  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.
