On analytical solutions of the DIS structure functions in the framework of GLR-MQ-ZRS equation

TL;DR

This paper derives analytical solutions for DIS structure functions within the GLR-MQ-ZRS framework, accounting for small-x gluon behavior and comparing results with HERA data.

Contribution

It introduces analytical solutions for structure functions considering both constant and Q^2-dependent strong coupling, enhancing understanding of small-x gluon dynamics.

Findings

Analytical solutions match HERA data well.

Solutions incorporate Regge-like small-x gluon behavior.

Results valid in specified x and Q^2 ranges.

Abstract

We computed the deep inelastic scattering (DIS) structure functions $F_2 (x,Q^2)$ and $F_L (x,Q^2)$ in the framework of Gribov-Levin-Ryskin-Mueller-Qiu, Zhu-Ruan-Shen (GLR-MQ-ZRS) equation. Both $x$ and $Q^2$ evolutions of the structure functions are studied in the kinematic range of $10^{-6}\leq x \leq 10^{-2}$ and $5 \leq Q^2 \leq 100\,,GeV^2$ respectively. we have suggested analytical solutions to the structure functions, our results are inspired by Regge like behaviour of gluons at small-x. The solutions of structure functions are obtained for two particular cases: (i) treating the strong coupling constant $\alpha_s$ as an arbitrary constant, and (ii) considering the $Q^2$ dependency of $\alpha_s$. Our predicted results are in good agreement with the latest available high precision HERA data.