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

A measurement is presented of decay-time-dependent $CP$ violation in the decays $B^0rightarrow J/psi K^0_mathrm{S}$ and $B^0rightarrowpsi(2S) K^0_mathrm{S}$, where the $J/psi$ is reconstructed from two electrons and the $psi(2S)$ from two muons. The analysis uses a sample of $pp$ collision data recorded 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} Cleft(B^0rightarrow J/psi K^0_mathrm{S}right)&=phantom{+},0.12,pm,0.07pm,0.02,, Sleft(B^0rightarrow J/psi K^0_mathrm{S}right)&=phantom{+},0.83,pm,0.08pm,0.01,, Cleft(B^0rightarrowpsi(2S) K^0_mathrm{S}right)&=-,0.05,pm,0.10pm,0.01,, Sleft(B^0rightarrowpsi(2S) K^0_mathrm{S}right)&=phantom{+},0.84,pm,0.10pm,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 $B^0$-$overline{B}^0$ oscillation. The first uncertainties are statistical and the second are systematic. The two sets of results are compatible with the previous LHCb measurement using $B^0rightarrow J/psi K^0_mathrm{S}$ decays, where the $J/psi$ meson was reconstructed from two muons. The averages of all three sets of LHCb results are begin{equation*} begin{aligned} Cleft(B^0rightarrow[cbar{c}]K^0_mathrm{S}right)&=-0.017 pm 0.029,, Sleft(B^0rightarrow[cbar{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.