Search for CP violation using $T$-odd correlations in $D^+\rightarrow K^+K^0_S\pi^+\pi^-$ and $D_s^+\rightarrow K^+ K^0_S\pi^+\pi^-$ decays

We search for CP violation in a sample of 20000 Cabibbo-suppressed decays, $D^+\rightarrow K^+K^0_S\pi^+\pi^-$, and 30000 Cabibbo-favored decays, $D_s^+\rightarrow K^+K^0_S\pi^+\pi^-$. We use 520 $fb^{-1}$ of data recorded by the BaBar detector at the PEP-II asymmetric-energy $e^+e^-$ collider operating at center of mass energies near 10.6 $GeV$. We search for CP violation in the difference between the $T$-odd asymmetries obtained using triple product correlations of the $D^+$ ($D_s^+$) and $D^-$ ($D_s^-$) decays, respectively. The $T$ violation parameter values obtained are $\mathcal{A}_T(D^+) = (-12.0 \pm 10.0_{stat} \pm 4.6_{syst})\times 10^{-3}$ and $\mathcal{A}_T(D_s^+) = (-13.6 \pm 7.7_{stat} \pm 3.4_{syst}) \times10^{-3}$, which are consistent with the standard model expectations.