  We describe an effective theory of interaction between pairs of dark matter
particles and pairs of photons. Such an interaction could accomodate
$\chi\bar{\chi}\rightarrow\gamma\gamma$ processes which might be the cause of
the observed feature in the FermiLAT spectrum, as well as
$\gamma^*/Z\rightarrow \gamma\chi\bar{\chi}$ processes, which would predict
excesses at the LHC in the $\gamma+\missET$ final-state. We reinterpret an
ATLAS $\gamma+\missET$ analysis and the observed Fermi feature in the parameter
space of our new effective theory to assess their consistency.
