Time-dependent CP violation at LHCb

The LHCb experiment has conducted precision measurements of time-dependent CP violation (TD-CPV) in key decay modes, including $B^0\to\psi K_S^0$, $B^0_s\to J/\psi K^+K^-$, and $B_s^0\to D_s^\mp K^\pm$ allowing extraction of CKM phases $\beta$, $\beta_s$, and $\gamma$. In the charm sector, where CP asymmetries are expected to be highly suppressed, TD-CPV analyses in $D^0\to K^\mp\pi^\pm$ and $D^0\to\pi^+\pi^-\pi^0$ decays provide sensitive tests of the Standard Model (SM). These measurements offer world-leading constraints on CP-violating parameters and show no significant deviations from SM predictions.