Analytical solution of surface tension of quark-hadron phase transition

Abstract

By using the finite temperature field theory, the one-loop effective potential and the dynamics of the quantum chromodynamics deconfinement phase transition in the framework of Friedberg-Lee model are studied at finite temperature and density. Our results show that there is a first-order deconfinement phase transition for the full phase diagram, and the critical temperature is about 119.8 MeV for a zero chemical potential whereas the critical chemical is around 256.4 MeV when the temperature is fixed at <i>T</i> = 50 MeV. Moreover, in the thin-wall approximation, we investigate the dynamics of a strong first-order quark-hadron transition via homogeneous bubble nucleation in the Friedberg-Lee model. Under an appropriate boundary condition, the equation of motion for the <inline-formula><tex-math id="M3">\begin{document}$ \sigma $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M3.png"/></alternatives></inline-formula> field is solved, then the evolutions of the bubble critical configuration with radius <inline-formula><tex-math id="M4">\begin{document}$ r $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20220659_M4.png"/></alternatives></inline-formula> at different temperatures and densities are calculated. The surface tension, the typical radius of the critical bubble and the shift in the coarse-grained free energy each as a function of temperature and chemical potential are obtained. In order to gain the reliability and advantages of the thin-wall approximation, our analytical results based on the thin-wall approximation are compared with those obtained by the exact numerical method accordingly. Finally, some consequences and possible applications of our results in the quark meson model and Polyakov quark meson model are also presented in the end of this paper.