Nuclear phenomena derived from quark-gluon strings

We propose a quantum chromodynamics (QCD) based many-body model for the nucleus where the strong coupling regime is controlled by a three-body string force, and the weak coupling regime is dominated by a pairing force. This model operates effectively with a quark-gluon Lagrangian containing a pairing force from instantons, and a baryonic string term which contains a confining potential. The unified model for weak and strong coupling regimes is, however, only consistent at the border of perturbative QCD. The baryonic string force is necessary, as a stability and compressibility analysis shows, for the occurrence of the phases of nuclear matter. The model exhibits a quark deconfinement transition and chiral restoration, which are ingredients of QCD and give qualitatively correct numerics. The effective model is shown to be isomorphic to the Nambu–Jona-Lasinio model and exhibits the correct chirality provided that the chiral fields are identified with the two-particle strings, which are natural in a QCD framework. Moreover, the model is able to reconcile qualitatively such aspects of hadronic physics as saturation density and binding energy of nuclear matter, surface density of finite nuclei, mass of the scalar particle, medium range NN interaction, and $f_{\pi }$ value in vacuum.

Figure 1

Baryonic string configurations. (a) The angles of the triangle defined by a three-quark cluster are all less than $2\pi /3$. (b) One of the angles of the triangle defined by a three-quark cluster is greater than $2\pi /3$. (c) A six-quark cluster. This configuration is here included as a possibility but not used in the full picture. It will be discussed in a forthcoming paper.

Figure 2

Phase diagram of hadronic matter energy as a function of the density. The dotted line applies to a quark gas. The dash-dotted curve corresponds to the so-called NL3 parametrization of the Walecka model [15]. The solid curve and the long-dashed curve present, respectively, the results of ESMI and ESMII. The dashed curve corresponds to the quark-meson coupling model [6].

Figure 3

Effective mass of the nucleon and σ field as function of the density for ESMI and ESMII. Chiral symmetry restoration occurs when these quantities vanish.

Figure 4

Pressure versus density for ESMI and ESMII. Phase transitions are shown as discontinuities in the slopes of the curves.