Twist-two operators and the BFKL regime - nonstandard solutions of the Baxter equation

TL;DR

This paper introduces new analyticity conditions for solving the Baxter equation directly for complex spin values, connecting BFKL physics with twist-two operators and enabling potential integration into exact integrability frameworks.

Contribution

It proposes analyticity conditions for Baxter equation solutions that work for any complex spin, facilitating direct analytical continuation without relying solely on harmonic sums.

Findings

Constructed solutions up to 2-loop level.

Revealed surprising asymptotics of solutions.

Potential for integration into TBA/FiNLIE/QSC methods.

Abstract

The link between BFKL physics and twist-two operators involves an analytical continuation in the spin of the operators away from the physical even integer values. Typically this is done only after obtaining an analytical result for integer spin through nested harmonic sums. In this paper we propose analyticity conditions for the solution of Baxter equation which would work directly for any value of complex spin and reproduce results from the analytical continuation of harmonic sums. We carry out explicit contructions up to 2-loop level. These nonstandard solutions of the Baxter equation have rather surprising asymptotics. We hope that these analyticity conditions may be used for incorporating them into the exact TBA/FiNLIE/QSC approaches valid at any coupling.