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 4πv. 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.

A new Higgs effective field theory and the new no-lose theorem

“…The invalidity of the dimension six EFT for the non-decoupling case has also pointed out in Refs. [25][26][27]. In contrast with the dimension six EFT, the naHEFT agrees with the complete one-loop calculations even for r 1.…”

“…New physics effects are encoded in polynomials, M 2 (h), F(h), K(h), Y(h), and Ŷ(h). If there is no non-decoupling effects, the effective Lagrangian is expressed by polynomials in |Φ| 2 = (v + h) 2 /2 rather than polynomials in h [24][25][26][27]. The EFT described by polynomials in |Φ| 2 is known as the "Standard Model Effective Field Theory (SMEFT) [20][21][22][23]".…”

“…One of the widely used EFT frameworks is the "Standard Model Effective Field Theory (SMEFT) [20][21][22][23]", in which new physics effects are expressed in polynomials of the SM fields transforming linearly under the electroweak gauge symmetry (SU (2) L × U (1) Y ) transformation. It has been recently pointed out, however, that the SMEFT cannot be applied to describe the non-decoupling physics [24][25][26][27]. This is because the non-decoupling effects in the Higgs sector typically cannot be expressed by a polynomial in the Higgs doublet fields.…”

Electroweak phase transition in the nearly aligned Higgs effective field theory

“…As clarified in Refs. [38,42,45,63,64], the non-analytic Higgs operators parameterize the nondecoupling new physics effects to the Higgs sector. Another widely used EFT framework is so-called the Standard model effective field theory (SMEFT) [65][66][67][68], in which f (|Φ| 2 ) is restricted to be a polynomial in |Φ| 2 as…”

Non-Decoupling New Particles

“…2 that limits the radius of convergence of the SMEFT expansion, see [10]. 7 Despite appearances the effective Lagrangian is well behaved when…”