A Peculiar Property of theJP=1+ρ0π−andε0π−States at LowM3πinπ−p→π+π−π−p

The usefulness of the isobar model for analysis of multiparticle final states depends a great deal on the choice of basis states with qualitatively different behavior in the relevant kinematic variables. We have discovered that the $1^{+}$ state formed in ${\pi }^{+}{\pi }^{-}{\pi }^{-}$ near $M_{3\pi }=0.9\mathrm{}$ GeV by a ${\rho }^0{\pi }^{-}$ $S$-wave system is quite similar in many important features to that formed by an ${\epsilon }^0{\pi }^{-}$ $P$-wave system, once symmetrization in the identical ${\pi }^{-}$ particles is accomplished. This similarity, which is quite marked for $M_{3\pi }<1.1\mathrm{}$ GeV, is due to a combination of kinematical and dynamical effects. It makes partial-wave analysis of $3\pi$ data in this region rather tricky. Persons applying isobar-model analysis to other systems should be alert for similar difficulties.