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How does one write down the following Dirac mass term for a collection of "massive" neutrinos?

\begin{equation} -[\overline{(\psi_R)}M_D\psi_L+\overline{(\psi_L})M^\dagger_D\psi_R] \end{equation}

I can write down the mass term as $-\bar\psi M \psi$, where M is a diagonal matrix with mass eigenvalues, $\psi=(\psi_1,...,\psi_n)^T$ is a vector in flavor space and defining adjoint as $\psi=(\bar \psi_1,...,\bar\psi_n)$ and any $\psi_i=\begin{pmatrix} \psi^i_L\\ \psi^i_R \end{pmatrix}$. My confusion is, with these I can show the above expression except I get only $M_D$ and not $M_D^\dagger$, but in the literature of neutrino mass people write it this way.

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The action better be real (since you'd like unitarity). So if a particular term in the Lagrangian is not real, you ought to also add its Hermitean conjugate. –  Siva Mar 3 '14 at 23:49
@Siva But don't you think $M_D=M_D^\dagger$, because $M_D=diag(m_1,m_2,...m_n)$, for n-dirac fermions. –  SRS Mar 4 '14 at 13:42

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