Analysis of rescattering effects in $3\pi$ final states

Abstract

Decays into three particles are often described in terms of two-body resonances and a non-interacting spectator particle. To go beyond this simplest isobar model, crossed-channel rescattering effects need to be accounted for. We quantify the importance of these rescattering effects in three-pion systems for different decay masses and angular-momentum quantum numbers. We provide the amplitude decompositions for four decay processes with total $J^{PC}=0^{--}$, $1^{--}$, $1^{-+}$, and $2^{++}$, all of which decay predominantly as $\rho \pi$ states. Two-pion rescattering is described in terms of an Omnès function, which incorporates the $\rho$ resonance. Inclusion of crossed-channel effects is achieved by solving the Khuri-Treiman integral equations. The unbinned log-likelihood estimator is used to determine the significance of the rescattering effects beyond two-body resonances; we compute the minimum number of events necessary to unambiguously find these in future Dalitz-plot analyses. Kinematic effects that enhance or dilute the rescattering are identified for the selected set of quantum numbers and various masses.

arXiv comment22 pages, 13 figures; v2: reconstruction theorem for 2++ channel corrected

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• Measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ cross section from threshold to 1.2 GeV with the CMD-3 detector
• A phenomenological estimate of isospin breaking in hadronic vacuum polarization
• Khuri-Treiman analysis of $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$
• Dispersive analysis of the $J/\psi \to {\pi }^0{\gamma }^{\ast }$ transition form factor with $\rho$-$\omega$ mixing effects
• Dalitz-plot decomposition for the $e^{+}{e}^{-}\to J/\psi \pi \pi (K\bar{K})$ and $e^{+}{e}^{-}\to h_c\pi \pi$ processes
• Understanding large localized CP violation in $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ using dispersive methods
• Measurement of the branching fraction of $J/\psi \to \rho \pi$ at KEDR