Thanks !
But in fact I am not sure it is right...
Look double beta decay : right (chirality) antineutrino is first emitted, then its helicity is flipped (massive neutrino) : it becomes a left helicity antineutrino still with right chirality. And, if Majorana, this left helicity antineutrino is equal to a left helicity neutrino which is absorbed by the second neutron...
From the beginning to the end it is a right chiral particle and a right chiral particle cannot give the weak process V-A : n + neutrino -> p + e-
So here it seems that the process is governed by the helicity ! and not by the chirality ! This is where I am lost...