An EFT hunter's guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes

Abstract

We derive the contact terms contributing to the four-point amplitudes of the standard-model particles, keeping terms with up to quartic energy growth. Imposing just the unbroken low-energy symmetry, and treating the electroweak gauge bosons and the Higgs as independent degrees of freedom, we obtain the most general four-point contact-term amplitudes, corresponding to the HEFT framework. The contact terms are spanned by a basis of Stripped Contact Terms (SCTs), which carry the polarization information, multiplied by polynomials in the Mandelstam invariants. For terms with quadratic energy growth, we also derive the low-energy SMEFT predictions, via on-shell Higgsing of the massless SMEFT contact terms. We discuss several aspects of bottom-up versus top-down on-shell derivations of the HEFT and SMEFT amplitudes, highlighting in particular the simple counting of HEFT dimensions in the on-shell approach and the transparent relation between perturbative unitarity and gauge-invariance in the little-group covariant massive spinor formalism. Our results provide a formulation of EFT analyses directly in terms of observable quantities. For terms with quadratic energy growth, we also provide the mapping to the Warsaw basis.

38 pages, 1 figure

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• A Higgs-Higgs bound state due to New Physics at a TeV
• A Periodic Table of Effective Field Theories
• Hilbert Series, the Higgs Mechanism, and HEFT
• Complete NLO Operators in the Higgs Effective Field Theory
• On-shell Higgsing for EFTs
• Complete NNLO Operator Bases in Higgs Effective Field Theory
• Amplitude/Operator Basis in Chiral Perturbation Theory

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• The Art of Counting: a reappraisal of the HEFT expansion
• Primary Observables for Electroweak Gauge Boson Collider Signals
• Multi-Higgs Amplitudes Bootstrapped: Dissecting SMEFT and HEFT
• Hidden U(N) Symmetry behind N=1 Superamplitudes
• General Signals for Charged Lepton Flavor Violating Decays
• Quantifying EFT Uncertainties in LHC Searches
• Higgs pair production in gluon fusion to higher orders in Higgs Effective Field Theory
• Probing Compressed Mass Spectrum Supersymmetry at the LHC with the Vector Boson Fusion Topology
• Massive Gauge Theories from Consistency Conditions of Amplitudes