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Title: Precision studies of duality in the 't Hooft model

Abstract

We address the numerical aspects of local quark-hadron duality using the example of the exactly solvable 't Hooft model, two-dimensional QCD with N{sub c}{yields}{infinity}. The primary focus of these studies is the total semileptonic decay widths relevant for extracting |V{sub cb}| and |V{sub ub}|. We compare the exact channel-by-channel sum of exclusive modes to the corresponding rates obtained in the standard 1/m{sub Q} 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. We find the ''small velocity'' sum rules to be exceptionally well saturated already by the first excited state. We also obtain a convincing degree of duality in the differential distributions and in an analogue of R{sub e{sup +}e{sup -}}(s). Finally, we discuss possible lessons for semileptonic decays of actual heavy quarks in QCD.

Authors:
;
Publication Date:
Sponsoring Org.:
(US)
OSTI Identifier:
40205177
Resource Type:
Journal Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 62; Journal Issue: 9; Other Information: DOI: 10.1103/PhysRevD.62.094011; Othernumber: PRVDAQ000062000009094011000001; 046021PRD; PBD: 1 Nov 2000; Journal ID: ISSN 0556-2821
Publisher:
The American Physical Society
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; SEEDS; SEMILEPTONIC DECAY; SUM RULES; VELOCITY

Citation Formats

Lebed, Richard F, and Uraltsev, Nikolai G. Precision studies of duality in the 't Hooft model. United States: N. p., 2000. Web. doi:10.1103/PhysRevD.62.094011.
Lebed, Richard F, & Uraltsev, Nikolai G. Precision studies of duality in the 't Hooft model. United States. https://doi.org/10.1103/PhysRevD.62.094011
Lebed, Richard F, and Uraltsev, Nikolai G. 2000. "Precision studies of duality in the 't Hooft model". United States. https://doi.org/10.1103/PhysRevD.62.094011.
@article{osti_40205177,
title = {Precision studies of duality in the 't Hooft model},
author = {Lebed, Richard F and Uraltsev, Nikolai G},
abstractNote = {We address the numerical aspects of local quark-hadron duality using the example of the exactly solvable 't Hooft model, two-dimensional QCD with N{sub c}{yields}{infinity}. The primary focus of these studies is the total semileptonic decay widths relevant for extracting |V{sub cb}| and |V{sub ub}|. We compare the exact channel-by-channel sum of exclusive modes to the corresponding rates obtained in the standard 1/m{sub Q} 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. We find the ''small velocity'' sum rules to be exceptionally well saturated already by the first excited state. We also obtain a convincing degree of duality in the differential distributions and in an analogue of R{sub e{sup +}e{sup -}}(s). Finally, we discuss possible lessons for semileptonic decays of actual heavy quarks in QCD.},
doi = {10.1103/PhysRevD.62.094011},
url = {https://www.osti.gov/biblio/40205177}, journal = {Physical Review D},
issn = {0556-2821},
number = 9,
volume = 62,
place = {United States},
year = {Wed Nov 01 00:00:00 EST 2000},
month = {Wed Nov 01 00:00:00 EST 2000}
}