# Helicity of the positron in zero mass limit

Hi...

I read somewhere that positron, in the massless, limit will have the same helicity as the antineutrino.

This must be because they are in the same SU(2) doublet.

So helicity operator must commute with the SU(2) generators.

Bill_K
What happens in the massless limit is that the left-handed and right-handed components of a fermion decouple from each other. Right-handed fermions couple only to the neutral weak current (Z meson) and electromagnetic current, and form weak isospin singlets. Left-handed fermions couple as well to the charged weak current (W meson) and form weak isospin doublets.

Thanks...I understand that...

Now, antineutrinos are right-handed....so positrons also will be right-handed in the mass-less limit, since the electrons will be left-handed...

It is observed in nature that neutrinos are left-handed and anti-neutrinos are right-handed..
It is also true that the neutrinos have SU(2)_L interactions...so the antineutrinos have an SU(2)_R, right?

How do we know that, when we turn off masses, electrons wont end up being all right-handed?

Bill_K