Breakdown of QCD Factorization for P-Wave Quarkonium Production at Low Transverse Momentum

TL;DR

This paper investigates the validity of TMD factorization in P-wave quarkonium production at low transverse momentum, revealing it holds at one-loop for certain states but is violated beyond that, impacting gluon distribution extraction.

Contribution

The study demonstrates the one-loop validity and higher-order violation of TMD factorization for specific P-wave quarkonium states, highlighting limitations in current theoretical frameworks.

Findings

TMD factorization holds at one-loop for $J^{PC}=0^{++}, 2^{++}$ P-wave states.

TMD factorization is violated beyond one-loop for these states.

Other P-wave quarkonium states also violate TMD factorization at one-loop.

Abstract

Quarkonium production at low transverse momentum in hadron collisions can be used to extract Transverse-Momentum-Dependent(TMD) gluon distribution functions, if TMD factorization holds there. We show that TMD factorization for the case of P-wave quarkonium with $J^{PC}=0^{++}, 2^{++}$ holds at one-loop level, but is violated beyond one-loop level. TMD factorization for other P-wave quarkonium is also violated already at one-loop.