Prong Inequalities fore+e−→γ→Nπ

I consider the ratio of the total cross section for $e^{+}{e}^{-}\to \gamma \to N\pi$ with $2p$ visible prongs to that with two visible prongs. For any fixed $N$ and all $2p$, nontrivial and optimal lower isospin bounds are derived for these ratios. The preliminary data indicate that these bounds may be experimentally significant.