Ablikim, M.Achasov, M. N.Ai, X. C.Albayrak, O.Albrecht, M.Ambrose, D. J.Amoroso, A.Lou, XinchouBESIII Collaboration2018-05-242018-05-242017-01-062017-01-060031-9007http://hdl.handle.net/10735.1/5760Based on a sample of 1.31 x 10⁹ J/ψ events collected with the BESIII detector, an amplitude analysis of the isospin-violating decays η′ → π⁺π⁻π⁰ and η′ → π⁰π⁰π⁰ is performed. A significant P-wave contribution from η′ → ρ^{±} π^{∓} is observed for the first time in η′ → π⁺π⁻π⁰. The branching fraction is determined to be ℬ(η′ → ρ^{±} π^{∓}) = (7.44 ± 0.60 ± 1.26 ± 1.84) x 10⁻⁴, where the first uncertainty is statistical, the second systematic, and the third model dependent. In addition to the nonresonant S-wave component, there is a significant σ meson component. The branching fractions of the combined S-wave components are determined to be ℬ(η′ → π⁺π⁻π⁰)s = (37.63 ± 0.77 ± 2.22 ± 4.48) x 10⁻⁴ and ℬ(η′ → π⁰π⁰π⁰) = (35.22 ± 0.82 ± 2.54) x 10⁻⁴, respectively. The latter one is consistent with previous BESIII measurements.en©2017 American Physical Society. All Rights Reserved.Hadron interactionsHadrons—DecayField theory (Physics)Quantum field theorySeismic wavesBranching fractions (Nuclear physics)Isobaric spinShear wavesarticleAblikim, M., M. N. Achasov, X. C. Ai, O. Albayrak, et al. 2017. "Amplitude Analysis of the Decays η′ → π⁺π⁻π⁰ and η′ → π⁰π⁰π⁰." Physical Review Letters 118(1), doi:10.1103/PhysRevLett.118.0120011181