Search for the CP-violating strong decays η → π⁺π⁻ and η^'(958)→π⁺π⁻

A search for the CP-violating strong decays η→π⁺π⁻ and η^'(958)→π⁺π⁻ has been performed using approximately 2.5×10⁷ events of each of the decays D⁺→π⁺π⁺π⁻ and D_s ⁺→π⁺π⁺π⁻, recorded by the LHCb experiment. The data set corresponds to an integrated luminosity of 3.0 fb⁻¹ of pp collision data recorded during LHC Run 1 and 0.3 fb⁻¹ recorded in Run 2. No evidence is seen for D_(s) ⁺→π⁺η^(') with η^(')→π⁺π⁻, and upper limits at 90% confidence level are set on the branching fractions, B(η→π⁺π⁻)<1.6×10⁻⁵ and B(η^'→π⁺π⁻)<1.8×10⁻⁵. The limit for the η decay is comparable with the existing one, while that for the η^' is a factor of three smaller than the previous limit.