  While many interactions of dark matter (DM) with the standard model (SM)
affect direct detection and LHC searches, there are only a few operators
generating annihilation of DM into photons. All of these operators, except four
of them, give rise to unsuppressed rates, rendering indirect detection superior
to other search strategies. For two of the four effective interactions with
velocity-suppressed annihilation cross sections, we identify a new type of loop
effect which significantly enhances the associated direct detection rates. As a
result, relevant constraints from next-generation direct detection experiments
on DM-SM interactions, so far only bounded by the LHC, are obtained.
