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Register a new userInfluences of statistics and initial size fluctuation on high-order cumulants of conserved quantities in relativistic heavy ion collisions
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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.
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We study statistics dependence of the probability distributions and the means of measured moments of conserved quantities, respectively. The required statistics of all interested moments and their products are estimated based on a simple simulation. We also explain why the measured moments are underestimated when the statistics are insufficient.With the statistics at RHIC/BES, the second and third order moments can be reliably obtained based on the method of Centrality bin width correction (CBWC), which can not be applied for the fourth order moments at low energy. With planning statistics at RHIC/BES II, and improved CBWC method, $kappasigma^2$ in a finer centrality bin scale should be measurable. This will help us to understand the current observation of energy and centrality dependence of high-order moments.
Higher order symmetric cumulants of global collective observables in heavy ion collisions are studied. The symmetric cumulants can be straightforwardly constructed for scalar observables: the average transverse momentum, the multiplicity, and the squares of harmonic flow vectors. Third and fourth order cumulants are calculated in the hydrodynamic model. A linear predictor of the average transverse momentum and harmonic flow coefficients in a collision is used to predict the value of the cumulants from the moments of the initial distribution. The symmetric cumulants divided by the averages (or the standard deviations) of the considered observables can be used as a fine tool to study correlations present in the initial state of the collision.
We discuss properties and applications of factorial cumulants of various particle numbers and for their mixed channels measured by the event-by-event analysis in relativistic heavy-ion collisions. After defining the factorial cumulants for systems with multi-particle species, their properties are elucidated. The uses of the factorial cumulants in the study of critical fluctuations are discussed. We point out that factorial cumulants play useful roles in understanding fluctuation observables when they have underlying physics approximately described by the binomial distribution. As examples, we suggest novel utilization methods of the factorial cumulants in the study of the momentum cut and rapidity window dependences of fluctuation observables.
We initialize the Quantum Chromodynamic conserved charges of baryon number, strangeness, and electric charge arising from gluon splitting into quark-antiquark pairs for the initial conditions of relativistic heavy-ion collisions. A new Monte Carlo procedure that can sample from a generic energy density profile is presented, called Initial Conserved Charges in Nuclear Geometry (ICCING), based on quark and gluon multiplicities derived within the color glass condensate (CGC) effective theory. We find that while baryon number and electric charge have nearly identical geometries to the energy density profile, the initial strangeness distribution is considerable more eccentric and is produced primarily at the hot spots corresponding to temperatures of $Tgtrsim 400$ MeV for PbPb collisions at $sqrt{s_{NN}}=5.02$ TeV.
We study effects of eccentricity fluctuations on the elliptic flow coefficient v_2 at mid-rapidity in both Au+Au and Cu+Cu collisions at sqrt{s_NN}=200 GeV by using a hybrid model that combines ideal hydrodynamics for space-time evolution of the quark gluon plasma phase and a hadronic transport model for the hadronic matter. For initial conditions in hydrodynamic simulations, both the Glauber model and the color glass condensate model are employed to demonstrate the effect of initial eccentricity fluctuations originating from the nucleon position inside a colliding nucleus. The effect of eccentricity fluctuations is modest in semicentral Au+Au collisions, but significantly enhances v_2 in Cu+Cu collisions.
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