Is SMEFT Enough?

TL;DR

This paper develops geometric criteria to distinguish SMEFT from HEFT, showing that many models require HEFT and thus SMEFT alone is insufficient for describing all possible new physics scenarios.

Contribution

It introduces a geometric reformulation to identify when HEFT is necessary over SMEFT, clarifying the limitations of SMEFT in capturing certain UV theories.

Findings

HEFT encompasses SMEFT, but many UV theories require HEFT as their low-energy limit.

Two cases necessitate HEFT: when new particles get all their mass from EWSB, or when additional EWSB sources are present.

HEFT offers a more convergent parametrization near the weak scale.

Abstract

There are two canonical approaches to treating the Standard Model as an Effective Field Theory (EFT): Standard Model EFT (SMEFT), expressed in the electroweak symmetric phase utilizing the Higgs doublet, and Higgs EFT (HEFT), expressed in the broken phase utilizing the physical Higgs boson and an independent set of Goldstone bosons. HEFT encompasses SMEFT, so understanding whether SMEFT is sufficient motivates identifying UV theories that require HEFT as their low energy limit. This distinction is complicated by field redefinitions that obscure the naive differences between the two EFTs. By reformulating the question in a geometric language, we derive concrete criteria that can be used to distinguish SMEFT from HEFT independent of the chosen field basis. We highlight two cases where perturbative new physics must be matched onto HEFT: (i) the new particles derive all of their mass from electroweak symmetry breaking, and (ii) there are additional sources of electroweak symmetry breaking. Additionally, HEFT has a broader practical application: it can provide a more convergent parametrization when new physics lies near the weak scale. The ubiquity of models requiring HEFT suggests that SMEFT is not enough.