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

Abstract

Abstract 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 $$ {\alpha}_s^n{\ln}^{n-1} $$ α s n ln n − 1 (1/z), to the CF hard-scattering coefficient, where z = M2/$$ \hat{s} $$ s ̂ with M and $$ \hat{s} $$ s ̂ 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 $$ {\alpha}_s^2 $$ α s 2 ln(1/z) is predicted from HEF.