Exploring semi-relativistic $p$-wave dark matter annihilation in minimal Higgs portal near supermassive black hole

Abstract: We conduct a comprehensive analysis of potential annihilation processes of light dark matter (DM) in minimal Higgs portal models near supermassive black hole (Sgr A$^{\star}$) in the Galactic Center, considering interactions between DM particles mediated by either a light scalar or pseudoscalar with couplings $ c_s $ and $ c_p $. Accelerated by the supermassive black hole, DM particles can reach velocities up to half the speed of light, significantly enhancing the $ p $-wave annihilation cross-section, allowing forbidden annihilation channels within specific mass ranges, and producing unique gamma-ray spectral signals. Utilizing gamma-ray observation from Fermi Large Area Telescope (Fermi-LAT) in the direction of Sgr $A^{\star}$, we constrain light DM parameter in the mass range of $ 0.3-10 \, \text{GeV} $ . Our results indicate that the couplings $ c_s $ and $ c_p $ are constrained to the order of $ 10^{-5} $, corresponding to a DM annihilation cross-section as low as $ 10^{-38} $$ {\rm cm}^3/{\rm s}$. In the future, the Very Large Gamma-ray Space Telescope (VLAST), with a larger detection area and broader detection range from $1$ MeV to $1$ TeV, will enhance our ability to probe sub-GeV DM and offer the opportunity to further study the forbidden annihilation scenario.