On the origin of families of fermions and their mass matrices - Approximate analyses of properties of four families within approach unifying spins and charges

The approach unifying all the internal degrees of freedom - proposed by one of us[1, 2, 3, 4, 5, 6, 7, 8, 9, 10] - is offering a new way of understanding families of quarks and leptons. Spinors, namely, living in d (= 1 + 13)−dimensional space, manifest in the observed d(= 1 + 3)-dimensional space (at ”physical energies”) all the known charges of quarks and leptons (with the mass protection property of the Standard model - only the left handed quarks and leptons carry the weak charge while the right handed ones are weak chargeless - included), while a part of the starting Lagrange density in d (= 1 + 13) transforms the right handed quarks and leptons into the left handed ones, manifesting a mass term in d = 1 + 3. Since a spinor carries two kinds of spins and interacts accordingly with two kinds of the spin connection fields, the approach predicts families and the corresponding Yukawa couplings. In the paper[11] the appearance of families of quarks and leptons within this approach was investigated and the explicit expressions for the corresponding Yukawa couplings, following from the approach after some approximations and simplifications, presented. In this paper we continue investigations of this new way of presenting families of quarks and leptons by further analyzing properties of mass matrices, treating quarks and leptons in an equivalent way. We connect free parameters of the approach with the known experimental data and investigate a possibility that the fourth family of quarks and leptons appears at low enough energies to be observable with the new generation of accelerators.