Higgs-like field interactions before symmetry breaking

We investigate the Brout-Englert-Higgs mechanism of spontaneous symmetry breaking and show that, before symmetry breaking, the interaction of Higgs fields with massless gauge fields leads to the production of particles with negative squared mass.

💡 Research Summary

The paper investigates a hitherto under‑explored aspect of the Higgs‑like sector: the behavior of the tachyonic short‑wavelength modes that exist before the electroweak symmetry is broken. Starting from the simplest scalar field model with a “Mexican‑hat’’ potential, the authors emphasize that the field configuration at the origin (φ = 0) is a local maximum and, for small fluctuations, the scalar behaves as a tachyon (negative‑mass‑squared). While the long‑wavelength tachyonic modes (|p| < m) are well known to grow exponentially and drive the symmetry‑breaking transition, the short‑wavelength sector (|p| ≥ m) possesses real energies and can be interpreted as genuine particle excitations.

To treat these excitations consistently, the authors adopt the “twin‑space’’ formalism introduced in their earlier work (Phys. Rev. D 110, 015006 (2024)). In this approach the tachyonic field operator ˆφ is defined on an enlarged Fock space F ⊗ F* so that it transforms as a scalar under the Lorentz group, thereby restoring covariance that would otherwise be lost in a single‑Fock‑space treatment. The mode expansion of ˆφ includes only momenta satisfying |k| ≥ m, with dispersion ω_k = √(k² − m²). The massless partner field ψ is quantized in the standard way.

The core of the analysis is a Yukawa‑type interaction H_int = g φ ψ². At first order in perturbation theory the authors compute the S‑matrix element for the process in which an incoming massless particle of momentum k emits a tachyon of momentum l and continues as a massless particle of momentum p (k → p + l). The amplitude is simply A = g, manifestly Lorentz‑invariant. From this they derive the decay width Γ by integrating over the final‑state phase space, carefully imposing the tachyonic momentum constraint |l| ≥ m (which is automatically satisfied by the delta‑function). The resulting expression, \