Closing the Window on Light Charged Higgs Bosons in the NMSSM

Abstract

In the Next-to-Minimal SuperSymmetric Model (NMSSM) the lightest CP-odd Higgs bosons (𝑎₁) can be very light. As a consequence, in addition to the standard charged Higgs boson (ℎ^±) decays considered in the MSSM for a light charged Higgs (𝑚_ℎ^±<𝑚_𝑡), the branching fraction for ℎ^±→𝑎₁𝑊 can be dominant. We investigate how this signal can be searched for in 𝑡𝑡 production at the Large Hadron Collider (LHC) in the case that (𝑚_𝑎1≳2𝑚_𝐵) with the 𝑎₁ giving rise to a single 𝑏𝑏-jet and discuss to what extent the LHC experiments are able to discover such a scenario with an integrated luminosity ~20 fb⁻¹. We also discuss the implications of the possible Higgs-signal observed at the LHC.

1. Introduction

With the successful start-up of the LHC and the intriguing results from the first year of data-taking at the center of mass energy of 7 TeV and an integrated luminosity close to ≈5 fb⁻¹ for each of the ATLAS and CMS experiments, the ongoing run in 2012 is set to be a milestone in particle physics. The possible signal for a Higgs boson around 125 GeV may or may not be confirmed and the search for physics Beyond the Standard Model (BSM) will continue. Contrary to the neutral Higgs boson, which if discovered may need to be analyzed in detail regarding its branching fraction into various channels in order to determine whether it is the Standard Model (SM) Higgs boson or not, the discovery of a charged Higgs boson would be an unmistakable sign of BSM physics.

The charged Higgs boson arises in theories with more than one Higgs doublet. The prime example is the MSSM [1, 2] which has two Higgs doublets, leading to two CP-even Higgs bosons (ℎ,𝐻) and one CP-odd (𝐴) in the case of CP-conservation and two charged states (𝐻^±) after electroweak symmetry breaking. In this case the two Higgs doublets are required by supersymmetry with one of them giving masses to the uptype fermions and one to the downtype ones. For a complete introduction to the Higgs sector in the MSSM we refer to [3].

The main reason for introducing supersymmetry (for a general introduction to supersymmetric theories we refer to [4]) is to solve the so-called hierarchy problem, that is, why the scale of the electroweak interaction is so much smaller than the cut-off of the SM, normally taken to be the Planck mass where gravity becomes the dominant force and the SM breaks down. With the Higgs boson being a scalar particle, the higher-order corrections to its mass are proportional to this cut-off and with the SM only being an effective theory this cut-off dependence cannot be renormalized away. In a supersymmetric theory this problem is essentially solved by the introduction of the fermionic partners of the Higgs fields, which only get logarithmic corrections to their masses and thereby avoids fine-tuning. In turn this means that the Higgs boson masses are also protected from receiving quadratic corrections as long as supersymmetry is not broken or only softly broken.

In addition to solving the hierarchy problem supersymmetry also offers a candidate for cold dark matter [5, 6] in the case that 𝑅-symmetry is preserved, which in turn is introduced to avoid terms in the Lagrangian that otherwise would mediate proton decay. In this case the lightest supersymmetric particle (LSP) is stable and generically it has the right mass and cross-section to constitute the observed dark matter. Supersymmetry also improves the unification of gauge forces at an hypothesized grand unification scale although the unification is not exact and it does depend on the details of the spectrum of SUSY-particles.

As is well known, the MSSM by itself is not without problems. Leaving the question of the precise mechanism for supersymmetry breaking aside, the MSSM faces the so-called 𝜇-problem. This relates to the magnitude of the dimensionful 𝜇-parameter which couples the two Higgs doublets to each other in the superpotential. In order to avoid large cancellations between this contribution to the Higgs masses and the soft supersymmetry breaking terms as well as having a phenomenologically viable supersymmetric theory (mainly having a large enough chargino mass), the magnitude of 𝜇 should be of order the electroweak or supersymmetry breaking scales. The problem is then that there is no a priori reason for this parameter to have any particular value, in principle it could be anything up to the Planck scale, so why is it similar to the electroweak or supersymmetry breaking scales?

In the NMSSM the 𝜇-problem is solved by introducing an additional Higgs singlet into the theory. After supersymmetry breaking this field gets a vacuum expectation value (vev) that effectively acts as a 𝜇-term. The original 𝜇-term in the superpotential can then be set to zero without spoiling the viability of the theory. For a more detailed review of the NMSSM we refer to [7, 8].

The additional Higgs singlet has important consequences for the phenomenology of the Higgs sector. In the MSSM, the masses of the heavy Higgs bosons (𝐻,𝐴,𝐻^±) are closely related to each other as they originate from the same (second) Higgs doublet if viewed in the Higgs basis where only one (the first) of the Higgs doublets has a vev. For example, at tree-level the masses of the CP-odd and charged Higgs bosons are related by 𝑚²_𝐻^±=𝑚²_𝐴+𝑚²_𝑊. As a consequence the decay 𝐻^±→𝐴𝑊 is typically not open.

In the NMSSM the additional Higgs singlet means that there is one more CP-even and one more CP-odd field with a separate mass scale introduced into the Higgs sector. As a consequence, the by now three CP-even and two CP-odd electroweak states will mix into the respective mass eigenstates. Thus the mass-relations from the MSSM will be altered. This is particularly evident in the CP-odd sector where the lightest state 𝑎₁ may now be much lighter than the charged Higgs boson—even after taking experimental constraints into account as discussed below—opening up the possibility for the ℎ^±→𝑎₁𝑊 decay to be dominant. In turn this means that the search for charged Higgs bosons, in 𝑡-quark decays for example, has to be widened also to include this decay channel.

The decay ℎ^±→𝑎₁𝑊 has already been considered to different levels of detail [9–11] in the literature and there are constraints from the DELPHI experiment for 𝑚_𝑎1>12 GeV [12], as well as the CDF experiment for the case 𝑎₁→𝜏⁺𝜏⁻ [13]. In this paper we want to focus on the region in parameter space where the 𝑎₁ mass is above the 𝑏𝑏 threshold but still so close to it that the two 𝑏-quarks will fragment into a single 𝑏𝑏-jet. The viability of scenarios with light 𝑎₁’s has also been considered by [14–18].

Our paper is organized as follows. In the next section we give some basic properties of the Higgs sector in the NMSSM that are relevant to our discussion. We then discuss the constraints on the parameter space in Section 3, including the latest results from LHC. In Section 4 we illustrate how the signal ℎ^±→𝑎₁𝑊 can be searched for in 𝑡𝑡-production taking into account the appropriate backgrounds. Section 5 contains a discussion of the implications of the possible Higgs signal from the ATLAS and CMS experiments and in Section 6 we summarize and conclude.

2. Basic Properties of The NMSSM

We consider the 𝑍₃-symmetric version of the NMSSM with the superpotential given by 𝑊_NMSSM=𝑊_MSSM+𝜆𝑆𝐻_𝑢⋅𝐻_𝑑+𝜅𝑆³, (2.1) where 𝑊_MSSM is the superpotential of the MSSM with 𝜇 set to zero. The soft supersymmetry breaking potential relative to the MSSM is then given by 𝑉^NMSSM_soft=𝑉^MSSM_soft+𝑚²_𝑆|𝑆|²+𝜆𝐴_𝜆𝑆𝐻_𝑢⋅𝐻_𝑑+13𝜅𝐴_𝜅𝑆³+ℎ.𝑐., (2.2) where the part of 𝑉^{M𝑆𝑆𝑀}_soft only depending on the Higgs fields is given by, 𝑉^MSSM_soft,higgs=𝑚²_𝐻𝑢𝐻_𝑢²+𝑚²_𝐻𝑑𝐻_𝑑². (2.3)

In addition 𝑉^MSSM_soft contains all the dependence on the other soft supersymmetry breaking parameters: the gaugino masses 𝑀₁,𝑀₂,𝑀₃, the trilinear couplings 𝐚_𝑢,𝐚_𝑑,𝐚_𝑒, the squark masses 𝐌_𝑄,𝐌_𝑢,𝐌_𝑑, and finally the slepton masses 𝐌_𝐿,𝐌_𝑒. In the following we will assume minimal flavour violation so that the sfermion mass matrices are diagonal and the trilinear couplings are proportional to the corresponding Yukawa coupling matrices 𝐚_𝑢=𝐴_𝑢𝐲_𝑢, and so forth.

After electroweak symmetry breaking, and assuming that CP is conserved, the Higgs sector will contain three CP-even Higgs bosons (ℎ₁,ℎ₂,ℎ₃), two CP-odd (𝑎₁,𝑎₂), and one charged (ℎ^±), where the states are ordered in terms of increasing mass. In the same way as in the MSSM the minimization conditions for the Higgs potential allow one to trade the 𝑚_𝐻𝑢,𝑚_𝐻𝑑 parameters for the doublet vev 𝑣≈174 GeV and tan𝛽=𝑣_𝑢/𝑣_𝑑. Similarly 𝑚_𝑆 can be expressed in terms of the singlet vev 𝑣_𝑠 which in turn gives rise to the effective 𝜇-parameter, 𝜇=𝜆𝑣_𝑠. All in all this leaves us with 6 unknown parameters describing the Higgs sector of NMSSM at tree-level: tan𝛽,𝜇,𝜆,𝜅,𝐴_𝜆,𝐴_𝜅. Below we will trade the latter two parameters for the masses 𝑚_ℎ^± and 𝑚_𝑎1.

As already alluded to the mass-eigenstates are mixtures of the electroweak eigenstates. More specifically, writing 𝑆^weak=(Re(𝐻_𝑢),Re(𝐻_𝑑),Re(𝑆)) we have ℎ_𝑖=𝐒_𝑖𝑗𝑆^weak_𝑗. (In the MSSM limit this means that 𝐒₁₂=−sin𝛼.) Similarly for the CP-odd states we have 𝑎_𝑖=𝐀_𝑖𝑗𝐴^weak_𝑗 with 𝐴^weak=(Im(cos𝛽𝐻_𝑢+sin𝛽𝐻_𝑑),Im(𝑆)). Here the mixing matrix is simply 𝐀=^{cos𝜃𝐴sin𝜃𝐴}_{−sin𝜃𝐴cos𝜃𝐴}. Together with the ratio of the two doublet vevs (or equivalently the rotation angle needed to go to the Higgs basis where only one of the doublets have a vev) tan𝛽, the mixing matrices 𝐒 and 𝐀 specify the reduced couplings to fermions and gauge bosons as given in Table 1.

Table 1 

Reduced Higgs couplings in the NMSSM compared to the MSSM and the SM (when applicable). Note that the reduced couplings to fermions are identical for all three generations, even if only the third generation is displayed here. The couplings to ℎ₃ can be obtained from the ℎ₁ ones by the replacements 𝐒₁₁→𝐒₃₁ and 𝐒₁₂→𝐒₃₂ whereas the couplings to 𝑎₂ can be obtained from the 𝑎₁ ones by the replacement cos𝜃_𝐴→sin𝜃_𝐴.

3. Experimental Constraints

In this section we will explore to what extent the process we are interested in is constrained by existing experimental data. Since we are interested in a light ℎ^± (with 𝑚_ℎ^±<𝑚_𝑡) and a light 𝑎₁ there are constraints both from collider experiments as well as low-energy flavour experiments. However, before going into the various constraints we will specify the scenarios that we have considered and then come back to the question of experimental constraints.

3.1. Specification of SUSY Scenario Considered

In the following we will consider a variant of the well motivated 𝑚_ℎ^max-scenario in the MSSM [19], similarly to what was done in [17]. Thus we will consider a universal scale 𝑀_SUSY for the sfermion masses at the supersymmetry breaking scale. In other words we assume, as already stated, that the sfermion mass matrices (𝐌_𝑄 etc.) are diagonal, and furthermore we assume that all diagonal entries are equal to 𝑀_SUSY which we keep fixed at 1 TeV. In addition we assume that the gaugino masses are related as in the constrained MSSM, where supersymmetry breaking is assumed to be mediated by gravity, namely, 𝑀₁=100 GeV, 𝑀₂=200 GeV, 𝑀₃=800 GeV. Finally we will assume that 𝐴_𝑡=𝐴_𝑏=𝐴_𝜏 but contrary to what was done in [17] we will let them vary in the range 𝐴_𝑡∈[−5000,5000] GeV so that the amount of mixing between the 𝑡_𝐿̃ and 𝑡_𝑅̃ is unconstrained.

For the Higgs sector we will let all six parameters vary freely. However, as was done in [17], we will trade the 𝐴_𝜅 parameter for 𝑚_𝑎1 and 𝐴_𝜆 parameter for 𝑚_ℎ^± using an iterative procedure starting from the tree-level relations: 𝑚²_ℎ^±=2𝜇𝐴sin2𝛽^𝜆+𝜅𝜆𝜇+𝑚²_𝑊−𝜆²𝑣²ℳ²_𝑃=2𝜇𝐴sin2𝛽^𝜆+𝜅𝜆𝜇𝜆𝑣𝐴_𝜆𝜅−2𝜆𝜇𝜆𝑣𝐴_𝜆𝜅−2𝜆𝜇𝜆²𝑣²sin2𝛽𝐴2𝜇^𝜆𝜅+4𝜆𝜇𝜅−3𝜆𝐴_𝜅𝜇, (3.1) where the latter gives the masses of the mass-eigenstates 𝑎₁, 𝑎₂ after diagonalisation. Thus the parameters we consider with their respective ranges are: [],[],[],[]𝑚tan𝛽∈1,60𝜆∈0,0.7𝜅∈−0.7,0.7𝜇∈125,1000GeV,_ℎ±∈[]𝑚80,170GeV,_𝑎1∈[4,150]GeV. (3.2)

The limits for the various parameters have been chosen as follows: For tan𝛽, 𝜅 and 𝜆 we impose perturbativity up to the GUT scale which effectively means that any value out side the above regions is bound to fail. (In addition some points inside these regions also fail because of this requirement.) The lower limits on 𝜇 and 𝑚_ℎ^± are dictated by experimental constraints. The upper limit on 𝜇 is not a hard one but follows from the implicit assumption that 𝜇 should be of order the electroweak scale whereas the upper limit on 𝑚_ℎ^± is given by the condition that the decay 𝑡→𝑏ℎ⁺ should be open. The reason for letting 𝜇 vary freely is mainly that this decreases the correlations between the masses of the Higgs bosons as will be discussed more below. Finally the lower limit on 𝑚_𝑎1 is chosen in order to have 𝑎₁→𝜏⁺𝜏⁻ open whereas the upper limit follows from having 𝑚_ℎ^±<170 GeV.

In order to calculate the resulting models from the inputs we use the package NMSSMTools version 3.2.0 [20, 21] with default settings. Among other things this means that we impose perturbativity of the model up to the GUT scale. Finally, in all scans we generate ~1 M points (with flat priors in the parameters considered) which fulfill the theoretical constraints implemented in NMSSMTools.

3.2. Current Experimental Constraints

The most important constraints come from the direct searches for Higgs bosons for which we use the package HiggsBounds version 3.7.0 [22, 23]. In addition there are also constraints from direct searches for supersymmetric particles, various flavour constraints and in principle also the anomalous magnetic moment of the muon as well as the relic density of dark matter. We have not applied the latter two constraints for the following reasons. To investigate the amount of dark matter in the various models one would also need to vary the gaugino masses as was done in [24]. Since we keep these fixed we have not applied the dark matter constraints. On the same vain we have not applied the constraint from the anomalous magnetic moment of the muon, since this depends on the masses of the scalar partners of the muon and the neutrinos, apart from requiring 𝜇 to be positive.

When it comes to the flavour constraints the situation is more involved in that various constraints have different level of model dependence. On the one hand there are constraints from tree-level mediated processes such as 𝐵_𝑢→𝜏⁺𝜈_𝜏, which only depend on the Higgs sector and on the other hand there are constraints from loop-mediated processes such as 𝐵_𝑠→𝜇⁺𝜇⁻ and 𝑏→𝑠𝛾 which depend on details of the supersymmetric sector of the model. In the following we will limit ourselves to applying the most severe constraints from 𝐵_𝑢→𝜏⁺𝜈_𝜏, which limits the available parameter space in [𝑚_ℎ^±,tan𝛽] and 𝐵_𝑠→𝜇⁺𝜇⁻ which puts limits on [𝑚_𝑎1,tan𝛽]. The latter constraint is especially important since we will consider light 𝑎₁ which is very constrained by the data from LHCb and CMS [25, 26]. Finally we apply the direct constraints from searches for supersymmetric particles. For all constraints except the Higgs bosons we use NMSSMTools version 3.2.0.

The results from the scan are displayed in Figure 1 with black points being viable models from a theory point of view but excluded by the direct searches for Higgs bosons and coloured points being allowed by the same constraint. Of primary interest are the allowed regions in [𝑚_𝑎1,𝑚_ℎ^±]. As is clear from the figure there is a distinct region of points with 𝑚_𝑎1∼2𝑚_𝐵≈10.6 GeV allowed by all constraints (indicated by green colour) for essentially any value of 𝑚_ℎ^±≳90 GeV. The same is also true in the constrained 𝑚_ℎ^max scenario where 𝜇=200 GeV and 𝐴_𝑡=−√6𝑀_SUSY+𝜇cot𝛽 are fixed as was already noted in [17]. However, at difference to the constrained 𝑚_ℎ^max scenario there are regions with larger 𝑚_𝑎1 that are allowed also for 𝑚_ℎ^±≲120 GeV.

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Figure 1 

Correlations between the parameters of the scan in the scenario under consideration (see text for details) with the various constraints applied as follows. All points in black are viable model points but are excluded by HiggsBounds. The coloured points are allowed by HiggsBounds and plotted in the following order: red points are excluded by 𝐵𝑠→𝜇+𝜇−, blue points are excluded by 𝐵𝑢→𝜏+𝜈𝜏, yellow points are excluded by direct searches for supersymmetric particles, and finally green points are allowed by all constraints considered.

Looking at the [𝑚_ℎ^±,tan𝛽]-plane, one clearly sees the constraint from 𝐵_𝑢→𝜏⁺𝜈_𝜏 for intermediate tan𝛽 (shown as blue points). For larger tan𝛽 there is a cancellation between the SM and ℎ^± contributions, which makes this region allowed by 𝐵_𝑢→𝜏⁺𝜈_𝜏, but instead the constraints from 𝐵_𝑠→𝜇⁺𝜇⁻ come into play (red points). It should be noted that the points excluded by 𝐵_𝑢→𝜏⁺𝜈_𝜏 are plotted on top of the constraints from 𝐵_𝑠→𝜇⁺𝜇⁻. Similarly the constraints from searches for supersymmetric particles are plotted (in yellow) on top of the constraints from 𝐵-decays, but with the cut 𝜇>125 GeV there are hardly any points excluded by this constraint. Finally we note that for tan𝛽≲15 there are allowed points in parameter space for essentially any value of 𝑚_ℎ^±≳90 GeV.

Turning to the [𝑚_𝑎1,tan𝛽]-plane we see that the region 𝑚_𝑎1∼2𝑚_𝐵 is allowed by all constraints up to tan𝛽≲10, whereas for larger tan𝛽 there are points allowed by direct Higgs boson searches but not allowed by 𝐵_𝑠→𝜇⁺𝜇⁻ and 𝐵_𝑢→𝜏⁺𝜈_𝜏. Given the uncertainties related to the indirect constraints from 𝐵-decays we conclude that there is a region in parameter space with 𝑚_𝑎1∼2𝑚_𝐵, 𝑚_ℎ^±∈[90,170] GeV, and tan𝛽∈[1,60] that should be searched for by the ATLAS and CMS experiments. It should also be noted that values both above and below the threshold 𝑚_𝑎1=2𝑚_𝐵 are allowed by the constraints.

Before turning to the signal of interest, that is, 𝐵𝑟(ℎ^±→𝑎₁𝑊), we also show in Figure 1 the effects of the various constraints when projected onto the [𝜅,𝜆] and [𝐴_𝑡,𝜇]-planes. From the first of these plots one clearly sees the constraint 𝜅²+𝜆²≲0.7 which arises from requiring perturbativity up to the GUT scale. From the second we see that the constraints imply |𝐴_𝑡|≲3500 GeV, which essentially follows from the radiative corrections to the lightest CP-even Higgs becoming small or even negative for large |𝐴_𝑡| relative to the value 𝑀_SUSY=1 TeV that we are using. We also see that for 𝜇 there are hardly no experimental constraints in the region considered. On the other hand, if we would extend 𝜇 to values smaller than 125 GeV then all those points would be excluded by searches for supersymmetric particles.

As promised we turn now to the resulting branching ratios for the decay ℎ^±→𝑎₁𝑊. From Figure 2 we observe the following general feature, the branching ratio can be large as soon as the channel is open (𝑚_𝑎1<𝑚_ℎ^±−𝑚_𝑊) except for large tan𝛽 where the decay ℎ^±→𝜏𝜈_𝜏 becomes dominant. Concentrating on those points that pass all the constraints considered and the region 𝑚_𝑎1∼2𝑚_𝐵 we also see from the lower right plot that 𝐵𝑟(ℎ^±→𝑎₁𝑊)≲0.9 as long as tan𝛽≲10 and 𝑚_ℎ^±≳100 GeV. Thus we can conclude that not only is the parameter space region 𝑚_𝑎1∼2𝑚_𝐵, 𝑚_ℎ^±∈[100,170] GeV, and tan𝛽∈[1,10] allowed in this region, but the decay ℎ^±→𝑎₁𝑊 is also dominant. In the next section we will exemplify how the so far unexplored region of parameter space with 𝑚_𝑎1∈[10,12] GeV can be probed by searching for ℎ^±→𝑎₁𝑊 with 𝑎₁→𝑏𝑏 in 𝑡𝑡-production at the LHC.

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Figure 2 

The branching ratio for ℎ±→𝑎1𝑊 when scanning over the parameters in the scenario under consideration (see text for details) with the various constraints applied. The colour coding is the same as in Figure 1.

Before ending this section we also show in Figure 3 the branching rations for the decay chains of interest, that is, 𝑡→𝑏ℎ⁺, 𝑡→𝑏ℎ⁺→𝑏𝑎₁𝑊, and 𝑡→𝑏ℎ⁺→𝑏𝑎₁𝑊→𝑏𝑏𝑏𝑊 as a function of tan𝛽 when restricting to parameter space points with 𝑚_ℎ^±<160 GeV. As can be seen from the figure, points with 𝐵𝑟(𝑡→𝑏ℎ⁺) as large as 0.2 are still allowed when the decay ℎ^±→𝑎₁𝑊 is included. This should be compared with the experimental constraints from ATLAS and CMS which so far have assumed that 𝐵𝑟(ℎ^±→𝜏𝜈_𝜏)=1 giving a limit 𝐵𝑟(𝑡→𝑏ℎ⁺)≲ few percent [27, 28].

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Figure 3 

The branching ratios for the decay chains 𝑡→𝑏ℎ+, 𝑡→𝑏ℎ+→𝑏𝑎1𝑊, and 𝑡→𝑏ℎ+→𝑏𝑎1𝑊→𝑏𝑏𝑏𝑊, respectively, when scanning over the parameters in the scenario under consideration (see text for details) with the various constraints applied and only considering points with 𝑚ℎ±<160 GeV. The colour coding is the same as in Figure 1.

4. Search Strategy

In the following section we will perform a signal-to-background analysis for three different charged Higgs masses: 𝑚_ℎ⁺=100,130 and 150 GeV, respectively. For definiteness we have used tan𝛽=50 when simulating the signal but the end results will not depend on this value. The mass of the 𝑎₁ is set to 11 GeV throughout as an example of a small 𝑎₁ mass that is just above 𝑏𝑏-threshold. The three charged Higgs masses are chosen to illustrate different kinematic properties: at 𝑚_ℎ^±=150 GeV the 𝑏-jet from the 𝑡→𝑏ℎ⁺ decay will be rather soft whereas the 𝑎₁ from the ℎ⁺ will be harder. For 𝑚_ℎ^±=100 GeV the situation will be the opposite, and in the intermediate case 𝑚_ℎ^±=130 GeV both jets can be relatively hard and in addition the available phase-space will be largest.

We aim to reconstruct the signal process where one of the 𝑡-quarks decays leptonically via ℎ^±→𝑎₁𝑊 with 𝑊→ℓ𝜈_ℓ and the other hadronically via 𝑊→𝑗𝑗 as illustrated in Figure 4. All cross-sections have been corrected for these enforced W decays as well as a factor of 2 for taking account of the process also with interchanged roles between the 𝑡 and the 𝑡. Because the 𝑎₁ is supposed to decay close to threshold to 𝑏𝑏, we aim for a reconstruction where the two 𝑏’s from the 𝑎₁ are clustered together to give a single 𝑏𝑏-jet.

Figure 4 

Illustrations of 𝑡𝑡 production in proton-proton collisions with the subsequent decay chain considered in this paper.

As backgrounds to the process we consider the irreducible 𝑡𝑡𝑏𝑏 as well as, because of its higher magnitude, 𝑡𝑡 with one jet being accidentally 𝑏-tagged (weighted with a mistagging probability, assumed to be 0.01 [29, 30]). In order to include also the single top contributions to the background we have simulated the processes 𝑡𝑏𝑊⁺𝑏𝑏 and 𝑡𝑏𝑊⁺, respectively, but in the following we will denote them as 𝑡𝑡𝑏𝑏 and 𝑡𝑡 for simplicity. For other reducible backgrounds, such as 𝑊+𝑏 jets, we assume that similar procedures can be applied as in the 𝑡𝑡 cross-section determination. For example, requiring two 𝑏-tagged jets reduces the 𝑊+𝑏 jets background to 𝑡𝑡 production to about 10% [31]. Several cuts are applied to strengthen the signal and to suppress the background as will be discussed in the following.

A center-of-mass energy of 8 TeV at the Large Hadron Collider is assumed throughout the whole analysis. For the generation of the hard matrix elements, we use MadGraph 5 [32] with a fixed renormalization and factorization scale (set as default to the 𝑍 mass) and the “CTEQ6L1” parton distribution functions. To supply MadGraph with the proper parameters of the signal we have for simplicity used a simple two Higgs Doublet Model with the masses given above as implemented in the Two Higgs Doublet Model Calculator 2HDMC [33]. The only important difference to the NMSSM then arises from the ℎ^±→𝑎₁𝑊 decay giving and extra factor cos²𝜃_𝐴 (cf. Table 1). All other steps to generate complete events, such as radiation, underlying events, and hadronization, are carried out using Pythia 8. We start from bare samples of 100000 events for the different signals as well as the 𝑡𝑡𝑏𝑏 background whereas for the 𝑡𝑡 background we have 50 times higher statistics to start with. There is no detector simulation included in this exploratory analysis but we have simulated 𝑏-tagging in a simplified way as detailed below.

For all processes we use the leading order cross-sections obtained from MadGraph. On the one hand this means that there is an overall scale factor which is more or less the same for both signal and background. On the other hand the rates will be lower than what would have been resulted if higher order cross-sections had been used. All in all this means that the signal over background rates we find will be underestimated in this respect. For example we get a LO cross-section for 𝑝𝑝→𝑡𝑡 process in the SM of 138 pb to be compared with the NNLL resummed result of 232 pb [34].

4.1. Reconstruction of the Leptonic 𝑊

To reconstruct the leptonic 𝑊, we first need to identify the charged lepton (𝑒 or 𝜇) associated to the hard process. The transverse momentum (𝑝_⟂) and pseudorapidity (𝜂)-distributions are shown in Figure 5. After applying cuts on the lepton kinematics (𝑝_⟂>20 GeV, |𝜂|<2.5), we require the summed 𝑝_⟂ of the surrounding particles in an (𝜂,𝜙)-cone of size Δ𝑅=Δ𝜂²+Δ𝜙²=0.3 around the lepton to be less than 10 GeV to call it isolated. (The numerical values for the 𝑝_⟂ cut and the cone size have been optimized by observation of the changes in efficiency and purity when varying the cuts). On the whole event then, we require to have precisely one isolated lepton in the final state.

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Figure 5 

Transverse momentum and pseudorapidity of the charged lepton from the 𝑊 decay and missing transverse energy (MET) before applying cuts.

The next step in reconstructing the leptonic 𝑊 is to identify the missing energy (MET)/missing ^→𝑝_⟂ of the event with the transverse momentum of the neutrino. Assuming the 𝑊 to be on mass-shell and using a mass-less neutrino then leaves two possible solutions for the longitudinal momentum of the neutrino 𝑝_𝜈𝑧=𝐴±√𝐷 with 𝑚𝐴=^2𝑊𝑝_𝑙𝑧+2𝑝_𝑙𝑧^→𝑝^→_𝜈⟂𝑝_𝑙⟂2𝑚²_⟂𝑙,𝐸𝐷=^2𝑙𝑚⁴_⟂𝑙𝑚⁴_𝑊4−^→𝑝_𝜈⟂^2→𝑝_𝑙⟂²+^→𝑝^→_𝜈⟂𝑝_𝑙⟂²+^→𝑝^→_𝜈⟂𝑝_𝑙⟂𝑚²_𝑊. (4.1)

In order to have a more accurate reconstruction of 𝑝_𝜈𝑧 we have applied a cut /^𝐸_⟂^>30 GeV. In addition, different selection criteria for the choice of the sign have been examined, for example, the invariant mass of the reconstructed ℎ^±. Among these, the most viable one turned out to be a simple selection of the smaller |𝑝_𝜈𝑧|, which is correct in roughly three quarters of the signal events.

4.2. Jet Reconstruction and Tagging

For the reconstruction of the hadronic part of the event, we consider different jet clustering schemes (anti-kT [35], Cambridge/Aachen [36], kT [37, 38]) as well as cone-sizes. All particles, except neutrinos and the isolated lepton, in the rapidity range |𝜂|<4.9 are fed into FastJet [39, 40]. The resulting clustered jets are required to have 𝑝_⟂>20 GeV. Afterwards, a simplified 𝑏-tagging is simulated for all jets in the region |𝜂|<2.5 by comparing the (𝜂,𝜙) of the jets to the 𝑏-quarks of the hard process. All jets within Δ𝑅=0.4 are then classified as 𝑏-jets.

The jet-algorithms require to specify the distance measure 𝑅 used when calculating the jet measure. Since we want to cluster the 𝑏𝑏 pair from the 𝑎₁ into one jet, it is crucial that the distance between the two subjets is not too large. Figure 6 shows the distance measure between the two 𝑏-quarks on parton level for different 𝑎₁ masses. As can be seen from the figure, for reasonable clustering cone sizes (around 0.4 to 0.6) and with 𝑚_𝑎1 in the region of interest for this analysis, the two 𝑏-quarks will most likely be clustered together as a single jet.

Figure 6 

The distance between the two 𝑏-quarks coming from the 𝑎1-decay on parton level for the signal with 𝑚ℎ±=130 GeV.

As an ideal reconstruction will now give rise to three 𝑏-jets, the correct reconstruction of the ℎ^± will be enhanced by the identification of the “wrong” 𝑏-jet which comes from the 𝑡 together with the hadronically decaying 𝑊⁻. The strategy to achieve this here is to first find the pair of untagged jets that is closest to the 𝑊 mass and then combine this pair with the 𝑏-jet that gives a mass closest to the 𝑡 mass. This 𝑏-jet will then be excluded in the ℎ^± reconstruction, reducing the number of 𝑏-jets which have to be considered (in an event with a so far correct clustering in the desired way) to two. In addition to this, we put cuts on the quality of the reconstruction by requiring the reconstructed masses shown in Figure 7 to be in the regions 𝑚_𝑊±20 GeV or 𝑚_𝑡±30 GeV, respectively. We have checked that the reconstruction of the 𝑊 and 𝑡 masses is quite independent of the choice of jet clustering scheme and cone-size as is also shown in Figure 7. Only the 0.3 cone size gives a slightly inferior top reconstruction, but then the 𝑎₁ will also not give rise to a single 𝑏-jet. If not mentioned differently, we thus use the anti-kT algorithm with 𝑅=0.5 in the following.

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Figure 7 

Mass reconstruction of the hadronically decaying 𝑊 (a) and 𝑡-quark (b) for the signal with 𝑚ℎ±=130 GeV when 𝑅=0.5 (a) and using the anti-kT algorithm (b).

Using the jet-reconstruction outlined above we obtain the jet and 𝑏-jet multiplicity, respectively, shown in Figure 8. As is clear from the figure, the number of jets peaks around the expected five and the number of 𝑏-jets is typically smaller than ideal which is due to the limited 𝑏-tagging region enforced. Also note the large decrease in 𝑏-jet multiplicity for the 𝑡𝑡 sample from 2 to 3. Here the 3𝑏-jet sample arises from gluon splitting into 𝑏𝑏 and we do not take it into account below since that would amount to double counting with the 𝑡𝑡𝑏𝑏 background.

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Figure 8 

Jet (a) and 𝑏-jet (b) multiplicity for the signal and backgrounds when using the anti-kT algorithm with 𝑅=0.5.

Given the large background from 𝑡𝑡 for the two 𝑏-jet sample we resort to requiring at least three 𝑏-jets. Assuming that one of the 𝑏-jets has been identified as coming from the 𝑡-quark this leaves two 𝑏-jets that may originate from the ℎ^±. Due to the strong dependence of the hardness of the 𝑏-jet from the 𝑡→ℎ⁺𝑏 decay on the ℎ^± mass, we consider both of these remaining solutions in general as possible candidates for the ℎ^± reconstruction. The resulting distributions when combining with the leptonically decaying 𝑊 are shown in Figure 9. In the ℎ^± reconstruction, we thus require 3𝑏-jets for the signals and the 𝑡𝑡𝑏𝑏 background, while we require 2𝑏-jets in the 𝑡𝑡 sample. For the latter we then assume that any of the non 𝑏-jets inside the 𝑏-tagger region (|𝜂|<2.5) can be mistagged with a probability of 0.01 per jet [29, 30].

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Figure 9 

Reconstructed charged Higgs masses, using either the higher-𝑝⟂ (a) or the lower-𝑝⟂ (b) 𝑏-jet combined with the leptonically decaying 𝑊.

4.3. Signal Significance and Reach

To estimate the signal reach as well as its significance, we choose a common window of 90 to 160 GeV to integrate the signal as well as the backgrounds. We correct for 𝑏-tagging efficiencies which we assume to be 0.6 per 𝑏-jet. The resulting cross-sections are shown in Table 2.

Table 2 

Integrated signal cross-sections (cf. Figure 9) for the three different charged Higgs masses as well as the two backgrounds. The integration region is 90 to 160 GeV.

𝑆/√𝐵 ratios for the three different mass cases are then calculated for an integrated luminosity of 20 fb⁻¹) and summarized in Table 3. The table also shows the branching ratios at the simulated parameter points, as well as the extrapolations to branching ratios necessary for a 5𝜎 discovery. From the table it is clear that for 𝑚_ℎ^±∼130 GeV, the discovery reach is maximal. For smaller or larger 𝑚_ℎ^±, the limitations in phase space will reduce the branching ratio for ℎ^±→𝑎₁𝑊 and 𝑡→ℎ^±𝑏 respectively. In the former case this means that the standard decay channel ℎ^±→𝜏𝜈_𝜏 will also be significant.

Table 3 

The 𝑆/√𝐵 ratios obtained for an integrated luminosity of 20 fb⁻¹ for the different signals considered together with the branching ratios for the total decay chain 𝑡→𝑏ℎ⁺→𝑏𝑎₁𝑊→𝑏𝑏𝑏𝑊 of the respective parameter points and a linear extrapolation to the critical branching ratio necessary for a 5𝜎 discovery.

Before ending this section we note that similarly to the standard decay modes of the charged Higgs boson it should be possible to use the spin-correlations between the decay products of the two top quarks as a way of enhancing the signal [41–43].

5. Compatibility with Possible Higgs Signal

Recently the ATLAS and CMS experiments announced the combined results of the SM Higgs (𝜙) searches using ≈5 fb⁻¹ of data from 2011 [44, 45]. In short they can be summarized as follows: the CMS experiment has ruled out the region 𝑚_𝜙∈[129,600] GeV at the 95% confidence level as expected whereas in the region [118,129] GeV they have not been able to make any exclusion at all even though they expected to be able to do so at the 95% confidence level, the ATLAS experiment has similarly ruled out the regions 𝑚_𝜙∈[112.9,115.5] GeV, 𝑚_𝜙∈[131,238] GeV, and 𝑚_𝜙∈[251,466] GeV at the 95% confidence level whereas they had expected to rule out the region [125,519] GeV.

Instead, both experiments have found an excess of events in the regions 𝑚_𝜙∼126 GeV and 𝑚_𝜙∼124 GeV for ATLAS and CMS, respectively, which when corrected for the so-called look-elsewhere-effect and combining the different channels has a statistical significance of about 2𝜎 for each of the two experiments. Although not statistically significant these results have stirred a lot of excitement in the high-energy physics community [24, 46–54]. It will most likely not be possible to draw any final conclusions about whether this is a true signal or not before the end of the run in 2012 which will give another ~20 fb⁻¹ of data.

One of the most important properties of the possible signal at the LHC is that the 𝜙→𝛾𝛾 channel is similar to what is expected from the SM. Therefore we start by considering the would-be signal from the ℎ₁ as well as the ℎ₂ compared to what is expected in the SM for a Higgs boson (𝜙) with the same mass. Assuming that gluon-gluon fusion dominates the production, which we have verified is always the case in the scenarios we consider, this ratio is given by 𝑅^ℎ𝑖_{𝑔𝑔𝛾𝛾}=𝜎𝑔𝑔→ℎ_𝑖NMSSM𝜎𝑔𝑔→𝜙_SM𝐵𝑟ℎ_𝑖→𝛾𝛾_NMSSM𝐵𝑟𝜙→𝛾𝛾_SM≃Γℎ_𝑖→𝑔𝑔_NMSSMΓ𝜙→𝑔𝑔_SM𝐵𝑟ℎ_𝑖→𝛾𝛾_NMSSM𝐵𝑟𝜙→𝛾𝛾_SM, (5.1) where in the second equality, following for example [47, 50], we have made the implicit assumption that the difference in radiative corrections for the production and decay processes are canceled in the ratio.

The results obtained for this quantity when using the same scan as in Section 3 are displayed in Figure 10. From the figure it is clear that if the possible signal seen at the LHC is the ℎ₁ then we would have to have 𝑚_𝑎1≳60 GeV. Even so 𝑅^ℎ1_{𝑔𝑔𝛾𝛾} does not become larger than ∼0.5 for 𝑚_ℎ1≳120 GeV in our scan and there appears to be an upper bound 𝑚_ℎ1≲122 GeV. However, the difference in mass compared to the possible observation is so small that it should be considered to be within the theoretical uncertainty. (For example, including the full one-loop corrections and the two-loop ones from the 𝑡 and 𝑏 Yukawa couplings could push the ℎ₁ mass bit higher in compliance with the possible signal. Similarly increasing 𝑀_SUSY would also increase 𝑚_ℎ1.) In any case it is clear that it is hardly possible to have a light 𝑎₁ if it is the ℎ₁ that has been seen at the LHC.

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Figure 10 

The signal for ℎ1→𝛾𝛾 (left) and ℎ2→𝛾𝛾 (right) relative to the standard model when scanning over the parameters in the scenario under consideration (see text for details) with the various constraints applied. The colour coding is the same as in Figure 1.

Next we turn to the possibility that it is the ℎ₂ that has been seen by the LHC experiments. The results of the scan are also shown in Figure 10. As can be seen from the figure the results are more promising in this case. There are points with 𝑅^ℎ2_{𝑔𝑔𝛾𝛾}≳0.1 also for small 𝑚_𝑎1 and intermediate 𝑚_ℎ^± that have 𝑚_ℎ2 in the region indicated by the LHC experiments.

In order to explore this possibility more closely we show in Figure 11 the results when fixing the 𝑎₁ mass to 11 GeV as was done in Section 4 for the three cases 𝑚_ℎ^±=100,130,160 GeV. As can be seen from the figure, for the intermediate charged Higgs mass it is possible to reach 𝑅^ℎ2_{𝑔𝑔𝛾𝛾}∼0.15. However it should be noted that in this case, as also shown in the figure, the branching fraction for ℎ^±→𝑎₁𝑊 is quite small meaning that the standard decay channel ℎ^±→𝜏𝜈_𝜏 can be used even though with a slightly reduced branching fraction.

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Figure 11 

The signal for ℎ2→𝛾𝛾 relative to the standard model (left) and the branching fraction for ℎ±→𝑎1𝑊 (right) in a scan with 𝑚𝑎1=11 GeV and 𝑚ℎ± fixed at 100 (top), 130 (middle), and 160 (bottom) GeV, respectively. The colour coding for the various constraints is the same as in Figure 1.

The last logical possibility would be that it is the ℎ₃ that has been observed by the CERN experiments. However, in the scenarios we consider it turns out that 𝑅^ℎ3_{𝑔𝑔𝛾𝛾} is always small.

The trends seen in Figure 11 can be understood on more general grounds from the difficulties of having a light 𝑎₁ with mass 𝑚_𝑎1<𝑚_ℎ𝑖/2 and at the same time have a large 𝑅^ℎ𝑖_{𝑔𝑔𝛾𝛾}. The first problem is that unless the triple Higgs coupling 𝑔_{ℎ𝑖𝑎1𝑎1} is small the decay ℎ_𝑖→𝑎₁𝑎₁ will become dominant. Looking at the structures of 𝑔_{ℎ𝑖𝑎1𝑎1}, which for example can be found in [8], this means that both 𝜆 and 𝜅 typically have to be small. Secondly the decay ℎ_𝑖→𝑎₁𝑍 will also dominate if 𝑚_𝑎1<𝑚_ℎ𝑖−𝑚_𝑍 unless the corresponding reduced coupling given in Table 1 is small. In other words we need (cos𝛽𝐒_𝑖1−sin𝛽𝐒_𝑖2)cos𝜃_𝐴 to be small. There are essentially three ways to achieve this. If cos𝜃_𝐴 is small then 𝑎₁ will be mainly singlet like and decouple. However, then ℎ^±→𝑎₁𝑊 will also be small. The second possibility is that 𝐒_𝑖1 and 𝐒_𝑖2 are small, but then the would-be-signal would be mainly singlet-like and not produced in the first place, so 𝐒_𝑖3 has to be small. Finally then, the combination (cos𝛽𝐒_𝑖1−sin𝛽𝐒_𝑖2) could be small but then the complementary combination (sin𝛽𝐒_𝑖1+cos𝛽𝐒_𝑖2) would have to be large giving an increased coupling ℎ_𝑖→𝑉𝑉. All in all this means that is difficult to have a light 𝑎₁ that it is not decoupled and still have a large 𝑅^ℎ𝑖_{𝑔𝑔𝛾𝛾}, although it cannot be completely ruled out.

6. Summary and Conclusions

We have considered a well motivated class of supersymmetric extensions of the standard model with nonminimal Higgs sector, namely, the CP-conserving NMSSM. In these types of models the additional Higgs singlet can modify the phenomenology of the Higgs sector in many different ways. In this paper we have specifically addressed the possibility of having a light CP-odd Higgs boson close to, but still above the 𝑏𝑏 threshold. This in turn means that the light charged Higgs boson, with mass 𝑚_ℎ^±<𝑚_𝑡, can decay into 𝑎₁𝑊 in addition to the standard decays ℎ^±→𝜏𝜈_𝜏, thus invalidating the interpretations made of charged Higgs bosons searches assuming that 𝐵𝑟(ℎ^±→𝜏𝜈_𝜏)=1.

When investigating the viability of these types of scenarios we have found that the experimental constraints from direct searches are quite weak even when taking the latest constraints from LHC into account. The constraints from indirect searches in 𝐵-decays are more constraining but also more model dependent. Even when including the results from the most important ones, namely 𝐵_𝑢→𝜏𝜈_𝜏 and 𝐵_𝑠→𝜇⁺𝜇⁻, we still find a region of parameter space that is allowed with tan𝛽∈[1,10]. This is precisely the same region as the one where the decay ℎ^±→𝑎₁𝑊 can be dominant.

The phenomenology of these types of scenarios is special in that, due to its low mass, the 𝑎₁ will decay into a single 𝑏𝑏 jet. Even so we have shown that it is possible to reconstruct the decay ℎ^±→𝑎₁𝑊 using standard jet finding algorithms when the 𝑊 decays leptonically. This requires to use the missing transverse momentum to calculate the four momentum of the 𝑊, which can then be combined with the 𝑎₁-jet to give a mass peak at 𝑚_ℎ^±. The other 𝑡 quark is assumed to decay hadronically according to 𝑡→𝑏𝑗𝑗 giving an additional handle to identify the events of interest. The most important background is thus the irreducible one from 𝑡𝑡𝑏𝑏 production but we have also taken into account the 𝑡𝑡 background by considering the possibility of mistagging ordinary jets as 𝑏-jets.

Based on our study we find that with an integrated luminosity of 20 fb⁻¹ it should be possible to discover a charged Higgs bosons in these types of scenarios as long as the combined branching fraction for the decay chain 𝑡→𝑏ℎ⁺→𝑏𝑎₁𝑊→𝑏𝑏𝑏𝑊 is larger than ≈0.01.

Finally we have also investigated the phenomenological consequences of the possible Higgs signal seen at the LHC on the types of scenarios we consider. We find that it is difficult to have a light 𝑎₁ that is not decoupled and at the same time have a combined production and decay into 𝛾𝛾 for one of the CP-even Higgs bosons with mass ~125 GeV. As a consequence we have not been able to find regions of parameter space where the ℎ^±→𝑎₁𝑊 decay dominates and at the same time are compatible with the possible Higgs signal. This means that irrespectively of whether the possible Higgs signal is substantiated or not, the LHC experiments should be able to either discover or put very tight constraints on a light charged Higgs bosons also in the NMSSM.

Note Added

On July 4, 2012 the ATLAS and CMS experiments announced the discovery of a new Higgs-like particle in the same mass region as the previous observations already cited in the text.

Acknowledgments

The authors thank Oscar Stål for helpful communications. Furthermore, they would like to thank Stefan Prestel for his kind advice and help, especially regarding the technical realization. This work is supported in part by the Swedish Research Council Grant 621-2011-5333.