In the framework of the classical Glauber approach, the analytical expressions for the variance of the number of wounded nucleons and binary collisions in AA interactions at a given centrality are presented. Along with the optical approximation term, they contain additional contact terms arising only in the case of nucleus-nucleus collisions. The magnitude of the additional contributions, e.g., for PbPb collisions at SPS energies, is larger than the contribution of the optical approximation at some values of the impact parameter. The sum of the additional contributions is in good agreement with the results of independent Monte Carlo simulations of this process. Due to these additional terms, the variance of the total number of participants for peripheral PbPb collisions and the variance of the number of collisions at all values of the impact parameter exceed several multiples of the Poisson variances. The correlator between the numbers of participants in colliding nuclei at fixed centrality is also analytically calculated.
A recent study of 5 TeV $p$-Pb centrality combined a Glauber model of $p$-Pb collision geometry with an assumption of linear scaling between $n_{ch}$ (charge) integrated within some $η$ acceptance and the number of nucleon participants $N_{part}$. The study concluded that $N_{part}$ increases to nearly 16 in central collisions, and the high-$p_t$ region of $p$-Pb $p_t$ spectra rescaled by the Glauber-estimated number of $p$-N binary collisions remains consistent with a $p$-$p$ spectrum for the same energy, independent of $p$-Pb centrality. However, the relation between $N_{part}$ and $n_{ch}$ …
We improve the centrality definition in impact parameter in PACIAE model responding the fact reported by the ALICE, ATLAS, and CMS collaborations that the maximum impact parameter in heavy ion collisions should be extended to 20 $fm$. Meanwhile the PACIAE program is updated to a new version of PACIAE 2.2.2 with convenience of studying the elementary nuclear collisions, proton-nucleus collisions, and the nucleus-nucleus collisions in one unified program version. The new impact parameter definition together with the optical Glauber model calculated impact parameter bin, $N_{part}$, and $N_{coll}…
We discuss multiplicity fluctuations of charged particles produced in nuclear collisions measured event-by-event by the NA49 experiment at CERN SPS within the Glauber Monte Carlo approach. We use the concepts of wounded nucleons and wounded quarks in the mechanism of multiparticle production to characterize multiplicity fluctuations expressed by the scaled variance of multiplicity distribution. Although Wounded Nucleon Model correctly reproduce the centrality dependence of the average multiplicity in Pb+Pb collisions, it completely fails in description of corresponding centrality dependence of…
A power-law description of heavy ion collision centrality
重离子碰撞$n_{ch}$的最小偏置分布可用幂律形式$n_{ch}^{-3/4}$很好地近似，表明将变量改为$n_{ch}^{1/4}$可以更精确地获得分布的结构和A-A碰撞中心性.我们提出了一个详细的中心性研究的海京-1.37 Monte Carlo数据在200 GeV的幂律格式。我们发现，$n_{participant}^{1/4}$上的最小偏差分布，确定与Glauber蒙特卡罗模拟，是均匀的，除了5%的正弦变化。幂律格式揭示了Glauber参数$n_{part}$和$n_{bin}$与分数截面之间的精确线性关系。适用于RHIC数据的幂律格式便于将外推约束的数据和Glauber分布，以获得一个10倍的改进，在周边碰撞的中心精度。
Recent data on the nuclear modification of W and Z boson production measured by the ATLAS collaboration in PbPb collisions at $\sqrt{s_{\rm nn}}=5.02$ TeV show an enhancement in peripheral collisions, seemingly contradicting predictions of the Glauber model. The data were previously explained by arguing that the nucleon-nucleon cross section may be shadowed in nucleus-nucleus collisions, and hence suppressed compared to the proton-proton cross section at the same collision energy. This interpretation has quite significant consequences for the understanding of heavy-ion data, in particular in t…
A Monte Carlo model, initially developed for soft pp and AA collisions at high energy, is applied for proton-lead interaction at the LHC energy. Elementary collisions are implemented at the partonic level and do not involve the usual Glauber supposition of independent nucleon-nucleon collisions. The average number of participating nucleons and charged multiplicity in p-Pb collisions were calculated and compared with the predictions of Glauber model and experimental data. It was demonstrated that taking into account the energy conservation results in the number of participating nucleons conside…
We study, within the Monte-Carlo Glauber model, centrality dependence of the midrapidity charged multiplicity density $dN_{ch}/dη$ and of the anisotropy coefficients $\varepsilon_{2,3}$ in Pb+Pb collisions at $\sqrt{s}=5.02$ TeV and in Xe+Xe collisions at $\sqrt{s}=5.44$ TeV. Calculations are performed for versions with and without nucleon meson cloud. The fraction of the binary collisions, $α$, has been fitted to the data on $dN_{ch}/dη$ in Pb+Pb collisions. We obtain $α\approx 0.09(0.13)$ with (without) meson cloud. The effect of meson cloud on the $dN_{ch}/dη$ is relatively small. For Xe+Xe…
The production of forward $J/ψ$ mesons in proton-nucleus collisions can provide important information on gluon saturation. In a previous work we studied this process in the Color Glass Condensate framework, describing the target using a dipole cross section fitted to HERA inclusive data and extrapolated to the case of a nuclear target using the optical Glauber model. In this work we study the centrality dependence of the nuclear suppression in this model and compare our results with recent LHC data for this observable.
The nuclear suppression of forward $J/ψ$ production in high energy proton-nucleus collisions can be used as a probe of gluon saturation at small $x$. In an earlier work we studied this suppression in minimum bias collisions in the Color Glass Condensate formalism, relying on the optical Glauber model to obtain the dipole cross section of the nucleus from the one of the proton fitted to HERA DIS data. Here we study how the impact parameter dependence of this model can be used to compare our results with recent LHC data on the centrality dependence of this suppression.
Forward $J/ψ$ production and suppression in high energy proton-nucleus collisions can be an important probe of gluon saturation. In an earlier work we studied this process in the Color Glass Condensate framework and showed that using the Glauber approach to extrapolate the dipole cross section of a proton to a nucleus leads to results closer to experimental data than previous calculations in this framework. Here we investigate the centrality dependence of the nuclear suppression in this model and show a comparison of our results with recent LHC data.
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 perip…
We present predictions of the mean multiplicity yields for different centrality classes of Pb-Pb collisions at $\sqrt{s} = 5.02$ TeV at the LHC, obtained using the Monte-Carlo Modified Glauber model (MGM) [1]. Contrary to generally used standard Glauber calculations, the MGM takes into account the energy conservation in the soft particles production. The only one efficient model parameter was tuned and fixed previously (k=0.35) by fitting the available data on multiplicity for all colliding systems up to RHIC energies. The MGM has shown already a good predictive capability for the yields at $\…
The charged-particle multiplicity distribution and the transverse-energy distribution measured in heavy-ion collisions at top RHIC and LHC energies are described using the two-component model approach based on a convolution of the Monte Carlo Glauber model with the Weibull model for particle production. The model successfully describes the multiplicity and transverse-energy distribution of minimum-bias collision data for a wide range of energies. The Weibull-Glauber model can be used to determine the centrality classes in heavy-ion collisions as an alternative to the conventional negative bino…
We propose a new way to correct for finite centrality bin width effect i.e. participant fluctuations in fluctuation analysis in high energy nucleus-nucleus collisions. The MMCP method allows to separate participant fluctuations and obtain fluctuations from one participant - a source - from a combination of the experimentally measured first four moments. The EPOS model is used for the numerical check of the MMCP for the net electric charge fluctuations in the forward rapidity region in Ar+Sc reactions at beam momentum 150 GeV/c. We show that using the existing methods - decreasing a centrality …
We study the initial conditions for Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV using the two component Monte-Carlo Glauber model with shadowing of the nucleons in the interior by the leading ones. The model parameters are fixed by comparing to the multiplicity data of p+Pb and Pb+Pb at $\sqrt{s_{\rm NN}}=5.02$ and $2.76$ TeV respectively. We then compute the centrality dependence of the eccentricities upto the fourth order as well as their event by event distributions. The inclusion of shadowing brings the Monte-Carlo Glauber model predictions in agreement with data as well as with resul…
The ability to accurately compute the series of coefficients $v_n$ characterizing the momentum space anisotropies of particle production in ultrarelativistic heavy ion collisions as a function of centrality is widely regarded as a triumph of fluid dynamics as description of the bulk matter evolution. A key ingredient to fluid dynamical modeling is however the initial spatial distribution of matter as created by a yet not completely understood equilibration process. A measurement directly sensitive to this initial state geometry is therefore of high value for constraining models of pre-equilibr…
The magnitude of long-range correlations between observables in two separated rapidity windows, proposed as a signature of the string fusion and percolation phenomenon, is studied in the framework of non-Glauber Monte Carlo string-parton model, based on the picture of elementary collisions of color dipoles. The predictions, obtained with and without string fusion, demonstrate effects of color string fusion on the observables in Pb-Pb collisions at the LHC: decrease of n-n correlation coefficient with centrality and negative pt-n correlations, if the sufficiently effective centrality estimator …
We present the results of an improved Monte Carlo Glauber (MCG) model of relevance for collisions involving nuclei at center-of-mass energies of BNL RHIC ($\sqrt{s_{\rm NN}}=0.2$ TeV), CERN LHC ($\sqrt{s_{\rm NN}}=2.76$-$8.8$ TeV), and proposed future hadron colliders ($\sqrt{s_{\rm NN}}\approx 10$-$63$ TeV). The inelastic pp cross sections as a function of $\sqrt{s_{\rm NN}}$ are obtained from a precise data-driven parametrization that exploits the many available measurements at LHC collision energies. We describe the nuclear transverse profile with two separated 2-parameter Fermi distributio…
The recently proposed participant dissipating effective-energy approach is applied to describe the dependence on centrality of the multiplicity of charged particles measured in heavy-ion collisions at the collision energies up to the highest LHC energy of 5 TeV. The effective-energy approach relates multihadron production in different types of collisions, by combining, under the proper collision energy scaling, the constituent quark picture with Landau relativistic hydrodynamics. The measurements are shown to be well described in terms of the centrality-dependent effective energy of participan…
We study within the Monte Carlo Glauber model the influence of collective quantum effects in the Pb nucleus on the azimuthal anisotropy coefficients $ε_{2,3}$ in Pb+Pb collisions at the LHC energies. To account for the quantum effects, we modify the sampling of the nucleon positions by applying suitable filters that guarantee that the colliding nuclei have the mean squared quadrupole and octupole moments consistent with the ones extracted from the experimental quadrupole and octupole strength functions for the Pb nucleus with the help of the energy weighted sum rule. Our Monte Carlo Glauber mo…
In the process of understanding nuclear collisions, reliable extrapolations from pp collisions, based on Glauber models, are highly desirable, though seldomly accurate. We review the inclusion of diffractive excitations and argue that they provide an important contribution to centrality observables in pA collisions. We present a method for distinguishing between diffractively and non-diffractively wounded nucleons, and a proof-of-principle for an extrapolation of multiparton interaction models built on this.
The PYTHIA Monte Carlo (PMC) has been applied broadly to simulations of high-energy $p$-$p$ and $p$-$\bar p$ collisions. The PMC is based on several assumptions, such as that most hadrons result from jet production (multiple parton interactions or MPIs), that $p$-$p$ centrality is relevant and that color reconnection (CR) strongly influences fragmentation to jets. An alternative description is provided by the two-component (soft + hard) model (TCM) of hadron production. TCM analysis of $p$-Pb ensemble-mean-$p_t$ data reveals centrality trends quite different from those estimated via a geometri…
The triangular flow in ultrarelativistic $^3$He-Au collisions at RHIC energies is enhanced due to the triangular arrangement of the nucleon configurations in $^3$He. We study the fireball eccentricities in the Glauber Monte Carlo model and find that since the configurations of the projectile $^3$He are elongated triangles, the created fireball has a large ellipticity and a smaller triangularity. The dependence of the triangularity on centrality is weak, so it cannot be extracted from the centrality dependence of the triangular flow $v_3$, as it is dominated by the centrality dependence of the …
The dependence on centrality, or on the number of nucleon participants, of the midrapidity density of charged particles measured in heavy-ion collisions at the collision energy of about 20 GeV at RHIC to the highest LHC energy of 5 TeV is investigated within the recently proposed effective-energy approach. This approach relates multihadron production in different types of collisions by combining, under the proper scaling of the collision energy, the constituent quark picture with Landau relativistic hydrodynamics. The measurements are shown to be well described based on the similarity of multi…
In ultrarelativistic heavy-ion experiments, one estimates the centrality of a collision by using a single observable, say $n$, typically given by the transverse energy or the number of tracks observed in a dedicated detector. The correlation between $n$ and the impact parameter, $b$, of the collision is then inferred by fitting a specific model of the collision dynamics, such as the Glauber model, to experimental data. The goal of this paper is to assess precisely which information about $b$ can be extracted from data without any specific model of the collision. Under the sole assumption that …
We investigate the influence of the central two-body NN correlations on several quantities observed in relativistic heavy-ion collisions. It is demonstrated with explicit Monte Carlo simulations, that the basic correlation measures, such as the fluctuations of participant eccentricity, initial size fluctuations, or the fluctuations of the number of sources producing particles, are all sensitive to the inclusion of the two-body correlations. The effect is at the level of about 10-20%. Moreover, the realistic (Gaussian) correlation function gives indistinguishable results from the hard-core repu…
Centrality dependence of charged particles multiplicity, transverse momentum spectra, integrated and differential elliptic flow, in $\sqrt{s}_{NN}$=200 GeV Au+Au collisions are analyzed using event by event ideal hydrodynamics. Monte-Carlo Glauber model of initial condition, constrained to reproduce experimental charged particle's multiplicity in 0-10% Au+Au collisions, reasonably well reproduces all the experimental observables, e.g. centrality dependence of charged particles multiplicity, integrated and differential elliptic flow. Model predictions for higher flow harmonics, $v_3$, $v_4$ how…
The process of formation of the participant system in heavy-ion collisions is investigated in the framework of a simplified analytic Glauber-like model, which is based on the relativistic Boltzmann transport equation. The key point lies in the time-dependent partition of the nucleon system into two groups: nucleons, which did not take part in any interaction before a given time and nucleons, which already have interacted. In the framework of the proposed model we introduce a natural energy-dependent temporal scale $t_c$, which allows us to remove all dependencies of the model on the collision …
Recent studies reveal that at high energies, collisions of small system like $p+p$ gives signatures similar to that widely observed in heavy ion collisions hinting towards a possibility of forming a medium with collective behaviour. With this motivation, we have used the Glauber model, which is traditionally applied to heavy ion collisions, in small system using anisotropic and inhomogeneous density profile of proton and found that the proposed model reproduces the charged particle multiplicity distribution of $p+p$ collisions at LHC energies very well. Collision geometric properties like mean…
A class of simple superposition models based on the Glauber picture of multiple collisions is compared with the data on the centrality dependence of the multiplicity distributions in a central rapidity bin. We show how the results depend on the specific assumptions concerning the distributions in the number of participants and their relations to the distributions of the number of produced hadrons in various phase space bins. None of the versions of the model describes satisfactorily the centrality dependence of the scaled dispersion.
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. …
The dependencies of charged particle pseudorapidity density and transverse energy pseudorapidity density at midrapidity on the collision energy and on the number of nucleon participants, or centrality, measured in nucleus-nucleus collisions are studied in the energy range spanning a few GeV to a few TeV per nucleon. The model in which the multiparticle production is driven by the dissipating effective energy of participants is introduced. The model is based on the earlier proposed approach, combining the constituent quark picture together with Landau relativistic hydrodynamics shown to interre…
We have estimated centrality variation of chemical freeze-out parameters from yield data at mid-rapidity of $π^\pm$, $K^\pm$ and $p$, $\bar{p}$ for collision energies of RHIC (Relativistic Heavy Ion Collider), Beam Energy Scan (RHIC-BES) program, and LHC (Large Hadron Collider). We have considered a simple hadron resonance gas model and employed a formalism involving conserved charges ($B, Q, S$) of QCD for parameterization. Along with temperature and three chemical potentials ($T,μ_B,μ_Q,μ_S$), a strangeness under-saturation factor ($γ_S$) has been used to incorporate the partial equilibratio…
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…
A simple approach based on the separation of wounded nucleons in an A-A collision in two categories, those suffering single collisions - corona and the rest - core, estimated within a Glauber Monte-Carlo approach, explains the centrality dependence of the light flavor hadrons production in Pb-Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV. The core contribution does not include any dependence of any process on the fireball shape as a function of the impact parameter. Therefore, the ratios of the $p_T$ distributions to the one corresponding to the minimum bias pp collisions at the same energy, each …
We collected the experimental data of transverse momentum spectra of identified particles produced in proton-proton ($p$-$p$), deuteron-gold ($d$-Au or $d$-$A$), gold-gold (Au-Au or $A$-$A$), proton-lead ($p$-Pb or $p$-$A$), and lead-lead (Pb-Pb or $A$-$A$) collisions measured by the ALICE, CMS, LHCb, NA49, NA61/SHINE, PHENIX, and STAR collaborations at different center-of mass energies. The multisource thermal model at the quark level or the participant quark model is used to describe the experimental data. The free parameters, the effective temperature $T$, entropy index-related $n$, and rev…
We show that the event-by-event fluctuations of the transverse size of the initial source, which follow directly from the Glauber treatment of the earliest stage of relativistic heavy-ion collisions, cause, after hydrodynamic evolution, fluctuations of the transverse flow velocity at hadronic freeze-out. This in turn leads to event-by-event fluctuations of the average transverse momentum, p_T. Simulations with GLISSANDO for the Glauber phase, followed by a realistic hydrodynamic evolution and statistical hadronization carried out with THERMINATOR, lead to agreement with the RHIC data. In parti…
Intense transient electric ({\bf E}) and magnetic ({\bf B}) fields are produced in the high energy heavy-ion collisions. The electromagnetic fields produced in such high-energy heavy-ion collisions are proposed to give rise to a multitude of exciting phenomenon including the Chiral Magnetic Effect. We use a Monte Carlo (MC) Glauber model to calculate the electric and magnetic fields, more specifically their scalar product $\bf{E}\cdot\bf{B}$, as a function of space-time on an event-by-event basis for the Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV for different centrality classes. We also calc…
A model for computing the probability density of event-by-event participant center-of-mass rapidity y^{c.m.} is presented. The evaluations of the y^{c.m.} distribution are performed for different collision energies and different centralities. We show that for certain conditions the rapidity distribution is described by a Gaussian with a variance determined mostly by the collision centrality. It is found that the width of the y^{c.m.} distribution increases strongly for more peripheral collisions, while it depends weakly on the collision energy. Other theoretical estimates of rapidity distribut…
Further investigation of the participant plane correlations within a Glauber model framework is presented, focusing on correlations between three or four participant planes of different order. A strong correlation is observed for $\cos(2Φ_{2}^*+3Φ_{3}^*-5Φ_{5}^*)$ which is a reflection of the elliptic shape of the overlap region. The correlation between the corresponding experimental reaction plane angles can be easily measured. Strong correlations of similar geometric origin are also observed for $\cos(2Φ_{2}^*+4Φ_{4}^*-6Φ_{6}^*)$, $\cos(2Φ_2^*-3Φ_3^*-4Φ_4^*+5Φ_5^*)$, $\cos(6Φ_2^*+3Φ_3^*-4Φ_4…
The Glauber modeling plays a key role in centrality-dependent measurements of heavy-ion collisions. A central input parameter in Glauber models is the inelastic nucleon-nucleon cross section $σ_{\text{nn}}^{\text{inel}}$ which is nearly always taken from proton-proton measurements. At the LHC energies $σ_{\text{nn}}^{\text{inel}}$ depends on the QCD dynamics at small $x$ and low interaction scales where the shadowing/saturation phenomena are expected to become relatively more important for larger nuclei than for the proton. Thus, $σ_{\text{nn}}^{\text{inel}}$ e.g. in Pb+Pb collisions may well …
We investigate the properties of light (anti)nuclei and (anti)hypertriton production in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}=2.76$ TeV, based on the parton and hadron cascade and dynamically constrained phase-space coalescence (PACIAE + DCPC) model. We found that the yields of light (anti)nuclei and (anti)hypertriton strongly depend on the centrality, i.e., their yields decrease rapidly with the increase of centrality bins, but their yield ratios are independent of centrality. The results of theoretical model are well consistent with ALICE data. Furthermore, we found that the integrated yie…
Results from proton-proton ($pp$) collisions have routinely been used as a baseline to analyze and understand the production of QCD matter expected to be produced in nuclear collisions. But recent studies of small systems formed in $pp$ collisions at the LHC energies hint at the possibility of producing medium with collective behavior. Therefore, results from $pp$ collisions required more careful investigation to understand whether QCD matter is produced in high multiplicity $pp$ collisions. With this motivation, the Glauber model traditionally used to study the heavy-ion collision dynamics at…
Experimental data on the onset of a so-called anomalous J/psi suppression in PbPb collisions at the SPS are considered in the framework of string percolation model. This onset is observed at a certain collision centrality, characterized by the number of nucleons-participants (Npart) related to the impact-parameter. Modified Bjorken formula calculations are performed for the local energy densities in AA collisions at different impact-parameters and with detailed account of the latest data available on the charged particles densities at midrapidity. Finally we compare variations of mean local en…
The dependencies of charged particle pseudorapidity density and transverse energy pseudorapidity density at midrapidity on the collision energy and on the number of nucleon participants, or centrality, measured in nucleus-nucleus collisions are studied in the energy range spanning a few GeV to a few TeV per nucleon. The study is based on the earlier proposed model, combining the constituent quark picture together with Landau relativistic hydrodynamics and shown to interrelate the measurements from different types of collisions. Within this picture, the dependence on the number of participants …
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)…
The centrality dependence of pseudorapidity density of charged particles and transverse energy is studied for a wide range of collision energies for heavy-ion collisions at midrapidity from 7.7 GeV to 5.02 TeV. A two-component model approach has been adopted to quantify the soft and hard components of particle production, coming from nucleon participants and binary nucleon-nucleon collisions, respectively. Within experimental uncertainties, the hard component contributing to the particle production has been found not to show any clear collision energy dependence from RHIC to LHC. The effect of…
