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Title: Baryon Wilson loop area law in QCD

Abstract

There is still confusion about the correct form of the area law for the baryonic Wilson loop (BWL) of QCD. Strong-coupling (i.e., finite lattice spacing in lattice gauge theory) approximations suggest the form exp[{minus}{ital KA}{sub {ital Y}}], where {ital K} is the {ital q{bar q}} string tension and {ital A}{sub {ital Y}} is the global minimum area, generically a three-bladed area with the blades joined along a Steiner line ({ital Y} configuration). However, the correct answer is exp[{minus}({ital K}/2)({ital A}{sub 12}+{ital A}{sub 13}+{ital A}{sub 23})], where, e.g., {ital A}{sub 12} is the minimal area between quark lines 1 and 2 ({Delta} configuration). This second answer was given long ago, based on certain approximations, and is also strongly favored in lattice computations. In the present work, we derive the {Delta} law from the usual vortex-monopole picture of confinement, and show that, in any case, because of the 1/2 in the {Delta} law, this law leads to a larger value for the BWL (smaller exponent) than does the {ital Y} law. We show that the three-bladed, strong-coupling surfaces, which are infinitesimally thick in the limit of zero lattice spacing, survive as surfaces to be used in the non-Abelian Stokes{close_quote} theorem for themore » BWL, which we derive, and lead via this Stokes{close_quote} theorem to the correct {Delta} law. Finally, we extend these considerations, including perturbative contributions, to gauge groups SU({ital N}), with {ital N}{gt}3. {copyright} {ital 1996 The American Physical Society.}« less

Authors:
 [1]
  1. Physics Department, University of California, 405 S. Hilgard Avenue, Los Angeles, California 90095-1547 (United States)
Publication Date:
OSTI Identifier:
389504
Resource Type:
Journal Article
Journal Name:
Physical Review, D
Additional Journal Information:
Journal Volume: 54; Journal Issue: 10; Other Information: PBD: Nov 1996
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; QUANTUM CHROMODYNAMICS; WILSON LOOP; BARYONS; STRONG-COUPLING MODEL; MONOPOLES; CONFINEMENT; SU GROUPS

Citation Formats

Cornwall, J M. Baryon Wilson loop area law in QCD. United States: N. p., 1996. Web. doi:10.1103/PhysRevD.54.6527.
Cornwall, J M. Baryon Wilson loop area law in QCD. United States. https://doi.org/10.1103/PhysRevD.54.6527
Cornwall, J M. 1996. "Baryon Wilson loop area law in QCD". United States. https://doi.org/10.1103/PhysRevD.54.6527.
@article{osti_389504,
title = {Baryon Wilson loop area law in QCD},
author = {Cornwall, J M},
abstractNote = {There is still confusion about the correct form of the area law for the baryonic Wilson loop (BWL) of QCD. Strong-coupling (i.e., finite lattice spacing in lattice gauge theory) approximations suggest the form exp[{minus}{ital KA}{sub {ital Y}}], where {ital K} is the {ital q{bar q}} string tension and {ital A}{sub {ital Y}} is the global minimum area, generically a three-bladed area with the blades joined along a Steiner line ({ital Y} configuration). However, the correct answer is exp[{minus}({ital K}/2)({ital A}{sub 12}+{ital A}{sub 13}+{ital A}{sub 23})], where, e.g., {ital A}{sub 12} is the minimal area between quark lines 1 and 2 ({Delta} configuration). This second answer was given long ago, based on certain approximations, and is also strongly favored in lattice computations. In the present work, we derive the {Delta} law from the usual vortex-monopole picture of confinement, and show that, in any case, because of the 1/2 in the {Delta} law, this law leads to a larger value for the BWL (smaller exponent) than does the {ital Y} law. We show that the three-bladed, strong-coupling surfaces, which are infinitesimally thick in the limit of zero lattice spacing, survive as surfaces to be used in the non-Abelian Stokes{close_quote} theorem for the BWL, which we derive, and lead via this Stokes{close_quote} theorem to the correct {Delta} law. Finally, we extend these considerations, including perturbative contributions, to gauge groups SU({ital N}), with {ital N}{gt}3. {copyright} {ital 1996 The American Physical Society.}},
doi = {10.1103/PhysRevD.54.6527},
url = {https://www.osti.gov/biblio/389504}, journal = {Physical Review, D},
number = 10,
volume = 54,
place = {United States},
year = {Fri Nov 01 00:00:00 EST 1996},
month = {Fri Nov 01 00:00:00 EST 1996}
}