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

Based on the k(t)-factorization framework, it is intended to report a detailed study of the differential cross section of the isolated prompt-photon pairs (IPPP) production in high-energy inelastic hadron-hadron collisions. 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 function (PDF) libraries of Martin et al, i.e. the MMHT2014. The computations are performed in accordance with the different experimental constraints of the latest existing experiment of the D0, CDF, CMS and ATLAS collaborations. It is shown that the 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 are detected experimentally, are observed and discussed. The possible double countings between 2 -> 2 and 2 -> 3 processes are studied. Finally, in agreement to the work of Golec-Biernat and Stasto, it is shown that there is not any dispute about the application of the AOC and the cut-off, in the above prescriptions, at least in the calculation of the various IPPP differential cross sections. However, mostly the LO and NLO-MRW frameworks are the upper and lower bands of the KNIR prescriptions, otherwise they predicate the data.