= Trilinear scalar vertices in the Wess–Zumino model
{c}
{title2=$V_{\phi\phi\phi^*}=-2im^*g$}
For canonical <Kähler potential> and $W=m\Phi^2/2+g\Phi^3/3$, eliminating the <auxiliary field> gives $V=|m\phi+g\phi^2|^2$. The cubic interaction Lagrangian is $-m^*g\phi^*\phi^2-mg^*\phi(\phi^*)^2$. Differentiating with respect to the three external fields gives the all-incoming <Feynman rules> $V_{\phi\phi\phi^*}=-2im^*g$ and $V_{\phi^*\phi^*\phi}=-2img^*$; the factor two counts identical scalar legs. For real $m,g$ and $\phi=(A+iB)/\sqrt2$, the cubic Lagrangian is $-mgA(A^2+B^2)/\sqrt2$, giving $V_{AAA}=-3\sqrt2img$ and $V_{ABB}=-\sqrt2img$.
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