Duality in semileptonic inclusive B-decays in potential models: regular versus singular potentials

Making use of the nonrelativistic potential model for the description of me sons, and working in the Shifman-Voloshin limit, we compare the integrated rate Gamma (B --> X(c)lv) calculated as a sum of the individual decay rates to the quantum-mechanical analog of the OPE. In the case of a potential re gular at the origin, we find a well-defined duality violation, which is, ho wever, exponentially small. It corresponds to the charm resonances kinemati cally forbidden in the decay process, but apparently picked up by the OPE. For singular potentials, we do not obtain a full OPE series, but only a lim ited Taylor expansion, since the coefficients become infinite beyond some o rder. In this case, we do not find an indication of duality violation: the difference is smaller than the last term of the limited expansion. This emp hasizes that the case of singular potentials, which may be relevant for QCD , deserves further study. (C) 2001 Published by Elsevier Science B.V.