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Register a new userNet-proton number fluctuations in the presence of the QCD critical point
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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.
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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.
Observations from collisions of heavy-ion at relativistic energies have established the formation of a new phase of matter, Quark Gluon Plasma (QGP), a deconfined state of quarks and gluons in a specific region of the temperature versus baryonic chemical potential phase diagram of strong interactions. A program to study the features of the phase diagram, such as a possible critical point, by varying the collision energy ($sqrt{s_{rm NN}}$), is performed at the Relativistic Heavy-Ion Collider (RHIC) facility. Non-monotonic variation with $sqrt{s_{rm NN}}$ of moments of the net-baryon number distribution, related to the correlation length and the susceptibilities of the system, is suggested as a signature for a critical point. We report the first evidence of a non-monotonic variation in kurtosis $times$ variance of the net-proton number (proxy for net-baryon number) distribution as a function of $sqrt{s_{rm NN}}$ with 3.1$sigma$ significance, for head-on (central) gold-on-gold (Au+Au) collisions measured using the STAR detector at RHIC. Non-central Au+Au collisions and models of heavy-ion collisions without a critical point show a monotonic variation as a function of $sqrt{s_{rm NN}}$.
The non-monotonic beam energy dependence of the higher cumulants of net-proton fluctuations is a widely studied signature of the conjectured presence of a critical point in the QCD phase diagram. In this work we study the effect of resonance decays on critical fluctuations. We show that resonance effects reduce the signatures of critical fluctuations, but that for reasonable parameter choices critical effects in the net-proton cumulants survive. The relative role of resonance decays has a weak dependence on the order of the cumulants studied with a slightly stronger suppression of critical effects for higher-order cumulants.
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.
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