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

We study the spin-exotic \(J^{PC} = 1^{-+}\) amplitude in single-diffractive dissociation of 190 GeV\(/c\) pions into \(\pi^-\pi^-\pi^+\) using a hydrogen target and confirm the \(\pi_1(1600) \to \rho(770) \pi\) 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 their experimental findings. We study the nonresonant contributions to the \(\pi^-\pi^-\pi^+\) final state using pseudo-data generated on the basis of a Deck model. Subjecting pseudo-data 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 \(J^{PC} = 1^{-+}\) amplitude and also for amplitudes with other \(J^{PC}\) quantum numbers. We investigate for the first time the amplitude of the \(\pi^-\pi^+\) subsystem with \(J^{PC} = 1^{--}\) in the \(3\pi\) amplitude with \(J^{PC} = 1^{-+}\) employing the novel freed-isobar analysis scheme. We reveal this \(\pi^-\pi^+\) amplitude to be dominated by the \(\rho(770)\) for both the \(\pi_1(1600)\) and the nonresonant contribution. We determine the \(\rho(770)\) resonance parameters within the three-pion final state. These findings largely confirm the underlying assumptions for the isobar model used in all previous partial-wave analyses addressing the \(J^{PC} = 1^{-+}\) amplitude.