  We explore the possibility of explaining a gamma-ray excess in the Galactic
Center, originally pointed out by Hooper, collaborators, and other groups, in
an effective field theory framework. We assume that dark matter annihilation is
mediated by particles heavy enough to be integrated out, and that such
particles couple to all quark families. We calculate the effective coupling
required to explain the annihilation signal in the Galactic Center, and compare
with bounds from direct detection, collider searches, and the requirement that
the dark matter particle make up the appropriate fraction of the universal
energy budget. We find that only a very small set of operators can explain the
gamma-ray excess while being consistent with other constraints. Specifically,
for scalar dark matter the viable options are one scalar-type coupling to
quarks and one interaction with gluons, while for fermionic (Dirac) dark matter
the viable options are two scalar-type dimension-7 operators or a dimension-6
vector-type operator. In all cases, future searches with the Large Hadron
Collider should probe the relevant operators' effective energy scale, while all
viable interactions should escape direct detection experiments.
