Heavy-ion collisions create deformed quark-gluon plasma (QGP) fireballs which explode anisotropically. The viscosity of the fireball matter determines its ability to convert the initial spatial deformation into momentum anisotropies that can be measured in the final hadron spectra. A quantitatively precise empirical extraction of the QGP viscosity thus requires a good understanding of the initial fireball deformation. This deformation fluctuates from event to event, and so does the finally observed momentum anisotropy. We present a harmonic decomposition of the initial fluctuations in shape and orientation of the fireball and perform event-by-event ideal fluid dynamical simulations to extract the resulting fluctuations in the magnitude and direction of the corresponding harmonic components of the final anisotropic flow at midrapidity. The final harmonic flow coefficients are found to depend non-linearly on the initial harmonic eccentricity coefficients. We show that, on average, initial density fluctuations suppress the buildup of elliptic flow relative to what one obtains from a smooth initial profile of the same eccentricity, and discuss implications for the phenomenological extraction of the QGP shear viscosity from experimental elliptic flow data.
We show that fluctuations of the fireball shape in the longitudinal direction generate nontrivial rapidity correlations that depend not only on the rapidity difference, y_{1} - y_{2}, but also on the rapidity sum, y_{1} + y_{2}. This is explicitly demonstrated in a simple wounded nucleon model, and the general case is also discussed. We show how to extract different components of the fluctuating fireball shape from the measured two-particle rapidity correlation function. The experimental possibility of studying the longitudinal initial conditions in heavy-ion and proton-proton collisions is em…
A zone of reactions is determined and then exploited as a tool in studying the space-time structure of an interacting system formed in a collision of relativistic nuclei. The time dependence of the reaction rates integrated over spatial coordinates is also considered. Evaluations are made with the help of the microscopic transport model UrQMD. The relation of the boundaries of different zones of reactions and the hypersurfaces of sharp chemical and kinetic freeze-outs is discussed.
We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision dat…
New, analytic solutions of relativistic viscous hydrodynamics are presented, describing expanding fireballs with Hubble-like velocity profile and ellipsoidal symmetry, similar to fireballs created in heavy ion collisions. We find that with these specifications, one obtains solutions where the shear viscosity essentially does not influence the time evolution of the system, thus these solutions are particularly adept tools to study the effect of bulk viscosity alone, which always results in a slower decrease of energy density as well as temperature compared to the case of perfect fluid. We inves…
The production of light nuclei in relativistic heavy-ion collisions is well described by both the thermal model, where light nuclei are in equilibrium with all other hadron species present in a fireball, and by the coalescence model, where light nuclei are formed due to final state interactions after the fireball decays. A method is proposed to falsify one of the models. We suggest to measure a hadron-deuteron correlation function which carries information about the source of the deuterons and allows one to determine whether a deuteron is directly emitted from the fireball or if it is formed a…
We show that the fluctuations in the wounded-nucleon model of the initial stage of relativistic heavy-ion collisions, together with the natural assumption that the forward (backward) moving wounded nucleons emit particles preferably in the forward (backward) direction, lead to an event-by-event torqued fireball. The principal axes associated with the transverse shape are rotated in the forward region in the opposite direction than in the backward region. On the average, the standard deviation of the relative torque angle between the forward and backward rapidity regions is about 20deg for the …
The splitting of elliptic flow measured in different regions of the momentum space of produced hadrons has been recently studied in transport models and proposed as a sensitive probe of the angular momentum carried by the fireball produced in a relativistic heavy ion collision. The initial state angular momentum also gives rise to rapidity odd directed flow which has been measured. We consider a relativistic hydrodynamic framework with the initial matter distribution suitably calibrated to describe the observed directed flow and apply it to study the spilt in the elliptic flow. Our study sugge…
We calculate the elliptic flow of bottomonia produced in Pb$\,+\,$Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV. We consider temperature-dependent decay widths for the anisotropic escape of various bottomonium states and observe that the transverse momentum dependence of bottomonia elliptic flow provides a tomographic information about the QGP fireball at different stages of its evolution. For the space-time evolution of the fireball, we employ simulation results from the 3+1D quasiparticle anisotropic hydrodynamic model. We find that our results for transverse momentum dependence of bottomoni…
We argue that energy and momentum deposition from hard partons into quark-gluon plasma induces an important contribution to the final state hadron anisotropies. We also advocate a novel method of Event Shape Sorting which allow to analyse the azimuthal anisotropies of the fireball dynamics in more detail. A use of the method in femtoscopy is demonstrated.
Thermal dilepton radiation from the hot fireballs created in high-energy heavy-ion collisions provides unique insights into the properties of the produced medium. We first show how the predictions of hadronic many-body theory for a melting $ρ$ meson, coupled with QGP emission utilizing a modern lattice-QCD based equation of state, yield a quantitative description of dilepton spectra in heavy-ion collisions at the SPS and the RHIC beam energy scan program. We utilize these results to systematically extract the excess yields and their invariant-mass spectral slopes to predict the excitation func…
Statistical fluctuations in the transverse distribution of sources in relativistic heavy ion collisions and an asymmetric emission profile associated with the wounded nucleons lead to rapidity dependence of the reaction plane. The size of this effect is estimated for the gold-gold collisions at the highest RHIC energy ($\sqrt{s_{NN}}=200 \mathrm{GeV}$) in the Glauber model using GLISSANDO. The hydrodynamical evolution of the resulting torqued fireball is carried out in 3+1 dimensions considering a perfect fluid. Hadronization is simulated using THERMINATOR including non-flow contribution comin…
The paper briefly presents history, status, and plans of the search for the critical structures - the onset of fireball, the onset of deconfinement, and the deconfinement critical point - in high energy nucleus-nucleus collisions. First, the basic ideas are introduced, the history of the observation of strongly interacting matter in heavy ion collisions is reviewed, and the path towards the quark-gluon plasma discovery is sketched. Then the status of the search for critical structures is discussed - the discovery of the onset of deconfinement, indications for the onset of fireball, and still i…
The solutions of relativistic viscous hydrodynamics for longitudinal expanding fireballs is investigated with the Navier-Stokes theory and Israel-Stewart theory. The energy and Euler conservation equations for the viscous fluid are derived in Rindler coordinates with the longitudinal expansion effect is small. Under the perturbation assumption, an analytical perturbation solution for the Navier-Stokes approximation and numerical solutions for the Israel-Stewart approximation are presented. The temperature evolution with both shear viscous effect and longitudinal acceleration effect in the long…
In this paper we use methods developed in Part 1 of The Dipion Cocktail, to fit the $p_t$ dependence of dipions for mid-central Au-Au collisions at $\sqrt{s_{NN}}$=200 GeV. For the minijet fragmentation part we use PYTHIA fragmentation as described in Part 1. For the thermal resonance production we use an exponential growth behavior. The interference between the direct production of dipion pairs from non-resonance minijet fragmentation and re-scattering through resonance states gives a measure of the size of the re-scattering region. This size is contain in the $α$ parameter of Part1. We assum…
In nuclear collisions at highest accessible LHC energies, often more than one dijet pairs deposit momentum into the deconfined expanding medium. With the help of 3+1 dimensional relativistic hydrodynamic simulation we show that this leads to measurable contribution to the anisotropy of collective transverse expansion. Hard partons generate streams in plasma which merge if they come close to each other. This mechanism correlates the resulting contribution to flow anisotropy with the fireball geometry and causes an increase of the elliptic flow in non-central collisions.
In the article, the fireball formed in the collision of relativistic nuclei is considered as a quantum object. Based on this, an attempt is made to explain the difference in the measurements of hyperon yields in the two experiments - NA49 and NA57. Using the basic principles of quantum mechanics, it was shown that a fireball can have two quantum states - with and without ignited Quark-Gluon Plasma (QGP). With an increase of the collision energy of heavy ions, the probability of QGP ignition increases. At the same time, the probability of the formation of fireball without QGP ignition also rema…
In high energy collisions involving small nuclei (p+p or x+Au collisions where x=p, d, or $^3$He) the fluctuating size, shape and internal gluonic structure of the nucleon is shown to have a strong effect on the initial size and shape of the fireball of new matter created in the collision. A systematic study of the eccentricity coefficients describing this initial fireball state for several semi-realistic models of nucleon substructure and for several practically relevant collision systems involving small nuclei is presented. The key importance of multiplicity fluctuations in such systems is p…
We apply the ``zone of reactions'' as a tool in studying the interacting system formed in a collision of relativistic nuclei. With the use of the intensity of collisions of particles (the number of collisions in unit volume per unit time), we study the space-time structure of a fireball. In this approach, three basic regions for the evolution of a system are separated by the scale of the intensity of collisions: the zone of a hot fireball, the zone of a cold fireball, and the zone of residual interaction. It is shown that the conception of a zone of reactions can be used for the determination …
Utilizing a recently found class of exact, analytic rotating solutions of non-relativistic fireball hydrodynamics, we calculate analytically the single-particle spectra, the elliptic flows and two-particle Bose-Einstein correlation functions for rotating and expanding fireballs with spheroidal symmetry. We demonstrate, that rotation generates final state momentum anisotropies even for a spatially symmetric, spherical initial geometry of the fireball. The mass dependence of the effective temperatures, as well as the HBT radius parameters and the elliptic flow are shown to be sensitive not only …
The interferometric radii in the system formed in ultra-relativistic proton-lead collisions are investigated in a framework based on event-by-event 3+1 dimensional viscous hydrodynamics. We argue that the most central p-Pb collisions undergoing collective expansion behave similarly to the peripheral nucleus-nucleus collisions. The interferometric observables can serve as signatures of the formation of an extended fireball.
Predictions are made for elliptic flow in collisions of polarized deuterons with a heavy nucleus. It is shown that the eccentricity of the initial fireball, evaluated with respect to the deuteron polarization axis perpendicular to the beam direction, has a substantial magnitude for collisions of highest multiplicity. Within the Glauber approach we obtain $\sim 7\%$ for the deuteron states with spin projection 0, and $\sim -3 \%$ for spin projection $\pm 1$. We propose to measure the elliptic flow coefficient as the second order harmonic coefficient in the azimuthal distribution of produced cha…
The expansion of the fireball created in Au-Au collisions at 200GeV and Pb-Pb collisions at 2.76TeV is modelled using the relativistic viscous hydrodynamics. The experimentally observed interferometry radii are well reproduced. Additional pre-equilibrium flow improves slightly the results for the lower energies studied.
We review the potential of precise measurements of electromagnetic probes in relativistic heavy-ion collisions for the theoretical understanding of strongly interacting matter. The penetrating nature of photons and dileptons implies that they can carry undistorted information about the hot and dense regions of the fireballs formed in these reactions and thus provide a unique opportunity to measure the electromagnetic spectral function of QCD matter as a function of both invariant mass and momentum. In particular we report on recent progress on how the medium modifications of the (dominant) iso…
We argue that relativistic nuclear collisions may provide experimental evidence of alpha clustering in light nuclei. A light alpha-clustered nucleus has a large intrinsic deformation. When collided against a heavy nucleus at very high energies, this deformation transforms into the deformation of the fireball in the transverse plane. The subsequent collective evolution of the fireball leads to harmonic flow reflecting the deformation of the initial shape, which can be measured with standard methods of relativistic heavy-ion collisions. We illustrate the feasibility of the idea by modeling the 1…
我们确定的主要物理学里程碑的发展奇怪的强子作为一个可观察的夸克-胶子等离子体的形成，并随后爆炸解体的解除约束的物质火球形成的相对论性重离子碰撞在160- 20 A GeV。我们描述了QGP相的物理性质，并根据强子丰度的分析表明与预期一致。我们还证明了强子谱的m_t形状与过冷QGP火球的突然破裂是定性一致的。
Many probes are proposed to determine the quark-gluon plasma and explore its properties in ultra-relativistic heavy-ion collisions. Some of them are related to initial states of the collisions, such as collective flow, Hanbury-Brown-Twiss (HBT) correlation, chiral magnetic effects and so on. The initial states can come from geometry overlap of the colliding nuclei, fluctuations or nuclear structure with the intrinsic geometry asymmetry. The initial geometry asymmetry can transfer to the final momentum distribution in the aspect of hydrodynamics during the evolution of the fireball. Different f…
格点QCD的结果提供了一个机会，模型，并外推到有限重子密度，性质的夸克-胶子等离子体（QGP）。在将热耦合常数和真空能的标度固定到格点数据上后，得到了QGP状态方程的性质。结果表明，我们提出的QGP-EoS模型能很好地描述CERN SPS实验中重离子碰撞形成的致密物质火球的物理性质。我们还估计了在核碰撞的早期阶段形成的火球的属性，并认为，QGP的形成必须预计到40 A GeV的中心铅-铅相互作用。
We study the effect of vorticity present in heavy ion collisions (HICs) on the temperature evolution of hot quark-gluon plasma in the presence of spin-vorticity coupling. The initial global rotation entails a nontrivial dependence of the longitudinal flow velocity on the transverse coordinates and also develops a transverse velocity component that depends upon the longitudinal coordinate. Both of these velocities lead to a 2+1 dimensional expansion of the fireball. It is observed that with finite vorticity and spin-polarization the fireball cools faster as compared to the case without vorticit…
We attempt to describe the rapidity and transverse momentum spectra of strange as well as non-strange hadrons e.g. cascade,cascadebar, lambda , lambdabar, proton, protonbar,(omega+omegabar, Kaon, anti-Kaon and their ratios in the ultra-relativistic collisions of gold nuclei at (Root sNN)=200 GeV. This is done by using a statistical thermal freeze-out model which incorporates the rapidity (collision) axis as well as transverse direction boosts developed within an expanding hot and dense hadronic fluid (fireball) till the final freeze-out. We determine the thermo-chemical freeze-out conditions p…
Baryon and energy densities, which are reached in central Au+Au collisions at collision energy of $\sqrt{s_{NN}}= 39$ GeV, are estimated within the model of three-fluid dynamics. It is shown that the initial thermalized mean proper baryon and energy densities in a sizable central region approximately are $n_B/n_0 \approx$ 10 and $\varepsilon\approx$ 40 GeV/fm$^3$, respectively. The study indicates that the deconfinement transition at the stage of interpenetration of colliding nuclei makes the system quite opaque. The final fragmentation regions in these collisions are formed not only by primor…
We show how ultra-relativistic collisions of light nuclei with heavy targets may be used to record snap-shots of the ground-state configurations and reveal information on cluster correlations. The development of collective flow in the formed fireball, which reflects the geometric correlations in the initial state, is essential for the method. As an illustration we analyze the 12C-208Pb collisions.
We discuss the torque effect in the initial fireball formed in relativistic heavy-ion collisions, manifesting itself, on the event-by-event basis, in a relative angle between the principal axes of the transverse momentum distributions in the forward and backward rapidity regions. The torque follows from two natural features: 1) the sources of particles (e.g. wounded nucleons) emit predominantly in their forward hemispheres, and 2) there exist fluctuations in the transverse distribution of sources from the two colliding nuclei. On the average, the standard event-by-event deviation of the relati…
A new exact and analytic solution of non-relativistic fireball hydrodynamics is presented. It describes an expanding triaxial ellipsoid that rotates around one of its principal axes. The observables are calculated using simple analytic formulas. Azimuthal oscillation of the off-diagonal Bertsch-Pratt radii of Bose-Einstein correlations as well as rapidity dependent directed and third flow measurements provide means to determine the magnitude of the rotation of the fireball. Observing this rotation and its dependence on collision energy may lead to new information on the equation of state of th…
Nuclei are nearly transparent to each other when they collide at high energy, but the collisions do produce high energy density matter in the central rapidity region where most experimental measurements are made. What happens to the receding nuclear fireballs? We calculate the energy loss of the nuclei using the color glass condensate model. We then use a simple space-time picture of the collision to calculate the baryon and energy densities of the receding fireballs. For central collisions of large nuclei at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider we find ba…
We study the effect that initial state fluctuations have on final particle correlations in heavy ion collisions. More precisely, we focus on the propagation of initial perturbations on top of the expanding fireball using the conformal solution derived by Gubser and Yarom for central collisions. For small perturbations, the hydrodynamic equations are solved by separation of variables and the solutions for different modes are added up to construct initial point-like perturbations, that are then allowed to evolve until freeze-out. The Cooper-Frye prescription is used to determine the final partic…
The production of the $X(3872)$ particle in heavy-ion collisions has been contemplated as an alternative probe of its internal structure. To investigate this conjecture, we perform transport calculations of the $X(3872)$ through the fireball formed in nuclear collisions at the LHC. Within a kinetic-rate equation approach as previously used for charmonia, the formation and dissociation of the $X(3872)$ is controlled by two transport parameters, i.e., its inelastic reaction rate and thermal-equilibrium limit in the evolving hot QCD medium. While the equilibrium limit is controlled by the charm p…
