Real next-to-next-to-leading-order QCD corrections to J/psi and Upsilon hadroproduction in association with a photon

We update the study of the QCD corrections to direct J/psi and Upsilon hadroproduction in association with a photon in the QCD-based approach of the Colour-Singlet (CS) Model. After comparison with the recent full next-to-leading-order (NLO) computation for this process, we provide an independent confirmation to the inclusive case that NLO QCD corrections to quarkonium-production processes whose LO exhibits a non-leading P_T behaviour can be reliably computed at mid and large P_T by considering only the real emission contributions accompanied with a kinematical cut. In turn, we evaluate the leading part of the alpha^4_S alpha contributions, namely those coming from (J/psi,Upsilon)+gamma associated with two light partons. We find that they are dominant at mid and large P_T. This confirms our expectations from the leading P_T scaling of the new topologies appearing at NNLO. We obtain that the yield from the CS becomes one order of magnitude larger than the upper value of the potential Colour-Octet yield. The polarization of the 3S1 quarkonia produced in association with a photon is confirmed to be longitudinal at mid and large P_T.