In this thesis, we present measurements of the branching fraction and CP asymmetry of rare B decay B → ΦΦK. These measurements are based on a 414 fb^{-1} data sample, which contains 447 × 10^6 B Bbar pairs, collected with the Belle detector at the KEKB asymmetric-engry e^+e^- (3.5 on 8 GeV) collider operating at the ?(4S) resonance. We observe the B^+ → ΦΦK^+ decay and report the evidence for B^0 → ΦΦK^0 decay. The branching fractions are measured to be:
● B(B^+ → ΦΦK^+)= [3.18^{+0.60}_{-0.52}(stat) ± 0.27(sys)] × 10^{-6}
● B(B^0 → ΦΦK^0) = [2.31^{+1.00}_{-0.74}(stat) ± 0.24(sys)] × 10^{-6}
for a ΦΦ invariant mass below 2.85 GeV/c^2, with significances including systematic uncertainty of 9.53 and 4.74 standard deviations, respectively.
In addition, we also study the charmonium decays, related to the ΦΦK.
The measured branching ratios are:
● B(η_c → ΦΦ) = (3.01^{+1.06}_{-1.02} ± 0.19) × 10^{-3}
● B(η_c → ΦK^+K^-) = (4.35^{+1.45}_{-1.44} ± 0.29) × 10^{-3}
● B(η_c → 2(K^+K^-)) = (2.62^{+0.93}_{-0.90} ± 0.18) × 10^{-3}
● B(J/Ψ → ΦK^+K^-) = (1.45^{+0.30}_{-0.27} ± 0.11) × 10^{-3}
● B(J/Ψ → 2(K^+K^-)) = (9.73^{+1.77}_{-1.61} ± 0.84) × 10^{-4}
The measured width of η_c is 25.17^{+7.72}_{-5.98} ± 0.32 MeV.