# Help counting the number of real parameters in simple seesaw Lagrangian

The seesaw Lagrangian is $$-\mathcal{L}_{\rm mass}=\frac{Y^\ell_{ab}\langle H^0\rangle}{\sqrt{2}}\bar{\ell}_{aL}\ell_{bR}+\frac{Y^\nu_{ab}\langle H^0\rangle}{\sqrt{2}}\bar{\nu}_{aL}\nu_{bR}+\frac{1}{2}M_{ab}\bar{\nu}^C_{aR}\nu_{bR}+\text{h.c.}$$ For $$3$$ left(right)-handed charged leptons $$\ell_{L(R)}$$, $$3$$ left(right)-handed neutrinos $$\nu_{L(R)}$$, there are $$18+18$$ real parameters coming from the complex $$3\times 3$$ Yukawa matrices $$Y^\ell, Y^\nu$$ and $$12$$ more from complex symmetric $$3\times 3$$ Majorana matrix $$M$$. Therefore, the total real parameters in this Lagrangian is $$48$$.