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

TL;DR

This paper develops a method to accurately predict heavy-quarkonium production cross sections by combining NLO calculations with high-energy resummation, improving physical consistency and providing new NNLO predictions.

Contribution

It introduces a novel matching procedure in z-space using Inverse-Error Weighting to combine NLO and high-energy resummed calculations for quarkonium production.

Findings

Resummation cures unphysical NLO results.

First use of InEW matching in this context.

Predicts NNLO coefficient proportional to α_s^2 ln(1/z).

Abstract

The energy dependence of the total hadroproduction cross section of pseudo-scalar quarkonia is computed via matching Next-to-Leading Order (NLO) Collinear-Factorisation (CF) results with resummed higher-order corrections, proportional to $\alpha_s^{n}\ln^{n-1}(1/z)$, to the CF hard-scattering coefficient, where $z=M^2/\hat{s}$ with $M$ and $\hat{s}$ 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 $\alpha_s^2\ln(1/z)$ is predicted from HEF.