Proper TMD factorization for quarkonia production: $pp\to\eta_{c,b}$ as a study case

Understand

Quarkonia production in different high-energy processes has recently been proposed in order to probe gluon transverse-momentum-dependent parton distribution and fragmentation functions (TMDs in general).

• However, no proper factorization theorems have been derived for the discussed processes, but rather just ansatzs, whose main assumption is the factorization of the two soft mechanisms present in the process: soft-gluon radiation and the formation of the bound state.
• In this paper it is pointed out that, at low transverse momentum, these mechanisms are entangled and thus encoded in a new kind of non-perturbative hadronic quantities beyond the TMDs: the TMD shape functions.
• This is illustrated by deriving the factorization theorem for the process $pp\to \eta_{c,b}$ at low transverse momentum.