Bose-Einstein Correlation Functions Research Articles

Hadron production and QCD coherence at LEP

Two analyses are presented based on the high statistics sample of hadronic Z0 decays recorded at LEP with the OPAL detector. First, Bose-Einstein correlation functions are studied in intervals of the average pair transverse momentum and of the pair rapidity, in order to study possible correlations between the pion production points and their momenta. The Yano-Koonin and the Bertsch-Pratt parameterizations are fitted to the measured correlation functions to estimate the space-time parameters of the source. The source rapidity is found to scale approximately with the pair rapidity, and both the longitudinal and transverse source dimensions decrease for increasing average pair transverse momenta, indicating that the source of pions expands during particle emission. In the second analysis, QCD coherence effects are studied measuring the correlations of particles with restricted transverse momenta. Due to colour coherence, the multiplicity distribution of particles with restricted transverse momenta is predicted to become Poissonian as the cut in transverse momentum decreases. The expected correlation pattern is observed for cuts down to ≈ 1 GeV but not at lower transvers momenta. This study indicates difficulties with the Local Parton-Hadron Duality (LPHD) hypothesis when applied to many-particle inclusive observables of soft hadrons.

Parametrization of Bose–Einstein correlations and reconstruction of the space–time evolution of pion production in e+e− annihilation

A parametrization of the Bose–Einstein correlation function of pairs of identical pions produced in hadronic e+e− annihilation is proposed within the framework of a model (the τ-model) in which space–time and momentum space are very strongly correlated. Using information from the Bose–Einstein correlations as well as from single-pion spectra, it is then possible to reconstruct the space–time evolution of pion production.

Shortest Movie from Bose–Einstein Correlation Functions in e + e − Annihilations

Bose-Einstein correlations of identical charged-pion pairs produced in hadronic Z decays are analyzed in terms of various parametrizations. A good description is achieved using Levy stable distributions. The source function is reconstructed with the help of the τ model.

Measurement and analysis of two- and three-particle correlations

Allowed regions of core fraction versus partial coherence are obtained from analysis of both two- and three-pion Bose-Einstein correlations measured at PHENIX in s N N = 200 GeV Au+Au collisions. Two-pion Bose-Einstein correlation functions for different average transverse momenta are used to analyze chiral symmetry restoration.

Improved Description of Bose–Einstein Correlation Function

The L3 data on Bose-Einstein correlations of equally charged pion pairs produced in hadronic Z decays are analyzed in terms of various parametrizations. Preliminary results are presented here.

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.

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.

Hydrodynamical analysis of hadronic spectra in the 130 GeV/nucleonAu+Aucollisions

We study one-particle spectra and a two-particle correlation function in the 130 GeV/nucleon Au+Au collisions at RHIC by making use of a hydrodynamical model. We calculate the one-particle hadronic spectra and present the first analysis of Bose-Einstein correlation functions based on the numerical solution of the hydrodynamical equations which takes both longitudinal and transverse expansion into account appropriately. The hydrodynamical model provides excellent agreement with the experimental data in the pseudorapidity and the transverse momentum spectra of charged hadrons, the rapidity dependence of anti-proton to proton ratio, and almost consistent result for the pion Bose-Einstein correlation functions. Our numerical solution with simple freeze-out picture suggests the formation of the quark-gluon plasma with large volume and low net-baryon density.

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.

On transverse mass of identical bosons in the string model

Transverse mass dependence of the Bose-Einstein correlation function radius parameters in experimental data on two-pion correlation in hadronic decays of Z 0, is compared to the intrinsic properties of the string model, using as an example production of identical kaon pairs by the J etset event generator.

Continuous emission versus freeze-out via Hanbury Brown–Twiss

The effect of the continuous emission hypothesis on the two-pion Bose-Einstein correlation function is discussed and compared with the corresponding results based on the usual freeze-out. Sizable differences in the correlation function appear in these different descriptions of the decoupling process. This means that, when extracting properties of the hot matter formed in high-energy heavy-ion collisions from the data, completely different conclusions may be reached according to the description of the particle emission process adopted.

Coulomb wave function corrections for n-particle Bose–Einstein correlations

The effect of multi-particle Coulomb final state interactions on higher-order intensity correlations is determined in general, based on a scattering wave function which is a solution of the n-body Coulomb Schrodinger equation in (a large part of) the asymptotic region of n-body configuration space. In particular, we study Coulomb effects on the n-particle Bose–Einstein correlation functions of similarly charged particles and remove a systematic error as big as 100% from higher-order multi-particle Bose–Einstein correlation functions.

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.

Coulomb wave function corrections for

The effect of multi-particle Coulomb final state interactions on higher-order intensity correlations is determined in general, based on a scattering wave function which is solution of the n-body Coulomb Schr\"odinger equation in (a large part of) the asymptotic region of n-body configuration space. In particular, we study Coulomb effects on the n-particle Bose-Einstein correlation functions of similarly charged particles and remove a systematic error as big as 100% from higher-order multi-particle Bose-Einstein correlation functions.

Coulomb corrections to the three-body correlation function in high-energy heavy ion reactions

Starting from an asymptotically correct three-body Coulomb wave-function, we determine the effect of Coulomb final state interaction on the three-particle Bose-Einstein correlation function of similarly charged particles. We numerically estimate that the Riverside approximation is not precise enough to determine the three-body Coulomb correction factor in the correlation function, if the characteristic HBT radius parameter is 5–10 fm, which is the range of interest in high-energy heavy ion physics.

Partial coherence in the core–halo picture of Bose–Einstein n-particle correlations

We study the influence of a possible coherent component in the boson source on the two-, three- and $n$-particle correlation functions in a generalized core/halo type of boson-emitting source. In particular, a simple formula is presented for the strengh of the $n$-particle correlation functions for such systems. Graph rules are obtained to evaluate the correlation functions of arbitrary high order. The importance of experimental determination of the 4-th and 5-th order Bose-Einstein correlation function is emphasized.

Appearance of an artificial length scale in JETSET Bose-Einstein simulation

This work studies the algorithm which implements the Bose-Einstein correlation effect in the JETSET 7.4 event generator. This algorithm attempts to reproduce an expected correlation function with a given correlation radius and amplitude. The two-particle correlation function is studied in the generated \(Z^0\) hadronic decays for different values of the built-in radius parameter. Samples consisting of only charged particles are used, as well as subsamples of pions, pions coming from the string decay and pions from the resonance decays. The Bose-Einstein correlation function, extracted from the generated events, is parameterized analogously to the built-in JETSET correlation function and its parameters are compared with the input ones. We found that the measured correlation function reproduces the built-in one, if the input radius parameter is larger than 1 fm. For lower input radii an artificial new length scale appears due to the way the Bose-Einstein correlation is implemented.

Bose-Einstein correlations and the equation of state of nuclear matter

Within a relativistic hydrodynamic framework, we use four different equations of state of nuclear matter to compare to experimental spectra from CERN/SPS experiments NA44 and NA49. Freeze-out hypersurfaces and Bose-Einstein correlation functions for identical pion pairs are discussed. We find that two-pion Bose-Einstein interferometry measures the relationship between the temperature and the energy density in the equation of state during the late hadronic stage of the fireball expansion. Little sensitivity of the light-hadron data to a quark-gluon plasma phase-transition is seen.

Observation of PartialUA(1)Restoration from Two-Pion Bose-Einstein Correlations

The effective intercept parameter of the two-pion Bose-Einstein correlation function, ${\ensuremath{\lambda}}_{*}$, is found to be sensitive to the partial restoration of ${\mathrm{U}}_{A}(1)$ symmetry in ultra-relativistic nuclear collisions. An increase in the yield of the ${\ensuremath{\eta}}^{\ensuremath{'}}$ meson, proposed earlier as a signal of partial ${\mathrm{U}}_{A}(1)$ restoration, is shown to create a ``hole'' in the low ${p}_{t}$ region of ${\ensuremath{\lambda}}_{*}$. A comparison with NA44 data and central $\mathrm{S}+\mathrm{Pb}$ collisions at $200A\mathrm{GeV}$ is made, and implications for future heavy ion experiments are discussed.

Testing the core-halo model on Bose-Einstein correlation functions

Having first performed a Monte Carlo simulation to justify the analysis technique to be used, we then analyze the Bose-Einstein correlation functions from CERN experiment NA44 in the context of the core-halo model. Although experimental resolution and error bar distribution prevents a direct observation of the halo structure, the values for the core radius and the core fraction of pions can be obtained in a straight-forward manner. These are found to be independent of the structure of the correlation function at small relative momenta of Q pi + pi + X reaction at CERN SPS. As we find that the model-independent HBT radii yield results that are quantitatively as well as qualitatively unreliable for systems with long-lived resonances, we present their corrected form that applies for correlation functions with lambda(K) < 1.