On the discrepancy of the low-x evolution kernels

TL;DR

This paper investigates the differences between the BFKL and BK kernels at NLO, showing that many discrepancies can be attributed to energy scale choices and establishing identities in supersymmetric theories.

Contribution

It demonstrates that the main differences in the kernels can be removed by a scale transformation and proves the NLO identity of the kernels in N=4 SYM.

Findings

Most of the kernel difference is due to energy scale choices.

The functional identity of kernels holds at LO and NLO in N=4 SYM.

Transformation rules for the nonforward BFKL kernel are derived.

Abstract

It is shown that in the case of the forward scattering the most part of the difference between the M\"obius form of the BFKL kernel and the BK kernel in the next-to-leading order (NLO) can be eliminated by the transformation related to the choice of the energy scale in the representation of scattering amplitudes. Change of the nonforward BFKL kernel under this transformation is derived as well. The functional identity of the forward BFKL kernel in the momentum and M\"obius representations in the leading order (LO) is exhibited and its NLO validity in N=4 supersymmetric Yang-Mills theory is proved.