Initial State Of Heavy-ion Collisions Research Articles

Efficient Solver of Relativistic Hydrodynamics with an Implicit Runge–Kutta Method

Abstract We propose a new method to solve the relativistic hydrodynamic equations based on implicit Runge–Kutta methods with a locally optimized fixed-point iterative solver. For numerical demonstration, we implement our idea for ideal hydrodynamics using the one-stage Gauss–Legendre method as an implicit method. The accuracy and computational cost of our new method are compared with those of explicit ones for the (1+1)D Riemann problem, as well as the (2+1)D Gubser flow and event-by-event initial conditions for heavy-ion collisions generated by TRENTo. We demonstrate that the solver converges with only one iteration in most cases, and as a result, the implicit method requires a smaller computational cost than the explicit one at the same accuracy in these cases, while it may not converge with an unrealistically large Δt. By showing a relationship between the one-stage Gauss–Legendre method with the iterative solver and the two-step Adams–Bashforth method, we argue that our method benefits from both the stability of the former and the efficiency of the latter.

Characterizing the initial conditions of heavy-ion collisions at the LHC with mean transverse momentum and anisotropic flow correlations

The study of the initial conditions of relativistic heavy-ion collisions and the subsequent development of hot and dense nuclear matter at the LHC is fundamental for the understanding of the strong nuclear force. The traditional approach of comparing observables with hydrodynamical models based on different initial conditions typically fails to isolate the effects of the initial conditions due to the sensitivity of the observables to the collective behaviour of the expanding system. Correlations of the mean transverse momentum [p T] and the anisotropic flow Fourier coefficients v n have been shown to serve as a unique probe of the initial conditions of the heavy-ion collisions with little to no bias from final state effects.In this talk, correlations between [p T] and v 2 or v 3 are presented as a function of centrality in Pb−Pb and Xe−Xe collisions at TeV and TeV, respectively, measured with ALICE. Additionally, measurements of the higher-order correlation between [p T], v 2, and v 3 is measured for the first time. All of these measurements are compared with hydrodynamical models using IP-Glasma or TRENTo initial conditions. The former is based on Color Glass Condensate effective theory with gluon saturation and the latter is a parameterized model with nucleons as the relevant degrees of freedom. The data is best described by models using IP-Glasma initial conditions, whereas the TRENTo based models fail to describe the data regardless of the parametrization.

Observation of flow angle and flow magnitude fluctuations in Pb-Pb collisions at sNN=5.02TeV at the CERN Large Hadron Collider

This Letter reports on the first measurements of transverse momentum dependent flow angle $\Psi_n$ and flow magnitude $v_n$ fluctuations, determined using new four-particle correlators. The measurements are performed for various centralities in Pb-Pb collisions at a centre-of-mass energy per nucleon pair of $\sqrt{s_{\rm NN}}$ = 5.02 TeV with ALICE at the CERN Large Hadron Collider. Both flow angle and flow magnitude fluctuations are observed in the presented centrality ranges and are strongest in the most central collisions and for a transverse momentum $p_{\rm T}>2$ GeV/$c$. Comparison with theoretical models, including iEBE-VISHNU, MUSIC, and AMPT, show that the measurements exhibit unique sensitivities to the initial state of heavy-ion collisions.

Characterizing the initial conditions of heavy-ion collisions at the LHC with mean transverse momentum and anisotropic flow correlations

Correlations between mean transverse momentum [pT] and anisotropic flow coefficients v2 or v3 are measured as a function of centrality in Pb–Pb and Xe–Xe collisions at sNN=5.02 TeV and 5.44 TeV, respectively, with ALICE. In addition, the recently proposed higher-order correlation between [pT], v2, and v3 is measured for the first time, which shows an anticorrelation for the presented centrality ranges. These measurements are compared with hydrodynamic calculations using IP-Glasma and TRENTo initial-state shapes, the former based on the Color Glass Condensate effective theory with gluon saturation, and the latter a parameterized model with nucleons as the relevant degrees of freedom. The data are better described by the IP-Glasma rather than the TRENTo based calculations. In particular, Trajectum and JETSCAPE predictions, both based on the TRENTo initial state model but with different parameter settings, fail to describe the measurements. As the correlations between [pT] and vn are mainly driven by the correlations of the size and the shape of the system in the initial state, these new studies pave a novel way to characterize the initial state and help pin down the uncertainty of the extracted properties of the quark–gluon plasma recreated in relativistic heavy-ion collisions.

Collective dynamics of heavy ion collisions in ATLAS

The latest measurements of collective behaviour in a variety of collision systems with the ATLAS detector at the LHC, including collisions at 13 TeV, collisions at 5.44 TeV, and \mbox{Pb+Pb}Pb+Pb collisions at 5.02 TeV, are presented. They include v_nvn-[p_{T}pT] correlations, which carry important information about the initial-state geometry of the quark-gluon plasma and can shed light on any quadrupole deformation in the Xe nucleus, and measurements of flow decorrelations differential in rapidity, which probe the longitudinal structure of the colliding system. These measurements furthermore provide stringent tests of the theoretical understanding of the initial state in heavy ion collisions.

Monte Carlo event generator for initial conditions of conserved charges in nuclear geometry

At top collider energies where baryon stopping is negligible, the initial state of heavy-ion collisions is overall charge neutral and predominantly composed of gluons. Nevertheless, there can also be significant local fluctuations of the baryon number, strangeness, and electric charge densities about zero, perturbatively corresponding to the production of quark/antiquark pairs. These previously ignored local charge fluctuations can permit the study of charge diffusion in the quark-gluon plasma (QGP), even at top collider energies. In this paper we present a new model denoted ICCING (initial conserved charges in nuclear geometry) which can reconstruct the initial conditions of conserved charges in the QGP by sampling a ($g\ensuremath{\rightarrow}q\overline{q}$) splitting probability over the initial energy density. We find that the new charge distributions generally differ from the bulk energy density; in particular, the strangeness distribution is significantly more eccentric than standard bulk observables and appears to be associated with the geometry of hot spots in the initial state. The new information provided by these conserved charges opens the door to studying a wealth of new charge- and flavor-dependent correlations in the initial state and ultimately the charge transport parameters of the QGP.

Model investigations of the correlation between the mean transverse momentum and anisotropic flow in shape-engineered events

The correlation between the event mean-transverse momentum [pT], and the anisotropic flow magnitude vn, ρ(vn2,[pT]), has been argued to be sensitive to the initial conditions in heavy-ion collisions. We use simulated events generated with the AMPT and EPOS models for Au+Au at sNN = 200 GeV, to investigate the model dependence and the response and sensitivity of the ρ(v22,[pT]) correlator to collision-system size and shape, and the viscosity of the matter produced in the collisions. We find good qualitative agreement between the correlators for the string melting version of the AMPT model and the EPOS model. The model investigations for shape-engineered events as well as events with different viscosity (η/s), indicate that ρ(v22,[pT]) is sensitive to the initial-state geometry of the collision system but is insensitive to sizable changes in η/s for the medium produced in the collisions. These findings suggest that precise differential measurements of ρ(v22,[pT]) as a function of system size, shape, and beam-energy could provide more stringent constraints to discern between initial-state models and hence, more reliable extractions of η/s.

Gluonic hot spot initial conditions in heavy-ion collisions

The initial conditions in heavy-ion collisions are calculated in many different frameworks. The importance of nucleon position fluctuations within the nucleus and sub-nucleon structure has been established when modeling initial conditions for input to hydrodynamic calculations. However, there remain outstanding puzzles regarding these initial conditions, including the measurement of the near equivalence of the elliptical $v_{2}$ and triangular $v_{3}$ flow coefficients in ultra-central 0-1% Pb+Pb collisions at the LHC. Recently a calculation termed MAGMA incorporating gluonic hot spots via two-point correlators in the Color Glass Condensate framework, and no nucleons, provided a simultaneous match to these flow coefficients measured by the ATLAS experiment, including in ultra-central 0-1% collisions. Our calculations reveal that the MAGMA initial conditions do not describe the experimental data when run through full hydrodynamic SONIC simulations or when the hot spots from one nucleus resolve hot spots from the other nucleus, as predicted in the Color Glass Condensate framework. We also explore alternative initial condition calculations and discuss their implications.

Probing the structure of the initial state of heavy-ion collisions with pT -dependent flow fluctuations

The connection between initial-state geometry and anisotropic flow can be quantified through a well-established mapping between $p_T$-integrated flow harmonics and cumulants of the initial transverse energy distribution. In this paper we successfully extend this mapping to also include $p_T$-differential flow. In doing so, we find that subleading principal components of anisotropic flow can reveal previously unobserved details of the hydrodynamic response, in both the linear and the nonlinear regimes. Most importantly, we show that they provide novel information on the small-scale structures present in the initial stage of relativistic heavy-ion collisions.

Correlations in the Initial Conditions of Heavy-Ion Collisions

Ultracentral collisions of heavy nuclei, in which the impact parameter is nearly zero, are especially sensitive to the details of the initial state model and the microscopic mechanism for collective flow. In a hydrodynamic “flow” picture, the final state momentum correlations are a direct response to the fluctuating initial geometry, although models of the initial geometry differ widely. Alternatively, dynamical mechanisms based in the color glass condensate (CGC) formalism can naturally lead to many-body correlations with very different systematics. Here we present a calculation of event-by-event elliptic flow in both the hydrodynamic and CGC paradigms and show that they can be qualitatively distinguished in ultracentral collisions of deformed nuclei. Specifically, the multiplicity dependence in such collisions is qualitatively opposite, with the CGC correlations increasing with multiplicity while the hydrodynamic correlations decrease. The consistency of the latter with experimental data on UU collisions appears to rule out a CGC-mediated explanation. We find that these qualitative features also persist in small deformed systems and can therefore be a valuable test of the microscopic physics in that regime. The authors acknowledge support from the US-DOE Nuclear Science Grant No. DE-SC0019175, and the Alfred P. Sloan Foundation, and the Zuckerman STEM Leadership Program.

Fluctuations in heavy-ion collisions generated by QCD interactions in the color glass condensate effective theory

Since their discovery, fluctuations in the initial state of heavy-ion collisions have been understood as originating mostly from the random positions of nucleons within the colliding nuclei. We consider an alternative approach where all the focus is on fluctuations generated by QCD interactions, that we evaluate at leading logarithmic accuracy in the color glass condensate effective theory. We validate our approach using BNL Relativistic Heavy Ion Collider (RHIC) and CERN Large Hadron Collider (LHC) data on anisotropic flow. In particular, we show that, compared to standard Glauber-inspired calculations, our formalism provides a better description of the centrality dependence of the ratio of elliptic flow and triangular flow. It also naturally explains the evolution of elliptic flow fluctuations between RHIC and LHC energies.

3-D Glasma initial state from small-x evolution

We present an ab-initio approach to compute the longitudinal dependence of the initial state in heavy-ion collisions by including small-x evolution of the nuclear gluon distributions. Extending the IP-Glasma model by including JIMWLK rapidity evolution, we compute event-by-event rapidity distributions of produced gluons and the early time energy momentum tensor as a function of space-time rapidity and transverse coordinates. We show how the effects of small-x evolution manifest themselves in longitudinal (rapidity) correlations of event-by-event multiplicities and transverse geometry and compare our results to various phenomenological models and experimental observations.

Initial state of Heavy-Ion Collisions: Isotropization and thermalization

I discuss how local thermal equilibrium and hydrodynamical flow are reached in heavy-ion collisions in the weak coupling limit.

Initial-State Quantum Fluctuations in the Little Bang

We review recent developments in the ab initio theoretical description of the initial state in heavy-ion collisions. We emphasize the importance of fluctuations, both for the phenomenological description of experimental data from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) and for the theoretical understanding of the nonequilibrium early-time dynamics and thermalization of the medium.

Measuring the gluon distribution in nuclei at an electron–ion collider

Despite the successes of the HERA collider, where much information was gained on the structure of the nucleon, data on the structure of the nucleus at moderate-to-small x remains elusive, as only fixed-target high- x data currently exist. The small- x region, however, is of great interest. The nucleon structure in this region is dominated by gluons which show a rapid rise with decreasing x . At low- x , this growth must be tamed and the gluon distribution will be saturated. This saturation phenomena is expected to be universal, appearing in both nucleons and nuclei. A knowledge of this regime is of vital importance to understanding the underlying physics which governs the initial conditions of heavy-ion collisions at both the LHC and RHIC, where particle production is dominated by gluons from this unknown region. However, only tantalising hints of this have been observed so far. Therefore, the construction of an Electron–Ion Collider (EIC), colliding polarised electrons with polarised protons and also a wide variety of nuclei, will allow an exploration of the region of small- x in great detail (with luminosities 100 x that of HERA), answering questions on both the spatial and momentum distributions of gluons and sea quarks in nuclei. In particular, the saturation region is more accessible in nuclei due to the amplification of the saturation scale with nuclear size ( Q S ∝ A 1 / 3 ). In this paper I present the current status of measuring the gluon distribution in nuclei in e + A collisions at an EIC.

Directed Flow of Charged Particles at Midrapidity Relative to the Spectator Plane in Pb-Pb Collisions atsNN=2.76 TeV

The directed flow of charged particles at midrapidity is measured in Pb-Pb collisions at √(s(NN))=2.76 TeV relative to the collision symmetry plane defined by the spectator nucleons. A negative slope of the rapidity-odd directed flow component with approximately 3 times smaller magnitude than found at the highest RHIC energy is observed. This suggests a smaller longitudinal tilt of the initial system and disfavors the strong fireball rotation predicted for the LHC energies. The rapidity-even directed flow component is measured for the first time with spectators and found to be independent of pseudorapidity with a sign change at transverse momenta p(T) between 1.2 and 1.7 GeV/c. Combined with the observation of a vanishing rapidity-even p(T) shift along the spectator deflection this is strong evidence for dipolelike initial density fluctuations in the overlap zone of the nuclei. Similar trends in the rapidity-even directed flow and the estimate from two-particle correlations at midrapidity, which is larger by about a factor of 40, indicate a weak correlation between fluctuating participant and spectator symmetry planes. These observations open new possibilities for investigation of the initial conditions in heavy-ion collisions with spectator nucleons.

Phenomenology of High Gluon Density QCD and Heavy-Ion Physics at ISMD 2011: $x$ Smaller than Ever!

I provide a brief summary of the theory presentations at ISMD 2011 related to the phenomenology of small-x QCD evolution and its application to particle production and fluctuations in high-energy hadron and heavy-ion collisions. I also mention some challenges for quantitative phenomenology which emerged from the LHC, such as understanding the long-range "ridge" in high-multiplicity p+p collisions, the transverse momentum distributions in p+p at semi-hard pT, and the origin and scale of density fluctuations in the initial state of heavy-ion collisions.

Quantifying the glue - understanding the initial conditions at RHIC and the LHC

Recent results on the suppression of hadrons at forward rapidities from the STAR collaboration indicate that high gluon densities play an important role in the initial conditions of heavy-ion collisions. The study of these initial conditions is therefore crucial in the next stage of understanding and quantifying the data from RHIC and the LHC. The best way to perform these measurements is through Deep Inelastic Scattering measurements on nuclei. Currently, there are no accelerator facilities which are able to perform this measurement. In this paper, I will outline the latest developments of the eRHIC proposal at BNL as well as preliminary designs of a new detector as well as an assessment of the current detectors (PHENIX and STAR) abilities to run in an eRHIC era.