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Register a new userFirst Study of the Negative Binomial Distribution Applied to Higher Moments of Net-charge and Net-proton Multiplicity Distributions
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A study of the first four moments (mean, variance, skewness, and kurtosis) and their products ($kappasigma^{2}$ and $Ssigma$) of the net-charge and net-proton distributions in Au+Au collisions at $sqrt{rm s_{NN}}$ = 7.7-200 GeV from HIJING simulations has been carried out. The skewness and kurtosis and the collision volume independent products $kappasigma^{2}$ and $Ssigma$ have been proposed as sensitive probes for identifying the presence of a QCD critical point. A discrete probability distribution that effectively describes the separate positively and negatively charged particle (or proton and anti-proton) multiplicity distributions is the negative binomial (or binomial) distribution (NBD/BD). The NBD/BD has been used to characterize particle production in high-energy particle and nuclear physics. Their application to the higher moments of the net-charge and net-proton distributions is examined. Differences between $kappasigma^{2}$ and a statistical Poisson assumption of a factor of four (for net-charge) and 40% (for net-protons) can be accounted for by the NBD/BD. This is the first application of the properties of the NBD/BD to describe the behavior of the higher moments of net-charge and net-proton distributions in nucleus-nucleus collisions.
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We report the first measurements of the kurtosis (kappa), skewness (S) and variance (sigma^2) of net-proton multiplicity (N_p - N_pbar) distributions at midrapidity for Au+Au collisions at sqrt(s_NN) = 19.6, 62.4, and 200 GeV corresponding to baryon chemical potentials (mu_B) between 200 - 20 MeV. Our measurements of the products kappa sigma^2 and S sigma, which can be related to theoretical calculations sensitive to baryon number susceptibilities and long range correlations, are constant as functions of collision centrality. We compare these products with results from lattice QCD and various models without a critical point and study the sqrt(s_NN) dependence of kappa sigma^2. From the measurements at the three beam energies, we find no evidence for a critical point in the QCD phase diagram for mu_B below 200 MeV.
We report the beam energy (sqrt s_{NN} = 7.7 - 200 GeV) and collision centrality dependence of the mean (M), standard deviation (sigma), skewness (S), and kurtosis (kappa) of the net-proton multiplicity distributions in Au+Au collisions. The measurements are carried out by the STAR experiment at midrapidity (|y| < 0.5) and within the transverse momentum range 0.4 < pT < 0.8 GeV/c in the first phase of the Beam Energy Scan program at the Relativistic Heavy Ion Collider. These measurements are important for understanding the Quantum Chromodynamic (QCD) phase diagram. The products of the moments, Ssigma and kappasigma^{2}, are sensitive to the correlation length of the hot and dense medium created in the collisions and are related to the ratios of baryon number susceptibilities of corresponding orders. The products of moments are found to have values significantly below the Skellam expectation and close to expectations based on independent proton and anti-proton production. The measurements are compared to a transport model calculation to understand the effect of acceptance and baryon number conservation, and also to a hadron resonance gas model.
We report the first measurements of a complete second-order cumulant matrix of net-charge, net-proton and net-kaon multiplicity distributions for the first phase of the beam energy scan program at RHIC. This includes the centrality and, for the first time, the pseudorapidity window dependence of both diagonal and off-diagonal cumulants in Au+Au collisions at sNN~= 7.7-200 GeV. Within the available acceptance of $|eta|<0.5$, the cumulants grow linearly with the pseudorapidity window. Relative to the corresponding measurements in peripheral collisions, the ratio of off-diagonal over diagonal cumulants in central collisions indicates an excess correlation between net-charge and net-kaon, as well as between net-charge and net-proton. The strength of such excess correlation increases with the collision energy. The correlation between net-proton and net-kaon multiplicity distributions is observed to be negative at sNN~= 200 GeV and change to positive at the lowest collision energy. Model calculations based on non-thermal (UrQMD) and thermal (HRG) production of hadrons cannot explain the data. These measurements will help map the QCD phase diagram, constrain hadron resonance gas model calculations and provide new insights on the energy dependence of baryon-strangeness correlations.
The moments and moment products of conserved charges are believed to be sensitive to critical fluctuations, which have been adopted in determining the QCD critical point. Using a dynamical multiphase transport model, we reproduce the centrality and energy dependences of moments and moment products of net-charge multiplicity distributions in Au+Au collisions measured by the Beam Energy Scan program at the RHIC. No non-monotonic energy dependence is observed. We infer that the moment products develop during the dynamical evolution of heavy-ion collisions. The observed difference based on the expectation of the Poisson baseline indicates a positive two-particle correlation between positively and negatively charged particles, which can arise from different dynamical processes at different stages. Therefore, to adopt moments and moment products of net-charge multiplicity distributions in determining the QCD critical point of relativistic heavy-ion collisions, it is essential to take the dynamical evolution.
Fluctuations of conserved quantities such as baryon number, charge, and strangeness are sensitive to the correlation length of the hot and dense matter created in relativistic heavy-ion collisions and can be used to search for the QCD critical point. We report the first measurements of the moments of net-kaon multiplicity distributions in Au+Au collisions at $sqrt{s_{rm NN}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV. The collision centrality and energy dependence of the mean ($M$), variance ($sigma^2$), skewness ($S$), and kurtosis ($kappa$) for net-kaon multiplicity distributions as well as the ratio $sigma^2/M$ and the products $Ssigma$ and $kappasigma^2$ are presented. Comparisons are made with Poisson and negative binomial baseline calculations as well as with UrQMD, a transport model (UrQMD) that does not include effects from the QCD critical point. Within current uncertainties, the net-kaon cumulant ratios appear to be monotonic as a function of collision energy.
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