  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.
