Related papers: Is the quark- mixing matrix moduli symmetric?
In the standard model, several forms of quark mass matrices which correspond to the choice of weak bases lead to the same left-handed mixings $V_L=V_{CKM}$, while the right-handed mixings $V_R$ are not observable quantities. Instead, in a…
Using unitarity, unlike the approaches available in the literature, we have constructed 9 independent representations of CKM matrix starting with each of the 9 elements of the matrix. The relationship of these independently constructed…
We deduce pertinent relations between the elements of the CKM matrix, and find that not all of these are totally compatible with experiment and/or the assumption of the $3 \times 3$ unitarity. We identify complex phases in the CKM-elements…
It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…
We express the oblique parameters $S$, $T$, $U$, $V$, $W$, and $X$ in terms of the corresponding mixing matrices in the framework of three BSM models with three CP-even neutral scalars. We consider three types of the extension of the scalar…
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…
The effects of virtual light quark pairs on the charmonium spectrum are studied. Pair creation is modelled with a ``$^{3}P_{0}$" vertex and intermediate states are summed up to 2S excitations. Quark model parameters are obtained by fitting…
We show that any nonsingular (real or complex) square matrix can be factorized into a product of at most three normal matrices, one of which is unitary, another selfadjoint with eigenvalues in the open right half-plane, and the third one is…
We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the pure…
Stimulated by a successful quark mass matrix model based on U(3)$\times$U(3)$'$ family symmetry, a phenomenological neutrino mass matrix for the Majorana neutrinos $(\nu_L, \nu_R^c, N_L, N_R^c)$ is proposed. The model has only three…
As an attempt to give an unified description of quark and lepton mass matrices M_f, the following mass matrix form is proposed: the form of the mass matrices are invariant under a cyclic permutation (f_1 \to f_2, f_2 \to f_3, f_3 \to f_1)…
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural projective embedding. This question…
We propose parametrizations of the neutrino mixing matrix. We discuss several Ansatzes: in some of them $V_{e3}=0$ but in others $V_{e3}$ typically ``comes out'' to be of order $\simeq 0.05.$
The triangular basis is proposed as an efficient way of analyzing general quark mass matrices. Applying the method to hermitian hierarchical matrices with five texture zeros, analytic predictions for quark mixing can be readily obtained.…
We parametrize lepton mixing matrix, known as PMNS matrix, in terms of three parameters which account deviations of three mixing angles from their bi-maximal or tri-bimaximal values. On the basis of this parametrization we can determine…
We systematically investigate general forms of mass matrices for three-generation up and down quarks, including asymmetrical ones in generation space. Viable zero matrix elements are explored which are compatible with the current…
We derive a new set of sum rules between the neutrino mass and mixing parameters in vacuum and their effective counterparts in matter. The moduli of nine genuine lepton mixing matrix elements can then be calculated in terms of the…
We consider the Friedberg-Lee symmetry for the quark sector and show that the symmetry closely relates to both quark masses and mixing angles. We also extend our scheme to the fourth generation quark model and find the relation…
Using the binary tetrahedral group $T^{'}$, the three angles and phase of the quark CKM mixing matrix are pursued by symmetry-breaking which involves $T^{'}$-doublet VEVs and the Chen-Mahanthappa CP-violation mechanism. The NMRT$^{'}$M,…
Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of…