THE COEFFICIENT ETA(3) OF THE VERTICAL-BAR-DELTA-S-VERTICAL-BAR=2-HAMILTONIAN IN THE NEXT-TO-LEADING ORDER

I present the calculation of the QCD short distance coefficient eta(3) Of the \Delta S\ = 2-Hamiltonian in the next-to-leading order (NLO) o f renormalization group improved perturbation theory. It involves the two-loop mixing of bilocal structures composed of two \Delta S\ = 1 op erators into \Delta S\ = 2 operators. The next-to-leading order correc tions enhance eta(3) by 27% to eta(3) = 0.47(-0.04)(+0.03) thereby aff ecting the phenomenology of the CP-parameter epsilon(K) sizeably. eta( 3) depends on the physical input parameters m(t), m(c) and Lambda(<(MS )over bar>) only weakly. The quoted error stems from factorization sca le dependences, which have reduced compared to the old leading log res ult. We further discuss some field theoretical aspects of the calculat ion such as the renormalization group equation for Green's functions w ith two operator insertions and the renormalization scheme dependence caused by the presence of evanescent operators. This article is based on work done in collaboration with U. Nierste.