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Charged Higgs Bosons in the MSSM at CMS: Discovery Reach and Parameter Dependence

The search for MSSM Higgs bosons will be an important goal at the LHC. In order to analyze the search reach of the CMS experiment for the charged MSSM Higgs bosons, we combine the latest results for the CMS experimental sensitivities based on full simulation studies with state-of-the-art theoretical predictions of MSSM Higgs-boson production and decay properties. The experimental analyses are done assuming an integrated luminosity of 30 fb^-1 for the two cases M_H+-m_t. The results are interpreted as 5 sigma discovery contours in M_H+- - tan_beta planes of the MSSM for various benchmark scenarios. We study the dependence of the 5 sigma contours on the variation of the relevant SUSY parameters. Particular emphasis is put on analyzing the variation of the discovery contours with the Higgs mixing parameter mu. The variation of mu can shift the prospective discovery reach in tan_beta by up to Delta tan_beta = 40.


Introduction
One of the main goals of the LHC is the identification of the mechanism of electroweak symmetry breaking. The most frequently investigated models are the Higgs mechanism within the Standard Model (SM) and within the Minimal Supersymmetric Standard Model (MSSM) [1]. Contrary to the case of the SM, in the MSSM two Higgs doublets are required. This results in five physical Higgs bosons instead of the single Higgs boson in the SM. These are the light and heavy CP-even Higgs bosons, h and H, the CP-odd Higgs boson, A, and the charged Higgs bosons, H ± . The Higgs sector of the MSSM can be specified at lowest order in terms of the gauge couplings, the ratio of the two Higgs vacuum expectation values, tan β ≡ v 2 /v 1 , and the mass of the CP-odd Higgs boson, M A (or M H ± , the mass of the charged Higgs boson). Consequently, the masses of the CP-even neutral and the charged Higgs bosons are dependent quantities that can be predicted in terms of the Higgs-sector parameters, e.g.
where M W denotes the mass of the W boson. The same applies to the production and decay properties of the MSSM Higgs bosons 1 . Higgsphenomenology in the MSSM is strongly affected by higher-order corrections, in particular from the sector of the third generation quarks and squarks, so that the dependencies on various other MSSM parameters can be important, see e.g. Refs. [2][3][4] for reviews.
Searches for the charged Higgs bosons of the MSSM (or a more general Two Higgs Doublet Model (THDM)) have been carried out at LEP [5], yielding a bound of M H ± > ∼ 80 GeV [6,7]. The Tevatron placed additional bounds on the MSSM parameter space from charged Higgsboson searches, in particular at large tan β and low M A [8]. At the LHC the charged Higgs bosons will be accessible best at large tan β up to M A < ∼ 800 GeV [9][10][11]. At the ILC, for M H ± < ∼ √ s/2 a high-precision determination of the charged Higgs boson properties will be possible [12][13][14][15].
The prospective sensitivities at the LHC are usually displayed in terms of the parameters M A and tan β (or M H ± and tan β) that characterize the MSSM Higgs sector at lowest order. The other MSSM parameters are conventionally fixed according to certain benchmark scenarios [16]. The respective LHC analyses of the 5 σ discovery contours for the charged Higgs boson are given in Ref. [17] for ATLAS and in Refs. [18,19] for CMS. However, within these analyses the variation with relevant SUSY parameters as well as possibly relevant loop corrections in the Higgs production and decay [11] have been neglected.
We focus in this paper on the 5 σ discovery contours for the charged MSSM Higgs boson for the two cases M H ± < m t and M H ± > m t , within the m max h scenario and the no-mixing scenario [11,16] (i.e. we concentrate on the CP-conserving case). They are obtained by using the latest CMS results [18,19] derived in a model-independent approach, i.e. making no assumption on the Higgs boson production mechanism or decays. However, the detection relies on the decay mode of the charged Higgs bosons to τ ν τ . Furthermore only SM backgrounds have been assumed. These experimental results are combined with up-to-date theoretical predictions for charged Higgs production and decay in the MSSM, taking into account also the decay to SUSY particles that can in principle suppress the branching ratio of the charged Higgs boson decay to τ ν τ .
For the interpretation of the exclusion bounds and prospective discovery contours in the benchmark scenarios it is important to assess how sensitively the results depend on those parameters that have been fixed according to the benchmark prescriptions. In Refs. [11,20] this issue has been analyzed for the neutral heavy MSSM Higgs bosons, and it has been found that the by far largest effect arises from the variation of the Higgs-mixing parameter µ. Consequently, we investigate how the 5 σ discovery regions in the M H ± -tan β plane for the charged MSSM Higgs boson obtainable with the CMS experiment at the LHC are affected by a variation of the mixing parameter µ.

Experimental analysis
The main production channels at the LHC are and The decay used in the analysis to detect the charged Higgs boson is The analyses described below correspond to CMS experimental sensitivities based on full simulation studies, assuming an integrated luminosity of 30 fb −1 . In these analyses a top quark mass of m t = 175 GeV has been assumed.

The light charged Higgs Boson
The "light charged Higgs boson" is characterized by M H ± < m t . The main production channel is given in eq. (1). Close to threshold also eq. (2) contributes. The relevant (i.e. detectable) decay channel is given by eq. (3). The experimental analysis, based on 30 fb −1 collected with CMS, is presented in Ref. [18]. The events were required to be selected with the single lepton trigger, thus exploiting the W → ℓν decay mode of a W boson from the decay of one of the top quarks in eq. (1). The total number of events leading to final states with the signal characteristics is evaluated, including their respective experimental efficiencies. The various channels and the corresponding efficiencies can be found in Tab. 1. The efficiencies are given for M H ± = 160 GeV, but vary only insignificantly over the parameter space under investigation. The number of signal-like events is evaluated as the sum of background and Higgs-boson signal events, N ev = N background (from the processes in Tab. 1) where L denotes the luminosity, and the experimental efficiency is given in Tab. 1. A 5 σ discovery can be achieved if a parameter point results in more than 5260 events (with 30 fb −1 ).
The next-to-leading order LHC cross section for top quark pairs is taken to be 840 pb [21]. For the W ± +3 jets background the leading order cross section for the process pp → W ± + 3 jets, W ± → ℓ ± ν (ℓ = e, µ) of 840 pb was used, as given by the MadGraph [22] generator. channel exp. efficiency Table 1: Relevant signal (first line) and background channels for the light charged Higgs boson and their respective experimental efficiencies. The charge conjugated processes ought to be included. The efficiency for the charged Higgs production is given for M H ± = 160 GeV, but varies only insignificantly over the relevant parameter space. ℓ denotes e or µ.

The heavy charged Higgs Boson
The "heavy charged Higgs boson" is characterized by M H ± > ∼ m t . Here eq. (2) gives the largest contribution to the production cross section, and very close to threshold eq. (1) can contribute somewhat. The relevant decay channel is again given in eq. (3). The experimental analysis, based on 30 fb −1 collected with CMS, has been presented in Ref. [19]. The fully hadronic final state topology was considered, thus events were selected with the single τ trigger at Level-1 and the combined τ -E miss T High Level trigger. The backgrounds considered were tt, W ± t, W ± + 3 jets as well as QCD multi-jet background. The tt and QCD multi-jet processes were generated with PYTHIA [23], W ± t was generated with the TopRex generator [24] and W ± + 3 jets with MadGraph [22]. The production cross sections for the tt background processes were normalized to the NLO cross sections [21]. The total background amounts (after cuts) to 1.7 ± 1 events, independently of the charged Higgs boson mass. The number of signal events is evaluated as where L denotes the luminosity, and the experimental efficiency is given in Tab. 2 as a function of M H ± . A 5 σ discovery corresponds to a number of signal events larger than 14.1.  The efficiency for the charged Higgs boson production over the full mass range considered was evaluated with the PYTHIA [23] generator processes 401 (gg → tbH ± ) and 402 (qq → tbH ± ) implemented as described in Ref. [25].

Calculation of cross section and branching ratios
While the phenomenology of the production and decay processes of the charged MSSM Higgs bosons at the LHC is mainly characterized by the parameters M A (or M H ± ) and tan β that govern the Higgs sector at lowest order, other MSSM parameters enter via higher-order contributions (see e.g. Ref. [11] and references therein), and also via the kinematics of Higgsboson decays into supersymmetric particles. The other MSSM parameters are usually fixed in terms of benchmark scenarios. The most commonly used scenarios are the "m max h " and "no-mixing" benchmark scenarios [11,16]. According to the definition of Ref. [16] the m max h scenario is given by, Here M SUSY denotes the diagonal soft SUSY-breaking parameters in the sfermion mass ma- The value of the top-quark mass in Ref. [16] was chosen according to the experimental central value at that time. For our numerical analysis below, we use the value, m t = 175 GeV, see Sect. 2. Using the current value of m t = 172.6 GeV [26] would lead to a small shift of the discovery contours right at threshold, but is insignificant for the qualitative results of this analysis. In Ref. [11] it was suggested that in the search for heavy MSSM Higgs bosons the m max h and no-mixing scenarios, which originally were mainly designed for the search for the light CP-even Higgs boson h, should be extended by several discrete values of µ (see below), µ = ±200, ±500, ±1000 GeV .
For the calculation of cross sections and branching ratios we use a combination of up-todate theory evaluations. The interaction of the charged Higgs boson with the t/b doublet can be expressed in terms of an effective Lagrangian [27], Here m b denotes the running bottom quark mass including SM QCD corrections. The prefactor 1/(1 + ∆ b ) in eq. (10) arises from the resummation of the leading tan β-enhanced corrections to all orders. The explicit form of ∆ b in the limit of heavy SUSY masses and tan β ≫ 1 reads [28] Here mt 1 , mt 2 , mb 1 , mb 2 denote thet andb masses. α s is the strong coupling constant, while α t ≡ h 2 t /(4π) is defined via the top Yukawa coupling. The analytical expression for I(. . .) can be found in Ref. [11]. Large negative values of (µ mg) and (µ A t ) (it should be noted that both benchmark scenarios have positive mg and A t ) can lead to a strong enhancement of the H ± tb coupling, while large positive values lead to a strong suppression. Concerning the m max h and the no-mixing benchmark scenarios, as discussed in Refs. [11,20] the ∆ b effects are much more pronounced in the m max h scenario, where the two terms in eq. (11) are of similar size. In the no-mixing scenario the first term in eq. (11) dominates, while the second term is small. A further suppression is caused by the larger value of M SUSY (see eq. (8)) in comparison with the m max h scenario. Consequently, the total effect of ∆ b is smaller in the no-mixing scenario (see also the discussion in Ref. [11]).
For the production cross section in eq. (1) we use the SM cross section σ(pp → tt) = 840 pb [21] 2 times the BR(t → H ± b) including the ∆ b corrections described above. The production cross section in eq. (2) is evaluated as given in Refs. [30,31]. In addition also the ∆ b corrections of eq. (10) are applied. Finally the BR(H ± → τ ν τ ) is evaluated taking into account all decay channels, among which the most relevant are H ± → tb, cs, W ( * ) h. Also possible decays to SUSY particles are taken into account. For the decay to tb again the ∆ b corrections are included. All the numerical evaluations are performed with the program FeynHiggs [32][33][34][35], see also Ref. [36].

Numerical analysis
The numerical analysis has been performed in the m max h and the no-mixing scenarios [11,16] for µ = −1000, −200, +200, +1000 GeV. We separately present the results for the light and the heavy charged Higgs and finally compare with the results in the CMS PTDR, where the results had been obtained fixing µ = +200 GeV and neglecting the ∆ b corrections, as well as neglecting the charged Higgs-boson decays to SUSY particles.

The light charged Higgs boson
In Fig. 1 we show the results for the 5 σ discovery contours for the light charged Higgs boson, corresponding to the experimental analysis in Sect. 2.1, where the charged Higgs boson discovery will be possible in the areas above the curves shown in Fig. 1

The heavy charged Higgs boson
In Fig. 2 we show the results for the 5 σ discovery contours for the heavy charged Higgs boson, corresponding to the experimental analysis in Sect. 2.2. The Higgs boson discovery will be possible in the areas above the curves. 3 As before, the experimental analysis was performed for the CMS detector and 30 fb −1 . The top quark mass is set to m t = 175 GeV. The thick (thin) lines correspond to positive (negative) µ, and the solid (dotted) lines have |µ| = 1000(200) GeV.  (2), contribute, the theoretical uncertainties are somewhat larger than in the other regions. For M H ± = 300 GeV the variation in the 5 σ discovery contours goes from tan β = 38 to tan β = 54. For µ = −1000 GeV and larger tan β values the bottom Yukawa coupling becomes so large that a perturbative treatment would no longer be reliable in this region, and correspondingly we do not continue the respective curve(s).
The shape of the µ = +1000 GeV curve has a local minimum at M H ± ≈ 300 GeV that is not (or only very weakly) present in the other curves, and that is also not visible in the original CMS analysis in Ref. [19] (obtained for µ = +200 GeV, but neglecting the ∆ b effects). The reason for the local minimum can be traced back to the strongly improved experimental efficiency going from M H ± = 200 GeV to 300 GeV, see Tab. 2. The better efficiency at M H ± = 300 GeV corresponds to a lower required cross section (∝ tan 2 β ) and/or a lower BR(H ± → τ ν τ ) to obtain the same number of signal events. On the other hand, going from M H ± = 200 GeV to 300 GeV this effect is in most cases overcompensated by a decrease of the cross section due to the increase in M H ± . The overcompensation results in an increase in tan β for the higher M H ± value. For µ = +1000 GeV, however, ∆ b is very large, suppressing strongly the charged Higgs production cross section as well as the BR(H ± → tb). The overall effect is a somewhat better reach in tan β for M H ± = 300 GeV than for M H ± = 200 GeV.
In comparison with the analysis of Ref. [11], based on the older CMS analysis given in Ref. [39], several differences can be observed. The feature of the local minimum is absent in Ref. [11], the variation of the 5 σ discovery contours with µ is weaker, and the effect of the decay of the charged Higgs boson to a chargino and a neutralino is more pronounced in Ref. [11]. The reason for these differences is the strongly reduced discovery region in the new CMS analysis [19] employed here as compared to the old CMS analysis [39] used in Ref. [11]. The reach in tan β is worse by ∼ 15 (30) for M A = 200(400) GeV in the new analysis. 4 Thus, at the substantially worse (i.e. higher) tan β values employed here the ∆ b effects are more pronounced, leading to the local minimum for µ = +1000 GeV and to a larger absolute variation in tan β with the size and the sign of µ, see Sect. 3. In the high tan β region furthermore the ∆ b effects dominate over the impact of the decay of the charged Higgs to charginos and neutralinos. As an example, for µ = +200 GeV and M H ± = 400 GeV the old analysis in Ref. [11] found that the discovery region starts at tan β = 32, where BR(H ± →χ ±χ0 ) ≈ 15%. Here we find that the discovery region starts at tan β = 64, where BR(H ± →χ ±χ0 ) ≈ 3%.
The no-mixing scenario is shown in the right plot of Fig. 2. The features are the same as in the m max h scenario. However, due to the smaller size of |∆ b |, see Sect. 3, they are much less pronounced. The variation in tan β stays at or below the level of ∆ tan β = 10 for the whole range of M H ± .

Comparison with the CMS PTDR
In Fig. 3 we show the combined results for the 5 σ discovery contours for the light and the heavy charged Higgs boson, corresponding to the experimental analyses in the m max h scenario as presented in the two previous subsections. They are compared with the results presented in the CMS PTDR [10]. Contrary to the previous sections, we now show the 5 σ discovery contours in the M A -tan β plane. The thick (thin) lines correspond to positive (negative) µ, and the solid (dotted) lines have |µ| = 1000(200) GeV. The thickened dotted (red/blue) lines represent the CMS PTDR results, obtained for µ = +200 GeV and neglecting the ∆ b effects.
Apart from the variation in the 5 σ discovery contours with the size and the sign of |µ|, two differences can be observed in the comparison of the PTDR results to the new results obtained here, i.e. including the ∆ b corrections in the production and decay of the charged Higgs boson as well as taking the decay to SUSY particles into account. For the light charged Higgs analysis the discovery contours are now shifted to smaller M A values, for negative µ even "bending over" for larger tan β values. The reason is the more complete inclusion of higher-order corrections (full one-loop and leading O(α t α s ) two-loop) to the relation between This gap is largest for µ = +1000 GeV and smallest for µ = −1000 GeV, where it amounts only up to ∼ 5 GeV. Possibly the heavy charged Higgs analysis strategy exploiting the fully hadronic final state can be extended to smaller M A values to completely close the gap. For the interpretation of Fig. 3 it should be kept in mind that the accessible area in the heavy Higgs analysis also "bends over" to smaller M A values for larger tan β, thus decreasing the visible gap in Fig. 3.

Conclusions
We have studied the variation of the 5 σ discovery contours for the search for the charged MSSM Higgs boson with the SUSY parameters. We combine the latest results for the CMS experimental sensitivities based on full simulation studies with state-of-the-art theoretical predictions of MSSM Higgs-boson properties. The experimental analyses are done assuming an integrated luminosity of 30 fb −1 for the two cases, M H ± < m t and M H ± > m t .
The numerical analysis has been performed in the m max h and the no-mixing scenarios for µ = ±200, ±1000 GeV. The impact of the variation of µ enters in particular via the higher-order correction ∆ b , affecting the charged Higgs production cross section and branching ratios. Also the decays of the charged Higgs boson to SUSY particles have been taken into account. As a general feature, large negative µ values give the largest reach, while large positive values yield the smallest 5 σ discovery areas.
The search for the light charged Higgs boson covers the the area of large tan β and M H ± < ∼ 160 GeV. The variation with µ within the m max h scenario induces a strong shift in the 5 σ discovery contours with ∆ tan β = 15 for M H ± = 100 GeV, rising up to ∆ tan β = 40 for larger M H ± values. The discovery region is largest (smallest) for µ = −(+)1000 GeV, corresponding to the largest (smallest) production cross section. The effects are similar, but much less pronounced, in the no-mixing scenario.
The search for the heavy charged Higgs boson reaches up to M H ± < ∼ 400 GeV for large tan β. Within the m max h scenario the variation of µ induces a very strong shift in the 5 σ discovery contours of up to ∆ tan β = 40 for M H ± > ∼ m t . As in the light charged Higgs case, within the no-mixing scenario the effects show the same qualitative behavior, but are much less pronounced.
Combining the search for the light and the heavy charge Higgs boson, we find a small gap, while in the CMS Physics Technical Design Report analysis all charged Higgs masses could be accessed. Possibly the heavy charged Higgs analysis strategy exploiting the fully hadronic final state can be extended to smaller M A values to completely close the gap. This issue deserves further studies.