# Why Majorana phases cannot be removed?

Why is the extra two Majorana phases in the PMNS matrix cannot be removed if neutrinos are Majorana fermions? Or in other words, why are the Majorana phases cannot be absorbed into the redefinition of phases of the neutrino fields, if neutrinos are Majorana-type (and also why is it possible if it is Dirac-type)?

• simple remark: even in the case of Dirac-type neutrinos, the PMNS matrix has still 1 phase that cannot be absorbed by a re-definition of the fields. – Paganini Jan 2 '15 at 9:23
• @ Paganini- Yes that is true. But it doesn't answer my question. – SRS Jan 2 '15 at 12:49

My understanding is that if neutrinos are of Majorana type, you have an additional mass term in the Lagrangian: $m ~\overline{\nu^C_L} ~\nu_L$. This term is not invariant under a redefinition of the phase $\nu_L \to e^{i\phi} \nu_L \Rightarrow m ~\overline{\nu^C_L} ~\nu_L \to e^{i2\phi} m ~\overline{\nu^C_L} ~\nu_L$, so you can't use this freedom.