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Elliptic flow integrated over the pt range 0.2<pt<5.0 GeV/c, as a function of event centrality, for the 2- and 4-particle cumulant methods, a fit of the distribution of the flow vector, and the Lee-Yang zeros method. For the cumulants the measurements are shown for all charged particles (full markers) and same charge particles (open markers). Data points are shifted for visibility. RHIC measurements for Au-Au at sNN=200 GeV, integrated over the pt range 0.15<pt<2.0 GeV/c, for the event plane v2{EP} and Lee-Yang zeros are shown by the solid curves.
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We report the first measurement of charged particle elliptic flow in Pb-Pb collisions at sqrt[S(NN)] =2.76 TeV with the ALICE detector at the CERN Large Hadron Collider. The measurement is performed in the central pseudorapidity region (|η|<0.8) and transverse momentum range 0.2<p t<5.0 GeV/c. The elliptic flow signal v₂, measured using the 4-parti...
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Citations
... One of the most interesting and unique features of ultrarelativistic heavy-ion collisions is the collective flow of the final state particles [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. This collective dynamics originate as an effect of the initial state of the collision and of the collective expansion of the fireball. ...
... This spatial azimuthal anistoropy of the entropy or energy density distribution, through the evolution and collective expansion, translates into the azimuthal anisotropy of the momentum distribution of final state particles. This azimuthal anisotropy can be understood through different order of flow harmonics (v n ) such as the elliptic flow, triangular flow etc [61][62][63][64]54]. ...
In this thesis, we focus on the fluctuations and correlations of the collective observables such as the mean transverse momentum per particle () and harmonic flow coefficients () of particles produced in the ultrarelativistic heavy-ion collisions at RHIC and the LHC. Specifically, we show that the fluctuations of harmonic flow can be probed by the factorization-breaking coefficients between flow vectors in different -bins. Experimental difficulty can be reduced by taking one of the flow vectors momentum averaged. Fluctuations cause a decorrelation between the flow vectors, which can be attributed to equal contributions from the flow magnitude and flow angle decorrelation. We study fluctuations of mean transverse momentum per particle () in ultra-central collisions and show that our model can explain the steep fall of its variance observed by the ATLAS collaboration. We also present robust predictions for the skewness and kurtosis, and highlight the role of impact parameter fluctuations in ultracentral collisions. We study the Pearson correlation coefficients between and , which can map the initial state correlations between the shape and size of the fireball. We show that higher order normalized and symmetric cumulants between these observables can be constructed, which put useful additional constraints on the initial state properties. Furthermore, we study the momentum dependent Pearson correlation between and the transverse momentum dependent flow. It shows sensitivity to the Gaussian width of the nucleon at the initial state. Finally, we show that such correlations and fluctuations of collective observables can be used to study nuclear deformation and put robust constraints on their deformation parameters through high energy nuclear collisions.
... The impact parameter driven spatial geometry of the fireball and nucleonic fluctuations lead to various anisotropic flow harmonics. The secondorder elliptic flow (v 2 ) originates from the geometry of the overlap region [90][91][92][93][94][95][96], while the third-order triangular flow (v 3 ) arises from event-by-event nucleon and subnucleon fluctuations [35,[97][98][99][100]. These flow harmonics are sensitive to the equation of state (EoS) and transport properties of the fireball, such as viscosity [101][102][103][104][105]. ...
We study symmetric and asymmetric cumulants as well as rapidity-even dipolar flow in O+O collisions at ~GeV to explore -clustering phenomena in light nuclei within the viscous relativistic hydrodynamics framework. Signatures of -clustering manifest in the anisotropic flow coefficients and their correlations -- particularly in observables involving elliptic-triangular flow correlations. We show that final-state symmetric and asymmetric cumulants -- especially and -- are sensitive to the initial nuclear geometry. Additionally, we observe a significant difference in rapidity-even dipolar flow, , between -clustered and Woods--Saxon configurations in high-multiplicity events. These findings underscore the pivotal role of nuclear structure in heavy-ion collision dynamics and provide observables for distinguishing nuclear geometries, particularly in ultra-central collisions.
... TeV, measured in the ALICE experiment [85]. The top 5% of events, which produce the highest yield of charged particles in the mid-rapidity region, are categorized as 0-5% centrality events. ...
This thesis aims to elucidate the role of initial baryon stopping and its diffusion in heavy-ion collisions (HIC) using hydrodynamic model. In this regard, we have studied the observable-directed flow () of identified hadrons, particularly the of baryons and antibaryons, as well as the splitting observed between them in detail. We propose a new ansatz for the initial baryon distribution. By employing this initial baryon deposition model alongside a tilted energy distribution as inputs to a hybrid framework, we successfully describe the rapidity-odd of identified hadrons, including the elusive baryon-antibaryon splitting of across a wide range of . Our model, incorporating baryon stopping and it's subsequent diffusion within a relativistic hydrodynamic framework and employing a crossover equation of state derived from lattice QCD calculations, establishes a non-critical baryonic baseline. Moreover, we demonstrate that recent STAR measurements of the centrality and system-size dependence of splitting between oppositely charged hadrons-attributed to electromagnetic field effects-are significantly influenced by background contributions from baryon stopping and its diffusion. Furthermore, we show that the rapidity dependence of the splitting of the rapidity-even component of between p and is highly sensitive to the initial baryon deposition scheme. If measured experimentally, this could constraint the rapidity dependence of the initial baryon deposition profile. Moreover, it could offer valuable phenomenological insights into the baryon junction picture and help refine constraints on the baryon diffusion coefficient of the medium. Notably, utilizing this phenomenologically successful baryon deposition model, we present the first estimation of the baryon diffusion coefficient for the strongly interacting QCD matter created in HIC.
... However, obtaining v n via the two-particle Q-cumulant method suffers from contributions from non-flow effects [34]. Thus, we introduce a pseudorapidity gap which can substantially reduce these nonflow effects [35][36][37][38]. ...
Anisotropic flow and fluctuations are sensitive observables to the initial state effects in heavy ion collisions and are characterized by the medium properties and final state interactions. Using event-shape observables, one can constrain the probability distributions of anisotropic flow coefficients, thus reducing the linear and nonlinear contributions in the measured higher-order harmonics. In this paper, we use transverse spherocity as an event shape observable to study the flow coefficients and elliptic flow fluctuations. Transverse spherocity is found to have a strong correlation with elliptic flow and its fluctuations. We exploit this feature of transverse spherocity to remove the contribution of elliptic flow from higher-order harmonics. The study is performed in Pb--Pb collisions at TeV using a multi-phase transport model. The multi-particle Q-cumulant method estimates the anisotropic flow coefficients, which reduces the non-flow contributions. We observe a stronger system response to the flow coefficients for the events with smaller values of elliptic flow.
... Anisotropic flow measurements at RHIC and the LHC have shown that the QGP behaves as a near-perfect liquid [8][9][10][11][12][13][14][15][16][17][18], with a shear viscosity over entropy density ratio close to the lowest limit predicted by AdS/CFT theory [19]. The anisotropic flow studies are typically performed via multi-particle azimuthal correlations [20], providing insight into various aspects of QGP dynamics. ...
Multi-particle correlations between azimuthal angle and mean transverse momentum are a powerful tool for probing size and shape correlations in the initial conditions of heavy-ion collisions. These correlations have also been employed to investigate nuclear structure, including potential nuclear shape phase transitions at the energy frontier. However, their implementation is highly nontrivial, and prior studies have been mostly limited to lower-order correlations, such as the modified Pearson correlation coefficient, . This paper presents a unified framework that employs a recursive algorithm, enabling the efficient evaluation of arbitrary-order correlations while maintaining computational efficiency. This framework is demonstrated using widely adopted transport models, including AMPT and HIJING. The proposed unified algorithm for multi-particle correlations between azimuthal angle and transverse momentum provides a systematic and efficient approach for multi-particle correlation analyses. Its application in experiments at the Relativistic Heavy Ion Collider and the Large Hadron Collider facilitates the exploration of nuclear structure at ultra-relativistic energies.
... One of the foremost signals of the formation of a quarkgluon plasma (QGP) during a heavy ion collision is the elliptic flow of the bulk medium [1][2][3][4][5], in semicentral collisions. 1 Due to the geometry of the collision, the overlap region of the two nuclei is not circular, and contains azimuthal anisotropies in density. Pressure gradients created by these spatial inhomogeneities lead to azimuthal anisotropies in the momentum distribution [6], quantified by the Fourier coefficients of the differential hadronic yield, ...
... To further explore the azimuthal anisotropies arising from TMDPDFs, we compute higher order harmonics v 3 and v 4 , which are displayed in Fig. 11. The experimental results of v 3 and v 4 display a different behavior than v 2 . While v 2 starts decreasing with p T already at p T 5 GeV, v 3 and v 4 are increasing up to the highest data points (p T 10 and p T 4, respectively). ...
... The experimental results of v 3 and v 4 display a different behavior than v 2 . While v 2 starts decreasing with p T already at p T 5 GeV, v 3 and v 4 are increasing up to the highest data points (p T 10 and p T 4, respectively). However, the data display large uncertainties at high p T and are limited to p T 10 GeV. ...
Various azimuthal anisotropies ( v 1 , v 2 , v 3 , v 4 ), at high transverse momentum (high p T ), are shown to arise from the asymmetric scattering of transverse polarized quarks and gluons, arising from unpolarized nucleons (the Boer-Mulders effect) and resulting in unpolarized hadrons (the Collins effect). Combined with the asymmetric scattering of partons from polarization independent but transverse momentum dependent (TMD) distributions, we obtain a possible mechanism to understand the azimuthal anisotropy of hadrons at large transverse momentum observed in p − p collisions. Constraining the ratio of polarization dependent TMD distributions to polarization independent distributions by comparing with the data from p − p collisions, we find that scaling the acquired transverse momentum of the initial state partons from the proton, due to prescattering before the hard interaction, with the length of the nucleus ( k ⊥ 2 ∝ A 1 / 3 ), straightforwardly yields the azimuthal anisotropy at high p T in p − A collisions.
Published by the American Physical Society 2025
... Not only does it provide a window into the properties of strongly interacting matter but also serves as a key observable in constraining theoretical models of collision dynamics. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] An elliptic flow, denoted by 2, measures the anisotropic distribution of particles produced in the azimuthal direction with respect to the reaction plane ( rp) in heavy-ion collisions. This is defined as the second Fourier coefficient in the Fourier decomposition of the par-ticle yield as a function of the azimuthal angle: [1] ...
Significant differences exist in the elliptic flow v2 for particles and their corresponding anti-particles. These differences, which are more significant for baryons and anti-baryons, were observed from the solenoidal tracker (STAR) experiment during Beam Energy Scan I (BES-I) at relativistic heavy ion collider (RHIC). By employing the simulated many-accelerated strongly interacting hadrons (SMASH) model, we studied the v2 differences between protons and anti-protons as well as between Λ and Λ¯ in Au + Au collisions at sNN=7.7 GeV as a function of the evolution time. It was found that as the evolution time increases, the v2 differences between protons and anti-protons become more significant than those between Λ and Λ¯ . This phenomenon can be explained by the different constituent quarks of protons and Λ. Given that some of the u and d quarks come from the colliding nuclei and are transported to midrapidity, they undergo more interactions than the produced quarks, resulting in protons Δv2 being larger than Λ Δv2. We compared the SMASH calculations with STAR BES-I data and concluded that higher-precision data from BES-II will set constraints on theoretical frameworks to interpret the v2 differences between particles and anti-particles.
... Finite azimuthal anisotropy has been well observed in heavy-ion collision experiments so far * e-mail: Barnafoldi.Gergely@wigner.hun-ren.hu at RHIC and LHC energies up to higher-order cumulants with various analysis methods [3][4][5][6]. Here, we present our deep learning feed-forward network for estimating elliptic flow (v 2 ) coefficients, which we compare to heavy-ion collision data from RHIC to LHC energies. ...
We developed a deep learning feed-forward network for estimating elliptic flow (v2) coefficients in heavy-ion collisions from RHIC to LHC energies. The success of our model is mainly the estimation of v2 from final state particle kinematic information and learning the centrality and the transverse momentum (pT) dependence of v2 in wide pT regime. The deep learning model is trained with AMPT-generated Pb-Pb collisions at √sNN = 5.02 TeV minimum bias events. We present v2 estimates for π±, K±, and p + p¯ in heavy-ion collisions at various LHC energies. These results are compared with the available experimental data wherever possible.
... The QGP is an extremely hot and dense system where (anti-)quarks and gluons exist as deconfined, quasi-free partons. Past comparisons between experimental anisotropic flow measurements and theoretical models (i.e., hydrodynamics [3][4][5] and kinetic transport methods [6-9]) suggest that the QGP behaves like a near-perfect fluid with a very small shear-viscosity to entropy-density ratio above the KSS lower bound η/s = 1/(4π) (ℏ = k B = c = 1) [10]. At temperatures exceeding the Hagedorn temperature, T H ≃ 150 MeV [11], the partons in the QGP resemble an ideal thermal gas. ...
... The cooling of the thermalized QGP can be modeled using Newton's cooling law, assuming an exponential decay of the temperature over time. This approximation is consistent with the rapid expansion and cooling dynamics observed in heavy-ion collisions [1][2][3][4][5]. Using the boundary conditions T = 550 MeV at t = 0 fm/c and T = 150 MeV at t = 10 fm/c, the temperature as a function of time is given by ...
Transport properties of the quark-gluon plasma are instrumental to testing perturbative quantum chromodynamics and understanding the extreme conditions of relativistic heavy-ion collisions. This study presents an analytical investigation of the shear viscosity and the shear viscosity-to-entropy density ratio of the QGP using a novel multi-component Chapman-Enskog framework assuming full thermalization. The approach incorporates species-specific contributions from gluons and (anti-)quarks into the plasma shear viscosity, temperature-dependent running parameters for the Debye mass and strong coupling, and a time-dependent cooling model. Our findings show that both and are enhanced by the inclusion of (anti-)quarks with gluons, and the parameters decrease over time due to the cooling and expansion of the QGP. These results align with perturbative QCD predictions, offering a more optimistic representation of QGP transport properties under dynamic conditions. This multi-component framework is compared with a multi-phase transport model that treats the QGP as a gluon gas with (anti-)quark augmentation.
... It proposes a progression from a high-density, high-temperature state, where the universe underwent successive phase transitions. The scientific community constructed heavy-ion colliders to scrutinize the Quantum Chromodynamic (QCD) phase transition, facilitating controlled experiments that emulate the primordial Big Bang conditions, often called the "mini bang" [2][3][4]. Figure 1 illustrates the envisioned phases of the quark and gluon-rich medium based on QCD [5]. The QCD phase diagram, introduced in 1975 [6], consists of two major regions: one representing the confining state where quarks and gluons are bound within hadrons and another representing the deconfined state where quarks and gluons move freely beyond hadronic boundaries. ...
This review explores the current understanding of collective excitations and the dynamics of heavy quark propagation in the quark-gluon plasma (QGP) formed in relativistic heavy-ion collisions. We focus on three core aspects: the theoretical modelling of the QGP, including momentum anisotropy, medium-induced collisions, finite chemical potential, and non-ideal interactions; the collective behaviours within the plasma; and the interaction dynamics of heavy quarks as they traverse the medium. Along with the polarization energy loss mechanisms, we also review the possibility of energy gain due to thermal field fluctuations. Lastly, we discuss how these theoretical insights can be tested through experiments and outline possible directions for future research.
