LHCb: Measurement of the time-dependent CP asymmetry in $B^{0} \rightarrow J/\psi K_S^0$

The LHCb is one of the LHC experiments, specially designed to study CP violation and rare decays of b-quark. In this scenario, the decay $B^{0} \rightarrow J/\psi K_S^0$ is a well-known mode to study CP violation. The final state is the same for both CP eigenstates $B^0$ and $\overline{B^0}$, which enables the interference through the b-quark oscillations.The CKM angle $\beta$ can be extracted from the above decay. The time dependent decay rate asymmetry can be written as: $$ \mathcal{A}_{J/\psi K_S^0} (t) = S_{J/\psi K_S^0} \sin(\Delta m_d t) - C_{J/\psi K_S^0} \cos( \Delta m_d t) $$ where, in the standard model, the parameters $S_{J/\psi K_S^0}$ and $C_{J/\psi K_S^0}$ are connected to the CKM angle $\beta$ through: $$S_{J/\psi K_S^0} = \sin 2 \beta \, \rm{ and } \, C_{J/\psi K_S^0} = 0 $$ Here we report the time-dependent analysis in the $B^{0} \rightarrow J/\psi (\mu^{+} \mu^{-}) K_S^0 (\pi^{+} \pi^{-})$ decays. Using the $1fb^{-1}$ of integrated luminosity data collected in 2011 at LHCb operating at $7 TeV$ on center of mass, we performed a 2 dimensional log-likelihood fit dependent on the $B^{0}$ proper time and its invariant mass, which yields: $$S_{J/\psi K_S^0} = 0.73 \pm 0.07 \textrm{(stat.)} \pm 0.04 \textrm{(syst.)}$$ $$C_{J/\psi K_S^0} = 0.03 \pm 0.09 \textrm{(stat.)} \pm 0.01 \textrm{(syst.)}$$ Both values are consistent with the current world average of these parameters. This is the most precise measurement of these quantities in a hadronic environment.