Search for the $C\text{\hspace{0.17em}⁣}P$-violating strong decays $\eta \to {\pi }^{+}{\pi }^{-}$ and ${\eta }^{\mathrm{\prime }}(958)\to {\pi }^{+}{\pi }^{-}$

A search for the $C\text{\hspace{0.17em}⁣}P$-violating strong decays $\eta \to {\pi }^{+}{\pi }^{-}$ and ${\eta }^{\mathrm{\prime }}(958)\to {\pi }^{+}{\pi }^{-}$ has been performed using approximately $2.5 \times 10^{7}$eventsofeachofthedecays$D^+ \to \pi^+\pi^+\pi^-$and$D_s^+ \to \pi^+\pi^+\pi^-$, 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 $D_{(s)}^{+}\to {\pi }^{+}{\eta }^{(\mathrm{\prime })}$ with $\eta^{(\prime)} \to \pi^+\pi^-$, and upper limits at 90% confidence level are set on the branching fractions, $\mathcal{B}(\eta \to {\pi }^{+}{\pi }^{-})<1.6\times {10}^{-5}$ and $\mathcal{B}({\eta }^{\mathrm{\prime }}\to {\pi }^{+}{\pi }^{-})<1.8\times {10}^{-5}$. The limit for the $\eta$ decay is comparable with the existing one, while that for the ${\eta }^{\mathrm{\prime }}$ is a factor of three smaller than the previous limit.