Estimating of CP Violation in B₂ B K^0+B K⁰ B ^ e^ ₄ Decays

In this paper, we investigate the CP asymmetries A₂₏^pm and A₂₏^mp in B₂^ B^ K^0+B^ K⁰ B^ ^ e^ ₄ and B₂^ B^ K^0+B^ K⁰ B^ ^ e^ ₄ decays, both of them consist of three parts: the indirect CP violations in K⁰ -K⁰ mixing A₂₏, ₌₈ₗ^pm and A₂₏, ₌₈ₗ^mp, the direct CP violations in B₂ decay A₂₏, ₃₈ₑ^pm and A₂₏, ₃₈ₑ^mp, the new CP violation effects A₂₏, ₈₍ₓ^pm and A₂₏, ₈₍ₓ^mp, which originate from the interference between the amplitude of the B₂^- B^- K^0 (K⁰) B^- ^- e^+ ₄ (^+ e^- ₄) decay with the difference between the oscillating effect of K⁰ K⁰ and that of K⁰ K⁰. The strong phase differences of the direct CP asymmetries A₂₏, ₃₈ₑ^pm and A₂₏, ₃₈ₑ^mp arising from K⁰-K⁰ mixing parameters. A₂₏^pm and A₂₏^mp are of the order O (10^-4) and O (10^-3), respectively. The new CP violation effect A₂₏, ₈₍ₓ^pm plays a dominant role in A₂₏^pm, the CP asymmetry A₂₏^mp is dominated by the indirect CP violation A₂₏, ₌₈ₗ^mp, so the CP asymmetry A₂₏^pm provides an ideal place to study the new CP violation effect. We derive another two asymmetry observables A₂₏^pp and A₂₏^mm, which are dominated by K⁰-K⁰ mixing. The observables A₂₏^pm, A₂₏^mp, A₂₏^pp and A₂₏^mm are hopefully to be marginally observed at the LHC experiment and the HL-LHC experiment.