Snowmass White Paper: Effective Field Theory Matching and Applications

TL;DR

This white paper reviews recent advances in functional methods for effective field theory matching, highlighting their automation and application to Standard Model EFT, with the problem fully solved up to one-loop order.

Contribution

It summarizes the current status of functional matching, including automation and applicability to phenomenology within the Standard Model EFT framework.

Findings

Matching for relativistic theories is fully solved up to one-loop order.

Functional matching can be automated for phenomenological studies.

The method applies to arbitrary order in EFT expansion.

Abstract

Mapping UV theories onto low energy effective descriptions is a procedure known as matching. The last decade has seen tremendous progress in the development of new tools for efficiently performing matching calculations, by relying on so-called functional methods. This white paper summarizes the status of functional matching. Specifically, matching for relativistic theories is a fully solved problem up to one-loop order in perturbation theory, and to arbitrary order in the effective field theory expansion. A streamlined prescription that has been partially automated facilitates the application of functional matching to phenomenological studies in the Standard Model EFT framework.