Production Effects and Final-state Interactions in $\ddot{I}{€}_1\to 3\ddot{I}€$

Abstract

We investigate the $\ddot{I}{€}_1(1600)$ signal channel of $3\ddot{I}€$ in the $J^{PC}=1^{-+}[\ddot{I}€\ddot{I}€{]}_{1^{--}}\ddot{I}€P$-wave. This channel has recently been analyzed by the COMPASS collaboration using the ``freed-isobar" technique which provides direct experimental access to the lineshape modifications of the $P$-wave $\ddot{I}€\ddot{I}€$ sub-channel arising from both final state interactions and production processes such as the Deck mechanism. We motivate a unified formalism combining production effects and final state interactions using the Khuri-Treiman formalism, which is consistent with low-energy unitarity, analyticity, and crossing symmetry, seeded by an initial production amplitude. We demonstrate that the precise lineshape of the $\ddot{I}€\ddot{I}€$ mass spectrum can be used to determine the relative strength and complex phase of different production mechanisms contributing to the $3\ddot{I}€$ final state. We conduct a global fit of the $\ddot{I}{€}_1$ freed-isobar data set, yielding a multi-dimensional parameterization of the $\ddot{I}{€}_1\to 3\ddot{I}€$ decay amplitude at COMPASS as a function of both decay and production variables. We identify the contributions from short-range production and the Deck mechanism and extract the total $3\ddot{I}€$ invariant mass dependence which will be important for a future extraction of the $\ddot{I}{€}_1$ pole position in the $\ddot{I}\ddot{I}€$ channel.

24 pages, 18 figures

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