Comment on Neutrino Masses and Oscillations in an SU(3)L×U(1)NSU(3)_L \times U(1)_N Model with Radiative Mechanism

We discussed how neutrino masses and oscillations are radiatively generated in an $SU(3)_L$ $\times$ $U(1)_N$ gauge model with a symmetry based on $L_e-L_\mu-L_\tau$ ($\equiv$$L^\prime$). The model is characterized by lepton triplets $\psi^i=(\nu^i,\ell^{-i},E^{-i})$, where $E^{-i}$ are negatively charged heavy leptons, an $SU(3)_L$ triplet Higgs scalar $\xi$ and a singlet Higgs scalar $k^{++}$. These Higgs scalars can be interpreted as a Zee's and Zee-Babu's scalar for radiative mechanisms. We demonstrated that the mass hierarchy of $\Delta m_{atm}^2$ $\gg$ $\Delta m_\odot^2$ arise as a consequence of the dynamical hierarchy between $L^\prime$-conserving one-loop effects and $L^\prime$-violating two-loop effects, and our model is relevant to yield quasivacuum solution for solar neutrino problem.Comment: 6 Pages, Latex2e, RevTex macr

Scotogenic dark matter and single-zero textures of the neutrino mass matrix

The scotogenic model can simultaneously account for the presence of dark matter and the origin of neutrino masses. We assume that the flavor neutrino mass matrix has one zero element and Yukawa matrix elements are real in the scotogenic model. It turns out that only one pattern of the flavor neutrino mass matrix in the one-zero-texture scheme within the scotogenic model is viable with the observed neutrino oscillation data, the relic abundance of the dark matter, and the upper limit of the branching ratio of the $\mu \rightarrow e \gamma$ process.Comment: 8 pages, 6 figures, references added, Accepted for publication in Physical Review

Clockwork origin of neutrino mixings

The clockwork mechanism provides a natural way to obtain hierarchical masses and couplings in a theory. We propose a clockwork model that has nine clockwork generations. In this model, the candidates of the origin of the neutrino mixings are nine Yukawa mass matrix elements $Y^{a\beta}$ that connect neutrinos and clockwork fermions, nine clockwork mass ratios $q_{a\beta}$, and nine numbers of clockwork fermions $n_{a\beta}$, where $a, \beta=1,2,3$. Assuming $|Y^{a\beta}|=1$, the neutrino mixings originate from the pure clockwork sector. We show that the observed neutrino mixings are exactly obtained from a clockwork model in the case of the $q_{a\beta}$ origin scenario. In the $n_{a\beta}$ origin scenario, the correct order of magnitude of the observed neutrino mixings is obtained from a clockwork model.Comment: 9 pages, 4 figures. Accepted for publication in Physical Review

Two-loop Radiative Corrections to Neutrino Masses in SU(3)L×U(1)NSU(3)_L \times U(1)_N Gauge Models

We have constructed two $SU(3)_L \times U(1)_N$ gauge models with the $L^\prime = L_e-L_\mu-L_\tau$ symmetry, which accommodate tiny neutrino masses generated by one-loop and two-loop radiative effects. The heavy neutral leptons and heavy charged leptons are employed to specify the lepton triplets in $SU(3)_L$, respectively, accompanied by ($\phi^0$, $\phi^-$, $h^+$) and ($\phi^+$, $\phi^0$, $h^+$), where $\phi$ stands for the standard Higgs scalar and $h^+$ is a key ingredient for radiative mechanisms. From our numerical calculations, we find that both our models are relevant to yield the VO solution to the solar neutrino problem.Comment: Talk at Post Summer Institute 2000 on Neutrino Physics, August 21-24, 2000, Fuji-Yoshida, Japa

Neutrino Oscillations Induced by Two-loop Radiative Effects

Phenomena of neutrino oscillations are discussed on the basis of two-loop radiative neutrino mechanism. Neutrino mixings are experimentally suggested to be maximal in both atmospheric and solar neutrino oscillations. By using $L_e - L_\mu - L_\tau$ ($\equiv L^\prime$)-conservation, which, however, only ensures the maximal solar neutrino mixing, we find that two-loop radiative mechanism dynamically generates the maximal atmospheric neutrino mixing and that the estimate of $\Delta m^2_\odot/\Delta m^2_{atm} \sim\epsilon m_e/m_\tau$ explains $\Delta m^2_\odot/\Delta m^2_{atm} \ll 1$ because of $m_e/m_\tau \ll 1$, where $\epsilon$ measures the breaking of the $L^\prime$-conservation. Together with $\Delta m^2_{atm} \approx 3\times 10^{-3}$ eV$^2$, this estimate yields $\Delta m^2_\odot \sim 10^{-7}$ eV$^2$ for $\epsilon \sim 0.1$, which corresponds to the LOW solution to the solar neutrino problem. Neutrino mass scale is given by $(16\pi^2)^{-2} m_em_\tau /M$ ($M \sim$ 1 TeV), which is of order 0.01 eV.Comment: 10 pages,6 figures,Talk given at the Post Summer Institute 2000 on Neutrino Physics, August 21-24, 2000, Fuji-Yoshida, Yamanashi, Japa

Fermi-Boltzmann statistics of neutrinos and relativistic effective degrees of freedom

We investigate the effect of the presence of non-pure fermionic neutrinos on the relativistic effective degrees of freedom in the early universe. The statistics of neutrinos is transformed continuously from Fermi-Dirac to Maxwell-Boltzmann statistics. We find that the relativistic degrees of freedom decreases with the deviation from pure Fermi-Dirac statistics of neutrinos if there are constant and large lepton asymmetries. Additionally, we confirm that the change of the statistics of neutrinos from Fermi-Dirac to Maxwell-Boltzmann is not sufficient to cover the excess of the effective number of neutrinos.Comment: 15 pages, 5 figures, version to appear in Modern Physics Letters

Asymmetric dark matter and effective number of neutrinos

We study the effect of the MeV-scale asymmetric dark matter annihilation on the effective number of neutrinos $N_{\rm eff}$ at the epoch of the big bang nucleosynthesis. If the asymmetric dark matter $\chi$ couples more strongly to the neutrinos $\nu$ than to the photons $\gamma$ and electrons $e^-$, $\Gamma_{\chi\gamma, \chi e} \ll \Gamma_{\chi\nu}$, or $\Gamma_{\chi\gamma, \chi e} \gg \Gamma_{\chi\nu}$, the lower mass limit on the asymmetric dark matter is about $18$ MeV for $N_{\rm eff}\simeq 3.0$.Comment: 13 pages, 14 figures, version accepted for publication in Physical Review

Formulae for flavour neutrino masses and its application to texture two zeros

We demonstrate the usefulness of flavour neutrino masses expressed in terms of $M_{ee},M_{e\mu}$ and $M_{e\tau}$. The analytical expressions for the flavour neutrino masses, mass eigenstates and physical CP-violating Majorana phases for texture two zeros are obtained exactly.Comment: 8 pages, 2 figures, version accepted for publication in Physical Review

Spinor Representation of O(3)O(3) for S4S_4

All possible permutations in the discrete $S_4$ group are classified by three rotation angles associated with the orthogonal group $O(3)$. We construct a spinor representation ${\bf 2}_D$ of $O(3)$, which is transformed by three 4$\times$4 matrices corresponding to three Pauli matrices in $SO(3)$. An irreducible decomposition of ${\bf 2}_D \otimes {\bf 2}_D$ supplies a vector representation of {\bf 3} of $O(3)$, thereby, of $S_4$. Our construction is consistent with the mathematical fact that $O(3)=SO(3)\times \boldsymbol{Z}_2$. The $\boldsymbol{Z}_2$ parity in the spinorial space is described by a block off-diagonal matrix as the spinorial parity operator, whose eigenvalues are $\pm 1$ consistent with $\boldsymbol{Z}_2$.Comment: 11 page

Parafermionic dark mater

To discuss the possible contribution of parafermions to the dark matter abundance, we extend the Boltzmann equation for fermionic dark matter to include parafermions. Parafermions can accommodate $r$ particles per quantum state $(2\le r<\infty)$, where the parafermion of order $r=1$ is identical to the ordinary fermion. It is found that the parafermionic dark matter can be more abundant than the fermionic dark matter in the present universe.Comment: 7 pages, 7 figures. Some changes in the wording. Accepted for publication in Physical Review