  In the framework of the kt-factorization approach, we study the production of
prompt photons associated with heavy (charm and beauty) quarks in hadron-hadron
collisions at high energies. Our consideration is based on the amplitude for
the production of a single photon associated with a quark pair in the fusion of
two off-shell gluons. The total and differential cross sections are presented
and the conservative error analysis is performed. Two sets of unintegrated
gluon distributions in the proton have been used in numerical calculation: the
one obtained from Ciafaloni-Catani-Fiorani-Marchesini evolution equation and
the other from Kimber-Martin-Ryskin prescription. The theoretical results are
compared with recent experimental data taken by the CDF collaboration at the
Fermilab Tevatron. Our analysis extends to specific angular correlations
between the produced prompt photons and muons originating from semileptonic
decays of the final charmed or beauty quarks. We point out the importance of
such observables, which can serve as a crucial test for the unintegrated gluon
densities in a proton. Finally, we extrapolate the theoretical predictions to
the CERN LHC energies. This paper is dedicated to the memory of P.F. Ermolov,
who died on May 14, 2008.
