Process dependence of the gluon Sivers function in p↑p→J/ψ+X within a TMD scheme in NRQCD

We consider the transverse single-spin asymmetry (SSA) for J/ψ production in p↑p→J/ψ+X within a phenomenological transverse momentum dependent scheme in nonrelativistic QCD. Extending a previous study [U. D'Alesio, Eur. Phys. J. C 79, 1029 (2019)EPCFFB1434-604410.1140/epjc/s10052-019-7551-4], we employ here the color-gauge invariant generalized parton model (CGI-GPM), in which spin and intrinsic transverse momentum effects are taken into account, together with leading-order initial- and final-state interactions (ISIs and FSIs). We find that, even when the heavy-quark pair is produced in a color-octet state, ISIs and FSIs lead to a nonvanishing SSA, allowing us, in principle, to test the process dependence of the gluon Sivers function (GSF). We show that of the two independent contributions, due to the so-called f- and d-type GSFs, appearing in the CGI-GPM, the d-type one turns out to be dynamically suppressed. Therefore, as already found adopting the Color-Singlet Model approach for the J/ψ formation [U. D'Alesio, Phys. Rev. D 96, 036011 (2017)PRVDAQ2470-001010.1103/PhysRevD.96.036011], only the f-type GSF could play a role in phenomenology. A comparison with the corresponding results obtained in the generalized parton model, without the inclusion of ISIs and FSIs, is also carried out.