Parametrizations of collinear and k_T-dependent parton densities in a proton

TL;DR

This paper introduces a new parametrization method for proton parton distribution functions that incorporates Q^2-evolution and extends to transverse momentum dependent distributions, with analytical expressions valid across x ranges.

Contribution

It develops a novel parametrization framework for collinear and k_T-dependent parton densities, including analytical formulas for TMD distributions at all x values.

Findings

Valence and nonsinglet parts obey sum rules.

Momentum conservation is incorporated for singlet quark and gluon densities.

First derivation of analytical expressions for TMD distributions at low and large x.

Abstract

A new type of parametrization for parton distribution functions in a proton, based on their $Q^2$-evolution at large and small $x$ values, is constructed. In our analysis, the valence and nonsinglet parts obey the Gross-Llewellyn-Smith and Gottfried sum rules, respectively. For the singlet quark and gluon densities momentum conservation is taken into account. Then, using the Kimber-Martin-Ryskin prescription, we extend the consideration to Transverse Momentum Dependent (TMD, or unintegrated) gluon and quark distributions in a proton, which currently plays an important role in a number of phenomenological applications. The analytical expressions for the latter, valid for both low and large $x$, are derived for the first time.