Measurement of the differential cross sections for the production of an isolated photon with associated jet in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$~TeV

The process $p\bar{p} \rightarrow \gamma + {\mathrm{jet}} + X$ is studied using 8.7~fb$^{-1}$ of data collected by the D0 detector at the Fermilab Tevatron collider at a center-of-mass energy $\sqrt{s} = 1.96$~TeV. Photons are reconstructed with rapidities $|y_{\gamma}| < 1.0$ and $1.5 < |y_{\gamma}| < 2.5$ with transverse momenta in the range $30 < p_{T \gamma} < 400$~GeV, while jets are reconstructed in four rapidity regions up to $|y_{\mathrm{jet}}| < 3.2$. The differential cross section $d^3\sigma/dP_{T \gamma} dy_{\gamma} dy_{\mathrm{jet}}$ is measured as a function of $p_{T \gamma}$ in 16 regions, differing by the relative orientations of the photon and the jet in rapidity. Results are compared with next-to-leading order calculations and to the {\sc pythia} and {\sc sherpa} Monte Carlo event generators.