Abstract
CPodd scalars are an integral part of many extensions of the Standard Model. Recently, electroweakscale pseudoscalars have received increased attention in explaining the diffuse gammaray excess from the Galactic Centre. Elusive due to absence of direct couplings to gauge bosons, these particles receive only weak constraints from direct searches at LEP or searches performed during the first LHC runs. We investigate the LHC’s sensitivity in probing a CPodd scalar in the mass range \(20 \le m_A \le 100\) GeV via ditopassociated production using jetsubstructurebased reconstruction techniques. We parameterise the scalar’s interactions using a simplified model approach and relate the obtained upper limits to couplings within typeI and typeII 2HDMs as well as the NMSSM. We find that in ditopassociated production, experiments at the LHC can set tight limits on CPodd scalars that fit the Galactic Centre excess. However, direct sensitivity to light CPodd scalars from the NMSSM remains challenging.
Introduction
The recent discovery of the Higgs boson [1, 2] marked a new era for fundamental physics. For the first time an electroweakscale scalar resonance has been discovered, supposedly a remnant of the mechanism underlying electroweak symmetry breaking [3–6].
While elementary scalar particles have been observed in nature for the first time, they are often an integral part of Standard Model (SM) extensions, e.g. supersymmetry or general NHiggs Doublet Models. When these extensions contain complex scalar fields, as a result, CPodd scalars are introduced in the spectrum of the theory. Hence, since their existence would be evidence for physics beyond the SM, searches for CPodd scalars are at the core of the current LHC program.
Recently, CPodd scalars as mediators between Dark Matter (DM) and SM particles have received attention as possible explanations of the diffuse gammaray excess from the Galactic Centre [7–10] in the contexts of the socalled Coy Dark Matter models [11–14], and the NexttoMinimalSupersymmetricStandardModel (NMSSM) [15, 16] (for subsequent discussions in the NMSSM, see [17–21]). Hence, they are included as mediators in simplified models by the ATLAS and CMS collaborations to recast searches for jets and missing transverse energy (‘monojet’) during the upcoming LHC runs [22, 23].
In contrast to the widely accepted paradigm that new physics particles have to be heavy, i.e. with masses of \(\mathcal {O}\)(1) TeV or beyond, the mass of CPodd scalars is almost unconstrained by direct searches. As interactions between gauge bosons and CPodd scalars are only induced via higherdimensional operators, e.g. \(\frac{1}{2} A \epsilon _{\mu \nu \sigma \rho } V_{\sigma \rho } V^{\mu \nu }\), limits from LEP are fairly weak. The main collider sensitivities may primarily arise from bottom quark or top quarkassociated productions (for recent explorations, see [24, 25]). Further, due to the predicted velocity suppression in direct detection experiments for CPodd scalar mediators, even light CPodd scalars are still in agreement with experimental observations. Some constraints from flavour physics exist but limits are again weak if \(m_A \gtrsim 5\) GeV [26], assuming the CPodd scalar interacts with fermions in agreement with the hypothesis of minimal flavour violation [27].
Therefore, indirect detection experiments and direct searches at the LHC appear to be the most sensitive ways to search for the existence of electroweakscale CPodd scalar particles. Most previous studies of direct searches for CPodd scalars at the LHC have been focussed on the gluonfusion production mechanism [28, 29]. Instead, in this paper we explore the direct production of such particles in association with a top quark pair and subsequent decay into a bottom quark pair, \(p p \rightarrow t \bar{t} A \rightarrow t \bar{t} b \bar{b}\). Thus, we derive limits on the mass and coupling strength of the CPodd scalar in a process with unsuppressed fermion couplings only.^{Footnote 1}
This paper is organised as follows. In Sect. 2 we briefly outline the way we incorporate the CPodd scalar into the theory, using a simplified model approach. The event generation and details of the final state reconstruction are described in Sects. 3 and 4. In Sect. 5 we derive limits on the mass of the CPodd scalar and its couplings to top quarks. Such limits can be applied to models where the CPodd scalar arises as part of a Higgs multiplet. In Sect. 6 we recast these limits in the context of a twoHiggsdoublet model (2HDM) and the NexttoMinimal Supersymmetric Standard Model (NMSSM). Finally, in Sect. 7 we offer conclusions.
Simplified model
While CPodd scalars are present in many extensions of the SM, for simplicity and generality of our results, we use a simplified model approach [30] to parameterise the contribution of this particle to the process \(p p \rightarrow t \bar{t} A \rightarrow t \bar{t} b \bar{b}\). More precisely, we add couplings of the CPodd scalar with the bottom and top quarks to the full SM Lagrangian
where
and \(g_i\) (\(i=t,b\)) parameterises the deviation from the SM Yukawa coupling \(y_i = m_i/v\).
Recently, a similar approach was proposed to recast monojet searches at the LHC in terms of scalar mediators between the SM and a secluded sector [31–34]. In a similar way, we will focus on the minimal set of free parameters relevant to the process considered. Throughout this paper we will assume A to be a narrow resonance with \(2 m_b \le m_A < 2m_t\). Hence, in our approach the CPodd scalar decays exclusively into bottom quarks with \(\mathrm {BR}(A\rightarrow b\bar{b})=1\) and its width \(\Gamma _A\) is completely determined by the value of \(g_b\). For a narrow resonance, the kinematic distributions are expected to remain largely independent of the value of \(\Gamma _A\) and interference effects with other electroweakscale particles, necessarily present in a UVcomplete model, are expected to be small [35, 36].
The purpose of our simplified model approach is to explicitly include the degrees of freedom of a UVcomplete model that contribute to the process of interest, i.e. the process \(pp \rightarrow t\bar{t} A \rightarrow t\bar{t}b\bar{b} \). Hence, the CPodd scalar A and its couplings to top and bottom quarks are to be understood as residual lowenergy states and interactions of welldefined UV models.^{Footnote 2} To minimise potential contributions of electroweakscale resonances to our signal region we use a “bump hunt” inspired reconstruction approach, as discussed in Sects. 3–4.
Event generation and simulation details
Signal and background modelling
Signal and background samples corresponding to pp collisions at \(\sqrt{s}=14\) TeV are generated using the Madgraph5 2.1.1 [38] leadingorder (LO) generator and the CTEQ6L1 [39] set of parton distribution functions (PDF), interfaced to Pythia v6.427 [40] for parton showering and fragmentation and using the Perugia2011C [41] underlying event tune. In all cases, a top quark mass of 172 GeV is assumed and top quarks are decayed inclusively by Pythia.
Samples of \(t\bar{t}A\) signal events are generated for different values of the A boson mass, \(m_A = 20, 30,40, 60, 80\) and 100 GeV, and assuming \(g_t=1\) and \(\mathrm {BR}(A \rightarrow b\bar{b})=1\). A model corresponding to the Lagrangian shown in Eq. (1) is implemented using Feynrules 2.1 [42] and is imported as an UFO model [43] in Madgraph5. The LO signal cross section predicted by Madgraph5 (see Table 1) is scaled by a kfactor of 1.3. This kfactor is obtained as the ratio of the NLO to LO cross sections for \(t\bar{t}h\) production, where h is a CPeven Higgs boson. It has been checked that this kfactor is rather constant as a function of \(m_h\), varied between 20 and 125 GeV. Figure 1a compares the production cross section between \(t\bar{t}h\) and \(t\bar{t}A\) as a function of the Higgs boson mass, in both cases assuming \(g_t=1\). The ratio between both cross sections varies significantly versus mass, with the \(t\bar{t}h\) cross section being about a factor of 20 larger than the \(t\bar{t}A\) cross section at a mass of 20 GeV, and only about a factor of 2 larger at a mass of 120 GeV [44]. This difference results from the presence of the extra \(\gamma _5\) factor in the interaction between a CPodd Higgs boson and the top quark, compared to the case of a CPeven Higgs boson. Another consequence of the different interaction is that a CPodd Higgs boson has a substantially harder \(p_\mathrm{{T}}\) spectrum compared to the CPeven case, particularly at low mass, as illustrated in Fig. 1b. This is a key feature exploited in this analysis, as discussed in Sect. 4.
A large sample of \(t\bar{t}\)+jets background events is generated including treelevel diagrams with up to two additional partons in the 5F scheme (i.e. including b and cquarks). To avoid doublecounting of partonic configurations generated by both the matrixelement calculation and the parton shower, a parton–jet matching scheme (“MLM matching”) [45] is employed. The sample is normalised to a cross section of 990 pb obtained using Top \(++\) v2.0 [46] at nexttonexttoleading order (NNLO) in QCD, including resummation of nexttonexttoleading logarithmic (NNLL) soft gluon terms [47–51], and using the MSTW 2008 NNLO [52, 53] PDF set. The \(t\bar{t}\)+jets sample is generated inclusively, but events are categorised depending on the flavour content of additional particle jets in the event (i.e. jets not originating from the decay of the \(t\bar{t}\) system). Particle jets are reconstructed with the anti\(k_t\) [54–56] algorithm with a radius parameter \(R=0.4\) and are required to have \(p_\mathrm{{T}}>15\) GeV and \(\eta <2.5\). Events where at least one such particle jet is matched within \(\Delta R<0.4\) to a bhadron with \(p_\mathrm{{T}}>5\) GeV not originating from a top quark decay are generically labelled as \(t\bar{t}+{\ge }1b\) events. Similarly, events where at least one such particle jet is matched within \(\Delta R<0.4\) to a chadron with \(p_\mathrm{{T}}>5\) GeV not originating from a W boson decay, and that are not labelled already as \(t\bar{t}+{\ge }1b\), are labelled as \(t\bar{t}+{\ge }1c\) events. Events labelled as either \(t\bar{t}+{\ge }1b\) or \(t\bar{t}+\ge 1c\) are generically referred to below as \(t\bar{t}+ \)HF events, where HF stands for “heavy flavour”. We do not apply dedicated corrections to the normalisation of \(t\bar{t}+ \)HF events, since Run 1 searches at the LHC [57] showed that the LO prediction from Madgraph5 using the same settings as us is consistent with data within \({\sim } 20\,\%\), and a larger systematic uncertainty will be assumed in this study. As in Ref. [57], a finer categorisation of \(t\bar{t}+ \)HF events is considered for the purpose of assigning systematic uncertainties associated with the modelling of heavyflavour production in different topologies. In this way, a distinction is made between events with only one extra heavyflavour jet satisfying the above cuts (referred to as \(t\bar{t}+b\) or \(t\bar{t}+c\)), events with two extra heavyflavour jets (referred to as \(t\bar{t}+b\bar{b}\) or \(t\bar{t}+c\bar{c}\)) and events with one extra heavyflavour jet containing two b or chadrons (referred to as \(t\bar{t}+B\) or \(t\bar{t}+C\)). The remaining events are labelled as \(t\bar{t}+\) lightjet events, including those with no additional jets.
Additional background samples corresponding to \(t\bar{t}W\), \(t\bar{t}Z\) and \(t\bar{t}h_\mathrm{SM}\) production, where \(h_\mathrm{SM}\) is the SM Higgs boson, are also produced. The \(t\bar{t}W\) sample is generated requiring at least one W boson in the event to decay leptonically, and is normalised to the corresponding LO cross section, 0.404 pb, times a kfactor of 1.4 [58]. The \(t\bar{t}Z\) sample is generated requiring \(Z \rightarrow q\bar{q}\) decays and is normalised to the corresponding LO cross section, 0.353 pb, times a kfactor of 1.3 [58]. Finally, the \(t\bar{t}h_\mathrm{SM}\) sample is generated assuming \(m_h=125\) GeV and requiring \(h \rightarrow b\bar{b}\) decays. It is normalised to the NLO cross section [59–61], 0.611 pb, times the \(h_\mathrm{SM} \rightarrow b\bar{b}\) branching ratio of 57.7 % [62–65], collected in Ref. [66]. In these samples \(Z \rightarrow q\bar{q}\) and \(h_\mathrm{SM} \rightarrow b\bar{b}\) decays are performed by Madgraph5 and top quarks and W bosons are decayed by Pythia.
Event reconstruction
The generated samples at the particle level are processed through a simplified simulation of the detector response and object reconstruction.
Isolated leptons (electrons or muons) are required to have \(p_\mathrm{{T}}>25\) GeV and \(\eta <2.5\). Furthermore, they are required to not overlap with jets, as discussed below. A typical perlepton identification efficiency of 80 % is assumed.
Stable particles from Pythia, except for muons and neutrinos, are processed through a simplified simulation of a calorimeter. The fourmomenta of particles falling within the same window in \(\eta \phi \) space of size \(\Delta \eta \times \Delta \phi = 0.1\times 0.1\) are added together to simulate the finite granularity of calorimeter cells. For each cell, the total threemomentum is rescaled such as to make the cell massless. Cells with energy larger than 0.1 GeV and \(\eta <5.0\) become the inputs to the jet algorithm. Several types of jets are considered in this analysis.
The anti\(k_t\) algorithm is used to reconstruct jets with two different radius parameters, \(R=0.2\) and \(R=0.4\), referred to as AKT2 and AKT4 jets, respectively. The minimum jet \(p_\mathrm{{T}}\) threshold for reconstruction is 5 GeV. During jet reconstruction, no distinction is made between identified electrons and jet energy deposits, and so every electron is also associated with a reconstructed jet. In order to remove this double counting, if any of the jets in the AKT2 and AKT4 collections lie within \(\Delta R=0.2\) of a selected electron, the closest jet from each jet collection is discarded. Since this analysis has a large number of bquark initiated jets, for which a significant fraction of energy is carried away by muons in semimuonic bhadron decays, the fourmomenta of all reconstructed muons with \(p_\mathrm{{T}}>4\) GeV that are ghostassociated [67, 68] to a jet are added to the calorimeter jet fourmomentum. After this correction, a minimum \(p_\mathrm{{T}}\) requirement of 15 and 25 GeV is made for AKT2 and AKT4 jets, respectively. All jets are required to satisfy \(\eta <2.5\). Finally, any electron or muon within \(\Delta R=0.4\) of a selected AKT4 jet is discarded. In this analysis AKT4 jets are used to define the minimum jet multiplicity required in the event selection, while AKT2 jets are used to define the btag multiplicity of the event. The latter is particularly important since at low \(m_A\) values the bquarks from the \(A \rightarrow b\bar{b}\) decay emerge with small angular separation. The flavour of an AKT2 jet is determined by matching it within \(\Delta R=0.15\) with a bhadron or a chadron (not originating from a bhadron decay), resulting in the jet being labelled as bjet or cjet, respectively. The rest of the jets are taken to originate from the fragmentation of a light quark or gluon and are labelled as “light jets”. Heavyflavour tagging is modelled in a probabilistic fashion by assigning a perjet efficiency of 70 % to bjets, 20 % to cjets, and 0.7 % to light jets.
In addition, jets are reconstructed with the Cambridge–Aachen (C/A) algorithm [69, 70] for the purpose of reconstructing the \(A \rightarrow b\bar{b}\) decay, taking advantage of the boost with which A bosons are produced in the \(t\bar{t}A\) process (see Fig. 1b). Two radius parameters are considered for C/A jets, \(R^\mathrm{C/A}=0.6\) and 0.8, referred to as CA6 and CA8 jets, respectively. The choice of radius for C/A jets is optimised in order to optimally reconstruct the \(t\bar{t}A\) signal depending on the value of \(m_A\). To minimise the impact of soft radiation and pileup (the latter not modelled in this analysis), the massdrop (a.k.a. BDRS) filtering algorithm [71, 72] is applied to the reconstructed C/A jets. For BDRS filtering, the following parameters are used: \(\mu _\mathrm{frac}=0.67\) and \(y_\mathrm{cut}=0.09\) [73]. A semimuonic energy correction is also applied to the C/A jet fourmomentum, as in the case of AKT2 and AKT4 jets.
Experimental analysis
Analysis strategy and event selection
This search is focussed on the \(t\bar{t}A \rightarrow W^+b W^ \bar{b}b\bar{b}\) process, with one of the W bosons decaying leptonically and the other W boson decaying hadronically. The resulting final state signature is thus characterised by one electron or muon, and high jet and bjet multiplicities that can be exploited to suppress the background, dominated by \(t\bar{t}\)+jets production. Therefore, the following preselection requirements are made: exactly one electron or muon, \(\ge \)5 AKT4 jets and \(\ge \)3 AKT2 btagged jets, in the following simply referred to as \(\ge \)5 jets and \(\ge \)3 btags. In order to optimise the sensitivity of the search, the selected events are categorised into two separate channels depending on the number of btags (3 and \(\ge \)4). The channel with \(\ge \)5 jets and \(\ge \)4 btags has the largest signaltobackground ratio and therefore drives the sensitivity of the search. It is dominated by \(t\bar{t}\)+HF background. The channel with 3 btags has significantly lower signaltobackground ratio and the background is enriched in \(t\bar{t}+ \)light jets. The simultaneous analysis of both channels is useful to calibrate insitu the \(t\bar{t}+\) jets background prediction (including its heavyflavour content) and constrain the related systematic uncertainties, as will be discussed in Sect. 4.3. This is a common strategy used in many experimental searches in the ATLAS and CMS collaborations [57, 74, 75], which we mimic here in order to obtain more realistic projected sensitivities.
An extra handle is provided by the significant boost of the A boson in a fraction of signal events, which results in the two bjets from the \(A \rightarrow b\bar{b}\) decay emerging with small angular separation between them. This is particularly relevant for low \(m_A\) values, as shown in Fig. 2. As a result, the A boson decay products can be reconstructed into a single fat jet, whose mass distribution would show a resonant structure peaked at the correct \(m_A\) value. This feature is also very powerful to discriminate against the background. Therefore, a further requirement is made to have at least one C/A BDRSfiltered jet with radius parameter \(R^\mathrm{CA}\) and minimum \(p_\mathrm{{T}}\) depending on the \(m_A\) hypothesis being tested. In order to correctly reconstruct a significant fraction of the signal while rejecting as much background as possible, CA6 jets are used for \(m_A \le 40\) GeV, while CA8 jets are used for higher \(m_A\) values (up to 100 GeV). The minimum \(p_\mathrm{{T}}\) requirements on the C/A jets are 60, 100, 120, 150, 200 and 250 GeV for \(m_A=20, 30, 40, 60, 80\) and 100 GeV, respectively. As shown in Fig. 2, for high values of \(m_A\) only a small fraction of signal events would have the A decay products contained within the CA8 jet. The small signal acceptance comes with the benefit of improved background rejection and the ability to reconstruct the A boson mass, desirable in such simple analysis. However, it is expected that a dedicated multivariate analysis focussed on the sample rejected by this analysis, similar in spirit to the ATLAS and CMS searches for the SM Higgs boson in \(t\bar{t} h\), \(h \rightarrow b\bar{b}\) [57, 74], could also achieve significant signal sensitivity at high \(m_A\). Evaluating this possibility is beyond the scope of this study. The number of btags inside the C/A jet is determined by matching the btagged AKT2 jets within a cone of radius \(\Delta R =0.75 R^\mathrm{C/A}\). Finally, a requirement is made that the C/A jets have \(\ge \)2 btags inside. In the case of more than one selected C/A jet, the leading \(p_\mathrm{{T}}\) one is chosen.
Table 2 presents the expected yields for signal and the SM backgrounds per fb\(^{1}\) of integrated luminosity as a function of the selection cuts applied in each of the analysis channels under consideration: (\(\ge \)5j, 3b) and (\(\ge \)5j, \(\ge \)4b). In the case of the (\(\ge \)5j, 3b) channel, the dominant background after final selection is \(t\bar{t}\)+light jets, where typically the two bquarks from the top quark decays, as well as the cquark from the \(W \rightarrow c\bar{s}\) decay, are btagged. In contrast, in the (\(\ge \)5j, \(\ge \)4b) channel half of the background is \(t\bar{t}+{\ge }1b\), with \(t\bar{t}\)+\(b\bar{b}\) being its leading contribution. The rest of the background is approximately equally split between \(t\bar{t}+{\ge }1c\) and \(t\bar{t}+\) light jets. In this table the expected contribution from \(t\bar{t}A\) signal is obtained under the assumptions that \(g_t=2\) and \(\mathrm {BR}(A\rightarrow b\bar{b})=1\). Both analysis channels have approximately the same amount of signal, while the background is about a factor of 4 higher in the (\(\ge \)5j, 3b) channel than in the (\(\ge \)5j, \(\ge \)4b) channel. Together with the different composition of the background, the very different signaltobackground ratio between both channels is the primary motivation for analysing them separately.
The final discriminating variable is the invariant mass of the selected C/A jet, referred to as “BDRS jet mass”. Figures 3 and 4 show the expected distribution of the BDRS jet mass for signal and background in each of the analysis channels, for the different \(m_A\) values considered. The distributions correspond to \(\sqrt{s}=14\) TeV and are normalised to an integrated luminosity of 30 fb\(^{1}\). For the assumed values of \(g_t=2\) and \(\mathrm {BR}(A\rightarrow b\bar{b})=1\), the signal is clearly visible on top of the background.
Systematic uncertainties
Several sources of systematic uncertainty are considered that can affect the normalisation of signal and background and/or the shape of the BDRS jet mass distribution. Individual sources of systematic uncertainty are considered uncorrelated. For each systematic uncertainty, correlations are maintained across processes and analysis channels. The choices of what uncertainties to consider and their magnitude are inspired by recent \(t\bar{t}h_\mathrm{SM}\), \(h_\mathrm{SM}\rightarrow b\bar{b}\) searches at the LHC [57].
A 15 % normalisation uncertainty is assigned to the \(t\bar{t}\)+lightjet background corresponding to the modelling of the jet multiplicity spectrum. A 30 % normalisation uncertainty is assigned to each of the \(t\bar{t}+ \)HF background components (\(t\bar{t}+b\), \(t\bar{t}+b\bar{b}\), \(t\bar{t}+B\), \(t\bar{t}+c\), \(t\bar{t}+c\bar{c}\), \(t\bar{t}+C\)), and taken to be uncorrelated among them. These uncertainties are expected to be conservative given the recent progress in NLO predictions for \(t\bar{t}\) production with up to two jets merged with a parton shower [76], as well as NLO predictions for \(t\bar{t}+{\ge } 1b\) production in the 4F scheme matched to a parton shower [77]. Cross section uncertainties for \(t\bar{t}W\), \(t\bar{t}Z\) and \(t\bar{t}h_\mathrm{SM}\) backgrounds are taken to be 30 % for each process. Uncertainties associated with jet energy and jet mass calibrations are taken to be 5 % per jet, fully correlated between energy and mass and across all jets in the event. Finally, uncertainties on the b, c and lightjet tagging efficiencies are taken to be 3, 6 and 15 %, respectively. These uncertainties are taken as uncorrelated between bjets, cjets and light jets. As shown in Figs. 3 and 4, the resulting total background normalisation uncertainty is about 20 %, although the different uncertainty components have different shape in the final distribution.
Statistical method
The BDRS jet mass distribution in the two analysis channels under consideration (see Figs. 3, 4) are tested for the presence of a signal. To obtain the most realistic possible sensitivity projection, a sophisticated statistical analysis is performed, following very closely the strategy adopted in the experimental searches at the LHC.
For each \(m_A\) hypothesis, 95 % CL upper limits on the \(t\bar{t}A\) production cross section times branching ratio, \(\sigma (t\bar{t}A) \times \mathrm {BR}(A \rightarrow b\bar{b})\), are obtained with the CL\(_\mathrm{{s}}\) method [78, 79] using a profile likelihood ratio as test statistic implemented in the RooFit package [80, 81]. The likelihood function \(L(\mu ,\theta )\) depends on the signalstrength parameter \(\mu \), a multiplicative factor to the theoretical signal production cross section, and \(\theta \), a set of nuisance parameters that encode the effect of systematic uncertainties in the analysis. The likelihood function is constructed as a product of Poisson probability terms over all bins of the distributions analysed, and of Gaussian or lognormal probability terms, each corresponding to a nuisance parameter. For a given assumed value of \(\mu \), the profile likelihood ratio \(q_\mu \) is defined as:
where \(\hat{\hat{\theta }}_\mu \) are the values of the nuisance parameters that maximise the likelihood function for a given value of \(\mu \), and \(\hat{\mu }\) and \(\hat{\theta }\) are the values of the parameters that maximise the likelihood function (with the constraint \(0\le \hat{\mu } \le \mu \)). The maximisation of the likelihood function over the nuisance parameters allows variations of the expectations for signal and background in order to improve the agreement with (pseudo)data, yielding a background prediction with reduced overall uncertainty and thus resulting in an improved sensitivity. For a given \(m_A\) hypothesis, values of the production cross section (parameterised by \(\mu \)) yielding CL\(_\mathrm{{s}}<\)0.05, where CL\(_\mathrm{{s}}\) is computed using the asymptotic approximation [82], are excluded at \(\ge \)95 % CL.
Estimated limits on a light CPodd scalar
Following the analysis steps and the statistical method outlined in Sects. 2–4, we estimate expected 95 % CL upper limits on the production cross section times branching ratio, \(\sigma (t\bar{t}A) \times \mathrm {BR}(A\rightarrow b\bar{b})\), as a function of \(m_A\) (see Fig. 5). Table 3 summarises the 95 % CL upper limits on \(\sigma (t\bar{t}A) \times \mathrm {BR}(A\rightarrow b\bar{b})\) as a function of \(m_A\) for different values of the integrated luminosity. Under the assumption that \(\mathrm {BR}(A\rightarrow b\bar{b})=1\), the upper limits on \(\sigma (t\bar{t}A) \times \mathrm {BR}(A\rightarrow b\bar{b})\) can be translated into upper limits on \(g_t\), which are summarised in Table 4.
Using the reconstruction strategy outlined in Sect. 4.1, a CPodd scalar that couples with \(g_t=1\) can be excluded for \(20 \le m_A \le 90\) GeV with only \(30~\mathrm {fb}^{1}\) of data (see Fig. 5). With an increased statistics of \(300~\mathrm {fb}^{1}\) couplings as low as \(g_t \simeq 0.5\) can be constrained over a large mass range, i.e. \(30 \le m_A \le 80\) GeV.
Interpretation of limits
A light CPodd Higgs boson (\(m_A < 125\) GeV), which may or may not be related to global symmetries being present, exists in many extensions of the SM. Its couplings with gauge bosons are generically suppressed, yielding weak bounds from LEP. If \(m_A<m_{h_\mathrm{SM}}/2\), it may be searched via the decay \(h_\mathrm{SM} \rightarrow AA\). Although such decay sometimes has a large branching ratio, being in conflict with current Higgs precision data, there do exist scenarios, in both supersymmetric and nonsupersymmetric theories, where the \(\mathrm {BR}(h_\mathrm{SM}\rightarrow AA)\) is suppressed. Therefore, new strategies for collider searches that could cover as large as possible model parameter space with a light CPodd Higgs boson, are necessary. Next, we will interpret our collider analysis of \(t\bar{t} A\) in several representative beyondSM scenarios.
2HDM
In the Minimal Supersymmetric Standard Model (MSSM), a supersymmetric extension of a typeII 2HDM, a scenario with a light CPodd Higgs boson is hard to achieve, given constraints from precision Higgs data. This is not surprising since there are only two free parameters at tree level in the Higgs sector, due to supersymmetric interrelations. The picture, however, is changed in the 2HDM without supersymmetry. With a softly broken \(Z_2\) symmetry (\(\Phi _1 \rightarrow \Phi _1\), \(\Phi _2 \rightarrow \Phi _2\)), which is often introduced to suppress scalarmediated flavourchanging processes, the Higgs potential of the 2HDM is given by
where \(\Phi _{1,2}\) are complex \(SU(2)_L\) doublets. Assuming no CPviolation, the model has two CPeven and one CPodd spin0 neutral eigenstates, denoted as h, H, and A, respectively. Such a setup contains seven free parameters at tree level (including all Higgs masses), yielding a large parameter space that can accommodate a light CPodd Higgs boson.
Theoretically, the SMlike Higgs boson \(h_\mathrm{SM}\), with mass of 125 GeV, could be either the light CPeven Higgs boson (h) or the heavy one (H). If \(m_A < m_{h_\mathrm{SM}}/2\), the decay \(h_\mathrm{SM}\rightarrow AA\) is kinematically allowed. Often the partial width for \(h_\mathrm{SM}\rightarrow AA\) becomes comparable or ever dominant over that of \(h_\mathrm{SM}\rightarrow b\bar{b}\), given that the latter is suppressed by the small value of the bquark mass. Therefore, \(h_\mathrm{SM} \rightarrow AA\) decays become a good probe for these light bosonic particles. However, as discussed recently [83],^{Footnote 3} in the alignment limit [\(\cos (\beta \alpha )=0\) if \(h_\mathrm{SM}=h\), and \(\sin (\beta \alpha )=0\) if \(h_\mathrm{SM}=H\)], which is favoured by current precision Higgs measurements, the Higgs coupling \(g_{h_\mathrm{SM} AA}\) is reduced to:
In the case that \(2 m_A^2 + m_{h_\mathrm{SM}}^2 \sim 4 m_{12}^2/\sin 2\beta \), the decay \(h_\mathrm{SM}\rightarrow AA\) would be greatly suppressed. Therefore, collider strategies are needed to probe these scenarios with \(m_A < m_{h_\mathrm{SM}}/2\), as well as the scenarios with \(m_A > m_{h_\mathrm{SM}}/2\).
We should note that the perturbation requirement for Higgs couplings yields bounds on \(\tan \beta \). Particularly, the coupling \(\lambda _1\) is related to the Higgs boson mass via the relation [83]:
Assuming \(g_{h_\mathrm{SM}\rightarrow AA}=0\), it becomes
Given that \(m_H^2  m_{h_\mathrm{SM}}^2/2  m_A^2 > 0\) for \(m_A < m_{h_\mathrm{SM}}/2\), the perturbativity condition \(\lambda _1 < 4\pi \) immediately sets an upper bound on \(\tan \beta \) in this region:
These features are illustrated in Fig. 6. Additionally, the perturbation requirement for top Yukawa couplings can bound the \(\tan \beta \) value from below. So we will limit our discussions for \(\tan \beta > 0.1\).
The expected sensitivities for probing these scenarios in the 2HDM via \(b\bar{b}A\) and \(t\bar{t}A\) production are presented in Fig. 7. The \(b\bar{b}A\) reach is estimated based on the projections from Ref. [85], neglecting systematic uncertainties. For illustration, we focus on typeI and typeII 2HDMs. Within a typeII 2HDM, the \(t\bar{t}A\) and \(b\bar{b}A\) channels are complementary to each other in searching for light CPodd Higgs bosons, since the coupling \(g_{bbA}\) is \(\tan \beta \)enhanced whereas \(g_{ttA}\) is \(\cot \beta \)enhanced. With integrated luminosities in excess of 300 fb\(^{1}\), the whole parameter region can be covered except a corner with relatively large \(m_A\) and moderate \(\tan \beta \). This is interesting given that low \(\tan \beta \) is particularly favoured by perturbativity. In contrast, within a typeI 2HDM, the coupling \(g_{bbA}\) would also be \(\cot \beta \)enhanced, so both search channels are no longer probing complementary \(\tan \beta \) regions. As a matter of fact, in such scenario the \(t\bar{t}A\) channel provides better sensitivity to search for the light CPodd Higgs boson over the whole mass range of \(20~\mathrm{GeV} < m_A < 100~\mathrm{GeV}\), although the high\(\tan \beta \) region remains difficult to probe.
Searches for \(t\bar{t}A\) and \(b\bar{b} A\) also provide a probe for DM physics. For example, consider a Dirac fermion \(\chi \) that is a DM candidate, with mass \(m_\chi \), and coupling to the CPodd scalar A via:
Integrating out A yields a dimensionsix effective operator:
Such an operator implies swave DM annihilation \(\chi \chi \rightarrow b\bar{b}\) with
allowing an explanation for the recently observed diffuse gammaray excess from the Galactic Centre [7, 86]. In Fig. 7, the \(\tan \beta m_A\) values consistent with an explanation of the gammaray excess are indicated, yielding a DM annihilation cross section of \(\langle \sigma v \rangle \simeq 12.5 \times 10^{26} \mathrm{cm}^3 \mathrm{s}^{1}\), under the assumptions that \(m_{\chi }=50\) GeV [87] and \(y_\chi = 0.3\). This scenario results in a spindependent and pwavesuppressed direct detection signal, resulting in a weak bound from current direct detection searches. Monojet searches at the LHC would also be insensitive since the decay \(A \rightarrow \chi \chi \) would be kinematically forbidden, while the \(t\bar{t}A\), \(A \rightarrow b\bar{b}\) search would provide an effective probe.
NMSSM
Another class of benchmark scenarios for light CPodd Higgs bosons arise in the NMSSM, with the superpotential and soft supersymmetrybreaking terms of its Higgs sector given by
where \(H_d\), \(H_u\) and S denote the neutral Higgs fields of the \(\mathbf{H_d}\), \(\mathbf{H_u}\) and \(\mathbf{S}\) supermultiplets, respectively. For convenience, let us define its CPeven and CPodd mass eigenstates as \(H_i\), \(i=1,2,3\), and \(A_j\), \(j=1,2\), respectively.
In contrast with the 2HDM case, the light CPodd Higgs boson in the NMSSM often results from breaking an approximate global symmetry spontaneously, serving as an axion or a pseudoGoldstone boson. Its appearance is thus less “artificial” than in a 2HDM (including the MSSM). Let us start with the treelevel mass matrix of the CPodd Higgs bosons in the NMSSM:
which yields a determinant
Necessarily, the scenarios with a light \(A_1\) (\(A_1\) denotes the lightest CPodd Higgs boson) or \(m_{A_1} \rightarrow 0\) yield \(\det (\mathcal {M}^2_{P}) \rightarrow 0\) and vice versa, if such a stable vacuum exists. Among various possibilities, two have been studied extensively: Rsymmetry (or Rlimit) and Peccei–Quinn (PQ)symmetry (or PQlimit), both of which yield a vanishing determinant at tree level.
Another difference with a 2HDM is that the light CPodd Higgs boson in the NMSSM is typically singletlike. This can be understood since the Goldstone boson of a spontaneously broken global U(1)symmetry is manifested as
Here \(v_{U(1)} = \sqrt{\sum q_i^2 v_i^2}\) is the U(1) breaking scale and \(q_i\) is the U(1) charge of \(\Phi _i\). An effective parameter \(\mu = \lambda \langle v_S\rangle \) of the electroweak scale with \(\lambda \sim \mathcal O(0.1)\) naturally yields \(v_S \gg v_u, v_d\), and hence a singletlike pseudoGoldstone boson. This feature renders such a light boson much more difficult to probe at colliders, compared to the 2HDM case.
Next, we evaluate the collider constraints on the two NMSSM scenarios discussed above:

1.
Rlimit: \(A_\lambda \rightarrow 0\), \(A_\kappa \rightarrow 0\), where the theory is approximately invariant under the transformation
$$\begin{aligned}&H_u \rightarrow H_u \exp (i \phi _\mathrm{R}), \quad H_d \rightarrow H_d \exp (i \phi _\mathrm{R}),\nonumber \\&S \rightarrow S \exp (i \phi _\mathrm{R}), \end{aligned}$$(16)and the treelevel couplings of the Raxion \(A_1\) with the top and bottom quarks are given by
$$\begin{aligned} y_{A_1 tt} = \frac{2 \lambda v \cos ^2 \beta }{\mu },\quad y_{A_1 bb} = \frac{2 \lambda v \sin ^2 \beta }{\mu }. \end{aligned}$$(17)In this scenario, both \(\lambda \) and \(\kappa \) can be large, yielding a sizeable contribution to the mass of the SMlike Higgs boson at tree level. Hence, a large value for \(\tan \beta \) is unnecessary. A scan in the parameter space in this scenario is performed using NMSSMTools 4.2.1 [88–93] including all builtin constraints, such as from Higgs searches, superpartner searches, muon \(g2\), flavour physics, invisible Zboson decay and the constraints from \(\Upsilon \) decays (with the exception of the Landau pole test and DM relatedconstraints, which are not considered). The resulting values for the \(y_{A_1tt}\) and \(y_{A_1bb}\) couplings are compared to the expected collider bounds in Fig. 8a. Depending on the parameter values, the magnitude of \(y_{A_1tt}\) in this scenario can be up to \(\sim 0.5\). Only for an integrated luminosity of 3000 fb\(^{1}\) the LHC can probe a coupling \(y_{A_1tt}\) as small as 0.5 via the \(t\bar{t} A_1\), \(A_1 \rightarrow b\bar{b}\) channel. Therefore this scenario is difficult to probe, even at the HLLHC.

2.
PQlimit: \(\frac{\kappa }{\lambda } \rightarrow 0\), \(A_\kappa \rightarrow 0\), where the theory is approximately invariant under the transformation
$$\begin{aligned}&H_u \rightarrow H_u \exp (i \phi _\mathrm{PQ}),\quad H_d \rightarrow H_d \exp (i \phi _\mathrm{PQ}), \nonumber \\&\quad S \rightarrow S \exp (2i \phi _\mathrm{PQ}), \end{aligned}$$(18)and the treelevel mass of the PQ pseudoGoldstone boson \(A_1\) are given by
$$\begin{aligned} m_{A_1} =  \frac{3 \kappa A_\kappa \mu }{\lambda }. \end{aligned}$$(19)This scenario has been proposed as a supersymmetric benchmark for subelectroweak scale (singlinolike) DM [84], since its lightest neutralino is generically singlinolike and lighter than the electroweak scale. Particularly, in this scenario \(A_1\) can serve as the mediator for DM annihilation into a bottom quark pair and explain the diffuse gammaray excess from the Galactic Centre [15, 16]. In this limit, the treelevel couplings of \(A_1\) with the top and bottom quarks are given by
$$\begin{aligned} y_{A_1 tt} = \frac{\lambda v \cos ^2 \beta }{\mu }, \quad y_{A_1 bb} = \frac{\lambda v \sin ^2 \beta }{\mu }, \end{aligned}$$(20)and so they are smaller by a factor of 2 than the corresponding couplings in the Rlimit. Furthermore, a smaller \(\lambda \) is favoured in this limit and a relatively large \(\tan \beta \) is needed to generate a mass of 125 GeV for the SMlike Higgs boson. Therefore, the coupling \(y_{A_1 tt}\) tends to be smaller than in the Rlimit scenario. The resulting values for the \(y_{A_1tt}\) and \(y_{A_1bb}\) couplings are compared to the expected collider bounds in Fig. 8b. For most of the points, the magnitude of \(y_{A_1 tt}\) is below 0.1, which renders this scenario extremely difficult to probe at the LHC using the \(t\bar{t}A_1\) channel.^{Footnote 4}
Finally, we stress that the \(b\bar{b} A_1\) channel does not help much in probing the R and PQlimit scenarios. The sensitivities of both searches are suppressed by the mixture with the singlet. Even worse, the mixing is approximately \(\tan \beta \) enhanced, further suppressing the sensitivity of the \(b\bar{b} A_1\) in probing the large \(\tan \beta \) region in both scenarios (Fig. 9).
Conclusions
Searches for CPodd scalars, as predicted by many extensions of the Standard Model and motivated by some recent astroparticle observations, are part of the core program of upcoming LHC runs at \(\sqrt{s}=13\) and 14 TeV. Searches at LEP and during Run 1 of the LHC at \(\sqrt{s}=7\) and 8 TeV have placed only weak constraints on the coupling strengths of CPodd scalars with top and bottom quarks, or in their allowed mass range.
Using a simplified model approach for the signal, we have carried out a detailed study to evaluate the prospects at the LHC for probing scenarios with a CPodd scalar with mass \(20 \le m_A < 100\) GeV, via the process \(pp \rightarrow t\bar{t}A\) with subsequent decay \(A\rightarrow b\bar{b}\). To separate the signal from the large background from \(t\bar{t} +\) jets production, we apply jetsubstructure techniques, reconstructing the mass of the CPodd scalar as the mass of a largeradius jet containing two btagged subjets. The chosen method allows for a socalled “bump hunt” over a fairly smooth background, and it may be the most promising strategy for searching for a CPodd scalar with mass \({\lesssim } 50\) GeV, i.e. about twice the typical minimum \(p_\mathrm{{T}}\) cut for narrow jets used in standard LHC searches. A significant effort has been made to develop a semirealistic experimental analysis, including a fairly complete description of systematic uncertainties. For more realistic estimates, sophisticated statistical tools are used to constrain insitu the effect of systematic uncertainties, thus limiting their impact on the search sensitivity. We then derive expected upper limits on the production cross section times branching ratio using the CL\(_\mathrm{{s}}\) method.
In specific models, e.g. 2HDM or NMSSM, the coupling of the A boson with the top quark is related to other couplings in a welldefined way. Hence, the upper limits obtained on this coupling for a given mass \(m_A\) can be used to bound other couplings of these models indirectly or as input for a global coupling fit. We find that in a typeI and typeII 2HDM the LHC can constrain a large fraction of the \((m_A, \tan \beta )\) parameter space, including the region preferred to explain the diffuse gammaray excess from the Galactic Centre as darkmatter annihilation via a CPodd scalar mediator which decays into \(b\bar{b}\). However, in the case of the NMSSM with a light CPodd scalar, a Goldstone boson of either a spontaneously broken R or PQsymmetry, the LHC appears to have very limited sensitivity in probing these models. Hence, depending on the concrete embedding of the scalar sector into a UVcomplete theory, the LHC can provide complementary information, not accessible at either indirect detection experiments or electron–positron colliders, on the existence of CPodd scalars, their mass, and their couplings to thirdgeneration fermions.
Notes
We note that, if the pseudoscalar couples for example in a universal way to fermions as part of a UVcomplete model, thereby not respecting Yukawalike coupling hierarchies, other production and decay channels might be more sensitive. However, the analysis we provide is still valid as a subset of possible search channels.
For a brief discussion of the limitations of simplified models see Ref. [37].
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Acknowledgments
This research was supported in part by the European Commission through the “HiggsTools” Initial Training Network PITNGA2012316704 (M.S.) and by the Spanish Ministerio de Economía y Competitividad under projects FPA201238713 and Centro de Excelencia Severo Ochoa SEV20120234 (M.C., T.F. and A.J). T.L. is supported by his startup fund at the HKUST. T.L. would also like to thank Y. Jiang for useful discussions and acknowledge the hospitality of the Jockey Club Institute for Advanced Study, HKUST, where part of this work was completed.
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Casolino, M., Farooque, T., Juste, A. et al. Probing a light CPodd scalar in ditopassociated production at the LHC. Eur. Phys. J. C 75, 498 (2015). https://doi.org/10.1140/epjc/s100520153708y
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DOI: https://doi.org/10.1140/epjc/s100520153708y
Keywords
 Higgs Boson
 Minimal Supersymmetric Standard Model
 Systematic Uncertainty
 Parton Shower
 Parton Distribution Function