Double-logs, Gribov-Lipatov reciprocity and wrapping

TL;DR

This paper investigates the analytical structure of five-loop anomalous dimensions of twist-2 operators at negative even spins, proposing generalizations of double-logarithmic equations and reciprocity-respecting functions to predict all-order pole structures and wrapping corrections.

Contribution

It introduces two new generalizations of double-logarithmic equations and reciprocity-respecting functions to predict higher-order poles and wrapping corrections in twist-2 operators.

Findings

Predicted all-order pole structures of anomalous dimensions.

Connected reciprocity-respecting functions with wrapping corrections.

Provided a framework for reconstructing wrapping effects from lower-order data.

Abstract

We study analytical properties of the five-loop anomalous dimension of twist-2 operators at negative even values of Lorentz spin. Following L. N. Lipatov and A. I. Onishchenko, we have found two possible generalizations of double-logarithmic equation, which allow to predict a lot of poles of anomalous dimension of twist-2 operators at all orders of perturbative theory from the known results. Second generalization is related with the reciprocity-respecting function, which is a single-logarithmic function in this case. We have found, that the knowledge of first orders of the reciprocity-respecting function gives all-loop predictions for the highest poles. Obtained predictions can be used for the reconstruction of a general form of the wrapping corrections for twist-2 operators.