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Register a new userMode Softening near the critical point within effective approaches to QCD
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We study the soft mode along the critical line in the phase diagram with the tricritical point, using the Nambu--Jona-Lasinio model. At the critical point with finite quark mass, the ordering density becomes a linear combination of the scalar, quark number and energy densities, and their susceptibilities diverge with the same exponent. Based on the conservation law, it is argued that the divergent susuceptibility of a conserved density must be accompanied by a critically--slowing hydrodynamic mode. The shift of the soft mode from the sigma meson to the hydrodynamic mode occurs at the tricritical point on the critical line.
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We investigate the evolution of the net-proton kurtosis and the kurtosis of the chiral order parameter near the critical point in the model of nonequilibrium chiral fluid dynamics. The order parameter is propagated explicitly and coupled to an expanding fluid of quarks and gluons in order to describe the dynamical situation in a heavy-ion collision. We study the critical region near the critical point on the crossover side. There are two sources of fluctuations: non-critical initial event-by-event fluctuations and critical fluctuations. These fluctuations can be distinguished by comparing a mean-field evolution of averaged thermodynamic quantities with the inclusion of fluctuations at the phase transition. We find that while the initial state fluctuations give rise to flat deviations from statistical fluctuations, critical fluctuations reveal a clear structure of the phase transition. The signals of the critical point in the net-proton and sigma field kurtosis are affected by the nonequilibrium dynamics and the inhomogeneity of the space-time evolution but develop clearly.
We present a fully dynamical model to study the chiral and deconfinement transition of QCD simultaneously. The quark degrees of freedom constitute a heat bath in local equilibrium for both order parameters, the sigma field and a dynamical Polyakov loop. The nonequilibrium evolution of these fields is described by Langevin equations including dissipation and noise. In several quench scenarios we are able to observe a delay in the relaxation times near the transition temperature for a critical point as well as a first-order phase transition scenario. During the hydrodynamical expansion of a hot quark fluid we find a strong enhancement of thermal fluctuations at the first-order transition compared to a scenario with a critical point.
The evolution of non-hydrodynamic slow processes near the QCD critical point is explored with the novel Hydro+ framework, which extends the conventional hydrodynamic description by coupling it to additional explicitly evolving slow modes describing long wavelength fluctuations. Their slow relaxation is controlled by critical behavior of the correlation length and is independent from gradients of matter density and pressure that control the evolution of the hydrodynamic quantities. In this exploratory study we follow the evolution of the slow modes on top of a simplified QCD matter background, allowing us to clearly distinguish, and study both separately and in combination, the main effects controlling the dynamics of critical slow modes. In particular, we show how the evolution of the slow modes depend on their wave number, the expansion of and advection by the fluid background, and the behavior of the correlation length. Non-equilibrium contributions from the slow modes to bulk matter properties that affect the bulk dynamics (entropy, pressure, temperature and chemical potential) are discussed and found to be small.
Fireballs created in relativistic heavy-ion collisions at different beam energies have been argued to follow different trajectories in the QCD phase diagram in which the QCD critical point serves as a landmark. Using a (1+1)-dimensional model setting with transverse homogeneity, we study the complexities introduced by the fact that the evolution history of each fireball cannot be characterized by a single trajectory but rather covers an entire swath of the phase diagram, with the finally emitted hadron spectra integrating over contributions from many different trajectories. Studying the phase diagram trajectories of fluid cells at different space-time rapidities, we explore how baryon diffusion shuffles them around, and how they are affected by critical dynamics near the QCD critical point. We find a striking insensitivity of baryon diffusion to critical effects. Its origins are analyzed and possible implications discussed.
We investigate the QCD phase diagram and the location of the critical end point (CEP) in the SU(2) Polyakov$-$Nambu$-$Jona-Lasinio model with entanglement interaction giving special attention to the $pi$ and $sigma$-mesons properties, namely the decay widths $sigmarightarrowpipi$, for several conditions around the CEP: we focus on the possible $sigmarightarrowpipi$ decay along the isentropic trajectories close to the CEP since the hydrodynamical expansion of a heavy-ion collision fireball nearly follows trajectories of constant entropy. It is expected that the type of transition the dense medium goes through as it expands after the thermalization determines the behavior of this decay. It is shown that no pions are produced from the sigma decay in the chirally symmetric phase if the isentropic lines approach the first order line from chemical potentials above it. Near the CEP or above the $sigmarightarrowpipi$ decay is possible with a high decay width.
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