Event-plane Angles Research Articles

Measuring differential particle correlations in relativistic nuclear collisions

This study explores the transverse momentum (pT) dependencies of symmetric and asymmetric correlations (SC and ASC) with one and two particles of interest in Au+Au collisions at 200 GeV. Leveraging a multiphase transport (AMPT) model, the investigation delves into the sensitivity of these correlations to the final state effects, providing valuable insights into their potential for constraining the final state effects' pT dependencies. The HIJING model is employed as a benchmark for nonflow correlations, shedding light on their impact on interpreting SC and ASC data. Moreover, the study points out that differential SC and ASC with one and two particles of interest (POIs) typically incorporate contributions from event-plane angle fluctuations. Consequently, this work highlights the significance of SC and ASC with one and two POIs as valuable tools for investigating the pT nature of the final state effects and advocates for comprehensive experimental measurements across various beam energies and system sizes to enhance understanding and provide additional constraints for theoretical models. Published by the American Physical Society 2024

Modification of charged-particle jets in event-shape engineered Pb–Pb collisions at [formula omitted] TeV

Charged-particle jet yields have been measured in semicentral Pb–Pb collisions at center-of-mass energy per nucleon–nucleon collision sNN=5.02 TeV with the ALICE detector at the LHC. These yields are reported as a function of the jet transverse momentum, and further classified by their angle with respect to the event plane and the event shape, characterized by ellipticity, in an effort to study the path-length dependence of jet quenching. Jets were reconstructed at midrapidity from charged-particle tracks using the anti-kT algorithm with resolution parameters R = 0.2 and 0.4, with event-plane angle and event-shape values determined using information from forward scintillating detectors. The results presented in this letter show that, in semicentral Pb–Pb collisions, there is no significant difference between jet yields in predominantly isotropic and elliptical events. However, out-of-plane jets are observed to be more suppressed than in-plane jets. Further, this relative suppression is greater for low transverse momentum (< 50 GeV/c) R = 0.2 jets produced in elliptical events, with out-of-plane to in-plane jet-yield ratios varying up to 5.2σ between different event-shape classes. These results agree with previous studies indicating that jets experience azimuthally anisotropic suppression when traversing the QGP medium, and can provide additional constraints on the path-length dependence of jet energy loss.

Elliptic flow of inclusive charged hadrons in Au+Au collisions at E lab = 35 A GeV using the PHSD model

Elliptic flow (v 2) of inclusive charged hadrons at mid-rapidity (∣η∣ < 1.0) in Au+Au collisions at E lab = 35 A GeV using the parton hadron string dynamics (PHSD) model are presented as a function of centrality, transverse momentum (p T) and pseudo-rapidity (η). The v 2 results are obtained using the η-sub event plane method with respect to the event plane angle (ψ 2) and participant plane angle (). p T-integrated charged hadron v 2 shows a strong centrality dependence in Au+Au collisions at E lab = 35 A GeV. The eccentricity-scaled elliptic flow (v 2/ε 2) also shows centrality dependence. The higher values of v 2/ε 2 in central collisions suggest the development of stronger collectivity. The calculations are compared with the results from Au+Au collisions at published by the STAR experiment at RHIC. We also compare the results of HSD and PHSD modes to investigate the contribution of hadronic and partonic phases of the medium on the calculated v 2. The current results serve as a prediction of the collective behavior of the matter produced in baryon-rich and moderate temperature conditions for the upcoming multi-purpose detector at the nuclotron-based Ion collider facility (NICA) and compressed baryonic matter experiment at the facility for antiproton and ion research. These predictions are also useful for interpreting data measured at relativistic heavy ion collider (RHIC) beam energy scan program.

Bayesian analysis of heavy ion collisions with the heavy ion computational framework Trajectum

We introduce a model for heavy ion collisions named Trajectum, which includes an expanded initial stage with a variable free streaming velocity $v_{\rm fs}$ and a hydrodynamic stage with three varying second order transport coefficients. We describe how to obtain a Gaussian Emulator for this 20-parameter model and show results for key observables. This emulator can be used to obtain Bayesian posterior estimates on the parameters, which we test by an elaborate closure test as well as a convergence study. Lastly, we employ the optimal values of the parameters found in [1] to perform a detailed comparison to experimental data from PbPb and $p$Pb collisions. This includes both observables that have been used to obtain these values as well as wider transverse momentum ranges and new observables such as correlations of event-plane angles.

Correlation of flow harmonics and mean transverse momentum in 5.02 TeV p+Pb and Pb+Pb collisions and event-plane dependence of HBT radii in high-multiplicity p+Pb collisions with the ATLAS detector

To assess the properties of the quark-gluon plasma formed in heavy ion collisions, correlations between the mean transverse momentum, [pT], and the magnitude of the flow harmonics, νn, are measured by the ATLAS experiment at the LHC. The analysis uses data samples of Pb+Pb and p+Pb collisions at sNN=5.02TeV, corresponding to integrated luminosities of 22 μb−1 and 28 nb−1, respectively. The correlations are measured using a modified Pearson coefficient that is independent of multiplicity fluctuations. To suppress any short-range correlations, the [pT] is measured at mid-rapidity and the flow harmonics are measured at forward rapidity. In Pb+Pb collisions, significant (non-zero) values of the correlation coefficients are observed for all studied harmonics, which show a strong centrality dependence but vary only weakly with the charged particle pT range used in the measurement. On the other hand, in p+Pb collisions, the correlation coefficient measured for the 2nd harmonic is found to show only a weak centrality dependence. The predictions of a 3+1D viscous-hydrodynamic model are found to be qualitatively consistent with the data, indicating hydrodynamic origin of these correlations in p+Pb collisions. As an independent test for the hydrodynamic description of collectivity observed in p+Pb collisions, measurements of two-pion HBT correlations as a function of the angle of the pion pair with respect to the second-order event plane angle are presented. The HBT correlation functions, corrected for event plane resolution, are measured as a function of qout, qside and qlong in intervals of pair transverse momentum and second-order flow-vector magnitude. The correlation functions are fit using the Bowler-Sinyukov form with the exponential HBT correlation function. The extracted HBT radii, Rout, Rside and Rlong and a significant out-side cross-term are found to exhibit significant modulation with respect to the second-order event plane, similar to that observed in heavy-ion collisions. Results of the measurements and physics implications of the result, will be discussed.

Rapidity decorrelation of anisotropic flow caused by hydrodynamic fluctuations

We investigate the effect of hydrodynamic fluctuations on the rapidity decorrelations of anisotropic flow in high-energy nuclear collisions using a (3+1)-dimensional integrated dynamical model. The integrated dynamical model consists of twisted initial conditions, fluctuating hydrodynamics, and hadronic cascades on an event-by-event basis. To understand the rapidity decorrelation, we analyze the factorization ratio in the longitudinal direction. Comparing the factorization ratios between fluctuating hydrodynamics and ordinary viscous hydrodynamics, we find a sizable effect of hydrodynamic fluctuations on rapidity decorrelations. We also propose to calculate the Legendre coefficients of the flow magnitude and the event-plane angle to understand the decorrelation of anisotropic flow in the longitudinal direction.

Investigation of the linear and mode-coupled flow harmonics in Au+Au collisions at [formula omitted] = 200 GeV

Flow harmonics (vn) of the Fourier expansion for the azimuthal distributions of hadrons are commonly employed to quantify the azimuthal anisotropy of particle production relative to the collision symmetry planes. While lower order Fourier coefficients (v2 and v3) are more directly related to the corresponding eccentricities of the initial state, the higher-order flow harmonics (vn>3) can be induced by a mode-coupled response to the lower-order anisotropies, in addition to a linear response to the same-order anisotropies. These higher-order flow harmonics and their linear and mode-coupled contributions can be used to more precisely constrain the initial conditions and the transport properties of the medium in theoretical models. The multiparticle azimuthal cumulant method is used to measure the linear and mode-coupled contributions in the higher-order anisotropic flow, the mode-coupled response coefficients, and the correlations of the event plane angles for charged particles as functions of centrality and transverse momentum in Au+Au collisions at nucleon-nucleon center-of-mass energy sNN= 200 GeV. The results are compared to similar LHC measurements as well as to several viscous hydrodynamic calculations with varying initial conditions.

Measurement of two-particle correlations with respect to second- and third-order event planes in Au + Au collisions at sNN=200 GeV

We present measurements of azimuthal correlations of charged hadron pairs in $\sqrt{s_{_{NN}}}=200$ GeV Au$+$Au collisions for the trigger and associated particle transverse-momentum ranges of $1<p_T^t<10$~GeV/$c$ and $0.5<p_T^a<10$~GeV/$c$. After subtraction of an underlying event using a model that includes higher-order azimuthal anisotropy $v_2$, $v_3$, and $v_4$, the away-side yield of the highest trigger-\pt ($p_T^t>4$~GeV/$c$) correlations is suppressed compared to that of correlations measured in $p$$+$$p$ collisions. At the lowest associated particle $p_T$ ($0.5<p_T^a<1$ GeV/$c$), the away-side shape and yield are modified relative to those in $p$$+$$p$ collisions. These observations are consistent with the scenario of radiative-jet energy loss. For the low-$p_T$ trigger correlations ($2<p_T^t<4$ GeV/$c$), a finite away-side yield exists and we explore the dependence of the shape of the away-side within the context of an underlying-event model. Correlations are also studied differentially versus event-plane angle $\Psi_2$ and $\Psi_3$. The angular correlations show an asymmetry when selecting the sign of the difference between the trigger-particle azimuthal angle and the $\Psi_2$ event plane. This asymmetry and the measured suppression of the pair yield out of plane is consistent with a path-length-dependent energy loss. No $\Psi_3$ dependence can be resolved within experimental uncertainties.

Longitudinal decorrelation measures of flow magnitude and event-plane angles in ultrarelativistic nuclear collisions

We discuss the forward-backward correlations of harmonic flow in Pb+Pb collisions at the CERN Large Hadron Collider (LHC), applying standard multibin measures, as well as proposed here new measures. We illustrate the methods with hydrodynamic model simulations based on event-by-event initial conditions from the wounded quark model with asymmetric rapidity emission profiles. Within the model we examine independently the event-plane angle and the flow magnitude decorrelations. We find specific hierarchy between various flow decorrelation measures and confirm certain factorization relations. We find qualitative agreement of the model and the data from the ATLAS and CMS Collaborations.

Chiral magnetic effect search in p+Au, d+Au and Au+Au collisions at RHIC

Metastable domains of fluctuating topological charges can change the chirality of quarks and induce local parity violation in quantum chromodynamics. This can lead to observable charge separation along the direction of the strong magnetic field produced by spectator protons in relativistic heavy-ion collisions, a phenomenon called the chiral magnetic effect (CME). A major background source for CME measurements using the charge-dependent azimuthal correlator (Δϒ) is the intrinsic particle correlations (such as resonance decays) coupled with the azimuthal elliptical anisotropy (v2). In heavy-ion collisions, the magnetic field direction and event plane angle are correlated, thus the CME and the v2-induced background are entangled. In this report, we present two studies from STAR to shed further lights on the background issue. (1) The Δϒ should be all background in small system p+Au and d+Au collisions, because the event plane angles are dominated by geometry fluctuations uncorrelated to the magnetic field direction. However, significant Δϒ is observed, comparable to the peripheral Au+Au data, suggesting a background dominance in the latter, and likely also in the mid-central Au+Au collisions where the multiplicity and v2 scaled correlator is similar. (2) A new approach is devised to study Δϒ as a function of the particle pair invariant mass (minv) to identify the resonance backgrounds and hence to extract the possible CME signal. Signal is consistent with zero within uncertainties at high minv. Signal at low minv, extracted from a two-component model assuming smooth mass dependence, is consistent with zero within uncertainties.

Event-by-Event Hydrodynamics+Jet Energy Loss: A Solution to the R_{AA}⊗v_{2} Puzzle.

High p_{T}>10 GeV elliptic flow, which is experimentally measured via the correlation between soft and hard hadrons, receives competing contributions from event-by-event fluctuations of the low-p_{T} elliptic flow and event-plane angle fluctuations in the soft sector. In this Letter, a proper account of these event-by-event fluctuations in the soft sector, modeled via viscous hydrodynamics, is combined with a jet-energy-loss model to reveal that the positive contribution from low-p_{T} v_{2} fluctuations overwhelms the negative contributions from event-plane fluctuations. This leads to an enhancement of high-p_{T}>10 GeV elliptic flow in comparison to previous calculations and provides a natural solution to the decade-long high-p_{T} R_{AA}⊗v_{2} puzzle. We also present the first theoretical calculation of high-p_{T} v_{3}, which is shown to be compatible with current LHC data. Furthermore, we discuss how short-wavelength jet-medium physics can be deconvoluted from the physics of soft, bulk event-by-event flow observables using event-shape engineering techniques.

Pinning down QCD-matter shear viscosity in ultrarelativistic heavy-ion collisions via EbyE fluctuations using pQCD + saturation + hydrodynamics

We introduce an event-by-event pQCD + saturation + hydro (”EKRT”) framework for high-energy heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading order (NLO) perturbative QCD (pQCD) using saturation to control soft particle production, and describe the space-time evolution of the QCD matter with viscous hydrodynamics, event by event (EbyE). We compare the computed centrality dependence of hadronic multiplicities, pT spectra and flow coefficients vn against LHC and RHIC data. We compare also the computed EbyE probability distributions of relative fluctuations of vn, as well as correlations of 2 and 3 event-plane angles, with LHC data. Our systematic multi-energy and -observable analysis not only tests the initial state calculation and applicability of hydrodynamics, but also makes it possible to constrain the temperature dependence of the shear viscosity-to-entropy ratio, η/s(T), of QCD matter in its different phases. Remarkably, we can describe all these different flow observables and correlations consistently with η/s(T) that is independent of the collision energy.

Soft probes of the QGP: Pb-Pb and p-Pb CMS results

The CMS collaboration measured second-order single-particle anisotropy, ν2, using 2-, 4-, 6- and 8-particle correlations as well as the Lee-Yang Zero method in pPb and PbPb collisions. This result shows that the correlations found in the small and highly asymmetric pPb collision system are long-range and have a many-particle origin. Deeper insight into the nature of these correlations is achieved by studying the factorization breaking effect which appears trough a pT-dependent event plane angle, caused by the initial-state fluctuations. The effect is largest for the most-central PbPb collisions (up to 20%), while it is on the level of few percent for peripheral PbPb and high-multiplicity pPb events. Hydrodynamics models which include a pT-dependent event plane angle semi-quantitatively describe the data and suggest that the effect is mainly determined by the initial-state conditions.

Decorrelation of anisotropic flow along the longitudinal direction

The initial energy density distribution and fluctuation in the transverse direction lead to anisotropic flows of final hadrons through collective expansion in high-energy heavy-ion collisions. Fluctuations along the longitudinal direction, on the other hand, can result in decorrelation of anisotropic flows in different regions of pseudo rapidity ($\eta$). Decorrelation of the $2$nd and $3$rd order anisotropic flows with different $\eta$ gaps for final charged hadrons in high-energy heavy-ion collisions is studied in an event-by-event (3+1)D ideal hydrodynamic model with fully fluctuating initial conditions from A Multi-Phase Transport (AMPT) model. The decorrelation of anisotropic flows of final hadrons with large $\eta$ gaps are found to originate from the spatial decorrelation along the longitudinal direction in the AMPT initial conditions through hydrodynamic evolution. The decorrelation is found to consist of both a linear twist and random fluctuation of the event-plane angles. The agreement between our results and recent CMS data in most centralities suggests that the string-like mechanism of initial parton production in AMPT model captures the initial longitudinal fluctuation that is responsible for the measured decorrelation of anisotropic flows in Pb+Pb collisions at LHC. Our predictions for Au+Au collisions at the highest RHIC energy show stronger longitudinal decorrelation, indicating larger longitudinal fluctuations at lower beam energies. Our study also calls into question some of the current experimental methods for measuring anisotropic flows and extraction of transport coefficients through comparisons to hydrodynamic simulations that do not include longitudinal fluctuations.

Event-by-event fluctuations in a perturbative QCD + saturation + hydrodynamics model: Determining QCD matter shear viscosity in ultrarelativistic heavy-ion collisions

We introduce an event-by-event perturbative-QCD + saturation + hydro ("EKRT") framework for ultrarelativistic heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading order perturbative QCD using a saturation conjecture to control soft particle production, and describe the space-time evolution of the QCD matter with dissipative fluid dynamics, event by event. We perform a simultaneous comparison of the centrality dependence of hadronic multiplicities, transverse momentum spectra, and flow coefficients of the azimuth-angle asymmetries, against the LHC and RHIC measurements. We compare also the computed event-by-event probability distributions of relative fluctuations of elliptic flow, and event-plane angle correlations, with the experimental data from Pb+Pb collisions at the LHC. We show how such a systematic multi-energy and multi-observable analysis tests the initial state calculation and the applicability region of hydrodynamics, and in particular how it constrains the temperature dependence of the shear viscosity-to-entropy ratio of QCD matter in its different phases in a remarkably consistent manner.

Predictions for 5.023 TeV Pb + Pb collisions at the CERN Large Hadron Collider

We compute predictions for various low-transverse-momentum bulk observables in $\sqrt{{s}_{NN}}=5.023$ TeV Pb+Pb collisions at the CERN Large Hadron Collider (LHC) from the event-by-event next-to-leading-order perturbative-QCD + saturation + viscous hydrodynamics (``EKRT'') model. In particular, we consider the centrality dependence of charged hadron multiplicity, flow coefficients of the azimuth-angle asymmetries, and correlations of event-plane angles. The centrality dependencies of the studied observables are predicted to be very similar to those at 2.76 TeV, and the magnitudes of the flow coefficients and event-plane angle correlations are predicted to be close to those at 2.76 TeV. The flow coefficients may, however, offer slightly more discriminating power on the temperature dependence of QCD matter viscosity than the 2.76 TeV measurements. Our prediction for the multiplicity in the 0--5 % centrality class, obtained using the two temperature-dependent shear-viscosity-to-entropy ratios that give the best overall fit to BNL Relativistic Heavy Ion Collider (RHIC) and LHC data is $d{N}_{\mathrm{ch}}/d\ensuremath{\eta}{|}_{|\ensuremath{\eta}|\ensuremath{\le}0.5}=1876\ensuremath{\cdots}2046$. We also predict a power-law increase from 200 GeV Au+Au collisions at RHIC to 2.76 and 5.023 TeV Pb+Pb collisions at the LHC, $d{N}_{\mathrm{ch}}/d\ensuremath{\eta}{|}_{|\ensuremath{\eta}|\ensuremath{\le}0.5}\ensuremath{\propto}{s}^{0.164\ensuremath{\cdots}0.174}$.

The torque effect and fluctuations of entropy deposition in rapidity in ultra-relativistic nuclear collisions

The decorrelation of the orientation of the event-plane angles in the initial state of relativistic Pb–Pb and p–Pb collisions, the “torque effect”, is studied in a model of entropy deposition in the longitudinal direction involving fluctuations of the longitudinal source profile on large scales. The radiation from a single wounded nucleon is asymmetric in space–time rapidity. It is assumed that the extent in rapidity of the region of deposited entropy is random. Fluctuations in the deposition of entropy from each source increase the event-plane decorrelation: for Pb–Pb collisions the change is moderate, while for p–Pb collisions the mechanism is absolutely essential to generate any sizable decorrelation. We also show that the experimental data for rank-four flow may be explained via folding of the elliptic flow. The results suggest the existence of long range fluctuations in the space–time distribution of entropy in the initial stages of relativistic nuclear collisions.

Hydrodynamic modeling of pseudorapidity flow correlations in relativistic heavy-ion collisions and the torque effect

We analyze correlations between the event-plane angles in different intervals of pseudorapidity within the 3+1-dimensional viscous hydrodynamics with the Glauber-model initial conditions. As predicted earlier, the fluctuations in the particle production mechanism in the earliest stage, together with asymmetry of the emission profiles in pseudorapidity from the forward and backwardgoing wounded nucleons, lead to the torque effect, namely, decorrelation of the event-plane angles in distant pseudorapidity bins. We use two- or three-bin measures of correlation functions to quantify the effect, with the latter compared to the recent data from the CMS collaboration. We find a sizable torque effect, with magnitude larger at the BNL Relativistic Heavy Ion Collider than at the CERN Large Hadron Collider.

Possible observables for the chiral electric separation effect in Cu + Au collisions

The quark-gluon plasma (QGP) generated in relativistic heavy-ion collisions could be locally parity-odd. In parity-odd QGP, the electric field may induce a chiral current which is called the chiral electric separation effect (CESE). We propose two possible observables for CESE in Cu + Au collisions: The first one is the correlation $\zeta_{\alpha\beta}=\langle \cos[2(\phi_\alpha+\phi_\beta-2\Psi_{\rm RP})]\rangle$; the second one is the charge-dependent event-plane angle $\Psi^{q}_2$ with $q=\pm$ being charge. Nonzero $\Delta\zeta=\zeta_{opp}-\zeta_{same}$ and $\Delta\Psi=\langle|\Psi_2^+-\Psi_2^-|\rangle$ may signal the CESE in Cu + Au collisions. Within a multiphase transport model, we study how the final state interaction affects these observables. We find that the correlation $\gamma_{\alpha\beta}=\langle\cos(\phi_{\alpha}+\phi_{\beta}-\Psi_{\rm RP})\rangle$ is sensitive to the out-of-plane charge separation caused by the chiral magnetic effect and to the in-plane charge separation caused by the in-plane electric field, but it is not sensitive to the CESE. On the other hand, $\Delta\zeta$ and $\Delta\Psi$ are sensitive to the CESE. Therefore, we suggest that the future experiments measure the above observables in Cu+Au collisions in order to disentangle different chiral and charge separation mechanisms.

Probing initial-state fluctuations with pT-dependent event-plane angle in pPb and PbPb collisions

Abstract The technique of two-particle correlations has been widely used in studying flow via azimuthal anisotropy in relativistic heavy-ion collisions. A key assumption imposed in this approach is the factorization of Fourier coefficients extracted from two-particle correlations into a product of single-particle anisotropies of trigger and associated particles. It was recently predicted by hydrodynamics that due to initial-state participant fluctuations, a transverse momentum ( p T ) dependence of the event-plane angle would be induced, leading to a breakdown of factorization, even if hydrodynamic flow is the only source of correlations. We present a systematic examination of the factorization assumption in pPb and PbPb collisions at a nucleon–nucleon center-of-mass energy of 5.02 TeV and 2.76 TeV, respectively, with the CMS experiment. Significant breakdown of factorization (up to 20%) is observed in a large sample of ultra-central (0–0.2%) triggered PbPb events, where initial-state fluctuations play a dominant role. Comparison of data and viscous hydrodynamic predictions, as a function of p T and centrality, allows new constraints on the modeling of initial condition and shear viscosity to entropy density ( η / s ) ratio of the medium created in heavy-ion collisions. Furthermore, the measurement is also extended to high-multiplicity pPb collisions. As the initial-state geometry of a pPb collision is expected to be entirely a consequence of fluctuations, quantitative studies of factorization breakdown will help to investigate the nature of the observed long-range correlations in pPb collisions, particularly in the context of hydrodynamic models.