Two-particle Correlation Function Research Articles

Exploring formation of Quark-Gluon Plasma through two-particle correlations functions in A+A and p+p data

This paper is the result of team’s hard work, which delves into the correlation functions in proton-proton and PbPb(Lead-Lead) collisions, scrutinizing their relevance in the formation of quark-gluon plasma. This project first simulated these high-energy collisions and generated a comprehensive dataset of proton-proton and PbPb(Proton-Proton) interactions. The entire analysis is designed around the task of calculating azimuthal and pseudorapidity correlation functions, and wish to compare the differences and similarities between the two collision types. Also delved into these correlation functions in proton-proton collisions as potential evidence for QGP(Quark-gluon plasma), a type of matter typically found in heavy metal collisions such as Pb-Pb. The results reveal unique patterns lurking in the correlation functions that suggest that QGPs may form even in smaller collision systems. Also Quark-Gluon Plasma (QGP) is a state where quarks and gluons move freely at extremely high energy densities. The two-particle correlation function helps identify QGP by measuring how particles are correlated after a collision. Specific patterns in these correlations, like a “ridge” structure, indicate the collective behavior of particles, signaling the formation of QGP. These findings are expected to shed more light on the intricate dynamics in particle collisions and the specific conditions that lead to the formation of QGPs.

The Theoretical Research of Two Particle Angular Correlation in PbPb Collisions

This literature review explores the significance of two-particle angular correlation in comprehending the complex dynamics of proton-heavy ion collisions in the quark gluon plasma (QGP) and the CMS detector at the LHC. We present a detailed account of the experimental setup and the findings derived from our measurements. The oneparticle distribution equation and the two-particle angular correlation functions are fundamental components for comprehensively investigating the theoretical aspects of the two-particle angular correlation. Following that, we present a concise summary of significant metrics, such as centrality, uncertainty, and Fourier coefficient, that may be determined from the available data. Additionally, we provide a concise summary of prior investigations into the two-particle angular correlation in collisions involving pp, p-Pb, or Pb-Pb at various energy levels. Specifically, we have utilized the MC model for the analysis and modeling of collision data. Various MC models are listed and evaluated using specific situations. Higher order correlations are now possible to help clarify information from proton or heavy ion collisions.

Correlation functions of weakly inhomogeneous plasma

This article focuses on the kinetic theory of inhomogeneous plasma and explores the interaction between a high-frequency electric field and weakly inhomogeneous plasma. Particularly, it examines the impact of an external variable field on the kinetic and high-frequency properties of the plasma, including kinetic equations, correlation functions, and distribution functions of charged particles. The study derives expressions for the pair (two-particle) correlation function and the corresponding distribution function, taking into ac- count the spatial inhomogeneity of the plasma and electric field, as well as the collisions between charged particles. The results were obtained using the kinetic equation for the spatial-temporal spectral density of fluctuations and the method of successive approximations (separation of slow motions and fast oscillations). The field amplitude is considered a slowly varying function of time and coordinates. The calculations neglect the contribution of the magnetic component of the electromagnetic field, which is applicable to longitudinal electric fields. The results obtained in this article are primarily of theoretical interest, they reveal the picture of the interaction of a weakly inhomogeneous plasma with a high-frequency electric field and can be used in the construction of a kinetic theory of an inhomogeneous plasma located in high-frequency electromagnetic fields. Note that for charged particles of the same sign, the correlation function is negative, and for particles of different signs it is positive. In addition, the correlation function is exponentially small when the distance between the particles is greater than the Debye radius. In all calculations, the contribution of the magnetic component of the electromagnetic field is neglected, which is quite true for the longitudinal electric field.

Long-range near-side correlation in e+e− collisions at 183-209 GeV with ALEPH archived data

The first measurement of two-particle angular correlations for charged particles with LEP-II data is presented. The study is performed using archived hadronic e+e− data collected by ALEPH at center-of-mass energies up to 209 GeV, above the W+W− production threshold, which provide access to unprecedented charged-particle multiplicities and more complex color-string configurations if compared to previous measurements at LEP-I energies. An intriguing long-range near-side excess is observed in the correlation function measured with respect to the thrust axis in the highest multiplicity interval (Ntrk≥50). Such a structure is not predicted by the Monte-Carlo simulation. The harmonic anisotropy coefficients vn, which result from the Fourier expansion of the two-particle correlation functions, were also measured for the first time in e+e− data, and compared to pythia 6 predictions and to the results obtained in proton-proton collisions. The results presented in the Letter provide novel experimental constraints on the formation of collective phenomena in point-like e+e− collisions.

Studying the interaction between charm and light-flavor mesons

The two-particle momentum correlation functions between charm mesons (D*± and D±) and charged light-flavor mesons (π± and K±) in all charge combinations are measured for the first time by the ALICE Collaboration in high-multiplicity proton–proton collisions at a center-of-mass energy of s=13 TeV. For DK and D*K pairs, the experimental results are in agreement with theoretical predictions of the residual strong interaction based on quantum chromodynamics calculations on the lattice and chiral effective field theory. In the case of Dπ and D*π pairs, tension between the calculations including strong interactions and the measurement is observed. For all particle pairs, the data can be adequately described by Coulomb interaction only, indicating a shallow interaction between charm and light-flavor mesons. Finally, the scattering lengths governing the residual strong interaction of the Dπ and D*π systems are determined by fitting the experimental correlation functions with a model that employs a Gaussian potential. The extracted values are small and compatible with zero. © 2024 CERN, for the ALICE Collaboration 2024 CERN

Investigating the composition of the K[formula omitted] state with π±K[formula omitted] correlations at the LHC

The first measurements of femtoscopic correlations with the particle pair combinations π±KS0 in pp collisions at s=13 TeV at the Large Hadron Collider (LHC) are reported by the ALICE experiment. Using the femtoscopic approach, it is shown that it is possible to study the elusive K0⁎(700) particle that has been considered a tetraquark candidate for over forty years. Source and final-state interaction parameters are extracted by fitting a model assuming a Gaussian source to the experimentally measured two-particle correlation functions. The final-state interaction in the π±KS0 system is modeled through a resonant scattering amplitude, defined in terms of a mass and a coupling parameter, The extracted mass and Breit–Wigner width, derived from the coupling parameter, of the final-state interaction are found to be consistent with previous measurements of the K0⁎(700). The small value and increase of the correlation strength with increasing source size support the hypothesis that the K0⁎(700) is a four-quark state, i.e. a tetraquark state of the form (q1,q2‾,q3,q3‾) in which q1, q2 and q3 indicate the flavor of the valence quarks of the π and KS0. This latter trend is also confirmed via a simple geometric model that assumes a tetraquark structure of the K0⁎(700) resonance.

Toward extracting the scattering phase shift from integrated correlation functions. II. A relativistic lattice field theory model

In the present work, a relativistic relation that connects the difference of interacting and noninteracting integrated two-particle correlation functions in finite volume to infinite volume scattering phase shift through an integral is derived. We show that the difference of integrated finite volume correlation functions converges rapidly to its infinite volume limit as the size of the periodic box is increased. The fast convergence of our proposed formalism is illustrated by analytic solutions of a contact interaction model, the perturbation theory calculation, and also the Monte Carlo simulation of a complex ϕ4 lattice field theory model. Published by the American Physical Society 2024

Emergent Flow Signal and the Colour String Fusion

In this study, we develop the colour string model of particle production, based on the multi-pomeron exchange scenario, to address the controversial origin of the flow signal measured in proton–proton inelastic interactions. Our approach takes into account the string–string interactions but does not include a hydrodynamic phase. We consider a comprehensive three-dimensional dynamics of strings that leads to the formation of strongly heterogeneous string density in an event. The latter serves as a source of particle creation. The string fusion mechanism, which is a major feature of the model, modifies the particle production and creates azimuthal anisotropy. Model parameters are fixed by comparing the model distributions with the ATLAS experiment proton–proton data at the centre-of-mass energy s=13 TeV. The results obtained for the two-particle angular correlation function, C(Δη,Δϕ), with Δη and Δϕ differences in, respectively, pseudorapidities and azimuthal angles between two particles, reveal the resonance contributions and the near-side ridge. Model calculations of the two-particle cumulants, c2{2}, and second order flow harmonic, v2{2}, also performed using the two-subevent method, are in qualitative agreement with the data. The observed absence of the away-side ridge in the model results is interpreted as an imperfection in the definition of the time for the transverse evolution of the string system.

Multiplicity Distributions and Modified Combinants in the Multipomeron Model of pp Interaction at High Energies

The multiplicity distributions of charged particles and their combinants for pp collisions at LHC energies are studied within the Multipomeron Exchange Model (MEM) that takes into account the phenomenon of string fusion. It is shown that the use of Gaussian-type distributions for multiplicity distributions at a fixed number of pomerons allows, within the MEM framework, the reproduction of the resulting multiplicity distributions and the oscillatory behavior of combinants, found in the ALICE and CMS pp collision data at LHC energies. It is important that in the proposed approach, the parameters of these Gaussian-type distributions are not considered free, but are calculated from the two-particle correlation function of a single string.

A novel method for calculating Bose–Einstein correlation functions with Coulomb final-state interaction

Measurements of Bose–Einstein correlations played a crucial role in the discovery and the subsequent detailed exploration of the Quark-Gluon-Plasma (QGP) created in high-energy collisions of heavy nuclei. Such measurements gave rise to femtoscopy, a flourishing sub-field of high-energy physics, and there are important new directions to explore and discoveries to be made in the near future. One of these important current topics is the precise investigation of the shape of the correlation functions utilizing Lévy-stable sources. In this paper, we utilize Lebesgue’s dominated convergence theorem and Fubini’s theorem to present a novel method of calculating the shape of the two-particle correlation functions, including the Coulomb final-state interaction. This method relies on an exact calculation of a large part of the necessary integrals of the Coulomb wave function and can be utilized to calculate the correlation function for any source function with an easily accessible Fourier transform. In this way, it is eminently applicable to Lévy-stable source functions. In this particular case, we find that the new method is more robust and allows the investigation of a wider parameter range than the previously utilized techniques. We present an easily applicable software package that is ready to use in experimental studies.

Holstein polaron transport from numerically "exact" real-time quantum dynamics simulations.

Numerically "exact" methods addressing the dynamics of coupled electron-phonon systems have been intensively developed. Nevertheless, the corresponding results for the electron mobility μdc are scarce, even for the one-dimensional (1d) Holstein model. Building on our recent progress on single-particle properties, here we develop the momentum-space hierarchical equations of motion (HEOM) method to evaluate real-time two-particle correlation functions of the 1d Holstein model at a finite temperature. We compute numerically "exact" dynamics of the current-current correlation function up to real times sufficiently long to capture the electron's diffusive motion and provide reliable results for μdc in a wide range of model parameters. In contrast to the smooth ballistic-to-diffusive crossover in the weak-coupling regime, we observe a temporally limited slow-down of the electron on intermediate time scales already in the intermediate-coupling regime, which translates to a finite-frequency peak in the optical response. Our momentum-space formulation lowers the numerical effort with respect to existing HEOM-method implementations, while we remove the numerical instabilities inherent to the undamped-mode HEOM by devising an appropriate hierarchy closing scheme. Still, our HEOM remains unstable at too low temperatures, for too strong electron-phonon coupling, and for too fast phonons.

Disentanglement of hard and soft QCD processes using two-particle correlation functions

Transverse spherocity (S 0) has evolved as a powerful method to distinguish between soft and hard contributions in an event in small collision systems. We used the two-particle differential-number correlation functions (R 2) and transverse momentum correlation functions (P 2) of charged particles produced in pp collisions at TeV with the PYTHIA8 model to explore this phenomena. The Δφ projections of these correlation functions in different multiplicity and S 0 classes are discussed. We find that these correlation functions show different shapes and sizes in both near- and away-side with multiplicity and S 0 classes. We observe a strong correlation in the near- and away-side of these correlation functions for jetty-like (hard QCD processes), which become weaker for isotropic (soft QCD processes) in spherocity classes as compared to multiplicity classes. Finally, it is observed that S 0 should be a good observable as compared to multiplicity to disentangle hard and soft QCD processes in a small collision system.

ACFlow: An open source toolkit for analytic continuation of quantum Monte Carlo data

The purpose of analytic continuation is to establish a real frequency spectral representation of single-particle or two-particle correlation function (such as Green's function, self-energy function, spin and charge susceptibilities) from noisy data generated in finite temperature quantum Monte Carlo simulations. It requires numerical solutions of a family of Fredholm integral equations of the first kind, which is indeed a challenging task. In this paper, an open source toolkit (dubbed ACFlow) for analytic continuation of quantum Monte Carlo data is presented. We first give a short introduction to the analytic continuation problem. Next, three popular analytic continuation algorithms, including the maximum entropy method, the stochastic analytic continuation, and the stochastic optimization method, as implemented in this toolkit are reviewed. And then we elaborate on the major features, implementation details, basic usage, inputs, and outputs of this toolkit. Finally, four representative examples, including analytic continuations of Matsubara self-energy function, Matsubara and imaginary time Green's functions, and current-current correlation function, are shown to demonstrate the usefulness and flexibility of the ACFlow toolkit. Program summaryProgram Title: ACFlowCPC Library link to program files:https://doi.org/10.17632/th6w74gwjm.1Developer's repository link:https://github.com/huangli712/ACFlowLicensing provisions: GNU General Public License Version 3Programming language: JuliaNature of problem: Most of the quantum Monte Carlo methods work on imaginary axis. In order to extract physical observables and compare them with the experimental results, analytic continuation must be done in the post-processing stage to convert the quantum Monte Carlo simulated data from imaginary axis to real axis.Solution method: Three well-established analytic continuation methods, including the maximum entropy method, the stochastic analytic continuation (both A. W. Sandvik's and K. S. D. Beach's algorithms), and the stochastic optimization method, have been implemented in the ACFlow toolkit.Additional comments including restrictions and unusual features: The ACFlow toolkit is written in pure Julia language. It is highly optimized and parallelized. It can be executed interactively in a Jupyter notebook environment.

One- and Two-Particle Correlation Functions in the Cluster Perturbation Theory for Cuprates.

The physics of high-Tc superconducting cuprates is obscured by the effect of strong electronic correlations. One way to overcome this problem is to seek an exact solution at least within a small cluster and expand it to the whole crystal. Such an approach is at the heart of cluster perturbation theory (CPT). Here, we developed CPT for the dynamic spin and charge susceptibilities (spin-CPT and charge-CPT), with the correlation effects explicitly taken into account by the exact diagonalization. We applied spin-CPT and charge-CPT to the effective two-band Hubbard model for the cuprates obtained from the three-band Emery model and calculated one- and two-particle correlation functions, namely, a spectral function and spin and charge susceptibilities. The doping dependence of the spin susceptibility was studied within spin-CPT and CPT-RPA, that is, the CPT generalization of the random phase approximation (RPA). In the underdoped region, both our methods resulted in the signatures of the upper branch of the spin excitation dispersion with the lowest excitation energy at the (π,π) wave vector and no presence of low-energy incommensurate excitations. In the high doping region, both methods produced a low energy response at four incommensurate wave vectors in qualitative agreement with the results of the inelastic neutron scattering experiments on overdoped cuprates.

Particle interferometry in a moat regime

Dense strongly interacting matter can exhibit regimes with spatial modulations, akin to crystalline phases. In this case particles can have a moat spectrum with minimal energy at nonzero momentum. We show that particle interferometry is a sensitive probe of such a regime in heavy-ion collisions. To this end, we develop a field-theoretical formalism that relates particle spectra to in-medium real-time correlation functions of quantum fields on curved hypersurfaces of spacetime. This is then applied to the study of Bose-Einstein correlations in a moat regime in heavy-ion collisions. The resulting two-particle spectra exhibit peaks at nonzero average pair momentum, in contrast to the two-particle spectra in a normal phase, which peak at zero momentum. These peaks lead to nontrivial structures in the ratio of two-particle correlation functions, which should be experimentally measurable if the resolution in the direction of average pair momentum is sufficiently large. We propose these structures in the correlation-function ratios as clear signature of a moat regime and spatially modulated phases in quantum chromodynamics (QCD).

Complementary two-particle correlation observables for relativistic nuclear collisions

Two-particle correlations are a widely used tool for studying relativistic nuclear collisions. Multiplicity fluctuations comparing charge and particle species have been studied as a possible signal for quark-gluon plasma (QGP) and the QCD critical point. These fluctuation studies all make use of particle variances which can be shown to originate with a two-particle correlation function. Momentum correlations and covariances of momentum fluctuations, which arise from the same correlation function, have also been used to extract properties of the nuclear collision medium such as the shear viscosity to entropy density ratio, the shear relaxation time, and temperature fluctuations. Searches for critical fluctuations are also done with these correlation observables. We derive a mathematical relationship between several number and momentum density correlation observables and outline the different physics mechanisms often ascribed to each. This set of observables also contains a new multiplicity-momentum correlation. Our mathematical relation can be used as a validation tool for measurements, as a method for interpreting the relative contributions of different physics mechanisms on correlation observables, and as a test for theoretical and phenomenological models to simultaneously explain all observables. We compare an independent source model to simulated events from pythia for all observables in the set.

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.

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.

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.

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.