The Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order

TL;DR

This paper computes the four-loop rapidity anomalous dimension in QCD and applies it to achieve N$^4$LL resummation of the Energy-Energy Correlation event shape, reducing theoretical uncertainties significantly.

Contribution

It provides the first four-loop calculation of the rapidity anomalous dimension and applies it to high-order resummation of event shapes in QCD.

Findings

Four-loop rapidity anomalous dimensions for quarks and gluons are obtained.

First N$^4$LL resummation of an event shape achieved.

Perturbative uncertainties reduced to below 1%.

Abstract

We obtain the quark and gluon rapidity anomalous dimension to fourth order in QCD. We calculate the N$^3$LO rapidity anomalous dimensions to higher order in the dimensional regulator and make use of the soft/rapidity anomalous dimension correspondence in conjunction with the recent determination of the N$^4$LO threshold anomalous dimensions to achieve our result. We show that the results for the quark and gluon rapidity anomalous dimensions at four loops are related by generalized Casimir scaling. Using the N$^4$LO rapidity anomalous dimension, we perform the resummation of the Energy-Energy Correlation in the back-to-back limit at N$^4$LL, achieving for the first time the resummation of an event shape at this logarithmic order. We present numerical results and observe a reduction of perturbative uncertainties on the resummed cross section to below 1%.