The NLO unintegrated parton distribution functions (PDF) in the KMR and the MRW frameworks using the MSTW2008 PDF

The next-to-leading order (NLO) unintegrated parton distribution functions (UPDF) are calculated in the two schemes by using the latest version of the integrated parton distribution functions (PDF) of Martin et al. (MSTW2008) as the inputs and the final results are compared among each others. In the first method, so-called the Kimber–Martin–Ryskin (KMR) prescription, the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) collinear approximation is used, instead of the Ciafaloni–Catani–Fiorani–Marchesini (CCFM) evolution equations and the dependence of PDF on the second scale, image (the partons transverse momenta), beside the first scale, μ (μ is the probe scale), is included in the last step of DGLAP evolution equation. In the second approach, which has been proposed by Martin, Ryskin and Watt (MRW), the current scale, the splitting functions, etc are modified in the KMR procedure. The three-dimensional UPDF are presented in terms of different image-planes for the large values of x (the longitudinal fraction of parton momentum) at image and image. It is shown that as in MRW calculations, at each image a kink is observed around image and image for the KMR and the MRW formalisms, respectively. Finally, it is demonstrated that the MRW gluon UPDF decrease with respect to the KMR ones, except of the small image regions, i.e. the Higgs production domain, so it can be concluded that the application of the MRW procedure may improve the exclusive reaction cross sections.