Unitarity Violation and the Geometry of Higgs EFTs

Abstract

We derive the scale of unitarity violation from the geometry of Effective Field Theory (EFT) extensions of the Standard Model Higgs sector. The high-energy behavior of amplitudes with more than four scalar legs depends on derivatives of geometric invariants with respect to the physical Higgs field $h$, such that higher-point amplitudes begin to reconstruct the scalar manifold away from our vacuum. In theories whose low-energy limit can be described by the Higgs EFT (HEFT) but not the Standard Model EFT (SMEFT), non-analyticities in the vicinity of our vacuum limit the radius of convergence of geometric invariants, leading to unitarity violation at energies below $4\pi v$. Our results unify approaches to the HEFT/SMEFT dichotomy based on unitarity, analyticity, and geometry, and more broadly illustrate the sense in which observables probe the geometry of an EFT. Along the way, we provide novel basis-independent results for Goldstone/Higgs boson scattering amplitudes expressed in terms of geometric covariant quantities.

42+12 pages, 6 figures. v2: Added references. v3: Journal version

References in corpus (3)

• Is SMEFT Enough?
• Constructing massive on-shell contact terms
• Higgs Coupling Measurements and the Scale of New Physics

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• Geometry in Scattering Amplitudes
• The flair of Higgsflare: Distinguishing electroweak EFTs with $W_L{W}_L\to n\times h$
• On-Shell Covariance of Quantum Field Theory Amplitudes
• Monolepton production in SMEFT to $\mathcal{O}(1/{\Lambda }^4)$ and beyond
• Electroweak phase transition in the nearly aligned Higgs effective field theory
• A new Higgs effective field theory and the new no-lose theorem
• Unitarity Bounds on Effective Field Theories at the LHC