Measurement of the differential cross sections for isolated direct photon pair production in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV

We present measurements of direct photon pair production cross sections using 8.5 fb${}^{-1}$ of data collected with the D0 detector at the Fermilab Tevatron $p\bar{p}$ collider. The results are presented as differential distributions of the photon pair invariant mass $d\sigma \mathrm{/}d{M}_{\gamma \gamma }$, pair transverse momentum $d\sigma \mathrm{/}d{p}_T^{\gamma \gamma }$, azimuthal angle between the photons $d\sigma \mathrm{/}d\mathrm{\Delta }{\varphi }_{\gamma \gamma }$, and polar scattering angle in the Collins-Soper frame $d\sigma \mathrm{/}d\mathrm{\mid }\cos {\theta }^{\ast }\mathrm{\mid }$. Measurements are performed for isolated photons with transverse momenta $p_T^{\gamma }>18(17)$ GeV for the leading (next-to-leading) photon in $p_T$, pseudorapidities $\mathrm{\mid }{\eta }^{\gamma }\mathrm{\mid }<0.9$, and a separation in $\eta -\varphi$ space $\Delta\mathcal R_{\gamma\gamma} > 0.4$. We present comparisons with the predictions from Monte Carlo event generators {\sc diphox} and {\sc resbos} implementing QCD calculations at next-to-leading order, $2\gamma${\sc nnlo} at next-to-next-to-leading order, and {\sc sherpa} using matrix elements with higher-order real emissions matched to parton shower.