We investigate the rapidity dependence of the elliptical flow in heavy ion collisions at 200 GeV (cms), by employing a three-dimensional hydrodynamic evolution, based on different initial conditions, and different freeze-out scenarios. It will be shown that the form of pseudo-rapidity ($η$) dependence of the elliptical flow is almost identical to space-time-rapidity ($η_{s}$) dependence of the initial energy distribution, independent of the freeze-out prescriptions.
We discuss the implications of the eikonal amplitude on the pair production probability in ultrarelativistic heavy-ion transits. In this context the Weizsäcker-Williams method is shown to be exact in the ultrarelativistic limit, irrespective of the produced particles' mass. A new equivalent single-photon distribution is derived which correctly accounts for the Coulomb distortions. As an immediate application, consequences for unitarity violation in photo-dissociation processes in peripheral heavy-ion encounters are discussed.
Recent theoretical developments of relativistic hydrodynamics applied to ultrarelativistic heavy-ion collisions are briefly reviewed. In particular, the concept of a formal gradient expansion is discussed, which is a tool to compare different hydrodynamic models with underlying microscopic theories.
We study the generation of directed flow in the hydrodynamic expansion of the hot matter formed in ultrarelativistic heavy-ion collisions at 200GeV. The experimentally observed negative directed flow in a wide range of central pseudorapidities isreproduced assuming that the fireball is tilted away from the collision axis. The tilt of the source is consistent with a preferential emission in the forward/backward hemisphere from forward/backward participating nucleons. The model reproduces the experimentally observed scaling of the directed flow when going from Au-Au to Cu-Cu systems.
Motivated by forthcoming experiments at RHIC and LHC, we study event-by-event fluctuations in ultrarelativistic heavy-ion collisions in participant nucleon as well as thermal models. The calculated physical observables, including multiplicity, kaon to pion ratios, and transverse momenta agree well with recent NA49 data at the SPS, and indicate that such studies do not yet reveal the presence of new physics. Finally, we present a simple model of how a first order phase transition can be signaled by very large fluctuations.
I present the motivation for studying nuclear collisions at ultrarelativistic energies which is to map the phase diagram of strongly interacting matter under very extreme conditions. The relevant experimental efforts are overviewed and problems in connecting observables with physics of the hot and dense matter are pointed out. I review the current highlights of the experimental programme: excitation functions of various quantities from the SPS which suggest a possibility of the onset of deconfinement, and the evidence of deconfined perfect fluid at RHIC.
We study the disintegration of nuclei by strong electromagnetic fields induced by ultrarelativistic heavy ions. The proposed multi-step model includes 1) the absorption of a virtual photon by a nucleus, 2) intranuclear cascades of produced hadrons and 3) statistical decay of the excited residual nucleus. The combined model describes well existing data on projectile fragmentation at energy 200 GeV per nucleon. Electromagnetic multifragmentation of nuclei is predicted to be an important reaction mechanism at RHIC and LHC energies.
Kinetic theory is used to check the applicability of parton cascade in 1 dimensional expansion. Using the information provided by 3 dimensional parton cascade, we model the transverse expansion by an effective area. With this model, kinetic theory is able to give prediction of the time development of transverse energy which is in good agreement with the parton cascade results.
A Monte Carlo program solving Boltzmann equation for partons via cascade method is presented. At presented, only gluon-gluon elastic scattering is included. The scattering cross section is regulated by a medium generated screening mass. Three different geometric modes (3 dimension expansion, 1-d expansion, and scattering inside a box) are provided for theoretical study of the parton transport and the applicability of the cascade method. Space cell division is available to save the number of computer operations. This improves the speed of the calculation by a large factor and makes the code bes…
We investigate the fluctuations of pion elliptic flow, triangular flow, and Hanbury-Brown-Twiss (HBT) correlation functions for the hydrodynamic sources with fluctuating initial conditions in the heavy ion collisions of the Au-Au at $\sqrt{s_{NN}}=200$ GeV and the Pb-Pb at $\sqrt{s_{NN}} =2.76$ TeV. A method based on event-subcollection analysis is used to detect these fluctuations in ultrarelativistic heavy ion collisions. We introduce a granularity length to describe the granular inhomogeneity of the initial sources, and investigate its relationships with the fluctuations of the flow harmoni…
We study the simultaneous dissociation of heavy ultrarelativistic nuclei followed by the forward-backward neutron emission in peripheral collisions at colliders. The main contribution to this particular heavy-ion dissociation process, which can be used as a beam luminosity monitor, is expected to be due to the electromagnetic interaction. The Weizsacker-Williams method is extended to the case of simultaneous excitation of collision partners which is simulated by the RELDIS code. A contribution to the dissociation cross section due to grazing nuclear interactions is estimated within the abrasio…
We study the time scale for pressure equilibration in heavy ion collisions at AGS energies within the three-fluid hydrodynamical model and a microscopic cascade model (UrQMD). We find that kinetic equilibrium is reached in both models after a time of 5 fm/c (center-of-mass time). Thus, observables which are sensitive to the early stage of the reaction differ considerably from the expectations within the instant thermalization scenario (one-fluid hydrodynamical model).
The behavior of hadronic matter at high baryon densities is studied within Ultrarelativistic Quantum Molecular Dynamics (URQMD). Baryonic stopping is observed for Au+Au collisions from SIS up to SPS energies. The excitation function of flow shows strong sensitivities to the underlying equation of state (EOS), allowing for systematic studies of the EOS. Dilepton spectra are calculated with and without shifting the $ρ$ pole. Except for S+Au collisions our calculations reproduce the CERES data.
A higher order QED calculation of the ultraperipheral heavy ion cross section for mu+ mu- pair production at RHIC and LHC is carried out. The so-called "Coulomb corrections" lead to an even greater percentage decrease of mu+ mu- production from perturbation theory than the corresponding decrease for e+ e- pair production. Unlike the e+ e- case, the finite charge distribution of the ions (form factor) and the necessary subtraction of impact parameters with matter overlap are significant effects in calculation an observable ultraperipheral mu+ mu- total cross section.
There exist several proposals to use Weizsäcker-Williams photons generated by ultrarelativistic heavy ions to produce exotic particles in $γγ$ fusion reactions. To estimate the background conditions for such reactions we analyze various mechanisms of meson production in very peripheral collisions of ultrarelativistic heavy ions at RHIC and LHC energies. Besides $γγ$ fusion they include also electromagnetic $γA$ interactions and strong nucleon-nucleon interactions in grazing $AA$ collisions. All these processes are characterised by low multiplicities of produced particles. $γA$ and $AA$ events …
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 nonequilibrium 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 $t_{CM}^{eq}\approx 5~fm/c\simeq 2R_{Au}/γ_{CM}$. Observables which are sensitive to the early stage of the collision (like e.g. nuc…
We study nuclear reactions induced by virtual photons associated with Lorentz-boosted Coulomb fields of ultrarelativistic heavy ions. Evaporation, fission and multifragmentation mechanisms are included in a new RELDIS code, which describes the deexcitation of residual nuclei formed after single and double photon absorption in peripheral heavy-ion collisions. Partial cross sections for different dissociation channels, including the multiple neutron emission ones, are calculated and compared with data when available. Rapidity and transverse momentum distributions of nucleons, nuclear fragments a…
In ultrarelativistic heavy ion collisions, the multiplicity of multi-strange baryons per participating nucleon increases with centrality in a different fashion for different systems and energies. At RHIC, for copper+copper (CuCu) collisions the increase is much steeper than for gold-gold (AuAu) collisions. We show that this system size dependence is due to a core-corona effect: the relative importance of the corona as compared to the core (thermalized matter) contribution varies and the contribution of a corona nucleon to the multiplicity differs from that of a core nucleon. $ϕ$ mesons follow …
We investigate the two-pion interferometry in ultrarelativistic heavy ion collisions in the granular source model of quark-gluon plasma droplets. The pion transverse momentum spectra and HBT radii of the granular sources agree well with the experimental data of the $\sqrt{s_{NN}}=200$ GeV Au-Au and $\sqrt{s_{NN}}=2.76$ TeV Pb-Pb most central collisions. In the granular source model the larger initial system breakup time may lead to the larger HBT radii $R_{\rm out}$, $R_{\rm side}$, and $R_{\rm long}$. However, the large droplet transverse expansion and limited average relative emitting time o…
The time-dependent Dirac equation can be solved exactly for ionization induced by ultrarelativistic heavy ion collisions. Ionization calculations are carried out in such a framework for a number of representative ion-ion pairs. For each ion-ion pair, the computed cross section consists of two terms, a constant energy independent term and a term whose coefficient is ln(gamma). Scaled values of both terms are found to decrease with increasing Z of the nucleus that is ionized.
We calculate the asymptotic high-energy amplitude for electrons scattering at one ion as well as at two colliding ions, respectively, by means of perturbation theory. We show that the interaction with one ion eikonalizes and that the interaction with two ions causally decouples. We are able to put previous results on perturbative grounds and propose further applications for the obtained rules for interactions on the light cone. The formalism will be of use for the calculation of Coulomb corrections to electron-positron pair creation in heavy ion collisions. Finally we discuss the results and i…
A temperature dependent bulk viscosity coefficient is used in 3+1D hydrodynamic simulations. I study the effect of the increase of bulk viscosity around the critical temperature on the system dynamics in central Pb+Pb collisions at $\sqrt{s_{NN}}=2760$~GeV. With increasing bulk viscosity the life-time of the system increases slightly. Also the shape of the freeze-out hypersurface changes, the outer layers of the fireball live longer. This effect causes a small reduction of the ratio of two interferometry radii $R_{out}/R_{side}$, improving the agreement with experimental data.
We discuss the elementary physics of the final state Coulomb interactions in Hanbury-Brown Twiss interferometry, showing -- with explicit comparison to E877 data for $π^+π^-$ and $π^\pm p$ -- that the Coulomb corrections in the pair correlation function can be well understood in terms of simple classical physics. We connect the classical picture with descriptions in terms of Coulomb wave functions, and investigate the influence of the ``central'' Coulomb potential on the pair correlation function.
Employing NEXUS, one of the most recent simulation programs for heavy ions collisions, we investigate in detail the Hanbury-Twiss correlation function for charged pions for reactions 158 GeV Pb+Pb. For this study we supplement the standard simulation program by electromagnetic interactions. We find that the string fragmentation introduces strong space-momentum correlations and the freeze out times of the correlated pairs have a wide distribution. Both has a strong influence on the apparent source radius determined from the measured correlation correlation function.An equally strong influence i…
The validity of a delta-function approximation for the electromagnetic interaction of relativistic heavy ions is investigated. The production of e+e- pairs, with electron capture, is used as a test of the approximation.
We study mutual dissociation of heavy nuclei in peripheral collisions at ultrarelativistic energies. Earlier this process was proposed for beam luminosity monitoring via simultaneous registration of forward and backward neutrons in zero degree calorimeters at Relativistic Heavy Ion Collider. Electromagnetic dissociation of heavy ions is considered in the framework of the Weizsacker-Williams method and simulated by the RELDIS code. Photoneutron cross sections measured in different experiments and calculated by the GNASH code are used as input for the calculations of dissociation cross sections.…
Relativistic dissipative fluid dynamics is a common tool to describe the space-time evolution of the strongly interacting matter created in ultrarelativistic heavy-ion collisions. For a proper comparison to experimental data, fluid-dynamical calculations have to be performed on an event-by-event basis. Therefore, fluid dynamics should be able to reproduce, not only the event-averaged momentum anisotropies, $<v_{n}>$, but also their distributions. In this paper, we investigate the event-by-event distributions of the initial-state and momentum anisotropies $ε_n$ and $v_n$, and their correlations…
The polarization of direct photons produced in an ultrarelativistic heavy-ion collision reflects the momentum anisotropy of the quark-gluon plasma created in the collision. This paper presents a general framework, based on the photon spectral functions in the plasma, for analyzing the angular distribution and thus the polarization of dileptons in terms of the plasma momentum anisotropies. The rates of dilepton production depend, in general, on four independent spectral functions, corresponding to two transverse polarizations, one longitudinal polarization, and -- in plasmas in which the moment…
Medium effects which include color screening and Landau-Pomeranchuk-Migdal suppression of induced radiation are discussed in connection with the equilibration of dense partonic system in ultrarelativistic heavy ion collisions. Taking into account of these medium effects, the equilibration rate for a gluonic gas are derived and the consequences are discussed.
We explore the consequences of a freeze-out criterion for heavy-ion collisions, based on pion escape probabilities from the hot and dense but rapidly expanding collision region. The influence of the expansion and the scattering rate on the escape probability is studied. The temperature dependence of this scattering rate favors a low freeze-out temperature of ~100 MeV. In general, our results support freeze-out along finite four-volumes rather than sharp three-dimensional hypersurfaces, with high-pt particles decoupling earlier from smaller volumes. We compare our approach to the proposed unive…
Transverse mass spectra of pions and protons measured in central collisions of heavy ions at the SPS and at RHIC are compared to a hydrodynamic parameterization. While the chemical temperature needed at RHIC is significantly higher compared to SPS, the spectra may be described using kinetic freeze-out parameters which are similar for both beam energies. At RHIC either the temperature or the flow velocity is higher, but the data provide no unambiguous proof for much stronger transverse flow. The contribution of such hydrodynamic emission at high transverse momenta is investigated in detail. It …
The role of minijet production as initial conditions for QGP production at $τ\sim 0.1 fm/c$ in nuclear collisions at the LHC and RHIC energies is discussed.
We calculate the centrality dependence of inclusive cross section of large-pT charmed-meson ($D^{0}$, $D^{*}$, $D^{*+}$, and $D_{s}^{+}$) from heavy quark fragmentation by the hard photoproduction processes for the nucleus-nucleus collisions in ultrarelativistic heavy ion collisions. The numerical results indicate that the modification of the hard photoproduction processes cannot be negligible for the charmed-meson production in Au-Au collisions at Relativistic Heavy Ion Collider (RHIC) and Pb-Pb collisions at Large Hadron Collider (LHC).
Coulomb corrections to perturbation theory for producing electron-positron pairs in ultrarelativistic heavy ion collisions are considered in a part-analytical, part-numerical approach. Production probabilities are reduced from perturbation theory with increasing charge of the colliding heavy ions, as has been previously argued in the literature. It is shown here that the reduction from perturbation theory comes from the appropriate physical spatial cutoff of the electromagnetic potentials arising from the colliding ultrarelativistic heavy ions.
An exact solution of the two center time-dependent Dirac equation for pair production induced by ultrarelativistic heavy ion collisions is presented. Cross sections to specific final states approach those of perturbation theory. Multiplicity rates are reduced from perturbation theory.
An exact solution of the time-dependent Dirac equation for ionization and pair production induced by ultrarelativistic heavy ion collisions is presented. Exact transition probabilities, equivalent to those that would be obtained in an untruncated basis coupled channels calculation, are presented. Exact bound-electron positron pair production probabilities are calculated to be mostly smaller than those calculated with the same potential in perturbation theory at impact parameters small enough for differences to occur.
Posterior distributions for physical parameters describing relativistic heavy-ion collisions, such as the viscosity of the quark-gluon plasma, are extracted through a comparison of hydrodynamic-based transport models to experimental results from 100$A$ GeV + 100$A$ GeV Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). By simultaneously varying six parameters and by evaluating several classes of observables, we are able to explore the complex intertwined dependencies of observables to model parameters. We obtain a full multi-dimensional posterior distribution for the model output …
The delta function gauge of the electromagnetic potential allows semiclassical formulas to be obtained for the probability of exciting a single electron out of the ground state in an ultrarelativistic heavy ion reaction. Exact formulas have been obtained in the limits of zero impact parameter and large, perturbative, impact parameter. The perturbative impact parameter result can be exploited to obtain a semi-empirical cross section formula of the form, sigma = A ln(gamma) + B, for single electron ionization. A and B can be evaluated for any combination of target and projectile, and the resulti…
In a previous paper, we have shown that a double phi peak structure appears in the dilepton invariant mass spectrum if a first order QCD phase transition occurs in ultrarelativistic heavy ion collisions. Furthermore, the transition temperature can be determined from the transverse momentum distribution of the low mass phi peak. In this work, we extend the study to the case that a smooth crossover occurs in the quark-gluon plasma to the hadronic matter transition. We find that the double phi peak structure still exists in the dilepton spectrum and thus remains a viable signal for the formation …
In recent works [Segev,Wells; Baltz, McLerran; Eichmann, Reinhardt, Schramm, Greiner] it was claimed that the Coulomb correction to the $e^+e^-$ production cross section in relativistic heavy-ion collisions is absent. We point out that this statement is in obvious contradiction to some well known results. We obtain large Coulomb corrections in the pair production cross section for the RHIC and LHC heavy-ion colliders.
We review the production of lepton pairs during high energy nuclear collisions. We highlight the information being carried out of the hot and dense strongly interacting medium. We describe the phenomenon of scalar-vector mixing that can take place in a dense medium and suggest possible measurable signatures of this effect in high energy heavy ion collisions.
If the bulk viscosity of QCD matter is large, the effective pressure of the hot and dense matter created in ultrarelativistic heavy ion collisions can become negative, leading to instabilities in the evolution of the plasma. In the context of heavy ion collisions, this effect is sometimes referred to as cavitation. In this contribution we discuss the onset of cavitation in event-by-event hydrodynamic simulations of ultrarelativistic heavy ion collisions at LHC energies. We estimate how large the bulk viscosity of the QGP has to be in the QCD (pseudo) phase transition region in order for the ef…
Dilepton production associated with minijets is calculated in ultrarelativistic heavy ion collisions using the first order approximation of the dilepton fragmentation functions of quarks and gluons. The full QCD evolution of the fragmentation functions is also studied. We find that the dilepton pairs from the fragmentation of minijets are comparable to direct Drell-Yan at $\sqrt{s}=200$ AGeV for small dilepton invariant mass $M\sim$ 1-2 GeV/c$^2$ while dominant over a large range of mass at $\sqrt{s}=6400$ AGeV.
We employ the Langevin equation and Wigner function to describe the bottom equark dynamical evolutions and their formation into a bound state in the expanding Quark Gluon Plasma (QGP). The additional suppressions from parton inelastic scatterings are supplemented in the regenerated bottomonium. Hot medium modifications on $Υ(1S)$ properties are studied consistently by taking the bottomonium potential to be the color-screened potential from Lattice results, which affects both $Υ(1S)$ regeneration and dissociation rates. Finally, we calculated the $Υ(1S)$ nuclear modification factor $R_{AA}^{\rm…
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.
We discuss a new approach to ultrarelativistic heavy-ion collisions based on classical hadrodynamics for extended nucleons, corresponding to nucleons of finite size interacting with massive meson fields. This new theory provides a natural covariant microscopic approach that includes automatically spacetime nonlocality and retardation, nonequilibrium phenomena, interactions among all nucleons and particle production. In the current version of our theory, we consider $N$ extended unexcited nucleons interacting with massive neutral scalar ($σ$) and neutral vector ($ω$) meson fields. The resulting…
I first review the early history of the ultrarelativistic heavy ion program, starting with the 1974 Bear Mountain Workshop, and the 1983 Aurora meeting of the U.S. Nuclear Science Committee, just one billion seconds ago, which laid out the initial science goals of an ultrarelativistic collider. The primary goal, to discover the properties of nuclear matter at the highest energy densities, included finding new states of matter -- the quark-gluon plasma primarily -- and to use collisions to open a new window on related problems of matter in cosmology, neutron stars, supernovae, and elsewhere. To…
The effect of shadowing on the early state of ultrarelativistic heavy ion collisions is investigated along with transverse energy and hard process production, specifically Drell-Yan, $J/ψ$, and $Υ$ production. We choose several parton distributions and parameterizations of nuclear shadowing, as well as the spatial dependence of shadowing, to study the influence of shadowing on relevant observables. Results are presented for Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV and Pb+Pb collisions at $\sqrt{s_{NN}} = 5.5$ TeV.
Highly excited nuclear matter created in ultrarelativistic heavy-ion collisions possibly reaches the phase of quark deconfinement. It quickly cools down and hadronises. We explain that the process of hadronisation may likely be connected with disintegration into fragments. Observable signals of such a scenario are proposed.
Recent results on minijet production in nuclear collisions at the RHIC and LHC energies are reviewed. Initial conditions of the QGP at $τ=0.1$ fm$/c$, especially parton chemistry, thermalization and net baryon number-to-entropy ratio are discussed. Also, contribution of minijets from a hard BFKL-pomeron ladder will be estimated.
The Coulomb potential produced by an ultrarelativistic particle (such as a heavy ion) in uniform motion is shown in the appropriate gauge to factorize into a longitudinal Dirac delta function of (z - t) times the simple two dimensional potential solution in the transverse direction. This form makes manifest the source of the energy independence of the interaction.
A two phase cascade, LUCIFER II, developed for the treatment of ultra high energy ion-ion collisions is applied to the production of strangeness at SPS energies $\sqrt{s}=17-20$. This simulation is able to simultaneously describe both hard processes such as Drell-Yan and slower, soft processes such as the production of light mesons, including strange mesons, by separating the dynamics into two steps, a fast cascade involving only nucleons in the original colliding relativistic ions followed, after an appropriate delay, by multiscattering of the resulting excited baryons and mesons produced vir…
We show how anisotropy in momentum of the gluon distribution in ultrarelativistic heavy ion collisions gives rise to polarization of direct photons produced via gluon-quark Compton scattering, as well as by quark-antiquark annihilation into a gluon-photon pair. We estimate the polarization asymmetry from the Compton process within a toy model where the polarized photons are produced from thermal gluons scattered by heavy-quark scattering centers moving with Bjorken boost-invariant flow, and find that it could be as large as 10%. We conclude that polarization measurements of directly produced p…
Screening of initial parton production due to the presence of on-shell partons in high-energy heavy-ion collisions is discussed. It is shown that the divergent cross sections in the calculation of parton production can be regulated self-consistently without an {\it ad hoc} cut-off, and that the resultant parton production and transverse energy production rate are finite. Consequences on the energy density estimates are discussed.
Anisotropic flow phenomena is a key probe of the existence of Quark-Gluon Plasma. Several new observable associated with correlations between anisotropic flow harmonics are developed, which are expected to be sensitive to the initial fluctuations and transport properties of the created matter in heavy ion collisions. I review recent developments of correlations of anisotropic flow harmonics. The experimental measurements, together with the comparisons to theoretical model calculations, open up new opportunities of exploring novel QCD dynamics in heavy-ion collisions.
Using the quasiclassical Green's function in the Coulomb field, we analyze the probabilities of single and multiple $e^+e^-$-pair production at fixed impact parameter $b$ between colliding ultrarelativistic heavy nuclei. We perform calculations in the Born approximation with respect to the parameter $Z_Bα$, and exactly in $Z_Aα$, $Z_{A}$ and $Z_{B}$ are the charge numbers of the corresponding nuclei. We also obtain the approximate formulas for the probabilities valid for $Z_Aα, Z_Bα\lesssim 1$.
