I investigate the volume corrections on cumulants of total charge distributions and net proton distributions. The required volume information is generated by an optical Glauber model. I find that the corrected statistical expectations of multiplicity distributions mimic the negative binomial distributions at non-central collisions, and they tend to approach the Poisson ones at most-central collisions due to the "boundary effects," which suppress the volume corrections. However, net proton distributions and reference multiplicity distributions are sensitive to the external volume fluctuations at most-central collisions, which imply that one has to consider the details of volume distributions in event-by-event multiplicity fluctuation studies.
We construct a multiplicity distribution characterized by large factorial cumulants (integrated correlation functions) from a simple combination of two ordinary multiplicity distributions characterized by small factorial cumulants. We find that such a model, which could be interpreted as representing two event classes, reproduces the preliminary data for the proton cumulants measured by the STAR collaboration at $7.7$ GeV very well. This model then predicts very large values for the fifth and sixth order factorial cumulants, which can be tested in experiment.
We study the influence of quantum interference and colour flow on three point correlations described by asymmetric cumulants in high multiplicity events in pp collisions. We use the model previously developed for the study of the collectivity in symmetric cumulants. We show that the resulting three point asymmetric cumulant is in qualitative agreement with the experimental data for the same parameters of the model as it was with the symmetric cumulants. Our results show that the initial state correlations must play a major role and may be even dominant in the explanation of the correlations in…
In this note we extend previous work on efficiency corrections for cumulant measurements [1,2]. We will discuss the limitations of the methods presented in these papers. Specifically we will consider multiplicity dependent efficiencies as well as a non-binomial efficiency distributions. We will discuss the most simple and straightforward methods to implement those corrections.
We studied the centrality selection effect on cumulants (up to fourth order) and the cumulants ratios of net-proton multiplicity distributions in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 7.7, 19.6 and 200 GeV from UrQMD model. The net-proton cumulants are calculated with collision centralities by using charged particle multiplicity from different pesudorapidity ($η$) region. By comparing the results from various collision centralities, we found that the autocorrelation effects are not significant in the results with collision centralities "refmult-3" and "refmult-2", which are using mid-…
We investigate the measurement of the sixth order cumulant and its ratio to the second order cumulant ($C_6/C_2$) in relativistic heavy-ion collisions. The influence of statistics and different methods of centrality bin width correction on $C_6/C_2$ of net-proton multiplicity distributions is demonstrated. There is no satisfactory method to extract $C_6/C_2$ with the current statistics recorded at lower energies by STAR at RHIC. With statistics comparable to the expected statistics at the planned future RHIC Beam Energy Scan II (BES II), no energy dependence of $C_6/C_2$ is observed in central…
Within the ultra-relativistic quantum molecular dynamics (UrQMD) model, in which the Lorentz-covariant treatment of nuclear mean-field potential is considered, the fluctuations of net-baryon, net-charge and deuterons multiplicity distributions in Au+Au head-on collisions at $\sqrt{s_{NN}}=3.0-5.0$ GeV are calculated. The results show that the nuclear mean-field potential can significantly enhance the magnitude of baryon number fluctuations in narrow rapidity windows, and this enhancement rapidly weakens with increasing beam energy. However, for proton and net-charge number fluctuations, the me…
Fluctuations of conserved quantities are sensitive observables to probe the signature of QCD phase transition and critical point in heavy-ion collisions. With the UrQMD model, we have studied the centrality and energy dependence of various order cumulants and cumulant ratios (up to fourth order) of net-proton,net-charge and net-kaon multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}}$= 7.7, 11.5, 19.6, 27, 39, 62.4, 200 GeV. The model results show that the production mechanism of the particles and anti-particles have significant impacts on the cumulants of net-particles multiplici…
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)…
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.
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…
We propose a method to remove the contributions of pileup events from higher-order cumulants and moments of event-by-event particle distributions. Assuming that the pileup events are given by the superposition of two independent single-collision events, we show that the true moments in each multiplicity bin can be obtained recursively from lower multiplicity events. In the correction procedure the necessary information are only the probabilities of pileup events. Other terms are extracted from the experimental data. We demonstrate that the true cumulants can be reconstructed successfully by th…
We determine the net-baryon multiplicity distribution which reproduces all cumulants measured so far by lattice QCD. We present the dependence on the volume and temperature of this distribution. We find that for temperatures and volumes encountered in heavy ion reactions, the multiplicity distribution is very close to the Skellam distribution, making the experimental determination of it rather challenging. We further provide estimates for the statistics required to measure cumulants of the net-baryon and net-proton distributions.
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 …
We analyze the rapidity and transverse momentum dependence for the cumulants of the net-proton and net-baryon distributions in Au+Au collisions at $\sqrt{s_{\text{NN}}} = 5\,\text{GeV}$ with a microscopic hadronic transport (JAM) model. To study the effects of mean field potential and softening of equation of state (EoS) on the fluctuations of net-proton (baryon) in heavy-ion collisions, the calculations are performed with two different modes. The softening of EoS is realized in the model by implementing the attractive orbit in the two-body scattering to introduce a reduction pressure of the s…
We performed systematic studies on the effects of event-by-event efficiency fluctuations on efficiency correction for cumulant analysis in relativistic heavy-ion collision experiments. Experimentally, particle efficiencies of events measured under different experimental conditions should be different. For fluctuation measurements, the final event-by-event multiplicity distributions should be the superposed distributions of various type of events measured under different conditions. We demonstrate efficiency fluctuation effects using numerical simulation, in which we construct an event ensemble…
We investigate the effect of the global charge conservation on the cumulants of conserved charges observed in relativistic heavy ion collisions in a finite rapidity window, $Δη$, with a special emphasis on the time evolution of fluctuations in the hadronic medium. It is argued that the experimental result of the net-electric charge fluctuation observed by ALICE does not receive effects from the global charge conservation, because of the finite diffusion distance of charged particles in the hadronic stage. We emphasize that the magnitude of the effect of the global charge conservation can be es…
Volume or centrality fluctuations (CF) is one of the main uncertainties for interpreting the centrality dependence of many experimental observables. The CF is constrained by centrality selection based on particle multiplicity in a reference subevent, and contributes to observables measured in another subevent. Using a Glauber-based independent source model, we study the influence of CF on several distributions of multiplicity $N$ and eccentricities $ε_n$: $p(N)$, $p(ε_n)$, $p(ε_n,ε_m)$ and $p(N,ε_n)$, where the effects of CF is quantified using multi-particle cumulants of these distributions. …
Higher-order cumulants of the distributions of conserved charges, such as net-baryon number, are sensitive to the quantum chromodynamics(QCD) phase transition and the QCD critical point. We calculate the cumulants and correlation functions of proton, antiproton, and net-proton multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}} = 7.7$ GeV using a multiphase transport model(AMPT). The AMPT model can basically describe the trends of cumulants, cumulant ratios, (normalized) correlation functions of the proton and net-proton measured by the STAR experiment. The multiproton (baryon) co…
A series of new flow observables mixed harmonic multi-particle cumulants (MHC), which allow for the first time to quantify the correlations strength between different order of flow coefficients with various moments, was investigated using hydrodynamic model. These new observables are constructed based on multi-particle cumulants, and thus by design will be less sensitive to the non-flow contaminations. In addition to the previous study of correlation involving two flow coefficients with their second moments, both correlations of three flow coefficients and the correlations of higher order mome…
The probability density functions of proton, anti-proton, and net-proton multiplicity distributions are constructed from the Beam Energy Scan results of the STAR experiment using the Pearson curve method. The constructed distributions of proton and anti-proton are compared with Poisson and Binomial distributions. The net-proton probability distributions are compared with Skellam distributions to study the O(4) criticality near the chiral crossover transition. The $C_{6}/C_{2}$ results estimated from the obtained PDFs are compared with Skellam and Binomial baselines for the Beam Energy Scan dat…
We calculate the cumulants and correlation functions of net-kaon multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}} = 7.7$ GeV using a multiphase transport model (AMPT) with both a new coalescence mechanism and all charge conservation laws. The AMPT model can qualitatively describe the centrality dependences of the net-kaon cumulants and cumulant ratios measured by the STAR experiment. By focusing on the stage evolution of the cumulants, cumulant ratios, and correlation functions, we reveal several key effects on the fluctuations and correlations of strangeness during the dynamic…
We propose a general procedure for the detector-response correction (including efficiency correction) of higher order cumulants observed by the event-by-event analysis in heavy-ion collisions. This method makes use of the moments of the response matrix characterizing the property of a detector, and is applicable to a wide variety of response matrices such as those having non-binomial responses and including the effects of ghost tracks. A procedure to carry out the detector-response correction of realistic detectors is discussed. In test analyses, we show that this method can successfully re- c…
We study the effects of correlations on cumulants and their ratios of net-proton multiplicity distributions which have been measured for central (0\%-5\%) Au + Au collisions at the Relativistic Heavy Ion Collider (RHIC). This effect has been studied assuming individual proton and anti-proton distributions as a Poisson or Negative Binomial Distribution (NBD). In-spite of significantly correlated production due to baryon number, electric charge conservation and kinematical correlations of protons and anti-protons, the measured cumulants of the net-proton distribution follow the independent produ…
We perform a systematic study on the effect of non-uniform track efficiency correction in higher-order cumulant analysis in heavy-ion collisions. Through analytical derivation, we find that the true values of cumulants can be successfully reproduced by the efficiency correction with an average of the realistic detector efficiency for particles with the same charges within each single phase space. The theoretical conclusions are supported by a toy model simulation by tuning the non-uniformity of the efficiency employed in the track-by-track efficiency correction method. The valid averaged effic…
In this paper, we present a novel event-shaped cumulants (ESC) response approach, based on a multi-phase transport (AMPT) model simulations, to analyze p-Pb collisions at $\sqrt{s_{NN}}$= 5.02 TeV. We find that the Pearson coefficients between the subset cumulants of the final harmonics $v_{2}\{2k\}~(k=1,2,3,4)$ and the subset cumulants of initial eccentricity $\varepsilon_{2}\{2k\}$ in the ESC basis are significantly enhanced. These Pearson coefficients are strongly-dependent on the charged multiplicity, the set number of events (SNE), and only weakly-dependent on the order of the multi-parti…
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.
By relating the charge multiplicity distribution and the temperature of a de-exciting nucleus through a deep neural network, we propose that the charge multiplicity distribution can be used as a thermometer of heavy-ion collisions. Based on an isospin-dependent quantum molecular dynamics model, we study the caloric curve of reaction $^{103}$Pd + $^9$Be with the apparent temperature determined through the charge multiplicity distribution. The caloric curve shows a characteristic signature of nuclear liquid-gas phase transition around the apparent temperature $T_{\rm ap}$ $=$ $6.4~\rm MeV$, whic…
We have studied the effect of limited statistics of data on measurement of the different order of cumulants of net-proton distribution assuming that the proton and antiproton distributions follow Possionian and Binomial distributions with initial parameters determined from experimental results for two top center of mass energies ($\sqrt{s_{\mathrm{NN}}}=200$ and $62.4$ GeV) in most central ($0-5$%) Au$+$Au collisions at Relativistic Heavy Ion Collider (RHIC). In this simulation, we observe that the central values for higher order cumulants have a strong dependence on event sample size and due …
Higher-order cumulants of conserved charge distributions are sensitive observables to probe the critical fluctuations near QCD critical point in heavy-ion collisions. Due to high interaction rate, pileup event can be one of the major sources of background in the measurements of higher-order cumulants. In this paper, we studied the effects of pileup events on higher-order cumulants of proton multiplicity distributions using UrQMD model. It is found that the proposed pileup correction fails if the correction parameters are determined by the Glauber fitting of charged particle multiplicities, whi…
The evolution of multiplicity distribution of a species which undergoes chemical reactions can be described with the help of a master equation. We study the master equation for a fixed temperature, because we want to know how fast different moments of the multiplicity distribution approach their equilibrium value. We particularly look at the 3rd and 4th factorial moments and their equilibrium values from which central moments, cumulants and their ratios can be calculated. Then we study the situation in which the temperature of the system decreases. We find out that in the non-equilibrium state…
We study the dependence of the normalized moments of the net-proton multiplicity distributions on the definition of centrality in relativistic nuclear collisions at a beam energy of $\sqrt{s_{\mathrm{NN}}}= 7.7$ GeV. Using the UrQMD model as event generator we find that the centrality definition has a large effect on the extracted cumulant ratios. Furthermore we find that the finite efficiency for the determination of the centrality introduces an additional systematic uncertainty. Finally, we quantitatively investigate the effects of event-pile up and other possible spurious effects which may …
We present a method that may allow an estimate of the value of the speed of sound as well as its logarithmic derivative with respect to the baryon number density in matter created in heavy-ion collisions. To this end, we utilize well-known observables: cumulants of the baryon number distribution. In analyses aimed at uncovering the phase diagram of strongly interacting matter, cumulants gather considerable attention as their qualitative behaviour along the explored range of collision energies is expected to aid in detecting the QCD critical point. We show that the cumulants may also reveal the…
Mix-cumulants of conserved charge distributions are sensitive observables for probing properties of the QCD medium and phase transition in heavy-ion collisions. To perform precise measurements, efficiency correction is one of the most important step. In this study, using the binomial efficiency model, we derive efficiency correction formulas for mutually exclusive and inclusive variables. The UrQMD model is applied to verify the validity of these formulas for different types of correlations. Furthermore, we investigate the effect of the multiplicity loss and contamination emerging from the par…
In this note we discuss subtleties associated with the efficiency corrections for measurements of off-diagonal cumulants and factorial moments for a situation when one deals with overlapping sets of particles, such as correlations between numbers of protons and positively charged particles. In particular, we discuss the situation commonly encountered in heavy-ion experiments, where first all charges are reconstructed and then protons are selected from these charges by an additional particle identification procedure. We present the efficiency correction formulas for the case when the detection …
Fluctuations of the baryon number in relativistic heavy-ion collisions are a promising observable to explore the structure of the QCD phase diagram. The cumulant ratios in heavy ion collisions at intermediate energies ($\sqrt{s_{\textrm{NN}}} < 7$ GeV) have not been studied to date. We investigate the effects of mean field potential and clustering on the cumulant ratios of baryon and proton number distributions in Au+Au collisions at beam energy of 1.23 GeV$/$nucleon as measured by the HADES Collaboration at GSI. Ultrarelativistic Quantum Molecular Dynamics (UrQMD) and the JAM model are used t…
The centrality or the number of initial-state sources $V$ of the system produced in heavy ion collision is a concept that is not uniquely defined and subject to significant theoretical and experimental uncertainties. We argue that a more robust connection between the initial-state sources with final-state multiplicity could be established from the event-by-event multiplicity correlation between two subevents separated in pseudorapidity, $N_a$ vs $N_b$. This correlation is sensitive to two main types of centrality fluctuations (CF): 1) particle production for each source $p(n)$ which smears the…
The effect of nuclear interactions on measurable net-proton number fluctuations in heavy ion collisions at the SIS18/GSI accelerator is investigated. The state of the art UrQMD model including interaction potentials is employed. It is found that the nuclear forces enhance the baryon number cumulants, as predicted from grand canonical thermodynamical models. The effect however is smeared out for proton number fluctuations due to iso-spin randomization and global baryon number conservation, which decreases the cumulant ratios. For a rapidity acceptance window larger than $Δy> 0.4$ the effects of…
Cumulants of baryon number are given considerable attention in analyses of heavy-ion collision experiments as possible signatures of the QCD critical point. In this work, we show that the values of the lowest three cumulants can also be utilized to recover information about the isothermal speed of sound and its logarithmic derivative with respect to the baryon number density. This result provides a new method for obtaining information about fundamental properties of nuclear matter studied in heavy-ion collisions, with consequences for both the search for the QCD critical point and neutron star…
