Measurement of the $B^0_s$ Width Difference and Mixing Phase in the Decay $B^0_s\rightarrow J/\psi \phi$

In the standard model (SM), the light ($L$) and heavy ($H$) mass eigenstates of the mixed ($B^0_s$, $\bar{B^0_s}$) system are expected to have a sizable mass and decay width difference, $\Delta M \equiv M_H - M_L$ and $\Delta \Gamma \equiv \Gamma_L - \Gamma_H$. The CP violating phase, $\phi_{s}$, defined as the relative phase of the off-diagonal elements of the mass and decay matrices in the $B^0_s$ $-$ $\bar{B^0_s}$ basis, is predicted to be small. From an analysis of the ``untagged'' $B^0_s\rightarrow J/\psi \phi$ time-dependent angular distributions, we measure the average lifetime ($\overline \tau$), $\Delta \Gamma$, and $\phi_ {s}$. To improve the sensitivity of the measurement, we have extended this analysis by using flavor tagging information when available.