The Geometric Universal One-Loop Effective Action

TL;DR

This paper develops universal geometric formulas for one-loop effective actions in scalar field theories, facilitating the integration of heavy fields in extensions of the Standard Model with applications demonstrated.

Contribution

It introduces a geometric approach to derive universal one-loop effective actions, simplifying calculations in scalar field theories and effective field theory matching.

Findings

Derived universal one-loop effective action formulas

Applied formulas to Standard Model extensions with scalar fields

Highlighted the importance of field redefinitions and geometric basis choices

Abstract

We derive universal formulae for integrating out heavy degrees of freedom in scalar field theories up to one-loop level in terms of covariant quantities associated with the geometry of the field manifold. The universal matching results can be readily applied to phenomenologically interesting extensions of the Standard Model, as we demonstrate using a singlet scalar example. We also discuss the role of field redefinitions in effective field theory matching and simplifications resulting from going to a field basis where interactions are encoded in a nontrivial metric on the field manifold.