Master formulae for Delta F=2 NLO-QCD factors in the Standard Model and beyond

We present analytic formulae for the QCD renormalization group factors rela ting the Wilson coefficients C-i (mu (t)) and C-i (mu), with mu (t) = O(m(t )) and mu < mu (t), of the DeltaF = 2 dimension six four-quark operators Q( i) in the Standard Model and in all of its extensions. Analogous analytic f ormulae for the QCD factors relating the matrix elements [Q(i) (2 GeV)] and [Q(i)(mu (K))] with mu (K) < 2 GeV are also presented. The formulae are gi ven in the NDR scheme. The strongest renormalization-group, effect, are fou nd for the operators with the Dirac structures (1 - gamma (5)) x (1 + gamma (5)) and (1 - gamma (5)) x (1 - gamma (5)). We calculate the matrix elemen ts ((K) over bar (0) \Q(i)\ K-0) in the NDR scheme using the lattice result s in the LRI scheme. We give expressions for the mass differences DeltaM(K) and DeltaM(B) and the CP-violating parameter epsilon (K) in terms of the n on-perturbative parameters B-j and the Wilson coefficients C-i (mu (t)). Th e latter summarize the dependence on new physics contributions. (C) 2001 El sevier Science B.V. All rights reserved.