e

Physics Letters B 559 (2003) 131–143

www.elsevier.com/locate/np

Bose–Einstein correlations ofπ0 pairs from hadronicZ0 decays

OPAL Collaboration

G. Abbiendib, C. Ainsleye, P.F. Åkessonc, G. Alexanderu, J. Allisono, P. Amaralh,G. Anagnostoua, K.J. Andersonh, S. Arcellib, S. Asaiv, D. Axenz, G. Azuelosq,1,I. Baileyy, E. Barberiog,16, R.J. Barlowo, R.J. Batleye, P. Bechtlex, T. Behnkex,

K.W. Bell s, P.J. Bella, G. Bellau, A. Bellerivef, G. Benellid, S. Bethkeae, O. Biebelad,I.J. Bloodwortha, O. Boeriui, P. Bockj, D. Bonacorsib, M. Boutemeurad, S. Braibantg,

L. Brigliadori b, R.M. Browns, K. Buesserx, H.J. Burckhartg, S. Campanad,R.K. Carnegief, B. Caronaa, A.A. Carterl, J.R. Cartere, C.Y. Changp, D.G. Charltona,2,

A. Csilling g,7, M. Cuffianib, S. Dadot, A. De Roeckg, E.A. De Wolfg,19, K. Deschx,B. Dienesac, M. Donkersf, J. Dubbertad, E. Duchovniw, G. Duckeckad, I.P. Duerdotho,

E. Elfgrenq, E. Etzionu, F. Fabbrib, L. Feldi, P. Ferrarig, F. Fiedlerad, I. Flecki,M. Forde, A. Freyg, A. Fürtjesg, P. Gagnonk, J.W. Garyd, G. Gayckenx,

C. Geich-Gimbelc, G. Giacomellib, P. Giacomellib, M. Giuntad, J. Goldbergt,E. Grossw, J. Grunhausu, M. Gruwég, P.O. Güntherc, A. Guptah, C. Hajduab,

M. Hamannx, G.G. Hansond, K. Harderx, A. Harelt, M. Harin-Diracd, M. Hauschildg,C.M. Hawkesa, R. Hawkingsg, R.J. Hemingwayf, C. Henselx, G. Herteni,

R.D. Heuerx, J.C. Hille, K. Hoffmanh, R.J. Homera, D. Horváthab,3, P. Igo-Kemenesj,K. Ishii v, H. Jeremieq, P. Jovanovica, T.R. Junkf, N. Kanayay, J. Kanzakiv,G. Karapetianq, D. Karlenf, K. Kawagoev, T. Kawamotov, R.K. Keelery,

R.G. Kelloggp, B.W. Kennedys, D.H. Kim r, K. Klein j,20, A. Klier w, S. Kluthae,T. Kobayashiv, M. Kobelc, S. Komamiyav, L. Kormosy, T. Krämerx, T. Kressd,

P. Kriegerf,12, J. von Kroghj, D. Kropk, K. Krugerg, T. Kuhl x, M. Kupperw,G.D. Laffertyo, H. Landsmant, D. Lanskem, J.G. Layterd, A. Leinsad, D. Lellouchw,

J. Letts15, L. Levinsonw, J. Lillich i, S.L. Lloydl, F.K. Loebingero, J. Luz, J. Ludwigi,A. Macphersonaa,9, W. Maderc, S. Marcellinib, A.J. Martinl, G. Masettib,

T. Mashimov, P. Mättig13, W.J. McDonaldaa, J. McKennaz, T.J. McMahona,R.A. McPhersony, F. Meijersg, W. Mengesx, F.S. Merritth, H. Mesf,1, A. Michelini b,S. Miharav, G. Mikenbergw, D.J. Millern, S. Moedt, W. Mohri, T. Mori v, A. Mutteri,

K. Nagail, I. Nakamurav, H.A. Nealaf, R. Nisiusae, S.W. O’Nealea, A. Ohg,A. Okparaj, M.J. Oregliah, S. Oritov, C. Pahlae, G. Pásztord,7, J.R. Patero,

0370-2693 2003 Elsevier Science B.V.doi:10.1016/S0370-2693(03)00337-X

Open access under CC BY license.

132 OPAL Collaboration / Physics Letters B 559 (2003) 131–143

G.N. Patricks, J.E. Pilcherh, J. Pinfoldaa, D.E. Planeg, B. Polib, J. Polokg, O. Poothm,M. Przybycieng,14, A. Quadtc, K. Rabbertzg,18, C. Rembserg, P. Renkelw, H. Rickd,

J.M. Roneyy, S. Rosatic, Y. Rozent, K. Rungei, K. Sachsf, T. Saekiv,E.K.G. Sarkisyang,10, A.D. Schailead, O. Schailead, P. Scharff-Hanseng, J. Schieckae,T. Schörner-Sadeniusg, M. Schröderg, M. Schumacherc, C. Schwickg, W.G. Scotts,

R. Seusterm,6, T.G. Shearsg,8, B.C. Shend, P. Sherwoodn, G. Sirolib, A. Skujap,A.M. Smithg, R. Sobiey, S. Söldner-Remboldo,4, F. Spanoh, A. Stahlc, K. Stephenso,

D. Stromr, R. Ströhmerad, S. Taremt, M. Tasevskyg, R.J. Taylorn, R. Teuscherh,M.A. Thomsone, E. Torrencer, D. Toyav, P. Trand, A. Tricoli b, I. Triggerg,

Z. Trócsányiac,5, E. Tsuru, M.F. Turner-Watsona, I. Uedav, B. Ujvári ac,5,C.F. Vollmerad, P. Vanneremi, R. Vértesiac, M. Verzocchip, H. Vossg,17, J. Vossebeldg,8,

D. Wallerf, C.P. Warde, D.R. Warde, P.M. Watkinsa, A.T. Watsona, N.K. Watsona,P.S. Wellsg, T. Wenglerg, N. Wermesc, D. Wetterlingj, G.W. Wilsono,11, J.A. Wilsona,

G. Wolf w, T.R. Wyatto, S. Yamashitav, D. Zer-Ziond, L. Zivkovic w

a School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UKb Dipartimento di Fisica dell’ Università di Bologna and INFN, I-40126 Bologna, Italy

c Physikalisches Institut, Universität Bonn, D-53115 Bonn, Germanyd Department of Physics, University of California, Riverside, CA 92521, USA

e Cavendish Laboratory, Cambridge CB3 0HE, UKf Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada

g CERN, European Organisation for Nuclear Research, CH-1211 Geneva 23, Switzerlandh Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637, USA

i Fakultät für Physik, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germanyj Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany

k Indiana University, Department of Physics, Bloomington, IN 47405, USAl Queen Mary and Westfield College, University of London, London E1 4NS, UK

m Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germanyn University College London, London WC1E 6BT, UK

o Department of Physics, Schuster Laboratory, The University, Manchester M13 9PL, UKp Department of Physics, University of Maryland, College Park, MD 20742, USA

q Laboratoire de Physique Nucléaire, Université de Montréal, Montréal, Québec H3C 3J7, Canadar University of Oregon, Department of Physics, Eugene, OR 97403, USA

s CLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UKt Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israelu Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel

v International Centre for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo 113-0033,and Kobe University, Kobe 657-8501, Japan

w Particle Physics Department, Weizmann Institute of Science, Rehovot 76100, Israelx Universität Hamburg/DESY, Institut für Experimentalphysik, Notkestrasse 85, D-22607 Hamburg, Germany

y University of Victoria, Department of Physics, PO Box 3055, Victoria BC V8W 3P6, Canadaz University of British Columbia, Department of Physics, Vancouver BC V6T 1Z1, Canada

aaUniversity of Alberta, Department of Physics, Edmonton AB T6G 2J1, Canadaab Research Institute for Particle and Nuclear Physics, PO Box 49, H-1525 Budapest, Hungary

ac Institute of Nuclear Research, PO Box 51, H-4001 Debrecen, Hungaryad Ludwig-Maximilians-Universität München, Sektion Physik, Am Coulombwall 1, D-85748 Garching, Germany

aeMax-Planck-Institute für Physik, Föhringer Ring 6, D-80805 München, Germanyaf Yale University, Department of Physics, New Haven, CT 06520, USA

Received 27 January 2003; received in revised form 26 February 2003; accepted 5 March 2003

Editor: L. Montanet

OPAL Collaboration / Physics Letters B 559 (2003) 131–143 133

r source,

action of

Abstract

We observe Bose–Einstein correlations inπ0 pairs using back-to-back two jet hadronic events fromZ0 decays in the datasample collected by the OPAL detector at LEP 1 from 1991 to 1995. Using a static Gaussian picture for the pion emittewe obtain the chaoticity parameterλ= 0.55±0.10±0.10 and the source radiusR = (0.59±0.08±0.05) fm. According to theJETSET and HERWIG Monte Carlo models, the Bose–Einstein correlations in our data sample largely connectπ0s originatingfrom the decays of different hadrons. Prompt pions formed at string break-ups or cluster decays only form a small frthe sample. 2003 Elsevier Science B.V. Open access under CC BY license.

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1. Introduction

The Bose–Einstein correlations (BEC) effect haquantum-mechanical origin. It arises from the requment to symmetrise the wave function of a systemtwo or more identical bosons. It was introduced inparticle reactions leading to multi-hadron final staas the GGLP effect [1] in the study of theπ+π+ andπ−π− systems. The distributions of the opening an

1 And at TRIUMF, Vancouver, Canada V6T 2A3.2 And Royal Society University Research Fellow.3 And Institute of Nuclear Research, Debrecen, Hungary.4 And Heisenberg Fellow.5 And Department of Experimental Physics, Lajos Koss

University, Debrecen, Hungary.6 And MPI München.7 And Research Institute for Particle and Nuclear Phys

Budapest, Hungary.8 Now at University of Liverpool, Department of Physic

Liverpool L69 3BX, UK.9 And CERN, EP Division, 1211 Geneva 23.

10 Now at University of Nijmegen, HEFIN, NL-6525 ED Nijmegen, The Netherlands, on NWO/NATO Fellowship B 64-29.

11 Now at University of Kansas, Department of Physics aAstronomy, Lawrence, KS 66045, USA.

12 Now at University of Toronto, Department of Physics, ToronCanada.

13 Current address: Bergische Universität, Wuppertal, Germa14 And University of Mining and Metallurgy, Cracow, Poland.15 Now at University of California, San Diego, CA, USA.16 Now at Physics Department Southern Methodist Univers

Dallas, TX 75275, USA.17 Now at IPHE Université de Lausanne, CH-1015 Lausan

Switzerland.18 Now at IEKP Universität Karlsruhe, Germany.19 Now at Universitaire Instelling Antwerpen, Physics Depa

ment, B-2610 Antwerpen, Belgium.20 Now at RWTH Aachen, Germany.

between the momenta in pairs of like-sign pions wshifted towards smaller values compared to the cosponding distributions for unlike-sign pairs. A relateffect was exploited earlier in astronomy [2] to mesure the radii of stars.

In high energy physics, for examplee+e− col-lisions at LEP, a quantitative understanding ofBEC effect allows tests of the parton fragmention and hadronisation models. This would in tuhelp in achieving a more precise measurementhe W boson mass and better knowledge of seral Standard Model (SM) observables [3]. The frmentation models presently used are those of strand clusters implemented, respectively, in the JSET [4] and HERWIG [5] Monte Carlo generators.

Numerous studies of BEC in pairs of identicbosons already exist, see for example [6]. Due toexperimental difficulties in photon andπ0 reconstruc-tion, only very few studies [7] exist for BEC inπ0

pairs, even though they offer the advantage of befree of final state Coulomb corrections.

The string model predicts a larger BEC strengthchaoticity and a smaller effective radius of the emittsource forπ0 pairs compared toπ± pairs whilethe cluster fragmentation model predicts the sasource strength and size [8,9]. However, neither moof primary hadron production has a mechanismallow BEC betweenπ0s produced in different strondecays. The string model prediction is a consequeof electric charge conservation in the local area whthe string breaks up. Similar expectations canderived if the probabilities in the string break-umechanism are interpreted as the squares of quamechanical amplitudes [8,10]. A small differenbetweenπ± pairs andπ0 pairs is also expecte

134 OPAL Collaboration / Physics Letters B 559 (2003) 131–143

se–pinEC

hehan

t

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heela-itysta-

eentlec-torthever-grsT

Thes theho-rb-

l

ndad-(thend-he

toarethe

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ingted

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from a pure quantum statistical approach to BoEinstein symmetry [11]. In addition, based on isosinvariance, suggestions exist on how to relate Bin the pion-pair systems, i.e.,π0π0, π±π±, andπ+π− and how to extend it toπ±π0 [12]. TheL3 Collaboration has recently reported [7] that tradius of the neutral-pion source may be smaller tthat of charged pions,Rπ±π± − Rπ0π0 = (0.150±0.075(stat)±0.068(syst)) fm, in qualitative agreemenwith the string fragmentation prediction.

This paper presents a study of BEC inπ0 pairs us-ing the full hadronic event sample collected at cenof-mass energies at and near theZ0 peak by the OPALdetector at LEP from 1991 to 1995. This correspoto about four million hadronicZ0 decays. A highlypure sample ofπ0 mesons is reconstructed using tlead-glass electromagnetic calorimeter. The corrtion function is obtained after accounting for purand resonant background. It is parametrised with atic picture of a Gaussian emitting source [1,2].

2. Selection of hadronic Z0 decays

A full description of the OPAL detector can bfound in [13]. The sub-detectors relevant to the presanalysis are the central tracking detector and the etromagnetic calorimeter. The central tracking detecconsists of a silicon micro-vertex detector, close tobeam pipe, and three drift chamber devices: thetex detector, a large jet chamber and surroundinz-chambers.21 In combination, the three drift chambesitting inside a solenoidal magnetic field of 0.435yield a momentum resolution of

σpt

pt≈

√0.022 + (0.0015pt)2

for |cos(θ)| < 0.7, wherept (in GeV) is the trans-verse momentum with respect to the beam axis.electromagnetic calorimeter detects and measureenergies and positions of electrons, positrons and ptons for energies above 0.1 GeV. It is a total abso

21 The OPAL coordinate system is defined so that thez-axis isin the direction of the electron beam, thex-axis points towards thecentre of the LEP ring, andθ andφ are the polar and azimuthaangles, defined relative to the+z- and +x-axes, respectively. Incylindrical polar coordinates, the radial coordinate is denotedr .

ing calorimeter, and is mounted between the coil athe iron yoke of the magnet. It consists of 11704 leglass blocks arranged in three large assembliesbarrel that surrounds the magnet coil, and two ecaps) which together cover 98% of the solid angle. Tintrinsic energy resolution isσE/E � 5%/

√E, where

E is the electromagnetic energy in GeV.Standard OPAL selection criteria are applied

tracks and electromagnetic clusters [14]. Tracksrequired to have at least 20 measured points injet chamber, a measured momentum greater0.1 GeV, an impact parameter|d0| in the r–φ planesmaller than 2 cm, az position at the point oclosest approach to the origin in ther–φ plane within25 cm of the interaction point, and a measured pangle with respect to the beam axis greater t20◦. Electromagnetic clusters are required to haveenergy greater than 0.1 GeV if they are in the barrepart of the detector (i.e.,|cosθ | � 0.82) or greaterthan 0.3 GeV if they are in the endcap parts. HadroZ0 decays are selected by requiring for each evmore than 7 measured tracks, a visible energy lathan 60 GeV and an angle larger than 25◦ and smallerthan 155◦ between the calculated event thrust [1axis and the beam axis. The visible energy isenergy sum of all detected tracks, electromagnclusters not associated to tracks and electromagnclusters associated to tracks after correcting for doucounting. For the requirements of the analysis met(see Section 5), only well defined back-to-back twjet events are retained, i.e., events having trust vT > 0.9. A sample of 1.86 millionZ0 hadronic decaysis selected for which the total background, consistmainly of τ pairs, is less than 1% and is neglecthroughout the analysis.

Detector effects and detection efficiencies forspectra ofπ0 pairs are evaluated using eight millioMonte Carlo hadronicZ0 decays. Events are geneated using the JETSET 7.4 program, tuned to repduce the global features of hadronic events as msured with the OPAL detector [14], with the BEC efect explicitly switched off. Samples generated wthe HERWIG 5.9 program without the BEC effeare used for comparison. The generated events wpassed through a full simulation of the OPAL detetor [16] and were analysed using the same reconsttion and selection programs as were applied todata.

OPAL Collaboration / Physics Letters B 559 (2003) 131–143 135

areruc-g-

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3. Reconstruction of π0 mesons

For the selected event sample, neutral pionsreconstructed from photon pairs. Photon reconsttion is performed in the barrel part of the electromanetic calorimeter where both the photon reconstrtion efficiency and the energy resolution are goThe procedure of [17] which resolves photon candates in measured electromagnetic clusters is uIt employs a parametrisation of the expected lateenergy distribution of electromagnetic showers. Itoptimised to resolve as many photon candidatespossible from the overlapping energy deposits inelectromagnetic calorimeter in a dense environmenhadronic jets. The photon candidate energies aretween 200 MeV and half the centre-of-mass eneThe purity of the photon sample is further increasusing a likelihood-type function [17] that associateseach photon candidate a weightw for being a true photon. The weightw depends on five variables, namethe energy of the photon candidate, the energy ofnearest cluster to the considered photon candidateopening angle between the photon candidate andnearest cluster, the opening angle between the phcandidate and the closest reconstructed tracks, anamount of energy that could be attributed to tracksan array of 3× 3 lead glass blocks. Photon candidawith higherw are more likely to be true photons.

All possible pairs of photon candidates are thconsidered. Each pair was assigned a probabilitPfor both candidates being correctly reconstructedphotons. This probability is simply the productthe w-weights associated with the two candidatThe largest momentum ofπ0 candidates is abou18 GeV due to the opening angle limitation. Tcombinatorial background consists of a mixturethree components: (i) wrong pairing of two correcreconstructed photons, (ii) pairing of two fake photoand (iii) pairing of one correctly reconstructed photwith a fake one. Choosing only photon pairs with hivalues ofP leaves combinatorial background mosfrom component (i).

Theπ0 reconstruction efficiency and purity arelustrated in Fig. 1 for different cuts onP. The effi-ciency is defined as the ratio of the number of correreconstructedπ0s over the number of generatedπ0s,and theπ0 purity is defined as the ratio of signal ov

.

Fig. 1. The π0 reconstruction efficiency (top) and the puri(bottom) for different cuts on the weightP = wi × wj of theij photon pair. The purity and efficiency are estimated fromJETSET Monte Carlo. The corresponding statistical errorssmaller than 1%.

total entries in a photon-pair mass window betwe100 and 170 MeV.

4. Selection of π0 pairs

The average number ofπ0s produced inZ0 decayshas been measured [18] to be 9.76±0.26,which is re-produced by our Monte Carlo simulations. This leato about 45 possibleπ0 pairings per event. Consideing only π0 candidates withP > 0.1 (i.e., 17% effi-ciency and 36% purity), we reconstruct at the dettor level 4.7π0 candidates on average per event. Tleads to about 8 pairings among which only 1 pairaverage is really formed by trueπ0s. Here, the detectolevel means that detector response, geometrical actance and photon reconstruction efficiency are tainto account. Therefore, theπ0 pair sample is background dominated and the study ofπ0 pair correla-tions or invariant mass spectra is subject to very labackground subtraction. Monte Carlo must be usepredict both the shape and amount of backgrounbe subtracted, leading to large systematic errors inmeasurements of the BEC source parameters.

136 OPAL Collaboration / Physics Letters B 559 (2003) 131–143

enormalised

Fig. 2. Distribution of two-photon invariant mass,M2γ , for selected events which have exactly two reconstructedπ0 candidates per event. Thsmooth curves represent the total Monte Carlo expectation (solid line) and the background (dashed line) expectation. The curves areto the same number of total selected hadronicZ0 decays as in the data. Theπ0 signal region (100–170 MeV) is also indicated.

d.V.

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agelotstonatex.

To avoid this, theπ0 selection criteria are tighteneWe selectπ0s which have a momentum above 1 GeThis cut reduces the fraction of fakeπ0s. In addition,it removesπ0s produced by hadronic interactionsthe detector material for which the Monte Carlo siulation is not adequate. The probabilityP associatedto eachπ0 candidate is required to be greater than 0In the case where a photon is associated with mthan one pair, only the pair with the highest probaity is considered as aπ0 candidate. Among the evenwith four or more reconstructed photon candidaonly those leading to a possibleπ0 pair with four dis-tinct photon candidates are retained for further ansis. Events with six or more photon candidates leing to more than twoπ0 candidates are rejected. Threpresent about 10% of the retained sample and wincrease the sensitivity to unwanted resonance sigif they were not rejected. Fig. 2 shows the photon pmass,M2γ , for the selected events. The average puof theπ0 sample is 79% in the mass window betwe

100 and 170 MeV. The background is estimatedrectly from data by a second-order polynomial fitthe side bands of the peak and by Monte Carlo simlation. The two background estimations yield compible results and the Monte Carlo reproduces correthe data. The superimposed curves are not the rof a fit to the data, but smoothed histograms ofMonte Carlo expectations for signal and backgrounormalised to the total number of selected hadroZ0 decays.

A clear π0 pair signal is obtained as shownFig. 3 where the two values ofM2γ are shown forthe retained events. Aπ0 pair is considered assignal candidate if both values ofM2γ are within themass window between 100 and 170 MeV. The averπ0 pair signal purity is 60% and the Monte Carsimulation describes the data well. Kinematic fiwere made, constraining the mass of pairs of phocandidates to theπ0 mass, with the assumption ththe photons come from the primary interaction vert

OPAL Collaboration / Physics Letters B 559 (2003) 131–143 137

Fig. 3. The two values ofM2γ for each selected event. The cell size is 8× 8 MeV2.

6%

in

le,

eixust

kntsin

f-orlyo-

h

and

irs.edtages,

nre-ent

Monte Carlo studies showed that this gives a 2improvement in the resolution of theπ0 momentum.

5. The BEC function

The correlation function is defined as the ratio,

(1)C(Q)= ρ(Q)

ρ0(Q),

whereQ is a Lorentz-invariant variable expressedterms of the twoπ0 four-momentap1 and p2 viaQ2 = −(p1 − p2)

2, ρ(Q) = (1/N)dN/dQ is themeasuredQ distribution of the twoπ0s andρ0(Q)

is a reference distribution which should, in principcontain all the correlations included inρ(Q) exceptthe BEC. For the measurement ofρ0(Q), we considerthe two commonly used methods [6]:

• Event Mixing: Mixedπ0 pairs are formed fromπ0s belonging to differentZ0 decay events in thdata. To remove the ambiguity on how to mevents, we select two-jet events having a thr

value T > 0.9, i.e., well defined back-to-bactwo-jet events. The thrust axes of the two eveare required to be in the same direction with(#cosθ × #φ) = (0.05× 10◦). Mixing is thenperformed by swapping aπ0 from one event witha π0 from another event. To avoid detection eficiency problems arising from different detectregions, swapping of two pions is performed onif they point to the same region of the electrmagnetic barrel detector within(#cosθ ×#φ)=(0.05× 10◦). With this procedure, we start wittwo hadronicZ0 events each having twoπ0 can-didates and can end up with between zerofour pairs of mixedπ0 candidates. TheQ vari-able is then calculated for each of the mixed paIf the contributions from background are removor suppressed, this method offers the advanof being independent of Monte Carlo simulationsinceC(Q) can be obtained from data alone.

• Monte Carlo Reference Sample: Theρ0 distribu-tion is constructed from Monte Carlo simulatiowithout BEC. The Monte Carlo is assumed toproduce correctly all the other correlations pres

138 OPAL Collaboration / Physics Letters B 559 (2003) 131–143

gy–wnthe

entssis

e is

-

byref-

ndorand

ck-atatheh

ro-

ideso

is

ele-

d

th-,ap-

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byheble

for

eichro-onef-onsd tode-

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herealrtex

ionten-tedirs

ingnly

m-le-

in the data, mainly those corresponding to enermomentum conservation and those due to knohadron decays. In order to be consistent withfirst method, the cutT > 0.9 is also applied forboth data and Monte Carlo.

In the following, the distributionsρ(Q) andρ0(Q)

are measured from the same sample of selected evThe mixing technique is used as the main analymethod and the Monte Carlo reference techniquapplied only for comparison.

6. The measured BEC function and backgroundcontribution

The correlation function,C(Q), corresponds experimentally to the average number ofπ0 pairs, cor-rected for background, in the data sample dividedthe corresponding corrected average number in theerence sample. Thus, we can write

(2)C(Q)= ρ(Q)

ρ0(Q)= ρ

m(Q)− ρb(Q)

ρm0 (Q)− ρb

0(Q),

where ρm and ρm0 are the measured values, a

ρb and ρb0 are the corresponding corrections f

background contributions. For both the numeratordenominator, the background consists mainly ofπ0

pairs in which one or bothπ0 candidates are fake.The background distributionsρb and ρb

0 are ob-tained from the Monte Carlo information. These baground distributions can also be obtained from dusing a side band fit to the projected spectra oftwo-dimensionalM2γ distributions (see Fig. 3) in eac400 MeV interval of the measuredQ variable. The re-sulting background distributions are correctly repduced by Monte Carlo. However, for the smallerQ in-tervals as used in this analysis, i.e., 100 MeV, the sband fit is subject to large statistical fluctuations,the Monte Carlo distributions have to be used.

In the region of interest where the BEC effectobserved,Q < 700 MeV, pion pairs from particle(resonance) decays could mimic the effect. The rvant decays are:K0

s → π0π0, f0(980)→ π0π0, andη→ π0π0π0 with branching ratios of 39%, 33% an32%, respectively. Pion pairs fromη decay contributeonly to the regionQ< 315 MeV. According to Monte

.

Carlo studies, the number of reconstructedK0s in the

2π0 channel is very small. Furthermore, the hypoesis that eachπ0 originates from the primary vertexas used in the kinematic fits (Section 4), does notply. This is an advantage for this analysis since theK0

speak is flattened, making its effect on theQ distribu-tion negligible. The Monte Carlo estimates of this pticle decay backgrounds are included in the distrition ρb(Q), adjusting the rate of individual hadronsthe LEP average [18] where necessary.

For our analysis we selectπ0 candidates withmomentum greater than 1 GeV. This is dictatedthe observation of correlations at smallQ even forMonte Carlo events generated without any BEC effIndeed, as shown in Fig. 4, a clear BEC-type effis visible in the correlation function obtained froMonte Carlo events without BEC for different low cuon π0 momentum. Using Monte Carlo informatiowe find that these correlations are mainly causedπ0s originating from secondary interactions with tdetector material. They would constitute an irreducibackground to the BEC effect if low momentumπ0sare considered in the analysis. This effect vanishesπ0 momenta greater than 1 GeV.

We rely on Monte Carlo simulation only to definthe appropriate momentum cut (i.e., 1 GeV) whcompletely suppresses the effect of soft pions pduced in the detector material, rather than relyingits prediction for the exact shape and size of thisfect. The reason is that, in contrast to charged piwhere the measured track information can be usesuppress products of secondary interactions in thetector material, the neutral pions have to be assuto originate from the main interaction vertex. Furthmore, with this assumption the kinematic fits (Setion 4) bias the energy of soft pions emitted in tdetector material towards larger values since theopening angle between the photons is larger (vecloser to the calorimeter) than the assumed one.

With the above selection criteria, the compositof the selectedπ0 pair sample is studied using MonCarlo simulations. According to the string fragmetation model implemented in JETSET, the selecsample consists of about 97.9% of mixed pion-pafrom different hadron decays, 2% of pairs belongto the decay products of the same hadron and o0.1% prompt pairs from the string break-ups. Siilarly, using the cluster fragmentation model imp

OPAL Collaboration / Physics Letters B 559 (2003) 131–143 139

on the

Fig. 4. The correlation distributionC(Q) determined for JETSET Monte Carlo events (generated without BEC effect) for different cutsπ0 momenta,pπ .

s ofbe-ands.ne-the

na-ar--ityor

ionsity

hrce

alf

-

nd-fit-dthere

mented in HERWIG, the selected sample consist97% of pairs from different hadron decays, 2.3%longing to the decay products of the same hadrononly 0.7% originating directly from cluster decayIt is worth mentioning that even if the direct piopairs from string break-up (JETSET) or cluster dcays (HERWIG) were all detected and accepted byanalysis procedure, they would be diluted in combition with other pions and would constitute only a mginal fraction (< 1% ) of the total number of reconstructedπ0 pairs. Thus, our analysis has no sensitivto direct pion pairs originating from string break-upcluster decay.

7. Results

The correlation distributionC(Q) (Eq. (2)) is para-metrised using the Fourier transform of the expressfor a static sphere of emitters with a Gaussian den

(see, e.g., [19]):

(3)C(Q)=N[1+ λexp

(−R2Q2)](1+ δQ+ εQ2).Here λ is the chaoticity of the correlation (whicequals zero for a fully coherent (non-chaotic) souand one for a chaotic source),R is the radius of thesource, andN a normalisation factor. The empiricterm,(1 + δQ+ εQ2), accounts for the behaviour othe correlation function at highQ due to any remaining long-range correlations. TheC(Q) distribution fordata is shown in Fig. 5 as the points with correspoing statistical errors, and the smooth curve is theted correlation function in theQ range between 0 an2.5 GeV. A clear BEC enhancement is observed inlow Q region of the distribution. The parameters adetermined to be:

λ= 0.55± 0.10,

R = (0.59± 0.08) fm,

N = 1.10± 0.08,

140 OPAL Collaboration / Physics Letters B 559 (2003) 131–143

dottedresents the

Fig. 5. The correlation distributionC(Q) as measured for OPAL data. The smooth curve is the fitted correlation function and thehistogram is the correlation distribution obtained for JETSET Monte Carlo events generated without BEC. The dashed histogram repmeasured correlation function before the subtraction of the contributions from known hadron decays.

the

ramual

edhedionion,thethatontion

ors

ke

nce

Weentt on

ius

tsptterwe

δ = (−0.14± 0.05)GeV−1,

ε = (0.07± 0.03)GeV−2,

where the quoted errors are statistical only andχ2/ndf of the fit is 14.7/19.

The distributionC(Q) obtained for Monte Carloevents generated with no BEC is shown as a histogin the same figure. It shows that there is no residcorrelation at lowQ and indicates that the observenhancement is present in the data only. The dasline histogram of Fig. 5 represents the correlatfunction obtained from data but before the subtractusing the Monte Carlo estimates, of pairs fromdecay products of the same hadron, indicatingthese contributions have only a minor influencethe measured parameters. In addition, the correlafunction constructed with backgroundπ0 pairs doesnot show any enhancement at lowQ (not shown).Here, backgroundπ0 pairs are defined as pairs fwhich one or both of theπ0s are outside the mas

-

window 100–170 MeV, i.e., these are likely to be faπ0 candidates.

The second method, which uses the MC referesample, yields the following results:

λ= 0.50± 0.10,

R = (0.46± 0.08) fm.

These results are quoted for comparison only.choose to quote the results obtained with the evmixing method since they are much less dependendetails of the Monte Carlo modelling.

The string model predicts a smaller source radand a larger chaoticity in the BEC effect forπ0 pairsthan for π± pairs, while the cluster model predicno difference. These predictions hold only for promboson pairs produced directly from the string or clusdecays. According to our Monte Carlo simulations,have no sensitivity to these pairs.

OPAL Collaboration / Physics Letters B 559 (2003) 131–143 141

sti-rsardd in

sof

V

d

arte

ecte-es-

in-ti-me

n

for

ed-

d

edhe

yin

ctsET

C.tic--ithreen-nt

del

8. Systematic uncertainties

Potential sources of systematic error are invegated. In each case the effect on the parameteRandλ and their deviations with respect to the standanalysis are estimated. The results are summariseTable 1.

• Bin width resolution: After the kinematic fit(Section 4), the resolution on the invariant masstwo pions, or on the variableQ, is approximately60 MeV. We have chosen a bin width of 100 Mefor the fit to the measuredC(Q) distribution. Thisbin width is varied from 100 MeV to 80 MeV anto 120 MeV.

• Fit range: The low end of the fit range is set to statQ= 350 MeV (fourth bin). The high end of thfit range is changed to stop atQ= 2 GeV.

• Effect of hadron decays: To estimate the effof the π0 pairs from the same resonance dcay on the measured BEC parameters, thetimated contribution is varied by±10% whichrepresents the typical error on the measureddividual hadron rates [18]. In order to invesgate the dependence of the measured paraters R and λ on the π0 momentum cut, theanalysis is repeated forπ0 momenta larger tha1.2 GeV.

-

• Analysis procedure: The analysis is repeatedseveral variations of the selection criteria.(1) The π0 selection mass window is chang

from 100–170 MeV to 110–165 MeV (increases theπ0 purity by 5%).

(2) The probability forπ0 selection is changefrom 0.6 to 0.5 (reduces theπ0 purity by5%).

(3) The thrust value for two-jet events is changfrom 0.9 to 0.85 and to 0.92 (changes toverall event sample size by±5%).

(4) The factor 1+ δQ+ εQ2 is replaced by 1+δQ.

(5) π0 from different events are mixed if thepoint to the same region of the detector with(#cosθ × #φ) = (0.10 × 15◦) instead of(0.05× 10◦).

• Model dependence: Correction for detector effeand detection efficiencies are based on JETSand HERWIG Monte Carlo samples without BETo check for any residual dependence, in parular at smallQ, theπ0 pair efficiency as a function ofQwas compared for JETSET samples wand without BEC. The efficiencies obtained agwithin the statistical error (about 1%) over the etire Q range. We conclude that with the preseimplementation of BEC in JETSET [4] theπ0 pairefficiency is not affected, and the residual modependence is negligible.

Table 1Systematic errors

Item λ R [fm] #λ #R

Basic result 0.55± 0.10 0.59± 0.08 +0.00 +0.00Bin width = 80 MeV 0.54± 0.13 0.58± 0.12 −0.01 −0.01Bin width = 120 MeV 0.57± 0.09 0.60± 0.07 +0.02 +0.01Low end of the fit range= 350 MeV 0.64± 0.14 0.62± 0.12 +0.09 +0.03High end of the fit range= 2 GeV 0.58± 0.11 0.56± 0.10 +0.03 −0.03Resonance contribution+10% 0.54± 0.10 0.59± 0.08 −0.01 +0.00Resonance contribution−10% 0.55± 0.10 0.58± 0.09 −0.00 −0.01Momentum cut= 1.2 GeV 0.53± 0.11 0.60± 0.08 −0.02 +0.01

Analysis procedure:(1) π0-signal mass window 0.55± 0.10 0.58± 0.09 +0.00 −0.01(2) Photon-pair probability 0.57± 0.09 0.57± 0.08 +0.02 −0.02(3) Thrust value 0.55± 0.10 0.60± 0.09 +0.00 +0.01(4) Long range corr. term 0.56± 0.10 0.58± 0.10 +0.01 −0.01(5) Mixing condition 0.54± 0.08 0.59± 0.07 −0.01 +0.00

Total sys. error 0.10 0.05

142 OPAL Collaboration / Physics Letters B 559 (2003) 131–143

rat-e.

of-

drix-edr to-e ise0],

dal-

ref-ion

EP

sti-tedorbe-that

nt

natur

f atge

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ion

g,

ch,

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120

;

43

;65.rsend,

ofPol.

2)

The final systematic errors are obtained from quadically adding the deviations from the central valuThus,

λ= 0.55± 0.10± 0.10,

R = (0.59± 0.08± 0.05) fm.

9. Conclusions

We have observed Bose–Einstein correlationsπ0 pairs produced in hadronicZ0 decays. Assuming a Gaussian shape for the source, we obtainλ =0.55± 0.10± 0.10 for the chaoticity parameter anR = (0.59± 0.08± 0.05) fm for the radius. In ordeto construct a reference sample with the event ming method, this analysis is restricted to well definback-to-back two-jet events. Furthermore, in orderemoveπ0s not originating from the primary interaction vertex the considered momentum phase spacrestricted topπ0 > 1 GeV. The measured value of thsource radius is smaller than our former value [2R = (1.002± 0.016+0.023

−0.096) fm, obtained for chargepions for which the measured track parameterslowed access to lower momenta and where theerence sample was constructed with unlike-sign ppairs. However, the value is compatible with the Linclusive average [21],R = (0.74± 0.01± 0.14) fm,for charged pions. Pions from strong decays contute the dominant part of our sample of reconstrucπ0 pairs. We have no sensitivity to test the stringcluster model predictions concerning differencestween neutral and charged pion pairs. We deduceBose–Einstein correlations exist betweenπ0 pairs inwhich eachπ0 is a strong decay product of a differehadron.

Acknowledgements

We particularly wish to thank the SL Divisiofor the efficient operation of the LEP acceleratorall energies and for their close cooperation with oexperimental group. In addition to the support stafour own institutions we are pleased to acknowledthe

− Department of Energy, USA,

− National Science Foundation, USA,− Particle Physics and Astronomy Research Co

cil, UK,− Natural Sciences and Engineering Research C

cil, Canada,− Israel Science Foundation, administered by

Israel Academy of Science and Humanities,− Benoziyo Center for High Energy Physics,− Japanese Ministry of Education, Culture, Spo

Science and Technology (MEXT) and a graunder the MEXT International Science ReseaProgram,

− Japanese Society for the Promotion of Scie(JSPS),

− German–Israeli Bi-national Science Foundat(GIF),

− Bundesministerium für Bildung und ForschunGermany,

− National Research Council of Canada,− Hungarian Foundation for Scientific Resear

OTKA T-029328, and T-038240,− The NWO/NATO Fund for Scientific Reasearc

The Netherlands.

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