THE ANATOMY OF EPSILON(')/EPSILON BEYOND LEADING LOGARITHMS WITH IMPROVED HADRONIC MATRIX-ELEMENTS

We use the recently calculated two-loop anomalous dimensions of current-current operators, QCD and electroweak penguin operators to construct the effective hamiltonian for DELTAS = 1 transitions beyond the leading logarithmic approximation. We solve the renormalization-group equations involving alpha(s) and alpha up to two-loop level and we give the numerical values of Wilson coefficient functions Ci(i)(mu) beyond the leading logarithmic approximation in various renormalization schemes. Numerical results for the Wilson coefficients in DELTAB = 1 and DELTAC = 1 hamiltonians are also given. We discuss several aspects of renormalization scheme dependence and demonstrate the scheme independence of physical quantities. We stress that the scheme dependence of the Wilson coefficients C(i)(mu) can only be cancelled by the one present in the hadronic matrix elements [Q(i)(mu)]. This requires also the calculation of O(alpha) corrections to [Q(i)(mu)]. We propose a new semi-phenomenological approach to hadronic matrix elements which incorporates the data for CP-conserving K --> pipi amplitudes and allows to determine the matrix elements of all (V - A) x (V - A) operators in any renormalization scheme. Our renormalization-group analysis of all hadronic matrix elements [Q(i)(mu)] reveals certain interesting features. We compare critically our treatment of these matrix elements with those given in the literature. When matrix elements of dominant QCD penguin (Q6) and electroweak penguin (Q8) operators are kept fixed the effect of next-to-leading order corrections is to lower considerably epsilon'/epsilon in the 't Hooft-Veltman (HV) renormalization scheme with a smaller effect in the dimensional regularization scheme with anticommuting gamma5 (NDR). Taking m(t) = 130 GeV, lambda(MSBAR) = 300 MeV and calculating [Q6] and [Q8] in the 1/N approach with m(s) (1 GeV) = 175 MeV, 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 [Q6] by only a factor of two gives epsilon'/epsilon = (20.0 +/- 6.5) x 10(-4) in agreement with the result of NA31. The dependence of epsilon'/epsilon on lambda(MSBAR), m(t) and [Q6,8] is presented. A detailed anatomy of various contributions and comparison with the analyses of Rome and Dortmund groups are given.