48 research outputs found
Kobayashi-Maskawa matrix moduli, decay constants and form factors determination from experimental data
The aim of the paper is to propose another tool for phenomenological analyses
of experimental data from superallowed nuclear and neutron decays, and
from leptonic and semileptonic decays, that allows the finding of the most
probable numerical form of the CKM matrix, as well as the determination of
decay constants, , and of various form factors , by using
another implementation of unitarity constraints. In particular this approach
allows the determination of semileptonic form factors that is illustrated on
the existing data from and
decays
Complex Hadamard matrices from Sylvester inverse orthogonal matrices
A novel method to obtain parametrizations of complex inverse orthogonal
matrices is provided. These matrices are natural generalizations of complex
Hadamard matrices which depend on non zero complex parameters. The method we
use is via doubling the size of inverse complex conference matrices. When the
free parameters take values on the unit circle the inverse orthogonal matrices
transform into complex Hadamard matrices, and in this way we find new
parametrizations of Hadamard matrices for dimensions n= 8,10,12.Comment: revised form of the paper published in Open Systems & Information
Dynamics, 16 (2009) 387-40
A new type fit for the CKM matrix elements
The aim of the paper is to propose a new type of fits in terms of invariant
quantities for finding the entries of the CKM matrix from the quark sector, by
using the mathematical solution to the reconstruction problem of 3 x 3 unitary
matrices from experimental data, recently found. The necessity of this type of
fit comes from the compatibility conditions between the data and the
theoretical model formalised by the CKM matrix, which imply many strong
nonlinear conditions on moduli which all have to be satisfied in order to
obtain a unitary matrix.Comment: 12 page
Motion on the n-dimensional ellipsoid under the influence of a harmonic force revisited
The integrals in involution for the motion on the -dimensional
ellipsoid under the influence of a harmonic force are explicitly found. The
classical separation of variables is given by the inverse momentum map. In the
quantum case the Schr\"odinger equation separates into one-dimensional
equations that coincide with those obtained from the classical separation of
variables. We show that there is a more general orthogonal parametrisation of
Jacobi type that depends on two arbitrary real parameters. Also if there is a
certain relation between the spring constants and the ellipsoid semiaxes the
motion under the influence of such a harmonic potential is equivalent to the
free motion on the ellipsoid.Comment: Latex2e, 18 page
New results on the parametrisation of complex Hadamard matrices
In this paper we provide an analytical procedure which leads to a system of
polynomial equations whose solutions give the parameterisation of
the complex Hadamard matrices. It is shown that in general the
Hadamard matrices depend on a number of arbitrary phases and a lower bound for
this number is given. The moduli equations define interesting geometrical
objects whose study will shed light on the parameterisation of Hadamard
matrices, as well as on some interesting geometrical varieties defined by them.Comment: 27 page
CP nonconservation in the leptonic sector
In this paper we use an exact method to impose unitarity on moduli of the
neutrino PMNS matrix recently determined, and show how one could obtain
information on CP non-conservation from a limited experimental information. One
suggests a novel type of global fit by expressing all the theoretical
quantities in terms of convention independent parameters: the Jarlskog
invariant and the moduli , able to resolve the positivity
problem of . In this way the fit will directly provide a value for
, and if it is different from zero it will prove the existence of CP
violation in the available experimental data. If the best fit result,
, from M. Maltoni {\em et al}, New J.Phys. {\bf 6} (2004) 122 is
confirmed, it will imply a new physics in the leptonic sector.Comment: This submission has been withdrawn by arXiv administrators because it
is duplicated in arXiv:1101.408
A new method for a global fit of the CKM matrix
We report on a new method to a global fit of the CKM matrix by using the
necessary and sufficient condition the data have to satisfy in order to find a
unitary matrix compatible with them. This condition writes as where is the phase that accounts for CP violation. By
using it we get that the experimental data are to a high degree compatible to
unitarity and that takes values around , in contrast to the
previous determinations. Numerical results are provided for the CKM matrix
entries, the mixing angles between generations and all the angles of the
standard unitarity triangle.Comment: Revtex4, 5 pages, corrected a typos in formula (8), checked up
numerical calculation
Geodesic Flow on the n-Dimensional Ellipsoid as a Liouville Integrable System
We show that the motion on the n-dimensional ellipsoid is complete integrable
by exhibiting n integrals in involution. The system is separable at classical
and quantum level, the separation of classical variables being realized by the
inverse of the momentum map. This system is a generic one in a new class of
n-dimensional complete integrable Hamiltonians defined by an arbitrary function
f(q,p) invertible with respect to momentum p and rational in the coordinate q.Comment: Latex, 8 pages, no figure
Circulant conference matrices for new complex Hadamard matrices
The circulant real and complex matrices are used to find new real and complex
conference matrices. With them we construct Sylvester inverse orthogonal
matrices by doubling the size of inverse complex conference matrices. When the
free parameters take values on the unit circle the inverse orthogonal matrices
transform into complex Hadamard matrices. The method is used for
conference matrices and in this way we find new parametrisations of Hadamard
matrices for dimension
Separation of unistochastic matrices from the double stochastic ones. Recovery of a 3 x 3 unitary matrix from experimental data
The aim of the paper is to provide a constructive method for recovering a
unitary matrix from experimental data. Since there is a natural immersion of
unitary matrices within the set of double stochastic ones, the problem to solve
is to find necessary and sufficient criteria that separate the two sets. A
complete solution is provided for the 3-dimensional case, accompanied by a
test necessary for the reconstruction of a unitary matrix from error
affected data.Comment: 28 page