High power n of m{sub b} in b-flavored widths and n={bold 5{r_arrow}{infinity}} limit
- Department of Physics, University of Notre Dame du Lac, Notre Dame, Indiana 46556 (United States)
- Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455 (United States)
- TH Division, CERN, CH 1211 Geneva 23 (Switzerland)
- Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188350 (Russia)
- Budker Institute of Nuclear Physics, Novosibirsk 630090 (Russia)
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 n and the width can be studied in the limit n{r_arrow}{infinity}. The resulting expansion elucidates why the small velmcity (SV) treatment is relevant for the inclusive semileptonic b{r_arrow}c transition. The extended SV limit (ESV limit) is introduced. The leading terms in the perturbative {alpha}{sub 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 m{sub b}/n are appropriate. On the other hand, the scale cannot be too small since the factorially divergent perturbative corrections associated with running of {alpha}{sub s} show up. Both requirements are met if we use the short-distance mass normalized at a scale around m{sub b}/n{approximately}1GeV. A convenient definition of such low-scale operator-product-expansion-compatible masses is briefly discussed. {copyright} {ital 1997} {ital The American Physical Society}
- Research Organization:
- Univ. of Minnesota, Minneapolis, MN (United States)
- DOE Contract Number:
- FG02-94ER40823
- OSTI ID:
- 542753
- Journal Information:
- Physical Review, D, Vol. 56, Issue 7; Other Information: PBD: Oct 1997
- Country of Publication:
- United States
- Language:
- English
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