Helicity of the positron in zero mass limit

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Discussion Overview

The discussion revolves around the helicity of positrons in the massless limit, particularly in relation to their behavior and interactions as compared to antineutrinos. Participants explore theoretical implications within the framework of weak isospin and SU(2) symmetry, addressing both conceptual and technical aspects of particle physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that in the massless limit, positrons will have the same helicity as antineutrinos due to their association in the same SU(2) doublet.
  • Another participant explains that in the massless limit, left-handed and right-handed components of fermions decouple, with right-handed fermions forming weak isospin singlets and left-handed fermions forming weak isospin doublets.
  • A participant asserts that since antineutrinos are right-handed, positrons must also be right-handed in the massless limit, while noting that neutrinos are left-handed.
  • Another participant counters that both right- and left-handed positrons and electrons will still exist, emphasizing that in the massless limit, the states decouple rather than disappear.
  • There is a discussion about the implications of the massless limit, with one participant pointing out the discomfort some have with the concept of massless charged particles, while noting that electrons are nearly massless already.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of positrons and electrons in the massless limit, particularly regarding the existence and interaction of right- and left-handed states. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

Participants reference the decoupling of helicity states and the implications of SU(2) interactions, but there are limitations in the assumptions made about the massless limit and the definitions of the states involved.

Sphysicist
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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.

Please confirm.
 
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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 won't end up being all right-handed?
 
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? :smile:)

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!
 

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