Finely tuned Nambu--Jona-Lasinio and linear. sigma. models

Journal Article · Sat Aug 15 04:00:00 EDT 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.46.1768· OSTI ID:7158255

Fishbane, P M ^[1]; Norton, R E; Truong, T N ^[2]

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1. Laboratoire de Physique Theorique et Haute Energies, Universite de Paris-XI, Batiment 211, Orsay (France)
2. Centre de Physique Theorique, Ecole Polytechnique, 91128 Palaiseau (France)

It is argued anew that the Nambu--Jona-Lasinio (NJL) model is renormalizable in the sense that all cutoff dependence (ignoring inverse powers of the cutoff) can be absorbed into a renormalized mass parameter and renormalized Yukawa and four-scalar coupling constants {ital G} and {lambda}, respectively. These couplings are not independent, although the relation between them depends upon subtle details of the cutoff procedure. At energies very much less than the cutoff the NJL model is equivalent to the linear {sigma} model. From the renormalization group equations of the latter model, it is shown that at scales very much less than the cutoff the couplings {ital G} and {lambda} are small and the ratio {lambda}/{ital G}{sup 2} is approximately determined to within an error which for {ital N}{lt}{infinity} ({ital N}= number of colors'') is less than the corrections coming from one loop. The average {sigma} field {ital v}, the {sigma} mass {ital M}{sub {sigma}}, and the fermion mass {ital m} are calculated in the one-loop (fermion or scalar) approximation.

• DOE Contract Number: AS05-89ER40518
• OSTI ID: 7158255
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 46:4; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662120 -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSON-EXCHANGE MODELS
COUPLING CONSTANTS
FERMIONS
MASS RENORMALIZATION
MATHEMATICAL MODELS
NUCLEAR POTENTIAL
PARTICLE MODELS
PERIPHERAL MODELS
POTENTIALS
PROPAGATOR
RENORMALIZATION
SCALAR FIELDS
SIGMA MODEL
SYMMETRY BREAKING
YUKAWA POTENTIAL