New Physics in the Third Family and its Effect on Low Energy Data

We investigate, in detail, a model in which the third family fermions are subjected to an SU(2) dynamics different from the first two families. Constrained by the precision Z-pole data, the heavy gauge boson mass is bounded from below to be about 1.7 TeV at the $2\sigma$ level. The flavor-changing neutral current (FCNC) in the lepton sector can be significant in $\tau\leftrightarrow e$ and $\tau \leftrightarrow \mu$ transitions. In the latter case, the ratio $Br(\tau\to \mu \bar{\nu_\mu} \nu_\tau)/ Br(\tau\to e \bar{\nu_e} \nu_\tau)$ and $Br(\tau\to \mu \mu \mu)$ can constrain the model better than LEP/SLC data in some region of the parameter space. Furthermore, FCNCs are unavoidable in the quark sector. Significant effects to the $B^0-\bar{B^0}$ mixing and the rare decays of the K and B mesons, such as $K^\pm \to \pi^\pm \nu {\bar \nu}$, $b \to s \nu {\bar \nu}, B_s \to \tau^+\tau^-, \mu^+\mu^-$ and $B_{s,d} \to \mu^\pm \tau^\mp$, are expected.