Eur. Phys. J. Plus (2013) 128: 119
https://doi.org/10.1140/epjp/i2013-13119-8

Regular Article

An approximate approach to the nonlinear DGLAP evaluation equation

Physics Department, Razi University, 67149, Kermanshah, Iran

^* e-mail: grboroun@gmail.com
^** e-mail: boroun@razi.ac.ir

Received: 1 July 2013
Revised: 15 September 2013
Accepted: 21 September 2013
Published online: 21 October 2013

Abstract

We determined the effects of the first nonlinear corrections to the gluon distribution using the solution of the QCD nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (NLDGLAP) evolution equation at small x. By using a Laplace-transform technique, the behavior of the gluon distribution is obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu (GLR-MQ) evolution equation with the nonlinear shadowing term incorporated. We show that the strong rise that is corresponding to the linear QCD evolution equations at small x can be tamed by screening effects. Consequently, the nonlinear effects for the gluon distributions are calculated and compared with the results for the integrated gluon density from the Balitsky-Kovchegov (BK) equation. The resulting analytic expression allows us to predict the shadowing correction to the logarithmic derivative F ₂(x, Q ²) with respect to ln Q ² and to compare the results with H1 data and a QCD analysis fit.