B. Buschbeck

The Correlation integral as probe of multiparticle correlations

Abstract We report on a considerable improvement of the usual factorial moment method used in the study of correlations and in particular of intermittency: by means of integrals of the correlation functions over a strip domain, we obtain greater stability and smaller statistical errors. The benefit of using correlation integrals rises with increasing order of the moment and with increasing dimension of the variables. An algorithm for the actual computation of the so-called strip integrals directly from experimental data is explained in detail. Illustrations of the power of the correlation integral method are given in terms of the NA22 spike event, a two-dimensional JETSET calculation and the p -model.

Integral correlation measures for multiparticle physics.

We report on a considerable improvement in the technique of measuring multiparticle correlations via integrals over correlation functions. A modification of measures used in the characterization of chaotic dynamical systems permits fast and flexible calculation of factorial moments and cumulants as well as their differential versions. Higher-order correlation integral measurements even of large multiplicity events such as encountered in heavy ion collisions are now feasible. The change from ordinary to factorial powers may have important consequences in other fields such as the study of galaxy correlations and Bose-Einstein interferometry.

Higher order pion interferometry: Moments and cumulants

Abstract Pion interferometry can be viewed as intermittency analysis in terms of momentum transfer of like-sign particles. By putting the common practice of event mixing on a sound footing and extending its use, we provide the tools to eliminate the combinatoric background contained in the usual correlation functions. Information on true higher order correlations can now be extracted and the question whether these play any role in interferometry addressed experimentally.

Multiplicity dependence of correlation functions in p̄p reactions at √s=630 GeV

Abstract Discussions about Bose–Einstein correlations between decay products of coproduced W-bosons again raise the question about the behaviour of correlations if several strings are produced. This is studied by the multiplicity dependence of correlation functions of particle pairs with like-sign and opposite-sign charge in p p reactions at s =630 GeV.

Generalized moments and cumulants for samples of fixed multiplicity

Factorial moments and cumulants are usually defined with respect to the unconditioned Poisson process. Conditioning a sample by selecting events of a given overall multiplicity {ital N} necessarily introduces correlations. By means of Edgeworth expansions, we derive generalized cumulants which define correlations with respect to an arbitrary process rather than just the Poisson case. The results are applied to correlation measurements at fixed {ital N}, to redefining short-range versus long-range correlations and to normalization issues. {copyright} {ital 1996 The American Physical Society.}

Transverse-longitudinal HBT correlations in pp¯ collisions at s=630 GeV

Abstract Correlations of like-sign pion pairs emerging from proton–antiproton collisions are analysed in the two-dimensional ( q L , q T ) decomposition of the three-momentum difference q. While the data cannot be adequately represented by Gaussian, exponential, power-law or Edgeworth parametrisations, more elaborate ones such as Levy and an exponential with a cross term do better. A two-scale model using a hard cut to separate small and large scales may indicate a core that is more prolate than the halo. Consideration not only of the interference peak at small ( q L , q T ) , but also of the shape of the correlation distribution at intermediate momentum differences is crucial to understanding the data.

Transverse-longitudinal HBT correlations in proton-antiproton collisions at root(s) = 630 GeV

Abstract Correlations of like-sign pion pairs emerging from proton–antiproton collisions are analysed in the two-dimensional ( q L , q T ) decomposition of the three-momentum difference q. While the data cannot be adequately represented by Gaussian, exponential, power-law or Edgeworth parametrisations, more elaborate ones such as Levy and an exponential with a cross term do better. A two-scale model using a hard cut to separate small and large scales may indicate a core that is more prolate than the halo. Consideration not only of the interference peak at small ( q L , q T ) , but also of the shape of the correlation distribution at intermediate momentum differences is crucial to understanding the data.

Internal cumulants for femtoscopy with fixed charged multiplicity

A detailed understanding of all effects and influences on higher-order correlations is essential. At low charged multiplicity, the effect of a non-Poissonian multiplicity distribution can significantly distort correlations. Evidently, the reference samples with respect to which correlations are measured should yield a null result in the absence of correlations. We show how the careful specification of desired properties necessarily leads to an average-of-multinomials reference sample. The resulting internal cumulants and their averaging over several multiplicities fulfill all requirements of correctly taking into account non-Poissonian multiplicity distributions as well as yielding a null result for uncorrelated fixed- samples. Various correction factors are shown to be approximations at best. Careful rederivation of statistical variances and covariances within the frequentist approach yields errors for cumulants that differ from those used so far. We finally briefly discuss the implementation of the analysis through a multiple event buffer algorithm.

Transverse-longitudinal HBT correlations in p over(p, ̄) collisions at sqrt(s) = 630 GeV

Abstract Correlations of like-sign pion pairs emerging from proton–antiproton collisions are analysed in the two-dimensional ( q L , q T ) decomposition of the three-momentum difference q. While the data cannot be adequately represented by Gaussian, exponential, power-law or Edgeworth parametrisations, more elaborate ones such as Levy and an exponential with a cross term do better. A two-scale model using a hard cut to separate small and large scales may indicate a core that is more prolate than the halo. Consideration not only of the interference peak at small ( q L , q T ) , but also of the shape of the correlation distribution at intermediate momentum differences is crucial to understanding the data.