Matching next-to-leading-order and high-energy-resummed calculations of heavy-quarkonium-hadroproduction cross sections

The energy dependence of the total hadroproduction cross section of pseudoscalar quarkonia is computed via matching Next-to-Leading Order (NLO) Collinear-Factorisation (CF) results with resummed higher-order corrections, proportional to α_s^nln^n-1 (1 /z ), to the CF hard-scattering coefficient, where z = M 2 / ŝ with M and ŝ being the quarkonium mass and the partonic center-of-mass energy squared. The resummation is performed using High-Energy Factorisation (HEF) in the Doubly-Logarithmic (DL) approximation, which is a subset of the leading logarithmic ln(1 /z ) approximation. Doing so, one remains strictly consistent with the NLO and NNLO DGLAP evolution of the PDFs. By improving the treatment of the small- z asymptotics of the CF coefficient function, the resummation cures the unphysical results of the NLO CF calculation. The matching is directly performed in the z -space and, for the first time, by using the Inverse-Error Weighting (InEW) matching procedure. As a by-product of the calculation, the NNLO term of the CF hard-scattering coefficient proportional to α_s^2 ln(1 /z ) is predicted from HEF.