@article{84ff19d3adf34cb98ad4f36729710d87, title = "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", abstract = "A measurement is presented of decay-time-dependent $CP$ violation in the decays $B^0\rightarrow J/\psi K^0_\mathrm{S}$ 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 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} 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 $B^0$-$\overline{B}^0$ oscillation. The first uncertainties are statistical and the second are systematic. The two sets of results are compatible with the previous LHCb measurement using $B^0\rightarrow J/\psi K^0_\mathrm{S}$ 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} 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.", author = "Peter Clarke and Greig Cowan and Stephan Eisenhardt and Franz Muheim and Matthew Needham and Stephen Playfer and LHCb Collaboration", year = "2017", month = nov, day = "27", doi = "10.1007/JHEP11(2017)170", language = "English", volume = "1711", pages = "170", journal = " Journal of High Energy Physics", issn = "1126-6708", publisher = "Springer-Verlag", }