Coupled-channel dynamics in the Nambu--Jona-Lasinio model

Journal Article · Sat May 01 00:00:00 EDT 1993 · Physical Review, C (Nuclear Physics); (United States)

DOI:https://doi.org/10.1103/PhysRevC.47.2356· OSTI ID:6645189

Celenza, L S; Pantziris, A; Shakin, C M; Szweda, J ^[1]

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1. Department of Physics and Center for Nuclear Theory, Brooklyn College of the City University of New York, Brooklyn, New York 11210 (United States)

We study the scalar-isoscalar sector of the Nambu--Jona-Lasinio (NJL) model and extend the model to include a description of the coupling of the quark-antiquark states to the two-pion continuum. The [ital q[bar q]] interaction gives rise to a sigma meson, which takes on a width and energy shift that depends upon the strength of the coupling for [ital q]+[ital [bar q]][r arrow][pi]+[pi]. (For weak channel coupling, the resonance is located at the mass of the sigma, [ital m][sub [sigma]][congruent]2[ital m][sub [ital q]][sup cons], where [ital m][sub [ital q]][sup cons] is the constituent quark mass of the NJL model.) We consider two models for the [ital q[bar q]][r arrow][pi][pi] coupling. In the first model, we find a low-energy resonance, with the resonance energy [ital E][sub [ital R]][le]2[ital m][sub [ital q]][sup cons]. We then see that the values, obtained from the analysis of experimental data, of the scalar-isoscalar phase shift describing [pi][pi] scattering [delta][sub 0][sup 0], are not compatible with the existence of a low-mass sigma. In the second model, the resonance is pushed upward into the region of the two-quark continuum, [ital E][sub [ital R]][gt]2[ital m][sub [ital q]][sup cons]. This second model provides an example of a phenomenon where the behavior of the [ital q[bar q]] [ital T] matrix is parametrized for [ital q][sup 2][le]0 by a mass that is [ital smaller] than the physical mass that characterizes the pole in the [ital T] matrix. The behavior of the second model suggests how the absence of experimental evidence for a low-mass sigma may be reconciled with the importance of such a meson in nuclear structure studies.

• OSTI ID: 6645189
• Journal Information: Physical Review, C (Nuclear Physics); (United States), Journal Name: Physical Review, C (Nuclear Physics); (United States) Vol. 47:5; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

662230* -- Quantum Chromodynamics-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYONS
BOSONS
COMPOSITE MODELS
COUPLED CHANNEL THEORY
ELEMENTARY PARTICLES
FERMIONS
FIELD THEORIES
HADRONS
HYPERONS
MATHEMATICAL MODELS
MESONS
NUCLEAR STRUCTURE
PARTICLE MODELS
PIONS
PSEUDOSCALAR MESONS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARK MODEL
QUARKONIUM
RESONANCE
SCALAR FIELDS
SIGMA BARYONS
STRANGE PARTICLES