Gluon density and $F_{2}$ functions from BK equation with impact parameter dependence

TL;DR

This paper refines a model for gluon density and the structure function $F_2$ using the BK equation with impact parameter dependence, showing good agreement with established parameterizations.

Contribution

It introduces a fixed initial condition for the BK equation with impact parameter dependence and compares resulting gluon and $F_2$ functions with GRV parameterization.

Findings

Gluon density and $F_2$ functions match GRV results for various $Q^2$ values.

Initial conditions similar to GBW ansatz are effective.

Model provides a good description of proton structure functions.

Abstract

In this note we fix the preliminary results obtained in the study of gluon density function of the paper \cite{bom3}. The LO BK equation for unintegrated gluon density with impact parameter dependence is considered in order to fix the parameters of the proposed model. In particular the form of initial condition for the equations of proton-proton scattering from \cite{bom3} is determined, which is similar to the form of fenomenological GBW ansatz. The gluon density function and $F_{2}$ function are also calculated and compared with the results for the gluon density and $F_{2}$ functions from the GRV parameterization for different values of $Q^2$. It is shown, that the results for $F_2$ structure function of the considered model are in the good accordance with the results obtained from the GRV parameterization of parton densities.