Tagged time-dependent angular analysis of $B_s\to J/\psi\phi$ decays with 337~pb$^{-1}$ at LHCb

The interference between $B_s$ decays to $J/\psi\phi$ either directly or via $B_s-\overline{B}_s$ oscillation gives rise to a $CP$ violating phase $\phi_s^{J\psi\phi}$. Using a sample of $8276 \pm 94$ $B_s\to J/\psi\phi$ events extracted from 337~pb$^{-1}$ of $pp$ collisions collected during the 2011 LHC run at $\sqrt{s}=7$~TeV, we fit for nine physics parameters, among which the phase $\phi_s^{J\psi\phi}$, the decay width difference $\Delta\Gamma_s$ and the decay width $\Gamma_s$. For one of two ambiguous solutions ($\phi_s^{J\psi\phi} \leftrightarrow \pi - \phi_s^{J\psi\phi};~\Delta \Gamma_s \leftrightarrow - \Delta \Gamma_s$) we find \[ \begin{array}{ccllllllll} \phi_s^{J\psi\phi} &\;=\; & 0.13 &\pm & 0.18 & \text{(stat)} &\pm & 0.07 & \text{(syst)} & \text{rad},\\ \Gamma_s &\;=\; & 0.656 &\pm & 0.009 & \text{(stat)} &\pm & 0.008& \text{(syst)} & \text{ps}^{-1}, \\ \Delta\Gamma_s &\;=\; & 0.123 &\pm & 0.029 & \text{(stat)} &\pm & 0.011& \text{(syst)} & \text{ps}^{-1}, \\ \end{array} \] in good agreement with the Standard Model predictions. This is the most precise measurement of $\phi_s^{J\psi\phi}$ and $\Gamma_s$. Furthermore, it is the first direct experimental evidence of a non-zero value of $\Delta\Gamma_s$.