Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 304 / 2 / d / Solution

For momenta much smaller than $M$,Expanding the source functional to order $g^2$, equivalently integrating out the heavy scalar by its field equation, producesThus the four-spinor coefficient is $g^2/(2M^2)$ in this normalization. Since $[\psi ]=3/2$ and $[g]=0$ in four dimensions, $(\bar{\psi }\psi {)}^2$ has dimension six and its coefficient has the required dimension $-2$.