ATLAS on-Z excess via gluino-Higgsino-singlino decay chains in the NMSSM

Recently the ATLAS experiment has reported 3.0 σ excess in an on-Z signal region in searches for supersymmetric particles. We find that the next-to-minimal supersymmetric standard model can explain this excess by the production of gluinos which mainly decay via g˜→gχ˜2,30→gZχ˜10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde{g}\to g{\tilde{\chi}}_{2,3}^0\to gZ{\tilde{\chi}}_1^0 $$\end{document} where χ˜2,30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\tilde{\chi}}_{2,3}^0 $$\end{document} and χ˜10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\tilde{\chi}}_1^0 $$\end{document} are the Higgsino and the singlino-like neutralinos, respectively. We show that the observed dark matter density is explained by the thermal relic density of the singlino-like neutralino, simultaneously. We also discuss the searches for the Higgs sector of this scenario at the Large Hadron Collider.


Introduction
The supersymmetric (SUSY) models are attractive candidates for physics beyond the standard model (SM) because the hierarchy problem can be solved and dark matter is naturally introduced when the R-parity is conserved. Among various possibilities, the minimal SUSY standard model (MSSM) has been the prime candidate for the realistic supersymmetric model. A drawback of the MSSM is, however, that it contains a dimensionful parameter µ, the mass term of the Higgs multiplets. This reintroduces an additional fine-tuning problem, the so-called µ problem [1]. The size of µ is required to be of the order of other soft SUSY breaking parameters for successful electroweak symmetry breaking whereas they are essentially unrelated with each other.
The simplest solution of the µ problem is to introduce an additional gauge-singlet superfieldŜ [2] whose vacuum expectation value (VEV) is controlled by soft SUSY breaking parameters. By making an effective µ term generated by the VEV ofŜ, the size of µ is naturally interrelated to the size of the soft SUSY breaking parameters. The next-tominimal SUSY standard model (NMSSM) is one of the simplest singlet extensions of the MSSM where a discrete Z 3 symmetry is imposed [2][3][4].
Recently, the ATLAS experiment has reported excess events in the SUSY particle searches with dileptons, jets and missing transverse energy (E miss T ) in data of 20.3 fb −1 at √ s = 8 TeV [5]. They have observed 29 (16 for ee and 13 for µµ) same-flavour oppositesign dilepton pairs whose invariant masses are in the Z boson mass window, 81 GeV < m < 101 GeV ("on-Z" signal region). The expected number of SM background events is 10.6±3.2 pairs. The observed event number corresponds to excess of 3.0 σ local significance (3.0 σ for ee and 1.7 σ for µµ, separately). In this paper, we call this excess "ATLAS on-Z excess". This excess seems to imply an existence of a gluino whose mass is lighter than 1.2 TeV or squarks lighter than 1.4 TeV [6]. The caveat is, though, that the CMS experiment has also analyzed the dileptons+jets+E miss T final state using √ s = 8 TeV data

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in which the kinematical cut is different from the ATLAS one, and a significant excess has not been observed in the on-Z signal region [7]. After the report, many scenarios in the MSSM as well as in the NMSSM have been proposed to explain the ATLAS on-Z excess without conflicting with constraints from various SUSY searches including the CMS on-Z result [6,[8][9][10][11][12][13][14][15][16][17][18][19][20]. To have on-shell Z bosons in final states while escaping other SUSY search constraints, scenarios with a gravitino as the lightest SUSY particle (LSP) seems to be one of the simplest possibilities. The lightest neutralino decays into a pair of a Z boson and a gravitino, while the decay of colored SUSY particles into the gravitino with a large E miss T are suppressed. Unfortunately, however, the simplified general gauge mediation model with the gravitino LSP cannot explain the ATLAS on-Z excess [9,10], where the produced Z bosons are rather hard due to the lightness of the gravitino and are caught in the mesh of the SUSY searches with multi jets + E miss T . In ref. [16], it has been shown that this problem can be evaded by introducing a non-MSSM massive particle, a goldstiniG , into which the lightest neutralino mainly decays. Due to the massiveness of the goldstini, the Z bosons are emitted softly, and hence, the constraints from 0 lepton + multi jets + E miss T searches become weaker. In this scenario, similar to the gravitino LSP scenario, the couplings between the goldstini and the MSSM particles are suppressed. Besides, the sfermion masses are assumed to be rather larger than the gaugino masses and the lightest neutralino is assumed to be the Higgsino-like. With this setup, the ATLAS on-Z excess is successfully explained by the gluino production via a decay chain,g → gχ 0 1,2 → gZG , whereχ 0 1,2 are the Higgsino-like neutralinos. The above goldstini nature is also realized in the NMSSM with a singlino-like neutralino LSP, where the singlino is the fermionic component of the additional singlet superfieldŜ. Actually, some literature investigated this possibility with decay chains ofg → qqχ 0 2 → qqZχ 0 1 [9,12], andq → qχ 0 2 → qZχ 0 1 [17,19], where in both casesχ 0 2 andχ 0 1 are the bino and singlino-like neutralinos, respectively.
In this paper, we discuss another possibility in the NMSSM and consider the gluino pair production whose decay chain isg → gχ 0 2,3 → gZχ 0 1 , whereχ 0 2,3 andχ 0 1 are the Higgsino-like and the singlino-like neutralinos, respectively (see figure 1). It should be noted that the two-body gluino decay modesg → gχ 0 2,3 at one-loop level are the dominant ones when the mass differences between the gluino and the Higgsinos are moderate and the squark masses are in the several TeV range [15,21,22]. Besides, as we will show, the radiative decay of the gluino reproduces the distribution of the jet multiplicity observed in the ATLAS results well.
We also investigate the properties of dark matter in the NMSSM, and find two distinct benchmark parameter sets. Eventually, we show that the ATLAS on-Z excess and the observed relic abundance of dark matter can be simultaneously explained in the NMSSM, without conflicting with other experimental constraints, including the CMS on-Z result.
We organize the rest of this paper as follows. In section 2, we briefly review the mass matrices of the Higgs-sector and neutralinos in the NMSSM. Next in section 3, we give an explanation of the ATLAS on-Z excess using the NMSSM with the singlino-like neutralino LSP. In section 4, the property of the dark matter around our benchmark points is discussed. In section 5, we discuss the searches for the Higgs sector at the LHC. The final section is devoted to conclusion.

NMSSM
In this paper, we investigate a possible explanation of the ATLAS on-Z excess in the NMSSM. Motivated by the study about the goldstini [16], we consider the case of the singlino-like neutralino LSP.
In this section, we quickly review the mass spectrum of the NMSSM by paying particular attention to the dependence on parameters. The detail of the NMSSM is given in ref. [23]. The superpotential and the scalar potential of the Higgs-sector in the NMSSM are given as where fields with hats are superfields, andŜ,Ĥ 1,2 are the singlet and the down-type and up-type Higgs doublets, respectively. κ and λ are coupling constants in the superpotential, and g and g are gauge coupling constants of the SU(2) L and U(1) Y gauge interactions. Due to the discrete Z 3 symmetry under whichŜ as well asĤ 1,2 rotate with unit charges, the superpotential does not have dimensionful parameters. The dimensionful parameters in the scalar potential are the soft SUSY breaking parameters, i.e., m 2 1,2,s and A λ,κ . For simplicity, we assume all parameters to be real in this paper. When the electroweak symmetry is broken, three neutral scalar bosons obtain VEVs and they are expanded around their VEVs as follows, (174.1 GeV) 2 and we use tan β ≡ v 2 /v 1 in the following. Then the effective µ term is generated, Since the singlet VEV v s is the same scale as the SUSY breaking dimensionful terms, the µ problem is solved.
In the NMSSM, the singlino is the one of the neutralino components. The neutralino mass matrix for the basis ψ 0 = B ,W 0 ,H 0 1 ,H 0 2 ,S is given as Typically, the mass of the singlino-like neutralino is given as mS |2κv s |.
The Higgs mass matrices for the basis (H , h , S R ) and (A , S I , G) (defined below) are given as Here, the convenient basis (H , h , S R ) and (A , S I , G) are defined by One of the NMSSM specific A terms A λ plays two important roles in determining the properties of the singlet particles and the Higgs mass spectrum. First, the mass scale of the heavy Higgs in eq. (2.17) can be controlled by A λ . Second, a singlet-doublet mixing for the SM-like Higgs boson can also be controlled by A λ . Even if the mass of the singlet-like Higgs boson is heavy, the effect of the singlet-doublet mixing does not decouple. When the lightest CP even Higgs boson is the SM-like one and M A is very large, the contribution of an off-diagonal mass termM 2 R23 (eq. (2.13)) to the mass of the SM-like Higgs boson is roughly estimated as follows, 1 which leads to a too light SM-like Higgs boson mass. This undesirable negative contribution via the singlet-doublet mixing can be avoided if λ 1 or when the following condition is satisfied, These conditions also suppress the off-diagonal mass termM 2 R23 .

Explanation of the ATLAS on-Z excess
In this section, we give an explanation of the ATLAS Z+jets+E miss T excess in the NMSSM. In order to explain the signals of the ATLAS on-Z excess by the gluino pair production, we consider the following mass spectrum, The reason to choose the above mass spectrum is described below.

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In order to explain the ATLAS on-Z excess by the gluino production, the following items are required.
• The gluino mass is required to be lighter than about 1.2 TeV for a large enough production cross section to explain the number of the excess [6].
• In the dominant gluino decay chain, at least one Z boson emission likeg → X+ NLSP → X + Z+ LSP is required, where X denotes SM colored particles.
• Since Z bosons dominantly decay hadronically, multi jets+E miss T searches put severe constraints. In order to ameliorate these constraints, the Z boson is required to be emitted rather softly. In addition, the decay of the NLSP into the Higgs boson + LSP is required to be suppressed so that the Z boson production is enhanced. This requirement also helps to evade the multi-jets constraints caused by the Higgs boson decay.
• In order to shift the jet multiplicity distribution to smaller values as is favored by the ATLAS result, the loop-induced gluino two-body decay is required to become dominant channel. This requirement is also advantageous to evade the multi-jets constraints.
To satisfy the above conditions, we consider the following mass spectrum in the NMSSM. First, in order to enhance the soft Z boson production, we assume a slight degeneracy between the NLSP and the LSP; m Z < m NLSP − m LSP < m h .
Next, in order for the gluino two-body decay to be a dominant channel, we assume that the gluino is lighter than the squarks, the bino, and the wino, while it is heavier than the Higgsinos and the singlino. 2 Besides, to suppress the decay of the gluino into tt(tb, bt) + Higgsino kinematically, we assume a slight degeneracy between the gluino and the Higgsino; mg − m Higgsino 300 GeV. Finally, to suppress the decay of the gluino into bb + Higgsino, we take the squark masses to be of order of 10 TeV. Note that the loopinduced gluino two-body decay into the gluon + Higgsino is relatively enhanced by a factor (ln(mt/m t )) 2 [15,21,22].
With the above mass spectrum, the Z boson is produced by the decay of the NLSP Higgsino-like neutralino into the LSP singlino-like neutralino. In terms of the model parameters, the Higgsino mass is typically given by |λv s | and the singlino mass is given by |2κv s |. Hence, λ ∼ 2κ to achieve the above mass spectrum.
Altogether, we consider the mass spectrum in eq. (3.1), in which the typical decay chain of the gluino isg → gχ 0 2,3 → gZχ 0 1 , whereχ 0 2,3 andχ 0 1 are the Higgsino and the singlino-like neutralinos, respectively. The diagram is drawn in figure 1. Note that due to small couplings between the singlino and the colored sector, the direct decay of the gluino into the singlino-like neutralino is suppressed. This is the advantage of the singlino-like

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LSP compared with the bino LSP scenario where the gluino decay mode into the bino LSP with jets can be comparable to the mode into the Higgsino NLSP depending on tan β.
Keeping above arguments in mind, we find two distinct valid parameter regions where the ATLAS on-Z excess can be explained. One is a region with a small λ and the other is the one with a large λ. As we will discuss in the next section, these two regions have different dark matter properties. It should be noted that the NMSSM in the small λ region is almost the same with the MSSM plus an additional gauge singlet fermion whose couplings to the MSSM sector are suppressed as in the simplified goldstini model [16]. In this region, the analyses of ref. [16] would be applied. In table 1, we show the two benchmark parameter sets in the two distinct parameter regions which exemplify the small λ and the large λ regions, respectively. In our analysis, we use the spectrum calculator NMSSMTools 4.7.0 [26,27] and also use the decay width calculator NMSDECAY [28]. In the table, we also show the properties of the dark matter which are calculated using MicrOMEGAs4.1.8 [29,30] (see next section). Note that we take M 1 = M 2 = 1.5 TeV in both benchmark points, and the bino and winos are decoupled enough.
At the small λ benchmark point, the mass of the SM-like Higgs boson is given by the radiative correction from the stop loop diagrams, which requires a large tan β. This large tan β leads to a large decay width ofg → bb(tb, bt) + Higgsino via an enhancement of the bottom Yukawa. Even for a rather large tan β, however, we have confirmed that the dominant decay channel of the gluino isg → g + Higgsino (see table 1).
At the large λ benchmark point, the mass of the SM-like Higgs boson is given by both the radiative correction and an additional F -term contribution which requires a small tan β (see eq. (2.9)). Such a large λ also brings the undesirable negative contribution to the lightest CP-even Higgs mass in eq. (2.20). To avoid this problem, we choose A λ that suppresses this negative contribution according to eq. (2.21). 3 Note that when one takes A λ to be O(1) TeV, this equation also suggests the small tan β. The large λ also leads to a certain singlino-Higgsino mixing, so that the decay branchg → g + singlino-like neutralino exists. Even with such contributions, we have again confirmed that the dominant decay channel isg → g + Higgsino (see table 1).
To investigate the number of the SUSY events in the ATLAS on-Z search and to check the experimental constraints from the other SUSY searches at the ATLAS and CMS collaborations, we use CheckMATE 1.2.1 [12,31] which incorporates DELPHES 3 [32] and FastJet [33,34] internally. Signal events are generated by MadGraph5 v2.2.3 [35,36] connected to Pythia 6.4 [37] where the MLM matching scheme is used with a matching scale at 150 GeV [38]. The parton distribution functions are CTEQ6L1 [39]. We use the gluino production cross sections at the next-to-leading-logarithmic accuracy given in ref.
As a result, we find that the SUSY events can explain the ATLAS on-Z excess within 1 σ without conflicting with any LHC constraints at 95% CL, including the CMS on-Z result for both benchmark points. In addition, the lightest CP-even Higgs boson mass is 125 GeV and the relic abundance of the singlino-like neutralino is also consistent with the observed values within 2 σ [46].
Let us comment on the uncertainty in the calculation of the Higgs boson mass. In NMSSMTools 4.7.0, the Higgs boson masses are calculated at full one-loop plus two-loop O(α t α s +α b α s ) level [47]. When the squark mass is about 10 TeV, a theoretical uncertainty of the SM-like Higgs boson mass from higher order corrections by the MSSM particles is about 5 GeV. Including the higher order corrections within the effective field theory approach, this uncertainty can be reduced to around 1 GeV with the similar central value

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in the case of the MSSM [48]. Thus, we simply use the result of NMSSMTools 4.7.0. Note that FeynHiggs [49] yields a larger Higgs mass by about 5 GeV. If this is the case, the required squark mass should be smaller by a factor of a few and the branching ratio of the radiative decay of the gluino becomes smaller. In the case of the large λ, we may change tan β as well as λ and obtain the similar LHC signal.
Before closing this section, let us comment on the distributions of the jet multiplicity, E miss T and H T in the on-Z signal region. In figure 2, we show the distributions of the jet multiplicity, E miss T and H T for the small λ and large λ benchmark points, respectively. Note that we combine the ee and µµ channels of the ATLAS results, although the efficiencies of the channels are different from each other. As shown in ref. [5], the jet multiplicity of the observed data is typically 2-5 jets while the multiplicity larger than 6 is disfavored. For both benchmark points, the jet multiplicity of the NMSSM contributions is peaked at around 4-5, which originates from two gluon jets in two gluino decays, two quarks from a Z-boson decay in one of the gluino decay chain, and an occasionally radiated jet. The predicted distributions of the jet multiplicity fit the ATLAS data very well, which confirms the advantage of the dominance of the gluino two body decay [16]. It can be seen that the distributions of E miss T and H T are also consistent with the data.

Dark matter property
In this section, we discuss the properties of dark matter in the small and large λ regions as exemplified in the above two benchmark points (see table 1). In the small λ region, the lightest neutralino is almost singlino-like. In most cases, such a singlino-like LSP results in overabundant dark matter in the universe because its annihilation cross section is too small. The overabundance is, however, avoided when the heavy Higgs masses are about twice of the mass of the singlino dark matter. Such a mass spectrum can be achieved by tuning the parameter A λ [50]. With this tuning, the singlino-like neutralino annihilates resonantly via the s-channel heavy Higgs boson exchange, which significantly enhances the annihilation cross section. 4 In this way, the observed dark matter density is explained by the singlino-like neutralino at the small λ benchmark point in spite of the weakness of couplings. It should be noted that due to a suppressed coupling between the singlino and the SM-like Higgs boson, the spin-independent dark matter-nucleon elastic scattering cross section is much lower than the reaches in currently proposed direct dark mater searches.
In the large λ region, on the other hand, there is a certain singlino-Higgsino mixing. The Higgsino components in the LSP can enhance the annihilation cross section, so that the tuning of the heavy Higgs mass is not required. In addition, sizable κ can also enhance the annihilation cross section. It is because that contributions of diagrams of s-cannel a s boson exchange into fermions [53] and t-channelχ

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The singlino-Higgsino mixing also contributes to the spin-independent dark matternucleon elastic scattering cross section at the large λ benchmark point. We found that the typical scattering cross section around the benchmark point is a little smaller than a current experimental bound by LUX [54], and proposed future experiments for the direct dark matter search can probe around this benchmark point [55][56][57][58].

Higgs sector searches at the LHC
In this section, we discuss the searches for the Higgs sector at the LHC. First, we consider the heavy doublet-like Higgses h 3 and a 2 . Successful parameter points in the small λ region always predict that the heavy doublet-like Higgses have masses around 1 TeV so that the singlino-like neutralino annihilates resonantly via the s-channel heavy Higgses exchanges. Interestingly, the 14 TeV LHC with a luminosity of 300 fb −1 can probe such a charged Higgs directly by the channel of pp → tbH + → tbtb due to a tan β enhancement of the bottom Yukawa [59]. 5 In the large λ region, although the production cross section of the heavy doublet-like Higgses is small, a high-luminosity LHC can probe them through the top Yukawa via the same channel [59].
Next, we consider the singlet-like scalars h 2 and a 1 . The masses of the singlet-like scalars tend to be within the TeV range in our scenario. This is because typical masses of the singlet scalars are controlled by κv s , which also determines the singlino mass and is taken as about 500 GeV in our scenario.
The singlet-like CP-even Higgs boson h 2 mainly decays into W W and ZZ due to an enhancement of the longitudinally polarized gauge bosons when the decay width into double Higgs, h 1 h 1 , is suppressed. In our benchmark points, we find that the gluongluon (vector boson) fusion cross sections of pp → h 2 (jj) → W W (jj) are 8 fb (1 fb) at the small λ benchmark point, and 0.2-20 fb (0.2-4 fb) at the large λ benchmark point for √ s = 14 TeV, where we vary A λ in the range of 1500-1100 GeV in the large λ benchmark point. Within this range of A λ , the reduction of the SM-like Higgs boson mass (see eq. (2.20)) can be compensated by taking a large trilinear coupling between the up-type Higgs doublet and stops. For a smaller A λ , h 2 contains more doublet components and hence the production cross section is larger. The current experimental upper bounds for the gluon-gluon (vector boson) fusion cross sections are 200 (100) fb for m h 2 = 500 GeV at √ s = 8 TeV [62].
On the other hand, the singlet-like CP-odd Higgs boson a 1 mainly decays into tt. The cross section of pp → a 1 → tt is 1 fb at √ s = 14 TeV at the large λ benchmark point. 6 The current upper bound is 2 pb for m a 1 = 500 GeV at √ s = 8 TeV [63]. Therefore, the direct search for such the singlet-like Higgses would be challenging. It is recently shown that the precision measurement of the double Higgs production can probe the singletlike Higgs bosons through the interference effect between a resonance production of the 5 In the small λ region, another promising channel for the heavy doublet-like Higgs searches is pp → h3/a2 → τ τ [60,61]. 6 In the small λ benchmark point, a1 → tt is forbidden by the kinematics, and mainly decays into bb.
However, pp → a1 → bb cannot be probed due to enormous background.

Conclusion
In this paper, we have studied a possible explanation of the ATLAS on-Z excess in the NMSSM by the gluino production via typical decay chains,g → gχ 0 2,3 → gZχ 0 1 , withχ 0 2,3 andχ 0 1 being the Higgsino and the singlino-like neutralinos, respectively. We found two distinct benchmark parameter sets. At the benchmark points, the observed dark matter density is also explained by the thermal relic abundance of the singlino-like neutralino. In addition, it is found that the expected distributions of the jet multiplicity, E miss T and H T for our benchmark points are consistent with the ATLAS data.
In the small λ region, we find that the 14 TeV LHC with a luminosity of 300 fb −1 can probe the 1 TeV charged Higgs directly by the channel of pp → tbH + → tbtb. On the other hand, in the large λ region, we find that proposed future experiments for the direct dark matter search can probe our scenario at around the benchmark point.