Two-particle Correlations Research Articles

Two-point Correlation Function Studies for the Milky Way: Discovery of Spatial Clustering from Disk Excitations and Substructure

We introduce a two-particle correlation function (2PCF) for the Milky Way, constructed to probe spatial correlations in the orthogonal directions of the stellar disk in the Galactic cylindrical coordinates of R, ϕ, and z. We use this new tool to probe the structure and dynamics of the Galaxy using the carefully selected set of solar neighborhood stars (d ≲ 3 kpc) from Gaia Data Release 2 that we previously employed for studies of axial symmetry breaking in stellar number counts. We make additional, extensive tests, comparing to reference numerical simulations, to ensure our control over possibly confounding systematic effects. Supposing either axial or north–south symmetry, we divide this data set into two nominally symmetric sectors and construct the 2PCF, in the manner of the Landy–Szalay estimator, from the Gaia data. In so doing, working well away from the midplane region in which the spiral arms appear, we have discovered distinct symmetry-breaking patterns in the 2PCF in its orthogonal directions, thus establishing the existence of correlations in stellar number counts alone at subkiloparsec length scales for the very first time. In particular, we observe extensive wavelike structures of amplitude greatly in excess of what we would estimate if the system were in a steady state. We study the variations in these patterns across the Galactic disk, and with increasing ∣z∣, and we show how our results complement other observations of non-steady-state effects near the Sun, such as vertical asymmetries in stellar number counts and the Gaia snail.

Two-particle tight-binding description of higher-harmonic generation in semiconductor nanostructures

We develop a quantum mechanical theory to describe the optical response of semiconductor nanostructures with a particular emphasis on higher-order harmonic Generation. Based on a tight-binding approach we take all two-particle correlations into account thus describing the creation, evolution and annihilation of electron and holes. In the limiting case of bulk materials, we obtain the same precision as that achieved by solving the well-established semiconductor Bloch Equations. For semiconducting structures of finite extent, we also incorporate the surrounding space thus enabling a description of electron emission. In addition, we incorporate different relaxation mechanisms such as dephasing and damping of intraband currents. Moreover, the advantage of our description is that, starting from extremely precise material data as e.g., from tight-binding parameters obtained from density-functional-theory calculations, we obtain a numerical description being by far less computationally challenging and resource-demanding as comparable ab-initio approaches, e.g., those based on time-dependent density functional theory.

Multiplicity-Momentum Correlations in Relativistic Nuclear Collisions

We introduce a two-particle correlation observable that measures multiplicity-momentum correlations and may facilitate an estimate of the level of equilibration of the medium created in relativistic nuclear collisions. We calculate that multiplicity-momentum correlations should vanish in equilibrium in the Grand Canonical Ensemble, therefore non-zero measured values may indicate that the system has not reached local thermal equilibrium. Information about the level of equilibration of the system is important because many state-of-the-art models assume local equilibration either directly or through the use of an equation of state that makes this assumption. We make estimates of multiplicity-momentum correlations using PYTHIA/Angantyr and find positive values comparable in magnitude to well-measured correlations of transverse momentum fluctuations. We then outline a formalism that can use multiplicity-momentum correlations and correlations of transverse momentum fluctuations to quantify the level of partial thermalization of the system.

Determination of the shear viscosity and light quark diffusivity of QGP with two-particle correlation functions

We discuss measurements of general balance functions recently reported by the ALICE collaboration in the context of a two-stage quark production model and towards the determination of light quark diffusivity.

A Second Order Upper Bound for the Ground State Energy of a Hard-Sphere Gas in the Gross–Pitaevskii Regime

We prove an upper bound for the ground state energy of a Bose gas consisting of N hard spheres with radius mathfrak {a}/N, moving in the three-dimensional unit torus Lambda . Our estimate captures the correct asymptotics of the ground state energy, up to errors that vanish in the limit N rightarrow infty . The proof is based on the construction of an appropriate trial state, given by the product of a Jastrow factor (describing two-particle correlations on short scales) and of a wave function constructed through a (generalized) Bogoliubov transformation, generating orthogonal excitations of the Bose–Einstein condensate and describing correlations on large scales.

Projections of two-particle correlations onto transverse rapidity in Au+Au collisions at sNN=200 GeV at STAR

Two-particle correlation measurements projected onto two-dimensional, transverse rapidity coordinates (yT1,yT2) provide an independent, orthogonal view of the multidimensional correlation distribution that is most often studied via angular projections. As such, these independent transverse projections allow access to manifestations of dynamical fluctuations in relativistic heavy-ion collisions that angular-correlation measurements may not be sensitive to. We report nonidentified charged-particle correlations for Au+Au minimum-bias collisions at sNN=200 GeV taken by the STAR experiment at the Relativistic Heavy-Ion Collider (RHIC). Correlations are presented as two-dimensional functions of transverse rapidity for like-sign, unlike-sign, and all charged-particle pairs, as well as for particle pairs whose relative azimuthal angles lie on the near-side, the away-side, or at all relative azimuth. The correlations are constructed using charged particles with transverse momentum pT≥0.15 GeV/c, pseudorapidity from −1 to 1, and azimuthal angles from −π to π. The significant correlation structures that are observed evolve smoothly with collision centrality. The major correlation features include a saddle shape plus a broad peak with maximum near yT≈3, corresponding to pT≈1.5 GeV/c. The broad peak is observed in both like- and unlike-sign charge combinations and in near- and away-side relative azimuthal angles. The all-charge, all-azimuth correlation measurements are compared with the predictions of hijing and epos to provide theoretical context for these new measurements. The results indicate that the correlations for peripheral to mid-central collisions can be approximately described as a superposition of nucleon + nucleon collisions with minimal effects from the quantum chromodynamics medium. Strong medium effects are indicated in mid- to most-central collisions.1 MoreReceived 22 April 2022Accepted 28 September 2022DOI:https://doi.org/10.1103/PhysRevC.106.044906©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasParticle correlations & fluctuationsRelativistic heavy-ion collisionsNuclear Physics

First study of the two-body scattering involving charm hadrons

This article presents the first measurement of the interaction between charm hadrons and nucleons. The two-particle momentum correlations of $\mathrm{pD^-}$ and $\mathrm{\overline{p}D}^+$ pairs are measured by the ALICE Collaboration in high-multiplicity pp collisions at $\sqrt{s} = 13~\mathrm{TeV}$. The data are compatible with the Coulomb-only interaction hypothesis within (1.1-1.5)$\sigma$. The level of agreement slightly improves if an attractive nucleon(N)$\overline{\mathrm{D}}$ strong interaction is considered, in contrast to most model predictions which suggest an overall repulsive interaction. This measurement allows for the first time an estimation of the 68% confidence level interval for the isospin $\mathrm{I}=0$ inverse scattering length of the $\mathrm{N\overline{D}}$ state ${f_{0,~\mathrm{I}=0}^{-1} \in [-0.4,0.9]~\mathrm{fm^{-1}}}$, assuming negligible interaction for the isospin $\mathrm{I}=1$ channel.

Effect of isolation on two-particle correlations in pilot-wave hydrodynamics

A bouncing droplet with its associated wavefield forms a hydrodynamic analog of de Broglie's pilot-wave. Two bouncing droplets are trapped in their respective cavities and become correlated oscillators at a distance. Then a wide barrier suddenly isolates the two oscillators which transition to new and identical distributions, as a consequence of the previously established correlations. These distributions are different from what they would have been had the oscillators been isolated at the onset.

Implications of correlations and fluctuations in small systems

The small collision systems like p+p and p+A collisions have shown new features like A+A collisions in the relativistic regime. These new aspects in small systems which have altered our research and understanding on the two-particle correlation measurements have been provided. Additionally, a critical observation of the fluctuation measurements provides new ways to infer such novel happening in the small collision systems. The ongoing and future endeavors towards the new measurements are also discussed.

Multi-differential studies to explore strangeness enhancement in pp with ALICE at the LHC

The study of energy and multiplicity dependence of strange hadron production in proton-proton collisions provides a powerful tool to understand similarities and differences between small and large collision systems. In order to better understand the origin of strangeness enhancement in pp new multi-differential analyses have been performed. The first separates the contribution of soft and hard processes, such as jets, to strange hadron production through two-particle correlation techniques. The second exploits the concept of the effective energy available for particle production in the event, which is estimated by an anti-correlation with the energy deposited in ALICE's Zero Degree Calorimeters. The results indicate that strangeness production emerges from the growth of the underlying event and confirm it is related to the final state multiplicity.

K[formula omitted]K[formula omitted] and K[formula omitted]K± femtoscopy in pp collisions at [formula omitted] and 13 TeV

Femtoscopic correlations with the particle pair combinations KS0KS0 and KS0K± are studied in pp collisions at s=5.02 and 13 TeV by the ALICE experiment. At both energies, boson source parameters are extracted for both pair combinations, by fitting models based on Gaussian size distributions of the sources, to the measured two-particle correlation functions. The interaction model used for the KS0KS0 analysis includes quantum statistics and strong final-state interactions through the f0(980) and a0(980) resonances. The model used for the KS0K± analysis includes only the final-state interaction through the a0 resonance. Source parameters extracted in the present work are compared with published values from pp collisions at s=7 TeV and the different pair combinations are found to be consistent. From the observation that the strength of the KS0KS0 correlations is significantly greater than the strength of the KS0K± correlations, the new results are compatible with the a0 resonance being a tetraquark state of the form (q1,q2‾,s,s‾), where q1 and q2 are u or d quarks.

Studying the mechanisms for strange particle production with ALICE at LHC

The main goal of the ALICE experiment is to study the physics of strongly interacting matter, focusing on the properties of the quark-gluon plasma (QGP). The relative production of strange hadrons with respect to non-strange hadrons in heavy-ion collisions was historically considered as one of the signatures of QGP formation. However, the latest results in proton-proton (pp) and proton-lead (p-Pb) collisions have revealed an increasing trend in the yield ratio of strange hadrons to pions with the charged-particle multiplicity in the event, showing a smooth evolution across different collision systems and energies. We present the new studies which are performed with the aim of better understanding the production mechanisms for strange particles and hence the strangeness enhancement phenomenon in small collision systems. In one of the recent studies, the very forward energy transported by beam remnants (spectators) and detected by the Zero Degree Calorimeters (ZDC) is used to classify events. The contribution of the effective energy and the particle multiplicity on strangeness production is studied using a multi-differential approach in order to disentangle initial and final state effects. In the second study, the origin of strangeness enhancement with multiplicity in pp has been further investigated by separating the contribution of soft and hard processes, such as jets, to strange hadron production. Techniques involving full jet reconstruction or two-particle correlations have been exploited. The results indicate that the increased relative strangeness production emerges from the growth of the underlying event, being disconnected from initial state properties, and suggest that soft (out-of-jets) processes are the dominant contribution to strange hadron production.

Two-particle correlations and the metal-insulator transition: Iterated perturbation theory revisited

Recent advances in many-body physics have made it possible to study correlated electron systems at the two-particle level. In Dynamical Mean-Field theory, it has been shown that the metal-insulator phase diagram is closely related to the eigenstructure of the susceptibility. So far, this situation has been studied using accurate but numerically expensive solvers. Here, the Iterated Perturbation Theory (IPT) approximation is used instead. Its simplicity makes it possible to obtain analytical results for the two-particle vertex and the DMFT Jacobian. The limited computational cost also enables a detailed comparison of analytical expressions for the response functions to results obtained using finite differences. At the same time, the approximate nature of IPT precludes an interpretation of the metal-insulator transition in terms of a Landau free energy functional.

The Glauber Model And Flow Analysis with Pb-Pb Collisions at

This work presents data analysis on Pb-Pb collisions with in centrality 40%-50%. Introduction and Monte-Carlo simulation results on the Glauber model are presented, which shed light on the initial geometric configuration of heavy ion collisions. Three-dimensional correlation function is plotted, and Fourier decomposition is carried out in order to obtain elliptic flow. Based on the assumption that non-flow effect is less prominent in long-range area, we separate it from the second Fourier decomposition of two-particle correlation function by making polynomial curve fitting.

Expansion of a one-dimensional Bose gas: the role of interactions and kinetic-energy driving

We study the expansion of a one-dimensional boson gas by initialising it in a small region of a chain, and then suddenly allowing it to expand into the remainder of the chain. We consider three initial ground-state configurations: the Mott insulator, the conventional superfluid, whose momentum density is sharply peaked at zero momentum, and the cat-like state with momentum peaks at ±π/2, produced by kinetic driving, the latter being a particular case of a flat-band system. In turn, we consider three types of expansion: spectroscopic (with interactions tuned to zero), dynamic (with standard short-range repulsive interactions), and under kinetic driving. The numerical calculations are exact. We compute the momentum and real-space one-particle densities, as well as the two-particle momentum correlations. We find that the spectroscopic time-of-flight experiment reflects the initial momentum distribution except for the larger number of momentum states and at high momenta. For the dynamic expansion starting from an insulator, we recover the non-equilibrium quasi-condensation into momenta ±π/2, provide a physical explanation in terms of interacting bosons that is confirmed by the numerical simulation, and note the existence of nontrivial correlations in the momentum distribution. Under kinetic driving the expansion is comparatively slow, but we conjecture that at high densities it will be much faster. We compare various measures of the two-particle momentum correlations, noting that some of them tend to conceal the possible cat-like structure of a many-body state.

Interplay of femtoscopic and charge-balance correlations

Correlations driven by the constraints of local charge conservation have been shown to provide insight into the chemical evolution and diffusivity of the high-temperature matter created in ultra-relativistic heavy ion collisions. Two-particle correlations driven by final-state interactions have allowed the extraction of critical femtoscopic space-time information about the expansion and dissolution of the same collisions. Whereas correlations from final-state interactions mainly appear at small relative momenta, a few tens of MeV/$c$, charge-balance correlations extend over a range of hundreds of MeV/$c$. In nearly all previous analyses, this separation of scales is used to focus solely on one class or the other. The purpose of this study is to quantitatively understand the degree to which correlations from final-state interactions distort the interpretation of charge-balance correlations and vice versa.

Measurement of Two-Particle Correlations of Hadrons in e^{+}e^{-} Collisions at Belle.

The measurement of two-particle angular correlation functions in high-multiplicity e^{+}e^{-} collisions at sqrt[s]=10.52 GeV is reported. In this study, the 89.5 fb^{-1} of hadronic e^{+}e^{-} annihilation data collected by the Belle detector at KEKB are used. Two-particle angular correlation functions are measured in the full relative azimuthal angle (Δϕ) and three units of pseudorapidity (Δη), defined by either the electron beam axis or the event-shape thrust axis, and are studied as a function of charged-particle multiplicity. The measurement in the thrust axis analysis, with mostly outgoing quark pairs determining the reference axis, is sensitive to the region of additional soft gluon emissions. No significant anisotropic collective behavior is observed with either coordinate analyses. Near-side jet correlations appear to be absent in the thrust axis analysis. The measurements are compared to predictions from various event generators and are expected to provide new constraints to the phenomenological models in the low-energy regime.

The effect of substrate waviness on random sequential adsorption packing properties

Random sequential adsorption of spheres on a wavy surface was studied. It was determined how surface structure influences random packing properties such as the packing fraction, the kinetics of packing growth and the two-particle density correlation function. Until the substrate varies within the range one order of magnitude smaller than the particle’s diameter, the properties of the packings obtained do not differ significantly from those on a flat surface. On the other hand, for the higher amplitude of unevenness, the packing fraction, low-density growth kinetics and the density autocorrelation function change significantly, while asymptotic growth kinetics seems to be barely sensitive to surface waviness. Besides fundamental significance, the study suggests that the experimental measurement of the aforementioned basic properties of adsorption monolayers can reveal the surface’s porous structure without investigating the surface itself.

Checking nonflow assumptions and results via PHENIX published correlations in p+p , p+Au , d+Au , and He3+Au at sNN=200 GeV

Recently the PHENIX Collaboration has made available two-particle correlation Fourier coefficients for multiple detector combinations in minimum bias p+p and 0-5% central p+Au, d+Au, 3He+Au collisions at 200 GeV [1]. Using these coefficients for three sets of two-particle correlations, azimuthal anisotropy coefficients $v_2$ and $v_3$ are extracted for midrapidity charged hadrons as a function of transverse momentum. In this paper, we use the available coefficients to explore various non-flow hypotheses as well as compare the results with theoretical model calculations. The non-flow methods fail basic closure tests with AMPT and PYTHIA/ANGANTYR, particularly when including correlations with particles in the low multiplicity light-projectile going direction. In data, the non-flow adjusted $v_2$ results are modestly lower in p+Au and the adjusted $v_3$ results are more significantly higher in p+Au and d+Au. However, the resulting higher values for the ratio $v_3/v_2$ in p+Au at RHIC compared to p+Pb at the LHC is additional evidence for a significant over-correction. Incorporating these additional checks, the conclusion that these flow coefficients are dominated by initial geometry coupled with final-state interactions (e.g.~hydrodynamic expansion of quark-gluon plasma) remains true, and explanations based on initial-state glasma are ruled out. The detailed balance between intrinsic and fluctuation-driven geometry and the exact role of weakly versus strongly-coupled pre-hydrodynamic evolution remains an open question for triangular flow, requiring further theoretical and experimental investigation.

Kinematic dependence of azimuthal anisotropies in p+Au, d+Au, and He3+Au at sNN=200GeV

There is strong evidence for the formation of small droplets of quark-gluon plasma in $p/d/^{3}$He+Au collisions at the Relativistic Heavy Ion Collider (RHIC) and in $p$+$p$/Pb collisions at the Large Hadron Collider. In particular, the analysis of data at RHIC for different geometries obtained by varying the projectile size and shape has proven insightful. In the present analysis, we find excellent agreement with the previously published PHENIX at RHIC results on elliptical and triangular flow with an independent analysis via the two-particle correlation method, which has quite different systematic uncertainties and an independent code base. In addition, the results are extended to other detector combinations with different kinematic (pseudorapidity) coverage. These results provide additional constraints on contributions from nonflow and longitudinal decorrelations.