QCD Factorization for Quarkonium Production in Hadron Collions at Low Transverse Momentum

TL;DR

This paper demonstrates that TMD factorization for low transverse momentum quarkonium production in hadron collisions holds at one-loop level, with all leading-twist gluon distributions involved, ensuring gauge invariance and accounting for off-shell initial gluons.

Contribution

It provides a comprehensive one-loop level analysis of TMD factorization involving all leading-twist gluon distributions, including the cancellation of super-leading contributions.

Findings

Factorization holds at one-loop level for all leading-twist TMD gluon distributions.

Super-leading contributions from off-shell gluons cancel in the sum over diagrams.

The resulting cross-section expression is explicitly gauge-invariant.

Abstract

Inclusive production of a quarkonium $\eta_{c,b}$ in hadron collisions at low transverse momentum can be used to extract various Transverse-Momentum-Dependent(TMD) gluon distributions of hadrons, provided the TMD factorization for the process holds. The factorization involving unpolarized TMD gluon distributions of unpolarized hadrons has been examined with on-shell gluons at one-loop level. In this work we study the factorization at one-loop level with diagram approach in the most general case, where all TMD gluon distributions at leading twist are involved. We find that the factorization holds and the perturbative effects are represented by one perturbative coefficient. Since the initial gluons from hadrons are off-shell in general, there exists the so-called super-leading region found recently. We find that the contributions from this region can come from individual diagrams at one-loop level, but they are cancelled in the sum. Our factorized result for the differential cross-section is explicitly gauge-invariant.