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Register a new userChiral-symmetry restoration in the linear sigma model at nonzero temperature and baryon density
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We study the chiral phase transition in the linear sigma model with 2 quark flavors and $N_c$ colors. One-loop calculations predict a first-order phase transition at both $mu=0$ and $mu eq 0$. We also discuss the phase diagram and make a comparison with a thermal parametrization of existing heavy-ion experimental data.
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Modifications of baryon properties due to the restoration of the chiral symmetry in an external hot and dense baryon medium are investigated in an effective chiral quark-meson theory. The nucleon arises as a soliton of the Gell-Mann - Levi $zs$-model, the parameters of which are chosen to be the medium-modified meson values evaluated within the Nambu - Jona-Lasinio model. The nucleon properties are obtained by means of variational projection techniques. The nucleon form factors as well as the nucleon delta transition form factors are evaluated for various densities and temperatures of the medium. Similar to the chiral phase transition line the critical curve in the $T-zr$ plane for delocalization of the nucleon is non-monotonic and this feature is reflected in all nucleon properties. At medium densities of about $(2-3) rnm$ the baryonic phase exists only at intermediate temperatures. For finite temperature and densities the nucleon form factors get strongly reduced at finite transfer momenta.
We study chiral symmetry restoration by analyzing thermal properties of QCDs (pseudo-)Goldstone bosons, especially the pion. The meson properties are obtained from the spectral densities of mesonic imaginary-time correlation functions. To obtain the correlation functions, we solve the Dyson-Schwinger equations and the inhomogeneous Bethe-Salpeter equations in the leading symmetry-preserving rainbow-ladder approximation. In the chiral limit, the pion and its partner sigma degenerate at the critical temperature $T_c$. At $T gtrsim T_c$, it is found that the pion rapidly dissociates, which signals deconfinement phase transition. Beyond the chiral limit, the pion dissociation temperature can be used to define the pseudo-critical temperature of chiral phase crossover, which is consistent with that obtained by the maximum point of the chiral susceptibility. The parallel analysis for kaon and pseudoscalar $sbar{s}$ suggests that heavy mesons may survive above $T_c$.
We study the production of strange hadrons in nucleus-nucleus collisions from 4 to 160 A GeV within the Parton-Hadron-String Dynamics (PHSD) transport approach that is extended to incorporate essentials aspects of chiral symmetry restoration (CSR) in the hadronic sector (via the Schwinger mechanism) on top of the deconfinement phase transition as implemented in PHSD. Especially the $K^+/pi^+$ and the $(Lambda+Sigma^0)/pi^-$ ratios in central Au+Au collisions are found to provide information on the relative importance of both transitions. The modelling of chiral symmetry restoration is driven by the pion-nucleon $Sigma$-term in the computation of the quark scalar condensate $<q {bar q}>$ that serves as an order parameter for CSR and also scales approximately with the effective quark masses $m_s$ and $m_q$. Furthermore, the nucleon scalar density $rho_s$, which also enters the computation of $<q {bar q}>$, is evaluated within the nonlinear $sigma-omega$ model which is constraint by Dirac-Brueckner calculations and low energy heavy-ion reactions. The Schwinger mechanism (for string decay) fixes the ratio of strange to light quark production in the hadronic medium. We find that above $sim$80 A GeV the reaction dynamics of heavy nuclei is dominantly driven by partonic degrees-of-freedom such that traces of the chiral symmetry restoration are hard to identify. Our studies support the conjecture of quarkyonic matter in heavy-ion collisions from about 5 to 40 A GeV and provide a microscopic explanation for the maximum in the $K^+/pi^+$ ratio at about 30 A GeV which only shows up if a transition to partonic degrees-of-freedom is incorporated in the reaction dynamics and is discarded in the traditional hadron-string models.
We consider chiral symmetry breaking at nonzero chemical potential and discuss the relation with the spectrum of the Dirac operator. We solve the so called Silver Blaze Problem that the chiral condensate at zero temperature does not depend on the chemical potential while this is not the case for the Dirac spectrum and the weight of the partition function.
The properties of hot hadronic matter are of great importance to the studies of heavy-ion collisions, cosmology and compact star formation. I briefly outline the current methods in use in the lattice simulations of QCD thermodynamics at zero and nonzero density. I discuss the most recent results for the QCD phase transition, critical behavior and the equation of state.
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