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This thesis describes a measurement of the proper lifetime of the B{sub s}{sup 0} mesons produced in proton-antiproton collisions at a center of mass energy of 1.96 TeV, collected by the CDF experiment at Fermilab. The B{sub s}{sup 0} meson lifetime is measured in its semileptonic decay mode, B{sub s}{sup 0} {yields} {ell}{sup +}{nu}{sub {ell}}D{sub s}{sup -}. The D{sub s}{sup -} meson candidates are reconstructed in the decay mode D{sub s}{sup -} {yields} {phi}{pi}, with {phi} {yields} K{sup +}K{sup -}, in a trigger sample which requires a muon or an electron and another track which has a large impact parameters. The large impact parameter track is required by the silicon vertex trigger which is an innovative triggering device which has not previously been used in lifetime measurements. A total of 905 {+-} B{sub s}{sup 0} candidates are reconstructed in a sample which has an integrated luminosity of 140 pb{sup -1} using data gathered between February 2002 and August 2003. The pseudo-proper lifetime distribution of these candidates is fitted with an unbinned maximum likelihood fit. This fit takes into account the missing momentum carried by the neutrino and the bias caused by requiring a track with large impact parameter by modeling these effects in simulations. The fit yields the result for the B{sub s}{sup 0} proper lifetime: c{tau}(B{sub s}{sup 0}) = 419 {+-} 28{sub -13}{sup +16} {micro}m and {tau}(B{sub s}{sup 0}) = 1.397 {+-} 0.093{sub -0.043}{sup +0.053} ps where the first error is statistical and the second is systematic

A Measurement of the Bs Lifetime at CDF Run II