Spin Dependence of Associated Production of a Prompt Photon and a Charm Quark at Next-to-Leading Order in QCD

A second order, $O(\alpha ^2_s)$, calculation in perturbative quantum chromodynamics is presented of the longitudinal spin dependence of the cross section for the two particle inclusive reaction $p + p \to \gamma + c + X$ for large values of the transverse momentum of the prompt photon and charm quark. Differential distributions are provided for the spin-averaged cross section and for the two-spin longitudinal polarization asymmetry $A_{LL}$ at the energy of the Brookhaven Relativistic Heavy Ion Collider. An assessment is given of the prospects for determination of the spin dependence of the charm quark density.