Particle number fluctuations and correlations in nucleus-nucleus collisions at SPS and RHIC energies are studied within microscopic transport approaches. In this review we focus on the Hadron-String-Dynamics (HSD) and Ultra-relativistic-Quantum-Molecular-Dynamics (UrQMD) models The obtained results are compared with the available experimental data as well as with the statistical models and the model of independent sources. In particular the role of the experimental centrality selection and acceptance is discussed in detail for a variety of experimental fluctuations and correlation observables with the aim to extract information on the critical point in the $(T,μ_B)$ plane of strongly interacting matter.
High-energy nucleus-nucleus collisions are studied in multi-chain model with successive collision. Analytic forms for single-particle distribution are derived.
We show that we can reach a global and coherent description of bottomonium suppression in both proton-nucleus and nucleus-nucleus collisions at the LHC energies. The measured relative suppression of the excited bottomonium states as compared to their ground state allows us to constrain the scattering cross sections between the bottomonia and the comovers created during the collisions. Our result hints at a similar energy distribution of these comovers in the environment created by proton-nucleus and nucleus-nucleus collisions. Along the way of our study, we also update our knowledge for the bo…
We show that a special choice of light-cone gauge can greatly simplify the calculation of the classical color field created in the initial stages of nucleus-nucleus collisions. Within this gauge, we can in particular construct explicitly the conserved color current and calculate exactly the gauge field immediately after the collision. This field is used as a boundary condition in an iterative solution of the Yang-Mills equations in the forward light-cone. In leading order, which corresponds to a linearization of the Yang-Mills equation in the forward light-cone, we obtain a simple formula for …
It is recently discovered that at high multiplicy, the proton-nucleus ($pA$) collisions give rise to two particle correlations that are strikingly similar to those of nucleus-nucleus ($AA$) collisions at the same multiplicity, although the system size is smaller in $pA$. Using an independent cluster model and a simple conformal scaling argument, where the ratio of the mean free path to the system size stays constant at fixed multiplicity, we argue that flow in $pA$ emerges as a collective response to the fluctuations in the position of clusters, just like in $AA$ collisions. With several physi…
We show that we can reproduce all the features of bottomonium suppression in both proton-nucleus and nucleus-nucleus collisions at LHC energies in a comover-interaction picture. For each collisions system, we use the measured {\it relative} suppression of the excited $Υ$(2S) and $Υ$(3S) states to $Υ$(1S) by ATLAS and CMS to parametrise the scattering cross sections of all $S$- and $P$-wave bottomonia with the comoving particles created during the collisions. In addition to a single nonpertubative parameter, these cross sections depend on the momentum distribution of these comovers which we fou…
This talk is a brief overview of the present status of our understanding of nucleus-nucleus collisions at high energy and the search for signals of the quark-gluon plasma.
Event-by-event multiplicity fluctuations in nucleus-nucleus collisions are studied within the HSD and UrQMD transport models. The scaled variances of negative, positive, and all charged hadrons in Pb+Pb at 158 AGeV are analyzed in comparison to the data from the NA49 Collaboration. We find a dominant role of the fluctuations in the nucleon participant number for the final hadron multiplicity fluctuations. This fact can be used to check different scenarios of nucleus-nucleus collisions by measuring the final multiplicity fluctuations as a function of collision centrality. The analysis reveals s…
Predictions on fluctuations of hadron production properties in central heavy ion collisions are presented. They are based on the Statistical Model of the Early Stage and extend previously published results by considering the strongly intensive measures of fluctuations. In several of the considered cases a significant change in collision energy dependence of calculated quantities as a result of the phase transition is predicted. This provides an opportunity to observe new signals of the onset of deconfinement in heavy ion collisions experiments.
The extension of the factorization theorems of perturbative QCD to power corrections associated with re-scattering in nuclear collisions is reviewed. The importance of hadron-nucleus collisions is discussed.
The parton and hadron cascade model PACIAE is used to investigate strange particle production in Au + Au collisions at GeV in different centralities and at 39, 11.5 and 7.7 GeV in the most central collision, respectively. It is shown that the transverse momentum distributions of strange particles by the PACIAE model fit the RHIC Beam Energy Scan experimental results well.
In a recent Letter, Geiger presents calculations of the dilepton emission from the early stage of ultrarelativistic heavy ion collisions using the parton cascade model (PCM). He shows that the $M_\perp$ scaling is not observed. In this Comment, we point out that this is largely due to a defect in the PCM.
We argue that a decrease of the chiral scalar meson mass is responsible for re-creation of $Ψ'$ from $J/Ψ$ in ultrarelativistic nucleus-nucleus collisions. This causes the charmonium yields to freeze out at temperatures close to the chiral symmetry restoration temperature $T_c$. As a result $Ψ'/Ψ$ may serve as a thermometer for $T_c$ itself. Results in a detailed reaction model support the conjecture. They show good agreement with recent data of NA38 and NA50 for $J/Ψ$ and $Ψ'$ production in S on U and Pb on Pb collisions.
We study the A+B -> l+ l- + jet +X process in nucleus-nucleus collisions at relativistic energies. The dilepton as well as the jet will pass through the matter produced in such collisions. The recoiling dilepton will carry information about the kinematical features of the jet, and will thus prove to be a very effective tool in isolating in-medium effects such as energy-loss and fragmentation function modifications. We estimate the contributions due to correlated charm and bottom decay and we identify a window where they are small as compared to pairs from the NLO Drell-Yan process.
We discuss properties of the specific strongly interacting transient collective state of matter in hadron and nuclei reactions and emphasize similarity in their dynamics. We consider elliptic flow introduced for description of nucleus collisions and discuss its possible behavior in hadronic reactions.
PACIAE, a parton and hadron cascade model, is utilized to systematically investigate strange particle production and strangeness enhancement in Au+Au collision and in Pb+Pb collision with the 200GeV at RHIC and 2.76TeV at LHC, respectively. The experimental results at different centrality, which come from the STAR collaboration and the ALICE collaboration, are well described by the PACIAE model. This may represent the importance of the parton and hadron rescatterings, as well as the reduction mechanism of strange quark suppression, added in the PACIAE model.
Within the statistical model, the net strangeness conservation and incomplete total strangeness equilibration lead to the suppression of strange particle multiplicities. Furthermore, suppression effects appear to be stronger in small systems. By treating the production of strangeness within the canonical ensemble formulation we developed a simple model which allows to predict the excitation function of $K^+/π^+$ ratio in nucleus-nucleus collisions. In doing so we assumed that different values of $K^+/π^+$, measured in p+p and Pb+Pb interactions at the same collision energy per nucleon, are dri…
A zone of reactions is determined and then exploited as a tool in studying the space-time structure of an interacting system formed in a collision of relativistic nuclei. The time dependence of the reaction rates integrated over spatial coordinates is also considered. Evaluations are made with the help of the microscopic transport model UrQMD. The relation of the boundaries of different zones of reactions and the hypersurfaces of sharp chemical and kinetic freeze-outs is discussed.
On the basis of the proposed algorithm for calculation of the hadron reaction rates, the space-time structure of the relativistic nucleus-nucleus collisions is studied. The reaction zones and the reaction frequencies for various types of reactions are calculated for AGS and SPS energies within the microscopic transport model. The relation of the reaction zones to the kinetic and chemical freeze-out processes is discussed. It is shown that the space-time freeze-out layer is most extended in time in the central region, while, especially for higher collision energies, the layer becomes very narro…
We propose to use the ratio of the pion-proton correlation functions evaluated under different conditions to study the relative space-time asymmetries in pion and proton emission (pion and nucleon source relative shifts) in high energy heavy ion collision. We address the question of the non-central collisions, where the sources can be shifted spatially both in the longitudinal and in the transverse directions in the reaction plane. We use the RQMD event generator to illustrate the effect and the technique.
We calculate the photon production cross-section in $pA$ collisions under the assumption that the nucleus has reached the saturation regime, while the proton can be described by the standard parton distribution functions. We show that due to the strong classical field $O(1/g)$ of the nucleus, bremsstrahlung diagrams become dominant over the direct photon diagrams. In particular, we show that $γ-$jet transverse momentum spectrum and correlations are very sensitive to gluon saturation effects in the nucleus.
The cross section for exclusive $π^+π^-$ and $π^0π^0$ meson pairs production in peripheral ultrarelativistic heavy-ion collisions is calculated at the energy available at the CERN Large Hadron Collider, i.e., $\sqrt{s_{NN}}=3.5$ TeV. The cross section for elementary $γγ\toππ$ process is calculated with the help of the pQCD Brodsky-Lepage approach with the distribution amplitude used recently to describe the pion transition form factor measured by the BaBar Collaboration.
We demonstrate that jet observables are highly sensitive to the characteristics of the vacuum and the in-medium QCD parton showers and propose techniques that exploit this sensitivity to constrain the mechanism of quark and gluon energy loss in strongly-interacting plasmas. As a first example, we calculate the inclusive jet cross section in high-energy nucleus-nucleus collisions to ${\cal O}(α_s^3)$. Theoretical predictions for the medium-induced jet broadening and the suppression of the jet production rate due to cold and hot nuclear matter effects in Au+Au and Cu+Cu reactions at RHIC are pre…
The bremsstrahlung produced when heavy nuclei collide is estimated for central collisions at the Relativistic Heavy Ion Collider. Bremsstrahlung photons with energies below 100 to 200 MeV are sufficient to discern the gross features of the space-time evolution of electric charge, if they can be separated from other sources of photons experimentally. This is illustrated explicitly by considering two very different models, one Bjorken-like, the other Landau-like, both of which are constructed to give the same final charge rapidity distribution.
New results of the NA61/SHINE Collaboration at the CERN SPS on mean hadron multiplicities in proton-proton (p+p) interactions are analyzed within the transport models and the hadron resonance gas (HRG) statistical model. The chemical freeze-out parameters in p+p interactions and central Pb+Pb (or Au+Au) collisions are found and compared with each other in the range of the center of mass energy of the nucleon pair $\sqrt{s_{NN}}=3.2-17.3$ GeV. The canonical ensemble formulation of the HRG model is used to describe mean hadron multiplicities in p+p interactions and the grand canonical ensemble i…
We describe the origin of, and the solution to, the negativity problem which occurs in the perturbative calculation of the cross-section for single-inclusive particle production in proton-nucleus collisions at next-to-leading-order.
A Monte Carlo simulator is presented to reproduce data of nucleus-nucleus interactions at high energies. The program is designed in a microscopic point of view, where the cascade approach is applied. Moreover, each nucleon from both the target and the projectile is followed up on the time scale along the collision time. The effect of the mean field that depends on the nuclear density is considered. Elastic and inelastic scattering are allowed for the nucleon binary collisions during the cascade according to their center of mass energies. Particle productions are studied through the fragmentati…
We use the Drell-Yan differential distribution dN_{DY}^{AB}/dE_T in high-energy nucleus-nucleus collisions to obtain a relation between the transverse energy E_T and the impact parameter b. Such a relation is then utilized to study the transverse-energy dependence of J/psi production in Pb-Pb collisions, using the J/psi absorption model presented previously. The anomalous Pb-Pb suppression data at 158A GeV can be explained if one assumes the occurrence of a new phase of strong J/psi absorption when the energy density exceeds 4.2 GeV/fm^3. The results are extended to make predictions for J/psi …
The influence of the underlying nucleon-nucleon collision geometry on evaluations of the nuclear overlap function ($T_{AB}$) and number of binary collisions ($N_{coll}$) is studied. A narrowing of the spatial distribution of the hard-partons with large light-cone fraction $x$ in nucleons leads to a downward correction for $N_{coll}$ and $T_{AB}$, which in turn, results in an upward correction for the nuclear modification factor $R_{AB}$. The size of this correction is estimated for several experimentally motivated nucleon-nucleon overlap functions for hard-partons. It is found to be significan…
In proton-nucleus and nucleus-nucleus collision experiments, one determines the centrality of a collision according to the multiplicity or energy deposited in a detector. This serves as a proxy for the true collision centrality, as defined by the impact parameter. We show that the probability distribution of impact parameter in a given bin of experiment-defined centrality can be reconstructed without assuming any specific model for the collision dynamics, in both proton-nucleus and nucleus-nucleus systems. The reconstruction is reliable up to about 10\% centrality, and is more accurate for nuc…
In p-p collisions the average transverse momentum is known to be correlated with the multiplicity of produced particles. The correlation is shown to survive in a superposition model of nucleus-nucleus collisions. When properly parameterized, the correlation strength appears to be independent of the collision centrality - it is the same in p-p and central A-A collisions. However, the correlation is strongly suppressed by the centrality fluctuations.
Azimuthal correlations of particles produced in nucleus-nucleus collisions at CERN SPS are discussed. The correlations quantified by the integral measure Phi are shown to be dominated by effects of collective flow.
In this lecture note, we discuss the global properties of nucleus-nucleus collisions. After a brief introduction to heavy-ion collisions, we introduce useful kinematics and then discuss the bulk hadron production in A+A collisions. At the end we discuss the hadronization and hadronic freeze-out in A+A collisions. We have tried to cover the topic from very fundamental arguments especially for the beginners in the field. We also give very useful formulae frequently used by experimentalists, from a first principle derivation.
We calculate the classical single-gluon production amplitude in nucleus-nucleus collisions including the first saturation correction in one of the nuclei (the projectile) while keeping multiple-rescattering (saturation) corrections to all orders in the other nucleus (the target). In our approximation only two nucleons interact in the projectile nucleus: the single-gluon production amplitude we calculate is order-g^3 and is leading-order in the atomic number of the projectile, while resumming all order-one saturation corrections in the target nucleus. Our result is the first step towards obtain…
We propose a new parametrization of the distribution of the initial eccentricity in a nucleus-nucleus collision at a fixed centrality, which we name the Elliptic Power distribution. It is a two-parameter distribution, where one of the parameters corresponds to the intrinsic eccentricity, while the other parameter controls the magnitude of eccentricity fluctuations. Unlike the previously used Bessel- Gaussian distribution, which becomes worse for more peripheral collisions, the new Elliptic Power distribution fits several Monte Carlo models of the initial state for all centralities.
We apply the successful Monte Carlo Glauber and IP-Glasma initial state models of heavy ion collisions to the much smaller size systems produced in proton-proton, proton-nucleus and deuteron- nucleus collisions. We observe a significantly greater sensitivity of the initial state geometry to details of multi-particle production in these models compared to nucleus-nucleus collisions. In particular, we find that the size of the system produced in p+A collisions is very similar to the one produced in p+p collisions, and predict comparable Hanbury-Brown-Twiss radii in the absence of flow in both sy…
According to the usual application of the sequential-suppression picture to the dynamics of heavy quarkonia in the hot medium formed in ultrarelativistic nuclear collisions, quark-antiquark pairs created in a given bound or unbound state remain in that same state as the medium evolves. We argue that this scenario implicitly assumes an adiabatic evolution of the quarkonia, and we show that the validity of the adiabaticity assumption is questionable.
A method to study event--by--event fluctuations of the `chemical' (particle type) composition of the final state of high energy collisions is proposed.}
The collision smearing of the nucleon momenta about their initial values during relativistic nucleus-nucleus collisions is investigated. To a certain degree, our model belongs to the transport type, and we investigate the evolution of the nucleon system created at a nucleus-nucleus collision. However, we parameterize this development by the number of collisions of every particle during evolution rather than by the time variable. It is assumed that the group of nucleons which leave the system after the same number of collisions can be joined in a particular statistical ensemble. The nucleon non…
We perform the first study on asymmetric longitudinal decorrelations of elliptic, triangular and quadrangular flows in proton-nucleus collisions at the LHC and RHIC energies. To measure the longitudinal flow decorrelations for asymmetric collision systems, we propose a new set of rapidity-asymmetric flow decorrelation functions. Our event-by-event hydrodynamic calculations show that the flow decorrelations in proton-going direction are larger than those in nucleus-going direction. We also find that proton-nucleus collisions at RHIC have larger longitudinal flow decorrelation effects than those…
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…
We show that the statistics of fluctuation-driven initial-state anisotropies in proton-proton, proton-nucleus and nucleus-nucleus collisions is to a large extent universal. We propose a simple parametrization for the probability distribution of the Fourier coefficient $\varepsilon_n$ in harmonic $n$, which is in good agreement with Monte-Carlo simulations. Our results provide a simple explanation for the 4-particle cumulant of triangular flow measured in Pb-Pb collisions, and for the 4-particle cumulant of elliptic flow recently measured in p-Pb collisions. Both arise as natural consequences o…
The strong electromagnetic fields in peripheral heavy ion collisions give rise to photon-photon and photon-nucleus interactions. I present a general survey of the photon-photon and photon-hadron physics accessible in these collisions. Among these processes I discuss the nuclear fragmentation through the excitation of giant resonances, the Coulomb dissociation method for application in nuclear astrophysics, and the production of particles.
The bremsstrahlung produced when heavy nuclei collide is estimated for central collisions at the Relativistic Heavy Ion Collider. Soft photons can be used to infer the rapidity distribution of the outgoing charge. An experimental design is outlined.
At large collision energy sqrt(s) and relatively low momentum transfer Q, one expects a new regime of Quantum Chromo-Dynamics (QCD) known as "saturation". This kinematical range is characterized by a very large occupation number for gluons inside hadrons and nuclei; this is the region where higher twist contributions are as large as the leading twist contributions incorporated in collinear factorization. In this talk, I discuss the onset of and dynamics in the saturation regime, some of its experimental signatures, and its implications for the early stages of Heavy Ion Collisions.
The $Δ$-scaling method has been applied to ultra-relativistic p+p, C+C and Pb+Pb collision data simulated using a high energy Monte Carlo package, LUCIAE 3.0. The $Δ$-scaling is found to be valid for some physical variables, such as charged particle multiplicity, strange particle multiplicity and number of binary nucleon-nucleon collisions from these simulated nucleus-nucleus collisions over an extended energy ranging from $E_{lab}$ = 20 to 200 A GeV. In addition we derived information entropy from the multiplicity distribution as a function of beam energy for these collisions.
The propagation of the heavy quarks produced in relativistic nucleus-nucleus collisions at RHIC and LHC is studied within the framework of Langevin dynamics in the background of an expanding deconfined medium described by ideal and viscous hydrodynamics. The transport coefficients entering into the relativistic Langevin equation are evaluated by matching the hard-thermal-loop result for soft collisions with a perturbative QCD calculation for hard scatterings. The heavy-quark spectra thus obtained are employed to compute the differential cross sections, the nuclear modification factors R_AA and…
Particle correlations are very actively studied in heavy-ion collisions at ultra-relativistic energies. Here, an attempt is made at determining a proper reference for such studies, by taking properly into account the multiparticle correlations induced by the conservation of total momentum in the collisions.
We study the scaled variances of multiplicity fluctuations in nucleus-nucleus collisions at SPS and RHIC energies within the HSD transport model. The HSD results are compared with proton-proton data and with predictions of the hadron-resonance gas statistical model. We find that the HSD scaled variances $ω_i$ for negatively, positively, and all charged hadrons in central nucleus-nucleus collisions remain close to the $ω_i$ values in proton-proton collisions and increase with collision energy as the corresponding multiplicities per participating nucleon. The statistical model predicts very diff…
We make a theoretical and experimental summary of the state-of-the-art status of hot and dense QCD matter studies on selected topics. We review the Beam Energy Scan program for the QCD phase diagram and present the current status of search for QCD Critical Point, particle production in high baryon density region, hypernuclei production, and global polarization effects in nucleus-nucleus collisions. The available experimental data in the strangeness sector suggests that a grand canonical approach in thermal model at high collision energy makes a transition to the canonical ensemble behavior at …
In 2007 Mark I. Gorenstein celebrated his 60th birthday. This report is dedicated to Mark and it sketches the results obtained during the past ten years of our collaboration and friendship. They concern search for and study of the onset of deconfinement in high energy nucleus-nucleus collisions.
Elastic parton-parton-parton scattering is briefly reviewed and is included in transport equations of quark-gluon matter. We solve the transport equations and get thermal states from initially produced quark-gluon matter. Both gluon matter and quark matter take early thermalization, but gloun matter has a shorter thermalization time than quark matter.
Heavy nuclei at collider energies are a source of high energy Weizsaecker-Williams photons. This photon flux may be utilized to study high energy photon-nucleus interactions. Here we concentrate on the coherent diffractive production of heavy vector mesons on nuclear targets and show how it probes the unintegrated glue of the nucleus in the saturation domain. We present predictions for rapidity distributions of exclusive coherent J/Psi and Upsilon mesons which can be measured by the ALICE experiment at the LHC.
A generic expression of double-parton scattering cross sections in high-energy nucleus-nucleus (A-A) collisions is derived as a function of the corresponding single-parton hard cross sections and of the A-A event centrality. We consider the case of prompt-J/psi production in lead-lead (Pb-Pb) at the CERN Large Hadron Collider and find that about 20% (35%) of the J/psi events in minimum-bias (most central) collisions contain a second J/psi from double parton interactions. In Pb-Pb at 5.5 TeV, in the absence of final-state effects, about 240 double-J/psi events are expected per unit midrapidity …
A phenomenological analysis of diffractive dissociation of nuclei in proton-nucleus and meson-nucleus collisions is presented. The theoretical approach employed here is able to take into account at once data of the HELIOS and EHS/NA22 collaborations that exhibit quite different atomic mass dependences. Possible extensions of this approach to hard diffraction in nuclear processes are also discussed.
We present a study of the heavy-flavor dynamics in nucleus-nucleus collisions. The initial (hard) production of c and b quarks is taken from NLO pQCD predictions. The presence of a hot medium (a Quark Gluon Plasma described by hydrodynamics) affects the final spectra of open-charm (beauty) hadrons and their decay electrons with respect to what found in pp collisions. The propagation of c and b quarks in the plasma is based on a picture of multiple uncorrelated random collisions, described by a relativistic Langevin equation. A microscopic evaluation of the transport coefficients is provided wi…
This is a review of theoretical attempts to describe production of heavy quark bound states in nucleus-nucleus collisions, in particular, the relative suppression of $J/ψ$ and $ψ'$ production observed in these reactions. The review begins with a survey of experimental data for proton-induced reactions and their theoretical interpretation. The evidence for additional suppression in nucleus-nucleus collisions is discussed and various theoretical models of charmonium absorption by comoving matter are presented and analyzed. The review concludes with suggestions for future research that would help…
We propose a mechanism of thermalization of nucleons in relativistic nucleus-nucleus collisions. Our model belongs, to a certain degree, to the transport ones; we consider the evolution of the system, but we parametrize this development by the number of collisions of every particle in the system rather than by the time variable. We based on the assumption that the nucleon momentum transfer after several nucleon-nucleon (-hadron) collisions becomes a random quantity driven by a proper distribution.
Using a hadron-string cascade model, JPCIAE, we study the effect of nuclear deformation on J/Psi suppression in the collision of uranium nuclei at 200A GeV/c. We find that the J/Psi survival probability is much smaller if the major axes of both deformed nuclei are along the beam direction than if they are perpendicular to the beam direction.
Pion and photon production cross sections are analyzed in proton-proton and proton-nucleus collisions at energies 20 GeV < s^1/2 < 60 GeV. We separate the proton-proton and nuclear contributions to transverse-momentum broadening and suggest a new mechanism for the nuclear enhancement in the high transverse-momentum region.
