A simple model for PDFs and nPDFs
A. V. Kotikov, A. V. Lipatov
TL;DR
The work derives analytical LO PDFs by solving the DGLAP equations with exact small-$x$ and large-$x$ asymptotics, constrained by momentum conservation and the Gross-Llewellyn-Smith and Gottfried sum rules, and fits them to 933 $F_2(x,Q^2)$ data points across broad $x$ and $Q^2$ ranges. It then extends to nuclear targets using a $Q^2$-rescaling model combined with Fermi motion, performing a global fit to $F_2^A(x,Q^2)/F_2^D(x,Q^2)$ data to extract rescaling parameters and predict nuclear PDFs. The results show good proton data description with $ abla^2$-dependent parameters and indicate weaker gluon shadowing but significant quark anti-shadowing at large $x$ in nuclei, highlighting differences with some other nPDF determinations and the need for future precision measurements. Overall, the paper provides analytic insight into PDFs and nPDFs across the full kinematic range, offering practical predictions for $pA$ and $AA$ collisions at current and future colliders.
Abstract
We present the main results of our recent papers, where we derived an analytical solution of the QCD evolution equations for parton distribution functions. The valence and non-singlet quark components satisfy the Gross-Llewellyn-Smith and Gottfried sum rules, respectively, while momentum conservation is maintained for the singlet quark and gluon densities. Several phenomenological parameters were extracted from a combined fit to precision data on the proton structure function $F_2(x,Q^2)$ collected by the BCDMS, H1, and ZEUS Collaborations, comprising a total of 933 points from 5 datasets. We proposed a model for nuclear medium modifications of parton densities. The approach is based on a global analysis of available deep inelastic scattering data for different nuclear targets within the rescaling model, incorporating Fermi motion effects. By fitting the rescaling parameters to experimental data on the ratio $F_2^A(x,Q^2)/F_2^{D}(x,Q^2)$ for several nuclear targets $A$, we obtained predictions for nuclear parton distribution functions.