Extended collinearly-improved Balitsky-Kovchegov evolution equation in target rapidity

TL;DR

This paper derives an extended version of the Balitsky-Kovchegov evolution equation incorporating running coupling corrections, demonstrating significant impact on scattering amplitude suppression through numerical analysis.

Contribution

The paper introduces a new derivation of the BK evolution equation in target rapidity with running coupling effects included, highlighting their importance.

Findings

Running coupling corrections significantly suppress the scattering amplitude.

Numerical solutions show the importance of including running coupling in the evolution equation.

The extended equation provides a more accurate description of high-energy QCD evolution.

Abstract

An extended collinearly-improved Balitsky-Kovchegov evolution equation in the target rapidity representation is derived by including the running coupling corrections during the expansion of the "real" $S$-matrix. We find that the running coupling brings important corrections to the evolution equation, as one can see that there are extra contributions to the evolution kernel once the running coupling is included. To identify the significance of the corrections, we numerically solve the evolution equation with and without the running coupling contributions during the $S$-matrix expansion. The numerical results show that the scattering amplitude is largely suppressed by the running coupling corrections, which indicate that one needs to consider the running coupling contributions during the derivation of the non-linear evolution equation in the target rapidity representation.