Flavor unification,τdecay, andbdecay within the six-quark—six-lepton Weinberg-Salam model

Abstract

The leptons ${\ensuremath{\nu}}_{e}$, $e$, ${\ensuremath{\nu}}_{\ensuremath{\mu}}$, $\ensuremath{\mu}$, ${\ensuremath{\nu}}_{\ensuremath{\tau}}$, $\ensuremath{\tau}$, and analogously the quarks $u$, $d$, $c$, $s$, $t$, $b$, are unified within the Weinberg-Salam S${\mathrm{U}}_{2}$\ifmmode\times\else\texttimes\fi{}${\mathrm{U}}_{1}$ gauge model without enlarging the gauge group. The result is a theory in which the familiar leptons, quarks, and gauge bosons, plus some extra Higgs bosons necessary for unification, all carry a new multiplicatively conserved quantum number $\ensuremath{\pi}=\ifmmode\pm\else\textpm\fi{}1$. The most striking results of this unification are (1) $\ensuremath{\pi}$ conservation forbids $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ but allows the Higgs-boson-mediated decays $\ensuremath{\tau}\ensuremath{\rightarrow}l\ensuremath{\gamma}$ ($l=e or \ensuremath{\mu}$) and $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\mathrm{ee} or e\ensuremath{\mu}\ensuremath{\mu}$, at a calculable rate with a calculable lower limit; (2) for quarks, two of the three Cabibbo angles must be zero, so that the $b$ quark (assumed lighter than $t$) decays only via Higgs-boson exchange, always semileptonically and always with lepton-number violation, e.g., $b\ensuremath{\rightarrow}d{e}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. This singular prediction will confirm or exclude the model as soon as $b$-flavored mesons are discovered. These and other phenomenological consequences of this unification are explained, and rates are estimated.