The energy spectrum of cosmic neutrinos, which was recently reported by the IceCube collaboration, shows a gap between 400 TeV and 1 PeV. An unknown neutrino interaction mediated by a field with a mass of the MeV scale is one of the possible solution
s to this gap. We examine if the leptonic gauge interaction L_{mu} - L_{tau} can simultaneously explain the two phenomena in the lepton sector: the gap in the cosmic neutrino spectrum and the unsettled disagreement in muon anomalous magnetic moment. We illustrate that there remains the regions in the model parameter space, which account for both the problems. Our results also provide a hint for the distance to the source of the high-energy cosmic neutrinos.
We consider a situation where the leading-order neutrino mass matrix is derived by a theoretical ansatz and reproduces the experimental data well, but not completely. Then, the next stage is to try to fully reproduce the data by adding small perturba
tion terms. In this paper, we obtain the analytical method to diagonalize the perturbed mass matrix and find a consistency condition that parameters should satisfy not to change sintheta_{12} much. This condition could cause parameter tuning and plays a crucial role in relating the added perturbation terms with the prediction analytically, in particular, for the case of the partially quasi-degenerated neutrino masses (m_2 simeq m_1) where neutrinoless double beta decays would be observed in the phase-II experiments.
Following the way proposed recently by Hernandez and Smirnov, we seek possible residual symmetries in the quark sector with a focus on the von Dyck groups. We begin with two extreme cases in which both $theta_{13}$ and $theta_{23}$ or only $theta_{13
}$ are set to zero. Then, cases where all the Cabibbo-Kobayashi-Maskawa parameters are allowed to take nonzero values are explored. The $Z_7$ symmetry is favorable to realize only the Cabibbo angle. On the other hand, larger groups are necessary in order to be consistent with all the mixing parameters. Possibilities of embedding the obtained residual symmetries into the $Delta(6N^2)$ series are also briefly discussed.
By postulating the relation theta_{23} simeq 45^circ + etatheta_{13}, we seek preferable correction terms to tri-bi-maximal mixing and discuss their origins. Global analyses of the neutrino oscillation parameters favor eta=pm 1/sqrt{2}; this correspo
nds to the relation found by Edy, Frampton, and Matsuzaki some years ago in the context of a T^prime flavor symmetry. In contrast, the results of the u_mu disappearance mode reported by the T2K and Super-Kamiokande collaborations seem to prefer eta=0, which gives an almost maximal theta_{23}. We derive a general condition for ensuring theta_{23} simeq 45^circ + etatheta_{13} and find that the condition is complicated by the neutrino masses and CP violating phases. We investigate the condition under simplified environments and arrive at several correction terms to the mass matrices. It is found that the obtained correction terms can arise from flavor symmetries or one-loop radiative corrections.
Inspired by the small mass-squared difference measured in the solar neutrino oscillation experiments and by the testability, we suggest that a limit of the partial mass degeneracy, in which masses of the first two generation fermions are degenerate,
may be a good starting point for understanding the observed fermion mass spectra and mixing patterns. The limit indicates the existence of a two-dimensional rotation symmetry, such as $O(2)$, $D_N$ and so on, in flavor space of the first two generations. We propose simple models for the lepton sector based on $D_N$ and show that the models can successfully reproduce the experimental data without imposing unnatural hierarchies among dimensionless couplings, although at least $10%$ tuning is necessary in order to explain a large atmospheric mixing. It is especially found that the $Z_2$ subgroup of the $D_N$ symmetry plays an important role in understanding the smallness of the electron mass and $theta_{13}^{rm PMNS}$. We also discuss testability of the models by the future neutrinoless-double-beta-decay experiments and cosmological observations.
Augmenting the Standard Model by three right-handed neutrinos allows for an anomaly-free gauge group extension G_max = U(1)_(B-L) x U(1)_(L_e-L_mu) x U(1)_(L_mu-L_tau). While simple U(1) subgroups of G_max have already been discussed in the context o
f approximate flavor symmetries, we show how two-zero textures in the right-handed neutrino Majorana mass matrix can be enforced by the flavor symmetry, which is spontaneously broken very economically by singlet scalars. These zeros lead to two vanishing minors in the low-energy neutrino mass matrix after the seesaw mechanism. This study may provide a new testing ground for a zero-texture approach: the different classes of two-zero textures with almost identical neutrino oscillation phenomenology can in principle be distinguished by their different Z interactions at colliders.
The extension of the minimal standard model by three right-handed sterile neutrinos with masses smaller than the electroweak scale (nuMSM) is discussed in a Q_6 flavor symmetry framework. The lightness of the keV sterile neutrino and the near mass de
generacy of two heavier sterile neutrinos are naturally explained by exploiting group properties of Q_6. A normal hierarchical mass spectrum and an approximately mu-tau symmetric mass matrix are predicted for three active neutrinos. Nonzero theta_{13} can be obtained together with a deviation of theta_{23} from the maximality, where both mixing angles are consistent with the latest global data including T2K and MINOS results. Furthermore, the tiny active-sterile mixing is related to the mass ratio between the lightest active and lightest sterile neutrinos.
We study finite quantum corrections for several well known neutrino mixing matrices and find that it is hard to account for the large value of theta_13 recently reported by T2K and MINOS. To nicely reproduce all experimentally favored neutrino mixing
angles and masses, we propose a new neutrino mixing pattern. We also demonstrate a simple realization by slightly extending the standard model to illustrate the quantum corrections.
We derive anomaly constraints for Abelian and non-Abelian discrete symmetries using the path integral approach. We survey anomalies of discrete symmetries in heterotic orbifolds and find a new relation between such anomalies and the so-called `anomalous U(1).
