Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form

We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott(HPS) form.These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector.The perturbing matrix is assumed to be purely imaginary(thus maximally T-violating) and to have a strength in energy scale no greater(but perhaps smaller) than the muon mass.As we shall show,it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than O((mμ/mτ)2) ≈ 3.5 × 10?3 from their HPS values.Assuming that(mμ/mτ)2 can be neglected,we derive two simple constraints on the four parameters θ12,θ23,θ31,and δ of the mapping matrix.These constraints are independent of the details of the imaginary T-violating perturbation of the charged lepton mass matrix.We also show that the e and μ parts of the mapping matrix have a definite form governed by two parameters α and β;any deviation of order mμ/mτ can be accommodated by adjusting these two parameters.     

Deviations of the lepton mapping matrix from the Harrison-Perkins- Scott form

We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott （HPS） form. These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector. The perturbing matrix is assumed to be purely imaginary （thus maximally T-violating） and to have a strength in energy scale no greater （but perhaps smaller） than the muon mass. As we shall show, it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than O（（mμ/mτ）^2） ≈ 3.5 ×10^-3 from their HPS values. Assuming that （mμ/mτ）^2 can be neglected, we derive two simple constraints on the four parameters θ12,θ23, θ31, and δ of the mapping matrix. These constraints are independent of the details of the imaginary T-violating perturbation of the charged lepton mass matrix. We also show that the e and μ parts of the mapping matrix have a definite form governed by two parameters α and β; any deviation of order mμ/mτ can be accommodated by adjusting these two parameters.     

Model with strong γ4T-violation

We extend the T violating model of the paper on "Hidden symmetry of the CKM and neutrino mapping matrices" by assuming its T-violating phases X↑ and X↓ to be large and the same,with X = X↑= X↓.In this case,the model has 9 real parameters:α↑,β↑T,ξ↑,η↑ for the ↑-quark sector,α↑,β↑T,ξ↑,η↑ for the ↓sector and a common X.We examine whether these nine parameters are compatible with ten observables:the six quark masses and the four real parameters that characterize the CKM matrix (i.e.,the Jarlskog invariant J and three Eulerian angles).We find that this is possible only if the T violating phase X is large,between -120° to -135°.In this strong T violating model,the smallness of the Jarlskog invariant J ≌ 3 × 10-5 is mainly accounted for by the large heavy quark masses,with mc/mt＜ ms/mb≈ 0.02,as well as the near complete overlap of t and b quark,with (c|b)=-0.04.     

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 quarks, arise from a pseudoscalar interaction with a new spin 0 field τ(x), odd in P and T, but even in C. This interaction contains a factor iγ₅ in the quark and lepton Dirac algebra, so that the full Hamiltonian is conserving; but by spontaneous symmetry breaking, the new field τ(x) has a nonzero expectation value τ≠0 that breaks P and T symmetry. Oscillations of τ(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 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 and the Jarlskog invariant of the neutrino mapping matrix.