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The leading term in the semileptonic width of heavy flavor hadrons depends onthe fifth power of the heavy quark mass. We present an analysis where thispower can be self-consistently treated as a free parameter n and the width canbe studied in the limit n -> oo. The resulting expansion elucidates why thesmall velocity (SV) treatment is relevant for the inclusive semileptonic b->ctransition. The extended SV limit (ESV limit) is introduced. The leading termsin the perturbative alpha_s expansion enhanced by powers of n are automaticallyresummed by using the low-scale Euclidean mass. The large-n treatment explainswhy the scales of order m_b/n are appropriate. On the other hand, the scalecannot be too small since the factorially divergent perturbative correctionsassociated with running of alpha_s show up. Both requirements are met if we usethe short-distance mass normalized at a scale around m_b/n \sim 1 GeV. Aconvenient definition of such low-scale OPE-compatible masses is brieflydiscussed.Comment: 26 pages, 1 figure; plain LaTe

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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