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The data of the four experiments have been statistically combined. The results are interpreted within the 2HDM for Type I and Type II benchmark scenarios. No statistically significant excess has been observed when compared to the Standard Model background prediction, and the combined LEP data exclude large regions of the model parameter space. Charged Higgs bosons with mass below 80&nbsp; ${\rm GeV}/c^{2}$ (Type II scenario) or 72.5 ${\rm GeV}/c^{2}$ (Type I scenario, for pseudo-scalar masses above 12 ${\rm GeV}/c^{2}$ ) are excluded at the 95&nbsp;% confidence level."/> <meta name="prism.issn" content="1434-6052"/> <meta name="prism.publicationName" content="The European Physical Journal C"/> <meta name="prism.publicationDate" content="2013-07-03"/> <meta name="prism.volume" content="73"/> <meta name="prism.number" content="7"/> <meta name="prism.section" content="OriginalPaper"/> <meta name="prism.startingPage" content="1"/> <meta name="prism.endingPage" content="9"/> <meta name="prism.copyright" content="2013 The Author(s)"/> <meta name="prism.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="prism.url" content="https://link.springer.com/article/10.1140/epjc/s10052-013-2463-1"/> <meta name="prism.doi" content="doi:10.1140/epjc/s10052-013-2463-1"/> <meta name="citation_pdf_url" content="https://link.springer.com/content/pdf/10.1140/epjc/s10052-013-2463-1.pdf"/> <meta name="citation_fulltext_html_url" content="https://link.springer.com/article/10.1140/epjc/s10052-013-2463-1"/> <meta name="citation_journal_title" content="The European Physical Journal C"/> <meta name="citation_journal_abbrev" content="Eur. 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No statistically significant excess has been observed when compared to the Standard Model background prediction, and the combined LEP data exclude large regions of the model parameter space. Charged Higgs bosons with mass below 80 ${\rm GeV}/c^{2}$ (Type II scenario) or 72.5 ${\rm GeV}/c^{2}$ (Type I scenario, for pseudo-scalar masses above 12 ${\rm GeV}/c^{2}$ ) are excluded at the 95 % confidence level."/> <meta property="og:image" content="https://static-content.springer.com/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig1_HTML.gif"/> <meta name="format-detection" content="telephone=no"> <link rel="apple-touch-icon" sizes="180x180" href=/oscar-static/img/favicons/darwin/apple-touch-icon-92e819bf8a.png> <link rel="icon" type="image/png" sizes="192x192" href=/oscar-static/img/favicons/darwin/android-chrome-192x192-6f081ca7e5.png> <link rel="icon" type="image/png" sizes="32x32" href=/oscar-static/img/favicons/darwin/favicon-32x32-1435da3e82.png> <link rel="icon" type="image/png" sizes="16x16" href=/oscar-static/img/favicons/darwin/favicon-16x16-ed57f42bd2.png> <link rel="shortcut icon" data-test="shortcut-icon" 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Search for charged Higgs bosons: combined results using LEP data </div> <div data-test="inCoD" data-track-context="sticky banner"> <div class="c-pdf-container"> <div class="c-pdf-download u-clear-both u-mb-16"> <a href="/content/pdf/10.1140/epjc/s10052-013-2463-1.pdf" class="u-button u-button--full-width u-button--primary u-justify-content-space-between c-pdf-download__link" data-article-pdf="true" data-readcube-pdf-url="true" data-test="pdf-link" data-draft-ignore="true" data-track="content_download" data-track-type="article pdf download" data-track-action="download pdf" data-track-label="button" data-track-external download> <span class="c-pdf-download__text">Download PDF</span> <svg aria-hidden="true" focusable="false" width="16" height="16" class="u-icon"><use xlink:href="#icon-eds-i-download-medium"/></svg> </a> </div> </div> </div> </div> </div> <div class="c-article-header"> <header> <ul class="c-article-author-list c-article-author-list--short" data-test="authors-list" data-component-authors-activator="authors-list"><li class="c-article-author-list__item"><a data-test="author-name" data-author-popup="group-1" href="#group-1">ALEPH Collaboration</a>, </li><li class="c-article-author-list__item"><a data-test="author-name" data-author-popup="group-2" href="#group-2">DELPHI Collaboration</a>, </li><li class="c-article-author-list__item"><a data-test="author-name" data-author-popup="group-3" href="#group-3">L3 Collaboration</a>, </li><li class="c-article-author-list__item"><a data-test="author-name" data-author-popup="group-4" href="#group-4">OPAL Collaboration</a> & </li><li class="c-article-author-list__item"><a data-test="author-name" data-author-popup="group-5" href="#group-5">The LEP working group for Higgs boson searches</a></li></ul><button aria-expanded="false" class="c-article-author-list__button"><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" 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aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-altmetric-medium"></use> </svg>1 <span class="app-article-metrics-bar__label">Altmetric</span></p> </li> <li class="app-article-metrics-bar__item app-article-metrics-bar__item--metrics"> <p class="app-article-metrics-bar__details"><a href="/article/10.1140/epjc/s10052-013-2463-1/metrics" data-track="click" data-track-action="view metrics" data-track-label="link" rel="nofollow">Explore all metrics <svg class="u-icon app-article-metrics-bar__arrow-icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-arrow-right-medium"></use> </svg></a></p> </li> </ul> </div> <div class="u-mt-32"> </div> </header> </div> <div data-article-body="true" data-track-component="article body" class="c-article-body"> <section aria-labelledby="Abs1" data-title="Abstract" lang="en"><div class="c-article-section" id="Abs1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Abs1">Abstract</h2><div class="c-article-section__content" id="Abs1-content"><p>The four LEP collaborations, ALEPH, DELPHI, L3 and OPAL, have searched for pair-produced charged Higgs bosons in the framework of Two Higgs Doublet Models (2HDMs). The data of the four experiments have been statistically combined. The results are interpreted within the 2HDM for Type I and Type II benchmark scenarios. No statistically significant excess has been observed when compared to the Standard Model background prediction, and the combined LEP data exclude large regions of the model parameter space. Charged Higgs bosons with mass below 80 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> (Type II scenario) or 72.5 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> (Type I scenario, for pseudo-scalar masses above 12 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>) are excluded at the 95 % confidence level.</p></div></div></section> <div data-test="cobranding-download"> </div> <section aria-labelledby="inline-recommendations" data-title="Inline Recommendations" class="c-article-recommendations" data-track-component="inline-recommendations"> <h3 class="c-article-recommendations-title" id="inline-recommendations">Similar content being viewed by others</h3> <div class="c-article-recommendations-list"> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-019-7561-2/MediaObjects/10052_2019_7561_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1140/epjc/s10052-019-7561-2?fromPaywallRec=false" data-track="select_recommendations_1" data-track-context="inline recommendations" data-track-action="click recommendations inline - 1" data-track-label="10.1140/epjc/s10052-019-7561-2">A 96 GeV Higgs boson in the N2HDM </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">03 January 2020</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3Aplaceholder%2Fimages/placeholder-figure-springernature.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1007/JHEP05(2018)012?fromPaywallRec=false" data-track="select_recommendations_2" data-track-context="inline recommendations" data-track-action="click recommendations inline - 2" data-track-label="10.1007/JHEP05(2018)012">Charged fermions below 100 GeV </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">03 May 2018</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3Aplaceholder%2Fimages/placeholder-figure-springernature.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1007/JHEP01(2016)120?fromPaywallRec=false" data-track="select_recommendations_3" data-track-context="inline recommendations" data-track-action="click recommendations inline - 3" data-track-label="10.1007/JHEP01(2016)120">Searches of exotic Higgs bosons in general mass spectra of the Georgi-Machacek model at the LHC </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">20 January 2016</span> </div> </div> </article> </div> </div> </section> <script> window.dataLayer = window.dataLayer || []; window.dataLayer.push({ recommendations: { recommender: 'semantic', model: 'specter', policy_id: 'NA', timestamp: 1732811557, embedded_user: 'null' } }); </script> <section aria-labelledby="content-related-subjects" data-test="subject-content"> <h3 id="content-related-subjects" class="c-article__sub-heading">Explore related subjects</h3> <span class="u-sans-serif u-text-s u-display-block u-mb-24">Discover the latest articles, news and stories from top researchers in related subjects.</span> <ul class="c-article-subject-list" role="list"> <li class="c-article-subject-list__subject"> <a href="/subject/experimental-particle-physics" data-track="select_related_subject_1" data-track-context="related subjects from content page" data-track-label="Experimental Particle Physics">Experimental Particle Physics</a> </li> </ul> </section> <div class="app-card-service" data-test="article-checklist-banner"> <div> <a class="app-card-service__link" data-track="click_presubmission_checklist" data-track-context="article page top of reading companion" data-track-category="pre-submission-checklist" data-track-action="clicked article page checklist banner test 2 old version" data-track-label="link" href="https://beta.springernature.com/pre-submission?journalId=10052" data-test="article-checklist-banner-link"> <span class="app-card-service__link-text">Use our pre-submission checklist</span> <svg class="app-card-service__link-icon" aria-hidden="true" focusable="false"><use xlink:href="#icon-eds-i-arrow-right-small"></use></svg> </a> <p class="app-card-service__description">Avoid common mistakes on your manuscript.</p> </div> <div class="app-card-service__icon-container"> <svg class="app-card-service__icon" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-clipboard-check-medium"></use> </svg> </div> </div> <div class="main-content"> <section data-title="Introduction"><div class="c-article-section" id="Sec1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec1"><span class="c-article-section__title-number">1 </span>Introduction</h2><div class="c-article-section__content" id="Sec1-content"><p>A charged Higgs boson appears in many extensions of the Higgs sector beyond the Standard Model (SM). Indeed, its discovery would signal unambiguously that the Higgs-like particle recently discovered at LHC [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 1" title="
ATLAS Coll., Phys. Lett. B 716, 1 (2012)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR1" id="ref-link-section-d1562255e371">1</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 2" title="
CMS Coll., Phys. Lett. B 716, 30 (2012)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR2" id="ref-link-section-d1562255e374">2</a>] is not the SM neutral Higgs boson. It is thus of great interest to search for a charged Higgs boson.</p><p>More than twelve years after the end of data-taking at LEP, it is important to add to the LEP legacy the outcome of the searches for a charged Higgs boson. In fact, the charged Higgs boson searches at a lepton collider are significantly less model-dependent than the corresponding searches at hadron colliders, due to the very simple production mechanism.</p><p>Since the previous communication by the LEP working group for Higgs boson searches (LEPHWG) on charged Higgs boson, in 2001 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 3" title="
Search for Charged Higgs bosons: preliminary combined results using LEP data collected at energies up to 209 GeV. LHWG Note/2001-05, July 2001, and 
 arXiv:hep-ex/0107031
 
 
 " href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR3" id="ref-link-section-d1562255e382">3</a>], the LEP experiments have published their final results on these searches and have, in some cases, also added searches for new final states not previously considered. The four LEP collaborations have searched for charged Higgs bosons in the framework of Two Higgs Doublet Models (2HDMs). Based on the final results obtained by ALEPH [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 4" title="
A. Heister et al. (ALEPH Collaboration), Phys. Lett. B 543, 1 (2002)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR4" id="ref-link-section-d1562255e385">4</a>], DELPHI [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 5" title="
J. Abdallah et al. (DELPHI Collaboration), Eur. Phys. J. C 34, 399 (2004)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR5" id="ref-link-section-d1562255e388">5</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 6" title="
P. Abreu et al. (DELPHI Collaboration), Phys. Lett. B 460, 484 (1999)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR6" id="ref-link-section-d1562255e391">6</a>], L3 [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 7" title="
P. Achard et al. (L3 Collaboration), Phys. Lett. B 575, 208 (2003)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR7" id="ref-link-section-d1562255e394">7</a>] and OPAL [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 8" title="
G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 72, 2076 (2012)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR8" id="ref-link-section-d1562255e398">8</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 9" title="
G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 7, 407 (1999)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR9" id="ref-link-section-d1562255e401">9</a>], the LEPHWG has performed a statistical combination of the data taken at center-of-mass energies, <span class="mathjax-tex">$\sqrt{s}$</span>, from 183 GeV to 209 GeV. The total luminosity used in this combination is 2.6 fb<sup>−1</sup>.</p><p>In 2HDMs [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 11" title="
S.L. Glashow, S. Weinberg, Phys. Rev. D 15, 1958 (1977)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR11" id="ref-link-section-d1562255e420">11</a>–<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 14" title="
A.G. Akeroyd, Nucl. Phys. B 544, 557 (1999)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR14" id="ref-link-section-d1562255e423">14</a>], there are five physical Higgs bosons: the CP-even h and H, the CP-odd A and the charged Higgs bosons, H<sup>±</sup>. The charged Higgs couplings to the photon and the Z boson are completely specified in terms of the electric charge and the weak mixing angle, <i>θ</i> <sub>W</sub>, and therefore, at tree level, the production cross-section depends only on the charged Higgs boson mass. Higgs bosons couple proportionally to the particle mass and therefore decay preferentially to heavy particles, but the precise branching ratios may vary significantly depending on the model. Two scenarios are considered in this paper. The first one effectively allows the charged Higgs boson to decay to fermions only, which is the case in type II 2HDM for not too small values of <i>m</i> <sub>A</sub> (the neutral CP-odd A boson mass) or tan<i>β</i> (the ratio of the two Higgs doublet vacuum expectation values). In this model the isospin <span class="mathjax-tex">$+\frac{1}{2}$</span> fermion-couplings to the charged Higgs boson are proportional to 1/tan<i>β</i>, while the isospin <span class="mathjax-tex">$-\frac{1}{2}$</span> fermion-couplings are proportional to tan<i>β</i>. This scenario is treated in Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Sec2">2</a>. In the second scenario, type I 2HDM, all fermions couple proportionally to 1/tan<i>β</i>. Consequently, the second scenario effectively allows the charged Higgs boson to also decay into gauge (possibly off-shell) bosons and Higgs bosons (see Sect. <a data-track="click" data-track-label="link" data-track-action="section anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Sec3">3</a>).</p><p>Pair-production of charged Higgs bosons via s-channel exchange of a <span class="mathjax-tex">$\mathrm{Z^{0}}$</span> boson would modify the decay width of the <span class="mathjax-tex">$\mathrm{Z^{0}}$</span> boson. Therefore electroweak precision measurements set indirect bounds on the mass of the charged Higgs boson regardless of its decay branching ratios. The difference between the measured decay width of the <span class="mathjax-tex">$\mbox{$\mathrm{Z^{0}}$}$</span> (<i>Γ</i> <sub>Z</sub>) and the prediction from the SM sets a limit on any non-standard (non SM) contribution to <span class="mathjax-tex">$\mbox {$\mathrm{Z^{0}}$}$</span> decay. The <span class="mathjax-tex">$\mbox{$\mathrm{Z^{0}}$}$</span> decay width has been measured precisely during the first phase of LEP (LEP-1). The final LEP result [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 15" title="
The LEP Collaborations, the SLD Collaboration, the LEP Electroweak working group, the SLD Electroweak and Heavy Flavour Groups. Phys. Rep. 427, 257 (2006)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR15" id="ref-link-section-d1562255e545">15</a>] set the limit <span class="mathjax-tex">$\varGamma_{\rm non SM}<2.9$</span> MeV/<i>c</i> <sup>2</sup> (95 % C.L.), which translates to <span class="mathjax-tex">$\mbox{$m_{\mathrm{H}^{\pm}}$}>$</span> 39.6 GeV/<i>c</i> <sup>2</sup> (95 % C.L.). Direct searches during the LEP-1 period set a lower bound for the charged Higgs boson mass at 44.1 GeV/<i>c</i> <sup>2</sup> at 95 % C.L. for type II 2HDM [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 16" title="
D. Decamp et al. (ALEPH Collaboration), Phys. Rep. 216, 253 (1992)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR16" id="ref-link-section-d1562255e586">16</a>–<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 19" title="
G. Alexander et al. (OPAL Collaboration), Phys. Lett. B 370, 174 (1996)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR19" id="ref-link-section-d1562255e590">19</a>]. The combination in this paper is performed for charged Higgs boson masses of 43 GeV/<i>c</i> <sup>2</sup> or larger, since the region below 43 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> has been covered by individual experiments.</p><p>For this combination of data, the cross-sections (and branching ratios for type II 2HDM) are calculated within the HZHA program package [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 20" title="
G. Ganis, P. Janot, The HZHA Generator: CERN Report 96-01, vol. 2, p. 309 (1996). Version 3, released in December 1999, 
 https://janot.web.cern.ch/janot/Generators.html
 
 
 " href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR20" id="ref-link-section-d1562255e612">20</a>], and the branching ratios of the charged Higgs boson in type I 2HDM are taken from Ref. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 21" title="
A.G. Akeroyd et al., Eur. Phys. J. C 12, 451 (2000)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR21" id="ref-link-section-d1562255e615">21</a>].</p><p>The input from the four experiments [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 4" title="
A. Heister et al. (ALEPH Collaboration), Phys. Lett. B 543, 1 (2002)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR4" id="ref-link-section-d1562255e621">4</a>–<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 9" title="
G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 7, 407 (1999)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR9" id="ref-link-section-d1562255e624">9</a>] which is used in the combination procedure is provided on a channel-by-channel basis. The word “channel” designates any subset of the data where a Higgs boson search has been carried out. Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Tab1">1</a> shows a summary of all channels available for this combination. It amounts to 22 channels from ALEPH, 43 from DELPHI, 12 from L3 and 45 from OPAL. </p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-1"><figure><figcaption class="c-article-table__figcaption"><b id="Tab1" data-test="table-caption">Table 1 Overview of the searches for charged Higgs bosons performed by the four LEP experiments, whose results are used in this combination. Where relevant, <i>m</i> <sub>A</sub> varies from 2<i>m</i> <sub> <i>b</i> </sub> to <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span>. Each experiment analyzed typically around 650 pb<sup>−1</sup>of data</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-013-2463-1/tables/1" aria-label="Full size table 1"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <p>Each experiment generated and simulated the detailed detector response in Monte Carlo event samples for the Higgs signal and the various background processes, at center-of-mass energies of 183, 189, 192, 196, 200, 202, 204, 206, 208 and 209 GeV to estimate background and signal contributions in the data collected between 1997 and 2000. Particular care has been taken when simulating the four-fermion background, especially from W-pair background, using the most advanced codes available at that time. ALEPH used KORALW [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 22" title="
M. Skrzypek et al., Comput. Phys. Commun. 94, 216 (1996)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR22" id="ref-link-section-d1562255e1248">22</a>] as the generator and RACOONWW [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 23" title="
A. Denner et al., Phys. Lett. B 475, 127 (2000)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR23" id="ref-link-section-d1562255e1251">23</a>] and YFSWW [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 24" title="
S. Jadach et al., Phys. Rev. D 61, 113010 (2000)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR24" id="ref-link-section-d1562255e1254">24</a>] for the cross-section calculation, while DELPHI used WPHACT [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 25" title="
A. Ballestrero et al., Comput. Phys. Commun. 152, 175 (2003)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR25" id="ref-link-section-d1562255e1257">25</a>], L3 YFSWW and OPAL GRC4F [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 26" title="
J. Fujimoto et al., Comput. Phys. Commun. 100, 128 (1997)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR26" id="ref-link-section-d1562255e1260">26</a>] and KORALW. Other generators were used for systematic studies. Furthermore, each of the four experiments used different values for the W mass in these background simulations (respectively 80.45, 80.40, 80.356 and 80.33 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> for ALEPH, DELPHI, L3 and OPAL), while the LEP combined measured value is 80.376±0.033 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 27" title="
The LEP Collaborations, ALEPH, DELPHI, L3, OPAL, and the LEP Electroweak Working Group, Phys. Rep. (2013, submitted). 
 arXiv:1302.3415
 
 [hep-ex]
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR27" id="ref-link-section-d1562255e1286">27</a>], thus introducing an additional source of systematic uncertainty due to the broadening of the W peak when adding the four background simulations.</p><p>The statistical procedure adopted for the combination of the data and the precise definitions of the confidence levels CL<sub> <i>b</i> </sub>, CL<sub> <i>s</i> </sub>, CL<sub> <i>s</i>+<i>b</i> </sub> by which the search results are expressed, have been described previously [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 28" title="
ALEPH, DELPHI, L3, OPAL Collaborations, The LEP working group for Higgs boson searches, Phys. Lett. B 565, 61 (2003)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR28" id="ref-link-section-d1562255e1313">28</a>]. The main sources of systematic uncertainty affecting the signal and background predictions are included, using an extension of the method of Cousins and Highland [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 29" title="
R.D. Cousins, V.L. Highland, Nucl. Instrum. Methods Phys. Res., Sect. A 320, 331 (1992)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR29" id="ref-link-section-d1562255e1316">29</a>] where the <i>p</i>-values are averaged over a large ensemble of Monte Carlo experiments. The correlations between search channels, LEP collision energies and individual experiments have not been taken into account, but these correlations are estimated to have only small effects, about 500 <span class="mathjax-tex">${\rm MeV}/c^{2}$</span>, to the final results.</p></div></div></section><section data-title="Combined searches in the framework of type II 2HDM"><div class="c-article-section" id="Sec2-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec2"><span class="c-article-section__title-number">2 </span>Combined searches in the framework of type II 2HDM</h2><div class="c-article-section__content" id="Sec2-content"><p>In type II 2HDM, one Higgs doublet couples to up-type fermions and the other to down-type fermions. The Higgs sector of the Minimal Supersymmetric Standard Model (MSSM) is a particular case of such models. In the MSSM, at tree-level, the H<sup>±</sup> is constrained to be heavier than the W boson and the radiative corrections to the charged Higgs mass are positive, except for very specific parameter choices. Thus, experimentally finding evidence of a charged Higgs boson with mass below the W boson mass would set very strong constraints on the MSSM parameters. However, in the following we will concentrate on the general type II 2HDM without any supersymmetric assumptions. Results on the search for neutral MSSM Higgs bosons can be found in [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="
The LEP collaborations, The LEP working group for Higgs boson searches, Eur. Phys. J. C 47, 547 (2006)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR30" id="ref-link-section-d1562255e1344">30</a>].</p><p>For the charged Higgs masses accessible at LEP energies, the decays into <i>τ</i> <sup>+</sup> <i>ν</i> <sub> <i>τ</i> </sub> and <span class="mathjax-tex">$\mathrm{c} \bar{\mathrm{s}}$</span> (and their charge conjugates) are expected to dominate. The searches are carried out under the assumption that the two decays <span class="mathjax-tex">$\mathrm{H}^{+}\rightarrow \mathrm{c} \bar{\mathrm{s}}$</span> and H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i> exhaust the H<sup>+</sup> decay width, but the relative branching ratio is free. This assumption is valid as long as <i>m</i> <sub>A</sub> is larger than 60 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> (MSSM case) or tan<i>β</i> is larger than a few units. Thus, the searches encompass the following H<sup>+</sup>H<sup>−</sup> final states: (<span class="mathjax-tex">$\mathrm{c} \bar{\mathrm{s}}$</span> )(<span class="mathjax-tex">$\bar{\mathrm{c}} \mathrm{s}$</span>), (<i>τ</i> <sup>+</sup> <i>ν</i>)(<i>τ</i> <sup>−</sup> <span class="mathjax-tex">$\bar{\nu}$</span>) and the mixed mode (<span class="mathjax-tex">$\mathrm{c} \bar{\mathrm{s}}$</span>)(<i>τ</i> <sup>−</sup> <span class="mathjax-tex">$\bar{\nu}$</span>) or (<span class="mathjax-tex">$\bar{\mathrm{c}} \mathrm{s}$</span>)(<i>τ</i> <sup>+</sup> <i>ν</i>). The combined search results are presented as a function of the branching ratio Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>).</p><p>Details of the searches done by the individual experiments can be found in Refs. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 4" title="
A. Heister et al. (ALEPH Collaboration), Phys. Lett. B 543, 1 (2002)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR4" id="ref-link-section-d1562255e1532">4</a>–<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 9" title="
G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 7, 407 (1999)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR9" id="ref-link-section-d1562255e1535">9</a>]. Two features in these analyses are worth noting: the main background is W pair production, which is partly irreducible, and the reconstructed mass is one of the discriminant variables used in the final hypothesis testing in the two channels where this is relevant (mixed and hadronic channels). The results from the four LEP experiments are summarized in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Tab2">2</a>, together with the 95 % C.L. observed and median expected lower limits on the charged Higgs boson mass. The mass limits are quoted separately for Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>)=0,1, and independently of the charged Higgs decay. </p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-2"><figure><figcaption class="c-article-table__figcaption"><b id="Tab2" data-test="table-caption">Table 2 Individual search results for the e<sup>+</sup>e<sup>−</sup>→H<sup>+</sup>H<sup>−</sup> fermionic final states. All limits are given at the 95 % C.L. The OPAL selection is mass-dependent; the numbers of events given here are for <span class="mathjax-tex">$m_{\mathrm{H}^{\pm }}= 80~{\rm GeV}/c^{2}$</span> </b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-013-2463-1/tables/2" aria-label="Full size table 2"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <p>In a first step, the statistical combination software was run separately on the data provided by the four collaborations and the results compared to the published results of each. The differences between this check and the published results (of the order of ±200 <span class="mathjax-tex">${\rm MeV}/c^{2}$</span> in the limits) reflect the differences between the statistical methods used by the four collaborations. The biggest difference has been found for the expected limit from OPAL at Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>)=1 and amounts to 600 <span class="mathjax-tex">${\rm MeV}/c^{2}$</span>. This difference is compatible in size with the estimated effect of about 500 <span class="mathjax-tex">${\rm MeV}/c^{2}$</span> of not taking into account the correlations between systematic uncertainties. All mass limits have thus been rounded down to the nearest half a <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>.</p><p>Combining the results from the four experiments, a scan in the branching ratio Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>) versus charged Higgs boson mass plane has been performed, and the limit-setting procedure was repeated for each scan point. This two-dimensional scan was performed with the following ranges and steps: <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span> from 43 to 95 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> with 1 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> steps, and Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>) from 0 to 1 with 0.05 steps.</p><p>Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig1">1</a> shows the observed background confidence level CL<sub> <i>b</i> </sub> as a function of <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span> and Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>). The observed confidence level is everywhere within ±2<i>σ</i> of the background prediction, except for three small regions, as shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig1">1</a>. Such regions result from the combination of small excesses, as compared to the background expectation, observed by two or three experiments. The first two mass regions, around 43 and 55 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>, are due to a slight excess of data in the hadronic channel, and the third one, around 90 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>, arises from an excess of events in the mixed channel. Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Tab3">3</a> gives the combined CL<sub> <i>b</i> </sub> together with the values from each experiment for these three domains (the values chosen for Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>) are given in the second column). </p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-1" data-title="Fig. 1"><figure><figcaption><b id="Fig1" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 1</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/1" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig1_HTML.gif?as=webp"><img aria-describedby="Fig1" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig1_HTML.gif" alt="figure 1" loading="lazy"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-1-desc"><p>Type II 2HDM: contours based on the observed p-values CL<sub> <i>b</i> </sub> as a function of <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span> and the branching ratio Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>), indicating the statistical significance, <i>N</i> <sub> <i>σ</i> </sub>, of local departures from the background expectation. The <i>black solid line</i> indicates the change of sign of this significance, i.e. where there is a transition from excess to deficit</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/1" data-track-dest="link:Figure1 Full size image" aria-label="Full size image figure 1" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-3"><figure><figcaption class="c-article-table__figcaption"><b id="Tab3" data-test="table-caption">Table 3 Combined and individual CL<sub> <i>b</i> </sub> values for the three mass points with a deviation from expectation larger than 2<i>σ</i>. All values, obtained with the statistical procedure of the overall combination, compare well to those published by the experiments. (*) ALEPH and L3 did not provide inputs for this mass</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-013-2463-1/tables/3" aria-label="Full size table 3"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <p>The combined results for the Type II 2HDM are summarized in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig2">2</a>, which shows the expected median and observed mass limits, while the contribution of each of the three decay channels to the overall limit is presented in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig3">3</a>. It is worth noting that: </p><ul class="u-list-style-dash"> <li> <p>The purely leptonic channel alone excludes charged Higgs masses above the W mass, down to Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>) around 0.45. In this channel, the mass of the Higgs boson cannot be reconstructed, due to the presence of two neutrinos in the final state. As a consequence, the W boson pair background is diluted and the analysis is sensitive up to <span class="mathjax-tex">$\sqrt{s}/2$</span>. The limit drops rapidly for Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>) below 0.45, due to a rapid decrease of the signal rate in this final state.</p> </li> <li> <p>The mixed channel alone cannot exclude charged Higgs mass values up to the W mass, even when it contributes maximally, for Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>)=0.5. For this value, the observed limit is only slightly above 79 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>, due to the large e<sup>+</sup>e<sup>−</sup>→W<sup>+</sup>W<sup>−</sup> background. This channel has the best coverage in terms of Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>), as shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig3">3</a>.</p> </li> <li> <p>The hadronic channel is the most difficult one; for masses close to the W mass, the sensitivity is reduced due to the large e<sup>+</sup>e<sup>−</sup>→W<sup>+</sup>W<sup>−</sup> background. The sensitivity at higher masses is improved (a gain of 10 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> on the expected limit), and the observed limit as well (note the excluded “island” at Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>) close to zero) with respect to the results of individual experiments.</p> </li> <li> <p>The difference between the expected and observed limit seen in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig2">2</a> for Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>) from 0.35 to 0.85 results from the excess of observed events already mentioned (see Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig1">1</a>) in the mixed channel above <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}} = 84~{\rm GeV}/c^{2}$</span>. </p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-2" data-title="Fig. 2"><figure><figcaption><b id="Fig2" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 2</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/2" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig2_HTML.gif?as=webp"><img aria-describedby="Fig2" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig2_HTML.gif" alt="figure 2" loading="lazy"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-2-desc"><p>Type II 2HDM: excluded regions in the Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>) vs <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span> plane, based on the combined data collected by the four LEP experiments at center-of-mass energies from 183 to 209 GeV. The <i>shaded area</i> is excluded at the 95 % or higher C.L. The expected exclusion limit (at the 95 % C.L.) is indicated by the <i>thin solid line</i> and the <i>thick dotted line</i> inside the <i>shaded area</i> is the observed limit at the 99.7 % C.L.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/2" data-track-dest="link:Figure2 Full size image" aria-label="Full size image figure 2" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-3" data-title="Fig. 3"><figure><figcaption><b id="Fig3" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 3</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/3" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig3_HTML.gif?as=webp"><img aria-describedby="Fig3" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig3_HTML.gif" alt="figure 3" loading="lazy"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-3-desc"><p>Type II 2HDM: regions in the Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>) vs <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span> plane excluded at the 95 % or higher C.L., based on the combined data collected by the four LEP experiments at center-of-mass energies from 183 to 209 GeV, for each of the three decay channels separately. The <i>solid</i> (<i>dashed</i>) <i>lines</i> are the observed (expected) limits</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/3" data-track-dest="link:Figure3 Full size image" aria-label="Full size image figure 3" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> </li> </ul> <p>The combined 95 % C.L. <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span> lower limits are listed in Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Tab4">4</a> for Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>)=0, 1, together with the limit that is independent of the fermionic decay mode. Taking the lowest of the observed limits from Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Tab4">4</a>, we quote a 95 % C.L. lower bound of 80 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> for the mass of the charged Higgs boson in type II 2HDM under the assumption of pure fermionic decays of the charged Higgs boson. Thus the hypothesis of a charged Higgs boson degenerate in mass with the W boson is not excluded at the 95 % confidence level with LEP data. The limits around the W mass are very sensitive to the modeling of the W pairs background. Taking the uncertainties in the background modeling (including the uncertainty due to different simulated W masses) into account results in a downward shift of these limits by 600 and 500 <span class="mathjax-tex">${\rm MeV}/c^{2}$</span> for Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>)=0 and 0.5, respectively. </p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-4"><figure><figcaption class="c-article-table__figcaption"><b id="Tab4" data-test="table-caption">Table 4 The combined 95 % C.L. lower bounds on the mass of the charged Higgs boson (in <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>), expected and observed, for fixed values of the branching ratio Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>) and for any Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>). All mass limits have been rounded down to the nearest half a <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> to take into account the effect of neglecting the correlations between systematic uncertainties. (*) The interval from 83 to 88 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> is also excluded at the 95% C.L.</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-013-2463-1/tables/4" aria-label="Full size table 4"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <p>Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig4">4</a> shows the 95 % C.L. upper bound on the e<sup>+</sup>e<sup>−</sup>→H<sup>+</sup>H<sup>−</sup> cross-section (with ± 1<i>σ</i> and ± 2<i>σ</i> bands) for four values of Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>), namely 1, 0.5, 0.2 (which corresponds to the weakest limit) and 0. The thick black curve is the 2HDM tree-level prediction for that cross-section. </p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-4" data-title="Fig. 4"><figure><figcaption><b id="Fig4" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 4</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/4" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig4_HTML.gif?as=webp"><img aria-describedby="Fig4" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig4_HTML.gif" alt="figure 4" loading="lazy"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-4-desc"><p>Type II 2HDM: the 95 % C.L. upper limits on the production cross-section as a function of <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span> for four different values of the branching ratio Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>), combining the data collected by the four LEP experiments at center-of-mass energies from 183 to 209 GeV. The <i>solid lines</i> represent the observed exclusion limits, while the expected exclusion limits are indicated by the <i>dashed lines</i>. The <i>shaded bands</i> represent the ±1<i>σ</i> and ±2<i>σ</i> excursions around the expected limits. The intersections of the curves (<i>solid</i> or <i>dashed</i>) with the <i>thick line</i> showing the theoretical (tree-level) charged Higgs cross-section represent the (observed or expected) 95 % C.L. lower limits on the charged Higgs boson mass</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/4" data-track-dest="link:Figure4 Full size image" aria-label="Full size image figure 4" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> </div></div></section><section data-title="Combined searches in 2HDM of type I"><div class="c-article-section" id="Sec3-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec3"><span class="c-article-section__title-number">3 </span>Combined searches in 2HDM of type I</h2><div class="c-article-section__content" id="Sec3-content"><p>An alternative set of models, type I 2HDMs, assume that all fermions couple to the same Higgs doublet. In this case all fermions couple proportionally to 1/tan<i>β</i> to the charged Higgs boson and fermionic decays are suppressed for medium to large tan<i>β</i> values. Consequently, if a neutral Higgs boson Φ (representing either A or the lightest CP-even scalar h) is sufficiently light, the decay to W<sup>∗</sup>Φ can be dominant even in the range of charged Higgs masses of interest at LEP (where W<sup>∗</sup> indicates an off-shell W boson). While searches for a CP-even neutral Higgs boson exclude such a particle for masses below 82 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> independently of its decay [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 31" title="
G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 27, 311 (2003)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR31" id="ref-link-section-d1562255e3213">31</a>], the existence of a light CP-odd neutral Higgs boson, A, is not excluded by experiment [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 32" title="
J. Abdallah et al. (DELPHI Collaboration), Eur. Phys. J. C 38, 1 (2004)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR32" id="ref-link-section-d1562255e3216">32</a>]. Hence, the search for the process H<sup>±</sup>→W<sup>∗</sup>A is fully justified. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig5">5</a> shows the predicted branching ratios of the charged Higgs bosons for various choices of parameters of type I models. For all kinematically allowed values of the A mass, <i>m</i> <sub>A</sub>, the possible charged Higgs boson decays are predominantly fermionic for low tan<i>β</i> and predominantly bosonic for high tan<i>β</i>. Between these two extreme cases, the branching ratios change rapidly as a function of tan<i>β</i> (between typically 0.1 and 10) and slower as a function of <i>m</i> <sub>A</sub>, appearing earlier in tan<i>β</i> for lower <i>m</i> <sub>A</sub>. The ratio between the two competing fermionic decays (<i>τν</i> over <span class="mathjax-tex">$\mathrm{c} \bar{\mathrm {s}}$</span>) is almost independent of the charged Higgs boson mass (see lower part of the figure), as expected from the Yukawa coupling which only depends upon the masses involved. </p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-5" data-title="Fig. 5"><figure><figcaption><b id="Fig5" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 5</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/5" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig5_HTML.gif?as=webp"><img aria-describedby="Fig5" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig5_HTML.gif" alt="figure 5" loading="lazy"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-5-desc"><p>Type I 2HDM: decay branching fractions as functions of the boson masses and tan<i>β</i> </p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/5" data-track-dest="link:Figure5 Full size image" aria-label="Full size image figure 5" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <p>To cover the possibility of a light A boson the final states W<sup>∗</sup>AW<sup>∗</sup>A and <span class="mathjax-tex">$\mbox{$\mathrm{W^{*}A}\tau^{-}\bar{\nu_{\tau}}$}$</span> were also searched for by DELPHI [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 5" title="
J. Abdallah et al. (DELPHI Collaboration), Eur. Phys. J. C 34, 399 (2004)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR5" id="ref-link-section-d1562255e3309">5</a>] and OPAL [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 8" title="
G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 72, 2076 (2012)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR8" id="ref-link-section-d1562255e3312">8</a>]. The channel <span class="mathjax-tex">$\mbox{$\mathrm{W^{*}A}\bar{\mathrm {c}}\mathrm{s}$}$</span> was not considered because its contribution is expected to be small for all tan<i>β</i>. The A boson was searched for through its decay into two b-jets, restricting the A mass to be above 12 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>. Type I models are explored through the combination of all five decay channels, namely the final states <span class="mathjax-tex">$\mathrm{c} \bar{\mathrm{s}}$</span> <span class="mathjax-tex">$\bar{\mathrm {c}} \mathrm{s}$</span>, <span class="mathjax-tex">$\mathrm{c} \bar{\mathrm{s}}$</span> <i>τν</i>, <i>τ</i> <sup>+</sup> <i>ντ</i> <sup>−</sup> <span class="mathjax-tex">$\bar{\nu}$</span>, W<sup>∗</sup>AW<sup>∗</sup>A and <span class="mathjax-tex">$\mbox {$\mathrm{W^{*}A}\tau^{-}\bar{\nu_{\tau}}$}$</span> (and their charge conjugates). The combination of the experimental search results is performed for branching ratio values predicted by the model as a function of tan<i>β</i> and <i>m</i> <sub>A</sub>. Where there was a possible overlap between two search channels, the one providing less expected sensitivity was ignored to avoid double counting. This is the case in the intermediate region in tan<i>β</i> for purely hadronic channels (W<sup>∗</sup>AW<sup>∗</sup>A and <span class="mathjax-tex">$\mathrm{c} \bar{\mathrm{s}}$</span> <span class="mathjax-tex">$\bar{\mathrm{c}} \mathrm {s}$</span>) on the one hand and the semi-leptonic channels (<span class="mathjax-tex">$\mbox{$\mathrm{W^{*}A}\tau^{-}\bar{\nu_{\tau}}$}$</span> and <span class="mathjax-tex">$\mathrm{c} \bar{\mathrm{s}}$</span> <i>τ</i> <sup>−</sup> <span class="mathjax-tex">$\bar {\nu}$</span>) on the other. A three-dimensional scan was performed with the following ranges and steps: <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span> from 43 to 95 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> in 1 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> steps, <i>m</i> <sub>A</sub> covering 12 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>, then 15 to 75 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> in 5 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> steps, and tan<i>β</i> from 0.1 to 100 in steps of 0.2 in log(tan<i>β</i>).</p><p>Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig6">6</a> shows the observed CL<sub> <i>b</i> </sub>, for four values of <i>m</i> <sub>A</sub> and two values of tan<i>β</i>. A slight excess for low and intermediate A masses in the high tan<i>β</i> region where the bosonic decays dominate is observed, resulting in observed limits generally weaker than expected (see Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig7">7</a>). Three main features are visible in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig7">7</a>, two plateaux and a valley between them: </p><ul class="u-list-style-bullet"> <li> <p>The first plateau, at low tan<i>β</i>, corresponds to the case when the fermionic channels dominate. Both expected and observed limits are above 86 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>.</p> </li> <li> <p>The valley is somewhat of an artefact. It is due to the conservative approach of considering only the most sensitive channel when two overlapping channels contribute. The difference between expected and observed mass limits reaches 4.5 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> in the extreme case (when tan<i>β</i>=1.6 and <i>m</i> <sub>A</sub>=12 GeV/<i>c</i> <sup>2</sup>).</p> </li> <li> <p>The second plateau, at high tan<i>β</i>, corresponds to the case when the bosonic channels dominate. The small excess seen in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig6">6</a> corresponds to a small difference between expected and observed charged Higgs mass limits, which is always less than 2.2 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>. </p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-6" data-title="Fig. 6"><figure><figcaption><b id="Fig6" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 6</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/6" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig6_HTML.gif?as=webp"><img aria-describedby="Fig6" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig6_HTML.gif" alt="figure 6" loading="lazy"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-6-desc"><p>Type I 2HDM: contours based on the observed p-values CL<sub> <i>b</i> </sub> as a function of <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span> and tan<i>β</i> or <i>m</i> <sub>A</sub>, indicating the statistical significance, N<sub> <i>σ</i> </sub>, of local departures from the background expectation, for four values of <i>m</i> <sub>A</sub> and two values of tan<i>β</i>. The <i>black solid line</i> indicates the change of sign of this significance, i.e. where there is a transition from excess to deficit</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/6" data-track-dest="link:Figure6 Full size image" aria-label="Full size image figure 6" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-7" data-title="Fig. 7"><figure><figcaption><b id="Fig7" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 7</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/7" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig7_HTML.gif?as=webp"><img aria-describedby="Fig7" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig7_HTML.gif" alt="figure 7" loading="lazy"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-7-desc"><p>Type I 2HDM: Observed (<i>left</i>) and expected (<i>right</i>) 95 % C.L. lower limits on the mass of the charged Higgs boson. The color-mass correspondence is indicated on the right hand side (units are <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>)</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/7" data-track-dest="link:Figure7 Full size image" aria-label="Full size image figure 7" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> </li> </ul> <p>Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Fig8">8</a> shows the excluded regions at the 95 % C.L. in the plane (<span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span>, tan<i>β</i>) for four values of <i>m</i> <sub>A</sub>, namely 12, 30, 50 and 70 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>, together with the expected exclusion limits. </p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-8" data-title="Fig. 8"><figure><figcaption><b id="Fig8" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 8</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/8" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig8_HTML.gif?as=webp"><img aria-describedby="Fig8" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjc%2Fs10052-013-2463-1/MediaObjects/10052_2013_2463_Fig8_HTML.gif" alt="figure 8" loading="lazy"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-8-desc"><p>Type I 2HDM: Excluded regions at 95 % C.L. in the (<span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span>, tan<i>β</i>) plane for different values of <i>m</i> <sub>A</sub>: 12, 30, 50 and 70 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>. The <i>dashed line</i> represents the expected exclusion limit</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1140/epjc/s10052-013-2463-1/figures/8" data-track-dest="link:Figure8 Full size image" aria-label="Full size image figure 8" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> <p>Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/article/10.1140/epjc/s10052-013-2463-1#Tab5">5</a> summarizes these results. For low tan<i>β</i> (tan<i>β</i> below 0.5) where the bosonic contribution is vanishingly small, the <span class="mathjax-tex">$m_{\mathrm{H}^{\pm}}$</span> lower limits (above 86 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>) are almost independent of <i>m</i> <sub>A</sub>. On the other hand, for high tan<i>β</i> (equal to or greater than 10) where the bosonic channels dominate, the sensitivity is maximal for intermediate A masses (<i>m</i> <sub>A</sub> around 50 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>). Outside the valley, the limit is always above 84 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>. Finally, the lowest limits always correspond to the cases in the valley, thus depending both on tan<i>β</i> and <i>m</i> <sub>A</sub>. The lowest (observed) limit is 72.5 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>, for tan<i>β</i>=1.6 and <span class="mathjax-tex">$m_{\mathrm{A}} =12~{\rm GeV}/c^{2}$</span>. This limit rises to 76.5 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> for <span class="mathjax-tex">$m_{\mathrm{A}} =20~{\rm GeV}/c^{2}$</span> and the difference between expectation and observation is reduced to 1 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>. </p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-5"><figure><figcaption class="c-article-table__figcaption"><b id="Tab5" data-test="table-caption">Table 5 Observed lower limits on the charged Higgs mass in <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> at 95 % C.L. for different values of <i>m</i> <sub>A</sub> (in <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>) and tan<i>β</i>. The expected median limits are shown in parentheses. The last column (last row) show the weakest limit for a fixed A mass and any tan<i>β</i> (for a fixed tan<i>β</i> and any A mass). The mass limits have been rounded down to the nearest half a <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> to take into account the effect of neglecting correlations between systematic uncertainties</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/article/10.1140/epjc/s10052-013-2463-1/tables/5" aria-label="Full size table 5"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div> </div></div></section><section data-title="Summary"><div class="c-article-section" id="Sec4-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec4"><span class="c-article-section__title-number">4 </span>Summary</h2><div class="c-article-section__content" id="Sec4-content"><p>The results of the searches carried out by the four LEP experiments for charged Higgs bosons have been statistically combined and interpreted in 2HDMs. No significant excess over the SM background is observed, and the exclusion limits are extended by several <span class="mathjax-tex">${\rm GeV}/c^{2}$</span> with respect to the final results of the individual collaborations [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 4" title="
A. Heister et al. (ALEPH Collaboration), Phys. Lett. B 543, 1 (2002)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR4" id="ref-link-section-d1562255e4369">4</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 5" title="
J. Abdallah et al. (DELPHI Collaboration), Eur. Phys. J. C 34, 399 (2004)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR5" id="ref-link-section-d1562255e4372">5</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 7" title="
P. Achard et al. (L3 Collaboration), Phys. Lett. B 575, 208 (2003)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR7" id="ref-link-section-d1562255e4375">7</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 8" title="
G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 72, 2076 (2012)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR8" id="ref-link-section-d1562255e4378">8</a>] and the previous combination [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 3" title="
Search for Charged Higgs bosons: preliminary combined results using LEP data collected at energies up to 209 GeV. LHWG Note/2001-05, July 2001, and 
 arXiv:hep-ex/0107031
 
 
 " href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR3" id="ref-link-section-d1562255e4382">3</a>]. In the type II 2HDM scenario, assuming that the two decays <span class="mathjax-tex">$\mathrm{H}^{+} \rightarrow\mathrm{c} \bar{\mathrm{s}}$</span> and H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i> exhaust the H<sup>+</sup> decay width, mass limits are obtained as a function of the branching ratio Br(H<sup>+</sup>→<i>τ</i> <sup>+</sup> <i>ν</i>). A 95 % C.L. lower limit on the charged Higgs mass, independent of its fermionic decay modes, is found to be 80 <span class="mathjax-tex">${\rm GeV}/c^{2}$</span>. Thanks to analyses by DELPHI and OPAL in the bosonic W<sup>∗</sup>A decay channels, a new scenario, for type I 2HDM, is also studied. 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The LEP working group for Higgs boson searches would also like to thank the members of the four LEP experiments for providing their results and for valuable discussions concerning their combination.</p> <h3 class="c-article__sub-heading">Open Access</h3> <p>This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.</p> </div></div></section><section aria-labelledby="author-information" data-title="Author information"><div class="c-article-section" id="author-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="author-information">Author information</h2><div class="c-article-section__content" id="author-information-content"><h3 class="c-article__sub-heading" id="affiliations">Authors and Affiliations</h3><ol class="c-article-author-affiliation__list"></ol><h3 class="c-article__sub-heading" id="groups">Consortia</h3><div class="c-article-author-institutional-author" id="group-1"><h3 class="c-article-author-institutional-author__name u-h3">ALEPH Collaboration</h3></div><div class="c-article-author-institutional-author" id="group-2"><h3 class="c-article-author-institutional-author__name u-h3">DELPHI Collaboration</h3></div><div class="c-article-author-institutional-author" id="group-3"><h3 class="c-article-author-institutional-author__name u-h3">L3 Collaboration</h3></div><div class="c-article-author-institutional-author" id="group-4"><h3 class="c-article-author-institutional-author__name u-h3">OPAL Collaboration</h3></div><div class="c-article-author-institutional-author" id="group-5"><h3 class="c-article-author-institutional-author__name u-h3">The LEP working group for Higgs boson searches</h3></div></div></div></section><section data-title="Additional information"><div class="c-article-section" id="additional-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="additional-information">Additional information</h2><div class="c-article-section__content" id="additional-information-content"><p>The authors are listed in Refs. [<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 4" title="
A. Heister et al. (ALEPH Collaboration), Phys. Lett. B 543, 1 (2002)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR4" id="ref-link-section-d1562255e345">4</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 5" title="
J. Abdallah et al. (DELPHI Collaboration), Eur. Phys. J. C 34, 399 (2004)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR5" id="ref-link-section-d1562255e348">5</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 7" title="
P. Achard et al. (L3 Collaboration), Phys. Lett. B 575, 208 (2003)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR7" id="ref-link-section-d1562255e351">7</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 8" title="
G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 72, 2076 (2012)
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR8" id="ref-link-section-d1562255e354">8</a>, <a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 10" title="
The LEP Working Group for Higgs Boson Searches consists of members of the four LEP collaborations and of theorists among whom S. Heinemeyer is co-author of this paper
" href="/article/10.1140/epjc/s10052-013-2463-1#ref-CR10" id="ref-link-section-d1562255e357">10</a>]. Corresponding author: Pierre Lutz belongs to the DELPHI Collaboration and the LEP working group for Higgs boson searches; e-mail: lutz@in2p3.fr. Postal address: DSM/IRFU/SPP, CEA Saclay, 91191 Gif sur Yvette Cedex, France</p></div></div></section><section data-title="Rights and permissions"><div class="c-article-section" id="rightslink-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="rightslink">Rights and permissions</h2><div class="c-article-section__content" id="rightslink-content"> <p><b>Open Access</b> This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (<a href="https://creativecommons.org/licenses/by/2.0" rel="license">https://creativecommons.org/licenses/by/2.0</a>), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</p> <p class="c-article-rights"><a data-track="click" data-track-action="view rights and permissions" data-track-label="link" href="https://s100.copyright.com/AppDispatchServlet?title=Search%20for%20charged%20Higgs%20bosons%3A%20combined%20results%20using%20LEP%20data&author=&contentID=10.1140%2Fepjc%2Fs10052-013-2463-1&copyright=The%20Author%28s%29&publication=1434-6044&publicationDate=2013-07-03&publisherName=SpringerNature&orderBeanReset=true&oa=CC%20BY">Reprints and permissions</a></p></div></div></section><section aria-labelledby="article-info" data-title="About this article"><div class="c-article-section" id="article-info-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="article-info">About this article</h2><div class="c-article-section__content" id="article-info-content"><div class="c-bibliographic-information"><div class="c-bibliographic-information__column"><h3 class="c-article__sub-heading" id="citeas">Cite this article</h3><p class="c-bibliographic-information__citation">ALEPH Collaboration., DELPHI Collaboration., L3 Collaboration. <i>et al.</i> Search for charged Higgs bosons: combined results using LEP data. <i>Eur. 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