INDIRECT CP VIOLATION IN THE NEUTRAL KAON SYSTEM BEYOND LEADING LOGARITHMS

We have calculated the short distance QCD coefficient eta(3) Of the effective \Delta S\=2 Hamiltonian in the next-to-leading order of renormalization-group improved perturbation theory. Since now all coefficients eta(1), eta(2), and eta(3) are known beyond the leading log approximation, one can achieve a much higher precision in the theoretical analysis of epsilon(K), the parameter of indirect CP violation in K-0-(K-0) over bar-mixing. The measured value for epsilon(K) yields a lower bound on each of \V-cb\, \V-ub/V-cb\, the top quark mass m(t), and the nonperturbative parameter B-K as a function of the remaining three quantities. For example, m(t)(pole) = 176 GeV, \V-cb\ = 0.040, and B-K = 0.75 implies \V-ub/V-cb\ less than or equal to 0.0778, if the measured value for epsilon(K) is attributed solely to standard model physics. We further discuss the implications on the CKM phase delta, \V-td\, and the key quantity for all CP-violating processes, Im lambda(t) = Im [V-ts*V-td]. These quantities and the improved Wolfenstein parameters <(rho)over bar> and <(eta)over bar> rare tabulated and the shape of the unitarity triangle is discussed. We compare the range for \V-td\ with the one -o obtained from the analysis of B-d(0)-(B) over bar(d)(0)-mixing. For 0.037 less than or equal to \V-cb\ less than or equal to 0.043, 0.06 less than or equal to \V-ub/V-cb\ less than or equal to 0.10, and 0.65 less than or equal to B-K less than or equal to 0.85 we find from a combined analysis of epsilon(K) and the B-d(0)-(B) over bar(d)(0)-mixing paramater x(d): 49 degrees less than or equal to delta less than or equal to 146 degrees, 7.4 x 10(-3) less than or equal to \V-td\ less than or equal to 12.4 x 10(-3), 0.85 x 10(-4) less than or equal to Im lambda(t) less than or equal to 1.60 x 10(-4), -0.36 less than or equal to <(rho)over bar> less than or equal to 0.28, and 0.21 less than or equal to <(eta)over bar> less than or equal to 0.44. We predict the mass difference of the B-s(0) system to lie id the range 6.5 ps(-1) less than or equal to Delta m(Bs) less than or equal to 28 ps(-1). Finally we have a 1995 look at the K-L-K-S-mass difference.