The Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order
Abstract
We obtain the quark and gluon rapidity anomalous dimension to fourth order in QCD. We calculate the NLO 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 NLO 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 NLO rapidity anomalous dimension, we perform the resummation of the Energy-Energy Correlation in the back-to-back limit at NLL, 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%.
Keywords
Cite
@article{arxiv.2205.02242,
title = {The Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order},
author = {Claude Duhr and Bernhard Mistlberger and Gherardo Vita},
journal= {arXiv preprint arXiv:2205.02242},
year = {2022}
}
Comments
5 pages, 3 figures, 2 ancillary files. v2: corrected typo in tabled values from ref [28] in eq. 10 and 11. Analytic formulae, EEC section and ancillary files unchanged