Two-particle Correlation Function Research Articles

K^{-}p Correlation Function from High-Energy Nuclear Collisions and Chiral SU(3) Dynamics.

The two-particle momentum correlation function of a K^{-}p pair from high-energy nuclear collisions is evaluated in the K[over ¯]N-πΣ-πΛ coupled-channel framework. The effects of all coupled channels together with the Coulomb potential and the threshold energy difference between K^{-}p and K[over ¯]^{0}n are treated completely for the first time. Realistic potentials based on the chiral SU(3) dynamics are used which fit the available scattering data. The recently measured correlation function is found to be well reproduced by allowing variations of the source size and the relative weight of the source function of πΣ with respect to that of K[over ¯]N. The predicted K^{-}p correlation function from larger systems indicates that the investigation of its source size dependence is useful in providing further constraints in the study of the K[over ¯]N interaction.

Two-particle correlation functions in cluster perturbation theory: Hubbard spin susceptibilities

Cluster Perturbation Theory (CPT) is a computationally economic method commonly used to estimate the momentum and energy resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Green's function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin-susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. We benchmark the method with the one-dimensional Fermi-Hubbard model at half filling by comparing with known results.

Beam-energy dependence of identified two-particle angular correlations in sNN=7.7–200 GeV Au+Au collisions

The two-particle angular correlation functions, $R_2$, of pions, kaons, and protons in Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV were measured by the STAR experiment at RHIC. These correlations were measured for both like-sign and unlike-sign charge combinations and versus the centrality. The correlations of pions and kaons show the expected near-side ({\it i.e.}, at small relative angles) peak resulting from short-range mechanisms. The amplitudes of these short-range correlations decrease with increasing beam energy. However, the proton correlation functions exhibit strong anticorrelations in the near-side region. This behavior is observed for the first time in an A+A collision system. The observed anticorrelation is $p_{T}$-independent and decreases with increasing beam energy and centrality. The experimental results are also compared to the Monte Carlo models UrQMD, Hijing, and AMPT.

Measurement of strange baryon–antibaryon interactions with femtoscopic correlations

Two-particle correlation functions were measured for pp‾, pΛ‾, p‾Λ, and ΛΛ‾ pairs in Pb–Pb collisions at sNN=2.76 TeV and sNN=5.02 TeV recorded by the ALICE detector. From a simultaneous fit to all obtained correlation functions, real and imaginary components of the scattering lengths, as well as the effective ranges, were extracted for combined pΛ‾ and p‾Λ pairs and, for the first time, for ΛΛ‾ pairs. Effective averaged scattering parameters for heavier baryon–antibaryon pairs, not measured directly, are also provided. The results reveal similarly strong interaction between measured baryon–antibaryon pairs, suggesting that they all annihilate in the same manner at the same pair relative momentum k⁎. Moreover, the reported significant non-zero imaginary part and negative real part of the scattering length provide motivation for future baryon–antibaryon bound state searches.

Measurement of long-range two-particle azimuthal correlations in Z-boson tagged pp collisions at sqrt{s}=8 and 13\xa0TeV

Results are presented from the measurement by ATLAS of long-range (|Delta eta |>2) dihadron angular correlations in sqrt{s}=8 and 13 TeV pp collisions containing a Z boson. The analysis is performed using 19.4 mathrm {fb}^{-1} of sqrt{s}=8 TeV data recorded during Run 1 of the LHC and 36.1 mathrm {fb}^{-1} of sqrt{s}=13 TeV data recorded during Run 2. Two-particle correlation functions are measured as a function of relative azimuthal angle over the relative pseudorapidity range 2<|Delta eta |<5 for different intervals of charged-particle multiplicity and transverse momentum. The measurements are corrected for the presence of background charged particles generated by collisions that occur during one passage of two colliding proton bunches in the LHC. Contributions to the two-particle correlation functions from hard processes are removed using a template-fitting procedure. Sinusoidal modulation in the correlation functions is observed and quantified by the second Fourier coefficient of the correlation function, v_{2,2}, which in turn is used to obtain the single-particle anisotropy coefficient v_{2}. The v_{2} values in the Z-tagged events, integrated over 0.5<p_{mathrm {T}}<5 GeV, are found to be independent of multiplicity and sqrt{s}, and consistent within uncertainties with previous measurements in inclusive pp collisions. As a function of charged-particle p_{mathrm {T}}, the Z-tagged and inclusive v_{2} values are consistent within uncertainties for p_{mathrm {T}}<3 GeV.

THE ONSET OF JET QUENCHING PHENOMENON

The aim of this study is to set a baseline for the jet quenching measurements of the Quark Gluon Plasma (QGP) formed in the large system size Nucleus-Nucleus (A-A) at top central collisions, via studying simulated small system size, Nucleon-Nucleon (N-N) collisions. The proton-proton (p-p) collisions were simulated using PYTHIA, at center of mass energies $\sqrt{s_{_{NN}}} = 200$ $GeV$ and $\sqrt{s_{_{NN}}} = 13$ $TeV$ corresponding to the available energies at the current collider experiments; the Relativistic Heavy Ion Collider (RHIC), and the Large Hadron Collider (LHC). At both energies, the two-particle azimuthal correlation functions have been considered, and the yield associated with the high transverse momentum ($p_{_{T}}$) particles were extracted at its near-side ($\Delta\phi \approx 0$) and away-side ($\Delta\phi \approx \pi$) at mid pseudo rapidity ($|\eta| \le 2$). The ratio between the near-side yields in the high multiplicity events to these of the low multiplicity events ($I_{_{HL}}^{^{N}}$), as well as, the ratio of the away-side yields ($I_{_{HL}}^{^{A}}$) were calculated at both energies as a function of the hadron fractional energy $z_{_{T}}$ of the high-$p_{_{T}}$ particle. At both energies, the values of $I_{_{HL}}^{^{N}}$ and $I_{_{HL}}^{^{A}}$ were less than unity, and of trivial dependence on $z_{_{T}}$. The values of $I_{_{HL}}^{^{A}}$ are always less than these of $I_{_{HL}}^{^{N}}$ at the same multiplicity and energy, and both quantities show a pattern of systematic decreases with the multiplicity. Such multiplicity dependence cannot be used neither to exclude the jet quenching nor to prove it in the high multiplicity events in p-p collisions, as the suppressions have been found at both sides, near and away of the high-$p_{_{T}}$ particle.

Onset of the Jet Quenching Phenomenon

The aim of this study is to set a baseline for the jet quenching measurements of the Quark Gluon Plasma (QGP) formed in the large system size Nucleus-Nucleus (A-A) at top central collisions, via studying simulated small system size, Nucleon-Nucleon (N-N) collisions. The proton-proton (p-p) collisions were simulated using PYTHIA, at center of mass energies $\sqrt{s_{_{NN}}} = 200$ $GeV$ and $\sqrt{s_{_{NN}}} = 13$ $TeV$ corresponding to the available energies at the current collider experiments; the Relativistic Heavy Ion Collider (RHIC), and the Large Hadron Collider (LHC). At both energies, the two-particle azimuthal correlation functions have been considered, and the yield associated with the high transverse momentum ($p_{_{T}}$) particles were extracted at its near-side ($\Delta\phi \approx 0$) and away-side ($\Delta\phi \approx \pi$) at mid pseudo rapidity ($|\eta| \le 2$). The ratio between the near-side yields in the high multiplicity events to these of the low multiplicity events ($I_{_{HL}}^{^{N}}$), as well as, the ratio of the away-side yields ($I_{_{HL}}^{^{A}}$) were calculated at both energies as a function of the hadron fractional energy $z_{_{T}}$ of the high-$p_{_{T}}$ particle. At both energies, the values of $I_{_{HL}}^{^{N}}$ and $I_{_{HL}}^{^{A}}$ were less than unity, and of trivial dependence on $z_{_{T}}$. The values of $I_{_{HL}}^{^{A}}$ are always less than these of $I_{_{HL}}^{^{N}}$ at the same multiplicity and energy, and both quantities show a pattern of systematic decreases with the multiplicity. Such multiplicity dependence cannot be used neither to exclude the jet quenching nor to prove it in the high multiplicity events in p-p collisions, as the suppressions have been found at both sides, near and away of the high-$p_{_{T}}$ particle.

Particle spatial arrangement metrics for near-crack-tip stress

Motivated by the lack of spatial information in fracture mechanics formulations, this work updates near-crack-tip stress field equations by introducing two scalar order metrics that capture particle arrangement. These metrics are based on the two-particle and three-particle spatial correlation functions. By evaluating these order metrics in particle distributions generated as stochastic perturbations of a regular grid, we study their behavior as a function of a perturbation parameter. To incorporate the scalar measures into the closed-form solution of the stress field near the crack tip, we introduce a correction factor containing both measures. The limits of these factors are established using existing results from computational fracture toughness experiments. The present study provides new tools to improve the description of material microstructure and allows us to describe the sensitivity of crack-tip stress to the particle arrangement. This will be useful for manufacturing techniques like additive manufacturing, where feature description of material microstructure is required.

Simulation studies of R2(Δη,Δφ) and P2(Δη,Δφ) correlation functions in pp collisions with the PYTHIA and HERWIG models

We report studies of charge-independent (CI) and charge-dependent (CD) two-particle differential-number correlation functions, $\rm{R_{2}}(\Delta\eta, \Delta\varphi)$, and transverse momentum ($p_{\rm T}$) correlation functions, $\rm{P_{2}}(\Delta\eta, \Delta\varphi)$, of charged particles in $\sqrt{\textit{s}}$ = 2.76 TeV pp collisions with the PYTHIA and HERWIG models. Model predictions are presented for inclusive charged hadrons ($h^\pm$), as well as pions ($\pi^\pm$), kaons (K$^\pm$), and (anti-)protons ($\rm \bar{p}$/p) in the ranges $0.2 < \textit{p}_{\rm T} \le 2.0~\rm{GeV}/\textit{c}$, $2.0 < \textit{p}_{\rm T} \le 5.0~\rm{GeV}/\textit{c}$, and $5.0 < \textit{p}_{\rm T} \le 30.0~\rm{GeV}/\textit{c}$, with full azimuthal coverage in the range $|\eta|< 1.0$. We compare the model predictions for the strength and shape of the $\rm{R_{2}}$ and $\rm{P_{2}}$ correlators as these pertain to recent measurements by the ALICE collaboration. The $\rm{R_{2}}$ and $\rm{P_{2}}$ correlation functions estimated with PYTHIA and HERWIG exhibit qualitatively similar near-side and away-side correlation structures but feature important differences. Our analysis indicates that comparative studies of $\rm{R_{2}}$ and $\rm{P_{2}}$ correlation functions would provide valuable insight towards the understanding of particle production in pp collisions, and by extension, should also be useful in studies of heavy-ion collisions. Comparison of the $\Delta \eta$ dependence of $\rm{R_{2}}$ and $\rm{P_{2}}$ could contribute, in particular, to a better understanding and modeling of the angular ordering of particles produced by hadronization in jets, as well as a better description of jet fragmentation functions of identified species at low momentum fraction $(z)$.

Quantum critical properties of Bose–Hubbard models

The Mott insulator-to-superfluid transition exhibited by the Bose–Hubbard model on a two-dimensional square lattice occurs for any value of the chemical potential, but becomes critical at the tips of the so-called Mott lobes only. Employing a numerical approach based on a combination of high-order perturbation theory and hypergeometric analytic continuation we investigate how quantum critical properties manifest themselves in computational practice. We consider two-dimensional triangular lattices and three-dimensional cubic lattices for comparison, providing accurate parametrizations of the phase boundaries at the tips of the respective first lobes. In particular, we lend strong support to a recently suggested inequality which bounds the divergence exponent of the one-particle correlation function in terms of that of the two-particle correlation function, and which sharpens to an equality if and only if a system becomes critical.

Quasi equilibrium state of expanding quantum fields and two-pion Bose-Einstein correlations in pp collisions at the LHC

We argue that the two-particle momentum correlation functions of high-multiplicity $p+p$ collisions at the LHC provide a signal for a ground state structure of a quasi equilibrium state of the longitudinally boost-invariant expanding quantum field which lies in the future light cone of a collision. The physical picture is that pions are produced by the expanding quantum emitter with two different scales approximately attributed to the expanding ideal gas in local equilibrium state and ground-state condensate. Specifically, we show that the effect of suppressing the two-particle Bose-Einstein momentum correlation functions increases with increasing transverse momentum of a like-sign pion pair due to different momentum-dependence of the corresponding particle emission regions.

Investigation of structural ordering in network forming ionic liquids: A molecular dynamics study.

Molecular dynamics simulations reveal anomalous short- and medium-range ordering with increasing temperature in network-forming ionic liquids (NIL) consisting of alkyl-diammonium cations with long side chains of 6 carbon atoms and citrate anions (NIL 5-6). This effect is weaker, and only a short-range order is observed in equivalent systems with side chains shortened to 3 C atoms (NIL 5-3). The short-range ordering can be attributed to volume expansion during heating, but the intermediate range order requires volume expansion as well as an increase in temperature. We find that the cross (cation-anion) interactions are the major contributors to the observed trend and the development of complex 3D correlations in the two-particle correlation functions. The simulations suggest that the above phenomenon can be correlated to local trapping of cation molecules in a variety of configurations at lower temperatures where molecular shape distributions show great variability; as temperature increases, the distribution of molecular radii of gyration becomes narrower, enabling the increased ordering.

Characterization of the topology of proton-proton collisions

In the LHC’s high-energy proton-proton collision experiments, a great amount of particles are produced after the interaction processes. To better understand the production mechanisms of such particles, it is convenient to study and characterize their topology. To do so, we shall study two-particle correlation functions. These functions are calculated with data generated by the PYTHIA event simulator, and in several different intervals of correlated particle’s transverse momentum. In this way, we may observe a particle jet structure, observed in the experiments and previewed by perturbative QCD, and how such structure is affected by different hadronization models.

Strongly Intensive Observables in the Model with String Fusion

We calculate the strongly intensive observables for multiplicities in two rapidity windows in the model with independent identical strings taking into account the charge sign of particles. We express the observables through the string pair correlation functions describing the correlations between the same and opposite sign particles produced in a string decay. We extract these charge-wise string two-particle correlation functions from the ALICE data on the forward-backward correlations and the balance function. Using them we predict the behavior of the charge-wise strongly intensive observables in the model with independent identical strings. We also show that the observable between multiplicities in two acceptance windows separated in rapidity, which is a strongly intensive in the case with independent identical strings, loses this property, when we take into account string fusion effects and a formation of strings of a few different types takes place in a collision. We predict the changes in the behaviour of this observable with energy and collision centrality, arising due to the string fusion phenomena.

Strongly intensive observable between multiplicities in two acceptance windows in a string model

The strongly intensive observable between multiplicities in two acceptance windows separated in rapidity and azimuth is calculated in the model with quark-gluon strings acting as sources. The dependence of this observable on the two-particle correlation function of a string, the width of observation windows and the rapidity gap between them is analyzed. In the case with independent identical strings the model calculation confirms the strongly intensive character of this observable: it is independent of both the mean number of string and its fluctuation. For this case the peculiarities of its behaviour for particles with different electric charges are also analyzed. In the case when the string fusion processes are taken into account and a formation of strings of a few different types takes place in a collision, this observable is proved to be equal to a weighted average of its values for different string types. Unfortunately, in this case through the weight factors this observable becomes dependent on collision conditions and, strictly speaking, can not be considered any more as strongly intensive variable. For a comparison the results of the calculation of considered observable with the PYTHIA event generator are also presented.

String model calculation of the strongly intensive observables for multiplicities in two windows

We calculate the strongly intensive observables for multiplicities in two rapidity windows in the model with independent identical strings taking into account the charge sign of particles. We express the observables through the string pair correlation functions describing the correlations between the same and opposite sign particles produced in a string decay. We extract these charge-wise string two-particle correlation functions from the ALICE data on the forward-backward correlations and the balance function. Using them we predict the behavior of the charge-wise strongly intensive observables in the model with independent identical strings.

Fermion-boson vertex within dynamical mean-field theory

In the study of strongly interacting systems, correlations on the two-particle level are receiving more and more attention. In this work, we study a particular two-particle correlation function: the fermion-boson vertex. It describes the response of the Green's function when an external field is applied and is an important ingredient of diagrammatic extensions of Dynamical Mean-Field Theory. We provide several perspectives on this object, using Ward identities, sum rules, perturbative analysis and asymptotic relations. We then use these tools to study the vertex across the doping-driven metal-insulator transition and find a divergence in the imaginary part.

Spectra of correlated many-electron systems: From a one- to a two-particle description

State-of-the-art spectroscopic techniques allow for a comprehensive understanding of one-electron excitations in various physically interesting and/or technologically relevant materials. While for weakly-correlated systems the corresponding one-particle spectral function A(ω, k) contains essentially all information about their physical properties the situation is much more complicated in the presence of strong electronic correlations. In fact, in the latter case different theoretical treatments often lead to very different explanations of the origin of specific features in the spectrum. A typical example is the pseudogap in the cuprates, i.e., the momentum-selective suppression of spectral weight at the Fermi level, which has been related to spin, charge or (d-wave) pairing fluctuations by different authors. This ambiguity about the underlying physical mechanism at work can be overcome by considering two-particle correlation functions as they are able to describe the collective modes of the system and can be also related to certain ground state properties. In this work, we will present different theoretical approaches for analyzing the spectrum of correlated systems by exploiting the information contained in these two-particle correlation functions. For the specific case of the pseudogap these procedures have allowed us (1) to identify antiferromagnetic spin fluctuations as microscopic origin of this spectral feature which (2) can be related to the formation of a resonating valence bond ground state in the system.

Harmonic decomposition of three-particle azimuthal correlations at energies available at the BNL Relativistic Heavy Ion Collider

We present measurements of three-particle correlations for various harmonics in Au+Au collisions at energies ranging from $\sqrt{s_{{\rm NN}}}=7.7$ to 200 GeV using the STAR detector. The quantity $\langle\cos(m\phi_1+n\phi_2-(m+n)\phi_3)\rangle$ is evaluated as a function of $\sqrt{s_{{\rm NN}}}$, collision centrality, transverse momentum, $p_T$, pseudo-rapidity difference, $\Delta\eta$, and harmonics ($m$ and $n$). These data provide detailed information on global event properties like the three-dimensional structure of the initial overlap region, the expansion dynamics of the matter produced in the collisions, and the transport properties of the medium. A strong dependence on $\Delta\eta$ is observed for most harmonic combinations consistent with breaking of longitudinal boost invariance. Data reveal changes with energy in the two-particle correlation functions relative to the second-harmonic event-plane and provide ways to constrain models of heavy-ion collisions over a wide range of collision energies.

The Two-Particle Correlation Function for Systems with Long-Range Interactions

In this paper, we study the truncated two-particle correlation function in particle systems with long range interactions. For Coulombian and soft potentials, we define and give well-posedness results for the equilibrium correlations. In the Coulombian case, we prove the onset of the Debye screening length in the equilibrium correlations, for suitable velocity distributions. Additionally, we give precise estimates on the effective range of interaction between particles. In the case of soft potential interaction the equilibrium correlations and their fluxes in the space of velocities are shown to be linearly stable.