Entropy, confinement, and chiral symmetry breaking

Journal Article · Fri Apr 01 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.076001· OSTI ID:21537756

Cornwall, John M ^[1]

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1. Department of Physics and Astronomy, University of California, Los Angeles California 90095 (United States)

This paper studies the way in which confinement leads to chiral symmetry breaking (CSB) through a gap equation. We argue that a combination of entropic effects, related to fluctuations of Wilson loops with massless constituents, and an Abelian gauge invariance of the confinement action as expressed in terms of the usual confining effective propagator 8{pi}K{sub F{delta}{mu}{nu}}/k{sup 4}, in effect removes infrared singularities coming from use of this propagator in a standard gap equation (K{sub F} is the string tension). Beginning from an Abelian gauge-invariant description of CSB that differs from this standard gap equation, we show how to extract a corresponding gap equation that incorporates both entropic effects and Abelian gauge invariance by replacement of the confining propagator with 8{pi}K{sub F{delta}{mu}{nu}}/(k{sup 2}+m{sup 2}){sup 2}. Here the finite mass m turns out to be {approx_equal}M(0)[M(p{sup 2}) is the running quark mass], based on an extension of an old calculation of the author. This massive propagator gives semiquantitatively two critical properties of confinement: (1) a negative contribution to the confining potential coming from entropy; (2) an infrared cutoff required by Abelian gauge invariance. Entropic effects lead to a qq condensate and contribute a negative term {approx}-K{sub F}/M(0), essential for a massless pion, to the pion Hamiltonian. The resulting gap equation leads to M{sup 2}(0){approx_equal}K{sub F}/{pi}. We argue that one-gluon exchange is not strong enough in the IR to drive quark CSB, but in any case is necessary to get the correct renormalization-group ultraviolet behavior. We find the standard renormalization-group result with the improvement that the prefactor (related to <qq>) can be calculated from the confining solution. Finally, we briefly point out the Minkowski-space virtues of using a principal-part propagator to describe confinement.

• OSTI ID: 21537756
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 7; Other Information: DOI: 10.1103/PhysRevD.83.076001; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRAL SYMMETRY
CONDENSATES
CONFINEMENT
ENTROPY
FLUCTUATIONS
GAUGE INVARIANCE
GLUONS
HAMILTONIANS
MASS
MINKOWSKI SPACE
PIONS
PROPAGATOR
QUARKS
RENORMALIZATION
SINGULARITY
SYMMETRY BREAKING
WILSON LOOP
BOSONS
ELEMENTARY PARTICLES
FERMIONS
HADRONS
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MESONS
PHYSICAL PROPERTIES
PSEUDOSCALAR MESONS
QUANTUM OPERATORS
SPACE
SYMMETRY
THERMODYNAMIC PROPERTIES
VARIATIONS