Search for $CP$ violation in $D_s^+ o K_S^0 pi^+$, $D^+ o K_S^0 K^+$ and $D^+ o phi pi^+$ decays.

A search for charge-parity ($CP$) violation in Cabibbo-suppressed $D_s^+to K_S^0 pi^+$, $D^+to K_S^0 K^+$ and $D^+to phi pi^+$ decays is reported using proton-proton collision data, corresponding to an integrated luminosity of 3.8 fb$^{-1}$, collected at a center-of-mass energy of 13 TeV with the LHCb detector. High-yield samples of kinematically and topologically similar Cabibbo-favored $D_{(s)}^+$ decays are analyzed to subtract nuisance asymmetries due to production and detection effects, including those induced by $CP$ violation in the neutral kaon system. The results are begin{align*} mathcal{A}_{CP}(D_s^+to K_S^0 pi^+) u0026=left(phantom{-}1.3phantom{0}pm1.9phantom{0}pm0.5phantom{0}right)times10^{-3}, mathcal{A}_{CP}(D^+to K_S^0 K^+) u0026=left(-0.09pm0.65pm0.48right)times10^{-3}, mathcal{A}_{CP}(D^+to phi pi^+) u0026=left(phantom{-}0.05pm0.42pm0.29right)times10^{-3}, end{align*} where the first uncertainties are statistical and the second systematic. They are the most precise measurements of these quantities to date, and are consistent with $CP$ symmetry.