The anatomy of $\varepsilon$'/$\varepsilon$ beyond leading logarithms with improved hadronic matrix elements

Results of a recent calculation of the effective $\Delta S$ Hamiltonian at the next-to-leading order will be presented\footnote{Work done in collaboration with A. J. Buras and M. E. Lautenbacher.. These, together with an improved treatment of hadronic matrix elements, are used to evaluate the measure for direct CP-violation, $\epsilon'/\epsilon$, at the next-to-leading order. Taking $m_t=130 ,GeV$, $\Lambda_{MS}$=300,MeV and calculating <$Q_6$> and <$Q_8$> in the 1/N approach, we find in the NDR scheme $\epsilon'/\epsilon$ = (6.7 ± 2.6) x $10^{-4}$ in agreement with the experimental findings of E731. We point out however that the increase of $<Q_6>$ by only a factor of two gives $\epsilon'/\epsilon$ = (20.0 ± 6.5) x $10^{-4}$ in agreement with the result of NA31. The dependencies of $\epsilon'/\epsilon$ on $\Lambda_{MS}$, $m_t$, and some $B$-parameters, parameterizing hadronic matrix elements, are briefly discussed.