Some New Isospin Bounds in Multipion Production

Reactions are considered in which $N$ pions are produced, subject to the constraint that the over-all isospin of the $N\pi$ system does not exceed the value one. For any $N$, bounds are given on the ratio of neutral to charged pions. From these $N$-dependent bounds, one obtains "enveloping bounds," valid for all $N$. The proofs rest on an earlier remark that all of the (generally many) $N\pi$ states with a given mixed symmetry (and with $I\le 1$) have the same branching ratios for generating various charge partitions.