Spectrum of the SU(2) scalar-fermion-gauge system under the influence of the Brout-Englert-Higgs effect

TL;DR

The paper investigates the spectrum of a gauge-invariant SU(2) scalar-fermion-gauge system in BEH-like regime using non-perturbative lattice methods. It implements the Fröhlich-Morchio-Strocchi mechanism to relate gauge-invariant bound states to the SM-like spectrum, and extends the analysis to a fermionic sector with dynamical vector-like leptons, enabling a gauge-invariant view of the Higgs, W/Z, and leptons. The results show a stable Higgs-like bound state with a SM-like mass ratio $m_{0^+}/m_{1^-}$ and reveal a fermion mass defect where the physical fermion can lie below $m_{0^+}$ for small $m_ extPsi/m_{1^-}$, consistent with FMS and indicating additional Higgs contributions in the fermionic sector. The work lays the groundwork for a Lüscher analysis of scattering and cross-sections, aiming for direct comparison with future collider data and highlighting qualitative differences between perturbative and gauge-invariant weak physics.

Abstract

Gauge invariance requires physical states to be composite, even in the weak sector of the Standard Model (SM). The Fröhlich-Morchio-Strocchi (FMS) mechanism resolves this subtlety and predicts additional Higgs contributions in SM processes. While this has been supported by theoretical investigations in the bosonic sector, its impact on fermionic observables remains largely unexplored. We use non-perturbative lattice techniques within a gauge-invariant framework to study a proxy theory of the weak sector with dynamical fermions. We determine the physical spectrum of the theory and interpret the results in the context of the FMS mechanism. Additionally, we identify suitable simulation points for a scattering analysis as a first step toward cross-sections relevant to (future lepton) colliders.

Figures (1)

• Figure 1: Dependence of the scalar, vector boson, fermion, and leptonium masses on the fermion mass, computed for the parameters listed in Table \ref{['tab:param']}. All masses are extracted from correlators constructed from gauge-invariant composite operators. Error bars are mostly smaller than the symbol size.