Large transition magnetic moment of the neutrino from horizontal symmetry

The apparent anticorrelation of the solar-neutrino signal with the 11-yr sunspot cycle observed by Davis can be understood if the electron neutrino has a large magnetic moment. We discuss extensions of the standard model, where the existence of a leptonic ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_H$-horizontal symmetry between the electron and muon generations provides a way to understand such a large magnetic moment, while keeping the neutrino mass naturally small. A global $l_e-l_{\mu }$ symmetry ($l_i=i\mathrm{th}\mathrm{lepton}\mathrm{number}$) is maintained even after spontaneous gauge symmetry breaking, so that the neutrino is of Zeldovich-Konopinski-Mahmoud type with $m_{{\nu }_e}^2-m_{{\nu }_{\mu }}^2=0\mathrm{}$. This condition automatically guarantees that the neutrino spin precession in the magnetic field of the Sun is not suppressed. Of the two extensions of the standard model that we discuss, the first one is a local ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_H$ model with the horizontal symmetry broken completely at a TeV scale. We show how a global ${\mathrm{U}\mathrm{}\left(1\right)\mathrm{}}_{l_e-l_{\mu }}$ can be maintained although $l_e-l_{\mu }$ is a subgroup of the gauged ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_H$. The second example is the minimal supersymmetric extension of the standard model with $R$-parity-violating [but ($l_e-l_{\mu }$)-conserving] interactions. An approximate ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_H$ symmetry between the $e-\mu$ families is imposed in order to suppress the neutrino mass, but not its magnetic moment. We provide a detailed theoretical and phenomenological investigation of these two models and discuss their tests at the colliders as well as in low-energy experiments. The models generally predict $m_{{\nu }_e}\simeq 1-10$ eV and the existence of charged scalar particles in the mass range of 100 GeV.