Estimates for the single-spin asymmetries in the p ↑ p →J /ψ X process at PHENIX RHIC and SPD NICA

We study the transverse single-spin asymmetry (TSSA) in ${p}^{\ensuremath{\uparrow}}p\ensuremath{\rightarrow}J/\ensuremath{\psi}X$ reaction, incorporating both transverse momentum and spin effects. To predict production cross section of prompt $J/\ensuremath{\psi}$, we use two different approaches, the color-singlet model and the improved color evaporation model, and show how the predicted results for TSSAs depend on the choice of hadronization model. For initial-state factorization, we also consider two options: the standard generalized parton model and the color gauge-invariant version of it. Estimates for the TSSAs in ${p}^{\ensuremath{\uparrow}}p\ensuremath{\rightarrow}J/\ensuremath{\psi}X$ process for the conditions of the future Spin Physics Detector Nuclotron-based Ion Collider fAcility (NICA) experiment are presented for the first time.