The structure of the soft anomalous dimension for gauge-theory amplitudes

by Tommaso Saracco (Nikhef, Amsterdam)

Monday 9 Dec 2024, 14:00 → 15:00 Europe/Rome

Aula Grassano

Understanding the infrared behaviour of gauge theories is a fundamental step in making accurate Standard Model predictions. Infrared divergences are known to exponentiate in scattering amplitudes, and we focus our attention on the soft anomalous dimension, which is the fundamental object governing the infrared behaviour of a theory. The soft anomalous dimension can be computed diagrammatically using special types of Feynman diagrams, known as web diagrams. We review the role of infrared divergences in scattering amplitudes, and how to calculate the anomalous dimension in the simplest cases. Webs without three or four-gluon vertices are shown to be rather well understood, even at high-loop order. However, webs with gluon-gluon interactions are strikingly more difficult to handle, even in the simplest cases. To avoid direct computation of webs, we explore the bootstrap approach to calculate the soft anomalous dimension . This approach relies on making an ansatz on the basis of functions on which the anomalous dimension takes values, and then determining the coefficients of the linear combination of the basis elements by studying suitable limits. To reduce the dimensionality of the basis of functions, we explore factorisation properties of webs. Formal proofs of two factorisation theorems are obtained for webs composed of two connected subdiagrams, holding at any loop order.