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 $\tau \to \mu \gamma$, $\mu \to e\gamma$ and $\tau \to e\gamma$ as well as the $\mu$-$e$ conversion ratio $R_{\mu e}$. We find that $\Gamma (\mu \to e\gamma )$, $\Gamma (\tau \to e\gamma )$ and $R_{\mu e}$ 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 $\Gamma (\tau \to \mu \gamma )/m_{\tau }^5$, $\Gamma (\mu \to e\gamma )/m_{\mu }^5$ and $\Gamma (\tau \to e\gamma )/m_{\tau }^5$ are approximately in the ratio $1:2|V_{e3}{|}^2:2|V_{e3}{|}^2$ if $|V_{e3}|$ is much larger than $\mathcal{O}(10^{-2})$, and in the ratio $2(\Delta m_{\mathrm{atm}}^2{)}^2:(\Delta m_{\mathrm{sun}}^2{)}^2:(\Delta m_{\mathrm{sun}}^2{)}^2$ if $|V_{e3}|$ is much lower than $\mathcal{O}(10^{-3})$, where $\Delta m_{\mathrm{atm}}^2$ and $\Delta m_{\mathrm{sun}}^2$ are the corresponding mass-squared differences of atmospheric and solar neutrino oscillations.

Comments: LaTex 6 pages (2 PS figures). Phys. Rev. D (in printing)