The three-loop cusp anomalous dimension in QCD

TL;DR

With this result, infrared divergences of planar scattering processes with massive particles can be predicted to that order and a closely related quantity in terms of an effective coupling defined by the lightlike cusp anomalies dimension is defined.

Abstract

We present the full analytic result for the three-loop angle-dependent cusp anomalous dimension in QCD. With this result, infrared divergences of planar scattering processes with massive particles can be predicted to that order. Moreover, we define a closely related quantity in terms of an effective coupling defined by the light-like cusp anomalous dimension. We find evidence that this quantity is universal for any gauge theory, and use this observation to predict the non-planar $n_{f}$-dependent terms of the four-loop cusp anomalous dimension.

Figures (2)

• Figure 1: Sample Feynman diagram producing a contribution to the three-loop cusp anomalous dimension in QCD. Thick lines denote two semi-infinite segments forming a cusp of angle $\phi$, and wavy lines represent gauge fields.
• Figure 2: $\theta$ dependence of the cusp anomalous dimension $\Omega(a,e^{-\theta})$ at one (solid), two (dashed), and three (dotted) loops.