On the Casimir scaling violation in the cusp anomalous dimension at small angle

TL;DR

This paper calculates a specific four-loop contribution to the QCD cusp anomalous dimension at small angles, revealing Casimir scaling violation and providing insights into its all-order structure.

Contribution

It presents the first gauge-invariant four-loop calculation of a non-planar contribution to the cusp anomalous dimension, testing a recent theoretical conjecture.

Findings

Identifies Casimir scaling violation at four loops.

Provides the four-loop HQET wave function anomalous dimension.

Offers explicit small-angle expansion results.

Abstract

We compute the four-loop $n_f$ contribution proportional to the quartic Casimir of the QCD cusp anomalous dimension as an expansion for small cusp angle $\phi$. This piece is gauge invariant, violates Casimir scaling, and first appears at four loops. It requires the evaluation of genuine non-planar four-loop Feynman integrals. We present results up to ${\mathcal O}(\phi^4)$. One motivation for our calculation is to probe a recent conjecture on the all-order structure of the cusp anomalous dimension. As a byproduct we obtain the four-loop HQET wave function anomalous dimension for this color structure.