Two-loop anomalous dimension for the resummation of non-global observables

TL;DR

This paper derives the two-loop anomalous dimension essential for resumming subleading logarithms in non-global jet observables, advancing precision in theoretical predictions of soft radiation effects.

Contribution

It provides the first extraction of the two-loop anomalous dimension for non-global observables, addressing the challenge of collinear singularities in soft amplitude limits.

Findings

Derived the two-loop anomalous dimension for non-global observables

Predicted subleading non-global logarithms in two-jet cross sections

Validated results through consistency checks with known logarithms

Abstract

The soft radiation emitted in jet cross sections can resolve the directions and colors of individual hard partons, leading to a complicated pattern of logarithmically enhanced terms in the perturbative series. Starting from a factorization theorem and solving the renormalization group equations for its ingredients, these large logarithms can be resummed. In this paper, we extract the two-loop anomalous dimension governing the resummation of subleading logarithms in jet cross sections and other non-global observables. This anomalous dimension can be obtained by considering soft limits of hard amplitudes, but the presence of collinear singularities in intermediate expressions makes its extraction delicate. As a consistency check, we use our results to predict the known subleading non-global logarithms in the two-jet cross section.