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 $$J^{PC} = 0^{--}$$ , $$1^{--}$$ , $$1^{-+}$$ , 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.
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"title": "Analysis of rescattering effects in $$3\\pi $$ <math> <mrow> <mn>3</mn> <mi>\u03c0</mi> </mrow> </math> final states"
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"value": "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 $$J^{PC} = 0^{--}$$ <math> <mrow> <msup> <mi>J</mi> <mrow> <mi>PC</mi> </mrow> </msup> <mo>=</mo> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mo>-</mo> </mrow> </msup> </mrow> </math> , $$1^{--}$$ <math> <msup> <mn>1</mn> <mrow> <mo>-</mo> <mo>-</mo> </mrow> </msup> </math> , $$1^{-+}$$ <math> <msup> <mn>1</mn> <mrow> <mo>-</mo> <mo>+</mo> </mrow> </msup> </math> , and $$2^{++}$$ <math> <msup> <mn>2</mn> <mrow> <mo>+</mo> <mo>+</mo> </mrow> </msup> </math> , all of which decay predominantly as $$\\rho \\pi $$ <math> <mrow> <mi>\u03c1</mi> <mi>\u03c0</mi> </mrow> </math> states. Two-pion rescattering is described in terms of an Omn\u00e8s function, which incorporates the $$\\rho $$ <math> <mi>\u03c1</mi> </math> resonance. Inclusion of crossed-channel effects is achieved by solving the Khuri\u2013Treiman 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."
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