jmheer said:
So if I understand what you are saying, there are currently no accepted theories and the lepton masses are considered to be arbitrary free parameters, for practical purposes. That was my understanding - thank you for confirming it, and sharing the arXiv links.
-Joe
The masses come from coupling to the Higgs field ("yukawa couplings"). These are the quantities which, in the standard model, are free parameters, i.e. their values are to be determined by experiment.
It is easy to formulate extensions to the standard model in which these couplings are constrained in some way. For example, one can postulate symmetries which force the yukawa couplings to have specific relations to each other.
In terms of the development of theory, the constraints on the masses which arise most naturally, are those which stem from "grand unification" of the forces. Positing that gluons and photons and weak bosons are all aspects of a unified force, also implies that e.g. certain leptons and quarks are aspects of the same ensemble of matter particles, which in turn implies that their yukawas aren't independent.
The simplest forms of grand unification are all but falsified, but there are hundreds of papers proposing variations on grand unification, plus various "flavor symmetries" affecting the yukawas; and these are field theories which naturally arise in string theory. In the context of string theory, the couplings are not merely constrained, but their exact values should follow from the shape of the extra dimensions, and so forth (though in practice, such calculations are still mostly beyond reach).
So there is a huge theoretical edifice in terms of which predictions are possible, and there are innumerable papers which fit into that edifice, and which make different predictions. The main problem is that such unified theories always predict other phenomena (this is how the simplest versions of grand unification were falsified), and none of those
other predictions have been confirmed, though one may always hope that the latest bump at the colliders is a new particle showing up, or that the extra particles in one's unified theory can explain dark matter, inflation, or the cosmic excess of matter over antimatter...
But be aware: the mass predictions which come from this paradigm are typically like "the top quark is much heavier than everything else", or "electrons and up quarks are light". They are very qualitative predictions. For the most part, numerically exact predictions await the utopia in which string theory learns how to calculate particle masses; and most algebraic formulas that have been found for particle masses, lack an actual theory.
Out of such "numerological" formulas, the Koide formula maximizes the combination of elegance, intricacy, and attention from actual physicists. But, while there really is some attention to the formula from actual physicists, it's still a very marginal topic, because it is a relationship between "pole masses", whereas theory suggests that relationships should arise among "running masses" (pole mass and running mass being different technical definitions of mass, in quantum field theory). Also, the formula itself has an unusual form, compared to the mass relationships that normally appear in unified theories.
Nonetheless, a little bit of work has been done on how to obtain it, notably by Yoshio Koide himself, and I am definitely one of the Koide fans from the "Beyond the Standard Models" subforum.
