On%20the%20Fukugita-Tanimoto-Yanagida%20Ansatz%20with%20Partially%20Non-degenerate%20Right-handed%20Majorana%20Neutrinos

1
On the Fukugita-Tanimoto-Yanagida Ansatz with
Partially Non-degenerate Right-handed Majorana
Neutrinos
29 October, 2006 High Energy Physics
Meeting_at_Guilin
IHEP Midori Obara
(?? ?)
M. O. and Z.Z. Xing, hep-ph/0608280
2
1. Introduction
Recent neutrino experimental results (at 99 C.L.)
Mixing angles
Mass-squared differences
Neutrinos have two large mixing angles and one
small mixing angle.
Cosmological bound on neutrino masses
Neutrinos have very small masses.
3
Why are neutrino masses so small?
Seesaw Mechanism
Various phenomenological ansatz for lepton mass
matrices have been actively studied.
Texture zeros
An empirical relation
S. Weinberg (1977), H. Fritzsch (1977), F.
Wilczek and A. Zee (1977)
R. Gatto, G. Sartori and M. Tonin (1968), N.
Cabibbo and Maiani (1968), R.J. Oakes (1969)
Fritzsch texture
for lepton mass matrices
Z.Z. Xing (2002)
4
Within the seesaw framework ...
M. Fukugita. M. Tanimoto and T. Yanagida (2003)
Fukugita-Tanimoto-Yanagida (FTY) ansatz
with
In this work
We generalize the FTY ansatz by allowing
the masses of to be partially non-degenerate
and examined how the deviation from the mass
degeneracy can affect the neutrino observables.
(A)
(B)
(C)
5
Contents
1. Introduction 2. Model 3. Numerical
Analysis 4. Summary
6
2. Model
7
We take the Fritzsch texture for and .
can be decomposed by diagonal phase matrix as
where
Similarly,
where
8
is given as follows
Here we assume
9
Mass splitting parameter
where
(A)
(B)
(C)
10
where
where we have neglected the terms of
and by assuming
and .
11
where
and
with
Parametrization
12
3. Numerical Analysis
13
We have seven parameters in our model
These parameters are constrained by the neutrino
experimental results.
Results
In the case of
(the FTY case)
Predicted values
14
In the case of
In the case of
The differences of parameter regions between
and cases can be distinguishable in
.
We show the allowed range for the parameters at
the typical value of in the three
cases.
(A)
(B)
(C)
15
(A)
16
(B)
17
(C)
18
Typical results at
Experimental upper bounds
19
Remarks
The maximal atmospheric neutrino mixing angle
can only be achieved in the cases B and C.


In all cases, is not well restricted.
The smallest mixing angle has an lower
bound in each case.
In future experiments
In all cases, the allowed range for is
roughly the same.
could be measured in the future
long-baseline neutrino experiments.
20
4. Summary
We have generalized the FTY ansatz by allowing
the masses of to be partially non-degenerate
and examined how the deviation from the mass
degeneracy can affect the neutrino observables.
(A)
(B)
(C)
The dependence of mixing angles on
The case C is the most sensitive to the effect of
the deviation from the mass degeneracy.
21
Future work
Including the complex phases into and/or .
Leptogenesis