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

We update the study of the QCD corrections to direct J/ψ and ϒ 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 PT behaviour can be reliably computed at mid and large PT by considering only the real emission contributions accompanied with a kinematical cut. In turn, we evaluate the leading part of the αS4α contributions, namely those coming from (J/ψ,ϒ)+γ associated with two light partons. We find that they are dominant at mid and large PT. This confirms our expectations from the leading PT 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 polarisation of the S13 quarkonia produced in association with a photon is confirmed to be longitudinal at mid and large PT.