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A search for the $C\!P$-violating strong decays $\eta \to \pi^+\pi^-$ and$\eta^\prime(958) \to \pi^+\pi^-$ has been performed using approximately $2.5\times 10^{7}$ events of each of the decays $D^+ \to \pi^+\pi^+\pi^-$ and$D_s^+ \to \pi^+\pi^+\pi^-$, recorded by the LHCb experiment. The data setcorresponds to an integrated luminosity of 3.0 fb$^{-1}$ of $pp$ collision datarecorded during LHC Run 1 and 0.3 fb$^{-1}$ recorded in Run 2. No evidence isseen for $D^+_{(s)} \to \pi^+ \eta^{(\prime)}$ with $\eta^{(\prime)} \to\pi^+\pi^-$, and upper limits at 90% confidence level are set on the branchingfractions, $\mathcal{B}(\eta \to \pi^+\pi^-) < 1.6 \times 10^{-5}$ and$\mathcal{B}(\eta^\prime \to \pi^+\pi^-) < 1.8 \times 10^{-5}$. The limit forthe $\eta$ decay is comparable with the existing one, while that for the$\eta^\prime$ is a factor of three smaller than the previous limit.

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