Question

Am I correct in thinking that applying the charge conjugation operator does not change the helicity of a particle, despite it replacing the particle with its anti-particle?

Answer 1

Applying the charge conjugation operator does not change the helicity. Because charge conjugation operator gives the antiparticle of the particle which has just the opposite of charge of particle like for electron it gives positron. Both electron and positron have same spin. But in the case of weak forces we see applying the charge conjugation on neutrino gives antineutrino, which is different from it's particle in only helicity. As we have seen the CP violation in weak interaction, it changes the helicity on charge conjugation operator ,only in the case of neutrino.