  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) of
renormalization group improved perturbation theory. It involves the two-loop
mixing of bilocal structures composed of two $|\Delta S|=1$ operators into
$|\Delta S|=2$ operators. The next-to-leading order corrections enhance
$\eta_3$ by 27\% to $\eta_3=0.47\errorpm{0.03}{0.04}$ thereby affecting the
phenomenology of the CP-parameter $\epsilon_K$ sizeably. $\eta_3$ depends on
the physical input parameters $m_t$, $m_c$ and $\Lambda_{MSbar}$ only weakly.
The quoted error stems from factorization scale dependences, which have reduced
compared to the old leading log result. We further discuss some field
theoretical aspects of the calculation such as the renormalization group
equation for Green's functions with 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.

High Energy Physics - Phenomenology