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 JPC = 0 − −, 1 − −, 1 − +, and 2 + +, all of which decay predominantly as ρπ states. Two-pion rescattering is described in terms of an Omn{`e}s function, which incorporates the 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.
The main numerics is done with c++/python code which can be found in the repository HISKP-ph/khuri_treiman_solver.
KTMC.jl/scr source code the Khuri-Treiman Monte-Carlo projectKTMC.jl/scripts several exploratory scripts for the projectKTMC.jl/plots preliminary plotsN-001-cartesian-pions [code] Relation of the physical decay to the isospin amplitudes in cartesian coordinatesN-002-covariant3pi [code] Evaluation of the covariant structures in the s-channelN-003-omega [code] early-stage MC experiments on discriminating models