Boosting perturbative QCD stability in quarkonium production

TL;DR

The paper addresses the perturbative instability of high-$P_T$ heavy quarkonium production in QCD by introducing STOP, an infrared-safe framework that stabilizes calculations using tree-level amplitudes (via HELAC-Onia) and carefully designed phase-space cuts. By incorporating finite remainders of P-wave counterterms and validating STOP against known NLO results across several Fock states, it provides a fast and reliable method to reproduce NLO behavior and offers partial NNLO estimates for the ${^3S^{[1]}_1}$ channel. The approach avoids full higher-order computations while preserving essential fragmentation physics, enabling practical predictions for inclusive and associated quarkonium production and enabling polarization studies. This work promises broad applicability to quarkonium phenomenology, with potential extensions to complete NNLO calculations and more sophisticated fragmentation-function treatments.

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 $\mathcal{O}(α_s^5)$, which is a NNLO term in the $α_s$ 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.

Figures (26)

• Figure 1: Comparison of spin-summed differential cross sections for the Fock state ${\bigl.^3\space S^{[1]}_1}$ between our aNLO calculations and the complete NLO calculations.
• Figure 2: Comparisons of spin-dependent differential cross sections for the Fock state ${\bigl.^3\space S^{[1]}_1}$ between our aNLO calculations and the complete NLO calculations.
• Figure 3: Comparisons of spin-summed differential cross sections for the Fock state ${\bigl.^3\space S^{[8]}_1}$ between LO (left), aNLO (right) calculations and the complete NLO calculations.
• Figure 4: Schematic depiction of inclusive quarkonium ${\cal O}_n$ production.
• Figure 5: Infrared unsafe configurations to be considered in inclusive quarkonium production, where the first 3 subfigures are for the onium jet $j_{{\cal O}_n}$ and the last one is for the light-flavoured jets.