Soluções das equações de evolução DGLAP e GLR-MQ em cromodinâmica quântica via transformada de Laplace

Abstract

The structure of the proton consists of a very large number of partons (collective denomination of quarks and gluons), which interact with each other according to the theory of strong interactions, Quantum Chromodynamics (QCD). Parton density in the proton is described by means of evolution equations that depend on kinematic variables. In this work the equations studied were the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations and the Gribov-Levin-Ryskin and Mueller-Qiu (GLR-MQ) equations. These equations present an analytical solution for small $x$, and the DGLAP equation predicts an indefinite increase in the density of the gluons and to slow this growth it is necessary to consider a process of recombination of the gluons, which leads to saturation of the density of these particles. In this work we study some methods of analytical and numerical solutions for the particle evolution equations. First we use an ansatz as solution of the evolution equations, and we obtain analytical and numerical results that have been compared with Parton Distributions Functions (PDFs). The main objective of this work was to obtain the distribution of gluons by solving the equations of analytical evolution and numerically using the Laplace transform method. We obtained analytical results for DGLAP and GLR-MQ and numerical only for DGLAP, where it was observed through the Laplace transform the saturation occurred even without the contribution of the nonlinear term that corresponds to the GLR-MQ equation.