$$\frac{1}{(E-E_0)^2+ \frac{\Gamma^2}{4}}$$
where $$E$$ is the energy in the centre of mass frame, $$E_0$$ is the rest energy of the propagator particle, and $$\Gamma$$ is its decay width. I was under the impression that divergences in transition rates are necessarily supressed because $$\Gamma$$ is always non-zero. However I have now come across a decay $$\pi^0 \rightarrow \gamma \gamma$$ where the intermediate particle is an up quark. From wat I am aware, these have a vanishing decay rate. How then does the rate for this process not diverge?