Calculation of the soft anomalous dimensions with time-like and light-like Wilson lines

by Zehao Zhu

Thursday 6 Mar 2025, 14:00 → 15:00 Europe/London

Soft singularities of scattering amplitudes are important for both theoretical and practical reasons. It is well known that these singularities are captured by correlators of Wilson lines which follow the classical trajectory of energetic partons participating in the process and intersect at the hard interaction vertex. Such correlators feature ultraviolet singularities, which allow us to compute the soft anomalous dimension, provided the infrared is regularized. However, while correlators of time-like Wilson lines which intersect each other are multiplicatively renormalizable, strictly light-like Wilson lines feature also collinear singularities and lose multiplicative renormalizability. This feature complicates their regularization and the separation between infrared and ultraviolet singularities. Indeed, the soft anomalous dimensions of massless scattering amplitudes is rather different from that of massive ones, and the relation between them is subtle. 

In this talk, I will show that by using the method of regions and differential equations, multiplicative renormalizability can be recovered so that two-loop soft anomalous dimensions involving massless particles are related to the computations with strictly lightlike Wislon lines. I will then turn to three loops, where I present an unfinished calculation with one time-like and three light-like Wilson lines.