Hidden Higgs Portal Vector Dark Matter for the Galactic Center Gamma-Ray Excess from the Two-Step Cascade Annihilation, and Muon g-2

We have built a lepton-specific next-to-minimal two-Higgs-doublet-portal vector dark matter model. The vector dark matter in the hidden sector does not directly couple to the visible sector, but instead annihilates into the hidden Higgs bosons which decay through a small coupling into the CP-odd Higgs bosons. In this model, the Galactic center gamma-ray excess is mainly due to the 2-step cascade annihilation with $\tau$'s in the final state. The obtained mass of the CP-odd Higgs $A$ in the Galactic center excess fit can explain the muon $g-2$ anomaly at the 2$\sigma$ level without violating the stringent constraints from the lepton universality and $\tau$ decays. We show three different freeze-out types of the dark matter relic, called (i) the conventional WIMP dark matter, (ii) the unconventional WIMP dark matter and (iii) the cannibally co-decaying dark matter, depending on the magnitudes of the mixing angles between the hidden Higgs and visible two-Higgs doublets. The dark matter in the hidden sector is secluded from detections in the direct searches or colliders, while the dark matter annihilation signals are not suppressed in a general hidden sector dark matter model. We discuss the constraints from observations of the dwarf spheroidal galaxies and the Fermi-LAT projected sensitivity.