Direct Photon Production in Association with a Heavy Quark

The inclusive cross section for a direct photon and a heavy quark (charm or bottom), $p+\bar p (p) \rightarrow \gamma +Q +X$, is calculated up to second order in the strong coupling constant $\alpha_s$. The photon fragmentation function, which is of order $\alpha/\alpha_s$, where $\alpha$ is the electromagnetic coupling constant, needs to be convoluted with all QCD subprocesses of order $\alpha_s^3$ containing a heavy quark in the final state so that the cross section is complete to next-to-leading order (NLO). This calculation extends previous efforts by including this NLO contribution. The cross section for photon plus heavy quark production can provide a useful check of the method used for the calculation of the heavy quark's parton distribution functions, which are currently determined with the use of the Altarelli-Parisi equation. The dependence of the cross section on the photon and heavy quark transverse momenta and rapidities will be examined. Predictions for both the Tevatron and the LHC will be presented.