🚀 go-pugleaf

I wrote:
* If you give the neutrino a Majorana mass... then when you overtake the
* light left-handed neutrino you will see a light right-handed antineutrino!
* Majorana masses violate any quantum number which the particle carries...
* so "particle" and "antiparticle" are not... well-distinguished...

vijay@wiliki.eng.hawaii.edu (Vijay Fafat) responded:
> What would I see if the same neutrino was AT REST in my frame? ...
> What about its chirality?

The particle would be light (rest-mass is a Lorentz invariant!), and
neither its chirality, nor its helicity, nor its lepton number (i.e.
neutrino vs. anti-neutrino) would be defined.

From Halzen & Martin, p.116: "For a massive fermion... handedness
[chirality] is not a good quantum number... gamma_5 does not commute with
the Hamiltonian...  [H]elicity is conserved but is frame-dependent."
Remember chirality and helicity are not the same thing: chirality is the
eigenvalue of gamma_5, while helicity is the projection of spin onto the
3-momentum unit vector.

> At what point in the experiment does the switch from left- to
> right-neutrino occur?

Its helicity switches as you pass through p=0.

You could ask why I used the terms "neutrino" and "anti-neutrino" in my
original statement if these terms are not well-defined.  I think the answer
is that for large momenta and small Majorana mass, lepton-number is nearly
conserved, i.e. processes which violate it are suppressed by m/p.

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