Modeling a Framework for Comprehensive Analysis of $\boldsymbol{p^\uparrow\!{A}}$ Transverse Analyzing Power Measurements at the RHIC HJET

We present a model for calculating the forward elastic analyzing power $A_\text{N}^{pA}(t)$ in proton-nucleus scattering, based on the Glauber approximation and incorporating soft-photon exchange corrections. The model is tested against 100 GeV HJET measurements for several nuclei, including Au, Ru, Zr, Al, O, C, and the deuteron. The calculations use Woods-Saxon parameters to describe the nuclear density distributions, as well as the proton-proton and proton-neutron hadronic spin-flip amplitudes, with the latter constrained by a Regge fit to HJET $pp$ data. Using the nominal input parameters, the calculations provide a reasonable description of the measured analyzing powers, although further refinement is needed to achieve a satisfactory fit. Allowing the input parameters to vary in the fits substantially improves the agreement with the data, yielding effective parametrizations of $A_\text{N}^{pA}(t)$ in terms of three or four parameters, depending on the nucleus. Notably, the nominal values of the imaginary part of the effective proton-nucleus spin-flip parameter $r_5^{pA}$ agree well with the fitted values for all nuclei considered. Subject to the limitations of the present model, this observation concerning $\operatorname{Im} r_5^{pA}$ is consistent with the proton-proton spin-flip amplitudes measured at HJET and supports the interpretation of a non-zero Pomeron spin-flip coupling. The results presented in this paper also motivate further investigation of the energy dependence of the proton-nucleon spin-flip amplitude using HJET measurements over a broad range of beam energies, with potential applications to proton-carbon and $^3$He polarimetry at the Electron-Ion Collider.