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

A measurement is presented of decay-time-dependent CP violation in the decays B$^{0}$ → J/ψ K$_{S}^{0}$ and B$^{0}$ → ψ(2S)K$_{S}^{0}$ , where the J/ψ is reconstructed from two electrons and the ψ(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 fb$^{−1}$. The CP -violation observables are measured to be $ \begin{array}{l}C\left({B}^0\to J/\psi \kern0.5em {K}_{\mathrm{S}}^0\right)=0.12\pm 0.07\pm 0.02,\\ {}S\left({B}^0\to J/\psi \kern0.5em {K}_{\mathrm{S}}^0\right)=0.83\pm 0.08\pm 0.01,\\ {}C\left({B}^0\to \psi (2S){K}_{\mathrm{S}}^0\right)=-0.05\pm 0.10\pm 0.01,\\ {}S\left({B}^0\to \psi (2S){K}_{\mathrm{S}}^0\right)=0.84\pm 0.10\pm 0.01,\end{array} $ 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$^{0}$ → J/ψ K$_{S}^{0}$ decays, where the J/ψ meson was reconstructed from two muons. The averages of all three sets of LHCb results are $ \begin{array}{l}C\left({B}^0\to \left[c\overline{c}\right]{K}_{\mathrm{S}}^0\right)=-0.017\pm 0.029,\\ {}S\left({B}^0\to \left[c\overline{c}\right]{K}_{\mathrm{S}}^0\right)=0.760\pm 0.034,\end{array} $ under the assumption that higher-order contributions to the decay amplitudes are negligible. The uncertainties include statistical and systematic contributions.