Matrix Elements of 4-fermion Operators with Quenched Wilson Fermions

Abstract

We presents results for the matrix elements of a variety of four-fermion operators calculated using quenched Wilson fermions. Our simulations are done on 170 lattices of size $32^3 x 64$ at $\beta = 6.0$. We find $B_K=0.74 +- 0.04 +- 0.05$, $B_D= 0.78 +- 0.01$, $B_7^{3/2}= 0.58 +- 0.02 {+0.07 \atop -0.03}$, $B_8^{3/2}= 0.81 +- 0.03 {+.03 \atop -0.02}$, with all results being in the NDR scheme at $\mu=2 GeV$. We also calculate the B-parameter for the operator $\CQ_s$, which is needed in the study of the difference of B-meson lifetimes. Our best estimate is $B_s(NDR,\mu=1/a)=0.80 +- 0.01$. This is given at the lattice scale since the required 2-loop anomalous dimension matrix is not known. In all these estimates, the first error is statistical, while the second is due to the use of truncated perturbation theory to match continuum and lattice operators. Errors due to quenching and lattice discretization are not included. We also present new results for the perturbative matching coefficients, extending the calculation to all Lorentz scalar four-fermion operators, and using NDR as the continuum scheme.