Scalar vertices of an adjoint triplet Higgs model ($hhh,hhhh,h{W}^{+}{W}^{-},hh{W}^{+}{W}^{-}$)

For a real triplet with potential $\lambda ({\Phi }^2-v^2{)}^2/8$, unitary gauge gives $\Phi =(0,0,v+h)$ and scalar interaction terms $-\lambda v{h}^3/2-\lambda h^4/8+2e^{2}vh{W}^{+}{W}^{-}+e^2{h}^2{W}^{+}{W}^{-}$. Functional differentiation, including identical-field multiplicities, gives vertices $-3i\lambda v$, $-3i\lambda$, $2i{e}^{2}v{g}_{\mu \nu }$ and $2i{e}^2{g}_{\mu \nu }$ respectively. The physical scalar is neutral under the residual U(1), so there are no $hAA$ or $hhAA$ vertices.