My question is about the mass of tau and mu. Is there some reason for them to be

Question

My question is about the mass of tau and mu. Is there some reason for them to be in the GeV range, where QCD masses -proton and pion, if you wish, or glue and chiral scales- are?

I am asking for theories justifying this. For instance, Alejandro Cabo tries to produce first the quark masses from the one of the top quark via QCD, very much as Georgi-Glashow electron-muon in the early seventies, and then he expects that the leptons should have masses similar to the quarks via the electromagnetic/electroweak coupling (albeit some group theoretical reason could be enough).

Hierarchically, and from the point of view that any near zero value for a coupling is a hint for a broken symmetry (so that in the limit where this symmetry is unbroken, the coupling is exactly zero), what I would expect is a symmetry protecting all the yukawas except the top, and then still a subgroup protecting the first generation.

Explanation / Answer

The anthropic principle might explain it.

The difference in mass of the neutron and proton is roughly the difference in mass between that of the down and up quarks, which is comparable to that of the electron mass. If the proton were significantly heavier, they would decay into neutrons

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