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 $\beta$ 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, $f_{P}$, and of various form factors $f_+(q^2)$, 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 $D\rightarrow \pi l \nu$ and $D\rightarrow K l\nu$ 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 $n$ integrals in involution for the motion on the $n$-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 $(n-2)^2$ polynomial equations whose solutions give the parameterisation of the complex $n\times n$ 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 $J$ and the moduli $|U_{\alpha i}|$, able to resolve the positivity problem of $|U_{e 3}|$. In this way the fit will directly provide a value for $J$, 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, $|U_{e3}|^2<0$, 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 $-1\le \cos\phi\le 1$ where $\phi$ 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 $\phi$ takes values around $90^0$, 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 $n=6$ conference matrices and in this way we find new parametrisations of Hadamard matrices for dimension $n=12$

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 $\chi^2$ test necessary for the reconstruction of a unitary matrix from error affected data.Comment: 28 page