Probing the CP-violating light neutral Higgs in the charged Higgs decay at the LHC

The CP-violating MSSM allows existence of a light neutral Higgs boson ($M_{H_1} \lapp 50$ GeV) in the CPX scenario in the low $\tan \beta (\lapp 5)$ region, which could have escaped the LEP searches due to a strongly suppressed $H_1 Z Z$ coupling. This parameter space corresponds to a relatively light $H^\pm$ ($M_{H^\pm}<M_t$), which is predicted to decay dominantly into the $W H_1$ channel. Thus one expects to see a striking $t \bar t$ signal at the LHC, where one of the top quarks decays into the $bb \bar b W$ channel, via $t \to b H^\pm, H^\pm \to W H_1$ and $H_1 \to b \bar b$. The characteristic correlation between the $b \bar b$, $b \bar b W$ and $b b \bar b W$ invariant mass peaks is expected to make this signal practically free of the SM background. Our parton level Monte Carlo simulation yields upto 5000 events, for ${\cal L} = 30$ fb$^{-1}$, over the parameter space of interest, after taking into account the b-tagging efficiency for three or more b-tagged jets.


Introduction
The search for Higgs bosons and study of their properties is one of the main goals of physics studies at the Tevatron upgrade (Run 2) and the upcoming Large Hadron Collider (LHC). The precision measurements with Electro-Weak (EW) data indicate the existence of a light Higgs boson (M h < 246 GeV at 95% C.L.) whereas direct searches rule out the case M h < 114.4 GeV [1] [2]. Naturalness arguments along with the indication of a light Higgs state suggest that Supersymmetry (SUSY) is a likely candidate for new physics Beyond the Standard Model (BSM). Even in the SUSY case, a mass for the lightest neutral Higgs smaller than ∼ 90 GeV is ruled out [3] if the SUSY parameters as well as the SUSY breaking parameters are real and CP is conserved. However, in presence of CP-violation in the Higgs sector, the lower limit can get diluted due to a reduction in the H 1 ZZ coupling [4].
CP violation, initially observed only in the K 0 -K 0 system, is one feature of the Standard Model (SM) that still defies clear theoretical understanding. It is in fact one of the necessary ingredients for generating the observed excess of baryons over antibaryons in the Universe [5,6]. The amount of CP violation present in the quark sector described very satisfactorily in the CKM picture, is however, too small to generate a baryon asymmetry of the observed level of N B /N γ ≃ 6.1 × 10 −10 [7]. New sources of CP violation beyond the SM are therefore a necessity [8].
The Minimal Supersymmetric Standard Model(MSSM), in principle, admits a large number of phases which can not be rotated away by a simple redefinition of the fields and hence provide new sources of CP-violation. A large number of these phases involving the first two generations of sparticles are strongly constrained by the electric dipole moments of the electron and neutron (EDMs) [9,10] and mercury atoms [11]. However, these constraints are model-dependent. It has been demonstrated that cancellations among different diagrams allow certain combinations of these phases to be large in a general MSSM. Furthermore, if the sfermions of the first two generations are sufficiently heavy, above the 1 TeV range, the EDM constraints on the phase of the higgsino mass parameter µ = |µ|e iφµ , in general constrained to φ µ < ∼ 10 −2 , get weaker; the sfermions of the third generation can still be light. In a version of MSSM where the Higgsino mass term µ, the gaugino masses M i and the trilinear couplings A f are complex the Higgs sector, even with CP-conserving tree level scalar potential, has loop induced CP-violation [12,13,14,15,16,17]. The LEP data can allow a much lighter Higgs with a mass < ∼ 40-50 GeV [18,19,3] due to a reduction in the H 1 ZZ coupling in the CPX scenario [13], which corresponds to a certain choice of the CP-violating SUSY parameters, chosen so as to showcase the CP-violation in the Higgs sector in this case. In a large portion of this region all the usual search channels of such a light Higgs at the LHC are also not expected to be viable [18] due to the simultaneous reduction in the coupling of the Higgs to a vector boson pair as well as the tt pair. As a matter of fact presence of CP-violation in Supersymmetry and hence the Higgs sector, can affect the Higgs decays as well as their production rates at the colliders substantially and has been a subject of many investigations [20,18].
It is interesting to note that in the same region of the parameter space where the coupling of the lightest mass eigenstate H 1 to a pair of Z-bosons: the H 1 ZZ coupling, is suppressed the H + W − H 1 coupling is enhanced because these two sets of couplings satisfy a sum-rule. The strong suppression of the H 1 ZZ coupling also means that the H 1 is dominated by the pseudo-scalar component in this region and hence implies a light charged Higgs boson (M H + < M t ). These two features suggest that H ± → H 1 W ± is the dominant decay mode of the H ± over the parameter space of interest. This motivated us to study the possibility of probing at the LHC, such a light Higgs scenario in CP violating MSSM Higgs model through the process pp → ttX → (bW ± )(bH ∓ )X → (bℓν)(bH 1 W )X → (bℓν)(bbb)(jj)+X along with the hadronic and leptonic decays of the two W ′ s interchanged. Thus the signal will consist of three or more b-tagged jets and two untagged jets along with a hard lepton and missing p T . Similar studies have been done in the context of charged Higgs search in NMSSM model [21]. In the next section we present the notation and some details of the calculation, followed by presentation of the results in the section after that and we end by making some concluding remarks.

Notation and Formalism
As already mentioned in the introduction the non-vanishing phases of µ and/or the trilinear scalar couplings A t,b can induce explicit CP-violation in the Higgs sector via loop corrections. Thus the Higgs potential, even though invariant under CP-transformation at tree level, receives CP-violating contributions on loop corrections. Due to large Yukawa interactions of the Higgs bosons to top and bottom squarks, Arg(µ) and Arg(A t ), Arg(A b ) are the relevant CP phases. These generate contributions to the off diagonal block M 2 SP in the 3 × 3 neutral Higgs boson mass-squared matrix M 2 ij , mixing the scalar (S) and the pseudo-scalar (P ) Higgs fields [12,13,14,15,16,17]. These may be given approximately by [13]: where Φ CP = Arg(A t µ), v = 246 GeV. From the above expression it is clear that sizeable scalar-pseudoscalar mixing is possible for large CP violating phase Φ CP , | µ | and | A t | (> M SUSY ). The mass scale M SUSY is defined by (m 2 )/2. After diagonalizing the 3 × 3 symmetric Higgs mass-squared matrix M 2 ij by an orthogonal matrix O, the physical mass eigenstates H 1 , H 2 and H 3 (in ascending order of mass) are states of indefinite CP parity. In this case M H ± is more appropriate parameter for description of the MSSM Higgs-sector in place of the M A used usually in the CP-conserving case.
As a result of the CP-mixing in the neutral Higgs sector, their couplings to the gauge bosons and the fermions get modified. For the purpose of illustration we provide the couplings of H i V V , H i H j Z and H i H ± W ∓ below. More details can be found in Ref. [13].
where, g H i V V , g H i H j Z and g H i H + W − are Higgs gauge boson couplings normalized to the standard model value and can be written as, These couplings obey the following sum rules: From the above sum rules one can see that if two of the g H i ZZ are known, then the whole set of couplings of the neutral Higgs boson to the gauge bosons are determined. It is interesting to see from Eq. (9) that in the presence of large CP-violating effects, with large scalar-pseudo-scalar mixing, the suppressed H 1 V V coupling means an enhanced H 1 H + W − coupling. This enhancement will play a significant role in our analysis. Equally important is the correlation between the mass of the charged Higgs M H ± and that of the pseudo-scalar state that exists in the MSSM. A suppressed H 1 V V coupling implies a light pseudo-scalar state, which in turn implies a light charged Higgs, with M H + < M t . As has been discussed before, the quantity sin Φ CP /M 2 SUSY needs to be large to get significant CP-mixing in the Higgs sector. The CP-violating benchmark scenario (CPX) has been suggested [13] to showcase this CP-violation and provides a suitable set of parameters which can be used to study the phenomenology of the CP-violating MSSM Higgs sector: Arg In the next section we first summarize the current constraints from LEP on the MSSM parameter space and hence on the Higgs masses in the CPX scenario and then discuss the phenomenology of the charged and the neutral Higgs search in the region of the low M H 1 window that is still allowed by LEP [18,19,3] for the case of CP-violating MSSM.

Results and discussion
Recently the OPAL Collaboration [19] reported their results for the Higgs boson searches in the CPviolating MSSM Higgs sector using the parameters defined in the CPX scenario as mentioned above and found that for certain values of phases and M H + , the lower mass limit on the neutral Higgs is diluted, at times vanishing completely. This results in windows in the tan β-M H + plane which are  still allowed by the LEP data. The LEP bounds are essentially evaded in this window as the lightest state is largely a pseudo-scalar with highly suppressed coupling to the ZZ pair. There exist two programs; CPSuperH [22] and FeynHiggs 2.0 [23] to calculate the masses and mixing in the Higgs sector in the CP-violating case. Due to the different approximations made in the two calculations as well as differences in the inclusion of different higher order terms, at least in the CPX scenario, the two programs give somewhat different results and the experimentalists use the lower prediction of the two for the expected cross-sections to get the most conservative constraints. The constraints also depend sensitively on the mass of the top quark used in the calculation [3]. The preliminary results from a combined analysis of all the LEP results [3], provide exclusion regions in the M H 1 − tan β plane for different values of the CP-violating phases, for the following values of the parameters: Combining the results of Higgs searches from ALEPH, DELPHI, L3 and OPAL, the authors in Ref. [18] have also provided exclusion regions in the M H 1 -tan β plane as well as M H + -tan β plane for the same set of parameters. While the exact exclusion regions differ somewhat in the three analyses [18,19,3] they all show that for phases Φ CP = 90 • and 60 • LEP cannot exclude the presence of a light Higgs boson at low tan β, mainly because of the suppressed H 1 ZZ coupling. The analysis of Ref. [18] further shows that in the same region the H 1 tt coupling is suppressed as well. Thus this particular region in the parameter space can not be probed either at the Tevatron where the associated production W/ZH 1 mode is the most promising one; neither can this be probed at the LHC as the reduced ttH 1 coupling suppresses the inclusive production mode and the associated production modes W/ZH 1 and ttH 1 , are suppressed as well. This region of Ref. [18]   As mentioned already, in the same region of the parameter space where H 1 ZZ coupling is suppressed, the H + W − H 1 coupling is enhanced because these two sets of couplings satisfy a sum-rule as shown in Eq. (9). Further, in the MSSM a light pseudo-scalar implies a light charged Higgs, lighter than the top quark. Tables 1 and 2 show the behaviour of the M H + , M H 1 and the BR (H + → H 1 W + ), for values of tan β corresponding to the above mentioned window in the tan β-M H 1 plane, of Ref. [18]. It is to be noted here that indeed the H ± is light (lighter than the top) over the entire range, making its production in t decay possible. Further, the H ± decays dominantly into H 1 W , with a branching ratio larger than 47% over the entire range where the decay is kinematically allowed, which covers practically the entire parameter range of interest; viz. M H 1 < 50(40) GeV for Φ CP = 90 • (60 • ). It can be also seen from both the tables that the BR(H ± → H 1 W ) is larger than 90% over most of the parameter space of interest. So not only that H + can be produced abundantly in the t decay giving rise to a possible production channel of H 1 through the decay H ± → H 1 W ± , but this decay mode will be the only decay channel to see this light (M H ± < M t ) H ± . The traditional decay mode of H ± → τ ν is suppressed by over an order of magnitude and thus will no longer be viable. Thus the process will allow a probe of both the light H 1 and a light H ± in this parameter window in the CP-violating MSSM in the CPX scenario. The signal will consist of three or more b-tagged and two un-tagged jets along with a hard lepton and missing p T . For a b tagging efficiency e, the suppression factor SF due to the demand of three or more tagged b jets is given by Assuming e = 0.5 we get 5/16 for this suppression factor. In our parton-level Monte Carlo analysis we employ following strategies to identify final state jets and leptons: 1. | η |< 2.5 for all jets and leptons, where η denotes pseudo-rapidity, 2. p T of the hardest three jets to be higher than 30 GeV, 3. p T of all the other jets, lepton, as well as the missing p T to be larger than 20 GeV, 4. A minimum separation of ∆R = (∆φ) 2 + (∆η) 2 = 0.4. between the lepton and jets as well as each pair of jets. If ∆R between two partons is less than 0.4 we merge them into a single jet.  Figure 1. These numbers should be multiplied by ∼ 0.5 to get the signal cross-section as explained in the text. The same mass window cuts as mentioned in Figure 1 have been used in this case.
6. We demand three or more tagged b-jets in the final state assuming a b-tagging efficiency of 50%.
7. The missing p T is obtained by vector summation of the transverse momenta of the lepton and the jets after Gaussian smearing.
Below we outline the mass reconstruction strategy we employ. The leptonically decaying W in the above decay chain is reconstructed from the lepton momentum p l and the missing transverse momentum p T within a quadratic ambiguity using the constraint that the invariant mass of the ℓν pair m ℓν = M W . In case of complex solutions the imaginary part is discarded and the two solutions coalesce. The hadronically decaying W is reconstructed from that pair of untagged jets, whose invariant mass is closest to M W . One top is then reconstructed from one of the reconstructed W's and one of the remaining jets chosen such that the invariant mass m W jet is closest to M t . Similarly the H 1 is then reconstructed from a pair from among the remaining jets, such that the invariant mass of the pair is closest to M H 1 . Then the H ± is reconstructed from this H 1 and the remaining reconstructed W. In case of a quadratic ambiguity for the latter, the one giving invariant mass closer to M H± is chosen.
Although the masses of the H 1 and H ± may not be known, one can select the right combinations on the basis of a clustering algorithm. Finally the second top is reconstructed by combining this H ± with the remaining jet.The signal cross-sections shown in Figs 1 and 2 are obtained using mass window cuts of M W ± 15 GeV, M t ± 25 GeV, M H 1 ± 15 GeV and M H ± ± 25 GeV on the reconstructed W, t, H 1 and H ± masses. Only the M W and M t mass window cuts are retained in Figures 3 and 4, showing the distributions in the reconstructed H 1 and H + masses.
In Figure 1 we show the variation of the cross-section with M H + (a) and M H 1 (b) for the CPviolating phase Φ CP = 60 • while the choice of other MSSM parameters are defined through Eqs. (11)(12)(13)(14)(15)(16). We have used the CPSuperH program [22] with M t = 175 GeV, to calculate the masses and the couplings of the Higgs-bosons in the CPX scenario. We have used the CTEQ 4L parametrisation of the parton density distributions and the QCD scale chosen is 2M t . The numbers presented in the figure contain neither the suppression factor due to b-tagging efficiency nor the K-factor(1.3-1.4) due to the NLO corrections to the tt cross-sections. Taking into account both, the numbers in the figure should be multiplied by 5/16 × 1.3-1.4 ∼ 0.5 to get the signal cross-section at the LHC. It may also be stated that the expected cross-sections at the Tevatron are far too small for this process to be useful there.
As can be seen from the figure the signal cross-section decreases with increase in tan β. This can be explained by the fact that H + → H 1 W + as well as t → bH + branching ratio decreases with the increase in tan β for a fixed H 1 mass. In this scenario, the largest signal cross-section (∼ 160 fb) can be obtained for tan β = 2 and M H + = 135 GeV, which corresponds to M H 1 = 54.3 GeV. The crosssection is ∼ 125 fb for M H + = 130 GeV corresponding to M H 1 = 40 GeV. In principle there exists a physics background to the signal arising from the decay H ± → W ±b b, via the virtual tb channel, but over this particular range of M H ± and tan β the corresponding branching ratio is negligibly small [24].
In Figure 2, we show variation of the signal cross-section with M H + (a) and M H 1 (b) for the CP-violating phase Φ CP = 90 • keeping other MSSM parameters fixed as in Figure 1. Apart from the choice of the phase, the main difference from Figure 1 is in the values of tan β. In this case we have somewhat larger values of tan β, namely 3.6, 4., 4.6 and 5., corresponding to the light Higgs window of Ref. [18] for Φ CP = 90 • . The largest signal cross-section in this case is ∼ 38 fb. Note that in both cases the signal cross-section is > ∼ 20 fb for M H 1 > ∼ 15 GeV.
In Figure 3 (a) we show the three-dimensional plot for the correlation between m bb and m bbW invariant mass distribution for Φ CP = 60 • , tan β = 2 and M H + = 125.6 GeV. The light Higgs mass corresponding to this set of input parameter is 24.8 GeV. It is clear from Figure 3 that there is simultaneous clustering in the m bb distribution around ≃ M H 1 and in the m bbW distribution around M H ± . Figure 3(b) shows the same, in terms of cross-section distribution in bb, bbW and bbW b invariant masses for the signal. The clustering feature can be used to distinguish the signal over the standard model background. As a matter of fact we estimated the background to the signal coming from the QCD production of ttbb. Even though the starting LO cross-section for ttbb production is as high as ∼ 8.5 pb, once all the cuts (including the mass window cuts) are applied we are left with a contribution to the signal type events of less than 0.5 fb. The major reduction is brought about by requiring that the invariant mass of the bbbW be within 25 GeV of M t 1 . This makes it very clear that the detectability 1 Preliminary studies in ATLAS collaboration presented at Les Houches Workshop [25] also find that this background Note further that this process would be the only channel of discovery for the charged Higgs-boson H ± as well in this scenario, as the traditional decay mode of H ± → ντ is suppressed by over an order of magnitude. Figure 4(a) shows the three-dimensional plot for the correlation between m bb and m bbW invariant mass distribution for Φ CP = 90 • , and somewhat higher values of tan β and M H + , tan β = 5 and M H + = 133 GeV. The light Higgs mass corresponding to this set of input parameter is 51 GeV. The Figure 4(b) shows the same, in terms of cross-section distribution in bb,bbW andbbbW invariant can be suppressed to negligible levels by similar requirements.  Figure 3. It should be mentioned here that the combinatorial background has already been included in the inclusive bb and bbW invariant mass distributions plotted in Figures 3-4 whereas the three dimensional plots showing the correlation do not include this. Within the framework of the mass reconstruction strategy outlined before, after the reconstruction of t → bW , one is left with three b jets and a W . The former correspond to three possible invariant bb masses for each MC point. It is seen from Figures  3 and 4 that even after inclusion of all the possible pairs at each point the peak at the H 1 mass is clearly visible. Now for further reconstruction one can choose the pair with invariant mass closest to the peak and then calculate the bbW invariant mass by combining this pair with the remaining W. In case of quadratic ambiguity for the W both the values for the W bb invariant mass are retained. Again, we see a clear peak at the H + mass. Finally combining this with the remaining b gives the W bbb invariant mass which peaks at M t . In case of quadratic ambiguity for the W we have chosen the W bb combination with invariant mass closer to the H + mass peak. In the three dimensional plot of Figures 3-4 we show the pair of invariant masses corresponding to this combination of W bb as well as the bb invariant mass closest to H 1 mass. We have found that about 50% of the signal events will have more than one combination of the bb and bbW invariant masses in the window M H 1 ± 15 GeV and M H + ± 25 GeV respectively, when one includes all the combinations. Thus the combinatorial background is important but does not seem to overwhelm the signal.
A comment about the M t dependence of our results is in order. If the value of M t used is increased from 175 to 178 GeV, typically the mass difference M H + -M H 1 goes up by about 7-8 GeV and thus the curves in Figures 1 and 2 will extend to M H 1 values higher by about 7-8 GeV. We, however, have used the more conservative value of 175 GeV for M t . as the window in the tan β-M H + window which we explore, has been obtained using M t = 175 GeV in Ref. [18]. Since the size of the window where LEP has no reach also gets bigger with an increased value of M t [19,3], the above observation simply implies that the region which the process t → bH ± → bH 1 W → bbbW can probe will also be bigger in that case.

Conclusions
Thus we have looked in the CPX scenario, in the CP-violating MSSM, at the region in the tan β-M H ± plane, where a light H 1 signal might have been lost at LEP due to strong suppression of the H 1 ZZ coupling and where the Tevatron and the LHC will have no reach due to a simultaneous suppression of the H 1 tt coupling as well. Specifically, we concentrated in the MSSM parameter space 3.5 < tan β < 5, M H 1 < ∼ 50 GeV and 2 < tan β < 3, M H 1 < ∼ 40 GeV, for the common CP violating phase Φ CP = 90 • and 60 • respectively, which correspond to the light H 1 window of [18]. We find that a light charged Higgs (M H ± < M t ) with a large value for the branching ratio for the decay H ± → H 1 W is realised almost over the entire parameter space that we considered. We find that such a light H 1 and light H ± , can be probed at the LHC in tt signal where one of the top quarks decays into the bbbW channel, via t → bH ± , H ± → W H 1 and H 1 → bb. Our parton-level Monte Carlo yields upto ∼ 1100-5000 events for a L = 30 fb −1 corresponding to the CP-violating phase Φ CP = 90 • and 60 • respectively. The events will show a very characteristic correlation between the bb, bbW and bbbW invariant mass peaks, indicating that the SM background may be negligible. Further, in a considerable part of this region, the branching ratio for the H ± → τ ν channel, that is normally used for the charged Higgs search, is reduced by over an order of magnitude. Thus, this tt signal will be a probe of both a light neutral H 1 and a light charged Higgs H ± . It is imperative that this investigation is followed up with a more exact simulation using event generator level Monte Carlo and detector acceptance effects, which is beyond our means. We hope that the encouraging results from this parton level Monte Carlo study will induce the CMS and the ATLAS collaborations to undertake such investigations. 05HT1RDA/6. DKG would also like to thank US DOE contract numbers DE-FG03-96ER40969 for financial support during the initial stages of this work.