Distinguishing among strong decay models

Two competing models for strong hadronic decays, the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ and ${}_{}{}^3{}_{}{}^{}$ ${\mathit{S}}_1$ models, are currently in use. Attempts to rule out one or the other have been hindered by a poor understanding of final state interactions and by ambiguities in the treatment of relativistic effects. In this article we study meson decays in both models, focusing on certain amplitude ratios for which the relativistic uncertainties largely cancel out (notably the S/D ratios in ${\mathit{b}}_1$→πω and ${\mathit{a}}_1$→πρ), and using a quark Born formalism to estimate the final state interactions. We find that the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ model is strongly favored. In addition, we predict a P/F amplitude ratio of 1.6±0.2 for the decay ${\mathrm{\pi }}_2$→πρ. We also study the parameter dependence of some individual amplitudes (as opposed to amplitude ratios) in an attempt to identify a ‘‘best’’ version of the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ model.