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arXiv · 2205.02249

The Four Loop QCD Rapidity Anomalous Dimension

Ian Moult·Hua Xing Zhu·Yu Jiao Zhu
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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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Ian Moult, Hua Xing Zhu, Yu Jiao Zhu. 2022-05-04. The Four Loop QCD Rapidity Anomalous Dimension. https://doi.org/10.1007/jhep08(2022)280

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