Stage Of Ultrarelativistic Heavy-ion Collisions Research Articles

Jet polarisation in an anisotropic medium

We study the evolution of an energetic jet which propagates in an anisotropic quark-gluon plasma, as created in the intermediate stages of ultrarelativistic heavy-ion collisions. We argue that the partons of the jet should acquire a non-zero average polarisation proportional to the medium anisotropy. We first observe that the medium anisotropy introduces a difference between the rates for transverse momentum broadening along the two directions perpendicular to the jet axis. In turn, this difference leads to a polarisation-dependent bias in the BDMPS-Z rates for medium-induced gluon branching. Accordingly, the daughter gluons in a branching process can carry net polarisation even if their parent gluon was unpolarised. Using these splitting rates, we construct kinetic equations which describe the production and transmission of polarisation via multiple branching in an anisotropic medium. The solutions to these equations show that polarisation is efficiently produced via quasi-democratic branchings, but then it is rapidly washed out by the subsequent branchings, due to the inability of soft gluons to keep trace of the polarisation of their parents. Based on that, we conclude that a net polarisation for the jet should survive in the final state if and only if the medium anisotropy is sizeable as the jet escapes the medium.

Hydrodynamic Attractors in Phase Space.

Hydrodynamic attractors have recently gained prominence in the context of early stages of ultrarelativistic heavy-ion collisions at the RHIC and LHC. We critically examine the existing ideas on this subject from a phase space point of view. In this picture the hydrodynamic attractor can be seen as a special case of the more general phenomenon of dynamical dimensionality reduction of phase space regions. We quantify this using principal component analysis. Furthermore, we adapt the well known slow-roll approximation to this setting. These techniques generalize easily to higher dimensional phase spaces, which we illustrate by a preliminary analysis of a dataset describing the evolution of a five-dimensional manifold of initial conditions immersed in a 16-dimensional representation of the phase space of the Boltzmann kinetic equation in the relaxation time approximation.

GLISSANDO 3: GLauber Initial-State Simulation AND mOre, ver. 3

We present ver. 3 of GLISSANDO, a versatile Monte-Carlo generator for Glauber-like models of the initial stages of ultra-relativistic heavy-ion collisions. The present version incorporates the wounded parton model, which is phenomenologically successful in reproducing multiplicities of particle production at the RHIC and the LHC. Within this model, one can study the nucleon substructure fluctuation effects, recently explored in p-A collisions. In addition, the code includes the possibility of investigating collisions of light nuclei, such as 3He and 3H, or the α-clustered 7,9Be, 12C, and 16O, where the deformation of the intrinsic wave function influences the transverse shape of the initial state. The current version, being down-compatible, retains the functionality of the previous releases, such as incorporation of various variants of Glauber-like models, a smooth NN inelasticity profile in the impact parameter obtained from a parameterization of experimental data, fluctuating strength of the entropy deposition, or realistic nuclear distributions of heavy nuclei with deformation. The code can provide output in the format containing the event-by-event source location, which may be further used in modeling the intermediate evolution phase, e.g., with hydrodynamics or transport models. The interface is simplified, such that in the control input file the user may supply only the very basic information, such as the collision energy, the mass numbers of the colliding nuclei, and the model type. GLISSANDO 3 is integrated with the CERN ROOT platform. The package includes numerous illustrative and useful ROOT scripts to compute and plot various results. Program summaryProgram Title:GLISSANDO 3 ver. 3.42Program Files doi:http://dx.doi.org/10.17632/yfrzxkrcvr.1Licensing provisions: CC By 4.0Programming language:C++ with the ROOT librariesNature of problem: The code implements in a versatile way the Glauber modeling of the initial stages of ultra-relativistic nuclear collisions, including the wounded nucleon and wounded quark models, with possible admixture of binary collisions. A state-of-the art inelastic nucleon–nucleon collision profile is implemented. A statistical distribution of the strength of the sources can be overlaid. The α clustered structure of light nuclei is built in.Solution method: Monte-Carlo simulation of nuclear collisions, analyzed off-line with numerous ROOT scripts. The software allows for a straightforward event-by-event analysis of eccentricity coefficients and their correlations, size fluctuations, or multiplicity distributions.Additional comments including restrictions and unusual features: The input may consist only of the model type, the mass numbers of the nuclei and the collision energy. The output can also be used as initial conditions for further hydrodynamic studies.

Heavy quarks in turbulent QCD plasmas

.The quark-gluon plasma, which is produced at an early stage of ultrarelativistic heavy-ion collisions, is expected to be initially strongly populated with chromodynamic fields. We address the question of how heavy quarks interact with such a turbulent plasma in comparison with an equilibrated one of the same energy density. For this purpose we derive a Fokker-Planck transport equation of heavy quarks embedded in a plasma of light quarks and gluons. We first discuss the equilibrium plasma and then the turbulent one applying the same approach, where the heavy quarks interact not with the plasma constituents but rather with the long wavelength classical fields. We first consider the three schematic models of isotropic trubulent plasma and then the simplified model of glasma with the chromodynamic fields only along the beam direction. The momentum broadening and collisional energy loss of a test heavy quark are computed and compared to those of the equilibrium plasma of the same energy density.

Open heavy-flavour measurements with ALICE at the LHC

Heavy quarks are produced in the early stages of ultra-relativistic heavy-ion collisions, and their number is preserved throughout the subsequent evolution of the system. Therefore, they constitute ideal probes for characterising the Quark-Gluon Plasma (QGP) medium and for the study of its transport properties. In particular, heavy quarks interact with the partonic constituents of the plasma, losing energy, and are expected to be sensitive to the medium collective motion induced by its hydrodynamical evolution. In pp collisions, the measurement of heavy-flavour hadron production provides a reference for heavyion studies, and allows also testing perturbative QCD calculations in a wide range of collision energies. Similar studies in p-Pb collisions help in disentangling cold nuclear matter effects from modifications induced by the presence of a QGP medium, and are also useful to investigate the possible existence of collective phenomena also in this system. The ALICE detector provides excellent performances in terms of particle identification and vertexing capabilities. Hence, it is fully suited for the reconstruction of charmed mesons and baryons and of electrons from heavy-flavour hadron decays at central rapidity. Furthermore, the ALICE muon spectrometer allows reconstructing heavy-flavour decay muons at forward rapidity. A review of the main ALICE results on open heavy flavour production in pp, p-Pb and Pb-Pb collisions is presented. Recent, more differential measurements are also shown, including azimuthal correlations of heavy-flavour particles with charged hadrons in p-Pb collisions, and D-meson tagged-jet production in p-Pb and Pb-Pb collisions.

Kinetic description of Bose-Einstein condensation with test particle simulations

We present a kinetic description of Bose-Einstein condensation for particle systems being out of thermal equilibrium, which may happen for gluons produced in the early stage of ultra-relativistic heavy-ion collisions. The dynamics of bosons towards equilibrium is described by a Boltzmann equation including Bose factors. To solve the Boltzmann equation with the presence of a Bose-Einstein condensate we make further developments of the kinetic transport model BAMPS (Boltzmann Approach of MultiParton Scatterings). In this work we demonstrate the correct numerical implementations by comparing the final numerical results to the expected solutions at thermal equilibrium for systems with and without the presence of Bose-Einstein condensate. In addition, the onset of the condensation in an over-populated gluon system is studied in more details. We find that both expected power-law scalings denoted by the particle and energy cascade are observed in the calculated gluon distribution function at infrared and intermediate momentum regions, respectively. Also, the time evolution of the hard scale exhibits a power-law scaling in a time window, which indicates that the distribution function is approximately self-similar during that time.

Entropy production in chemically nonequilibrium quark-gluon plasma created in centralPb+Pbcollisions at energies available at the CERN Large Hadron Collider

We study the possibility that partonic matter produced at early stage of ultrarelativistic heavy-ion collisions is out of chemical equilibrium. It is assumed that initially this matter is mostly composed of gluons, but quarks and antiquarks are produced at later times. The dynamical evolution of partonic system is described by the Bjorken-like ideal hydrodynamics with a time dependent quark fugacity. The results of this model are compared with those obtained by assuming the complete chemical equilibrium of partons already at the initial stage. It is shown that in a chemically non-equilibrium scenario the entropy gradually increases, and about 25% of the total final entropy is generated during the hydrodynamic evolution of deconfined matter. We argue that the (anti)quark suppression included in this approach may be responsible for reduced (anti)baryon to meson ratios observed in heavy-ion collisions at LHC energies.

Classical gluon fields and collective dynamics of color-charge systems

An investigation of color fields that arise in collisions of relativistic heavy ions reveals that, in the non-Abelian case, a change in the color charge leads to the appearance of an extra term that generates a sizable contribution of color-charge glow in chromoelectric and chromomagnetic fields. The possibility of the appearance of a color echo in the scattering of composite color particles belonging to the dipole type is discussed. Arguments are adduced in support of the statement that such effects are of importance in simulating the first stage of ultrarelativistic heavy-ion collisions,where the initial parton state is determined by a high nonequilibrium parton density and by strong local color fluctuations.

Relativistic Boltzmann transport approach with Bose-Einstein statistics and the onset of gluon condensation

We study the evolution of a gluon system under conditions of density and temperature similar to those explored in the early stage of ultrarelativistic heavy-ion collisions. We first describe the implementation of the relativistic Boltzmann-Nordheim (RBN) transport approach that includes in the collision integral the quantum effects of Bose-Einstein statistics. Then, we describe the evolution of a spatially uniform gluon system in a box under elastic collisions solving the RBN for various initial conditions. We discuss the critical phase-space density that leads to the onset of a Bose-Einstein condensate (BEC) and the time scale for this process to occur. In particular, thanks to the fact that RBN allows one to relax the small angle approximation, we study the effect at both small and large screening mass ${m}_{D}$. For small ${m}_{D}\ensuremath{\ll}T$ we see that our solution of RBN is in agreement with the recent extensive studies within a Fokker-Planck scheme in small angle approximation. For the same total cross section but with large ${m}_{D}\ensuremath{\simeq}2\phantom{\rule{0.16em}{0ex}}T$ (large angle scatterings), we see a significant time speed-up of the onset of BEC with respect to small ${m}_{D}\ensuremath{\ll}T$. This further strengthens the possibility that at least a transient BEC is formed in the early stage of ultrarelativistic heavy-ion collisions.

Equilibration of anisotropic quark-gluon plasma produced by decays of color flux tubes

A set of kinetic equations is used to study equilibration of the anisotropic quark-gluon plasma produced by decays of color flux tubes possibly created at the very early stages of ultra-relativistic heavy-ion collisions. The decay rates of the initial color fields are given by the Schwinger formula, and the collision terms are treated in the relaxation-time approximation. By connecting the relaxation time with viscosity we are able to study production and thermalization processes in the plasma characterized by different values of the ratio of the shear viscosity to entropy density, eta/s. For the lowest (KSS) value of this ratio, 4 pi eta/s = 1, and realistic initial conditions for the fields, the system approaches the viscous-hydrodynamics regime within 1-2 fm/c. On the other hand, for larger values of the viscosity, 4 pi eta/s greater or equal to 3, the collisions in the plasma become inefficient to destroy collective phenomena which manifest themselves as oscillations of different plasma parameters. The presence of such oscillations brings in differences between the kinetic and hydrodynamic descriptions, which suggest that the viscous-hydrodynamics approach after 1-2 fm/c is not complete if 4 pi eta/s is greater or equal to 3 and should be extended to include dissipative phenomena connected with color conductivity.

Schwinger mechanism enhanced by the Nielsen–Olesen instability

We discuss gluon production by the Schwinger mechanism in collinear color-electric and magnetic fields which may be realized in pre-equilibrium stages of ultra-relativistic heavy-ion collisions. Fluctuations of non-Abelian gauge fields around a purely color-magnetic field contain exponentially growing unstable modes in a longitudinally soft momentum region, which is known as the Nielsen–Olesen instability. With a color-electric field imposed parallelly to the color-magnetic field, we can formulate this instability as the Schwinger mechanism. This is because soft unstable modes are accelerated by the electric fields to escape from the instability condition. Effects of instability remain in the transverse spectrum of particle modes, leading to an anomalously intense Schwinger particle production.

General formulation of transverse hydrodynamics

General formulation of hydrodynamics describing transversally thermalized matter created at the early stages of ultrarelativistic heavy-ion collisions is presented. Similarities and differences with the standard three-dimensionally thermalized relativistic hydrodynamics are discussed. The role of the conservation laws as well as the thermodynamic consistency of two-dimensional thermodynamic variables characterizing transversally thermalized matter is emphasized.

Fluctuating initial conditions in heavy ion collisions from the Glauber approach

In the framework of the Glauber approach applied to the initial stage of ultra-relativistic heavy-ion collisions we analyze the shape parameters of the early-formed system (fireball) and their event-by-event fluctuations. We test a variety of models: the conventional wounded-nucleon model, a model admixing binary collisions to the wounded nucleons, a model with hot spots, and the hot-spot model where the deposition of energy occurs with a superimposed probability distribution. We look in detail at the so-called participant harmonic moments, {epsilon}*, obtained by an averaging procedure where in each event the system is translated to its center of mass and aligned with the major principal axis of the ellipse of inertia. Quantitative comparisons indicate substantial relative effects for {epsilon}* in variants of Glauber models. However, the dependence of the scaled standard deviation {delta}{epsilon}*/, {epsilon}* on the chosen model is weak. For all models the values range from about 0.5 for the central collisions to about 0.3-0.4 for peripheral collisions, for both gold-gold and copper-copper collisions. They are dominated by statistics and change only by 10-15% from model to model. We provide an approximate analytic expansion for the harmonic moments and their fluctuations given in terms of the fixed-axes moments. For centralmore » collisions and in the absence of correlations the expansion gives the simple formula {delta}{epsilon}*/{epsilon}*{approx_equal}{radical}(4/{pi}-1)=0.52. Similarly, we obtain expansions for the radial profiles of the higher harmonics. We investigate the relevance of the shape-fluctuation effects for jet quenching and find them important only for very central events. Finally, we make some comments of relevance for hydrodynamics, the elliptic flow, and its fluctuations. We argue how smooth hydrodynamics leads to the known result v{sub 4}{approx}v{sub 2}{sup 2} and, further, to the prediction {delta}v{sub 4}/v{sub 4}=2{delta}v{sub 2}/v{sub 2}.« less

Baryon deceleration by strong chromofields in ultrarelativistic nuclear collisions

It is assumed that strong chromofields are generated at early stages of ultrarelativistic heavy-ion collisions which give rise to a collective deceleration of baryons from colliding nuclei. We have solved classical equations of motion for baryonic slabs under the action of a time-dependent longitudinal chromoelectric field. It is demonstrated that the slab final rapidities are rather sensitive to the strength and decay time of the chromofield as well as to the back reaction of the produced partonic plasma. The net-baryon rapidity loss $\ensuremath{\langle}\ensuremath{\delta}y\ensuremath{\rangle}=2.0$, found for most central Au-Au collisions at RHIC, can be explained by the action of chromofields with the initial energy density of about 50 GeV/fm${}^{3}$. Predictions of the baryon stopping for the LHC energy are made.

Event anisotropy measurement in 200GeV Au+Au collisions at RHIC-PHENIX experiment

Event anisotropy is expected to have sensitivity to the early stage of ultra-relativistic heavy-ion collisions at RHIC. The possible formation of a quark gluon plasma (QGP) could affect how the initial anisotropy in the space coordinate is transferred into the momentum space for the final state. The anisotropy parameter (v 2) is an amplitude of the 2nd harmonic parameter of the azimuthal distribution with respect to the reaction plane. We present here v 2 of identified ( π +, π −, K +, K −, p and p ) and inclusive charged particles measured in the PHENIX central arm detector (| η| < 0.35) with respect to the reaction plane defined at | η| = 3 ∼ 4 in 200 GeV Au+Au collisions.

Identified charged particle azimuthal anisotropy in PHENIX at RHIC

Event anisotropy is expected to have sensitivity to the early stage of ultra-relativistic heavy-ion collisions at RHIC. The possible formation of a quark gluon plasma (QGP) could affect how the initial anisotropy in the space coordinate is transfered into the momentum space for the initial state. The anisotropy parameter (v 2) is an amplitude of the 2nd harmonic parameter of the azimuthal distribution with respect to the reaction plane. We present here v 2 of identified and inclusive charged particles measured in the PHENIX central arm detector (∣η∣ < 0.35) with respect to the reaction plane defined at ∣η∣ = 3 ∼ 4 in 200 GeV Au + Au collisions. We find that v 2 increases from central to mid-central collisions reaching a maximum at about 50% of the geometric cross section and then decreases again for more peripheral collisions. As a function of transverse momentum in minimum-bias collisions, the v 2 parameter increases linearly with p T up to p T ≅ 2 GeV/c and then saturates for inclusive charged particles. the v 2 parameter of identified particles (π +, π −, K +, K −, p and p ¯ follow a hydro-dynamic behavior up to 2 GeV/c in p T, where the lighter mass particles haver larger v 2 at a given p T. However there is an indication that this trend is reversed at around p T ≅ 2GeV/c, where p and p ¯ have larger v 2 than π and K.

Density fluctuations in the quark-gluon plasma

Using the kinetic theory we discuss how the particle and energy densities of the quark-gluon plasma fluctuate in a space-time cell. The fluctuations in the equilibrium plasma and in one from the early stage of ultrarelativistic heavy-ion collisions are estimated. Within the physically interesting values of the parameters involved the fluctuations appear sizable in both cases.

Non-equilibrium fluid-dynamics in the early stage of ultrarelativistic heavy-ion collisions

To describe ultrarelativistic heavy-ion collisions we construct a three-fluid hydrodynamical model. In contrast to one-fluid hydrodynamics, it accounts for the finite stopping power of nuclear matter, i.e. for non-equilibrium effects in the early stage of the reaction. Within this model, we study baryon dynamics in the BNL-AGS energy range. For the system Au+Au we find that kinetic equilibrium between projectile and target nucleons is established only after a time t cm eq ≈ 5 fm c ⋍ 2R Au γ cm . Observables that are sensitive to the early stage of the collision (like e.g. nucleon flow) therefore differ considerably from those calculated in the one-fluid model.

Color collective effects at the early stage of ultrarelativistic heavy-ion collisions.

Hard and semihard processes lead to a copious production of partons at the early stage of ultrarelativistic heavy-ion collisions. Since the parton momentum distribution is strongly anisotropic, the system can be unstable with respect to the specific plasma modes. The conditions of instability are found and the characteristic time of its development is estimated. Then, the screening of the static chromoelectric field in the nonequilibrium plasma is studied. Importance of the two phenomena for heavy-ion collisions at the Brookhaven Relativistic Heavy Ion Collider and the CERN Large Hadron Collider is critically discussed.

Non-equilibrium quark-gluon plasma at the initial stage of ultrarelativistic heavy-ion collisions

There are discussed unstable plasma modes and screening lengths in the many-parton system created due to hard and semihard processes at the initial stage of ultrarelativistic heavy-ion collisions. Hard and semihard processes are expected to lead to a copious production of partons, mainly gluons, in ultrarelativistic heavy-ion collisions [1–8]. The number of gluons generated at the initial stage of central Au-Au collision is estimated [6] as 570 at RHIC and 8100 at LHC. Since the longitudinal momenta of the produced partons are, in average, much greater than the transverse momenta, one expects instability of such a many-parton system due to specific plasma modes. Using the Penrose criterion [9] we discuss the stability conditions and then we find explicitly the unstable mode. In the second part of this note we consider screening of the chromoelectric field in the many-parton system.