Handedness of neutrinos and antineutrinos

[lizzie96]

Could anybody explain why neutrinos have only ever been observed to be left-handed and antineutrinos right-handed? If neutrinos travel slower than light and have mass (albeit very small), as shown by neutrino oscillation experiments, why can neutrinos not change their handedness?

 

[Bill_K]

It's because of the way they interact. The weak interaction takes place through exchange of a W boson, which couples only to left-handed fermions. Thus a right-handed neutrino, if it does exist, will be "sterile" with respect to the standard model interactions. Which means you can't produce them, and if they already exist you can't detect them. (You certainly can't slow them down!)

 

[Vanadium 50]

Furthermore, there are two kinds of handedness, called "helicity" and "chirality". The handedness that governs the interaction is chirality. The kind you describe is helicity.

 

[lizzie96]

Thank you. Could you explain the difference between helicity and chirality?

 

[Vanadium 50]

Not easily, at the undergraduate level. For massless particles, they are identical.

 

[Bill_K]

When we speak about the handedness of a fermion, we really mean its chirality. In terms of a Dirac spinor, the chirality operator is γ⁵, and has eigenvalues ±1. It's directly involved in the weak interaction, because the interaction Hamiltonian has the projection operator (1 - γ⁵) in front of every fermion. We say the weak interaction is V - A.

Chirality is a Lorentz invariant quantity, i.e. observing the fermion from a different rest frame doesn't change its chirality. If you write the Hamiltonian for a free particle, H = α·p + βm and ask what [H, γ⁵] is, you find that γ⁵ commutes with the first term but not the βm. So for a massless fermion, such as a massless neutrino, chirality is a constant of the motion. But it is not a constant of the motion for electrons and neutrinos with mass.

Helicity is the spin projection in the direction of motion, represented by the operator Σ·p. Differs from chirality in two respects: (a) for a free particle it IS a constant of the motion, and (b) it is NOT Lorentz invariant. You can change the particle's helicity by running past it. For massless fermions, chirality and helicity turn out to be equal and we don't have to worry about the distinction. If neutrinos do have mass, the distinction becomes relevant.

 

[kurros]

Chirality is a Lorentz invariant quantity, i.e. observing the fermion from a different rest frame doesn't change its chirality. If you write the Hamiltonian for a free particle, H = α·p + βm and ask what [H, γ⁵] is, you find that γ⁵ commutes with the first term but not the βm. So for a massless fermion, such as a massless neutrino, chirality is a constant of the motion. But it is not a constant of the motion for electrons and neutrinos with mass.

I am not super clear on this, so let me just ask: isn't this only true for Dirac masses? If neutrinos have Majorana masses then won't their chirality be a constant of motion?

 

[Bill_K]

Yes, that's true. Chirality would commute with a Majorana mass term like (ν_R)^cν_R.