In the framework of the kt-factorization approach, the isolated prompt photon pair production in pp and p \bar p collisions at high energies is studied. The consideration is based on the quark-antiquark annihilation, quark-gluon scattering and gluon-gluon fusion subprocesses, where the non-zero transverse momenta of incoming partons are taken into account. The unintegrated quark and gluon densities in a proton are determined using the Kimber-Martin-Ryskin prescription. The numerical analysis covers the total and differential production cross sections and extends to specific angular correlations between the produced prompt photons. Theoretical uncertainties of our evaluations are studied and comparison with the NLO pQCD calculations is performed. The numerical predictions are compared with the recent experimental data taken by the D0, CDF, CMS and ATLAS collaborations at the Tevatron and LHC energies.
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