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Title: Topological susceptibility in the SU(3) gauge theory

Abstract

We compute the topological susceptibility for the SU(3) Yang-Mills theory by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r{sub 0}{sup 4}{chi} = 0.059(3), which corresponds to {chi} = (191 {+-} 5 MeV)4 if FK is used to set the scale. Our result supports the Witten-Veneziano explanation for the large mass of the {eta}'. Comments on the large-volume distribution of the topological charge are presented.

Authors:
 [1]
  1. CERN, Department of Physics, TH Division, CH-1211 Geneva 23 (Switzerland)
Publication Date:
OSTI Identifier:
20787629
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 806; Journal Issue: 1; Conference: International workshop on quantum chromodynamics: Theory and experiment, Conversano, Bari (Italy), 16-20 Jun 2005; Other Information: DOI: 10.1063/1.2163756; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHARGE DENSITY; DISTRIBUTION; ETA PRIME-958 MESONS; FERMIONS; GAUGE INVARIANCE; MEV RANGE; QUANTUM CHROMODYNAMICS; REST MASS; SU-3 GROUPS; TOPOLOGY; YANG-MILLS THEORY

Citation Formats

Del Debbio, Luigi. Topological susceptibility in the SU(3) gauge theory. United States: N. p., 2006. Web. doi:10.1063/1.2163756.
Del Debbio, Luigi. Topological susceptibility in the SU(3) gauge theory. United States. doi:10.1063/1.2163756.
Del Debbio, Luigi. Thu . "Topological susceptibility in the SU(3) gauge theory". United States. doi:10.1063/1.2163756.
@article{osti_20787629,
title = {Topological susceptibility in the SU(3) gauge theory},
author = {Del Debbio, Luigi},
abstractNote = {We compute the topological susceptibility for the SU(3) Yang-Mills theory by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r{sub 0}{sup 4}{chi} = 0.059(3), which corresponds to {chi} = (191 {+-} 5 MeV)4 if FK is used to set the scale. Our result supports the Witten-Veneziano explanation for the large mass of the {eta}'. Comments on the large-volume distribution of the topological charge are presented.},
doi = {10.1063/1.2163756},
journal = {AIP Conference Proceedings},
number = 1,
volume = 806,
place = {United States},
year = {Thu Jan 12 00:00:00 EST 2006},
month = {Thu Jan 12 00:00:00 EST 2006}
}
  • The topological susceptibility in a gauge theory with the SU(3) symmetry group is calculated by the Monte Carlo method. The result agrees with that calculated previously for the SU(2) group and is roughly two orders of magnitude smaller than that required for the solution assumed for the U/sub A/(1) problem.
  • The topological susceptibility is calculated within the Hamiltonian approach to Yang-Mills theory in Coulomb gauge, using the vacuum wave functional previously determined by a variational solution of the Yang-Mills Schroedinger equation. The numerical result agrees qualitatively with the predictions of lattice simulations.
  • The topological susceptibility of the SU(3) random vortex world-surface ensemble, an effective model of infrared Yang-Mills dynamics, is investigated. The model is implemented by composing vortex world surfaces of elementary squares on a hypercubic lattice, supplemented by an appropriate specification of vortex color structure on the world surfaces. Topological charge is generated in this picture by writhe and self-intersection of the vortex world surfaces. Systematic uncertainties in the evaluation of the topological charge, engendered by the hypercubic construction, are discussed. Results for the topological susceptibility are reported as a function of temperature and compared to corresponding measurements in SU(3) latticemore » Yang-Mills theory. In the confined phase, the topological susceptibility of the random vortex world-surface ensemble appears quantitatively consistent with Yang-Mills theory. As the temperature is raised into the deconfined regime, the topological susceptibility falls off rapidly, but significantly less so than in SU(3) lattice Yang-Mills theory. Possible causes of this deviation, ranging from artefacts of the hypercubic description to more physical sources, such as the adopted vortex dynamics, are discussed.« less
  • The renormalization functions involved in the determination of the topological susceptibility in the SU(2) lattice gauge theory are extracted by direct measurements, without relying on perturbation theory. The determination exploits the phenomenon of critical slowing down to allow the separation of perturbative and nonperturbative effects. The results are in good agreement with perturbative computations.