Two-loop anomalous dimensions of generic dijet soft functions

TL;DR

This paper derives compact formulas for two-loop anomalous dimensions of soft functions in SCET, enabling precise resummation of logarithms in collider observables and confirming previous results while providing new predictions.

Contribution

It introduces a unified integral representation for two-loop soft anomalous dimensions applicable to various SCET soft functions, including new predictions for angularity and jet grooming.

Findings

Confirmed existing two-loop results for multiple dijet soft functions.

Provided new predictions for angularity event shapes.

Extended formalism to both SCET-1 and SCET-2 soft functions.

Abstract

We present compact integral representations for the calculation of two-loop anomalous dimensions for a generic class of soft functions that are defined in terms of two light-like Wilson lines. Our results are relevant for the resummation of Sudakov logarithms for e+ e- event-shape variables and inclusive hadron-collider observables at next-to-next-to-leading logarithmic accuracy within Soft-Collinear Effective Theory (SCET). Our formalism applies to both SCET-1 and SCET-2 soft functions and we clarify the relation between the respective soft anomalous dimension and the collinear anomaly exponent. We confirm existing two-loop results for about a dozen dijet soft functions and obtain new predictions for the angularity event shape and the soft-drop jet-grooming algorithm.