We derive a high energy factorization theorem for inclusive gluon production in A+A collisions. Our factorized formula resums i) all order leading logarithms (g^2 \ln(1/x_{1,2}))^n of the incoming partons momentum fractions, and ii) all contributions (g ρ_{1,2})^n that are enhanced when the color charge densities in the two nuclei are of order of the inverse coupling-- ρ_{1,2}\sim g^{-1}. The resummed inclusive gluon spectrum can be expressed as a convolution of gauge invariant distributions W[ρ_{1,2}] from each of the nuclei with the leading order gluon number operator. These distributions are shown to satisfy the JIMWLK equation describing the evolution of nuclear wavefunctions with rapidity. As a by-product, we demonstrate that the JIMWLK Hamiltonian can be derived entirely in terms of retarded light cone Green's functions without any ambiguities in their pole prescriptions. We comment on the implications of our results for understanding the Glasma produced at early times in A+A collisions at collider energies.
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.
We extend previous results (arXiv:0804.2630 [hep-ph]) on factorization in high-energy nucleus-nucleus collisions by computing the inclusive multigluon spectrum to next-to-leading order. The factorization formula is strictly valid for multigluon emission in a slice of rapidity of width ΔY< 1/α_s. Our results show that often neglected disconnected graphs dominate the inclusive multigluon spectrum and are essential to prove factorization for this quantity. These results provide a dynamical framework for the Glasma flux tube picture of the striking "ridge"-like correlation seen in heavy ion collis…
High-energy nucleus-nucleus collisions are studied in multi-chain model with successive collision. Analytic forms for single-particle distribution are derived.
We obtain a novel result in QCD for long range rapidity correlations between gluons produced in the collision of saturated high energy hadrons or nuclei. This result, obtained in a high energy factorization framework, provides strong justification for the Glasma flux tube picture of coherent strong color fields. Our formalism can be applied to "near side ridge" events at RHIC and in future studies of long range rapidity correlations at the LHC.
We review the origin, and salient features, of the breaking of the conventional linear $k_{\perp}$-factorization for an in-nucleus hard pQCD processes. A realization of the nonlinear $k_{\perp}$-factorization which emerges instead is shown to depend on color properties of the underlying pQCD subprocesses. We discuss the emerging universality classes and extend nonlinear $k_{\perp}$-factorization to AGK unitarity rules for the excitation of the target nucleus.
Single inclusive particle production at next-to-leading order in proton-nucleus collisions at forward rapidities: hybrid approach meets TMD factorization
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.
Global perturbative QCD analyses, based on large data sets from electron-proton and hadron collider experiments, provide tight constraints on the parton distribution function (PDF) in the proton. The extension of these analyses to nuclear parton distributions (nPDF) has attracted much interest in recent years. nPDFs are needed as benchmarks for the characterization of hot QCD matter in nucleus-nucleus collisions, and attract further interest since they may show novel signatures of non- linear density-dependent QCD evolution. However, it is not known from first principles whether the factorizat…
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.
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 …
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…
In the present work, it is intended to calculate the unintegrated parton distribution functions (UPDFs) of the $^6{Li}$ nucleus, which depend not only on the longitudinal momentum fraction $x$ (the Bjorken variable) and the factorization scale $μ$ of partons, but also on their transverse momentum ($k_t$). Therefore, the KMR and MRW procedures are applied to generate the $k_t$-dependent parton distributions from the familiar integrated parton densities (PDFs), which were determined in our recent related work, using the constituent quark exchange model (CQEM) for the $^6Li$ nucleus. Then, the re…
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…
Revealing a deep connection between factorization and saturation: New insight into modeling high-energy proton-proton and nucleus-nucleus scattering in the EPOS4 framework
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.
The high-energy QCD factorization for Deep Inelastic Scattering and for proton-nucleus collisions using Wilson line formalism and factorization in rapidity is discussed. We show that in DIS the factorization in rapidity reduces to the $k_{\rm T}$-factorization when the 2-gluon approximation is applied, provided that the composite Wilson line operator is used in the high-energy Operator Product Expansion. We then show that the inclusive forward cross-section in proton-nucleus collisions factorizes in parton distribution functions, fragmentation functions and dipole gluon distribution function a…
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 study Higgs boson production from gluon-gluon fusion at mid-rapidity in high energy proton-nucleus collisions. For this process the presently still little known gluon distribution function $h_1^{\perp g}$ gives a numerically relevant contribution. We show by explicite calculation that using CGC (color glass condensate) model input the result obtained in the naive k_t factorization approach matches the result obtained in the TMD factorization framework for a dilute medium. We also verify the earlier finding that the k_t factorization formalism for Higgs production breaks down in a dense medi…
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.
Single and double inclusive cross-sections in nucleus-nucleus collisions are derived in the perturbative QCD with interacting BFKL pomerons in the quasi-classical approximation.
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.
It has been observed recently that while continuum dilepton production and open charm production in high-energy $pA$ collisions can be described in terms of the superposition of $pp$ collisions, dilepton yields in S+U collisions are in excess of similar extrapolations. This feature can be explained as arising from the interaction of gluons produced in different soft baryon-baryon collisions, leading to additional open-charm pairs in nucleus-nucleus collisions but not in $pA$ collisions.
We explore the relationship between the Glasma framework and the String Percolation Model by introducing a simple model for the rapidity distributions in nucleus-nucleus collisions. The model is solved for both symmetrical and asymmetrical collisions. The phenomenon of limiting fragmentation is briefly discussed.
At the partonic level, a typical final state in small-x deep inelastic scattering off nuclei and hard proton-nucleus collisions can be characterized by the multiplicity of color-excited nucleons. Within reggeon field theory, each color-excited nucleon is associated with the unitarity cut of the pomeron exchanged between the projectile and nucleus. In this communication we derive the unitarity rules for the multiplicity of excited nucleons, alias cut pomerons, alias topological cross sections, for typical hard dijet production processes. We demonstrate how the coupled-channel non-Abelian intran…
We calculate the nuclear suppression for $J/Ψ$ and $Ψ'$ production within a coupled channel approach in the subspace of the $J/Ψ$ and $Ψ'$ states. We are able to explain, why (i) the $J/Ψ$ and $Ψ'$ show the same suppression from $200\ GeV$ to $800\ GeV$ in proton-nucleus collisions and why (ii) the $Ψ'$ is absorbed more strongly than the $J/Ψ$ in nucleus-nucleus collisions at $200\ GeV$. The numerical result which includes only interactions with nucleons acconts for half of the observed suppression in sulphur-uranium collisions.
In this paper the Dynamical String Model is applied to the numerical simulation of the ultrarelativistic heavy-ion collision S(200 GeV/n)+S. The results are in qualitative agreement with experimental data.
In this paper, it is shown that in hadron-nucleus and nucleus-nucleus collisions, the main source for central exclusive diffractive Higgs production is photon-photon fusion. At the LHC energy, the total cross section for this process is about 0.6 pb (for proton-gold scattering), and 3.9 nb (for gold-gold collision) while the gluon-gluon fusion leads to the value of the cross section for CED Higgs production which is about 0.1 nb and 3.9 pb respectively.
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…
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…
We argue that the large suppression of the $ψ(2S)$ inclusive cross-section relative to the $J/ψ$ inclusive cross-section in proton-nucleus (p+A) collisions can be attributed to factorization breaking effects in the formation of quarkonium. These factorization breaking effects arise from soft color exchanges between charm-anticharm pairs undergoing hadronization and comoving partons that are long-lived on time scales of quarkonium formation. We compute the short distance pair production of heavy quarks in the Color Glass Condensate (CGC) effective field theory and employ an improved Color Evapo…
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…
