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Using a data sample of pp collisions corresponding to an integrated luminosity of $3~ \rm fb^{-1}$, the $\Xi_b^-$ and $\Omega_b^-$ baryons are reconstructed in the $\Xi_b^- \rightarrow J/\psi \Xi^-$ and $\Omega_b^- \rightarrow J/\psi \Omega^-$ decay modes and their lifetimes measured to be $\tau (\Xi_b^-) = 1.55\, ^{+0.10}_{-0.09}~{\rm(stat)} \pm 0.03\,{\rm(syst)}$ ps, $\tau (\Omega_b^-) = 1.54\, ^{+0.26}_{-0.21}~{\rm(stat)} \pm 0.05\,{\rm(syst)}$ ps.
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