Classifying the special functions of Feynman integrals

My research will focus on developing our understanding of the mathematical properties of scattering amplitudes, which allow us to make particle physics predictions using quantum field theory. Traditionally, scattering amplitudes have been computed using Feynman diagrams. However, Feynman diagrams turn out to be incredibly difficult to compute.

As a result, a great deal of research has been devoted to evaluating Feynman diagrams that contribute to the Standard Model---which describes the particles and interactions that occur in the real world---as these diagrams are required for making predictions in collider experiments.

However, another more illuminating approach to computing scattering amplitudes has recently become feasible. Scattering amplitudes are highly structured mathematical objects, whose properties are constrained by basic physical principles such as causality and unitarity. Bootstrap approaches to evaluating scattering amplitudes seek to leverage this fact by constructing amplitudes directly from these expected physical and mathematical properties, thereby circumventing the difficult integrals that must be evaluated in more traditional approaches.

However, in order to get bootstrap methods off of the ground, one must be able to predict what types of special functions a given Feynman diagram will give rise to. The ultimate goal of my project is thus to systematically classify the types of special functions that can arise in important Standard Model processes.

The Baikov representation of the integrals associated with Feynman diagrams has seen renewed interest in the past decade, because its structure makes manifest more clearly these relevant analytical properties. However, many aspects of the Baikov representation have not been studied. Thus, in addition to prediction what types of special functions will arise, I will explore whether additional properties---such as the location of algebraic and logarithmic branch cuts---is made transparent by this representation.

This will lead to great advances in our ability to bootstrap scattering amplitudes of phenomenological relevance at the Lare Hadron Collider.