Related papers: Quaternionic Electroweak Theory and CKM Matrix
In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an…
The Dirac equation with Lorentz violation involves additional coefficients and yields a fourth-order polynomial that must be solved to yield the dispersion relation. The conventional method of taking the determinant of $4\times 4$ matrices…
In order to obtain a consistent formulation of octonionic quantum mechanics (OQM), we introduce left-right barred operators. Such operators enable us to find the translation rules between octonionic numbers and $8\times 8$ real matrices (a…
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
After the recent high precision determinations of $V_{us}$ and $V_{ud}$, the first row of the CKM matrix shows more than $4\sigma$ deviation from unitarity. Two possible scenarios beyond the Standard Model can be investigated in order to…
The structure of the mixing matrix, in the electroweak quark sector with four generations of quarks is investigated. We conclude that the area of the unitarity quadrangle is not a good choice as a possible measure of the CP~violation. In…
Some comments are made on the matrices which serve as the basis of a quaternionic algebra. We show that these matrices are related with the quaternionic action of the imaginary units from the left and from the right.
Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…
The scalar composite representations of the electroweak symmetry group of the Standard Model are exhibited in the case of two generations of quarks. The link between `strong' and `electroweak' eigenstates is investigated, showing that the…
We study leptonic CKM mixing matrices when the neutrino Yukawa matrices are antisymmetric which gives rise to mass patterns suitable to explain solar, atmospheric and LSND neutrino oscillation experiments. Taking diagonal leptonic matrices…
We construct quark mixing matrices within a group theoretic framework which is easily applicable to any number of generations. Familiar cases are retrieved and related, and it is hoped that our viewpoint may have advantages both…
Investigating the CKM matrix in different parametrization schemes, it is noticed that those schemes can be divided into a few groups where the sine values of the CP phase for each group are approximately equal. Using those relations,…
We obtain a sufficient condition for the convexity of quaternionic numerical range for complex matrices in terms of its complex numerical range. It is also shown that the Bild coincides with complex numerical range for real matrices. From…
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We…
The electroweak theory contains too many empirical parameters. Most of them are related to the flavor part of particle physics. In this paper we discuss a relevant simple idea: the complicated system of actual dimensionless, small versus…
Experiment shows that the top quark is far heavier than the other elementary fermions. This finding has stimulated research on theories of electroweak and flavor symmetry breaking that include physics beyond the standard model. Efforts to…
The renewed interest in investigating quaternionic quantum mechanics, in particular tunneling effects, and the recent results on quaternionic differential operators motivate the study of resolution methods for quaternionic differential…
The angle gamma of the standard CKM unitarity triangle can be determined from B -> D K decays with a very small irreducible theoretical error, which is only due to second-order electroweak corrections. We study these contributions and…
We analyze the possibility of the leptonic mixing matrix having a Wolfenstein form at the Grand Unified Theory scale. The renormalization group evolution of masses and mixing angles from the high scale to electroweak scale, in certain new…
In this talk I review the current status of the CKM matrix. A special emphasis is also given to several discrepancies between experiments and the standard model at the level of about three standard deviations. Recent results that appeared…