Every nonsingular fermion mass matrix, by an appropriate unitary transformation of right-chiral fields, is equivalent to a triangular matrix. Using the freedom in choosing bases of right-chiral fields in the minimal standard model, reduction to triangular form reduces the well-known ambiguities in reconstructing a mass matrix to trivial phase redefinitions. Furthermore, diagonalization of the quark mass sectors can be shifted to one charge sector only, without loosing the concise and economic triangular form. The corresponding effective triangular mass matrix is reconstructed, up to trivial phases, from the moduli of the CKM matrix elements, and vice versa, in a unique way. A new formula for the parametrization independent CP-measure in terms of observables is derived and discussed.Comment: 13 pages, Late

A recently proposed, new construction of the Standard Model based on the graded Lie algebra SU (2|1) is analyzed in some depth. The essential ingredient is an algebraic superconnection which incorporates both the gauge fields and the Higgs fields and whose curvature automatically leads to a spontaneously broken realization of the theory. The mechanism of hiding the original algebraic structure is unorthodox and is due to the specific, "noncommutative" realization of SU (2|1). The model is characterized by a constant background supercurvature which is invariant under arbitrary, constant SU (2|1) gauge transformations. This background field whose effect is analogous to the action of a constant magnetic field on a spherical atom, is traced back to the differential in the space of (super)matrices by means of which the supercurvature is constructed. The same background field is responsible for the fact that the ground state has no more than the U (1) e.m. symmetry of electromagnetism, the SU (2)L × U (1) symmetry of the Standard Model being recovered only after "backshifting" the Higgs fields. Thus, the Higgs mechanism receives a new and geometrical interpretation.

Triangular mass matrices for neutrinos and their charged partners contain full information on neutrino mixing in a most concise form. Although the scheme is general and model independent, triangular matrices are typical for reducible but indecomposable representations of graded Lie algebras which, in turn, are characteristic for the standard model in noncommutative geometry. The mixing matrix responsible for neutrino oscillations is worked out analytically for two and three lepton families. The example of two families fixes the mixing angle to just about what is required by the Mikheyev-Smirnov-Wolfenstein resonance oscillation of solar neutrinos. In the case of three families we classify all physically plausible choices for the neutrino mass matrix and derive interesting bounds on some of the moduli of the mixing matrix.

QERN L.IBRFIRIES» GENE'··/H empirical inputs.plain sorne of the qualitative features of the standard model which previously were confirm our previous experience: models based on non-cornmutative geometry ex functions of the mass eigenvalues and a small number of parameters. Our results fully analytic expressions for the mass matrices and the mixing matrices which are ment with experiment but derived from a very different physical picture. `We present CKM mixing identical with, or very close to, published empirical analyses in agree ing electroweak interactions for the observed splittings) we find mass matrices and interactions. Assuming the quark generations to be initially degenerate (thus blam posable representation which provides a natural framework for inter-generational classify three quark generations in a twelve-dimensional, reducible, but indecom-A version of the standard model based on non-commutative geometry allows to Abstract e-mail: (name)©VIPMZW.Physik.Uni-Mainz.DE

We propose a new and efficient method of reconstructing quark mass matrices from their eigenvalues and a complete set of mixing observables. By a combination of the principle of NNI bases which are known to cover the general case, and of the polar decomposition theorem that allows us to convert arbitrary nonsingular matrices to triangular form, we achieve a parametrization where the remaining freedom is reduced to one complex parameter. While this parameter runs through the domain bounded by the circle with radius R ϭͱ(m t 2 Ϫm u 2 )/(m t 2 Ϫm c 2 ) around the origin in the complex plane one sweeps the space of all mass matrices compatible with the given set of data.