Transverse Momentum Dependent Factorization for Quarkonium Production at Low Transverse Momentum

TL;DR

This paper investigates the validity of TMD factorization in low transverse momentum quarkonium production, determining one-loop perturbative coefficients and highlighting the necessity of a soft factor for divergence cancellation.

Contribution

It provides the first one-loop level analysis of TMD factorization for quarkonium production, including the role of a soft factor beyond tree level.

Findings

One-loop perturbative coefficients are calculated.

A soft factor is necessary to cancel soft divergences.

Potential complications for p-wave quarkonium are discussed.

Abstract

Quarkonium production in hadron collisions at low transverse momentum $q_\perp \ll M$ with $M$ as the quarkonium mass can be used for probing transverse momentum dependent (TMD) gluon distributions. For this purpose, one needs to establish the TMD factorization for the process. We examine the factorization at the one-loop level for the production of $\eta_c$ or $\eta_b$. The perturbative coefficient in the factorization is determined at one-loop accuracy. Comparing the factorization derived at tree level and that beyond the tree level, a soft factor is, in general, needed to completely cancel soft divergences. We have also discussed possible complications of TMD factorization of p-wave quarkonium production.