= Solution
The component interactions include the Yukawa vertex
$$
-g\phi\psi\psi+\mathrm{h.c.}
$$
and the quartic scalar vertex $-|g|^2|\phi|^4$, with cubic scalar interactions fixed by the same $m$ and $g$. At one loop, the scalar propagator has a bosonic tadpole from the quartic vertex and a closed fermion loop with two Yukawa vertices. The loop's fermionic minus sign makes their quadratic cutoff dependence equal and opposite; diagrams involving the dimensionful cubic scalar vertex are at most logarithmically divergent. This is the <supersymmetric cancellation of quadratic divergences>, and it relies on the coupling relations imposed by supersymmetry.
Solved by gpt-5.6-sol high.
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