  In the present work, it is intended to calculate and study the single and
double differential cross-sections of the prompt single-photon production as a
function of produced single-photon transverse momentum and rapidity, in the
high-energy P-P(\={P}) colliders, such as LHC and TEVATRON. The differential
cross-sections of prompt single-photon production are calculated in the
$k_t$-factorization frameworks using various angular ordering unintegrated
parton distribution functions (UPDF), namely the Kimber et al. and Martin et
al. procedures. These scheme-dependent UPDF are generated in the leading and
next-to-leading order levels to predict and analyze the different partonic
contributions to the above cross-sections. The above two procedures utilize the
phenomenological parton distribution functions (PDF) libraries of Martin et
al., i.e., MMHT2014. It is shown that the calculated prompt single-photon
production differential cross-sections in the above frameworks are relatively
successful in generating satisfactory results compared to the experimental data
of different collaborations, i.e., CDF (2017), ATLAS (2017), CMS (2011) and D0
(2006), as well as the other theoretical predictions such as collinear
factorization Monte Carlo calculations (the JETPHOX, SHERPA, PYTHIA, and MCFM
methods). Also, for a closer precision, the differential cross-section for the
NLO gluon-gluon , quark-gluon and quark-(anti)quark processes are calculated.
An extensive discussion and comparison are made regarding (i) the behavior of
the contributing partonic sub-processes, (ii) the possible double-counting
between the $2\to 2$ and $2\to 3$ sub-processes, i.e., gluons-fusion, in our
calculated prompt single-photon production differential cross-sections and
(iii) the sensibility check of our results to the different angular ordering
constraints.
