A non-Standard Standard Model

Abstract

We examine the Standard Model under the electroweak symmetry group $U_{EW}(2)$ subject to the Lie algebra condition $\mathfrak{u}_{EW}(2)\not\cong \mathfrak{su}_{I}(2)\oplus \mathfrak{u}_{Y}(1)$. Physically, the condition ensures that all electroweak gauge bosons interact with each other prior to symmetry breaking. This represents a crucial shift in the identification of physical gauge bosons: Unlike the Standard Model which posits a change of Lie algebra basis induced by spontaneous symmetry breaking, here the basis is unaltered and $A,\,Z^0,\,W^\pm$ represent the physical bosons both before and after spontaneous symmetry breaking. Our choice of $\mathfrak{u}_{EW}(2)$ requires some modification of the matter field representation of the Standard Model. For $U_{EW}(2)$, there are two pertinent representations ${\mathbf{2}}$ and its $U(2)$-conjugate ${\mathbf{2^c}}$ related by a global gauge transformation that squares to minus the identity. The product group structure calls for strong-electroweak degrees of freedom in the $(\mathbf{3},\mathbf{2})$ and the $(\mathbf{3},{\mathbf{2^c}})$ of $SU_C(3)\times U_{EW}(2)$ that possess integer electric charge just like leptons. These degrees of freedom play the role of quarks, and they lead to a modified Lagrangian that nevertheless reproduces transition rates and cross sections equivalent to the Standard Model. The close resemblance between quark and lepton electroweak doublets suggests a mechanism for a speculative phase transition between quarks and leptons that stems from the product structure of the symmetry group. Our hypothesis is that the strong and electroweak bosons see each other as a source of decoherence. In effect, lepton representations get identified with the $SU(3)$-trace-reduced quark representations. This mechanism allows for possible extensions of the Standard Model that don't require large inclusive multiplets of matter fields.