Critical fluctuations in a dynamically expanding heavy-ion collision
Masakiyo Kitazawa, Grégoire Pihan, Nathan Touroux, Marcus Bluhm, Marlene Nahrgang
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4 pages 5 figures, contribution to the proceedings of XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2019)
For the discovery of the QCD critical point it is crucial to develop dynamical models of the fluctuations of the net-baryon number that can be embedded in simulations of heavy-ion collisions. In this proceeding, we study the dynamical formation of the critical fluctuations of the net-baryon number near the QCD critical point and their survival in the late stages in an expanding system. The stochastic diffusion equation with a non-linear free energy functional is employed for describing the evolution of conserved-charge fluctuations along trajectories in the crossover and first-order transition regions near the QCD critical point.
We calculate the Lambda polarization in an exact analytical, rotating model based on parameters extracted 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
The question of decoupling and freeze-out is reinvestigated and analysed in terms of transparent semi-classical decoupling formulae, which provide a smooth decoupling in time both, for single and two particle inclusive spectra. They generalise frequently employed instantaneous freeze-out procedures and provide simple relations between the damping width and the duration of the decoupling process. The implications on physical phenomena arising from the expansion and decay dynamics of the highly compressed hadronic matter generated in high energy nuclear collisions are discussed.
The work distribution of an expanding extreme relativistic gas is shown to be a gamma distribution with a different shape parameter as compared with its non-relativistic counterpart. This implies that the shape of the transverse energy distribution in relativistic heavy ion collisions depends on the particle contents during the evolution of the hot and dense matter. Therefore, transverse energy fluctuations provide additional insights into the Quark-Gluon Plasma produced in these collisions.
We present a relativistic molecular dynamics approach based on the Nambu--Jona-Lasinio Lagrangian. We derive the relativistic time evolution equations for an expanding plasma, discuss the hadronization cross section and how they act in such a scenario. We present in detail how one can transform the time evolution equation to a simulation program and apply this program to study the expansion of a plasma created in experiments at RHIC and LHC. We present first results on the centrality dependence of $v_2$ and of the transverse momentum spectra of pions and kaons and discuss in detail the hadroni…
The freeze out (FO) of the expanding systems, created in relativistic heavy ion collisions, is discussed. We start with kinetic FO model, which realizes complete physical FO in a layer of given thickness, and then combine our gradual FO equations with Bjorken type system expansion into a unified model. We shall see that the basic FO features, pointed out in the earlier works, are not smeared out by the expansion.
We study viscous effects on heavy quark radiative energy loss in a dynamically screened medium with boost-invariant longitudinal expansion. We calculate, to first order in opacity, the energy loss by incorporating viscous corrections in the single-particle phase-space distribution function within relativistic dissipative hydrodynamics. We consider the Grad's 14-moment and the Chapman-Enskog-like methods for the nonequilibrium distribution functions. Our numerical results for the charm quark radiative energy loss show that, as compared to static fluid, an expanding ideal (nonviscous) fluid caus…
We propose Kolmogorov-Smirnov test as a means for recognising event-by-event fluctuations of rapidity distributions in relativistic heavy ion collisions. Such fluctuations may be induced by the spinodal decomposition of the rapidly expanding system during the 1st order quark-hadron phase transition.
Peripheral heavy ion reactions at ultra relativistic energies have large angular momentum that can be studied via two particle correlations using the Differential Hanbury Brown and Twiss method. We analyze the possibilities and sensitivity of the method in a rotating system. We also study an expanding solution of the fluid dynamical model of heavy ion reactions.
We use kinetic theory in order to study the role of quantum fluctuations in the isotropization of the pressure tensor in a system subject to fast longitudinal expansion, such as the matter produced in the early stages of a heavy ion collision.
We present a realistic expanding source model with nine parameters that are necessary and sufficient to describe the main physics occuring during hydrodynamical freezeout of the excited hadronic matter produced in relativistic heavy-ion collisions. As a first test of the model, we compare it to data from central Si + Au collisions at p_lab/A = 14.6 GeV/c measured in experiment E-802 at the AGS. An overall chi-square per degree of freedom of 1.055 is achieved for a fit to 1416 data points involving invariant pi^+, pi^-, K^+, and K^- one-particle multiplicity distributions and pi^+ and K^+ two-p…
We introduce a new realistic expanding source model for invariant one-particle multiplicity distributions and two-particle correlations in nearly central relativistic heavy-ion collisions that contains nine adjustable parameters, which are necessary and sufficient to properly characterize the gross properties of the source during its freezeout from a hydrodynamical fluid into a collection of noninteracting, free-streaming hadrons. These nine physically relevant parameters fall into three categories of three parameters each, with the first category corresponding to the source's longitudinal mot…
We propose intensity interferometry with identical lepton pairs as an efficient tool for the estimation of the source size of the expanding hot zone produced in relativistic heavy ion collisions. This can act as a complementary method to two photon interferometry. The correlation function of two electrons with the same helicity has been evaluated for RHIC energies. The thermal shift of the rho meson mass has negligible effects on the HBT radii.
We consider the (3+1) dimensional expansion and cooling of the chirally-restored and deconfined matter at finite net-baryon densities as expected in heavy-ion collisions at moderate energies. In our approach, we consider chiral fields and the Polyakov loop as dynamical variables coupled to a medium represented by a quark-antiquark fluid. The interaction between the fields and the fluid leads to dissipation and noise, which in turn affect the field fluctuations. We demonstrate how inhomogeneities in the net-baryon density may form during an evolution through the spinodal region of the first-ord…
We explore the ability of a recently proposed jet substructure technique, Dynamical Grooming, to pin down the properties of the Quark-Gluon Plasma formed in ultra-relativistic heavy-ion collisions. In particular, we compute, both analytically and via Monte-Carlo simulations, the opening angle $θ_g$ of the hardest splitting in the jet as defined by Dynamical Grooming. Our calculation, grounded in perturbative QCD, accounts for the factorization in time between vacuum-like and medium-induced processes in the double logarithmic approximation. We observe that the dominating scale in the $θ_g$-dist…
We study the radiation of thermal photons and dileptons likely to be produced in relativistic heavy ion collisions. We find that the thermal photon multiplicity scales with the charged pion multiplicity as $dN_{ch}/dy)^α$ with $α\sim 1.2$ for a transversely expanding system, contrary to the general belief of a quadratic dependence. The scaling is shown to be valid, both for real and virtual photons. The coefficient of proportionality at a given energy may help us identify the appropriate equation of state of hot hadronic matter produced in such collisions.
We develop a new dynamical model for high energy heavy-ion collisions in the beam energy region of the highest net-baryon densities on the basis of non-equilibrium microscopic transport model JAM and macroscopic 3+1D hydrodynamics by utilizing a dynamical initialization method. In this model,dynamical fluidization of a system is controlled by the source terms of the hydrodynamic fields. In addition, time dependent core-corona separation of hot regions is implemented. We show that our new model describes multiplicities and mean transverse mass in heavy-ion collisions within a beam energy region…
We present for the first time quantitative results for the coupled dynamics of second order fluctuations in the three conserved charges of QCD based on stochastic diffusion equations for a Bjorken-type expanding hadronic medium.
We investigate the instability of classical Yang-Mills field in an expanding geometry under a color magnetic background field within the linear regime. We consider homogeneous, boost-invariant and time-dependent color magnetic fields simulating the glasma configuration. We introduce the conformal coordinates which enable us to map an expanding problem approximately into a nonexpanding problem. We find that the fluctuations with finite longitudinal momenta can grow exponentially due to parametric instability. Fluctuations with finite transverse momenta can also show parametric instability, but …
The bulk and shear viscosities ($η$ and $ζ$) have been studied for quark-gluon-plasma produced in relativistic heavy ion collisions within semi-classical transport theory, in a recently proposed quasi-particle model of (2+1)-flavor lattice QCD equation of state. These transport parameters have been found to be highly sensitive to the interactions present in hot QCD. Contributions to the transport coefficients from both the gluonic sector and the matter sector have been investigated. The matter sector is found to be significantly dominating over the gluonic sector, in both the cases of $η$ and …
Axial charge production at the early stage of heavy-ion collisions is investigated within the framework of real-time lattice simulations at leading order in QCD coupling. Starting from color glass condensate initial conditions, the time evolution of quantum quark fields under classical color gauge fields is computed on a lattice in longitudinally expanding geometry. We consider simple color charge distributions in Lorentz contracted nuclei that realize flux tube-like configurations of color fields carrying nonzero topological charge after a collision. By employing the Wilson fermion extended t…
We derive expressions for various correlators of the gauge field and find the propagators in Hamiltonian dynamics which employs a new gauge $A^τ=0$. This gauge is a part of the wedge form of relativistic dynamics suggested earlier as a tool for the study of quantum dynamics in ultra-relativistic heavy ion collisions. We prove that the gauge is completely fixed. The gauge field is quantized and the field of radiation and the longitudinal fields are unambiguously separated. The new gauge puts the quark and gluon fields of the colliding hadrons in one Hilbert space and thus allows one to avoid fa…
In two previous works [arXiv:1009.4363,arXiv:1107.0668], we studied the time evolution of a system of real scalar fields with quartic coupling which shares important features with the Color Glass Condensate description of heavy ion collisions. Our primary objective was to understand how such a system, when initialized with a non-perturbatively large classical field configuration, reaches thermal equilibrium. An essential goal of these works was to highlight the role played by the quantum fluctuations. However, these studies considered only a system confined within a box of fixed volume. In the…
We present theoretical approaches to high energy nuclear collisions in detail putting a special emphasis on technical aspects of numerical simulations. Models include relativistic hydrodynamics, Monte-Carlo implementation of k_T-factorization formula, jet quenching in expanding fluids, a hadronic transport model and the Vlasov equation for colored particles.
We propose a new scenario characterizing the transition of the quark-gluon plasma (QGP) produced in heavy-ion collisions from a highly non-equilibrium state at early times toward a fluid described by hydrodynamics at late times. We develop an analogy to the evolution of a quantum mechanical system that is governed by the instantaneous ground states. In the simplest case, these slow modes are "pre-hydrodynamic" in the sense that they are initially distinct from, but evolve continuously into, hydrodynamic modes. For a class of collision integrals, the pre-hydrodynamic mode represents the angular…
By solving the rate equation in an expanding quark-gluon plasma, we study thermal production of charm quarks in central Pb+Pb collisions at the Future Circular Collider. With the charm quark production cross section taken from the perturbative QCD at the next-to-leading order, we find that charm quark production from the quark-gluon plasma can be appreciable compared to that due to initial hard scattering between colliding nucleons.
We report an extension of the source imaging method for analyzing three-dimensional sources from three-dimensional correlations. Our technique consists of expanding the correlation data and the underlying source function in spherical harmonics and inverting the resulting system of one-dimensional integral equations. With this strategy, we can image the source function quickly, even with the finely binned data sets common in three-dimensional analyses.
The time evolution of collective modes in an expanding ultarelativistic and (effectively) Abelian plasma is studied in the hard-loop approximation semi-analytically by means of integro-differential equations. A previous treatment is generalized to arbitrary orientation of wave vectors with respect to the direction of anisotropy and thus to a fully 3+1 dimensional situation. Moreover, initial fluctuations are allowed in both gauge fields and currents, which is necessary in the case of (stable) longitudinal modes. For unstable (Weibel) modes, this generalization of initial conditions reduces dra…
Due to long chemical equilibration times within standard hadronic reactions during the hadron gas phase in relativistic heavy ion collisions it has been suggested that the hadrons are "born" into equilibrium after the quark gluon plasma phase. Here we develop a dynamical scheme in which possible Hagedorn states contribute to fast chemical equilibration times of baryon anti-baryon pairs (as well as kaon anti-kaon pairs) inside a hadron gas and just below the critical temperature. Within this scheme, we use master equations and derive various analytical estimates for the chemical equilibration t…
Bose-Einstein correlations and invariant momentum distributions are analyzed for longitudinally expanding finite systems, like jets in elementary particle collisions or systems created in high energy heavy ion reactions. Cross-term generating hyperbolic mixing angle is introduced for HBT. Temporal or spatial temperature gradients are shown to contribute to thermal length and time scales for HBT. Results are illustrated in three figures.
An expanding fireball model with two freeze-outs, which assumes that the chemical freeze-out occurs earlier at higher temperature and the thermal freeze-out occurs later at lower temperature, is developed and successfully applied to fit simultaneously the hadron ratios, transverse momentum spectra of measured hadrons and rapidity distribution of charged hadrons measured in Au+Au collision at 200 A$\cdot$GeV by STAR, PHENIX and PHOBOS collaborations. The quality of all the fittings is very good and the resulting parameters are in agreement with published values.
The influence of the nuclear Coulomb field on transverse spectra of $π^+$ and $π^-$ measured in $Pb+Pb$ reactions at 158 A GeV has been investigated. Pion trajectories are calculated in the field of an expanding fireball. The observed enhancement of the $π^-/π^+$ ratio at small momenta depends on the temperature and transverse expansion velocity of the source, the rapidity distribution of the net positive charge, and mainly the time of the freeze-out.
Hot gluons are the dominant components of the QCD plasma to be formed in future high energy heavy ion experiments. In this paper we study the elementary processes in the plasma medium for gluon multiplication based on all orders of the tree-diagrams in perturbative QCD. When applying to the chemical equilibration in the expanding system, we found that the gluons reaches chemical equilibrium well within its plasma phase. The inclusion of all the next-to-leading order processes makes the equilibration considerably faster than the simple $gg\leftrightarrow ggg$ one considered previously.
The formation of Mach cones is studied in a full $(3+1)$-dimensional setup of ultrarelativistic heavy-ion collisions, considering a transverse and longitudinal expanding medium at Relativistic Heavy-Ion Collider energies. For smooth initial conditions and central collisions the jet-medium interaction is investigated using high-energy jets and various values of the ratio of shear viscosity over entropy density, $η/s$. For small viscosities, the formation of Mach cones is proven, whereas for larger viscosities the characteristic structures smear out and vanish eventually. The formation of a doub…
Evolution of spatially anisotropic perturbation created in the system formed after Relativistic Heavy Ion Collisions has been studied. The microscopic evolution of the fluctuations has been examined within the ambit of Boltzmann Transport Equation (BTE) in a hydrodynamically expanding background. The expansion of the background composed of Quark Gluon Plasma (QGP) is treated within the framework of relativistic hydrodynamics. Spatial anisotropic fluctuations with different geometry have been evolved through Boltzmann equation. It is observed that the trace of such fluctuation survive the evolu…
Collective phenomena in quantum many-body systems are often described in terms of hydrodynamics, an appropriate framework when the involved particle numbers are effectively macroscopic. We propose to use experiments on expanding clouds of few and many interacting cold atoms to investigate the emergence of hydrodynamics as a function of particle number. We consider gases confined in two-dimensional elliptically-deformed traps, and we employ the manifestation of elliptic flow as an indicator of collective behavior. We quantify the response of the gas to the deformation of the trapping potential,…
We present a concise review of the recent development of relativistic hydrodynamics and its applications to heavy-ion collisions. Theoretical progress on the extended formulation of hydrodynamics towards out-of-equilibrium systems is addressed, emphasizing the so-called attractor solution. On the other hand, recent phenomenological improvements in the hydrodynamic modeling of heavy-ion collisions with respect to the ongoing Beam Energy Scan program, the quantitative characterization of transport coefficients in the three-dimensionally expanding quark-gluon plasma, the fluid description of smal…
Within the AMPT Monte Carlo model, hot spots in the initial transverse parton density are shown to lead to harmonic flows which all contribute to dihadron azimuthal correlation. The net back-to-back dihadron correlation after subtraction of harmonic flows still has a double-peak that is independent of the initial geometric triangularity at a fixed impact-parameter and unique to the structure of jet-induced Mach cone and expanding hot spots dragged by radial flow. The longitudinal structure of hot spots also leads to a near-side ridge in dihadron correlation with a large rapidity gap. By succes…
