Nonlinear GLR-MQ evolution equation and $$Q^2$$ Q 2 -evolution of gluon distribution function

Mayuri Devee,J K Sarma

doi:10.1140/epjc/s10052-014-2751-4

Abstract

In this paper we have solved the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu (GLR-MQ) evolution equation for gluon distribution function G(x,Q^2) and studied the effects of the nonlinear GLR-MQ corrections to the Leading Order (LO) Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. Here we incorporate a Regge like behaviour of gluon distribution function to obtain the solution of GLR-MQ evolution equation. We have also investigated the Q^2-dependence of gluon distribution function from the solution of GLR-MQ evolution equation. Moreover it is interesting to observe from our results that nonlinearities increase with decreasing correlation radius (R) between two interacting gluons. Results also confirm that the steep behavior of gluon distribution function is observed at R=5 GeV^{-1}, whereas it is lowered at R=2 GeV^{-1} with decreasing x as Q^2 increases. In this work we have also checked the sensitivity of \lambda_G in our calculations. Our computed results are compared with those obtained by the global DGLAP fits to the parton distribution functions viz. GRV, MRST, MSTW and with the EHKQS model.

Highlights

The most precise determinations of the gluon momentum distribution in the proton can be obtained from a measurement of the deep inelastic scattering (DIS) proton structure function F2(x, Q2) and its scaling violation
The GLR-MQ equation is based on two processes in the parton cascade: the emission induced by the quantum chromodynamics (QCD) vertex g→g + g with a probability which is proportional to αsρ and the annihilation of a gluon by the same vertex g + g→g with a probability which is proportional to αs2r 2ρ2, where ρ(x, Q2)=xg(x, Q2)/π R2 is the density of gluons in the transverse plane, π R2 is the target area, and R is the correlation radius between two interacting gluons
In this paper we have solved the nonlinear GLR-MQ evolution equation in order to determine the Q2-dependence of the gluon distribution function G(x, Q2)

Summary

Introduction

The most precise determinations of the gluon momentum distribution in the proton can be obtained from a measurement of the deep inelastic scattering (DIS) proton structure function F2(x, Q2) and its scaling violation. These effects lead to nonlinear power corrections to the DGLAP equations These nonlinear terms lower the growth of the gluon distribution in this kinematic region where αs is still small but the density of partons becomes very large. The main features of this equation are that it predicts saturation of the gluon distribution at very small-x, it predicts a critical line separating the perturbative regime from the saturation regime, and it is only valid in the border of this critical line [29,33] It is an amazing property of the GLR-MQ equation that it introduces a characteristic momentum scale Q2s , which is a measure of the density of the saturated gluons. In the present work we intend to obtain a solution of the nonlinear GLR-MQ evolution equation for the calculation of the gluon distribution function in leading order.

Theory

Results and discussions

Conclusions