Weak matrix elements on the lattice - Circa 1995

Status of weak matrix elements is reviewed. In particular, epsilon'/epsilon, B --> K*gamma, B-K, B-B and B-B. are discussed and the overall situation with respect to the lattice effort and some of its phenomenological implications are summarised. For epsilon'/epsilon the need for the relevant matrix elements is stressed in view of the forthcoming improved experiments. For some of the operators, (e.g. O-s), even bounds on their matrix elements would be very helpful. On B --> K*gamma, 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 --> rho gamma. On B-K, the preliminary result from JLQCD appears to contradict Sharpe et al. JLQCD data seems to fit very well to linear a dependence and leads to an appreciably lower value of BK. Four studies of BK 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-hl) for the heavy-light mesons via B-hl = constant + constants'/m(ht) 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 end 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.