Transverse and longitudinal Bose-Einstein correlations in hadronic Z^0 decays

Bose-Einstein correlations in pairs of identical charged pions produced in a sample of 4.3 million Z hadronic decays are studied as a function of the three components of the momentum difference, transverse (“out” and “side”) and longitudinal with respect to the thrust direction of the event. A significant difference between the transverse, r, and longitudinal, r, dimensions is observed, indicating that the emitting source of identical pions, as observed in the Longitudinally CoMoving System, has an elongated shape. This is observed with a variety of selection techniques. Specifically, the values of the parameters obtained by fitting the extended Goldhaber parametrisation to the correlation function ${\mathrm C'} ={\mathrm C^{DATA}}/{\mathrm C^{MC}}$ for two-jet events, selected with the Durham algorithm and resolution parameter y = 0.04, are r = (0.809 0.009 (stat) (syst)) fm, r = (0.989 0.011 (stat) ({\it syst})) fm and r/r = 1.222 0.027 (stat) (syst). The results are discussed in the context of a recent model of Bose-Einstein correlations based on string fragmentation. The results of a unidimensional analysis are also presented. Received: 3 January 2000 / Published online: 8 June 2000     

Resonance decays,correlations and intermittency in hadronic collisions

We study a very simple model of correlations and intermittency of identical final state pions in hadronic collisions. Final state pions are either products of resonance decays or they are “directly” produced. The “direct” production is simulated by an immediate decay of a resonance. For “direct pions” forming about a half of final state pions and for formation times of resonances less than 0.5fin/c we get density of sources which via Hanbury-Brown and Twiss interference leads to correlations of two identical pions consistent with recent data and shows intermittency patterns for the second factorial moment. The essential ingredient of the scheme is the combination of pions from resonance decays and direct pions. Due to life-times of resonances taken from experiment, pions from resonance decays are responsible for short-range correlations in the longitudinal momentum, whereas directly produced pions, due to their fast production, dominate in the region of longitudinal momentum difference of the order of 100 MeV/c. The combination of both can give an approximate scaling leading to intermittency.     

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 hadronic 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 and a strength of . The Coulomb correction was found to increase the value by 9% and to reduce by 6%. The measured corresponds to a value of when one takes into account the three-pion sample purity. A relation between the two-pion and the three-pion source parameters is discussed. Received: 7 May 1998 / Published online: 12 August 1998     

Three-pion correlations for studying partial coherence in nuclear collisions

Use of three-particle correlations provides a unique tool for studying partial coherence in relativistic heavy-ion collisions. Here a theory is presented for multiple coherent source components of partially coherent pion radiation. Results are given for the relative probabilities of emission of one, two, or three pions. The calculations on the relation between two- and three-pion correlators give some evidence, when compared with available experimental data, for the existence of partial coherence and multiple coherent components in heavy-ion collisions.     

The production of neutral kaons in Z0 decays and their Bose-Einstein correlations

Updated measurements of the B⁰ and B⁺ meson lifetimes are presented. From a data sample of 1.72 million hadronic Z⁰ decays recorded during the period 1991 to 1993, a sample of approximately 1000 semileptonic B meson decays containing a D⁰, D⁺ or D^*+ has been isolated. From the distribution of decay times in the different samples the lifetimes of the B⁰ and B⁺ mesons are determined to be 1.53±0.12±0.08 ps and 1.52±0.14±0.09 ps, respectively, where the first error is statistical and the second systematic. The ratio of the B⁺ to B⁰ lifetimes is measured to be 0.99±0.14 _–0.04 ^+0.05 , confirming expectations that the lifetimes are similar.     

Bose-Einstein and colour interference in W-pair decays

We study effects on the W mass measurements at LEP2 from non-perturbative interference effects in the fully hadronic decay channel. Based on a model for Bose-Einstein interference, which is in agreement with LEP1 data, we argue that there are no Bose-Einstein correlations between bosons coming from the different W's. For small reconnection probabilities we rule out the possible experimental signal of colour interference at LEP2, suggested in [1]. The conclusions from this paper are that the theoretical uncertainties in the W mass determination should be smaller than the experimental statistical error. Received: 3 November 1997 / Published online: 10 March 1998     

Condensates and Bose-Einstein correlations

We discuss the conditions under which Bose-Einstein correlation can be used to determine the presence of condensates. One starts from the fact that any condensate is a coherent state and uses then the formalism of quantum optics. The case of final state interactions is considered explicitly in a Landau-Ginzburg type approach as used in laser physics. By applying a mean field Hartree approximation for the many mode problem we find that the second order correlation function for identical bosons $\text{C}{}_2\text{(}\text{p}{}_1\text{?}\text{p}{}_2\text{=0)}$ does effectively not depend on the phenomenological coupling constant g and thus C₂(0) can be used to determine the amount of coherence and hence the existence of condensates. On the other hand $\text{C}{}_2\text{(}\text{p}{}_1\text{?}\text{p}{}_2\text{≠0)}$ does depend on g and therefore its measurement provides information about g. The implications of these findings for the determination of the size and lifetime of the source á la Hanbury-Brown-Twiss are discussed. Our conclusions apply both to condensates in nuclear (pion condensates, alpha and deuteron condensates) and hadronic matter.     

Bose-Einstein correlations and isospin

Bose-Einstein correlations between pions are analysed in terms of isospin. The lack of Bose-Einstein correlation between π⁺ and π⁰ is explicitly demonstrated.     

Bose-Einstein correlations and color strings

It is shown that correlations between like-sign bosons (the “Bose-Einstein effect”) arise naturally in string fragmentation models for e⁺e⁻ annihilation. Via the area dependence of Wilson loop integrals, the correlation length in momentum space can be related to the string tension.     

Hyperon decays and quark-quark correlations

The nonleptonic weak Hamiltonian strongly favours the annihilation and creation of correlated quark pairs in spin zero and colour antitriplet states. It is demonstrated that bothS- andP-wave nonleptonic hyperon decays are well described by this mechanism if supplemented by factorization contributions. Apart from the use of mass values and the -nucleon coupling constant, the results are obtained in a parameter free way. Since the diquark properties applied are identical to the ones used in the calculation ofK2 decays and the long range contribution to theK _L –K _S mass difference, a coherent physical picture of dominant nonperturbative effects in the low energy domain is reached.Supported in part by the Bundersministerium für Forschung und Technologie, Bonn, FRG     

Bose-Einstein correlations in thermal field theory

Two-particle correlation functions are calculated for bosons emitted from a localized thermal source (the “glow” of a “hot spot”). In contrast to existing work, non-equilibrium effects up to first order in gradients of the particle distribution function are taken into account. The spectral width of the bosons is shown to be an important quantity: if it is too small, they do not equilibrate locally and therefore strongly increase the measured correlation radius.     

Bose-Einstein correlations in the Lund model

By providing the Lund model fragmentation process with a quantum mechanical framework we extend the results of Andersson and Hofmann [Phys. Lett. B 169 (1986) 364] to situations where there are very many identical bosons. We investigate the features of the weight distributions in some detail and in particular exhibit three-particle BE correlations, the influence on the ϱ-spectrum and the difference between charged and neutral pion correlations.     

Bose-Einstein correlations of pion wavepackets

A wavepacket model for a system of free pions, which takes into account the full permutation symmetry of the wavefunction and which is suitable for any phase space parametrization is developed. The properties of the resulting mixed ensembles and the two-particle correlation function are discussed. A physical interpretation of the chaoticity λ as localization of the pions in the source is presented. Two techniques to generate test-particles, which satisfy the probability densities of the wavepacket state, are studied:

1. A Monte Carlo procedure in momentum space based on the standard Metropolis technique.
2. A molecular dynamic procedure using Bohm’s quantum theory of motion. In order to reduce the numerical complexity, the separation of the wavefunction into momentum space clusters is discussed. In this context the influence of an unauthorized factorization of the state, i. e. the omission of interference terms, is investigated. It is shown that the correlation radius remains almost uneffected, but the chaoticity parameter decreases substantially. A similar effect is observed in systems with high multiplicities, where the omission of higher order corrections in the analysis of two-particle correlations causes a reduction of the chaoticity and the radius. The approximative treatment of the Coulomb interaction between pions and the source is investigated. The results suggest that Coulomb effects on the correlation radii are not symmetric for pion pairs of different charges. For (π^?,π^?) pairs the radius, integrated over the whole momentum spectrum, increases substantially, while for (π⁺,π⁺) pairs the radius remains almost unchanged.

     

Intermittency and correlations in hadronic Z^0 decays

A multidimensional study of local multiplicity fluctuations and multiparticle correlations of hadrons produced in Z decays is performed. The study is based on the data sample of more than events recorded with the OPAL detector at LEP. The fluctuations and correlations are analysed in terms of the normalized scaled factorial moments and cumulants up to the fifth order. The moments are observed to have intermittency-like behaviour, which is found to be more pronounced with increasing dimension. The large data sample allows for the first time a study of the factorial cumulants in annihilation. The analysis of the cumulants shows the existence of genuine multiparticle correlations with a strong intermittency rise up to higher orders. These correlations are found to be stronger in higher dimensions. The decomposition of the factorial moments into lower-order correlations shows that the dynamical fluctuations have important contributions from genuine many-particle correlations. The Monte Carlo models Jetset 7.4 and Herwig 5.9 are found to reproduce the trend of the measured moments and cumulants but they underestimate the magnitudes. The results are found to be consistent with QCD jet formation dynamics, although additional contributions from other mechanisms cannot be excluded. Received: 8 February 1999 / Published online: 8 September 1999     

Coulomb and strong interactions for Bose-Einstein correlations

We present an analytical formula for the Bose-Einstein correlations (BEC) which includes effects of both Coulomb and strong final state interactions (FSI). It was obtained by using Coulomb wave function together with the scattering partial wave amplitude of the strong interactions describing data on thes-wave phase shift. We have proved numerically that this method is equivalent to solving Schrödinger equation with Coulomb and thes-wave strong interaction potentials. As an application we have analysed, using our formula which includes the degree of coherence and the long range correlation, the data fore ⁺ e ^? annihilations. We have found that the degree of coherence present in our formula approaches approximately unity whereas the long range correlation parameter becomes approximately zero. These results suggest that the physical meanings of the fractional degree of coherence and the long range correlation observed in various other analyses can most probably be attributed to FSI.     

Bose-Einstein correlations in neutrino and antineutrino interactions in deuterium

Bose-Einstein correlations between pions of equal charge have been observed in Charged Current and Neutral Current (anti)neutrino-deuterium interactions in the BEBC bubble chamber exposed to the SPS wide band beam. The pion emission region is found to be essentially spherical with a mean radius of (0.48±0.07) fm; the chaoticity parameter is 0.36±0.04.