Local scale-invariance breaking in the standard model by two-measure theory

Abstract

We introduce Weyl's scale invariance as additional local symmetry in the standard model of electroweak interactions. Under this, the gauge symmetry of the standard model now is $SU(3)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0ex}{0ex}}U(1)\ifmmode\times\else\texttimes\fi{}\stackrel{\texttildelow{}}{U}(1)$, where $\stackrel{\texttildelow{}}{U}(1)$ is for local scale invariance, and its gauge boson is called the Weylon. Also introduced are two new scalars ${\ensuremath{\sigma}}_{1}$ and ${\ensuremath{\sigma}}_{2}$ with the common scaling weight $\ensuremath{-}1$. The mechanism for spontaneous breaking of scale invariance is invoked by coupling ${\ensuremath{\sigma}}_{2}$ to a metric-independent measure defined in terms of an additional four scalars ${\ensuremath{\phi}}^{I}(I=1,2,3,4)$. Weyl's scale invariance is now implemented by combining it with internal diffeomorphisms of the four scalars ${\ensuremath{\phi}}^{i}$. We show that once local scale invariance is broken, the phenomenon (a) generates Newton's gravitational constant ${G}_{N}$ and (b) triggers spontaneous symmetry breaking in the conventional manner resulting in masses for the conventional fermions and bosons. The scale at which Weyl's scale symmetry breaks is of order Planck mass. If right-handed neutrinos are also introduced, their absence at present energy scales is attributed to their mass being tied to the scale at which scale invariance breaks. New $C$- and $CP$-violating effects can also be induced by mixing the Weylon with the hypercharge gauge boson of the standard model.