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class="vector-toc-list"> </ul> </li> <li id="toc-Higgs_boson" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Higgs_boson"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Higgs boson</span> </div> </a> <ul id="toc-Higgs_boson-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Theoretical_aspects" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Theoretical_aspects"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Theoretical aspects</span> </div> </a> <button aria-controls="toc-Theoretical_aspects-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Theoretical aspects subsection</span> </button> <ul id="toc-Theoretical_aspects-sublist" class="vector-toc-list"> <li id="toc-Construction_of_the_Standard_Model_Lagrangian" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Construction_of_the_Standard_Model_Lagrangian"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Construction of the Standard Model Lagrangian</span> </div> </a> <ul id="toc-Construction_of_the_Standard_Model_Lagrangian-sublist" class="vector-toc-list"> <li id="toc-Quantum_chromodynamics_sector" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Quantum_chromodynamics_sector"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Quantum chromodynamics sector</span> </div> </a> <ul id="toc-Quantum_chromodynamics_sector-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electroweak_sector" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Electroweak_sector"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2</span> <span>Electroweak sector</span> </div> </a> <ul id="toc-Electroweak_sector-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Higgs_sector" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Higgs_sector"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.3</span> <span>Higgs sector</span> </div> </a> <ul id="toc-Higgs_sector-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Yukawa_sector" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Yukawa_sector"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.4</span> <span>Yukawa sector</span> </div> </a> <ul id="toc-Yukawa_sector-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Fundamental_interactions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fundamental_interactions"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Fundamental interactions</span> </div> </a> <button aria-controls="toc-Fundamental_interactions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Fundamental interactions subsection</span> </button> <ul id="toc-Fundamental_interactions-sublist" class="vector-toc-list"> <li id="toc-Gravity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gravity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Gravity</span> </div> </a> <ul id="toc-Gravity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electromagnetism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electromagnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Electromagnetism</span> </div> </a> <ul id="toc-Electromagnetism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Weak_nuclear_force" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Weak_nuclear_force"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Weak nuclear force</span> </div> </a> <ul id="toc-Weak_nuclear_force-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Strong_nuclear_force" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Strong_nuclear_force"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Strong nuclear force</span> </div> </a> <ul id="toc-Strong_nuclear_force-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Tests_and_predictions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tests_and_predictions"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Tests and predictions</span> </div> </a> <ul id="toc-Tests_and_predictions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Challenges" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Challenges"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Challenges</span> </div> </a> <ul id="toc-Challenges-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Further reading</span> </div> </a> <button aria-controls="toc-Further_reading-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Further reading subsection</span> </button> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> <li id="toc-Introductory_textbooks" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Introductory_textbooks"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.1</span> <span>Introductory textbooks</span> </div> </a> <ul id="toc-Introductory_textbooks-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Advanced_textbooks" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Advanced_textbooks"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.2</span> <span>Advanced textbooks</span> </div> </a> <ul id="toc-Advanced_textbooks-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Journal_articles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Journal_articles"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.3</span> <span>Journal articles</span> </div> </a> <ul id="toc-Journal_articles-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Standard Model</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 78 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-78" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">78 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Standaardmodel" title="Standaardmodel – Afrikaans" lang="af" hreflang="af" data-title="Standaardmodel" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Standardmodell" title="Standardmodell – Alemannic" lang="gsw" hreflang="gsw" data-title="Standardmodell" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D9%86%D9%85%D9%88%D8%B0%D8%AC_%D8%A7%D9%84%D9%85%D8%B9%D9%8A%D8%A7%D8%B1%D9%8A" title="نظرية النموذج المعياري – Arabic" lang="ar" hreflang="ar" data-title="نظرية النموذج المعياري" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Modelu_est%C3%A1ndar_de_la_f%C3%ADsica_de_part%C3%ADcules" title="Modelu estándar de la física de partícules – Asturian" lang="ast" hreflang="ast" data-title="Modelu estándar de la física de partícules" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Standart_Model" title="Standart Model – Azerbaijani" lang="az" hreflang="az" data-title="Standart Model" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%AE%E0%A6%BF%E0%A6%A4_%E0%A6%AE%E0%A6%A1%E0%A7%87%E0%A6%B2" title="প্রমিত মডেল – Bangla" lang="bn" hreflang="bn" data-title="প্রমিত মডেল" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D1%82%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D0%B4%D1%8D%D0%BB%D1%8C" title="Стандартная мадэль – Belarusian" lang="be" hreflang="be" data-title="Стандартная мадэль" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D1%82%D0%B5%D0%BD_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB" title="Стандартен модел – Bulgarian" lang="bg" hreflang="bg" data-title="Стандартен модел" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Standardni_model" title="Standardni model – Bosnian" lang="bs" hreflang="bs" data-title="Standardni model" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Model_est%C3%A0ndard_de_f%C3%ADsica_de_part%C3%ADcules" title="Model estàndard de física de partícules – Catalan" lang="ca" hreflang="ca" data-title="Model estàndard de física de partícules" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D1%82%D0%BB%C4%83_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C" title="Стандартлă модель – Chuvash" lang="cv" hreflang="cv" data-title="Стандартлă модель" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Standardn%C3%AD_model" title="Standardní model – Czech" lang="cs" hreflang="cs" data-title="Standardní model" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Standardmodellen" title="Standardmodellen – Danish" lang="da" hreflang="da" data-title="Standardmodellen" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Standardmodell" title="Standardmodell – German" lang="de" hreflang="de" data-title="Standardmodell" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Osakestef%C3%BC%C3%BCsika_standardmudel" title="Osakestefüüsika standardmudel – Estonian" lang="et" hreflang="et" data-title="Osakestefüüsika standardmudel" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%B1%CE%B8%CE%B9%CE%B5%CF%81%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%A0%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF" title="Καθιερωμένο Πρότυπο – Greek" lang="el" hreflang="el" data-title="Καθιερωμένο Πρότυπο" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Modelo_est%C3%A1ndar_de_la_f%C3%ADsica_de_part%C3%ADculas" title="Modelo estándar de la física de partículas – Spanish" lang="es" hreflang="es" data-title="Modelo estándar de la física de partículas" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Norma_modelo" title="Norma modelo – Esperanto" lang="eo" hreflang="eo" data-title="Norma modelo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Eredu_Estandarra" title="Eredu Estandarra – Basque" lang="eu" hreflang="eu" data-title="Eredu Estandarra" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AF%D9%84_%D8%A7%D8%B3%D8%AA%D8%A7%D9%86%D8%AF%D8%A7%D8%B1%D8%AF" title="مدل استاندارد – Persian" lang="fa" hreflang="fa" data-title="مدل استاندارد" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Mod%C3%A8le_standard_de_la_physique_des_particules" title="Modèle standard de la physique des particules – French" lang="fr" hreflang="fr" data-title="Modèle standard de la physique des particules" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/An_tSamhail_Chaighde%C3%A1nach" title="An tSamhail Chaighdeánach – Irish" lang="ga" hreflang="ga" data-title="An tSamhail Chaighdeánach" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Modelo_est%C3%A1ndar" title="Modelo estándar – Galician" lang="gl" hreflang="gl" data-title="Modelo estándar" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%91%9C%EC%A4%80_%EB%AA%A8%ED%98%95" title="표준 모형 – Korean" lang="ko" hreflang="ko" data-title="표준 모형" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8D%D5%BF%D5%A1%D5%B6%D5%A4%D5%A1%D6%80%D5%BF_%D5%B4%D5%B8%D5%A4%D5%A5%D5%AC" title="Ստանդարտ մոդել – Armenian" lang="hy" hreflang="hy" data-title="Ստանդարտ մոդել" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AE%E0%A4%BE%E0%A4%A8%E0%A4%95_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BF%E0%A4%AE%E0%A4%BE%E0%A4%A8" title="मानक प्रतिमान – Hindi" lang="hi" hreflang="hi" data-title="मानक प्रतिमान" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Standardni_model" title="Standardni model – Croatian" lang="hr" hreflang="hr" data-title="Standardni model" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Model_Standar" title="Model Standar – Indonesian" lang="id" hreflang="id" data-title="Model Standar" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Sta%C3%B0all%C3%ADkan" title="Staðallíkan – Icelandic" lang="is" hreflang="is" data-title="Staðallíkan" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Modello_standard" title="Modello standard – Italian" lang="it" hreflang="it" data-title="Modello standard" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%9E%D7%95%D7%93%D7%9C_%D7%94%D7%A1%D7%98%D7%A0%D7%93%D7%A8%D7%98%D7%99" title="המודל הסטנדרטי – Hebrew" lang="he" hreflang="he" data-title="המודל הסטנדרטי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%A6%E0%B2%BF_%E0%B2%B8%E0%B3%8D%E0%B2%9F%E0%B2%BE%E0%B2%82%E0%B2%A1%E0%B2%B0%E0%B3%8D%E0%B2%A1%E0%B3%8D_%E0%B2%AE%E0%B2%BE%E0%B2%A1%E0%B3%86%E0%B2%B2%E0%B3%8D_%E0%B2%B8%E0%B2%BF%E0%B2%A6%E0%B3%8D%E0%B2%A7%E0%B2%BE%E0%B2%82%E0%B2%A4" title="ದಿ ಸ್ಟಾಂಡರ್ಡ್ ಮಾಡೆಲ್ ಸಿದ್ಧಾಂತ – Kannada" lang="kn" hreflang="kn" data-title="ದಿ ಸ್ಟಾಂಡರ್ಡ್ ಮಾಡೆಲ್ ಸಿದ್ಧಾಂತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%A2%E1%83%90%E1%83%9C%E1%83%93%E1%83%90%E1%83%A0%E1%83%A2%E1%83%A3%E1%83%9A%E1%83%98_%E1%83%9B%E1%83%9D%E1%83%93%E1%83%94%E1%83%9A%E1%83%98" title="სტანდარტული მოდელი – Georgian" lang="ka" hreflang="ka" data-title="სტანდარტული მოდელი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Mod%C3%A8l_standar_(fizik_di_s%C3%A9_partikil)" title="Modèl standar (fizik di sé partikil) – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Modèl standar (fizik di sé partikil)" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Standartmodelis" title="Standartmodelis – Latvian" lang="lv" hreflang="lv" data-title="Standartmodelis" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Standardmodell" title="Standardmodell – Luxembourgish" lang="lb" hreflang="lb" data-title="Standardmodell" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Standartinis_modelis" title="Standartinis modelis – Lithuanian" lang="lt" hreflang="lt" data-title="Standartinis modelis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Model_standard_(f%C3%ACzica_de_le_partezele)" title="Model standard (fìzica de le partezele) – Lombard" lang="lmo" hreflang="lmo" data-title="Model standard (fìzica de le partezele)" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Standard_modell" title="Standard modell – Hungarian" lang="hu" hreflang="hu" data-title="Standard modell" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D0%B4%D0%B5%D0%BD_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB" title="Стандарден модел – Macedonian" lang="mk" hreflang="mk" data-title="Стандарден модел" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B5%8D%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B4%BE%E0%B5%BB%E0%B4%A1%E0%B5%87%E0%B5%BC%E0%B4%A1%E0%B5%8D_%E0%B4%AE%E0%B5%8B%E0%B4%A1%E0%B5%BD" title="സ്റ്റാൻഡേർഡ് മോഡൽ – Malayalam" lang="ml" hreflang="ml" data-title="സ്റ്റാൻഡേർഡ് മോഡൽ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Mudell_Standard" title="Mudell Standard – Maltese" lang="mt" hreflang="mt" data-title="Mudell Standard" data-language-autonym="Malti" data-language-local-name="Maltese" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%BE%E0%A4%A3_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%83%E0%A4%A4%E0%A5%80" title="प्रमाण प्रतिकृती – Marathi" lang="mr" hreflang="mr" data-title="प्रमाण प्रतिकृती" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Model_Piawai" title="Model Piawai – Malay" lang="ms" hreflang="ms" data-title="Model Piawai" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D1%82_%D0%B7%D0%B0%D0%B3%D0%B2%D0%B0%D1%80" title="Стандарт загвар – Mongolian" lang="mn" hreflang="mn" data-title="Стандарт загвар" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Standaardmodel_van_de_deeltjesfysica" title="Standaardmodel van de deeltjesfysica – Dutch" lang="nl" hreflang="nl" data-title="Standaardmodel van de deeltjesfysica" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%A8%99%E6%BA%96%E6%A8%A1%E5%9E%8B" title="標準模型 – Japanese" lang="ja" hreflang="ja" data-title="標準模型" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Standardmodellen" title="Standardmodellen – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Standardmodellen" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Standardmodellen" title="Standardmodellen – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Standardmodellen" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%95%E0%AD%8D%E0%AC%B7%E0%AD%81%E0%AC%A6%E0%AD%8D%E0%AC%B0%E0%AC%95%E0%AC%A3_%E0%AC%AC%E0%AC%BF%E0%AC%9C%E0%AD%8D%E0%AC%9E%E0%AC%BE%E0%AC%A8%E0%AC%B0_%E0%AC%86%E0%AC%A6%E0%AC%B0%E0%AD%8D%E0%AC%B6_%E0%AC%AE%E0%AC%BE%E0%AC%A8%E0%AC%A6%E0%AC%A3%E0%AD%8D%E0%AC%A1" title="କ୍ଷୁଦ୍ରକଣ ବିଜ୍ଞାନର ଆଦର୍ଶ ମାନଦଣ୍ଡ – Odia" lang="or" hreflang="or" data-title="କ୍ଷୁଦ୍ରକଣ ବିଜ୍ଞାନର ଆଦର୍ଶ ମାନଦଣ୍ଡ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AE%E0%A8%BF%E0%A8%85%E0%A8%BE%E0%A8%B0%E0%A9%80_%E0%A8%A8%E0%A8%AE%E0%A9%82%E0%A8%A8%E0%A8%BE" title="ਮਿਅਾਰੀ ਨਮੂਨਾ – Punjabi" lang="pa" hreflang="pa" data-title="ਮਿਅਾਰੀ ਨਮੂਨਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%85%DB%8C%D8%B9%D8%A7%D8%B1%DB%8C_%D9%86%D9%85%D9%88%D9%86%DB%81" title="میعاری نمونہ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="میعاری نمونہ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Standad_Magl" title="Standad Magl – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Standad Magl" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Model_standardowy" title="Model standardowy – Polish" lang="pl" hreflang="pl" data-title="Model standardowy" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Modelo_Padr%C3%A3o" title="Modelo Padrão – Portuguese" lang="pt" hreflang="pt" data-title="Modelo Padrão" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Modelul_standard" title="Modelul standard – Romanian" lang="ro" hreflang="ro" data-title="Modelul standard" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D1%82%D0%BD%D0%B0%D1%8F_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C" title="Стандартная модель – Russian" lang="ru" hreflang="ru" data-title="Стандартная модель" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Standard_Model" title="Standard Model – Simple English" lang="en-simple" hreflang="en-simple" data-title="Standard Model" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C5%A0tandardn%C3%BD_model" title="Štandardný model – Slovak" lang="sk" hreflang="sk" data-title="Štandardný model" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Standardni_model" title="Standardni model – Slovenian" lang="sl" hreflang="sl" data-title="Standardni model" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%85%DB%86%D8%AF%DB%8E%D9%84%DB%8C_%D8%B3%D8%AA%D8%A7%D9%86%D8%AF%D8%A7%D8%B1%D8%AF" title="مۆدێلی ستاندارد – Central Kurdish" lang="ckb" hreflang="ckb" data-title="مۆدێلی ستاندارد" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D0%B4%D0%BD%D0%B8_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB" title="Стандардни модел – Serbian" lang="sr" hreflang="sr" data-title="Стандардни модел" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Standardni_model_%C4%8Destica" title="Standardni model čestica – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Standardni model čestica" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Mod%C3%A9l_Baku" title="Modél Baku – Sundanese" lang="su" hreflang="su" data-title="Modél Baku" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Hiukkasfysiikan_standardimalli" title="Hiukkasfysiikan standardimalli – Finnish" lang="fi" hreflang="fi" data-title="Hiukkasfysiikan standardimalli" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Standardmodellen" title="Standardmodellen – Swedish" lang="sv" hreflang="sv" data-title="Standardmodellen" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Pamantayang_Modelo" title="Pamantayang Modelo – Tagalog" lang="tl" hreflang="tl" data-title="Pamantayang Modelo" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%80%E0%AE%B0%E0%AF%8D%E0%AE%AE%E0%AE%B0%E0%AE%AA%E0%AF%81_%E0%AE%92%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81%E0%AE%B0%E0%AF%81" title="சீர்மரபு ஒப்புரு – Tamil" lang="ta" hreflang="ta" data-title="சீர்மரபு ஒப்புரு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D1%82_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C" title="Стандарт модель – Tatar" lang="tt" hreflang="tt" data-title="Стандарт модель" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%9A%E0%B8%9A%E0%B8%88%E0%B8%B3%E0%B8%A5%E0%B8%AD%E0%B8%87%E0%B8%A1%E0%B8%B2%E0%B8%95%E0%B8%A3%E0%B8%90%E0%B8%B2%E0%B8%99" title="แบบจำลองมาตรฐาน – Thai" lang="th" hreflang="th" data-title="แบบจำลองมาตรฐาน" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Theory of forces and subatomic particles</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about a non-mathematical general overview of the Standard Model of particle physics. For a mathematical description, see <a href="/wiki/Mathematical_formulation_of_the_Standard_Model" title="Mathematical formulation of the Standard Model">Mathematical formulation of the Standard Model</a>. For other uses, see <a href="/wiki/Standard_model_(disambiguation)" class="mw-disambig" title="Standard model (disambiguation)">Standard model (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": 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0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><th class="sidebar-title"><a class="mw-selflink selflink">Standard Model</a> of <a href="/wiki/Particle_physics" title="Particle physics">particle physics</a></th></tr><tr><td class="sidebar-image"><figure class="skin-invert-image noresize mw-ext-imagemap-desc-bottom-right" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/240px-Standard_Model_of_Elementary_Particles.svg.png" decoding="async" width="240" height="230" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/360px-Standard_Model_of_Elementary_Particles.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/480px-Standard_Model_of_Elementary_Particles.svg.png 2x" data-file-width="1390" data-file-height="1330" usemap="#ImageMap_af1b7d82cba73703" resource="/wiki/File:Standard_Model_of_Elementary_Particles.svg" /></span><map name="ImageMap_af1b7d82cba73703"><area href="/wiki/Up_quark" shape="rect" coords="17,48,59,89" alt="Up quark" title="Up quark" /><area href="/wiki/Charm_quark" shape="rect" coords="60,48,102,89" alt="Charm quark" title="Charm quark" /><area href="/wiki/Top_quark" shape="rect" coords="104,48,145,89" alt="Top quark" title="Top quark" /><area href="/wiki/Gluon" shape="rect" coords="149,48,190,89" alt="Gluon" title="Gluon" /><area href="/wiki/Higgs_boson" shape="rect" coords="194,48,235,89" alt="Higgs boson" title="Higgs boson" /><area href="/wiki/Down_quark" shape="rect" coords="17,91,59,132" alt="Down quark" title="Down quark" /><area href="/wiki/Strange_quark" shape="rect" coords="60,91,102,132" alt="Strange quark" title="Strange quark" /><area href="/wiki/Bottom_quark" shape="rect" coords="104,91,145,132" alt="Bottom quark" title="Bottom quark" /><area href="/wiki/Photon" shape="rect" coords="149,91,190,132" alt="Photon" title="Photon" /><area href="/wiki/Electron" shape="rect" coords="17,137,59,178" alt="Electron" title="Electron" /><area href="/wiki/Muon" shape="rect" coords="60,137,102,178" alt="Muon" title="Muon" /><area href="/wiki/Tau_(particle)" shape="rect" coords="104,137,145,178" alt="Tau (particle)" title="Tau (particle)" /><area href="/wiki/W_and_Z_bosons#Z_bosons}Z_boson" shape="rect" coords="149,137,190,178" alt="W and Z bosons#Z bosons}Z boson" title="W and Z bosons#Z bosons}Z boson" /><area href="/wiki/Electron_neutrino" shape="rect" coords="17,180,59,221" alt="Electron neutrino" title="Electron neutrino" /><area href="/wiki/Muon_neutrino" shape="rect" coords="60,180,102,221" alt="Muon neutrino" title="Muon neutrino" /><area href="/wiki/Tau_neutrino" shape="rect" coords="104,180,145,221" alt="Tau neutrino" title="Tau neutrino" /><area href="/wiki/W_and_Z_bosons" shape="rect" coords="149,180,190,221" alt="W and Z bosons" title="W and Z bosons" /><area href="/wiki/Standard_Model" shape="rect" coords="16,8,224,19" alt="Standard Model" title="Standard Model" /><area href="/wiki/Fermion" shape="rect" coords="17,24,145,38" alt="Fermion" title="Fermion" /><area href="/wiki/Boson" shape="rect" coords="149,24,235,38" alt="Boson" title="Boson" /><area href="/wiki/Quark" shape="rect" coords="6,93,14,133" alt="Quark" title="Quark" /><area href="/wiki/Lepton" shape="rect" coords="6,176,12,219" alt="Lepton" title="Lepton" /><area href="/wiki/Scalar_boson" shape="rect" coords="227,92,233,172" alt="Scalar boson" title="Scalar boson" /><area href="/wiki/Gauge_boson" shape="rect" coords="196,143,202,219" alt="Gauge boson" title="Gauge boson" /><area href="/wiki/Vector_boson" shape="rect" coords="205,165,209,219" alt="Vector boson" title="Vector boson" /></map><figcaption></figcaption></figure><div class="sidebar-caption"><a href="/wiki/Elementary_particle" title="Elementary particle">Elementary particles</a> of the Standard Model</div></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Background</div><div class="sidebar-list-content mw-collapsible-content"><a href="/wiki/Particle_physics" title="Particle physics">Particle physics</a><br /><a class="mw-selflink selflink">Standard Model</a><br /><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a> <br /> <a href="/wiki/Gauge_theory" title="Gauge theory">Gauge theory</a> <br /> <a href="/wiki/Spontaneous_symmetry_breaking" title="Spontaneous symmetry breaking">Spontaneous symmetry breaking</a><br /> <a href="/wiki/Higgs_mechanism" title="Higgs mechanism">Higgs mechanism</a></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Constituents</div><div class="sidebar-list-content mw-collapsible-content"><a href="/wiki/Electroweak_interaction" title="Electroweak interaction">Electroweak interaction</a><br /> <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">Quantum chromodynamics</a><br /> <a href="/wiki/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa_matrix" title="Cabibbo–Kobayashi–Maskawa matrix">CKM matrix</a><br /><a href="/wiki/Mathematical_formulation_of_the_Standard_Model" title="Mathematical formulation of the Standard Model">Standard Model mathematics</a></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Limitations</div><div class="sidebar-list-content mw-collapsible-content"><a href="/wiki/Strong_CP_problem" title="Strong CP problem">Strong CP problem</a><br /><a href="/wiki/Hierarchy_problem" title="Hierarchy problem">Hierarchy problem</a><br /><a href="/wiki/Neutrino_oscillation" title="Neutrino oscillation">Neutrino oscillations</a><br /><a href="/wiki/Physics_beyond_the_Standard_Model" title="Physics beyond the Standard Model">Physics beyond the Standard Model</a></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed hlist"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Rutherford</a></li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">Thomson</a></li> <li><a href="/wiki/James_Chadwick" title="James Chadwick">Chadwick</a></li> <li><a href="/wiki/Satyendra_Nath_Bose" title="Satyendra Nath Bose">Bose</a></li> <li><a href="/wiki/E._C._George_Sudarshan" title="E. C. George Sudarshan">Sudarshan</a></li> <li><a href="/wiki/Raymond_Davis_Jr." title="Raymond Davis Jr.">Davis Jr</a></li> <li><a href="/wiki/Carl_David_Anderson" title="Carl David Anderson">Anderson</a></li> <li><a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Fermi</a></li> <li><a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac</a></li> <li><a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman</a></li> <li><a href="/wiki/Carlo_Rubbia" title="Carlo Rubbia">Rubbia</a></li> <li><a href="/wiki/Murray_Gell-Mann" title="Murray Gell-Mann">Gell-Mann</a></li> <li><a href="/wiki/Henry_Way_Kendall" title="Henry Way Kendall">Kendall</a></li> <li><a href="/wiki/Richard_E._Taylor" title="Richard E. Taylor">Taylor</a></li> <li><a href="/wiki/Jerome_Isaac_Friedman" title="Jerome Isaac Friedman">Friedman</a></li> <li><a href="/wiki/C._F._Powell" title="C. F. Powell">Powell</a></li> <li><a href="/wiki/Philip_Warren_Anderson" class="mw-redirect" title="Philip Warren Anderson">Anderson</a></li> <li><a href="/wiki/Sheldon_Glashow" title="Sheldon Glashow">Glashow</a></li> <li><a href="/wiki/John_Iliopoulos" title="John Iliopoulos">Iliopoulos</a></li> <li><a href="/wiki/Leon_M._Lederman" title="Leon M. Lederman">Lederman</a></li> <li><a href="/wiki/Luciano_Maiani" title="Luciano Maiani">Maiani</a></li> <li><a href="/wiki/Simon_van_der_Meer" title="Simon van der Meer">Meer</a></li> <li><a href="/wiki/Clyde_Cowan" title="Clyde Cowan">Cowan</a></li> <li><a href="/wiki/Yoichiro_Nambu" title="Yoichiro Nambu">Nambu</a></li> <li><a href="/wiki/Owen_Chamberlain" title="Owen Chamberlain">Chamberlain</a></li> <li><a href="/wiki/Nicola_Cabibbo" title="Nicola Cabibbo">Cabibbo</a></li> <li><a href="/wiki/Melvin_Schwartz" title="Melvin Schwartz">Schwartz</a></li> <li><a href="/wiki/Martin_Lewis_Perl" title="Martin Lewis Perl">Perl</a></li> <li><a href="/wiki/Ettore_Majorana" title="Ettore Majorana">Majorana</a></li> <li><a href="/wiki/Steven_Weinberg" title="Steven Weinberg">Weinberg</a></li> <li><a href="/wiki/Tsung-Dao_Lee" title="Tsung-Dao Lee">Lee</a></li> <li><a href="/wiki/John_Clive_Ward" title="John Clive Ward">Ward</a></li> <li><a href="/wiki/Abdus_Salam" title="Abdus Salam">Salam</a></li> <li><a href="/wiki/Makoto_Kobayashi_(physicist)" class="mw-redirect" title="Makoto Kobayashi (physicist)">Kobayashi</a></li> <li><a href="/wiki/Toshihide_Maskawa" title="Toshihide Maskawa">Maskawa</a></li> <li><a href="/wiki/Robert_Mills_(physicist)" title="Robert Mills (physicist)">Mills</a></li> <li><a href="/wiki/Yang_Chen-Ning" title="Yang Chen-Ning">Yang</a></li> <li><a href="/wiki/Hideki_Yukawa" title="Hideki Yukawa">Yukawa</a></li> <li><a href="/wiki/Gerard_%27t_Hooft" title="Gerard 't Hooft">'t Hooft</a></li> <li><a href="/wiki/Martinus_J._G._Veltman" title="Martinus J. G. Veltman">Veltman</a></li> <li><a href="/wiki/David_Gross" title="David Gross">Gross</a></li> <li><a href="/wiki/Abraham_Pais" title="Abraham Pais">Pais</a></li> <li><a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Pauli</a></li> <li><a href="/wiki/Hugh_David_Politzer" title="Hugh David Politzer">Politzer</a></li> <li><a href="/wiki/Frederick_Reines" title="Frederick Reines">Reines</a></li> <li><a href="/wiki/Julian_Schwinger" title="Julian Schwinger">Schwinger</a></li> <li><a href="/wiki/Frank_Wilczek" title="Frank Wilczek">Wilczek</a></li> <li><a href="/wiki/James_Cronin" title="James Cronin">Cronin</a></li> <li><a href="/wiki/Val_Logsdon_Fitch" title="Val Logsdon Fitch">Fitch</a></li> <li><a href="/wiki/John_Hasbrouck_Van_Vleck" title="John Hasbrouck Van Vleck">Vleck</a></li> <li><a href="/wiki/Peter_Higgs" title="Peter Higgs">Higgs</a></li> <li><a href="/wiki/Fran%C3%A7ois_Englert" title="François Englert">Englert</a></li> <li><a href="/wiki/Robert_Brout" title="Robert Brout">Brout</a></li> <li><a href="/wiki/C._R._Hagen" title="C. R. Hagen">Hagen</a></li> <li><a href="/wiki/Gerald_Guralnik" title="Gerald Guralnik">Guralnik</a></li> <li><a href="/wiki/Tom_Kibble" title="Tom Kibble">Kibble</a></li> <li><a href="/wiki/Santiago_Ant%C3%BAnez_de_Mayolo" title="Santiago Antúnez de Mayolo">de Mayolo</a></li> <li><a href="/wiki/C%C3%A9sar_Lattes" title="César Lattes">Lattes</a></li> <li><a href="/wiki/George_Zweig" title="George Zweig">Zweig</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Standard_model_of_particle_physics" title="Template:Standard model of particle physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Standard_model_of_particle_physics" title="Template talk:Standard model of particle physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Standard_model_of_particle_physics" title="Special:EditPage/Template:Standard model of particle physics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The <b>Standard Model</b> of <a href="/wiki/Particle_physics" title="Particle physics">particle physics</a> is the <a href="/wiki/Scientific_theory" title="Scientific theory">theory</a> describing three of the four known <a href="/wiki/Fundamental_force" class="mw-redirect" title="Fundamental force">fundamental forces</a> (<a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetic</a>, <a href="/wiki/Weak_interaction" title="Weak interaction">weak</a> and <a href="/wiki/Strong_interaction" title="Strong interaction">strong interactions</a> – excluding <a href="/wiki/Gravity" title="Gravity">gravity</a>) in the <a href="/wiki/Universe" title="Universe">universe</a> and classifying all known <a href="/wiki/Elementary_particle" title="Elementary particle">elementary particles</a>. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> with the current formulation being finalized in the mid-1970s upon <a href="/wiki/Experimental_confirmation" class="mw-redirect" title="Experimental confirmation">experimental confirmation</a> of the existence of <a href="/wiki/Quark" title="Quark">quarks</a>. Since then, proof of the <a href="/wiki/Top_quark" title="Top quark">top quark</a> (1995), the <a href="/wiki/Tau_neutrino" title="Tau neutrino">tau neutrino</a> (2000), and the <a href="/wiki/Higgs_boson" title="Higgs boson">Higgs boson</a> (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of <a href="/wiki/Weak_neutral_current" class="mw-redirect" title="Weak neutral current">weak neutral currents</a> and the <a href="/wiki/W_and_Z_bosons" title="W and Z bosons">W and Z bosons</a> with great accuracy. </p><p>Although the Standard Model is believed to be theoretically self-consistent<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>note 1<span class="cite-bracket">]</span></a></sup> and has demonstrated some success in providing <a href="/wiki/Experimental_prediction" class="mw-redirect" title="Experimental prediction">experimental predictions</a>, it leaves some <a href="/wiki/Physics_beyond_the_standard_model" class="mw-redirect" title="Physics beyond the standard model">physical phenomena unexplained</a> and so falls short of being a <a href="/wiki/Theory_of_everything" title="Theory of everything">complete theory of fundamental interactions</a>.<sup id="cite_ref-NYT-20230911_4-0" class="reference"><a href="#cite_note-NYT-20230911-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> For example, it does not fully explain <a href="/wiki/Baryon_asymmetry" title="Baryon asymmetry">why there is more matter than anti-matter</a>, incorporate the full <a href="/wiki/Theory_of_gravitation" class="mw-redirect" title="Theory of gravitation">theory of gravitation</a><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> as described by <a href="/wiki/General_relativity" title="General relativity">general relativity</a>, or account for the <a href="/wiki/Accelerating_expansion_of_the_universe" title="Accelerating expansion of the universe">universe's accelerating expansion</a> as possibly described by <a href="/wiki/Dark_energy" title="Dark energy">dark energy</a>. The model does not contain any viable <a href="/wiki/Dark_matter" title="Dark matter">dark matter</a> particle that possesses all of the required properties deduced from observational <a href="/wiki/Physical_cosmology" title="Physical cosmology">cosmology</a>. It also does not incorporate <a href="/wiki/Neutrino_oscillation" title="Neutrino oscillation">neutrino oscillations</a> and their non-zero masses. </p><p>The development of the Standard Model was driven by <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical</a> and <a href="/wiki/Experimental_physics" title="Experimental physics">experimental</a> particle physicists alike. The Standard Model is a paradigm of a <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a> for theorists, exhibiting a wide range of phenomena, including <a href="/wiki/Spontaneous_symmetry_breaking" title="Spontaneous symmetry breaking">spontaneous symmetry breaking</a>, <a href="/wiki/Anomaly_(physics)" title="Anomaly (physics)">anomalies</a>, and non-perturbative behavior. It is used as a basis for building more exotic models that incorporate <a href="/wiki/Hypothetical_particle" class="mw-redirect" title="Hypothetical particle">hypothetical particles</a>, <a href="/wiki/Extra_dimensions" title="Extra dimensions">extra dimensions</a>, and elaborate symmetries (such as <a href="/wiki/Supersymmetry" title="Supersymmetry">supersymmetry</a>) to explain experimental results at variance with the Standard Model, such as the existence of dark matter and neutrino oscillations. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historical_background">Historical background</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=1" title="Edit section: Historical background"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">History of quantum field theory</a>, <a href="/wiki/History_of_subatomic_physics" title="History of subatomic physics">History of subatomic physics</a>, <a href="/wiki/Julian_Schwinger" title="Julian Schwinger">Julian Schwinger</a>, and <a href="/wiki/John_Clive_Ward" title="John Clive Ward">John Clive Ward</a></div> <p>In 1928, <a href="/wiki/Paul_Dirac" title="Paul Dirac">Paul Dirac</a> introduced the <a href="/wiki/Dirac_equation" title="Dirac equation">Dirac equation</a> which implied the existence of <a href="/wiki/Antimatter" title="Antimatter">antimatter</a>. </p><p>In 1954, <a href="/wiki/Yang_Chen-Ning" title="Yang Chen-Ning">Yang Chen-Ning</a> and <a href="/wiki/Robert_Mills_(physicist)" title="Robert Mills (physicist)">Robert Mills</a> extended the concept of <a href="/wiki/Gauge_theory" title="Gauge theory">gauge theory</a> for <a href="/wiki/Abelian_group" title="Abelian group">abelian groups</a>, e.g. <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a>, to <a href="/wiki/Nonabelian_group" class="mw-redirect" title="Nonabelian group">nonabelian groups</a> to provide an explanation for <a href="/wiki/Strong_interaction" title="Strong interaction">strong interactions</a>.<sup id="cite_ref-YM_6-0" class="reference"><a href="#cite_note-YM-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In 1957, <a href="/wiki/Chien-Shiung_Wu" title="Chien-Shiung Wu">Chien-Shiung Wu</a> demonstrated <a href="/wiki/Parity_(physics)" title="Parity (physics)">parity</a> was not conserved in the <a href="/wiki/Weak_interaction" title="Weak interaction">weak interaction</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>In 1961, <a href="/wiki/Sheldon_Glashow" title="Sheldon Glashow">Sheldon Glashow</a> combined the <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetic</a> and <a href="/wiki/Weak_interaction" title="Weak interaction">weak interactions</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> In 1964, Murray Gell-Mann and George Zweig introduced quarks and that same year <a href="/wiki/Oscar_W._Greenberg" title="Oscar W. Greenberg">Oscar W. Greenberg</a> implicitly introduced color charge of quarks.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> In 1967 <a href="/wiki/Steven_Weinberg" title="Steven Weinberg">Steven Weinberg</a><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Abdus_Salam" title="Abdus Salam">Abdus Salam</a><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> incorporated the <a href="/wiki/Higgs_mechanism" title="Higgs mechanism">Higgs mechanism</a><sup id="cite_ref-Englert1964_12-0" class="reference"><a href="#cite_note-Englert1964-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Peter_W._Higgs_1964_508–509_13-0" class="reference"><a href="#cite_note-Peter_W._Higgs_1964_508–509-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-G.S._Guralnik,_C.R._Hagen,_T.W.B._Kibble_1964_585–587_14-0" class="reference"><a href="#cite_note-G.S._Guralnik,_C.R._Hagen,_T.W.B._Kibble_1964_585–587-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> into Glashow's <a href="/wiki/Electroweak_interaction" title="Electroweak interaction">electroweak interaction</a>, giving it its modern form. </p><p>In 1970, Sheldon Glashow, John Iliopoulos, and Luciano Maiani introduced the <a href="/wiki/GIM_mechanism" title="GIM mechanism">GIM mechanism</a>, predicting the <a href="/wiki/Charm_quark" title="Charm quark">charm quark</a>.<sup id="cite_ref-:2_15-0" class="reference"><a href="#cite_note-:2-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> In 1973 Gross and Wilczek and Politzer independently discovered that non-Abelian gauge theories, like the color theory of the strong force, have <a href="/wiki/Asymptotic_freedom" title="Asymptotic freedom">asymptotic freedom</a>.<sup id="cite_ref-:2_15-1" class="reference"><a href="#cite_note-:2-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> In 1976, Martin Perl discovered the <a href="/wiki/Tau_lepton" class="mw-redirect" title="Tau lepton">tau lepton</a> at the <a href="/wiki/SLAC_National_Accelerator_Laboratory" title="SLAC National Accelerator Laboratory">SLAC</a>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> In 1977, a team led by Leon Lederman at Fermilab discovered the bottom quark.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>The Higgs mechanism is believed to give rise to the <a href="/wiki/Mass" title="Mass">masses</a> of all the <a href="/wiki/Elementary_particle" title="Elementary particle">elementary particles</a> in the Standard Model. This includes the masses of the <a href="/wiki/W_and_Z_bosons" title="W and Z bosons">W and Z bosons</a>, and the masses of the <a href="/wiki/Fermion" title="Fermion">fermions</a>, i.e. the <a href="/wiki/Quark" title="Quark">quarks</a> and <a href="/wiki/Lepton" title="Lepton">leptons</a>. </p><p>After the <a href="/wiki/Neutral_current" title="Neutral current">neutral weak currents</a> caused by <a href="/wiki/Subatomic_particle" title="Subatomic particle">Z boson</a> exchange <a href="/wiki/Gargamelle" title="Gargamelle">were discovered</a> at <a href="/wiki/CERN" title="CERN">CERN</a> in 1973,<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979 <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a> for discovering it. The W<sup>±</sup> and Z<sup>0</sup> <a href="/wiki/Boson" title="Boson">bosons</a> were discovered experimentally in 1983; and the ratio of their masses was found to be as the Standard Model predicted.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>The theory of the <a href="/wiki/Strong_interaction" title="Strong interaction">strong interaction</a> (i.e. <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">quantum chromodynamics</a>, QCD), to which many contributed, acquired its modern form in 1973–74 when <a href="/wiki/Asymptotic_freedom" title="Asymptotic freedom">asymptotic freedom</a> was proposed<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> (a development which made QCD the main focus of theoretical research)<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> and experiments confirmed that the <a href="/wiki/Hadron" title="Hadron">hadrons</a> were composed of fractionally charged quarks.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><p>The term "Standard Model" was introduced by <a href="/wiki/Abraham_Pais" title="Abraham Pais">Abraham Pais</a> and <a href="/wiki/Sam_Treiman" title="Sam Treiman">Sam Treiman</a> in 1975,<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> with reference to the electroweak theory with four quarks.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Steven_Weinberg" title="Steven Weinberg">Steven Weinberg</a>, has since claimed priority, explaining that he chose the term Standard <a href="/wiki/Model" title="Model">Model</a> out of a sense of modesty<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template noprint noexcerpt Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:NOTRS" class="mw-redirect" title="Wikipedia:NOTRS"><span title="The current source is insufficiently reliable (WP:NOTRS). (March 2022)">better source needed</span></a></i>]</sup> and used it in 1973 during a talk in Aix-en-Provence in France.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Particle_content">Particle content</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=2" title="Edit section: Particle content"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Standard Model includes members of several classes of elementary particles, which in turn can be distinguished by other characteristics, such as <a href="/wiki/Color_charge" title="Color charge">color charge</a>. </p><p>All particles can be summarized as follows: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Elementary_particles" title="Template:Elementary particles"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Elementary_particles" title="Template talk:Elementary particles"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Elementary_particles" title="Special:EditPage/Template:Elementary particles"><abbr title="Edit this template">e</abbr></a></li></ul></div> <table style="border-spacing: 0px; border-collapse: separate; margin: 0 auto; font-size:85%"> <tbody><tr style="height:1px;text-align:center"><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="6" rowspan="2" style="border:2px solid;padding:0.2em"><span style="font-size:120%"><b>Elementary particles</b></span></td></tr><tr style="height:1px;text-align:center"></tr> <tr style="height:1px;text-align:center"><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td style="height:1em;width:1em"></td><td style="height:1em;border-bottom:1px solid;width:1em"></td><td colspan="2" style="height:1em;border-bottom:1px solid;width:2em"></td><td colspan="2" style="height:1em;border-bottom:1px solid;width:2em"></td><td colspan="2" style="height:1em;border-bottom:1px solid;width:2em"></td><td style="border-right:1px solid;border-bottom:1px solid;height:1em;width:1em"></td><td style="height:1em;border-bottom:1px solid;width:1em"></td><td colspan="2" style="height:1em;border-bottom:1px solid;width:2em"></td><td colspan="2" style="height:1em;border-bottom:1px solid;width:2em"></td><td colspan="2" style="height:1em;border-bottom:1px solid;width:2em"></td><td style="height:1em;border-bottom:1px solid;width:1em"></td><td rowspan="2" style="height:2em;width:1em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td></tr><tr style="height:1px;text-align:center"><td style="border-right:1px solid;height:1em;width:1em"></td><td style="height:1em;width:1em"></td><td colspan="2" style="height:1em;width:2em"></td><td colspan="2" style="height:1em;width:2em"></td><td colspan="2" style="height:1em;width:2em"></td><td colspan="2" style="height:1em;width:2em"></td><td colspan="2" style="height:1em;width:2em"></td><td colspan="2" style="height:1em;width:2em"></td><td colspan="2" style="height:1em;width:2em"></td><td style="border-right:1px solid;height:1em;width:1em"></td></tr> <tr style="height:1px;text-align:center"><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="6" rowspan="2" style="border:2px solid;padding:0.2em"><big style="display:block; border-bottom:1px solid black"><b>Elementary <a href="/wiki/Fermion" title="Fermion">fermions</a></b></big><small style="display:block"><a href="/wiki/Half-integer" title="Half-integer">Half-integer</a> <a href="/wiki/Spin_(particle_physics)" class="mw-redirect" title="Spin (particle physics)">spin</a></small><small style="display:block">Obey the <a href="/wiki/Fermi%E2%80%93Dirac_statistics" title="Fermi–Dirac statistics">Fermi–Dirac statistics</a></small></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="6" rowspan="2" style="border:2px solid;padding:0.2em"><big style="display:block; border-bottom:1px solid black"><b>Elementary <a href="/wiki/Boson" title="Boson">bosons</a></b></big><small style="display:block"><a href="/wiki/Integer" title="Integer">Integer</a> spin</small><small style="display:block">Obey the <a href="/wiki/Bose%E2%80%93Einstein_statistics" title="Bose–Einstein statistics">Bose–Einstein statistics</a></small></td></tr><tr style="height:1px;text-align:center"></tr> <tr style="height:1px;text-align:center"><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td style="height:1em;width:1em"></td><td style="height:1em;border-bottom:1px solid;width:1em"></td><td colspan="2" style="height:1em;border-bottom:1px solid;width:2em"></td><td style="border-right:1px solid;border-bottom:1px solid;height:1em;width:1em"></td><td style="height:1em;border-bottom:1px solid;width:1em"></td><td colspan="2" style="height:1em;border-bottom:1px solid;width:2em"></td><td style="height:1em;border-bottom:1px solid;width:1em"></td><td rowspan="2" style="height:2em;width:1em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td style="height:1em;width:1em"></td><td style="height:1em;border-bottom:1px solid;width:1em"></td><td colspan="2" style="height:1em;border-bottom:1px solid;width:2em"></td><td style="border-right:1px solid;border-bottom:1px solid;height:1em;width:1em"></td><td style="height:1em;border-bottom:1px solid;width:1em"></td><td colspan="2" style="height:1em;border-bottom:1px solid;width:2em"></td><td style="height:1em;border-bottom:1px solid;width:1em"></td><td rowspan="2" style="height:2em;width:1em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td></tr><tr style="height:1px;text-align:center"><td style="border-right:1px solid;height:1em;width:1em"></td><td style="height:1em;width:1em"></td><td colspan="2" style="height:1em;width:2em"></td><td colspan="2" style="height:1em;width:2em"></td><td colspan="2" style="height:1em;width:2em"></td><td style="border-right:1px solid;height:1em;width:1em"></td><td style="border-right:1px solid;height:1em;width:1em"></td><td style="height:1em;width:1em"></td><td colspan="2" style="height:1em;width:2em"></td><td colspan="2" style="height:1em;width:2em"></td><td colspan="2" style="height:1em;width:2em"></td><td style="border-right:1px solid;height:1em;width:1em"></td></tr> <tr style="height:1px;text-align:center"><td colspan="6" rowspan="2" style="border:2px solid;padding:0.2em;vertical-align:top"><span style="display:block; border-bottom:1px solid black"><b><a href="/wiki/Quark" title="Quark">Quarks</a> and antiquarks</b></span><small style="display:block">Spin = <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span></small><small style="display:block">Have <a href="/wiki/Color_charge" title="Color charge">color charge</a></small><small style="display:block">Participate in <a href="/wiki/Strong_interaction" title="Strong interaction">strong interactions</a> </small><small style="display:block">and <a href="/wiki/Electroweak" class="mw-redirect" title="Electroweak">electroweak</a> interactions</small></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="6" rowspan="2" style="border:2px solid;padding:0.2em;vertical-align:top"><span style="display:block; border-bottom:1px solid black"><b><a href="/wiki/Lepton" title="Lepton">Leptons</a> and antileptons</b></span><small style="display:block">Spin = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span></small><small style="display:block">No color charge</small><small style="display:block"><a href="/wiki/Electroweak" class="mw-redirect" title="Electroweak">Electroweak</a> interactions</small></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="6" rowspan="2" style="border:2px solid;padding:0.2em;vertical-align:top"><span style="display:block; border-bottom:1px solid black"><b><a href="/wiki/Gauge_boson" title="Gauge boson">Gauge bosons</a></b></span><small style="display:block">Spin = 1</small><small style="display:block"><a href="/wiki/Force_carrier" title="Force carrier">Force carriers</a></small></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="6" rowspan="2" style="border:2px solid;padding:0.2em;vertical-align:top"><span style="display:block; border-bottom:1px solid black"><b><a href="/wiki/Scalar_boson" title="Scalar boson">Scalar bosons</a></b></span><small style="display:block">Spin = 0</small></td></tr><tr style="height:1px;text-align:center"></tr> <tr style="height:1px;text-align:center"><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td rowspan="2" style="border-right:1px solid;height:2em;width:1em"></td><td rowspan="2" style="height:2em;width:1em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td rowspan="2" style="border-right:1px solid;height:2em;width:1em"></td><td rowspan="2" style="height:2em;width:1em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td rowspan="2" style="border-right:1px solid;height:2em;width:1em"></td><td rowspan="2" style="height:2em;width:1em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td rowspan="2" style="border-right:1px solid;height:2em;width:1em"></td><td rowspan="2" style="height:2em;width:1em"></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td></tr><tr style="height:1px;text-align:center"></tr> <tr style="height:1px;text-align:center"><td colspan="6" rowspan="2" style="border:2px solid;padding:0.2em;vertical-align:top"><div style="text-align:left"><a href="/wiki/Quark#Table_of_properties" title="Quark"><b>Three generations</b></a><ol style="margin-left:2ch"><li><a href="/wiki/Up_quark" title="Up quark">Up</a> (u),<br /><a href="/wiki/Down_quark" title="Down quark">Down</a> (d)</li><li><a href="/wiki/Charm_quark" title="Charm quark">Charm</a> (c),<br /><a href="/wiki/Strange_quark" title="Strange quark">Strange</a> (s)</li><li><a href="/wiki/Top_quark" title="Top quark">Top</a> (t),<br /><a href="/wiki/Bottom_quark" title="Bottom quark">Bottom</a> (b)</li></ol></div></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="6" rowspan="2" style="border:2px solid;padding:0.2em;vertical-align:top"><div style="text-align:left"><b>Three generations</b><ol style="margin-left:2ch"><li><a href="/wiki/Electron" title="Electron">Electron</a> (<span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>e<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>),<sup><a href="#dagger1"> [†] </a></sup><br /><span class="nowrap"><a href="/wiki/Electron_neutrino" title="Electron neutrino">Electron neutrino</a> (<span class="texhtml"><span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>ν<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">e</sub></span></span></span></span>)</span></li><li><a href="/wiki/Muon" title="Muon">Muon</a> (<span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>μ<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>),<br /><a href="/wiki/Muon_neutrino" title="Muon neutrino">Muon neutrino</a> (<span class="texhtml"><span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>ν<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">μ</sub></span></span></span></span>)</li><li><a href="/wiki/Tau_(particle)" title="Tau (particle)">Tau</a> (<span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>τ<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>),<br /><a href="/wiki/Tau_neutrino" title="Tau neutrino">Tau neutrino</a> (<span class="texhtml"><span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>ν<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">τ</sub></span></span></span></span>)</li></ol></div></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="6" rowspan="2" style="border:2px solid;padding:0.2em;vertical-align:top"><div style="text-align:left"><b>Three kinds</b><ol style="margin-left:2ch"><li><a href="/wiki/Photon" title="Photon">Photon</a><br />(<span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>γ<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>; <a href="/wiki/Electromagnetic_interaction" class="mw-redirect" title="Electromagnetic interaction">electromagnetic interaction</a>)</li><li><a href="/wiki/W_and_Z_bosons" title="W and Z bosons">W and Z bosons</a><br />(<span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>W<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>, <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>W<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>, <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>Z<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">0</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>; <a href="/wiki/Weak_interaction" title="Weak interaction">weak interaction</a>)</li><li>Eight types of <a href="/wiki/Gluon" title="Gluon">gluons</a><br />(<span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>g<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>; <a href="/wiki/Strong_interaction" title="Strong interaction">strong interaction</a>)</li></ol></div></td><td colspan="2" rowspan="2" style="height:2em;width:2em"></td><td colspan="6" rowspan="2" style="border:2px solid;padding:0.2em;vertical-align:top"><b>One kind</b><br /><br /><a href="/wiki/Higgs_boson" title="Higgs boson">Higgs boson</a> (<span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">0</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>)</td></tr><tr style="height:1px;text-align:center"></tr> </tbody></table> <p><small style="display:block"><i>Notes</i>:<br /> [†]<span class="anchor" id="dagger1"></span> An anti-electron (<span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>e<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>) is conventionally called a "<a href="/wiki/Positron" title="Positron">positron</a>".<br /> </small> </p> <div class="mw-heading mw-heading3"><h3 id="Fermions">Fermions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=3" title="Edit section: Fermions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Standard Model includes 12 <a href="/wiki/Elementary_particle" title="Elementary particle">elementary particles</a> of <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a> <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span>, known as <a href="/wiki/Fermion" title="Fermion">fermions</a>.<sup id="cite_ref-:0_35-0" class="reference"><a href="#cite_note-:0-35"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> Fermions respect the <a href="/wiki/Pauli_exclusion_principle" title="Pauli exclusion principle">Pauli exclusion principle</a>, meaning that two <a href="/wiki/Indistinguishable_particles" title="Indistinguishable particles">identical fermions</a> cannot simultaneously occupy the same quantum state in the same atom.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> Each fermion has a corresponding <a href="/wiki/Antiparticle" title="Antiparticle">antiparticle</a>, which are particles that have corresponding properties with the exception of <a href="/wiki/Additive_inverse" title="Additive inverse">opposite</a> <a href="/wiki/Charge_(physics)" title="Charge (physics)">charges</a>.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> Fermions are classified based on how they interact, which is determined by the charges they carry, into two groups: <a href="/wiki/Quark" title="Quark">quarks</a> and <a href="/wiki/Lepton" title="Lepton">leptons</a>. Within each group, pairs of particles that exhibit similar physical behaviors are then grouped into <a href="/wiki/Generation_(particle_physics)" title="Generation (particle physics)">generations</a> (see the table). Each member of a generation has a greater mass than the corresponding particle of generations prior. Thus, there are three generations of quarks and leptons.<sup id="cite_ref-:1_38-0" class="reference"><a href="#cite_note-:1-38"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> As first-generation particles do not decay, they comprise all of ordinary (<a href="/wiki/Baryon" title="Baryon">baryonic</a>) matter. Specifically, all atoms consist of electrons orbiting around the <a href="/wiki/Atomic_nucleus" title="Atomic nucleus">atomic nucleus</a>, ultimately constituted of up and down quarks. On the other hand, second- and third-generation charged particles decay with very short <a href="/wiki/Half-life" title="Half-life">half-lives</a> and can only be observed in high-energy environments. Neutrinos of all generations also do not decay, and pervade the universe, but rarely interact with baryonic matter. </p><p>There are six quarks: <a href="/wiki/Up_quark" title="Up quark">up</a>, <a href="/wiki/Down_quark" title="Down quark">down</a>, <a href="/wiki/Charm_quark" title="Charm quark">charm</a>, <a href="/wiki/Strange_quark" title="Strange quark">strange</a>, <a href="/wiki/Top_quark" title="Top quark">top</a>, and <a href="/wiki/Bottom_quark" title="Bottom quark">bottom</a>.<sup id="cite_ref-:0_35-1" class="reference"><a href="#cite_note-:0-35"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_38-1" class="reference"><a href="#cite_note-:1-38"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> Quarks carry <a href="/wiki/Color_charge" title="Color charge">color charge</a>, and hence interact via the <a href="/wiki/Strong_interaction" title="Strong interaction">strong interaction</a>. The <a href="/wiki/Color_confinement" title="Color confinement">color confinement</a> phenomenon results in quarks being strongly bound together such that they form color-neutral composite particles called <a href="/wiki/Hadron" title="Hadron">hadrons</a>; quarks cannot individually exist and must always bind with other quarks. Hadrons can contain either a quark-antiquark pair (<a href="/wiki/Meson" title="Meson">mesons</a>) or three quarks (<a href="/wiki/Baryon" title="Baryon">baryons</a>).<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> The lightest baryons are the <a href="/wiki/Nucleon" title="Nucleon">nucleons</a>: the <a href="/wiki/Proton" title="Proton">proton</a> and <a href="/wiki/Neutron" title="Neutron">neutron</a>. Quarks also carry <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a> and <a href="/wiki/Weak_isospin" title="Weak isospin">weak isospin</a>, and thus interact with other fermions through <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> and <a href="/wiki/Weak_interaction" title="Weak interaction">weak interaction</a>. The six leptons consist of the <a href="/wiki/Electron" title="Electron">electron</a>, <a href="/wiki/Electron_neutrino" title="Electron neutrino">electron neutrino</a>, <a href="/wiki/Muon" title="Muon">muon</a>, <a href="/wiki/Muon_neutrino" title="Muon neutrino">muon neutrino</a>, <a href="/wiki/Tau_(particle)" title="Tau (particle)">tau</a>, and <a href="/wiki/Tau_neutrino" title="Tau neutrino">tau neutrino</a>. The leptons do not carry color charge, and do not respond to strong interaction. The main leptons carry an <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a> of -1 <i><a href="/wiki/Elementary_charge" title="Elementary charge">e</a></i>, while the three <a href="/wiki/Neutrino" title="Neutrino">neutrinos</a> carry a neutral electric charge. Thus, the neutrinos' motion are only influenced by <a href="/wiki/Weak_interaction" title="Weak interaction">weak interaction</a> and <a href="/wiki/Gravity" title="Gravity">gravity</a>, making them difficult to observe. </p> <div class="mw-heading mw-heading3"><h3 id="Gauge_bosons">Gauge bosons</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=4" title="Edit section: Gauge bosons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right skin-invert-image" typeof="mw:File/Thumb"><a href="/wiki/File:Standard_Model_%E2%80%93_All_Feynman_diagram_vertices.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Standard_Model_%E2%80%93_All_Feynman_diagram_vertices.svg/330px-Standard_Model_%E2%80%93_All_Feynman_diagram_vertices.svg.png" decoding="async" width="330" height="389" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Standard_Model_%E2%80%93_All_Feynman_diagram_vertices.svg/495px-Standard_Model_%E2%80%93_All_Feynman_diagram_vertices.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Standard_Model_%E2%80%93_All_Feynman_diagram_vertices.svg/660px-Standard_Model_%E2%80%93_All_Feynman_diagram_vertices.svg.png 2x" data-file-width="899" data-file-height="1059" /></a><figcaption>Interactions in the Standard Model. All Feynman diagrams in the model are built from combinations of these vertices. <i>q</i> is any quark, <i>g</i> is a gluon, <i>X</i> is any charged particle, γ is a photon, <i>f</i> is any fermion, <i>m</i> is any particle with mass (with the possible exception of the neutrinos), <i>m</i><sub>B</sub> is any boson with mass. In diagrams with multiple particle labels separated by / one particle label is chosen. In diagrams with particle labels separated by | the labels must be chosen in the same order. For example, in the four boson electroweak case the valid diagrams are WWWW, WWZZ, WWγγ, WWZγ. The conjugate of each listed vertex (reversing the direction of arrows) is also allowed.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The Standard Model includes 4 kinds of <a href="/wiki/Gauge_boson" title="Gauge boson">gauge bosons</a> of <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a> 1,<sup id="cite_ref-:0_35-2" class="reference"><a href="#cite_note-:0-35"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> with bosons being quantum particles containing an integer spin. The gauge bosons are defined as <a href="/wiki/Force_carrier" title="Force carrier">force carriers</a>, as they are responsible for mediating the <a href="/wiki/Fundamental_interaction" title="Fundamental interaction">fundamental interactions</a>. The Standard Model explains the four fundamental forces as arising from the interactions, with fermions <a href="/wiki/Static_forces_and_virtual-particle_exchange" title="Static forces and virtual-particle exchange">exchanging</a> <a href="/wiki/Virtual_particle" title="Virtual particle">virtual</a> force carrier particles, thus mediating the forces. At a macroscopic scale, this manifests as a <a href="/wiki/Force" title="Force">force</a>.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> As a result, they do not follow the Pauli exclusion principle that constrains fermions; bosons do not have a theoretical limit on their <a href="/wiki/Volume_number_density" class="mw-redirect" title="Volume number density">spatial density</a>. The types of gauge bosons are described below. </p> <ul><li><a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetism</a>: <a href="/wiki/Photon" title="Photon">Photons</a> mediate the electromagnetic force, responsible for interactions between electrically charged particles. The photon is massless and is described by the theory of <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">quantum electrodynamics</a> (QED).</li> <li><a href="/wiki/Strong_interaction" title="Strong interaction">Strong Interactions</a>: <a href="/wiki/Gluon" title="Gluon">Gluons</a> mediate the strong interactions, which binds quarks to each other by influencing the <a href="/wiki/Color_charge" title="Color charge">color charge</a>, with the interactions being described in the theory of <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">quantum chromodynamics</a> (QCD). They have no mass, and there are eight distinct gluons, with each being denoted through a color-anticolor charge combination (e.g. red–antigreen).<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>note 2<span class="cite-bracket">]</span></a></sup> As gluons have an effective color charge, they can also interact amongst themselves.</li> <li><a href="/wiki/Weak_interaction" title="Weak interaction">Weak Interactions</a>: The <a href="/wiki/W_and_Z_bosons" title="W and Z bosons"><span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>W<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>, <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>W<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>, and <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>Z<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span></a> gauge bosons mediate the weak interactions between all fermions, being responsible for <a href="/wiki/Radioactive_decay" title="Radioactive decay">radioactivity</a>. They contain mass, with the <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>Z<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> having more mass than the <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>W<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">±</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span>. The weak interactions involving the <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>W<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">±</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> act only on <a href="/wiki/Chirality_(physics)" title="Chirality (physics)"><i>left-handed</i> particles and <i>right-handed</i> antiparticles</a>. The <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>W<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">±</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> carries an electric charge of +1 and −1 and couples to the electromagnetic interaction. The electrically neutral <span style="white-space:nowrap;"><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:right"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span>Z<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.0em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> boson interacts with both left-handed particles and right-handed antiparticles. These three gauge bosons along with the photons are grouped together, as collectively mediating the <a href="/wiki/Electroweak" class="mw-redirect" title="Electroweak">electroweak</a> interaction.</li> <li><a href="/wiki/Gravity" title="Gravity">Gravity</a>: It is currently unexplained in the Standard Model, as the hypothetical mediating particle <a href="/wiki/Graviton" title="Graviton">graviton</a> has been proposed, but not observed.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> This is due to the incompatibility of quantum mechanics and <a href="/wiki/General_relativity" title="General relativity">Einstein's theory of general relativity</a>, regarded as being the best explanation for gravity. In general relativity, gravity is explained as being the geometric curving of spacetime.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup></li></ul> <p>The <a href="/wiki/Feynman_diagram" title="Feynman diagram">Feynman diagram</a> calculations, which are a graphical representation of the <a href="/wiki/Perturbation_theory_(quantum_mechanics)" title="Perturbation theory (quantum mechanics)">perturbation theory</a> approximation, invoke "force mediating particles", and when applied to analyze <a href="/wiki/Particle_accelerator" title="Particle accelerator">high-energy scattering experiments</a> are in reasonable agreement with the data. However, perturbation theory (and with it the concept of a "force-mediating particle") fails in other situations. These include low-energy quantum chromodynamics, <a href="/wiki/Bound_state" title="Bound state">bound states</a>, and <a href="/wiki/Soliton" title="Soliton">solitons</a>. The interactions between all the particles described by the Standard Model are summarized by the diagrams on the right of this section. </p> <div class="mw-heading mw-heading3"><h3 id="Higgs_boson">Higgs boson</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=5" title="Edit section: Higgs boson"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Higgs_boson" title="Higgs boson">Higgs boson</a></div> <p>The Higgs particle is a massive <a href="/wiki/Scalar_field_theory" title="Scalar field theory">scalar</a> elementary particle theorized by <a href="/wiki/Peter_Higgs" title="Peter Higgs">Peter Higgs</a> (<a href="/wiki/1964_PRL_symmetry_breaking_papers" title="1964 PRL symmetry breaking papers">and others</a>) in 1964, when he showed that Goldstone's 1962 theorem (generic continuous symmetry, which is spontaneously broken) provides a third polarisation of a massive vector field. Hence, Goldstone's original scalar doublet, the massive spin-zero particle, was <a href="/wiki/1964_PRL_symmetry_breaking_papers" title="1964 PRL symmetry breaking papers">proposed as the Higgs boson</a>, and is a key building block in the Standard Model.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> It has no intrinsic <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a>, and for that reason is classified as a <a href="/wiki/Boson" title="Boson">boson</a> with spin-0.<sup id="cite_ref-:0_35-3" class="reference"><a href="#cite_note-:0-35"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>The Higgs boson plays a unique role in the Standard Model, by explaining why the other elementary particles, except the <a href="/wiki/Photon" title="Photon">photon</a> and <a href="/wiki/Gluon" title="Gluon">gluon</a>, are massive. In particular, the Higgs boson explains why the photon has no mass, while the <a href="/wiki/W_and_Z_bosons" title="W and Z bosons">W and Z bosons</a> are very heavy. Elementary-particle masses and the differences between <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> (mediated by the photon) and the <a href="/wiki/Weak_force" class="mw-redirect" title="Weak force">weak force</a> (mediated by the W and Z bosons) are critical to many aspects of the structure of microscopic (and hence macroscopic) matter. In <a href="/wiki/Electroweak_interaction" title="Electroweak interaction">electroweak theory</a>, the Higgs boson generates the masses of the leptons (electron, muon, and tau) and quarks. As the Higgs boson is massive, it must interact with itself. </p><p>Because the Higgs boson is a very massive particle and also decays almost immediately when created, only a very high-energy <a href="/wiki/Particle_accelerator" title="Particle accelerator">particle accelerator</a> can observe and record it. Experiments to confirm and determine the nature of the Higgs boson using the <a href="/wiki/Large_Hadron_Collider" title="Large Hadron Collider">Large Hadron Collider</a> (LHC) at <a href="/wiki/CERN" title="CERN">CERN</a> began in early 2010 and were performed at <a href="/wiki/Fermilab" title="Fermilab">Fermilab</a>'s <a href="/wiki/Tevatron" title="Tevatron">Tevatron</a> until its closure in late 2011. Mathematical consistency of the Standard Model requires that any mechanism capable of generating the masses of elementary particles must become visible<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="Isn't "apparent" or "manifest" needed here instead of "visible"? (July 2013)">clarification needed</span></a></i>]</sup> at energies above <span class="nowrap"><span data-sort-value="6993224304708179999♠"></span>1.4 <a href="/wiki/Electronvolt" title="Electronvolt">TeV</a></span>;<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> therefore, the LHC (designed to collide two <span class="nowrap"><span data-sort-value="6994112152354090000♠"></span>7 TeV</span> proton beams) was built to answer the question of whether the Higgs boson actually exists.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p><p>On 4 July 2012, two of the experiments at the LHC (<a href="/wiki/ATLAS_experiment" title="ATLAS experiment">ATLAS</a> and <a href="/wiki/Compact_Muon_Solenoid" title="Compact Muon Solenoid">CMS</a>) both reported independently that they had found a new particle with a mass of about <span class="nowrap"><span data-sort-value="7002125000000000000♠"></span>125 <a href="/wiki/Electronvolt#Mass" title="Electronvolt">GeV/<i>c</i><sup>2</sup></a></span> (about 133 proton masses, on the order of <span class="nowrap"><span data-sort-value="6975100000000000000♠"></span>10<sup>−25</sup> kg</span>), which is "consistent with the Higgs boson".<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-NYT-20120704_50-0" class="reference"><a href="#cite_note-NYT-20120704-50"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> On 13 March 2013, it was confirmed to be the searched-for Higgs boson.<sup id="cite_ref-CERN_20130314_51-0" class="reference"><a href="#cite_note-CERN_20130314-51"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CERN_EPS2017_52-0" class="reference"><a href="#cite_note-CERN_EPS2017-52"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Theoretical_aspects">Theoretical aspects</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=6" title="Edit section: Theoretical aspects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Mathematical_formulation_of_the_Standard_Model" title="Mathematical formulation of the Standard Model">Mathematical formulation of the Standard Model</a></div> <div class="mw-heading mw-heading3"><h3 id="Construction_of_the_Standard_Model_Lagrangian">Construction of the Standard Model Lagrangian</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=7" title="Edit section: Construction of the Standard Model Lagrangian"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable collapsible collapsed"> <tbody><tr> <th colspan="6">Parameters of the Standard Model </th></tr> <tr> <th># </th> <th>Symbol </th> <th>Description </th> <th>Renormalization<br /> scheme (point) </th> <th>Value </th></tr> <tr> <td>1 </td> <td><i>m</i><sub>e</sub> </td> <td>Electron mass </td> <td> </td> <td>0.511 MeV </td></tr> <tr> <td>2 </td> <td><i>m</i><sub>μ</sub> </td> <td>Muon mass </td> <td> </td> <td>105.7 MeV </td></tr> <tr> <td>3 </td> <td><i>m</i><sub>τ</sub> </td> <td>Tau mass </td> <td> </td> <td>1.78 GeV </td></tr> <tr> <td>4 </td> <td><i>m</i><sub>u</sub> </td> <td>Up quark mass </td> <td><i>μ</i><sub><span style="text-decoration:overline;">MS</span></sub> = 2 GeV </td> <td>1.9 MeV </td></tr> <tr> <td>5 </td> <td><i>m</i><sub>d</sub> </td> <td>Down quark mass </td> <td><i>μ</i><sub><span style="text-decoration:overline;">MS</span></sub> = 2 GeV </td> <td>4.4 MeV </td></tr> <tr> <td>6 </td> <td><i>m</i><sub>s</sub> </td> <td>Strange quark mass </td> <td><i>μ</i><sub><span style="text-decoration:overline;">MS</span></sub> = 2 GeV </td> <td>87 MeV </td></tr> <tr> <td>7 </td> <td><i>m</i><sub>c</sub> </td> <td>Charm quark mass </td> <td><i>μ</i><sub><span style="text-decoration:overline;">MS</span></sub> = <i>m</i><sub>c</sub> </td> <td>1.32 GeV </td></tr> <tr> <td>8 </td> <td><i>m</i><sub>b</sub> </td> <td>Bottom quark mass </td> <td><i>μ</i><sub><span style="text-decoration:overline;">MS</span></sub> = <i>m</i><sub>b</sub> </td> <td>4.24 GeV </td></tr> <tr> <td>9 </td> <td><i>m</i><sub>t</sub> </td> <td>Top quark mass </td> <td>On shell scheme </td> <td>173.5 GeV </td></tr> <tr> <td>10 </td> <td><i>θ</i><sub>12</sub> </td> <td>CKM 12-mixing angle </td> <td> </td> <td>13.1° </td></tr> <tr> <td>11 </td> <td><i>θ</i><sub>23</sub> </td> <td>CKM 23-mixing angle </td> <td> </td> <td>2.4° </td></tr> <tr> <td>12 </td> <td><i>θ</i><sub>13</sub> </td> <td>CKM 13-mixing angle </td> <td> </td> <td>0.2° </td></tr> <tr> <td>13 </td> <td><i>δ</i> </td> <td>CKM CP violation Phase </td> <td> </td> <td>0.995 </td></tr> <tr> <td>14 </td> <td><i>g</i><sub>1</sub> or <i>g</i><span class="nowrap" style="padding-left:0.1em;">'</span> </td> <td>U(1) gauge coupling </td> <td><i>μ</i><sub><span style="text-decoration:overline;">MS</span></sub> = <i>m</i><sub>Z</sub> </td> <td>0.357 </td></tr> <tr> <td>15 </td> <td><i>g</i><sub>2</sub> or <i>g</i> </td> <td>SU(2) gauge coupling </td> <td><i>μ</i><sub><span style="text-decoration:overline;">MS</span></sub> = <i>m</i><sub>Z</sub> </td> <td>0.652 </td></tr> <tr> <td>16 </td> <td><i>g</i><sub>3</sub> or <i>g</i><sub>s</sub> </td> <td>SU(3) gauge coupling </td> <td><i>μ</i><sub><span style="text-decoration:overline;">MS</span></sub> = <i>m</i><sub>Z</sub> </td> <td>1.221 </td></tr> <tr> <td>17 </td> <td><i>θ</i><sub>QCD</sub> </td> <td>QCD vacuum angle </td> <td> </td> <td>~0 </td></tr> <tr> <td>18 </td> <td><i>v</i> </td> <td>Higgs vacuum expectation value </td> <td> </td> <td>246 GeV </td></tr> <tr> <td>19 </td> <td><i>m</i><sub>H</sub> </td> <td>Higgs mass </td> <td> </td> <td><span class="nowrap"><span data-sort-value="6992200416256758830♠"></span>125.09<span style="margin-left:0.3em;margin-right:0.15em;">±</span>0.24 GeV</span> </td></tr></tbody></table> <p>Technically, <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a> provides the mathematical framework for the Standard Model, in which a <a href="/wiki/Lagrangian_(field_theory)" title="Lagrangian (field theory)">Lagrangian</a> controls the dynamics and kinematics of the theory. Each kind of particle is described in terms of a dynamical <a href="/wiki/Field_(physics)" title="Field (physics)">field</a> that pervades <a href="/wiki/Space-time" class="mw-redirect" title="Space-time">space-time</a>.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> The construction of the Standard Model proceeds following the modern method of constructing most field theories: by first postulating a set of symmetries of the system, and then by writing down the most general <a href="/wiki/Renormalization" title="Renormalization">renormalizable</a> Lagrangian from its particle (field) content that observes these symmetries. </p><p>The <a href="/wiki/Global_symmetry" class="mw-redirect" title="Global symmetry">global</a> <a href="/wiki/Poincar%C3%A9_group" title="Poincaré group">Poincaré symmetry</a> is postulated for all relativistic quantum field theories. It consists of the familiar <a href="/wiki/Translational_symmetry" title="Translational symmetry">translational symmetry</a>, <a href="/wiki/Rotational_symmetry" title="Rotational symmetry">rotational symmetry</a> and the inertial reference frame invariance central to the theory of <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a>. The <a href="/wiki/Local_symmetry" class="mw-redirect" title="Local symmetry">local</a> SU(3)×SU(2)×U(1) <a href="/wiki/Gauge_symmetry" class="mw-redirect" title="Gauge symmetry">gauge symmetry</a> is an <a href="/wiki/Internal_symmetries" class="mw-redirect" title="Internal symmetries">internal symmetry</a> that essentially defines the Standard Model. Roughly, the three factors of the gauge symmetry give rise to the three fundamental interactions. The fields fall into different <a href="/wiki/Representation_of_a_Lie_group" title="Representation of a Lie group">representations</a> of the various symmetry groups of the Standard Model (see table). Upon writing the most general Lagrangian, one finds that the dynamics depends on 19 parameters, whose numerical values are established by experiment. The parameters are summarized in the table (made visible by clicking "show") above. </p> <div class="mw-heading mw-heading4"><h4 id="Quantum_chromodynamics_sector">Quantum chromodynamics sector</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=8" title="Edit section: Quantum chromodynamics sector"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">Quantum chromodynamics</a></div> <p>The quantum chromodynamics (QCD) sector defines the interactions between quarks and gluons, which is a <a href="/wiki/Yang%E2%80%93Mills_theory" title="Yang–Mills theory">Yang–Mills gauge theory</a> with SU(3) symmetry, generated by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T^{a}=\lambda ^{a}/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <mo>=</mo> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T^{a}=\lambda ^{a}/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f290eaca89deceb27e294b45c5d7eef69f368919" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.702ex; height:2.843ex;" alt="{\displaystyle T^{a}=\lambda ^{a}/2}"></span>. Since leptons do not interact with gluons, they are not affected by this sector. The Dirac Lagrangian of the quarks coupled to the gluon fields is given by </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {L}}_{\text{QCD}}={\overline {\psi }}i\gamma ^{\mu }D_{\mu }\psi -{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu },}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>QCD</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo accent="false">¯</mo> </mover> </mrow> <mi>i</mi> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mi>ψ</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msubsup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msubsup> <msubsup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msubsup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}_{\text{QCD}}={\overline {\psi }}i\gamma ^{\mu }D_{\mu }\psi -{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu },}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b0b7887d9441531a621c36261e44d6c83363d3f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:31.578ex; height:5.176ex;" alt="{\displaystyle {\mathcal {L}}_{\text{QCD}}={\overline {\psi }}i\gamma ^{\mu }D_{\mu }\psi -{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu },}"></span> </p><p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span> is a three component column vector of <a href="/wiki/Dirac_spinor" title="Dirac spinor">Dirac spinors</a>, each element of which refers to a quark field with a specific <a href="/wiki/Color_charge" title="Color charge">color charge</a> (i.e. red, blue, and green) and summation over <a href="/wiki/Flavour_(particle_physics)" title="Flavour (particle physics)">flavor</a> (i.e. up, down, strange, etc.) is implied. </p><p>The gauge covariant derivative of QCD is defined by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{\mu }\equiv \partial _{\mu }-ig_{s}{\frac {1}{2}}\lambda ^{a}G_{\mu }^{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo>≡</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo>−</mo> <mi>i</mi> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <msubsup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{\mu }\equiv \partial _{\mu }-ig_{s}{\frac {1}{2}}\lambda ^{a}G_{\mu }^{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b15c329be3ab10997fe5d72e3d086969acb2d7c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.965ex; height:5.176ex;" alt="{\displaystyle D_{\mu }\equiv \partial _{\mu }-ig_{s}{\frac {1}{2}}\lambda ^{a}G_{\mu }^{a}}"></span>, where </p> <ul><li><span class="texhtml mvar" style="font-style:italic;">γ<span style="padding-left:0.12em;"><sup>μ</sup></span></span> are the <a href="/wiki/Dirac_matrices" class="mw-redirect" title="Dirac matrices">Dirac matrices</a>,</li> <li><span class="texhtml mvar" style="font-style:italic;">G<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">a</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">μ</sub></span></span></span> is the 8-component (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=1,2,\dots ,8}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mn>8</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=1,2,\dots ,8}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/584f686125120403ab10cfd5b783fefe8e6d7121" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.028ex; height:2.509ex;" alt="{\displaystyle a=1,2,\dots ,8}"></span>) SU(3) gauge field,</li> <li><span class="texhtml mvar" style="font-style:italic;">λ<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">a</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span></span> are the 3 × 3 <a href="/wiki/Gell-Mann_matrices" title="Gell-Mann matrices">Gell-Mann matrices</a>, generators of the SU(3) color group,</li> <li><span class="texhtml mvar" style="font-style:italic;">G<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">a</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">μν</sub></span></span></span> represents the <a href="/wiki/Gluon_field_strength_tensor" title="Gluon field strength tensor">gluon field strength tensor</a>, and</li> <li><span class="texhtml mvar" style="font-style:italic;">g<sub>s</sub></span> is the strong coupling constant.</li></ul> <p>The QCD Lagrangian is invariant under local SU(3) gauge transformations; i.e., transformations of the form <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi \rightarrow \psi '=U\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo stretchy="false">→</mo> <msup> <mi>ψ</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>U</mi> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi \rightarrow \psi '=U\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84a9551de66e75e4d79772d14265223ff7b05ab8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.719ex; height:2.843ex;" alt="{\displaystyle \psi \rightarrow \psi '=U\psi }"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U=e^{-ig_{s}\lambda ^{a}\phi ^{a}(x)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>i</mi> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <msup> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U=e^{-ig_{s}\lambda ^{a}\phi ^{a}(x)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/086a876065b936c79684a50e0b135cca44b92d75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.515ex; height:2.843ex;" alt="{\displaystyle U=e^{-ig_{s}\lambda ^{a}\phi ^{a}(x)}}"></span> is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3\times 3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3\times 3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddc0d4d6106875f8006be1d898512ca5843bad8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.165ex; height:2.176ex;" alt="{\displaystyle 3\times 3}"></span> unitary matrix with determinant 1, making it a member of the group SU(3), and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi ^{a}(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi ^{a}(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37df4c1c86a7b6f8812c30cfcd93bbd4783cf3a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.626ex; height:2.843ex;" alt="{\displaystyle \phi ^{a}(x)}"></span> is an arbitrary function of spacetime. </p> <div class="mw-heading mw-heading4"><h4 id="Electroweak_sector">Electroweak sector</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=9" title="Edit section: Electroweak sector"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Electroweak_interaction" title="Electroweak interaction">Electroweak interaction</a></div> <p>The electroweak sector is a <a href="/wiki/Yang%E2%80%93Mills_theory" title="Yang–Mills theory">Yang–Mills gauge theory</a> with the symmetry group U(1) × SU(2)<sub>L</sub>, </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {L}}_{\text{EW}}={\overline {Q}}_{Lj}i\gamma ^{\mu }D_{\mu }Q_{Lj}+{\overline {u}}_{Rj}i\gamma ^{\mu }D_{\mu }u_{Rj}+{\overline {d}}_{Rj}i\gamma ^{\mu }D_{\mu }d_{Rj}+{\overline {\ell }}_{Lj}i\gamma ^{\mu }D_{\mu }\ell _{Lj}+{\overline {e}}_{Rj}i\gamma ^{\mu }D_{\mu }e_{Rj}-{\tfrac {1}{4}}W_{a}^{\mu \nu }W_{\mu \nu }^{a}-{\tfrac {1}{4}}B^{\mu \nu }B_{\mu \nu },}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>EW</mtext> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>Q</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> <mi>j</mi> </mrow> </msub> <mi>i</mi> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> <mi>j</mi> </mrow> </msub> <mi>i</mi> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>d</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> <mi>j</mi> </mrow> </msub> <mi>i</mi> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ℓ</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> <mi>j</mi> </mrow> </msub> <mi>i</mi> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>e</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> <mi>j</mi> </mrow> </msub> <mi>i</mi> <msup> <mi>γ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msubsup> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msubsup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}_{\text{EW}}={\overline {Q}}_{Lj}i\gamma ^{\mu }D_{\mu }Q_{Lj}+{\overline {u}}_{Rj}i\gamma ^{\mu }D_{\mu }u_{Rj}+{\overline {d}}_{Rj}i\gamma ^{\mu }D_{\mu }d_{Rj}+{\overline {\ell }}_{Lj}i\gamma ^{\mu }D_{\mu }\ell _{Lj}+{\overline {e}}_{Rj}i\gamma ^{\mu }D_{\mu }e_{Rj}-{\tfrac {1}{4}}W_{a}^{\mu \nu }W_{\mu \nu }^{a}-{\tfrac {1}{4}}B^{\mu \nu }B_{\mu \nu },}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb742e1b52f87adea9049004d083e331b89b3e75" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:112.128ex; height:3.843ex;" alt="{\displaystyle {\mathcal {L}}_{\text{EW}}={\overline {Q}}_{Lj}i\gamma ^{\mu }D_{\mu }Q_{Lj}+{\overline {u}}_{Rj}i\gamma ^{\mu }D_{\mu }u_{Rj}+{\overline {d}}_{Rj}i\gamma ^{\mu }D_{\mu }d_{Rj}+{\overline {\ell }}_{Lj}i\gamma ^{\mu }D_{\mu }\ell _{Lj}+{\overline {e}}_{Rj}i\gamma ^{\mu }D_{\mu }e_{Rj}-{\tfrac {1}{4}}W_{a}^{\mu \nu }W_{\mu \nu }^{a}-{\tfrac {1}{4}}B^{\mu \nu }B_{\mu \nu },}"></span> </p><p>where the subscript <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span> sums over the three generations of fermions; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{L},u_{R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{L},u_{R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0c331e0daf380932ea1e60798aa92ba620f8bd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.033ex; height:2.509ex;" alt="{\displaystyle Q_{L},u_{R}}"></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d_{R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df56a3afd4b194ddabfc645c5553b9da6a781802" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.689ex; height:2.509ex;" alt="{\displaystyle d_{R}}"></span> are the left-handed doublet, right-handed singlet up type, and right handed singlet down type quark fields; and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell _{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell _{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ebbe64726d0ded087547eb3c97ca2b3934311f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.321ex; height:2.509ex;" alt="{\displaystyle \ell _{L}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e_{R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e_{R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a1d0de48b69c5f8a6850b73e5103c3b71e9a396" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.563ex; height:2.009ex;" alt="{\displaystyle e_{R}}"></span> are the left-handed doublet and right-handed singlet lepton fields. </p><p>The electroweak <a href="/wiki/Gauge_covariant_derivative" title="Gauge covariant derivative">gauge covariant derivative</a> is defined as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{\mu }\equiv \partial _{\mu }-ig'{\tfrac {1}{2}}Y_{\text{W}}B_{\mu }-ig{\tfrac {1}{2}}{\vec {\tau }}_{\text{L}}{\vec {W}}_{\mu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo>≡</mo> <msub> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo>−</mo> <mi>i</mi> <msup> <mi>g</mi> <mo>′</mo> </msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>W</mtext> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mo>−</mo> <mi>i</mi> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>τ</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>W</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{\mu }\equiv \partial _{\mu }-ig'{\tfrac {1}{2}}Y_{\text{W}}B_{\mu }-ig{\tfrac {1}{2}}{\vec {\tau }}_{\text{L}}{\vec {W}}_{\mu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78e05c60adee36a88046b5a6f44606aef696000c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:34.736ex; height:3.676ex;" alt="{\displaystyle D_{\mu }\equiv \partial _{\mu }-ig'{\tfrac {1}{2}}Y_{\text{W}}B_{\mu }-ig{\tfrac {1}{2}}{\vec {\tau }}_{\text{L}}{\vec {W}}_{\mu }}"></span>, where </p> <ul><li><span class="texhtml mvar" style="font-style:italic;">B<sub>μ</sub></span> is the U(1) gauge field,</li> <li><span class="texhtml"><i>Y</i><sub>W</sub></span> is the <a href="/wiki/Weak_hypercharge" title="Weak hypercharge">weak hypercharge</a> – the generator of the U(1) group,</li> <li><span class="texhtml"><i>W</i><span style="position:relative; margin-right:-0.75em; right:0.75em; bottom:0.75em;;"><small>→</small></span><sub><i>μ</i></sub></span> is the 3-component SU(2) gauge field,</li> <li><span class="texhtml"><i>τ</i><sub>L</sub><span style="position:relative; margin-right:-0.75em; right:0.75em; bottom:0.75em;;"><small>→</small></span></span> are the <a href="/wiki/Pauli_matrices" title="Pauli matrices">Pauli matrices</a> – infinitesimal generators of the SU(2) group – with subscript L to indicate that they only act on <i>left</i>-chiral fermions,</li> <li><span class="texhtml mvar" style="font-style:italic;">g'</span> and <span class="texhtml mvar" style="font-style:italic;">g</span> are the U(1) and SU(2) coupling constants respectively,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W^{a\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W^{a\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a93ca35bec9eef586d6eb6b379c6047fd200bf8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.472ex; height:2.343ex;" alt="{\displaystyle W^{a\mu \nu }}"></span> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=1,2,3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=1,2,3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26e89beb689f72161ecea41ea832a68113d8c239" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.884ex; height:2.509ex;" alt="{\displaystyle a=1,2,3}"></span>) and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B^{\mu \nu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> <mi>ν</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B^{\mu \nu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb1aedcb45482f596c64eb5fc96eba754d5eeaad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.859ex; height:2.343ex;" alt="{\displaystyle B^{\mu \nu }}"></span> are the <a href="/wiki/Field_strength_tensor" class="mw-redirect" title="Field strength tensor">field strength tensors</a> for the weak isospin and weak hypercharge fields.</li></ul> <p>Notice that the addition of fermion mass terms into the electroweak Lagrangian is forbidden, since terms of the form <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m{\overline {\psi }}\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ψ</mi> <mo accent="false">¯</mo> </mover> </mrow> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m{\overline {\psi }}\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b96616c4307954df9f951c501fd9c5f35a94973c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.182ex; height:3.343ex;" alt="{\displaystyle m{\overline {\psi }}\psi }"></span> do not respect U(1) × SU(2)<sub>L</sub> gauge invariance. Neither is it possible to add explicit mass terms for the U(1) and SU(2) gauge fields. The Higgs mechanism is responsible for the generation of the gauge boson masses, and the fermion masses result from Yukawa-type interactions with the Higgs field. </p> <div class="mw-heading mw-heading4"><h4 id="Higgs_sector">Higgs sector</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=10" title="Edit section: Higgs sector"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Higgs_mechanism" title="Higgs mechanism">Higgs mechanism</a></div> <p>In the Standard Model, the <a href="/wiki/Higgs_field" class="mw-redirect" title="Higgs field">Higgs field</a> is an <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {SU} (2)_{\text{L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>SU</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {SU} (2)_{\text{L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6893c4b12b93bc5c39cc31d4971ea8401cb21573" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.267ex; height:2.843ex;" alt="{\displaystyle \operatorname {SU} (2)_{\text{L}}}"></span> doublet of complex <a href="/wiki/Scalar_(physics)" title="Scalar (physics)">scalar</a> fields with four degrees of freedom: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi ={\begin{pmatrix}\varphi ^{+}\\\varphi ^{0}\end{pmatrix}}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}\varphi _{1}+i\varphi _{2}\\\varphi _{3}+i\varphi _{4}\end{pmatrix}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>i</mi> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mi>i</mi> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi ={\begin{pmatrix}\varphi ^{+}\\\varphi ^{0}\end{pmatrix}}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}\varphi _{1}+i\varphi _{2}\\\varphi _{3}+i\varphi _{4}\end{pmatrix}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86d706e3335d1e731c4d82501fbd8c862ff03bd2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:32.466ex; height:6.509ex;" alt="{\displaystyle \varphi ={\begin{pmatrix}\varphi ^{+}\\\varphi ^{0}\end{pmatrix}}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}\varphi _{1}+i\varphi _{2}\\\varphi _{3}+i\varphi _{4}\end{pmatrix}},}"></span> where the superscripts + and 0 indicate the electric charge <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> of the components. The weak hypercharge <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y_{\text{W}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>W</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{\text{W}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/832ea281734f232f063dc72cdaf2b16a7defb76a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.272ex; height:2.509ex;" alt="{\displaystyle Y_{\text{W}}}"></span> of both components is 1. Before symmetry breaking, the Higgs Lagrangian is <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {L}}_{\text{H}}=\left(D_{\mu }\varphi \right)^{\dagger }\left(D^{\mu }\varphi \right)-V(\varphi ),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>H</mtext> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <msup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msup> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}_{\text{H}}=\left(D_{\mu }\varphi \right)^{\dagger }\left(D^{\mu }\varphi \right)-V(\varphi ),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1121d1b03dd17bdfb3fcda4d20348f0aa3afc07c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:29.074ex; height:3.509ex;" alt="{\displaystyle {\mathcal {L}}_{\text{H}}=\left(D_{\mu }\varphi \right)^{\dagger }\left(D^{\mu }\varphi \right)-V(\varphi ),}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{\mu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{\mu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/267983ed233945e70f42935df28e623cfce15c12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.148ex; height:2.843ex;" alt="{\displaystyle D_{\mu }}"></span> is the electroweak gauge covariant derivative defined above and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V(\varphi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(\varphi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35516139da223f6fe5129764734d9932abe27673" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.117ex; height:2.843ex;" alt="{\displaystyle V(\varphi )}"></span> is the potential of the Higgs field. The square of the covariant derivative leads to three and four point interactions between the electroweak gauge fields <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{\mu }^{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W_{\mu }^{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/900a6ee8c880be1e7089aa8bef2aa29b02de241e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.61ex; height:2.843ex;" alt="{\displaystyle W_{\mu }^{a}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{\mu }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{\mu }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fe5f2581724819fecf73ea084522e1278fcde4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.987ex; height:2.843ex;" alt="{\displaystyle B_{\mu }}"></span> and the scalar field <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span>. The scalar potential is given by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V(\varphi )=-\mu ^{2}\varphi ^{\dagger }\varphi +\lambda \left(\varphi ^{\dagger }\varphi \right)^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msup> <mi>φ</mi> <mo>+</mo> <mi>λ</mi> <msup> <mrow> <mo>(</mo> <mrow> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msup> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(\varphi )=-\mu ^{2}\varphi ^{\dagger }\varphi +\lambda \left(\varphi ^{\dagger }\varphi \right)^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f704fe82b0ec9fade63b6781ff21326c042778a6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:28.511ex; height:3.843ex;" alt="{\displaystyle V(\varphi )=-\mu ^{2}\varphi ^{\dagger }\varphi +\lambda \left(\varphi ^{\dagger }\varphi \right)^{2},}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu ^{2}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu ^{2}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0772c3f1368864f3d8d1eb4ec89927740b52f88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.717ex; height:3.176ex;" alt="{\displaystyle \mu ^{2}>0}"></span>, so that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> acquires a non-zero <a href="/wiki/Vacuum_expectation_value" title="Vacuum expectation value">Vacuum expectation value</a>, which generates masses for the Electroweak gauge fields (the Higgs' mechanism), and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eea25afc0351140f919cf791c49c1964b8b081de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.616ex; height:2.176ex;" alt="{\displaystyle \lambda >0}"></span>, so that the potential is bounded from below. The quartic term describes self-interactions of the scalar field <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span>. </p><p>The minimum of the potential is degenerate with an infinite number of equivalent <a href="/wiki/Ground_state" title="Ground state">ground state</a> solutions, which occurs when <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi ^{\dagger }\varphi ={\tfrac {\mu ^{2}}{2\lambda }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msup> <mi>φ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>λ</mi> </mrow> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi ^{\dagger }\varphi ={\tfrac {\mu ^{2}}{2\lambda }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4086c2d9f31abc2c4793611a551ae4600494cb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:9.76ex; height:4.509ex;" alt="{\displaystyle \varphi ^{\dagger }\varphi ={\tfrac {\mu ^{2}}{2\lambda }}}"></span>. It is possible to perform a <a href="/wiki/Unitary_gauge" class="mw-redirect" title="Unitary gauge">gauge transformation</a> on <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> such that the ground state is transformed to a basis where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{4}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{4}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ceff904baec83e124b9e1a3e4cc7ecd1075cfb5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.181ex; height:2.676ex;" alt="{\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{4}=0}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi _{3}={\tfrac {\mu }{\sqrt {\lambda }}}\equiv v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>μ</mi> <msqrt> <mi>λ</mi> </msqrt> </mfrac> </mstyle> </mrow> <mo>≡</mo> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{3}={\tfrac {\mu }{\sqrt {\lambda }}}\equiv v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2eab2210a4ec31a287f7052e682748591360368b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.062ex; height:4.176ex;" alt="{\displaystyle \varphi _{3}={\tfrac {\mu }{\sqrt {\lambda }}}\equiv v}"></span>. This breaks the symmetry of the ground state. The expectation value of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> now becomes <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle \varphi \rangle ={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0\\v\end{pmatrix}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mi>φ</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>v</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle \varphi \rangle ={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0\\v\end{pmatrix}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/969ca007ecefec4d8cabe897f7856626278d32c4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:16.344ex; height:6.509ex;" alt="{\displaystyle \langle \varphi \rangle ={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0\\v\end{pmatrix}},}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span> has units of mass and sets the scale of electroweak physics. This is the only dimensional parameter of the Standard Model and has a measured value of ~<span class="nowrap"><span data-sort-value="7002246000000000000♠"></span>246 GeV/<i>c</i><sup>2</sup></span>. </p><p>After symmetry breaking, the masses of the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{W}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>W</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{W}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c2d00245e075824f4e403c08e4d8a4ab43bac58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.389ex; height:2.176ex;" alt="{\displaystyle {\text{W}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{Z}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Z</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{Z}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99f643acd962d347b3e6e43f7154653d770a5b76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.42ex; height:2.176ex;" alt="{\displaystyle {\text{Z}}}"></span> are given by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{\text{W}}={\frac {1}{2}}gv}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>W</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>g</mi> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\text{W}}={\frac {1}{2}}gv}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a28416839d0fba95d0a40b9b712d4522c1205016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.302ex; height:5.176ex;" alt="{\displaystyle m_{\text{W}}={\frac {1}{2}}gv}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{\text{Z}}={\frac {1}{2}}{\sqrt {g^{2}+g'^{2}}}v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>Z</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>g</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </msqrt> </mrow> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\text{Z}}={\frac {1}{2}}{\sqrt {g^{2}+g'^{2}}}v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/843bb536945512340849f536ba9b9fb5e5301ad8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.463ex; height:5.176ex;" alt="{\displaystyle m_{\text{Z}}={\frac {1}{2}}{\sqrt {g^{2}+g'^{2}}}v}"></span>, which can be viewed as predictions of the theory. The photon remains massless. The mass of the <a href="/wiki/Higgs_Boson" class="mw-redirect" title="Higgs Boson">Higgs Boson</a> is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{\text{H}}={\sqrt {2\mu ^{2}}}={\sqrt {2\lambda }}v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>H</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mi>λ</mi> </msqrt> </mrow> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\text{H}}={\sqrt {2\mu ^{2}}}={\sqrt {2\lambda }}v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10b856dffa86ff43b2cdfab4c632525604e590bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:21.225ex; height:4.843ex;" alt="{\displaystyle m_{\text{H}}={\sqrt {2\mu ^{2}}}={\sqrt {2\lambda }}v}"></span>. Since <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> are free parameters, the Higgs' mass could not be predicted beforehand and had to be determined experimentally. </p> <div class="mw-heading mw-heading4"><h4 id="Yukawa_sector">Yukawa sector</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=11" title="Edit section: Yukawa sector"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Yukawa_interaction" title="Yukawa interaction">Yukawa interaction</a> terms are: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {L}}_{\text{Yukawa}}=(Y_{\text{u}})_{mn}({\bar {Q}}_{\text{L}})_{m}{\tilde {\varphi }}(u_{\text{R}})_{n}+(Y_{\text{d}})_{mn}({\bar {Q}}_{\text{L}})_{m}\varphi (d_{\text{R}})_{n}+(Y_{\text{e}})_{mn}({\bar {\ell }}_{\text{L}})_{m}{\varphi }(e_{\text{R}})_{n}+\mathrm {h.c.} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>Yukawa</mtext> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>u</mtext> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>Q</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>φ</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>R</mtext> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>Q</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mi>φ</mi> <mo stretchy="false">(</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>R</mtext> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ℓ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi>φ</mi> </mrow> <mo stretchy="false">(</mo> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>R</mtext> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> <mo>.</mo> <mi mathvariant="normal">c</mi> <mo>.</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {L}}_{\text{Yukawa}}=(Y_{\text{u}})_{mn}({\bar {Q}}_{\text{L}})_{m}{\tilde {\varphi }}(u_{\text{R}})_{n}+(Y_{\text{d}})_{mn}({\bar {Q}}_{\text{L}})_{m}\varphi (d_{\text{R}})_{n}+(Y_{\text{e}})_{mn}({\bar {\ell }}_{\text{L}})_{m}{\varphi }(e_{\text{R}})_{n}+\mathrm {h.c.} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/631781a4722c53e78373c44dc84b75dbe69f0a26" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:84.959ex; height:3.176ex;" alt="{\displaystyle {\mathcal {L}}_{\text{Yukawa}}=(Y_{\text{u}})_{mn}({\bar {Q}}_{\text{L}})_{m}{\tilde {\varphi }}(u_{\text{R}})_{n}+(Y_{\text{d}})_{mn}({\bar {Q}}_{\text{L}})_{m}\varphi (d_{\text{R}})_{n}+(Y_{\text{e}})_{mn}({\bar {\ell }}_{\text{L}})_{m}{\varphi }(e_{\text{R}})_{n}+\mathrm {h.c.} }"></span> </p><p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y_{\text{u}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>u</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{\text{u}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/981c3edfdac996c9d21da2440a206e692692cf74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.497ex; height:2.509ex;" alt="{\displaystyle Y_{\text{u}}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y_{\text{d}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{\text{d}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e39cac0d67e06243c7e65ffc0a78b748eb0455a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.497ex; height:2.509ex;" alt="{\displaystyle Y_{\text{d}}}"></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y_{\text{e}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{\text{e}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6edaf2398a78c9c4ad6924a848d3438fcd430ddc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.313ex; height:2.509ex;" alt="{\displaystyle Y_{\text{e}}}"></span> are <span class="texhtml">3 × 3</span> matrices of Yukawa couplings, with the <span class="texhtml mvar" style="font-style:italic;">mn</span> term giving the coupling of the generations <span class="texhtml mvar" style="font-style:italic;">m</span> and <span class="texhtml mvar" style="font-style:italic;">n</span>, and h.c. means Hermitian conjugate of preceding terms. The fields <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{\text{L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{\text{L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d5eb41c53113e98d2d4a6b0d8f3f993a7579e06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:2.509ex;" alt="{\displaystyle Q_{\text{L}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell _{\text{L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell _{\text{L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fd2bf7c575e8ba912406fdff1557d6620f49bba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.229ex; height:2.509ex;" alt="{\displaystyle \ell _{\text{L}}}"></span> are left-handed quark and lepton doublets. Likewise, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{\text{R}},d_{\text{R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>R</mtext> </mrow> </msub> <mo>,</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>R</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{\text{R}},d_{\text{R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c7cc85cecf632eb69375061b163e8c5eb18f613" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.456ex; height:2.509ex;" alt="{\displaystyle u_{\text{R}},d_{\text{R}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e_{\text{R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>R</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e_{\text{R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2898f8fed9bc6d9cde28f60f7af1883eede490bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.525ex; height:2.009ex;" alt="{\displaystyle e_{\text{R}}}"></span> are right-handed up-type quark, down-type quark, and lepton singlets. Finally <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> is the Higgs doublet and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {\varphi }}=i\tau _{2}\varphi ^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>φ</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mo>=</mo> <mi>i</mi> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {\varphi }}=i\tau _{2}\varphi ^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70704c70119d005759715c450a1f1d6813def007" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.08ex; height:2.843ex;" alt="{\displaystyle {\tilde {\varphi }}=i\tau _{2}\varphi ^{*}}"></span> is its charge conjugate state. </p><p>The Yukawa terms are invariant under the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {SU} (2)_{\text{L}}\times \operatorname {U} (1)_{\text{Y}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>SU</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> <mo>×</mo> <mi mathvariant="normal">U</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>1</mn> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Y</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {SU} (2)_{\text{L}}\times \operatorname {U} (1)_{\text{Y}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7c31e658a37afaf5b9a740b87ff5244f9e013be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.287ex; height:2.843ex;" alt="{\displaystyle \operatorname {SU} (2)_{\text{L}}\times \operatorname {U} (1)_{\text{Y}}}"></span> gauge symmetry of the Standard Model and generate masses for all fermions after spontaneous symmetry breaking. </p> <div class="mw-heading mw-heading2"><h2 id="Fundamental_interactions">Fundamental interactions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=12" title="Edit section: Fundamental interactions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Fundamental_interaction" title="Fundamental interaction">Fundamental interaction</a></div> <p>The Standard Model describes three of the four fundamental interactions in nature; only gravity remains unexplained. In the Standard Model, such an interaction is described as an exchange of <a href="/wiki/Boson" title="Boson">bosons</a> between the objects affected, such as a <a href="/wiki/Photon" title="Photon">photon</a> for the electromagnetic force and a <a href="/wiki/Gluon" title="Gluon">gluon</a> for the strong interaction. Those particles are called <a href="/wiki/Force_carrier" title="Force carrier">force carriers</a> or messenger <a href="/wiki/Particles" class="mw-redirect" title="Particles">particles</a>.<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p> <table style="margin: 1em auto 1em auto;" class="wikitable floatcenter"> <caption><b>The four fundamental interactions of nature</b><sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </caption> <tbody><tr> <th style="" rowspan="2">Property/Interaction </th> <th style="background-color:#8080BF" rowspan="2">Gravitation </th> <th style="background-color:#BFA080" colspan="2">Electroweak </th> <th style="background-color:#80BF80" colspan="2">Strong </th></tr> <tr> <th style="background-color:#BFBF80">Weak </th> <th style="background-color:#BF8080">Electromagnetic </th> <th style="background-color:#AAD4AA"><small>Fundamental</small> </th> <th style="background-color:#D5EAD5"><small>Residual</small> </th></tr> <tr> <td>Mediating particles </td> <td align="center" style="background:var(--background-color-interactive, #eee); color: var(--color-base, #000);vertical-align:middle;text-align:center;">Not yet observed<br /><small>(<a href="/wiki/Graviton" title="Graviton">Graviton</a> hypothesised)</small> </td> <td align="center"><a href="/wiki/W_and_Z_bosons" title="W and Z bosons">W<sup>+</sup>, W<sup>−</sup> and Z<sup>0</sup></a> </td> <td align="center"><a href="/wiki/Photon" title="Photon">γ</a> (photon) </td> <td align="center">Gluons </td> <td align="center"><a href="/wiki/Pion" title="Pion">π</a>, <a href="/wiki/Rho_meson" title="Rho meson">ρ</a> and <a href="/wiki/Omega_meson" title="Omega meson">ω</a> <a href="/wiki/Meson" title="Meson">mesons</a> </td></tr> <tr> <td>Affected particles </td> <td align="center">All particles </td> <td align="center">Left-handed <a href="/wiki/Fermions" class="mw-redirect" title="Fermions">fermions</a> </td> <td align="center">Electrically charged </td> <td align="center">Quarks, <a href="/wiki/Gluon" title="Gluon">gluons</a> </td> <td align="center"><a href="/wiki/Hadron" title="Hadron">Hadrons</a> </td></tr> <tr> <td>Acts on </td> <td align="center"><a href="/wiki/Stress%E2%80%93energy_tensor" title="Stress–energy tensor">Stress–energy tensor</a> </td> <td align="center"><a href="/wiki/Flavour_(particle_physics)" title="Flavour (particle physics)">Flavour</a> </td> <td align="center">Electric charge </td> <td align="center"><a href="/wiki/Color_charge" title="Color charge">Color charge</a> </td> <td align="center"> </td></tr> <tr> <td>Bound states formed </td> <td align="center">Planets, stars, galaxies, galaxy groups </td> <td align="center" data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <td align="center">Atoms, molecules </td> <td align="center">Hadrons </td> <td align="center">Atomic nuclei </td></tr> <tr> <td>Strength at the scale of quarks<br /> (relative to electromagnetism) </td> <td align="center"><span class="nowrap"><span data-sort-value="6959100000000000000♠"></span>10<sup>−41</sup></span> <small>(predicted)</small> </td> <td align="center"><span class="nowrap"><span data-sort-value="6996100000000000000♠"></span>10<sup>−4</sup></span> </td> <td align="center">1 </td> <td align="center">60 </td> <td align="center" style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Not applicable <br />to quarks </td></tr> <tr> <td>Strength at the scale of <br />protons/neutrons <br /> (relative to electromagnetism) </td> <td align="center"><span class="nowrap"><span data-sort-value="6964100000000000000♠"></span>10<sup>−36</sup></span> <small>(predicted)</small> </td> <td align="center"><span class="nowrap"><span data-sort-value="6993100000000000000♠"></span>10<sup>−7</sup></span> </td> <td align="center">1 </td> <td align="center" style="background:#FFC7C7;color:black;vertical-align:middle;text-align:center;" class="table-no">Not applicable <br />to hadrons </td> <td align="center">20 </td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Standard_Model" title="Special:EditPage/Standard Model">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">June 2021</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Gravity">Gravity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=13" title="Edit section: Gravity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a> and <a href="/wiki/Gravity" title="Gravity">Gravity</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Fundamental_Interactions.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Fundamental_Interactions.png/220px-Fundamental_Interactions.png" decoding="async" width="220" height="216" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Fundamental_Interactions.png/330px-Fundamental_Interactions.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Fundamental_Interactions.png/440px-Fundamental_Interactions.png 2x" data-file-width="750" data-file-height="735" /></a><figcaption>Fundamental Interactions of the Standard Model including the hypothetical Graviton.</figcaption></figure> <p>Despite being perhaps the most familiar fundamental interaction, gravity is not described by the Standard Model, due to contradictions that arise when combining general relativity, the modern theory of gravity, and quantum mechanics. However, gravity is so weak at microscopic scales, that it is essentially unmeasurable. The <a href="/wiki/Graviton" title="Graviton">graviton</a> is postulated to be the mediating particle, but has not yet been proved to exist. </p> <div class="mw-heading mw-heading3"><h3 id="Electromagnetism">Electromagnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=14" title="Edit section: Electromagnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetism</a> and <a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">Quantum electrodynamics</a></div> <p>Electromagnetism is the only long-range force in the Standard Model. It is mediated by photons and couples to electric charge.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> Electromagnetism is responsible for a wide range of phenomena including <a href="/wiki/Electron_shell" title="Electron shell">atomic electron shell structure</a>, <a href="/wiki/Chemical_bonds" class="mw-redirect" title="Chemical bonds">chemical bonds</a>, <a href="/wiki/Electric_circuit" class="mw-redirect" title="Electric circuit">electric circuits</a> and <a href="/wiki/Electronics" title="Electronics">electronics</a>. Electromagnetic interactions in the Standard Model are described by quantum electrodynamics. </p> <div class="mw-heading mw-heading3"><h3 id="Weak_nuclear_force">Weak nuclear force</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=15" title="Edit section: Weak nuclear force"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Weak_interaction" title="Weak interaction">Weak interaction</a> and <a href="/wiki/Electroweak_interaction" title="Electroweak interaction">Electroweak interaction</a></div> <p>The weak interaction is responsible for various forms of <a href="/wiki/Particle_decay" title="Particle decay">particle decay</a>, such as <a href="/wiki/Beta_decay" title="Beta decay">beta decay</a>. It is weak and short-range, due to the fact that the weak mediating particles, W and Z bosons, have mass. W bosons have electric charge and mediate interactions that change the particle type (referred to as flavour) and charge. Interactions mediated by W bosons are <a href="/wiki/Charged_current_interaction" class="mw-redirect" title="Charged current interaction">charged current interactions</a>. Z bosons are neutral and mediate neutral current interactions, which do not change particle flavour. Thus Z bosons are similar to the photon, aside from them being massive and interacting with the neutrino. The weak interaction is also the only interaction to violate <a href="/wiki/Parity_violation" class="mw-redirect" title="Parity violation">parity</a> and <a href="/wiki/CP_violation" title="CP violation">CP</a>. Parity violation is maximal for charged current interactions, since the W boson interacts exclusively with left-handed fermions and right-handed antifermions. </p><p>In the Standard Model, the weak force is understood in terms of the electroweak theory, which states that the weak and electromagnetic interactions become united into a single <i>electroweak</i> interaction at high energies. </p> <div class="mw-heading mw-heading3"><h3 id="Strong_nuclear_force">Strong nuclear force</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=16" title="Edit section: Strong nuclear force"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Strong_interaction" title="Strong interaction">Strong interaction</a>, <a href="/wiki/Nuclear_force" title="Nuclear force">Nuclear force</a>, and <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">Quantum chromodynamics</a></div> <p>The strong nuclear force is responsible for hadronic and <a href="/wiki/Nuclear_binding_energy" title="Nuclear binding energy">nuclear binding</a>. It is mediated by gluons, which couple to color charge. Since gluons themselves have color charge, the strong force exhibits <a href="/wiki/Color_confinement" title="Color confinement">confinement</a> and <a href="/wiki/Asymptotic_freedom" title="Asymptotic freedom">asymptotic freedom</a>. Confinement means that only color-neutral particles can exist in isolation, therefore quarks can only exist in hadrons and never in isolation, at low energies. Asymptotic freedom means that the strong force becomes weaker, as the energy scale increases. The strong force overpowers the <a href="/wiki/Electrostatic" class="mw-redirect" title="Electrostatic">electrostatic</a> repulsion of protons and quarks in nuclei and hadrons respectively, at their respective scales. </p><p>While quarks are bound in hadrons by the fundamental strong interaction, which is mediated by gluons, nucleons are bound by an emergent phenomenon termed the <i>residual strong force</i> or <i><a href="/wiki/Nuclear_force" title="Nuclear force">nuclear force</a></i>. This interaction is mediated by mesons, such as the <a href="/wiki/Pion" title="Pion">pion</a>. The color charges inside the nucleon cancel out, meaning most of the gluon and quark fields cancel out outside of the nucleon. However, some residue is "leaked", which appears as the exchange of virtual mesons, that causes the attractive force between nucleons. The (fundamental) strong interaction is described by quantum chromodynamics, which is a component of the Standard Model. </p> <div class="mw-heading mw-heading2"><h2 id="Tests_and_predictions">Tests and predictions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=17" title="Edit section: Tests and predictions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Standard Model predicted the existence of the <a href="/wiki/W_and_Z_bosons" title="W and Z bosons">W and Z bosons</a>, <a href="/wiki/Gluon" title="Gluon">gluon</a>, <a href="/wiki/Top_quark" title="Top quark">top quark</a> and <a href="/wiki/Charm_quark" title="Charm quark">charm quark</a>, and predicted many of their properties before these particles were observed. The predictions were experimentally confirmed with good precision.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p><p>The Standard Model also predicted the existence of the <a href="/wiki/Higgs_boson" title="Higgs boson">Higgs boson</a>, which was found in 2012 at the <a href="/wiki/Large_Hadron_Collider" title="Large Hadron Collider">Large Hadron Collider</a>, the final fundamental particle predicted by the Standard Model to be experimentally confirmed.<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Challenges">Challenges</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=18" title="Edit section: Challenges"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Physics_beyond_the_Standard_Model" title="Physics beyond the Standard Model">Physics beyond the Standard Model</a></div> <style data-mw-deduplicate="TemplateStyles:r1233989161">.mw-parser-output .unsolved{margin:0.5em 0 1em 1em;border:#ccc solid;padding:0.35em 0.35em 0.35em 2.2em;background-color:var(--background-color-interactive-subtle);background-image:url("https://upload.wikimedia.org/wikipedia/commons/2/26/Question%2C_Web_Fundamentals.svg");background-position:top 50%left 0.35em;background-size:1.5em;background-repeat:no-repeat}@media(min-width:720px){.mw-parser-output .unsolved{clear:right;float:right;max-width:25%}}.mw-parser-output .unsolved-label{font-weight:bold}.mw-parser-output .unsolved-body{margin:0.35em;font-style:italic}.mw-parser-output .unsolved-more{font-size:smaller}</style> <div role="note" aria-labelledby="unsolved-label-physics" class="unsolved"> <div><span class="unsolved-label" id="unsolved-label-physics">Unsolved problem in physics</span>:</div> <div class="unsolved-body"> <ul><li>What gives rise to the Standard Model of particle physics?</li> <li>Why do particle masses and <a href="/wiki/Coupling_constant" title="Coupling constant">coupling constants</a> have the values that we measure?</li> <li>Why are there three <a href="/wiki/Generation_(particle_physics)" title="Generation (particle physics)">generations</a> of particles?</li> <li>Why is there more matter than <a href="/wiki/Antimatter" title="Antimatter">antimatter</a> in the universe?</li> <li>Where does <a href="/wiki/Dark_matter" title="Dark matter">dark matter</a> fit into the model? Does it even consist of one or more new particles?</li></ul> </div> <div class="unsolved-more"><a href="/wiki/List_of_unsolved_problems_in_physics" title="List of unsolved problems in physics">(more unsolved problems in physics)</a></div> </div> <p>Self-consistency of the Standard Model (currently formulated as a non-<a href="/wiki/Abelian_group" title="Abelian group">abelian</a> gauge theory quantized through path-integrals) has not been mathematically proved. While regularized versions useful for approximate computations (for example <a href="/wiki/Lattice_gauge_theory" title="Lattice gauge theory">lattice gauge theory</a>) exist, it is not known whether they converge (in the sense of S-matrix elements) in the limit that the regulator is removed. A key question related to the consistency is the <a href="/wiki/Yang%E2%80%93Mills_existence_and_mass_gap" title="Yang–Mills existence and mass gap">Yang–Mills existence and mass gap</a> problem. </p><p>Experiments indicate that <a href="/wiki/Neutrinos" class="mw-redirect" title="Neutrinos">neutrinos</a> have <a href="/wiki/Mass" title="Mass">mass</a>, which the classic Standard Model did not allow.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> To accommodate this finding, the classic Standard Model can be modified to include neutrino mass, although it is not obvious exactly how this should be done. </p><p>If one insists on using only Standard Model particles, this can be achieved by adding a non-renormalizable interaction of leptons with the Higgs boson.<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> On a fundamental level, such an interaction emerges in the <a href="/wiki/Seesaw_mechanism" title="Seesaw mechanism">seesaw mechanism</a> where heavy right-handed neutrinos are added to the theory. This is natural in the <a href="/wiki/Left-right_symmetry" class="mw-redirect" title="Left-right symmetry">left-right symmetric</a> extension of the Standard Model<sup id="cite_ref-Minkowski1977_61-0" class="reference"><a href="#cite_note-Minkowski1977-61"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-MohapatraSenjanovic1980_62-0" class="reference"><a href="#cite_note-MohapatraSenjanovic1980-62"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> and in certain <a href="/wiki/Grand_unified_theory" class="mw-redirect" title="Grand unified theory">grand unified theories</a>.<sup id="cite_ref-Gell-Mann1979_63-0" class="reference"><a href="#cite_note-Gell-Mann1979-63"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> As long as new physics appears below or around 10<sup>14</sup> <a href="/wiki/Electronvolt" title="Electronvolt">GeV</a>, the neutrino masses can be of the right order of magnitude. </p><p>Theoretical and experimental research has attempted to extend the Standard Model into a <a href="/wiki/Unified_field_theory" title="Unified field theory">unified field theory</a> or a <a href="/wiki/Theory_of_everything" title="Theory of everything">theory of everything</a>, a complete theory explaining all physical phenomena including constants. Inadequacies of the Standard Model that motivate such research include: </p> <ul><li>The model does not explain <a href="/wiki/Gravitation" class="mw-redirect" title="Gravitation">gravitation</a>, although physical confirmation of a theoretical particle known as a <a href="/wiki/Graviton" title="Graviton">graviton</a> would account for it to a degree. Though it addresses strong and electroweak interactions, the Standard Model does not consistently explain the canonical theory of gravitation, <a href="/wiki/General_relativity" title="General relativity">general relativity</a>, in terms of <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>. The reason for this is, among other things, that quantum field theories of gravity generally break down before reaching the <a href="/wiki/Planck_scale" class="mw-redirect" title="Planck scale">Planck scale</a>. As a consequence, we have no reliable theory for the very early universe.</li> <li>Some physicists consider it to be <i>ad hoc</i> and inelegant, requiring 19 numerical constants whose values are unrelated and arbitrary.<sup id="cite_ref-BlumhoferHutter1997_64-0" class="reference"><a href="#cite_note-BlumhoferHutter1997-64"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> Although the Standard Model, as it now stands, can explain why neutrinos have masses, the specifics of neutrino mass are still unclear. It is believed that explaining neutrino mass will require an additional 7 or 8 constants, which are also arbitrary parameters.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup></li> <li>The Higgs mechanism gives rise to the <a href="/wiki/Hierarchy_problem" title="Hierarchy problem">hierarchy problem</a> if some new physics (coupled to the Higgs) is present at high energy scales. In these cases, in order for the weak scale to be much smaller than the <a href="/wiki/Planck_scale" class="mw-redirect" title="Planck scale">Planck scale</a>, severe fine tuning of the parameters is required; there are, however, other scenarios that include <a href="/wiki/Asymptotic_safety_in_quantum_gravity" title="Asymptotic safety in quantum gravity">quantum gravity</a> in which such fine tuning can be avoided.<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> There are also issues of <a href="/wiki/Quantum_triviality" title="Quantum triviality">quantum triviality</a>, which suggests that it may not be possible to create a consistent quantum field theory involving elementary scalar particles.<sup id="cite_ref-TrivPurs_67-0" class="reference"><a href="#cite_note-TrivPurs-67"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup></li> <li>The model is inconsistent with the emerging <a href="/wiki/Lambda-CDM_model" title="Lambda-CDM model">Lambda-CDM model</a> of cosmology. Contentions include the absence of an explanation in the Standard Model of particle physics for the observed amount of <a href="/wiki/Cold_dark_matter" title="Cold dark matter">cold dark matter</a> (CDM) and its contributions to <a href="/wiki/Dark_energy" title="Dark energy">dark energy</a>, which are many orders of magnitude too large. It is also difficult to accommodate the observed predominance of matter over antimatter (<a href="/wiki/Matter" title="Matter">matter</a>/<a href="/wiki/Antimatter" title="Antimatter">antimatter</a> <a href="/wiki/Baryon_asymmetry" title="Baryon asymmetry">asymmetry</a>). The <a href="/wiki/Isotropic" class="mw-redirect" title="Isotropic">isotropy</a> and <a href="/wiki/Homogeneity_(physics)" title="Homogeneity (physics)">homogeneity</a> of the visible universe over large distances seems to require a mechanism like cosmic <a href="/wiki/Inflation_(cosmology)" class="mw-redirect" title="Inflation (cosmology)">inflation</a>, which would also constitute an extension of the Standard Model.</li></ul> <p>Currently, no proposed <a href="/wiki/Theory_of_everything" title="Theory of everything">theory of everything</a> has been widely accepted or verified. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=19" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 27em;"> <ul><li><a href="/wiki/Yang%E2%80%93Mills_theory" title="Yang–Mills theory">Yang–Mills theory</a></li> <li><a href="/wiki/Fundamental_interaction" title="Fundamental interaction">Fundamental interaction</a>: <ul><li><a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">Quantum electrodynamics</a></li> <li><a href="/wiki/Strong_interaction" title="Strong interaction">Strong interaction</a>: <a href="/wiki/Color_charge" title="Color charge">Color charge</a>, <a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">Quantum chromodynamics</a>, <a href="/wiki/Quark_model" title="Quark model">Quark model</a></li> <li><a href="/wiki/Weak_interaction" title="Weak interaction">Weak interaction</a>: <a href="/wiki/Electroweak_interaction" title="Electroweak interaction">Electroweak interaction</a>, <a href="/wiki/Fermi%27s_interaction" title="Fermi's interaction">Fermi's interaction</a>, <a href="/wiki/Weak_hypercharge" title="Weak hypercharge">Weak hypercharge</a>, <a href="/wiki/Weak_isospin" title="Weak isospin">Weak isospin</a></li></ul></li> <li><a href="/wiki/Gauge_theory" title="Gauge theory">Gauge theory</a>: <a href="/wiki/Introduction_to_gauge_theory" title="Introduction to gauge theory">Introduction to gauge theory</a></li> <li><a href="/wiki/Generation_(particle_physics)" title="Generation (particle physics)">Generation</a></li> <li><a href="/wiki/Higgs_mechanism" title="Higgs mechanism">Higgs mechanism</a>: <a href="/wiki/Higgs_boson" title="Higgs boson">Higgs boson</a>, <a href="/wiki/Alternatives_to_the_Standard_Higgs_Model" title="Alternatives to the Standard Higgs Model">Alternatives to the Standard Higgs Model</a></li> <li><a href="/wiki/Lagrangian_(field_theory)" title="Lagrangian (field theory)">Lagrangian</a></li> <li>Open questions: <a href="/wiki/CP_violation" title="CP violation">CP violation</a>, <a href="/wiki/Neutrino_mass" class="mw-redirect" title="Neutrino mass">Neutrino masses</a>, <a href="/wiki/QCD_matter" title="QCD matter">QCD matter</a>, <a href="/wiki/Quantum_triviality" title="Quantum triviality">Quantum triviality</a></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a></li> <li>Standard Model: <a href="/wiki/Mathematical_formulation_of_the_Standard_Model" title="Mathematical formulation of the Standard Model">Mathematical formulation of</a>, <a href="/wiki/Physics_beyond_the_Standard_Model" title="Physics beyond the Standard Model">Physics beyond the Standard Model</a></li> <li><a href="/wiki/Electron_electric_dipole_moment" title="Electron electric dipole moment">Electron electric dipole moment</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=20" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">There are mathematical issues regarding quantum field theories still under debate (see e.g. <a href="/wiki/Landau_pole" title="Landau pole">Landau pole</a>), but the predictions extracted from the Standard Model by current methods applicable to current experiments are all self-consistent.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text">Although nine color–anticolor combinations mathematically exist, gluons form color octet particles. As one color-symmetric combination is linear and forms a color singlet particles, there are eight possible gluons.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=21" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFR._Oerter2006" class="citation book cs1">R. Oerter (2006). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/theoryofalmostev0000oert"><i>The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics</i></a></span> (Kindle ed.). <a href="/wiki/Penguin_Group" title="Penguin Group">Penguin Group</a>. p. <a rel="nofollow" class="external text" href="https://archive.org/details/theoryofalmostev0000oert/page/2">2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-236678-6" title="Special:BookSources/978-0-13-236678-6"><bdi>978-0-13-236678-6</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">28 March</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Theory+of+Almost+Everything%3A+The+Standard+Model%2C+the+Unsung+Triumph+of+Modern+Physics&rft.pages=2&rft.edition=Kindle&rft.pub=Penguin+Group&rft.date=2006&rft.isbn=978-0-13-236678-6&rft.au=R.+Oerter&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ftheoryofalmostev0000oert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span> <sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged March 2022">dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFR._Mann2010" class="citation book cs1">R. 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"Neutrino masses and mixings and...". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-ph/0606054">hep-ph/0606054</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Neutrino+masses+and+mixings+and...&rft.date=2006&rft_id=info%3Aarxiv%2Fhep-ph%2F0606054&rft.aulast=Strumia&rft.aufirst=Alessandro&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></span> </li> <li id="cite_note-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-66">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSalvioStrumia2018" class="citation journal cs1">Salvio, Alberto; Strumia, Alessandro (2018). <a rel="nofollow" class="external text" href="http://inspirehep.net/record/1286134">"Agravity"</a>. <i>Journal of High Energy Physics</i>. <b>2014</b> (6): 080. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1403.4226">1403.4226</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014JHEP...06..080S">2014JHEP...06..080S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FJHEP06%282014%29080">10.1007/JHEP06(2014)080</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6560704">6560704</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/31258400">31258400</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+High+Energy+Physics&rft.atitle=Agravity&rft.volume=2014&rft.issue=6&rft.pages=080&rft.date=2018&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC6560704%23id-name%3DPMC&rft_id=info%3Abibcode%2F2014JHEP...06..080S&rft_id=info%3Aarxiv%2F1403.4226&rft_id=info%3Apmid%2F31258400&rft_id=info%3Adoi%2F10.1007%2FJHEP06%282014%29080&rft.aulast=Salvio&rft.aufirst=Alberto&rft.au=Strumia%2C+Alessandro&rft_id=http%3A%2F%2Finspirehep.net%2Frecord%2F1286134&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></span> </li> <li id="cite_note-TrivPurs-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-TrivPurs_67-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFD.J.E._Callaway1988" class="citation journal cs1"><a href="/wiki/David_J_E_Callaway" class="mw-redirect" title="David J E Callaway">D.J.E. Callaway</a> (1988). "Triviality Pursuit: Can Elementary Scalar Particles Exist?". <i><a href="/wiki/Physics_Reports" title="Physics Reports">Physics Reports</a></i>. <b>167</b> (5): 241–320. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1988PhR...167..241C">1988PhR...167..241C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0370-1573%2888%2990008-7">10.1016/0370-1573(88)90008-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Reports&rft.atitle=Triviality+Pursuit%3A+Can+Elementary+Scalar+Particles+Exist%3F&rft.volume=167&rft.issue=5&rft.pages=241-320&rft.date=1988&rft_id=info%3Adoi%2F10.1016%2F0370-1573%2888%2990008-7&rft_id=info%3Abibcode%2F1988PhR...167..241C&rft.au=D.J.E.+Callaway&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=22" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOerter2006" class="citation book cs1">Oerter, Robert (2006). <i>The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics</i>. Plume. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-452-28786-0" title="Special:BookSources/978-0-452-28786-0"><bdi>978-0-452-28786-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Theory+of+Almost+Everything%3A+The+Standard+Model%2C+the+Unsung+Triumph+of+Modern+Physics&rft.pub=Plume&rft.date=2006&rft.isbn=978-0-452-28786-0&rft.aulast=Oerter&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchumm2004" class="citation book cs1">Schumm, Bruce A. (2004). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/deepdownthingsbr00schu"><i>Deep Down Things: The Breathtaking Beauty of Particle Physics</i></a></span>. Johns Hopkins University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8018-7971-5" title="Special:BookSources/978-0-8018-7971-5"><bdi>978-0-8018-7971-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Deep+Down+Things%3A+The+Breathtaking+Beauty+of+Particle+Physics&rft.pub=Johns+Hopkins+University+Press&rft.date=2004&rft.isbn=978-0-8018-7971-5&rft.aulast=Schumm&rft.aufirst=Bruce+A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fdeepdownthingsbr00schu&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.symmetrymagazine.org/standard-model/">"The Standard Model of Particle Physics Interactive Graphic"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Standard+Model+of+Particle+Physics+Interactive+Graphic&rft_id=http%3A%2F%2Fwww.symmetrymagazine.org%2Fstandard-model%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Introductory_textbooks">Introductory textbooks</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=23" title="Edit section: Introductory textbooks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFI._AitchisonA._Hey2003" class="citation book cs1">I. Aitchison; A. Hey (2003). <i>Gauge Theories in Particle Physics: A Practical Introduction</i>. Institute of Physics. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-585-44550-2" title="Special:BookSources/978-0-585-44550-2"><bdi>978-0-585-44550-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gauge+Theories+in+Particle+Physics%3A+A+Practical+Introduction.&rft.pub=Institute+of+Physics&rft.date=2003&rft.isbn=978-0-585-44550-2&rft.au=I.+Aitchison&rft.au=A.+Hey&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFW._GreinerB._Müller2000" class="citation book cs1">W. Greiner; B. Müller (2000). <i>Gauge Theory of Weak Interactions</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-67672-0" title="Special:BookSources/978-3-540-67672-0"><bdi>978-3-540-67672-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gauge+Theory+of+Weak+Interactions&rft.pub=Springer&rft.date=2000&rft.isbn=978-3-540-67672-0&rft.au=W.+Greiner&rft.au=B.+M%C3%BCller&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJ.E._DoddB.M._Gripaios2020" class="citation book cs1">J.E. Dodd; B.M. Gripaios (2020). <i>The Ideas of Particle Physics: An Introduction for Scientists</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-108-72740-2" title="Special:BookSources/978-1-108-72740-2"><bdi>978-1-108-72740-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Ideas+of+Particle+Physics%3A+An+Introduction+for+Scientists&rft.pub=Cambridge+University+Press&rft.date=2020&rft.isbn=978-1-108-72740-2&rft.au=J.E.+Dodd&rft.au=B.M.+Gripaios&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFD.J._Griffiths1987" class="citation book cs1">D.J. Griffiths (1987). <i>Introduction to Elementary Particles</i>. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-60386-3" title="Special:BookSources/978-0-471-60386-3"><bdi>978-0-471-60386-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Elementary+Particles&rft.pub=John+Wiley+%26+Sons&rft.date=1987&rft.isbn=978-0-471-60386-3&rft.au=D.J.+Griffiths&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFG.L._Kane1987" class="citation book cs1">G.L. Kane (1987). <i>Modern Elementary Particle Physics</i>. Perseus Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-11749-3" title="Special:BookSources/978-0-201-11749-3"><bdi>978-0-201-11749-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modern+Elementary+Particle+Physics&rft.pub=Perseus+Books&rft.date=1987&rft.isbn=978-0-201-11749-3&rft.au=G.L.+Kane&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Advanced_textbooks">Advanced textbooks</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=24" title="Edit section: Advanced textbooks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFT.P._ChengL.F._Li2006" class="citation book cs1">T.P. Cheng; L.F. Li (2006). <i>Gauge theory of elementary particle physics</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-851961-4" title="Special:BookSources/978-0-19-851961-4"><bdi>978-0-19-851961-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gauge+theory+of+elementary+particle+physics&rft.pub=Oxford+University+Press&rft.date=2006&rft.isbn=978-0-19-851961-4&rft.au=T.P.+Cheng&rft.au=L.F.+Li&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span> Highlights the <a href="/wiki/Gauge_theory" title="Gauge theory">gauge theory</a> aspects of the Standard Model.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJ.F._DonoghueE._GolowichB.R._Holstein1994" class="citation book cs1">J.F. Donoghue; E. Golowich; B.R. Holstein (1994). <i>Dynamics of the Standard Model</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-47652-2" title="Special:BookSources/978-0-521-47652-2"><bdi>978-0-521-47652-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dynamics+of+the+Standard+Model&rft.pub=Cambridge+University+Press&rft.date=1994&rft.isbn=978-0-521-47652-2&rft.au=J.F.+Donoghue&rft.au=E.+Golowich&rft.au=B.R.+Holstein&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span> Highlights dynamical and <a href="/wiki/Phenomenology_(particle_physics)" class="mw-redirect" title="Phenomenology (particle physics)">phenomenological</a> aspects of the Standard Model.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFL._O'Raifeartaigh1988" class="citation book cs1">L. O'Raifeartaigh (1988). <i>Group structure of gauge theories</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-34785-3" title="Special:BookSources/978-0-521-34785-3"><bdi>978-0-521-34785-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Group+structure+of+gauge+theories&rft.pub=Cambridge+University+Press&rft.date=1988&rft.isbn=978-0-521-34785-3&rft.au=L.+O%27Raifeartaigh&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNagashima2013" class="citation book cs1">Nagashima, Yorikiyo (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=QYlX6AL4CtwC"><i>Elementary Particle Physics: Foundations of the Standard Model, Volume 2</i></a>. Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-527-64890-0" title="Special:BookSources/978-3-527-64890-0"><bdi>978-3-527-64890-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elementary+Particle+Physics%3A+Foundations+of+the+Standard+Model%2C+Volume+2&rft.pub=Wiley&rft.date=2013&rft.isbn=978-3-527-64890-0&rft.aulast=Nagashima&rft.aufirst=Yorikiyo&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DQYlX6AL4CtwC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span> 920 pages.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchwartz2014" class="citation book cs1">Schwartz, Matthew D. (2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=HbdEAgAAQBAJ"><i>Quantum Field Theory and the Standard Model</i></a>. Cambridge University. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-107-03473-0" title="Special:BookSources/978-1-107-03473-0"><bdi>978-1-107-03473-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Field+Theory+and+the+Standard+Model&rft.pub=Cambridge+University&rft.date=2014&rft.isbn=978-1-107-03473-0&rft.aulast=Schwartz&rft.aufirst=Matthew+D.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DHbdEAgAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span> 952 pages.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLangacker2009" class="citation book cs1">Langacker, Paul (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=dpANo3e_pS8C"><i>The Standard Model and Beyond</i></a>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4200-7907-4" title="Special:BookSources/978-1-4200-7907-4"><bdi>978-1-4200-7907-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Standard+Model+and+Beyond&rft.pub=CRC+Press&rft.date=2009&rft.isbn=978-1-4200-7907-4&rft.aulast=Langacker&rft.aufirst=Paul&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DdpANo3e_pS8C&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span> 670 pages. Highlights <a href="/wiki/Finite_group" title="Finite group">group-theoretical</a> aspects of the Standard Model.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Journal_articles">Journal articles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=25" title="Edit section: Journal articles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFE.S._AbersB.W._Lee1973" class="citation journal cs1">E.S. Abers; B.W. Lee (1973). "Gauge theories". <i><a href="/wiki/Physics_Reports" title="Physics Reports">Physics Reports</a></i>. <b>9</b> (1): 1–141. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1973PhR.....9....1A">1973PhR.....9....1A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0370-1573%2873%2990027-6">10.1016/0370-1573(73)90027-6</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Reports&rft.atitle=Gauge+theories&rft.volume=9&rft.issue=1&rft.pages=1-141&rft.date=1973&rft_id=info%3Adoi%2F10.1016%2F0370-1573%2873%2990027-6&rft_id=info%3Abibcode%2F1973PhR.....9....1A&rft.au=E.S.+Abers&rft.au=B.W.+Lee&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFM._Baak2012" class="citation journal cs1">M. Baak; et al. (2012). 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Novaes (2000). "Standard Model: An Introduction". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/hep-ph/0001283">hep-ph/0001283</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Standard+Model%3A+An+Introduction&rft.date=2000&rft_id=info%3Aarxiv%2Fhep-ph%2F0001283&rft.au=S.F.+Novaes&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFD.P._Roy1999" class="citation arxiv cs1">D.P. Roy (1999). 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"The Universe Is A Strange Place". <i>Nuclear Physics B: Proceedings Supplements</i>. <b>134</b>: 3. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0401347">astro-ph/0401347</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004NuPhS.134....3W">2004NuPhS.134....3W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.nuclphysbps.2004.08.001">10.1016/j.nuclphysbps.2004.08.001</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:28234516">28234516</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nuclear+Physics+B%3A+Proceedings+Supplements&rft.atitle=The+Universe+Is+A+Strange+Place&rft.volume=134&rft.pages=3&rft.date=2004&rft_id=info%3Aarxiv%2Fastro-ph%2F0401347&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A28234516%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.nuclphysbps.2004.08.001&rft_id=info%3Abibcode%2F2004NuPhS.134....3W&rft.au=F.+Wilczek&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStandard+Model" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Standard_Model&action=edit&section=26" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style 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href="http://home.web.cern.ch/about/physics/standard-model">The Standard Model</a> on the CERN website explains how the basic building blocks of matter interact, governed by four fundamental forces.</li> <li><a rel="nofollow" class="external text" href="https://av.tib.eu/series/56">Particle Physics: Standard Model</a>, <a href="/wiki/Leonard_Susskind" title="Leonard Susskind">Leonard Susskind</a> lectures (2010).</li></ul> <div style="clear:both;" class=""></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output 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class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Standard_model_of_physics" title="Template:Standard model of physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Standard_model_of_physics" title="Template talk:Standard model of physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Standard_model_of_physics" title="Special:EditPage/Template:Standard model of physics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Standard_Model" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Standard Model</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Background</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Particle_physics" title="Particle physics">Particle physics</a> <ul><li><a href="/wiki/Fermion" title="Fermion">Fermions</a></li> <li><a href="/wiki/Gauge_boson" title="Gauge boson">Gauge boson</a></li> <li><a href="/wiki/Higgs_boson" title="Higgs boson">Higgs boson</a></li></ul></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a></li> <li><a href="/wiki/Gauge_theory" title="Gauge theory">Gauge theory</a></li> <li><a href="/wiki/Strong_interaction" title="Strong interaction">Strong interaction</a> <ul><li><a href="/wiki/Color_charge" title="Color charge">Color charge</a></li> <li><a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">Quantum chromodynamics</a></li> <li><a href="/wiki/Quark_model" title="Quark model">Quark model</a></li></ul></li> <li><a href="/wiki/Electroweak_interaction" title="Electroweak interaction">Electroweak interaction</a> <ul><li><a href="/wiki/Weak_interaction" title="Weak interaction">Weak interaction</a></li> <li><a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">Quantum electrodynamics</a></li> <li><a href="/wiki/Fermi%27s_interaction" title="Fermi's interaction">Fermi's interaction</a></li> <li><a href="/wiki/Weak_hypercharge" title="Weak hypercharge">Weak hypercharge</a></li> <li><a href="/wiki/Weak_isospin" title="Weak isospin">Weak isospin</a></li></ul></li></ul> </div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/150px-Standard_Model_of_Elementary_Particles.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/225px-Standard_Model_of_Elementary_Particles.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/300px-Standard_Model_of_Elementary_Particles.svg.png 2x" data-file-width="1390" data-file-height="1330" /></span></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Constituents</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cabibbo%E2%80%93Kobayashi%E2%80%93Maskawa_matrix" title="Cabibbo–Kobayashi–Maskawa matrix">CKM matrix</a></li> <li><a href="/wiki/Spontaneous_symmetry_breaking" title="Spontaneous symmetry breaking">Spontaneous symmetry breaking</a></li> <li><a href="/wiki/Higgs_mechanism" title="Higgs mechanism">Higgs mechanism</a></li> <li><a href="/wiki/Mathematical_formulation_of_the_Standard_Model" title="Mathematical formulation of the Standard Model">Mathematical formulation of the Standard Model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Physics_beyond_the_Standard_Model" title="Physics beyond the Standard Model">Beyond the<br />Standard Model</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Evidence</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hierarchy_problem" title="Hierarchy problem">Hierarchy problem</a></li> <li><a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a></li> <li><a href="/wiki/Cosmological_constant" title="Cosmological constant">Cosmological constant</a> <ul><li><a href="/wiki/Cosmological_constant_problem" title="Cosmological constant problem">problem</a></li></ul></li> <li><a href="/wiki/CP_violation" title="CP violation">Strong CP problem</a></li> <li><a href="/wiki/Neutrino_oscillation" title="Neutrino oscillation">Neutrino oscillation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Technicolor_(physics)" title="Technicolor (physics)">Technicolor</a></li> <li><a href="/wiki/Kaluza%E2%80%93Klein_theory" title="Kaluza–Klein theory">Kaluza–Klein theory</a></li> <li><a href="/wiki/Grand_Unified_Theory" title="Grand Unified Theory">Grand Unified Theory</a></li> <li><a href="/wiki/Theory_of_everything" title="Theory of everything">Theory of everything</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Supersymmetry" title="Supersymmetry">Supersymmetry</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Minimal_Supersymmetric_Standard_Model" title="Minimal Supersymmetric Standard Model">MSSM</a></li> <li><a href="/wiki/Next-to-Minimal_Supersymmetric_Standard_Model" title="Next-to-Minimal Supersymmetric Standard Model">NMSSM</a></li> <li><a href="/wiki/Split_supersymmetry" title="Split supersymmetry">Split supersymmetry</a></li> <li><a href="/wiki/Supergravity" title="Supergravity">Supergravity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/String_theory" title="String theory">String theory</a></li> <li><a href="/wiki/Superstring_theory" title="Superstring theory">Superstring theory</a></li> <li><a href="/wiki/Loop_quantum_gravity" title="Loop quantum gravity">Loop quantum gravity</a></li> <li><a href="/wiki/Causal_dynamical_triangulation" title="Causal dynamical triangulation">Causal dynamical triangulation</a></li> <li><a href="/wiki/Canonical_quantum_gravity" title="Canonical quantum gravity">Canonical quantum gravity</a></li> <li><a href="/wiki/Superfluid_vacuum_theory" title="Superfluid vacuum theory">Superfluid vacuum theory</a></li> <li><a href="/wiki/Twistor_theory" title="Twistor theory">Twistor theory</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Experiments</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Laboratori_Nazionali_del_Gran_Sasso" title="Laboratori Nazionali del Gran Sasso">Gran Sasso</a></li> <li><a href="/wiki/India-based_Neutrino_Observatory" title="India-based Neutrino Observatory">INO</a></li> <li><a href="/wiki/Large_Hadron_Collider" title="Large Hadron Collider">LHC</a></li> <li><a href="/wiki/Sudbury_Neutrino_Observatory" title="Sudbury Neutrino Observatory">SNO</a></li> <li><a href="/wiki/Super-Kamiokande" title="Super-Kamiokande">Super-K</a></li> <li><a href="/wiki/Tevatron" title="Tevatron">Tevatron</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Category:Standard_Model" title="Category:Standard Model">Category</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Standard_Model_(physics)" class="extiw" title="commons:Category:Standard Model (physics)">Commons</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Particles_in_physics" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align: center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Particles" title="Template:Particles"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Particles" title="Template talk:Particles"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Particles" title="Special:EditPage/Template:Particles"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Particles_in_physics" style="font-size:114%;margin:0 4em"><a href="/wiki/Particle_physics" title="Particle physics">Particles in physics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Elementary_particle" title="Elementary particle">Elementary</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;"><a href="/wiki/Fermion" title="Fermion">Fermions</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Quark" title="Quark">Quarks</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Up_quark" title="Up quark">Up (quark</a></li> <li><a href="/wiki/Up_antiquark" class="mw-redirect" title="Up antiquark">antiquark)</a></li> <li><a href="/wiki/Down_quark" title="Down quark">Down (quark</a></li> <li><a href="/wiki/Down_antiquark" class="mw-redirect" title="Down antiquark">antiquark)</a></li> <li><a href="/wiki/Charm_quark" title="Charm quark">Charm (quark</a></li> <li><a href="/wiki/Charm_antiquark" class="mw-redirect" title="Charm antiquark">antiquark)</a></li> <li><a href="/wiki/Strange_quark" title="Strange quark">Strange (quark</a></li> <li><a href="/wiki/Strange_antiquark" class="mw-redirect" title="Strange antiquark">antiquark)</a></li> <li><a href="/wiki/Top_quark" title="Top quark">Top (quark</a></li> <li><a href="/wiki/Top_antiquark" class="mw-redirect" title="Top antiquark">antiquark)</a></li> <li><a href="/wiki/Bottom_quark" title="Bottom quark">Bottom (quark</a></li> <li><a href="/wiki/Bottom_antiquark" class="mw-redirect" title="Bottom antiquark">antiquark)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Lepton" title="Lepton">Leptons</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Electron" title="Electron">Electron</a></li> <li><a href="/wiki/Positron" title="Positron">Positron</a></li> <li><a href="/wiki/Muon" title="Muon">Muon</a></li> <li><a href="/wiki/Muon" title="Muon">Antimuon</a></li> <li><a href="/wiki/Tau_(particle)" title="Tau (particle)">Tau</a></li> <li><a href="/wiki/Tau_(particle)" title="Tau (particle)">Antitau</a></li> <li><a href="/wiki/Neutrino" title="Neutrino">Neutrino</a> <ul><li><a href="/wiki/Electron_neutrino" title="Electron neutrino">Electron neutrino</a></li> <li><a href="/wiki/Neutrino#Antineutrinos" title="Neutrino">Electron antineutrino</a></li> <li><a href="/wiki/Muon_neutrino" title="Muon neutrino">Muon neutrino</a></li> <li><a href="/wiki/Neutrino#Antineutrinos" title="Neutrino">Muon antineutrino</a></li> <li><a href="/wiki/Tau_neutrino" title="Tau neutrino">Tau neutrino</a></li> <li><a href="/wiki/Neutrino#Antineutrinos" title="Neutrino">Tau antineutrino</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;"><a href="/wiki/Boson" title="Boson">Bosons</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:4em;font-weight:normal; text-align: center;"><a href="/wiki/Gauge_boson" title="Gauge boson">Gauge</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Photon" title="Photon">Photon</a></li> <li><a href="/wiki/Gluon" title="Gluon">Gluon</a></li> <li><a href="/wiki/W_and_Z_bosons" title="W and Z bosons">W and Z bosons</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:4em;font-weight:normal; text-align: center;"><a href="/wiki/Scalar_boson" title="Scalar boson">Scalar</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Higgs_boson" title="Higgs boson">Higgs boson </a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;;font-weight:normal; text-align: center;"><a href="/wiki/Ghost_(physics)" title="Ghost (physics)">Ghost fields</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Faddeev%E2%80%93Popov_ghost" title="Faddeev–Popov ghost">Faddeev–Popov ghosts</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;"><a href="/wiki/Hypothetical_particles" class="mw-redirect" title="Hypothetical particles">Hypothetical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal; text-align: center;"><a href="/wiki/Superpartner" title="Superpartner">Superpartners</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal; text-align: center;"><a href="/wiki/Gaugino" title="Gaugino">Gauginos</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gluino" title="Gluino">Gluino</a></li> <li><a href="/wiki/Gravitino" title="Gravitino">Gravitino</a></li> <li><a href="/wiki/Photino" title="Photino">Photino</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal; text-align: center;">Others</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Axino" title="Axino">Axino</a></li> <li><a href="/wiki/Chargino" title="Chargino">Chargino</a></li> <li><a href="/wiki/Higgsino" title="Higgsino">Higgsino</a></li> <li><a href="/wiki/Neutralino" title="Neutralino">Neutralino</a></li> <li><a href="/wiki/Sfermion" title="Sfermion">Sfermion</a> (<a href="/wiki/Stop_squark" title="Stop squark">Stop squark</a>)</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal; text-align: center;">Others</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Axion" title="Axion">Axion</a></li> <li><a href="/wiki/Curvaton" title="Curvaton">Curvaton</a></li> <li><a href="/wiki/Dilaton" title="Dilaton">Dilaton</a></li> <li><a href="/wiki/Dual_graviton" title="Dual graviton">Dual graviton</a></li> <li><a href="/wiki/Graviphoton" title="Graviphoton">Graviphoton</a></li> <li><a href="/wiki/Graviton" title="Graviton">Graviton</a></li> <li><a href="/wiki/Inflaton" title="Inflaton">Inflaton</a></li> <li><a href="/wiki/Leptoquark" title="Leptoquark">Leptoquark</a></li> <li><a href="/wiki/Magnetic_monopole" title="Magnetic monopole">Magnetic monopole</a></li> <li><a href="/wiki/Majoron" title="Majoron">Majoron</a></li> <li><a href="/wiki/Majorana_fermion" title="Majorana fermion">Majorana fermion</a></li> <li><a href="/wiki/Dark_photon" title="Dark photon">Dark photon</a></li> <li><a href="/wiki/Preon" title="Preon">Preon</a></li> <li><a href="/wiki/Sterile_neutrino" title="Sterile neutrino">Sterile neutrino</a></li> <li><a href="/wiki/Tachyon" title="Tachyon">Tachyon</a></li> <li><a href="/wiki/W%E2%80%B2_and_Z%E2%80%B2_bosons" title="W′ and Z′ bosons">W′ and Z′ bosons</a></li> <li><a href="/wiki/X_and_Y_bosons" title="X and Y bosons">X and Y bosons</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Bound_state" title="Bound state">Composite</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Hadrons" scope="row" class="navbox-group" style="width:1%;text-align: center;"><a href="/wiki/Hadron" title="Hadron">Hadrons</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal; text-align: center;"><a href="/wiki/Baryon" title="Baryon">Baryons</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nucleon" title="Nucleon">Nucleon</a> <ul><li><a href="/wiki/Proton" title="Proton">Proton</a></li> <li><a href="/wiki/Antiproton" title="Antiproton">Antiproton</a></li> <li><a href="/wiki/Neutron" title="Neutron">Neutron</a></li> <li><a href="/wiki/Antineutron" title="Antineutron">Antineutron</a></li></ul></li> <li><a href="/wiki/Delta_baryon" title="Delta baryon">Delta baryon</a></li> <li><a href="/wiki/Lambda_baryon" title="Lambda baryon">Lambda baryon</a></li> <li><a href="/wiki/Sigma_baryon" title="Sigma baryon">Sigma baryon</a></li> <li><a href="/wiki/Xi_baryon" title="Xi baryon">Xi baryon</a></li> <li><a href="/wiki/Omega_baryon" title="Omega baryon">Omega baryon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal; text-align: center;"><a href="/wiki/Meson" title="Meson">Mesons</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pion" title="Pion">Pion</a></li> <li><a href="/wiki/Rho_meson" title="Rho meson">Rho meson</a></li> <li><a href="/wiki/Eta_meson" class="mw-redirect" title="Eta meson">Eta and eta prime mesons</a></li> <li><a href="/wiki/Bottom_eta_meson" title="Bottom eta meson">Bottom eta meson</a></li> <li><a href="/wiki/Phi_meson" title="Phi meson">Phi meson</a></li> <li><a href="/wiki/J/psi_meson" title="J/psi meson">J/psi meson</a></li> <li><a href="/wiki/Omega_meson" title="Omega meson">Omega meson</a></li> <li><a href="/wiki/Upsilon_meson" title="Upsilon meson">Upsilon meson</a></li> <li><a href="/wiki/Kaon" title="Kaon">Kaon</a></li> <li><a href="/wiki/B_meson" title="B meson">B meson</a></li> <li><a href="/wiki/D_meson" title="D meson">D meson</a></li> <li><a href="/wiki/Quarkonium" title="Quarkonium">Quarkonium</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal; text-align: center;"><a href="/wiki/Exotic_hadron" title="Exotic hadron">Exotic hadrons</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Tetraquark" title="Tetraquark">Tetraquark</a> (<a href="/wiki/Double-charm_tetraquark" title="Double-charm tetraquark">Double-charm tetraquark</a>)</li> <li><a href="/wiki/Pentaquark" title="Pentaquark">Pentaquark</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;;font-weight:normal; text-align: center;">Others</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Atomic_nucleus" title="Atomic nucleus">Atomic nuclei</a></li> <li><a href="/wiki/Atom" title="Atom">Atoms</a></li> <li><a href="/wiki/Exotic_atom" title="Exotic atom">Exotic atoms</a> <ul><li><a href="/wiki/Positronium" title="Positronium">Positronium</a></li> <li><a href="/wiki/Muonium" title="Muonium">Muonium</a></li> <li><a href="/wiki/Tauonium" class="mw-redirect" title="Tauonium">Tauonium</a></li> <li><a href="/wiki/Onium" title="Onium">Onia</a></li> <li><a href="/wiki/Pionium" title="Pionium">Pionium</a></li> <li><a href="/wiki/Protonium" title="Protonium">Protonium</a></li></ul></li> <li><a href="/wiki/Superatom" title="Superatom">Superatoms</a></li> <li><a href="/wiki/Molecule" title="Molecule">Molecules</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;"><a href="/wiki/Category:Hypothetical_composite_particles" title="Category:Hypothetical composite particles">Hypothetical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Baryons</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hexaquark" title="Hexaquark">Hexaquark</a></li> <li><a href="/wiki/Heptaquark" title="Heptaquark">Heptaquark</a></li> <li><a href="/wiki/Skyrmion" title="Skyrmion">Skyrmion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Mesons</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Glueball" title="Glueball">Glueball</a></li> <li><a href="/wiki/Theta_meson" title="Theta meson">Theta meson</a></li> <li><a href="/wiki/T_meson" title="T meson">T meson</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal; text-align: center;;font-weight:normal; text-align: center;">Others</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mesonic_molecule" title="Mesonic molecule">Mesonic molecule</a></li> <li><a href="/wiki/Pomeron" title="Pomeron">Pomeron</a></li> <li><a href="/wiki/Diquark" title="Diquark">Diquark</a></li> <li><a href="/wiki/R-hadron" title="R-hadron">R-hadron</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Quasiparticle" title="Quasiparticle">Quasiparticles</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anyon" title="Anyon">Anyon</a></li> <li><a href="/wiki/Davydov_soliton" title="Davydov soliton">Davydov soliton</a></li> <li><a href="/wiki/Dropleton" title="Dropleton">Dropleton</a></li> <li><a href="/wiki/Exciton" title="Exciton">Exciton</a></li> <li><a href="/wiki/Fracton_(subdimensional_particle)" title="Fracton (subdimensional particle)">Fracton</a></li> <li><a href="/wiki/Electron_hole" title="Electron hole">Hole</a></li> <li><a href="/wiki/Magnon" title="Magnon">Magnon</a></li> <li><a href="/wiki/Phonon" title="Phonon">Phonon</a></li> <li><a href="/wiki/Plasmaron" title="Plasmaron">Plasmaron</a></li> <li><a href="/wiki/Plasmon" title="Plasmon">Plasmon</a></li> <li><a href="/wiki/Polariton" title="Polariton">Polariton</a></li> <li><a href="/wiki/Polaron" title="Polaron">Polaron</a></li> <li><a href="/wiki/Roton" title="Roton">Roton</a></li> <li><a href="/wiki/Trion_(physics)" title="Trion (physics)">Trion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Lists</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_baryons" title="List of baryons">Baryons</a></li> <li><a href="/wiki/List_of_mesons" title="List of mesons">Mesons</a></li> <li><a href="/wiki/List_of_particles" title="List of particles">Particles</a></li> <li><a href="/wiki/List_of_quasiparticles" title="List of quasiparticles">Quasiparticles</a></li> <li><a href="/wiki/Timeline_of_particle_discoveries" title="Timeline of particle discoveries">Timeline of particle discoveries</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_subatomic_physics" title="History of subatomic physics">History of subatomic physics</a> <ul><li><a href="/wiki/Timeline_of_atomic_and_subatomic_physics" title="Timeline of atomic and subatomic physics">timeline</a></li></ul></li> <li><a class="mw-selflink selflink">Standard Model</a> <ul><li><a href="/wiki/Mathematical_formulation_of_the_Standard_Model" title="Mathematical formulation of the Standard Model">mathematical formulation</a></li></ul></li> <li><a href="/wiki/Subatomic_particle" title="Subatomic particle">Subatomic particles</a></li> <li><a href="/wiki/Particle" title="Particle">Particles</a></li> <li><a href="/wiki/Antiparticle" title="Antiparticle">Antiparticles</a></li> <li><a href="/wiki/Nuclear_physics" title="Nuclear physics">Nuclear physics</a></li> <li><a href="/wiki/Eightfold_way_(physics)" title="Eightfold way (physics)">Eightfold way</a> <ul><li><a href="/wiki/Quark_model" title="Quark model">Quark model</a></li></ul></li> <li><a href="/wiki/Exotic_matter" title="Exotic matter">Exotic matter</a></li> <li><a href="/wiki/Massless_particle" title="Massless particle">Massless particle</a></li> <li><a href="/wiki/Relativistic_particle" title="Relativistic particle">Relativistic particle</a></li> <li><a href="/wiki/Virtual_particle" title="Virtual particle">Virtual particle</a></li> <li><a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">Wave–particle duality</a></li> <li><a href="/wiki/Particle_chauvinism" title="Particle chauvinism">Particle chauvinism</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align: center;"><div><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Symbol_portal_class.svg" class="mw-file-description" title="Portal"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></a></span> <b><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></b></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Quantum_field_theories" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Quantum_field_theories" title="Template:Quantum field theories"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_field_theories" title="Template talk:Quantum field theories"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Quantum_field_theories" title="Special:EditPage/Template:Quantum field theories"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Quantum_field_theories" style="font-size:114%;margin:0 4em"><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theories</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algebraic_quantum_field_theory" title="Algebraic quantum field theory">Algebraic QFT</a></li> <li><a href="/wiki/Axiomatic_quantum_field_theory" title="Axiomatic quantum field theory">Axiomatic QFT</a></li> <li><a href="/wiki/Conformal_field_theory" title="Conformal field theory">Conformal field theory</a></li> <li><a href="/wiki/Lattice_field_theory" title="Lattice field theory">Lattice field theory</a></li> <li><a href="/wiki/Noncommutative_quantum_field_theory" title="Noncommutative quantum field theory">Noncommutative QFT</a></li> <li><a href="/wiki/Gauge_theory" title="Gauge theory">Gauge theory</a></li> <li><a href="/wiki/Quantum_field_theory_in_curved_spacetime" title="Quantum field theory in curved spacetime">QFT in curved spacetime</a></li> <li><a href="/wiki/String_theory" title="String theory">String theory</a></li> <li><a href="/wiki/Supergravity" title="Supergravity">Supergravity</a></li> <li><a href="/wiki/Thermal_quantum_field_theory" title="Thermal quantum field theory">Thermal QFT</a></li> <li><a href="/wiki/Topological_quantum_field_theory" title="Topological quantum field theory">Topological QFT</a></li> <li><a href="/wiki/Two-dimensional_conformal_field_theory" title="Two-dimensional conformal field theory">Two-dimensional conformal field theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Models</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Regular</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Born%E2%80%93Infeld_model" title="Born–Infeld model">Born–Infeld</a></li> <li><a href="/wiki/Euler%E2%80%93Heisenberg_Lagrangian" title="Euler–Heisenberg Lagrangian">Euler–Heisenberg</a></li> <li><a href="/wiki/Ginzburg%E2%80%93Landau_theory" title="Ginzburg–Landau theory">Ginzburg–Landau</a></li> <li><a href="/wiki/Non-linear_sigma_model" title="Non-linear sigma model">Non-linear sigma</a></li> <li><a href="/wiki/Proca_action" title="Proca action">Proca</a></li> <li><a href="/wiki/Quantum_electrodynamics" title="Quantum electrodynamics">Quantum electrodynamics</a></li> <li><a href="/wiki/Quantum_chromodynamics" title="Quantum chromodynamics">Quantum chromodynamics</a></li> <li><a href="/wiki/Quartic_interaction" title="Quartic interaction">Quartic interaction</a></li> <li><a href="/wiki/Scalar_electrodynamics" title="Scalar electrodynamics">Scalar electrodynamics</a></li> <li><a href="/wiki/Scalar_chromodynamics" title="Scalar chromodynamics">Scalar chromodynamics</a></li> <li><a href="/wiki/Soler_model" title="Soler model">Soler</a></li> <li><a href="/wiki/Yang%E2%80%93Mills_theory" title="Yang–Mills theory">Yang–Mills</a></li> <li><a href="/wiki/Yang%E2%80%93Mills%E2%80%93Higgs_equations" title="Yang–Mills–Higgs equations">Yang–Mills–Higgs</a></li> <li><a href="/wiki/Yukawa_interaction" title="Yukawa interaction">Yukawa</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Low dimensional</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Two-dimensional_Yang%E2%80%93Mills_theory" title="Two-dimensional Yang–Mills theory">2D Yang–Mills</a></li> <li><a href="/wiki/Bullough%E2%80%93Dodd_model" title="Bullough–Dodd model">Bullough–Dodd</a></li> <li><a href="/wiki/Gross%E2%80%93Neveu_model" title="Gross–Neveu model">Gross–Neveu</a></li> <li><a href="/wiki/Schwinger_model" title="Schwinger model">Schwinger</a></li> <li><a href="/wiki/Sine-Gordon_equation" title="Sine-Gordon equation">Sine-Gordon</a></li> <li><a href="/wiki/Thirring_model" title="Thirring model">Thirring</a></li> <li><a href="/wiki/Thirring%E2%80%93Wess_model" title="Thirring–Wess model">Thirring–Wess</a></li> <li><a href="/wiki/Toda_field_theory" title="Toda field theory">Toda</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Conformal</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Massless_free_scalar_bosons_in_two_dimensions" title="Massless free scalar bosons in two dimensions">2D free massless scalar</a></li> <li><a href="/wiki/Liouville_field_theory" title="Liouville field theory">Liouville</a></li> <li><a href="/wiki/Minimal_model_(physics)" title="Minimal model (physics)">Minimal</a></li> <li><a href="/wiki/Polyakov_action" title="Polyakov action">Polyakov</a></li> <li><a href="/wiki/Wess%E2%80%93Zumino%E2%80%93Witten_model" title="Wess–Zumino–Witten model">Wess–Zumino–Witten</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Supersymmetric</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/4D_N_%3D_1_global_supersymmetry" title="4D N = 1 global supersymmetry">4D N = 1</a></li> <li><a href="/wiki/N_%3D_1_supersymmetric_Yang%E2%80%93Mills_theory" title="N = 1 supersymmetric Yang–Mills theory">N = 1 super Yang–Mills</a></li> <li><a href="/wiki/Seiberg%E2%80%93Witten_theory" title="Seiberg–Witten theory">Seiberg–Witten</a></li> <li><a href="/wiki/Super_QCD" title="Super QCD">Super QCD</a></li> <li><a href="/wiki/Wess%E2%80%93Zumino_model" title="Wess–Zumino model">Wess–Zumino</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Superconformal</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/6D_(2,0)_superconformal_field_theory" title="6D (2,0) superconformal field theory">6D (2,0)</a></li> <li><a href="/wiki/ABJM_superconformal_field_theory" title="ABJM superconformal field theory">ABJM</a></li> <li><a href="/wiki/N_%3D_4_supersymmetric_Yang%E2%80%93Mills_theory" title="N = 4 supersymmetric Yang–Mills theory">N = 4 super Yang–Mills</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Supergravity</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pure_4D_N_%3D_1_supergravity" title="Pure 4D N = 1 supergravity">Pure 4D N = 1</a></li> <li><a href="/wiki/4D_N_%3D_1_supergravity" title="4D N = 1 supergravity">4D N = 1</a></li> <li><a href="/wiki/N_%3D_8_supergravity" title="N = 8 supergravity">4D N = 8</a></li> <li><a href="/wiki/Higher-dimensional_supergravity" title="Higher-dimensional supergravity">Higher dimensional</a></li> <li><a href="/wiki/Type_I_supergravity" title="Type I supergravity">Type I</a></li> <li><a href="/wiki/Type_IIA_supergravity" title="Type IIA supergravity">Type IIA</a></li> <li><a href="/wiki/Type_IIB_supergravity" title="Type IIB supergravity">Type IIB</a></li> <li><a href="/wiki/Eleven-dimensional_supergravity" title="Eleven-dimensional supergravity">11D</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Topological</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/BF_model" title="BF model">BF</a></li> <li><a href="/wiki/Chern%E2%80%93Simons_theory" title="Chern–Simons theory">Chern–Simons</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Particle theory</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chiral_model" title="Chiral model">Chiral</a></li> <li><a href="/wiki/Fermi%27s_interaction" title="Fermi's interaction">Fermi</a></li> <li><a href="/wiki/Minimal_Supersymmetric_Standard_Model" title="Minimal Supersymmetric Standard Model">MSSM</a></li> <li><a href="/wiki/Nambu%E2%80%93Jona-Lasinio_model" title="Nambu–Jona-Lasinio model">Nambu–Jona-Lasinio</a></li> <li><a href="/wiki/Next-to-Minimal_Supersymmetric_Standard_Model" title="Next-to-Minimal Supersymmetric Standard Model">NMSSM</a></li> <li><a class="mw-selflink selflink">Standard Model</a></li> <li><a href="/wiki/Stueckelberg_action" title="Stueckelberg action">Stueckelberg</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Casimir_effect" title="Casimir effect">Casimir effect</a></li> <li><a href="/wiki/Cosmic_string" title="Cosmic string">Cosmic string</a></li> <li><a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">History</a></li> <li><a href="/wiki/Loop_quantum_gravity" title="Loop quantum gravity">Loop quantum gravity</a></li> <li><a href="/wiki/Loop_quantum_cosmology" title="Loop quantum cosmology">Loop quantum cosmology</a></li> <li><a href="/wiki/On_shell_and_off_shell" title="On shell and off shell">On shell and off shell</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a></li> <li><a href="/wiki/Quantum_dynamics" title="Quantum dynamics">Quantum dynamics</a></li> <li><a href="/wiki/Quantum_foam" title="Quantum foam">Quantum foam</a></li> <li><a href="/wiki/Quantum_fluctuation" title="Quantum fluctuation">Quantum fluctuations</a> <ul><li><a href="/wiki/Template:Quantum_electrodynamics" title="Template:Quantum electrodynamics">links</a></li></ul></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a> <ul><li><a href="/wiki/Template:Quantum_gravity" title="Template:Quantum gravity">links</a></li></ul></li> <li><a href="/wiki/Quantum_hadrodynamics" title="Quantum hadrodynamics">Quantum hadrodynamics</a></li> <li><a href="/wiki/Quantum_hydrodynamics" title="Quantum hydrodynamics">Quantum hydrodynamics</a></li> <li><a href="/wiki/Quantum_information" title="Quantum information">Quantum information</a></li> <li><a href="/wiki/Quantum_information_science" title="Quantum information science">Quantum information science</a> <ul><li><a href="/wiki/Template:Quantum_information" title="Template:Quantum information">links</a></li></ul></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Quantum_thermodynamics" title="Quantum thermodynamics">Quantum thermodynamics</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><i>See also:</i> <span class="noviewer" typeof="mw:File"><span title="Template"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/16px-Symbol_template_class_pink.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/23px-Symbol_template_class_pink.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/31px-Symbol_template_class_pink.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Template:Quantum_mechanics_topics" title="Template:Quantum mechanics topics">Template:Quantum mechanics topics</a></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Major_branches_of_physics" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Branches_of_physics" title="Template:Branches of physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Branches_of_physics" title="Template talk:Branches of physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Branches_of_physics" title="Special:EditPage/Template:Branches of physics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Major_branches_of_physics" style="font-size:114%;margin:0 4em">Major <a href="/wiki/Branches_of_physics" title="Branches of physics">branches of physics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Divisions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Basic_research" title="Basic research">Pure</a></li> <li><a href="/wiki/Applied_physics" title="Applied physics">Applied</a> <ul><li><a href="/wiki/Engineering_physics" title="Engineering physics">Engineering</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Approaches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Experimental_physics" title="Experimental physics">Experimental</a></li> <li><a href="/wiki/Theoretical_physics" title="Theoretical physics">Theoretical</a> <ul><li><a href="/wiki/Computational_physics" title="Computational physics">Computational</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Classical_physics" title="Classical physics">Classical</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a> <ul><li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newtonian</a></li> <li><a href="/wiki/Analytical_mechanics" title="Analytical mechanics">Analytical</a></li> <li><a href="/wiki/Celestial_mechanics" title="Celestial mechanics">Celestial</a></li> <li><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum</a></li></ul></li> <li><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a></li> <li><a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">Classical electromagnetism</a></li> <li><a href="/wiki/Classical_optics" class="mw-redirect" title="Classical optics">Classical optics</a> <ul><li><a href="/wiki/Geometrical_optics" title="Geometrical optics">Ray</a></li> <li><a href="/wiki/Physical_optics" title="Physical optics">Wave</a></li></ul></li> <li><a href="/wiki/Thermodynamics" title="Thermodynamics">Thermodynamics</a> <ul><li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical</a></li> <li><a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Modern_physics" title="Modern physics">Modern</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Relativistic_mechanics" title="Relativistic mechanics">Relativistic mechanics</a> <ul><li><a href="/wiki/Special_relativity" title="Special relativity">Special</a></li> <li><a href="/wiki/General_relativity" title="General relativity">General</a></li></ul></li> <li><a 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