Missing energy signatures of dark matter at the LHC

We use ATLAS and CMS searches in the monojet $+$ missing energy and monophoton $+$ missing energy final state to set limits on the couplings of dark matter to quarks and gluons. Working in an effective field theory framework we compare several existing monojet analyses and find that searches with high ${p}_{T}$ cuts are more sensitive to dark matter. We constrain the suppression scale of the effective dark matter--standard model interactions and convert these limits into bounds on the cross sections relevant to direct and indirect detection. We find that, for certain types of operators, in particular, spin-independent dark matter--gluon couplings and spin-dependent dark matter--quark couplings, LHC constraints from the monojet channel are competitive with, or superior to, limits from direct searches up to dark matter masses of order 1 TeV. Comparing to indirect searches, we exclude, at 90% C.L., dark matter annihilating to quarks with the annihilation cross section of a thermal relic for masses below $\ensuremath{\sim}15--70\text{ }\text{ }\mathrm{GeV}$, depending on the Lorentz structure of the effective couplings. Monophoton limits are somewhat weaker than monojet bounds but still provide an important cross check in the case of a discovery in monojets. We also discuss the possibility that dark matter--standard model interactions at LHC energies cannot be described by effective operators, in which case we find that constraints can become either significantly stronger, or considerably weaker, depending on the mass and width of the intermediate particle. Further, we discuss the special case of dark matter coupling to the Higgs boson, and we show that searches for invisible Higgs decays would provide superior sensitivity, particularly for a light Higgs mass and light dark matter.