| This thesis reports a time dependent measurement of the B0s-B&d1; 0s oscillation frequency Deltams using semileptonic decays B0s → D-sℓ+X . We use a data sample of 1 fb-1 of p p collisions at s = 1.96 TeV collected with the CDF II detector at the Fermilab Tevatron Collider to reconstruct ∼61,500 semileptonic B0s decays. This analysis of B0s-B&d1; 0s mixing has a sensitivity of 19.4 ps-1 and shows an evidence of B0s oscillations at Deltams ∼17.75 ps -1 with an amplitude significance of ∼2. In combination with the analyses of ∼8,700 hadronic B0s decays at CDF, we have made the first direct observation of time-dependent B0s-B&d1; 0s flavor oscillations measuring Deltams = 17.77+0.09-0.10 (stat) +/- 0.07 (syst) ps-1. The obtained value of Deltams agrees with the Standard Model expectation. When combined with the world average values for Delta md, mB0 and mB0s&d1; , along with other theoretical input, this result yields the ratio of CKM matrix elements |Vtd/Vts| = 0.2060 +/- 0.0007 exp) +0.0081-0.0060 (theor). |
