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

Hongkai Liu (Physics Department, Technion — Israel Institute of Technology, Technion city, Haifa, 3200003, Israel) ; Teng Ma (Physics Department, Technion — Israel Institute of Technology, Technion city, Haifa, 3200003, Israel; Department of Physics and IFAE-BIST, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Barcelona, Spain) ; Yael Shadmi (Physics Department, Technion — Israel Institute of Technology, Technion city, Haifa, 3200003, Israel) ; Michael Waterbury (Physics Department, Technion — Israel Institute of Technology, Technion city, Haifa, 3200003, Israel)

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 Higgs Effective Field Theory (HEFT) framework. The contact terms are spanned by a basis of Stripped Contact Terms, which carry the polarization information, multiplied by polynomials in the Mandelstam invariants. For terms with quadratic energy growth, we also derive the low-energy Standard Model Effective Field Theory (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 Effective Field Theory analyses directly in terms of observable quantities. For terms with quadratic energy growth, we also provide the mapping to the Warsaw basis.

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      "source": "Springer", 
      "value": "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 Higgs Effective Field Theory (HEFT) framework. The contact terms are spanned by a basis of Stripped Contact Terms, which carry the polarization information, multiplied by polynomials in the Mandelstam invariants. For terms with quadratic energy growth, we also derive the low-energy Standard Model Effective Field Theory (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 Effective Field Theory analyses directly in terms of observable quantities. For terms with quadratic energy growth, we also provide the mapping to the Warsaw basis."
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Published on:
31 May 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 5
Pages 1-33
DOI:
https://doi.org/10.1007/JHEP05(2023)241
arXiv:
2301.11349
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: