Unitarity violation and the geometry of Higgs EFTs

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