Two-particle Bose-Einstein Correlations Research Articles

Two-particle Bose–Einstein correlations in { pp } collisions at mathbf {sqrt{s} = 13} TeV measured with the ATLAS detector at the LHC

This paper presents studies of Bose–Einstein correlations (BEC) in proton–proton collisions at a centre-of-mass energy of 13 TeV, using data from the ATLAS detector at the CERN Large Hadron Collider. Data were collected in a special low-luminosity configuration with a minimum-bias trigger and a high-multiplicity track trigger, accumulating integrated luminosities of 151 upmu b^{-1} and 8.4 nb^{-1}, respectively. The BEC are measured for pairs of like-sign charged particles, each with |eta | < 2.5, for two kinematic ranges: the first with particle p_{mathrm {T}} > 100 MeV and the second with particle p_{mathrm {T}} > 500 MeV. The BEC parameters, characterizing the source radius and particle correlation strength, are investigated as functions of charged-particle multiplicity (up to 300) and average transverse momentum of the pair (up to 1.5 GeV). The double-differential dependence on charged-particle multiplicity and average transverse momentum of the pair is also studied. The BEC radius is found to be independent of the charged-particle multiplicity for high charged-particle multiplicity (above 100), confirming a previous observation at lower energy. This saturation occurs independent of the transverse momentum of the pair.

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.

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.

Two-particle Bose-Einstein correlations in pp collisions at [Formula: see text] 0.9 and 7 TeV measured with the ATLAS detector.

The paper presents studies of Bose–Einstein Correlations (BEC) for pairs of like-sign charged particles measured in the kinematic range p_mathrm{T}> 100 MeV and |eta |< 2.5 in proton collisions at centre-of-mass energies of 0.9 and 7 TeV with the ATLAS detector at the CERN Large Hadron Collider. The integrated luminosities are approximately 7 upmu b^{-1}, 190 upmu b^{-1} and 12.4 nb^{-1} for 0.9 TeV, 7 TeV minimum-bias and 7 TeV high-multiplicity data samples, respectively. The multiplicity dependence of the BEC parameters characterizing the correlation strength and the correlation source size are investigated for charged-particle multiplicities of up to 240. A saturation effect in the multiplicity dependence of the correlation source size parameter is observed using the high-multiplicity 7 TeV data sample. The dependence of the BEC parameters on the average transverse momentum of the particle pair is also investigated.

Bose-Einstein correlations of light hadrons and the stochastic scale of particle emitter source

Based on quantum field theory at finite temperature, we obtained new results for two-particle Bose-Einstein correlation (BEC) function C2(Q) in case of light hadrons. The important parameters of BEC function related to the size of emitting source, mean multiplicity, stochastic forces range and correlation radius with the particle energy and the mass dependence, and the temperature of the source are obtained in analytical form for the first time. Not only is the correlation between identical bosons explored but also the off-correlation between non-identical particles is proposed.

Bose-Einstein correlations of neutral gauge bosons in pp collisions

The theory for Bose-Einstein correlations in case of neutral gauge bosons in pp collisions at high energies is presented. Based on quantum field theory at finite temperature, the two-particle Bose-Einstein correlations of neutral gauge bosons are carried out for the first time. As a result, the important parameters of the correlation functions can be obtained for the Z 0 Z 0 pairs.

Analysis of Identified Particle Yields and Bose–Einstein (HBT) Correlations in p+p Collisions at RHIC

Simultaneous Buda-Lund hydro model fits are presented to identified particle spectra and two-particle Bose-Einstein correlations as measured by the STAR collaboration in $\sqrt{s}=200$ GeV p+p collisions at RHIC. Preliminary results are compared to similar results in Au+Au collisions at RHIC, hadron+p reactions as well as Pb+Pb collisions at CERN SPS.

Bose-Einstein correlations for Lévy stable source distributions

The peak of the two-particle Bose-Einstein correlation functions has a very interesting structure. It is often believed to have a multivariate Gaussian form. We show here that for the class of stable distributions, characterized by the index of stability $0 < \alpha \le 2$, the peak has a stretched exponential shape. The Gaussian form corresponds then to the special case of $\alpha = 2$. We give examples for the Bose-Einstein correlation functions for univariate as well as multivariate stable distributions, and check the model against two-particle correlation data.

The Reconstructed Final State of Au + Au Collisions from PHENIX and STAR Data at [ s ] 1/2 = 130 AGeV - Indication for Quark Deconfinement at RHIC

The final state of Au+Au collisions at √s=130 AGeV at RHIC has been reconstructed within the framework of the Buda-Lund hydrodynamical model, by performing a simultaneous fit to final data on twoparticle Bose-Einstein correlations of the STAR and PHENIX Collaboration, and final identified single-particle spectra as measured by the PHENIX Collaboration. The results indicate a strongly three dimensional expansion, with a four-velocity field that is almost a spherically symmetric Hubble flow. We find large transverse geometrical source sizes, R G=9.8±1.2 fm, relatively short mean freeze-out time, τ0=6.1±0.3 fm/c and a short duration of particle emission, Δτ=0.02±1.5 fm/c. Most strikingsly, we find an indication for a hot central part of the hydrodynamically evolving core, characterized by a central temperature T 0=202±13 MeV that is close to (or even above) the deconfinement temperature of the quark-hadron phase transition. The best fit indicates a cold surface temperature T s=110±16 MeV. When the possibility of the hot center is excluded, the confidence level of the fit decreases from 28.9% to 1.0%. Predictions are made for the rapidity dependence of the slope parameters and for the transverse mass depedence of the rapidity width of the single-particle spectra, and the transverse mass dependence of the non-identical particle correlations.

Observables and initial conditions for self-similar ellipsoidal flows

Single-particle spectra and two-particle Bose-Einstein correlation functions are determined analytically utilizing a self-similar solution of nonrelativistic hydrodynamics for ellipsoidally symmetric, expanding fireballs, by assuming that the symmetry axes of the ellipsoids are tilted in the frame of the observation. The directed, elliptic, and third flows are calculated analytically. The mass dependences of the slope parameters in the principal directions of the expansion, together with the mass and angular dependences of the HBT radius parameters, reflect directly the ellipsoidal properties of the flow.

Wigner Functions in High Energy Physics

Recent developments are (meta)reviewed in the applications of Wigner functions to describe the observed single-particle spectra and two-particle Bose-Einstein (or Hanbury Brown-Twiss) correlations in high energy particle and nuclear physics, with examples from hadron-proton and Pb+Pb collisions at CERN SPS.

Particle interferometry, binary sources and oscillations in two-particle correlations

The basics and the formalism of Bose-Einstein correlations is briefly reviewed. The invariant Buda-Lund form is summarized. Tools are presented that can be utilized in a model-independent search for non-Gaussian structuctures in the two-particle Bose-Einstein correlation functions. The binary source formalism of particle interferometry is presented and related to oscillations in the two-particle Bose-Einstein and Fermi-Dirac correlation functions. The frequency of the observed oscillations in the NA49 two-proton correlation function in Pb+Pb collisions at CERN SPS energies is explained with the help of the reconstructed space-time picture of particle production and the binary nature of the proton source in this reaction.

Particle Interferometry from 40 MeV to 40 TeV

Recent developments are summarized in the theory of Bose-Einstein and Fermi-Dirac correlations, with emphasis on the necessity of a simultaneous analysis of particle spectra and quantum statistical correlations for a detailed reconstruction of the space-time picture of particle emission. This review is limited to the following topics: basics and formalism of quantum-statistical correlations; the core/halo picture for n-particle Bose-Einstein correlations; particle interferometry in e+e- collisions including the Andersson-Hofmann model; the invariant Buda-Lund particle interferometry; the Buda-Lund, the Bertsch-Pratt and Yano-Koonin-Podgoretskii parameterizations, the Buda-Lund hydro model and its applications to (π/K)+p and Pb+Pb collisions at CERN SPS, and to low-energy heavy-ion collisions; the binary-source formalism and the related oscillations in the two-particle Bose-Einstein and Fermi-Dirac correlation functions; the experimental signals of expanding rings of fire and shells of fire in particle and heavy-ion physics and their similarity to planetary nebulae in stellar astronomy.

Reconstructing the Freeze-out State in Pb+Pb Collisions at 158 A GeV/ c a

For a class of analytical parametrizations of the freeze-out state of relativistic heavy ion collisions, we perform a simultaneous analysis of the single-particle m_t-spectra and two-particle Bose-Einstein correlations measured in central Pb+Pb collisions at the CERN SPS. The analysis includes a full model parameter scan with chi^2 confidence levels. A comparison of different transverse density profiles for the particle emission region allows for a quantitative discussion of possible model dependencies of the results. Our fit results suggest a low thermal freeze-out temperature T approximately 95 +- 15 MeV and a large average transverse flow velocity of about 0.55c +- 0.07c. Moreover, the fit favours a box-shaped transverse density profile over a Gaussian one. We discuss the origins and the consequences of these results in detail. In order to reproduce the measured pion multiplicity our model requires a positive pion chemical potential. A study of the pion phase-space density indicates \mu_\pi approximately 60 MeV for T = 100 MeV.

Isotopic spin effect in two-pion and three-pion Bose-Einstein correlations

Bose-Einstein correlations of pions are calculated in the presence of both statistical and coherent pion production. An isotopic spin conservation is taken into account for the coherent component. Additional contributions due to the isospin effect in pion correlation functions are found. Moreover, the experimental data of two-particle Bose-Einstein correlations for neutral pions are analyzed in this scheme.

Bose-Einstein weights for event generators

A simple new algorithm for the calculation of two-particle Bose-Einstein correlations from classical event generators is derived and discussed.

Particle correlations in Pb+Pb collisions at the CERN-SPS — results from the NA49 experiment

Preliminary results of the multidimensional two-particle Bose-Einstein correlation analysis of negatively charged particles are presented for Pb+Pb collisions at a beam energy of 158 GeV per nucleon. The data show the characteristics of a dynamic pion source which mainly expands along the collision axis in a non boost invariant way. Evidence for a finite duration of the particle emission process is found. The dependence of the Coulomb correlation function for π + π − pairs on the source size is discussed. The analysis of the higher order correlation integrals shows that multiparticle correlations are dominated by two body correlations.

Bose-Einstein correlations in the invariant Q2 variable and intermittency.

The dependence of two-particle Bose-Einstein correlations on the squared invariant momentum difference [ital Q][sup 2] has been calculated in several models with fixed space-time sizes of the pion source. The complex relationship between the apparent radius and incoherence factor of the source measured with the help of [ital Q], and the true'' radii and incoherence factors is established. The resulting correlation functions have a sharp and approximately powerlike peak at small [ital Q] in agreement with preliminary data of the UA1 Collaboration. The appearance of this powerlike peak at small [ital Q] due to the kinematics of the [ital Q] variable imples that the observed [ital Q] dependence does not necessarily constitute evidence either for intermittency or for a fractal nature of the source.

Relationship between Bose-Einstein correlations and intermittency revisited

The dependence of two-particle Bose-Einstein correlations on the squared invariant momentum difference Q 2 has been calculated in models with fixed space-time sizes of the pion source. The resulting correlation functions have a sharp and approximately power-like peak at small Q in agreement with recent data of the UA1 Collaboration. The kinematical origin of the small Q peak is established thus showing that the observed Q-dependence does not necessarily imply evidence for intermittency.

Hadron interferometry revisited

The emperical relation for the two-particle Bose-Einstein correlation function used in many experimental and theoretical studies and involving one exponential is in contradiction with quantum statistics. It is shown that the correct formula contains two exponentials, the ratio of which depends only on the radius R and the chaoticity p of the source. The corresponding three-particle correlation is also derived. Possible important implications of these result for the determination of p and R are discussed.