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 Meeting@Guilin IHEP Midori Obara (小原 绿) M. O. and Z.Z. Xing, hep-ph/0608280

§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.

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)

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)

Contents §1. Introduction §2. Model §3. Numerical Analysis §4. Summary

§2. Model

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

is given as follows: Here we assume

Mass splitting parameter where (A) (B) (C)

where where we have neglected the terms of and by assuming and .

where with and Parametrization

§3. Numerical Analysis

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

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)

(A)

(B)

(C)

Typical results at Experimental upper bounds:

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.

§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.

Future work ・ Including the complex phases into and/or . Leptogenesis