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I've been reading Mark Srednicki's book on Quantum Field Theory, and toward the end (Chapter 88), he describes how the different generations of leptons acquire mass via Yukawa interactions. However, I'm trying to work out why exactly the different families of leptons (electrons, muons and tauons) have different masses to eachother.

Can anyone explain? Or is this somehow linked to the unanswered question of why any of the fermions have the particular masses that they do?

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The fermion masses result from Yukawa interactions after EWSB: $$ m_f = \frac1{\sqrt 2} y_f v $$ Thus the Yukawa couplings govern lepton and quark masses.

Of course the masses should be diagonalized. For the leptons, as there no neutrino masses in the SM, the lepton interactions and masses can be simultaneously diagonlized, whereas differences in up- and down-type mixing results in a CKM matrix for quarks.

Why are the Yukawa matrices what they are? No one knows. Possible approaches include:

  • Yukawas can be exactly predicted in a more fundamental theory.
  • Yukawas are selected by anthropics in e.g. string landscape. Perhaps we require exactly one light lepton.
  • No explanation/mechanism behind Yukawas. They just are what they are.

A possibility of the first kind is that the Yukawas are unified at high energy, but deviate at low energy due to calculable RG effects. But I don't think complete is successfully realised in any GUT models.

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