Polarization Measurements of $p^{\uparrow}$ and $^3$He$^\uparrow$ Beams at RHIC and Future EIC Using the Polarized Atomic Hydrogen Gas Jet Target

Abstract: At the Relativistic Heavy-Ion Collider (RHIC), the Polarized Atomic Hydrogen Gas Jet Target polarimeter (HJET) is employed for the precise measurement of the absolute transverse (vertical) polarization of proton beams, achieving low systematic uncertainties of approximately $\sigma^\text{syst}_P/P\leq0.5\%$. The acquired experimental data not only facilitated the determination of single $A_\text{N}(t)$ and double $A_\text{NN}(t)$ spin analyzing powers for 100 and 255 GeV proton beams but also revealed a non-zero Pomeron spin-flip contribution through a Regge fit. Preliminary results obtained for forward inelastic $p^{\uparrow}p$ and elastic $p^{\uparrow}A$ analyzing powers will be discussed. The success of HJET at RHIC suggests its potential application for proton beam polarimetry at the upcoming Electron-Ion Collider (EIC), aiming for an accuracy of 1\%. Moreover, the provided analysis indicates that the RHIC HJET target can serve as a tool for the precision calibration, with the required accuracy, of the $^3$He beam polarization at the EIC.