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

TL;DR

This study confirms the existence of the exotic $ ho(770) o ext{pi}$ decay in the $ ho(770) ext{pi}$ channel, clarifies previous conflicting results through analysis model comparison, and introduces a novel freed-isobar analysis scheme for the $3 ext{pi}$ final state.

Contribution

It provides a comprehensive partial-wave analysis of the $J^{PC} = 1^{-+}$ amplitude, reconciling previous discrepancies and introducing a new freed-isobar analysis method for the $3 ext{pi}$ system.

Findings

Confirmed the $ ho(770) ext{pi}$ decay amplitude of $ ho(770)$ in the $1^{-+}$ channel.

Reconciled conflicting previous results by analyzing analysis models and kinematic dependencies.

Introduced a novel freed-isobar analysis scheme revealing the $ ho(770)$ dominance in the $3 ext{pi}$ system.

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.