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.
We give predictions for the ratio) at small values of Bjorken variable x in the first three orders of perturbation theory. We show an approximateQ ), irrespectively on the gluon density in a proton used in the calculations. This observation could be useful in subsequent phenomenological studies of the heavy flavor production at future lepton-hadron and hadron-hadron colliders.
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