Tagged time-dependent angular analysis of $B_s^0 \to J/\psi\phi$ decays at LHCb

The interference between $B_s^0$ decays to $J/\psi \phi$ either directly or via $B_s^0-\bar{B}_s^0$ oscillation gives rise to a $CP$ violating phase $\phi_s$. Using a sample of about $21,200$ $B_s^0\to J/\psi \phi$ events extracted from 1$fb^{-1}$ of $pp$ collisions collected during the 2011 LHC run at a center of mass energy of $\sqrt{s}=7$ TeV, we fit for nine physics parameters, including the phase $\phi_s$, the mean decay width difference $\Delta\Gamma_s$ and the decay width $\Gamma_s$. We find the following result: \begin{align} \phi_s \, \, = \, \, -0.001 \, \, \pm \, \, 0.101 \, \, \text{(stat)} \, \, \pm \, \, 0.027 \, \, \text{(syst)} \, \, \text{rad}, \\ \, \, \Gamma_s \, \, = \, \, 0.6580 \, \, \pm \, \, 0.0054 \, \, \text{(stat)} \, \, \pm \, \, 0.0066 \, \, \text{(syst)} \text{ps} ^{-1}, \\ \Delta\Gamma_s \, \, = \, \, 0.116 \, \, \pm \, \, 0.018 \, \, \text{(stat)} \, \, \pm \, \, 0.006 \text{(syst)} \, \, \text{ps} ^{-1} . \end{align