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Title: Predictive formulation of the Nambu-Jona-Lasinio model

Abstract

A novel strategy to handle divergences typical of perturbative calculations is implemented for the Nambu-Jona-Lasinio model and its phenomenological consequences investigated. The central idea of the method is to avoid the critical step involved in the regularization process, namely, the explicit evaluation of divergent integrals. This goal is achieved by assuming a regularization distribution in an implicit way and making use, in intermediary steps, only of very general properties of such regularization. The finite parts are separated from the divergent ones and integrated free from effects of the regularization. The divergent parts are organized in terms of standard objects, which are independent of the (arbitrary) momenta running in internal lines of loop graphs. Through the analysis of symmetry relations, a set of properties for the divergent objects are identified, which we denominate consistency relations, reducing the number of divergent objects to only a few. The calculational strategy eliminates unphysical dependencies of the arbitrary choices for the routing of internal momenta, leading to ambiguity-free, and symmetry-preserving physical amplitudes. We show that the imposition of scale properties for the basic divergent objects leads to a critical condition for the constituent quark mass such that the remaining arbitrariness is removed. The model becomesmore » predictive in the sense that its phenomenological consequences do not depend on possible choices made in intermediary steps. Numerical results are obtained for physical quantities at the one-loop level for the pion and sigma masses and pion-quark and sigma-quark coupling constants.« less

Authors:
 [1];  [2];  [3]
  1. Departamento de Fisica, Universidade Federal de Santa Maria, 97119-900 Santa Maria, Rio Grande do Sul (Brazil)
  2. Departamento de Ciencias Exatas, Universidade Federal de Lavras, Caixa Postal 37, 37200-000, Lavras, Minas Gerais (Brazil)
  3. Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, Sao Paulo (Brazil)
Publication Date:
OSTI Identifier:
21249878
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 77; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.77.065025; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; COUPLING CONSTANTS; DISTRIBUTION; EVALUATION; MASS; PIONS; QUARKS; SIGMA PARTICLES; SYMMETRY

Citation Formats

Battistel, O A, Dallabona, G, and Krein, G. Predictive formulation of the Nambu-Jona-Lasinio model. United States: N. p., 2008. Web. doi:10.1103/PHYSREVD.77.065025.
Battistel, O A, Dallabona, G, & Krein, G. Predictive formulation of the Nambu-Jona-Lasinio model. United States. https://doi.org/10.1103/PHYSREVD.77.065025
Battistel, O A, Dallabona, G, and Krein, G. 2008. "Predictive formulation of the Nambu-Jona-Lasinio model". United States. https://doi.org/10.1103/PHYSREVD.77.065025.
@article{osti_21249878,
title = {Predictive formulation of the Nambu-Jona-Lasinio model},
author = {Battistel, O A and Dallabona, G and Krein, G},
abstractNote = {A novel strategy to handle divergences typical of perturbative calculations is implemented for the Nambu-Jona-Lasinio model and its phenomenological consequences investigated. The central idea of the method is to avoid the critical step involved in the regularization process, namely, the explicit evaluation of divergent integrals. This goal is achieved by assuming a regularization distribution in an implicit way and making use, in intermediary steps, only of very general properties of such regularization. The finite parts are separated from the divergent ones and integrated free from effects of the regularization. The divergent parts are organized in terms of standard objects, which are independent of the (arbitrary) momenta running in internal lines of loop graphs. Through the analysis of symmetry relations, a set of properties for the divergent objects are identified, which we denominate consistency relations, reducing the number of divergent objects to only a few. The calculational strategy eliminates unphysical dependencies of the arbitrary choices for the routing of internal momenta, leading to ambiguity-free, and symmetry-preserving physical amplitudes. We show that the imposition of scale properties for the basic divergent objects leads to a critical condition for the constituent quark mass such that the remaining arbitrariness is removed. The model becomes predictive in the sense that its phenomenological consequences do not depend on possible choices made in intermediary steps. Numerical results are obtained for physical quantities at the one-loop level for the pion and sigma masses and pion-quark and sigma-quark coupling constants.},
doi = {10.1103/PHYSREVD.77.065025},
url = {https://www.osti.gov/biblio/21249878}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 6,
volume = 77,
place = {United States},
year = {Sat Mar 15 00:00:00 EDT 2008},
month = {Sat Mar 15 00:00:00 EDT 2008}
}