Abstract
We consider the transverse single-spin asymmetry (SSA) for $J/\psi$ production in $p^\uparrow p \to J/\psi + X$ within a TMD approach in non-relativistic QCD. Extending a previous study [1], 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, 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 $J/\psi$ formation [2], 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.
Highlights
The study of the three-dimensional structure of hadrons is of fundamental importance for our comprehension of their properties
Even when the heavy-quark pair is produced in a color-octet state, ISIs and FSIs lead to a nonvanishing single-spin asymmetry (SSA), allowing us, in principle, to test the process dependence of the gluon Sivers function (GSF)
II, we summarize the formalism for the computation of single-spin asymmetries in pp → J=ψ þ X, adopting the color-gauge invariant generalized parton model (CGI-generalized parton model (GPM)) framework within nonrelativistic QCD (NRQCD), which was presented in details in Refs. [12,22], while results are shown and discussed in Sec
Summary
The study of the three-dimensional structure of hadrons is of fundamental importance for our comprehension of their properties. Its success in describing many polarization observables and its role in looking for potential factorization breaking effects make it an important tool For these processes, the color-gauge invariant extension of the GPM, known as the CGI-GPM, has been developed in Refs. ISIs and FSIs are taken into account assuming a single eikonal gluon exchange between the struck parton and the remnants of the transversely polarized proton This approximation is basically the leading-order contribution, in a perturbative expansion of the Wilson line, in the definition of the Sivers function. It is worth mentioning that, for single-scale processes, like pp → h þ X, an alternative formalism, based on collinear factorization at next-to-leading twist (twist-3), has been developed and successfully applied [14,15,16] In this framework, SSAs are given by convolutions of hard scattering amplitudes with universal quark-gluonquark and three-gluon correlation functions. All the expressions for the hard scattering amplitudes squared, computed within the CGIGPM, are collected in the Appendix
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
