Abstract
A search is made for charged Higgs bosons predicted by TwoHiggsDoublet extensions of the Standard Model (2HDM) using electronpositron collision data collected by the OPAL experiment at \(\sqrt{s}=189\mbox{}209\ \mbox{GeV}\), corresponding to an integrated luminosity of approximately 600 pb^{−1}. Charged Higgs bosons are assumed to be pairproduced and to decay into \(\mathrm{q} \bar{\mathrm{q}}\), τν _{τ} or AW^{±}. No signal is observed. Modelindependent limits on the charged Higgsboson production cross section are derived by combining these results with previous searches at lower energies. Under the assumption \(\mathrm{BR} (\mathrm{H}^{\pm} \to \tau\nu_{\tau}) + \mathrm{BR} (\mathrm{H}^{\pm} \to \mathrm{q} \bar{\mathrm{q}}) = 1\), motivated by general 2HDM type II models, excluded areas on the \([m_{\mathrm{H}^{\pm}} , \mathrm{BR} (\mathrm {H}^{\pm} \to \tau\nu_{\tau})]\) plane are presented and charged Higgs bosons are excluded up to a mass of 76.3 GeV at 95 % confidence level, independent of the branching ratio BR(H^{±}→τν _{τ}). A scan of the 2HDM type I model parameter space is performed and limits on the Higgsboson masses \(m_{\mathrm{H}^{\pm}}\) and m _{A} are presented for different choices of tanβ.
Similar content being viewed by others
Avoid common mistakes on your manuscript.
1 Introduction
In the Standard Model (SM) [1–3], the electroweak symmetry is broken via the Higgs mechanism [4–6] generating the masses of elementary particles. This requires the introduction of a complex scalar Higgsfield doublet and implies the existence of a single neutral scalar particle, the Higgs boson. While the SM accurately describes the interactions between elementary particles, it leaves several fundamental questions unanswered. Therefore, it is of great interest to study extended models.
The minimal extension of the SM Higgs sector required, for example, by supersymmetric models contains two Higgsfield doublets [7] resulting in five Higgs bosons: two charged (H^{±}) and three neutral. If CPconservation is assumed, the three neutral Higgs bosons are CPeigenstates: h and H are CPeven and A is CPodd. TwoHiggsDoublet Models (2HDMs) are classified according to the Higgsfermion coupling structure. In type I models (2HDM(I)) [8, 9], all quarks and leptons couple to the same Higgs doublet, while in type II models (2HDM(II)) [10], downtype fermions couple to the first Higgs doublet, and uptype fermions to the second.
Charged Higgs bosons are expected to be pairproduced in the process e^{+}e^{−}→ H^{+}H^{−} at LEP, the reaction e^{+}e^{−}→H^{±}W^{∓} having a much lower cross section [11]. In 2HDMs, the treelevel cross section [12] for pair production is completely determined by the charged Higgsboson mass and known SM parameters.
The H^{±} branching ratios are modeldependent. In most of the 2HDM(II) parameter space, charged Higgs bosons decay into the heaviest kinematically allowed fermions, namely τν _{τ} and quark pairs.^{Footnote 1} The situation changes in 2HDM(I), where the decay H^{±}→AW^{±} can become dominant if the ratio of the vacuum expectation values of the two Higgsfield doublets is such that tanβ⪆1 and the A boson is sufficiently light [13, 14].
In this paper we search for charged Higgs bosons decaying into \(\mathrm {q}\bar {\mathrm {q}}\), τν _{τ} and AW^{±} using the data collected by the OPAL Collaboration in 1998–2000. The results are interpreted within general 2HDM(II) assuming \(\mbox {$\mathrm {BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $}\mbox {${\tau \nu _{\tau }}$})$}+ \mbox {$\mathrm {BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $}\mbox {$\mathrm {q}\bar {\mathrm {q}}$})$}= 1\) for the branching ratios and in 2HDM(I) taking into account decays of charged Higgs bosons via AW^{±}, as well. Our result is not confined to \(\mathrm{q} \bar{\mathrm{q}}=\{\mathrm{c}\bar{\mathrm{s}}, \bar {\mathrm{c}}\mathrm{s}\}\) although that is the dominant hadronic decay channel in most of the parameter space.
The previously published OPAL lower limit on the charged Higgsboson mass, under the assumption of \(\mbox {$\mathrm {BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $}\mbox {${\tau \nu _{\tau }}$})$}+ \mbox {$\mathrm {BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $}\mbox {$\mathrm {q}\bar {\mathrm {q}}$})$}= 1\), is \(m_{\mathrm{H}^{\pm}}>59.5\ \mbox{GeV}\) at 95 % confidence level (CL) using data collected at \(\sqrt{s}\leq183\ \mbox{GeV}\) [15, 16]. Lower bounds of 74.4–79.3 GeV have been reported by the other LEP collaborations [17–19] based on the full LEP2 data set. The DELPHI Collaboration also performed a search for H^{±}→AW^{±} decay and constrained the charged Higgsboson mass in 2HDM(I) [18] to be \(m_{\mathrm{H}^{\pm}}\geq76.7\ \mbox{GeV}\) at 95 %CL.
2 Experimental considerations
The OPAL detector is described in [20–23]. The events are reconstructed from chargedparticle tracks and energy deposits (clusters) in the electromagnetic and hadron calorimeters. The tracks and clusters must pass a set of quality requirements similar to those used in previous OPAL Higgsboson searches [24]. In calculating the total visible energies and momenta of events and individual jets, corrections are applied to prevent doublecounting of energy in the case of tracks and associated clusters [24].
The data analyzed in this paper were collected in 1998–2000 at centerofmass energies of 189–209 GeV as given in Table 1. Due to different requirements on the operational state of the OPAL subdetectors, the integrated luminosity of about 600 pb^{−1} differs slightly among search channels.
In this paper the following final states are sought:

\(\mathrm{H}^{+}\mathrm{H}^{}\to\tau^{+}\nu_{\tau}\tau^{}\bar{\nu}_{\tau}\) (twotau final state, 2τ),

\(\mathrm{H}^{+}\mathrm{H}^{}\to\mathrm{q}\bar{\mathrm{q}}\tau\nu_{\tau}\) (twojet plus tau final state, 2j+τ),

\(\mathrm{H}^{+}\mathrm{H}^{}\to\mathrm{q}\bar{\mathrm{q}}\mathrm{q}\bar{\mathrm{q}}\) (fourjet final state, 4j),

\(\mathrm{H}^{+}\mathrm{H}^{}\to \mathrm{AW}^{+*} \mathrm{AW}^{*}\to \mathrm{b} \bar{\mathrm{b}}\mathrm{q}\bar{\mathrm{q}}\mathrm{b} \bar{\mathrm{b}} \mathrm{q}\bar{\mathrm{q}}\) (eightjet final state, 8j),

\(\mathrm{H}^{+}\mathrm{H}^{}\to \mathrm{AW}^{+*} \mathrm{AW}^{*}\to \mathrm{b} \bar{\mathrm{b}}\mathrm{q}\bar{\mathrm{q}} \mathrm{b} \bar{\mathrm{b}}\ell\nu_{\ell}\) (sixjet plus lepton final state, 6j+ℓ),

\(\mathrm{H}^{+}\mathrm{H}^{}\to \mathrm{AW}^{\pm*}\tau\nu_{\tau}\to\mathrm{b} \bar{\mathrm{b}}\mathrm{q}\bar{\mathrm{q}} \tau\nu_{\tau}\) (fourjet plus tau final state, 4j+τ).
The signal detection efficiencies and accepted background cross sections are estimated using a variety of Monte Carlo samples. The HZHA generator [25] is used to simulate H^{+}H^{−} production at fixed values of the charged Higgsboson mass in steps of 1–5 GeV from the kinematic limit down to 50 GeV for fermionic decays and 40 GeV for bosonic decays.
The background processes are simulated primarily by the following event generators: PYTHIA [26, 27] and KK2F [28, 29] (\(Z/\gamma^{*}\to \mathrm{q}\bar{\mathrm{q}} (\gamma)\)), grc4f [30, 31] (fourfermion processes, 4f), BHWIDE [32] and TEEGG [33] (e^{+}e^{−}(γ)), KORALZ [34] and KK2F (μ ^{+} μ ^{−}(γ) and τ ^{+} τ ^{−}(γ)), PHOJET [35, 36], HERWIG [37], Vermaseren [38] (hadronic and leptonic twophoton processes).
The generated partons, both for the signal and the SM Monte Carlo simulations, are hadronized using JETSET [26, 27], with parameters described in [39]. For systematic studies, cluster fragmentation implemented in HERWIG for the process \(Z/\gamma^{*}\to \mathrm{q}\bar{\mathrm{q}} (\gamma)\) is used. The predictions of 4f processes are crosschecked using EXCALIBUR [40], KoralW [41] and KandY [42].
The obtained Monte Carlo samples are processed through a full simulation of the OPAL detector [43]. The event selection is described below.
3 Search for fourfermion final states
In most of the parameter space of 2HDM(II) and with a sufficiently heavy A boson in 2HDM(I), the fermionic decays of the charged Higgs boson dominate and lead to fourfermion final states. The most important decay mode is typically H^{±}→τν _{τ}, with the hadronic mode \(\mathrm{H}^{\pm}\to\mathrm{q}\bar{\mathrm{q}}\) reaching about 40 % branching ratio at maximum.
The search for the fully leptonic final state \(\mathrm{H}^{+}\mathrm{H}^{}\to \tau^{+}\nu_{\tau}\tau^{}{\bar{\nu}}_{\tau}\) is described in [44]. The searches for the \(\mathrm{H}^{+}\mathrm{H}^{} \to \mathrm{q}\bar{\mathrm{q}}\tau\nu_{\tau}\) and the \(\mathrm{H}^{+}\mathrm{H}^{}\to\mathrm{q}\bar{\mathrm{q}}\mathrm{q}\bar{\mathrm{q}}\) events are optimized using Monte Carlo simulation of \(\mathrm{H}^{+}\to\mathrm{c} \bar{\mathrm{s}}\) decays. The sensitivities to other quark flavors are similar and the possible differences are taken into account as systematic uncertainties. Therefore, our results are valid for any hadronic decay of the charged Higgs boson.
Fourfermion final states originating from H^{+}H^{−} production would have very similar kinematic properties to W^{+}W^{−} production, which therefore constitutes an irreducible background to our searches, especially when \(m_{\mathrm{H}^{\pm}}\) is close to \(m_{\mathrm {W}^{\pm }}\). To suppress this difficult SM background, a massdependent likelihood selection (similar to the technique described in [45]) is introduced. For each charged Higgsboson mass tested (m _{test}), a specific analysis optimized for a reference mass (m _{ref}) close to the hypothesized value is used.
We have chosen a set of reference charged Higgsboson masses at which signal samples are generated. Around these reference points, mass regions (labeled by m _{ref}) are defined with the borders centered between the neighboring points. For each individual mass region, at each centerofmass energy, we create a separate likelihood selection. The definition of the likelihood function is based on a set of histograms of channel specific observables, given in [16]. The signal histograms are built using events generated at m _{ref}. The background histograms are composed of the SM processes and are identical for all mass regions.
When testing the hypothesis of a signal with mass m _{test}, the background and data rate and discriminant (i.e. the reconstructed Higgsboson mass) distribution depend on the mass region to which m _{test} belongs. The signal quantities depend on the value of m _{test} itself and are determined as follows. The signal rate and discriminant distribution are computed, with the likelihood selection optimized for m _{ref}, for three simulated signal samples with masses m _{low}, m _{ref} and m _{high}. Here, m _{low} and m _{high} are the closest mass points to m _{ref} at which signal Monte Carlo samples are generated, with m _{low}<m _{ref}<m _{high}. The signal rate and discriminant distribution for m _{test} are then calculated by linear interpolation from the quantities for m _{low} and m _{ref} if m _{test}<m _{ref}, or for m _{ref} and m _{high} if m _{test}>m _{ref}.
When building the likelihood function three event classes are considered: signal, fourfermion background (including twophoton processes) and twofermion background. The likelihood output gives the probability that a given event belongs to the signal rather than to one of the two background sources.
3.1 The twojet plus tau final state
The analysis closely follows our published one at \(\sqrt{s}=183\ \mbox{GeV}\) [16]. It proceeds in two steps. First, events consistent with the final state topology of an isolated tau lepton, a pair of hadronic jets and sizable missing energy are preselected and are then processed by a likelihood selection. The sensitivity of the likelihood selection is improved by building massdependent discriminant functions as explained above.
Events are selected if their likelihood output (\({\mathcal{L}}\)) is greater than a cut value chosen to maximize the sensitivity of the selection at each simulated charged Higgsboson mass (m _{ref}). Apart from the neighborhood of the W^{+}W^{−} peak, the optimal cut does not depend significantly on the simulated mass and is chosen to be \({\mathcal{L}} > 0.85\). Around the W^{+}W^{−} peak, it is gradually reduced to 0.6.
The number of selected events per year is given in Table 2 for a test mass of \(m_{\mathrm{H}^{\pm}}=75\ \mbox{GeV}\). In total, 331 events are selected in the data sample with 316.9±3.2 (stat.) ±38.4 (syst.) events expected from SM processes. The sources of systematic uncertainties are discussed below. Fourfermion processes account for more than 99 % of the SM background and result in a large peak in the reconstructed mass centered at the W^{±} mass (with a second peak at the Z mass for test masses of \(m_{\mathrm{H}^{\pm}}>85\ \mbox{GeV}\)). The signal detection efficiencies for the various LEP energies are between 25 % and 53 % for any charged Higgsboson mass.
The likelihood output and reconstructed dijet mass distributions for simulated Higgsboson masses of 60 GeV and 75 GeV are presented in Figs. 1(a)–(d). The reconstructed Higgsboson mass resolution is 2.0–2.5 GeV [16]. Figure 2(a) gives the mass dependence of the expected number of background and signal events and compares them to the observed number of events at each test mass.
The systematic uncertainties are estimated for several choices of the charged Higgsboson mass from 50 GeV to 90 GeV at centerofmass energies of \(\sqrt{s}=189\ \mbox{GeV}\), 200 GeV and 206 GeV to cover the full LEP2 range. The following sources of uncertainties are considered: limited number of generated Monte Carlo events, statistical and systematic uncertainty on the luminosity measurement, modeling of kinematic variables in the preselection and in the likelihood selection, tau lepton identification, dependence of the signal detection efficiency on finalstate quark flavor, signal selection efficiency interpolation between generated Monte Carlo points, background hadronization model, and fourfermion background model. The contributions from the different sources are summarized in Table 3.
In the limit calculation, the efficiency and background estimates of the 2j+τ channel are reduced by 0.8–1.7 % (depending on the centerofmass energy) in order to account for accidental vetoes due to acceleratorrelated backgrounds in the forward detectors.
3.2 The fourjet final state
The event selection follows our published analysis at \(\sqrt{s}=183\ \mbox{GeV}\) [16]: first, wellseparated fourjet events with large visible energy are preselected; then a set of variables is combined using a likelihood technique. To improve the discriminating power of the likelihood selection, a new reference variable is introduced: the logarithm of the matrix element probability for W^{+}W^{−} production averaged over all possible jetparton assignments computed by EXCALIBUR [40]. Moreover, we introduce massdependent likelihood functions as explained above. As the optimal cut value on the likelihood output is not that sensitive to the charged Higgsboson mass in this search channel, we use the condition \({\mathcal{L}} > 0.45\) at all centerofmass energies and for all test masses.
There is a good agreement between the observed data and the SM Monte Carlo expectations at all stages of the selection. The number of selected events per year is given in Table 2 for a test mass of \(m_{\mathrm{H}^{\pm}}=75\ \mbox{GeV}\). In total, 1100 events are selected in the data, while 1117.8±5.9 (stat.) ±74.4 (syst.) events are expected from SM processes. The fourfermion processes account for about 90 % of the expected background and result in a large peak centered at the W^{±} mass and a smaller one at the Z boson mass. The signal detection efficiencies are between 41 % and 59 % for any test mass and centerofmass energy.
Typical likelihood output and reconstructed dijet mass distributions of the selected events together with the SM background expectation and signal shapes for simulated charged Higgsboson masses of 60 GeV and 75 GeV are plotted in Figs. 1(e)–(h). The Higgsboson mass can be reconstructed with a resolution of 1–1.5 GeV [16]. Figure 2(b) shows the mass dependence of the expected number of background and signal events and compares them to the observed number of events at each test mass. Systematic uncertainties are estimated in the same manner as for the 2j+τ search and are given in Table 3.
4 Search for AW^{+∗}AW^{−∗} events
In a large part of the 2HDM(I) parameter space, the branching ratio of H^{±}→AW^{±} dominates. The possible decay modes of the A boson and the W^{±} lead to many possible H^{+}H^{−}→AW^{+∗}AW^{−∗} event topologies. Above m _{A}≈12 GeV, the A boson decays predominantly into a \(\mathrm {b} \bar {\mathrm {b}}\) pair, and thus its detection is based on bflavor identification. Two possibilities, covering 90 % of the decays of two W^{±}, are considered: quark pairs from both W^{±} bosons or a quark pair from one and a leptonic final state from the other. The event topologies are therefore “eight jets” or “six jets and a lepton with missing energy”, with four jets containing bflavor in both cases.
The background comes from several Standard Model processes. ZZ and W^{+}W^{−} production can result in multijet events. While ZZ events can contain true bflavored jets, W^{+}W^{−} events are selected as candidates when cflavored jets fake bjets. Radiative QCD corrections to \(\mathrm{e}^{+}\mathrm{e}^{}\to\mathrm{q}\bar{\mathrm{q}}\) also give a significant contribution to the expected background.
Due to the complexity of the eightparton final state, it is more efficient to use general event properties and variables designed specifically to discriminate against the main background than a full reconstruction of the event. As a consequence, no attempt is made to reconstruct the charged Higgsboson mass.
The analysis proceeds in two steps. First a preselection is applied to select btagged multijet events compatible with the signal hypothesis. Then a likelihood selection (with three event classes: signal, fourfermion background and twofermion background) is applied.
The preselection of multijet events uses the same variables as the search for the hadronic final state in [16] with optimized cut positions. However, it introduces a very powerful new criterion, especially against the W^{+}W^{−} background, on a combined btagging variable (\({{\mathcal{B}}_{\mathrm{evt}}}\)) requiring the consistency of the event with the presence of bquark jets.
The neural network method used for btagging in the OPAL SM Higgsboson search [24] is used to calculate on a jetbyjet basis the discriminating variables \(f^{i}_{\mathrm{c/b}}\) and \(f^{i}_{\mathrm{uds/b}}\). These are constructed for each jet i as the ratios of probabilities for the jet to be c or udslike versus the probability to be blike. The inputs to the neural network include information about the presence of secondary vertices in a jet, the jet shape, and the presence of leptons with large transverse momentum. The Monte Carlo description of the neural network output was checked with LEP1 data with a jet energy of about 46 GeV. The main background in this search at LEP2 comes from fourfermion processes, in which the mean jet energy is about 50 GeV, very close to the LEP1 jet energy; therefore, an adequate modeling of the background is expected with the events reconstructed as four jets.
The AW^{+∗}AW^{−∗} signal topology depends on the Higgsboson masses. At m _{A}≈12 GeV or \(\mbox {$m_{\mathrm{A}}$}\approx m_{\mathrm{H}^{\pm}}\), the available energy in the A or W^{±} system is too low to form two clean, collimated jets. At high \(m_{\mathrm{H}^{\pm}}\), the boost of the A and W^{±} bosons is small in the laboratory frame and the original eight partons cannot be identified. At low \(m_{\mathrm{H}^{\pm}}\), the A and W^{±} bosons might have a boost, but it is still not possible to resolve correctly the two partons from their decay. From these considerations, one can conclude that it is not useful to require eight (or even six) jets in the event, as these jets will not correspond to the original partons. Consequently, to get the best possible modeling of the background, four jets are reconstructed with the Durham jetfinding algorithm [46–49] before the btagger is run.
The flavordiscriminating variables are combined for the four reconstructed jets by
The index i runs over the reconstructed jets (i=1,…,4) and the parameters α and β are numerical coefficients whose optimal values depend on the flavor composition of the signal and background final states. However, since the expected sensitivity of the search is only slightly dependent on the values of α and β, they are fixed at α=0.1 and β=0.7. Events are retained if \(\mbox {${{\mathcal{B}}_{\mathrm{evt}}}$}>0.4\).
The preselections of the two event topologies (8j and 6j+ℓ) are very similar. However, in the 6j+ℓ channel, no kinematic fit is made to the \(\mathrm{W}^{+}\mathrm{W}^{}\to\mathrm{q}\bar{\mathrm{q}}\mathrm{q}\bar{\mathrm{q}}\) hypothesis and, therefore, no cuts are made on the fit probabilities. No charged lepton identification is applied; instead the search is based on indirect detection of the associated neutrino by measuring the missing energy.
After the preselection the observed data show an excess over the predicted Monte Carlo background. This can partly be explained by the apparent difference between the gluon splitting rate into cc̅ and bb̅ pairs in the data and in the background Monte Carlo simulation. The measured rates at \(\sqrt{s}=91\ \mbox{GeV}\) are \(g_{\mathrm{c}\bar{\mathrm{c}}} = 3.2 \pm0.21 \pm0.38\ \%\) [50] and \(g_{\mathrm{b}\bar{\mathrm{b}}} = 0.307 \pm0.053 \pm0.097\ \%\) [51] from the LEP1 OPAL data. The gluon splitting rates in our Monte Carlo simulation are extracted from \(\mathrm{e}^{+}\mathrm{e}^{}\to\mathrm{ZZ}\to\ell^{+} \ell^{}\mathrm{q}\bar{\mathrm{q}}\) events, where the \(\mathrm{Z}\to \mathrm{q}\bar{\mathrm{q}}\) decays have similar kinematic properties to the ones in the LEP1 measurement. Note that \(\mathrm{e}^{+}\mathrm{e}^{}\to\mathrm{ZZ}\to \mathrm{q}\bar{\mathrm{q}}\mathrm{q}\bar{\mathrm{q}}\) events can not be used as the two \(\mathrm {q}\bar {\mathrm {q}}\) pairs interact strongly with each other. The rates are found to be \(g_{\mathrm{c}\bar{\mathrm{c}}}^{\mathrm{MC}} = 1.33 \pm0.06\ \%\) and \(g_{\mathrm{b}\bar{\mathrm{b}}}^{\mathrm{MC}} = 0.116 \pm0.0167\ \%\), averaged over all centerofmass energies. This mismodeling can be compensated by reweighting the SM Monte Carlo events with gluon splitting to heavy quarks and at the same time deweighting the nonsplit events to keep the total numbers of W^{+}W^{−}, ZZ and twofermion background events fixed at generator level. The reweighting factor is 2.41 for \(g\to \mathrm{c}\bar{\mathrm{c}}\) and 2.65 for \(\mathrm{g}\to \mathrm{b}\bar{\mathrm{b}}\). The same reweighting factors are used for W^{+}W^{−}, ZZ and twofermion events with gluon splitting at all LEP2 energies, noting that all background samples were hadronized with the same settings and assuming that the \(\sqrt{s}\) dependence of the gluon splitting of a fragmenting twofermion system is correctly modeled by the Monte Carlo generator. It is known that the generator reproduces the energy dependence predicted by QCD in the order α _{s} with resummed leadinglog and nexttoleading log terms [52]. This correction results in a background enhancement factor of 1.08 to 1.1 after the preselection, depending on the search channel and the centerofmass energy, but it does not affect the shape of the background distributions.
The numbers of preselected events after the reweighting are given in columns 2 and 3 of Table 4. At this stage of the analysis the 8j and 6j+ℓ data samples are highly overlapping. The observed rates still show an excess over the background predictions, adding up to about 1.6 standard deviations in both samples. Although this difference is statistically not significant, it can be shown that the Monte Carlo prediction has minor imperfections. For the 8j case, the distributions of three variables used in the analysis, namely y _{34}, y _{56} and \(\mathcal{B}_{\mathrm{evt}}\), are plotted in the right part of Fig. 3. As can be seen, the variable y _{56} is most powerful to reject the background. Both the y _{34} and the y _{56} distributions are slightly shifted towards the position of a hypothetical Higgs signal and the \(\mathcal{B}_{\mathrm{evt}}\) distribution shows an excess over the predicted background at intermediate \(\mathcal{B}_{\mathrm{evt}}\) values, but the excess events are not distributed according to the expectation for a Higgs signal. The shifts are visible with better statistical significance in the left part of Fig. 3. It shows the same variables for a background enriched data sample, where the preselection cuts on y _{34} and \(\mathcal{B}_{\mathrm{evt}}\) are dropped, except for the study of the y _{56} variable where we keep the cut on y _{34} to select multijet events. The resulting samples are completely dominated by background, the contribution of a Higgs signal being at most 0.5 %. Since heavy quark production in the Monte Carlo generator is already corrected, the origin of the discrepancies is likely a slight mismodeling of the topology of multijet events, especially if they contain heavy quarks. No further correction is applied to the estimated background. Excess events passing the final selection, even if they do not look signallike, are thus counted with a certain weight as signal events in the statistical analysis, to be discussed later.
As a final selection, likelihood functions are built to identify signal events. The reference distributions depend on the LEP energy, but they are constructed to be independent of the considered \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) combination. To this end, we form the signal reference distributions by averaging all simulated H^{+}H^{−} samples in the \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) mass range of interest.
Since the selections at \(\sqrt{s}=192\mbox{}209\ \mbox{GeV}\) are aimed at charged Higgsboson masses around the expected sensitivity reach of about 80–90 GeV, all masses up to the kinematic limit are included. On the other hand, at \(\sqrt{s}=189\ \mbox{GeV}\) only charged Higgsboson masses up to 50 GeV are included since the selections at this energy are optimized to reach down to as low as a charged Higgsboson mass of 40 GeV where the LEP1 exclusion limit lies. The input variables for the 8j final state are: the Durham jetresolution parameters^{Footnote 2} log_{10} y _{34} and log_{10} y _{56}, the oblateness [53] event shape variable, the opening angle of the widest jet defined by the size of the cone containing 68 % of the total jet energy, the cosine of the W production angle multiplied with the W charge (calculated from the jet charges [54]) for the \(\mathrm{e}^{+}\mathrm{e}^{} \rightarrow \mathrm{W}^{+}\mathrm{W}^{} \rightarrow \mathrm{q} \bar{\mathrm{q}} \mathrm{q}\bar{\mathrm{q}}\) interpretation, and the btagging variable \({{\mathcal{B}}_{\mathrm{evt}}}\). At \(\sqrt{s}=189\ \mbox{GeV}\), log_{10} y _{23}, log_{10} y _{45}, log_{10} y _{67}, and the maximum jet energy are also used. Moreover, the sphericity [55] event shape variable has more discriminating power and thus replaces oblateness. Although the y _{ij} variables are somewhat correlated, they contain additional information: their differences reflect the kinematics of the initial partons.
The input variables for the 6j+ℓ selection are: log_{10} y _{34}, log_{10} y _{56}, the oblateness, the missing energy of the event, and \({{\mathcal{B}}_{\mathrm{evt}}}\). At \(\sqrt{s}=189\ \mbox{GeV}\), log_{10} y _{23}, the maximum jet energy and the sphericity are also included.
Events are selected if they pass a lower cut on the likelihood output. The likelihood distributions are shown in Fig. 4. The positions of the likelihood cuts are indicated by vertical lines. The discrepancies observed in Fig. 3 in backgroundenriched samples, propagate into the likelihood distributions. Since the excess events in Fig. 3 are shifted relative to the background expectation, but do not agree with the Higgs distribution, they give likelihood values between the mean background and signal values in Fig. 4. With large statistical errors, the effect can be seen at intermediate likelihood values. Some of the excess events pass the final likelihood cut.
To assure that every event is counted only once in the final analysis, the overlapping 8j and 6j+ℓ event samples, as obtained after the final likelihood cut are redistributed into three event classes: (i) events exclusively classified as 8j candidates, (ii) events exclusively classified as 6j+ℓ candidates and (iii) events accepted by both selections. If an event falls into class (iii), the larger likelihood output of the two selections is kept for further processing. The final results using the above classification are quoted in Table 4. After all selection cuts, an excess of events appears in the 1999 data sample. The excess (1.9σ) is not statistically significant and it is consistent with the results of the other years. This modified channel definition not only removes the overlap but also increases the efficiency for detecting signal events by considering the crosschannel efficiencies (e.g. the efficiency to select \(\mathrm{H}^{+}\mathrm{H}^{}\to \mathrm{b} \bar{\mathrm{b}}\mathrm{q}\bar{\mathrm{q}}\mathrm{b} \bar{\mathrm{b}}\mathrm{q}\bar{\mathrm{q}}\) signal by the exclusive 6j+ℓ selection can be as high as 18 %, though it is typically only a few %). The efficiencies are determined independently for all simulated \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) combinations and interpolated to arbitrary \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) by twodimensional spline interpolation. The behavior of the selection efficiencies depends strongly on the targeted charged Higgsboson mass range and also varies with the mass difference \(\Delta m=m_{\mathrm{H}^{\pm }}m_{\mathrm{A}}\). In most cases the overlap channel has the highest efficiency. At \(\sqrt {s}=189\ \mbox{GeV}\) and \(m_{\mathrm{H}^{\pm}}=45\ \mbox{GeV}\), it reaches 32 % for the \(\mathrm{b} \bar{\mathrm{b}}\mathrm{q}\bar{\mathrm{q}}\mathrm{b} \bar{\mathrm{b}}\ell\nu_{\ell}\) and 44 % for the \(\mathrm{H}^{+}\mathrm{H}^{}\to \mathrm{b} \bar{\mathrm{b}}\mathrm{q}\bar{\mathrm{q}}\mathrm{b} \bar{\mathrm{b}}\mathrm{q}\bar{\mathrm{q}}\) signal. At \(\sqrt{s}=206\ \mbox{GeV}\) and \(m_{\mathrm{H}^{\pm}}=90\ \mbox{GeV}\), the overlap efficiency can be as high as 62 % for the \(\mathrm{b} \bar{\mathrm{b}}\mathrm{q}\bar{\mathrm{q}}\mathrm{b} \bar{\mathrm{b}}\ell\nu_{\ell}\) and 71 % for the \(\mathrm{H}^{+}\mathrm{H}^{}\to \mathrm{b} \bar{\mathrm{b}}\mathrm{q}\bar{\mathrm{q}}\mathrm{b} \bar{\mathrm{b}}\mathrm{q}\bar{\mathrm{q}}\) signal. The exclusive 6j+ℓ selection has efficiencies typically below 20–30 %, while the exclusive 8j selection below 10–15 %. Table 5 gives the selection efficiencies at selected \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) points.
The composition of the background depends on the targeted Higgsboson mass region. In the lowmass selection (\(\sqrt{s}=189\ \mbox{GeV}\)) that is optimized for \(m_{\mathrm{H}^{\pm}}=40\mbox{}50\ \mbox{GeV}\), the Higgs bosons are boosted and therefore the final state is twojetlike with the largest background contribution coming from twofermion processes: they account for 52 % in the exclusive 8j, 80 % in the exclusive 6j+ℓ and 76 % in the overlap channel. On the other hand, in the highmass analysis (\(\sqrt{s}=192\mbox{}209\ \mbox{GeV}\)) the fourfermion fraction is dominant: 69 % in the 8j, 56 % in the 6j+ℓ and 70 % in the overlap channel.
Systematic errors arise from uncertainties in the preselection and from mismodeling of the likelihood function. The variables y _{34} and \({{\mathcal{B}}_{\mathrm{evt}}}\) appear both in the preselection cuts and in the likelihood definition. The total background rate is known to be underestimated after the preselection step. The computation of upper limits on the production cross section, with this background rate subtracted, results in conservative limits, assuming the modeling of the other preselection variables and the signal and background likelihoods to be correct. Therefore, no systematic uncertainty is assigned to the percentage of events passing the y _{34} and \({{\mathcal{B}}_{\mathrm{evt}}}\) preselection cuts. The systematic errors related to preselection variables other than y _{34} and \({{\mathcal{B}}_{\mathrm{evt}}}\), evaluated from background enriched data samples, are taken into account.
As already mentioned, the discrepancies shown in Fig. 3 have an impact on the likelihood function. Eventbyevent correction routines for the variables y _{34} and \({{\mathcal{B}}_{\mathrm{evt}}}\) were developed to describe the observed shapes, keeping the normalization above the preselection cuts fixed. The systematic errors were estimated by computing the likelihood for all MC events with the modified values of y _{34} and \({{\mathcal{B}}_{\mathrm{evt}}}\) and counting the accepted MC events. The systematic errors related to all other reference variables were estimated in the same manner.
Systematic uncertainties also arise due to the gluon splitting correction. The experimental uncertainty on the gluon splitting rate translates into uncertainties on the total background rates. Moreover, there is an uncertainty due to the Monte Carlo statistics of the \(\mathrm{g}\to \mathrm{c}\bar{\mathrm{c}}\) and bb̅ events.
Finally, uncertainties due to the limited number of simulated signal and background events are included. The different contributions are summarized in Table 6. Uncertainties below the 1 % level are neglected.
5 Search for AW^{±} τν _{τ} events
In some parts of the 2HDM(I) parameter space, both the fermionic H^{±}→τν _{τ} and the bosonic H^{±}→AW^{±} decay modes contribute. To cover this transition region at small \(m_{\mathrm{H}^{\pm}}m_{\mathrm{A}}\) mass differences, a search for the final state H^{+}H^{−}→AW^{±} τν _{τ} is performed. The transition region is wide for small tanβ and narrow for large tanβ; therefore, this analysis is more relevant for lower values of tanβ.
Only the hadronic decays of W^{±} and the decay \(\mathrm{A}\to \mathrm{b} \bar{\mathrm{b}}\) are considered. Thus the events contain a tau lepton, four jets (two of which are bflavored) and missing energy. Separating the signal from the W^{+}W^{−} background becomes difficult close to \(m_{\mathrm{H}^{\pm}}=m_{\mathrm{W}^{\pm}}\).
The preselection is designed to identify hadronic events containing a tau lepton plus significant missing energy and transverse momentum from the undetected neutrino. In most cases it is not practical to reconstruct the four jets originating from the AW^{±} system. Instead, to suppress the main background from semileptonic W^{+}W^{−} events, we remove the decay products of the tau candidate and force the remaining hadronic system into two jets by the Durham algorithm. The requirements are then based on the preselection of Sect. 3.1 with additional preselection cuts on the effective centerofmass energy, log_{10} y _{12} and log_{10} y _{23} of the hadronic system, and the chargesigned W^{±} production angle.
The likelihood selection uses seven variables: the momentum of the tau candidate, the cosine of the angle between the tau momentum and the nearest jet, log_{10} y _{12} of the hadronic system, the cosine of the angle between the two hadronic jets, the chargesigned cosine of the W^{±} production angle, the invariant mass of the hadronic system, and the btagging variable \({{\mathcal{B}}_{\mathrm{evt}}}\). Here, \({{\mathcal{B}}_{\mathrm{evt}}}\) is defined using the two jets of the hadronic system using Eq. (1) of Sect. 4, with i=1,2 and α=β=1. To form the signal reference distributions, all simulated H^{+}H^{−} samples in the \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) mass range of interest are summed up. Since the search at \(\sqrt{s}=192\mbox{}209\ \mbox{GeV}\) targets intermediate charged Higgsboson masses (60–80 GeV), all masses up to the kinematic limit are included. At \(\sqrt{s}=189\ \mbox{GeV}\), only charged Higgsboson masses up to 50 GeV are included since the selection is optimized for low charged Higgsboson masses (40–50 GeV).
The likelihood output distributions are shown in Fig. 5. There is an overall agreement between data and background distributions, apart from a small discrepancy at 189 GeV. Events are selected if their likelihood output is larger than 0.9. In total, 15 data events survive the selection at \(\sqrt{s}=192\mbox{}209\ \mbox{GeV}\), to be compared with 14.8±0.6 (stat.) ±1.9 (syst.) events expected from background sources. At \(\sqrt{s}=189\ \mbox{GeV}\), where the selection is optimized for low Higgsboson masses, 13 data events are selected with 6.1±0.5 (stat.) ±1.3 (syst.) events expected. The contribution of fourfermion events, predominantly from semileptonic W^{+}W^{−} production, amounts to 67 % at \(\sqrt{s}=189\ \mbox{GeV}\) and to 90 % at \(\sqrt{s}=192\mbox{}209\ \mbox{GeV}\).
At \(\sqrt{s}=192\mbox{}209\ \mbox{GeV}\), the signal selection efficiency starts at about 5 % at \(m_{\mathrm{H}^{\pm}}=40\ \mbox{GeV}\), reaches its maximum of about 40 % (depending on the mass difference \(\Delta m=m_{\mathrm{H}^{\pm}}m_{\mathrm{A}}\)) at \(m_{\mathrm{H}^{\pm}}=60\ \mbox{GeV}\), then decreases to 12 % at \(m_{\mathrm{H}^{\pm}}=90\ \mbox{GeV}\). In the lowmass selection at \(\sqrt{s}=189\ \mbox{GeV}\), the efficiency depends strongly on the mass difference: at \(m_{\mathrm{H}^{\pm}}=40\ \mbox{GeV}\), it is 27 % for Δm=2.5 GeV and 60 % for Δm=10 GeV. The selection efficiency approaches its maximum at \(m_{\mathrm{H}^{\pm}}=50\ \mbox{GeV}\) (73 % for Δm=15 GeV) and then drops to zero at \(m_{\mathrm{H}^{\pm}}=80\ \mbox{GeV}\). Table 5 gives selection efficiencies at representative \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) points.
The systematic uncertainties due to the modeling of selection variables are evaluated with the method developed for the AW^{+∗}AW^{−∗} channels and summarized in Table 7.
6 Interpretation
None of the searches has revealed a signallike excess over the SM expectation. The results presented here and those published previously [16, 44] by the OPAL Collaboration are combined using the method of [56] to study the compatibility of the observed events with “backgroundonly” and “signal plus background” hypotheses and to derive limits on charged Higgsboson production. The statistical analysis is based on weighted event counting, with the weights computed from physical observables, also called discriminating variables of the candidate events (see Table 8). Systematic uncertainties with correlations are taken into account in the confidence level (pvalue) calculations. To improve the sensitivity of the analysis, they are also incorporated into the weight definition [56].^{Footnote 3}
The results are interpreted in two different scenarios: in the traditional, supersymmetryfavored 2HDM(II) (assuming that there are no new additional light particles other than the Higgs bosons) and in the 2HDM(I) where under certain conditions fermionic couplings are suppressed.
First, we calculate 1−CL _{b}, the confidence [56] under the backgroundonly hypothesis, and then proceed to calculate limits on the charged Higgsboson production cross section in the signal + background hypothesis. These results are used to provide exclusions in the model parameter space, and in particular, on the charged Higgsboson mass.
6.1 2HDM type II
First a general 2HDM(II) is considered, where \(\mathrm{BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $} \mbox {${\tau \nu _{\tau }}$}) + \mathrm{BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $}\mbox {$\mathrm {q}\bar {\mathrm {q}}$}) = 1\). This model was thoroughly studied at LEP. It is realized in supersymmetric extensions of the SM if no new additional light particles other than the Higgs bosons are present. As our previously published mass limit in such a model is \(m_{\mathrm{H}^{\pm}}>59.5\ \mbox{GeV}\) [16], only charged Higgsboson masses above 50 GeV are tested. Crosssection limits for lower masses can be found in [15]. In this model, the results of the 2τ, 2j+τ and 4j searches enter the statistical combination.
The confidence 1−CL _{b} is plotted for each channel separately in Fig. 6(a) and combined in Fig. 6(b). Note that 1−CL _{b}<0.5 translates to negative values of sigma (as indicated by the dual yaxis scales in Fig. 6(a)) and indicates an excess of events. No deviation reaches the 2σ level.
The results are used to set upper bounds on the charged Higgsboson pair production cross section relative to the 2HDM prediction as calculated by HZHA. The limits obtained are shown for each channel separately in Figs. 7(a)–(c) and combined in Fig. 7(d). The combined results are shown by “isolines” along which \(\sigma_{95}( \mbox {$\mathrm {H}^{+}$}\mbox {$\mathrm {H}^{}$})/\sigma_{\mathrm{2HDM}}\), the ratio of the limit on the production cross section and the 2HDM crosssection prediction, is equal to the number indicated next to the curves.
Excluded areas on the \([\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$\mathrm {BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $}\mbox {${\tau \nu _{\tau }}$})$}]\) plane are presented for each channel separately in Fig. 8(a) and combined in Fig. 8(b). The expected mass limit from simulated background experiments, assuming no signal, is also shown. For the combined results, the 90 % and 99 % CL contours are also given. Charged Higgs bosons are excluded up to a mass of 76.3 GeV at 95 % CL, independent of \(\mathrm {BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $}\mbox {${\tau \nu _{\tau }}$})\). Lower mass limits for different values of \(\mathrm {BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $}\mbox {${\tau \nu _{\tau }}$})\) are presented in Table 9.
6.2 2HDM type I
We present here for the first time an interpretation of the OPAL charged Higgsboson searches in an alternative theoretical scenario, a 2HDM(I). The novel feature of this model with respect to the more frequently studied 2HDM(II) is that the fermionic decays of the charged Higgs boson can be suppressed. If the A boson is light, the H^{±}→AW^{±} decay may play a crucial role.
The charged Higgsboson sector in these models is described by three parameters: \(m_{\mathrm{H}^{\pm}}\), m _{A} and tanβ. To test this scenario, the Higgsboson decay branching ratios H^{±}→τν _{τ}, \(\mathrm {c} \bar {\mathrm {s}}\), \(\mathrm {c} \bar {\mathrm {b}}\), AW^{±} and \(\mathrm{A}\to\mathrm{b} \bar{\mathrm{b}}\) are calculated by the program of Akeroyd et al. [13, 14], and the model parameters are scanned in the range: \(40\ \mbox{GeV} \leq m_{\mathrm{H}^{\pm}} \leq94\ \mbox{GeV}\), \(12\ \mbox{GeV} \leq \mbox {$m_{\mathrm{A}}$}< m_{\mathrm{H}^{\pm}}\), \(0\leq \mbox {$\tan \beta $}\leq 100\). Charged Higgsboson pair production is excluded below 40 GeV by the measurement of the Z boson width [57]. As the A boson detection is based on the identification of bquark jets, no limits are derived for m _{A}<2m _{b}.
Both the fermionic (2τ, 2j+τ and 4j) and the bosonic (4j+τ, 6j+ℓ and 8j) final states play an important role and therefore their results have to be combined. There is, however, a significant overlap between the events selected by the \(\mathrm{H}^{+}\mathrm{H}^{}\to\mathrm{q}\bar{\mathrm{q}}\mathrm{q}\bar{\mathrm{q}}\) and H^{+}H^{−}→AW^{+∗}AW^{−∗} selections, and the events selected by the \(\mathrm{H}^{+}\mathrm{H}^{}\to\mathrm{q}\bar{\mathrm{q}}\tau\nu_{\tau}\) and H^{+}H^{−}→AW^{±} τν _{τ} selections. Therefore, an automatic procedure is implemented to switch off the less sensitive of the overlapping channels, based on the calculation of the expected limit assuming no signal. In general the fermionic channels are used close to the \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) diagonal and for low tanβ, and the searches for H^{±}→AW^{±} are crucial for low values of m _{A} and high values of tanβ.
The confidence 1−CL _{b} is calculated for the combination of the 8j and 6j+ℓ searches and for the 4j+τ search, without requiring the 2HDM(I) branching ratios (model independent scan), and for tanβ dependent combinations of all channels, including the fermionic ones, taking the 2HDM(I) cross section predictions into account (model dependent scan).
The result for the 8j and 6j+ℓ combination is calculated assuming SM branching ratios [58] for the W^{±} decay and is shown in Fig. 9(a). Close to the \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) diagonal, the eight or sixjet structure of a H^{±}→AW^{±} signal becomes less pronounced and the final state turns out fourjetlike with a few soft extra particles. As the selection variables for the signal and the background become similar, the likelihood cut removes more signal events, resulting in a drop in efficiency and extrapolations towards the \(m_{\mathrm{H}^{\pm }}=m_{\mathrm{A}}\) limit are unreliable. Morever, within the 2HDM(I), the branching ratio for the bosonic Higgs decay vanishes at \(m_{\mathrm{H}^{\pm }}=m_{\mathrm{A}}\). Results for \(\mbox {$m_{\mathrm{A}}$}> m_{\mathrm{H}^{\pm}}3\ \mbox{GeV}\) are thus not included in Fig. 9(a). In this mass region, the branching ratios for both H^{+}H^{−}→8j and H^{+}H^{−}→6j+ℓ are always less than 10^{−4}. The largest deviation from background expectation, 1−CL _{b}=0.029, corresponding to 1.9σ is reached at \(m_{\mathrm{H}^{\pm}}=70\ \mbox{GeV}\) and m _{A}=64 GeV. Another local minimum at \(m_{\mathrm{H}^{\pm}}=60\ \mbox{GeV}\) and m _{A}=12 GeV, not visible in Fig. 9(a), has 1−CL _{b}=0.052. However, the mean background shift on the \([\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$}]\) plane amounts only to 1.1σ.
The 1−CL _{b} values for the 4j+τ channel is shown in Fig. 9(b). Mass combinations with \(\mbox {$m_{\mathrm{A}}$}> m_{\mathrm{H}^{\pm}} 2.5\ \mbox{GeV}\) are not included. In this mass region, the 2HDM(I) prediction for the H^{+}H^{−}→ 4j+τ branching ratio is less than 0.005. The largest deviation 1−CL _{b}=0.013 corresponding to 2.2σ appears for low charged Higgsboson masses (\(m_{\mathrm{H}^{\pm}}=40\ \mbox{GeV}\), m _{A}=21 GeV), reflecting the excess of events in the \(\sqrt{s}=189\ \mbox{GeV}\) search. The mean background shift for this channel is 0.8σ.
When all channels are combined within the 2HDM(I), the confidence levels shown in Figs. 9(c)–(d) are obtained. Close to the \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) diagonal, the results are determined by the analysis of the fermionic channels. The 2HDM(I) predicts BR(H^{±}→τν _{τ})≈0.65 for the branching ratio, depending only weakly on \(m_{\mathrm{H}^{\pm}}\). The upper parts of Figs. 9(c)–(d) correspond thus to an almost horizontal cut in Fig. 6(b) at BR(H^{±}→τν _{τ})=0.65. The lower parts of Figs. 9(c)–(d) are essentially weighted combinations of the results in Figs. 9(a)–(b), depending on tanβ and the masses involved. However, it has to be noted that also the decays \(\mathrm{H}^{+}\mathrm{H}^{}\to\tau^{+}\nu_{\tau}\tau^{}{\bar{\nu}}_{\tau}\) are included and that the event weights in the statistical analysis are somewhat different for the model independent scans in Figs. 9(a)–(b) and the model dependent scans in Figs. 9(c)–(d). In general, excesses in Figs. 9(a)–(b) add up to excesses less than 2σ in the combination. A few regions with a significance above 2σ are present. For tanβ=10, the largest excess 1−CL _{b}=0.014, corresponding to 2.2σ, is found at \(m_{\mathrm{H}^{\pm}}=55\ \mbox{GeV}\) and m _{A}=34 GeV (just before switching from the bosonic to the fermionic channels). This excess corresponds to a signal rate of 28.5 % of the 2HDM(I) expectation. Noting that the event weights depend on the hypothetical signal rate, structures in the 1−CL _{b} distribution as a function of \(\Delta m = m_{\mathrm{H}^{\pm}}  m_{\mathrm{A}}\) are due to the similar increase of the signal crosssection with Δm for different \(m_{\mathrm{H}^{\pm}}\) values. The rise of the crosssection is steeper for larger tanβ, therefore the low 1−CL _{b} region shrinks from Fig. 9(c) to Fig. 9(d).
In the limit of small m _{A} and large values of tanβ, the Higgs decay into the τν _{τ} channel is suppressed. The structures of the 1−CL _{b} bands close to m _{A}=12 GeV in Figs. 9(a) and 9(d) are therefore very similar.
As mentioned previously, the H^{±}→AW^{±} decay becomes dominant if the A boson is sufficiently light. The smaller tanβ is, the smaller m _{A} should be. This is clearly seen from the structure of the result in Figs. 9(c)–(d): for tanβ=10, the bosonic decay becomes dominant at \(m_{\mathrm{A}} \lessapprox m_{\mathrm{H}^{\pm}}18\ \mbox{GeV}\), while for tanβ=100, it dominates already at \(m_{\mathrm{A}} \lessapprox m_{\mathrm{H}^{\pm}} 6\ \mbox{GeV}\).
The modelindependent limits on the charged Higgsboson production cross section relative to the 2HDM prediction are presented in Fig. 10(a) for the H^{+}H^{−}→AW^{+∗}AW^{−∗} and in Fig. 10(b) for H^{+}H^{−}→AW^{±} τν _{τ} searches, with the only assumption that W^{±} decays with SM branching ratios. The exclusion line for 40 % of the total production cross section in Fig. 10(a) forms an island around \(m_{\mathrm{H}^{\pm}}=60\ \mbox{GeV}\) and m _{A}=12 GeV, corresponding to the minimum of 1−CL _{b} at this point.
The results combining all channels using 2HDM(I) branching ratios are shown in Fig. 11 for different choices of tanβ. For 0≤tanβ≤0.1, the excluded mass region is independent of m _{A}, since the AW^{±} final state does not contribute. The Higgs mass limit is identical to the 2HDM(II) limit at BR(H^{±}→τν _{τ})=0.65. This limit is also reached at the \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) diagonal for any value of tanβ. For intermediate and large values of tanβ, the boundary lines of the excluded mass regions have two local \(m_{\mathrm{H}^{\pm}}\) minima. The first minimum at m _{A}=12 GeV is due to the excess of events in the AW^{+∗}AW^{−∗} searches. The second minimum is at a region extending parallel to the \((\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$})\) diagonal (see the full and dotted black curves corresponding to a crosssection ratio of 1.0). This reflects the loss of sensitivity in the AW^{+∗}AW^{−∗} searches for mass combinations without a pronounced 8j or 6j+ℓ structure and is also due to the channel switching procedure implemented to avoid the use of overlapping events as explained above.
To further study the behavior of the unexcluded regions, 90 %, 95 % and 99 % CL excluded areas are shown in Fig. 12 for different choices of tanβ. The island at \(m_{\mathrm{H}^{\pm}}=60\ \mbox {GeV}\) can not be excluded at the 99 % CL.
Due to the excess of events in the H^{+}H^{−}→AW^{+∗}AW^{−∗} searches in the year 1999 data, the observed limit is lower than the expectation in all regions where the H^{±}→AW^{±} decay dominates. Our final results are presented, for all tanβ, in Fig. 13, and the limits on charged Higgsboson mass are summarized in Table 10. Since an excess is present in both the 8j and 6j+ℓ combination and the 4j+τ channel, and the relative weighting of these channels depends on tanβ, the size of the mentioned island is tanβ dependent. The absolute lower limit on the charged Higgs boson mass for 95 % CL is set by tanβ=3.5, as indicated in Fig. 13. It amounts to 56.8 GeV for \(0\leq \mbox {$\tan \beta $}\leq100\) and \(12\ \mbox{GeV} \leq \mbox {$m_{\mathrm{A}}$}\leq m_{\mathrm {H}^{\pm}}\), to be compared with an expectation of 71.1 GeV. The unexcluded island is no longer present at 90 % CL where the observed mass limit improves to 66.0 GeV.
For m _{A}>15 GeV, the tanβindependent lower limit on the charged Higgsboson mass at 95 % CL is 65.0 GeV with 71.3 GeV expected. The limit is found in the transition region where the bosonic and fermionic channels have comparable sensitivities. The 6 GeV difference is due to the excess observed in the H^{+}H^{−}→AW^{+∗}AW^{−∗} search.
7 Summary
A search is performed for the pair production of charged Higgs bosons in electronpositron collisions at LEP2, considering the decays H^{±}→τν _{τ}, \(\mathrm {q}\bar {\mathrm {q}}\) and AW^{±}. No signal is observed. The results are interpreted in the framework of TwoHiggsDoublet Models.
In 2HDM(II), required by the minimal supersymmetric extension of the SM, charged Higgs bosons are excluded up to a mass of 76.3 GeV (with an expected limit of 75.6 GeV) when \(\mbox {$\mathrm {BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $}\mbox {${\tau \nu _{\tau }}$})$}+ \mbox {$\mathrm {BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $}\mbox {$\mathrm {q}\bar {\mathrm {q}}$})$}= 1\) is assumed. \(\mathrm {BR}(\mbox {$\mathrm {H}^{\pm }$}\mbox {$\rightarrow $}\mbox {${\tau \nu _{\tau }}$})\)dependent limits are given in Fig. 8 and Table 9.
In 2HDM(I), where fermionic decays can be suppressed and H^{±}→AW^{±} can become dominant, a tanβindependent lower mass limit of 56.8 GeV is observed for m _{A}>12 GeV (with an expected limit of 71.1 GeV) due to an excess observed at \(\sqrt{s}=192\mbox{}202\ \mbox{GeV}\) in the H^{+}H^{−}→AW^{+∗}AW^{−∗} search, discussed in Sect. 4. For m _{A}>15 GeV, the observed limit improves to \(m_{\mathrm{H}^{\pm }} >65.0\ \mbox{GeV}\) (with an expected limit of 71.3 GeV). Figure 13 shows the excluded areas in the \([\mbox {$m_{\mathrm {H}^{\pm }}$}, \mbox {$m_{\mathrm{A}}$}]\) plane and Table 10 reports selected numerical results.
Notes
Throughout this paper charge conjugation is implied. For simplicity, the notation τν _{τ} stands for τ ^{+} ν _{τ} and \(\tau^{}\bar{\nu }_{\tau}\) and \(\mathrm {q}\bar {\mathrm {q}}\) for a quark and antiquark of any flavor combination.
Throughout this paper y _{ij} denotes the parameter of the Durham jet finder at which the event classification changes from ijet to jjet, where j=i+1.
For the weight definition, we use criteria (i) and (ii) in the 2HDM parameter scans and criterion (vii) in calculating model independent results. The generalized version of Eq. (2.9), given in Eq. (6.1), is used to include systematic errors in the event weights. The treatment of correlations between systematic errors is discussed in Sect. 5.1.
References
S.L. Glashow, Nucl. Phys. 22, 579 (1961)
S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967)
A. Salam, in Elementary Particle Theory, ed. by N. Svartholm (Almquist and Wiksells, Stockholm, 1968), 367 pp.
P.W. Higgs, Phys. Lett. 12, 132 (1964)
F. Englert, R. Brout, Phys. Rev. Lett. 13, 321 (1964)
G.S. Guralnik, C.R. Hagen, T.W.B. Kibble, Phys. Rev. Lett. 13, 585 (1964)
J.F. Gunion, H.E. Haber, G.L. Kane, S. Dawson, The Higgs Hunter’s Guide (AddisonWesley, Reading, 1990); and references therein
S.L. Glashow, S. Weinberg, Phys. Rev. D 15, 1977 (1958)
E.A. Paschos, Phys. Rev. D 15, 1977 (1966)
H.E. Haber et al., Nucl. Phys. B 161, 493 (1979)
S. Kanemura, Eur. Phys. J. C 17, 473 (2000)
A. Djouadi, J. Kalinowski, P.M. Zerwas, Z. Phys. C 57, 569 (1993)
A.G. Akeroyd, Nucl. Phys. B 544, 557 (1999)
A.G. Akeroyd, A. Arhrib, E. Naimi, Eur. Phys. J. C 20, 51 (2001)
OPAL Collaboration, K. Ackerstaff et al., Phys. Lett. B 426, 180 (1998)
OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. C 7, 407 (1999)
ALEPH Collaboration, A. Heister et al., Phys. Lett. B 543, 1 (2002)
DELPHI Collaboration, J. Abdallah et al., Eur. Phys. J. C 34, 399 (2004)
L3 Collaboration, P. Achard et al., Phys. Lett. B 575, 208 (2003)
OPAL Collaboration, K. Ahmet et al., Nucl. Instrum. Methods A 305, 275 (1991)
B.E. Anderson et al., IEEE Trans. Nucl. Sci. 41, 845 (1994)
S. Anderson et al., Nucl. Instrum. Methods A 403, 326 (1998)
G. Aguillion et al., Nucl. Instrum. Methods A 417, 266 (1998)
OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. C 26, 479 (2003)
G. Ganis, P. Janot, in Physics at LEP2, CERN 9601, vol. 2 (CERN, Geneva, 1996), p. 309
T. Sjöstrand, Comput. Phys. Commun. 82, 74 (1994)
T. Sjöstrand, LU TP 95–20 (1995)
S. Jadach, B.F.L. Ward, Z. Wa̧s, Comput. Phys. Commun. 130, 260 (2000)
S. Jadach, B.F. Ward, Z. Wa̧s, Phys. Lett. B 449, 97 (1999)
J. Fujimoto et al., Comput. Phys. Commun. 100, 128 (1997)
J. Fujimoto et al., in Physics at LEP2, CERN 9601, vol. 2 (CERN, Geneva, 1996), p. 30
S. Jadach, W. Płaczek, B.F.L. Ward, in Physics at LEP2, CERN 9601, vol. 2 (CERN, Geneva, 1996), p. 286; UTHEP951001
D. Karlen, Nucl. Phys. B 289, 23 (1987)
S. Jadach, B.F.L. Ward, Z. Wa̧s, Comput. Phys. Commun. 79, 503 (1994)
E. Budinov et al., in Physics at LEP2, CERN 9601, vol. 2 (CERN, Geneva, 1996), p. 216
R. Engel, J. Ranft, Phys. Rev. D 54, 4244 (1996)
G. Marchesini et al., Comput. Phys. Commun. 67, 465 (1992)
J.A.M. Vermaseren, Nucl. Phys. B 229, 347 (1983)
OPAL Collaboration, G. Alexander et al., Z. Phys. C 69, 543 (1996)
F.A. Berends, R. Pittau, R. Kleiss, Comput. Phys. Commun. 85, 437 (1995)
S. Jadach, W. Płaczek, M. Skrzypek, B.F.L. Ward, Z. Wa̧s, Comput. Phys. Commun. 119, 272 (1999)
S. Jadach, W. Płaczek, M. Skrzypek, B.F.L. Ward, Z. Wa̧s, Comput. Phys. Commun. 140, 475 (2001)
J. Allison et al., Nucl. Instrum. Methods A 317, 47 (1992)
OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. C 32, 453 (2004)
OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. C 18, 425 (2001)
N. Brown, W.J. Stirling, Phys. Lett. B 252, 657 (1990)
S. Bethke, Z. Kunszt, D. Soper, W.J. Stirling, Nucl. Phys. B 370, 310 (1992)
S. Catani et al., Phys. Lett. B 269, 432 (1991)
N. Brown, W.J. Stirling, Z. Phys. C 53, 629 (1992)
OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. C 13, 1 (2000)
OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. C 18, 447 (2001)
M.H. Seymour, Nucl. Phys. B 436, 163 (1995)
Mark J Collaboration, D.P. Barber et al., Phys. Rev. Lett. 43, 830 (1979)
OPAL Collaboration, R. Akers et al., Z. Phys. C 67, 365 (1995)
G. Hanson et al., Phys. Rev. Lett. 35, 1609 (1975)
P. Bock, J. High Energy Phys. 01, 080 (2007)
ALEPH, DELPHI, L3, OPAL and SLD Collaborations, LEP Electroweak Working Group, SLD Electroweak and Heavy Flavour Groups, S. Schael et al., Phys. Rep. 427, 257 (2006)
Particle Data Group, C. Amsler et al., Phys. Lett. B 667, 1 (2008)
Acknowledgements
We particularly wish to thank the SL Division for the efficient operation of the LEP accelerator at all energies and for their close cooperation with our experimental group. In addition to the support staff at our own institutions we are pleased to acknowledge the
Department of Energy, USA,
National Science Foundation, USA,
Particle Physics and Astronomy Research Council, UK,
Natural Sciences and Engineering Research Council, Canada,
Israel Science Foundation, administered by the Israel Academy of Science and Humanities,
Benoziyo Center for High Energy Physics,
Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and a grant under the MEXT International Science Research Program,
Japanese Society for the Promotion of Science (JSPS),
German Israeli Binational Science Foundation (GIF),
Bundesministerium für Bildung und Forschung, Germany,
National Research Council of Canada,
Hungarian Foundation for Scientific Research, OTKA T038240, and T042864,
The NWO/NATO Fund for Scientific Research, the Netherlands.
Author information
Authors and Affiliations
Consortia
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
The OPAL Collaboration., Abbiendi, G., Ainsley, C. et al. Search for charged Higgs bosons in e^{+}e^{−} collisions at \(\sqrt{s}=189\mbox{}209\ \mbox{GeV}\). Eur. Phys. J. C 72, 2076 (2012). https://doi.org/10.1140/epjc/s1005201220760
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjc/s1005201220760