Measurement of the $CP$ violating phase $\phi_s$ and $\phi_s^{sq\bar{q}}$ at LHCb

Precise measurements of the $B_s^0 - \overline{B}_s^0$ mixing parameters provide a powerful test of the Standard Model, offering potential hints to new physics. The LHCb collaboration has performed updated measurements of the $CP$-violating phases $\phi_s^{c\bar{c}s}$ and $\phi_s^{s\bar{s}s}$, which supersede previous results. Also, an alternative approach to determine $\Delta \Gamma_s$ is presented, bringing a new tool that may help to resolve the tension observed between measurements made in $B_s^0 \to J/\psi \phi$ by LHC experiments.