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The first measurement of decay-time-dependent CP asymmetries in the decay B-S(0) -> J/psi K-S(0) and an updated measurement of the ratio of branching fractions B(B-S(0) -> J/psi K-S(0))/B(B-0 -> J/psi K-S(0)) are presented. The results are obtained using data corresponding to an integrated luminosity of 3.0 fb(-1) of proton-proton collisions recorded with the LHCb detector at centre-of-mass energies of 7 and 8 TeV. The results on the CP asymmetries are A(Delta Gamma)(B-S(0) -> J/psi K-S(0)) = 0.49 +/- (0.77)(0.65)(stat) +/- 0.06(syst), C-dir(B-S(0) -> J/psi K-S(0)) = -0.28 +/- 0.41(stat) +/- 0.08(syst), S-mix(B-S(0) -> J/psi K-S(0)) = -0.08 +/- 0.40(stat) +/- 0.08(syst). The ratio B(B-S(0) -> J/psi K-S(0))/B(B-0 -> J/psi K-S(0)) is measured to be 0.0431 +/- 0.0017(stat) +/- 0.0012(syst) +/- 0.0025(f(s)/f(d)), where the last uncertainty is due to the knowledge of the B-S(0) and B-0 production fractions.
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