Review of Anisotropic Flow Correlations in Ultrarelativistic Heavy-Ion Collisions

The first results from heavy ion collisions at the Large Hadron Collider for charged particle spectra and elliptic flow are compared to an event-by-event hybrid approach with an ideal hydrodynamic expansion. This approach has been shown to successfully describe bulk observables at RHIC. Without changing any parameters of the calculation the same approach is applied to Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. This is an important test if the established understanding of the dynamics of relativistic heavy ion collisions is also applicable at even higher energies. Specifically, we employ the hybrid approach with two different equations of state and the pure hadronic transport approach to indicate sensitivities to finite viscosity. The centrality dependence of the charged hadron multiplicity, $p_T$ spectra and differential elliptic flow are shown to be in reasonable agreement with the ALICE data. Furthermore, we make predictions for the transverse mass spectra of identified particles and triangular flow. The eccentricities and their fluctuations are found to be surprisingly similar to the ones at lower energies and therefore also the triangular flow results are very similar. Any deviations from these predictions will indicate the need for new physics mechanisms responsible for the dynamics of heavy ion collisions.

These lectures are an elementary introduction to various experimental signatures of collective motion in ultrarelativistic heavy ion collisions: relation between transverse momenta and multiplicities, identified particle spectra, HBT correlations, and elliptic flow.

Anisotropic flows ($v_2$ and $v_4$) of hadrons and light nuclear clusters are studied by a partonic transport model and nucleonic transport model, respectively, in ultra-relativistic and intermediate energy heavy ion collisions. Both number-of-constituent-quark scaling of hadrons, especially for $\phi$ meson which is composed of strange quarks, and number-of-nucleon scaling of light nuclear clusters are discussed and explored for the elliptic flow ($v_2$). The ratios of $v_4/v_2^2$ of hadrons and nuclear clusters are, respectively, calculated and they show different constant values which are independent of transverse momentum. The above phenomena can be understood, respectively, by the coalescence mechanism in quark-level or nucleon-level.

We study the correlations between light flavor and heavy quarks (HQs) flow harmonics at LHC energy within a transport approach. We have investigated the role of transport coefficient in developing these anisotropic flows correlations. We suggest correlation and the relative fluctuations of anisotropic flows συη /〈υn 〉 as novel observables to constrain the HQ transport coefficients in quark gluon plasma. Finally, very strong electro-magnetic (E.M.) fields are created in Ultra-relativistic Heavy-Ion Collision (HIC). We show within relativistic Boltzmann transport approach coupled with E.M. field that the strong e.m. field is responsible for a splitting of directed flow υ 1 of D and anti-D mesons of few percent, i.e. much larger compared to the observed charged particles. Moreover, we discuss the role played by the initial large bulk vorticity on the build up of rapidity odd HQs directed flow υ 1.

We describe the propagation of heavy quarks (HQs), charm and bottom, in the quark-gluon plasma (QGP) by means of a full Boltzmann transport approach including event-by-event fluctuations within a coalescence plus fragmentation hadronization. The non-perturbative dynamics of the interaction between HQs and plasma particles have been taken into account through a Quasi-Particle Model (QPM). We show that the resulting charm in-medium evolution is able to correctly predict simultaneously not only the experimental data for the average D-mesons RAA(pT) and v2,3(pT) at LHC energies but also the extension of the analysis to the event-shape engineeering tecnique that classify events according to magnitude of the second-order harmonic reduced flow vector q2. In the same scheme we show predictions for RAA(pT) of electrons from semi-leptonic B-mesons decays at top LHC energies. Our results entail a determination of Ds which is consistent with the lattice QCD calculations.

Anisotropic flow can offer significant information of evolution dynamics in heavy-ion collisions. A systematic study of the directed flow $v_1$ and elliptic flow $v_2$ of hard photons and free nucleons is performed for $^{40}$Ca+$^{40}$Ca collisions in a framework of isospin dependent quantum molecular dynamics (IQMD) model. The study firstly reveals that thermal photons emitted in intermediate-energy heavy-ion collisions have the behaviors of directed and elliptic flows. The interesting phenomena of incident energy dependence of $v_1$ and $v_2$ for thermal photons in central collisions also confirmed that it can be regarded as a good probe of evolution dynamics. Moreover, the multiplicities of hard photons and free nucleons and their correlation are also investigated. We find that direct photon emission is positively related to free nucleons emission, however, there exists an anti-correlation for thermal photons with free nucleons.

The global and local (longitudinal) spin polarization measurements of $\Lambda$ ($\bar{\Lambda}$) hyperons by STAR and ALICE Collaborations open up an immense interest in investigating the spin polarization dynamics in heavy-ion collisions. Recent studies suggest the transverse component of the vorticity field is responsible for the global spin polarization. In contrast, the longitudinal component of the vorticity field accounts for the local spin polarization. The local spin polarization of $\Lambda$ hyperons arises due to the anisotropic flow in the transverse plane, indicating a quadrupole pattern of the longitudinal vorticity along the beam direction. In this study, we derive a simple solution relating the longitudinal mean spin vector with the second-order anisotropic flow coefficient due to the thermal shear tensor for an ideal uncharged fluid in a longitudinal boost invariant scenario. The present study focuses on the local spin polarization of $\Lambda$ and $\bar{\Lambda}$ in Au$+$Au and Pb$+$Pb collisions at $\sqrt{s_{NN}}$ = 200 GeV and 5.02 TeV, respectively. Further, we explore the azimuthal angle, centrality, and transverse momentum ($p_{\rm T}$) dependence study of longitudinal spin polarization using hydrodynamic and transport models. All these models predict a maximum longitudinal spin polarization in mid-central collisions around 30-50 \% centrality at $p_{\rm T} \approx$ 2.0 - 3.0 GeV/c. These findings on longitudinal spin polarization advocate the existence of a thermal medium in non-central heavy-ion collisions.

Anisotropic flow is recognized as one of the main observables providing information on the early dynamics in heavy-ion collisions. The large elliptic flow observed at the RHIC is considered to be evidence for almost perfect liquid behavior of the strongly coupled quark–gluon plasma produced in the collisions. In this report, we review our current understanding of this new state of matter and investigate the predictions for anisotropic flow at the LHC.

Collision of SU(2) gauge fields in 3+1 dimensions

Multi-particle cumulants of azimuthal angle correlations have been compelling tools to probe the properties of the Quark-Gluon Plasma (QGP) created in the ultra-relativistic heavy-ion collisions and the search for the QGP in small collision systems at RHIC and the LHC. However, only very few of them are available and have been studied in theoretical calculations and experimental measurements. In this paper, we present a generic recursive algorithm for multi-particle cumulants, which enables the calculation of arbitrary order multi-particle cumulants. Among them, the new 10-, 12-, 14-, and 16-particle cumulants of a single harmonic, named $c_{n}\{10\}$, $c_{n}\{12\}$, $c_{n}\{14\}$, and $c_{n}\{16\}$, and the corresponding $v_n$ coefficients, will be discussed for the first time. These new multi-particle cumulants can be readily used along with updates to the generic framework of multi-particle correlations to a very high order. Finally, we propose a particular series of mixed harmonic multi-particle cumulants, which measures the general correlations between any moments of different flow coefficients. The predictions of these new observables are shown based on an initial state model MC-Glauber, a toy Monte Carlo model, and the HIJING transport model for future comparisons between experimental data and theoretical model calculations. The study of these new multi-particle cumulants in heavy-ion collisions will significantly improve the understanding of the joint probability density function which involves both different harmonics of flow and also the symmetry planes. This will pave the way for more stringent constraints on the initial state and help to extract more precisely how the created hot and dense matter evolves. Meanwhile, the efforts applied to small systems could be very helpful in the understanding of the origin of the observed collectivity at RHIC and the LHC.

A consistent derivation of the equations of motion (EOMs) of test particles for solving the spin-dependent Boltzmann-Vlasov equation is presented. The resulting EOMs in phase space are similar to the canonical equations in Hamiltonian dynamics, and the EOM of spin is the same as that in the Heisenburg picture of quantum mechanics. Considering further the quantum nature of spin and choosing the direction of total angular momentum in heavy-ion reactions as a reference of measuring nucleon spin, the EOMs of spin-up and spin-down nucleons are given separately. The key elements affecting the spin dynamics in heavy-ion collisions are identified. The resulting EOMs provide a solid foundation for using the test-particle approach in studying spin dynamics in heavy-ion collisions at intermediate energies. Future comparisons of model simulations with experimental data will help constrain the poorly known in-medium nucleon spin-orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.

Dilepton as a probe of pion dynamics in heavy-ion collisions

The formation of quark-gluon plasma (QGP) has been confirmed in ultra-relativistic heavy-ion (i.e. Pb-Pb) collisions. Results from small collision systems, such as proton-ion (p–Pb) and proton-proton (pp) collisions at LHC energies, have revealed several notable features: a hardening of the pT-spectra and evidence of radial flow, an enhancement in (multi-)strange hadron production with increasing multiplicity, and non-zero anisotropic flow coefficients. These observations suggest the presence of collective effects, similar to those found in the QGP in heavy-ion collisions. In the searching of QGP formation in small collision systems, in particular, high-multiplicity (HM) p–Pb and pp collisions are essential as their charged-particle multiplicity is comparable to that of peripheral heavy-ion collisions. This proceeding presents the LHC Run 2 results of light-flavour hadron (π, K, p) production in high-multiplicity pp collisions at √s = 13 TeV with a focus on transverse momenta (pT) spectra, mean transverse momenta (〈pT〉), ratio of pT-spectra and the ratio of the integrated yields of kaon-to-pion and proton-to-pion. The results are compared with that of heavy-ion collisions. The anisotropic flow (v2) measurement in high-multiplicity p–Pb collisions at √sNN = 5.02 TeV and pp collisions at √s = 13 TeV are also shown and compared with the results from Pb–Pb collisions.

Transition to hot quark matter in relativistic heavy-ion collision

Results obtained from the search for the critical point of strongly interacting matter in relativistic heavy-ion collisions at the CERN-SPS (experiments NA49 and NA61/SHINE) and the RHIC beam energy scan program (experiments STAR and PHENIX) are discussed. Although some intriguing signals were found, establishing firm evidence for the critical point remains a challenging enterprise.