Abstract
The approach unifying all the internal degrees of freedom—proposed by one of us—offers a new way of understanding families of quarks and leptons: a part of the starting Lagrange density in d (=1+13), which includes two kinds of spin connection fields—the gauge fields of two types of Clifford algebra objects—transforms the right-handed quarks and leptons into left-handed ones manifesting in d=1+3 the Yukawa couplings of the Standard Model. We study the influence of the way of breaking symmetries on the Yukawa couplings and estimate properties of the fourth family—the quark masses and the mixing matrix, investigating the possibility that the fourth family of quarks and leptons appears at low enough energies to be observable with the new generation of accelerators.
Highlights
The starting symmetry—all the gauge fields assumed by the Standard Model, as well as the mass matrices leading to the observed masses of quarks and leptons and the measured mixing matrices
If we find out how and at which scales the break of S O(1, 7) to S O(1, 3) × SU (2) × U (1) (possibly via S O(1, 3) × S O(4)) occurs, the approach could offer the explanation of why we see spinors carrying beside the spin the weak, the electromagnetic and the color charge, why each of the charges couple with a different coupling constant to the corresponding gauge fields, what are the ratios of these coupling constants, why until now have we been able to see only three families, all three of different masses and at which energy scale the family occurs
We study the break of the symmetries from S O(1, 7) × U (1) × SU (3), down to S O(1, 3) × U (1) × SU (3), which occurs in the following steps
Summary
We point ωabα and ωabc = fcα ωabα. We simplify the index kl in the exponent of fields Akl±((ab), (cd)) to ±, omitting i. The way of breaking either of the two symmetries—the Poincaré one and the symmetry determined by the generators Sab in d = 1 + 13—strongly influences the Yukawa couplings of equation (10), relating the parameters ωabc and influencing the coupling constants. We assume two ways of breaking symmetries, and investigate under what conditions each of these two ways of breaking symmetries lead to the current measured properties of fermions
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