Geometric Effective Field Theory for the Higgs

Abstract: In this talk, I will review recent progress in using geometric methods to characterize Effective Field Theories (EFT) for the Higgs. I will argue that it is important to explore the properties of Higgs EFTs in terms of geometric quantities, in order to derive results that are manifestly invariant under field redefinitions. I will first explore an application of Riemannian geometry for deriving the scale of perturbative unitarity violation from Higgs/Goldstone scattering. Critically, this only accommodates field redefinitions without derivatives. I will then present a generalization of these methods which we call “functional geometry” that accommodates field redefinitions with derivatives. I will derive a novel off-shell recursion relation for amplitudes through the analogy of increasing the rank of a tensor by applying a covariant derivative. I will then show the sense in which the building blocks of this geometry are “on-shell covariant”, and will speculate about various applications of the functional geometry formalism.