The pseudoscalar vertex replaces $-i\lambda$ by $g\gamma^5$, so
$$
S_{fi}^{(5)}=(2\pi)^4\delta^{(4)}(k-p-q)
g\bar u^s(p)\gamma^5v^{s'}(q).
$$
Using $\gamma^5\not q\gamma^5=-\not q$ with the conjugation sign gives
$$
\mathcal P_5=\frac{g^2}{2}M^2.
$$
The interactions are experimentally distinguishable through the decay rate and its threshold behavior: scalar decay is proportional to $(1-4m^2/M^2)^{3/2}$, whereas pseudoscalar decay is proportional to $(1-4m^2/M^2)^{1/2}$. Spin and parity correlations provide further discrimination.


Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 3 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-301/3/b/solution