Applications of a nonlinear evolution equation I: the parton distributions in the proton

TL;DR

This paper uses a nonlinear QCD evolution equation with corrections to evaluate proton parton distributions, improving stability at low Q^2 and aligning with experimental data, thus bridging quark models and high-scale measurements.

Contribution

It introduces a nonlinear evolution approach with twist-4 corrections to better model proton parton distributions at low Q^2.

Findings

Nonlinear corrections enhance perturbative stability at low Q^2.

Proton sea quark distributions are positive and flat at small x.

Results are compatible with existing experimental data.

Abstract

The parton distributions in the proton are evaluated dynamically using a nonlinear QCD evolution equation - the DGLAP equation with twist-4 (the GLR-MQ-ZSR) corrections - starting from a low scale $\mu^2$, where the nucleon consists of valence quarks. We find that the negative nonlinear corrections can improve the perturbative stability of the QCD evolution equation at low $Q^2$. Our resulting parton distributions of the proton with four free parameters are compatible with the existing databases. We show that the sea quark distributions exhibit a positive and flattish behavior at small $x$ and low $Q^2$. This approach provides a powerful tool to connect the quark models of the hadron and various non-perturbative effects on them at scale $\mu^2$ with the measured structure functions at high scale $Q^2>> \mu^2$.