Quartic complex-scalar vertex in the Wess–Zumino model (${\mathcal{L}}_{\mathrm{int}}=-|g{|}^2{\phi }^{\ast 2}{\phi }^2\Rightarrow -4i|g{|}^2$)

In a canonical Wess–Zumino model with cubic superpotential $g{\Phi }^3/3$, auxiliary elimination gives a complex-scalar quartic interaction with two legs of each field type. With all momenta incoming and the displayed coefficient, its Feynman rule is $-i(2!2!)|g{|}^2$. For $\phi =(A+iB)/\sqrt{2}$, the same quartic scalar potential is $|g{|}^2(A^2+B^2{)}^2/4$, with real-field rules $-6i|g{|}^2$ for four identical legs and $-2i|g{|}^2$ for two of each. Factorials depend on how the coefficient is defined, not on a new physical coupling.