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A measurement is presented of decay-time-dependent $CP$ violation in thedecays $B^0\rightarrow J/\psi K^0_\mathrm{S}$ and $B^0\rightarrow\psi(2S)K^0_\mathrm{S}$, where the $J/\psi$ is reconstructed from two electrons and the$\psi(2S)$ from two muons. The analysis uses a sample of $pp$ collision datarecorded with the LHCb experiment at centre-of-mass energies of 7 and 8 TeV,corresponding to an integrated luminosity of 3 $\mathrm{fb}^{-1}$. The$CP$-violation observables are measured to be \begin{equation*} \begin{aligned}C\left(B^0\rightarrow J/\psiK^0_\mathrm{S}\right)&=\phantom{+}\,0.12\,\pm\,0.07\pm\,0.02\,,S\left(B^0\rightarrow J/\psiK^0_\mathrm{S}\right)&=\phantom{+}\,0.83\,\pm\,0.08\pm\,0.01\,,C\left(B^0\rightarrow\psi(2S)K^0_\mathrm{S}\right)&=-\,0.05\,\pm\,0.10\pm\,0.01\,,S\left(B^0\rightarrow\psi(2S)K^0_\mathrm{S}\right)&=\phantom{+}\,0.84\,\pm\,0.10\pm\,0.01\,, \end{aligned}\end{equation*} where $C$ describes $CP$ violation in the direct decay, and $S$describes $CP$ violation in the interference between the amplitudes for thedirect decay and for the decay after $B^0$-$\overline{B}^0$ oscillation. Thefirst uncertainties are statistical and the second are systematic. The two setsof results are compatible with the previous LHCb measurement using$B^0\rightarrow J/\psi K^0_\mathrm{S}$ decays, where the $J/\psi$ meson wasreconstructed from two muons. The averages of all three sets of LHCb resultsare \begin{equation*} \begin{aligned}C\left(B^0\rightarrow[c\bar{c}]K^0_\mathrm{S}\right)&=-0.017 \pm 0.029\,,S\left(B^0\rightarrow[c\bar{c}]K^0_\mathrm{S}\right)&=\phantom{+}0.760 \pm0.034\,, \end{aligned} \end{equation*} under the assumption that higher-ordercontributions to the decay amplitudes are negligible. The uncertainties includestatistical and systematic contributions.

Measurement of $CP$ violation in $B^0\rightarrow J/\psi K^0_\mathrm{S}$ and $B^0\rightarrow\psi(2S) K^0_\mathrm{S}$ decays