A SIMULTANEOUS ANALYSIS FOR THE ΔI = 1/2 RULE, DIRECT CP VIOLATION, AND MIXINGS

To have a consistent picture, a simultaneous analysis for the K → ππ isospin amplitudes A₀ and A₂, the ΔI = 1/2 rule, CP-violating ε′/ε, and and mixings within the standard model is made by employing the recent reanalyzed values of the parameters and relating the penguin matrix elements involved in the K → ππ decays to the known matrix elements of the ΔI = 1/2 operator (Q₂ − Q₁) and ΔI = 3/2 operator (Q₂ + 2Q₁). The allowed values for all the relevant quantities are calculated in detail. A general bound for top quark mass m_t, CP phase δ and ε′/ε is found: for δ in the second quadrant, 84GeV ≤ m_t ≤ 250GeV, δ ≤ 173° and 1 × 10⁻⁴ < ε′/ε ≤ 1 × 10⁻²; for δ in the first quadrant, 126GeV ≤ m_t ≤ 664GeV, δ ≥ 11º and 1 × 10⁻³ < ε′/ε ≤ 1 × 10⁻² as m_t ≤ 260GeV. Taking the plausible central values of the parameters — |V_cb| = 0.041, |V_ub|/|V_cb| = 0.12, B_K = 0.75, , x_B = 0.70, m_s = (100 ~ 125)MeV and Λ_QCD = (200 ~ 300)MeV — as a "standard" set, we then obtain from the simultaneous analysis a consistent prediction: A₀ = (3.24 ± 0.70) × 10⁻⁷, A₂ = (0.145 ± 0.007) × 10⁻⁷, ω = A₂/A₀ = 0.046 ± 0.007 and m_t ≃ 142GeV, δ ≃ 152°, ε′/ε ≃ (2.5 ± 1.0) × 10⁻³. The possible implications for the experiments are also discussed.