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 JPC=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 level.
Highlights
Collisions with hadrons provide important information about the interactions and inner structure of hadrons
Higgs-production[6, 7], quarkonium production [8], two-photon production[9] and the production of a quarkonium combined with a photon[10], are suggested to determine TMD gluon distribution functions
In the production of 1S0 quarkonium at low transverse momentum, TMD factorization is explicitly examined at one-loop level in [11], where the quarkonium will not interact with soft gluons at leading power
Summary
Collisions with hadrons provide important information about the interactions and inner structure of hadrons. In the production of 1S0 quarkonium at low transverse momentum, TMD factorization is explicitly examined at one-loop level in [11], where the quarkonium will not interact with soft gluons at leading power. All singular contributions from the virtual- and real correction are factorized into TMD gluon distribution functions and the soft factor.
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