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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 $dσ/dM_{γγ}$, pair transverse momentum $d σ/dp^{γγ}_T$, azimuthal angle between the photons $dσ/dΔϕ_{γγ}$, and polar scattering angle in the Collins-Soper frame $dσ/d|\cos θ^*|$. Measurements are performed for isolated photons with transverse momenta $p^γ_T>18 ~(17)$ GeV for the leading (next-to-leading) photon in $p_T$, pseudorapidities $|η^γ|<0.9$, and a separation in $η-ϕ$ space $Δ\mathcal R_{γγ} > 0.4$. We present comparisons with the predictions from Monte Carlo event generators {\sc diphox} and {\sc resbos} implementing QCD calculations at next-to-leading order, $2γ${\sc nnlo} at next-to-next-to-leading order, and {\sc sherpa} using matrix elements with higher-order real emissions matched to parton shower.