Boosting perturbative QCD stability in quarkonium production

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.