Exotic meson $\pi_1(1600)$ with $J^{PC} = 1^{-+}$ and its decay into $\rho(770)\pi

We study the spin-exotic JPC=1-+ amplitude in single-diffractive dissociation of 190 GeV/c pions into π-π-π+ using a hydrogen target and confirm the π1 ( 1600 ) → ρ ( 770 ) π amplitude, which interferes with a nonresonant 1-+ amplitude. We demonstrate that conflicting conclusions from previous studies on these amplitudes can be attributed to different analysis models and different treatment of the dependence of the amplitudes on the squared four-momentum transfer and we thus reconcile these experimental findings. We study the nonresonant contributions to the π-π-π+ final state using pseudodata generated on the basis of a Deck model. Subjecting pseudodata and real data to the same partial-wave analysis, we find good agreement concerning the spectral shape and its dependence on the squared four-momentum transfer for the JPC=1-+ amplitude and also for amplitudes with other JPC quantum numbers. We investigate for the first time the amplitude of the π-π+ subsystem with JPC=1-- in the 3π amplitude with JPC=1-+ employing the novel freed-isobar analysis scheme. We reveal this π-π+ amplitude to be dominated by the ρ ( 770 ) for both the π1 ( 1600 ) and the nonresonant contribution. These findings largely confirm the underlying assumptions for the isobar model used in all previous partial-wave analyses addressing the JPC=1-+ amplitude.