6533b839fe1ef96bd12a6d77

RESEARCH PRODUCT

A SIMULTANEOUS ANALYSIS FOR THE ΔI = 1/2 RULE, DIRECT CP VIOLATION, $K^0 -\bar K^0$ AND $B^0 -\bar B^0$ MIXINGS

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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 [Formula: see text] and [Formula: see text] 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 mt, CP phase δ and ε′/ε is found: for δ in the second quadrant, 84 GeV ≤ mt ≤ 250 GeV , δ ≤ 173° and 1 × 10−4 < ε′/ε ≤ 1 × 10−2; for δ in the first quadrant, 126 GeV ≤ mt ≤ 664 GeV , δ ≥ 11º and 1 × 10−3 < ε′/ε ≤ 1 × 10−2 as mt ≤ 260 GeV . Taking the plausible central values of the parameters — |Vcb| = 0.041, |Vub|/|Vcb| = 0.12, BK = 0.75, [Formula: see text], xB = 0.70, ms = (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 mt ≃ 142 GeV , δ ≃ 152°, ε′/ε ≃ (2.5 ± 1.0) × 10−3. The possible implications for the experiments are also discussed.