Field reparametrization in effective field theories

TL;DR

This paper discusses the choice of operator bases in Effective Field Theories, emphasizing the importance of basis equivalence for the S-matrix and analyzing the effects of non-linear field reparametrizations on EFT consistency.

Contribution

It revisits the equivalence theorem in EFT, clarifying the impact of non-linear, non-invariant field reparametrizations on basis choice and S-matrix equivalence.

Findings

All bases are equivalent for the S-matrix when properly defined.

Non-linear, non-invariant reparametrizations can connect different operator sets.

Phenomenological approaches may ignore some formal aspects without invalidating preliminary results.

Abstract

Debate topic for Effective Field Theory (EFT) is the choice of a "basis" for $\mrdim = 6$ operators Clearly all bases are equivalent as long as they are a "basis", containing a minimal set of operators after the use of equations of motion and respecting gauge invariance. From a more formal point of view a basis is characterized by its closure with respect to renormalization. Equivalence of bases should always be understood as a statement for the S-matrix and not for the Lagrangian, as dictated by the equivalence theorem. Any phenomenological approach that misses one of these ingredients is still acceptable for a preliminar analysis, as long as it does not pretend to be an EFT. Here we revisit the equivalence theorem and its consequences for EFT when two sets of higher dimensional operators are connected by a set of non-linear, noninvariant, field reparametrizations.