Source Function Determined from HBT Correlations by the Maximum Entropy Principle

We study the reconstruction of the source function in space-time directly from the measured HBT correlation function using the Maximum Entropy Principle. We find that the problem is ill-defined without at least one additional theoretical constraint as input. Using the requirement of a finite source lifetime for the latter we find a new Gaussian parametrization of the source function directly in terms of the measured HBT radius parameters and its lifetime, where the latter is a free parameter which is not directly measurable by HBT. We discuss the implications of our results for the remaining freedom in building source models consistent with a given set of measured HBT radius parameters.Comment: 12 pages, revte

Inflection point as a characteristic of the QCD critical point

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., van der Waals equation of fluid, magnetization of spin models 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 QCD critical point in heavy ion collisions.Comment: 10 pages, 3 figure

On the Stability of Rapidity Gap Analysis

It is argued that the newly introduced moments of rapidity gaps for the event-by-event fluctuations depends on the number of events and multiplicity. The interesting ones of them are unstable under ISR energies of h-h collisions. The instability get well improved when multiplicity increases.Comment: 6 pages, 3 figure

Investigation on the contribution of the particle mass to the interaction measure

Collective phenomena from RHIC and LHC experiments indicate a strongly coupled quark gluon plasma. Finite temperature lattice QCD calculations show the interaction measure, $\Delta\equiv(\epsilon-3p)/T^4$, is sizeable over a considerable range of temperatures above the deconfinement temperature, which may also indicate that the plasma is strongly interacting. For the ideal gas with massless particles, the interaction measure is zero. A nonzero value is probably due to either the interaction or the mass. In order to see the contribution of the particle mass to the interaction measure, in this paper we study a system without any interactions, i.e., an ideal gas with massive particles. After assembling the standard formulas of the quantum statistics with relativistic energy, we calculate the energy density, the pressure and the interaction measure. We find that their dependences on temperature reproduce the qualitative features of the lattice result. The interaction measure is nonzero for an ideal gas, which demonstrates that the particle mass contributes to the interaction measure. By our estimate, in the interaction measure obtained by the lattice calculation, quark mass contributes less than (40-50)%. There are sizeable residue interactions in the deconfined phase.Comment: 8 pages, 3 figure

Event-by-Event Fluctuations of Transverse Momentum in Elementary Collisions at 250 GeV/cc

We present a study of event-by-event fluctuations of transverse momentum in \pi^{+}\p and \K^{+}\p collisions at 250 GeV/$c$ and the corresponding PYTHIA Monte Carlo results for \pi^{+}\p collisions. The dependence of $\Phi_{p_{t}}$ on event and particle variables are investigated in detail. We find that $\Phi_{p_t}$ are all negative for different average transverse momentum per event sample. The $_N \sim N$ correlation may not be the only origin of $\Phi_{p_{t}}$.Comment: 4 pages, 5 figure (in epsi) talk given at XXXI International Symposium on Multiparticle Dynamics, Sep. 1-7, 2001, Datong China URL http://ismd31.ccnu.edu.cn

Is there hydrodynamic flow at RHIC ?

It is argued that the observation of anisotropic azimuthal distribution of final state particles alone is insufficient to show whether the formed matter at RHIC behaves like hydrodynamic flow. Examining the intrinsic interaction (or correlation) of the formed matter should provide more definite judgement. To the end, a spatial-dependent azimuthal multiplicity-correlation pattern is suggested. It shows clearly in the pattern that there are two kinds of interactions at the early stage of Au + Au collisions at \sqnn=200 GeV generated by RQMD with hadron re-scattering and AMPT with string melting. This is out of the expectation from the elliptic flow driven by anisotropic expansion.Comment: 4 pages, 2figure

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

Through the Monte Carlo simulation of the three-dimensional, three-state Potts model, which is a paradigm of finite-temperature pure gauge QCD, we study the fluctuations of generalized susceptibilities near the temperatures of external fields of first-, second-order phase transitions and crossover. Similar peak-like fluctuation appears in the second order susceptibility at three given external fields. Oscillation-like fluctuation appears in the third and fourth order susceptibilities. We find that these non-monotonic fluctuations are not only associated with the second-order phase transition, but also the first-order one and crossover in a system of finite-size. We further present the finite-size scaling analysis of the second and fourth order susceptibilities, respectively. The exponent of the scaling characterizes the order of the transitions, or the crossover.Comment: 9 pages, 5 figure

Eccentricity and elliptic flow at fixed centrality in Au+Au collisions at sqrt(s_NN)=200GeV in AMPT

To reduce the effect of the fluctuations of initial geometrical shape, elliptic flow are studied at fixed centrality in Au+Au collision at $\sqrt{s_{\rm NN}}$=200GeV. It is observed with the participant increasing, elliptic flow has an increase and a decrease at different fixed impact parameter, but not a trivial fluctuation. It is analyzed that the initial space anisotropy dominates the participant dependence of elliptic flow in near-central collisions(b=5fm) and mid-central collisions(b=8fm), while the interaction between particles can mainly answer for the behavior of elliptic flow in peripheral collisions(b=12fm). To distinguish the pure geometrical effect, elliptic flow scaled by initial eccentricity is studied. It is found that the ratio $v_{2}/\epsilon$ increases with participant and reaches a saturation when the participant is large enough, indicating that the collision system reach the local equilibrium.Comment: 4 pages, 3 figures, accepted by Chinese Physics

Influences of statistics and initial size fluctuation on high-order cumulants of conserved quantities in relativistic heavy ion collisions

By the generator of the UrQMD model, event statistics for the products of kurtosis ($\kappa$) and variance ($\sigma^2$) of net-proton and net-charge multiplicity distributions are carefully studied. It is shown that the statistics at RHIC/BES below $\sqrt {s_{NN}} < 19.6$ GeV are not sufficient for using the method of Centrality Bin Width Correction (CBWC). Corresponding results are systematically underestimated. A way to improve the CBWC method is proposed. It can remove the statistics dependence of the data and reduce the initial size fluctuation as well.Comment: 6 pages, 5 figure

Measurement of anisotropic radial flow in relativistic heavy ion collisions

We suggest the azimuthal distribution of mean transverse (radial) rapidity of the final state particles as a more direct measure of the transverse motion of the source than the standard azimuthal multiplicity distribution. Using a sample generated by the AMPT model with string melting, we demonstrate that the azimuthal amplitude of the suggested distribution characterizes the anisotropic radial flow, and coincides with the parameter of anisotropic radial rapidity extracted from a generalized blast-wave parametrization.Comment: 5 pages, 4 figure