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I am a bit confused about neutrinos in the standard model. The vertex of the weak interaction charged current, implies that any neutrino interacting through the charged current must be left handed. However the neutral current allows coupling to the right handed particles, too (and we see that in the interactions with charged leptons). Why is it not possible for a $Z$ boson to decay to a pair for neutrino-antineutrino, in which the neutrino is right-handed? I.e. why don't we have any right-handed neutrinos in the standard model?

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  • Short answer: vanishing weak hypercharge.

Unlike the charged leptons, neutrinos are electrically neutral, so for the weak isospin singlet neutrinos, $Y_W= 2 ( Q-T_3)=0$.

This means that right-handed neutrinos don't couple to the $W_3$, nor the $B$ gauge fields, hence neither to γ nor the Ζ, the physical Weinberg angle rotations thereof. They may only couple to left-handed neutrinos and the Higgs field in Yukawa couplings, if these develop Dirac masses. So it is not that one does not have them in the SM, it is more like that they hardly do anything in it if they are around...


The Yukawa coupling for the above, however, should be below $10^{-14}$. Now don't ask about the coupling to the neutral goldston with the same strength, so then...

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