Analytical and numerical study of the Schwinger-Dyson equation with four-fermion coupling

Journal Article · Sun Oct 15 04:00:00 EDT 1989 · Physical Review (Section) D: Particles and Fields; (USA)

DOI:https://doi.org/10.1103/PhysRevD.40.2697· OSTI ID:5354666

Takeuchi, T ^[1]

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1. Center for Theoretical Physics, Department of Physics, Yale University, New Haven, Connecticut 06511 (US)

The dressed ladder Schwinger-Dyson equation for the fermion self-energy {Sigma}(p{sup 2}) with an additional four-fermion coupling term is studied both analytically and numerically. We limit our analysis to asymptotically free theories with a large hierarchy between the confinement scale {Lambda}{sub c} and the ultraviolet cutoff {Lambda}. The dependence of the dynamical mass {Sigma}{sub 0} identical {Sigma}(0) and the fermion condensate {l angle} {Psi}{Psi}{r angle} on the four-fermion coupling strength {lambda} is derived. It is found that there exists a critical four-fermion coupling strength {lambda}{sub 2}, such that in the region {lambda}{lt}{lambda}{sub 2} the dynamical mass {Sigma}{sub 0} is of the order of the confinement scale {Lambda}{sub c}, while in the region {lambda}{gt}{lambda}{sub 2} the dynamical mass {Sigma}{sub 0} is of the order of the cutoff {Lambda}. In the region {lambda}{lt}{lambda}{sub 2}, the condensate {l angle} {Psi}{Psi}{r angle} picks up an enhancement factor {lambda}{sub 2}/({lambda}{sub 2}{minus}{lambda}), and in the limit {lambda}{r arrow}{lambda}{sub 2}, reaches the order of {Lambda}{sup 2}{Lambda}{sub c}. In the region {lambda}{gt}{lambda}{sub 2}, the condensate {l angle}{Psi}{Psi}{r angle} is of the order of {Lambda}{sup 3}. The application of the equation to technicolor theories is also discussed.

• OSTI ID: 5354666
• Journal Information: Physical Review (Section) D: Particles and Fields; (USA), Journal Name: Physical Review (Section) D: Particles and Fields; (USA) Vol. 40:8; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRAL SYMMETRY
COLOR MODEL
COMPOSITE MODELS
COUPLING
ELEMENTARY PARTICLES
ENERGY
FERMIONS
FIELD THEORIES
FOUR-BODY PROBLEM
GAUGE INVARIANCE
INTERACTIONS
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LADDER APPROXIMATION
MANY-BODY PROBLEM
MASS
MATHEMATICAL MODELS
PARTICLE INTERACTIONS
PARTICLE MODELS
POSTULATED PARTICLES
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARK MODEL
QUARKS
SELF-ENERGY
SYMMETRY
SYMMETRY BREAKING
ULTRAVIOLET DIVERGENCES