Connections Between Inclusive and Exclusive Semileptonic B Decay

Abstract

B decay sum rules relate exclusive B semileptonic decay matrix elements to forward B-meson matrix elements of operators in HQET. At leading order the operators that occur are the b-quark kinetic energy $\lambda_1$ and chromomagnetic energy $\lambda_2$. The latter is determined by the measured $B^*-B$ mass splitting. The derivation of these sum rules is reviewed and perturbative QCD corrections are discussed. A determination of $\lambda_1$ and the energy of the light degrees of freedom in a B-meson, $\bar\Lambda$, from semileptonic B decay data is presented. Future prospects for improving these sum rules are discussed.