Spontaneously Breaking Non-Abelian Gauge Symmetry in Non-Hermitian Field Theories

TL;DR

This paper extends PT-symmetric non-Hermitian gauge theories to non-Abelian symmetries, demonstrating a consistent gauge-invariant framework and revealing novel mass spectra for gauge bosons and scalars, opening new avenues in particle physics modeling.

Contribution

It introduces a gauge-invariant formulation of non-Hermitian non-Abelian gauge theories and analyzes the mass generation mechanism, extending previous Abelian results.

Findings

Gauge boson masses depend quartically on the non-Hermitian parameter mu.

The bosonic mass spectrum significantly differs from Hermitian models.

The framework maintains gauge invariance and BRST symmetry in non-Hermitian settings.

Abstract

We generalise our previous formulation of gauge-invariant PT-symmetric field theories to include models with non-Abelian symmetries and discuss the extension to such models of the Englert-Brout-Higgs-Kibble mechanism for generating masses for vector bosons. As in the Abelian case, the non-Abelian gauge fields are coupled to non-conserved currents. We present a consistent scheme for gauge fixing, demonstrating Becchi-Rouet-Stora-Tyutin invariance, and show that the particle spectrum and interactions are gauge invariant. We exhibit the masses that gauge bosons in the simplest two-doublet SU(2)xU(1) model acquire when certain scalar fields develop vacuum expectation values: they and scalar masses depend quartically on the non-Hermitian mass parameter mu. The bosonic mass spectrum differs substantially from that in a Hermitian two-doublet model. This non-Hermitian extension of the Standard Model opens a new direction for particle model building, with distinctive predictions to be explored further.