Three Loop Cusp Anomalous Dimension in QCD

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 lightlike cusp anomalous dimension. We find evidence that this quantity is universal for any gauge theory and use this observation to predict the nonplanar $n_f$-dependent terms of the four loop cusp anomalous dimension.

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 $\varphi$, and wavy lines represent gauge fields.

Figure 2

$\theta$ dependence of the cusp anomalous dimension $\mathrm{\Omega }(a,e^{-\theta })$ at one (solid), two (dashed), and three (dotted) loops.