Search for $CP$ violation in the decay ${\tau }^{\mathbf{-}}\to {\pi }^{\mathbf{-}}{K}_s^0\mathbf{(}\mathbf{\ge }O{\pi }^0\mathbf{)}{\nu }_{\tau }$

We report a search for $CP$ violation in the decay ${\tau }^{-}\to {\pi }^{-}{K}_S^0(\ge 0{\pi }^0){\nu }_{\tau }$ using a data set of $437\times {10}^6$ $\tau$-lepton pairs, corresponding to an integrated luminosity of $476{\mathrm{fb}}^{-1}$, collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ storage rings. The $CP$-violating decay-rate asymmetry is determined to be $(-0.36\pm 0.23\pm 0.11)\%$ approximately 2.8 standard deviations from the standard model prediction of $(0.36\pm 0.01)\%$.

Figure 1

Invariant-mass distributions for the combined $e$-tag and $\mu$-tag samples. The label in each plot indicates the reconstructed decay mode (including the charge conjugate mode). Points with error bars represent data whereas the histograms represent the simulated sample. The histogram labeled as “Signal” includes the ${\tau }^{-}\to {\pi }^{-}{K}_S^0(\ge 0{\pi }^0){\nu }_{\tau }$, residual ${\tau }^{-}\to K^{-}{K}_S^0(\ge 0{\pi }^0){\nu }_{\tau }$, and ${\tau }^{-}\to {\pi }^{-}{K}^0{\overline{K}}^0{\nu }_{\tau }$ modes. All selection criteria (including the likelihood ratio requirement), except the invariant-mass ($M_{\mathrm{rec}}$) criterion, have been applied. The vertical lines and arrows indicate the $M_{\mathrm{rec}}<1.8\mathrm{GeV}/c^2$ selection criterion.

Figure 2

The likelihood ratio $y(\tau )$ used to distinguish $\tau$ events from $q\overline{q}$ events (top plot) and the likelihood ratio $y(K_S^0)$ used to select $\tau$ decays with a $K_S^0\to {\pi }^{+}{\pi }^{-}$ (bottom plot). All selection cuts, except the plotted likelihood ratio requirement, have been applied. Points with error bars represent data while histograms correspond to simulated events. The histogram labeled as “Signal” includes the ${\tau }^{-}\to {\pi }^{-}{K}_S^0(\ge 0{\pi }^0){\nu }_{\tau }$, residual ${\tau }^{-}\to K^{-}{K}_S^0(\ge 0{\pi }^0){\nu }_{\tau }$, and ${\tau }^{-}\to {\pi }^{-}{K}^0{\overline{K}}^0{\nu }_{\tau }$ modes. The vertical lines indicate the selection criteria.

Figure 3

The relative selection efficiency as a function of $t/{\tau }_{K_S^0}$ obtained from the Monte Carlo sample. The top plot shows the region $0<t/{\tau }_{K_S^0}<1$ and the bottom plot the region $1<t/{\tau }_{K_S^0}<8$. The solid line is the fit to the points in the displayed region. The relative efficiency is normalized to be unity for the region $0.25<t/{\tau }_{K_S^0}<1.0$.