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

We search for $CP$ violation in a sample of 20 000 Cabibbo-suppressed decays, $D^{+}\to K^{+}{K}_S^0{\pi }^{+}{\pi }^{-}$, and 30 000 Cabibbo-favored decays, $D_s^{+}\to K^{+}{K}_S^0{\pi }^{+}{\pi }^{-}$. We use $520{\mathrm{fb}}^{-1}$ 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 ${\mathcal{A}}_T(D^{+})=(-12.0\pm {10.0}_{\mathrm{stat}}\pm {4.6}_{\mathrm{syst}})\times {10}^{-3}$ and ${\mathcal{A}}_T(D_s^{+})=(-13.6\pm {7.7}_{\mathrm{stat}}\pm {3.4}_{\mathrm{syst}})\times {10}^{-3}$, which are consistent with the standard model expectations.

Figure 1

Distributions of $p^{*}$, $P_1-P_2$, and $L_T$ for $D^{+}$ (top panels) and $D_s^{+}$ (bottom panels) candidates. The distributions for signal and background are shown as solid and dot-dashed histograms, respectively. All distributions are normalized to 1. Signal distributions are extracted from $D^{+}\to K_S^0{\pi }^{+}{\pi }^{+}{\pi }^{-}$ and $D_s^{+}\to K_S^0{K}^{-}{\pi }^{+}{\pi }^{+}$ for $D^{+}$ and $D_s^{+}$ decays, respectively. The background distributions are extracted from the $D_{(s)}^{+}\to K^{+}{K}_S^0{\pi }^{+}{\pi }^{-}$ sidebands.

Figure 2

The $K^{+}{K}_S^0{\pi }^{+}{\pi }^{-}$ mass spectrum in the $D^{+}$ mass region (a) before and (b) after the cut on the likelihood ratio. Similar plots (c) and (d) are drawn for $D_s^{+}$. The curves in (b) and (d) result from the fits described in the text. The distributions of the pull values are also shown. The ${\chi }^2/n_{\mathrm{dof}}$ values from the fits are 0.87 ($D^{+}$) and 0.95 ($D_s^{+}$).

Figure 3

Fits to the four $D^{+}\to K^{+}{K}_S^0{\pi }^{+}{\pi }^{-}$ data subsamples. The pull values are shown above each mass distribution. The ${\chi }^2/n_{\mathrm{dof}}$ values from the fit are 1.07 ($D^{+}$, $C_T>0$), 1.10 ($D^{+}$, $C_T<0$), 1.19 ($D^{-}$, ${\overline{C}}_T>0$), and 0.95 ($D^{-}$, ${\overline{C}}_T<0$).

Figure 4

Fits to the four $D_s^{+}\to K^{+}{K}_S^0{\pi }^{+}{\pi }^{-}$ data subsamples. The pull values are shown above each mass distribution. The ${\chi }^2/n_{\mathrm{dof}}$ values from the fit are 1.05 ($D_s^{+}$, $C_T>0$), 1.03 ($D_s^{+}$, $C_T<0$), 1.15 ($D_s^{-}$, ${\overline{C}}_T>0$), and 1.02 ($D_s^{-}$, ${\overline{C}}_T<0$).