A NEW ANALYSIS OF HADRON PROPERTIES IN THE MODIFIED LOGARITHMIC QUARK MODEL

A modi ed logarithmic mesonic potential is investigated in the framework of quantum chromodynamics (QCD) theory. The eld equations have been solved in the mean- eld approximation using the iteration method. The obtained results of nucleon properties are strongly improved in comparison with the original quark-sigma model. A comparison with the recent quark models such as the extended Skyrme model and the perturbative quark model is discussed. We conclude that the modi ed logarithmic quark model successfully predicts the nucleon properties that are in good agreement with experimental data. In addition, we avoid the physical di¢ culty found in previous works. 1. INTRODUCTION To understand the nucleon properties from a microscopic theory of the hadronic interaction discussed earlier QCD is not yet calculative tractable, so theorist have turned their attention to various models of the hadronic interaction which incorporate the important symmetries (e. g. chiral symmetry) of QCD [1]. One of the e¤ective models which shares the chiral symmetry is Gell-Mann and Levys linear sigma model [2]. After replacing the nucleon picture by the quark picture by the Birse and Banerjees quark-sigma model [3]. The model did not gives the correct phenomenology such as the value of the isoscalar pion-nucleon scattering length is too large. Another, weakness of the linear sigma model is that the value of sigma commutator is very large. There are attempts to solve these problems. By including the vectors meson which lead to more parameters in the model as in Refs. ([4] and [5]). By increasing higher-order mesonic interactions in the model as in Refs. ( [6], [7] and [8]). In the modi ed quark-sigma model ( [6], [7] and [8] ), authors deal with approximate models that the inclusion of the higher-order mesonic interactions make the model is in non-normalaizable model. A logarithmic mesonic potential is suggested by the replace original mesonic potential in the quark sigma model to provide a good description of nucleon properties ([9] and [10]). The logarithmic quark-sigma model [9] is solved in the mean- eld 2000 Mathematics Subject Classi cation. 81V05, 81V25, 82B26, 82B80. Key words and phrases. Chiral Lagrangian density, Mean- eld approximation, Nucleon Properties. 1 2 M. ABU-SHADY, A. K. ABU-NAB JFCA-2014/5(3S) approximation and the nucleon properties are improved in comparison with original quark-sigma but some nucleon properties are still large in comparison with experimental data. The same model is solved in the coherent-pair approximation to provide good description of nucleon properties in comparison with the mean eld approximation, but some nucleon properties are still large in comparison with experimental data [10]. In addition, the model has a weakness point which comes from singularity point at vanishing of mesonic contributions. The purpose of this work is to suggest the new form of logarithmic potential, in which the modi ed potential is based on chiral symmetry and avoid weakness point that found in Refs. ([9] and [10]). In addition, the e¤ect of radius distance and free parameters are examined on nucleon properties, which are not investigated in Refs. ([9] and [10]). The structure of the paper is as follows. In Sec. 2, the original linear sigma model with the modi ed logarithmic potential is explained. The numerical calculations and results are discussed in Sec. 3. A comparison with other works is presented in Sec. 4. Finally, the summery and conclusions are displayed in Sec. 5. 2. The MODIFIED CHIRAL QUARK-SIGMA MODEL The chiral quark-sigma model was proposed by Birse and Banerjee [3]. The basic approach is to couple quarks to mesons in a chirally invariant manner. The simplest realization of this idea has Lagrangian of the form of a Gell-Mann-Levy sigma model [2] with quarks in the place of nucleons. We consider a Lagrangian based on the linear sigma model L (r) = i @ + 1 2 (@ @ + @ :@ )+g ( + i 5 : ) U (0) 1 ( ; ) ; (1) where, the mesonic potential functional is given by