# Helicity of the positron in zero mass limit

## Main Question or Discussion Point

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.

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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
so positrons also will be right-handed in the mass-less limit, since the electrons will be left-handed...
No. There will still exist both right- and left-handed positrons and electrons. What I said was, in the massless limit the right- and left-handed states decouple from each other.

Right-handed electrons (And left-handed positrons) are SU2 singlets. They do not interact with the charged weak current, but they do interact with neutral currents. For this reason they can still be created in reactions. (Didn't I say this already? )

By "massless limit", you could mean either "imagine the coupling constant to the Higgs field is zero", or "high energy limit where the mass is negligible". Some people get uncomfortable talking about massless charged particles. But note two things: Such concerns would apply equally to both right- and left-handed fermions. And, electrons nearly are massless charged particles already!