= Cubic counterterm from a Yukawa fermion triangle
{title2=$\mathcal L_{\mathrm{ct}}=-\delta h\,\Phi\phi^2/2$}
For interactions $-G\bar\psi\psi\Phi-g\bar\psi\psi\phi$, the two <Yukawa fermion triangle> orientations generate a local divergent three-scalar vertex proportional to $mGg^2$. In $d=4-2\epsilon$, with $S-1=i\mathcal M$ convention, its loop pole is $\mathcal M_{\mathrm{div}}=-24mGg^2/(16\pi^2\bar\epsilon)$. A $\Phi\phi^2$ <counterterm> cancels it. The finite renormalized coefficient is additional data, fixed by a <renormalization condition>. Declaring this cubic absent from the displayed bare interaction is not by itself a prescription for its loop-generated finite value.
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