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 flavor changing neutral currents in the quark sector and the charged lepton sector that are suppressed by $m_s/m_b$ and $m_{\mu }/m_{\tau }$ in addition to the mass of the heavy Higgs boson of the second Higgs doublet. A Higgs boson mass of $m_H\sim 600–900\mathrm{GeV}$ can explain the deviation from the standard model reported in several rare $B$ decays. Predictions for other $B$ decays are made, and a new $CP$ phase is predicted in $B_s-{\overline{B}}_s$ mixing. The lepton flavor violating decays $\tau \to \mu \overline{l}(\overline{q})l(q)$ 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.

• Received 22 November 2005

DOI:https://doi.org/10.1103/PhysRevD.72.113002