A baryonic chemical potential (
Quantum Chromodynamics (QCD) is a fundamental theory of strong interactions since it is renormalizable. However, thermodynamics of QCD is not well understood because of its nonperturbative nature. In particular, QCD phase diagram is an essential for understanding not only natural phenomena such as compact stars and the early universe but also laboratory experiments such as relativistic heavy-ion collisions. The quantitative calculations of phase diagram from first-principle lattice QCD (LQCD) have the well-known sign problem when the baryon chemical potential is included
At nonzero baryonic chemical potential, standard numerical lattice simulations do not work well. Therefore our knowledge of the QCD phase diagram at nonzero
The baryonic chemical potential is studied in the linear sigma model at finite temperature as in [
The aim of this work is to calculate the effective mesonic potential in the presence of the baryonic chemical potential at finite temperature using the
This paper is organized as follows. In Section
The interactions of quarks via the exchange of
The purpose of this section is to include the finite temperature and chemical potential in (
The purpose of this subsection is to calculate the effective mesonic potential, the
In (
Sigma and pion masses are plotted as functions of temperature in the absence and presence of baryonic chemical potential.
At finite baryonic chemical potential, it is more difficult to predict the phase transition using lattice QCD. Phenomenology models such as the quark sigma model and the NJL model are used to describe the phase transition. Chen et al. [
In Figure
Sigma and pion masses are plotted as functions of temperature for two values of coupling constant
In Figure
Sigma and pion masses are plotted as functions temperature for two values of sigma mass.
Next, we need to examine the behavior of the pressure at finite temperature. In Figure
The pressure is plotted as a function of temperature for two values of
Next, we need to examine the energy density in the presence of the baryon chemical potential. In Figure
The energy density is plotted as a function of temperature for two values of
The energy density is plotted as function of temperature for two values of coupling constant
In this work, we investigated the effect of the baryon chemical potential on the meson properties, the pressure, and the energy density at finite temperature. The effective mesonic potential is calculated by using the N-midpoint method at finite of chemical potential. We found that the behavior of the meson properties is in good agreement in comparison with other models. The pressure and energy density are examined as functions of temperature at finite temperature. A comparison is presented with other works. In addition, we included the fermion sector in the linear sigma model. This sector is ignored in many previous studies such as in [
We conclude that the present technique successfully predicts the behavior of the meson properties, the critical point temperature, and the energy density in comparison with other works at finite chemical potential and avoid the difficulty that previously mentioned in [
In this appendix, we write the basic steps of the
The author declares that there is no conflict of interests regarding the publication of this paper.