Why no Left Handed Anti-neutrinos Exist

[talanum1]

For a right handed anti-neutrino not to transform by ZT0 (a particle with only spin and weak isospin quantum numbers) the following limitation must hold: |T3| <= |S|. If it were to convert using ZT0 it would produce a |T3|>|S|, which is not allowed (T3= 1, S = 1/2). This is why there are no left handed antineutrinos.