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

Abstract

The leptons ${\nu }_e$, $e$, ${\nu }_{\mu }$, $\mu$, ${\nu }_{\tau }$, $\tau$, and analogously the quarks $u$, $d$, $c$, $s$, $t$, $b$, are unified within the Weinberg-Salam S${\mathrm{U}}_2$×${\mathrm{U}}_1$ 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 $\pi =\pm 1$. The most striking results of this unification are (1) $\pi$ conservation forbids $\mu \to e\gamma$ but allows the Higgs-boson-mediated decays $\tau \to l\gamma$ ($l=e or \mu$) and $\tau \to \mu \mathrm{ee} or e\mu \mu$, 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., $b\to d{e}^{+}{\mu }^{-}$. 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.