Analytic calculation of prompt photon plus associated heavy flavor at next-to-leading order in QCD

Contributions through second order, $O\left({\alpha }_s^2\right)$, in perturbative quantum chromodynamics are calculated analytically for inclusive associated production of a prompt photon and a charm quark at large values of transverse momentum in high energy hadron-hadron collisions. Seven partonic subprocesses contribute at order ${\alpha }_s^2$. We find important corrections to the lowest order, $O\left({\alpha }_s\right)$, subprocess $\mathrm{cg}\to \gamma c$. We demonstrate to what extent data from $p+\overline{p}\to \gamma +c+X$ may serve to measure the charm quark density in the nucleon.