Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 307 / 1 / vi / b / Solution

The Yukawa matrix is $W_{ij}={\partial }_i{\partial }_{j}W$, 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.