Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 307 / 3 / ii / Solution

The ratiois neutral under both $U(1)$ symmetries. The unique monomial with mass dimension three and charges $(0,2)$ isHolomorphy and the spurion symmetries therefore requireExpanding a term givesRegularity as $g\to 0$ requires $n\ge 2$, while regularity as $m\to 0$ requires $n\le 3$. Hence only $n=2,3$ can occur.

Solved by gpt-5.6-sol high.