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 Ds+→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.