Prospects of mass measurements for neutral MSSM Higgs bosons in the intense-coupling regime at a Linear Collider

We analyze the prospects for detecting the three neutral Higgs bosons of the Minimal Supersymmetric extension of the Standard Model in the intense-coupling regime at e+e- colliders. Due to the small mass differences between the Higgs states in this regime and their relative large total decay widths, the discrimination between the particles is challenging at the LHC and in some cases even impossible. We propose to use the missing mass technique in the Higgs-strahlung process in e+e- collisions to distinguish between the two CP-even Higgs eigenstates h and H, relying on their b b-bar decay in the b,b-bar,l+,l- event sample. Ah and AH associated production is then studied in the 4b-jet event sample to probe the CP-odd A boson. At collider energies sqrt(s) = 300 GeV and an integrated luminosity of 500 fb-1, accuracies in the mass measurement of the CP-even Higgs bosons are expected to range from 100 to 300 MeV, while for the CP-odd A boson, accuracies of less than 500 MeV can be obtained.

In the Minimal Supersymmetric Standard Model (MSSM), two Higgs doublets are needed to break the electroweak symmetry and therefore, there are five physical Higgs states: two CP-even Higgs particles h and H, a CP-odd or pseudoscalar Higgs boson A, and two charged Higgs particles H ± [1]. The intense-coupling regime [2,3] is characterized by a rather large value of the ratio of the vacuum expectation values of the two doublet fields, tan β = v 2 /v 1 > ∼ 10, and a mass for the pseudoscalar A boson that is close to the maximal (minimal) value of the CP-even h (H) boson mass. In such a scenario, an almost mass degeneracy of the neutral Higgs particles occurs, M h ∼ M A ∼ M H ∼ 100-140 GeV. The couplings of both the CP-even h and H particles to gauge bosons and isospin up-type fermions are suppressed, and their couplings to down-type fermions, in particular to b-quarks and τ leptons, are strongly enhanced. The interactions of both Higgs particles therefore approach those of the pseudoscalar Higgs boson which does not couple to massive gauge bosons as a result of CP invariance, and for which the couplings to isospin − 1 2 (+ 1 2 ) fermions are (inversely) proportional to tan β. Because of this enhancement, the branching ratios of the h and H bosons into bb and τ + τ − final states are by far dominant, with values of ∼ 90% and ∼ 10%, respectively, similarly to the pseudoscalar Higgs case. A corollary of this feature is that the total decay widths of the three neutral Higgs particles are rather large, being of the same order as the mass differences.
As discussed in Ref. [3], this leads to a rather difficult situation for the detection of these particles at the LHC. The branching ratios of the interesting decays which allow the detection of the CP-even Higgs bosons, namely γγ, W W * → ℓℓνν and ZZ * → 4ℓ, are too small and prevent serious analyses. The bb decay mode has a too large QCD background to be useful. For τ + τ − decays, the expected experimental resolution on the invariant mass of the tau system is about 10-20 GeV and thus clearly too large for distinct Higgs particle observation; rather, one would simply observe a relatively broad excess over the background, corresponding to A and h and/or H production. A way out, as suggested in Ref. [3], is to rely on the decays into muon pairs with the Higgs bosons produced in association with bb pairs, gg/qq → bb + Φ with Φ = h, H and A; see also Ref. [4]. Although the decay is rare, BR(Φ → µ + µ − ) ∼ 3.3 × 10 −4 , the dimuon mass resolution is expected to be as good as 1 GeV, i.e. comparable to the Higgs total widths for M Φ ∼ 130 GeV 1 . However, even in this case, it is possible to resolve only two Higgs peaks in favorable situations. In general, the detection of the three individual Higgs bosons is very challenging, and in some cases even impossible at the LHC 2 .
1 The Higgs-strahlung and vector-boson fusion processes for the production of the h and H bosons, as well as associated production of the three neutral Higgs particles with top quarks, will have smaller cross sections than in the SM due to the suppressed couplings of the particles involved. The production of the three Higgs particles in the gluon-gluon process, gg → Φ → µ + µ − , although bearing large rates will suffer from the huge Drell-Yan pp → γ * , Z * → µ + µ − background process [3]. 2 An alternative possibility at the LHC is diffractive Higgs production [5] where, based on the recoil mass technique, very good proton beam energy resolution and precise luminosity measurements are crucial to resolve the Higgs signals and perform accurate mass determinations.
In e + e − collisions [6], the CP-even Higgs bosons can be produced in the Higgs-strahlung, e + e − → Z + h/H, and in the vector-boson fusion, e + e − → νν + h/H, processes. The CPodd particle cannot be probed in these channels due to its zero-couplings to gauge bosons at tree level, but it can be produced in association with the h or H bosons in the reactions e + e − → A + h/H. Earlier studies [7] indicated that the vector boson fusion processes are difficult to use in this context, as the full final state cannot be reconstructed. In turn, the Higgs-strahlung and the Higgs pair production processes, as will be demonstrated in this note, have a great potential to explore the individual h, H and A states in the intense-coupling regime and to allow the measurement of their masses.
The cross sections for the Higgs-strahlung and pair production processes are mutually complementary coming either with a coefficient sin 2 (β − α) or cos 2 (β − α), with α being the mixing angle in the CP-even Higgs sector: where σ SM is the SM Higgs cross section in the strahlung process andλ ∼1 for √ s ≫ M A accounts for P-wave suppression near the kinematical threshold for the production of two spin-zero particles. Since σ SM is rather large, being of the order of 50-100 fb for a Higgs boson with a mass ∼ 130 GeV at a c.m. energy √ s ∼ 300-500 GeV, the production and the detection of the three neutral Higgs bosons should be straightforward for an integrated luminosity of L ∼ 0.5-1 ab −1 , as expected at future linear e + e − colliders such as TESLA [7].
In Fig. 1, the production cross sections for the Higgs-strahlung and Higgs pair production of the neutral Higgs particles are shown as a function of the c.m. energy. We have chosen the same three representative scenarios P1, P2 and P3 discussed in Ref. [3]: tan β = 30 and M A = 125, 130 and 135 GeV. The maximal mixing scenario where the trilinear Higgs-stop coupling is given by A t ≃ √ 6M S with the common stop masses fixed to M S = 1 TeV has been adopted; the other SUSY parameter will play only a minor role and have been set to 1 TeV, while the top quark mass is fixed 3 to m t = 175 GeV. The resulting Higgs masses, couplings and branching ratios shown in Table 1 have been obtained using the program HDECAY [8] in which the routine FeynHiggsFast [9] is used for the implementation of the radiative corrections. As apparent from Fig. 1, values of √ s not too far above the kinematical thresholds of these reactions are favored within our scenarios with M Φ ∼ 130 GeV, since the cross sections scale like 1/s as the processes are mediated by s-channel gauge boson exchange. We will thus choose to operate the e + e − collider at √ s = 300 GeV in the present analysis, as the production cross sections are large enough for all cases considered.  The Higgs-strahlung processes offers the most promising way to discriminate between the two CP-even Higgs particles, since the pseudoscalar boson A is not involved. For the SM Higgs boson, as was widely demonstrated, the recoil mass technique in both leptonic and hadronic Z decays allow very precise determination of its mass; for instance an accuracy of ∼ 40 MeV for a mass of ∼ 120 GeV can be achieved [7]. In the intense-coupling scenario, where the two scalar h and H bosons are close in mass and are often produced with different rates, some of them being small, the impact of initial state radiation (ISR) and beamstrahlung is important and should be carefully taken into account. We have performed a detailed simulation, including the signal and all the main background reactions using the program package CompHEP [10] interfaced [11] with PYTHIA [12], as well as a simulation of the detector response with the code SIMDET [13]. The analysis reveals that the most promising way for measuring the h and H boson masses is to select first the ℓ + ℓ − bb event sample (ℓ = e/µ), followed by the recoil Z mass technique. However, without cuts and b-quark tagging, the signals from the h and H bosons cannot be resolved, as illustrated in Fig. 2 in the case of the parameter point P1. If some realistic b-tagging is applied and the surviving bbℓ + ℓ − events are required to pass the following cuts: i) the dilepton invariant mass is within M ℓ + ℓ − = 90 ± 6 GeV, i.e. compatible with the Z boson, ii) each jet energy has E j ≥ 12 GeV, iii) the angle between two jets is (j 1 , j 2 ) ≥ 95 degrees, the separation of the two Higgs signal peaks is possible and the masses are accessible. Simulation results for the case of TESLA, as an example, and for the MSSM parameter points P1, P2 and P3 are shown in Fig. 3. The selection efficiencies are found to be 68% for the signal reaction, while they are at the level of 22% for the ℓ + ℓ − bb, 6.4% for the ℓ + ℓ − cc and 0.1% for the ℓ + ℓ − qq (q = u, d, s) background processes. As evident from Fig. 3, the masses of the h and H particles can be determined with accuracies of the order of 100-300 MeV at a 300 GeV collider energy and with 500 fb −1 accumulated luminosity. Such uncertainties in the mass measurements are significantly smaller than the typical mass differences between the two Higgs states. They are however larger than the corresponding accuracy for the SM Higgs boson. At higher c.m. energies, the mass determination will be significantly worse as a consequence of the smaller production cross sections, degraded energy resolution of the more energetic leptons and the stronger impact of ISR and beamstrahlung. It would become very difficult to resolve the h and H signals as is demonstrated in Fig. 4 for √ s = 500 GeV and two times larger Once the h and H boson masses are known from the recoil mass technique, attention should be directed to the mass determination of the A particle which can be probed in the complementary pair production channels e + e − → A + h/H. This can be achieved either via the reconstruction of the bb and/or τ + τ − invariant masses or through a threshold scan. The first method has been discussed in Ref. [14] for the production of heavier Higgs bosons in the decoupling limit M A ∼ M H ≫ M Z , in the reaction e + e − → HA → 4b at √ s = 800 GeV. Accuracies of about 100 MeV for the H/A masses were obtained sufficiently above the reaction thresholds using the dominant bbbb and bbτ + τ − final states [15].
In the intense-coupling regime, the three neutral Higgs bosons contribute to the bbbb and bbτ + τ − final state signals. Since typical b-jet energy resolutions are close to or somewhat larger than the Higgs mass differences, it is challenging to discriminate between the A → bb and the h/H → bb decays, as illustrated in Fig. 5 where all possible bb mass combinations for the signal and the sum of signal and background events are shown for the parameter point P1 as an illustration.
To associate the correct bb mass combination to the A and h/H boson decay into 4b final state events, we use the "combinatorial mass difference" method. After selecting 4bjet events by means of b-tagging, we consider all three possible combinations of 2 b-jet pairs. Only one of them is the "physical" combination where both b-quarks in each pair correspond to one of the decaying Higgs particles, while the other two combinations are combinatorial background.
Because of the well defined kinematics in the process e + e − → A + h/H → bb bb, the angle between two b-jets in the Higgs decay is about 115 • for our parameter set and independent of the Higgs particles since their masses are almost degenerate. The influence of ISR and beamstrahlung leads to some smearing of the corresponding angular distribution as shown in the left-hand side of Fig. 6. A sharp distribution is evident for the "correct" or signal b-jet pair, while the combinatorial b-jet background pairing leads to a flat distribution.
In addition, b-jet pairs originating from Higgs decays are more centrally produced than the combinatorial background, as evident from the right-hand side of Fig. 6. Thus, the separation of the "physical" combinations from the combinatorial background might be achieved by means of the following cuts: i) −0.95 < cos θ b 1 b 2 < −0.3 and ii) | cos θ bb−pair | < 0.7, where θ b 1 b 2 is the angle between two b-jets and θ bb−pair the polar angle of the bb system. The "physical pairs" are selected with an efficiency of about 85%, whereas the background combinations are selected with an efficiency of about 20%.
In the discrimination between Ah and AH production, we use the average mass, M =  Finally, the selection of the pseudoscalar boson A from the Ah and AH pairing relies on some probability estimation based on the function If, for instance, the former step favors Ah production for a particular 4b-jet event, the function P gives the probability that the first chosen invariant mass M 1 is the mass of the h boson. This probability value is compared with a uniformly distributed random number r in the range [0, 1]. If P > r, the association M h = M 1 and M A = M 2 is performed, whereas for the opposite case P < r, we assign M h = M 2 and M A = M 1 . The same procedure is applied if AH pair production has been favored in the first step. Resulting bb mass spectra for the MSSM parameter points P1, P2 and P3 are shown in Fig. 7. Only the 2b-jet masses which have been assigned to the pseudoscalar A boson are displayed, and all 4b-jet background sources have been taken into account.
As fits to these histograms revealed, the mass of the pseudoscalar Higgs boson A can be measured with an accuracy of 300 to 500 MeV, once the measured masses of the h and H particles with their corresponding errors have been taken into account. Such experimental accuracies, although larger than those for the SM Higgs boson, are smaller than the typical mass differences M A − M h or M H − M A in the chosen scenarios.
One may expect a more precise determination of the mass values for the A boson by measuring the e + e − → A + h/H production cross sections near the respective kinematical thresholds, where the cross sections rise as σ ∼ β 3 with β ∼ 1 − 4M 2 A /s. This is very similar to scalar lepton pair production in e + e − collisions, e + e − →ll in supersymmetric models, which has many common characteristics with the process discussed here. Indeed, it has been shown [16] that slepton masses of the order of 100 GeV can be measured with an accuracy of less than 0.1% in a threshold scan. Whether this holds also true for e + e − → A + h/H production in the intense-coupling regime [the production cross sections are smaller but the final states are cleaner] has to be studied in detail, including ISR and beamstrahlung. This study is however beyond the scope of this note.
In conclusion, the intense-coupling regime in the MSSM Higgs sector, in which tan β is rather large and the three neutral h, H and A Higgs particles have comparable masses, is a difficult scenario to be resolved completely at the LHC. In e + e − collisions, thanks to the clean environment and to the complementarity of the available production channels, the separation of the three states is possible. The Higgs-strahlung processes allows first to probe the h and H bosons and to measure their masses from the recoiling mass spectrum against the Z boson; the best results are obtained by selecting the bb + ℓ + ℓ − event sample and imposing b-jet tagging. Then, associated CP-even and CP-odd Higgs production would allow to probe the pseudoscalar A boson by direct reconstruction of its decay products. At collider energies √ s ≃ 300 GeV and with integrated luminosities of 500 fb −1 , accuracies for the measurement of the masses of the three neutral Higgs particles are expected to range from 100 to 500 MeV, which is smaller than the typical Higgs mass differences in this scheme.
In the study of the intense-coupling regime, the interplay between the LHC and a future linear collider might be very important: on the one hand, any broad peak information observed at the LHC will assist the choice of the appropriate energy at the LC and on the other hand, characteristics of the Higgs states as measured at the linear collider could constrain techniques to access further observables at the LHC such as the gluon-gluon-Higgs couplings and the Φ → µ + µ − branching ratios, as the processes gg → Φ → µ + µ − might be then possible to detect, a posteriori.