Title: A Non-standard Standard Model,
Abstract: This paper examines the Standard Model under the strong-electroweak gauge
group $SU_S(3)\times U_{EW}(2)$ subject to the condition $u_{EW}(2)\not\cong
su_I(2)\oplus u_Y(1)$. Physically, the condition ensures that all electroweak
gauge bosons interact with each other prior to symmetry breaking --- as one
might expect from $U(2)$ invariance. This represents a crucial shift in the
notion 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 (modulo $U_{EW}(2)$ gauge
transformations) the physical bosons both \emph{before} and after spontaneous
symmetry breaking.
Our choice of $u_{EW}(2)$ basis requires some modification of the matter
field sector of the Standard Model. Careful attention to the product group
structure calls for strong-electroweak degrees of freedom in the
$(\mathbf{3},\mathbf{2})$ and the $(\mathbf{3},\overline{\mathbf{2}})$ of
$SU_S(3)\times U_{EW}(2)$ 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 in this
picture suggests a mechanism for a phase transition between quarks and leptons
that stems from the product structure of the gauge group. Our hypothesis is
that the strong and electroweak bosons see each other as a source of
decoherence. In effect, leptons get identified with the $SU_S(3)$-trace of
quark representations. This mechanism allows for possible extensions of the
Standard Model that don't require large inclusive multiplets of matter fields.
As an example, we propose and investigate a model that turns out to have some
promising cosmological implications.