Model For Heavy-ion Collisions Research Articles

Determination of Quark-Gluon-Plasma Parameters from a Global Bayesian Analysis

The quality of data taken at RHIC and LHC as well as the success and sophistication of computational models for the description of ultra-relativistic heavy-ion collisions have advanced to a level that allows for the quantitative extraction of the transport properties of the Quark-Gluon-Plasma. However, the complexity of this task as well as the computational effort associated with it can only be overcome by developing novel methodologies: in this paper we outline such an analysis based on Bayesian Statistics and systematically compare an event-by-event heavy-ion collision model to data from the Large Hadron Collider. We simultaneously probe multiple model parameters including fundamental quark-gluon plasma properties such as the temperature-dependence of the specific shear viscosity η/s, calibrate the model to optimally reproduce experimental data, and extract quantitative constraints for all parameters simultaneously. The method is universal and easily extensible to other data and collision models.

Coupling Constant Corrections in a Holographic Model of Heavy Ion Collisions.

We initiate a holographic study of coupling-dependent heavy ion collisions by analyzing, for the first time, the effects of leading-order, inverse coupling constant corrections. In the dual description, this amounts to colliding gravitational shock waves in a theory with curvature-squared terms. We find that, at intermediate coupling, nuclei experience less stopping and have more energy deposited near the light cone. When the decreased coupling results in an 80% larger shear viscosity, the time at which hydrodynamics becomes a good description of the plasma created from high energy collisions increases by 25%. The hydrodynamic phase of the evolution starts with a wider rapidity profile and smaller entropy.

The Elastic Cross Section in the Nambu–Jona-Lasinio Model

RésuméWe discuss the quark masses and the elastic cross sections at finite chemical potential in the Nambu–Jona-Lasinio model. We comment the generic features of the cross sections as functions of the chemical potential, temperature and collision energy. Finally, we discuss their relevance in the construction of a relativistic transport model for heavy-ion collisions based on this effective Lagrangian.

Implications of energy and momentum conservation for particle emission in A+A collisions at energies available at the CERN Super Proton Synchrotron

We construct a simple model of heavy ion collisions, local in the impact parameter plane, and appropriate for the SPS energy range. This model can be regarded as a new realization of the "fire-streak" approach, originally applied to studies of lower energy nucleus-nucleus reactions. Starting from local energy and momentum conservation, we nicely describe the broadening of the pion rapidity distribution when going from central to peripheral Pb+Pb collisions at $\sqrt{s_{NN}}$=17.3 GeV. The results of our calculations are compared with SPS experimental data. We discuss the resulting implications on the role of energy and momentum conservation for the dynamics of particle production in heavy ion collisions. A specific space-time picture emerges, where the longitudinal evolution of the system strongly depends on the position in the impact parameter (${b_x}$, ${b_y}$) plane. This picture is consistent with our earlier findings on the longitudinal evolution of the system as deduced from electromagnetic effects on charged pion directed flow, and can provide an explanation for specific low-$p_T$ phenomena seen in the fragmentation region of Pb+Pb collisions.

A ‘soft + hard’ model for heavy-ion collisions

We describe the spectra of neutral pions stemming from AuAu collisions at in a ‘soft + hard’ model. The model is based on the assumptions that hadrons stemming from hard processes are described via perturbative quantum chromodynamics improved parton model calculations, while those stemming from the Quark-Gluon Plasma (we refer to as soft yields) can be described in a super-statistical model induced by multiplicity uctuations. The obtained dependence of the parameters of the model on the event centrality is compared to what is observed in PbPb collisions at .

Elastic $qq$ Cross Sections at Finite Chemical Potential in the Nambu--Jona-Lasinio Lagrangian

We discuss the elastic qq cross sections at finite chemical potential in the Nambu–Jona-Lasinio model. We comment the generic features of the cross sections as functions of the chemical potential, temperature and collision energy. Finally, we discuss their relevance in the construction of a relativistic transport model for heavy-ion collisions based on this effective Lagrangian.

A viscous blast-wave model for heavy-ion collisions

We present a generalization of the blast-wave model by incorporating viscous effects in the fluid velocity profile as well as in the Cooper-Frye freeze-out. We apply this model to study the identified particles spectra and anisotropic flow at the Large Hadron Collider (LHC). We show that this improved viscous blast-wave model leads to good description of the transverse momentum distribution of particle multiplicities and elliptic as well as triangular flow. Within this model, we estimate the shear viscosity to entropy density ratio η/s ≃ 0.24 at the LHC.

Studies of three-particle correlations and reaction-plane correlators from STAR

We present STAR measurements of various harmonics of three-particle correlations in $\sqrt{s_{NN}}=200$ GeV Au+Au collisions at RHIC. The quantity $\langle\cos(m\phi_1+n\phi_2-(m+n)\phi_3)\rangle$ is measured for inclusive charged particles for different harmonics $m$ and $n$ as a function of collision centrality, transverse momentum $p_T$ and relative pseudorapidity $\Delta\eta$. These observables provide detailed information on global event properties like correlations between event planes of different harmonics and are particularly sensitive to the expansion dynamics of the matter produced in the collisions. We compare our measurements to different viscous hydrodynamic models. We argue that these measurements probe the three-dimensional structure of the initial state and provide unique ways to constrain the transport parameters involved in hydrodynamic modeling of heavy-ion collisions.

Exploring nonlocal observables in shock wave collisions

We study the time evolution of 2-point functions and entanglement entropy in strongly anisotropic, inhomogeneous and time-dependent N=4 super Yang-Mills theory in the large N and large 't Hooft coupling limit using AdS/CFT. On the gravity side this amounts to calculating the length of geodesics and area of extremal surfaces in the dynamical background of two colliding gravitational shockwaves, which we do numerically. We discriminate between three classes of initial conditions corresponding to wide, intermediate and narrow shocks, and show that they exhibit different phenomenology with respect to the nonlocal observables that we determine. Our results permit to use (holographic) entanglement entropy as an order parameter to distinguish between the two phases of the cross-over from the transparency to the full-stopping scenario in dynamical Yang-Mills plasma formation, which is frequently used as a toy model for heavy ion collisions. The time evolution of entanglement entropy allows to discern four regimes: highly efficient initial growth of entanglement, linear growth, (post) collisional drama and late time (polynomial) fall off. Surprisingly, we found that 2-point functions can be sensitive to the geometry inside the black hole apparent horizon, while we did not find such cases for the entanglement entropy.

Theory of collective dynamics: flow, fluctuations and correlations in heavy ion collisions

I review recent developments in the hydrodynamic modeling of ultra-relativistic heavy ion collisions and the extraction of the properties of bulk QCD matter from heavy ion collision measurements. I briefly summarize the current framework used for the theoretical modeling of heavy ion collisions and report the recent progress on the extraction of the temperature dependence of the shear and bulk viscosity coefficients, the development of statistical tools for data-to-model comparison, and anisotropic hydrodynamics. All these recent developments in our field pave the way for more quantitative determination of the transport properties of bulk QCD matter from the experimental heavy ion collision program.

Thermal and prompt photons at RHIC and the LHC

Thermal and prompt photon production in heavy ion collisions is evaluated and compared with measurements from both RHIC and the LHC. An event-by-event hydrodynamical model of heavy ion collisions that includes shear and bulk viscosities is used, along with up-to-date photon emission rates. Larger tension with measurements is observed at RHIC than at the LHC. The center-of-mass energy and centrality dependence of thermal and prompt photons is investigated.

Holographic heavy ion collisions with baryon charge

We numerically simulate collisions of charged shockwaves in Einstein-Maxwell theory in anti-de Sitter space as a toy model of heavy ion collisions with non-zero baryon charge. The stress tensor and the baryon current become well described by charged hydrodynamics at roughly the same time. The effect of the charge density on generic observables is typically no larger than 15\%. %The rapidity profile of the charge is wider than the profile of the local energy density. We find significant stopping of the baryon charge and compare our results with those in heavy ion collision experiments.

Semi-holography for heavy ion collisions: self-consistency and first numerical tests

We present an extended version of a recently proposed semi-holographic model for heavy-ion collisions, which includes self-consistent couplings between the Yang-Mills fields of the Color Glass Condensate framework and an infrared AdS/CFT sector, such as to guarantee the existence of a conserved energy-momentum tensor for the combined system that is local in space and time, which we also construct explicitly. Moreover, we include a coupling of the topological charge density in the glasma to the same of the holographic infrared CFT. The semi-holographic approach makes it possible to combine CGC initial conditions and weak-coupling glasma field equations with a simultaneous evolution of a strongly coupled infrared sector describing the soft gluons radiated by hard partons. As a first numerical test of the semi-holographic model we study the dynamics of fluctuating homogeneous color-spin-locked Yang-Mills fields when coupled to a homogeneous and isotropic energy-momentum tensor of the holographic IR-CFT, and we find rapid convergence of the iterative numerical procedure suggested earlier.

Production of photons in relativistic heavy-ion collisions

In this work it is shown that the use of a hydrodynamical model of heavy ion collisions which incorporates recent developments, together with updated photon emission rates greatly improves agreement with both ALICE and PHENIX measurements of direct photons, supporting the idea that thermal photons are the dominant source of direct photon momentum anisotropy. The event-by-event hydrodynamical model uses IP-Glasma initial states and includes, for the first time, both shear and bulk viscosities, along with second order couplings between the two viscosities. The effect of both shear and bulk viscosities on the photon rates is studied, and those transport coefficients are shown to have measurable consequences on the photon momentum anisotropy.

Deviations of the energy-momentum tensor from equilibrium in the initial state for hydrodynamics from transport approaches

Many hybrid models of heavy ion collisions construct the initial state for hydrodynamics from transport models. Hydrodynamics requires that the energy-momentum tensor $T^{\mu\nu}$ and four-currents $j^{\mu}$ do not deviate considerably from the equilibrium ideal-fluid form, but the ones constructed from transport do not necessarily possess this property. In this work we investigate the space-time picture of $T^{\mu\nu}$ deviations from equilibrium in Au+Au collisions using a coarse-grained transport approach. The collision energy is varied in the range $E_{lab} = 5-160A$ GeV. The sensitivity of $T^{\mu\nu}$ deviations from equilibrium to collision centrality, and other parameters such as the switching criterion, the amount of statistics used to construct the initial state, and the smearing parameter $\sigma$ is investigated. For low statistics deviations of $T^{\mu\nu}$ from equilibrium are large and dominated by the effect of finite sampling. For large statistics the pressure anisotropy plays the most significant role, while the off-diagonal components of $T^{\mu\nu}$ are small in a large volume during the whole evolution. For all considered energies and centralities the pressure anisotropy exhibits a similar feature: there is a narrow interval of time, when it rapidly drops in a considerable volume. This allows us to introduce an "isotropization time," which is found to decrease with energy and slightly increase with centrality. The isotropization times are larger than times typically used for initializing hydrodynamics.

Estimating ŋ/s of QCD matter at high baryon densities

We report on the application of a cascade + viscous hydro + cascade model for heavy ion collisions in the RHIC Beam Energy Scan range, √snn = 6.3…200 GeV. By constraining model parameters to reproduce the data we find that the effective (average) value of the shear viscosity over entropy density ratio ŋ/s decreases from 0.2 to 0.08 when collision energy grows from √sNN ≈ 7 to 39 GeV.

Λ polarization in an exact fluid dynamical model for heavy-ion collisions

Λ polarization is calculated in an exact analytical, rotating model based on parameters from a high resolution (3+1)D Particle-in-Cell Relativistic hydrodynamics calculation. The polarization is attributed to effects from thermal vorticity and for the first time the effects of the radial and axial acceleration are also studied separately.

Formation time of quark–gluon plasma in heavy-ion collisions in the holographic shock wave model

We estimate the thermalization time in two colliding shock waves holographic model of heavy-ion collisions. For this purpose we model the process by the Vaidya metric with a horizon defined by the trapped surface location. We consider two bottom-up AdS/QCD models that give, within the colliding shock waves approach, the dependence of multiplicity on the energy compatible with RHIC and LHC results. One model is a bottom-up AdS/QCD confining model and the other is related to an anisotropic thermalization. We estimate the thermalization time and show that increasing the confining potential decreases the thermalization time as well as an anisotropy accelerates the thermalization.

Center clusters in full QCD at finite temperature and background magnetic field

We study the center structure of full dynamical QCD at finite temperatures and nonzero values of the background magnetic field using continuum extrapolated lattice data. We concentrate on two particular observables characterizing center clusters: their fractality and the probability for percolation. For temperatures below and around the transition region, the fractal dimension is found to be significantly smaller than three, leading to a vanishing mean free path inside the cluster structure. This finding might be relevant for center symmetry-based models of heavy-ion collisions. In addition, the percolation probability is employed to define the transition temperature and to map out the QCD phase diagram in the magnetic field-temperature plane.

A semi-holographic model for heavy-ion collisions

We develop a semi-holographic model for the out-of-equilibrium dynamics during the partonic stages of an ultrarelativistic heavy-ion collision. The model combines a weakly-coupled hard sector, involving gluon modes with energy and momenta of the order of the saturation momentum and relatively large occupation numbers, with a strongly-coupled soft sector, which physically represents the soft gluons radiated by the hard partons. The hard sector is described by perturbative QCD, more precisely, by its semi-classical approximation (the classical Yang-Mills equations) which becomes appropriate when the occupation numbers are large. The soft sector is described by a marginally deformed conformal field theory, which in turn admits a holographic description in terms of classical Einstein's equations in $AdS_5$ with a minimally coupled massless `dilaton'. The model involve two free parameters which characterize the gauge-invariant couplings between the hard and soft sectors. Via these couplings, the hard modes provide dynamical sources for the gravitational equations at the boundary of $AdS_5$ and feel the feedback of the latter as additional soft sources in the classical Yang-Mills equations. Importantly, the initial conditions for this coupled dynamics are fully determined by the hard sector alone, i.e. by perturbative QCD, and are conveniently given by the color glass condensate (CGC) effective theory. We also develop a new semi-holographic picture of jets in the QGP by attaching a non-Abelian charge to the endpoint of the trailing string in $AdS_5$ representing a heavy quark. This leads to modified Nambu-Goto equations for the string which govern the (collisional and radiative) energy loss by the heavy quark towards both hard and soft modes.