Measurements of time-dependent $CP$ violation in $B^0\to \psi (2S)K_S^0$ decays

We report improved measurements of time-dependent $CP$ violation parameters for $B^0({\overline{B}}^0)\to \psi (2S)K_S^0$. This analysis is based on a data sample of $657\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB energy-asymmetric $e^{+}{e}^{-}$ collider. We fully reconstruct one neutral $B$ meson in the $\psi (2S)K_S^0$ $CP$-eigenstate decay channel, and the flavor of the accompanying $B$ meson is identified to be either $B^0$ or ${\overline{B}}^0$ from its decay products. $CP$ violation parameters are obtained from the asymmetries in the distributions of the proper-time intervals between the two $B$ decays: ${\mathcal{S}}_{\psi (2S)K_S^0}=+0.72\pm 0.09(\mathrm{stat})\pm 0.03(\mathrm{syst})$, ${\mathcal{A}}_{\psi (2S)K_S^0}=+0.04\pm 0.07(\mathrm{stat})\pm 0.05(\mathrm{syst})$. These results are in agreement with results from measurements of $B^0\to J/\psi K^0$.

Figure 1

(a) $\Delta E$ distribution within the $M_{\mathrm{bc}}$ signal region, (b) $M_{\mathrm{bc}}$ distribution within the $\Delta E$ signal region for $B^0\to \psi (2S)K_S^0$. The solid curves show the fits to the signal plus background distributions, while the dashed curves show the background contributions. The small contribution from peaking backgrounds is discussed in the text.

Figure 2

The top plot shows the $\Delta t$ distributions for $q=+1$ and $q=-1$ with no requirement on $r$. The dashed curve is the sum of backgrounds, while the solid curves are the sum of signal and backgrounds. The bottom plot is the raw asymmetry of well-tagged events ($r>0.5$, 45% of the total). The solid curve shows the result of the unbinned maximum-likelihood fit.