Shadowing correction to the gluon distribution behavior at small x

Abstract

We determined the saturation exponent of the gluon distribution using the solution of the QCD nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-parisi (NLDGLAP) evolution equation at small $x$. The very small $x$ 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. The form of initial condition for the equation is determined. We find, with decreasing $x$, the emergence of a singular behavior and the eventual taming (at $R=5Ge{V}^{-1}$) and the essential taming (at $R=2Ge{V}^{-1}$) of this singular behavior by shadowing term. The nonlinear gluon density functions are calculated and compared with the results for the integrated gluon density from the Balitsky- Kovchegov(BK) equation for the different values of $Q^2$. It is shown, that the results for the gluon density function are comparable with the results obtained from BK equation solution. Also we show that for each $x$, the $Q^2$ dependence of the data is well described by gluon shadowing corrections to GLR-MQ equation. The resulting analytic expression allow us to predict the logarithmic derivative $\frac{\partial F_2^s(x,Q^2)}{\partial ln{Q}^2}$ and to compare the results with H1 data and a QCD analysis fit.

5 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1402.0678

References in corpus (2)

• Analytic Expression for the Joint x and Q^2 Dependences of the Structure Functions of Deep Inelastic Scattering
• Gluon density and $F_2$ functions from BK equation with impact parameter dependence

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