Measurement of the CP-violating phase $\phi_s$ in the decay $B^{0}_s \to J/\psi \phi$

We present a measurement of the time-dependent $CP$-violating asymmetry in $B^{0}_s\to J/\psi\phi$ decays, using data collected with the LHCb detector at the LHC. The decay time distribution of $B^{0}_s\to J/\psi\phi$ is characterized by the decay widths $\Gamma_{\mathrm{H}}$ and $\Gamma_{\mathrm{L}}$ of the heavy and light mass eigenstates of the $B^{0}_s-\overline{B}^{0}_s$ system and by a $CP$-violating phase $\phi_s$. In a sample of about 8500 $B^{0}_s\to J/\psi\phi$ events isolated from $0.37$~fb$^-1$ of $pp$ collisions at $\sqrt{s}=7$ TeV we measure $\phi_s \: = \: 0.15 \: \pm \: 0.18 \; \mathrm{(stat)} \: \pm \: 0.06 \; \mathrm{(syst)}$ rad. We also find an average $B_s$ decay width $\Gamma_s \equiv (\Gamma_{\mathrm{L}}+\Gamma_{\mathrm{H}})/2 \: = \: 0.657 \: \pm \: 0.009 \; \mathrm{(stat)} \: \pm \: 0.008 \; \mathrm{(syst)}$ ps$^{-1}$ and a decay width difference $\Delta\Gamma_s \equiv \Gamma_{\mathrm{L}} - \Gamma_{\mathrm{H}} \: = \: 0.123 \: \pm \: 0.029 \; \mathrm{(stat)} \: \pm \: 0.011 \; \mathrm{(syst)}$ ps$^{-1}$. Our measurement is insensitive to the transformation $(\phi_s,\Delta\Gamma_s) \mapsto (\pi-\phi_s,-\Delta\Gamma_s)$.