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You are right that that the symmetry breaking breaks all three symmetries of $SU(2)$. Thus the $SU(2)$ generators give you three goldstone bosons in the theory with broken symmetry. However, we have not yet considered all of the symmetries of the original theory. We know that the full symmetry group has six generators and that five of them must be broken. ...

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what would happen if weak bosons wouldn't interact with higgs field The Higgs field is a pair of complex scalar fields that transform as an electroweak doublet. So, on this view, if the fields don't have weak isopin charge and weak hypercharge, they're not components of the Higgs field; they're something else entirely. Essentially, you're asking what ...

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Well if you turned the coupling off, the Higgs mechanism wouldn't apply, and the symmetry would never be spontaneously broken. And then rather than having massive fields, you'd have massless fields and the interaction in the Lagrangian that would have been a mass term would instead be a Yukawa interaction. It'd be very similar to what happens at high ...

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