Next-to-leading order QCD predictions for the signal of Dark Matter and photon associated production at the LHC

We study the potential of the LHC to discover the signal of dark matter associated production with a photon induced by a dimension six effective operator, including next-to-leading order QCD corrections. We investigate the main backgrounds from the standard model, i.e. $Z$ boson and a photon associated production with invisible decay of $Z$ boson, and $Z$ boson and a jet production with the jet misidentified as a photon. We find that the ${p}_{T}^{\ensuremath{\gamma}}$ distributions of the backgrounds decrease faster than that of the signal with increasing of the transverse momentum of the photon. The ${\ensuremath{\eta}}^{\ensuremath{\gamma}}$ distributions of the backgrounds are almost flat in the full range of ${\ensuremath{\eta}}^{\ensuremath{\gamma}}$. In contrast, the signal lies mainly in the central region of ${\ensuremath{\eta}}^{\ensuremath{\gamma}}$. These characteristics may help to select the events in experiments. We show that in the parameter space allowed by the relic abundance constraint, which we have calculated at the next-to-leading-order QCD level, the LHC with $\sqrt{S}=7\text{ }\text{ }\mathrm{TeV}$ may discover this signal at the $5\ensuremath{\sigma}$ level after collecting an integrated luminosity of $1\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. On the other hand, if this signal is not observed at the LHC, we can set a lower limit on the new physics scale at the $3\ensuremath{\sigma}$ level.