HIGH-POWER N-OF-M(B) IN B-FLAVORED WIDTHS AND N=5-]INFINITY LIMIT

The leading term in the semileptonic width of heavy flavor hadrons dep ends on the fifth power of the heavy quark mass. We present an analysi s where this power can be self-consistently treated as a free paramete r n and the width can be studied in the limit n --> infinity. The resu lting expansion elucidates why the small velocity (SV) treatment is re levant for the inclusive semileptonic bic transition. The extended SV limit (ESV Limit) is introduced. The leading terms in the perturbative alpha(s) expansion enhanced by powers of n are automatically resummed by using the low-scale Euclidean mass. The large-n treatment explains why the scales of order mb in are appropriate. On the other hand, the scale cannot be too small since the factorially divergent perturbativ e corrections associated with running of alpha(s), show up. Both requi rements are met if we use the short-distance mass normalized at a scal e around m(b)/n similar to 1 GeV. A convenient definition of such low- scale operator-product-expansion-compatible masses is briefly discusse d.