Boosting perturbative QCD stability in quarkonium production

TL;DR

This paper introduces a method to stabilize perturbative QCD calculations for heavy quarkonium production at high momentum transfers using only tree-level generators, effectively capturing important higher-order effects without full computations.

Contribution

The paper presents a novel approach to incorporate power-enhanced perturbative contributions in quarkonium production, improving stability and accuracy of predictions with minimal computational complexity.

Findings

Reproduces NLO results with a tree-level generator

Estimates the missing NNLO contribution, finding negligible impact on magnitude

Applicable to broad quarkonium production processes without full higher-order calculations

Abstract

The aim of this paper is to introduce a general way to stabilize the perturbative QCD computations of heavy quarkonium production in the boosted or high-momentum transferring region with tree-level generators only. Such an approach is possible by properly taking into account the power-enhanced perturbative contributions in a soft and collinear safe manner without requiring any complete higher-order computations. The complicated NLO results for inclusive quarkonium hadroproduction can be well reproduced within our approach based on a tree-level generator {\sc\small HELAC-Onia}. We have applied it to estimate the last missing leading-twist contribution from the spin-triplet color-singlet S-wave production at $\mathcal{O}(\alpha_s^5)$, which is a NNLO term in the $\alpha_s$ expansion for the quarkonium $P_T$ spectrum. We conclude that the missing NNLO contribution will not change the order of the magnitude of the short-distance coefficient. Such an approach is also quite appealing as it foresees broad applications in quarkonium-associated production processes, which are mostly absent of complete higher-order computations and fragmentation functions.