Search for $CP$ violation in $D^+_s\to K_S^0\pi^+$, $D^+\to K_S^0K^+$ and $D^+\to\phi\pi^+$ decays

A search for charge-parity ($CP$) violation in Cabibbo-suppressed $D^+_s\to K_S^0\pi^+$, $D^+\to K_S^0K^+$ 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^+) &=\left(\phantom{-}1.3\phantom{0}\pm1.9\phantom{0}\pm0.5\phantom{0}\right)\times10^{-3},\\ \mathcal{A}_{CP}(D^+\to K_S^0 K^+) &=\left(-0.09\pm0.65\pm0.48\right)\times10^{-3},\\ \mathcal{A}_{CP}(D^+\to \phi \pi^+) &=\left(\phantom{-}0.05\pm0.42\pm0.29\right)\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. A combination with previous LHCb measurements, based on data collected at 7 and 8 TeV, is also reported.