arXiv subjects

Petre Dita

Publications and source records attributed to Petre Dita.

At least 19 recordsLinked to original sources

arXiv2016

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 $|U_{αi}|$, 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.

hep-ph↗

arXiv2012

Four-parameter families of complex Hadamard matrices of order six

In this paper we provide a general method to construct four-parameter families of complex Hadamard matrices of order six. Our approach is to write a 6-dimensional matrix as composed of four blocks, each one in the form of a circulant matrix. Use of Sylvester method of inverse orthogonal matrices leads to two constraints on the six parameters, and their fulfilment generates complex Hadamard matrices when the free parameters take values on the unit circle. We hope that the problem of mutually unbiased bases could be solved for six-level systems by using our results.

math-ph↗

arXiv2012

On Agaian Matrix

In this paper we discuss the isolation problem of the Agaian matrix among the 6-dimensional matrices. In general a matrix isolation could depend on the kind of equivalence one uses for complex Hadamard matrices. However the present form of Agaian matrix has such a big symmetry that both equivalence methods lead to the same result: the matrix is isolated.

math.CO↗

arXiv2011

Flavour physics parameters from data and unitarity

The aim of the paper is to show that the nowadays experimental data from superallowed nuclear and neutron $β$ decays, and from leptonic and semileptonic decays allow the finding of the most probable numerical form of the KM matrix, as well as the determination of decay constants, $f_{P}$, and of various form factors $f_+(q^2)$, by using a genuine implementation of unitarity constraints. In particular this approach allows the determination of semileptonic form factors that is illustrated on the existing data of $D\rightarrow πl ν$ and $D\rightarrow K lν$ decays.

hep-ph↗

arXiv2011

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$.

math-ph↗

arXiv2011

CP nonconservation in the leptonic sector

In this paper we use an exact method to impose unitarity on moduli of neutrino PMNS matrix recently determined, and show how one could obtain information on CP nonconservation from a limited experimental information. One suggests a novel type of global fit by expressing all theoretical quantities in terms of convention independent parameters: the Jarlskog invariant $J$ and the moduli $|U_{αi}|$, 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.

hep-ph↗

arXiv2010

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 $β$ 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 $D\rightarrow πl ν$ and $D\rightarrow K lν$ decays.

physics.gen-ph↗

arXiv2010

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.

math-ph↗

arXiv2010

Hadamard Matrices from Mutually Unbiased Bases

An analytical method for getting new complex Hadamard matrices by using mutually unbiased bases and a nonlinear doubling formula is provided. The method is illustrated with the n=4 case that leads to a rich family of eight-dimensional Hadamard matrices that depend on five arbitrary parameters whose modulus is equal to unity.

math-ph↗

arXiv2009

On one parametrization of Kobayashi-Maskawa matrix

An analysis of Wolfenstein parametrization for the Kobayashi-Maskawa matrix shows that it has a serious flaw: it depends on {\em three} independent parameters instead of {\em four} as it should be. Because this approximation is currently used in phenomenological analyzes from the quark sector, the reliability of almost all phenomenological results is called in question. Such an example is the latest PDG fit from \cite{CA}, p. 150. The parametrization cannot be fixed since even when it is brought to an exact form it has the same flaw and its use lead to many inconsistencies.

physics.gen-ph↗

arXiv2008

CKM matrix unitarity and a novel type of global fits

The aim of the paper is to propose one paradigm change of CKM global fits on experimental data from electroweak sector. The change refers to using in fits the exact unitarity constraints expressed in terms of four invariant parameters, such as moduli of the CKM matrix, and to take into account an important set of the available experimental data. In the paper we use data from nuclear beta decays, and from leptonic and semileptonic decays, in order to find the most probable numerical form of the CKM matrix, as well as the determination of decay constants, $f_{P}$, and of various form factors $f_+^{Pp}(0)$, directly from experimental results.

hep-ph↗

arXiv2007

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.

hep-ph↗

arXiv2006

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 $χ^2$ test necessary for the reconstruction of a unitary matrix from error affected data.

math-ph↗

arXiv2005

Global fits to the Cabibbo-Kobayashi-Maskawa matrix: unitarity condition method versus standard unitarity triangles approach

The aim of the paper is to make a comparison between the unitarity condition method and the standard version of the unitarity triangle approach by using as parameters four independent moduli $|U_{ij}|$. This choice is motivated by the measurability property and leads to a simple criterion for the separation of unistochastic matrices from the double stochastic ones, whose fulfillment is the key point of any global fit for the CKM entries. In our formulation both the methods are exact, do not depend on any assumption as the smallness of some parameter and both can be used to global fits in the quark and fermion sectors. Monte Carlo simulations show that the separation criterion puts very strong conditions requiring a fine tuning of all the CKM matrix elements.

hep-ph↗

arXiv2005

Unitarity condition method for global fits of the Cabibbo-Kobayashi-Maskawa matrix

We report on an exact method for global fits of the CKM matrix by using the necessary and sufficient conditions the data have to satisfy in order to find a unitary matrix compatible with them, and this method can be applied to both quark and lepton CKM matrices. The key condition writes $-1\le\cosδ\le 1$ where $δ$ is the phase that encodes the CP violation, and it is obtained when one describes the CKM matrix in terms of four moduli of its entries. We use it to reconstruct many approximate unitary matrices from the PDG data, and by using the double stochasticity property of the unitary matrices we find a strong dependence of $\sin 2β$ on $|U_{ub}|$, that implies also strong correlations between $|U_{ij}|$ themselves, proving the constraining power of this approach.

hep-ph↗

arXiv2004

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 $-1\le \cosϕ\le 1$ where $ϕ$ 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 $ϕ$ 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.

hep-ph↗

arXiv2004

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.

quant-ph↗

arXiv2003

Finite-level systems, Hermitian operators, isometries, and a novel parameterization of Stiefel and Grassmann manifolds

In this paper we obtain a description of the Hermitian operators acting on the Hilbert space $\C^n$, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of arbitrary $n$-dimensional operators, operators that may be considered either as Hamiltonians, or density matrices for finite-level quantum systems. It is shown that the spectral multiplicities are encoded in a flag unitary matrix obtained as an ordered product of special unitary matrices, each one generated by a complex $n-k$-dimensional unit vector, $k=0,1,...,n-2$. As a byproduct, an alternative and simple parameterization of Stiefel and Grassmann manifolds is obtained.

quant-ph↗