An approximate approach to the nonlinear DGLAP evaluation equation

• Published in: European physical journal plus Vol. 128; no. 10; p. 119
• Main Authors: Boroun, G. R., Zarrin, S.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 21.10.2013; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Complex Systems; Condensed Matter Physics; Gluons; Linear evolution equations; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Quantum chromodynamics; Regular Article; Theoretical; Gluon Distribution; DGLAP Equation; Tame; Gluon Distribution Function; Gluon Density
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/i2013-13119-8

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.