Contribution.J Revi.Jta Mexicana de Fí.5ica 39, No. Suplemento 1 (1999) S50-559

Bose-Einstein correlations in e+e- annihilationsand the string rnodel of fragrnentation

CERARDO HERRERADepartamento de Fí.<ica, Centro de Investigación y de Estudios AvanzadosInstituto Politécnico Nacional, Apartado postal 14-740, 07000 México, D.F.

ABSTRACT. Bose-Einstein correlations in the hadronic process following e+e- annihilation arestlldied. The reslllt is compared with the string rnodel approach to Base-Einstein correlation infragmentation.

HESUMEN. Se estudian la.,;;correlaciones de Bose-Einstein en procesos hadrónicos generados enaniquilaciones e+e-. Los resultados se comparan con la correlación y fragmentación predicha porel modelo de "string".

PACS: 13.75.Lb; 13.87.Fh

l. INTRODUCTION

One is able to explain, in a perturbative fashion, the reaction e+e- - qq III whichan electron and positron interact and two colored partons are produced. However, thephenomena occuring afterwards, i.e. the transformation of the outgoing colored partonsinto a set of color singlet hadrons, is up to now an open problem. This phenomenon isknown as fragmentation. Nowadays there exist probabilistic models of fragmentation. Theproduction of hadrons in these models, unfortunately does not explicitly indude quantumiuterference [1]. In this work we study the quant um mechanical interference of hadrons inthe fragmentation state. This interference is a manifestation of the quantum statistic ofhadrons which produces a correlation among ¡dentical partides. For identica! bosons theeffect is known as !lose-Einstein (!lE) Correlation [2, 3]. The interference occurs at thebeginnig of hadronization and therefore !lE correlations reftect, to a great extent, someaspects of the partide prod uction mechanism.In electron-positron annihilations at an energy in the center-of-ma." around 10 CeV,

it is interesting to make inferences about the qq and 3 gluon fragmentation process bycomparing the !lE correlation in the direct decay of the 1(1S) with those of the continuumnearby. \Ve call continuum data to the data da." consisting of e+e- annihilation into qqat center-of-mass energies of 9.3 and 10.5 CeV.

2. FORMALISM

In quantum mechanics the probability for partide production is delermined by the abso-lute square of the amplitudes for the process. This leads to cross terms in the square ofthe sum of different contributions to a process giving rise to interference in the same waya.' interference in light occurs. One usually study two partide correlations in terms of the

BOSE-EINSTEINCORRELATlONS... 51

+ e+ e- --4 qq-

! T(1S)--4ggg

K=0.3 GeV' -----K=0.2GeV'

0.50.0 0.2 04 0.6 0.8 1.0

Q[GeV]

FIGURE 1. Model predictions of Andersson and Hofmann for ditrerent values of the string param-eter compared with the ARGUS data in T(IS) decays (drdes) and in the continuum (crosses).

ratio of the joint probability for a pair of identica! partid es to be emmited P(PI,P2), tothe product P(p¡)' P(P2) of the single-partide probabilities, this is known as "correlationfunction" RaE(p¡,P2), where P¡,P2 are the four-momenta of the two partides,

(1)

One of the most succesful approaches to fragmentation in electron-positron reactionsis the "String Model" [4]. This model is dassical in the sense that does not considerwave functions to describe partide production. In order to incorporate the rea! quantumbehavior of the microscopic nature to this model a semidassical description of phase spacehas been proposed [5].This approach uses the fact that the probability for a particular fina! state with n

partides is suppressed by an exponentia! of the area spanned by the string in space-time.The exponential is interpreted as the square of a matrix element M.The amplitude for a fina! state with two identica! bosons shou!d consider the two

possible arrays j.e. the bosons interchange. It is therefore wr¡tten as the square of thesum of two exponentia!s,

where K is the string tension, b is a free parameter and Al(A2) represent the areas inspace-time of the n-partie!es configurations when the bosons are unpermuted (permuted).This amplitude is a function of the are a di!Terence óA = Al - A2• One can express thisarea in terms of the momenta and energy of the partides so that the enhancement ofthe probability which arises from the ÓA can be expressed as a function of the relativemomentum variable Q, (Q2 = -(PI - p2)2)[5J. After integrating over the who!e final statethe correlation function RaE computed is found to peak at low Q as can be seen in Fig.1 ",here the correlation function for diITerent values of the string parameters is shown.

52 GERARDO HERRERA

3. DATA ANALYSIS

The analysis is based on the data col!ected with the ARGUS detector at the DORIS IIstorage ring at OESY. The data sample comprises an integrated luminosity of 23.8 pb-1at the Y(IS) resonance and 43.6 pb-1 in the continuum nearby.The ARGUS detector is a 471" magnetic spectrometer. Oetails of the detector, the

trigger and the event reconstruction are discussed elsewhere [6]. By ARGUS, chargedparticle identification is made on the basis of specific energy loss in the drift chamber(dE/dx) and time-of-f1ight (TOF) measurements. This information was used to calculate,for al! charged tracks, a likelihood ratio for each particle hypothesis (e, Ji, 71", K, p).Since the detector is triggered not only by events of interest, global selection criteria

are needed to suppress the unwanted background. These selection criteria are discussed indetail in Ref. 3. After having selected multihadronic events sorne additional requirementsare imposed to the remaining events in order to reduce resonance effects and to avoidkinematical and experimental bias. Oetails on these requirements are given in Ref. 3.In order to measure BE correlations in like charged boson pairs, it is necessary to have

a comparison sample which does not exhibit the BE effect. We used like charged pions asidentical bosons and unlike charged pions as reference sample. The correlation functionis computed dividing the Q distribution of the like charged pairs by the Q distribution ofunlike charged pairs.Any particles which were misidentified as pions are not subject to the BE statistics.

They appear as an uncorrelated background and a special correction is needed. Withthe help of Monte CarIo data, the fraction of misidentified pions was determined and amisidentification correction applied.Many of the pions used to construct the correlation distribution come from decays

of resonances and long lived particles, this constitutes a background which reduces thestrength of the effect. Among the most abundant particles and resonances in the regionof Q2 that we are studying are 1/, 1/'(958), w(783), K2 and p(770)o. The productionrate of 1/ mesons has been measured by ARGUS. This al!owed us to subtract the decayproducts of this meson. An estimate of the w(783) and 1/'(958) efTectwas performed usingthe production rates as predicted by the LUNO.The correlation function obtained for the continuum and for the Y(lS) ful! corrected

data are shown in Fig. 1. A smal! suppression of the BE enhancement in Y(lS) data isobserved. This can be explained by the fact that resonance production is larger at Y(lS)energies than in the continuum.In Fig. 1 the experimental results are compared with the model predictions of Andersson

and Hofmann for different values of the string parameters. The solid line provides a gooddescription of the data.

4. CONCLUSION

In summary, from the point of view of BE correlations the hadronization of quarks donot differ from the gluonic one.

BOSE-EINSTEIN CORRELATIONS.. • 53

In comparing lhe measured correlalion function wilh lhe model prediction of Anclerssonand Hofmann a good description of the Bose-Einstein enhacement is observed.

REFERENCES

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243; 28 (1983) 229.5. B. Andersson, W. Hofmann, Phys. Let!. B169 (1986) 364.6. H. Albrccht et al., ARGUS Collab., Nud. Tnat. and Meth. A275 (1989) 1.