Paper detail

An approximate approach to the nonlinear DGLAP evaluation equation

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.