Search for charged Higgs bosons: combined results using LEP data
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Abstract
The four LEP collaborations, ALEPH, DELPHI, L3 and OPAL, have searched for pairproduced 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 \({\rm GeV}/c^{2}\) (Type II scenario) or 72.5 \({\rm GeV}/c^{2}\) (Type I scenario, for pseudoscalar masses above 12 \({\rm GeV}/c^{2}\)) are excluded at the 95 % confidence level.
Keywords
Higgs Boson Minimal Supersymmetric Standard Model Charged Higgs Boson Neutral Higgs Boson Minimal Supersymmetric Standard Model Parameter1 Introduction
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 Higgslike particle recently discovered at LHC [1, 2] is not the SM neutral Higgs boson. It is thus of great interest to search for a charged Higgs boson.
More than twelve years after the end of datataking 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 modeldependent than the corresponding searches at hadron colliders, due to the very simple production mechanism.
Since the previous communication by the LEP working group for Higgs boson searches (LEPHWG) on charged Higgs boson, in 2001 [3], 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 [4], DELPHI [5, 6], L3 [7] and OPAL [8, 9], the LEPHWG has performed a statistical combination of the data taken at centerofmass energies, \(\sqrt{s}\), from 183 GeV to 209 GeV. The total luminosity used in this combination is 2.6 fb^{−1}.
In 2HDMs [11, 12, 13, 14], there are five physical Higgs bosons: the CPeven h and H, the CPodd A and the charged Higgs bosons, H^{±}. 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, θ _{W}, and therefore, at tree level, the production crosssection 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 m _{A} (the neutral CPodd A boson mass) or tanβ (the ratio of the two Higgs doublet vacuum expectation values). In this model the isospin \(+\frac{1}{2}\) fermioncouplings to the charged Higgs boson are proportional to 1/tanβ, while the isospin \(\frac{1}{2}\) fermioncouplings are proportional to tanβ. This scenario is treated in Sect. 2. In the second scenario, type I 2HDM, all fermions couple proportionally to 1/tanβ. Consequently, the second scenario effectively allows the charged Higgs boson to also decay into gauge (possibly offshell) bosons and Higgs bosons (see Sect. 3).
Pairproduction of charged Higgs bosons via schannel exchange of a \(\mathrm{Z^{0}}\) boson would modify the decay width of the \(\mathrm{Z^{0}}\) 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 \(\mbox{$\mathrm{Z^{0}}$}\) (Γ _{Z}) and the prediction from the SM sets a limit on any nonstandard (non SM) contribution to \(\mbox {$\mathrm{Z^{0}}$}\) decay. The \(\mbox{$\mathrm{Z^{0}}$}\) decay width has been measured precisely during the first phase of LEP (LEP1). The final LEP result [15] set the limit \(\varGamma_{\rm non SM}<2.9\) MeV/c ^{2} (95 % C.L.), which translates to \(\mbox{$m_{\mathrm{H}^{\pm}}$}>\) 39.6 GeV/c ^{2} (95 % C.L.). Direct searches during the LEP1 period set a lower bound for the charged Higgs boson mass at 44.1 GeV/c ^{2} at 95 % C.L. for type II 2HDM [16, 17, 18, 19]. The combination in this paper is performed for charged Higgs boson masses of 43 GeV/c ^{2} or larger, since the region below 43 \({\rm GeV}/c^{2}\) has been covered by individual experiments.
For this combination of data, the crosssections (and branching ratios for type II 2HDM) are calculated within the HZHA program package [20], and the branching ratios of the charged Higgs boson in type I 2HDM are taken from Ref. [21].
Overview of the searches for charged Higgs bosons performed by the four LEP experiments, whose results are used in this combination. Where relevant, m _{A} varies from 2m _{ b } to \(m_{\mathrm{H}^{\pm}}\). Each experiment analyzed typically around 650 pb^{−1}of data
Expt (ref.)  Final state  \(\sqrt {s}\) (GeV)  \(m_{\mathrm{H}^{\pm}}\) range (GeV/c ^{2}) 

ALEPH [4]  \({\mathrm{H}}^{+}{\mathrm{H}}^{} \rightarrow\mbox{$\mathrm{c} \bar{\mathrm{s}}$}\mbox{$\bar {\mathrm{c}} \mathrm{s}$}\)  189–209  45–100 
\({\mathrm{H}}^{+}{\mathrm{H}}^{} \rightarrow\mbox{$\mathrm{c} \bar {\mathrm{s}}$}\tau\nu \)  189–209  55–100  
H^{+}H^{−}→τντν  189–209  45–100  
\({\mathrm{H}}^{+}{\mathrm{H}}^{} \rightarrow\mbox{$\mathrm{c} \bar{\mathrm {s}}$}\mbox{$\bar{\mathrm{c}} \mathrm{s}$}\)  183–209  40–100  
\({\mathrm{H}}^{+}{\mathrm{H}}^{} \rightarrow \mbox{$\mathrm{c} \bar{\mathrm{s}}$}\tau\nu\)  183–209  40–100  
H^{+}H^{−}→τντν  183–209  40–100  
H^{+}H^{−}→W^{∗}Aτν  189–209  40–100  
H^{+}H^{−}→W^{∗}AW^{∗}A  189–209  40–100  
L3 [7]  \({\mathrm{H}}^{+}{\mathrm{H}}^{} \rightarrow\mbox{$\mathrm{c} \bar{\mathrm{s}}$}\mbox{$\bar {\mathrm{c}} \mathrm{s}$}\)  183–209  50–100 
\({\mathrm{H}}^{+}{\mathrm{H}}^{} \rightarrow\mbox{$\mathrm{c} \bar {\mathrm{s}}$}\tau\nu\)  183–209  50–100  
H^{+}H^{−}→τντν  183–209  50–100  
\({\mathrm{H}}^{+}{\mathrm{H}}^{} \rightarrow\mbox{$\mathrm{c} \bar{\mathrm{s}}$}\mbox{$\bar {\mathrm{c}} \mathrm{s}$}\)  183–209  40–100  
\({\mathrm{H}}^{+}{\mathrm{H}}^{} \rightarrow \mbox{$\mathrm{c} \bar{\mathrm{s}}$}\tau\nu\)  183–209  40–100  
H^{+}H^{−}→τντν  183–209  45–100  
H^{+}H^{−}→W^{∗}Aτν  189–209  40–95  
H^{+}H^{−}→W^{∗}AW^{∗}A  189–209  40–95 
Each experiment generated and simulated the detailed detector response in Monte Carlo event samples for the Higgs signal and the various background processes, at centerofmass 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 fourfermion background, especially from Wpair background, using the most advanced codes available at that time. ALEPH used KORALW [22] as the generator and RACOONWW [23] and YFSWW [24] for the crosssection calculation, while DELPHI used WPHACT [25], L3 YFSWW and OPAL GRC4F [26] 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 \({\rm GeV}/c^{2}\) for ALEPH, DELPHI, L3 and OPAL), while the LEP combined measured value is 80.376±0.033 \({\rm GeV}/c^{2}\) [27], thus introducing an additional source of systematic uncertainty due to the broadening of the W peak when adding the four background simulations.
The statistical procedure adopted for the combination of the data and the precise definitions of the confidence levels CL_{ b }, CL_{ s }, CL_{ s+b } by which the search results are expressed, have been described previously [28]. The main sources of systematic uncertainty affecting the signal and background predictions are included, using an extension of the method of Cousins and Highland [29] where the pvalues 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 \({\rm MeV}/c^{2}\), to the final results.
2 Combined searches in the framework of type II 2HDM
In type II 2HDM, one Higgs doublet couples to uptype fermions and the other to downtype fermions. The Higgs sector of the Minimal Supersymmetric Standard Model (MSSM) is a particular case of such models. In the MSSM, at treelevel, the H^{±} 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 [30].
For the charged Higgs masses accessible at LEP energies, the decays into τ ^{+} ν _{ τ } and \(\mathrm{c} \bar{\mathrm{s}}\) (and their charge conjugates) are expected to dominate. The searches are carried out under the assumption that the two decays \(\mathrm{H}^{+}\rightarrow \mathrm{c} \bar{\mathrm{s}}\) and H^{+}→τ ^{+} ν exhaust the H^{+} decay width, but the relative branching ratio is free. This assumption is valid as long as m _{A} is larger than 60 \({\rm GeV}/c^{2}\) (MSSM case) or tanβ is larger than a few units. Thus, the searches encompass the following H^{+}H^{−} final states: (\(\mathrm{c} \bar{\mathrm{s}}\) )(\(\bar{\mathrm{c}} \mathrm{s}\)), (τ ^{+} ν)(τ ^{−} \(\bar{\nu}\)) and the mixed mode (\(\mathrm{c} \bar{\mathrm{s}}\))(τ ^{−} \(\bar{\nu}\)) or (\(\bar{\mathrm{c}} \mathrm{s}\))(τ ^{+} ν). The combined search results are presented as a function of the branching ratio Br(H^{+}→τ ^{+} ν).
Individual search results for the e^{+}e^{−}→H^{+}H^{−} fermionic final states. All limits are given at the 95 % C.L. The OPAL selection is massdependent; the numbers of events given here are for \(m_{\mathrm{H}^{\pm }}= 80~{\rm GeV}/c^{2}\)
Experiment  ALEPH [4]  DELPHI [5]  L3 [7]  OPAL [8] 

Total Int. luminosity (pb^{−1})  630  620  685  670 
Final states  Number of expected/observed events  
(\(\mathrm{c} \bar{\mathrm{s}}\))(\(\bar{\mathrm{c}} \mathrm{s}\))  2806.0/2742  2179.3/2179  2473.8/2578  1501.4/1471 
(\(\mathrm{c} \bar{\mathrm{s}}\))(τ ^{−} \(\bar{\nu}\))  289.3/280  1122.8/1129  494.5/470  526.3/569 
(τ ^{+} ν)(τ ^{−} \(\bar{\nu}\))  39.8/45  73.6/66  149.8/147  1103.4/1110 
Sum of all channels  3135.1/3067  3375.7/3374  3118.1/3195  3131.1/3150 
Mass limits in \({\rm GeV}/c^{2}\) Expected(median)/observed limit  
Br(H^{+}→τ ^{+} ν)=0  78.2/80.4  77.7/77.8  76.8/76.6  77.2/76.5 
Br(H^{+}→τ ^{+} ν)=1  89.2/87.8  88.9/90.1  84.3/83.7  89.2/91.3 
any Br(H^{+}→τ ^{+} ν)  77.1/79.3  76.3/74.4  75.7/76.4  75.6/76.3 
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 \({\rm MeV}/c^{2}\) 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^{+}→τ ^{+} ν)=1 and amounts to 600 \({\rm MeV}/c^{2}\). This difference is compatible in size with the estimated effect of about 500 \({\rm MeV}/c^{2}\) of not taking into account the correlations between systematic uncertainties. All mass limits have thus been rounded down to the nearest half a \({\rm GeV}/c^{2}\).
Combining the results from the four experiments, a scan in the branching ratio Br(H^{+}→τ ^{+} ν) versus charged Higgs boson mass plane has been performed, and the limitsetting procedure was repeated for each scan point. This twodimensional scan was performed with the following ranges and steps: \(m_{\mathrm{H}^{\pm}}\) from 43 to 95 \({\rm GeV}/c^{2}\) with 1 \({\rm GeV}/c^{2}\) steps, and Br(H^{+}→τ ^{+} ν) from 0 to 1 with 0.05 steps.
Combined and individual CL_{ b } values for the three mass points with a deviation from expectation larger than 2σ. 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
\(\mbox{$m_{\mathrm{H}^{\pm}}$}\) (\({\rm GeV}/c^{2}\))  Br(H^{+}→τ ^{+} ν)  combined CL_{ b }  ALEPH CL_{ b }  DELPHI CL_{ b }  L3 CL_{ b }  OPAL CL_{ b } 

43  0.0  0.998  (*)  0.99  (*)  0.96 
55  0.0  0.997  0.75  0.96  0.96  0.94 
89  0.35  0.988  0.98  0.63  0.88  0.80 

The purely leptonic channel alone excludes charged Higgs masses above the W mass, down to Br(H^{+}→τ ^{+} ν) 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 \(\sqrt{s}/2\). The limit drops rapidly for Br(H^{+}→τ ^{+} ν) below 0.45, due to a rapid decrease of the signal rate in this final state.

The mixed channel alone cannot exclude charged Higgs mass values up to the W mass, even when it contributes maximally, for Br(H^{+}→τ ^{+} ν)=0.5. For this value, the observed limit is only slightly above 79 \({\rm GeV}/c^{2}\), due to the large e^{+}e^{−}→W^{+}W^{−} background. This channel has the best coverage in terms of Br(H^{+}→τ ^{+} ν), as shown in Fig. 3.

The hadronic channel is the most difficult one; for masses close to the W mass, the sensitivity is reduced due to the large e^{+}e^{−}→W^{+}W^{−} background. The sensitivity at higher masses is improved (a gain of 10 \({\rm GeV}/c^{2}\) on the expected limit), and the observed limit as well (note the excluded “island” at Br(H^{+}→τ ^{+} ν) close to zero) with respect to the results of individual experiments.
The combined 95 % C.L. lower bounds on the mass of the charged Higgs boson (in \({\rm GeV}/c^{2}\)), expected and observed, for fixed values of the branching ratio Br(H^{+}→τ ^{+} ν) and for any Br(H^{+}→τ ^{+} ν). All mass limits have been rounded down to the nearest half a \({\rm GeV}/c^{2}\) to take into account the effect of neglecting the correlations between systematic uncertainties. (*) The interval from 83 to 88 \({\rm GeV}/c^{2}\) is also excluded at the 95% C.L.
Expected limit (median)  Observed limit  

Br(H^{+}→τ ^{+} ν)=0  88  80.5 (*) 
Br(H^{+}→τ ^{+} ν)=1  93.5  94 
Any Br(H^{+}→τ ^{+} ν)  79.5  80 
3 Combined searches in 2HDM of type I
To cover the possibility of a light A boson the final states W^{∗}AW^{∗}A and \(\mbox{$\mathrm{W^{*}A}\tau^{}\bar{\nu_{\tau}}$}\) were also searched for by DELPHI [5] and OPAL [8]. The channel \(\mbox{$\mathrm{W^{*}A}\bar{\mathrm {c}}\mathrm{s}$}\) was not considered because its contribution is expected to be small for all tanβ. The A boson was searched for through its decay into two bjets, restricting the A mass to be above 12 \({\rm GeV}/c^{2}\). Type I models are explored through the combination of all five decay channels, namely the final states \(\mathrm{c} \bar{\mathrm{s}}\) \(\bar{\mathrm {c}} \mathrm{s}\), \(\mathrm{c} \bar{\mathrm{s}}\) τν, τ ^{+} ντ ^{−} \(\bar{\nu}\), W^{∗}AW^{∗}A and \(\mbox {$\mathrm{W^{*}A}\tau^{}\bar{\nu_{\tau}}$}\) (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 tanβ and m _{A}. 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 tanβ for purely hadronic channels (W^{∗}AW^{∗}A and \(\mathrm{c} \bar{\mathrm{s}}\) \(\bar{\mathrm{c}} \mathrm {s}\)) on the one hand and the semileptonic channels (\(\mbox{$\mathrm{W^{*}A}\tau^{}\bar{\nu_{\tau}}$}\) and \(\mathrm{c} \bar{\mathrm{s}}\) τ ^{−} \(\bar {\nu}\)) on the other. A threedimensional scan was performed with the following ranges and steps: \(m_{\mathrm{H}^{\pm}}\) from 43 to 95 \({\rm GeV}/c^{2}\) in 1 \({\rm GeV}/c^{2}\) steps, m _{A} covering 12 \({\rm GeV}/c^{2}\), then 15 to 75 \({\rm GeV}/c^{2}\) in 5 \({\rm GeV}/c^{2}\) steps, and tanβ from 0.1 to 100 in steps of 0.2 in log(tanβ).

The first plateau, at low tanβ, corresponds to the case when the fermionic channels dominate. Both expected and observed limits are above 86 \({\rm GeV}/c^{2}\).

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 \({\rm GeV}/c^{2}\) in the extreme case (when tanβ=1.6 and m _{A}=12 GeV/c ^{2}).
 The second plateau, at high tanβ, corresponds to the case when the bosonic channels dominate. The small excess seen in Fig. 6 corresponds to a small difference between expected and observed charged Higgs mass limits, which is always less than 2.2 \({\rm GeV}/c^{2}\).
Observed lower limits on the charged Higgs mass in \({\rm GeV}/c^{2}\) at 95 % C.L. for different values of m _{A} (in \({\rm GeV}/c^{2}\)) and tanβ. The expected median limits are shown in parentheses. The last column (last row) show the weakest limit for a fixed A mass and any tanβ (for a fixed tanβ and any A mass). The mass limits have been rounded down to the nearest half a \({\rm GeV}/c^{2}\) to take into account the effect of neglecting correlations between systematic uncertainties
m _{A}  tanβ=0.1  tanβ=1  tanβ=10  tanβ=100  Minimum 

12  86.0 (86.0)  73.5 (77.0)  83.5 (86.0)  84.0 (86.0)  72.5 (77.0) 
20  86.5 (86.0)  76.5 (77.5)  85.5 (87.0)  85.5 (87.0)  76.5 (77.5) 
30  86.5 (86.5)  80.0 (79.5)  87.5 (89.0)  87.5 (89.0)  78.0 (79.5) 
50  86.5 (86.5)  84.0 (84.0)  89.0 (90.0)  89.5 (91.0)  81.0 (80.5) 
70  86.5 (86.5)  86.5 (86.5)  83.5 (83.5)  89.0 (90.5)  81.0 (81.0) 
Minimum  86.0 (86.0)  73.5 (77.0)  81.5 (81.0)  81.0 (81.0)  72.5 (77.0) 
4 Summary
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 \({\rm GeV}/c^{2}\) with respect to the final results of the individual collaborations [4, 5, 7, 8] and the previous combination [3]. In the type II 2HDM scenario, assuming that the two decays \(\mathrm{H}^{+} \rightarrow\mathrm{c} \bar{\mathrm{s}}\) and H^{+}→τ ^{+} ν exhaust the H^{+} decay width, mass limits are obtained as a function of the branching ratio Br(H^{+}→τ ^{+} ν). A 95 % C.L. lower limit on the charged Higgs mass, independent of its fermionic decay modes, is found to be 80 \({\rm GeV}/c^{2}\). Thanks to analyses by DELPHI and OPAL in the bosonic W^{∗}A decay channels, a new scenario, for type I 2HDM, is also studied. In this case, masses of the charged Higgs boson below 72.5 \({\rm GeV}/c^{2}\) are excluded at the 95 % C.L. for A masses above 12 \({\rm GeV}/c^{2}\).
Notes
Acknowledgements
We would like to thank the CERN accelerator division for the excellent performance of the LEP accelerator in its highenergy phase. 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.
Open Access
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