Search for the $C\!P$-violating strong decays $\eta \to \pi^+\pi^-$ and $\eta^\prime(958) \to \pi^+\pi^-$

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.