Nearly Bi-Maximal Neutrino Mixing, Muon g-2 Anomaly and Lepton-Flavor-Violating Processes

Abstract

We interpret the newly observed muon g-2 anomaly in the framework of a leptonic Higgs doublet model with nearly degenerate neutrino masses and nearly bi-maximal neutrino mixing. Useful constraints are obtained on the rates of lepton-flavor-violating rare decays $τ\to μγ$, $μ\to e γ$ and $τ\to e γ$ as well as the $μ$-$e$ conversion ratio $R_{μe}$. We find that $Γ(μ\to e γ)$, $Γ(τ\to e γ)$ and $R_{μe}$ depend crucially on possible non-zero but samll values of the neutrino mixing matrix element $V_{e3}$, and they are also sensitive to the Dirac-type CP-violating phase. In particular, we show that $Γ(τ\to μγ)/m^5_τ$, $Γ(μ\to e γ)/m^5_μ$ and $Γ(τ\to e γ)/m^5_τ$ are approximately in the ratio $1: 2|V_{e3}|^2: 2|V_{e3}|^2$ if $|V_{e3}|$ is much larger than ${\cal O}(10^{-2})$, and in the ratio $2 (Δm^2_{\rm atm})^2: (Δm^2_{\rm sun})^2:(Δm^2_{\rm sun})^2$ if $|V_{e3}|$ is much lower than ${\cal O}(10^{-3})$, where $Δm^2_{\rm atm}$ and $Δm^2_{\rm sun}$ are the corresponding mass-squared differences of atmospheric and solar neutrino oscillations.