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

Keywords

• Deep Inelastic Scattering or Small-X Physics
• Quarkonium
• Resummation
• Higher-Order Perturbative Calculations