Simple approach to soft-pion emission inp¯pinteractions near threshold

Viewed in the pion rest frame, the Feynman amplitude for emission of a soft pion is simply proportional to the amplitude of the core, each possible source nucleon contributing a term proportional to its chirality. Together with threshold approximations, this observation enables us to write, in a very simple way, a general expression relating the cross section $\sigma (\overline{p}p\to f+{\pi }^0)$ to $\sigma (\overline{p}p\to f)$, and the cross section $\sigma (\overline{p}p\to f+{\pi }^{+})$ to $\sigma (\overline{p}n\to f)$, near threshold. A comparison is made to data on the reactions $\overline{p}p\to \overline{p}p{\pi }^0$, $\overline{p}n{\pi }^{+}$, $\overline{\Lambda }\Lambda {\pi }^0$, ${\Sigma }^{-}{\Sigma }^{+}{\pi }^0$, $\Lambda \overline{p}{K}^{+}{\pi }^0$, and ${\Sigma }^{+}\overline{p}{K}^0{\pi }^0$, with varying degrees of success.