# One family of fermions SU(2)LXU(1)

1. ### Euphemia

12
Hello, all
If now I only have one family of fermions (a neutrino, a charged lepton, an up-type quark and a down quark), what is going to change of the Lagragian and also the Feynman rules of SU(2)LXU(1)
electroweak theory?
Euphemia

2. ### ofirg

114
Almost all the interactions in the SM, including those mediated by the Z, photon and gluons ( strong, electromagnetic and weak neutral current) don't mix between the different generations ( families) of fermions. For these interactions, the lagrangain is simply a sum of an identical lagrangian for each generation ( up to different masses, of course) with the same feynman rules for each generation.
Only the interaction mediated by the W boson (charged neutral current) mixes between the generations with coefficents given by the CKM matrix. This is where the fact that we have three generations and not one come to play.

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