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Is SMEFT Enough?
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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.
Forward citations
Cited by 10 Pith papers
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geoSCET: Soft Theorems from Power Counting
geoSCET derives geometric soft theorems for scalar field theories directly from effective-field-theory power counting and proves they are exact to all orders in perturbation theory when no potential is present.
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Geometry of soft scalars at one loop
The geometric soft theorem for scalar effective field theories is unchanged at one loop in derivative-coupled theories, and receives a universal leading correction when potential interactions are present.
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Towards the HEFT-hedron: the complete set of positivity constraints at NLO
Complete positivity constraints from causality and unitarity are derived for the 15 NLO HEFT operators contributing to longitudinal gauge-Higgs scattering, shrinking the allowed space to about 5 percent.
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Constraints on Loryons in a Two Higgs Doublet Model
In a two-Higgs-doublet model, neutral singlet scalar Loryons remain viable up to about 700 GeV, while charged Loryon representations are strongly constrained by unitarity and Higgs-to-diphoton measurements.
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The Potential of HEFT and the scale of New Physics
From a geometric recursion, the authors compute leading high-energy amplitudes with arbitrary multiplicities, resum them into unitarity bounds and cut-offs, and show that a dilaton HEFT reaches the SM as Δ→2 without p...
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Anomalous Couplings from the Electroweak Chiral Lagrangian for Off-Shell Higgs in $gg\to Z_L Z_L$
In the electroweak chiral Lagrangian, off-shell Higgs contributions to gg to Z_L Z_L at leading order reduce to two independent combinations of the anomalous couplings c_t, c_V, and c_ggh.
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Connecting $t$-channel Dark Matter Models to the Standard Model Effective Field Theory
One-loop SMEFT Wilson coefficients for leptophilic t-channel dark matter, combined with global fits, exclude large coupling regions, especially C_ell_ell for doublet mediators and C_ed above 3 TeV.
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High Energy Vector Boson Scattering in Four-Body Final States to Probe Higgs Cubic, Quartic, and HEFT interactions
With modified Higgs potentials, 2-to-4 vector boson scattering has unitarity violation scales around ten times lower than 2-to-3 scattering and can overtake its cross section at parton energies of a few TeV.
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Electroweak Symmetry Restoration and Radiation Amplitude Zeros
The paper defines a quantitative measure of electroweak symmetry restoration, δ = M_W/2E, and proposes W±γ, W±Z, and W±H cross-section ratios near radiation amplitude zeros as new high-energy collider observables for ...
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Effective Lagrangians from functional matching
Functional matching is reviewed and applied to the Higgs singlet extension; rewriting the resulting EFT in SMEFT form requires fermionic operators even when the heavy Higgs sector has no direct fermion couplings.
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