Renormalizable model for the Galactic Center gamma-ray excess from dark matter annihilation

Evidence for an excess of gamma rays with O(GeV) energy coming from the center of our galaxy has been steadily accumulating over the past several years. Recent studies of the excess in data from the Fermi telescope have cast doubt on an explanation for the excess arising from unknown astrophysical sources. A potential source of the excess is the annihilation of dark matter into standard model final states, giving rise to gamma ray production. The spectrum of the excess is well fit by 30 GeV dark matter annihilating into a pair of b quarks with a cross section of the same order of magnitude as expected for a thermal relic. Simple models that can lead to this annihilation channel for dark matter are in strong tension with null results from direct detection experiments. We construct a renormalizable model where dark matter-standard model interactions are mediated by a pseudoscalar that mixes with the CP-odd component of a pair of Higgs doublets, allowing for the gamma ray excess to be explained while suppressing the direct detection signal. We consider implications for this scenario from Higgs decays, rare B meson decays and monojet searches and also comment on some difficulties that any dark matter model explaining the gamma ray excess via direct annihilation into quarks will encounter.