  The tentative gamma-ray line in the Fermi data at ~135 GeV motivates a dark
matter candidate that couples to photons through loops of charged messengers.
It was recently shown that this model can explain the observed line, but
achieving the correct phenomenology requires a fairly sizable coupling between
the WIMP and the charged messengers. While strong coupling by itself is not a
problem, it is natural to wonder whether the phenomenological success is not
spoiled by higher order quantum corrections. In this work we compute the
dominant two-loop contributions to the electromagnetic form-factors of the WIMP
and show that over a large portion of the relevant parameter space these
corrections are under control and the phenomenology is not adversely affected.
We also discuss more generally the effects of these form-factors on signals in
direct-detection experiments as well as on the production of the WIMP candidate
in colliders. In particular, for low masses of the charged messengers the
production rate at the LHC enjoys an enhancement from the threshold singularity
associated with these charged states.
