Multiparticle Correlations Research Articles

Review of nonflow estimation methods and uncertainties in relativistic heavy-ion collisions

Abstract Collective anisotropic flow, where particles are correlated over the entire event, is a prominent phenomenon in relativistic heavy-ion collisions and is sensitive to the properties of the matter created in those collisions. It is often measured by two- and multi-particle correlations and is therefore contaminated by nonflow, those genuine few-body correlations unrelated to the global event-wise correlations. Many methods have been devised to estimate nonflow contamination with various degrees of successes and difficulties. Here, we review those methods pedagogically, discussing the pros and cons of each method, and give examples of ballpark estimate of nonflow contamination and associated uncertainties in relativistic heavy-ion collisions. We hope such a review of the various nonflow estimation methods in a single place would prove helpful to future researches.

Hurst Exponent and Event-by-Event Fluctuations in Relativistic Nucleus–Nucleus Collisions

A joint study of multi-particle pseudo-rapidity correlations and event-by-event fluctuations in the distributions of secondary particles and fragments of the target nucleus and the projectile nucleus was carried out in order to search for correlated clusters of secondary particles. An analysis of the collisions of the sulfur nucleus with photoemulsion nuclei at an energy of 200 A·GeV is presented based on experimental data obtained at the SPS at CERN. The analysis of multi-particle correlations was performed using the Hurst method. A detailed analysis of each individual event showed that in events of complete destruction of a projectile nucleus with a high multiplicity of secondary particles, long-distance multi-particle pseudo-rapidity correlations are observed. The distribution of average pseudo-rapidity in such events differs significantly from others, as it is much narrower, and its average value is noticeably shifted towards lower values <η>.

Symmetric cumulant sc2,4{4} and asymmetric cumulant ac2{3} from transverse momentum conservation and flow

Multiparticle cumulants method can be used to reveal long-range collectivity in small and large colliding systems. The four-particle symmetric cumulant sc2,4{4}, three-particle asymmetric cumulant ac2{3}, and the normalized cumulants nsc2,4{4} and nac2{3} from the transverse momentum conservation and flow are calculated. The interplay between the two effects is also investigated. Our results are in a good agreement with the recent ATLAS measurements of multiparticle azimuthal correlations with the subevent cumulant method, which provides insight into the origin of collective flow in small systems. Published by the American Physical Society 2024

Probing the nuclear structure with multiparticle correlation in Xe–Xe collisions

Probing the nuclear structure with multiparticle correlation in Xe–Xe collisions

Hierarchical Framework for Predicting Entropies in Bottom-Up Coarse-Grained Models.

The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However, performing additional CG simulations on top of model construction often leads to significant additional computational overhead. In this work, we propose a simple hierarchical framework for predicting the thermodynamic entropies of various molecular CG systems. Our approach employs a decomposition of the CG interactions, enabling the estimation of the CG partition function and thermodynamic properties a priori. Starting from the ideal gas description, we leverage classical perturbation theory to systematically incorporate simple yet essential interactions, ranging from the hard sphere model to the generalized van der Waals model. Additionally, we propose an alternative approach based on multiparticle correlation functions, allowing for systematic improvements through higher-order correlations. Numerical applications to molecular liquids validate the high fidelity of our approach, and our computational protocols demonstrate that a reduced model with simple energetics can reasonably estimate the thermodynamic entropy of CG models without performing any CG simulations. Overall, our findings present a systematic framework for estimating not only the entropy but also other thermodynamic properties of CG models, relying solely on information from the reference system.

Effective interaction between guest charges immersed in 2D jellium

The model under study is an infinite 2D jellium of pointlike particles with elementary charge e, interacting via the logarithmic potential and in thermal equilibrium at the inverse temperature β. Two cases of the coupling constant Γ≡βe2 are considered: the Debye–Hückel limit Γ→0 and the free-fermion point Γ=2 . In the most general formulation, two guest particles, the one with charge qe (the valence q being an arbitrary integer) and the hard core of radius σ > 0 and the pointlike one with elementary charge e, are immersed in the bulk of the jellium at distance d⩾σ . Two problems are of interest: the asymptotic large-distance behavior of the excess charge density induced in the jellium and the effective interaction between the guest particles. Technically, the induced charge density and the effective interaction are expressed in terms of multi-particle correlations of the pure (translationally invariant) jellium system. It is shown that the separation form of the induced charge density onto its radial and angle parts, observed previously in the limit Γ→0 , is not reproduced at the coupling Γ=2 . Based on an exact expression for the effective interaction between guest particles at Γ=2 , oppositely ( q=0,−1,−2,… ) charged guest particles always attract one another while likely ( q=1,2,… ) charged guest particles repeal one another up to a certain distance d between them and then the mutual attraction takes place up to asymptotically large (finite) distances.

Generic multi-particle transverse momentum correlations as a new tool for studying nuclear structure at the energy frontier

The mean transverse momentum of produced particles, [pT]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[p_\ extrm{T} ]$$\\end{document}, and its event-by-event fluctuations give direct access to the initial conditions of ultra-relativistic heavy-ion collisions and help probe the colliding nuclei’s structure. The [pT]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[p_\ extrm{T} ]$$\\end{document} fluctuations can be studied via multi-particle pT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_\ extrm{T}$$\\end{document} correlations; so far, only the lowest four orders have been studied. Higher-order fluctuations can provide stronger constraints on the initial conditions and improved sensitivity to the detailed nuclear structure; however, their direct implementation can be challenging and is still lacking. In this paper, we apply a generic recursive algorithm for the genuine multi-particle pT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_\ extrm{T}$$\\end{document} correlations, which enables the accurate study of higher-order [pT]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[p_\ extrm{T} ]$$\\end{document} fluctuations without heavy computational cost for the first time. With this algorithm, we will examine the power of multi-particle pT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_\ extrm{T}$$\\end{document} correlations through Monte Carlo model studies with different nuclear structures. The impact on the nuclear structure studies, including the nuclear deformation and triaxial structure, will be discussed. These results demonstrate the usefulness of multi-particle pT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_\ extrm{T}$$\\end{document} correlations for studying nuclear structure in high-energy nuclei collisions at RHIC and the LHC, which could serve as a complementary tool to existing low-energy nuclear structure studies.

Higher-order moments of the elliptic flow distribution in PbPb collisions at sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s_{\ extrm{NN}}} $$\\end{document} = 5.02 TeV

The hydrodynamic flow-like behavior of charged hadrons in high-energy lead-lead collisions is studied through multiparticle correlations. The elliptic anisotropy values based on different orders of multiparticle cumulants, v2{2k}, are measured up to the tenth order (k = 5) as functions of the collision centrality at a nucleon-nucleon center-of-mass energy of sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s_{\ extrm{NN}}} $$\\end{document} = 5.02 TeV. The data were recorded by the CMS experiment at the LHC and correspond to an integrated luminosity of 0.607 nb−1. A hierarchy is observed between the coefficients, with v2{2} > v2{4} ≳ v2{6} ≳ v2{8} ≳ v2{10}. Based on these results, centrality-dependent moments for the fluctuation-driven event-by-event v2 distribution are determined, including the skewness, kurtosis and, for the first time, superskewness. Assuming a hydrodynamic expansion of the produced medium, these moments directly probe the initial-state geometry in high-energy nucleus-nucleus collisions.

Pseudorapidity dependence of anisotropic flow and its decorrelations using long-range multiparticle correlations in Pb–Pb and Xe–Xe collisions

The pseudorapidity dependence of elliptic (v2), triangular (v3), and quadrangular (v4) flow coefficients of charged particles measured in Pb–Pb collisions at a centre-of-mass energy per nucleon pair of sNN=5.02TeV and in Xe–Xe collisions at sNN=5.44TeV with ALICE at the LHC are presented. The measurements are performed in the pseudorapidity range −3.5<η<5 for various centrality intervals using two- and multi-particle cumulants with the subevent method. The flow probability density function (p.d.f.) is studied with the ratio of flow coefficient v2 calculated with four- and two-particle cumulant, and suggests that the variance of flow p.d.f. is independent of pseudorapidity. The decorrelation of the flow vector in the longitudinal direction is probed using two-particle correlations. The results measured with respect to different reference regions in pseudorapidity exhibit differences, argued to be a result of saturating decorrelation effect above a certain pseudorapidity separation, in contrast to previous publications which assign this observation to non-flow effects. The results are compared to 3+1 dimensional hydrodynamic and the AMPT transport model calculations. Neither of the models is able to simultaneously describe the pseudorapidity dependence of measurements of anisotropic flow and its fluctuations. The results presented in this work highlight shortcomings in our current understanding of initial conditions and subsequent system expansion in the longitudinal direction. Therefore, they provide input for its improvement.

Many-body correlations for nuclear physics across scales: from nuclei to quark-gluon plasmas to hadron distributions

It is an experimental fact that multi-particle correlations in the final states of high-energy nucleus-nucleus collisions are sensitive to collective correlations of nucleons in the wave functions of the colliding nuclei. Here, I show that this connection is more direct than it intuitively seems. With an energy deposition scheme inspired by high-energy quantum chromodynamics, and within a linearized description of initial-state fluctuations in the quark-gluon plasma, I exhibit relations between N-particle correlations in the final states of nuclear collisions and N-nucleon density distributions in the colliding nuclei. This result formally justifies the sensitivity of the outcome of high-energy collisions to features such as nuclear deformations. It paves the way, thus, to systematic studies of the impact of state-of-the-art nuclear interactions in such processes.

Multiparticle correlations, cumulants, and moments sensitive to fluctuations in rare-probe azimuthal anisotropy in heavy ion collisions

Multiparticle correlations, cumulants, and moments sensitive to fluctuations in rare-probe azimuthal anisotropy in heavy ion collisions

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.

Transverse momentum decorrelation of the flow vector in Pb–Pb collisions at sqrt{s_{_{textrm{NN}}}} = 5.02 TeV

Anisotropic flow, typically defined as the azimuthal correlations of the produced particles with respect to the common symmetry plane over a large kinematic, has been a popular approach in the last three decades to explore the properties of hot and dense QCD matter in high-energy heavy-ion collisions. These flow studies are usually based on the multi-particle correlations method, assuming that multi-particle correlations can be factorized into the product of flow coefficients. However, recent LHC measurements, based on new four-particle correlation observables, show evidence of flow angle decorrelation and flow magnitude decorrelation. These decorrelations break the assumption of the common symmetry plane and factorization. In this paper, we perform systematic studies to investigate the decorrelation with A Multi-Phase Transport (AMPT) model. We examine different tunings of the initial conditions, partonic cross sections, and hadronic interactions, revealing that the decorrelations are mainly driven by the initial geometry fluctuations while weakly influenced by the system’s dynamic evolution. Comparison to experimental data and the AMPT calculations presented in this paper promotes a new possibility to further constraints on the initial conditions of the heavy-ion collisions.

Strange hadron collectivity in pPb and PbPb collisions

The collective behavior of {textrm{K}}_{textrm{S}}^0 and Lambda /overline{Lambda} strange hadrons is studied by measuring the elliptic azimuthal anisotropy (v2) using the scalar-product and multiparticle correlation methods. Proton-lead (pPb) collisions at a nucleon-nucleon center-of-mass energy sqrt{s_{textrm{NN}}} = 8.16 TeV and lead-lead (PbPb) collisions at sqrt{s_{textrm{NN}}} = 5.02 TeV collected by the CMS experiment at the LHC are investigated. Nonflow effects in the pPb collisions are studied by using a subevent cumulant analysis and by excluding events where a jet with transverse momentum greater than 20 GeV is present. The strange hadron v2 values extracted in pPb collisions via the four- and six-particle correlation method are found to be nearly identical, suggesting the collective behavior. Comparisons of the pPb and PbPb results for both strange hadrons and charged particles illustrate how event-by-event flow fluctuations depend on the system size.

Separating single- from multi-particle dynamics in nonlinear spectroscopy.

Quantum states depend on the coordinates of all their constituent particles, with essential multi-particle correlations. Time-resolved laser spectroscopy1 is widely used to probe the energies and dynamics of excited particles and quasiparticles such as electrons and holes2,3, excitons4-6, plasmons7, polaritons8 or phonons9. However, nonlinear signals from single- and multiple-particle excitations are all present simultaneously and cannot be disentangled without a priori knowledge of the system4,10. Here, we show that transient absorption-the most commonly used nonlinear spectroscopy-with N prescribed excitation intensities allows separation of the dynamics into N increasingly nonlinear contributions; in systems well-described by discrete excitations, these N contributions systematically report on zero to N excitations. We obtain clean single-particle dynamics even at high excitation intensities and can systematically increase the number of interacting particles, infer their interaction energies and reconstruct their dynamics, which are not measurable via conventional means. We extract single- and multiple-exciton dynamics in squaraine polymers11,12 and, contrary to common assumption6,13, we find that the excitons, on average, meet several times before annihilating. This surprising ability of excitons to survive encounters is important for efficient organic photovoltaics14,15. As we demonstrate on five diverse systems, our procedure is general, independent of the measured system or type of observed (quasi)particle and straightforward to implement. We envision future applicability in the probing of (quasi)particle interactions in such diverse areas as plasmonics7, Auger recombination2 and exciton correlations in quantum dots5,16,17, singlet fission18, exciton interactions in two-dimensional materials19 and in molecules20,21, carrier multiplication22, multiphonon scattering9 or polariton-polariton interaction8.

Frequency Combs with Parity-Protected Cross-Correlations and Entanglement from Dynamically Modulated Qubit Arrays.

We develop a general theoretical framework to dynamically engineer quantum correlations and entanglement in the frequency-comb emission from an array of superconducting qubits in a waveguide, rigorously accounting for the temporal modulation of the qubit resonance frequencies. We demonstrate that when the resonance frequencies of the two qubits are periodically modulated with a π phase shift, it is possible to realize simultaneous bunching and antibunching in cross-correlations as well as Bell states of the scattered photons from different sidebands. Our approach, based on the dynamical conversion between the quantum excitations with different parity symmetry, is quite universal. It can be used to control multiparticle correlations in generic dynamically modulated dissipative quantum systems.

Interplay between core and corona from small to large systems

We present new results in p+p and Pb+Pb collisions at the LHC energies from the updated dynamical core–corona initialization framework (DCCI2). The fractions of final hadron yields originating from equilibrated and non-equilibrated components are extracted as functions of multiplicity. We find that the contributions from non-equilibrated components are non-negligible even in Pb+Pb collisions and affect pT-integrated multi-particle correlations. These suggest the importance of non-equilibrated components for the sophisticated extraction of properties of the quark gluon plasma from comparisons between dynamical frameworks and experimental data.

ADVANCES IN SYSTEMS EVOLUTION THROUGH QUANTUM CORRELATIONS WITHIN ENGINEERING APPLICATIONS

In this paper, we explore the dynamics of quantum correlations in an isolated physical quantum under the influence of intrinsic coherence. We characterize the quantum correlations in the hybrid system using the granular model to investigate the amount of coherent-chaotic fractions, and we particularly use the spherical droplets to measure the specific correlations. Likewise, we examine the effect of coherence on the source evolution of these quantifiers within engineering applications. In particular, the behavior of the multiparticle correlations in terms of the system parameters and the coherence rate is investigated and analyzed in detail to explore the source intrinsic dimensions. We found that the correlations with genuine interferences behave slightly unsymmetrical for identical parameters characterizing the considered complex system and that the genuine correlations are more meaningful than primary interference which probed the chaotic peculiarities against the coherence phenomena. Our results also show that the robustness of quantum correlations can be modulated by adjusting the coherent rate, source physical properties and the initial conditions.

Multiparticle orientational correlations are responsible for the nonlinear dielectric effect: Analysis of temperature-dependent measurements for glycerol.

The nonlinear dielectric effect (NDE) is traditionally viewed as originating from saturation of the response of individual dipoles in a strong electric field. This mean-field view, mathematically described by the Langevin saturation function, predicts enhanced dielectric saturation at lower temperatures. In contrast, recent experiments for glycerol have shown a sharp increase of the NDE with increasing temperature. The formalism presented here splits the NDE into a sum of a term representing binary correlations of dipolar orientations and terms referring to three- and four-particle orientational correlations. Analysis of experimental data shows that the contribution of three- and four-particle correlations strongly increases at elevated temperatures. The mean-field picture of dielectric saturation as the origin of the NDE is inconsistent with observations. A positive NDE (increment of the field-dependent dielectric constant) is predicted for low-concentration solutions of polar molecules in nonpolar solvents. The dependence of the NDE on the concentration of the polar component is polynomial.

Enhanced interactions of interlayer excitons in free-standing heterobilayers.

Strong, long-range dipole-dipole interactions between interlayer excitons (IXs) can lead to new multiparticle correlation regimes1,2, which drive the system into distinct quantum and classical phases2-5, including dipolar liquids, crystals and superfluids. Both repulsive and attractive dipole-dipole interactions have been theoretically predicted between IXs in a semiconductor bilayer2,6-8, but only repulsive interactions have been reported experimentally so far3,9-16. This study investigated free-standing, twisted (51°, 53°, 45°) tungsten diselenide/tungsten disulfide (WSe2/WS2) heterobilayers, in which we observed a transition in the nature of dipolar interactions among IXs, from repulsive to attractive. This was caused by quantum-exchange-correlation effects, leading to the appearance of a robust interlayer biexciton phase (formed by two IXs), which has been theoretically predicted6-8 but never observedbefore in experiments. The reduced dielectric screening in a free-standing heterobilayer not only resulted in a much higher formation efficiency of IXs, but also led to strongly enhanced dipole-dipole interactions, which enabled us to observe the many-body correlations of pristine IXs at the two-dimensional quantum limit. In addition, we firstly observed several emission peaks from moiré-trapped IXs at room temperature in a well-aligned, free-standing WSe2/WS2 heterobilayer. Our findings open avenues for exploring new quantum phases with potential for applications in non-linear optics.