We examine the constraints on the MNS lepton mixing matrix =66rom the present and future experimental data of the neutrino oscillation, tritium beta decay, and neutrinoless double beta decay for Majorana neutrinos. We show that the small mixing angle
solutions for solar neutrino problem are disfavored for small averaged mass ($<m_ u>$) of neutrinoless double beta decay ($leq 0.01$ eV) in the inverse neutrino mass hierarchy scenario. This is the case even in the normal mass hierarchy scenario except for very restrictive value of the averaged neutrino mass ($bar{m_ u}$) of single beta decay. The lower mass bound for $bar{m_ u}$ is given from the present neutrino oscillation data. We obtain some relations between $<m_ u>$ and $bar{m_ u}$. The constraints on the Majorana CP violating phases are also given.
It is usually considered that the SO(10) model with one 10 and one 126 Higgs scalars cannot reproduce the observed quark and charged lepton masses. Against this conventional conjecture, we find solutions of the parameters which can give the observed
fermion mass spectra. The SO(10) model with one 10 and one 120 Higgs scalars is also discussed.
We illustrate the graphical method that gives the constraints on the parameters appearing in the neutrino oscillation experiments and the neutrinoless double beta decay. This method is applicable in three and four generations. Though this method is v
alid for more general case, we examine explicitly the cases in which the CP violating factors take $pm 1$ or $pm i$ in the neutrinoless double beta decay for illustrative clearance. We also discuss some mass matrix models which lead to the above CP violating factors.
We examine the constraints on the MNS lepton mixing matrix from the present and future experimental data of the neutrino oscillation and lepton number violation processes. We introduce a graphical representation of the CP violation phases which appea
r in the lepton number violation processes such as neutrinoless double beta decay, the $mu^--e^+$ conversion, and the K decay, $K^-topi^+mu^-mu^-.$ Using this graphical representation, we derive the constraints on the CP violation phases in the lepton sector.
We propose a model that all quark and lepton mass matrices have the same zero texture. Namely their (1,1), (1,3) and (3,1) components are zeros. The mass matrices are classified into two types I and II. Type I is consistent with the experimental data
in quark sector. For lepton sector, if seesaw mechanism is not used, Type II allows a large $ u_mu - u_tau$ mixing angle. However, severe compatibility with all neutrino oscillation experiments forces us to use the seesaw mechanism. If we adopt the seesaw mechanism, it turns out that Type I instead of II can be consistent with experimental data in the lepton sector too.
We discuss the constraints of lepton mixing angles from lepton number violating processes such as neutrinoless double beta decay, (mu^-)-(e^+) conversion and K decay, $K^- to pi^+mu^-mu^-$ which are allowed only if neutrinos are Majorana particles. T
he rates of these processes are proportional to the averaged neutrino mass defined by $<m_{ u} >_{a b}equiv |sum_{j=1}^{3}U_{a j} U_{b j}m_j|$ in the absence of right-handed weak coupling. Here $a, b (j)$ are flavour(mass) eigen states and $U_{a j}$ is the left-handed lepton mixing matrix. We obtain the consistency conditions which are satisfied irrelevant to the concrete values of CP violation phases (three phases in Majorana neutrinos). These conditions constrain the lepton mixing angles, neutrino masses $m_i$ and (< m_{ u} >_{a b}). By using these constraints we obtain the limits on the averaged neutrino masses for (mu^-)-(e^+) conversion and K decay, $K^- to pi^+mu^-mu^-$.
From the analyses of the recent data of neutrino oscillation experiments (especially the CHOOZ and the Super KAMIOKANDE experiments), we discuss how these data affect the neutrinoless double beta decay ($(beta beta)_{0 u}$) rate and vice versa assumi
ng that neutrinos are Majorana particles. For the case that $m_1 sim m_2 ll m_3$ ($m_i$ are neutrino masses), we obtain, from the data of the CHOOZ and Super KAMIOKANDE, $0.28 le sin^2theta_{23} le 0.76$ and $sin^2theta_{13} le 0.05$. Combining the latter constraint with the analysis of the averaged neutrino mass (< m_ u >) appeared in $(beta beta)_{0 u}$, we find that (frac{< m_ u >-m_2}{m_3-m_2}<sin^2 theta_{13} le 0.05), which leads to the constraint on (< m_ u >) as (< m_ u > le 0.05 m_3+(1-0.05)m_2). For the case that $m_1 ll m_2 sim m_3$, we find that the data of neutrino oscillation experiments and$(beta beta)_{0 u}$ imply the constraints of mixing angles.
Taking account of possible CP violation, we discuss about the constraints on the lepton mixing angles from the neutrinoless double beta decay and from the neutrino oscillation for the three flavour Majorana neutrinos. From the CHORUS oscillation expe
riment, combined with the data of neutrinoless double beta decay, we show that the large angle solution of (theta_{23}) is improbable if the neutrino mass (m_3) of the third generation is a candidate of hot dark matters.
