Measurement of CP Violation in $B_s^0 \to J\psi \phi$ decays

Precise measurements of CP violation provide stringent tests of the Standard Model towards a search for signs of New Physics. The decay-time dependent CP asymmetry in $B_s^0 \to J\psi \phi$ decays has been measured using proton-proton, $pp$, collision data, collected with the LHCb detector. The CP-violating phase $\phi_s$ is measured, along with the difference in decay widths of the light and heavy mass eigenstates of the $B_s^0-\overline{B}_s^0$ system, and the average $B_s^0$ decay width. Discussed are also data-driven corrections to simulated event samples, and the control of systematic effects using data control sample. Prospects for the sensitivity that can be achieved with future LHCb data taking periods will be also given.