Interpretations of galactic center gammaray excess confronting the PandaXII constraints on dark matterneutron spindependent scatterings in the NMSSM
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Abstract
The Weakly Interacting Massive Particle (WIMP) has been one of the most attractive candidates for Dark Matter (DM), and the lightest neutralino (\(\widetilde{\chi }^0_1\)) in the NexttoMinimal Supersymmetric Standard Model (NMSSM) is an interesting realization of the WIMP framework. The Galactic Center Excess (GCE) indicated from the analysis of the photon data of the Fermi Large Area Telescope (FermiLAT) in the gammaray wavelength \(\lesssim 1 \,\mathrm{fm}\), can be explained by WIMP DM annihilations in the sky, as shown in many existing works. In this work we consider an interesting scenario in the \(Z_3\)NMSSM where the singlet S and Singlino \(\widetilde{S}^0\) components play important roles in the Higgs and DM sector. Guided by our analytical arguments, we perform a sophisticated scan over the NMSSM parameter space by considering various observables such as the Standard Model (SM) Higgs data measured by the ATLAS and CMS experiments at the Large Hadron Collider (LHC), and the Bphysics observables \(BR(B_s\rightarrow X_s\gamma )\) and \(BR(B_s\rightarrow \mu ^+\mu ^)\). We first collect samples which can explain the GCE well while passing all constraints we consider except for the DM direct detection (DD) bounds from XENON1T and PandaXII experiments. We analyze the features of these samples suitable for the GCE interpretation and find that \(\widetilde{\chi }^0_1\) DM are mostly Singlinolike and annihilation products are mostly the bottom quark pairs \(\bar{b}b\) through a light singletlike CPodd Higgs \(A_1\). Moreover, a good fit to the GCE spectrum generically requires sizable DM annihilation rates \(\langle \sigma _{b\bar{b}} v \rangle _{0}\) in today’s Universe. However, the correlation between the coupling \(C_{A_1 b\bar{b}}\) in \(\langle \sigma _{b\bar{b}} v \rangle _{0}\) and the coupling \(C_{Z \widetilde{\chi }^0_1 \widetilde{\chi }^0_1}\) in DMneutron Spin Dependent (SD) scattering rate \(\sigma ^{SD}_{\widetilde{\chi }^0_1N}\) makes all samples we obtain for GCE explanation get excluded by the PandaXII results. Although the DM resonant annihilation scenarios may be beyond the reach of our analytical approximations and scan strategy, the aforementioned correlation can be a reasonable motivation for future experiments such as PandaXnT to further test the NMSSM interpretation of GCE.
1 Introduction
An excess of gammarays in the direction of the Galactic Center (GCE) has been reported by several groups analyzing the data from the Large Area Telescope on board the Fermi Gammaray Space Telescope (FermiLAT) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. Various interpretations have been proposed to provide additional gammaray sources which can be roughly classified into two categories. One is of astrophysical origin such as a large population of unresolved millisecond pulsars (MSPs) in the Galactic bulge [13, 14, 15, 16, 17, 18, 19, 20, 21] or a series of recent leptonic cosmicray outbursts [22, 23, 24]. Another category is of particle Dark Matter (DM) origin which annihilate into the Standard Model (SM) particles subsequently producing gammarays in the excess energy range (see e.g. [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46] and references therein). For the comparison between the two categories of GCE interpretation, it has been argued that [47] a sufficiently large population of MSPs would imply a large population of observable lowmass Xray binaries, limiting the contribution of MSPs to the GCE to \(\sim \) 4–23% and thus leaving annihilating DM as a contender. Another argument comes from [18] by comparing the GCE spectrum to that measured from 37 MSPs by Fermi experiment, which indicates that a population of unresolved MSPs exhibit a spectral shape that is too soft at subGeV energies to accommodate the GCE. Furthermore, [20] argued that after pulsars are expelled from a globular cluster, they continue to lose rotational kinetic energy and become less luminous. This makes the luminosity function of those MSPs depart from the steadystate distribution and thus MSPs born in globular clusters can account for only a few percent or less of the GCE. Consequently, pulsars located in the Galactic bulge or a Galactic halo of DM are both viable interpretations for the GCE.
The existence of DM has been verified by various cosmological and astrophysical observations. However, no direct evidence of DM particle interactions has been measured by any experiment. DM particle search is a promising strategy to find new particle physics principles Beyond the Standard Model (BSM). Weakly Interacting Massive Particle (WIMP) has been a popular DM candidate given that its scatterings off the SM nuclei mediated by the weak interaction may be detected [48, 49]. One of the most attractive WIMPs is the Lightest Supersymmetric Particle (LSP) in supersymmetric models (SUSY) such as the lightest neutralino (\(\widetilde{\chi }^0_1\)).
Among the various realizations of the SUSY framework, the Minimal Supersymmetric Standard Model (MSSM) is the simplest one and provides a promising WIMP DM. However, after a series of experiments upgraded their sensitivities and set stronger bounds, MSSM is no longer a favorable framework for WIMP. Firstly, the SMlike Higgs mass measured to be around 125 GeV by the ATLAS and CMS experiment at the Large Hadron Collider (LHC) [50, 51] requires a sizable loop radiative corrections through heavy top squark (\(\gtrsim 1\) TeV) which leads to a large fine tuning. Secondly, to generate the observed DM relic density while surviving the DM direct detection limits simultaneously, the Bino (\(\widetilde{B}^0\)) must be the dominant ingredient in the lightest neutralino. Consequently, the \(\mu \) parameter in MSSM have to be relatively large which further aggravates the fine tuning problem.
As a minimal extension of the MSSM, the NexttoMSSM (NMSSM) contains an additional gauge singlet superfield \(\hat{S}\) which can dynamically generate the \(\mu \) parameter in MSSM with a small value, in which case the fine tuning problem can be alleviated significantly [52]. Recently, several experiments including LUX [53], PandaX [54] and XENON [55] updated their results of DM direct detections (DD). At this moment, the strongest constraints on SpinIndependent (SI) and SpinDependent (SD) WIMPnucleon scattering cross sections come from XENON1T (\(\sigma ^{SI}_{\widetilde{\chi }^0_1\text {}P}\)) and PandaXII (\(\sigma ^{SD}_{\widetilde{\chi }^0_1\text {}N}\)), respectively. These stringent limits have already pushed the neutralino WIMP DM scenario in NMSSM into a challenging situation: one either imposes large cancelations in the DMnucleon interactions among different contributions, the socalled blind spot scenario [56, 57, 58, 59, 60, 61], or chooses a large value of \(\mu \) parameter as did in the MSSM [60]. Either choice makes the NMSSM also suffer from the difficulty of fine tuning.
In [46] we observed that a light neutralino \(\widetilde{\chi }_1^0\) in the \(Z_3\)NMSSM was able to explain the GCE meanwhile satisfying various other constraints including the observed DM relic density and the Higgs data measured by the ATLAS and CMS groups at the LHC, by adjusting the \(\widetilde{\chi }_1^0\) pair annihilation branch ratios into \(b\bar{b}\), \(W^+W^\) and \(A_1H_i\) (\(i=1,2\)). These DM annihilations can generate additional gammaray sources strong enough to interpret the observed GCE and present a close connection between the astrophysical gammaray observations and DM phenomenology. More interestingly, the LSP \(\widetilde{\chi }_1^0\) usually manifests itself as large missing transverse momentum at high energy colliders such as the LHC, which is one of the most important signals for searching SUSY.
In this work we present our dedicated analysis on a correlation pattern between the DM annihilation cross sections to explain the GCE and DMnucleon spindependent scattering rates in the direct detection experiments, in the \(Z_3\)NMSSM where the singlet S and Singlino \(\widetilde{S}^0\) components play important roles in the Higgs and DM sector. Guided by the analytical arguments, we perform a sophisticated scan by employing the Markov Chain Monte Carlo (MCMC) strategy over the NMSSM parameter space, to verify our expectations and explore whether numerical calculations can reveal NMSSM parameter space that can still explain the GCE while passing the limits from XENON1T and PandaXII.
We organize the paper as follows. In Sect. 2 we recapitulate the main features of neutralino DM in the NMSSM and the DM annihilation mechanisms to explain the GCE. Using the analytical approximations of spindependent DMnucleon scattering rate, we identify the correlation between the GCE interpretation and the scattering strength. In Sect. 3 we explain our scan strategies in detail. We present and analyze the results of our scan in Sect. 4 and summarize in Sect. 5.
2 Neutralino DM in the NMSSM
In this section, we briefly recapitulate the features of neutralino DM in NMSSM and the mechanisms to explain the GCE in terms of DM annihilations. Then we discuss the analytical approximations of neutralino DMnucleon spindependent scattering rate, based on which we identify the correlation between the GCE interpretation and the scattering strength in direct detection.
2.1 Lightest neutralino in NMSSM as WIMP DM
2.2 Explaining GCE with NMSSM neutralino DM
2.3 Correlation of GCE explanation to neutralino DMneutron SD scattering in NMSSM
3 Scan strategies
The scan over the NMSSM parameter space was performed by employing the MCMC method. We utilize NMSSMTools5.0 [68, 69] to calculate the NMSSM mass spectrums, particle decaying ratios and Bphysics observables, which are further interfaced to MicrOMEGAs [67, 70] to calculate the DM annihilation cross section, relic density, DMnucleon scattering rates, and the gammaray spectrum to compared with GCE. We build an overall \(\chi ^2\) function with which smaller values reflect better compatibility of a model sample in the NMSSM parameter space with the observables contained in \(\chi ^2\). The MCMC scan strategy is powerful in finding the NMSSM parameter regions meeting our physical goals.
3.1 NMSSM parameter simplifications and ranges
3.2 \(\chi ^2\) method in MCMC strategy
Now we briefly recapitulate the \(\chi ^2\) method based on which we embed our codes of MCMC chain into NMSSMTools5.0. Smaller \(\chi ^2\) of a NMSSM sample can be regarded as its better compatibility confronting the experimental observations built into the \(\chi ^2\). Smaller \(\chi ^2\) also result in higher acceptance probability of this sample which will act as the new starting point to search nearby parameter space better fitting the experiments. Note that a model point may still be accepted as a node in the scanning chain even if it predicts one or several observables outside the experimental bounds at some confidence level, as long as its \(\chi ^2\) is not very large. This strategy can help the codes avoid to get stuck in some corners of the total parameter space. When \(\chi ^2\) reaches a stable minimum after a long scan chain, we will apply a set of selection rules with respect to the relevant observables and name the kept points as GCEsamples.
 The first type of \(\chi ^2\) in Eq. (22), i.e. \(\chi ^2_{m_{h_{SM}}}\), \(\chi ^2_{BR(B_s \rightarrow X_s\gamma )}\), \(\chi ^2_{BR(B_s \rightarrow \mu ^+\mu ^)}\) and \(\chi ^2_{\varOmega _{\widetilde{\chi }^0_1} h^2}\), correspond to the case in which an observable has a theoretical prediction \(\mu _i\), an observed center value \(\mu _0\) and uncertainty \(\sigma _i\) (including both experimental and theoretical parts). In this case the \(\chi ^2_i\) is defined asin which the values of \(\mu _i,\mu _0,\sigma _i\) will be provided when we apply the finalstep selection cuts.$$\begin{aligned} \chi ^2_i=\left( \frac{\mu _i\mu _0}{\sigma _i}\right) ^2, \end{aligned}$$(23)
 The second type of \(\chi ^2\) in Eq. (22) is built based on the upper bounds of DMnucleon scattering cross sections, due to the absence of confirmed signals in DM direct detections. We utilize the forms of \(\chi ^2_{\sigma ^{SI}_{\widetilde{\chi }^0_1P}}\) and \(\chi ^2_{\sigma ^{SD}_{\widetilde{\chi }^0_1N}}\) according to [71]:$$\begin{aligned} \chi ^2_{\sigma ^{SI}_{\widetilde{\chi }^0_1P}}= & {} \frac{1}{2}\left( \frac{\sigma ^{SI}_{\widetilde{\chi }^0_1P}}{\delta \sigma ^{SI}_{\widetilde{\chi }^0_1P}}\right) ^2,\end{aligned}$$(24)with$$\begin{aligned} \chi ^2_{\sigma ^{SD}_{\widetilde{\chi }^0_1N}}= & {} \frac{1}{2}\left( \frac{\sigma ^{SD}_{\widetilde{\chi }^0_1N}}{\delta \sigma ^{SD}_{\widetilde{\chi }^0_1N}}\right) ^2, \end{aligned}$$(25)$$\begin{aligned} \delta \sigma ^{SI}_{\widetilde{\chi }^0_1P}= & {} \left( \sigma ^{SI,0}_{\widetilde{\chi }^0_1P}/1.64\right) ^2+(0.2\sigma ^{SI}_{\widetilde{\chi }^0_1P})^2,\end{aligned}$$(26)where \(\sigma ^{SI,0}_{\widetilde{\chi }^0_1P}\) and \(\sigma ^{SD,0}_{\widetilde{\chi }^0_1N}\) are upper limits of the cross sections for a given DM mass \(m_{\widetilde{\chi }^0_1}\) at \(90\%\) confidence level from XENON1T and PandaXII, respectively.$$\begin{aligned} \delta \sigma ^{SD}_{\widetilde{\chi }^0_1N}= & {} \left( \sigma ^{SD,0}_{\widetilde{\chi }^0_1N}/1.64\right) ^2+(0.2\sigma ^{SD}_{\widetilde{\chi }^0_1N})^2, \end{aligned}$$(27)
 Lastly, \(\chi ^2_{GCE}\) in Eq. (22) is constructed according to Eq. (5.1) of [3]:where \(d\bar{N}/dE_i=\mathcal {A} dN/dE_i\) and \(dN_0/dE_i\) are the gammaray spectrum predicted by NMSSM samples with a scaling factor \(\mathcal {A}\) and GCE spectrum extracted from FermiLAT data after background modeling, respectively, in the ith gammaray energy bin. \(\mathcal {A}\) is a tuning factor accommodating the Galactic DM halo profile uncertainties which scales the theoretical predictions of \(dN/dE_i\). We define \(\chi ^2_{GCE}\) as the minimum value of \(\chi ^2(\mathcal {A})\) with varying \(\mathcal {A}\) [46],$$\begin{aligned} \chi ^2(\mathcal {A}) = \sum \limits _{i,j=1}^{24} \left( \frac{d\bar{N}}{dE_i} \frac{dN_0}{dE_i}\right) \varSigma ^{1}_{ij}\left( \frac{d\bar{N}}{dE_j} \frac{dN_0}{dE_j}\right) , \nonumber \\ \end{aligned}$$(28)\(\chi ^2(\mathcal {A})\) can be understood as a generalization of the 1dimensional (1D) \(\chi ^2\) in Eq. (23) to the 2D case with \(\sigma _i^2 \rightarrow \varSigma _{ij}^{1}\), where \(\varSigma ^{1}_{ij}\) is the inverse of a covariance matrix \(\varSigma _{ij}\) which reflects the correlations among different energy bins, defined as [3]$$\begin{aligned} \chi ^2_{GCE} = min(\chi ^2(\mathcal {A})), \quad \mathcal {A} \in (0.2,5). \end{aligned}$$(29)where the average runs over the 22 test region of interests (ROIs) in [3]. With \(\chi ^2_{GCE}\) constructed in Eq. (28), all terms in Eq. (22) are consistent in the sense of statistic definition. We refer interested readers to [3] for more details about \(\varSigma _{ij}\).$$\begin{aligned} \varSigma _{ij} = \left\langle \frac{dN_0}{dE_i}\frac{dN_0}{dE_j} \right\rangle  \left\langle \frac{dN_0}{dE_i}\right\rangle \left\langle \frac{dN_0}{dE_j} \right\rangle , \end{aligned}$$(30)
 1.
The SM Higgs data [50, 51, 72]. We require NMSSM to accommodate a CPeven Higgs boson whose mass is near 125 GeV while decays and couplings satisfy the observed results by ATLAS and CMS. We implement this requirement by utilizing the packages HiggsBounds5.0.0 [73] and HiggsSignal2.0.0 [74]. The Higgs mass we use is \(m_{h_{SM}}=(125.36\pm 0.41\pm 2.0)\) GeV [72], indicating in order the experimental central value \(\mu _i\) in Eq. (23), the experimental uncertainty \(\sigma _{i,the}\) at \(1\sigma \) and the theoretical uncertainty \(\sigma _{i,exp}\) at \(1\sigma \). Thus the total uncertainty in Eq. (23) is \(\sigma _i=\sqrt{\sigma _{i,the}^2+\sigma _{i,exp}^2}\), which also applies to the following observables with similar format of data.
 2.
Bphysics constraints, i.e. \(BR(B_s \rightarrow X_s\gamma )=(3.43\pm 0.22\pm 0.24)*10^{4}\) [75] and \(BR(B_s\rightarrow \mu ^+\mu ^)=(2.9\pm 0.7\pm 0.29)\times 10^{9}\) [76], with the same form as \(m_{h_{SM}}\).
 3.
Constraints from SUSY searches at the LEP and LHC, which have been encoded in the package NMSSMTools5.0, such as the mass limits on SUSY particles.
 4.
Bounds on DM annihilations from FermiLAT gammaray observations of Milky Way dSphs [77] in which likelihood analysis codes are provided for constraining theoretical models.^{1} We input the predicted gammaray spectrum and DM annihilation cross sections of our NMSSM samples and follow the code analysis. We apply the selection cut \(\chi ^2_{dSph}<2.71/2\) suggested by the codes to pick out the NMSSM samples passing the dSph constraints.
 5.
Observed DM relic density \(\varOmega _{\widetilde{\chi }^0_1} h^2 = 0.1197\times (1\pm 10\%)\) [78], where the \(10\%\) is included to accommodate the uncertainty of numerical calculations in MicrOMEGAs [70].
 6.
For the GCE spectrum comparison between the theoretical and experimental results, we impose the final selection criterion \(\chi ^2_{GCE}<35.2\). This value corresponds to the explanation of GCE by our NMSSM samples at \(95\%\) confidence level with \(N_{exp.}N_{the.}=241\) degree of freedom (d.o.f) [46], where \(N_{exp.}=24\) is the number of GCE energy bins in the analysis of FermiLAT data [3] and \(N_{the.}=1\) is the theoretical scaling factor \(\mathcal {A}\) in Eq. (28).
4 Results from the scan
In this section we first present the main features of the GCEsamples obtained in Sect. 3. Then we discuss their compatibility with the latest DM direct detection bounds from XENON1T and PandaXII.
4.1 Features of the GCEsamples

DM masses \(m_{\widetilde{\chi }^0_1}\) of the GCEsamples mostly locate between 60 and 70 GeV with Singlino component dominated, and a resonant effect near \(m_{\widetilde{\chi }^0_1}\approx m_{h_{SM}}/2\) can be clearly identified. Since \(\widetilde{\chi }^0_1 \widetilde{\chi }^0_1\rightarrow t\bar{t},W^+W^,ZZ,hh...\) are not accessible for DM so light in today’s Universe, we checked that the dominant DM annihilation channel is \(\widetilde{\chi }^0_1 \widetilde{\chi }^0_1 \rightarrow b\bar{b}\). However, we checked that some samples with \(\widetilde{\chi }^0_1 \widetilde{\chi }^0_1 \rightarrow W^+W^\) also passed various requirements in Sect. 3 but failed to satisfy GCE fitting criterion \(\chi ^2_{GCE}<35.2\), which has been noticed and pointed out in our previous work [46] with a different construction of \(\chi ^2_{total}\). The difficulty of \(W^+W^\) channel to fit the GCE comes from the overboosted gammaray spectrum given the relatively large \(m_W\).

Generally speaking, for a given DM mass \(m_{\widetilde{\chi }^0_1}\), larger today’s DM annihilation cross sections \(\langle \sigma v\rangle _0\) correspond to smaller \(\chi ^2_{GCE}\), i.e. better compatibility of the predicted gammaray spectrum with the observed GCE, except for the strong resonant region \(m_{\widetilde{\chi }^0_1}\approx m_{h_{SM}}/2\). Understandably, a sufficiently strong production rate of the gammaray flux from DM annihilations is helpful to act as an additional gammaray source to explain the GCE.

Resonance enhancement near \(m_{\widetilde{\chi }^0_1}\approx m_{h_{SM}}/2\) alleviates the pressure on the NMSSM parameters of producing large couplings in \(\widetilde{\chi }^0_1 \widetilde{\chi }^0_1 \rightarrow b\bar{b}\), e.g. \(C_{A_i \widetilde{\chi }_1^0 \widetilde{\chi }_1^0}\) and \(C_{A_i b\bar{b}}\) in Eq. (8). Therefore this mass region can provide the NMSSM parameters more flexibility to fine tune the shape of the predicted gammaray spectrum to better fit to the GCE and result in smaller \(\chi ^2_{GCE}\).

Generically, smaller DM masses \(m_{\widetilde{\chi }^0_1}\) tend to produce smaller \(\chi ^2_{GCE}\), since the larger DM number density with smaller DM mass can provide higher probability for DM to find each other and annihilate, yielding stronger gammaray flux.
Note that the DM annihilation processes in Eq. (7) can also contribute to the DM annihilations in the early Universe which make DM freeze out from the SM thermal plasma. In Fig. 2 we project the GCEsamples on the plane of \(m_{\widetilde{\chi }^0_1}\) versus \(m_{A_1}\) with \(\chi ^2_{GCE}\) represented by colors, where a solid line indicating \(m_{A_1}/m_{\widetilde{\chi }^0_1}=2\) is provided. We can see that \(2m_{\widetilde{\chi }^0_1}/m_{A_1}\) is near the resonant region for most samples, implying that the light CPodd Higgs \(A_1\) also play an important role in the schannel annihilation in the early Universe, except in some other strong resonant scenarios such as \(m_{\widetilde{\chi }^0_1}\approx m_{h_{SM}}/2\). We note that schannel DM annihilations can also proceed through Z boson and the CPeven Higgs bosons \(H_i\). However, we checked that their contributions are small because the coupling \(C_{Z \widetilde{\chi }^0_1 \widetilde{\chi }^0_1}\) is week for a Singlinolike \(\widetilde{\chi }^0_1\) in the DM annihilations, and the mass relation \(2 m_{\widetilde{\chi }^0_1}/m_{H_1} \gtrsim \mathcal {O}(2)\) is mostly offresonant for the \(H_1\)mediation.
4.2 GCE confronting DM direct detection in NMSSM
Finally, in Fig. 4 we confront the GCEsamples with the updated limits from the DM direct detections of XENON1T and PandaXII. We project the GCEsamples on the plane of \(\sigma ^{SI}_{\widetilde{\chi }^0_1P}\) versus \(\sigma ^{SD}_{\widetilde{\chi }^0_1N}\) with color denoting the reduced coupling \(R_{C_{A_1 b\bar{b}}}\equiv C_{A_1b\bar{b}}/y_b\) in Eq. (13) included in the DM annihilation cross sections to explain the GCE. Since the bounds on \(\sigma ^{SI}_{\widetilde{\chi }^0_1P}\) and \(\sigma ^{SD}_{\widetilde{\chi }^0_1N}\) don’t change much for the narrow DM mass ranges between 60 GeV and 70 GeV indicated by Fig. 1, we choose their respective strongest limits at \(90\%\) confidence level near \(m_{\widetilde{\chi }^0_1}\simeq 62\ \mathrm {GeV}\), i.e. \(\sigma ^{SD}_{\widetilde{\chi }^0_1N}=4.6\times 10^{41}\ \mathrm {cm^2}\) and \(\sigma ^{SI}_{\widetilde{\chi }^0_1P}=9.8\times 10^{47}\ \mathrm {cm^2}\). As we can see from Fig. 4, all GCEsamples we obtain are excluded by \(\sigma ^{SD}_{\widetilde{\chi }^0_1N}\) from PandaXII but a small portion can still pass the \(\sigma ^{SI}_{\widetilde{\chi }^0_1P}\) constraints from XENON1T. The colors representing \(R_{C_{A_1 b\bar{b}}}\) clearly show that large \(C_{A_1 b\bar{b}}\) which can enhance \(\langle \sigma _{b\bar{b}} v \rangle _{0}\) for GCE explanation generally produce large scattering rate \(\sigma ^{SD}_{\widetilde{\chi }^0_1N}\), except for some strong resonant regions.
5 Summary
In this work we consider an interesting scenario in the \(Z_3\)NMSSM where the singlet S and Singlino \(\widetilde{S}^0\) components play important roles in the Higgs and DM sector. Guided by the analytical argument, we perform a sophisticated scan by considering various observables such as the SM Higgs data and the Bphysics observables . We first collect samples without applying the strict DM direct detection (DD) bounds and analyze their features about the GCE interpretation. We find that \(\widetilde{\chi }^0_1\) DM are mostly Singlinolike and annihilation products are mostly the bottom quark pairs \(\bar{b}b\) through a light singletlike CPodd Higgs \(A_1\). Moreover, a good fit to the GCE spectrum generically requires sizable DM annihilation rates \(\langle \sigma _{b\bar{b}} v \rangle _{0}\) in today’s Universe. However, the correlation between the coupling \(C_{A_1 b\bar{b}}\) in \(\langle \sigma _{b\bar{b}} v \rangle _{0}\) and the coupling \(C_{Z \widetilde{\chi }^0_1 \widetilde{\chi }^0_1}\) in DMneutron Spin Dependent (SD) scattering rate \(\sigma ^{SD}_{\widetilde{\chi }^0_1N}\) makes all samples we obtain for GCE explanation excluded by the PandaXII results. Although the DM resonant annihilation scenarios may be beyond the reach of our analytical approximations and scan strategy, the aforementioned correlation can be a reasonable motivation for future experiments such as PandaXnT to further test the NMSSM interpretation of GCE.
Footnotes
Notes
Acknowledgements
We thank Junjie Cao and Yang Zhang for helpful discussions, as well as Peiwen Wu for advices on the analytical arguments. This work was supported in part by the National Natural Science Foundation of China (NNSFC) under Grant no. 11705048.
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