Five-parton amplitudes with two-quark and two-photon at Next-to-Leading Order

We discuss one-loop five-parton amplitudes with two-quark two-photon or three-photon external legs. The amplitudes are required to evaluate the NLO corrections for the $\gamma \gamma jet$ production process at hadron colliders. The results have been already discussed by several groups in terms of QCD amplitudes. Here, we present more straightforward version of one-loop calculations without using the QCD amplitudes.