Advances in High Energy Physics

Volume 2015 (2015), Article ID 509847, 16 pages

http://dx.doi.org/10.1155/2015/509847

## Two Higgs Bosons near 125 GeV in the Complex NMSSM and the LHC Run I Data

^{1}School of Physics & Astronomy, University of Southampton, Southampton SO17 1BJ, UK^{2}Asia Pacific Center for Theoretical Physics, San 31, Hyoja-dong, Nam-gu, Pohang 790-784, Republic of Korea

Received 24 April 2015; Revised 14 July 2015; Accepted 30 July 2015

Academic Editor: Mark D. Goodsell

Copyright © 2015 Stefano Moretti and Shoaib Munir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

We analyse the impact of explicit CP-violation in the Higgs sector of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) on its consistency with the Higgs boson data from the Large Hadron Collider (LHC). Through detailed scans of the parameter space of the complex NMSSM for certain fixed values of one of its CP-violating (CPV) phases, we obtain a large number of points corresponding to five phenomenologically relevant scenarios containing ∼125 GeV Higgs boson(s). We focus, in particular, on the scenarios where the visible peaks in the experimental samples can actually be explained by two nearly mass-degenerate neutral Higgs boson states. We find that some points corresponding to these scenarios give an overall slightly improved fit to the data, more so for nonzero values of the CPV phase, compared to the scenarios containing a single Higgs boson near 125 GeV.

#### 1. Introduction

The Higgs sector of the NMSSM [1–4] (see, e.g., [5, 6] for reviews) contains two additional neutral mass eigenstates besides the three of the Minimal Supersymmetric Standard Model (MSSM). This is due to the presence of a Higgs singlet superfield besides the two doublet superfields of the MSSM. When all the parameters in the Higgs and sfermion sectors of the NMSSM are real, one of these new Higgs states is a scalar and the other a pseudoscalar. Hence, in total three scalars, , and two pseudoscalars, , make up the neutral Higgs boson content of the model. This extended Higgs sector of the NMSSM boasts some unique phenomenological possibilities, which are either precluded or experimentally ruled out in the MSSM. For example, in the NMSSM either of the two lightest CP-even Higgs bosons, or , can play the role of the ~125 GeV Standard Model- (SM-) like Higgs boson, , observed at the LHC [7–9].

Of particular interest in the NMSSM is the possibility that the SM-like Higgs boson can obtain a large tree-level mass in a* natural* way, that is, without requiring large radiative corrections from the supersymmetric sectors. This happens in a specific region of the parameter space, which we refer to as the natural NMSSM, where there is a significant singlet-doublet mixing and is typically . This scenario was used to explain [10–12] the enhancement in channel in the early LHC data. However, when the singlet-doublet mixing is too large, the properties of can deviate appreciably from an exact SM-like behaviour, resulting in a reduction of its fermionic partial decay widths. An alternative possibility in a very similar parameter space region is that of both and simultaneously having masses near 125 GeV [13–16]. In that case, the observed excess at the LHC could actually be due to a superposition of these two states, when their individual signal peaks cannot be resolved separately. One of these two Higgs bosons, typically , is the singlet-like neutral state. Moreover, in [17] it was noted that the lighter one of the two pseudoscalars, , when it is singlet-like, could also be nearly mass-degenerate with a SM-like near 125 GeV, instead of or even along with . However, such a pseudoscalar can only contribute visibly to the measured signal strength near 125 GeV if it is produced in association with pair.

One of the most important yet unresolved issues in particle physics is that of the observed matter-antimatter asymmetry in the universe. A plausible explanation for this asymmetry is electroweak (EW) baryogenesis [18, 19]. The necessary conditions for successful EW baryogenesis include the following [20]: baryon number violation, CP-violation, and departure from equilibrium at the critical temperature of the EW symmetry breaking (EWSB) phase transition, implying that it is strongly first order. In the SM, a strongly first order EW phase transition is not possible given the measured mass of the Higgs boson at the LHC. Besides, the only source of CP-violation in the SM, the Cabibbo-Kobayashi-Maskawa matrix, is insufficient. Therefore, beyond the SM, a variety of sources of CP-violation have been proposed in the literature (for a review, see [21] and references therein). In the context of supersymmetry (SUSY), a strongly first order phase transition is possible in the MSSM only if the lightest stop has a mass below that of the top quark. This possibility has now been ruled out by SUSY searches at the LHC [22–24]. Also, the MSSM Higgs sector does not violate CP at the tree level but does so only at higher orders [25–32]. The CPV phases, transmitted radiatively to the Higgs sector via couplings to the sfermions, are tightly constrained by the measurements of fermion electric dipole moments (EDMs) [33–35]. However, these EDM constraints can be relaxed under certain conditions [27, 28, 36–41].

The NMSSM has been shown to accommodate a strongly first order EW phase transition without a light stop [42–47]. Additionally, in this model, CP-violation can be invoked explicitly in the Higgs sector even at the tree level by assuming the Higgs self-couplings, and , to be complex. Beyond the Born approximation, the phase of the SUSY-breaking Higgs-sfermion-sfermion couplings, , where denotes a SM fermion, is also induced in the Higgs sector, as in the MSSM. In the presence of the associated complex phases, the five neutral Higgs bosons are CP-indefinite states, due to the mixing between the scalar and pseudoscalar interaction eigenstates. CPV phases can therefore influence the phenomenology of the NMSSM Higgs bosons by, for example, modifying their mass spectrum as well as their production and decay rates [48], similarly to the MSSM [49–59]. The impact of these phases in the complex NMSSM (cNMSSM), that is, the CPV NMSSM, on the necessary conditions for successful EW phase transition was also studied some time ago [60]. The consistency of scenarios yielding the correct baryon asymmetry with the LHC Higgs boson data still remains to be studied in depth though. However, even leaving aside these considerations, the possibly distinct phenomenological scenarios that the cNMSSM can yield make it a particularly interesting model for exploration at the Run II of the LHC.

The cNMSSM has therefore been the subject of several studies recently and, in particular, some important theoretical developments have been made in the model. The dominant 1-loop corrections to the neutral Higgs sector from the (s)quark and gauge sectors were studied in [61–64], in the renormalisation group equations-improved effective potential approach. The corrections from the gaugino sector were included in [65] and, more inclusively, recently in [66]. In the Feynman diagrammatic approach, the complete 1-loop Higgs mass matrix was derived in [67] and contributions to it were calculated in [68]. As far as the phenomenology of the Higgs bosons in the cNMSSM is concerned, the consistency of several CPV scenarios with the early results on from the LHC data was studied in detail in [48, 67]. Another distinct phenomenological scenario, possible only for nonzero CPV phases, has also been studied in [65].

The CMS and ATLAS collaborations have recently updated their measurements of signal rates in and channels [69, 70]. The fact that these rates also tend to favour a SM-like is increasingly jeopardising the above-mentioned natural NMSSM scenario with large singlet-doublet mixing but only with one Higgs boson, either or , around 125 GeV. This makes the scenario with both and contributing to the observed ~125 GeV signal all the more important, since it may potentially satisfy better the current Higgs boson data while still leaving plenty of room for new physics. In case of the cNMSSM, since the five neutral Higgs bosons are CP-mixed states, the scenario with mass-degenerate and can entail both the corresponding possibilities in the real NMSSM (rNMSSM), that is, mass-degenerate , or , .

In this study we therefore analyse and compare the prospects for scenarios with two mass-degenerate Higgs bosons against those with a single Higgs boson near 125 GeV in the -invariant cNMSSM. We perform scans of the relevant parameter space [13] of the model using the public program NMSSMCALC [71] to search for all possible ~125 GeV Higgs boson scenarios, with the CPV phase of the coupling set to five different values, including , the rNMSSM limit, in each case. The condition for mass-degeneracy between two Higgs bosons is imposed by requiring them to lie within 2.5 GeV of each other, which is consistent with the current mass resolution of the LHC [72], taking into account the uncertainties in the theoretical mass prediction. We then use fits to the Higgs boson data from the LHC Run I, both with TeV and TeV, as well as the Tevatron, performed using the program HiggsSignals [73], as the sole criterion for comparing the present likelihood of each of these scenarios. We also discuss how these mass-degenerate Higgs bosons can be identified at the LHC based on the signal rate double ratios introduced in [74].

The paper is organised as follows. In the next section we will briefly revisit the Higgs sector of the cNMSSM. In Section 3 we will provide details of our numerical scans and our procedure for fitting the model predictions for the Higgs boson(s) to the LHC data. In Section 4 we will discuss the results of our analysis and in Section 5 we will present our conclusions.

#### 2. The Higgs Sector of the cNMSSM

The NMSSM contains a singlet Higgs superfield, , besides the two doublet superfields,of the MSSM. The superpotential of the NMSSM is written aswhere and are dimensionless Yukawa couplings. This superpotential is scale invariant, since the term appearing in the MSSM superpotential has been removed by imposing a discrete symmetry. In this model, an effective -term, , is instead generated when the singlet field acquires a vacuum expectation value (VEV), , which is naturally of the order of the SUSY-breaking scale.

The tree-level Higgs potential of the NMSSM, obtained from the superpotential in (2), is written in terms of the neutral scalar components of the Higgs superfields, , , and , aswhere , with and being the and gauge couplings, respectively, and and are the soft SUSY-breaking Higgs trilinear couplings. The scalar fields , , and are developed around their respective VEVs, , , and , as

The Higgs coupling parameters appearing in the potential in (3) can very well be complex, implying , , , and . As a result, , evaluated at the vacuum, contains the phase combinationsFor correct EWSB, the Higgs potential should have a minimum at nonvanishing , , and , which is ensured by requiringThrough the above minimisation conditions the phase combinations and can be determined up to a twofold ambiguity by . Thus, is the only physical CP phase appearing in the NMSSM Higgs sector at the tree level. Also, using these conditions, the soft mass parameters , , and can be traded for the corresponding Higgs field VEVs.

The neutral Higgs mass matrix is obtained by taking the second derivative of evaluated at the vacuum. This matrix, , in the basis, from which the massless Nambu-Goldstone mode has been rotated away, can be diagonalised using an orthogonal matrix, , as . This yields the physical tree-level masses corresponding to the five mass eigenstates:such that . The elements, , of the mixing matrix then govern the couplings of the Higgs bosons to all the particles in the model.

The tree-level Higgs mass matrix is subject to higher order corrections from the SM fermions, from the gauge and chargino/neutralino sectors and the Higgs sector itself, as well as the sfermion sector, in case of which they are dominated by the stop contributions. Upon the inclusion of these corrections, , the Higgs mass matrix gets modified, so thatExplicit expressions for as well as can be found in [65–67]. Thus, beyond the Born approximation, the CPV phases of the gaugino mass parameters, , and of are also radiatively induced in the Higgs sector of the NMSSM.

Therefore, when studying the phenomenology of the Higgs bosons, one needs to take into account also the parameters from the other sectors of the model. However, the most general NMSSM contains more than 130 parameters at the EW scale. Assuming the matrices for the sfermion masses and for the trilinear scalar couplings to be diagonal considerably reduces the number of free parameters. One can further exploit the fact, mentioned above, that the corrections to the Higgs boson masses from the sfermions are largely dominated by the stop sector. For our numerical analysis in the following sections, we will thus impose the following supergravity-inspired universality conditions on the model parameters at the EW scale:where , , , , and are the squared soft masses of the sfermions, those of the gauginos, and the soft trilinear couplings. Altogether, the input parameters of the cNMSSM then include , , , , , , , , , , , , and , where and are the phases of the unified parameters and , respectively.

#### 3. Numerical Analysis

As noted in the Introduction, nonzero CPV phases can modify appreciably the masses and decay widths of the neutral Higgs bosons compared to the CP-conserving case for a given set of the remaining free parameters. In the case of candidate in the model, whether or or even , the CPV phases are thus strongly constrained by the LHC mass and signal rate measurements. This was analysed in detail in [48], where the scenarios with mass-degenerate Higgs bosons were, however, not taken into account. In the present study we thus test whether the said modifications in the Higgs boson properties with nonzero values of the phase (by which we imply , which is the actual physically meaningful phase, since can be absorbed into by a field redefinition) can lead to a relatively improved consistency with the experimental data.

The reason for choosing as the only variable phase while setting , , and to is that it is virtually unconstrained by the measurements of fermionic EDMs [63, 64, 67]. Furthermore, our aim here is to analyse the scenarios with a generic CPV phase and compare them with the rNMSSM limit rather than measure the effect of any of the individual phases. Note however that since only the difference enters the Higgs mass matrix at the tree level, the impact of a variation in is also quantified by that due to the variation in at this level. At higher orders though, a variation in has an impact on the sfermion and neutralino/chargino sectors which is independent of .

In our numerical analysis, we used the program NMSSMCALC-v1.03 [71] for computing the Higgs boson mass spectrum and decay branching ratios (BRs) for a given model input point. The public distribution of NMSSMCALC contains two separate packages, one for the rNMSSM only and the other for the cNMSSM. Some supersymmetric corrections to the Higgs boson decay widths are currently only available in the rNMSSM and hence are not included in the cNMSSM package. For consistency among our rNMSSM and cNMSSM results, we therefore set in the cNMSSM package for the rNMSSM case instead of using the dedicated rNMSSM package. Furthermore, using the cNMSSM code also for the rNMSSM limit makes it convenient to draw a one-on-one correspondence between case and each of cases in a given scenario. This is because in the cNMSSM package, even in the rNMSSM limit, the five neutral Higgs bosons are ordered by their masses and not separated on the basis of their CP-identities. Thus, the scenario with mass-degenerate , , which we will henceforth refer to as the scenario, takes into account both the ~125 GeV , and the ~125 GeV , solutions of the rNMSSM without distinguishing between them. If one, conversely, uses the rNMSSM package, these two scenarios ought to be considered separately. The same is true also for the scenario, wherein , are mass-degenerate.

The program NMSSMCALC allows one the option to include only the complete 1-loop contributions in the Higgs mass matrix or to add also the 2-loop corrections to it. In our analysis, for a better theoretical precision, we evaluated the Higgs boson masses at the 2-loop level. In the NMSSMCALC input, one also needs to choose between the modified dimensional regularisation () and on-shell renormalisation schemes for calculating contributions from the top/stop sector in the program. We opted for the scheme for each scenario. Note though that further inclusion of , , and the recently calculated NMSSM-specific 2-loop corrections [75] in NMSSMCALC may have a nonnegligible impact on the Higgs boson masses and observables [76]. We, however, maintain that such contributions will only result in a slight shifting of the parameter configurations yielding solutions of our interest here, but our overall results and conclusions should still remain valid.

We performed six sets of scans of the cNMSSM parameter space by linking NMSSMCALC with the MultiNest-v2.18 [77–79] package. MultiNest performs a multimodal sampling of a theoretical model’s parameter space based on Bayesian evidence estimation. However, we use this package not for drawing Bayesian inferences about the various NMSSM scenarios considered but simply to avoid a completely random sampling of the 9-dimensional model parameter space. In the program, we therefore defined a Gaussian likelihood function for in a given scan, assuming the experimental measurement of its mass to be 125 GeV and allowing up to ±2GeV error in its model prediction. We set the enlargement factor reduction parameter to 0.3 and the evidence tolerance factor to a rather small value of 0.2, so that while the package was sampled more concentratedly near the central mass value, a sufficiently large number of points were collected before the scan converged. In each of the first two sets of scans we required to be . In the third set we imposed this requirement of consistency with mass on , in the fourth set on , in the fifth set on both and , and in the sixth set on both and . Each of the six sets further contained five separate scans corresponding to , , , , and .

The scanned ranges of the nine free parameters (after fixing the phases) of the natural NMSSM, which are uniform across all its five scenarios considered, are given in Table 1(a). Only large values of and are used in this model (with the upper cut-off on them imposed to avoid the Landau pole). Since large radiative corrections from SUSY sectors are not necessary in the natural limit of the NMSSM, the parameters , , and are not required to take too large values. Note that while can in principle be both positive and negative, with a slightly different impact on the physical mass of the SM-like Higgs boson for an identical set of other input parameters in each case, we restricted the scans to its negative values only, in order to increase the scanning efficiency.