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$$ L= \begin{pmatrix} L^+ \\ L^0 \\ L^- \end{pmatrix} $$

Then the mass term is given by [1]:

$$ \mathcal{L} \supset -\frac m 2 \left( 2 L^+ L^- +L^0 L^0 \right) $$

I am wondering where the mass term is coming from.

I know that in the Standard Model the mass term for a doublet which is in two dimensional representation, is given by ## m \bar L L##.

Any ideas or comments appreciated.

**Reference:**

- Eqn (4) in arXiv:0710.1668v2 [hep-ph]