Solution (source code)

= Solution

The Yukawa matrix is $W_{ij}=\partial_i\partial_jW$, which vanishes for constant $W$. Therefore there is no scalar-fermion interaction vertex and no corresponding Feynman diagram. The requests in parts (vi)(a) and (vi)(b) would become nontrivial only after changing the field content or reducing the symmetry so that a nonzero invariant superpotential exists.

Solved by gpt-5.6-sol high.