Factorization approach for the Delta I=1/2 rule and epsilon '/epsilon in kaon decays

The DeltaI = 1/2 rule and direct CP violation epsilon/epsilon' in kaon deca ys are studied within the framework of the effective Hamiltonian approach i n conjunction with generalized factorization for hadronic matrix elements. We identify two principal sources responsible for the enhancement of ReA(0) /ReA(2): the vertex-type as well as penguin-type corrections to the matrix elements of four-quark operators, wh ich rend er the physical amplitude ren ormalization-sca le and -scheme independent, and the nonfactorized effect d ue to soft-gluon exchange, which is needed to suppress the DeltaI = 3/2 K - -> pi pi amplitude. Contrary to the chiraI approach which is limited to lig ht meson decays and fails to reproduce the Aa amplitude, the aforementioned approach for dealing with scheme and scale issues is applicable to heavy m eson decays. We obtain ReA(0)/ReA(2) = 13 - 15 if m(s)(1 GeV) lies in the r ange 125-175 MeV. The bag parameters Bi, which are often employed to parame trize the scale and scheme dependence of hadronic matrix elements, are calc ulated in two different renormalization schemes. It is found that B-S((2)) and B-6((0)), both of order 1.5 at mu 1 GeV, are nearly gamma (5) scheme in dependent, whereas B-3,5,7((0)) as well as B-7((2)) show a sizable scheme d ependence. Moreover, only B-1,3,4((0)) exhibit a significant m(s) dependenc e, while the other B-parameters are almost m, independent. For direct CP vi olation, we obtain epsilon'/epsilon = (0.5 - 1.3) x 10(-3) if m(s)(1 GeV) = 150 MeV and epsilon'/epsilon = (0.8 - 2.0) X 10(-3) if m(s) is as small as indicated by some recent lattice calculations.