The aim of the present work is to study the phenomenological behavior of unitegrated parton distribution functions (UPDF) by using the Kimber-Martin-Ryskin (KMR) and Martin-Ryskin-Watt (MRW) formalisms. In the first method, the leading order (LO) UPDF of the KMR prescription is extracted, by taking into account the PDF of Martin et al., i.e., MSTW2008-LO and MRST99-NLO and. While in the second scheme, the next-to-leading order (NLO) UPDF of the (MRW) procedure is generated through the set of MSTW2008-NLO PDFas the inputs. The different aspects of the UPDF in the two approaches, as well as the input PDF are discussed. Then, the deep inelastic proton structure functions, F 2 ðx; Q 2 Þ, are calculated from the above UPDF in the two schemes, and compared with the data, which are extracted from the ZEUS, NMC, and H1 þ ZEUS experimental measurements. In general, it is shown that the calculated structure functions based on the UPDF of two schemes, are consistent to the experimental data, and by a good approximation, they are independent to the input PDF. But the proton structure functions, which are extracted from the KMR prescription, have better agreement to the data with respect to that of MRW. Although the MRW formalism is in more compliance with the Dokshitzer-Bribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation requisites, but it seems in the KMR case, the angular ordering constraint spreads the UPDF to the whole transverse momentum region, and makes the results to sum up the leading DGLAP and Balitski-Fadin-Kuraev-Lipatov (BFKL) Logarithms. This point is under study by the authors.
In the present work, which is based on the k t -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 someMonte Carlo calculations (i.e. 2γNNLO, 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→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.
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