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

Abstract

We study the spin-exotic $J^{PC}=1^{-+}$ amplitude in single-diffractive dissociation of 190 GeV$/c$ pions into $\ddot{I}{€}^{-}\ddot{I}{€}^{-}\ddot{I}{€}^{+}$ using a hydrogen target and confirm the $\ddot{I}{€}_1(1600)\to \ddot{I}(770)\ddot{I}€$ 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 $\ddot{I}{€}^{-}\ddot{I}{€}^{-}\ddot{I}{€}^{+}$ 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 $\ddot{I}{€}^{-}\ddot{I}{€}^{+}$ subsystem with $J^{PC}=1^{--}$ in the $3\ddot{I}€$ amplitude with $J^{PC}=1^{-+}$ employing the novel freed-isobar analysis scheme. We reveal this $\ddot{I}{€}^{-}\ddot{I}{€}^{+}$ amplitude to be dominated by the $\ddot{I}(770)$ for both the $\ddot{I}{€}_1(1600)$ and the nonresonant contribution. We determine the $\ddot{I}(770)$ 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.