A sum rule from the shape function

Abstract

We present a sum rule relating the electron energy spectrum and the hadron mass distribution in semileptonic b -> u decays close to threshold. The relation found is free from non-perturbative effects and the theoretical error is expected to be O(5%). An experimental confirmation of this prediction can provide a check of the basic assumptions at the root of the theory of the shape function.

Comments: LaTeX file, 7 pages, no figures; minor changes, details on the derivation of the one-loop coefficient function added