The 2-3 symmetry: Flavour Changing $b$, $\tau$ Decays and Neutrino Mixing

Abstract

The observed pattern of neutrino mixing may be the result of a 2-3($ \mu- \tau$) symmetry in the leptonic sector. We consider a two Higgs doublet model with a 2-3 symmetry in the down type quark and the charged lepton sector. The breaking of the 2-3 symmetry by the strange quark mass and the muon mass leads to FCNC in the quark sector and the charged lepton sector that are suppressed by ${m_s \over m_b}$ and ${m_{\mu} \over m_{\tau}}$ in addition to the mass of the heavy Higgs boson of the second Higgs doublet. A Higgs boson mass of $ m_H \sim 600 - 900$ GeV can explain the deviation from standard model reported in several rare B decays. Predictions for other B decays are made and a new CP phase is predicted in $B_{s}-{\bar{B}_{s}}$ mixing. The lepton flavour violating decays $ \tau \to \mu \bar{l}(\bar{q}) l(q)$ are below the experimental limits. The breaking of 2-3 symmetry in the lepton sector can lead to deviations of the atmospheric neutrino mixing angle from the maximal value by $ \sim 2$ degrees.