Weak matrix elements on the Lattice — Circa 1995

Status of weak matrix elements is reviewed. In particular, ɛ'/ ɛ, B → K ^*γ , 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 ɛ'/ ɛ the need for the relevant matrix elements is stressed in view of the forthcoming improved experiments. For some of the operators, (e.g. O₆), even bounds on their matrix elements would be very helpful. On B → K ^*γ , a constant behavior of T₂ appears disfavored although dependence of T₂ 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_{t d} from B → ργ. 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 B _K. Four studies of B _K in the "full" ( n _ƒ = 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 _hl is suggested. A summary of an illustrative sample of hadron matrix elements is given and constraints on CKM parameters (e.g. V_{t d}/ V_{t s}), 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.