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The Four Loop QCD Rapidity Anomalous Dimension

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arxiv 2205.02249 v2 pith:EX7W47DX submitted 2022-05-04 hep-ph hep-thnucl-th

Ian Moult , Hua Xing Zhu , Yu Jiao Zhu This is my paper · ORCID
classification hep-phhep-thnucl-th
keywords anomalousdimensionrapidityfourfunctionlooprelationsoft
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

The rapidity anomalous dimension controls the scaling of transverse momentum dependent observables in the Sudakov region. In a conformal theory it is equivalent to the soft anomalous dimension, but in QCD this relation is broken by anomalous terms proportional to the $\beta$-function. In this paper we first give a simple proof of this relation using two different representations of the energy-energy correlator observable. We then calculate the anomalous terms to three loops by computing the three-loop fully differential soft function to $\mathcal{O}(\epsilon)$. Combined with recent perturbative data from the study of on-shell form factors and splitting functions, this allows us to derive the four loop rapidity anomalous dimension in QCD.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    At N4LL accuracy, a global fit to all available e+e- energy-energy correlation data shows the data are insensitive to the Collins-Soper kernel and alpha_s, contradicting a recent extraction claim.

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