On a residual freedom of the next-to-leading BFKL eigenvalue in color adjoint representation in planar $\mathcal{N} = 4$ SYM

TL;DR

This paper investigates the residual ambiguity in the next-to-leading BFKL eigenvalue within planar $ abla=4$ SYM theory, showing how to modify the eigenvalue without affecting the known remainder functions at NLA accuracy.

Contribution

It introduces a method to incorporate a modified NLO BFKL eigenvalue by shifting the impact factor, preserving the two and three loop remainder functions.

Findings

Residual freedom in NLO BFKL eigenvalue identified

Modified eigenvalue can be implemented without changing known remainder functions

Provides a way to explore eigenvalue ambiguities in planar $ abla=4$ SYM

Abstract

We discuss a residual freedom of the next-to-leading BFKL eigenvalue that originates from ambiguity in redistributing the next-to-leading~(NLO) corrections between the adjoint BFKL eigenvalue and eigenfunctions in planar $\mathcal{N}=4$ super-Yang-Mills~(SYM) Theory. In terms of the remainder function of the Bern-Dixon-Smirnov~(BDS) amplitude this freedom is translated to reshuffling correction between the eigenvalue and the impact factors in the multi-Regge kinematics~(MRK) in the next-to-leading logarithm approximation~(NLA). We show that the modified NLO BFKL eigenvalue suggested by the authors can be introduced in the MRK expression for the remainder function by shifting the anomalous dimension in the impact factor in such a way that the two and three loop remainder function is left unchanged to the NLA accuracy.