Heavy Light Weak Matrix Elements * Shep–96–21

In this review I will focus on calculations of selected matrix elements involving b quarks. The semileptonic decays B̄→πlν̄l and B̄→ρlν̄l depend on the CKM element Vub which fixes one side of the unitarity triangle. Lattice calculations open the possibility for a model independent extraction of this quantity. The rare radiative decay B̄→K∗γ is important for the determination of Vts and as a window on new physics. Calculations here are hampered by the necessity to impose models for form factors. For the B meson decay constant, the systematic uncertainty arising from continuum extrapolation is being reduced and quenching effects are being addressed. Combining with results for the mixing parameter, the phenomenologically relevant quantity f BBB will become better determined.