Effect of the A-Term on the Nucleon Properties in the Extended Linear Sigma Model

Abstract

In this paper, the effect of the gradient-expanded meson term on the nucleon properties is investigated. The A-term is included in the extended linear sigma model in the framework of some aspects of QCD. The field equations have been solved in the mean-field approximation for the hedgehog baryon state. We find that the inclusion of the new term improves the description of the nucleon properties in comparison with other models.Keywords Mean-field approximation · Nucleon properties · Linear sigma model IntroductionIt is now becoming clear that the chiral symmetry of the QCD Lagrangian and its spontaneous breaking [1] play a very important role in determining the structure of low-mass hadrons, which consist of u, d and s quarks, and simultaneously play a crucial role in hadron correlators in mediating the spontaneous chiral symmetry breaking [2, 3].One of the effective models in describing hadron properties is the linear sigma model which has been suggested earlier by Gell-Mann and Levy [4] to describe nucleons interacting via sigma (σ ) and pion (π ) exchanges. This model is a principal example of spontaneous symmetry breaking. Some of the consequences of this model, however, are known to be in conflict with observation. Notably, the isoscalar pion-nucleon (πN ) scattering length predicted by the model is larger than experimental value by an order of magnitude; see e.g. Refs.[5-8]. Many solutions for this model have already been suggested. Birse and Banerjee [5] constructed equations of motion treating both the σ -and π -fields as time-independent classical fields and quarks in the hedgehog spinor state. Birse [6] generalized this mean-field model to include angular and momentum and isospin projection. Goeke et al. [7] investigated hadron properties in a chiral model for the nucleon based on the linear sigma model with scalar-isoscalar and scalar-isovector mesons coupled to quarks using the coherent pair M. Abu-Shady ( )

Meson Properties at Finite Temperature in the Linear Sigma Model

“…3, 4, we examine the dependence of the sigma and pion fields on temperature T , which it has not been examined in previous calculations as in [1,2]. In our work, we used the same iteration method to calculate the pion and sigma fields in the case of the effective potential as we used before at zero temperature as in [19][20][21]. In Fig.…”

“…To solve (20), we integrate a suitable Green's function over the source fields as in [19][20][21], thus…”

Effect of a logarithmic mesonic potential on nucleon properties in the coherent-pair approximation

“…Broniowski and Golli [18] analyzed a particular extension of the linear σ model coupled to valence quarks containing an additional term with two ingredients of the chiral fields and they investigated the dynamic consequences of this term and its relevance to the phenomenology of soliton models of the nucleons. In addition, this model is investigated in the mean-field approximation [19] and the coherent-pair approximation [20] for hadron properties. Dmitrasinovic and Myhrer [21] used an extended linear σ model [22] in which a pair of extra terms are added to the original linear σ model in order to improve pion-nucleon scattering and the nucleon σ term.…”

Mid-point technique for calculating divergent integrals

“…In this work, we focus on the quark models that deal with strong interactions between quarks inside nucleon. There are different quark models such as the quark sigma model and its extension [9][10][11][12][13][14][15] and Nambu and Jona-Lasinio model (NJL) its extension [16][17][18][19]. The NJL is taken as a model for the divergent integral [16].…”