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Based on a sample of 1.31×10^{9} J/ψ events collected with the BESIII detector, an amplitude analysis of the isospin-violating decays η^{'}→π^{+}π^{-}π^{0} and η^{'}→π^{0}π^{0}π^{0} is performed. A significant P-wave contribution from η^{'}→ρ^{±}π^{∓} is observed for the first time in η^{'}→π^{+}π^{-}π^{0}. The branching fraction is determined to be B(η^{'}→ρ^{±}π^{∓})=(7.44±0.60±1.26±1.84)×10^{-4}, where the first uncertainty is statistical, the second systematic, and the third model dependent...

*January 6, 2017: Physical Review Letters*