We present a Principal Component Analysis for a hydrodynamic simulation and compare with CMS experimental data. While the results are reasonable for anisotropic flow, for multiplicity fluctuations they are qualitatively different. We argue that this is due to too large transverse momentum ($p_T$) fluctuations and $N-p_T$ covariance in the simulation than seen experimentally. In turn this is related to too large initial size fluctuations.
Higher moments of multiplicity fluctuations of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the canonical ensemble. Exact conservation of three charges, baryon number, electric charge, and strangeness, is enforced in the large volume limit. Moments up to the forth order of various particles are calculated at SPS, RHIC and LHC energies. The asymptotic fluctuations within a simplified model with only one conserved charge in the canonical ensemble are discussed where simple analytical expressions for moments of multiplicity distributi…
We study the multiplicity fluctuation and correlation of identified mesons and baryons formed at the hadronization by the quark combination mechanism in the context of ultra-relativistic heavy-ion collisions. Based on the statistical method of free quark combination, we derive the two-hadron multiplicity correlations such as meson-meson and meson-baryon correlations, and take the effects of quark number fluctuation at hadronization into account by a Taylor expansion method. After including the decay contributions, we calculate the dynamical fluctuation observable $ν_{dyn}$ for $\text{K}π$, $pπ…
Multiplicity fluctuations are one of the most crucial observables in the Beam Energy Scan program of the Relativistic Heavy Ion Collider. It is understood that they can be utilized to probe the whereabouts of the critical point on the phase diagram of the QCD matter. However, a significant portion of these fluctuations is, apart from that related to the QCD phase transition, attributed to the other origins, which we refer to as "noncritical" ones. The present study is dedicated to the noncritical aspects of the multiplicity fluctuations in heavy-ion collisions. In particular, we focus on those…
Three-dimensional, as well as one- and two-dimensional, studies of multiplicity fluctuation are performed using AMPT model to generate central Au-Au collision events at ${\sqrt s_{NN}}= 200$ GeV. Two- and three-dimensional normalized factorial moments in rapidity, transverse momentum and azimuthal angle are found to exhibit power-low scaling when partitioning with the same number of bins in each direction, indicating that the fluctuation are isotropic, i.e. the fractality is self-similar in multiparticle production of central Au-Au collisions. Further, we measured the parameter $ν$ which it ch…
In this paper, we investigate the multiplicity fluctuations of charged particles observed in high-energy nuclear collisions and relate them to the size of hadronizing systems which happen during such processes. We use the average multiplicities $\langle N\rangle $ and variances $Var\left(N\right)$ of multiplicity distributions of charged particles produced in centrality selected collisions of relativistic heavy-ion nuclei to evaluate the dynamic variable $Ω$ and study its dependence on the size of colliding nuclei. We connect the observed system-size dependence of multiplicity fluctuations wit…
In heavy-ion collisions, momentum-dependent pair correlations can be characterized by a principal component analysis (PCA), in which subleading modes are expected to reveal new information on flow fluctuations. However, we find that, as currently measured, these modes can be dominated by multiplicity fluctuations, which serve as an unwanted background. Here, we propose new PCA observables that are robust against multiplicity fluctuations and isolate novel sources of flow fluctuations, thus being suited to provide fresh insight into the initial stages of the system at small length scales.
The dynamical fluctuation and correlation of multiplicity distributions of identified baryons and antibaryons produced by the hadronization of the bulk quark system are systematically studied in quark combination model. Starting from the most basic dynamics of quark combination which are necessary for multiplicity study, we analyze moments (variance, skewness and kurtosis) of inclusive multiplicity distribution of identified baryons, two-baryon multiplicity correlations, and baryon-antibaryon multiplicity correlations after the hadronization of quark system with given quark number and antiquar…
We discuss multiplicity fluctuations of charged particles produced in nuclear collisions measured event-by-event by the NA49 experiment at CERN SPS within the Glauber Monte Carlo approach. We use the concepts of wounded nucleons and wounded quarks in the mechanism of multiparticle production to characterize multiplicity fluctuations expressed by the scaled variance of multiplicity distribution. Although Wounded Nucleon Model correctly reproduce the centrality dependence of the average multiplicity in Pb+Pb collisions, it completely fails in description of corresponding centrality dependence of…
This proceeding briefly summarizes our recent work on calculating the correlated fluctuations of net protons on the hydrodynamic freeze-out surface near the QCD critical point. For both Poisson and Binomial baselines, our calculations could roughly reproduce the energy dependent cumulant $C_4$ and $κσ^2$ of net protons, but always over-predict $C_2$ and $C_3$ due to the positive contributions from the static critical fluctuations.
The number of particles detected in a nucleus-nucleus collision strongly depends on the impact parameter of the collision. Therefore, multiplicity fluctuations, as well as rapidity correlations of multiplicities, are dominated by impact parameter fluctuations. We present a method based on Bayesian inference which allows for a robust reconstruction of fluctuations and correlations at fixed impact parameter. We apply the method to ATLAS data on the distribution of charged multiplicity and transverse energy. We argue that multiplicity fluctuations are smaller at large rapidity than around central…
By deriving a general expression for multiplicity distribution (a conditional probability distribution) in statistical model, we demonstrate the mismatches between experimental measurements and previous theoretical calculations on multiplicity fluctuations. From the corrected formula, we develop an improved baseline measure for multiplicity distribution under Poisson approximation in statistical model to replace the traditional Poisson expectations. We find that the ratio of the mean multiplicity to the corresponding reference multiplicity are crucial to systemically explaining the measured sc…
Multiplicity distributions and event-by-event multiplicity fluctuations in AuAu collisions at energies in future heavy-ion experiment at the Facility for Anti-proton and Ion Research (FAIR) are investigated. Events corresponding to FAIR energies are simulated in the frame work of Ultra Relativistic Quantum Molecular Dynamics (URQMD) model. It is observed that the mean and the width of multiplicity distributions monotonically increase with beam energy. The trend of variations of dispersion with mean number of participating nucleons for the centrality-bin width of 5\% are in accord with the Cent…
We study the production of $J/ψ$ vector mesons as a function of charged hadron multiplicity in p+p and p+Pb collisions at LHC energies. We employ the color glass condensate framework, using running coupling Balitsky-Kovchegov evolved dipole amplitudes, to compute gluon and $c\bar{c}$-pair production. We use fragmentation functions to obtain charged hadrons, and explore two different hadronization schemes for the $J/ψ$: non-relativistic quantum chromodynamics and the improved color evaporation model. In our framework, event-by-event multiplicity fluctuations of both hadrons and $J/ψ$ are driven…
Intrinsic Fluctuations of the Proton Saturation Momentum Scale in High Multiplicity p+p Collisions
本文用彩色玻璃凝聚体理论研究了p+p碰撞中的高多重数事例。我们表明，除了亚核色荷波动的质子饱和动量尺度的内在波动，需要解释非常高的多重尾分布在p+p碰撞。这种内在波动的起源大概是非微扰性质的。经典的杨米尔斯模拟使用IP-ARMAMA模型进行定量估计。我们发现，在RHIC和LHC的p+p数据中，饱和动量标度平均值的波动如$\cal O$（1）那么大，会导致罕见的高多重数事件。利用现有的多重数分布数据，我们试图约束质子饱和动量尺度的分布，并对13 TeV p+p碰撞中的多重数分布进行预测。
Multiplicity distributions of charged particles and their event-by-event fluctuations have been compiled for relativistic heavy-ion collisions from the available experimental data at Brookhaven National Laboratory and CERN and also by the use of an event generator. Multiplicity fluctuations are sensitive to QCD phase transition and to the presence of critical point in the QCD phase diagram. In addition, multiplicity fluctuations provide baselines for other event-by-event measurements. Multiplicity fluctuation expressed in terms of the scaled variance of the multiplicity distribution is an inte…
As one of the possible signals for the whereabouts of the critical point on the QCD phase diagram, recently, the multiplicity fluctuations in heavy-ion collisions have aroused much attention. It is a crucial observable of the Beam Energy Scan program of the Relativistic Heavy Ion Collider. In this work, we investigate the centrality dependence of the multiplicity fluctuations regarding the recent measurements from STAR Collaboration. By employing a hydrodynamical approach, the present study is dedicated to the noncritical aspects of the phenomenon. To be specific, in addition to the thermal fl…
We report the higher order cumulants and their ratios for baryon, charge and strangeness multiplicity in canonical and grand-canonical ensembles in ideal thermal model including all the resonances. When the number of conserved quanta is small, an explicit treatment of these conserved charges is required, which leads to a canonical description of the system and the fluctuations are significantly different from the grand canonical ensemble. Cumulant ratios of total charge and net-charge multiplicity as a function of collision energies are also compared in grand canonical ensemble.
The initial state is one of the greatest uncertainties in heavy-ion collisions. A model-agnostic approach is taken in the phenomenological Trento framework which constrains parameters using Bayesian analysis. However, the color-glass condensate (CGC) effective theory predicts initial energy densities that lie outside the recent Bayesian analyses due, in part, to the assumption in Trento of event-by-event multiplicity fluctuations following a $Γ$ distribution. We compare the Trento-preferred $\sqrt{T_{A}T_{B}}$ scaling to CGC-like $T_{A}T_{B}$ scaling coupled with log-normal fluctuations in $Au…
The independent participant model is generalized for skewness and kurtosis. The obtained relations allow to calculate the fluctuations of an arbitrarily high order. From the comparison with the SPS and the LHC data it is found that the participants are not nucleons. The contribution of the participant fluctuations increases with the order of fluctuations. The 5% centrality bins selected for the analysis at the LHC by ALICE seems to be too large. The fluctuations measures are dominated by the fluctuations of participants there. The method to quantify the value of participant number fluctuations…
An analysis method is proposed to study the forward-backward (FB) multiplicity fluctuation in high-energy nuclear collisions, built on the earlier work of Bzdak and Teaney. The method allows the decomposition of the centrality dependence of average multiplicity from the dynamical event-by-event (EbyE) fluctuation of multiplicity in pseudorapidity. Application of the method to AMPT and HIJING models shows that the long-range component of the FB correlation is captured by a few longitudinal harmonics, with the first component driven by the asymmetry in the number of participating nucleons in the…
One of the greatest uncertainties in heavy-ion collisions is the description of the initial state. Different models predict a wide range of initial energy density distributions based on their underlying assumptions. Final flow harmonics are sensitive to these differences in the initial state due to the nearly linear mapping between eccentricities and anisotropic flow harmonics. The Trento code uses a model-agnostic approach by phenomenologically parameterizing the initial state and constraining those parameters from a Bayesian analysis. There the multiplicity fluctuations were determined by a …
The multiplicity fluctuations are studied in the van der Waals excluded volume hadron-resonance gas model. The calculations are done in the grand canonical ensemble within the Boltzmann statistics approximation. The scaled variances for positive, negative and all charged hadrons are calculated along the chemical freeze-out line of nucleus-nucleus collisions at different collision energies. The multiplicity fluctuations are found to be suppressed in the van der Waals gas. The numerical calculations are presented for two values of hard-core hadron radius, $r=0.3$ fm and 0.5 fm, as well as for th…
Initial volume fluctuation (VF) arising from the participant fluctuation would be the background which should be subtracted experimentally from the measured higher-order cumulants. We study the validity of the Volume Fluctuation Correction (VFC) on higher-order net-proton cumulants by using simple toy model and UrQMD model in Au+Au collisions at \sqrt s_{NN} = 200 GeV for various centrality definitions. The results are compared to the conventional data driven method called Centrality Bin Width Correction (CBWC). We find VFC works well in toy model assuming independent particle production (IPP)…
