Parametrizations of Collinear and <i>k</i>_<i>T</i>-Dependent Parton Densities in Proton

Abstract

A new type of parametrization for parton distribution functions in the proton, based on their Q2-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 the proton, which currently plays an important role in a the number of phenomenological applications. The analytical expressions for the latter, valid for both low and large x, are derived for the first time.

Keywords

• QCD evolution
• parton density functions in the proton
• Kimber–Martin–Ryskin approach