A study on linear and non-linear parton evolution equations

TL;DR

This paper investigates both linear (DGLAP) and nonlinear (GLR-MQ) parton evolution equations in QCD, analyzing analytic solutions and comparing them with existing parton distribution functions to understand proton structure at high energies.

Contribution

It provides analytic solutions for parton evolution equations and compares these with parametrizations of parton distribution functions, exploring methods for solving nonlinear equations.

Findings

Analytic solutions for gluon distribution evolution equations.

Comparison with existing parton distribution functions.

Potential future application of Laplace transform method.

Abstract

In the high energy regime, the proton structure consists of a very large number of particles called partons (quarks and gluons) that interact with each other, according to the theory of strong interactions, Quantum Chromodynamics (QCD). Through QCD, the number of partons in the proton is described by equations of parton evolution that depend on kinematic variables. These equations can be linear, the DGLAP equations, and nonlinear, the GLR-MQ equation. We have studied some analytic solutions of the equations of parton evolution. In order to generate the preliminary results, we used an ansatz for the solution of the equations of evolution of the gluon distribution, and compared with results of parametrizations of Parton Distributions Functions (PDFs). Another method proposed in the literature is the solution via Laplace transform that will be applied in the future.