Pole decomposition of BFKL eigenvalue at zero conformal spin and the real part of digamma function

TL;DR

This paper develops a technique to analyze the powers of the BFKL eigenvalue at zero conformal spin, revealing how generalized polygamma functions emerge from pole separation of the digamma function in perturbative expansions.

Contribution

It introduces a novel method for calculating powers of the real part of the digamma function using pole separation, applicable to BFKL eigenvalues at zero conformal spin.

Findings

Demonstrates how generalized polygamma functions arise from pole separation

Provides a new technique for calculating powers of the real part of digamma function

Enhances understanding of BFKL eigenvalue structure at zero conformal spin

Abstract

We consider the powers of leading order eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov~(BFKL) equation at zero conformal spin. Using reflection identities of harmonic sums we demonstrate how involved generalized polygamma functions are introduced by pole separation of a rather simple digamma function. This generates higher weight generalized polygamma functions at any given order of perturbative expansion. As a byproduct of our analysis we develop a general technique for calculating powers of the real part of digamma function in a pole separated form.