overline{c}$ using prompt leptons Abdallah (et al.), J ...and Inst. de F´ısica, Univ. Estadual do...

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Measurement of the forward-backward asymmetries of $e^ + e^- \rightarrow Z \rightarrow b\overline{b}$ and $e^ + e^- \rightarrow Z \rightarrow c \overline{c}$ using prompt leptons

Abdallah (et al.), J.; Blom, H.M.; Kluit, P.M.; Ferreira-Montenegro, J.; Mulders, M.P.; Reid,D.W.; Timmermans, J.J.M.; van Dam, P.H.A.Published in:European Physical Journal C

DOI:10.1140/epjc/s2004-01708-6

Link to publication

Citation for published version (APA):Abdallah (et al.), J., Blom, H. M., Kluit, P. M., Ferreira-Montenegro, J., Mulders, M. P., Reid, D. W., ... van Dam,P. H. A. (2004). Measurement of the forward-backward asymmetries of $e^ + e^- \rightarrow Z \rightarrow b\overline{b}$ and $e^ + e^- \rightarrow Z \rightarrow c \overline{c}$ using prompt leptons. European PhysicalJournal C, 34, 109-125. https://doi.org/10.1140/epjc/s2004-01708-6

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https://doi.org/10.1140/epjc/s2004-01708-6

Digital Object Identifier (DOI) 10.1140/epjc/s2004-01708-6Eur. Phys. J. C 34, 109–125 (2004) THE EUROPEAN

PHYSICAL JOURNAL C

Measurement of the forward-backward asymmetriesof e+e− → Z → bb and e+e− → Z → cc using prompt leptons

The DELPHI Collaboration

J. Abdallah25, P. Abreu22, W. Adam51, P. Adzic11, T. Albrecht17, T. Alderweireld2, R. Alemany-Fernandez8,T. Allmendinger17, P. Allport23, U. Amaldi29, N. Amapane45, S. Amato48, E. Anashkin36, A. Andreazza28,S. Andringa22, N. Anjos22, P. Antilogus25, W-D. Apel17, Y. Arnoud14, S. Ask26, B. Asman44, E. Augustin25,A. Augustinus8, P. Baillon8, A. Ballestrero46, P. Bambade20, R. Barbier27, D. Bardin16, G. Barker17, A. Baroncelli39,M. Battaglia8, M. Baubillier25, K.-H. Becks53, M. Begalli6, A. Behrmann53, E. Ben-Haim20, N. Benekos32,A. Benvenuti5, C. Berat14, M. Berggren25, L. Berntzon44, D. Bertrand2, M. Besancon40, N. Besson40, D. Bloch9,M. Blom31, M. Bluj52, M. Bonesini29, M. Boonekamp40, L. Booth23, G. Borisov21, O. Botner49, B. Bouquet20,V. Bowcock23, I. Boyko16, M. Bracko43, R. Brenner49, E. Brodet35, P. Bruckman18, M. Brunet7, L. Bugge33,P. Buschmann53, M. Calvi29, T. Camporesi8, V. Canale38, F. Carena8, N. Castro22, F. Cavallo5, M. Chapkin42,Ph. Charpentier8, P. Checchia36, R. Chierici8, P. Chliapnikov42, J. Chudoba8, U. Chung8, K. Cieslik18, P. Collins8,R. Contri13, G. Cosme20, F. Cossutti47, J. Costa50, D. Crennell37, J. Cuevas34, J. D’Hondt2, J. Dalmau44, T. da Silva48,W. Da Silva25, G. Della Ricca47, A. De Angelis47, W. De Boer17, C. De Clercq2, B. De Lotto47, N. De Maria45,A. De Min36, L. de Paula48, L. Di Ciaccio38, A. Di Simone39, K. Doroba52, J. Drees53,8, M. Dris32, G. Eigen4, T. Ekelof49,M. Ellert49, M. Elsing8, C. Espirito Santo22, G. Fanourakis11, D. Fassouliotis11,3, M. Feindt17, J. Fernandez41,A. Ferrer50, F. Ferro13, U. Flagmeyer53, H. Foeth8, E. Fokitis32, F. Fulda-Quenzer20, J. Fuster50, M. Gandelman48,C. Garcia50, Ph. Gavillet8, E. Gazis32, R. Gokieli8,52, B. Golob43, G. Gomez-Ceballos41, P. Goncalves22, E. Graziani39,G. Grosdidier20, K. Grzelak52, J. Guy37, C. Haag17, A. Hallgren49, K. Hamacher53, K. Hamilton35, S. Haug33,F. Hauler17, V. Hedberg26, M. Hennecke17, H. Herr8, J. Hoffman52, S-O. Holmgren44, J. Holt8, A. Houlden23,K. Hultqvist44, N. Jackson23, G. Jarlskog26, P. Jarry40, D. Jeans35, K. Johansson44, D. Johansson44, P. Jonsson27,C. Joram8, L. Jungermann17, F. Kapusta25, S. Katsanevas27, E. Katsoufis32, G. Kernel43, P. Kersevan8,43,U. Kerzel17, A. Kiiskinen15, T. King23, J. Kjaer8, P. Kluit31, P. Kokkinias11, C. Kourkoumelis3, O. Kouznetsov16,Z. Krumstein16, M. Kucharczyk18, J. Lamsa1, G. Leder51, F. Ledroit14, L. Leinonen44, R. Leitner30, J. Lemonne2,V. Lepeltier20, T. Lesiak18, W. Liebig53, D. Liko51, A. Lipniacka44, H. Lopes48, M. Lopez34, D. Loukas11, P. Lutz40,L. Lyons35, J. MacNaughton51, A. Malek53, S. Maltezos32, F. Mandl51, J. Marco41, R. Marco41, B. Marechal48,M. Margoni36, J-C. Marin8, C. Mariotti8, A. Markou11, C. Martinez-Rivero41, J. Masik12, N. Mastroyiannopoulos11,F. Matorras41, C. Matteuzzi29, F. Mazzucato36, M. Mazzucato36, R. Mc Nulty23, C. Meroni28, E. Migliore45,W. Mitaroff51, U. Mjoernmark26, T. Moa44, M. Moch17, K. Moenig8,10, R. Monge13, J. Montenegro31, D. Moraes48,S. Moreno22, P. Morettini13, U. Mueller53, K. Muenich53, M. Mulders31, L. Mundim6, W. Murray37, B. Muryn19,G. Myatt35, T. Myklebust33, M. Nassiakou11, F. Navarria5, K. Nawrocki52, R. Nicolaidou40, M. Nikolenko16,9,A. Oblakowska-Mucha19, V. Obraztsov42, A. Olshevski16, A. Onofre22, R. Orava15, K. Osterberg15, A. Ouraou40,A. Oyanguren50, M. Paganoni29, S. Paiano5, P. Palacios23, H. Palka18, D. Papadopoulou32, L. Pape8, C. Parkes24,F. Parodi13, U. Parzefall8, A. Passeri39, O. Passon53, L. Peralta22, V. Perepelitsa50, A. Perrotta5, A. Petrolini13,J. Piedra41, L. Pieri39, F. Pierre40, M. Pimenta22, E. Piotto8, T. Podobnik43, V. Poireau8, E. Pol6, G. Polok18,P. Poropat47, V. Pozdniakov16, N. Pukhaeva2,16, A. Pullia29, J. Rames12, L. Ramler17, A. Read33, P. Rebecchi8,J. Rehn17, D. Reid31, R. Reinhardt53, P. Renton35, F. Richard20, J. Ridky12, M. Rivero41, D. Rodriguez41,A. Romero45, P. Ronchese36, P. Roudeau20, T. Rovelli5, V. Ruhlmann-Kleider40, D. Ryabtchikov42, A. Sadovsky16,L. Salmi15, J. Salt50, A. Savoy-Navarro25, U. Schwickerath8, A. Segar35, R. Sekulin37, M. Siebel53, A. Sisakian16,G. Smadja27, O. Smirnova26, A. Sokolov42, A. Sopczak21, R. Sosnowski52, T. Spassov8, M. Stanitzki17, A. Stocchi20,J. Strauss51, B. Stugu4, M. Szczekowski52, M. Szeptycka52, T. Szumlak19, T. Tabarelli29, C. Taffard23, F. Tegenfeldt49,J. Timmermans31, L. Tkatchev16, M. Tobin23, S. Todorovova12, B. Tome22, A. Tonazzo29, P. Tortosa50, P. Travnicek12,D. Treille8, G. Tristram7, M. Trochimczuk52, C. Troncon28, M-L. Turluer40, A. Tyapkin16, P. Tyapkin16,S. Tzamarias11, V. Uvarov42, G. Valenti5, P. Van Dam31, J. Van Eldik8, A. Van Lysebetten2, N. van Remortel2,I. Van Vulpen8, G. Vegni28, F. Veloso22, W. Venus37, P. Verdier27, V. Verzi38, D. Vilanova40, L. Vitale47, V. Vrba12,H. Wahlen53, J. Washbrook23, C. Weiser17, D. Wicke8, J. Wickens2, G. Wilkinson35, M. Winter9, M. Witek18,O. Yushchenko42, A. Zalewska18, P. Zalewski52, D. Zavrtanik43, V. Zhuravlov16, I. Zimin16, A. Zintchenko16,M. Zupan11

110 The DELPHI Collaboration: Measurement of e+e− → Z → bb and e+e− → Z → cc

1 Department of Physics and Astronomy, Iowa State University, Ames IA 50011-3160, USA2 Physics Department, Universiteit Antwerpen, Universiteitsplein 1, 2610 Antwerpen, Belgium

and IIHE, ULB-VUB, Pleinlaan 2, 1050 Brussels, Belgiumand Faculte des Sciences, Univ. de l’Etat Mons, Av. Maistriau 19, 7000 Mons, Belgium

3 Physics Laboratory, University of Athens, Solonos Str. 104, 10680 Athens, Greece4 Department of Physics, University of Bergen, Allegaten 55, 5007 Bergen, Norway5 Dipartimento di Fisica, Universit a di Bologna and INFN, Via Irnerio 46, 40126 Bologna, Italy6 Centro Brasileiro de Pesquisas Fısicas, rua Xavier Sigaud 150, 22290 Rio de Janeiro, Brazil

and Depto. de Fısica, Pont. Univ. Catolica, C.P. 38071 22453 Rio de Janeiro, Braziland Inst. de Fısica, Univ. Estadual do Rio de Janeiro, rua Sao Francisco Xavier 524, Rio de Janeiro, Brazil

7 College de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, 75231 Paris Cedex 05, France8 CERN, 1211 Geneva 23, Switzerland9 Institut de Recherches Subatomiques, IN2P3 – CNRS/ULP – BP20, 67037 Strasbourg Cedex, France

10 Now at DESY-Zeuthen, Platanenallee 6, 15735 Zeuthen, Germany11 Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, 15310 Athens, Greece12 FZU, Inst. of Phys. of the C.A.S. High Energy Physics Division, Na Slovance 2, 180 40, Praha 8, Czech Republic13 Dipartimento di Fisica, Universita di Genova and INFN, Via Dodecaneso 33, 16146 Genova, Italy14 Institut des Sciences Nucleaires, IN2P3-CNRS, Universite de Grenoble 1, 38026 Grenoble Cedex, France15 Helsinki Institute of Physics, P.O. Box 64, 00014 University of Helsinki, Finland16 Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, 101 000 Moscow, Russian Federation17 Institut fur Experimentelle Kernphysik, Universitat Karlsruhe, Postfach 6980, 76128 Karlsruhe, Germany18 Institute of Nuclear Physics,Ul. Kawiory 26a, 30055 Krakow, Poland19 Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, 30055 Krakow, Poland20 Universite de Paris-Sud, Lab. de l’Accelerateur Lineaire, IN2P3-CNRS, Bat. 200, 91405 Orsay Cedex, France21 School of Physics and Chemistry, University of Lancaster, Lancaster LA1 4YB, UK22 LIP, IST, FCUL - Av. Elias Garcia, 14-1o, 1000 Lisboa Codex, Portugal23 Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK24 Dept. of Physics and Astronomy, Kelvin Building, University of Glasgow, Glasgow G12 8QQ25 LPNHE, IN2P3-CNRS, Univ. Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, 75252 Paris Cedex 05, France26 Department of Physics, University of Lund, Solvegatan 14, 223 63 Lund, Sweden27 Universite Claude Bernard de Lyon, IPNL, IN2P3-CNRS, 69622 Villeurbanne Cedex, France28 Dipartimento di Fisica, Universita di Milano and INFN-MILANO, Via Celoria 16, 20133 Milan, Italy29 Dipartimento di Fisica, Univ. di Milano-Bicocca and INFN-MILANO, Piazza della Scienza 2, 20126 Milan, Italy30 IPNP of MFF, Charles Univ., Areal MFF, V Holesovickach 2, 180 00, Praha 8, Czech Republic31 NIKHEF, Postbus 41882, 1009 DB Amsterdam, The Netherlands32 National Technical University, Physics Department, Zografou Campus, 15773 Athens, Greece33 Physics Department, University of Oslo, Blindern, 0316 Oslo, Norway34 Dpto. Fisica, Univ. Oviedo, Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain35 Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK36 Dipartimento di Fisica, Universita di Padova and INFN, Via Marzolo 8, 35131 Padua, Italy37 Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK38 Dipartimento di Fisica, Universita di Roma II and INFN, Tor Vergata, 00173 Rome, Italy39 Dipartimento di Fisica, Universita di Roma III and INFN, Via della Vasca Navale 84, 00146 Rome, Italy40 DAPNIA/Service de Physique des Particules, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France41 Instituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros s/n, 39006 Santander, Spain42 Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation43 J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia and Laboratory for Astroparticle Physics, Nova Gorica Polytechnic,

Kostanjeviska 16a, 5000 Nova Gorica, Slovenia,and Department of Physics, University of Ljubljana, 1000 Ljubljana, Slovenia

44 Fysikum, Stockholm University, Box 6730, 113 85 Stockholm, Sweden45 Dipartimento di Fisica Sperimentale, Universita di Torino and INFN, Via P. Giuria 1, 10125 Turin, Italy46 INFN,Sezione di Torino, and Dipartimento di Fisica Teorica, Universita di Torino, Via P. Giuria 1, 10125 Turin, Italy47 Dipartimento di Fisica, Universita di Trieste and INFN, Via A. Valerio 2, 34127 Trieste, Italy

and Istituto di Fisica, Universita di Udine, 33100 Udine, Italy48 Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fundao 21945-970 Rio de Janeiro, Brazil49 Department of Radiation Sciences, University of Uppsala, P.O. Box 535, 751 21 Uppsala, Sweden50 IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, 46100 Burjassot (Valencia), Spain51 Institut fur Hochenergiephysik, Osterr. Akad. d. Wissensch., Nikolsdorfergasse 18, 1050 Vienna, Austria52 Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, 00681 Warsaw, Poland53 Fachbereich Physik, University of Wuppertal, Postfach 100 127, 42097 Wuppertal, Germany

The DELPHI Collaboration: Measurement of e+e− → Z → bb and e+e− → Z → cc 111

Received: 10 December 2003 / Revised version: 3 February 2004 /Published online: 9 March 2004 – c© Springer-Verlag / Societa Italiana di Fisica 2004

Abstract. The forward-backward asymmetries of the processes e+e− → Z → bb and e+e− → Z → ccwere measured from a sample of hadronic Z decays collected by the DELPHI experiment between 1993and 1995. Enriched samples of bb and cc events were obtained using lifetime information. The tagging of band c quarks in these samples was based on the semileptonic decay channels b/c → X+µ and b/c → X+ecombined with charge flow information from the hemisphere opposite to the lepton.

Combining the AbbFB and Acc

FB measurements presented in this paper with published results based on 1991and 1992 DELPHI data samples, the following pole asymmetries were obtained:

A0,bFB = 0.1021 ± 0.0052 (stat) ± 0.0024 (syst)

A0,cFB = 0.0728 ± 0.0086 (stat) ± 0.0063 (syst)

The effective value of the weak mixing angle derived from these measurements is

sin2 θleptW,eff = 0.23170 ± 0.00097.


1 Introduction

The polar angle, θ, of the final state fermion relative to theincoming electron in the reaction e+e− → ff , at

√s �

MZ , is distributed according to:

dσ

d cosθ∝ 1 + cos2θ +

83Aff

FB cosθ . (1)

The coefficient of the cosθ term, in the Electroweak Stan-dard Model and for pure Z exchange, is related, at thelowest order, to the vector (vf ) and axial vector (af ) cou-plings of the Z to the fermions by:

AffFB =

34AeAf =

34

2aeve

a2e + v2

e

2afvf

a2f + v2

f

. (2)

Higher order electroweak corrections can be accounted forin the above relations by defining the modified couplingsvf and af and an effective value sin2 θf

W,eff of the weakmixing angle:

vf

af= 1 − 4 |qf | sin2 θf

W,eff (3)

where qf is the electric charge of the fermion in units ofthe proton charge. The effective value of the weak mixingangle estimated in this paper is the one correspondingto the leptons (sin2 θlept

W,eff), small contributions specific tothe quark sector being corrected for using the programZFITTER [1].

Because of the values of the Z couplings to fermions,both the forward-backward asymmetry and its sensitivityto sin2 θlept

W,eff are larger in the Z → qq channel than in

the leptonic ones, thus making the AbbFB and Acc

FB mea-surements of particular interest. The determination of thequark asymmetries Abb

FB and AccFB requires:

– the tagging of the Z boson hadronic decays into bb andcc heavy quark final states;

– the reconstruction of the polar angle of the producedquark/anti-quark axis;

– the orientation of the corresponding axis as a functionof the quark direction1.

The analysis presented here is based on events withidentified muons or electrons produced in semileptonic de-cays of b and c hadrons, referred to as the “lepton sample”in the following. The main parameters used to analysethese events are:

– the kinematic variables associated with the lepton,namely the transverse (pT ) and longitudinal (pL) mo-mentum with respect to the direction of the closestjet;

– the sign of the lepton electric charge.

Prompt leptons with high pT and pL allow the selectionof a high purity sample of e+e− → Z → bb events and, atthe same time, the discrimination between quark and anti-quark jets on the basis of the charge correlation betweenthe lepton and the parent quark. Decay chains like b →c → l+ and B0B0 mixing reduce this charge correlation.Conversely the presence of background and the reducedcharge correlations limit the use of the largest fractionof the lepton sample at low pT and pL. Two additionalvariables were used in the present analysis to overcomethese limitations in the Abb

FB measurement:

– a b-tagging variable, based mainly on the probabilityto observe a given event, assuming the tracks comefrom the primary vertex, to isolate pure samples ofe+e− → Z → bb events;

– a momentum weighted average of the particle charges inthe hemisphere opposite to the lepton, to provide an in-dependent estimator of the charge of the primary quark.

By combining the information from the b-tagging andthe lepton pL and pT , a clean sample of Z → cc could alsobe selected, allowing the measurement of Acc

FB.The thrust axis (

−→T ) of the event, oriented by the jet

containing the lepton, was used to determine the directionof the primary quark.

1 This requirement implies that jets induced by a quark orby an anti-quark have to be distinguished.


The choice of these variables was driven not only by theobjective of optimising the statistical precision of the mea-sured asymmetries but also by the capability of calibratingthem on the data, thus controlling well the systematics.

The data used here were collected between 1993 and1995 at energies around the Z peak with the DELPHIdetector at LEP. This analysis extends the previously pub-lished results based on the events collected in 1990 [2], 1991and 1992 [3].

After a brief presentation of the DELPHI detector, theevent and lepton selections are described. The observablesused in the analysis are discussed together with their de-scription by the simulation and the associated sources ofsystematics. The measurement of the asymmetries Abb

FBand Acc

FB is presented in the last sections.

2 Detector description and event selection

2.1 The DELPHI detector

The DELPHI detector has been described in detail in [4].Only the components which were most relevant to thepresent analysis are discussed.

The innermost detector in DELPHI was the Vertex De-tector (VD), located just outside the LEP beam pipe. Itconsisted of three concentric cylindrical layers of silicon mi-crostrip detectors at average radii of 6.3, 9.0 and 10.9 cmfrom the beam line, called the Closer, Inner and Outerlayer, respectively. During 1993 it provided only the mea-surement of the RΦ 2 coordinate and the polar angle accep-tance for a particle crossing all the three layers was limitedby the extent of the Outer layer to 44◦ ≤ θ ≤ 136◦ [5].In 1994 the Closer and the Outer layers were equippedwith double sided silicon detectors, also measuring the zcoordinate [6]. At the same time the angular acceptanceof the Closer layer was enlarged from 30◦ ≤ θ ≤ 150◦to 25◦ ≤ θ ≤ 155◦. The measured intrinsic precision wasabout 8 µm for the RΦ measurement while for z it dependedon the polar angle of the incident track, going from about10 µm for tracks perpendicular to the modules, to 20 µmfor tracks with a polar angle of 25◦. For charged particletracks with hits in all three RΦ VD layers, the impactparameter3 precision was σRΦ = [61/(p sin3/2 θ) ⊕ 20]µmwhile for tracks with hits in both the Rz layers it wasσz = [67/(p sin5/2 θ) ⊕ 33]µm, where p is the momen-tum in GeV/c.

Outside the VD, between radii of 12 cm and 28 cm,the Inner Detector (ID) was located, which included ajet chamber providing up to 24 RΦ measurements and

2 In the DELPHI coordinate system, z is along the directionof the incoming electron beam, Φ and R are the azimuthalangle and radius in the xy plane, and θ is the polar angle withrespect to the z axis.

3 TheRΦ impact parameter is defined as the distance betweenthe point of closest approach of a charged particle in the xyplane to the reconstructed primary vertex. The distance in zbetween this point on the charged particle trajectory and theprimary vertex is called the z impact parameter.

five layers of proportional chambers with both RΦ and zinformation. The ID covered the angular range 29◦ ≤ θ ≤151◦. In 1995 a new ID was operational, with the samewire configuration in the inner drift chamber but a widerpolar angle acceptance of 15◦ ≤ θ ≤ 165◦.

The VD and the ID were surrounded by the main DEL-PHI tracking device, the Time Projection Chamber (TPC),a cylinder of 3 m length, of 30 cm inner radius and of 122 cmouter radius. The ionisation charge produced by particlescrossing the TPC volume was drifted to the ends of thedetector where it was measured in a proportional counter.Up to 16 space points could be measured in the angularregion 39◦ ≤ θ ≤ 141◦. The analysis of the pulse heightof the signals of up to 192 sense wires of the proportionalchambers allowed the determination for charged particlesof the specific energy loss, dE/dX, which was used forparticle identification.

The Outer Detector (OD) was located between radii of198 cm and 206 cm and consisted of five layers of drift cells.

In the forward regions two sets of planar wire chambers,at ± 160 cm and ± 270 cm in z, completed the chargedparticle reconstruction at low angle.

The muon identification relied mainly on the muonchambers, a set of drift chambers providing three-dimen-sional information situated at the periphery of DELPHIafter approximately 1 m of iron. One set of chambers waslocated 20 cm before the end of the hadronic calorimeter(HCAL), two further sets of chambers being outside. Atθ � 90◦ there were 7.5 absorption lengths between theinteraction point and the last muon detector.

In the Barrel part of the detector there were three layerseach including two active planes of chambers covering theregion | cos θ| < 0.63. The two external layers overlappedin azimuth to avoid dead spaces. In the Forward part, theinner and the outer layers consisted of two planes of driftchambers with anode wires crossed at right angles. Theresolution was 1.0 cm in z and 0.2 cm (0.4 cm) in RΦ forthe Barrel (Forward). In 1994 a further set of chambers(Surround Muon Chambers) was added to cover the regionbetween the Barrel and Forward chambers.

The electromagnetic calorimeter in the barrel region,| cos θ| < 0.73, was the High density Projection Cham-ber (HPC), situated inside the superconducting coil. Thedetector had a thickness of 17.5 radiation lengths and con-sisted of 144 modules arranged in 6 rings along z, eachmodule was divided into 9 drift layers separated by lead.It provided three-dimensional shower reconstruction. Inthe forward region, 0.80 < | cos θ| < 0.98, the electro-magnetic calorimeter EMF consisted of two disks of 5 mdiameter with a total of 9064 lead-glass blocks in the formof truncated pyramids, arranged almost to point towardsthe interaction region.

2.2 Selection of hadronic events

The selection of charged particle tracks and neutral clusterswas performed according to the requirements of Table 1.Hadronic events were then selected with an efficiency of95% requiring:


Table 1. Requirements on charged particle tracks and neutral clusters for hadronicevents selection. On selected events, the energy flow measurement and jets recon-struction were performed with an improved neutral clusters reconstruction, includingphotons of lower energy in the HPC (down to ∼ 0.3 GeV) and neutral showers ofmore than 1 GeV reconstructed in the HCAL

charged-particle tracks polar angle | cos θ| < 0.93length of track measured inside TPC > 30 cmimpact parameter (RΦ) < 5 cmimpact parameter |z| < 10 cmcharged particle momentum > 0.2 GeV/crelative uncertainty on the momentum < 100%

neutral clusters detected by HPC or EMFpolar angle | cos θ| < 0.98HPC (EMF) energy > 0.8(0.4) GeV

– at least 7 accepted charged particles;– a total measured energy of these charged particles, as-

suming pion masses, larger that 0.15 times the centre-of-mass energy,

√s.

A total of 2.7 million hadronic events was selected from1993–1995 data, at centre-of-mass energies within ± 2 GeVof the Z resonance mass. A set of 8.4 million simulatedhadronic events for years 1993 to 1995 was used, gener-ated using the JETSET 7.3 Parton Shower model [7] incombination with the full simulation of the DELPHI de-tector. The parameters of the generator were tuned to theDELPHI data as described in [8]. The detailed breakdownof the events used in data and simulation for each year isgiven in Table 2.

3 Lepton samples

The main kinematical variable used to measure the flavourcomposition of the leptonic sample was the transverse mo-mentum, pT , of the lepton with respect to the jet axis.To compute this axis the jet containing the lepton wasused, but its direction was reconstructed without the lep-ton. Jets were built using the JADE algorithm [9] with a

scaled invariant mass ycut = m2ij

E2vis

≥ 0.01 .To ensure a good determination of the thrust polar an-

gle, θT , the analysis was limited to events with |cos(θT )| <0.9. For events with more than one lepton candidate, onlythe highest pT lepton was used for the Abb

FB and AccFB mea-

surement.The lepton identification has been studied not only by

means of special data and simulation samples (for example: µ+µ−, K0 → π+π−, Compton events) but also using p,pT and b-tagging4 cuts to select, in hadronic events, lepton

4 The b-tagging method and its calibration will be presentedin detail in Sect. 4. b-tagged and anti-b-tagged samples refer,respectively, to the purer and to the most contaminated bsub-samples as defined in Sect. 4. The b-tagging is used inthis section to estimate the purity of the electron sample butis only used as a cross-check for the muon sample. For this

Table 2. The number of selected hadronic events for dataand simulation

Year # of events (in 103)Data Simulation

1993 696 22761994 1370 43001995 662 1829

Table 3. Number of events with at least one lepton candidatefor the different years and for the three centre-of-mass energies.The highest pT lepton is used to classify the event as “muon”or “electron”

Year Energy muons electrons89 GeV 6068 4240

1993 91 GeV 28791 2155393 GeV 9171 6536

1994 91 GeV 95183 6997189 GeV 5147 4062

1995 91 GeV 28600 2178693 GeV 8629 6443

sub-samples with different purity. In practice with only twosuch lepton sub-samples, two parameters, the efficiency andthe purity of the overall sample, can be compared betweendata and simulation.

The number of lepton candidates for the different yearsand centre-of-mass energies can be found in Table 3. Detailson the lepton identification and on the sample compositionare given in the next two sub-sections.

3.1 Muon sample

For the muon identification the tracks reconstructed in thecentral detectors were used to define a path along which

reason to avoid any sizable correlation in the tuning of thesimulation, the b-tagging calibration used in this section wasbased on events from the muon sample alone.


hits in the muon chambers were looked for. The identi-fication algorithm has been described extensively in [3].Muon candidates with a momentum, p, above 2.5 GeV/cand in the region of good geometrical acceptance were se-lected. The muon polar angle θµ was required to be inthe region 0.03 < |cos θµ| < 0.6 or 0.68 < |cos θµ| < 0.93.Only for a small fraction of the 1994 data sample the Sur-round Muon Chambers, which filled the gap between thebarrel and forward detectors, were able to provide usefulmuon identification.

The muon identification efficiency was measured inZ → µ+µ−, Z → τ+τ−and γγ → µ+µ− events, yield-ing on average about 0.85 for 45 GeV/c muons and 0.83 formomenta between 10 and 5 GeV/c.

In order to extract AbbFB and Acc

FB from the observedasymmetry the absolute lepton efficiency is not required,only a correct description of the sample purity is needed.The contamination from misidentified hadrons arises partlyfrom the decay of pions and kaons and, for momenta above3 GeV/c, mostly from energetic hadrons interacting at theend of the calorimeter and generating punch-throughs.K0

S particles decaying into two pions were used to mea-sure the rate of pion misidentification above 3 GeV/c show-ing that the fraction of pions misidentified as muons was1.79 ± 0.09 ± 0.05 and 1.41 ± 0.10 ± 0.03 times bigger indata than in the simulation for the barrel and the for-ward regions respectively. Muons from pion decays weresubtracted from the misidentified sample to compute thenumbers quoted above. The first error is due to the limitedstatistics, the second corresponds to a 15% change in thecontamination of muons from pion decays. The fraction ofmuons from π and K decays present in the selected muonsample was determined to this precision by comparing thesize of two muon sub-samples in hadronic events selectedby p,pT cuts5.

To measure further the sample composition directlyfrom the data, the number of muon candidates, normalisedto the number of hadronic Z decays, was compared be-tween data and simulation in sub-samples enriched inprompt muons or background by different sets of selectionsin p, pT or b-tagging. The stability of the misidentifica-tion correction quoted above was measured as a functionof p, pT and θ in b and anti-b-tagged samples. No dis-crepancy was observed outside expected statistical fluctu-ations. For example in the anti-b-tagged sub-sample, whichhad a purity of 30% in leptons from heavy flavour decay,a data/simulation comparison for 28 bins in momentumhad a 27% χ2 probability. In this same sub-sample the6.6% excess of positive particles due to the difference be-tween the K+ and K− cross-sections in the detector, wasalso perfectly described with a statistical precision of ±0.5%. These studies confirmed the correct description inthe tuned simulation of the different sources of backgroundwithin the uncertainties quoted above.

5 The first one was selected with p > 2.5 GeV/c and pT <0.7 GeV/c and the second one with p > 4 GeV/c and pT >0.7 GeV/c, the two samples having respectively 19% and 4% ofmuons from π and K decays.

Table 4. Full 1993–1995 lepton sample composition. The lep-tons from heavy flavour decays, when the heavy flavour quarkwas coming from a gluon splitting, are counted in “other”, line“h)”. The total efficiency to select a muon or an electron fromthe process “a)”is respectively (44.7±0.2)% and (35.4±0.4)%including all effects (momentum cuts and detector inefficien-cies) except the efficiency to select hadronic events

Lepton candidate source Sample composition in %µ e

Lepton from b hadron decay : “same sign” 32.5 35.1a) b → l− 29.0 31.6b) b → τ → l− 1.0 1.0c) b → c → l− ; b → c → τ → l− 2.5 2.5Lepton from b hadron decay : “opposite sign” 11.8 11.7d) b → c → l+ ; b → c → τ → l+

Lepton from b hadron decay : other source 0.3 0.3e) b → J/Ψ → l+l−

Lepton from c decay 16.8 15.9f) c → l+ ; c → τ → l+

Background 38.6 37.0g) Misidentification 26.3 18.2h) Light mesons decay / converted gammas / other 12.3 18.8

The comparison between data and simulation for thecos θµ distribution is presented in Fig. 1. The muon samplecomposition is given in Table 4.

3.2 Electron sample

The electron candidates of momentum higher than 2 GeV/cwere identified in the barrel (0.03 < |cos θe| < 0.7) by com-bining the electromagnetic shower information from theHPC and the track ionisation measured by the TPC, with aneural network. In the forward region (0.7 < |cos θe| < 0.9)only the ionisation measured by the TPC was used. Mainlydue to the large amount of material in front of the EMF,the calorimetric information in the forward regions was notused to identify electrons.

Electrons in the barrel region

In the barrel the contamination and efficiency of the elec-tron sample was tuned in the simulation using two sub-samples with p > 3 GeV/c and a b or anti-b-tag. Their con-tent of misidentified electrons was respectively 27% and89%. The efficiency was found to be correctly describedby the simulation, in agreement with a study based onCompton scattering and photon conversion samples [10].The misidentification probability was found in the data tobe a factor 0.9 lower than that in the simulation, with vari-ations within a few percent as a function of the year andangular region. A study based on sub-samples selected by pand pT cuts gave compatible results. The relative precisionon this correction was estimated to be ±5%.


a)

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Fig. 1a–d. cos θ distribution for muon, upper plots, and electron, lower plots, candidates. The lepton candidates have pT <0.7 GeV/c in a , c and pT > 0.7 GeV/c in b , d corresponding to samples enriched in background and signal respectively. The“b → µ/e right (wrong)” samples correspond to leptons with the same (opposite) sign as the primary b parton (see Sect. 6.1).Converted photons cause the strong cos θe dependence of the background in the c plot. Only the statistical errors are quotedin these plots. The systematics on the samples composition considered in the text are enough to cover the few discrepanciesobserved between the data and the simulation

The number of selected electron candidates in a lowp (p < 3 GeV/c) and pT (pT < 1 GeV/c) region for anti-b-tagged events agreed between data and simulation forthe standard and low converted gamma rejections (withconverted gamma rejections of 90% and 75% respectively).This study was statistically compatible with a correct de-scription of the converted gamma content of the electronsample at a ± 10% level.

Electrons in the forward regions

In the forward regions, where only the ionisation measuredby the TPC was used, the misidentification could be stud-ied with the muon sample, muons and pions having almostthe same ionisation signature in the TPC. This showed theneed to increase the misidentification by a factor 1.12±0.07in the simulation. The amount of electron from convertedphotons was determined with the help of the b-tagging and


p, pT requirements as above. This amount was found tobe correctly described by the simulation for the differentyears within a precision better than ± 10%.

The comparison between the data and the simulationfor the cos θe distribution is presented in Fig. 1. The com-position of the electron sample is quoted in Table 4.

4 Use of the b-tagging information

To improve the separation between heavy and light flavoursa b-tagging technique developed for the measurement of Rb,the partial width of Z into bb pairs, was used [11].Each event was divided into two hemispheres according tothe direction of the thrust axis, and the b-tagging proba-bility for a hemisphere to contain a b quark was given bythe jet with the highest b-tagging probability in the hemi-sphere.

The tagging technique was based on the combination ofup to four discriminating variables, xi (i=1 to 4), definedfor each jet:

– the jet lifetime probability, constructed from the posi-tively signed impact parameters of all tracks includedin a jet, is built from the probabilities to observe agiven set of impact parameters, assuming the trackscome from the primary vertex;

– the effective mass of the system of particles assignedto the secondary vertex 6;

– the rapidity of tracks associated to the secondary vertexwith respect to the jet direction;

– the fraction of the jet energy carried by charged parti-cles from the secondary vertex.

The correct description of these variables by the simulationis shown in [11].

For each jet containing a secondary vertex, the four vari-ables xi were then combined into a single tagging variabley by means of their probability density functions fuds

i (xi),fc

i (xi), f bi (xi), for uds, c and b quarks respectively, as de-

termined from simulation studies:

y = nc

∏ fci (xi)

f bi (xi)

+ nuds

∏ fudsi (xi)f b

i (xi),

nc, nuds being the fractions of c-jets and uds-jets with areconstructed secondary vertex normalised by the relation:nc + nuds = 1. Only the first variable was used if no sec-ondary vertex was reconstructed. Hemispheres with a jetcontaining a b-quark were characterised by a large valueof the variable ηHEM = − log10 y.

The value of the tagging variable for the whole eventwas computed from the corresponding values obtained in

6 A secondary vertex was required to contain at least 2 tracksnot compatible with the primary vertex and to have L/σL > 4where L is the distance from the primary to the secondaryvertex and σL is its error. Each track assigned to the secondaryvertex should have at least one measurement in the VD andat least 2 tracks should have measurements in both R−Φ andR− z planes of the VD.

each hemisphere as:

ηEVT = max(ηHEM1, ηHEM2).

The sample composition determination, as a function of thevalue of ηEVT, was needed to extract Abb

FB and AccFB from the

raw asymmetries. Since a separate tag for each hemispherewas used, the sample composition could be derived from thedata themselves with minimum input from the simulationby using a technique similar to the single tag versus doubletag method of the Rb analysis [11].

For events with the thrust axis situated within thebarrel acceptance (|cos θT | < 0.7), the distribution of thehemisphere b-tagging variable ηHEM was divided into threeintervals corresponding, respectively, to events enriched inuds (I), c (II) or b (III) flavours. For this low number ofintervals a direct measurement of their content in term ofuds, c and b can be implemented in the data as follows.

In each interval j the fraction f(j)E of events with at

least one hemisphere in that interval and the fraction f(j)H

of hemispheres in the interval itself, were expressed by thefollowing relations:

f(j)E =

∑q

rq

(2ε(j)

q − ε(j)D,q

)

=∑

q

rqε(j)q

[2 − ρ(j)

q − ε(j)q (1 − ρ(j)

q )]

,

f(j)H =

∑q

rqε(j)q , (4)

where ε(j)q were the fractions of hemispheres in the j−th

interval for the flavour q (q = uds, c, b), and the correla-tions ρ

(j)q = (ε(j)

D,q − ε(j) 2q )/(ε(j)

q (1 − ε(j)q )) accounted for

the probability (ε(j)D,q) of having both hemispheres in that

interval. The variables rq stand for the fractions of Z → qqevents in the selected leptonic sample.The requirement of an identified lepton in the final statestrongly enhanced the fraction of events with a Z decayinginto heavy quark pairs. Therefore the fractions rq were ob-tained from Rq, the Standard Model partial decay widthsof the Z, via the relation

rq = Rqeq,�

ehad,�q = uds, c, b (5)

where eq,� was the flavour dependent hadronic selectionefficiency, taken from the simulation, and ehad,� =

∑uds,c,b

×Rqeq,�. To determine the fractions ε(j)q,RD in real data for

the different intervals, it has been assumed that they differonly slightly from the ones in the simulation, ε

(j)q :

ε(j)q,RD = ε(j)

q (1 + δ(j)q )

In the approximation, confirmed by the data, of smallcorrections δ

(j)q , the set of Equations (4), including the


closure relations on the fractions ε(j)q,RD and ε

(j)q , gives at

first order in δ(j)q :

∑q

rqε(j)q

[2 − ρ(j)

q − 2ε(j)q (1 − ρ(j)

q )]δ(j)q

= f(j)E −

∑q

rqε(j)q

[2 − ρ(j)

q − ε(j)q (1 − ρ(j)

q )], (6)

∑q

rqε(j)q δ(j)

q = f(j)H −

∑q

rqε(j)q , (7)

Nint∑j

ε(j)q δ(j)

q = 0 , (8)

where ρ(j)q and ε

(j)q were taken from the simulation. For

Nint = 3 b-tagging intervals there are in total 9 unknownsδ(j)q and 9 equations. The rank of the matrix of the coeffi-

cients is 8 so that one input δ(j)q was required7. For Nint = 2

and merging together 2 flavours, the system reduces to 6equations and 4 unknowns. Since the rank of the matrixof the coefficients is 4 the system has one exact solution8.Therefore the δ

(j)q for Nint = 3 were obtained in two steps.

First we combined together the two highest bins of ηHEM,merged the c and b contributions and solved this reducedsystem with 4 unknowns. Then the full system was solvedfixing δ

(I)uds to the value obtained in the previous step.

For events with 0.7 < |cos θT | < 0.85, because of thereduced performances of b-tagging in the forward region,only the reduced system with 4 unknowns was solved. Nob-tagging information was used for events with |cos θT | >0.85 9.

Errors on δ(j)q due to the finite statistics of the simu-

lated sample were estimated in the following way. For eachflavour q, we considered the two dimensional distributions{ηHEM1, ηHEM2} which could be derived from the originalone in the simulation by adding −1, 0, and +1 standarddeviations to the content of each interval. This was doneconserving the total number of events of that flavour andwith the standard deviations given by the multinomial dis-tribution. For each configuration the coefficients ε

(j)q , ρ

(j)q

in (4) were recomputed and then the system solved. Thespread of the different solutions for the δ

(j)q was considered

as the simulation statistical error on these corrections.As a cross check of the method, the simulated sample

was divided into 6 different sub-samples of equal size. Foreach sub-sample, the system was solved and the uncertaintyon the solutions was evaluated by using the procedure de-scribed above. The spread of the solutions in the subsets

7 As by construction∑Nint

j ε(j)q = 1 implies

∑Nintj f

(j)H = 1,

one equation among the Equations (7) and (8) can be deducedfrom the other.

8 For Nint = 2, we have by definition ρ(1)q = ρ

(2)q which makes

in this case the two equations associated to (6) equivalent.9 For the 1993 data sample, due to the reduced length of the

micro-vertex detector, the b-tagging was performed only downto |cos θT | < 0.81.

Table 5. Values of the fractions (ε(j)q ), obtained from thesimulation, and of their respective corrections (1 + δ

(j)q ), fitted

on real data, using 1994 event samples

bin I II III(dominant flavour) (uds) (c) (b)Barrel region

ε(j)uds 0.71 0.23 0.06

1 + δ(j)uds 1.019 ± 0.003 0.950 ± 0.017 0.986 ± 0.072

ε(j)c 0.45 0.34 0.21

1 + δ(j)c 0.986 ± 0.007 1.046 ± 0.013 0.956 ± 0.031

ε(j)b 0.13 0.18 0.69

1 + δ(j)b 0.970 ± 0.009 0.946 ± 0.006 1.020 ± 0.002

Forward regions

ε(j)uds 0.70 .30

1 + δ(j)uds 1.000 ± 0.009 1.000 ± 0.021

ε(j)bc 0.36 .64

1 + δ(j)bc .931 ± 0.008 1.039 ± 0.005

was found to be in agreement with the estimation of theerror. The corrections 1 + δ

(j)q to the simulation fractions

found for the 1994 sample together with the error due tothe finite simulation statistics are shown in Table 5. For allthe samples, the corrections δ

(III)uds were found to be compat-

ible with zero indicating a good control of the backgroundlevel in the region most relevant in this measurement. Thefractions ε

(III)b were found instead 2–4 % higher in the

data than in the simulation.For the system with Nint = 3 the predicted correlations

have a sizable value only for ρ(III)b (= 0.027±0.005 in 1994).

The detector and QCD origins of such correlations havebeen studied in detail in [11]. In the present analysis even a100% change in the predicted correlation has a small impacton the estimated data sample composition. The variationinduced is of the same order as the one associated to thestatistical uncertainty on δ

(j)q .

For the system with Nint = 2 the predicted correlationswere up to ∼ 0.1 for the b/c flavours and still compatiblewith zero for the uds sample. The high value of ρ

(j)bc ob-

tained in this case is a pure artifact of the merging of theb and c samples and is just related, at first order, to thedifference in tagging efficiency of b and c.

The merging of b and c for Nint = 2 is justified bythe fact that for the b-tagging intervals used in this case,the δ

(j)q corrections are mainly related to the difference

in the description of the detector response between realdata and simulation and not to the details of the b and cphysics. This is supported by the fact that in the intervalI dominated by uds, which is the same both for Nint = 2and Nint = 3, the corrections δ

(I)c and δ

(I)b in the barrel

are compatible (cf. Table 5). To evaluate possible biasesfrom this merging procedure, another system, also withNint = 2, was built starting from the original one withNint = 3 but now combining the two lowest bins of ηHEM,bins I and II, and merging the uds and c flavours. The


Table 6. Values of σQjet,l , f and Qjet,l in the barrel for the subsample enriched in b, fitted in thedata and in the simulation before tuning in 1994. It should be noticed that, because of the constraintexpressed by (9), f and Qjet,l are fully anti-correlated. The first quoted error corresponds to the analysedstatistics and the other, in the case of data, to systematics

σQjet,l f in % Qjet,l

µ sample e sample µ sample e sampleData .2842 ± .0004 ± .0021 68.4 ± .6 ± .6 70.2 ± .8 ± .6 .099 ∓ .003 ∓ .003 .098 ∓ .004 ∓ .003Sim. .2894 ± .0003 69.3 ± .4 71.1 ± .4 .103 ∓ .002 .101 ∓ .002

changes found in AbbFB and Acc

FB were taken conservativelyas systematic errors (cf. Sect. 7).

5 Use of the jet charge information.

The jet charge measured in the event hemisphere, oppositeto the lepton, provides an additional information on thecharge of the parton from which the lepton originates. Thisinformation is particularly relevant for events with a lowpT lepton to be still able to distinguish between b → l−and b → c → l+ and for events with a high pT lepton to tagB0B0 oscillations. The jet charge was built by means of amomentum-weighted (pi) average of the charges (qi) of thecharged particles in the hemisphere opposite to the lepton:

Qopp =∑

hem qi|−→pi · −→T |K∑

hem |−→pi · −→T |K

with the event divided into two hemispheres by a planeperpendicular to the thrust axis

−→T .

With this definition the information coming from thetracks in the lepton hemisphere was not used in order toavoid the strong bias in the topology due to the presenceof a lepton. Based on the work presented in [12] K = 0.8was chosen to optimise the b/b separation. We restrictedthe use of the jet charge to the events with the thrust axisin the barrel (|cos θT | < 0.7) and belonging to the leptonsubsample enriched in b (bin III according to the definitiongiven in Sect. 4).

The distribution of the total event jet charge in thehadronic decays of the Z turned out to be systematicallydisplaced from zero (∼ +0.01), due to the hadronic inter-actions of particles inside the detector. It was checked thatthis shift was independent of the event flavour in each b-tagbin and is corrected for, separately in the data and in thesimulation, as a function of the thrust axis of the event.After this correction it was possible to treat in a consis-tent way positive and negative leptons, by using, as b/bdiscriminating variable, the product of the lepton chargetimes the opposite jet charge, Q�×Qopp. For a pure sampleof leptons coming from Z → bb decays, Q� × Qopp has aGaussian distribution centred at negative (positive) valuesin case of right (wrong) sign correlation between the leptonand the b parton from the opposite hemisphere. In the fol-lowing this central value will be quoted as ±Qjet,l and thewidth of the Gaussian as σQjet,l

. After normalisation bythe total number of leptons, the integral of the Gaussian

with the negative mean will be quoted as f , the integralof the other Gaussian being then equal to 1 − f .

A procedure of self calibration of Q� × Qopp with thedata was used so as not to rely on the simulation for thejet charge description. It also allowed the fraction f to bemore independent of the precise knowledge of the B0B0

mixing or of the branching fractions for the direct (b → �−)and cascade (b → c → �+) semileptonic decays.

The first step of the jet charge self calibration consistedin the tuning of the simulation in order to reproduce thetotal event jet charge distribution measured in data. Thetotal event jet charge measured in the full sample of b-tagged hadronic decays could be used. This distributiongives a direct estimate of σQjet,l

[12].As a second step the values of f and Qjet,l were ob-

tained by a double Gaussian fit of Q� × Qopp in the data.This has been done for each year for muon and electronseparately, after subtracting the background predicted bythe simulation. The statistical sensitivity of the fit was im-proved by reducing the number of fitted parameters usingthe following constraint:

〈Q� × Qopp〉 = (1–2f)Qjet,l. (9)

This constraint is derived from the definition of the twoGaussian distributions introduced above.

Subsequently the jet charge values in the simulationwere corrected to reproduce the measured distribution ofmean, Qjet,l, and width, σQjet,l

. Moreover, in each leptonsubsample, the events were re-weighted in order to repro-duce the fitted value of the fraction of right sign leptons,f . After this calibration the simulation describes the datacorrectly as can be seen in Fig. 2; event sub-samples en-riched, by kinematical cuts, in leptons from different originlike b → l− in the high pT region or b → c → l+ in the lowpT one, are well described even if they have quite differentvalues for 〈Q� × Qopp〉. Figure 2 gives a good consistencycheck of the overall simulation tuning regarding the leptonsample composition.

There are two sources of uncertainty related to the jetcharge self calibration method (see Table 6) :

– the σQjet,l, f and Qjet,l are measured with a statistical

uncertainty in the simulation and in the data,– the σQjet,l

, f and Qjet,l values are extracted from thedata after subtraction of the uds and c contamination.This subtraction, as it relies on estimates from the sim-ulation, induces systematic errors.These errors have been estimated using samples en-

riched in uds or c events, corresponding to the b-tagged


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Fig. 2. Jet charge distribution for the full muon sample. The muon candidates have pT < 1.3 GeV/c and p < 7 GeV/c (left) andpT > 1.3 GeV/c (right) corresponding to samples enriched in b → c → µ+ or b → µ− events respectively

events in bins (I) or (II). In such samples any difference inthe event charge or jet charge distributions between dataand the tuned simulation was entirely attributed to an im-perfect description in the simulation of the uds or c events.Using a new description of the event or jet charge for udsor c events to fix these differences, new values of σQjet,l

or f and Qjet,l were then estimated. The biggest changesin σQjet,l

, f and Qjet,l observed have been considered assystematic errors.

6 The fit of the asymmetries

The AbbFB and Acc

FB asymmetries were extracted from aminimum χ2 fit to the observed charge asymmetry, Aobs,i

FB ,defined as:

Aobs,iFB =

N−(i) − N+(i)N−(i) + N+(i)

where N+(i) and N−(i) are the numbers of events withan identified lepton in the i-th bin with, respectively, apositive and a negative electrical charge.

Four variables were used for binning the sample: cos θT ,which accounted for the polar angle dependence of theasymmetries, and three multivariate classification parame-ters, chosen to have bins enriched with leptons from a singleorigin. These last three parameters allowed the statisticalerrors of the Abb

FB and AccFB measurements to be reduced.

6.1 The multivariate parameters

The observables entering the multivariate parameters,whose values depend on the origin of the lepton candi-dates, were chosen to be:

– the transverse (pT ) and longitudinal (pL) momenta ofthe lepton;

– the event b-tagging, ηEVT;– the product of the lepton charge times the jet charge

of the opposite hemisphere, Q� × Qopp.Starting from these observables a multivariate tagging

of the lepton origin was built by considering four classes:1. br : leptons from b hadron decays in Z → bb events with

the right sign correlation (same sign) with respect tothe primary b quark;

2. bw : leptons from b hadron decays in Z → bb eventswith the wrong sign correlation (opposite sign) withrespect to the primary b quark;

3. c : prompt leptons from c decays in Z → cc;4. bkg : other processes (misidentified hadrons, leptons

from light hadron decay, electron and positron fromphoton conversion and leptons from heavy flavourhadron decays where the heavy flavour quarks wereproduced by gluon splitting).The sign correlation mentioned here refers to the one

between the lepton charge and the b/b flavour at produc-tion and therefore it includes possible effects due to B0B0

mixing (cf. Sect. 6.3 for a more extended discussion on themixing). The probability densities ppT ,pL

k and pbtag,jet−chk

of observing a set of (pT , pL) and (ηEVT, Q� × Qopp) val-ues for a lepton from the class k were computed by usingtwo-dimensional distributions from the tuned simulation.A likelihood ratio Pk was built to estimate the probabilitycorresponding to a given set of values within a class:

Pk =NkppT ,pL

k pbtag,jet−chk

Σk′Nk′ppT ,pL

k′ pbtag,jet−chk′

where Nk (Nk′) is the total number of leptons from theclass k (k′). The scaling of the likelihood ratio by Nk takes


into account the relative weights of each class. Neglectingsome of the correlations between the observables, such adefinition identifies Pk as the fraction of lepton candidateswith a given set of pT , pL, ηEVT and Q� × Qopp belongingto the class k.

This technique, used for the multivariate classification,extends that in [11] by considering probabilities in twodimensions and takes into account part of the correlationsbetween pairs of observables.

In order to consider the possible improvement by takinginto account all possible correlations, an approach basedon a classification with a neural network was also tried.The results obtained were in good agreement with thosefrom the multivariate approach but had a slightly worsestatistical precision. The multivariate approach was chosenas it allowed, for the small number of observables used, asimpler control of the analysis and an optimal use of theavailable simulation statistics.

The Pbr ,Pbw and Pc distributions for muons and elec-trons are shown in Fig. 3.

6.2 Measurement of AbbFB and Acc

FB

The asymmetries AbbFB and Acc

FB were extracted from a χ2

fit to the observed asymmetries Aobs,iFB over the different

bins of the (cos θT , Pbr-Pbw

, Pc) parameter space:

χ2 = (10)

∑i

(((f i

br− f i

bw

)Abb

FB + f icA

ccFB + f i

bkgAbkg,iFB

)W i

θT−Aobs,i

FB

)2

σ2i

where:

– W iθT

= 83

1Ni

data

∑Nidata

j=1cos θj

T

1+(cos θjT )2

takes into account thedependence of the asymmetry on the polar angle;

– σi is the statistical error including contributions fromboth data (Aobs,i

FB ) and simulation (f ik,Abkg,i

FB );– f i

k are the different fractions in each bin determinedfrom the tuned simulation.

To optimise the use of the available statistics, the multi-variate variables were computed separately for the differentyears and lepton samples and all samples were merged forthe χ2 fit. The data binning in the parameter space wasdone to have the same number of events per bin, ∼ 100,∼ 180 and ∼ 150 events for

√s = 89.43 GeV, 91.22 GeV

and 92.99 GeV respectively.Due to the opposite sign in the contribution of the br

and bw classes to the b asymmetry only the difference be-tween the fractions of br and bw classes matter in practice.It’s why the equi-populated bins for the χ2 fit were definedby using the combined variable Pbr − Pbw and Pc. A pos-sible third sampling corresponding to Pbkg has been foundof marginal interest, mainly due to the closure relation onthe Pk, and has not been used for the present fit.

A sign correlation between the lepton candidate andthe parent quark can exist also for the misidentified lep-tons thus leading to non-zero values for the background

asymmetry Abkg,iFB . Furthermore, since this correlation in-

creases with the particle momentum and as a function ofb-tagging value, Abkg,i

FB must be known in each bin. To op-timise the statistical precision of the estimated Abkg,i

FB , thesame factorisation technique as in the previous analysis [3]was adopted: the simulation was only used to determinethe charge correlation between the background and the ini-tial quark in each bin, while the quark asymmetries wereset to their Standard Model expectation for background inlight quark events10 or to the fitted parameters Abb

FB, AccFB

for background in b or c events.

6.3 Effect of the B0B0 mixing

The B0B0 mixing reduces the charge correlation betweenthe initial b/b produced from the Z decay and the leptonissued from the B hadron semileptonic decay. The size ofthe change depends on the proper decay time of the Bhadron and on its type, resulting in different values of theeffective mixing in the different bins of the lepton sample,for the following reasons:– the B0

d and B0s fractions in the b sample are not the

same for direct or cascade decay leptons due to differ-ences between the D+/D0/Ds production rates fromthe different B hadrons; this introduces, for example,a variation of the effective mixing as a function of pT ;

– the use of the b-tagging biases the content of the binsin terms of proper decay time, thus introducing sizablechanges in the effective mixing;

– the sign correlation between the lepton and the jetcharge, measured in the opposite hemisphere, dependsdirectly on the mixing.The B0B0 mixing is now well measured [13]. Follow-

ing the approach developed in the LEP oscillation workinggroup [14], the simulation was tuned to reproduce the mea-sured B fractions (fB± , fB0

d, fB0

s,fBbaryon) and the time

dependence of the oscillations (∆md and ∆ms). The val-ues and the corresponding uncertainties used to implementthe B0B0 mixing in the simulation are listed in Table 7.11

With this approach, the values estimated from thetuned simulation of f i

brand f i

bwincluded the expected

amount of mixing.

6.4 Results

The measured asymmetries and the corresponding statisti-cal errors using the 1993–1995 lepton samples are listed be-low:10 The uncertainty due to the exact knowledge of these asym-metries is negligible compared with the error on the chargecorrelation itself.11 The values used come from the LEP Lifetime Working group(lifetimes), the LEP oscillation working group (fractions, ∆md

and ∆ms) and the LEP Heavy Flavour working group (χ).The lower bound value quoted for ∆ms was used (∆ms >10.6ps−1), no sensitivity to the exact value of this parameter inthe allowed domain has been observed. All these numbers aretaken from [13].


0

10000

20000

30000

40000

50000

60000

70000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

DELPHI

multivariate b → µ right sign

Num

ber

of m

uon

cand

idat

es

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

DELPHI

multivariate b → e right sign

Num

ber

of e

lect

ron

cand

idat

es

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

DELPHI

multivariate b → µ wrong sign

Num

ber

of m

uon

cand

idat

es

0

10000

20000

30000

40000

50000

60000

70000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

DELPHI

multivariate b → e wrong sign

Num

ber

of e

lect

ron

cand

idat

es

0

10000

20000

30000

40000

50000

60000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

DELPHI

multivariate c → µ

Num

ber

of m

uon

cand

idat

es

0

10000

20000

30000

40000

50000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

DELPHI

multivariate c → e

Num

ber

of e

lect

ron

cand

idat

es

Fig. 3. Likelihood ratio Pbr (up), Pbw (middle) and Pc (bottom) distributions for muons (left) and electrons (right) for all years


Table 7. Different systematics in the χ2 fit of the 1993–1995 DELPHI lepton sampleat

√s = 91.22 GeV. The systematic errors at

√s = 89.43 GeV were estimated to be

± 0.0024 for AbbFB and ± 0.0046 for Acc

FB, and at√

s = 92.99 GeV the correspondingvalues were ± 0.0024 and ± 0.0070

Parameters Central Variations ∆ AbbFB ∆ Acc

FB

value applied Peak Peak

Br(b → l) 0.1056 ± 0.0026 ∓ 0.00048 ± 0.00062

Br(b → c → l) 0.0807 ± 0.0034 ∓ 0.00015 ∓ 0.00080

Br(b → c → l) 0.0162 +0.0044−0.0036 ± 0.00017 ± 0.00180

Br(b → τ → l) 0.00419 ± 0.00055 ∓ 0.00001 ± 0.00027

Br(b → J/ψ → l) 0.00072 ± 0.00006 ± 0.00005 ± 0.00002

Br(c → l) 0.0990 ± 0.0037 ± 0.00036 ∓ 0.00182

Γbb/Γhad 0.21644 ± 0.00075 ∓ 0.00007 ± 0.00007

Γcc/Γhad 0.1671 ± 0.0048 ± 0.00034 ∓ 0.00130

g → bb 0.00254 ± 0.00051 ± 0.00012 ± 0.00005

g → cc 0.0296 ± 0.0038 ± 0.00012 ± 0.00001

〈XE〉B 0.702 ± 0.008 ∓ 0.00016 ∓ 0.00019

〈XE〉D∗ in cc events 0.510 ± 0.0094 ± 0.00047 ∓ 0.00046

b decay model [15] ACCMM ISGWISGW∗∗ ∓ 0.00065 ∓ 0.00111

c decay model [15] CL1 CL2CL3 ± 0.00098 ∓ 0.00116

Total : Lepton Sample ± 0.0015 ± 0.0035

τB0d

1.548 ps ± 0.032 ± 0.00005 ± 0.00004

τB± 1.653 ps ± 0.028 ∓ 0.00002 ∓ 0.00003

τB0s

1.493 ps ± 0.062 ∓ 0.00025 ± 0.00001

τBbaryon 1.208 ps ± 0.051 ± 0.00004 ∓ 0.00002

〈τBhadron〉 1.564 ps ± 0.014 ± 0.00005 ± 0.00000

τB±/τB0d

1.062 ± 0.029 ± 0.00016 ± 0.00001

fb−baryon 0.115 ± 0.020 ∓ 0.00006 ± 0.00010

fB0s

0.117 ± 0.030 ± 0.00051 ± 0.00001

∆md 0.472 ps−1 ± 0.017 ∓ 0.00003 ± 0.00008

χ 0.1177 ± 0.0055 ± 0.00082 ± 0.00001

Total : Mixing ± 0.0010 ± 0.0001

Misidentified e see text ± 0.00011 ± 0.00021

Converted gammas in e sample ± 10 % ∓ 0.00019 ∓ 0.00050

Misidentified µ see text ± 0.00025 ± 0.00085

µ from π,K decay ± 15% ± 0.00027 ± 0.00092

background asymmetry ± 40 % ∓ 0.00076 ± 0.00421

pT reweight of background see text ∓ 0.00007 ± 0.00021

Energy flow correction see text ∓ 0.00009 ∓ 0.00020

Total : Lepton identification and pT measurement ± 0.0009 ± 0.0044

b-tag tuning see text ∓ 0.00009 ± 0.00028

Merging for Nint = 2 see text + 0.00061 − 0.00082

Jet charge stat see text ∓ 0.00052 ± 0.00070

Jet charge BKG subtraction see text ∓ 0.00069 ± 0.00084

Total : b-tag and jet charge calibration ± 0.0011 ± 0.0014

Total ± 0.0023 ± 0.0058


0

0.02

0.04

0.06

0.08

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

DELPHI

cosθT

Obs

erve

d A

sym

met

ry

Fig. 4. Observed AobsFB asymmetry at peak energy as a function

of cos θT for a data subsample enriched in b with the right sign(Pbr −Pbw > 0.6). The result of the fit is shown as a dashed line

At√

s = 89.43 GeV:

AbbFB = 0.066 ± 0.022 (stat)

AccFB = 0.030 ± 0.035 (stat)

with a correlation of 0.19 and χ2

ndf = 185208 , Prob(χ2)=0.87;

at√

s = 91.22 GeV:

AbbFB = 0.0958 ± 0.0061 (stat)

AccFB = 0.0585 ± 0.0098 (stat)


ndf = 14161453 , Prob(χ2)=0.75;

at√

s = 92.99 GeV:

AbbFB = 0.109 ± 0.018 (stat)

AccFB = 0.108 ± 0.028 (stat)


ndf = 204208 , Prob(χ2)=0.57.

The result of the fit for a data subsample is presentedwith the observed asymmetry in Fig. 4.

7 Systematic effects

The systematics from the different sources are listed in Ta-ble 7.

Lepton sampleTo estimate the systematics due to uncertainties in decaybranching ratios and spectra, the standard prescription ofthe LEP Heavy Flavour Working group was used [15]. Thecentral values and variation were taken from [13] and [16] .The b and c decay model and their associated changes weretaken from [15]. The variation considered for the leptonidentification was described in Sect. 3.MixingThe combined effects of the uncertainties quoted in Table 7for the parameters having a direct effect on the B0B0

mixing description give a precision of ± 0.014 on fB0s

and± 0.005 on χ [13] following the method described in [14].To take into account correctly the impact of the differentsources of uncertainty on the B0B0 mixing description,each of these measurements was varied within its error.Background asymmetryIt should be noted that, while the observed “BackgroundAsymmetry” systematic in Acc

FB comes from uds events,for Abb

FB, the main source is the charge correlation betweena fake lepton and the initial quark in b events themselves.Even if the charge correlation between the fake leptonsand the initial quark of the corresponding event has beentaken from the simulation, this correlation can be studiedin the data using the Q� × Qopp observable. Such chargecorrelation in b events is visible for example in the leftplot of Fig. 2. In this case the ∼ 10 % of the differencein the amount of background between the two extremeQ� × Qopp bins, originates from b → c → s → K−, wherethe K± is misidentified as a muon and behaves like a rightsign lepton.

From these studies a conservative change of ±20% inthe charge correlation, corresponding to ±40% variationin the background asymmetry, has been considered for thesystematics. Such a change increases by 1.8 the χ2 of thedata/simulation comparison computed in the left plot ofFig. 2 corresponding to b-tag events enriched in fake leptonsby a p,pT cut. The same comparison done in the anti-b-tagbin (I), enriched in fake leptons from uds events, gives anincrease of 1.3 in the χ2.

The AccFB systematics are dominated by the contribu-

tion of the background asymmetry. This underlines thedifficulty to separate the c events from the other flavours(see Fig. 3). The size of this systematic follows the variationof the asymmetries with

√s and explains most of the 50%

increase in the AccFB systematics between

√s = 89.43 GeV

and√

s = 92.99 GeV.Energy flow, pT reconstructionDue to a slightly worse energy reconstruction in the data, a1–2 % shift in the jet energy distribution between data andsimulation has been observed. This difference could havedifferent effects on the asymmetries depending on its exactsource (overall correction or sub-sample of charged/neutraltrack correction). The different possible sources were con-sidered and the biggest effect observed was taken as thesystematic error.In the anti-b-tagged sample the shape of the pT distribu-tion of the lepton candidate was not correctly describedby the simulation. This effect is known to be common to


all tracks from hadronisation in the tuned DELPHI simu-lation [8]. The full size of the correction estimated in theanti-b-tagged sample, was considered as a systematic er-ror. It corresponds to changes ∼ ±5% of the number ofmisidentified leptons as a function of pT .b-taggingTo take into account the effect of changes in the fractionrq, defined in (5), the b-tagging corrections, δ

(i)q , were re-

computed for each of the changes quoted in Table 7. Forthis reason all the quoted systematics also include possiblevariations induced by changes in the b-tagging tuning.

The systematic named b-tag tuning in Table 7, cor-responds to the effects of the finite simulation statisticsused to estimate the sample composition in the differentb-tagged intervals and to the sensitivity to the correlationρ(i)q as described in Sect. 4.

The full difference between the results obtained for thetwo considered Nint choices (see Sect. 4) is quoted as Merg-ing for Nint = 2.Jet chargeA jet charge tuning was performed for each computation ofthe systematics. For this reason, possible systematic errorsin the jet charge tuning arising from the variation of a givenparameter defined in Table 7 are included in the systematicerrors of this parameter.

The systematic named Jet charge stat in Table 7, corre-sponds to the effect of the finite statistics used to estimateσQjet,l

, f and Qjet,l. The systematic named Jet charge BKGsubtraction in Table 7, is associated to the uncertainty onthe jet charge description of non b events (see Sect. 5).

8 QCD corrections to themeasured asymmetries

The QCD corrections applied to the asymmetries wereobtained following the prescription given in [17]. This ap-proach takes into account changes in these corrections dueto experimental bias, like the suppression of events withan energetic gluon induced by the cut on the momentumof the selected leptons. The simulation sample, with anenlarged asymmetry 12 to improve the statistical precisionof the study, was used to estimate such a bias. The rel-ative change in the corrections due to experimental biaswas estimated for this analysis to be 0.58 ± 0.08 for Abb

FBand 0.42 ± 0.12 for Acc

FB. These scale factors were appliedto the theoretical QCD corrections 13 and give the follow-ing QCD corrections : AnoQCD,xx

FB = AxxFB/(1 − Cx) with

Cb = 0.0205 ± 0.0046 and Cc = 0.0172 ± 0.0057 .

12 A value of 0.73 was used, slightly smaller than the maximalasymmetry allowed (0.75) to avoid the boundary problem andconsequent asymmetric errors in the result of the fit13 Chad,T

b = 0.0354 ± 0.0063 and Chad,Tc = 0.0413 ± 0.0063 as

recommended in [16].

-0.05

0

0.05

0.1

0.15

89 90 91 92 93 94√s [GeV]

AF

B(√

s)

DELPHI

AFB

b

AFB

c

Fig. 5. Measured values of AbbFB and Acc

FB at different√

s com-pared to the Standard Model predictions for mt = 175 GeV/c2

and mH = 300 GeV/c2 (To avoid the overlap of the results atpeak-2 and peak+2, the Abb

FB and AccFB points have been shifted

respectively by +0.02 GeV and -0.02 GeV.)

9 Conclusion

The heavy flavour asymmetry measurements presented inthis paper, obtained with the 1993–1995 DELPHI data,can be combined with the 1991–1992 DELPHI measure-ments of Abb

FB and AccFB using leptons [3]. All asymmetry

measurements were QCD corrected before averaging andthe 1991–1992 DELPHI measurements were corrected tothe same inputs (branching ratios and mixing) as the onesused in this paper.

Taking into account the correlations between the dif-ferent systematic sources, the combined results are:

AbbFB = 0.067 ± 0.022 (stat) ± 0.002 (syst)

at√

s = 89.43 GeVAbb

FB = 0.1004 ± 0.0056 (stat) ± 0.0025 (syst)at

√s = 91.26 GeV

AbbFB = 0.112 ± 0.018 (stat) ± 0.002 (syst)

at√

s = 92.99 GeV

AccFB = 0.031 ± 0.035 (stat) ± 0.005 (syst)

at√

s = 89.43 GeVAcc

FB = 0.0631 ± 0.0093 (stat) ± 0.0065 (syst)at

√s = 91.26 GeV

AccFB = 0.110 ± 0.028 (stat) ± 0.007 (syst)

at√

s = 92.99 GeV.

Figure 5 shows the energy dependence of AbbFB and Acc

FBcompared to the Standard Model prediction.


Following the general procedure described in [15], theseresults have been corrected to the Z pole; the energy shiftfrom

√s to mZ (for

√s = 89.43 GeV: +0.0391, +0.0997; for√

s = 91.26 GeV: −0.0013,−0.0034 ; for√

s = 92.99 GeV:−0.0260, −0.0664), the effects of the initial state radia-tion (+0.0041,+0.0104) and γ exchange and γ/ Z inter-ference (−0.0003,−0.0008) have been corrected by addingthe quoted numbers respectively to Abb

FB and AccFB. The

averages of the pole asymmetries obtained after these cor-rections are :

A0,bFB = 0.1021 ± 0.0052 (stat) ± 0.0024 (syst)

A0,cFB = 0.0728 ± 0.0086 (stat) ± 0.0063 (syst)

in agreement with other DELPHI and LEP measurements[2, 18,19].

The total correlation between A0,bFB and A0,c

FB is +7%,with a correlation of +22% and -36% for the statisticaland systematic errors respectively.

The effective value of the weak mixing angle derivedfrom these measurements is

sin2 θleptW,eff = 0.23170 ± 0.00097.

Acknowledgements. We are greatly indebted to our technicalcollaborators, to the members of the CERN-SL Division forthe excellent performance of the LEP collider, and to the fund-ing agencies for their support in building and operating theDELPHI detector. We acknowledge in particular the support ofAustrian Federal Ministry of Education, Science and Culture,GZ 616.364/2-III/2a/98, FNRS–FWO, Flanders Institute toencourage scientific and technological research in the industry(IWT), Federal Office for Scientific, Technical and Culturalaffairs (OSTC), Belgium, FINEP, CNPq, CAPES, FUJB andFAPERJ, Brazil, Czech Ministry of Industry and Trade, GACR 202/99/1362, Commission of the European Communities(DG XII), Direction des Sciences de la Matiere, CEA, France,Bundesministerium fur Bildung, Wissenschaft, Forschung undTechnologie, Germany, General Secretariat for Research andTechnology, Greece, National Science Foundation (NWO) andFoundation for Research on Matter (FOM), The Netherlands,Norwegian Research Council, State Committee for ScientificResearch, Poland, SPUB-M/CERN/PO3/DZ296/2000, SPUB-M/CERN/PO3/DZ297/2000 and 2P03B 104 19 and 2P03B 6923(2002–2004) JNICT-Junta Nacional de Investigacao Cientı-fica e Tecnologica, Portugal, Vedecka grantova agentura MS SR,Slovakia, Nr. 95/5195/134, Ministry of Science and Technologyof the Republic of Slovenia, CICYT, Spain, AEN99-0950 andAEN99-0761, The Swedish Natural Science Research Council,Particle Physics and Astronomy Research Council, UK, De-partment of Energy, USA, DE-FG02-01ER41155, EEC RTNcontract HPRN-CT-00292-2002.

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