Abstract
We discuss the different Kimber-Martin-Ryskin (KMR) prescriptions for unintegrated parton distribution functions (uPDFs). We show that the strong-ordering (SO) and the angular-ordering (AO) cutoffs lead to strong discrepancies between the obtained cross sections. While the result obtained with the AO cutoff overestimates the heavy-flavor cross section by about a factor of 3, the SO cutoff gives the correct answer. We also solve the issue of the KMR uPDF definitions mentioned by Golec-Biernat and Sta\ifmmode \acute{s}\else \'{s}\fi{}to [Phys. Lett. B 781, 633 (2018)] and show that, in the case of the AO cutoff, the KMR uPDFs are ill defined.
Highlights
Understanding transverse-momentum-dependent parton distribution functions has been a topic of increasing theoretical and experimental interest
We will discuss several theoretical issues related to the angular-ordering cutoff, and see that the KMR/WMR unintegrated parton distribution functions (uPDFs) built with the strongordering cutoff are free of some of them. Another objective of this paper is to present a solution to the issue of the KMR/WMR uPDFs definitions addressed in Ref. [12]
In this paper we discussed the KMR and WMR prescriptions for uPDFs, and we underlined the fact that several recent studies that used the “KMR” prescription
Summary
Understanding transverse-momentum-dependent parton distribution functions has been a topic of increasing theoretical and experimental interest. Compared to the collinear PDFs, they provide additional information on the transverse dynamics of a parton inside the hadron. The TMD factorization [1,2,3,4] is valid for small kt=Q, where kt is the parton transverse momentum and Q is the hard scale of the process. The TMD PDFs, mainly studied in semi-inclusive deep inelastic scattering and Drell-Yan experiments, provide three-dimensional information on the hadron structure and could help to solve the proton-spin crisis. Kt is not restricted to small values It finds applications at the LHC, where the transverse momentum of incoming spacelike partons can be large, due to partonic evolutions
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