Numerical solution of the nonlinear evolution equation at small x with impact parameter and beyond the LL approximation

TL;DR

This paper numerically analyzes a nonlinear small-x evolution equation with impact parameter dependence, incorporating running coupling and kinematical effects beyond the leading logarithmic approximation, revealing sensitivities to infrared regularization and impact parameter constraints.

Contribution

It introduces a numerical approach to solve the nonlinear small-x evolution equation with impact parameter and includes effects beyond the LL approximation, such as running coupling and kinematical constraints.

Findings

Saturation scales and impact parameter expansion radius are extracted as functions of rapidity.

Solution sensitivity to infrared regularization is observed with running coupling.

Kinematical effects significantly influence evolution with impact parameter.

Abstract

Nonlinear evolution equation at small x with impact parameter dependence is analyzed numerically. Saturation scales and the radius of expansion in impact parameter are extracted as functions of rapidity. Running coupling is included in this evolution, and it is found that the solution is sensitive to the infrared regularization. Kinematical effects beyond leading logarithmic approximation are taken partially into account by modifying the kernel which includes the rapidity dependent cuts. While the local nonlinear evolution is not very sensitive to these effects, the kinematical constraints cannot be neglected in the evolution with impact parameter.