1. High Energy Physics Meeting@Guilin
On the Fukugita-Tanimoto-Yanagida Ansatz with Partially Non-degenerate Right-handed Majorana Neutrinos
29 October, 2006
High Energy Physics
IHEP
Midori Obara
(小原 绿)
M. O. and Z.Z. Xing, hep-ph/

2. §1. Introduction Mixing angles Mass-squared differences
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. In this work 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. can be decomposed by diagonal phase matrix as
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
with
and
Parametrization

12. §3. Numerical Analysis

13. Results We have seven parameters in our model: In the case of
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