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<!DOCTYPE html> <html > <head> <meta charset="utf-8"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <meta content="width=device-width, initial-scale=1" name="viewport"> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs"> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="RFRvdK_mC1cUBGyA4YQq31mZI3_3TGGiKp0dEHjG012iJJ9w0BP6miKE6HqNulk4CMu2CljIMrb8UmXN7pP_QA" /> <meta name="citation_title" content="Naturalness and Electroweak Symmetry Breaking" /> <meta name="citation_publication_date" content="2008/01/01" /> <meta name="citation_author" content="Romesh Kaul" /> <meta name="twitter:card" content="summary" /> <meta name="twitter:url" content="https://www.academia.edu/24498105/Naturalness_and_Electroweak_Symmetry_Breaking" /> <meta name="twitter:title" content="Naturalness and Electroweak Symmetry Breaking" /> <meta name="twitter:description" content="The Principle of Naturalness of small parameters of a theory is reviewed. While quantum field theories constructed from gauge fields and fermions only are natural, those containing elementary scalar fields are not. In particular the Higgs boson mass" /> <meta name="twitter:image" content="http://a.academia-assets.com/images/twitter-card.jpeg" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/24498105/Naturalness_and_Electroweak_Symmetry_Breaking" /> <meta property="og:title" content="Naturalness and Electroweak Symmetry Breaking" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="The Principle of Naturalness of small parameters of a theory is reviewed. While quantum field theories constructed from gauge fields and fermions only are natural, those containing elementary scalar fields are not. In particular the Higgs boson mass" /> <meta property="article:author" content="https://independent.academia.edu/RomeshKaul" /> <meta name="description" content="The Principle of Naturalness of small parameters of a theory is reviewed. While quantum field theories constructed from gauge fields and fermions only are natural, those containing elementary scalar fields are not. In particular the Higgs boson mass" /> <title>(PDF) Higgs Mass Stability and Naturalness Issues</title> <link rel="canonical" href="https://www.academia.edu/24498105/Naturalness_and_Electroweak_Symmetry_Breaking" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = 'b092bf3a3df71cf13feee7c143e83a57eb6b94fb'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1739815569000); window.Aedu.timeDifference = new Date().getTime() - 1739815569000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"The Principle of Naturalness of small parameters of a theory is reviewed. While quantum field theories constructed from gauge fields and fermions only are natural, those containing elementary scalar fields are not. In particular the Higgs boson mass in the Standard Model of electro-weak forces is not stable against radiative corrections. Two old canonical solutions of this problem are: (i)","author":[{"@context":"https://schema.org","@type":"Person","name":"Romesh Kaul","url":"https://independent.academia.edu/RomeshKaul"}],"contributor":[],"dateCreated":"2016-04-17","datePublished":"2008-01-01","headline":"Naturalness and Electroweak Symmetry Breaking","image":"https://attachments.academia-assets.com/44830213/thumbnails/1.jpg","inLanguage":"en","keywords":["Quantum Field Theory","Electroweak Symmetry Breaking","Standard Model","Higgs boson","Symmetry Breaking","Gauge Field"],"publisher":{"@context":"https://schema.org","@type":"Organization","name":null},"sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":null}],"thumbnailUrl":"https://attachments.academia-assets.com/44830213/thumbnails/1.jpg","url":"https://www.academia.edu/24498105/Naturalness_and_Electroweak_Symmetry_Breaking"}</script><style type="text/css">@media(max-width: 567px){:root{--token-mode: 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While quantum field theories constructed from gauge fields and fermions only are natural, those containing elementary scalar fields are not. In particular the Higgs boson mass in the Standard Model of electro-weak forces is not stable against radiative corrections. 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const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=24498105"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">The Principle of Naturalness of small parameters of a theory is reviewed. While quantum field theories constructed from gauge fields and fermions only are natural, those containing elementary scalar fields are not. In particular the Higgs boson mass in the Standard Model of electro-weak forces is not stable against radiative corrections. Two old canonical solutions of this problem are: (i)</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":44830213,"attachmentType":"pdf","workUrl":"https://www.academia.edu/24498105/Naturalness_and_Electroweak_Symmetry_Breaking"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":44830213,"attachmentType":"pdf","workUrl":"https://www.academia.edu/24498105/Naturalness_and_Electroweak_Symmetry_Breaking"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-premium-marketing"></div></div><div class="ds-signup-banner ds-signup-banner-premium-marketing"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="premium-banner-content"><div class="left"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><span>Get access to the world's latest research</span></div><div class="right"><div class="card free"><div class="header">Free</div><div class="feature-list"><div class="feature"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">check</span><span>Download one paper at a time</span></div><div class="feature"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">check</span><span>Save papers to bookmarks</span></div><div class="feature"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">check</span><span>Basic search</span></div></div><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--small ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"premium-banner-desktop-free"}">Sign up for free</button></div><div class="card premium"><div class="pill">Recommended</div><div class="header premium">Premium</div><div class="feature-list"><div class="feature"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">check</span><span>Get highly curated PDF packages</span></div><div class="feature"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">check</span><span>Track your impact with Mentions</span></div><div class="feature"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">check</span><span>Access advanced search filters</span></div><div class="feature"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">check</span><span>Support Academia’s mission</span></div><div class="feature"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">check</span><span>Create your personal website</span></div></div><button class="ds2-5-button ds2-5-button--small ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"premium-banner-desktop-upgrade","submitText":"Try Premium for $1"}">Try Premium for $1</button></div></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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The BSM tour will be guided by symmetry arguments. I shall pick up four specific BSM scenarios, namely, supersymmetry, Little Higgs, Gauge-Higgs unification, and the Higgsless approach. The discussion will be confined mainly on their electroweak symmetry breaking aspects.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Electroweak symmetry breaking and beyond the Standard Model physics — A review","attachmentId":72468966,"attachmentType":"pdf","work_url":"https://www.academia.edu/57691785/Electroweak_symmetry_breaking_and_beyond_the_Standard_Model_physics_A_review","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/57691785/Electroweak_symmetry_breaking_and_beyond_the_Standard_Model_physics_A_review"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="110697689" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/110697689/Electroweak_theory_without_spontaneous_symmetry_breaking_II">Electroweak theory without spontaneous symmetry breaking II</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="51281241" href="https://independent.academia.edu/MichaelD%C3%BCtsch">Michael Dütsch</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1996</p><p class="ds-related-work--abstract ds2-5-body-sm">A recent construction of the electroweak theory, based on quantum gauge invariance alone, is extended to the general case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance lead to an isolated solution for the fermionic couplings in agreement with the standard model. Third order gauge invariance determines the Higgs potential. The resulting massive gauge theory is manifestly gauge invariant, after construction. Work supported by Swiss National Science Foundation Work supported by Alexander von Humboldt Foundation</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Electroweak theory without spontaneous symmetry breaking II","attachmentId":108434716,"attachmentType":"pdf","work_url":"https://www.academia.edu/110697689/Electroweak_theory_without_spontaneous_symmetry_breaking_II","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/110697689/Electroweak_theory_without_spontaneous_symmetry_breaking_II"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="57691891" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/57691891/Electroweak_Symmetry_Breaking_and_Physics_Beyond_the_Standard_Model">Electroweak Symmetry Breaking and Physics Beyond the Standard Model</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="5232111" href="https://independent.academia.edu/HowardHaber">Howard Haber</a></div><p class="ds-related-work--abstract ds2-5-body-sm">In order to extend the Standard Model to TeV scale energies one must address two basic questions: (1) What is the complete description of the e ective theory of fundamental particles at and below the electroweak scale? and (2) What is the dynamics responsible for electroweak symmetry breaking? The answers to these questions are crucial for addressing the third outstanding question of particle physics: What are the origins of the Standard Model parameters? We brie y summarize current theoretical approaches to answering some of these questions.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Electroweak Symmetry Breaking and Physics Beyond the Standard Model","attachmentId":72469036,"attachmentType":"pdf","work_url":"https://www.academia.edu/57691891/Electroweak_Symmetry_Breaking_and_Physics_Beyond_the_Standard_Model","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/57691891/Electroweak_Symmetry_Breaking_and_Physics_Beyond_the_Standard_Model"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="125855354" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/125855354/Electroweak_Symmetry_Breaking_and_Beyond_the_Standard_Model">Electroweak Symmetry Breaking and Beyond the Standard Model</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="5232111" href="https://independent.academia.edu/HowardHaber">Howard Haber</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 1995</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Electroweak Symmetry Breaking and Beyond the Standard Model","attachmentId":119823990,"attachmentType":"pdf","work_url":"https://www.academia.edu/125855354/Electroweak_Symmetry_Breaking_and_Beyond_the_Standard_Model","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/125855354/Electroweak_Symmetry_Breaking_and_Beyond_the_Standard_Model"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="11307833" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/11307833/Naturalness_and_Theoretical_Constraints_on_the_Higgs_Boson_Mass">Naturalness and Theoretical Constraints on the Higgs Boson Mass</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="27347218" href="https://independent.academia.edu/MarcosSampaio">Marcos Sampaio</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Theoretical Physics, 2013</p><p class="ds-related-work--abstract ds2-5-body-sm">We verify that quadratic divergences responsible for the lack of naturalness in the Standard Model are intrinsically arbitrary and regularization dependent. Such arbitrariness may be fixed by demanding consistency of scale invariance breakdown by quantum corrections as argued by W. Bardeen. Besides eliminating a fine-tuning problem and restore validity of perturbation theory, this requirement allows to construct bounds for the Higgs boson mass in terms of δm 2 /m 2 H . These bounds together with the vacuum stability bound allow us to obtain intervals for the Higgs boson mass for a given energy scale.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Naturalness and Theoretical Constraints on the Higgs Boson Mass","attachmentId":46763318,"attachmentType":"pdf","work_url":"https://www.academia.edu/11307833/Naturalness_and_Theoretical_Constraints_on_the_Higgs_Boson_Mass","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/11307833/Naturalness_and_Theoretical_Constraints_on_the_Higgs_Boson_Mass"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="923590" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/923590/Structure_of_corrections_to_electroweak_interactions_in_Higgsless_models">Structure of corrections to electroweak interactions in Higgsless models</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="46250" href="https://michiganstate.academia.edu/ElizabethSimmons">Elizabeth Simmons</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review D, 2004</p><p class="ds-related-work--abstract ds2-5-body-sm">Recently, "Higgsless" models of electroweak symmetry breaking have been proposed. Based on compactified five-dimensional gauge theories, these models achieve unitarity of electroweak boson self-interactions through the exchange of a tower of massive vector bosons rather than the exchange of a scalar Higgs boson. In this paper, using deconstruction, we analyze the form of the corrections to the electroweak interactions in a large class of these models, allowing for arbitrary 5-D geometry, position-dependent gauge coupling, and brane kinetic energy terms. We show that many models considered in the literature, including those most likely to be phenomenologically viable, are in this class. By analyzing the asymptotic behavior of the correlation function of gauge currents at high momentum, we extract the exact form of the relevant correlation functions at tree-level and compute the corrections to precision electroweak observables in terms of the spectrum of heavy vector bosons. We determine when nonoblique corrections due to the interactions of fermions with the heavy vector bosons become important, and specify the form such interactions can take. In particular we find that in this class of models, so long as the theory remains unitary, S −4 cos 2 θ W T > O(1), where S and T are the usual oblique parameters. We concur with the result of Cacciapaglia et.al. that small or negative S is possible -though only at the expense of substantial negative T at tree-level. Although we stress our results as they apply to continuum 5-D models, they apply also to models of extended electroweak gauge symmetries motivated by models of hidden local symmetry.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Structure of corrections to electroweak interactions in Higgsless models","attachmentId":5617032,"attachmentType":"pdf","work_url":"https://www.academia.edu/923590/Structure_of_corrections_to_electroweak_interactions_in_Higgsless_models","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/923590/Structure_of_corrections_to_electroweak_interactions_in_Higgsless_models"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="923579" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/923579/Strong_dynamics_and_electroweak_symmetry_breaking">Strong dynamics and electroweak symmetry breaking</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="46250" href="https://michiganstate.academia.edu/ElizabethSimmons">Elizabeth Simmons</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Reports, 2003</p><p class="ds-related-work--abstract ds2-5-body-sm">The breaking of electroweak symmetry, and origin of the associated "weak scale," v weak = 1/ 2 √ 2G F = 175 GeV, may be due to a new strong interaction. Theoretical developments over the past decade have led to viable models and mechanisms that are consistent with current experimental data. Many of these schemes feature a privileged role for the top quark, and third generation, and are natural in the context of theories of extra space dimensions at the weak scale. We review various models and their phenomenological implications which will be subject to definitive tests in future collider runs at the Tevatron, and the LHC, and future linear e + e − colliders, as well as sensitive studies of rare processes. 5 Outlook and Conclusions 159 6 Acknowledgements 160 Appendix A: The Standard Model 161 Appendix B: The Nambu-Jona-Lasinio Model 168 Bibliography 172</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Strong dynamics and electroweak symmetry breaking","attachmentId":5617026,"attachmentType":"pdf","work_url":"https://www.academia.edu/923579/Strong_dynamics_and_electroweak_symmetry_breaking","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/923579/Strong_dynamics_and_electroweak_symmetry_breaking"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="18112069" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/18112069/The_universality_class_of_the_electroweak_theory">The universality class of the electroweak theory</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38063268" href="https://independent.academia.edu/MaximTsypin">Maxim Tsypin</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Nuclear Physics B, 1998</p><p class="ds-related-work--abstract ds2-5-body-sm">We study the universality class and critical properties of the electroweak theory at finite temperature. Such critical behaviour is found near the endpoint m H = m H,c of the line of first order electroweak phase transitions in a wide class of theories, including the Standard Model (SM) and a part of the parameter space of the Minimal Sypersymmetric Standard Model (MSSM). We find that the location of the endpoint corresponds to the Higgs mass m H,c = 72(2) GeV in the SM with sin 2 θ W = 0, and m H,c < 80 GeV with sin 2 θ W = 0.23. As experimentally m H > 88 GeV, there is no electroweak phase transition in the SM. We compute the corresponding critical indices and provide strong evidence that the phase transitions near the endpoint fall into the three dimensional Ising universality class.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The universality class of the electroweak theory","attachmentId":39881893,"attachmentType":"pdf","work_url":"https://www.academia.edu/18112069/The_universality_class_of_the_electroweak_theory","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/18112069/The_universality_class_of_the_electroweak_theory"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="923583" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/923583/Erratum_toStrong_dynamics_and_electroweak_symmetry_breaking_Phys_Rep_381_2003_235_402_">Erratum to``Strong dynamics and electroweak symmetry breaking''[Phys. Rep. 381 (2003) 235-402]</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="46250" href="https://michiganstate.academia.edu/ElizabethSimmons">Elizabeth Simmons</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Reports, 2004</p><p class="ds-related-work--abstract ds2-5-body-sm">The breaking of electroweak symmetry, and origin of the associated "weak scale," v weak = 1/ 2 √ 2G F = 175 GeV, may be due to a new strong interaction. Theoretical developments over the past decade have led to viable models and mechanisms that are consistent with current experimental data. Many of these schemes feature a privileged role for the top quark, and third generation, and are natural in the context of theories of extra space dimensions at the weak scale. We review various models and their phenomenological implications which will be subject to definitive tests in future collider runs at the Tevatron, and the LHC, and future linear e + e − colliders, as well as sensitive studies of rare processes. 5 Outlook and Conclusions 159 6 Acknowledgements 160 Appendix A: The Standard Model 161 Appendix B: The Nambu-Jona-Lasinio Model 168 Bibliography 172</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Erratum to``Strong dynamics and electroweak symmetry breaking''[Phys. Rep. 381 (2003) 235-402]","attachmentId":51162053,"attachmentType":"pdf","work_url":"https://www.academia.edu/923583/Erratum_toStrong_dynamics_and_electroweak_symmetry_breaking_Phys_Rep_381_2003_235_402_","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/923583/Erratum_toStrong_dynamics_and_electroweak_symmetry_breaking_Phys_Rep_381_2003_235_402_"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="6070500" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/6070500/Redesigning_Electroweak_Theory_Does_the_Higgs_Particle_Exist">Redesigning Electroweak Theory: Does the Higgs Particle Exist</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="9138154" href="https://independent.academia.edu/vttoth">Viktor T Toth</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2009</p><p class="ds-related-work--abstract ds2-5-body-sm">An electroweak model in which the masses of the W and Z bosons and the fermions are generated by quantum loop graphs through a symmetry breaking is investigated. The model is based on a regularized quantum field theory in which the quantum loop graphs are finite to all orders of perturbation theory and the massless theory is gauge invariant, Poincaré invariant, and unitary. The breaking of the electroweak symmetry SU(2) L ×U(1) Y is achieved without a Higgs particle. A fundamental energy scale Λ W ≃ 542 GeV (not to be confused with a naive cutoff) enters the theory through the regularization of the Feynman loop diagrams. The theory yields a prediction for the W mass m W that is accurate to about 0.5% without radiative corrections. The scattering amplitudes for W + L W − L →W + L W − L and e + e − →W + L W − L processes do not violate unitarity at high energies due to the suppression of the amplitudes by the running of the coupling constants at vertices.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Redesigning Electroweak Theory: Does the Higgs Particle Exist","attachmentId":32992392,"attachmentType":"pdf","work_url":"https://www.academia.edu/6070500/Redesigning_Electroweak_Theory_Does_the_Higgs_Particle_Exist","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/6070500/Redesigning_Electroweak_Theory_Does_the_Higgs_Particle_Exist"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":44830213,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":44830213,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_44830213" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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