Xue Pan

Inflection point as a characteristic of the QCD critical point

Abstract In the universality class of the critical point of QCD, the appearance of the inflection point in the equation of state (EoS) is associated with the second order phase transition. The high cumulants of conserved quantities near the critical point are corresponding to the high derivatives of the EoS near the inflection point. The critical behavior of high cumulants of conserved charge near the QCD critical point, in particular, the sign change, is closely related to the appearance of inflection point. We show in general how the times of sign change of high cumulants relate to the order of derivative. We also demonstrate that the character of inflection point of EoS is as visible as the sign change of high cumulants in 3 systems, i.e., the van der Waals equation of fluid, the energy of spin model and the baryon number density of QCD matter. Therefore, we propose that the EoS, or the mean of baryon number density, should be measured and studied together with its higher cumulants in exploring the QCD critical point in heavy ion collisions.

Statistical and dynamical fluctuations in the ratios of higher net-proton cumulants in relativistic heavy-ion collisions

With the help of transport and statistical models, we find that the ratios of higher net-proton cumulants measured at RHIC are dominated by Poisson-like statistical fluctuations. A way to eliminate this statistical fluctuation is suggested. The obtained dynamical ratios of higher net-proton cumulants are demonstrated to be more relevant to the underlying physics, i.e. the correlations between proton and antiproton, or the critical fluctuations.

Statistical and dynamical parts of the cumulants of conserved charges in relativistic heavy ion collisions

The Poisson-liked statistical fluctuations, which are caused by the finite number of produced particles, are firstly estimated for the cumulants of conserved charges, i.e., the cumulants of net-baryon, net-electric charge, and net-strangeness. They turn out to be the same as those baselines derived from Hadron Resonance Gas (HRG) model. The energy and centrality dependence of net-proton cumulants at the Relativistic Heavy-Ion Collider (RHIC) are demonstrated to be mainly caused by statistical fluctuations. Subtracting the statistical fluctuations, the dynamical kurtosis of net- and total-proton from two versions of the AMPT model and the UrQMD model at current RHIC beam energies are presented. It is found that the observed sign change in the kurtosis of net-proton can not be reproduced by these three transport models. There is no significant difference between net- and total-proton kurtosis in model calculations, in contrary to the data at RHIC.

Poisson baseline of net-charge fluctuations in relativistic heavy ion collisions

Taking the doubly charged particles and positive-negative charge pair production into account, the Poisson baseline of the fluctuations of net-charge is studied. Within the Poisson baseline, the cumulants of net-charge are derived. Comparing to the Skellam baseline of net-charge, we infer that the doubly charged particles broaden the distributions of net-charge, while the positive-negative charge pairs narrow the distributions. With ratios of the doubly charged particles and positive-negative charge pairs to the total positive charges from THERMINATOR 2, the first four orders of moments and the corresponding moment products are calculated in the Poisson baseline for Au + Au collisions at

Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model

\sqrt{s_{NN}}

High cumulants of conserved charges and their statistical uncertainties

= 200 GeV at RHIC/STAR. The results are closer to the data from RHIC/STAR than the Skellam baseline.Taking doubly charged particles, positive-negative charge pair production and the effects of volume fluctuations into account, the Poisson baseline of the fluctuations of net-charge is studied. Within the Poisson baseline, the cumulants of net-charge are derived. Comparing to the Skellam baseline of net-charge, we infer that doubly charged particles broaden the distributions of net-charge, while positive-negative charge pairs narrow the distributions. Using the ratios of doubly charged particles and positive-negative charge pairs from neutral resonance decays to the total positive charges from THERMINATOR 2, the first four orders of moments and the corresponding moment products are calculated in the Poisson baseline for Au + Au collisions at

Generalized susceptibilities along the phase boundary of the three-dimensional, three- state Potts model

\sqrt{s_{NN}}

Critical behavior of higher cumulants of order parameter in the 3D-Ising universality class

= 200 GeV at RHIC/STAR. We find that the standard deviation is mainly influenced by the resonance decay, while the third and fourth order moments and corresponding moment products are mainly modified and fit the data of RHIC/STAR much better after including the effects of volume fluctuations.

High-order cumulants from the 3-dimensional O(1,2,4) spin models

We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class.

Critical behavior of Binder ratios and ratios of higher order cumulants of conserved charges in QCD deconfinement phase transition

We study the influence of measured high cumulants of conserved charges on their associated statistical uncertainties in relativistic heavy-ion collisions. With a given number of events, the measured cumulants randomly fluctuate with an approximately normal distribution, while the estimated statistical uncertainties are found to be correlated with corresponding values of the obtained cumulants. Generally, with a given number of events, the larger the cumulants we measure, the larger the statistical uncertainties that are estimated. The error-weighted averaged cumulants are dependent on statistics. Despite this effect, however, it is found that the three sigma rule of thumb is still applicable when the statistics are above one million.