A timeon model of quark and lepton mass matrices

It is proposed that T violation in physics, as well as the masses of electron and u, d quarks, arise from a pseudoscalar interaction with a new spin 0 field tau(x), odd in P and T, but even in C. This interaction contains a factor i gamma(5) in the quark and lepton Dirac algebra, so that the full Hamiltonian is P; T conserving; but by spontaneous symmetry breaking, the new field tau(x) has a nonzero expectation value <tau > not equal 0 that breaks P and T symmetry. Oscillations of tau(x) about its expectation value produce a new particle, the "timeon". The mass of timeon is expected to be high because of its flavor-changing properties. The main body of the paper is on the low energy phenomenology of the timeon model. As we shall show, for the quark system the model gives a compact three-dimensional geometric picture consisting of two elliptic plates and one needle, which embodies the 10 observables: six quark masses, three Eulerian angles theta(12); theta(23); theta(31) and the Jarlskog invariant of the CKM matrix. For leptons, we assume that the neutrinos do not have a direct timeon interaction; therefore, the lowest neutrino mass is zero. The timeon interaction with charged leptons yields the observed nonzero electron mass, analogous to the up and down quark masses. Furthermore, the timeon model for leptons contains two fewer theoretical parameters than observables. Thus, there are two testable relations between the three angles theta(12); theta(23); theta(31) and the Jarlskog invariant of the neutrino mapping matrix. (C) 2009 Elsevier Inc. All rights reserved.