Abstract
A general reaction of the type is considered in which the final pions are produced in a state with definite isospin and charge . Rigorous bounds on the ratio of the number of neutral to the number of charged pions are derived, following from isospin invariance and Bose statistics alone. Previously known results are recovered for and new bounds are obtained for . The -pion state with fixed is appropriately symmetrized using the representation theory of SU(3) in an O(3) basis. We can deal with arbitrary values of , since we have resolved the SU(3) ⊃ O(3) missing-label problem. An example of the type of bounds we obtain is for the reaction , where . For and even, we obtain . Similar results are given for odd and also for reactions like .
- Received 29 April 1974
DOI:https://doi.org/10.1103/PhysRevD.10.1587
©1974 American Physical Society