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

Solution

- iλ

g γ^{5}

, so

S_{f i}^{(5)} = (2 π)^{4} δ^{(4)} (k - p - q) g \overset{u}{ˉ}^{s} (p) γ^{5} v^{s^{'}} (q) .

Using

γ^{5} \neq q γ^{5} = - \neq q

with the conjugation sign gives

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 - 4 m^{2} / M^{2})^{3/2}

, whereas pseudoscalar decay is proportional to

(1 - 4 m^{2} / M^{2})^{1/2}

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