Flavour tagged time dependent angular analysis of the $B_s \rightarrow J/\psi \phi$ decay and extraction of $\Delta \Gamma$ and the weak phase $\phi_s$ in ATLAS

A measurement of the $B_s \rightarrow J/\psi \phi$ decay parameters, updated to include flavour tagging is reported using $4.9$fb$^{-1}$ of integrated luminosity collected by the ATLAS detector from $pp$ collisions recorded in 2011. The values measured for the physical parameters are: \begin{eqnarray*} \phi_s = 0.12 \pm 0.25~\rm{(stat.)}\pm 0.11~\rm{(syst.)}~rad \\ \Delta \Gamma_s = 0.053 \pm 0.021~\rm{(stat.)}\pm 0.009~\rm{(syst.)~ps}^{-1} \\ \Gamma_s = 0.677 \pm 0.007 ~\rm{(stat.)}\pm 0.003 ~\rm{(syst.)~ps}^{-1}\\ |A_{0}(0)|^2 = 0.529 \pm 0.006 \rm{(stat.)}\pm 0.011~\rm{(syst.)}\\ |A_{\parallel}(0)|^2 = 0.220 \pm 0.008 \rm{(stat.)}\pm 0.009~\rm{(syst.)}\\ \delta_\perp = 3.89 \pm 0.46 ~\rm{(stat.)}\pm \ 0.13~\rm{(syst.)}~rad \\ \end{eqnarray*} where the parameter $\Delta\Gamma_s$ is constrained to be positive. The fraction $ |A_{S}(0)|^2 $, of $S$-wave $KK$ or $f_{0}$ contamination through the decays $B_s \rightarrow J/\psi K^+K^- (f_0)$ is also measured and is found to be compatible with zero. Results for $\phi_s$ and $\Delta \Gamma_s$ are also presented as $68\%$ and $95\%$ likelihood contours, which show agreement with Standard Model expectations.