A 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 of 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 ones. 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 become 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.

38 pages, 1 figure, To appear in Phy.Rev.D

References in corpus (12)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• NJL-model analysis of dense quark matter
• Baryons as non-topological chiral solitons
• Chiral Lagrangians and Nambu-Jona-Lasinio like models
• Pion Observables in the Extended NJL Model with Vector and Axial-Vector Mesons
• Role of Ambiguities and Gauge Invariance in the Calculation of the Radiatively Induced Chern-Simons Shift in Extended Q.E.D.
• Consistency in Regularizations of the Gauged NJL Model at One Loop Level
• Regularization in the Gauged Nambu--Jona-Lasinio Model
• Confined Chiral Solitons in the Spectral Quark Model
• Anomalies Dismissed of Ambiguities and the Neutral Pion Decay
• Anomalies in Ward Identities for Three-Point Functions Revisited
• Elimination of the vacuum instability for finite nuclei in the relativistic $\sigma$-$\omega$ model

Cited by in corpus (10)

• Charmed mesons with a symmetry-preserving contact interaction
• Thermodynamics and Phase Structure of the Two-Flavor Nambu--Jona-Lasinio Model Beyond Large-N_c
• Extension of the Nambu--Jona-Lasinio model at high densities and temperatures by using an implicit regularization scheme
• Symmetry-preserving contact interaction model for heavy-light mesons
• Charmed mesons at finite temperature and chemical potential
• From scale properties of physical amplitudes to a predictive formulation of the Nambu-Jona-Lasinio model
• Clifford algebra Cl(0,6) approach to beyond the standard model and naturalness problems
• Electroweak and Majorana Sector Higgs Bosons and Pseudo-Nambu-Goldstone Bosons
• Dynamical Symmetry Breaking and Negative Cosmological Constant
• Properties of predictive formulation of the Nambu-Jona-Lasinio model and ghost problem