Form factors and scattering amplitudes in supersymmetric gauge theories

Abstract

The study of scattering amplitudes in the maximally supersymmetric Yang-Mills theory (N = 4 SYM) is a thriving field of research. Since the reformulation of perturbative gauge theory as a twistor string theory by Witten, this area has witnessed a flurry of activity, leading to the discovery of a multitude of novel techniques, such as recursion relations and MHV diagrams, collectively referred to as on-shell methods. In parallel, many previously hidden properties and rich mathematical structures have been found, a powerful example of such being the dual superconformal symmetry. It is natural to ask whether this understanding can be extended to phenomenologically relevant theories as well as other quantities. The goal of the present work is to apply the modern on-shell methods to calculations of form factors, with particular focus on those which are relevant for describing Higgs production in QCD from the point of view of an effective field theory. Specifically, our analysis will be carried out in supersymmetric gauge theories at two-loop level and will consist of several steps. We focus first on operators in the SU(2j3) closed subsector of N = 4 SYM, in particular two non-protected, dimension-three operators. We then move on to consider the trilinear operator Tr(F3) and a related descendant of the Konishi operator which contains Tr(F3), also in N =4 SYM. Finally, we concentrate on two-loop form factors of these two operators in theories with less-than-maximal supersymmetry. The result of our investigation shows an emergence of a small number of universal building blocks, ultimately related to the two-loop form factor of a trilinear half-BPS operator. This finding suggests that the most complicated, maximally transcendental part of Higgs plus multi-gluon amplitudes in QCD can be equivalently computed in a remarkably simple way by considering form factors of half-BPS operators in N =4 SYM.