Collective flow of the final-state hadrons observed in ultrarelativistic heavy-ion collisions or even in smaller systems formed in high-multiplicity pp and p/d/$^3$He-nucleus collisions is one of the most important diagnostic tools to probe the initial state of the system and to shed light on the properties of the short-lived, strongly-interacting many-body state formed in these collisions. Limited, in the initial years, to the study of mainly the directed and elliptic flows -- the first two Fourier harmonics of the single-particle azimuthal distribution -- this field has evolved in recent years into a much richer area of activity. This includes not only higher Fourier harmonics and multiparticle cumulants, but also a variety of other related observables, such as the ridge seen in two-particle correlations, flow decorrelation, symmetric cumulants and event-plane correlators which measure correlations between the magnitudes or phases of the complex flows in different harmonics, coefficients that measure the nonlinear hydrodynamic response, statistical properties, such as the non-Gaussianity of the flow fluctuations, etc. We present a Tutorial Review of the modern flow picture and the various aspects of the collectivity -- an emergent phenomenon in quantum chromodynamics.
Hanbury Brown--Twiss interferometry (HBT) provides crucial insights into both the space-time structure and the momentum-space evolution of ultrarelativistic nuclear collisions at freeze-out. In particular, the dependence of the HBT radii on the transverse pair momentum $K_T$ and the system charged multiplicity $dN_{\mathrm{ch}}/dη$ may reflect the mechanisms driving collective behavior in small systems. This paper argues that certain features observed in the multiplicity dependence of the HBT radii can be naturally understood if small systems evolve hydrodynamically at high-multiplicity. This …
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.
We discuss the use of the hydrodynamic model for the description of the evolution of dense matter formed in ultrarelativistic heavy-ion collisions. The collective flow observed in heavy-ion collisions at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider is consistent with the assumption that a fireball of strongly interacting matter is formed. Experimental results from p-Pb and d-Au collisions show similar phenomena, which suggests that collective expansion appears in small systems as well. We review the recent application of the hydrodynamic model to small systems …
We analyze the phenomenon of size-flow transmutation in ultrarelativistic nuclear collisions in a model where the initial size fluctuations are driven by the wounded quarks and the collectivity is provided by viscous hydrodynamics. It is found that the model properly reproduces the data for the transverse momentum fluctuations measured for Pb+Pb collisions at 2.76TeV by the ALICE Collaboration. The agreement holds for a remarkably wide range of centralities, from 0-5% up to 70-80%, and displays a departure from a simple scaling with $(dN_{\rm ch}/dη)^{1/2}$ in the form seen in the data. The ov…
Collective flow and femtoscopy in ultrarelativistic 3He-Au collisions are investigated within the 3+1-dimensional (3+1D) viscous event-by-event hydrodynamics. We evaluate elliptic and triangular flow coefficients as functions of the transverse momentum. We find the typical long-range ridge structures in the two-particle correlations in the relative azimuth and pseudorapidity, in the pseudorapidity directions of both Au and 3He. We also make predictions for the pionic interferometric radii, which decrease with the transverse momentum of the pion pair. All features found hint on collectivity of …
At the colliders RHIC and LHC, nuclei at the ultrarelativistic energies of $100$ GeV/A and $2.7$ TeV/A will be smashed together with the hope of creating an elusive and short-lived state of matter called the quark gluon plasma. The initial conditions which determine the dynamical evolution of the quark gluon matter formed in the central region after the collision depend crucially on the small $x$ component of the nuclear wavefunction before the collision. In this comment, we discuss recent work which argues that, for large nuclei, weak coupling techniques in QCD can be used to calculate the di…
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.
It is possible that isospin violating dynamical effects are amplified due to coherence if a disoriented chiral condensate (or other source of a coherent pion state) is formed in a heavy ion collison. It is shown explicitly that altering the isospin of the coherent state by order of one unit can change the number of $π^0$'s in the condensate by some finite fraction of the total number. A possible signature of such amplified isospin violating effects is that the ratio of neutral to total low $p_T$ pions averaged over many events may differ markedly from 1/3. Such a signal would not be washed out…
We suggest that the ultrarelativistic collisions of heavy ions provide the simplest situation for the study of strong interactions which can be understood from first principles and without any model assumptions about the microscopic structure of the colliding nuclei. We argue that the boost-invariant geometry of the collision, and the existence of hard partons in the final states, both supported by the data, make a sufficient basis for the quantum theory of the phenomenon. We conclude that the quantum nature of the entire process is defined by its global geometry, which is enforced by a macros…
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 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…
The formation and collective expansion of the fireball formed in ultrarelativistic p-A and d-A collisions is discussed. Predictions of the hydrodynamic model are compared to recent experimental results. The presence of strong final state interaction effects in the small dense systems is consistent with the observed azimuthal anisotropy of the flow and with the mass dependence of the average transverse momentum and of the elliptic flow. This raises the question of the mechanism explaining such a rapid build up of the collective flow and the large degree of local equilibration needed to justify …
We study the role of anisotropic escape in generating the elliptic flow of bottomonia produced in ultrarelativistic heavy-ion collisions. We implement temperature-dependent decay widths for the various bottomonium states, to calculate their survival probability when traversing through the anisotropic hot medium formed in non-central collisions. We employ the recently developed 3+1d quasiparticle anisotropic hydrodynamic simulation to model the space-time evolution of the quark-gluon plasma. We provide a quantitative prediction for transverse momentum dependence of bottomonium elliptic flow and…
We consider the evolution of a parton system which is formed at the central rapidity region just after an ultrarelativistic heavy ion collision. The evolution of the system, which is composed of gluons, quarks and antiquarks, is described by a relativistic Boltzmann equations with collision terms including radiation and retardation effects. The equations are solved by the test particle method using Monte-Carlo sampling. Our simulations do not show any evidence of kinetic equilibration, unless the cross sections are artificially increased to unrealistically large values.
Anisotropic high energy density domains may be formed at early stages of ultrarelativistic heavy ion collisions, e.g. due to phase transition dynamics or non-equilibrium phenomena like (mini-)jets. Here we investigate hadronic observables resulting from an initially created anisotropic high energy density domain. Based on our studies using a transport model we find that the initial anisotropies are reflected in the freeze-out multiplicity distribution of both pions and kaons due to secondary hadronic rescattering. The anisotropy appears to be stronger for particles at high transverse momenta. …
Anomalous centrality evolution of two-particle angular correlations observed in Au-Au collisions at $\sqrt{s_{NN}} = 62$ and 200 GeV and the onset of ridge structures are considered in the model of interacting quark-gluon strings. We assume that at the given energy of nucleus-nucleus collisions the critical energy density may be reached at the specific centrality. In a string percolation model this might be treated equivalently to a formation of a large cluster of strings characterized by the critical string density, with a size comparable to the whole area of interaction of two nuclei. This h…
We explore predictions of the wounded quark model for particle production and properties of the initial state formed in ultrarelativistic heavy-ion collisions. The approach is applied uniformly to A+A collisions in a wide collision energy range, as well as for p+A and p+p collisions at the CERN Large Hadron Collider (LHC). We find that generically the predictions from wounded quarks for such features as eccentricities or initial sizes are close (within 15\%) to predictions of the wounded nucleon model with an amended binary component. A larger difference is found for the size in p+Pb system, w…
As a result of multiple mini-jet production, initial conditions of the QCD plasma formed in ultrarelativistic nuclear collisions may be inhomogeneous, with large fluctuations of the local energy density (hot spots), and turbulent, with a chaotic initial transverse velocity field. Assuming rapid local thermalization, the evolution of such plasmas is computed using longitudinal boost-invariant 3+1-dimensional hydrodynamics. We compare the evolution in case that the speed of sound in the plasma is constant to one resulting from an equation of state involving a strong first order transition, with …
Complete evolution of the strongly interacting matter formed in ultrarelativistic heavy-ion collisions is studied within a coupled Boltzmann and relativistic viscous hydrodynamics approach. For the initial nonequilibrium evolution phase, we employ the AMPT model that explicitly includes event-by-event fluctuations in the number and positions of the participating nucleons as well as of the produced partons with subsequent parton transport. The ensuing near-equilibrium evolution of quark-gluon and hadronic matter is modeled within the (2+1)-dimensional viscous hydrodynamics. We probe the role of…
