Genuine correlations of like-sign particles in hadronic Z0 decays
Introduction
Correlations in momentum space between hadrons produced in high energy interactions have been extensively studied over many decades in different contexts [1]. Being a measure of event-to-event fluctuations of the number of hadrons in a phase space domain of size Δ, correlations provide detailed information on the hadronisation dynamics, complementary to that derived from inclusive single-particle distributions and global event-shape characteristics.
The suggestion in [2] that multiparticle dynamics might possess (multi-)fractal properties or be “intermittent”, emphasized the importance of studying correlations as a function of the size of domains in momentum space. A key ingredient for such studies is the normalized factorial moment and factorial cumulant technique (see Section 2), which allows statistically meaningful results to be obtained even for very small phase space cells.
Unlike factorial moments, cumulants of order q are a direct measure of the stochastic interdependence among groups of exactly q particles emitted in the same phase space cell [3], [4], [5]. Therefore, they are well suited for the study of true or “genuine” correlations between hadrons.
Whereas earlier work dealt mainly with correlations between pairs, i.e., second-order correlations, the use of factorial cumulants in high-statistics experiments has established the presence of genuine correlations among groups comprising three or more hadrons, hereafter referred to as higher-order correlations.
Experimental results on hadron correlations are reviewed in [1], [6]. Except for heavy ion collisions, where correlations beyond second order are found to be small, as can be understood from a superposition of independent particle-production sources [7], in all other types of reactions, significant positive higher-order correlations are seen. In two- or three-dimensional (typically rapidity, azimuthal angle, transverse momentum) phase space cells, they rapidly increase as the cell-size, Δ, becomes smaller. Further studies of the dependence on particle charge confirm that, as conjectured in [8], correlations between hadrons with the same charge play an increasingly important role as Δ decreases, thus pointing to the influence of Bose–Einstein (BE) interference effects [9], [10]; for a recent review see [11]. In contrast, correlations in multiplets composed of particles with different charges, which are more sensitive to multiparticle resonance decays than like-sign ones, tend to saturate in small phase space domains [12], [13].
Two-particle Bose–Einstein correlations (BEC) have been observed in a wide range of multihadronic processes [11]. Such correlations were extensively studied at LEP [14], [15], [16]. Evidence for BEC among groups of more than two identical particles has also been reported [13], [17]. The subject has acquired particular importance in connection with high-precision measurements of the W-boson mass at LEP-II [18], [19]. For these, better knowledge of correlations in general is needed, as well as realistic Monte Carlo modelling of BEC [20], [21].
The OPAL Collaboration recently reported an analysis of the domain-size dependence of factorial cumulants in hadronic Z0 decays, using much larger statistics than in any previous experiment [22]. In that study, no distinction was made between multiplets composed of like-charge particles and those of mixed charge. Clear evidence was seen for large positive genuine correlations up to fifth order. Hard jet production was found to contribute significantly to the observed particle fluctuation patterns. However, Monte Carlo models based on parton showers and string or cluster fragmentation, gave only a qualitative description of the Δ-dependence of the cumulants. Quantitatively, the model studied, which did not explicitly include BE-type correlation effects, underestimated significantly correlations between hadrons produced very close together in momentum space.
In the present Letter, the high statistics OPAL data collected at and near the Z0 centre-of-mass energy are used to measure cumulants for multiplets of particles with the same charge, hereafter referred to as “like-sign cumulants”. They are compared to “all-charge” cumulants, corresponding to multiplets comprising particles of any (positive or negative) charge. Using the factorial cumulant technique, results of much higher precision than previously available are obtained on like-sign correlations up to fourth order. The role of Bose–Einstein-type effects is studied, using recently proposed BEC algorithms12 in the Monte Carlo event generator Pythia for e+e− annihilation [24]. Proceeding beyond the usual analyses of two-particle correlations, we show that, at least within the framework of this model, a good description can be achieved of the factorial cumulants up to fourth order in one-, two- and three-dimensional phase space domains.
The Letter is organized as follows. Section 2 explains the normalized factorial cumulant method which allows genuine particle correlations to be measured. The OPAL detector, the event selection and the track selection criteria are detailed in Section 3. The data on factorial cumulants are presented in Section 4. They are compared with Pythia predictions and, in particular, with several variants of a model to simulate the Bose–Einstein effect. The results are summarized in Section 5. A brief overview of some of the BEC algorithms implemented in Pythia is given in the appendix.
Section snippets
Factorial cumulant method
To measure genuine multiparticle correlations in multi-dimensional phase space cells, we use the technique of normalized factorial cumulant moments, Kq, or “cumulants” for brevity, as proposed in [5].
In the present Letter, the cumulants are computed as in a previous OPAL analysis [22]. A D-dimensional region of phase space (defined in Section 3) is partitioned into MD cells of equal size Δ. From the number of particles counted in each cell, nm (m=1,…,MD), event-averaged unnormalized factorial
Experimental details
The present analysis uses a sample of approximately 4.1×106 hadronic Z0 decays collected from 1991 through 1995. About 91% of this sample was taken at the Z0; the remaining part has a centre-of-mass energy, , within ±3 GeV of the Z0 peak.
The OPAL detector has been described in detail in [26]. The results presented here are mainly based on the information from the central tracking chambers, which consist of a silicon microvertex detector, a vertex chamber, a jet chamber with 24 sectors each
Like-sign and all-charge cumulants
The fully corrected normalized cumulants Kq (q=2,3,4) for all-charge15 and like-sign particle multiplets, calculated in one-dimensional (y and Φ) (1D), two-dimensional y×Φ (2D) and three-dimensional y×Φ× lnpT (3D) phase space cells, are displayed in Fig. 1, Fig. 2.
From Fig. 1 it is seen that, even in 1D, positive genuine correlations among groups of two,
Summary and conclusions
In this paper we have presented a comparative study of like-sign and all-charge genuine correlations between two and more hadrons produced in e+e− annihilation at the Z0 energy. The high-statistics data on hadronic Z0 decays recorded with the OPAL detector from 1991 through 1995 were used to measure normalized factorial cumulants as a function of the domain size Δ, in D-dimensional domains (D=1,2,3) in rapidity, azimuthal angle and (the logarithm of) transverse momentum, defined in the event
Acknowledgements
We particularly wish to thank the SL Division for the efficient operation of the LEP accelerator at all energies and for their close cooperation with our experimental group. We thank our colleagues from CEA, DAPNIA/SPP, CE-Saclay for their efforts over the years on the time-of-flight and trigger systems which we continue to use. In addition to the support staff at our own institutions we are pleased to acknowledge the Department of Energy, USA; National Science Foundation, USA; Particle Physics
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Cited by (0)
- 1
And at TRIUMF, Vancouver, Canada V6T 2A3.
- 2
And Royal Society University Research Fellow.
- 7
And Research Institute for Particle and Nuclear Physics, Budapest, Hungary.
- 3
And Institute of Nuclear Research, Debrecen, Hungary.
- 10
And CERN, EP Division, 1211 Geneva 23, Switzerland.
- 11
And Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel.
- 6
And MPI München, Germany.
- 8
Now at University of Liverpool, Department of Physics, Liverpool L69 3BX, UK.
- 4
And Heisenberg Fellow.
- 5
And Department of Experimental Physics, Lajos Kossuth University, Debrecen, Hungary.
- 9
And University of California, Riverside, High Energy Physics Group, CA 92521, USA.