Trilinear scalar vertices in the Wess–Zumino model ($V_{\varphi \varphi {\varphi }^{\ast }}=-2i{m}^{\ast }g$)

For canonical Kähler potential and $W=m{\Phi }^2/2+g{\Phi }^3/3$, eliminating the auxiliary field gives $V=|m\varphi +g{\varphi }^2{|}^2$. The cubic interaction Lagrangian is $-m^{\ast }g{\varphi }^{\ast }{\varphi }^2-m{g}^{\ast }\varphi ({\varphi }^{\ast }{)}^2$. Differentiating with respect to the three external fields gives the all-incoming Feynman rules $V_{\varphi \varphi {\varphi }^{\ast }}=-2i{m}^{\ast }g$ and $V_{{\varphi }^{\ast }{\varphi }^{\ast }\varphi }=-2im{g}^{\ast }$; the factor two counts identical scalar legs. For real $m,g$ and $\varphi =(A+iB)/\sqrt{2}$, the cubic Lagrangian is $-mgA(A^2+B^2)/\sqrt{2}$, giving $V_{AAA}=-3\sqrt{2}img$ and $V_{ABB}=-\sqrt{2}img$.