1,948 research outputs found

### 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 $U_{e3}$

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

### Constraints on flavour-dependent long-range forces from atmospheric neutrino observations at Super-Kamiokande

In the minimal standard model it is possible to gauge any one of the
following global symmetries in an anomaly free way: (i)$L_{e}-L_{\mu}$, (ii)
$L_{e}-L_{\tau}$ or (iii) $L_{\mu}-L_{\tau}$. If the gauge boson corresponding
to (i) or (ii) is (nearly) massless then it will show up as a long range
composition dependent fifth force between macroscopic objects. Such a force
will also influence neutrino oscillations due to its flavour-dependence. We
show that the latter effect is quite significant in spite of very strong
constraints on the relevant gauge couplings from the fifth force experiments.
In particular, the $L_{e}- L_{\mu,\tau}$ potential of the electrons in the Sun
and the earth is shown to suppress the atmospheric neutrino $\nu_\mu \to
\nu_\tau$ oscillations which have been observed at Super-Kamiokande. The
Super-K data of oscillation of multi-GeV atmospheric neutrinos can be used to
put an upper bound on coupling $\alpha_{e\tau}< 6.4 \times 10^{-52}$ and
$\alpha_{e\mu}< 5.5 \times 10^{-52}$at 90% CL when the range of the force is
the earth-sun distance. This is an improvement by two orders on the earlier
fifth force bounds in this range.Comment: 5 pages Latex, 3 figure

### 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 $\mu$-$\tau$ 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

### Predictive Framework with a Pair of Degenerate Neutrinos at a high scale

Radiative generation of the solar scale $\Delta_{\odot}$ is discussed in the
presence of leptonic CP violation. We assume that both the solar scale and
$U_{e3}$ are zero at a high scale and the weak radiative corrections generate
them. It is shown that all leptonic mass matrices satisfying these requirements
lead to a unique prediction $\Delta_{\odot} \cos 2\theta_{\odot}\approx 4
\delta_\tau \sin^2 \theta_A |m_{ee}|^2$ for the solar scale in terms of the
radiative correction parameter $\delta_\tau$, the physical solar (atmospheric)
mixing angles $\theta_{odot} (\theta_A)$ and the Majorana neutrino mass
$m_{ee}$ probed in neutrinoless double beta decay. This relation is independent
of the mixing matrix and CP-violating phases at the high scale. The presence of
CP-violating phases leads to dilution in the solar mixing angle defined at the
high scale. Because of this, bi-maximal mixing pattern at the high energy leads
to large but non-maximal solar mixing in the low-energy theory. An illustrative
model with this feature is discussed.Comment: 15 pages, including a postscript figur

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