Dalitz-Plot Analysis Including Duality

Using fairly general parametrizations of the Veneziano type for the decay amplitude, we study the annihilations of $\overline{N}N$ at rest (in the $T=1\mathrm{}$ channel) into three pions. Very good agreement is obtained for the wellknown $\overline{p}n$ channel in terms of four essential parameters. A previous model due to Lovelace is found to be inaccurate in fitting the data, and therefore his phenomenological interpretation is changed. If our predictions for other decay channels are confirmed, the generally accepted decoupling of the $\rho$ in $\overline{N}N$ ($T=1\mathrm{}$) is probably incorrect. It is suggested that our procedure is the right one for parametrizing decay amplitudes in order to check if duality is a true property of strong interactions.