Is anyone familiar with any sort of theoretical explanation of the number of chiral families? Any model or idea in this direction would be very interesting and useful.
Anomaly cancellation for three chiral families is interesting.
Does it say something deeper regarding number families ?
Heterotic string theories, when conpactified, yields three
chiral families, See:
String theory in four dimensions with three families of chiral fermions and standard gauge symmetry
Phys. Rev. D 34, 3780 – Published 15 December 1986
Da-Xi Li
Also a series of papers by Z Kakushadze investigate
string inspired three family models.
The most official answer I have always heard is that three is a minimum for CP violating phase. But not a strong argument.
Extra dimensions seem to like three generations, as it is known from compactification of superstrings, usually getting the number of families from some topological parameter. With extra dimensions, but without superstrings, some of my university teachers did a paper years ago: https://inspirehep.net/record/11555?ln=es (Phys.Rev. D26 (1982) 691-697)
My own guess is a very retorted mechanism: use the quarks as preons for the yet-to-be-found susy scalars. This is only possible with three generations.
Article Origin of inertia at rest and the number of generations
Thanks for your comments.
Had a look at work of Alonso et al. In their setting, I see two problems.
1. There is no chiral symmetry, which prevents leptons from becoming massive,
i.e. model do not carries symmetries of SM.
2. May be, above problem, by some elaboration, can be overcome; but the Lagrangian
Authors consider looks to me rather ad-hoc. If it can be derived by some fundamental principles, then conclusions would be more firm and waterproof.
However, their approach looks interesting and original, and may be worthwhile to think in that direction.
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