VANISHING OF 1/M CORRECTIONS AT THRESHOLD

Heavy-quark predictions for hadronic weak-decay transition amplitudes have O(1/m) corrections, but we show these always vanish at threshold. This follows from the nonrenormalization of the threshold effective currents at O(1/m), and an application of the Ademollo-Gatto theorem. The result, which we call Luke's theorem, holds for initial and final particles consisting of a heavy quark or scalar and light degrees of freedom in an arbitrary spin state.