Measurement of $\gamma +b+X$ and $\gamma +c+X$ Production Cross Sections in $p\overline{p}$ Collisions at $\sqrt{s}=1.96\mathrm{TeV}$

First measurements of the differential cross sections $d^3\sigma /(d{p}_T^{\gamma }d{y}^{\gamma }d{y}^{\mathrm{jet}})$ for the inclusive production of a photon in association with a heavy quark ($b$, $c$) jet are presented, covering photon transverse momenta $30<p_T^{\gamma }<150\mathrm{GeV}$, photon rapidities $|y^{\gamma }|<1.0$, jet rapidities $|y^{\mathrm{jet}}|<0.8$, and jet transverse momenta $p_T^{\mathrm{jet}}>15\mathrm{GeV}$. The results are based on an integrated luminosity of $1{\mathrm{fb}}^{-1}$ in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ recorded with the D0 detector at the Fermilab Tevatron Collider. The results are compared with next-to-leading order perturbative QCD predictions.