Renormalization Group Invariant Matrix Elements of DS = 2 and DI = 3/2 Four-Fermion Operators without Quark Masses

Abstract

We introduce a new parameterization of four-fermion operator matrix elements which does not involve quark masses and thus allows a reduction of systematic uncertainties. In order to simplify the matching between lattice and continuum renormalization schemes, we express our results in terms of renormalization group invariant B-parameters which are renormalization-scheme and scale independent. As an application of our proposal, matrix elements of DI=3/2 and SUSY DS =2 operators have been computed. The calculations have been performed using the tree-level improved Clover lattice action at two different values of the strong coupling constant (beta=6/g^2=6.0 and 6.2), in the quenched approximation. Renormalization constants and mixing coefficients of lattice operators have been obtained non-perturbatively. Using lowest order ChiPT, we also obtain <Pi Pi| O_7|K >^{NDR}_{I=2} = (0.11\pm 0.02) GeV^4 and <Pi Pi| O_8|K >^{NDR}_{I=2} = (0.51\pm 0.05) GeV^4 at mu=2 GeV.