Nontopological soliton in the Polyakov quark-meson model

Abstract

Within a mean-field approximation, we study a nontopological soliton solution of the Polyakov quark-meson model in the presence of a fermionic vacuum term with two flavors at finite temperature and density. The profile of the effective potential exhibits a stable soliton solution below a critical temperature $T\ensuremath{\le}{T}_{\ensuremath{\chi}}^{c}$ for both the crossover and the first-order phase transitions, and these solutions are calculated here with appropriate boundary conditions. However, it is found that only if $T\ensuremath{\le}{T}_{d}^{c}$ is the energy of the soliton ${M}_{N}$ less than the energy of the three free constituent quarks $3{M}_{q}$. As $T>{T}_{d}^{c}$, there is an instant delocalization phase transition from hadron matter to quark matter. The phase diagram together with the location of a critical end point has been obtained in the $T$ and $\ensuremath{\mu}$ plane. We notice that two critical temperatures always satisfy ${T}_{d}^{c}\ensuremath{\le}{T}_{\ensuremath{\chi}}^{c}$. Finally, we present and compare the result of thermodynamic pressure at zero chemical potential with lattice data.