Two-particle Correlation Function Research Articles

Higher-order anisotropies in the blast-wave model: Disentangling flow and density field anisotropies

We formulate a generalisation of the blast-wave model which is suitable for the description of higher order azimuthal anisotropies of the hadron production. The model includes anisotropy in the density profile as well as an anisotropy in the transverse expansion velocity field. We then study how these two kinds of anisotropies influence the single-particle distributions and the correlation radii of two-particle correlation functions. Particularly we focus on the third-order anisotropy and consideration is given to the averaging over different orientation of the event plane.

Boltzmann-Langevin approach to pre-equilibrium correlations in nuclear collisions

Correlations born before the onset of hydrodynamic flow can leave observable traces on the final state particles. Measurement of these correlations can yield important information on the isotropization and thermalization process. Starting from a Boltzmann-like kinetic theory in the presence of dynamic Langevin noise, we derive a new partial differential equation for the two-particle correlation function that respects the microscopic conservation laws. We illustrate how this equation can be used to study the effect of thermalization on long range correlations.

Application of the Two-Particle Correlation Function Approach to the Description of a Single-Pass Free Electron Laser Operated in SASE Mode

We describe the theory of a superluminescent single-pass free electron laser based on the Bogolyubov chain of equations for multiparticle distribution functions. Special choice of the variables eliminates the retardation of interaction. A small parameter (inverse number of particles per signal growth length in the accompanying reference system) for the chain truncation is found. Expansion over this parameter makes it possible to neglect three-particle correlation functions and solve only the equations containing a single-particle distribution function and two-particle correlation functions. The calculation results are in good agreement with the conclusions based on the previously developed quasilinear theory.

Flow Dominance and Factorization of Transverse Momentum Correlations in Pb-Pb Collisions at the LHC.

We present the first measurement of the two-particle transverse momentum differential correlation function, P_{2}≡⟨Δp_{T}Δp_{T}⟩/⟨p_{T}⟩^{2}, in Pb-Pb collisions at sqrt[s_{NN}]=2.76 TeV. Results for P_{2} are reported as a function of the relative pseudorapidity (Δη) and azimuthal angle (Δφ) between two particles for different collision centralities. The Δϕ dependence is found to be largely independent of Δη for |Δη|≥0.9. In the 5% most central Pb-Pb collisions, the two-particle transverse momentum correlation function exhibits a clear double-hump structure around Δφ=π (i.e., on the away side), which is not observed in number correlations in the same centrality range, and thus provides an indication of the dominance of triangular flow in this collision centrality. Fourier decompositions of P_{2}, studied as a function of the collision centrality, show that correlations at |Δη|≥0.9 can be well reproduced by a flow ansatz based on the notion that measured transverse momentum correlations are strictly determined by the collective motion of the system.

Femtoscopy in = 5.02 TeV p-Pb collisions with ATLAS

Bose-Einstein correlations between identified charged pions are measured for p+Pb collisions at = 5.02 TeV with the ATLAS detector using a total integrated luminosity of 28 nb−1. Pions are identified using ionisation energy loss measured in the pixel detector. Two-particle correlation functions and the extracted source radii are presented as a function of average transverse pair momentum (kT) and rapidity () as well as collision centrality. Pairs are selected with a rapidity −2 < < 1 and with an average transverse momentum 0.1 < kT < 0.8 GeV. The effect on the two-particle correlation function from jet fragmentation is studied, and a new method for constraining its contributions to the measured correlations is described. The measured source sizes are substantially larger in more central collisions and are observed to decrease with increasing pair kT. A correlation with the local single-particle multiplicity dNch/dy* is demonstrated. The scaling of the extracted radii with the mean number of participants is also used to compare a selection of initial-geometry models. The cross term Rol, which couples radial and longitudinal expansion, is measured as a function of rapidity, and a departure from zero is observed with 4.8 σ combined significance for > −1 in the most central events.

Femtoscopy in √SNN= 5.02 TeVp-Pb collisions withATLAS

Bose-Einstein correlations between identified charged pions are measured for p +Pb collisions at √S NN = 5.02 TeV with the ATLAS detector using a total integrated luminosity of 28 nb−1 . Pions are identified using ionisation energy loss measured in the pixel detector. Two-particle correlation functions and the extracted source radii are presented as a function of average transverse pair momentum (k T ) and rapidity (y ππ *) as well as collision centrality. Pairs are selected with a rapidity −2 ππ * T T . A correlation with the local single-particle multiplicity dN ch /dy * is demonstrated. The scaling of the extracted radii with the mean number of participants is also used to compare a selection of initial-geometry models. The cross term R o1 , which couples radial and longitudinal expansion, is measured as a function of rapidity, and a departure from zero is observed with 4.8 σ combined significance for y ππ * > −1 in the most central events.

Forward-backward multiplicity fluctuation and longitudinal harmonics in high-energy nuclear collisions

Forward-backward (FB) multiplicity fluctuation in high-energy nuclear collisions can be quantified by two-particle pseudo-rapidity correlation function and its expansion into Legendre polynomials. The corresponding coefficients represent different fluctuation modes in longitudinal direction. The leading term 〈a12〉 corresponds to the asymmetry of numbers of the participants from the two colliding nuclei. This method is tested in events generated from AMPT and HIJING model. The an signal are found to be strongly dampened in AMPT than in HIJIGN, due to weaker short-range correlaitons and final-state effects in AMPT. Two-particle correlation also reveals an intresting shallow minimum around Δη≈0 in AMPT events, which is absent in HIJING results. The method opens a new avenue to elucidate the particle production mechanism and early time dynamics in heavy-ion collisions.

Suppression and Two-Particle Correlations of Heavy Mesons in Heavy-Ion Collisions

We study the medium modification of heavy quarks produced in heavy-ion collisions. The evolution of heavy quarks inside the QGP is described using a modified Langevin framework that simultaneously incorporates their collisional and radiative energy loss. Within this framework, we provide good descriptions of the heavy meson suppression and predictions for the two-particle correlation functions of heavy meson pairs.

Two-particle correlation function and dihadron correlation approach

It is shown that, in the case of asymmetric nuclear interactions, the application of the traditional dihadron correlation approach to determining a two-particle correlation function C may lead to a form distorted in relation to the canonical pair correlation function C2. This result was obtained both by means of exact analytic calculations of correlation functions within a simple string model for proton–nucleus and deuteron–nucleus collisions and by means of Monte Carlo simulations based on employing the HIJING event generator. It is also shown that the method based on studying multiplicity correlations in two narrow observation windows separated in rapidity makes it possible to determine correctly the canonical pair correlation function C2 for all cases, including the case where the rapidity distribution of product particles is not uniform.

Quantum canonical ensemble and correlation femtoscopy at fixed multiplicities

Identical particle correlations at fixed multiplicity are considered by means of quantum canonical ensemble of finite systems. We calculate one-particle momentum spectra and two-particle Bose-Einstein correlation functions in the ideal gas by using a recurrence relation for the partition function. Within such a model we investigate the validity of the thermal Wick's theorem and its applicability for decomposition of the two-particle distribution function. The dependence of the Bose-Einstein correlation parameters on the average momentum of the particle pair is also investigated. Specifically, we present the analytical formulas that allow one to estimate the effect of suppressing the correlation functions in a finite canonical system. The results can be used for the femtoscopy analysis of the A+A and p+p collisions with selected (fixed) multiplicity.

Short-range two-particle correlations from statistical clusters

The two-particle short-range correlation functions in rapidity, azimuthal angle, and transverse momentum following from the decay of statistical clusters are evaluated and discussed.Received 2 September 2015DOI:https://doi.org/10.1103/PhysRevD.93.094015© 2016 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFragmentation into hadronsParticle productionParticles & Fields

Using RIXS to Uncover Elementary Charge and Spin Excitations

X-ray photons can be used as unique probes to understand the properties of elementary excitations. A theoretical study demonstrates that a complex x-ray scattering technique captures richer spectral information than simpler two-particle correlation functions in cuprate superconductors.

Measurement of Long-Range Near-Side Two-Particle Angular Correlations in pp Collisions at sqrt[s]=13 TeV.

Results on two-particle angular correlations for charged particles produced in pp collisions at a center-of-mass energy of 13TeV are presented. The data were taken with the CMS detector at the LHC and correspond to an integrated luminosity of about 270 nb^{-1}. The correlations are studied over a broad range of pseudorapidity (|η|<2.4) and over the full azimuth (ϕ) as a function of charged particle multiplicity and transverse momentum (p_{T}). In high-multiplicity events, a long-range (|Δη|>2.0), near-side (Δϕ≈0) structure emerges in the two-particle Δη-Δϕ correlation functions. The magnitude of the correlation exhibits a pronounced maximum in the range 1.0<p_{T}<2.0 GeV/c and an approximately linear increase with the charged particle multiplicity, with an overall correlation strength similar to that found in earlier pp data at sqrt[s]=7 TeV. The present measurement extends the study of near-side long-range correlations up to charged particle multiplicities N_{ch}∼180, a region so far unexplored in pp collisions. The observed long-range correlations are compared to those seen in pp, pPb, and PbPb collisions at lower collision energies.

Probing proton fluctuations with asymmetric rapidity correlations

Intrinsic fluctuations of the proton saturation momentum generate asymmetric rapidity distributions on an event-by-event basis. We argue that the asymmetric component, $\ensuremath{\langle}{a}_{1}^{2}\ensuremath{\rangle}$, of the orthogonal polynomial decomposition of the two-particle rapidity correlation function is a sensitive probe to this distribution of fluctuations. We present a simple model connecting the experimentally measured $\ensuremath{\langle}{a}_{1}^{2}\ensuremath{\rangle}$ to the variance, $\ensuremath{\sigma}$, of the distribution of the logarithm of the proton saturation scale. We find that $\ensuremath{\sigma}\ensuremath{\approx}0.5--1$ describes the asymmetric component of the rapidity correlations recently measured by the ATLAS Collaboration.

Observables and initial conditions for rotating and expanding fireballs with spheroidal symmetry

Utilizing a recently found class of exact, analytic rotating solutions of non-relativistic fireball hydrodynamics, we calculate analytically the single-particle spectra, the elliptic flows and two-particle Bose-Einstein correlation functions for rotating and expanding fireballs with spheroidal symmetry. We demonstrate, that rotation generates final state momentum anisotropies even for a spatially symmetric, spherical initial geometry of the fireball. The mass dependence of the effective temperatures, as well as the HBT radius parameters and the elliptic flow are shown to be sensitive not only to radial flow effects but also to the magnitude of the initial angular momentum.

Fluctuations of harmonic and radial flow in heavy ion collisions with principal components

We analyze the spectrum of harmonic flow, $v_n(p_T)$ for $n=0\text{--}5$, in event-by-event hydrodynamic simulations of Pb+Pb collisions at the CERN Large Hadron Collider ($\sqrt{s_{NN}}=2.76\,{\text{TeV}}$) with principal component analysis (PCA). The PCA procedure finds two dominant contributions to the two-particle correlation function. The leading component is identified with the event plane $v_n(p_T)$, while the subleading component is responsible for factorization breaking in hydrodynamics. For $v_0$, $v_1$, and $v_3$ the subleading flow is a response to the radial excitation of the corresponding eccentricity. By contrast, for $v_2$ the subleading flow in \emph{peripheral collisions} is dominated by the nonlinear mixing between the leading elliptic flow and radial flow fluctuations. In the $v_2$ case, the sub-sub-leading mode more closely reflects the response to the radial excitation of $\varepsilon_2$. A consequence of this picture is that the elliptic flow fluctuations and factorization breaking change rapidly with centrality, and in central collisions (where the leading $v_2$ is small and nonlinear effects can be neglected) the subsub-leading mode becomes important. Radial flow fluctuations and nonlinear mixing also play a significant role in the factorization breaking of $v_4$ and $v_5$. We construct good geometric predictors for the orientation and magnitudes of the leading and subleading flows based on a linear response to the geometry, and a quadratic mixing between the leading principal components. Finally, we suggest a set of measurements involving three point correlations which can experimentally corroborate the nonlinear mixing of radial and elliptic flow and its important contribution to factorization breaking as a function of centrality.

Insight into the electron–positron correlations in metals through the looking glass

A semi-empirical analysis of the positron annihilation experimental spectra indicates for a strong sensitivity of the two-particle electron–positron (e–p) enhancement factor to the l=s, p, d, f character of the initial electronic state [1,2]. The essential discrepancy between the models consists in the dependence of the relevant correlation functions on the energy of the annihilating electron. The present contribution contains a theoretical study of the e–p enhancement factors for s, p, d and f states as a function of the electron energy. The slope of the resulting characteristics is directly related to the degree of localisation of the s, p, d and f electrons in the electron density of states. This effect occurs especially for d electrons in transition metals, in favour to the approach of Ref. [1].The energy dependence of the two-particle correlation functions is also a source of controversy between various theoretical approaches. The energy dependent enhancement factors describe properly the positron interaction with delocalised s and p electrons, but this approach overestimates the high momentum components of the e–p momentum densities, dominated by the localised d and f states. On the contrary, the calculations that employ the energy averaged enhancement factors match better with experiment for localised d and f electrons, but they hardly reproduce experimental spectra for nearly-free electron populations. An attempt to visit two sides of the looking glass is made in the theory of the present work. The model combines the properties of both approaches. The resulting e–p momentum densities and enhancement factors are in good agreement with the experimental data for simple, noble and transition metals, both in the low and high momentum region.

Chaoticity and Coherence in Bose-Einstein Condensation and Correlations

We review the properties of chaoticity and coherence in Bose-Einstein condensation and correlations, for a dense boson system in its mean-field represented approximately by a harmonic oscillator potential. The order parameter and the nature of the phase transition from the chaotic to the condensate states are studied for different fixed numbers of bosons. The two-particle correlation function in momentum space is calculated to investigate how the Bose-Einstein correlation depends on the degree of condensation and other momentum variables. We generalize the Bose-Einstein correlation analysis to three-particle correlations to show its dependence on the degree of condensation.

Analytical Expressions for the Hard-Scattering Production of Massive Partons

We obtain explicit expressions for the two-particle differential cross section EcEKdσ(AB→cKX)/dcdk and the two-particle angular correlation function dσ(AB→cKX)/d∆ϕd∆y in the hard-scattering production of massive partons in order to exhibit the “ridge” structure on the away side in the hard-scattering process. The single-particle production cross section dσ(AB→cX)/dyccTdcT is also obtained and compared with the ALICE experimental data for charm production in pp collisions at 7 TeV at LHC.

Order-disorder transitions in a sheared many-body system.

Motivated by experiments on sheared suspensions that show a transition between ordered and disordered phases, we here study the long-time behavior of a sheared and overdamped two-dimensional system of particles interacting by repulsive forces. As a function of interaction strength and shear rate we find transitions between phases with vanishing and large single-particle diffusion. In the phases with vanishing single-particle diffusion, the system evolves towards regular lattices, usually on very slow time scales. Different lattices can be approached, depending on interaction strength and forcing amplitude. The disordered state appears in parameter regions where the regular lattices are unstable. Correlation functions between the particles reveal the formation of shear bands. In contrast to single-particle densities, the spatially resolved two-particle correlation functions vary with time and allow to determine the phase within a period. As in the case of the suspensions, motion in the state with low diffusivity is essentially reversible, whereas in the state with strong diffusion it is not.