Next-to-leading and resummed BFKL evolution with saturation boundary

TL;DR

This paper studies how saturation boundaries affect small-x evolution at next-to-leading order, revealing that nonlinear effects do not fix instabilities, thus requiring resummation of higher-order corrections, which significantly alters the saturation scale.

Contribution

It introduces a renormalization group improved resummed equation with saturation boundary, highlighting the necessity of resummation for stable nonlinear small-x evolution.

Findings

Instabilities in NLO BFKL are not cured by saturation effects.

Resummation reduces the saturation scale and delays saturation onset.

Resummed splitting function has a minimum at moderate small-x values.

Abstract

We investigate the effects of the saturation boundary on small-x evolution at the next-to-leading order accuracy and beyond. We demonstrate that the instabilities of the next-to-leading order BFKL evolution are not cured by the presence of the nonlinear saturation effects, and a resummation of the higher order corrections is therefore needed for the nonlinear evolution. The renormalization group improved resummed equation in the presence of the saturation boundary is investigated, and the corresponding saturation scale is extracted. A significant reduction of the saturation scale is found, and we observe that the onset of the saturation corrections is delayed to higher rapidities. This seems to be related to the characteristic feature of the resummed splitting function which at moderately small values of x possesses a minimum.