We report on a measurement of b-hadron lifetimes in the fully reconstructed decay modes B+→J/ψK+, B0→J/ψK*(892)0, B0→J/ψKs0, and Λb0→J/ψΛ0 using data corresponding to an integrated luminosity of 4.3 fb-1, collected by the CDF II detector at the Fermilab Tevatron. The measured lifetimes are τ(B+)=[1.639±0.009(stat)±0.009(syst)] ps, τ(B0)=[1.507±0.010(stat)±0.008(syst)] ps, and τ(Λb0)=[1.537±0.045(stat)±0.014(syst)] ps. The lifetime ratios are τ(B+)/τ(B0)=[1.088±0.009(stat)±0.004(syst)] and τ(Λb0)/τ(B0)=[1.020±0.030(stat)±0.008(syst)]. These are the most precise determinations of these quantities from a single experiment.
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