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Title: Hadron Physics and the Dyson-Schwinger Equations of QCD

Abstract

We use the Bethe-Salpeter equation in rainbow-ladder truncation to calculate the ground state mesons from the chiral limit to bottomonium, with an effective interaction that was previously fitted to the chiral condensate and pion decay constant. Our results are in reasonable agreement with the data, as are the vector and pseudoscalar decay constants. The meson mass differences tend to become constant in the heavy-quark limit. We also present calculations for the pion and rho electromagnetic form factors, and for the single-quark form factors of the {eta}c and J/{psi}.

Authors:
 [1]
  1. Dept. of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 (United States)
Publication Date:
OSTI Identifier:
21056913
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 892; Journal Issue: 1; Conference: QCHS7: 7. conference on quark confinement and the hadron spectrum, Ponta Delgada, Acores (Portugal), 2-7 Sep 2006; Other Information: DOI: 10.1063/1.2714348; (c) 2007 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; B QUARKS; BETHE-SALPETER EQUATION; BOTTOMONIUM; C QUARKS; CHIRALITY; ELECTROMAGNETIC FORM FACTORS; ETA C-2980 MESONS; GROUND STATES; J PSI-3097 MESONS; MASS DIFFERENCE; PIONS; QUANTUM CHROMODYNAMICS; REST MASS; RHO-770 MESONS; SCHWINGER FUNCTIONAL EQUATIONS; SCHWINGER SOURCE THEORY; T QUARKS

Citation Formats

Maris, Pieter. Hadron Physics and the Dyson-Schwinger Equations of QCD. United States: N. p., 2007. Web. doi:10.1063/1.2714348.
Maris, Pieter. Hadron Physics and the Dyson-Schwinger Equations of QCD. United States. doi:10.1063/1.2714348.
Maris, Pieter. Tue . "Hadron Physics and the Dyson-Schwinger Equations of QCD". United States. doi:10.1063/1.2714348.
@article{osti_21056913,
title = {Hadron Physics and the Dyson-Schwinger Equations of QCD},
author = {Maris, Pieter},
abstractNote = {We use the Bethe-Salpeter equation in rainbow-ladder truncation to calculate the ground state mesons from the chiral limit to bottomonium, with an effective interaction that was previously fitted to the chiral condensate and pion decay constant. Our results are in reasonable agreement with the data, as are the vector and pseudoscalar decay constants. The meson mass differences tend to become constant in the heavy-quark limit. We also present calculations for the pion and rho electromagnetic form factors, and for the single-quark form factors of the {eta}c and J/{psi}.},
doi = {10.1063/1.2714348},
journal = {AIP Conference Proceedings},
number = 1,
volume = 892,
place = {United States},
year = {Tue Feb 27 00:00:00 EST 2007},
month = {Tue Feb 27 00:00:00 EST 2007}
}
  • Dyson-Schwinger equations furnish a Poincare covariant framework within which to study hadrons. A particular feature is the existence of a nonperturbative, symmetry preserving truncation that enables the proof of exact results. The gap equation reveals that dynamical chiral symmetry breaking is tied to the long-range behavior of the strong interaction, which is thereby constrained by observables, and the pion is precisely understood, and seen to exist simultaneously as a Goldstone mode and a bound state of strongly dressed quarks. The systematic error associated with the simplest truncation has been quantified, and it underpins a one-parameter model efficacious in describing anmore » extensive body of mesonic phenomena. Incipient applications to baryons have brought successes and encountered challenges familiar from early studies of mesons, and promise a covariant field theory upon which to base an understanding of contemporary large momentum transfer data.« less
  • We apply Euclidean time methods to phenomenological Dyson-Schwinger models of hadrons. By performing a Fourier transform of the momentum space correlation function to Euclidean time and by taking the large Euclidean time limit, we project onto the lightest on-mass-shell hadron for given quantum numbers. The procedure, which actually resembles lattice gauge theory methods, allows the extraction of moments of structure functions, moments of light-cone wave functions, and form factors without {ital ad hoc} extrapolations to the on-mass-shell points. We demonstrate the practicality of the procedure with the example of the pion form factor. {copyright} {ital 1997} {ital The American Physicalmore » Society}« less
  • The Dyson-Schwinger equations (DSEs) are a tower of coupled integral equations that relate the Green functions of QCD to one another and include the equation for the quark self-energy, the analogue of the gap equation in superconductivity; the Bethe-Salpeter equation, the solution of which yields meson bound state amplitudes; and the covariant Fadde`ev equation, whose solution provides baryon bound state amplitudes. Solving the tower of DSEs provides the solution of QCD; a field theory being completely defined when all of its n-point functions are known. The nonperturbative DSE approach is being developed as a complement and computationally less-intensive alternative tomore » numerical simulations of lattice-QCD. Significant progress has recently been made and it is now possible to make direct comparisons between quantities calculated using the DSE approach and the results of numerical simulations of Abelian gauge theories. Cross-fertilization between numerical simulations of lattice-QCD and DSE studies is a presently underutilized but particularly useful means of developing a detailed understanding of nonperturbative QCD. In this presentation the author describes how symmetries are used to ensure that the sensitivity of calculated observables to the truncation of the tower of DSEs is small. A phenomenologically efficacious application of the DSE approach, which employs a parametrisation of the gluon propagator and facilitates the extrapolation application of known properties of QCD at large spacelike-q{sup 2} to the region of small spacelike-q{sup 2}, is discussed and illustrated via the calculation of hadronic observables, such as: {pi}{pi} scattering lengths; pion and kaon electromagnetic form factors; baryon spectroscopy and electromagnetic properties.« less
  • Continuum strong QCD is the application of models and continuum quantum field theory to the study of phenomena in hadronic physics, which includes; e.g., the spectrum of QCD bound states and their interactions; and the transition to, and properties of, a quark gluon plasma. We provide a contemporary perspective, couched primarily in terms of the Dyson-Schwinger equations but also making comparisons with other approaches and models. Our discourse provides a practitioners' guide to features of the Dyson-Schwinger equations [such as confinement and dynamical chiral symmetry breaking] and canvasses phenomenological applications to light meson and baryon properties in cold, sparse QCD.more » These provide the foundation for an extension to hot, dense QCD, which is probed via the introduction of the intensive thermodynamic variables: chemical potential and temperature. We describe order parameters whose evolution signals deconfinement and chiral symmetry restoration, and chronicle their use in demarcating the quark gluon plasma phase boundary and characterizing the plasma's properties. Hadron traits change in an equilibrated plasma. We exemplify this and discuss putative signals of the effects. Finally, since plasma formation is not an equilibrium process, we discuss recent developments in kinetic theory and its application to describing the evolution from a relativistic heavy ion collision to an equilibrated quark gluon plasma.« less
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