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

Abstract

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 amplitude decompositions for four decay processes with total $$J^{PC} = 0^{--}$$ J PC = 0 - - , $$1^{--}$$ 1 - - , $$1^{-+}$$ 1 - + , and $$2^{++}$$ 2 + + , all of which decay predominantly as $$\rho \pi $$ ρ π states. Two-pion rescattering is described in terms of an Omnès function, which incorporates the $$\rho $$ ρ 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.