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Title: Precision Studies of Duality in the 't Hooft Model

Abstract

The authors address numerical aspects of local quark-hadron duality using the example of the exactly solvable 't Hooft model, two-dimensional QCD with Nc ?8. The primary focus of these studies is total semileptonic decay widths relevant for extracting (Vcb) and (Vub). They compare the exact channel-by-channel sum of exclusive modes to the corresponding rates obtained in the standard 1/mQ expansion arising from the Operator Product Expansion. An impressive agreement sets in unexpectedly early, immediately after the threshold for the first hadronic excitation in the final state. Yet even at higher energy release it is possible to discern the seeds of duality-violating oscillations. They find the ''Small Velocity'' sum rules to be exceptionally well saturated already by the first excited state. They also obtain a convincing degree of duality in the differential distributions and in an analogue of Re+e-(s). Finally, they discuss possible lessons for semileptonic decays of actual heavy quarks in QCD.

Authors:
;
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility, Newport News, VA (US)
Sponsoring Org.:
USDOE Office of Energy Research (ER) (US)
OSTI Identifier:
760435
Report Number(s):
JLAB-THY-00-21; DOE/ER/40150-1738; hep-ph/0006346
TRN: US0100883
DOE Contract Number:  
AC05-84ER40150
Resource Type:
Journal Article
Journal Name:
Phys.Rev.D62:094011,2000
Additional Journal Information:
Journal Volume: D; Journal Issue: 62; Other Information: Submitted to Phys.Rev.D62:094011,2000; PBD: 1 Jun 2000
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DUALITY; EXCITATION; EXCITED STATES; OPERATOR PRODUCT EXPANSION; OSCILLATIONS; QUANTUM CHROMODYNAMICS; QUARKS; SEMILEPTONIC DECAY; SUM RULES; VELOCITY

Citation Formats

Lebed, R.F., and Uraltsev, N.G. Precision Studies of Duality in the 't Hooft Model. United States: N. p., 2000. Web. doi:10.1103/PhysRevD.62.094011.
Lebed, R.F., & Uraltsev, N.G. Precision Studies of Duality in the 't Hooft Model. United States. doi:10.1103/PhysRevD.62.094011.
Lebed, R.F., and Uraltsev, N.G. Thu . "Precision Studies of Duality in the 't Hooft Model". United States. doi:10.1103/PhysRevD.62.094011.
@article{osti_760435,
title = {Precision Studies of Duality in the 't Hooft Model},
author = {Lebed, R.F. and Uraltsev, N.G.},
abstractNote = {The authors address numerical aspects of local quark-hadron duality using the example of the exactly solvable 't Hooft model, two-dimensional QCD with Nc ?8. The primary focus of these studies is total semileptonic decay widths relevant for extracting (Vcb) and (Vub). They compare the exact channel-by-channel sum of exclusive modes to the corresponding rates obtained in the standard 1/mQ expansion arising from the Operator Product Expansion. An impressive agreement sets in unexpectedly early, immediately after the threshold for the first hadronic excitation in the final state. Yet even at higher energy release it is possible to discern the seeds of duality-violating oscillations. They find the ''Small Velocity'' sum rules to be exceptionally well saturated already by the first excited state. They also obtain a convincing degree of duality in the differential distributions and in an analogue of Re+e-(s). Finally, they discuss possible lessons for semileptonic decays of actual heavy quarks in QCD.},
doi = {10.1103/PhysRevD.62.094011},
journal = {Phys.Rev.D62:094011,2000},
number = 62,
volume = D,
place = {United States},
year = {2000},
month = {6}
}