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

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.

30 pages, 4 figures, revtex format; to match published version

References in corpus (4)

• Symmetries and conservation laws in non-Hermitian field theories
• Critical behavior of the PT-symmetric $i{\varphi }^3$ quantum field theory
• Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians
• Decay of the Higgs boson to ${\tau }^{-}{\tau }^{+}$ and non-Hermiticity of the Yukawa interaction

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• Massive gauge particles versus Goldstone bosons in non-Hermitian non-Abelian gauge theory
• 't Hooft-Polyakov monopoles in non-Hermitian quantum field theory
• PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• IR/UV mixing from local similarity maps of scalar non-Hermitian field theories
• Complex BPS solitons with real energies from duality
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• The phase diagram and vortex properties of PT-symmetric non-Hermitian two-component superfluid
• Schwinger-Dyson equations and mass generation for an axion theory with a PT symmetric Yukawa fermion interaction
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• Renormalisation group flows connecting a $4-\epsilon$ dimensional Hermitian field theory to a $\mathcal{P}\mathcal{T}$-symmetric theory for a fermion coupled to an axion
• Original study of the $g{\varphi }^2(i\varphi {)}^{\epsilon }$ theory. Analysis of all orders in $\epsilon$ and resummations
• Non-Hermiticity: a new paradigm for model building in particle physics
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• Decay of the Higgs boson $h\to {\tau }^{-}{\tau }^{+}\to {\pi }^{-}{\nu }_{\tau }{\pi }^{+}{\bar{\nu }}_{\tau }$ for a non-Hermitian Yukawa interaction
• Complex topological soliton with real energy in particle physics
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry
• Non-linear and weak-coupling expansion in Quantum Field Theory