THE DELTA-S=1 EFFECTIVE HAMILTONIAN INCLUDING NEXT-TO-LEADING ORDER QCD AND QED CORRECTIONS

In this paper we present a calculation of the DELTAS = 1 effective wea k hamiltonian including next-to-leading order QCD and QED corrections. At a scale mu of the order of a few GeV, the Wilson coefficients of t he operators are given in terms of the renormalization group evolution matrix and of the coefficients computed at a large scale approximatel y M(W). The expression of the evolution matrix is derived from the two -loop anomalous dimension matrix which governs the mixing of the relev ant current-current and penguin operators, renormalized in some given regularization scheme. We have computed the anomalous dimension matrix up to and including order alpha(s)2 and alpha(e)alpha(s) in two diffe rent renormalization schemes, NDR and HV, with consistent results. We give many details on the calculation of the anomalous dimension matrix at two loops, on the determination of the Wilson coefficients at the scale M(W) and of their evolution from M(W) to mu. We also discuss the dependence of the Wilson coefficients/operators on the regularization scheme.