New Criteria for Exchange of a Spin-Zero Meson

The Treiman-Yang test can be extended to give a new criterion for exchange of a spin-zero particle (SZE). The new test would be useful in a reaction (e.g., ${\pi }^{-}+p\to \rho +N^{*}$) in which the two final systems both have a detectable polarization. For such a case it would require that the polarizations of the two systems be uncorrelated, i.e., the cross section is a product of two factors, the first depending only on the polarization of one of the final systems and the second, only on the other. The analogous statements hold for correlations connecting one of the initial particles and the final system that communicates with it only through SZE, and also for correlations connecting the two initial particles. The new test would fail in the event that more than one spin-zero particle is exchanged, i.e., the collision amplitude is a superposition of several SZE amplitudes. In that case there could be correlation terms consisting of a scalar defined in the center-of-mass-frame (c.m.) of one of the final systems (with the momentum transfer as a preferred axis) multiplied by a scalar defined in the other final c.m. If the exchanged particles do not all have the same parity, then there may be additional terms containing a pseudoscalar in the first c.m. multiplied by a pseudoscalar in the second c.m. These effects do not violate the Treiman-Yang azimuthal-angle-independence and bombardment-energy-independence tests. Furthermore, the failure of the new criterion is only partial, since a multiple SZE model continues to forbid correlations of polarization components perpendicular to the momentum transfer in their respective frames of definition.