Tagged time-dependent angular analysis of $B^0_s \to J/\psi\phi$ decays with the 2010 LHCb data

The interference between $B^0_s$ decays to $J\psi\phi$ either directly or via $B^0_s-\bar{B}^0_s$ oscillation gives rise to a CP violating phase $\phi_s^{J/\psi\phi}$. In the Standard Model, this phase is approximately -2$\beta_s$, where $\beta_s$ = arg (-$V_{ts}V_{tb}^*/V_{cs}V_{cb}^*$). We have performed a measurement of $\phi^{J\psi\phi}_s$ using a sample that contains 836 $\pm$ 60 $B^0_s\to J/\psi\phi$ events extracted from 36 pb$^{-1}$ of $pp$ collisions collected during the 2010 LHC run at $\sqrt{s}$ = 7 TeV. The result is presented as a two-dimensional region in the $\phi_s$-$\Delta\Gamma_s$ plane. The probability of a fluctuation from the Standard Model expectation to the observed result for $\phi_s$ and $\Delta\Gamma_s$ is 22% (``1.2$\sigma$''). We derive a one-dimensional interval at 68% CL of $\phi_s \in$ [-2.7, -0.5] rad.