Transverse momentum dependent (TMD) parton distribution functions generated in the modified DGLAP formalism based on the valence-like distributions

Abstract

Transverse momentum dependent (TMD) parton distributions, also referred to as unintegrated parton distribution functions (UPDFs), are produced via the Kimber–Martin–Ryskin (KMR) prescription. The GJR08 set of parton distribution functions (PDFs) which are based on the valence-like distributions is used, at the leading order (LO) and the next-to-leading order (NLO) approximations, as inputs of the KMR formalism. The general and the relative behaviors of the generated TMD PDFs at LO and NLO and their ratios in a wide range of the transverse momentum values, i.e. [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are investigated. It is shown that the properties of the parent valence-like PDFs are imprinted on the daughter TMD PDFs. Imposing the angular ordering constraint (AOC) leads to the dynamical variable limits on the integrals which in turn increase the contributions from the lower scales at lower [Formula: see text]. The results are compared with our previous studies based on the MSTW2008 input PDFs and it is shown that the present calculation gives flatter TMD PDFs. Finally, a comparison of longitudinal structure function [Formula: see text] is made by using the produced TMD PDFs and those that were generated through the MSTW2008-LO PDF from our previous work and the corresponding data from H1 and ZEUS collaborations and a reasonable agreement is found.