Assessing (H)EFT theory errors by pitting EoM against Field Redefinitions

TL;DR

This paper explores how field redefinitions impact effective field theory truncations and proposes a method to validate power-counting schemes using invariance principles, with a case study in Higgs EFT.

Contribution

It introduces a framework for assessing EFT errors via invariance under field redefinitions, extending uncertainty estimation methods to non-renormalisable interactions.

Findings

Invariance under field redefinitions can validate power-counting schemes.

The approach generalizes SM uncertainty estimation procedures.

Case study in Higgs EFT highlights process-dependent sensitivities.

Abstract

Truncations of effective field theory expansions are technically necessary but inherently intertwined with the redundancies of general field redefinitions. This can be viewed as a juxtaposition of power-counting and theoretical uncertainties, which seek to estimate neglected higher-dimensional interactions through approaches based on community consensus. One can then understand the invariance of physics under field redefinitions as a data-informed validation of different power-counting schemes, or as a means of assigning theoretical errors in comparison with algebraic, equation of motion-based replacements. Such an approach generalises widely accepted procedures for estimating theoretical uncertainties within the SM to non-renormalisable interactions. We perform a case study for a representative example in Higgs Effective Field theory, focusing on universal Higgs properties tensioned against process-dependent sensitivity expectations.