Indirect CP-Violation in the Neutral Kaon System Beyond Leading Logarithms
Abstract
We have calculated the short distance QCD coefficient η3 of the effective | S|=2-hamiltonian in the next-to-leading order. Since now all coefficients η1, η2 and η3 are known beyond the leading log approximation, one can achieve a much higher precision in the theoretical analysis of εK. The measured value for εK yields a lower bound on each of |Vcb|, |Vub/Vcb|, the top quark mass mt and the non- perturbative parameter BK as a function of the remaining three quantities. We discuss the implications on the CKM phase δ, |Vtd| and the key quantity for all CP-violating processes, Im λt = Im [V*ts Vtd]. These quantities and the improved Wolfenstein parameters and η are tabulated and the shape of the unitarity triangle is discussed. We compare the range for |Vtd| with the one obtained from the analysis of B0--B0 mixing. For 0.037 ≤ |Vcb| ≤ 0.043, 0.06 ≤ |Vub/Vcb| ≤ 0.10 and 0.65 ≤ BK ≤ 0.85 we find from a combined analysis of εK and the B0--B0 mixing paramater xd: 49 ≤ δ ≤ 146, 7.4 · 10-3 ≤ |Vtd| ≤ 12.4 · 10-3, 0.85 · 10-4 ≤ λt ≤ 1.60 · 10-4, -0.36 ≤ ≤ 0.28 and 0.21 ≤ η ≤ 0.44. We predict the mass difference of the Bs0$ system to lie in the range 6.5 ps-1 ≤ mBs ≤ 28 ps-1. Finally we have a 1995 look at the KL--KS mass difference.
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