  Monojet and monophoton final states with large missing transverse energy
(${\not E}_T$) are important for dark matter (DM) searches at colliders. We
present analytic expressions for the differential cross sections for the
parton-level processes, $q\bar{q}(qg)\to g(q)\chi\bar{\chi}$ and $q\bar{q}\to
\gamma\chi\bar{\chi}$, for a neutral DM particle with a magnetic dipole moment
(MDM) or an electric dipole moment (EDM). We collectively call such DM
candidates dipole moment dark matter (DMDM). We also provide monojet cross
sections for scalar, vector and axial-vector interactions. We then use
ATLAS/CMS monojet${+\not E}_T$ data and CMS monophoton$+{\not E}_T$ data to
constrain DMDM. We find that 7 TeV LHC bounds on the MDM DM-proton scattering
cross section are about six orders of magnitude weaker than on the conventional
spin-independent cross section.
