CP violation in $B \to ΦK_S$ in a model III 2HDM

Abstract

The mixing induced time dependent CP asymmetry, direct CP asymmetry, and branching ratio in $B \to ΦK_S$ in a model III 2HDM are calculated, in particular, neutral Higgs boson contributions are included. It is shown that satisfying all the relevant experimental constraints, for time dependent CP asymmetry $S_{ϕK}$ the model III can agree with the present data, $S_{ϕk}=-0.39\pm 0.41$, within the $1σ$ error, and the direct CP asymmetry which is zero in SM can be about $ -8% \sim -20%$ in the reasonable regions of parameters.