We report on a measurement of the flavor-specific $B^{0}_{s}$ lifetime and of the $D^{-}_{s}$ lifetime using proton-proton collisions at center-of-mass energies of 7 and 8 TeV, collected by the LHCb experiment and corresponding to 3.0 fb$^{-1}$ of integrated luminosity. Approximately 407 000 $B^{0}_{s} rightarrow D^{(*)-}_{s} mu^{+} u_mu $ decays are partially reconstructed in the $K^{+}K^{-}pi^{-}mu^{+}$ final state. The $B^{0}_{s}$ and $D^{-}_{s}$ natural widths are determined using, as a reference, kinematically similar $B^{0} rightarrow D^{(*)-}mu^{+} u_mu$ decays reconstructed in the same final state. The resulting differences between widths of $B^{0}_{s}$ and $B^{0}$ mesons and of $D^{-}_{s}$ and $D^{-}$ mesons are $Delta_Gamma(B) =-0.0115 pm 0.0053 (stat) pm 0.0041 (syst)$ ps$^{-1}$ and $Delta_Gamma(D) = 1.0131 pm 0.0117 (stat) pm 0.0065 (syst)$ ps$^{-1}$, respectively. Combined with the known $B^{0}$ and $D^{-}$ lifetimes, these yield the flavor-specific $B^{0}_{s}$ lifetime, $tau^{rm fs}_{B^{0}_{s}} = 1.547 pm 0.013 (stat) pm 0.010 (syst) pm 0.004 (tau_{B})$ ps and the $D^{-}_{s}$ lifetime, $tau_{D^{-}_{s}} = 0.5064 pm 0.0030 (stat) pm 0.0017 (syst) pm 0.0017 (tau_{D})$ ps The last uncertainties originate from the limited knowledge of the $B^0$ and $D^{-}$ lifetimes. The results improve upon current determinations.
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