Phase structure of the linear sigma model with the non-standard symmetry breaking term

Abstract

The phase structure of the linear sigma model at finite isospin chemical potential μ and temperature T is systematically studied in the non-standard case of symmetry breaking by means of the Cornwall-Jackiw-Tomboulis effective potential. The latter quantity is calculated in the improved Hartree-Fock approximation which preserves the Goldstone theorem and the thermodynamic consistency. It results that the charged pions are condensed for μ equal to the pion mass in vacuum and the pion condensation corresponds to a first-order phase transition for 0 T 175.813 MeV, whereas at higher temperature it becomes a second-order phase transition. Moreover, the chiral-symmetry restoration, which is a first-order phase transition, occurs for 138.464 MeV T 147.168 MeV. The phase diagrams for both pion and chiral condensates are obtained.

Pion condensation in a soft-wall AdS/QCD model

“…The non-perturbative physics dominant near transition point requires methods beyond traditional perturbative expansion. Many efforts have been made in this area, including lattice simulations(LQCD) [5][6][7][8][9], functional renormalization group(FRG) [10,11], chiral perturbation theory(χPT) [12,13], perturbative methods [14], random matrix models [15,16], effective models [17][18][19][20][21][22][23] and so on. Different from baryon number density, finite isospin chemical potential would not cause sign problem, due to the opposite signs of the chemical potentials for u and d. Therefore, lattice simulations could be safely applied in this region.…”

Meson spectral functions at finite temperature and isospin density with the functional renormalization group

“…Since we are interested in the thermal excitations above but close to the critical temperature of the pion superfluid, we investigate the meson two-point functions only in the normal phase, where the meson fields φ = (σ, π) are the eigenstates of the system and the propagators G φ and G ψ in (25) are presented in (13) for mesons and (19) for quarks.…”

Neutrality Effects on the Phase Structure of the Linear Sigma Model with the Non-standard Symmetry Breaking

“…Hence, there are two distinct Hartree-Fock approximations: the one that respects the Goldstone theorem is called the improved Hartree-Fock (IHF) approximation and the other related to the absence of the Goldstone theorem is called briefly the usual HF approximation. In [18] we have established the renormalized CJT effective potential in IHF approximation,…”

“…In our previous work [17] the kaon condensation was considered in the linear sigma model, where we developed a self-consistent approach involving the renormalization prescription, the thermodynamic consistency and the preservation of the Goldstone theorem. Besides, in [18], making use of this method we considered the phase structure of linear sigma model in the non-standard case of explicitly symmetry breaking basing on the Cornwall-Jackiw-Tomboulis (CJT) effective potential, but there was no electric neutrality constraint.…”

“…The paper is structured as follows. In Section II, the calculation of renormalized CJT effective potential in [18] are resumed. In Section III the neutrality effects on the phase structure are numerically studied.…”