# 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 fi2048excited 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 (United States)

- Sponsoring Org.:
- USDOE Office of Energy Research (ER) (United States)

- OSTI Identifier:
- 5159417

- Report Number(s):
- JLAB-THY-00-21; DOE/ER/40150-1738; hep-ph/0006346

- DOE Contract Number:
- AC05-84ER40150

- Resource Type:
- Miscellaneous

- Resource Relation:
- Other Information: No journal information given for this preprint

- Country of Publication:
- United States

- Language:
- English

- Subject:
- DUALITY; EXCITATION; EXCITED STATES; OPERATOR PRODUCT EXPANSION; OSCILLATIONS; QUANTUM CHROMODYNAMICS; QUARKS; SEMILEPTONIC DECAY; SUM RULES; HADRONS; ENERGY-LEVEL TRANSITIONS; ENERGY LEVELS; SERIES EXPANSION; QUANTUM FIELD THEORY; FERMIONS; WEAK PARTICLE DECAY; EQUATIONS; ELEMENTARY PARTICLES; FIELD THEORIES; PARTICLE DECAY

### Citation Formats

```
Richard F. Lebed, and Nikolai G. Uraltsev.
```*Precision Studies of Duality in the 't Hooft Model*. United States: N. p., 2000.
Web.

```
Richard F. Lebed, & Nikolai G. Uraltsev.
```*Precision Studies of Duality in the 't Hooft Model*. United States.

```
Richard F. Lebed, and Nikolai G. Uraltsev. Thu .
"Precision Studies of Duality in the 't Hooft Model". United States.
```

```
@article{osti_5159417,
```

title = {Precision Studies of Duality in the 't Hooft Model},

author = {Richard F. Lebed and Nikolai G. Uraltsev.},

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 fi2048excited 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 = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2000},

month = {6}

}