b

Physics Letters B 576 (2003) 29–42

www.elsevier.com/locate/physlet

A measurement of the branching fractions of theb-quarkinto charged and neutralb-hadrons

DELPHI Collaboration

J. Abdallahab, P. Abreuy, W. Adambd, P. Adzicn, T. Albrechtt, T. Alderweireldb,c,d,R. Alemany-Fernandezl, T. Allmendingert, P.P. Allportz, U. Amaldiaf, N. Amapaneaw,S. Amatoba, E. Anashkinam, A. Andreazzaae, S. Andringay, N. Anjosy, P. Antilogusab,

W.-D. Apelt, Y. Arnoudq, S. Askac, B. Asmanav, J.E. Augustinab, A. Augustinusl,P. Baillonl, A. Ballestreroax, P. Bambadew, R. Barbierad, D. Bardins, G. Barkert,

A. Baroncelliap, M. Battaglial, M. Baubillierab, K.-H. Becksbf, M. Begallih,i,j ,A. Behrmannbf, E. Ben-Haimw, N. Benekosai, A. Benvenutig, C. Beratq,

M. Berggrenab, L. Berntzonav, D. Bertrandb,c,d, M. Besanconaq, N. Bessonaq,D. Blochm, M. Blomah, M. Bluj be, M. Bonesiniaf, M. Boonekampaq, P.S.L. Boothz,G. Borisovx, O. Botnerbb, B. Bouquetw, T.J.V. Bowcockz, I. Boykos, M. Brackoat,au,R. Brennerbb, E. Brodetal, P. Bruckmanu, J.M. Brunetk, L. Buggeaj, P. Buschmannbf,

M. Calvi af, T. Camporesil, V. Canaleao, F. Carenal, N. Castroy, F. Cavallog,M. Chapkinas, Ph. Charpentierl, P. Checchiaam, R. Chiericil , P. Chliapnikovas,J. Chudobal, S.U. Chungl, K. Ciesliku, P. Collinsl, R. Contrip, G. Cosmew,

F. Cossuttiay,az, M.J. Costabc, B. Crawleya, D. Crennellan, J. Cuevasak, J. D’Hondtb,c,d,J. Dalmauav, T. Da Silvaba, W. Da Silvaab, G. Della Riccaay,az, A. De Angelisay,az,W. De Boert, C. De Clercqb,c,d, B. De Lottoay,az, N. De Mariaaw, A. De Minam,

L. de Paulaba, L. Di Ciaccioao, A. Di Simoneap, K. Dorobabe, J. Dreesbf,l , M. Drisai,G. Eigenf, T. Ekelofbb, M. Ellert bb, M. Elsingl, M.C. Espirito Santoy, G. Fanourakisn,D. Fassouliotisn,e, M. Feindtt, J. Fernandezar, A. Ferrerbc, F. Ferrop, U. Flagmeyerbf,H. Foethl, E. Fokitisai, F. Fulda-Quenzerw, J. Fusterbc, M. Gandelmanba, C. Garciabc,

Ph. Gavilletl, E. Gazisai, R. Gokielil,be, B. Golobat,au, G. Gomez-Ceballosar,P. Goncalvesy, E. Grazianiap, G. Grosdidierw, K. Grzelakbe, J. Guyan, C. Haagt,

A. Hallgrenbb, K. Hamacherbf, K. Hamiltonal, S. Haugaj, F. Haulert, V. Hedbergac,M. Hennecket, H. Herrl, J. Hoffmanbe, S.-O. Holmgrenav, P.J. Holtl, M.A. Houldenz,K. Hultqvistav, J.N. Jacksonz, G. Jarlskogac, P. Jarryaq, D. Jeansal, E.K. Johanssonav,

P.D. Johanssonav, P. Jonssonad, C. Joraml, L. Jungermannt, F. Kapustaab,S. Katsanevasad, E. Katsoufisai, G. Kernelat,au, B.P. Kersevanl,at,au, U. Kerzelt,

0370-2693/$ – see front matter 2003 Elsevier B.V. All rights reserveddoi:10.1016/j.physletb.2003.09.070

.

30 DELPHI Collaboration / Physics Letters B 576 (2003) 29–42

A. Kiiskinenr, B.T. Kingz, N.J. Kjaerl, P. Kluit ah, P. Kokkiniasn, C. Kourkoumelise,O. Kouznetsovs, Z. Krumsteins, M. Kucharczyku, J. Lamsaa, G. Lederbd, F. Ledroitq,L. Leinonenav, R. Leitnerag, J. Lemonneb,c,d, V. Lepeltierw, T. Lesiaku, W. Liebigbf,

D. Liko bd, A. Lipniackaav, J.H. Lopesba, J.M. Lopezak, D. Loukasn, P. Lutzaq,L. Lyonsal, J. MacNaughtonbd, A. Malekbf, S. Maltezosai, F. Mandlbd, J. Marcoar,R. Marcoar, B. Marechalba, M. Margoniam, J.-C. Marinl, C. Mariottil , A. Markoun,

C. Martinez-Riveroar, J. Masiko, N. Mastroyiannopoulosn, F. Matorrasar,C. Matteuzziaf, F. Mazzucatoam, M. Mazzucatoam, R. Mc Nultyz, C. Meroniae,

W.T. Meyera, E. Miglioreaw, W. Mitaroff bd, U. Mjoernmarkac, T. Moaav, M. Mocht,K. Moenigl,1, R. Mongep, J. Montenegroah, D. Moraesba, S. Morenoy, P. Morettinip,U. Muellerbf, K. Muenichbf, M. Muldersah, L. Mundimh,i,j , W. Murrayan, B. Murynv,

G. Myattal, T. Myklebustaj, M. Nassiakoun, F. Navarriag, K. Nawrockibe,R. Nicolaidouaq, M. Nikolenkos,m, A. Oblakowska-Muchav, V. Obraztsovas,

A. Olshevskis, A. Onofrey, R. Oravar, K. Osterbergr, A. Ouraouaq, A. Oyangurenbc,M. Paganoniaf, S. Paianog, J.P. Palaciosz, H. Palkau, Th.D. Papadopoulouai, L. Papel,

C. Parkesaa, F. Parodip, U. Parzefalll, A. Passeriap, O. Passonbf, L. Peraltay,V. Perepelitsabc, A. Perrottag, A. Petrolinip, J. Piedraar, L. Pieriap, F. Pierreaq,M. Pimentay, E. Piottol, T. Podobnikat,au, V. Poireaul, M.E. Polh,i,j , G. Poloku,

P. Poropatay,az,2, V. Pozdniakovs, N. Pukhaevab,c,d,s, A. Pulliaaf, J. Rameso, L. Ramlert,A. Readaj, P. Rebecchil, J. Rehnt, D. Reidah, R. Reinhardtbf, P. Rentonal, F. Richardw,J. Ridkyo, M. Riveroar, D. Rodriguezar, A. Romeroaw, P. Roncheseam, E. Rosenberga,P. Roudeauw, T. Rovellig, V. Ruhlmann-Kleideraq, D. Ryabtchikovas, A. Sadovskys,L. Salmir, J. Saltbc, A. Savoy-Navarroab, U. Schwickerathl, A. Segaral, R. Sekulinan,M. Siebelbf, A. Sisakians, G. Smadjaad, O. Smirnovaac, A. Sokolovas, A. Sopczakx,

R. Sosnowskibe, T. Spassovl, M. Stanitzkit, A. Stocchiw, J. Straussbd, B. Stuguf,M. Szczekowskibe, M. Szeptyckabe, T. Szumlakv, T. Tabarelliaf, A.C. Taffardz,F. Tegenfeldtbb, J. Timmermansah, L. Tkatchevs, M. Tobinz, S. Todorovovao,B. Tomey, A. Tonazzoaf, P. Tortosabc, P. Travniceko, D. Treillel, G. Tristramk,M. Trochimczukbe, C. Tronconae, M.-L. Turlueraq, I.A. Tyapkins, P. Tyapkins,

S. Tzamariasn, V. Uvarovas, G. Valentig, P. Van Damah, J. Van Eldikl,A. Van Lysebettenb,c,d, N. van Remortelb,c,d, I. Van Vulpenl, G. Vegniae, F. Velosoy,

W. Venusan, P. Verdierad, V. Verzi ao, D. Vilanovaaq, L. Vitaleay,az, V. Vrbao,H. Wahlenbf, A.J. Washbrookz, C. Weisert, D. Wickel, J. Wickensb,c,d, G. Wilkinsonal,

M. Winterm, M. Witeku, O. Yushchenkoas, A. Zalewskau, P. Zalewskibe,D. Zavrtanikat,au, V. Zhuravlovs, N.I. Zimin s, A. Zintchenkos, M. Zupann

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

c IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgiumd Faculté des Sciences, Université de l’Etat Mons, Av. Maistriau 19, B-7000 Mons, Belgium

DELPHI Collaboration / Physics Letters B 576 (2003) 29–42 31

ic,

zil

e Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greecef Department of Physics, University of Bergen, Allégaten 55, NO-5007 Bergen, Norway

g Dipartimento di Fisica, Università di Bologna and INFN, Via Irnerio 46, IT-40126 Bologna, Italyh Centro Brasileiro de Pesquisas Físicas, rua Xavier Sigaud 150, BR-22290 Rio de Janeiro, Brazil

i Departamento de Física, Pont. Universidad Católica, C.P. 38071, BR-22453 Rio de Janeiro, Brazilj Institute de Física, Universidad Estadual do Rio de Janeiro, rua São Francisco Xavier 524, Rio de Janeiro, Brazil

k Collège de France, Laboratoire de Physique Corpusculaire, IN2P3-CNRS, FR-75231 Paris cedex 05, Francel CERN, CH-1211 Geneva 23, Switzerland

m Institut de Recherches Subatomiques, IN2P3-CNRS/ULP-BP20, FR-67037 Strasbourg cedex, Francen Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece

o FZU, Institute of Physics of the C.A.S. High Energy Physics Division, Na Slovance 2, CZ-180 40, Praha 8, Czech Republicp Dipartimento di Fisica, Università di Genova and INFN, Via Dodecaneso 33, IT-16146 Genova, Italy

q Institut des Sciences Nucléaires, IN2P3-CNRS, Université de Grenoble 1, FR-38026 Grenoble cedex, Francer Helsinki Institute of Physics, P.O. Box 64, University of Helsinki, FIN-00014 Helsinki, Finland

s Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, RU-101 000 Moscow, Russian Federationt Institut für Experimentelle Kernphysik, Universität Karlsruhe, Postfach 6980, DE-76128 Karlsruhe, Germany

u Institute of Nuclear Physics,Ul. Kawiory 26a, PL-30055 Krakow, Polandv Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, PL-30055 Krakow, Poland

w Université de Paris-Sud, Laboratoire de l’Accélérateur Linéaire, IN2P3-CNRS, Bât. 200, FR-91405 Orsay cedex, Francex School of Physics and Chemistry, University of Lancaster, Lancaster LA1 4YB, UK

y LIP, IST, FCUL, Av. Elias Garcia, 14-1, PT-1000 Lisboa codex, Portugalz Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK

aaDepartment of Physics and Astronomy, Kelvin Building, University of Glasgow, Glasgow G12 8QQ, UKab LPNHE, IN2P3-CNRS, Université de Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, FR-75252 Paris cedex 05, France

ac Department of Physics, University of Lund, Sölvegatan 14, SE-223 63 Lund, Swedenad Université Claude Bernard de Lyon, IPNL, IN2P3-CNRS, FR-69622 Villeurbanne cedex, France

aeDipartimento di Fisica, Università di Milano and INFN-MILANO, Via Celoria 16, IT-20133 Milan, Italyaf Dipartimento di Fisica, Università di Milano-Bicocca and INFN-MILANO, Piazza della Scienza 2, IT-20126 Milan, Italy

ag IPNP of MFF, Charles University, Areal MFF, V Holesovickach 2, CZ-180 00 Praha 8, Czech Republicah NIKHEF, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands

ai National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greeceaj Physics Department, University of Oslo, Blindern, NO-0316 Oslo, Norway

ak Departamento de la Fisica, Universidad Oviedo, Avda. Calvo Sotelo s/n, ES-33007 Oviedo, Spainal Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK

am Dipartimento di Fisica, Università di Padova and INFN, Via Marzolo 8, IT-35131 Padua, Italyan Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, UK

ao Dipartimento di Fisica, Università di Roma II and INFN, Tor Vergata, IT-00173 Rome, Italyap Dipartimento di Fisica, Università di Roma III and INFN, Via della Vasca Navale 84, IT-00146 Rome, Italy

aq DAPNIA/Service de Physique des Particules, CEA-Saclay, FR-91191 Gif-sur-Yvette cedex, Francear Instituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros s/n, ES-39006 Santander, Spain

as Institute for High Energy Physics, Serpukov P.O. Box 35, Protvino (Moscow region), Russian Federationat J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia and Laboratory for Astroparticle Physics, Nova Gorica Polytechn

Kostanjeviska 16a, SI-5000 Nova Gorica, Sloveniaau Department of Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia

av Fysikum, Stockholm University, Box 6730, SE-113 85 Stockholm, Swedenaw Dipartimento di Fisica Sperimentale, Università di Torino and INFN, Via P. Giuria 1, IT-10125 Turin, Italy

ax INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Università di Torino, Via P. Giuria 1, IT-10125 Turin, Italyay Dipartimento di Fisica, Università di Trieste and INFN, Via A. Valerio 2, IT-34127 Trieste, Italy

az Istituto di Fisica, Università di Udine, IT-33100 Udine, Italyba Universidad Federal do Rio de Janeiro, C.P. 68528 Cidade Universidad, Ilha do Fundão, BR-21945-970 Rio de Janeiro, Bra

bb Department of Radiation Sciences, University of Uppsala, P.O. Box 535, SE-751 21 Uppsala, Swedenbc IFIC, Valencia-CSIC, and D.F.A.M.N., Universidad de Valencia, Avda. Dr. Moliner 50, ES-46100 Burjassot (Valencia), Spain

bd Institut für Hochenergiephysik, Österr. Akad. d. Wissensch., Nikolsdorfergasse 18, AT-1050 Vienna, Austriabe Institute for Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland

bf Fachbereich Physik, University of Wuppertal, Postfach 100 127, DE-42097 Wuppertal, Germany2

Received 21 July 2003; accepted 8 September 2003

32 DELPHI Collaboration / Physics Letters B 576 (2003) 29–42

thee weakly-taken inn

Editor: M. Doser

Abstract

The production fractions of charged and neutralb-hadrons inb-quark events fromZ0 decays have been measured withDELPHI detector at LEP. An algorithm has been developed, based on a neural network, to estimate the charge of thdecayingb-hadron by distinguishing its decay products from particles produced at the primary vertex. From the datathe years 1994 and 1995, the fraction ofb-quarks fragmenting into positively charged weakly-decayingb-hadrons has beemeasured to be:

f+ = (42.09± 0.82(stat)± 0.89(syst)

)%.

Subtracting the rates for chargedΞ+b andΩ+

b baryons gives the production fraction ofB+ mesons:

fBu = (40.99± 0.82(stat)± 1.11(syst)

)%.

2003 Elsevier B.V. All rights reserved.

ndre-

seta--

oneess,hisar-

ain

as

en,

nd

ac-re

ac-here-

f-nic[3]

u-

d-

y.

1. Introduction

The branching fractions of theb-quark into the dif-ferent species ofb-hadrons are an important input asource of systematic uncertainty for many measuments in the heavy flavour sector whereb-hadrons areproduced in jets, e.g., analyses onB-meson oscilla-tions or CKM elements at LEP. Furthermore, theproduction fractions give insight into the fragmention process. Sinceb-quarks at LEP are mainly produced directly in the decay of theZ0 boson, with neg-ligible contributions from later processes like glusplitting g → bb, b-hadron production fractions arsensitive to a certain step in the fragmentation procnamely the beginning of the fragmentation chain. Tis not the case for analyses investigating inclusive pticle production rates of hadrons which do not conta primary heavy quark.

The b-hadron production fractions are definedthe probability of ab- or b-quark to fragment intothe correspondingb-hadron:fBu = BR(b → B+) =BR(b → B−), fBd = BR(b → B0) = BR(b → B0),fBs = BR(b → B0

s ) = BR(b → B0s ), fb-baryon =

BR(b → anti-b-baryon) = BR(b → b-baryon). Fur-

E-mail address:stocchi@mail.cern.ch (A. Stocchi).1 Now at DESY-Zeuthen, Platanenallee 6, D-15735 Zeuth

Germany.2 Deceased.

thermore, the production fractions for charged aneutral b-hadrons are defined asf+ = BR(b →X+B ) = BR(b → X−

B ) and f 0 = BR(b → X0B) =

BR(b→ X0B), whereX+

B , X−B andX0

B stand for anypositively charged, negatively charged or neutralb-hadron, respectively. With these definitions,fBi is alsothe production fraction of theb-hadron typeBi , parti-cle or antiparticle, inbb events.

A direct measurement of these production frtions using exclusive decays is difficult, since theare many decay channels with small branching frtions having large relative uncertainties [1]. For tdetermination offBs , the inputs used are measuments of the product branching ratio BR(b → B0

s ) ·BR(B0

s → D−s l

+νX) at LEP [2], measurements othe ratiofBs /(fBu + fBd ) using events with exclusively reconstructed charm particles in semileptob-decays or double semileptonic decays from CDFand the mixing parametersχ andχd . The integratedmixing probability χ , in an unbiased sample of netral B-mesons, has contributions fromB0- andB0

s -mesons:3 χ = fBdχd + fBsχs , whereχd andχs arethe integrated mixing probabilities forB0- andB0

s -mesons. This allows the extraction offBs quite pre-cisely. The baryon rate is estimated from similar pro

3 Sinceχ is mainly measured using leptons, the ratesfBd andfBs have to be weighted by ratios of lifetimes,τBd /τB andτBs /τB ,respectively. This has been omitted in the formulae for simplicit

DELPHI Collaboration / Physics Letters B 576 (2003) 29–42 33

theicsingle pioner,

Fig. 1. Schematic picture of the production mechanism ofb-hadrons. The rates, given in percent, of hadrons primarily produced infragmentation are denoted byf ′, the ones which decay through weak interaction (indicated by dashed lines) byf . Strong and electromagnetdecays are indicated by solid and dotted arrows, respectively, together with their (expected) branching ratios (for strong decays onlyand kaon transitions have been considered). The given rates are taken from simulation (JETSET7.3 Monte Carlo model with parton showoption and parameter settings according to the DELPHI-Tuning [7]). The parameters giving the suppression ofss pairs and diquarks arerespectively,γs = P (ss)/P (uu)= P (ss)/P (dd)= 0.28 andP (qq)/P (q)= 0.1.

ionof

gese

ro-

ish

-ion-

-

ing

e

uct branching ratios, usingΛ+c l

− andΞ−l− correla-tions [3,4], and a measurement of proton productin b-hadron decays [5]. No direct measurementsfBd or fBu have been published so far. The averafor weakly-decayingb-hadrons are listed in [1]. Thfollowing assumptions are made: theb-hadron pro-duction fractions are the same inZ → bb decays atLEP and in high-pt jets at the TEVATRON,fBs +fb-baryon+ fBu + fBd = 1 andfBu = fBd . The lattertwo are applied as constraints in the averaging pcedure. The combined result isfBs = (10.6 ± 1.3)%,fb-baryon= (11.8 ± 2.0)% andfBd = fBu = (38.8 ±1.3)%.

In Fig. 1 a schematic picture of theb-hadron pro-duction process is shown. One has to distingu

between the fractions ofb-hadrons which are directly produced in the non-perturbative fragmentatprocess, denotedf ′

i in the following, and the fractions of weakly-decayingb-hadrons,fi . Strong decaysof primarily producedb-hadrons can lead tof ′

i = fi ,e.g., the presence of orbitally excitedB∗∗

s -mesons withtheir expected decaysB∗∗

s → B(∗)K have the consequencef ′

Bs> fBs , f

′Bu< fBu andf ′

Bd< fBd . How-

ever, the equalityf ′Bu

= f ′Bd

, which originates fromisospin symmetry, remains valid for weakly-decayb-hadrons (fBu = fBd ).4

4 In contrast to theD-system, the presence ofB∗-mesons doesnot change the rates of charged and neutralB-mesons, becaus

34 DELPHI Collaboration / Physics Letters B 576 (2003) 29–42

ish

aryrges a

dtaHIon

nedd

ininlytion

3,

allide

4en

lar

rndl12

re

P,

24en5ofck

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odiieents

he

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.he

the

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gedassion

chr to-of-

het 7

al--p-

For the rates of charged and neutralb-hadrons, anefficient algorithm has been developed to distingucharged particles from weakB-decays, from theirfragmentation counterparts produced at the primevent vertex. This allows an estimate of the chaof the weakly-decaying hadron to be made and thumeasurement off+ andf 0. fBu can then be extractefrom f+ with small additional uncertainties. The dataken in the years 1994 and 1995, when the DELPdetector was equipped with a double sided silicvertex detector, have been used for the analysis.

The simulation used the JETSET 7.3 model [6]with parton shower option and parameters determifrom earlier QCD studies [7], followed by a detailedetector simulation [8].

2. The DELPHI detector and event selection

The DELPHI detector is described in detailreferences [9,10]. The present analysis relies maon charged particles, measured using informaprovided by the central tracking detectors.

• The microvertex detector(VD) consists of threelayers of silicon strip detectors at radii of 6.9.0 and 10.9 cm.Rφ coordinates5 in the planeperpendicular to the beam are measured inthree layers. The first and third layers also provz information. The polar angle (θ ) coverage fora particle passing all three layers is from 4to 136. The single point precision has beestimated from real data to be about 8 µm inRφand (for charged particles crossing perpendicuto the module) about 9 µm inz.

• The inner detector (ID) consists of an innedrift chamber with jet chamber geometry a5 cylindrical layers of multiwire proportionachambers (MWPC). The jet chamber, between

their dominant decay mode isB∗ → Bγ . This is also the case foorbitally excitedB∗∗-mesons, iffB∗∗

d= fB∗∗

u, and isospin rules ar

used to calculate the dominant single pion transitions.5 In the standard DELPHI coordinate system, thez-axis is along

the electron direction, thex-axis points towards the centre of LEand they-axis points upwards. The polar angle to thez-axis isdenoted byθ , and the azimuthal angle around thez-axis byφ; theradial coordinate isR =

√x2 + y2.

and 23 cm inR and 23 and 157 in θ , consistsof 24 azimuthal sectors, each providing up toRφ points. From 1995 on, a longer ID has beoperational, with polar angle coverage from 1to 165 and replacing the MWPC by 5 layersstraw tube detectors. The precision on local traelements has been measured in muon pair evto be about 45 µm inRφ.

• The time projection chamber(TPC) is the maintracking device of DELPHI. It provides up t16 space points per particle trajectory for rabetween 40 and 110 cm and polar angles betw39 and 141. The precision on the track elemenis about 150 µm inRφ and about 600 µm inz.For particle identification a measurement of tspecific energy loss (dE/dx) is provided by 192sense wires located at the end caps of the dvolume.

• The outer detector(OD) consists of 5 layers odrift tubes between radii of 197 and 206 cm.polar angle coverage is from 42 to 138. The ODprovides 3 space points and 2Rφ points per trackThe single point precision is about 110 µm in tRφ plane and about 3.5 cm in thez direction.

An event has been selected as multihadronic iffollowing requirements are satisfied:

• There must be at least five charged particin the event, each with momentum larger th400 MeV/c and polar angle between 20 and160.

• The total reconstructed energy of these charparticles has to exceed 12% of the centre-of-menergy (assuming all particles to have the pmass).

• The total energy of the charged particles in eahemisphere (defined by the plane perpendiculathe beam axis) has to exceed 3% of the centremass energy.

After these cuts, about 2 million events from t1994 and 1995 runs have been retained. Aboumillion simulatedZ0 → qq and 3.1 millionZ0 → bb

events have been selected with the same cuts.Jets have been reconstructed with the LUCLUS

gorithm [6] (djoin = 5 GeV/c) using charged and neutral particles. Two-jet events well within the acce

DELPHI Collaboration / Physics Letters B 576 (2003) 29–42 35

s by

gedfitsizeacttedatesndedsed.totailer thebleveasent.ere2].ostere

gedgeralre,

lcu-en--gedThemi-

tothehear-teder-

oton-hetheut

he

d

due

ingre

and toil in

-averge.m-he

ryteddis-in

e

riorint

s asworkthese

om

tance of the vertex detector (|cosθthrust|< 0.65) wereselected. The event was divided in two hemispherethe plane perpendicular to the thrust axis.

The most important variables to tag or antitagbbevents are the track impact parameters of charparticles with respect to the primary vertex which ison an event-by-event basis using the position andof the beamspot as constraints. From the track impparameters and their errors a probability is computhat a selected sample of charged particles originfrom the primary vertex. To increase efficiency apurity, additional information, e.g., from reconstructsecondary vertices and identified leptons are uA combined discriminating variable is then usedselectbb events. These methods are described in dein [11]. The tagging ofbb events was performed in thhemisphere opposite to the one which was used fomeasurement. The cut on the discriminating variaof the combinedb-tagging has been chosen to gia b-purity of about 97.5%. A secondary vertex wfit in the hemisphere considered for the measuremHadronic interactions in the detector material wreconstructed using the algorithm described in [1Since the particle causing the interaction is lost in mof the cases, hemispheres with such interactions wrejected.

3. Measurement of the rates of chargedand neutral b-hadrons

The basic idea for measuring the rates of charand neutralb-hadrons is to reconstruct the charof the weakly-decaying hadron. Based on a neunetwork, for each charged particle in a hemisphea probabilityPB that the particle originates from ab-hadron decay rather than from fragmentation is calated. Charged particles are accepted if their momtum exceeds 500 MeV/c and if at least one vertex detector hit has been associated. At least four charparticles had to be accepted in the hemisphere.maximum number of charged particles in the hesphere failing these acceptance cuts was limitedfour. The input variables to the neural network areprobability that the charged particle track fits to tprimary vertex, the momentum, the rapidity of the pticle with respect to the thrust axis, the reconstrucflight distance from the primary to the secondary v

tex in theRφ plane and its error. The last two are nspecific for the particles but for the hemisphere csidered. They give additional information about tseparation power of the other variables, especiallyvertex probability. The distributions of the net outpvariable6 are shown in Fig. 2.7

A secondary-vertex chargeQB is then constructedthrough

(1)QB =Nhem∑i=1

QiPB,i,

whereNhem is the number of accepted particles in themisphere,Qi the charge of particlei andPB,i itsprobability to stem from ab-hadron decay as defineabove. Assuming binomial statistics, an error onQBcan be defined as

(2)σQB =√√√√Nhem∑

i=1

PB,i(1− PB,i).

This quantity does not account for particle lossesto inefficiencies in the track reconstruction.σQB issmall if all charged particles are well classified, havvalues ofPB close to 0 or 1, and gets larger the moparticles have probabilities around 0.5.

Parameters in the simulation possibly havingeffect on the measurement have been adjustetheir measured values. They are discussed in detaSection 4 and listed also in Table 1.

The shapes of theQB distributions are directly affected by the number of charged particles which hbeen used in the reconstruction of the vertex chaThis number is larger in the data than in the siulation by 0.12 at a mean value of about 8.0. Tshape of the particle multiplicity distribution is vesimilar in the data and the simulation. The simulaevents are reweighted to get agreement in thistribution. The error of the vertex charge, definedEq. (2), also influences theQB distributions becaus

6 This variable can be interpreted as Bayesian a posteprobability.PB is computed from this variable taking into accouthe ratio ofb-hadron decay particles and fragmentation particletaken from simulation. This is necessary because the neural nethas been trained with equal numbers of charged particles fromtwo classes.

7 If not explicitly stated otherwise, all figures show the data fr1994 and 1995.

36 DELPHI Collaboration / Physics Letters B 576 (2003) 29–42

cles),ed at

Fig. 2. The output of the neural network used to separateB-decay particles from fragmentation particles. Shown are the data (closed cirthe simulation (solid histogram) and the contributions from weakB-decay particles (dotted) and their fragmentation counterparts producthe primary vertex (dashed). The latter distribution includes particles originating from strong decays of excitedb-hadrons.

nt,havee for. Forngng

g

e offla-

trib-ofor-m-

ass-All

iftsla-uteying

allc-

me-

fere

Table 1Breakdown of systematic errors onf+. For theb-hadron fractions,fBs and fb-baryon, their correlation has been taken into accoufor the other sources of systematic uncertainties the errorsbeen added in quadrature. The signs of the errors given aran upwards variation of the corresponding physics parameterBR(B0(+) → D−(0) +X), an upwards variation means increasiBR(B0 → D− + X) and adjusting the other, related branchiratios as explained in the text

Source Value and variation δf+ [%]τB0 (1.542± 0.016) ps +0.007τB+ (1.674± 0.018) ps −0.129τBs (1.461± 0.057) ps +0.027τb-baryon (1.208± 0.051) ps +0.010χd 0.181± 0.004 +0.038fBs (8.5± 1.3)% +0.217fb-baryon (9.5± 2.0)% +0.057fΞ−b

(1.1± 0.5)% −0.187

PB∗∗ 0.24± 0.04 +0.287PΣ(∗)B

0.10± 0.05 −0.027

Wrong sign charm rate (20.0± 3.3)% −0.001BR(B0(+) → D−(0) +X) text −0.183b fragmentation function text 0.201Min. # of acc. charged particles 4, 3 0.217QB calibration text 0.677Non-bb background ±30% +0.113

Total 0.886

it is directly related to its width. Incorrect modellinof the shape of theQB distribution in the simula-tion potentially biases the result. The dependencthe mean value and spread ofσQB on the number ocharged particles is shown in Fig. 3. Data and simution agree well, the deviations being within±3%. Thesimulated events are reweighted to get these disutions in agreement, individually for any numbercharged particles, to avoid any possible bias. To crect for the loss of charged particle tracks, the nuber of charged particles in the hemisphere not ping the track cuts is also brought into agreement.these corrections are small. Comparing theQB dis-tributions of data and simulation shows slight shof the data distribution with respect to the simution which is corrected depending on the absolvalue of the polar angleθ (these shifts are typicallaround 0.01 with the deviations from zero not bevery significant). Such shifts can be caused by smdifferences in the material distribution of the detetor in data and simulation causing a charge asymtry.

The vertex chargeQB is sensitive to the charge otheb-quark in the hemisphere, mainly in cases whchargedb-hadrons are produced. Sinceb- and b-

DELPHI Collaboration / Physics Letters B 576 (2003) 29–42 37

charge

tionrection

Fig. 3. 〈σQB 〉 (left) andσ(σQB ) (right) versus the number of charged particles which have been used for the estimation of the vertexfor data (closed circles) and simulation (histogram) before applying the correction as explained in the text. The ratios〈σQB 〉data/〈σQB 〉sim and0.1 · σ(σQB )data/σ(σQB )sim are shown as dashed lines. The deviations are within±3% over the whole range.

Fig. 4. The fraction of ‘opposite-sign’ events versusQcutB for 1994 (left) and 1995 (right) comparing data (circles with error bars) and simula

(histogram), used for the calibration ofQB . For 1994, the solid (dashed) histogram shows the simulation before (after) applying the corexplained in the text.

ei-anisallign’

’)both

SStheIn

be-oras-

quarks are produced in pairs inZ decays, events wherthe vertex chargeQB can be determined in both hemspheres (‘double tagged’ events in the following) cbe used to calibrateQB on the data themselves. Thisdone in the following way. For 20116 events, wherecuts are passed in both hemispheres, ‘opposite-s(called ‘OS’ in the following) and ‘same-sign’ (‘SSevents are defined through the vertex charges inhemispheres: OS:Q1

B ·Q2B < 0, SS:Q1

B ·Q2B > 0. To

be sensitive to the shape of the distributions,|Q1,2B |>

QcutB has been required. The fractions of OS and

events are directly related to the probability to tagcharge of theb-quark in the hemisphere correctly.Fig. 4, the fraction of OS events,fOS, versusQcut

B

is shown for the 1994 and 1995 data sets. It canseen that the probability to tag theb-quark charge correctly is slightly overestimated in the simulation f1994 (with a tendency to become worse when incre

38 DELPHI Collaboration / Physics Letters B 576 (2003) 29–42

fit), negativelyitively

Fig. 5. Distribution of the vertex charge,QB , of the weakly-decayingb-hadron for the data (points with error bars) with the result of thesuperimposed (solid histogram) on a linear scale and on a logarithmic scale (see inset). The shapes for neutral (dashed histogram(dashed-dotted) and positively (dotted) chargedb-hadrons obtained from the simulation (in the fit, one single component was used for posand negatively chargedb-hadrons) are also shown. The hatched histogram shows the contribution of non-bb events.

),rac-

-the

eding

ost

n

dis-atau-

eutraot

tive

odof

omnd-withu-

ng

ing QcutB , thus probing the wings of the distribution

whereas good agreement is found for 1995. The ftion of OS events is mainly determined by theQB dis-tributions of chargedb-hadrons. To correct for the disagreement between data and simulation in 1994,QB distributions for positively and negatively chargb-hadrons are reweighted in the simulation accordto w± = 1 − (±a1 ·QB − a2)

3. The following para-meters were found to make the fraction ofOS eventsin the simulation consistent with the data over almthe full range ofQcut

B (see Fig. 4):a1 = 0.31 anda2 = 0.34. Another, related, distribution is the fractioof double tagged events versusQcut

B with respect to alldouble tagged events. It has been verified that thistribution is in good agreement for both years of dtaking (after applying the correction to the 1994 simlation).

The measuredQB distribution has been fit by thcorresponding shapes expected for charged and neb-hadrons obtained from the simulation, while n

l

separating the shapes for the positive and negacharges.

A technique based on a binned log-likelihomethod taking into account the limited statisticsthe simulation has been used [13]. The non-bb back-ground has been fixed to the value obtained frsimulation. The real data distribution, correspoing to 103.285 selected hemispheres, togetherthe fit result and the simulation prediction for netral, positively and negatively chargedb-hadrons isshown in Fig. 5. The result forf+, the fraction ofchargedb-hadrons in a sample of weakly-decayib-hadrons produced inZ0 → bb decays, isf+ =(41.84± 0.99(stat))% for the 1994 data set andf+ =(42.65 ± 1.48(stat))% for 1995 giving a combinedvalue of

(3)f+ = (42.09± 0.82(stat)

)%.

The result forf 0 is given throughf 0 = 1 − f+ =(57.91±0.82(stat))%, withf+ andf 0 being fully an-

DELPHI Collaboration / Physics Letters B 576 (2003) 29–42 39

ts

e fitsedhas

theantons

on,orad–-ardf theentthe

ra-:

ng

ta-our-

hat

etry

eres

ole.

sege

flue

ure

y-arti-n-x)er-

-a

ticorrelated. Theχ2 per degree of freedom of the fiare 0.96 and 1.06 for the two years.

4. Systematic checks and uncertainties

Several cross-checks have been performed. Thrange and number of bins of the histograms uin the fit have been varied. The momentum cutbeen varied in the range from 300 to 800 MeV/cand the maximum number of rejected tracks inhemisphere between two and five. No significchange of the result has been found. The distributiof negatively and positively chargedb-hadrons havebeen fit separately. This gives

BR(b, b→X+B )=

(20.66± 0.60(stat)

)%,

BR(b, b→X−B )=

(21.16± 0.59(stat)

)%

for 1994 and

BR(b, b→X+B )=

(21.37± 0.87(stat)

)%,

BR(b, b→X−B )=

(21.29± 0.86(stat)

)%

for 1995. The two numbers are correlated (ρ± ≈0.44).

As already mentioned and used for the calibratithe vertex chargeQB can be used as flavour tag fhemispheres where theb- or b-quark fragmented intochargedb-hadron and is thus sensitive to the forwarbackward asymmetryAFB

b . The differential asymmetry, computed from the vertex charges in the forwand backward hemispheres, versus the direction othrust axis is shown in Fig. 6, showing good agreemwith the expectation from the measured value ofpole asymmetryAFB

b = 0.0982± 0.0017 (from [1]).To estimate systematic errors, the following pa

meters in the simulation and cuts have been varied

• lifetimes ofb-hadrons;• the oscillation frequency and thus the mixi

probability χd for B0-mesons. Mixing ofB0-mesons leaves the contribution from fragmention particles unchanged but reverses the flavof the weakly-decayingB-meson. The contributions to the vertex charge fromB0- and B0-mesons are slightly different. One reason is tB0-mesons produce dominantlyD−-mesons

Fig. 6. The dependence of the measured differential asymmAFB

diff on cosθthrust for the data.AFBdiff has been computed from

the vertex charges in the forward and backward hemisphas: AFB

diff = (〈QFWB

〉 − 〈QBWB

〉)/〈QbB

〉, where 〈QbB

〉 is the meanof the vertex charge for hemispheres containing ab-quark. Theerrors indicated are statistical only. The expectation for the pasymmetryAFB

b= 0.0982 (from [1]) is superimposed as solid line

whereasB0-mesons mainly giveD+, leading todifferent charges at the tertiary charm vertex;

• the rates of differentb-hadron species, becaudifferentb-hadrons contribute to a certain char(e.g., B0, B0

s , Λb, Ξ0b to Q = 0) and their

distributions look slightly different. The value ofBu(= fBd ) has been set to the measured vain this analysis. The values offBs andfb-baryonfrom [1] have been rescaled accordingly to ensfBs + fb-baryon+ fBu + fBd = 1;

• the rates of excitedb-hadrons, namely orbitallexcitedB∗∗

u,d,s -mesons andΣ(∗)b -baryons. The expected strong decays of these states produce pcles (pions or kaons) looking partly like fragmetation particles (coming from the primary verteand partly likeB-decay particles (having largrapidity). From the results in [14,15] an aveagePB∗∗

u,d= BR(b→ B∗∗

u,d )/BR(b→ b(u, d)) =0.24±0.04 is computed. It is assumed thatPB∗∗

s=

PB∗∗u,d

. ForΣ(∗)b production DELPHI gives an upper limit in [15]. The following value is taken asconservative choice:8 P

Σ(∗)b

= 0.10± 0.05;

8 PΣ(∗) is defined in the same way asPB∗∗ .

b

40 DELPHI Collaboration / Physics Letters B 576 (2003) 29–42

c-

of

lesre

hedgtentof

enental

a-d.

heonn-areg-

edfor

ma

ged

ed

lts

iftataap-nouse

mu-he

-

ngn ofult,

yr

ed

o

e

ty

ns

ly-ed

• the rate of so-called ‘wrong-sign charm’ prodution at the upperW vertex from [16];

• the branching ratios of ‘right-sign’ decaysB+- andB0-mesons intoD0- andD−-mesons.Because ofτ (D−) > τ(D0), b-hadron decayswith aD− in the final state have charged particfrom the tertiary charm decay which are modisplaced from the primary vertex than in tcase of aD0, affecting the vertex variables useas input to the neural network. The followinbranching ratios have been used, being consiswith the measured inclusive production ratesD0- and D−-mesons inB-decays: BR(B0 →D− +X)= 15.6%, BR(B0 → D0 +X)= 65.8%,BR(B+ →D− +X) = 29.3%, BR(B+ → D0 +X) = 52.1%. These branching ratios have bevaried by 5% (absolute). The variation has beperformed in a correlated way to keep the torate of D0- and D−-mesons inB-decays andBR(B0/B+ → D0 +X)+ BR(B0/B+ →D− +X) constant;

• the b-quark fragmentation function. The mesured function from DELPHI [17] has been useFor the systematic error the full difference to tmodel implemented in the simulation (Peterswith εb = 0.002326) has been taken. This is a coservative choice, since the measurement errorsmuch smaller than the deviations from the framentation function in the simulation;

• the cut on the minimum number of acceptcharged particles in the hemisphere usedthe calculation ofQB has been changed froan even to an odd number. This could havesystematic effect because charged (neutral)b-hadrons decay to an odd (even) number of charparticles;

• the calibration of the vertex charge (describin Section 3). The parametersa1 and a2 havebeen varied independently in a way which resuin a displacement of thefOS versusQcut

B curve(Fig. 4) in the simulation, corresponding to a shby one standard deviation with respect to the derrors. This procedure has been consistentlyplied also to the 1995 year simulation, even ifcorrection has been applied in this case, becaof the good agreement between data and silation. The error from the parameter giving tlargest variation inf+ has been chosen;

• the non-bb background (mainlycc) has been varied by±30%.

If not explicitly stated otherwise, the correspondinumbers have been taken from [1]. The breakdowthe systematic errors is shown in Table 1. The resincluding systematic errors, is:

(4)f+ = (42.09± 0.82(stat)± 0.89(syst)

)%.

5. Interpretation of the results

Weakly-decaying neutralb-hadrons areB0- andB0s -mesons, theΛb-baryon and the strangeb-baryonΞ0b . The rate of chargedb-hadrons is dominated b

theB+-meson, strangeb-baryons giving only a minocontribution (Ξ−

b ,Ω−b ). Formally, one gets:

f 0 = fBd + fBs + f 0b-baryon,

(5)f+ = fBu + f+b-baryon.

In [16], the fraction ofΞ−b -baryons has been estimat

analysing production rates ofΞ−l− final states:

fΞ−b

= BR(b→ Ξ+b )= BR(b→Ξ−

b )

= (1.1± 0.5)%.

This fraction is subtracted fromf+ to get the fractionof B+-mesons in a sample of weakly-decayingb-hadrons produced in the fragmentation ofb-quarks(the production fraction ofΩ−

b -baryons is expected tbe negligible). The result is

(6)fBu = (40.99± 0.82(stat)± 1.11(syst)

)%,

where the error fromfΞ−b

has been added to th

systematic error fromf+ taking into account thecorrelation arising from the fact that the uncertainof fΞ−

bis a source of uncertainty forf+ (compare

Table 1).

6. Conclusions

A precise measurement of the production fractioof weakly-decaying charged and neutralb-hadrons hasbeen presented for the first time. The fraction ofb-quarks fragmenting into positively charged weakdecayingb-hadrons, and thus the fraction of charg

DELPHI Collaboration / Physics Letters B 576 (2003) 29–42 41

ed

of a-by

re-n

o-orto

nd, in

ce

sci-us-l

J,

R

G

A,

ft,

ogy,

da-r-

nd,/nd

nalrtu-

No.

b-

;cil;un-

R-

66

89

95

1

4

9)

5)

5)

4

2

5

6)

.h-

h-

b-hadrons in a sample of weakly-decayingb-hadronsproduced inZ0 → bb decays, has been measurto be f+ = (42.09 ± 0.82(stat) ± 0.89(syst))% =(42.09± 1.21)%. Subtracting theΞ+

b rate (assumingthat theΩ+

b rate is negligible) givesfBu = (40.99±0.82(stat)± 1.11(syst))%= (40.99± 1.38)%. This is,so far, the most precise dedicated measurementproduction fraction of a specificb-hadron. The accuracy onfBu is comparable to the accuracy achievedcombining all other information available onb-hadronproduction fractions. This measurement thus repsents significant new information that will impact ocombinations of measurements to estimateb-hadronproduction fractions in jets.

Acknowledgements

We are greatly indebted to our technical collabrators, to the members of the CERN-SL Division fthe excellent performance of the LEP collider, andthe funding agencies for their support in building aoperating the DELPHI detector. We acknowledgeparticular, the support of:

– Austrian Federal Ministry of Education, Scienand Culture, GZ 616.364/2-III/2a/98;

– FNRS–FWO, Flanders Institute to encourageentific and technological research in the indtry (IWT), Federal Office for Scientific, Technicaand Cultural affairs (OSTC), Belgium;

– FINEP, CNPq, CAPES, FUJB and FAPERBrazil;

– Czech Ministry of Industry and Trade, GA C202/99/1362;

– Commission of the European Communities (DXII);

– Direction des Sciences de la Matière, CEFrance;

– Bundesministerium für Bildung, WissenschaForschung und Technologie, Germany;

– General Secretariat for Research and TechnolGreece;

– National Science Foundation (NWO) and Fountion for Research on Matter (FOM), The Nethelands;

– Norwegian Research Council;

– State Committee for Scientific Research, PolaSPUB-M/CERN/PO3/DZ296/2000, SPUB-MCERN/PO3/DZ297/2000 and 2P03B 104 19 a2P03B 69 23(2002-2004)JNICT—Junta Naciode Investigação Científica e Tecnológica, Pogal;

– Vedecka grantova agentura MS SR, Slovakia,95/5195/134;

– Ministry of Science and Technology of the Repulic of Slovenia;

– CICYT, Spain, AEN99-0950 and AEN99-0761– The Swedish Natural Science Research Coun– Particle Physics and Astronomy Research Co

cil, UK;– Department of Energy, USA, DE-FG02-01E

41155;– EEC RTN Contract HPRN-CT-00292-2002.

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