Search

We consider the transverse single-spin asymmetry (SSA) for $J/\ensuremath{\psi}$ production in ${p}^{\ensuremath{\uparrow}}p\ensuremath{\rightarrow}J/\ensuremath{\psi}+X$ within a phenomenological transverse momentum dependent scheme in nonrelativistic QCD. Extending a previous study [U. D'Alesio et al., Eur. Phys. J. C 79, 1029 (2019)], 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 $J/\ensuremath{\psi}$ formation [U. D'Alesio et al., Phys. Rev. D 96, 036011 (2017)], 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.

We calculate the Sivers asymmetry in the photoproduction of almost back-to-back J/ψ-jet pair in the process ep↑→J/ψ+jet+X, which will be possible at the future planned Electron-Ion Collider (EIC). We use the framework of a generalized parton model and nonrelativistic QCD for calculating the J/ψ production rate. We include contributions from both color singlet and color octet states in the asymmetry. We obtain sizable Sivers asymmetry that can be promising to determine the gluon Sivers function. We also investigate the effect of transverse momentum dependent evolution on the asymmetry.

The prediction of single-spin asymmetry in inelastic photoproduction of $J/\ensuremath{\psi}$ in $e{p}^{\ensuremath{\uparrow}}$ collision is presented. At next-to-leading order, the dominating process is photon-gluon fusion, $\ensuremath{\gamma}+g\ensuremath{\rightarrow}J/\ensuremath{\psi}+g$ for the production of $J/\ensuremath{\psi}$ in $e+{p}^{\ensuremath{\uparrow}}\ensuremath{\rightarrow}J/\ensuremath{\psi}+X$, which directly probes the gluon Sivers function. Using the nonrelativistic QCD based color octet model, the color octet states ${^{3}S}_{1}^{(8)}$, ${^{1}S}_{0}^{(8)}$ and ${^{3}P}_{J(0,1,2)}^{(8)}$ contribution to $J/\ensuremath{\psi}$ production is calculated. Sizable asymmetry is estimated as a function of transverse momentum ${P}_{T}$ and energy fraction $z$ of $J/\ensuremath{\psi}$ in the range $0l{P}_{T}\ensuremath{\le}1\text{ }\text{ }\mathrm{GeV}$ and $0.3lz\ensuremath{\le}0.9$. The unpolarized differential cross section of inelastic $J/\ensuremath{\psi}$ photoproduction is found to be in good agreement with H1 and ZEUS data.