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J. F. Gunion and H. E. Haber, “The CP conserving two Higgs doublet model: The Approach to the decoupling limit,” Phys. Rev. D
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R. Alonso, E. E. Jenkins, and A. V. Manohar, “A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space,” Phys. Lett
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2020

Is SMEFT Enough?

Cohen, Timothy, Craig, Nathaniel, Lu, Xiaochuan et al.

Understand

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.