Abstract:
The Beam Energy Scan program has been undertaken at the Relativistic Heavy Ion Collider (RHIC) to search for the QCD critical point. The presence of the critical point is expected to lead to non-monotonic behavior of several quantities. Here we report the result of higher moments of net-charge distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 39 GeV as measured by the STAR experiment. The STAR results are compared with results from HIJING event generator and Hadron Resonance (HRG) Models.

Abstract:
Dynamical fluctuations in global conserved quantities such as baryon number, strangeness, or charge may be observed near a QCD critical point. Results from new measurements of dynamical $K/\pi$, $p/\pi$, and $K/p$ ratio fluctuations are presented. The commencing of a QCD critical point search at RHIC has extended the reach of possible measurements of dynamical $K/\pi$, $p/\pi$, and $K/p$ ratio fluctuations from Au+Au collisions to lower energies. The STAR experiment has performed a comprehensive study of the energy dependence of these dynamical fluctuations in Au+Au collisions at the energies $\sqrt{s_{NN}}$ = 7.7, 11.5, 39, 62.4, and 200 GeV. New results are compared to previous measurements and to theoretical predictions from several models. The measured dynamical $K/\pi$ fluctuations are found to be independent of collision energy, while dynamical $p/\pi$ and $K/p$ fluctuations have a negative value that increases toward zero at top RHIC energy. Fluctuations of the higher moments of conserved quantities (net-proton and net-charge) distributions, which are predicted to be sensitive to the presence of a critical point, are also presented.

Abstract:
We present the STAR preliminary results on mid-rapidity and low transverse momentum mean, standard deviation, skewness, and kurtosis of net-charge and net-proton distributions in Au+Au and Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV for various collision centralities. All the measured high moments of these distributions can be scaled by the number of participating nucleons, consistent with the soft process emissions. The ratios of fourth to second order cumulants of both the net-charge and net-proton distributions are consistent with models without QCD critical point.

Abstract:
We calculate the first four moments of baryon number, electric charge and strangeness fluctuations within the hadron resonance gas model. Different moments and their ratios as well as skewness and kurtosis are evaluated on the phenomenologically determined freeze-out curve in the temperature, baryon chemical potential plane. The model results and its predictions as well as relations between different moments are compared with the first data on net proton fluctuations in Au-Au collisions obtained at RHIC by the STAR Collaboration. We find good agreement between the model calculations and experimental results. We also point out that higher order moments should be more sensitive to critical behavior and will also distinguish hadron resonance gas model calculations from results obtained from lattice QCD.

Abstract:
Recent results for moments of multiplicity distributions of net-protons and net-electric charge from the STAR collaboration are compared to lattice QCD results for higher order fluctuations of baryon number and electric charge by the Wuppertal-Budapest collaboration, with the purpose of extracting the freeze-out temperature and chemical potential. All lattice simulations are performed for a system of 2+1 dynamical quark flavors, at the physical mass for light and strange quarks; all results are continuum extrapolated. We show that it is possible to extract an upper value for the freeze-out temperature, as well as precise baryo-chemical potential values corresponding to the four highest collision energies of the experimental beam energy scan. Consistency between the freeze-out parameters obtained from baryon number and electric charge fluctuations is found. The freeze-out chemical potentials are now in agreement with the statistical hadronization model.

Abstract:
We discuss the relevance of higher order moments of net baryon number fluctuations for the analysis of freeze-out and critical conditions in heavy ion collisions at LHC and RHIC. Using properties of O(4) scaling functions, we discuss the generic structure of these higher moments at vanishing baryon chemical potential and apply chiral model calculations to explore their properties at non-zero baryon chemical potential. We show that the ratios of the sixth to second and eighth to second order moments of the net baryon number fluctuations change rapidly in the transition region of the QCD phase diagram. Already at vanishing baryon chemical potential they deviate considerably from the predictions of the hadron resonance gas model which reproduce the second to fourth order moments of the net proton number fluctuations at RHIC. We point out that the sixth order moments of baryon number and electric charge fluctuations remain negative at the chiral transition temperature. Thus, they offer the possibility to probe the proximity of the thermal freeze-out to the crossover line.

Abstract:
We calculate electric and baryonic charge fluctuations on the lattice. Results have been obtained with the highly improved staggered quark action (HISQ) and almost physical quark masses on lattices with spacial extent of $N_\tau=6,8,12$. Higher order cumulants of the net-charge distributions are increasingly dominated by a universal scaling behavior, which is arising due to a critical point of QCD in the chiral limit. Considering cumulants up to the sixth order, we observe that they generically behave as expected from universal scaling laws, which is quite different from the cumulants calculated within the hadron resonance gas model. Taking ratios of these cumulants, we obtain volume independent results that can be compared to the experimental measurements. Such a comparison will unambiguously relate the QCD transition temperature that has been determined on the lattice with the freeze out temperature of heavy ion collision at LHC and RHIC.

Abstract:
We analyze baryon number, strangeness and electric charge fluctuations as well as their correlations in QCD at high temperature. We present results obtained from lattice calculations performed with an improved staggered fermion action (p4-action) at two values of the lattice cut-off with almost physical up and down quark masses and a physical value for the strange quark mass. We compare these results, with an ideal quark gas at high temperature and a hadron resonance gas model at low temperature. We find that fluctuations and correlations are well described by the former already for temperatures about 1.5 times the transition temperature. At low temperature qualitative features of the lattice results are quite well described by a hadron resonance gas model. Higher order cumulants, which become increasingly sensitive to the light pions, however show deviations from a resonance gas in the vicinity of the transition temperature.

Abstract:
We analyze baryon number, strangeness and electric charge fluctuations as well as their correlations in QCD at high temperature. We present results obtained from lattice calculations performed with an improved staggered fermion action (p4-action) at two values of the lattice cut-off with almost physical up and down quark masses and a physical value for the strange quark mass. We compare these results, with an ideal quark gas at high temperature and a hadron resonance gas model at low temperature. We find that fluctuations and correlations are well described by the former already for temperatures about 1.5 times the transition temperature. At low temperature qualitative features of the lattice results are quite well described by a hadron resonance gas model. Higher order cumulants, which become increasingly sensitive to the light pions, however show deviations from a resonance gas in the vicinity of the transition temperature.

Abstract:
We consider a recent proposal by Horv\'ath {\em et al.} to address the question whether topological charge fluctuations in QCD are instanton dominated via the response of fermions using lattice fermions with exact chiral symmetry, the overlap fermions. Considering several volumes and lattice spacings we find strong evidence for chirality of a finite density of low-lying eigenvectors of the overlap-Dirac operator in the regions where these modes are peaked. This result suggests instanton dominance of topological charge fluctuations in quenched QCD.