Matrix Elements of 4-fermion Operators with Quenched Wilson Fermions

Details Matrix Elements of 4-fermion Operators with Quenched Wilson Fermions Matrix Elements of 4-fermion Operators with Quenched Wilson Fermions

1996-11-22

arxiv.org/abs/hep-lat/9611023v2

Phys.Rev. D55 (1997) 4036-4054

Physics

High Energy Physics

High Energy Physics - Lattice

35 pages. Typos in published version corrected. Makefile and modified "axis" figures included. Latex2e document. Uncomment hyp

Scientific paper

10.1103/PhysRevD.55.4036

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.

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