Weak matrix elements on the Lattice — Circa 1995

Abstract

Status of weak matrix elements is reviewed. In particular, $\epspeps$, $\bkastg$, $B_K$, $B_B$ and $B_{B_s}$ are discussed and the overall situation with respect to the lattice effort and some of its phenomenological implications are summarized. For $\epspeps$ the need for the relevant matrix elements is stressed in view of the forthcoming improved experiments. For some of the operators, (e.g.\ $O_6$), even bounds on their matrix elements would be very helpful. On $\bkastg$, a constant behavior of $T_2$ appears disfavored although dependence of $T_2$ could, of course, be milder than a simple pole. Improved data is badly needed to settle this important issue firmly, especially in view of its ramification for extractions of $V_{td}$ from $B\to\rho\gamma$. On $B_K$, the preliminary result from JLQCD appears to contradict Sharpe \etal\ JLQCD data seems to fit very well to linear $a$ dependence and leads to an appreciably lower value of $B_K$. Four studies of $B_K$ in the ``full'' ($n_f=2$) theory indicate very little quenching effects on $B_K$; the full theory value seems to be just a little less than the quenched result. Based on expectations from HQET, analysis of the $B$-parameter ($B_{h\ell}$) for the heavy-light mesons via $B_{h\ell}={}$constant${}+{}$constants$^\prime/m_{h\ell}$ is suggested. A summary of an illustrative sample of hadron matrix elements is given and constraints on CKM parameters (e.g.\ $V_{td}/V_{ts}$), on the unitarity triangle and on $x_s/x_d$, emerging from the lattice calculations along with experimental results are briefly discussed. In quite a few cases, for the first time, some indication of quenching errors on weak matrix elements are now becoming available.