Resummation of small-spin singularities in anomalous dimensions of twist-two operators

TL;DR

This paper explores the resummation of small-spin singularities in the anomalous dimensions of twist-two operators in QCD, linking higher-loop behavior with conformal theories and advanced mathematical frameworks.

Contribution

It introduces a novel resummation method for singularities in anomalous dimensions, connecting QCD results with conformal field theory insights and higher-order predictions.

Findings

Resummation predicts higher-loop singular behaviors.

Connections established with conformal Regge theory.

Insights into detector operators in QCD and conformal theories.

Abstract

Anomalous dimensions of leading-twist operators in QCD play an important role in precision predictions for high-energy processes, since they govern the scale evolution of parton distributions. Their analytic structure as a function of spin is particularly important due to the complexity of higher-loop computations. In these proceedings, we discuss the resummation of the certain type of such singularities that share common features with those appearing in the quark flavor-nonsinglet sector of QCD. Our main focus is on the interplay between Gross-Neveu-Yukawa model in $\epsilon$ expansion and Gross-Neveu in $1/N$ expansion. Such resummation allows one to predict the higher-loop singular behavior and reveals connections with the conformal Regge theory and recent studies of detector operators in QCD and various conformal field theories.