Gauge model for chiral-symmetry breaking and muon-electron mass ratio

Abstract

We present a unified gauge model of weak and electromagnetic interactions, which has the following features: (a) Chiral $\mathrm{U}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}{\mathrm{}\left(2\right)\mathrm{}}_R$ is an exact "natural" symmetry of strong interactions in zeroth order and therefore its violations (which arise in order $g^4$ are computable, and adjusting parameters suitably we can get $\frac{(\sqrt{2}{\epsilon }_0+{\epsilon }_8)}{(\sqrt{2}{\epsilon }_0-2\mathrm{}{\epsilon }_8)}\sim \alpha$; (b) violations of isospin symmetry as observed in, for example, $\Delta I\ne 0$ mass differences are, then, computable and of order $\alpha$; (c) this model can be extended to include leptons in such a way that $\frac{m_e}{m_{\mu }}$ is computable and is of order $g^4$. We also speculate on the possibility of spontaneous $\mathrm{CP}$ violation arising as a higher-order effect.