B-parameters of 4-fermion operators from lattice QCD

Reliable estimates of the matrix elements of 4-fermion operators between hadronic states are essential in order to quantify strong interaction corrections to weak processes. Here we report on calculations of mixing elements of (i) ∆s = 2 operators between K and K̄0 states (BK) that arise in the calculation of the CP violation parameter ǫ. The value of BK is an essential input in pinning down the Wolfenstein parameters ρ and η in the CKM matrix. (ii) The strong and electromagnetic penguin operators needed to predict ǫ/ǫ (B6 and B8). In particular, we consider B8, which is phenomenologically important since a smaller value means a larger ǫ/ǫ. (iii) The S+P operators needed in the study of the lifetime differences of B mesons (Bs).