Democracy of Fmilies and Nertrino Mass Matrix
On the basis of a seesaw-type mass matrix model for quarks and leprons,
$M_f \simeq m_L M^{-1}_F m_R$, where $m_L \propto m_R$ are universal for
$f = u, d, \nu$ and $e$ (up-quark-, down-quark-, neutrino- and charged lepron-sectors),
and $M_F$ is given by $M_F = K(1 + 3b_f X)$ ($1$ is a $3 \times 3$ unit matrix,
$X$ is a democratic-type matrix and $b_f$ is a complex parameter which
depends on $f$, neutrino mass spectrum and mixings are descussed. The
model can provide an explanation why $m_t \gg m_b$, while $m_u \sim m_d$
by taking $b_u = -1/3$, at which the detarminant of $M_F$ becomes zero.
At $b_\nu = -1/2$, the model can provide a large $\nu_\mu - \nu_\tau$ mixing,
$sin^2 2\theta_{23} \simeq 1$, with $m_{\nu 1} \ll m_{\nu 3}$, which is
favorable to the atmospheric and solar neutrino data.
Thermodynamic Properties, Phases and Classical Vacua of Two Dimensional
$R^2$-Gravity
Two dimensional quantum R$^2$-gravity is formulated
in the semiclassical method.
The thermodynamic properties,such as
the equation of state,
the temperature and the entropy, are explained.
The topology constraint and the area constraint are properly taken
into account. A total derivative term
and an infrared regularization play important roles.
The classical solutions (vacua)
of R$^2$-Liouville equation are obtained by making use of the well-known
solution of the
ordinary Liouville equation.
The positive and negative constant
curvature solutions are 'dual' each other.
Each solution has two branches($\pm$).
We characterize all phases.
The topology of a sphere is mainly considered.
MINBU Distribution of Two Dimensional Quantum Gravity: Simulation
Result and Semiclassical Analysis
Shoichi Ichinose, Noritsugu Tsuda and Tetsuyuki Yukawa
We analyse MINBU distribution of
2 dimensional quantum gravity. New data of R$^2$-gravity by the Monte Carlo
simulation and its theoretical analysis
by the semiclassical approach are presented.
The cross-over phenomenon takes place at some size of the baby universe
where the randomness competes with the smoothing force of $R^2$-term.
The dependence on the central charge $c_m$\
and on the $R^2$-coupling are
explained for the ordinary 2d quantum gravity and for $R^2$-gravity.
The $R^2$-Liouville solution plays the central role in the semiclassical
analysis.
A total derivative term (surface term) and the infrared regularization
play important roles .
The surface topology is that of a sphere .
- US - 95 - 04 and EHU - 95 - 03
(hep-ph/9505333): To be publised in Z.Phys. C72, 333 (1996)
U(3)-Family Nonet Higgs Boson and its Phenomenology
Yoshio Koide and Morimitu Tanimoto
In order to give a charged lepton mass formula, a model with U(3)-family
nonet Higgs boson is proposed. Since the Higgs boson $\phi_L$ ($\phi_R$)
couples only between light fermions (quarks and leptons) $f_L$ ($f_R$) and
super-heavy vector-like fermions $F_R$ ($F_L$), the model leads to a
seesaw-type mass matrix $M_f \simeq m_L M^{-1}_F m_R$ for quarks and leptons
$f = u, d, \nu$ and $e$. However,the model, in general, induces flavor changing
neutral currents. Lower bounds of the physical Higgs boson masses of
$\phi_L$ are deduced from the present experimental data and new physics from
the present scenario is speculated.
- US - 95 - 03 and AMU - 95 - 04
(hep-ph/9505201): Z. Phys. C71, 459 (1996).
Top Quark Mass Enhacement in a Seesaw-Type Quark Mass Matrix
Yoshio Koide and Hideo Fusaoka
We investigate the implications of a seesaw type mass matrix, i.e.,
$M_f\simeq m_L M_F^{-1} m_R$, for quarks and leptons $f$
under the assumption that
the matrices $m_L$ and $m_R$ are common to all flavors (up-/down-
and quark-/lepton- sectors)
and the matrices $M_F$ characterizing the heavy fermion sectors
have the form [(unit matrix)
+ $b_f$ (a democratic matrix)] where $b_f$ is a flavor parameter.
We find that by adjusting the complex parameter $b_f$,
the model can provide that
$m_t\gg m_b$ while at the same time keeping $m_u\sim m_d$
without assuming any parameter with
hierarchically different values between $M_U$ and $M_D$.
The model with three adjustable parameters
under the ``maximal" top quark mass enhancement can give
reasonable values of five quark mass ratios and
four KM matrix parameters.
(hep-th/9509073): to be published in Z. Phys. C (1996).
New Formulation of Anomaly, Anomaly Formula and Graphical
Representation
Shoichi Ichinose and Noriaki Ikeda
A general approach to anomaly in quantum field theory is newly formulated by
use of the propagator theory in solving the
heat-kernel equation. We regard the heat-kernel as a sort of
the point-splitting regularization in the space(-time) manifold.
Fujikawa's general standpoint that the anomalies come from
the path-integral measure is taken. We obtain some useful formulae
which are valid for general anomaly calculation.
They turn out to be the same as the
1-loop counter-term formulae except some important total derivative terms.
Various anomalies in 2 and 4 dimensional theories
are systematically calculated.
Some important relations between them are concretely shown.
As for the representation of general (global SO(n))
tensors, we introduce a graphical
one . It makes the tensor structure of invariants very transparent
and makes the tensor calculation so simple.
New Physics from U(3)-Family Nonet Higgs Boson Scenario
Being inspired by a phenomenological success of a charged lepton mass
formula, a model with U(3)-family nonet Higgs boson is proposed. Here,
the Higgs bosons $\phi_L$ ($\phi_R$) couple only between light fermions
(quarks and leptons) $f_L$ ($f_R$) and super-heavy vector-like fermions
$F_R$ ($F_L$), so that the model leads to a seesaw-type mass matrix
$M_f \simeq m_L M^{-1}_F m_R$ for quarks and leptons $f = u, d, \nu$ and
$e$. Lower bounds of the physical Higgs boson masses are deduced from
the present experimental data and possible new physics from the present
scenario is speculated.