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 two colliding nuclei. The higher-order longitudinal harmonics are found to be strongly damped in AMPT compare to HIJING, due to weaker short-range correlations as well as the final-state effects present in the AMPT model. Two-particle pseudorapidity correlation reveals interesting charge-dependent short-range structures that are absent in HIJING model. The proposed method opens an avenue to elucidate the particle production mechanism and early time dynamics in heavy-ion collisions. Future analysis directions and prospects of using the pseudorapidity correlation function to understand the centrality bias in $p$+$p$, $p$+A and A+A collisions are discussed.
Forward-backward multiplicity correlations have been studied in electron-positron, proton-proton and more recently in lead-lead collisions. For the proton-proton case, comparison of experimental results to different models reveals an incomplete understanding of the physical phenomenon associated with these correlations. In this work, we present a study of forward-backward multiplicity correlations in proton-proton collisions using the PYTHIA event generator, at LHC energies. A detailed analysis is presented with and without weak decays, splitting data samples into soft and hard QCD processes, …
The correlations between multiplicities in two separated rapidity windows, is studied in the framework of the Monte Carlo model based on the picture of string formation in elementary collisions of colour dipoles. The hardness of the elementary collisions is defined by a transverse size of the interacting dipoles. The dependencies of the forward-backward correlation strength on the width and position of the pseudorapidity windows, as well as on transverse momentum range of observed particles were studied. It is demonstrated that taking into account of the string fusion effects improves the agre…
The initial geometry effect on forward-backward multiplicity correlations $C(N_{f},N_{b})$ is studied in relativistic collisions between light nuclei by using a multiphase transport model (AMPT). It is found that tetrahedron $^{16}$O + $^{16}$O gives a more uniform and symmetrical fireball which produces a more isotropic distribution of final particles after the expansion and evolution, and leads to a small $C(N_{f},N_{b})$. Forward-backward multiplicity correlation could be taken as a useful probe to distinguish the pattern of $α$-clustered $^{16}$O in experiments by comparing the neighboring…
We study multiplicity correlations of hadrons in forward and backward hemispheres in $pp$ inelastic interactions at energies 200GeV $\leq \sqrt{s} \leq$ 13TeV within the microscopic quark-gluon string model. The model correctly describes (i) the almost linear dependence of average multiplicity in one hemisphere on the particle multiplicity in other hemisphere in the center-of-mass frame; (ii) the increase of the slope parameter $b_{corr}$ with rising collision energy; (iii) the quick falloff of the correlation strength with increase of the midrapidity gap; (iv) saturation of the forward-backwa…
The parton rescattering effect on the charged hadron forward-backward multiplicity correlation in $pp$ collisions at $\sqrt s$=200 GeV is studied by a parton and hadron cascade model, PACIAE, based on the PYTHIA model. The calculated multiplicity and pseudorapidity distribution of the final state charged hadron are well compared with experimental data. It turned out that the final state charged hadron pseudorapidity distribution are different from the initial state charged partons. The parton rescattering effect on the charged hadron forward-backward multiplicity correlation increases with inc…
It is argued that the superposition approach, where partons are independently emitted from longitudinally extended sources in the early stage, is fully compatible with the experimental results for the forward-backward multiplicity correlations in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76 \textrm{ TeV}$. The pertinent correlation analysis is based on the PhD Thesis of Ref. [1], which includes an unpublished analysis of data taken by the ALICE Collaboration. Our calculations show that in the experimentally covered pseudorapidity range $Δη=1.2$, the initial sources in the backward and forward bins …
We have studied the centrality dependence of charged particle forward-backward multiplicity correlation strength in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV with a parton and hadron cascade model, PACIAE, based on PYTHIA. The calculated results are compared with the STAR data. The experimentally observed correlation strength characters: (1) the approximately flat pseudorapidity dependence in central collisions and (2) the monotonous decrease with decreasing centrality are well reproduced. However the theoretical results are bigger than the STAR data for the peripheral collisions. A discussi…
We analyze the multiplicity correlations between distant forward and backward rapidity regions in relativistic heavy-ion collisions in a superposition framework, where the particle production occurs through independent emission from correlated sources. This in principle allows for inferring information on the long-range forward-backward correlations of the sources in the earliest phase of the collision, based solely on the experimental information on the statistical features of the observed particle distributions. Our three-stage study incorporates the fluctuations of parton production in the …
Probing Forward-Backward Multiplicity Correlations and Fluctuations Using the Strongly Intensive Observable $Σ$ in Pb-Pb Collisions at SPS Energies with UrQMD
Variable Energy Cyclotron Centre（可变能量回旋加速器中心）；GSI Helmholtzzentrum für Schwerionenforschung GmbH (GSI)（GSI亥姆霍兹重离子研究中心有限公司）
Color reconnection (CR) mechanism in PYTHIA model has been reported to be essential to describe the flow-like collective effect observed in high multiplicity $p$+$p$ and $p$+Pb collisions. In this work, we test this mechanism towards explaining the Forward-Backward multiplicity correlation (b$_{\mathrm {cor}}$) measurements in $p$+$p$ collisions at the LHC energies. Out of the three different CR schemes implemented in PYTHIA, (a) MPI based CR (default mechanism), (b) QCD based CR and (c) Gluon moved CR, we found that the QCD based CR scheme describes relatively better the ALICE measurements of…
We propose a forward-backward multiplicity correlation function $C^N_{FB}$, which is experimentally accessible, to measure the noncollectivity contribution. We find that $C^N_{FB}$ is sensitive to the jet contribution for the particle-rich case. Surprisingly, it will automatically decrease for the particle-rare case. Our study indicates that similar decreasing trend observed previously is mainly driven by particle scarcity instead of jets. The function is studied in Au+Au collision at $\sqrt{s_{NN}}=200$ GeV with a multiphase transport model (AMPT). We find that the jet fraction is about 10% a…
We argue that the transverse shape of the fireball created in heavy ion collision is controlled by event-by-event fluctuations of the eccentricity vectors for the forward-going and backward-going wounded nucleons: $\vecε_n^{\mathrm{F}}\equiv ε_n^{\mathrm{F}} e^{i nΦ_n^{\mathrm{*F}}}$ and $\vecε_n^{\mathrm{B}}\equiv ε_n^{\mathrm{B}} e^{i nΦ_n^{\mathrm{*B}}}$. Due to the asymmetric energy deposition of each wounded nucleon along its direction of motion, the eccentricity vector of the produced fireball is expected to interpolate between $\vecε_n^{\mathrm{F}}$ and $\vecε_n^{\mathrm{B}}$ along the …
We analyze a generic model where wounded quarks are amended with strings in which both end-point positions fluctuate in spatial rapidity. With the assumption that the strings emit particles independently of one another and with a uniform distribution in rapidity, we are able to analyze the model semi-analytically, which allows for its detailed understanding. Using as a constraint the one-body string emission functions obtained from the experimental data for collisions at $\sqrt{s_{NN}}=200$ GeV, we explore the two-body correlations for various scenarios of string fluctuations. We find that the…
The angular dependence of the cumulative particles production off nuclei near the kinematical boundary for multistep process is defined by characteristic polynomials in angular variables $J_N^2(z_N^θ)$, where $θ$ is the polar angle defining the momentum of the final (cumulative) particle, $z_N^θ= cos (θ/N)$, the integer $N$ being the multiplicity of the process (the number of interactions). Physical argumentation, exploring the small phase space method, leads to the appearance of equations for these polynomials $J_N^2[cos(π/N)]=0$. The recurrent relations between polynomials with different $N$…
The forward-backward (FB) charged particle multiplicity correlations between windows separated in rapidity and azimuth are analyzed using a model that treats strings as independent identical emitters. Both the short-range (SR) contribution, originating from the correlation between multiplicities produced from a single source, and the long-range (LR) contribution, originating from the fluctuation in the number of sources, are taken into account. The dependencies of the FB correlation coefficient, $b$, on the windows' rapidity and azimuthal acceptance and the gaps between these windows are studi…
We demonstrate that the investigations of the forward-backward correlations between intensive observables enable to obtain more clear signal about the initial stage of hadronic interaction, e.g. about the process of string fusion, compared to usual forward-backward multiplicity correlations. As an example, the correlation between mean-event transverse momenta of charged particles in separated rapidity intervals is considered. We performed calculations in the framework of dipole-based Monte Carlo string fusion model. We obtained the dependence of the correlation strength on the collision centra…
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…
The angular dependence of the cumulative particles production off nuclei near the kinematical boundary for multistep process is defined by characteristic polynomials in angular variables, describing spatial momenta of the particles in intermediate and final states. Physical argumentation, exploring the small phase space method, leads to the appearance of equations for these polynomials in $cos (θ/N)$, where $θ$ is the polar angle of the momentum of final (cumulative) particle, the integer $N$ being the multiplicity of the process (the number of interactions). It is shown explicitly how these e…
Investigating forward-backward asymmetry in D-meson production and anisotropic flow in p-Pb collisions at the LHC
Wuhan Textile University（武汉纺织大学）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（上海理论核物理中心，国家自然科学基金委员会与复旦大学）；Wuhan University of Technology（武汉理工大学）；China University of Geosciences (Wuhan)（中国地质大学（武汉））；East Carolina University（东卡罗来纳大学）；Institute of Modern Physics, Fudan University（复旦大学现代物理研究所）
Effects of strong longitudinal color fields (SCF) on the identified (anti)particle transverse momentum ($p_T$) distributions in $ pp$ collision at $\sqrt{s}$ = 7 TeV are investigated within the framework of the {\small HIJING/BB v2.0} model. The comparison with the experiment is performed in terms of the correlation between mean transverse momentum ($\langle p_t\rangle$) and multiplicity (N$_{ch}^*$) of charged particles at central rapidity, as well as the ratios of the $p_T$ distributions to the one corresponding to the minimum bias (MB) pp collisions at the same energy, each of them normaliz…
We have studied the centrality bin size dependence of charged particle forward-backward multiplicity correlation strength in 5%, 0-5%, and 0-10% most central Au+Au collisions at $\sqrt{s_NN}}$=200 GeV with a parton and hadron cascade model, PACIAE based on PYTHIA. The real (total), statistical, and NBD (Negative Binomial Distribution) correlation strengths are calculated by the real events, the mixed events, and fitting the charged particle multiplicity distribution to the NBD, respectively. It is turned out that the correlation strength increases with increasing centrality bin size monotonous…
We discuss the forward-backward correlations of harmonic flow in Pb+Pb collisions at the CERN Large Hadron Collider (LHC), applying standard multibin measures, as well as proposed here new measures. We illustrate the methods with hydrodynamic model simulations based on event-by-event initial conditions from the wounded quark model with asymmetric rapidity emission profiles. Within the model we examine independently the event-plane angle and the flow magnitude decorrelations. We find specific hierarchy between various flow decorrelation measures and confirm certain factorization relations. We f…
The forward-backward (FB) multiplicity correlations in two windows separated in rapidity and azimuth are analyzed in the framework of the model with independent identical emitters (strings). Along with the short-range contribution, originating from the correlation between particles produced by a single string, the long-range contribution, originating from the fluctuation in the number of strings, is taken into account. The connection of the FB multiplicity correlation coefficient with the two-particle correlation function and the di-hadron correlation analysis is traced. It's also shown that t…
The central-arbitrary bin and forward-backward bin multiplicity correlation patterns for Au+Au collisions at $\sqrt{s_{NN}} $= $7.7-62.4$ GeV are investigated within a multi-phase transport (AMPT) model. An interesting observation is that for $\sqrt{s_{NN}} <19.6$ GeV Au+Au collisions, these two correlation patterns both have an increase with the pseudorapidity gap, while for $\sqrt{s_{NN}} >19.6$ GeV Au+Au collisions, they decrease. We mainly discuss the influence of different evolution stages of collision system on the central-arbitrary bin correlations, such as the initial conditions, parto…
Realistic Expanding Source Model for Invariant One-Particle Multiplicity Distributions and Two-Particle Correlations in Relativistic Heavy-Ion Collisions
Fluctuations in the initial transverse energy-density distribution lead to anisotropic flows as observed in central high-energy heavy-ion collisions. Studies of longitudinal fluctuations of the anisotropic flows can shed further light on the initial conditions and dynamical evolution of the hot quark-gluon matter in these collisions. Correlations between anisotropic flows with varying pseudorapidity gaps in Pb+Pb collisions at the CERN Large Hadron Collider are investigated using both an event-by-event (3+1)-D ideal hydrodynamical model with fluctuating initial conditions and the a multiphase …
Long range correlations are searched for by analyzing the experimental data on 16O-AgBr and 32S-AgBr collisions at 200A GeV/c and the results are compared with the predictions of a multi phase transport (AMPT) model. The findings reveal that the observed forward-backward (F-B) multiplicity correlations are mainly of short-range in nature. The range of F-B correlations are observed to extend with increasing projectile mass. The observed extended range of F-B correlations might be due to overall multiplicity fluctuations arising because of nuclear geometry. The findings are not sufficient for ma…
We present a semi-analytic approach to forward-backward multiplicity correlations in ultra-relativistic nuclear collisions, based on particle emission from strings with fluctuating end-points. We show that with the constraints from rapidity spectra, one can obtain bounds for the magnitude of the standard measures of the forward-backward fluctuations. The method is generic under the assumption of independent production from sources. For definiteness, we use the wounded quark model for Au+Au and d+Au collisions at the energy of $\sqrt{s_{NN}}=200$ GeV.
The mid-rapidity transverse momentum spectra of hadrons (p, p-bar, K+, K-, K0-short, phi, Λ, Λ-bar, Ξ,Ξ-bar, (Ξ + Ξ-bar), Ω, and Ω-bar) and the available rapidity distributions of the strange hadrons K0-short, (Λ + Λ-bar), (Ξ + Ξ-bar) produced in p-p collisions at LHC energy root(sNN) = 0.9 TeV have been studied using a Unified Statistical Thermal Freeze-out Model (USTFM). The calculated results are found to be in good agreement with the experimental data. The theoretical fits of the transverse momentum spectra using the model calculations provide the thermal freeze-out conditions in terms of …
We analyze the forward-backward multiplicity correlation coefficient as measured by STAR. We show that in the most central Au+Au collisions bins located symmetrically around η= 0 with large separation in pseudorapidity are more strongly correlated than bins located asymmetrically with smaller separation. In proton-proton collisions the opposite effect is observed. It suggests a qualitatively different behavior of the two-particle correlation as a function of pseudorapidity sum in p+p and Au+Au collisions.
We present a formulation of the initial state of heavy ion collisions that generalizes the 2+1D boost invariant IP-Glasma \cite{Schenke:2012wb} to 3+1D through JIMWLK rapidity evolution of the pre-collision Wilson lines. The rapidity dependence introduced by the JIMWLK evolution leads us to modify the initial condition for the gauge fields, and to solve Gauss' law iteratively in order to allow for temporal evolution on a 3-dimensional lattice. While the transverse physics of QGP has been studied nearly exhaustively, the effect of longitudinal fluctuations introduced by the JIMWLK evolution has…
Soft processes in pp and AA interactions are considered in the framework of phenomenological model with color strings formation and fusion. Elementary parton collisions are realized in the model as the interaction of two colour dipoles from projectile and target nucleons. Modeling of the exclusive distributions of parton momentum fractions and transverse coordinates is performed. The interaction of colour strings in transverse plane is carried out in the framework of local string fusion model with the introduction of the lattice in the impact parameter plane and taking into account the finite …
We use the framework of the HIJING/BB v2.0 model to simulate high-multiplicity (HM) $p+p$ collision events at the Large Hadron Collider (LHC) to study observables sensitive to possible collective phenomena, such as strong longitudinal color fields (SLCF) modeled by an enhanced string tension ($κ$). We focus on the hyperon/meson yield ratios at center-of-mass (c.m.) energy $\sqrt{s}$ = 7 TeV, in the transverse momentum region, $1 < p_T < 4 $ GeV/{\it c}. For minimum bias events these ratios are well described assuming an energy dependence $κ= κ(s)= κ_{0} (s/s_{0})^{0.04} {\rm GeV/fm}$ ($κ_{0}$=…
We propose that flow fluctuations have the same origin as transverse momentum fluctuations. The common source of these fluctuations is the spatially inhomogeneous initial state that drives hydrodynamic flow. Longitudinal correlations from an early Glasma stage followed by hydrodynamic flow quantitatively account for many features of multiplicity and $p_t$ fluctuation data. We develop a framework for studying flow and its fluctuations in this picture. We then compute elliptic and triangular flow fluctuations, and study their connections to the ridge.
Multiplicity, rapidity and transverse momentum distributions of hadrons produced both in inelastic and nondiffractive $pp$ collisions at energies from $\sqrt{s} = 200$\,GeV to 14\,TeV are studied within the Monte Carlo quark-gluon string model (QGSM). Good agreement with the available experimental data up to $\sqrt{s} = 13$\,TeV is obtained, and predictions are made for the collisions at top LHC energy $\sqrt{s} = 14$\,TeV. The model indicates that Feynman scaling and extended longitudinal scaling remain valid in the fragmentation regions, whereas strong violation of Feynman scaling is observe…
We study the origin of the directed flow of charged particles produced in relativistic heavy-ion collisions. Three different initial conditions, Boz$\dot{\textrm{e}}$k-Wyskiel, CCNU and Shen-Alzhrani, of energy density distributions are coupled to the (3+1)-dimensional viscous hydrodynamic model CLVisc, and their effects on the development of the anisotropic medium geometry, pressure gradient and radial flow are systematically compared. By comparing to experimental data at both RHIC and LHC, we find that the directed flow provides a unique constraint on the tilt of the initial medium profile i…
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. …
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…
