Lattice Calculation of Weak Matrix Elements

Abstract

We present the first results from a small-lattice (${6}^{3}$ \ifmmode\times\else\texttimes\fi{} 10) calculation of nonleptonic weak matrix elements. The $\ensuremath{\Delta}I=\frac{1}{2}$ rule is studied as a test case. For a lattice meson of approximately the kaon mass we find a significantly enhanced $\ensuremath{\Delta}I=\frac{1}{2}$ amplitude and a $\ensuremath{\Delta}I=\frac{3}{2}$ amplitude compatible with zero within our statistics. The dominance of the $\ensuremath{\Delta}I=\frac{1}{2}$ amplitude appears to be due to a class of graphs called the eye graphs. Qualitatively similar results are found whether or not the charm quark is integrated out ab initio. We also report preliminary results on other weak matrix elements.