We discuss how one can determine the average kinetic energy of the heavy qauark mesons from differential distributions in semileptonic B decays. A new, the so-called third, sum rule for the b→c transition is derived in the small velocity (SV) limit. Using this sum rule and the measured momentum dependence of the B→D* transition (the slope of the Isgur-Wise function), we obtain a new lower bound on the parameter μπ2=(2MB)-〈B|b(iD )2b|B〉 proportional to the average kinetic energy of the b quaek inside a B meson. Existing data suggest μπ2 > 0.4 GeV and (from the "optical" sum rule) Λ > 500 MeV, albeit with some numerical uncertainties.
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We are grateful to L. Bellantoni, D. Cassel, Y. Kub-ota, R. Poling and J. Richman for useful discussions of the current experimental situation. A.G. would like to thank the CERN Theory Division for hospitality. This work was supported in part by the National Science Foundation under the grant number PHY 92-13313 and by DOE under the grant number DE-FG02-94ER40823, and by the Royal Society and PPARC, UK.