Moderate-to-Large-$x$ Gluon Helicity from $J/\psi$ Production at $\sqrt{s}=27~\mathrm{GeV}$
We present a feasibility study of the longitudinal double-spin asymmetry $A_{LL}$ in inclusive $J/\psi$ production in polarized proton-proton collisions at $\sqrt{s}\approx 27~\mathrm{GeV}$ at the Spin Physics Detector (SPD) of the Nuclotron-based Ion Collider fAcility (NICA). At these moderate energies, $J/\psi$ production is dominated by gluon-gluon fusion, probing gluon momentum fractions $x\approx 0.1$-$0.2$ at central rapidity and highly asymmetric configurations at forward rapidity, where one parton can reach $x\approx 0.5$-$0.9$. This provides direct sensitivity to the poorly constrained moderate- to large-$x$ region of the gluon helicity distribution $\Delta g(x)$. We estimate $A_{LL}$ as a function of transverse momentum and rapidity using polarized parton distribution functions, focusing on the underlying partonic spin asymmetry. Nonperturbative long-distance effects are treated in a simplified manner and largely cancel in the asymmetry, enabling a direct assessment of gluon polarization sensitivity. We find asymmetries reaching $|A_{LL}|\approx 0.09$ at $p_T=3~\mathrm{GeV}$, with enhanced sensitivity at forward rapidity. The dominant theoretical uncertainty arises from polarized parton distribution functions. These results demonstrate that inclusive $J/\psi$ measurements at SPD/NICA provide a sensitive and complementary probe of gluon polarization at moderate and large $x$, extending constraints from RHIC into a kinematic regime not directly accessible to the EIC.