Luminosity Systematic Studies for J/$\psi$ TSSA Measurements at SpinQuest

SpinQuest is a Fermilab high-luminosity Drell-Yan experiment designed to probe the Sivers functions of light sea quarks by scattering a 120~GeV proton beam off transversely polarized ammonia (NH$_3$) and deuterated ammonia (ND$_3$) targets. The experiment also aims to measure $J/\psi$ azimuthal asymmetries, which are sensitive to the gluon Sivers function. The polarized target system utilizes a split-pair 5~T superconducting magnet and a high-power $^4$He evaporation refrigerator operating at 1~K, enabling average polarizations of $\approx$~80\% for NH$_3$ and $\approx$~32\% for ND$_3$ via dynamic nuclear polarization. To enhance efficiency and repeatability, a fully automated annealing system is currently under development. This talk will provide an update on the extraction of $J/\psi$ azimuthal asymmetries, the automated annealing system, and present a comparative study of relative luminosity from GEANT4 simulations, which supports ongoing efforts to quantify experimental systematics.