A detail study of the LHC and TEVATRON hadron-hadron prompt-photon pair production experiments in the angular ordering constraint k_t-factorization approaches

In the present work, which is based on the k_-factorization framework, it is intended to make a detail study of the isolated prompt-photon pairs (IPPP) production in the high-energy inelastic hadron-hadron collisions differential cross section. The two scheme-dependent unintegrated parton distribution functions (UPDF) in which the angular ordering constraints (AOC) are imposed, namely the Kimber-Martin-Ryskin (KMR) and the Martin-Ryskin-Watt (MRW) approaches, in the leading and the next-to-leading orders (LO and NLO) are considered, respectively. These two prescriptions (KMR and MRW) utilize the phenomenological parton distribution functions (PDF) libraries of Martin et al, i.e. the MMHT2014. The computations are performed in accordance with the initial dynamics of latest existing experimental reports of the D0, CDF, CMS and ATLAS collaborations and the different experimental constraints. It is shown that above frameworks are capable of producing acceptable results, compared to the experimental data, the pQCD and some Monte Carlo calculations (i.e. 2\gamma-NNLO, SHERPA, DIPHOX and RESBOS). It is also concluded that the KMR framework produces better results in the higher center-of-mass energies, while the same thing can be argued about the LO-MRW prescription in lower energies. Additionally, these two schemes show different behavior in the regions where the fragmentation and higher pQCD effects become important. A clear prediction for the various shoulders and tails which were detected experimentally are observed and discussed in the present theoretical approaches. The possible double countings between 2 \rightarrow 2 and 2 \rightarrow 3 processes are studied.