Amplitude Analysis of the Decays η′ → π⁺π⁻π⁰ and η′ → π⁰π⁰π⁰

Based 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.