Study of Three Generation Seesaw Model with Dirac Mass Matrix of Four-zero Texture and CP Violation in Neutrino Sector

概要

Neutrino is a kind of lepton, which dose not have electric charge. It is known
that neutrino has tiny but non-zero mass by the neutrino oscillation. However,
Standard Model(SM) can not explain their mass, since it includes only lefthanded neutrinos and can not construct their mass terms. Seesaw mechanism
has been suggested to describe their masses and to understand why they are so
tiny [12]. It extends SM by introducing heavy right-handed neutrinos and by
assuming that they are Majorana particles. We study the type-I seesaw model
with three right-handed neutrinos. This mechanism leads to effective Majorana
mass term for light active neutrinos. It is written with Dirac mass matrix and
Majorana mass matrix for right-handed neutrinos.
the Dirac mass matrix and the Majorana mass matrix are parametrized by
15 and 3 parameters respectively in the real diagonal basis for the Majorana
mass matrix and charged-lepton mass matrix. The effective mass matrix is
then expressed by 18 parameters. The general model still has much parameters
by comparing with the number of phenomenological parameters; three mass
eigenvalues, three mixing angles and three CP phases. In this paper, we focus
on the four-zero texture model for the Dirac mass matrix [16, 13, 14, 17]. We
put four zero-elements onto the Dirac mass matrix by hand. The other five
elements remain non-zero. The effective mass matrix of four-zero texture model
is parametrized with seven parameters, which are comparable to the number of
measurements.
There are 9 C4 = 126 different configurations of Dirac mass matrix of fourzero texture model. We develop an efficient method to explore all the configurations without examining each form independently. In the method, different
form of Dirac matrices related to each other by permutation of their rows and
columns are classified into several groups. Phenomenological constraints on the
parameters are also imposed according to this classification.
Some flavor symmetries restrict the forms of the Dirac mass matrix and
the Majorana mass matrix [13, 14, 15]. Flavor symmetry reduces the number
of model parameters. The position of zeros on the Dirac mass matrix can be
restricted by some flavor symmetries.
The paper is organized as follows. In section 2, we introduce the type-I seesaw mechanism which explains the tiny but non-zero masses of neutrino. We
also mention the CP asymmetry in the neutrino sector via neutrino oscillation.
In section 3, we define the notation of our model by using the type-I seesaw
mechanism with three heavy right-handed Majorana neutrinos. We suggest two
specific models; four-zero texture model on Dirac mass matrix in subsection 3.2
and seesaw model with one massless neutrino in subsection 3.3. In section 4,
we study the four-zero texture model on Dirac mass matrix. The 126 different
patterns of zero-elements-configuration on the Dirac mass matrix are classified
into 7 classes. This classification serves for sorting which textures we have to
analyze. In section 5, we make numerical analysis. We first outline how to perform the numerical analysis and then explain the efficient method according to
the classification of textures. Some results of calculations are shown in subsection 5.3. In section 6, the hidden relations among the elements of the effective
Majorana mass are derived and the correlations found in the numerical analysis
are examined from a view point of the hidden relations. Section 7 is devoted to
the summary. ...