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Register a new userTime-evolution of net-baryon density fluctuations across the QCD critical region
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We investigate the role of a finite surface tension during the time-evolution of fluctuations in the net-baryon density. The systems in this study undergo a temperature evolution across the phase transition in the critical region of the QCD phase diagram. The occuring non-equilibrium effects are discussed.
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Event-by-event fluctuations of the net-proton number studied in heavy-ion collisions provide an important means in the search for the conjectured critical end point (CP) in the QCD phase diagram. We propose a phenomenological model in which the fluctuations of the chiral critical mode couple to protons and anti-protons. This allows us to study the behavior of the net-proton number fluctuations in the presence of the CP. Calculating the net-proton number cumulants, $C_n$ with n=1,2,3,4, along the phenomenological freeze-out line we show that the ratio of variance and mean $C_2/C_1$, as well as kurtosis $C_4/C_2$ resemble qualitative properties observed in data in heavy-ion collisions as a function of beam energy obtained by the STAR Collaboration at RHIC. In particular, the non-monotonic structure of the kurtosis and smooth change of the $C_2/C_1$ ratio with beam energy could be due to the CP located near the freeze-out line. The skewness, however, exhibits properties that are in contrast to the criticality expected due to the CP. The dependence of our results on the model parameters and the proximity of the chemical freeze-out to the critical point are also discussed.
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.
A quantitatively reliable theoretical description of the dynamics of fluctuations in non-equilibrium is indispensable in the experimental search for the QCD critical point by means of ultra-relativistic heavy-ion collisions. In this work we consider the fluctuations of the net-baryon density which becomes the slow, critical mode near the critical point. Due to net-baryon number conservation the dynamics is described by the fluid dynamical diffusion equation, which we extend to contain a white noise stochastic current. Including nonlinear couplings from the 3d Ising model universality class in the free energy functional, we solve the fully interacting theory in a finite size system. We observe that purely Gaussian white noise generates non-Gaussian fluctuations, but finite size effects and exact net-baryon number conservation lead to significant deviations from the expected behavior in equilibrated systems. In particular the skewness shows a qualitative deviation from infinite volume expectations. With this benchmark established we study the real-time dynamics of the fluctuations. We recover the expected dynamical scaling behavior and observe retardation effects and the impact of critical slowing down near the pseudo-critical temperature.
The experimental search for the QCD critical point by means of relativistic heavy-ion collisions necessitates the development of dynamical models of fluctuations. In this work we study the fluctuations of the net-baryon density near the critical point. Due to net-baryon number conservation the correct dynamics is given by the fluid dynamical diffusion equation, which we extend by a white noise stochastic term to include intrinsic fluctuations. We quantify finite resolution and finite size effects by comparing our numerical results to analytic expectations for the structure factor and the equal-time correlation function. In small systems the net-baryon number conservation turns out to be quantitatively and qualitatively important, as it introduces anticorrelations at larger distances. Including nonlinear coupling terms in the form of a Ginzburg-Landau free energy functional we observe non-Gaussian fluctuations quantified by the excess kurtosis. We study the dynamical properties of the system close to equilibrium, for a sudden quench in temperature and a Hubble-like temperature evolution. In the real-time dynamical systems we find the important dynamical effects of critical slowing down, weakening of the extremal value and retardation of the fluctuation signal. In this work we establish a set of general tests, which should be met by any model propagating fluctuations, including upcoming $3+1$ dimensional fluctuating fluid dynamics.
Net-proton number fluctuations can be measured experimentally and hence provide a source of important information about the matter created during relativistic heavy ion collisions. Particularly, they may give us clues about the conjectured QCD critical point. In this work the beam-energy dependence of ratios of the first four cumulants of the net-proton number is discussed. These quantities are calculated using a phenomenologically motivated model in which critical mode fluctuations couple to protons and anti-protons. Our model qualitatively captures both the monotonic behavior of the lowest-order ratio as well as the non-monotonic behavior of higher-order ratios, as seen in the experimental data from the STAR Collaboration. We also discuss the dependence of our results on the coupling strength and the location of the critical point.
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