New lattice approaches to the $ΔI=1/2$ rule

Details New lattice approaches to the $ΔI=1/2$ rule New lattice approaches to the $ΔI=1/2$ rule

1997-07-11

arxiv.org/abs/hep-lat/9707009v1

Nucl.Phys.B514:313-335,1998

Physics

High Energy Physics

High Energy Physics - Lattice

22 pages, 1 figure, uses epsfig

Scientific paper

10.1016/S0550-3213(97)00756-6

Lattice QCD should allow a derivation of the $\Delta I=1/2$ rule from first principles, but numerical calculations to date have been plagued by a variety of problems. After a brief review of these problems, we present several new methods for calculating $K\to\pi\pi$ amplitudes. These are designed for Wilson fermions, though they can be used also with staggered fermions. They all involve a non-perturbative determination of matching coefficients. We show how problems of operator mixing can be greatly reduced by using point-split hadronic currents, and how CP violating parts of the $K\to\pi\pi$ amplitudes can be calculated by introducing a fake top quark. Many of the methods can also be applied to the calculation of two body non-leptonic B-meson decays.

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