$B^0 \to \phi K^0_S$ Selection and Sensitivity Study

The mixing-induced CP asymmetry in the decay $B^0 \to \phi K^0_S$ is predicted to be almost the same as in $b\to c\bar{c} s$ dominated decay modes in the Standard Model, but is sensitive to new physics with extra $b\to s$ CP-violating phases. This note describes the selection of $B^0 \to \phi K^0_S$ in the LHCb experiment using data produced in Monte Carlo simulation. We expect about 920 signal events in 2 $fb^{-1}$ of data with a background to signal ratio $\rm 0.3< B/S < 1.1$ at $90\%$ confidence level. Based on this result we estimate that the mixing-induced CP asymmetry $\rm S = \sin2\beta^{eff}$ in $B^0 \to \phi K^0_S$ can be measured to a statistical precision of 0.23 (0.1) in 2 (10) $fb^{-1}$ of data.