Two-loop Radiative Neutrino Mechanism in an SU(3)L×U(1)NSU(3)_L\times U(1)_N Gauge Model

By using the $L_e$ - $L_\mu$ - $L_\tau$ symmetry, we construct an $SU(3)_L\times U(1)_N$ gauge model that provides two-loop radiative neutrino masses as well as one-loop radiative neutrino masses. The generic smallness of two-loop neutrino masses leading to $\Delta m^2_\odot$ compared with one-loop neutrino masses leading to $\Delta m^2_{atm}$ successfully explains $\Delta m^2_{atm}$ $>>$ $\Delta m^2_{\odot}$ by invoking the $L_e$ - $L_\mu$ - $L_\tau$ breaking. The Higgs scalar ($h^+$) that initiates radiative mechanisms is unified into a Higgs triplet together with the standard Higgs scalar ($\phi^+$, $\phi^0$) to form ($\phi^+$, $\phi^0$, $h^+$), which calls for three families of lepton triplets: ($\nu^i_L$, $\ell^i_L$, $\omega^i_L$) (i = 1,2,3), where $\omega^i$ denote heavy neutral leptons. The two-loop radiative mechanism is found possible by introducing a singly charged scalar, which couples to $\ell^i_R\omega^j_R$ (i,j = 2,3).Comment: with 10 pages, revtex, including 2 figures, accepted for publication in Phys. Rev. D (with undefined latex citation indices removed

Radiatively Induced Neutrino Masses and Oscillations in an SU(3)_LxU(1)_N Gauge Model

We have constructed an $SU(3)_L \times U(1)_N$ gauge model utilizing an $U(1)_{L^\prime}$ symmetry, where $L^\prime$ = $L_e-L_\mu-L_\tau$, which accommodates tiny neutrino masses generated by $L^\prime$-conserving one-loop and $L^\prime$-breaking two-loop radiative mechanisms. The generic smallness of two-loop radiative effects compared with one-loop radiative effects describes the observed hierarchy of $\Delta m_{atm}^2$ $\gg$ $\Delta m_\odot^2$. A key ingredient for radiative mechanisms is a charged scalar ($h^+$) that couples to charged lepton-neutrino pairs and $h^+$ together with the standard Higgs scalar ($\phi$) can be unified into a Higgs triplet as ($\phi^0$, $\phi^-$, $h^+$)$^T$. This assignment in turn requires lepton triplets ($\psi_L^i$) with heavy charged leptons ($\kappa_L^{+i}$) as the third member: $\psi_L^i=(\nu^i_L,\ell^i_L,\kappa^{+i}_L)^T$, where $i$ ($=1,2,3$) denotes three families. It is found that our model is relevant to yield quasi-vacuum oscillations for solar neutrinos.Comment: 11 pages, revtex, including 2 figures, accepted for publication in Phys. Rev. D with minor modification of our resul

Bilarge Neutrino Mixing and \mu - \tau Permutation Symmetry for Two-loop Radiative Mechanism

The presence of approximate electron number conservation and \mu-\tau permutation symmetry of S_2 is shown to naturally provide bilarge neutrino mixing. First, the bimaximal neutrino mixing together with U_{e3}=0 is guaranteed to appear owing to S_2 and, then, the bilarge neutrino mixing together with |U_{e3}|<<1 arises as a result of tiny violation of S_2. The observed mass hierarchy of \Delta m^2_{\odot}<<\Delta m^2_{atm} is subject to another tiny violation of the electron number conservation. This scenario is realized in a specific model based on SU(3)_L x U(1)_N with two-loop radiative mechanism for neutrino masses. The radiative effects from heavy leptons contained in lepton triplets generate the bimaximal structure and those from charged leptons, which break S_2, generate the bilarge structure together with |U_{e3}|<<1. To suppress dangerous flavor-changing neutral current interactions due to Higgs exchanges especially for quarks, this S_2 symmetry is extended to a discrete Z_8 symmetry, which also ensures the absence of one-loop radiative mechanism.Comment: 18 pages, 7 figures, to appear in Phys. Rev.