# NNLO solution of nonlinear GLR-MQ evolution equation to determine gluon distribution function using Regge like ansatz

## TL;DR

This paper presents an NNLO solution to the nonlinear GLR-MQ evolution equation for gluon distribution functions, incorporating Regge behavior and analyzing sensitivity to parameters, with results compared to recent global fits.

## Contribution

It introduces a novel NNLO analytical solution to the nonlinear GLR-MQ equation using a Regge-like ansatz, extending previous work to higher order accuracy.

## Key findings

- Results agree with recent global PDF fits
- Sensitivity analysis for correlation radius and Regge intercept
- Q^2 evolution of gluon distribution in the Regge region

## Abstract

In this work we have suggested a solution of the Gribov-Levin-Ryskin-Mueller-Qiu (GLR-MQ) nonlinear evolution equation at next-to-next-to-leading order (NNLO). The range of $Q^2$ in which we have solved the GLR-MQ equation is Regge region of the range $5 GeV^2 \leq Q^2 \leq 25 GeV^2$ and so we have incorporated the Regge like behavior to obtain $Q^2$ evolution of gluon distribution function $G(x, Q^2)$. We have also checked the sensitivity of our results for different values of correlation radius (R) between two interacting gluons, viz. $R=2 GeV^{-1}$ and $R= 5 GeV^{-1}$ as well as for different values of Regge intercept $\lambda_G$. Our computed results are compared with those obtained by the most recent global DGLAP fits to the parton distribution functions viz. PDF4LHC15, NNPDF3.0, HERAPDF15, CT14 and ABM12.