Two-pion Correlation Research Articles

Pion Interferometry of square root of (s(NN)) =130 GeV Au + Au collisions at RHIC.

Two-pion correlation functions in Au+Au collisions at square root of [s(NN)] = 130 GeV have been measured by the STAR (solenoidal tracker at RHIC) detector. The source size extracted by fitting the correlations grows with event multiplicity and decreases with transverse momentum. Anomalously large sizes or emission durations, which have been suggested as signals of quark-gluon plasma formation and rehadronization, are not observed. The Hanbury Brown-Twiss parameters display a weak energy dependence over a broad range in square root of [s(NN)].

Pion interferometry at RHIC: porobing a thermalized quark-gluon plasma?

We calculate the Gaussian radius parameters of the pion-emitting source in high-energy heavy-ion collisions, assuming a first-order phase transition from a thermalized quark-gluon plasma (QGP) to a gas of hadrons. Such a model leads to a very long-lived dissipative hadronic rescattering phase which dominates the properties of the two-pion correlation functions. The radii are found to depend only weakly on the thermalization time tau(i), the critical temperature Tc (and thus the latent heat), and the specific entropy of the QGP. The model calculations suggest a rapid increase of R(out)/R(side) as a function of KT if a thermalized QGP were formed.

Boundary and expansion effects on two-pion correlation functions in relativistic heavy-ion collisions

We examine the effects that a confining boundary together with hydrodynamical expansion play on two-pion distributions in relativistic heavy-ion collisions. We show that the effects arise from the introduction of further correlations due both to collective motion and the system's finite size. As is well known, the former leads to a reduction in the apparent source radius with increasing average pair momentum K. However, for small K, the presence of the boundary leads to a decrease of the apparent source radius with decreasing K. These two competing effects produce a maximum for the effective source radius as a function of K.

Quantum corrections for pion correlations involving resonance decays

A method is presented to include quantum corrections into the calculation of two-pion correlations for the case where particles originate from resonance decays. The technique uses classical information regarding the space-time points at which resonances are created. By evaluating a simple thermal model, the method is compared to semiclassical techniques that assume exponential decaying resonances moving along classical trajectories. Significant improvements are noted when the resonance widths are broad as compared to the temperature.

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.

Azimuthal dependence of pion interferometry at the AGS

Two-pion correlation functions, measured as a function of azimuthal emission angle with respect to the reaction plane, provide novel information on the anisotropic shape and orientation of the pion-emitting zone formed in heavy ion collisions. We present the first experimental determination of this information, for semi-central Au + Au collisions at 2–6 A GeV. The source extension perpendicular to the reaction plane is greater than the extension in the plane, and tilt of the pion source in coordinate space is found to be opposite its tilt in momentum space.

Dynamical pion production via parametric resonance from disoriented chiral condensates

We discuss a dynamical mechanism of pion production from disoriented chiral condensates (DCC). It leads to an explosive production of pions via the parametric amplification mechanism, which is similar to the reheating mechanism in inflationary cosmology. Classically, it is related with the instability in the solutions of the Mathieu equation and we explore the quantum aspects of the mechanism. We show that nonlinearlities and back reactions can be ignorable for sufficiently long time under the small amplitude approximations of background $\sigma$ oscillations, which may be appropriate for the late stage of nonequilibrium phase transition. It allows us to obtain an explicit quantum state of the produced pions and $\sigma$, the squeezed state of BCS type. Single particle distributions and two-pion correlation functions are computed within these approximations. The results obtained illuminate the characteristic features of multi-pion states produced through the parametric amplification mechanism. In particular, two-pion correlations of various charge combinations contain back-to-back correlations which cannot be masked by the identical particle interference effect.

Numerical analysis of a two-pion correlation function based on a hydrodynamical model

We will numerically investigate the two-particle correlation function of the CERN-SPS $158A$ GeV Pb+Pb central collisions in detail based on a (3+1)-dimensional relativistic hydrodynamical model with first order phase transition. We use the Yano-Koonin-Podgoretski\ifmmode \breve{\imath}\else \u{\i}\fi{} (YKP) parametrization as well as the usual Cartesian parametrization and analyze the pair momentum dependence of the Hanbury Brown--Twiss radii extracted from the parametrizations. We find that the interpretation of the temporal radius parameter as the time duration in the YKP parametrization is not available for the hydrodynamical model where the source became opaque naturally because of expansion and surface dominant freeze-out. Finally, the effect of the phase transition on the source opacity is also discussed.

Multiboson effects in multiparticle production

The influence of multiboson effects on pion multiplicities, single-pion spectra, and two-pion correlation functions is discussed in terms of an analytically solvable model. The applicability of its basic factorization assumption is clarified. An approximate scaling of the basic observables with the phase space density is demonstrated in the low density (gas) limit. This scaling and also its violation at high densities due to the condensate formation is described by approximate analytical formulas which allow, in principle, for the identification of the multiboson effects among others. For moderate densities indicated by the experimental data, a fast saturation of multiboson effects with the number of contributing cumulants is obtained, allowing for the account of these effects in realistic transport code simulations. At high densities, the spectra are mainly determined by the universal condensate term and the initially narrow Poisson multiplicity distribution approaches a wide Bose-Einstein one. As a result, the intercepts of the inclusive and fixed-$n$ correlation functions (properly normalized to 1 at large relative momenta) approach 2 and 1, respectively, and their widths logarithmically increase with the increasing phase space density. It is shown that the neglect of energy-momentum constraints in the model is justified except near a multipion threshold, where these constraints practically exclude the possibility of a very cold condensate production. It is argued that spectacular multiboson effects are likely to be observed only in the rare events containing sufficiently high density (speckle) fluctuations.

Bose-Einstein correlations in a space-time approach toe+e−annihilation into hadrons

A new treatment of Bose-Einstein correlations is incorporated in a space-time parton-shower model for ${e}^{+}{e}^{\ensuremath{-}}$ annihilation into hadrons. Two alternative algorithms are discussed, and we use a simple calculable model to demonstrate that they reproduce successfully the size of the hadron emission region. One of the algorithms is used to calculate two-pion correlations in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{Z}^{0}\ensuremath{\rightarrow}\mathrm{hadrons}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{W}^{+}{W}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{hadrons}.$ Results are shown with and without resonance decays, for correlations along and transverse to the thrust jet axis in these two classes of events.

Systematic Investigation of Two-pion Correlations at the AGS

We summarize recent HBT results from the Henry Higgins and Forward Spectrometers of BNL E866. These measurements are for pions of both signs in the mid- and forward-rapidity regions, 1.2 < Y < 2.3, for a range of mean pair momenta, 0.1 < kT < 0.5, spanning the full range of system-size and centrality from peripheral Si+Al to central Au+Au. All particles are identified as pions by time-of-flight to better than 3σ. Source radii are fit using Bertsch-Pratt and Yano-Koonin parameterizations. The transverse momentum dependences imply transverse expansion in all systems. The radii scaling with centrality is consistent with both geometric and freeze-out interpretations. Comparisons to geometric overlap of the projectile-target system also give evidence for expansion. Emission durations are in the range, 2–4 fm/c, and for the first time show a linear correlation with geometric size.

Systematic investigation of two-pion correlations at the AGS

We summarize recent HBT results from the Henry Higgins and Forward Spectrometers of BNL E866. These measurements are for pions of both signs in the mid- and forward-rapidity regions, 1.2 < Y < 2.3, for a range of mean pair momenta, 0.1 < k T < 0.5, spanning the full range of system-size and centrality from peripheral Si+Al to central Au+Au. All particles are identified as pions by time-of-flight to better than 3σ. Source radii are fit using Bertsch-Pratt and Yano-Koonin parameterizations. The transverse momentum dependences imply transverse expansion in all systems. The radii scaling with centrality is consistent with both geometric and freeze-out interpretations. Comparisons to geometric overlap of the projectile-target system also give evidence for expansion. Emission durations are in the range, 2–4 fm/c, and for the first time show a linear correlation with geometric size.

Combined effects of nuclear Coulomb field, radial flow, and opaqueness on two-pion correlations

Correlations of two like charged pions emitted from a hot and charged spherically expanding nuclear system are investigated. The motion of the pions is described quantum mechanically using the Klein-Gordon equation which includes Coulomb field and pion absorption. Flow modifies the radial distribution of the source function and rescales the pion wave functions. The radii extracted from the correlation functions are calculated in sideward and outward direction as a function of the pair momentum. Comparison with recent measurements at bombarding energies of 1 GeV and 11 GeV per nucleon is made.

Coalescence and flow in ultrarelativistic heavy ion collisions

Using a density matrix approach to describe the process of coalescence, we calculate the coalescence probabilities and invariant momentum spectra for deuterons and antideuterons. We evaluate our expressions with a hydrodynamically motivated parametrization for the source at freeze-out which implements rapid collective expansion of the collision zone formed in heavy ion collisions. We find that the coalescence process is governed by the same lengths of homogeneity which can be extracted from HBT interferometry. They appear in the absolute cluster yield via an effective volume factor as well as in a quantum mechanical correction factor which accounts for the internal structure of the deuteron cluster. Our analysis provides a new interpretation for the parameters in the popular phenomenological coalescence model and for the effective overlap volume in Hagedorn's model for cluster production in pp collisions. Using source parameters extracted from a recent HBT analysis of two-pion correlations, we successfully describe deuteron and antideuteron production data from Pb+Pb collisions at the CERN SPS as measured by the NA44 and NA52 collaborations. We also confirm the recent finding by Polleri et al. that the different measured slopes of nucleon and deuteron transverse mass spectra require a transverse density profile of the source which is closer to a box than to a Gaussian shape.

Pion correlations and two-particle bound states

A method to investigate possible loosely bound dibaryon states is suggested. The momentum dependence of a two-pion correlation function is shown to depend on the (non)existence of a bound state.

Short range rapidity correlations from the Bose-Einstein effect and multiplicity fluctuations in heavy-ion collisions— an experimental demonstration

A measurement of the two-particle correlation of identified pions was performed E802 E859 magnetic spectrometer on the interval 1.5 ≤ y ≤ 2.0, δφ = 0.4 rad, for central 28Si+Au collisions. It is demonstrated that the two-pion correlation in rapidity is entirely due to Bose-Einstein interference. The directly measured exponential correlation length is ζ y = 0.20 ± 0.03 for two π −, with strenght ( R(0, 0) ∼ 1%, in agreement with previous E802 indirect measurements derived from an analysis of intermittency using Negative Binomial Distributions.

Multiboson effects and the normalization of the two-pion correlation function

We discuss multiboson symmetrization effects on the normalization and shape of the two-pion correlation function, comparing two different popular definitions of the latter. Explicit algorithms for constructing absolutely normalized correlators from experiment are given.

High energy Pb+Pb collisions viewed by pion interferometry

Two-pion correlations from Pb+Pb collisions at 158 GeV/c per nucleon are measured by the NA44 experiment at CERN. Multidimensional fits characterize the emission volume, which is found to be larger than in {ital S}-induced collisions. Comparison to the RQMD model is used to relate the fit parameters to the actual emission volume. {copyright} {ital 1998} {ital The American Physical Society}

Bose-Einstein correlations of three charged pions in hadronic Z $^{\bf 0}$ decays

Bose-Einstein Correlations (BEC) of three identical charged pions were studied in $4 \times 10^6$ hadronic ${\rm Z}^0$ decays recorded with the OPAL detector at LEP. The genuine three-pion correlations, corrected for the Coulomb effect, were separated from the known two-pion correlations by a new subtraction procedure. A significant genuine three-pion BEC enhancement near threshold was observed having an emitter source radius of $r_3 = 0.580 \pm 0.004 \mbox{ (stat.)} \pm 0.029 \mbox{ (syst.)} \mbox{ fm}$ and a strength of $\lambda_3 = 0.504 \pm 0.010 \mbox{ (stat.)}\pm 0.041 \mbox{ (syst.)}$ . The Coulomb correction was found to increase the $\lambda_3$ value by $\sim $ 9% and to reduce $r_3$ by $\sim $ 6%. The measured $\lambda_3$ corresponds to a value of $0.707 \pm 0.014 \mbox{ (stat.)} \pm 0.078 \mbox{ (syst.)}$ when one takes into account the three-pion sample purity. A relation between the two-pion and the three-pion source parameters is discussed.

Two pion correlations as a possible experimental probe for disoriented chiral condensates

We discuss two-pion correlations as a possible experimental probe into disoriented chiral condensates. In particular, we point out that the iso-singlet squeezed states of the BCS type have peculiar two-particle correlations in the back-to-back and the identical momentum configurations which should be detectable experimentally. We motivate the examination of the squeezed state by showing that such state naturally appears in a final stage of nonequilibrium phase transitions via the parametric resonance mechanism proposed by Mrówczyński and Müller.