Measurement of $CP$ asymmetries in $D^{\pm}\rightarrow \eta^{\prime} \pi^{\pm}$ and $D_s^{\pm}\rightarrow \eta^{\prime} \pi^{\pm}$ decays

A search for $CP$ violation in $D^{\pm}\rightarrow \eta^{\prime} \pi^{\pm}$ and $D^{\pm}_{s}\rightarrow \eta^{\prime} \pi^{\pm}$ decays is performed using proton-proton collision data, corresponding to an integrated luminosity of $3$ fb$^{-1}$, recorded by the LHCb experiment at centre-of-mass energies of $7$ and $8$ TeV. The measured $CP$-violating charge asymmetries are $A_{CP}(D^{\pm} \rightarrow \eta^{\prime} \pi^{\pm})=(-0.61\pm 0.72 \pm 0.53 \pm 0.12)\%$ and $A_{CP}(D^{\pm}_{s}\rightarrow \eta^{\prime} \pi^{\pm})=(-0.82\pm 0.36 \pm 0.22 \pm 0.27)\%$, where the first uncertainties are statistical, the second systematic, and the third are the uncertainties on the $A_{CP}(D^{\pm} \rightarrow K^0_S \pi^{\pm})$ and $A_{CP}(D^{\pm}_{s}\rightarrow \phi \pi^{\pm})$ measurements used for calibration. The results represent the most precise measurements of these asymmetries to date.