Neutrino masses and mixing from flavour antisymmetry

We discuss consequences of assuming ($i$) that the (Majorana) neutrino mass matrix $M_\nu$ displays flavour antisymmetry, $S_\nu^T M_\nu S_\nu=-M_\nu$ with respect to some discrete symmetry $S_\nu$ contained in $SU(3)$ and ($ii$) $S_\nu$ together with a symmetry $T_l$ of the Hermitian combination $M_lM_l^\dagger$ of the charged lepton mass matrix forms a finite discrete subgroup $G_f$ of $SU(3)$ whose breaking generates these symmetries. Assumption ($i$) leads to at least one massless neutrino and allows only four textures for the neutrino mass matrix in a basis with a diagonal $S_\nu$ if it is assumed that the other two neutrinos are massive. Two of these textures contain a degenerate pair of neutrinos.Assumption ($ii$) can be used to determine the neutrino mixing patterns. We work out these patterns for two major group series $\Delta(3 N^2)$ and $\Delta(6 N^2)$ as $G_f$. It is found that all $\Delta(6 N^2)$ and $\Delta(3 N^2)$ groups with even $N$ contain some elements which can provide appropriate $S_\nu$. Mixing patterns can be determined analytically for these groups and it is found that only one of the four allowed neutrino mass textures is consistent with the observed values of the mixing angles $\theta_{13}$ and $\theta_{23}$. This texture corresponds to one massless and a degenerate pair of neutrinos which can provide the solar pair in the presence of some perturbations. The well-known groups $A_4$ and $S_4$ provide examples of the groups in respective series allowing correct $\theta_{13}$ and $\theta_{23}$. An explicit example based on $A_4$ and displaying a massless and two quasi degenerate neutrinos is discussed.Comment: 22 pages, 1 figur

Universal 2-3 symmetry

Possible maximal mixing seen in the oscillations of the atmospheric neutrinos has led to postulate of a $\mu$-$\tau$ symmetry which interchanges $\nu_\mu$ and $\nu_\tau$. We argue that such symmetry need not be special to neutrinos but can be extended to all fermions. The assumption that all fermion mass matrices are approximately invariant under interchange of the second and the third generation fields is shown to be phenomenologically viable and has interesting consequences. In the quark sector, the smallness of $V_{ub}$ and $V_{cb}$ can be a consequences of this approximate 2-3 symmetry. The same approximate symmetry can simultaneously lead to large atmospheric mixing angle and can describe the leptonic mixing quite well provided the neutrino spectrum is quasi degenerate. We present this scenario, elaborate on its consequences and discuss its realization.Comment: 13 pages, 1 figur

Summary of Model Predictions for Ue3U_{e3}

We present a short discussion on the expected magnitude of $|U_{e3}|$ in the context of various scenarios proposed to describe neutrino masses and mixing. Generic expectation is relatively large ($>0.05$) values for \ue3 which occur in many well-motivated theoretical scenarios and models.Comment: Updated version of the talk presented at the 5th Workshop on "Neutrino Oscillations and their Origin (NOON2004)", February 11-15, Tokyo, Japa

No-go for exactly degenerate neutrinos at high scale?

We show in a model independent manner that, if the magnitudes of Majorana masses of neutrinos are exactly equal at some high scale, the radiative corrections cannot reproduce the observed masses and mixing spectrum at the low scale, irrespective of the Majorana phases or the mixing angles at the high scale.Comment: 12 pages ReVTeX, A few typos corrected in the 2nd versio

Radiatively Generated νe\nu_e Oscillations: General Analysis, Textures and Models

We study the consequences of assuming that the mass scale $\Delta_{odot}$ corresponding to the solar neutrino oscillations and mixing angle $U_{e3}$ corresponding to the electron neutrino oscillation at CHOOZ are radiatively generated through the standard electroweak gauge interactions. All the leptonic mass matrices having zero $\Delta_{odot}$ and $U_{e3}$ at a high scale lead to a unique low energy value for the $\Delta_{odot}$ which is determined by the (known) size of the radiative corrections, solar and the atmospheric mixing angle and the Majorana mass of the neutrino observed in neutrinoless double beta decay. This prediction leads to the following consequences: ($i$) The MSSM radiative corrections generate only the dark side of the solar neutrino solutions. ($ii$) The inverted mass hierarchy ($m,-m,0$) at the high scale fails in generating the LMA solution but it can lead to the LOW or vacuum solutions. ($iii$) The $\Delta_{odot}$ generated in models with maximal solar mixing at a high scale is zero to the lowest order in the radiative parameter. It tends to get suppressed as a result of this and lies in the vacuum region. We discuss specific textures which can lead to the LMA solution in the present framework and provide a gauge theoretical realization of this in the context of the seesaw model.Comment: 19 pages, LATE

Pseudo-Dirac neutrinos from flavour dependent CP symmetry

Discrete residual symmetries and flavour dependent CP symmetries consistent with them have been used to constrain neutrino mixing angles and CP violating phases. We discuss here role of such CP symmetries in obtaining a pseudo-Dirac neutrino which can provide a pair of neutrinos responsible for the solar splitting. It is shown that if (a) $3\times 3$ Majorana neutrino matrix $M_\nu$ is invariant under a discrete $Z_2\times Z_2$ symmetry generated by $S_{1,2}$, (b) CP symmetry $X$ transform $M_\nu$ as $X^T M_\nu X=M_\nu^*$, and (c) $X$ and $S_{1,2}$ obey consistency conditions $X S_{1,2}^* X^\dagger=S_{2,1}$, then two of the neutrino masses are degenerate independent of specific forms of $X$, $S_1$ and $S_2$. Explicit examples of this result are discussed in the context of $\Delta(6 n^2)$ groups which can also be used to constrain neutrino mixing matrix $U$. Degeneracy in two of the masses does not allow complete determination of $U$ but it can also be fixed once the perturbations are introduced. We consider explicit perturbations which break $Z_2\times Z_2$ symmetries but respect CP. These are shown to remove the degeneracy and provide a predictive description of neutrino spectrum. In particular, a correlation $\sin 2\theta_{23}\sin\delta_{CP}=\pm {\rm Im}[p]$ is obtained between the atmospheric mixing angle $\theta_{23}$ and the CP violating phase $\delta_{CP}$ in terms of a group theoretically determined phase factor $p$. Experimentally interesting case $\theta_{23}=\frac{\pi}{4}$, $\delta_{CP}=\pm \frac{\pi}{2}$ emerges for groups which predict purely imaginary $p$. We present detailed predictions of the allowed ranges of neutrino mixing angles, phases and the lightest neutrino mass for three of the lowest $\Delta(6 n^2)$ groups with $n=2,4,6$.Comment: 17 pages, 4 figures; Minor modification, published versio

Generalized μ\mu-τ\tau symmetry and discrete subgroups of O(3)

The generalized $\mu$-$\tau$ interchange symmetry in the leptonic mixing matrix $U$ corresponds to the relations: $|U_{\mu i}|=|U_{\tau i}|$ with $i=1,2,3$. It predicts maximal atmospheric mixing and maximal Dirac CP violation given $\theta_{13} \neq 0$. We show that the generalized $\mu$-$\tau$ symmetry can arise if the charged lepton and neutrino mass matrices are invariant under specific residual symmetries contained in the finite discrete subgroups of $O(3)$. The groups $A_4$, $S_4$ and $A_5$ are the only such groups which can entirely fix $U$ at the leading order. The neutrinos can be (a) non-degenerate or (b) partially degenerate depending on the choice of their residual symmetries. One obtains either vanishing or very large $\theta_{13}$ in case of (a) while only $A_5$ can provide $\theta_{13}$ close to its experimental value in the case (b). We provide an explicit model based on $A_5$ and discuss a class of perturbations which can generate fully realistic neutrino masses and mixing maintaining the generalized $\mu$-$\tau$ symmetry in $U$. Our approach provides generalization of some of the ideas proposed earlier in order to obtain the predictions, $\theta_{23}=\pi/4$ and $\delta_{\rm CP} = \pm \pi/2$.Comment: 18 page

Fermion number conservation and two Higgs doublet models without tree level flavour changing neutral currents

The charged fermion mass matrices are always invariant under $U(1)^3$ symmetry linked to the fermion number transformation. A class of two Higgs doublet models (2HDM) can be identified by requiring that the definition of this symmetry in an arbitrary weak basis be independent of Higgs parameters such as the ratio of the Higgs vacuum expectation values. The tree level flavour changing neutral currents normally present in 2HDM are absent in this class of models but unlike the type I or type II Higgs doublet models, the charged Higgs couplings in these models contain additional flavour dependent CP violating phases. These phases can account for the recent hints of the beyond standard model CP violation in the $B_d$ and $B_s$ mixing. In particular, there is a range of parameters in which new phases do not contribute to the $K$ meson CP violation but give identical new physics contribution to the $B_d$ and $B_s$ meson mixing. Specific model realizations of the above scenario are briefly discussed.Comment: 12 page