Towards a new global QCD analysis: solution to the Balitsky–Kovchegov nonlinear equation at arbitrary impact parameter

Abstract

A numerical solution of the nonlinear evolution equation that governs the dynamics of high parton density QCD, is presented. A solution is obtained by restricting the kinematical region in which the equation is valid. It is shown that the angle-integrated solution at large values of the impact parameter b falls off exponentially, i.e., as e − m b . In impact parameter distributions the power-like tail of the amplitude appears only after the inclusion of dipoles of size larger than the target, a configuration for which the nonlinear equation is not valid. The value, energy and impact parameter of the saturation momentum Q s ( y = ln ( 1 / x ) , b ) are calculated both for fixed and running QCD coupling cases. It is shown that the solution exhibits geometrical scaling behavior. The radius of interaction increases with rapidity in accordance with the Froissart theorem. The solution we obtain differs from previous treatments, where an ansatz for the b behavior was made. For the particular case of large fixed α s , the behavior of the solution obtained is similar to that found for running α s . However, in general the solutions for running and small fixed α s differ: for running α s , we obtain a larger radius of interaction, a steeper rapidity dependence, and a larger value of the saturation momentum.