The four loop QCD rapidity anomalous dimension

Ian Moult

doi:10.1007/JHEP08(2022)280

The four loop QCD rapidity anomalous dimension

2022-08-29

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DOI：10.1007/JHEP08(2022)280

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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 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.

Keywords:

Factorization

Renormalization Group

Higher-Order Perturbative Calculations

Resummation

The four loop QCD rapidity anomalous dimension

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