  We study the production of prompt diphotons in the central region of rapidity
within the framework of the quasi-multi-Regge-kinematics approach applying the
hypothesis of quark and gluon Reggeization. We describe accurately and without
free parameters the experimental data which were obtained by the CDF
Collaboration at the Tevatron Collider. It is shown that the main contribution
to studied process is given by the direct fusion of two Reggeized gluons into a
photon pair, which is described by the effective Reggeon-Reggeon to
particle-particle vertex. The contribution from the annihilation of Reggeized
quark-antiquark pair into a diphoton is also considered. At the stage of
numerical calculations we use the Kimber-Martin-Ryskin prescription for
unintegrated quark and gluon distribution functions, with the
Martin-Roberts-Stirling-Thorne collinear parton densities for a proton as
input.
