Related papers: Natural Quark Mass Patterns
The use of quadratic residues to construct matrices with specific determinant values is a familiar problem with connections to many areas of mathematics and statistics. Our research has focused on using cubic residues to construct matrices…
We carry out a new study of quark mass matrices $M^{}_{\rm u}$ (up-type) and $M^{}_{\rm d}$ (down-type) which are Hermitian and have four zero entries, and find a new part of the parameter space which was missed in the previous works. We…
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex…
In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is…
We present analyses of the sixty hybrid textures of neutrino mass matrix, which have an equality of matrix elements and one zero. These textures are possibly derived in the models with discrete flavor symmetry. Only six textures among sixty…
We give an overview of recent progress in the study of fermion mass and flavor mixing phenomena. The hints exhibited by the quark and lepton mass spectra towards possible underlying flavor symmetries, from which realistic models of mass…
We study neutrino mass matrices with one texture equality and the neutrino mixing matrix having either its first (TM$_1$) or second (TM$_2$) column identical to that of the tribimaximal mixing matrix. We found that out of total fifteen…
We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.
In 1981, Yoshio Koide noticed that the square root values of the charged lepton masses satisfy the relation \[ Q=\frac{m_e+m_{\mu}+m_{\tau}}{(\sqrt{m_e}+\sqrt{m_{\mu}}+\sqrt{m_{\tau}})^2} \approx \frac{2}{3} \] Inspired by this relation, we…
The predictability of hierarchical quark mass matrices with symmetrically placed texture zeros is explored in the light of current precision measurements on quark masses and mixing data and interesting phenomenological relations among the…
A nearly historical account of quark mass matrix models is given, and the structure of quark mass matrices in the Standard Model is studied. For a minimal parameter basis suggested earlier, where $M_u$ is diagonal and $M_{d11}$, $M_{d13}$,…
We discuss recently discovered links of the statistical models of normal random matrices to some important physical problems of pattern formation and to the quantum Hall effect. Specifically, the large $N$ limit of the normal matrix model…
Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…
We consider a texture for the neutrino mass matrix characterized by one vanishing $2\times2$ subtrace. We analyze phenomenologically and analytically all the six possible patterns, and show that all non-singular ones are able to accommodate…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
The measurements of the neutrino and quark mixing angles satisfy the empirical relations called Quark-Lepton Complementarity. These empirical relations suggest the existence of a correlation between the mixing matrices of leptons and…
Let H be a positive semidefinite matrix partitioned into Hermitian blocks. Then, up to a direct sum operation, H is the average of matrices isometrically congruent to its partial trace. A few corollaries are given, related to important…
Different approaches to the quark-lepton mass problem are reviewed. The infrared quasifixed point predictions for the top quark mass are discussed for the Standard Model and its minimal supersymmetric extension, with particular reference to…
We consider an universal mass matrix model which has a seesaw-invariant structure with the most general texture based on flavor 2 (\leftrightarrow) 3 symmetry common to all quarks and leptons. The CKM quark mixing matrix of the model is…
We propose a simple phenomenological model of quarks-leptons mass matrices having fundamentally universal symmetry structure. These mass matrices consist of democratic and semi-democratic mass matrix terms commonly to the neutrino and the…