Probing gluon polarization in hadronic direct photon production

Inclusive direct photon production at large transverse momentum in proton-proton interactions with a longitudinally polarized beam and target is an incisive probe of the polarized gluon density in a proton. To help motivate future experiments and assist in their design, we provide predictions of the polarization asymmetry for a range of reasonable choices of the polarized gluon density. The cross sections are small at fixed-target energies, but the effort to measure them is necessary if the polarized gluon density $\Delta G(x, Q^2)$ is to be determined. In order to obtain our predictions, we parametrize spin-dependent parton densities and compute their evolution with $Q^2$. Our densities provide good agreement with the spin-dependent structure function $g_1^p(x, Q^2)$ measured in deep-inelastic lepton scattering.