Power corrections to the production of a prompt photon in association with a jet in the $N$-jettiness slicing scheme at NLO QCD

We compute the next-to-leading-power corrections in the $N$-jettiness variable to the production of a prompt photon and a jet at next-to-leading order in perturbative QCD in the $q\bar{q}$ annihilation channel. We employ the $k_{\perp }$ jet algorithm and assume that the $N$-jettiness value divided by the jet transverse momentum is the smallest parameter in the problem; in particular it should be small compared to the jet radius $R$.