# Small-x analysis on the effect of gluon recombinations inside hadrons in light of the GLR-MQ-ZRS equation

## TL;DR

This paper investigates the impact of antishadowing effects on gluon distribution functions at small-x using the GLR-MQ-ZRS nonlinear equation, solving it under different assumptions and comparing results with experimental data and existing PDFs.

## Contribution

It provides a novel analysis of gluon recombination effects at small-x by solving the GLR-MQ-ZRS equation with Regge behavior and comparing different QCD coupling scenarios.

## Key findings

- Gluon distribution functions are significantly affected by antishadowing effects.
- Results align well with experimental data and established PDFs.
- Predictions for the evolution of the proton's structure function derivative are consistent with HERA data.

## Abstract

We present a study of the contribution of antishadowing effects on the gluon distribution functions $G(x,Q^2)$ in light of the Gribov-Levin-Ryskin-Mueller-Qiu, Zhu-Ruan-Shen (GLR-MQ-ZRS) nonlinear equation at small-$x$, where $x$ is the momentum fraction or Bjorken variable and $Q^2$ is the four momentum transfer squared or photon virtuality. In this work, we have solved the GLR-MQ-ZRS nonlinear equation using Regge like the behavior of gluons in the kinematic range of $10^{-2}\leq x \leq 10^{-6}$ and $5\,GeV^2\, \leq Q^2\leq 100\, GeV^2$ respectively. We have obtained the solution of $G(x,Q^2)$ by considering two particular cases: (a) $\alpha_s$ fixed; and (b) the leading order QCD dependency of $\alpha_{s}$ on $Q^2$. A comparative analysis is also performed where we compare the gluon distribution function due to inclusion of the antishadowing effect with that of the gluon distribution without including the antishadowing effect. Our obtained results of $G(x,Q^2)$ are compared with NNPDF3.0, CT14 and PDF4LHC. We also compare our results with the result obtained from the IMParton C++ package. Using the solutions of $G(x,Q^2)$, we have also predicted $x$ and $Q^2$ evolution of the logarithmic derivative of proton's $F_2$ structure function i.e. $dF_2 (x,Q^2)/d\ln Q^2$. We incorporated both the leading order(LO) and next-to-leading order (NLO) QCD contributions of the gluon-quark splitting kernels, in $dF_2 (x,Q^2)/d\ln Q^2$. Our result of $dF_2 (x,Q^2)/d\ln Q^2$ agrees reasonably well with the experimental data recorded by HERA's H1 detector.