Flow Harmonics Research Articles

Measurement of forward charged hadron flow harmonics in peripheral PbPb collisions at sNN=5.02TeV with the LHCb detector

Flow harmonic coefficients, vn, which are the key to studying the hydrodynamics of the quark-gluon plasma (QGP) created in heavy-ion collisions, have been measured in various collision systems and kinematic regions and using various particle species. The study of flow harmonics in a wide pseudorapidity range is particularly valuable to understand the temperature dependence of the shear viscosity to entropy density ratio of the QGP. This paper presents the first LHCb results of the second- and the third-order flow harmonic coefficients of charged hadrons as a function of transverse momentum in the forward region, corresponding to pseudorapidities between 2.0 and 4.9, using the data collected from PbPb collisions in 2018 at a center-of-mass energy of 5.02 TeV. The coefficients measured using the two-particle angular correlation analysis method are smaller than the central-pseudorapidity measurements at ALICE and ATLAS from the same collision system but share similar features. ©2024 CERN, for the LHCb Collaboration 2024 CERN

Exploring electromagnetic field effects and constraining transport parameters of QGP using STAR BES-II data

Heavy-ion collisions undergo various stages in their evolution and it is crucial to disentangle the initial- and final-stage effects. In this work, we report measurements of two types of observables: (i) charge-dependent directed flow (Δv1), which is sensitive to the initial ultra-strong electromagnetic fields, and (ii) flow correlations, such as rn(η) which is sensitive to the initial longitudinal de-correlation, and correlations among flow harmonics. These measurements contribute to constraining the initial state of the collisions, and through a comprehensive beam energy scan, we gain significant insights into the system evolution in the presence of initial spatial asymmetry and electromagnetic fields.

A review on anisotropic flow in heavy-ion collisions

We present a review of published experimental measurements on anisotropic flow in heavy-ion collisions. Flow coefficients [Formula: see text] are presented for charged and identified hadrons at various beam energies ranging from [Formula: see text][Formula: see text]GeV to 200[Formula: see text]GeV at the Relativistic Heavy Ion Collider (RHIC) and [Formula: see text][Formula: see text]GeV at the Large Hadron Collider (LHC). We present [Formula: see text] and its slope [Formula: see text] and discuss possible first-order Quantum chromodynamics (QCD) phase transition. [Formula: see text] of particles containing heavy quarks (Charm quarks) is also discussed to illustrate the effect of the magnetic field produced in relativistic heavy-ion collisions. We also present flow harmonics ([Formula: see text], [Formula: see text] and [Formula: see text]) for inclusive charged and identified hadrons. We compare the charged particle [Formula: see text] coefficients with hydrodynamics to study and constrain initial conditions in the transport models. The results of identified particle [Formula: see text] from ideal and viscous hydrodynamics are discussed to understand the dynamics and mechanism of particle production in high-energy nuclear collisions.

Higher flow harmonics of strange hadrons in Au+Au collisions at $$\sqrt {s_{{{\text{NN}}}} }$$ = 200 GeV and Pb+Pb collisions at $$\sqrt {s_{{{\text{NN}}}} }$$ = 2.76 TeV with HYDJET++ model

Higher flow harmonics of strange hadrons in Au+Au collisions at $$\sqrt {s_{{{\text{NN}}}} }$$ = 200 GeV and Pb+Pb collisions at $$\sqrt {s_{{{\text{NN}}}} }$$ = 2.76 TeV with HYDJET++ model

Linear and nonlinear frequency-domain modelling of oscillatory flow over submerged canopies

An analytical and experimental study of flow velocities within submerged canopies of rigid cylinders under oscillatory flows is presented, providing insights into the momentum transfer mechanisms between the different flow harmonics. The experimental dataset covers an unprecedented wide range of flow amplitudes with in-canopy velocity reductions ranging between 0.2 and 0.8 of the free stream velocity (from inertia- to drag-dominated in-canopy flow). Results from the analytical model with nonlinear drag compare favourably to the experimental data. Having application of theories for free surface waves over canopies in mind, the effects of linearization of the drag are analysed by comparing sinusoidal and nonlinear model predictions. Finally, a unified prediction formula for in-canopy velocities for sinusoidal, velocity-skewed, and velocity-asymmetric free stream velocities is presented. The formula depends on two non-dimensional parameters related to inertia and drag forces, and the unified formula allows for easy assessment of the maximum in-canopy velocity.

Decomposition of multi-particle azimuthal correlations in Q-cumulant analysis* *Supported by the Ministry of Education Science and Technological Development, Republic of Serbia, the National Natural Science Foundation of China (12035006, 12075085, 12147219), and the U.S. Department of Energy (de-sc0012910).

The method of Q-cumulants is a powerful tool for studying the fine details of azimuthal anisotropies in high energy nuclear collisions. This paper presents a new method, based on mathematical induction, to evaluate the analytical form of high-order Q-cumulants. The capability of this method is demonstrated via a toy model that uses the elliptic power distribution to simulate the anisotropic emission of particles, quantified in terms of Fourier flow harmonics . The method can help in studying the large amount of event statistics that can be collected in the future and allow measurements of the very high central moments of the distribution. This can, in turn, facilitate progress in understanding the initial geometry, the input to the hydrodynamic calculations of medium expansion in high energy nuclear collisions, and the constraints on it.

Fourier coefficients of noninterdependent collective motions in heavy-ion collisions

We present a scenario in heavy-ion collisions where different modes of collective motions are noninterdependent, driven by factorized actions in the created nuclear medium. Such physics mechanisms could each dominate at a distinct evolution stage, or coexist simultaneously. If the probability of particle emission is modulated by each nondependent collective motion with a single-harmonic Fourier expansion, the particle azimuthal distribution should be the product of all these expansions. Consequently, nonleading cross terms between collectivity modes appear, and their contributions to experimental observables could be significant. In particular, we argue that the chiral magnetic effect (CME) and elliptic flow can develop separately, with their convolution affecting the observable that is sensitive to the shear-induced CME. We will use the event-by-event anomalous-viscous fluid dynamics model to illustrate the effects of this scenario. Besides giving insights into searches for the CME, we also propose feasible experimental tests based on conventional flow harmonics, and demonstrate the emergence of nonleading cross terms with a multiphase transport model.

Investigating the role of electric fields on flow harmonics in heavy-ion collisions

Using the blast-wave model, we explore the effect of electric fields on spectra and flow harmonics (especially the elliptic flow) for charged pions and protons. We incorporate the first-order correction to the single-particle distribution function due to the electric fields and the dissipative effect while calculating the invariant yields of hadrons in the Cooper–Frye prescription at the freezeout hypersurface. We find a noticeable correction to the directed and elliptic flow of pions and protons for unidirectional and azimuthal asymmetric electric fields of a magnitude in the transverse plane. Further, we observe mass dependency of the directed flow generated due to the electric fields. The splitting of particle and antiparticle’s elliptic flow due to the electric fields is also discussed.

Momentum-dependent flow correlations in deformed nuclei at collision energies available at the BNL Relativistic Heavy Ion Collider

Flow fluctuations in ultrarelativistic heavy-ion collisions can be probed by studying the momentum dependent correlations or the factorization-breaking coefficients between flow harmonics in separate kinematic bins (transverse momentum $p$ or pseudorapidity $\ensuremath{\eta}$). We study such factorization-breaking coefficients for collisions of deformed $^{238}\mathrm{U}+^{238}\mathrm{U}$ nuclei to see the effect of the nuclear deformation on momentum dependent coefficients. We also study momentum dependent mixed-flow correlations for the isobar collision system: $^{96}\mathrm{Ru}+^{96}\mathrm{Ru}$ and $^{96}\mathrm{Zr}+^{96}\mathrm{Zr}$, which have the same mass number but different nuclear structure, thus providing the ideal scenario to study nuclear deformation effect on such observables. We use the TRENTO $+$ MUSIC model for simulations and event-by-event analysis of those observables. We find that these momentum dependent correlation coefficients are not only excellent candidates to probe the fluctuation in heavy-ion collision, but also show significant sensitivity to the nuclear deformation.

Correlations between flow and transverse momentum in Xe+Xe and Pb+Pb collisions at the LHC with the ATLAS detector: A probe of the heavy-ion initial state and nuclear deformation

The correlations between flow harmonics $v_n$ for $n=2$, 3 and 4 and mean transverse momentum $[p_\mathrm{T}]$ in $^{129}$Xe+$^{129}$Xe and $^{208}$Pb+$^{208}$Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.44$ TeV and 5.02 TeV, respectively, are measured using charged particles with the ATLAS detector. The correlations are sensitive to the shape and size of the initial geometry, nuclear deformation, and initial momentum anisotropy. The effects from non-flow and centrality fluctuations are minimized, respectively, via a subevent cumulant method and event activity selection based on particle production in the very forward rapidity. The results show strong dependences on centrality, harmonic number $n$, $p_{\mathrm{T}}$ and pseudorapidity range. Current models describe qualitatively the overall centrality- and system-dependent trends but fail to quantitatively reproduce all the data. In the central collisions, where models generally show good agreement, the $v_2$-$[p_\mathrm{T}]$ correlations are sensitive to the triaxiality of the quadruple deformation. The comparison of model to the Pb+Pb and Xe+Xe data suggests that the $^{129}$Xe nucleus is a highly deformed triaxial ellipsoid that is neither a prolate nor an oblate shape. This provides strong evidence for a triaxial deformation of $^{129}$Xe nucleus using high-energy heavy-ion collision.

Impact of nuclear deformation on collective flow observables in relativistic U+U collisions

A Multi-Phase Transport (AMPT) model is used to investigate the efficacy of several flow observables to constrain the initial-state deformation of the Uranium nuclei in U$+$U collisions at nucleon-nucleon center-of-mass energy $\sqrt{s_{\mathrm{NN}}}$ = 193 GeV. The multiparticle azimuthal cumulant method is used to investigate the sensitivity of (I) a set of quantities that are sensitive to both initial- and final-state effects as well as (II) a set of dimensionless quantities that are more sensitive to initial-state effects to the Uranium nuclei quadrupole shape deformation. I find that the combined use of the flow harmonics, flow fluctuations and correlations, linear and nonlinear flow correlations to the quadrangular flow harmonic, and the correlations between elliptic flow and the mean-transverse momentum could serve to constrain the nuclear deformation of the Uranium nuclei. Therefore, a comprehensive set of measurements of such observables can provide a quantifying tool for the quadrupole shape deformation via data-model comparisons

Probing the nuclear deformation with three-particle asymmetric cumulant in RHIC isobar runs

4496Ru+4496Ru and 4096Zr+4096Zr collisions at sNN=200 GeV provide unique opportunities to study the geometry and fluctuations raised from the deformation of the colliding nuclei. Using iEBE-VISHNU hybrid model, we predict ac2{3} ratios between these two collision systems and demonstrate that the ratios of ac2{3}, as well as the ratios of the involving flow harmonics and event-plane correlations, are sensitive to quadrupole and octupole deformations, which could provide strong constrains on the shape differences between 96Ru and 96Zr. We also study the nonlinear response coefficients χ4,22, which show insensitivity to the deformation effect.

Precision Tests of the Nonlinear Mode Coupling of Anisotropic Flow via High-Energy Collisions of Isobars

Valuable information on dynamics of expanding fluids can be inferred from the response of such systems to perturbations in their initial geometry. We apply this technique in high-energy 96Ru+96Ru and 96Zr+96Zr collisions to scrutinize the expansion dynamics of the quark-gluon plasma, where the initial geometry perturbations are sourced by the differences in deformations and radial profiles between 96Ru and 96Zr, and the collective response is captured by the change in anisotropic flow Vn between the two collision systems. Using a transport model, we analyze how the nonlinear coupling between lower-order flow harmonics V 2 and V 3 to the higher-order flow harmonics V 4 and V 5, expected to scale as and V 5NL = χ 5 V 2 V 3, gets modified as one moves from 96Ru+96Ru to 96Zr+96Zr systems. We find that these scaling relations are valid to high precision: variations of order 20% in V 4NL and V 5NL due to differences in quadrupole deformation, octupole deformation, and nuclear skin modify χ 4 and χ 5 by about 1–2%. Percent-level deviations are however larger than the expected experimental uncertainties and could be measured. Therefore, collisions of isobars with different nuclear structures are a unique tool to isolate subtle nonlinear effects in the expansion of the quark-gluon plasma that would be otherwise impossible to access in a single collision system.

Beam Energy Dependence of the Linear and Mode-Coupled Flow Harmonics Using the a Multi-Phase Transport Model

In the framework of the A Multi-Phase Transport (AMPT) model, the multi-particle azimuthal cumulant method is used to calculate the linear and mode-coupled contributions to the quadrangular flow harmonic (v4) and the mode-coupled response coefficient as functions of centrality in Au+Au collisions at sNN = 200, 39, 27 and 19.6 GeV. This study indicates that the linear and mode-coupled contributions to v4 are sensitive to beam energy change. Nevertheless, the correlations between different-order flow symmetry planes and the mode-coupled response coefficients show weak beam energy dependence. In addition, the presented results suggest that the experimental measurements that span a broad range of beam energies can be an additional constraint for the theoretical model calculations.

Beam energy dependence of the linear and mode-coupled flow harmonics in Au+Au collisions

The linear and mode-coupled contributions to higher-order anisotropic flow are presented for Au+Au collisions at sNN = 27, 39, 54.4, and 200 GeV and compared to similar measurements for Pb+Pb collisions at the Large Hadron Collider (LHC). The coefficients and the flow harmonics' correlations, which characterize the linear and mode-coupled response to the lower-order anisotropies, indicate a beam energy dependence consistent with an influence from the specific shear viscosity (η/s). In contrast, the dimensionless coefficients, mode-coupled response coefficients, and normalized symmetric cumulants are approximately beam-energy independent, consistent with a significant role from initial-state effects. These measurements could provide unique supplemental constraints to (i) distinguish between different initial-state models and (ii) delineate the temperature (T) and baryon chemical potential (μB) dependence of the specific shear viscosity ηs(T,μB).

On differences between even and odd anisotropic-flow harmonics in non-equilibrated systems

To assess how anisotropic transverse flow is created in a system out of equilibrium, we compare several kinetic-theoretical models in the few-rescatterings regime. We compare the flow harmonics v_n from three types of transport simulations, with either 2rightarrow 2 or 2rightarrow 0 collision kernels and in the former case allowing the particles to rescatter several times or not, and from analytical calculations neglecting the gain term of the Boltzmann equation. We find that the even flow harmonics are similar in all approaches, while the odd ones differ significantly. This suggests that while even v_n harmonics may to a large extent be due to the anisotropic escape probability of particles, this is not the predominant mechanism underlying the odd v_n coefficients.

On Statistical Fluctuations in Collective Flows

In relativistic heavy-ion collisions, event-by-event fluctuations are known to have non-trivial implications. Even though the probability distribution is geometrically isotropic for the initial conditions, the anisotropic εn still differs from zero owing to the statistical fluctuations in the energy profile. On the other hand, the flow harmonics extracted from the hadron spectrum using the multi-particle correlators are inevitably subjected to non-vanishing variance due to the finite number of hadrons emitted in individual events. As one aims to extract information on the fluctuations in the initial conditions via flow harmonics and their fluctuations, finite multiplicity may play a role in interfering with such an effort. In this study, we explore the properties and impacts of such fluctuations in the initial and final states, which both notably appear to be statistical ones originating from the finite number of quanta of the underlying system. We elaborate on the properties of the initial-state eccentricities for the smooth and event-by-event fluctuating initial conditions and their distinct impacts on the resulting flow harmonics. Numerical simulations are performed. The possible implications of the present study are also addressed.

An empirical model for velocity in rough turbulent oscillatory boundary layers

A novel empirical model for the streamwise velocity in oscillatory boundary layer flow, valid in the rough turbulent regime, is presented. The model consists of simple expressions that require only the free-stream velocity time-series and equivalent sand-grain roughness length of the bed to be known a priori. A frequency-independent attenuation and phase lead is assumed for all flow harmonics, expressions for which are extracted from data from previous experimental studies made in 3 different oscillatory flow tunnels. Only the oscillating component of the flow is considered in the model; steady streaming is neglected. Errors in kinematics predicted by the model are typically two orders of magnitude smaller than the maximum oscillatory velocity in the free-stream. Hence, it is well-suited to engineering application due to its simplicity and accuracy.

Transverse Momentum Dependence on Fourier Elliptic and Triangular Flow Harmonics in Mid-Central Pbpb Collisions at

We have collected particle collision data from the experiment using CMS apparatus, where we studied charged ions in the nucleus-to-nucleus collision’s PbPb branch in Pb at the 2.76 TeV energy scale. So far for the present work, we report the anisotropy of the thermal observational flux in lead-lead nucleon collisions at sqrt = 2.76 TeV. We observed that the collisions produced a large ion azimuth angle ranging from −π to π radian and a pseudo-conductance ranging from -2.6 to 2.6. In this work, we report the correlation function of transverse momentum, Pt , Δη, and ΔΦ over a wide range of centroids. When the transverse momentum is about 1-2 GeV/c and Δη is in range -1 to 1, we observe a jet peak in the η and Φ correlation plot as the centrality increases. In the case of ν 2, which is an elliptic current signal, we measured it with a 4-part correlation method in the 40-50% centrality class. Asymptotic angular correlations in the far range have been studied by Fourier decomposition on the product of anisotropies when the cross-correlation is equal to 3-3.5 GeV/c. The obtained Fourier coefficients are factorized into the singular product of -ion Φ anisotropies. The assumptions of the hydrodynamic model with the shear viscosity correlation increase accordingly.

Event-shape engineering analysis of D meson in ultrarelativistic heavy-ion collisions

We describe the propagation of charm quarks in the quark-gluon plasma (QGP) by means of an event-by-event transport approach. In our calculations the non-perturbative interaction between heavy quarks and light partons has been taken into account through a quasi-particle approach with thermal light quark masses tuned to reproduce lQCD thermodynamics. We found that the flow observables v_2 and v_3 of D mesons are comparable with the experimental measurements for Pb + Pb collisions at 5.02 TeV in different ranges of centrality selections. The results are analyzed with event-shape engineering technique. The comparison of the anisotropic flow coefficients v_n with experimental data show a quite good agreement with experimental data for different flow vector q_2 selections, which confirms the strong coupling between charm quarks and light quarks in the QCD matter. Furthermore, we present here a novel study of the event-by-event correlations between flow harmonics of D mesons and soft hadrons at LHC energy with the event-shape engineering technique that can put further constraints on heavy quark transport coefficients toward a solid comparison between the phenomenological determination and the lattice QCD calculations.