Photoabsorption cross section in the low-$x$ and low-$Q^2$ domain, and DGLAP evolution

TL;DR

This paper investigates the gluon distribution in the proton at low-x and low-Q^2 using a two-gluon exchange model, deriving a reliable gluon distribution through DGLAP evolution with improved accuracy in the low-Q^2 domain.

Contribution

It introduces a method to accurately extract the gluon distribution at low-Q^2 by considering the scaling behavior and modifications to DGLAP evolution without altering high-Q^2 results.

Findings

Scaling of photoabsorption cross section in terms of $(W^2,Q^2)$

Improved gluon distribution extraction at low-Q^2

Quantitative validation of evolution modifications at low-Q^2

Abstract

The behavior of the gluon distribution of the proton in the low-$x$, low-$Q^2$ domain of deep inelastic electron-proton scattering (DIS) is being investigated. By considering two-gluon exchange as the dominant interaction in the low-$x$, low-$Q^2$ domain, we imply the well-known result of scaling of the photoabsorption cross section in terms of the scaling variable $\eta(W^2,Q^2)$. From this, we derive a reliable result for the gluon distribution at the leading order of the perturbative QCD improved parton model, based on evolution from a starting scale of $Q_0^2\cong 2$ GeV$^2$. The validity of evolution, when considering its quantitative modification at low-$Q^2$ without any alteration at larger values of $Q^2$, leads to a quantitative improvement in the extraction of the gluon distribution based on evolution from a starting scale of $Q^2$ conventionally chosen as $Q^2= Q_0^2\cong 2$ GeV$^2$.