Boosting perturbative QCD stability in quarkonium production

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.Comment: 40 pages, 26 figures, 3 tables; v2: journal version, fix a few typos fixed, add two figures, reorganize the figure