Search for $CP$ violation in $B^0 \to J/\psi K^0_S$ decays with first LHCb data

We report on the measurement of the well-established $CP$ violation in $B^0 \to J/\psi K^0_S$ decays. We perform a time-dependent analysis of the decays reconstructed in 35 pb$^{-1}$ of LHCb data that was taken in 2010. We measure the $CP$ asymmetry parameter $S_{J/\psi K^0_s}$, which is connected to the CKM angle $\beta$ through $S_{J/\psi K^0_s}$ = sin 2$\beta$, neglecting $CP$ violation in $B^0-\bar{B}^0$ mixing and decay. We find $S_{J/\psi K^0_s}$ = 0.53$^{+0.28}_{-0.29}$ (stat) $\pm$ 0.05 (syst).