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 $\frac{m_s}{m_b}$ and $\frac{m_{\mu }}{m_{\tau }}$ 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.

Comments: 21 pages, no figures. Reorganization and addition of text. Reference added and misprints corrected. Conclusions unchanged. Accepted for publication