PDF at small $x$ in the non-perturbative region

TL;DR

This paper investigates the behavior of parton distribution functions at small x in a proton, incorporating parton splitting and fusion, revealing saturation phenomena and comparing with perturbative QCD models.

Contribution

It introduces an upgraded parton model including both splitting and fusion, providing new insights into parton saturation at very small x.

Findings

Power-law behavior of parton density at moderately small x

Detection of saturation of parton density at very small x

Comparison with perturbative QCD equations

Abstract

Parton distribution function (PDF) at small $x$ in a fast-moving proton is investigated within an upgraded parton model that includes parton splitting with branching cascades and parton fusion. In the region of moderately small $x$, we obtain a power-law behavior of the parton density $x f(x)$ with an exponent proportional to the logarithm of the probability of parton splitting. Taking into account parton fusion leads to a nonlinear equation for the PDF. In the region of very small $x$, the phenomenon of saturation of the parton density is detected and a model estimate of its value in this regime is obtained. The results are compared with those obtained previously based on the analysis of equations in logarithmic approximations of perturbative QCD.