SUSY explanation of the Fermi Galactic Center Excess and its test at LHC Run-II

We explore the explanation of the Fermi Galactic Center Excess (GCE) in the Next-to-Minimal Supersymmetric Standard Model. We systematically consider various experimental constraints including the Dark Matter (DM) relic density, DM direct detection results and indirect searches from dwarf galaxies. We find that, for DM with mass ranging from $30 {\rm GeV}$ to $40 {\rm GeV}$, the GCE can be explained by the annihilation $\chi \chi \to a^\ast \to b \bar{b}$ only when the CP-odd scalar satisfies $m_a \simeq 2 m_\chi$, and in order to obtain the measured DM relic density, a sizable $Z$-mediated contribution to DM annihilation must intervene in the early universe. As a result, the higgsino mass $\mu$ is upper bounded by about 350 GeV. Detailed Monte Carlo simulations on the $3\ell+ E_T^{miss}$ signal from neutralino/chargino associated production at 14-TeV LHC indicate that the explanation can be mostly (completely) excluded at $95\%$ C.L. with an integrated luminosity of 100(200) fb$^{-1}$. We also discuss the implication of possible large $Z$ coupling to DM for the DM-nucleon spin dependent (SD) scattering cross section, and find that although the current experimental bounds on $\sigma^{\rm SD}_p$ is less stringent than the spin independent (SI) results, the future XENON-1T and LZ data may be capable of testing most parts of the GCE-favored parameter region.