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

A measurement is presented of decay-time-dependent $CP$ violation in the decays $B^0\to J\mathrm{/}\psi K_{\mathrm{S}}^0$ and $B^0\rightarrow\psi(2S) K^0_$\mathrm{S}$$,wherethe$J/\psi$isreconstructedfromtwoelectronsandthe$\psi(2S)$fromtwomuons\mathrm{.}Theanalysisusesasampleof$pp$ collision data recorded with the LHCb experiment at centre-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 ${\mathrm{f}\mathrm{b}}^{-1}$. The $CP$-violation observables are measured to be \begin{equation*} \begin{aligned} C\left(B^0\rightarrow J/\psi K^0_$\mathrm{S}$\right)&=\phantom{+},0.12,\pm,0.07\pm,0.02,, S\left(B^0\rightarrow J/\psi K^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 the direct decay and for the decay after $B^0$-${\bar{B}}^0$ oscillation. The first uncertainties are statistical and the second are systematic. The two sets of results are compatible with the previous LHCb measurement using $B^0\to J\mathrm{/}\psi K_{\mathrm{S}}^0$ decays, where the $J\mathrm{/}\psi$ meson was reconstructed from two muons. The averages of all three sets of LHCb results are \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 \pm 0.034,, \end{aligned} \end{equation*} under the assumption that higher-order contributions to the decay amplitudes are negligible. The uncertainties include statistical and systematic contributions.