Unitarity Violation and the Geometry of Higgs EFTs

TL;DR

This paper links the unitarity violation scale in Higgs EFTs to the geometric properties of the scalar manifold, revealing how high-energy behavior constrains EFT validity and unifies different EFT frameworks.

Contribution

It introduces a geometric approach to determine unitarity violation in Higgs EFTs and clarifies the distinction between HEFT and SMEFT based on geometric invariants.

Findings

Unitarity violation occurs below 4πv in certain Higgs EFTs.

Geometric invariants determine the high-energy behavior of scalar amplitudes.

New basis-independent formulas for Higgs and Goldstone scattering amplitudes.

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.