Neutinos are either Dirac particles or Majorana particles but can’t be both at the same time. Then how can we write a general mass term as the sum of a Dirac mass term and a Majorana mass term? When we write such a term what nature of neutrinos (Dirac or Mjorana) do we have in mind?
A massive Dirac field, has four independent degrees of freedom (DOF): $$\psi_L,\psi_R,(\psi_L)^c=(\psi^c)_R,(\psi_R)^c=(\psi^c)_L$$ In contrast with this, a Majorana fermion has only two independent DOF: $$\psi_L, (\psi_L)^c=(\psi^c)_R$$ Then, in particular, how is it possible to replace $\psi_L$ by $(\psi_R)^c$ in the Dirac mass term because $\psi_L=(\psi_R)^c$ is true only for Majorana particles and not for Dirac particles. This is the headache I have.