Interpretations of galactic center gamma-ray excess confronting the PandaX-II constraints on dark matter-neutron spin-dependent scatterings in the NMSSM

The Weakly Interacting Massive Particle (WIMP) has been one of the most attractive candidates for Dark Matter (DM), and the lightest neutralino (${\tilde{\chi }}_1^0$) in the Next-to-Minimal Supersymmetric Standard Model (NMSSM) is an interesting realization of WIMP. The Galactic Center Excess (GCE) can be explained by WIMP DM annihilations in the sky. In this work we consider the $Z_3$-NMSSM where the singlet $S$ and Singlino ${\tilde{S}}^0$ components play important roles in the Higgs and DM sector. Guided by our analytical arguments, we perform a numerical scan over the NMSSM parameter space for the GCE explanation by considering various observables such as the Standard Model (SM) Higgs data measured by the ATLAS and CMS experiments, and the $B$-physics observables $BR(B_s\to X_s\gamma )$ and $BR(B_s\to {\mu }^{+}{\mu }^{-})$. We find that the correlation between the coupling $C_{A_{1}b\bar{b}}$ in $⟨{\sigma }_{b\bar{b}}v{⟩}_0$ and the coupling $C_{Z \widetilde{\chi}^0_1 \widetilde{\chi}^0_1}$ in DM-neutron Spin Dependent (SD) scattering rate ${\sigma }_{{\tilde{\chi }}_1^0-N}^{SD}$ makes all samples we obtain for GCE explanation get excluded by the PandaX-II 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 PandaX-nT to further test the NMSSM interpretation of GCE.