Hadronic matrix elements from the lattice

Abstract

Lattice matrix elements are briefly reviewed. In the quenched approximation $f_B$, $B_B$ and $B_K$ are now under good control. Experimental hints for $f^{\rm expt}_{D_S}> f^{\rm QQCD}_{D_S}$ are noted; precise determination of $f_{D_S}$ from experiment as well as from the lattice is strongly advocated. Lattice calculations of the form factor for $B\toπ\ellν$ at relatively large value of $q^2$ have made good progress and should be useful in conjunction with precise measurement of the differential spectra expected from $B$-factories. Recent attempt at $K\to ππ$ using staggered quarks is briefly discussed; use of non-perturbative renormalization, improved actions and operators with staggered quarks is emphasized. Due to the good chiral behavior of domain wall quarks it would be useful to study $K\to ππ$ with this discretization.