Search for colour reconnection effects in e W through

Article

Reference

Search for colour reconnection effects in e

+

e

−

-> W

+

W

−

-> hadrons

through particle-flow studies at LEP

L3 Collaboration

ACHARD, Pablo (Collab.), et al.

Abstract

A search for colour reconnection effects in hadronic decays of W pairs is performed with the

L3 detector at centre-of-mass energies between 189 and 209 GeV. The analysis is based on

the study of the particle flow between jets associated to the same W boson and between two

different W bosons in qqqqevents. The ratio of particle yields in the different interjet regions is

found to be sensitive to colour reconnection effects implemented in some hadronization

models. The data are compared to different models with and without such effects. An extreme

scenario of colour reconnection is ruled out.

L3 Collaboration, ACHARD, Pablo (Collab.), et al. Search for colour reconnection effects in e

+

e

−

-> W

+

W

−

-> hadrons through particle-flow studies at LEP. Physics letters. B, 2003, vol. 561,

no. 3-4, p. 202-212

DOI : 10.1016/S0370-2693(03)00490-8

Available at:

http://archive-ouverte.unige.ch/unige:42650

Disclaimer: layout of this document may differ from the published version.

1 / 1

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Physics Letters B 561 (2003) 202–212

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Search for colour reconnection effectsin e+e− → W+W− → hadrons through particle-flow

studies at LEP

L3 Collaboration

P. Achardt, O. Adrianiq, M. Aguilar-Benitezx, J. Alcarazx, G. Alemanniv, J. Allabyr,A. Aloisio ab, M.G. Alviggi ab, H. Anderhubat, V.P. Andreevf,ag, F. Anselmoh,

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L3 Collaboration / Physics Letters B 561 (2003) 202–212 203

M.N. Kienzle-Focaccit, J.K. Kimap, J. Kirkbyr, W. Kittel ad, A. Klimentovm,aa,A.C. Königad, M. Kopalaq, V. Koutsenkom,aa, M. Kräberat, R.W. Kraemerah,

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G. Rahal-Callotat, M.A. Rahamani, P. Raicso, N. Rajai, R. Ramelliat, P.G. Rancoitaz,R. Ranieriq, A. Rasperezaas, P. Razisac, D. Renat, M. Rescignoal, S. Reucroftj,S. Riemannas, K. Rilesc, B.P. Roec, L. Romerox, A. Roscaas, S. Rosier-Leesd,

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D. Teyssierw, C. Timmermansad, Samuel C.C. Tingm, S.M. Tingm, S.C. Tonwari,J. Tóthl, C. Tully aj, K.L. Tungg, J. Ulbrichtat, E. Valenteal, R.T. Van de Wallead,R. Vasquezaq, V. Veszpremiy, G. Vesztergombil, I. Vetlitskyaa, D. Vicinanzaam,G. Viertelat, S. Villaak, M. Vivargentd, S. Vlachose, I. Vodopianovy, H. Vogelah,

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H.L. Zhuangg, A. Zichichih,r,s, B. Zimmermannat, M. Zöller a

a III. Physikalisches Institut, RWTH, D-52056 Aachen, Germany1

b National Institute for High Energy Physics, NIKHEF, and University of Amsterdam, NL-1009 DB Amsterdam, The Netherlandsc University of Michigan, Ann Arbor, MI 48109, USA

d Laboratoire d’Annecy-le-Vieux de Physique des Particules, LAPP, IN2P3-CNRS, BP 110, F-74941 Annecy-le-Vieux cedex, France

204 L3 Collaboration / Physics Letters B 561 (2003) 202–212

e Institute of Physics, University of Basel, CH-4056 Basel, Switzerlandf Louisiana State University, Baton Rouge, LA 70803, USA

g Institute of High Energy Physics, IHEP, 100039 Beijing, China6

h University of Bologna and INFN-Sezione di Bologna, I-40126 Bologna, Italyi Tata Institute of Fundamental Research, Mumbai, Bombay 400 005, India

j Northeastern University, Boston, MA 02115, USAk Institute of Atomic Physics and University of Bucharest, R-76900 Bucharest, Romania

l Central Research Institute for Physics of the Hungarian Academy of Sciences, H-1525 Budapest 114, Hungary2

m Massachusetts Institute of Technology, Cambridge, MA 02139, USAn Panjab University, Chandigarh 160 014, Indiao KLTE-ATOMKI, H-4010 Debrecen, Hungary3

p Department of Experimental Physics, University College Dublin, Belfield, Dublin 4, Irelandq INFN Sezione di Firenze and University of Florence, I-50125 Florence, Italy

r European Laboratory for Particle Physics, CERN, CH-1211 Geneva 23, Switzerlands World Laboratory, FBLJA Project, CH-1211 Geneva 23, Switzerland

t University of Geneva, CH-1211 Geneva 4, Switzerlandu Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029, China6

v University of Lausanne, CH-1015 Lausanne, Switzerlandw Institut de Physique Nucléaire de Lyon, IN2P3-CNRS, Université Claude Bernard, F-69622 Villeurbanne, France

x Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, CIEMAT, E-28040 Madrid, Spain4

y Florida Institute of Technology, Melbourne, FL 32901, USAz INFN-Sezione di Milano, I-20133 Milan, Italy

aa Institute of Theoretical and Experimental Physics, ITEP, Moscow, Russiaab INFN-Sezione di Napoli and University of Naples, I-80125 Naples, Italy

ac Department of Physics, University of Cyprus, Nicosia, Cyprusad University of Nijmegen and NIKHEF, NL-6525 ED Nijmegen, The Netherlands

aeCalifornia Institute of Technology, Pasadena, CA 91125, USAaf INFN-Sezione di Perugia and Università Degli Studi di Perugia, I-06100 Perugia, Italy

ag Nuclear Physics Institute, St. Petersburg, Russiaah Carnegie Mellon University, Pittsburgh, PA 15213, USA

ai INFN-Sezione di Napoli and University of Potenza, I-85100 Potenza, Italyaj Princeton University, Princeton, NJ 08544, USA

ak University of Californa, Riverside, CA 92521, USAal INFN-Sezione di Roma and University of Rome, “La Sapienza”, I-00185 Rome, Italy

am University and INFN, Salerno, I-84100 Salerno, Italyan University of California, San Diego, CA 92093, USA

ao Bulgarian Academy of Sciences, Central Laboratory of Mechatronics and Instrumentation, BU-1113 Sofia, Bulgariaap The Center for High Energy Physics, Kyungpook National University, 702-701 Taegu, South Korea

aq Purdue University, West Lafayette, IN 47907, USAar Paul Scherrer Institut, PSI, CH-5232 Villigen, Switzerland

asDESY, D-15738 Zeuthen, Germanyat Eidgenössische Technische Hochschule, ETH Zürich, CH-8093 Zürich, Switzerland

au University of Hamburg, D-22761 Hamburg, Germanyav National Central University, Chung-Li, Taiwan, ROC

aw Department of Physics, National Tsing Hua University, Taiwan, ROC

Received 13 March 2003; received in revised form 26 March 2003; accepted 27 March 2003

Editor: L. Rolandi

Abstract

A search for colour reconnection effects in hadronic decays of W pairs is performed with the L3 detector at centre-of-massenergies between 189 and 209 GeV. The analysis is based on the study of the particle flow between jets associated to the same Wboson and between two different W bosons in qq̄qq̄ events. The ratio of particle yields in the different interjet regions is found


to be sensitive to colour reconnection effects implemented in some hadronization models. The data are compared to differentmodels with and without such effects. An extreme scenario of colour reconnection is ruled out. 2003 Published by Elsevier Science B.V.

1. Introduction

According to the string model of hadronization, theparticles produced in the process e+e− → W+W− →hadrons originate, in the absence of colour reconnec-tion, from the fragmentation of two colour singletstrings each of which is stretched between the twoquarks from a W boson. In this case the hadrons areuniquely associated to a particular W and there is a di-rect correspondence between the jets formed by thesehadrons and the primary quarks from the W boson de-cays. Energy–momentum is separately conserved foreach of the W systems. However, it has been suggestedthat interactions may occur between the decay prod-ucts of the two W bosons [1–4]. The main justificationfor this “cross-talk” is the relatively short distance sep-arating the decay vertices of the W bosons produced ine+e− annihilation (≈ 0.1 fm) compared to the typicalhadronic scale (1 fm), which implies a large space–time overlap of the two hadronizing systems.

The main consequence of these interactions, calledcolour reconnection (CR) effects, is a modification ofthe distribution in phase-space of hadrons. CR effectsare thought to be suppressed in the hard perturbativephase, but may be more important in the soft gluonemission regime [2]. While hard gluons, with energygreater than the W width, are radiated independentlyfrom different colour singlets, soft gluons could inprinciple be affected by the colour strings of bothdecaying Ws. Such CR would affect the number of soft

1 Supported by the German Bundesministerium für Bildung,Wissenschaft, Forschung und Technologie.

2 Supported by the Hungarian OTKA fund under contractnumbers T019181, F023259 and T037350.

3 Also supported by the Hungarian OTKA fund under contractnumber T026178.

4 Supported also by the Comisión Interministerial de Ciencia yTecnología.

5 Also supported by CONICET and Universidad Nacional de LaPlata, CC 67, 1900 La Plata, Argentina.

6 Supported by the National Natural Science Foundation ofChina.

particles in specific phase-space regions, especiallyoutside the jet cores.

The study of CR is interesting not only for probingQCD dynamics but also for determining a possiblebias in the W mass measurement in the four-quarkchannel. CR could affect the invariant masses ofjet pairs originating from W decays. Therefore theprecision with which the W mass may be determinedusing the four-quark channel depends strongly on theunderstanding of CR effects. Events where only oneW decays hadronically are unaffected by CR.

Previous LEP studies of CR, performed at centre-of-mass energy

√s � 183 GeV, were based on charged

particle multiplicity and momentum distributions [5].The analysis presented in this Letter uses the meth-

od suggested in Ref. [6] based on energy and particleflow to probe the string topology of four-quark eventsto search for particular effects of particle depletionand enhancement. The results are based on 627 pb−1

of data collected with the L3 detector [7] at√s =

189–209 GeV. Comparisons with various models aremade at detector level and the compatibility withthe existence of CR effects in various models isinvestigated.

2. Colour reconnection models

Several phenomenological models have been pro-posed [2,3,8–11] to describe CR effects in e+e− →W+W− → hadrons events. The analysis presented inthis Letter is performed with some of those CR mod-els, which are implemented in the PYTHIA [12], ARI-ADNE [13], and HERWIG [14] Monte Carlo (MC)programs.

We investigate two models by Sjöstrand and Khoze[2] implemented in PYTHIA. They are based onrearrangement of the string configuration during thefragmentation process. They follow the space–timeevolution of the strings and allow local reconnectionsif the strings overlap or cross, depending on the stringdefinition (elongated bags or vortex lines).


In the type I model (SKI) the strings are associatedwith colour flux tubes having a significant transverseextension. The reconnection occurs when these tubesoverlap and only one reconnection is allowed, theone with the largest overlap volume. The reconnectionprobability depends on this volume of overlap and iscontrolled by one free parameter,kI , which can bevaried in the model to generate event samples withdifferent fractions of reconnected events. The relationwith the event reconnection probability (Preco) is givenby the following formula:

(1)Preco= 1− exp(−f kI),

wheref is a function of the overlap volume of the twostrings, which depends on W-pair kinematics varyingwith

√s. The default value ofkI is 0.6 [2], which

corresponds to a reconnection probability of about30% at

√s = 189 GeV. This analysis is performed

with three different values ofkI : 0.6, 3, and 1000,corresponding to reconnection probabilities at

√s =

189 GeV of about 30%, 66%, and nearly 100%,respectively.

In the type II model (SKII) the strings have nolateral extent and the reconnection occurs, with unitprobability, when they cross. The fraction of recon-nected events in this model is of the order of 30% at√s = 189 GeV.The CR model implemented in ARIADNE is based

on reconnection of coloured dipoles before the stringfragmentation takes place [9]. In the AR2 scheme,which is investigated here, reconnections are allowedif they reduce the string length. While reconnectionswithin a W are allowed at all scales, those betweenWs are only allowed after the parton showers haveevolved down to gluon energies less than 2 GeV. At√s = 189 GeV they affect about 55% of the events.The CR scheme implemented in HERWIG is, as

for the string fragmentation, a local phenomenon sincethe cluster fragmentation process follows the space–time development. In this model [10] the clusters arerearranged if their space–time extension is reduced.This rearrangement occurs with a probability equal to1/N2

colour, with default valueNcolour= 3, giving about23% of reconnected events.

All probabilities discussed above are derived asfraction of events where at least one reconnectionoccurs either within the same W or between two Ws.

3. Event selection

The energy measured in the electromagnetic andhadronic calorimeters and in the tracking chamber isused to select e+e− → W+W− → hadrons events.The total visible energy (Evis) and the energy imbal-ance parallel (E‖) and perpendicular (E⊥) to the beamdirection are measured. The number of clusters, de-fined as objects obtained from a non-linear combina-tion of charged tracks with a transverse momentumgreater than 100 MeV and calorimetric clusters witha minimum energy of 100 MeV, is denoted byNcluster.The selection criteria are:

Evis√s> 0.7,

E⊥Evis

< 0.2,

|E‖|Evis

< 0.2, Ncluster� 40.

In addition the events must have 4 jets reconstructedwith the Durham algorithm [15] withycut = 0.01. Toreduce the contamination from semileptonic W de-cays, events with energeticµ or e are rejected. Eventswith hard initial state radiation (ISR) are rejected asdescribed in Ref. [16]. Additional criteria select eventswith nearly perfect quark–jet association, necessaryfor the study of particle and energy flow between jets.The two largest interjet angles are required to be be-tween 100◦ and 140◦ and not adjacent. The two otherinterjet angles must be less than 100◦. This selectionguarantees similar sharing of energy between the fourprimary partons with the two strings evolving back-to-back and similar interjet regions between the two Ws.The above cuts are optimized by studying MC W+W−events at

√s = 189 GeV using the KORALW [17] MC

generator interfaced with the PYTHIA fragmentationmodel without CR. Relaxing the angular criteria in-creases the efficiency but gives lower probability tohave correct W-jet pairing due to the more complicatedevent topology.

The number of selected events, the number of ex-pected events, the selection efficiency and the percent-age of correct pairing are given in Table 1. After ap-plying all the cuts the full sample contains 666 eventswith an average efficiency of 12% and a purity of about85% for e+e− → W+W− → hadrons. The averageprobability to have the correct pairing between the Wbosons and their associated jets is estimated to be 91%.


Table 1Average centre-of-mass energies, integrated luminosities (L), num-ber of selected events (Nevents), number of expected events (NMC),selection efficiency (ε) and percentage of correct jet pairing (π ) forthe particle flow analysis. The combined figures are given in the lastrow

〈√s〉 (GeV) L (pb−1) Nevents NMC ε (%) π (%)

188.6 176.7 208 226.0 14.2 88191.6 29.7 38 37.9 14.3 90195.5 83.7 104 101.0 13.4 92199.5 84.3 97 91.9 12.2 93201.7 35.5 36 37.2 11.3 93205.1 77.8 75 74.8 10.3 93206.6 138.9 108 120.8 8.9 91

198.2 626.6 666 689.6 12.0 91

The background is composed of qq̄(γ ) eventsand Z-pair production events, in similar amounts.Background from semileptonic W pair decays is foundto be negligible (less than 0.3%). The qq̄(γ ) process ismodeled with the KK2F MC program [18], interfacedwith JETSET [19] routines to describe the QCDprocesses, and the background from Z-pair productionis simulated with PYTHIA. For CR studies W-pairevents are simulated with PYTHIA. All MC samplesare passed through a realistic detector simulation [20]which takes into account time dependent detectoreffects and inefficiencies.

4. Particle- and energy-flow distributions

The algorithm to build the particle- and energy-flowdistributions [6] (Fig. 1) starts by defining the planespanned by the most energetic jet (jet 1) and the closestjet making an angle with jet 1 greater than 100◦ whichis most likely associated to the same W (jet 2). Foreach event, the momentum vector direction of eachparticle is then projected on to this plane. The particleand energy flows are measured as a function of theangle,φ, between jet 1 and the projected momentumvector for the particles located between jets 1 and 2.In order to take into account the fact that the W-pair events are not planar a new plane is defined foreach remaining pair of adjacent jets. In this four-planeconfiguration the angleφ is defined as increasing fromjet 1 toward jet 2, then to the closest jet from theother W (jet 3) toward the remaining jet (jet 4) and

Fig. 1. Determination of theφi angle for the particlei.

back to jet 1. The angleφj,i of a particlei havinga projected momentum vector located between jetsj

andj + 1 is calculated in the plane spanned by thesetwo jets. A particlei making an angleφi with respectto jet 1 adds an entry equal to 1 in the particle-flowdistribution and adds an entry equal to its energy,normalized to the total event energy, in the energy-flowdistribution for the correspondingφ bin.

The distributions are calculated using, for the parti-cle definition, the clusters defined in the previous sec-tion.

Fig. 2 shows the particle- and energy-flow distrib-utions obtained for the data and the MC predictionsat detector level by using only the first plane for pro-jecting all the particles. The data and MC distributionsagree over the full angular range in both cases.

In order to compare the interjet regions the anglesin the planes are rescaled by the angle between the twoclosest jets. For a particlei located between jetsj andj + 1 the rescaled angle is

(2)φresci = j − 1+ φj,i

ψj,j+1,

whereφj,i is the angle between jetj and particlei andψj,j+1 is the angle between jetsj andj +1. With thisdefinition the four jets have fixed rescaled angle valuesequal to 0, 1, 2, and 3.

Fig. 3(a) shows the rescaled particle-flow distribu-tion normalized to the number of events after a bin-by-bin background subtraction for the data and MCpredictions without CR and for the SKI model withkI = 1000, later referred to as SKI 100%. As expected,the latter shows some depletion in the number of par-ticles in the intra-W regions spanned by the two Wbosons (regions A and B) and some particle enhance-ment in the two inter-W regions (regions C and D)when compared to the model without CR (no-CR).

To improve the sensitivity to CR effects the particleflows in regions A and B are averaged as are theparticle flows in regions C and D. The results are


Fig. 2. (a) Particle- and (b) energy-flow distributions at√s = 189–209 GeV for data and MC predictions.

Fig. 3. (a) Particle-flow distribution as a function of the rescaledangle for data and for PYTHIA MC predictions without CR, andwith the SKI 100% model. Distributions of (b) combined intra-Wparticle flow and (c) combined inter-W particle flow.

shown in Fig. 3(b) and (c) where the angle is redefinedto be in the range[0,1]. MC studies at particlelevel with particles having a momentum greater than100 MeV show that the CR effects are consistent withthe detector level results and have similar magnitudes.

The ratio of the particle flow between the quarksfrom the same W to that between quarks from differentWs is found to be a sensitive observable to cross-talk effects as predicted by the SKI model. Theseratios, computed from the particle- and energy-flowdistributions at detector level, are shown in Fig. 4 forthe data, the PYTHIA prediction without CR, the SKImodel withkI = 3 and SKI 100%.

The differences between the models with andwithout CR are larger in the middle of the interjetregions. Therefore, in order to quantify the CR effectsthe ratioR is computed in an interval, 0.2< φresc<

0.8, optimized with respect to the sensitivity to SKI100%. The corresponding variables for particle- andenergy-flow are defined as follows:

(3)

RN =∫ 0.8

0.2 fA+BN dφ

∫ 0.80.2 f

C+DN dφ

andRE = ∫ 0.8

0.2 fA+BE dφ

∫ 0.80.2 f

C+DE dφ

,

where, in a regioni,

(4)f iN = 1

Nevt

dn

dφand f iE = 1

E

dE

dφ.

The measured values ofRN and RE obtainedat each centre-of-mass energy are summarized inTable 2. Correlations in the particle rates betweenthe four interjet regions are taken into account byconstructing the full covariance matrix. This results inan increase of about 20% of the statistical uncertainty.The values obtained with the complete data sample


Fig. 4. Ratio of (a) particle- and (b) energy-flow distributions (Eq. (4)) in regions A+ B to that in regions C+ D. Statistical uncertainties areshown.

Table 2MeasuredRN and RE values as a function of energy with theirstatistical uncertainties

〈√s〉 (GeV) RN RE

188.6 0.820± 0.037 0.610± 0.047191.6 0.929± 0.093 0.822± 0.133195.5 0.948± 0.059 0.774± 0.077199.5 1.004± 0.067 0.871± 0.095201.7 0.770± 0.086 0.626± 0.130205.1 1.033± 0.083 0.756± 0.111206.6 0.958± 0.068 0.781± 0.096

are:

RN = 0.911± 0.023(stat.),

RE = 0.719± 0.035(stat.).

An estimate of the sensitivity to the SKI 100% model,shows thatRN is 2.6 times more sensitive thanRE.Accordingly, the following results and discussion areonly based onRN.

Fig. 5 shows the measuredRN as a function of√s together with PYTHIA no-CR and SKI model

predictions. The energy dependence originating fromthe different pairing purities and jet configurationsis in agreement with the model predictions. For thePYTHIA SKI predictions, the ratio decreases with thereconnection probability over the whole energy rangewith similar magnitude. The data indicate little or noCR.

Fig. 5. The ratioRN as a function of√s at detector level for

data and PYTHIA no-CR and SKI model predictions. The para-metrization of the energy dependence is obtained by fitting asecond order polynomial function to the predicted MC depen-dence. The parametrization obtained with PYTHIA no-CR givesRN(

√s )/RN(189 GeV) = −3.07× 10−4 s+ 0.1297

√s − 12.56.

The dependence obtained with the SKI model (kI = 3) leads to a2.3% change in the average rescaledRN value at 189 GeV.

5. Semileptonic decays

To verify the quality of the MC simulation ofthe W→ qq̄ fragmentation process and the possiblebiases which may arise when determining the particleyields between reconstructed jets in the detector, theparticle- and energy-flow distributions are investigatedin e+e− → W+W− → qq̄lν, wherel = e,µ. For thisanalysis events are selected with high multiplicity,large missing momentum and a high-energy electronor muon. The missing momentum is considered as


Fig. 6. Particle-flow distributions (a) before and (b) after angle rescaling for the semileptonic W decays for data and KORALW prediction.

a fictitious particle in order to apply the Durham jetalgorithm to select 4-jet events withycut = 0.01.

The same angular criteria on the four interjetangles as applied in the fully hadronic channel areused here. The purity obtained after selection isabout 96% and the efficiency is about 12%. Thenumber of selected semileptonic events is 315 with anexpectation of 314.5 events. Particle- and energy-flowdistributions are built in a similar way as in the fullyhadronic channel with the additional requirement thatthe charged lepton should be in jet 3 or 4. Fig. 6(a)shows the corresponding particle-flow distributionprojected on to the plane of jets 1 and 2 for thedata and the KORALW MC prediction. There is goodagreement between data and MC over the wholedistribution. Fig. 6(b) shows the rescaled particle-flowdistribution where the structure of the two different Wsis clearly visible. The region between jet 1 and jet 2corresponds to the hadronically decaying W (W1) andthe region between jet 3 and jet 4 corresponds to theW decaying semileptonically (W2). The activity in theW2 region is mainly due to low-energy fragments fromthe hadronic decay of the first W. A comparison of dataand MC for the particle flow obtained by summing theregionsW1 andW2 is shown in Fig. 7(a). The ratiobetween the data and the MC distributions is shownin Fig. 7(b). This ratio is consistent with unity over thewhole range. This result gives additional confidence inthe correctness of the modelling of the fragmentationprocess of quark pairs according to the fragmentationparameters used in KORALW and PYTHIA as well asthe particle flow definition and reconstruction.

Fig. 7. (a) Particle-flow distributions as a function of the rescaledangle for the semileptonic W decays for data and the KORALWprediction. (b) Ratio of data and MC as a function of the rescaledangle. (c) RatioR of the particle flow in hadronic events divided bytwice the particle flow in semileptonic events.

In the absence of CR effects, the activity foundin regions A+ B of a fully hadronic event shouldbe equivalent to twice the particle activity in the re-gionsW1 +W2 of the distribution for a semileptonicevent. Fig. 7(c) shows the ratio of the particle flow infour-quark events divided by twice the particle flow


in semileptonic events for the data and the predic-tions from no-CR PYTHIA MC and the SKI 100%model. The CR model shows the expected deficit in thehadronic channel compared to the semileptonic one.The data are consistent with the no-CR scheme butthe large statistical uncertainty prevents a quantitativestatement based on this model-independent compari-son.

6. Systematic uncertainties

Several sources of systematic uncertainties areinvestigated. The first important test is whether theresult depends on the definition of the particles.The analysis is repeated using calorimetric clustersonly. Half the difference between the two analyzes isassigned as the uncertainty due to this effect. This isfound to be the dominant systematic uncertainty.

The second source of systematic uncertainty is thelimited knowledge of quark fragmentation modelling.The systematic effect in the qq̄(γ ) background is es-timated by comparing results using the JETSET andHERWIG MC programs. The corresponding uncer-tainty is assigned to be half the difference between thetwo models.

The systematic uncertainty from quark fragmenta-tion modelling in W-pair events is estimated by com-paring results using PYTHIA, HERWIG and ARI-ADNE MC samples without CR. The uncertainty isassigned as the RMS between theRN values obtainedwith the three fragmentation models. Such compar-isons between different models test also possible ef-fects of different fragmentation schemes which are nottaken into account when varying only fragmentationparameters within one particular model.

Another source associated with fragmentation mod-elling is the effect of Bose–Einstein correlations (BEC)in hadronic W decays. This effect is estimated by re-peating the analysis using a MC sample with BEC onlybetween particles originating from the same W. An un-certainty is assigned equal to half the difference withthe default MC which includes full BEC simulation(BE32 option) [21] in W pairs. The sensitivity of theRN variable to BEC is found to be small.

The third main source of systematic uncertaintyis the background estimation. The qq̄(γ ) backgroundwhich is subtracted corresponds mainly to QCD four-

Table 3Contributions to the systematic uncertainties onRN

Source σRN

Energy flow objects 0.016qq̄ fragmentation 0.009WW fragmentation 0.008BEC 0.0034-jet background rate 0.004ZZ background 0.002

Total 0.021

jet events for which the rate is not well modelled byparton shower programs. PYTHIA underestimates, byabout 10%, the four-jet rate in the selected phase-spaceregion [22]. A systematic uncertainty is estimatedby varying the q̄q(γ ) cross-section by±5% aftercorrecting the corresponding background by+5%.This correction increases the value ofRN by 0.004.

A last and small systematic uncertainty is associ-ated with Z-pair production. It is estimated by varyingthe corresponding cross-section by±10%. This varia-tion takes into account all possible uncertainties per-taining to the hadronic channel, from final state in-teraction effects to the theoretical knowledge of thehadronic cross-section.

A summary of the different contributions to thesystematic uncertainty is given in Table 3.

The ratio obtained by taking into account thesystematic uncertainties is then:

RN = 0.915± 0.023(stat.)± 0.021(syst.).

7. Comparison with models

TheRN values predicted by the PYTHIA no-CR,SKI, SKII, ARIADNE no-CR, AR2, HERWIG no-CR, and HERWIG CR models are given in Table 4.

The data disfavour extreme scenarios of CR. A com-parison with ARIADNE and HERWIG shows that theCR schemes implemented in these two models do notmodify significantly the interjet particle activity in thehadronic W-pair decay events. Thus it is not possibleto constrain either of these models in the present analy-sis.

The dependence ofRN on the reconnection proba-bility is investigated with the SKI model. For this, fourMC samples are used: the no-CR sample and those


Table 4Measured value ofRN and model predictions

RNData 0.915± 0.023± 0.021

PYTHIA no-CR 0.918± 0.003SKI (kI = 0.6) 0.896± 0.003SKI (kI = 3.0) 0.843± 0.003SKI 100% 0.762± 0.003SKII 0.916± 0.003ARIADNE no-CR 0.929± 0.003AR2 0.919± 0.003HERWIG no-CR 0.948± 0.005HERWIG CR 0.946± 0.005

with kI = 0.6, 3, and 1000. In the SKI model the frac-tion of reconnected events is controlled by thekI para-meter and the dependence ofRN onkI is parametrizedasRN(kI) = p1(1 − exp(−p2kI)) + p3 wherepi arefree parameters. Aχ2 fit to the data is performed. Theχ2 minimum is atkI = 0.08. This value corresponds toabout 6% reconnection probability at

√s = 189 GeV.

Within the large uncertainty the result is also consis-tent with no CR effect.

The upper limits onkI at 68 and 95% confidencelevel are derived as 1.1 and 2.1, respectively. Thecorresponding reconnection probabilities at

√s =

189 GeV are 45 and 64%. The extreme SKI scenario,in which CR occurs in essentially all events, isdisfavoured by 4.9σ .

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