Can Right-Handed Neutrinos Be Integrated into the Standard Model?

[lalo_u]

I am reading Mohapatra's book: "Massive Neutrinos in Physics and Astrophysics". At the beginning of chapter 7, it is sought expressions where the right neutrino was considered in the Electroweak Standard Model.
Everything was fine until I found the expression \overline{N^c_{l'L}}\nu^c_{lR}=\overline{\nu_{lL}}N_{l'R}.
Where N_{l'R} is the right handed field associated with right handed neutrinos and the subsctipts l,l' indicate the lepton flavors.

Well, I'm trying to prove this, but I get stuck on the following expression:

\overline{N^c_{l&#039;L}}\nu^c_{lR} =\overline{\left(N_{l&#039;L}\right)^c}\left(\nu_{lR}\right)^c<br /> = \overline{N_{l&#039;R}}\nu_{lL}
And I'm assuming that they are Majorana neutrinos.

To complete the test I should justify why the conjugate for the last expression can be taken and remain unchanged, someone could help?

 

[member 553083]

To prove the expression \overline{N^c_{l'L}}\nu^c_{lR}=\overline{\nu_{lL}}N_{l'R}, you can use the fact that Majorana particles are their own antiparticles. This means that the conjugate of a Majorana particle is equal to itself. Thus, taking the conjugate of the last expression will not change it: \overline{N_{l'R}}\nu_{lL} = \overline{\left(N_{l'R}\right)^c}\left(\nu_{lL}\right)^c = \overline{\nu_{lL}}N_{l'R}.