CP violation in $B_s^0$ mixing with LHCb

The determination of the CP-violating phase ${\varphi }_s$ in $B^0_s \rightarrow J/\psi \phi$ decays is one of the key goals of the LHCb experiment. Its value is predicted to be very small in the Standard Model but can be significantly enhanced in many models of new physics. An angular analysis of the decay $\text{PBs}\to \text{PJpsi}\text{Pphi}$ using about 340\invpicobarn of data is presented resulting in a Standard Model compatible value of ${\varphi }_s^{\text{PJpsi}\text{Pphi}}=0.13\pm 0.18(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.07(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})\mathrm{r}\mathrm{a}\mathrm{d}$. An additional extraction of ${\varphi }_s$ from the decay $\text{PBs}\to \text{PJpsi}{f}_0(980)$ is performed for the first time in LHCb. A combination results in ${\varphi }_s=0.05\pm 0.17(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.07(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})\mathrm{r}\mathrm{a}\mathrm{d}$. To resolve the fast mixing frequency is an essential prerequisite of this analysis. This is demonstrated by a precision measurement of $\Delta m_s=17.725\pm0.041($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}$)\pm0.026($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}$)\ps^{-1}$.