The exotic meson ${\pi }_1(1600)$ with $J^{PC}=1^{-+}$ and its decay into $\rho (770)\pi$

Abstract

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.

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