High power [Formula presented] of [Formula presented] in [Formula presented]-flavored widths and [Formula presented] limit

The leading term in the semileptonic width of heavy flavor hadrons depends on the fifth power of the heavy quark mass. We present an analysis where this power can be self-consistently treated as a free parameter [Formula presented] and the width can be studied in the limit [Formula presented] The resulting expansion elucidates why the small velocity (SV) treatment is relevant for the inclusive semileptonic [Formula presented] transition. The extended SV limit (ESV limit) is introduced. The leading terms in the perturbative [Formula presented] expansion enhanced by powers of [Formula presented] are automatically resummed by using the low-scale Euclidean mass. The large-[Formula presented] treatment explains why the scales of order [Formula presented] are appropriate. On the other hand, the scale cannot be too small since the factorially divergent perturbative corrections associated with running of [Formula presented] show up. Both requirements are met if we use the short-distance mass normalized at a scale around [Formula presented] A convenient definition of such low-scale operator-product-expansion-compatible masses is briefly discussed.