Facets of confinement and dynamical chiral symmetry breaking
The gap equation is a cornerstone in understanding dynamical chiral symmetry breaking and may also provide clues to confinement. A symmetry-preserving truncation of its kernel enables proofs of important results and the development of an efficacious pheno
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THE EUROPEAN PHYSICAL JOURNAL
A
Facets of confinement and dynamical chiral symmetry breaking P. Maris!, A. Raya2 , C.D. Roberts 3 ,4,a, and S.M. Schmidt 5 Department of Physics, North Carolina State University, Raleigh NC 27695-8202, USA 1nstituto de F(sica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Apartado Postal 2-82, Morelia, Michoacan, Mexico 3 Physics Division, Argonne National Laboratory, Argonne 1L 60439-4843, USA 4 Fachbereich Physik, Un ivers it at Rostock, D-18051 Rostock, Germany 5 Helmholtz-Gemeinschaft, Ahrstrasse 45, D-53175 Bonn, Germany 1
2
Received: 30 September 2002 / Published online: 22 October 2003 -
© Societa 1taliana di
Fisica / Springer-Verlag 2003
Abstract. The gap equation is a cornerstone in understanding dynamical chiral symmetry breaking and may also provide clues to confinement. A symmetry-preserving truncation of its kernel enables proofs of important results and the development of an efficacious phenomenology. We describe a model of the kernel that yields: a momentum-dependent dressed-quark propagator in fair agreement with quenched latticeQCD results; and chirallimit values, f~ = 68 MeV and (qq) = -(190 MeV)3. It is compared with models inferred from studies of the gauge sector.
PACS. 12.38.Aw General properties of QCD (dynamics, confinement, etc.) - 1l.30.Rd Chiral symmetries
1 Introduction We will address these topics from the perspective of QeD's Dyson-Schwinger equations (DSEs) [1]. The DSEs are a keystone in proving renormalisability and provide a generating tool for perturbation theory. The latter point is very important in applications to low-energy phenomena because it means that the model-dependence which necessarily appears in continuum studies of nonperturbative QCD is restricted to the infrared; i.e., to momentum scales :S 1 GeV 2 . This feature has successfully been exploited in applications to the spectra [2,3], and strong [1] and electroweak [5] interactions of mesons. It also mitigates, to a useful extent, some of the problems with the approach; e.g., it helps in developing reliable truncations for the coupled system of DSEs. Recent successes are founded on an accurate understanding of dynamical chiral symmetry breaking (DCSB), and its role in resolving the dichotomy of the pion [6] (as both a Goldstone mode and a massless bound state of massive constituents) and its relation to the long-range behaviour of the effective coupling between quarks [7].
a
e-mail: [email protected]
2 Dynamical chiral symmetry breaking This is a purely nonperturbative phenomenon that can be studied via QCD's gap equation:
(1) wherein Tn is the current-quark bare mass, g is the coupling constant, D jJ,V (p- q) is the dressed-gluon propagator, r:; (q, p) is the dressed-quark-gluon vertex; and the solution is the dressed-quark propagator
S (p) =
1
--,.-;-:::-:-=-:--::-:-
ir . p A(p2) + B(p2)
(2)
(Equation (1) is the unrenormalised equation: renormalisation will only be mentioned as necessary.) As noted in the introduction, one can use the gap equation
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