Indirect CP-Violation in the Neutral Kaon System Beyond Leading Logarithms

Abstract

We have calculated the short distance QCD coefficient η_3 of the effective |ΔS|=2-hamiltonian in the next-to-leading order. Since now all coefficients η_1, η_2 and η_3 are known beyond the leading log approximation, one can achieve a much higher precision in the theoretical analysis of ε_K. The measured value for ε_K$ yields a lower bound on each of |V_{cb}|, |V_{ub}/V_{cb}|, the top quark mass $m_t$ and the non- perturbative parameter B_K as a function of the remaining three quantities. We discuss the implications on the CKM phase δ, |V_{td}| and the key quantity for all CP-violating processes, Im λ_t = Im [V^*_{ts} V_{td}]. These quantities and the improved Wolfenstein parameters \barρand \barηare tabulated and the shape of the unitarity triangle is discussed. We compare the range for |V_{td}| with the one obtained from the analysis of B^0--\bar{B^0} mixing. For 0.037 \leq |V_{cb}| \leq 0.043, 0.06 \leq |V_{ub}/V_{cb}| \leq 0.10 and 0.65 \leq B_K \leq 0.85 we find from a combined analysis of ε_K and the B^0--\bar{B^0} mixing paramater x_d: 49^{\circ} \leq δ\leq 146^{\circ}, 7.4 \cdot 10^{-3} \leq |V_{td}| \leq 12.4 \cdot 10^{-3}, 0.85 \cdot 10^{-4} \leq \imag λ_t \leq 1.60 \cdot 10^{-4}, -0.36 \leq \barρ\leq 0.28 and 0.21 \leq \barη\leq 0.44. We predict the mass difference of the $B_s^0$ system to lie in the range 6.5 ps^{-1} \leq Δm_{B_s} \leq 28 ps^{-1}. Finally we have a 1995 look at the K_L--K_S mass difference.