Z. Phys. C 74, 423–435 (1997) ZEITSCHRIFTFUR PHYSIK Cc© Springer-Verlag 1997

Measurement of the semileptonic branching fractionof inclusive b baryon decays toΛOPAL Collaboration

K. Ackerstaff8, G. Alexander23, J. Allison16, N. Altekamp5, K. Ametewee25, K.J. Anderson9, S. Anderson12, S. Arcelli2,S. Asai24, D. Axen29, G. Azuelos18,a, A.H. Ball17, E. Barberio8, R.J. Barlow16, R. Bartoldus3, J.R. Batley5, J. Bechtluft14,C. Beeston16, T. Behnke8, A.N. Bell1, K.W. Bell20, G. Bella23, S. Bentvelsen8, P. Berlich10, S. Bethke14, O. Biebel14,A. Biguzzi2, V. Blobel27, I.J. Bloodworth1, J.E. Bloomer1, M. Bobinski10, P. Bock11, H.M. Bosch11, M. Boutemeur34,B.T. Bouwens12, S. Braibant12, R.M. Brown20, H.J. Burckhart8, C. Burgard8, R. Burgin10, P. Capiluppi2, R.K. Carnegie6,A.A. Carter13, J.R. Carter5, C.Y. Chang17, D.G. Charlton1,b, D. Chrisman4, P.E.L. Clarke15, I. Cohen23, J.E. Conboy15,O.C. Cooke16, M. Cuffiani2, S. Dado22, C. Dallapiccola17, G.M. Dallavalle2, S. De Jong12, L.A. del Pozo8, K. Desch3,M.S. Dixit7, E. do Couto e Silva12, M. Doucet18, E. Duchovni26, G. Duckeck34, I.P. Duerdoth16, J.E.G. Edwards16,P.G. Estabrooks6, H.G. Evans9, M. Evans13, F. Fabbri2, P. Fath11, F. Fiedler27, M. Fierro2, H.M. Fischer3, R. Folman26,D.G. Fong17, M. Foucher17, A. Furtjes8, P. Gagnon7, A. Gaidot21, J.W. Gary4, J. Gascon18, S.M. Gascon-Shotkin17,N.I. Geddes20, C. Geich-Gimbel3, F.X. Gentit21, T. Geralis20, G. Giacomelli2, P. Giacomelli4, R. Giacomelli2, V. Gibson5,W.R. Gibson13, D.M. Gingrich30,a, D. Glenzinski9, J. Goldberg22, M.J. Goodrick5, W. Gorn4, C. Grandi2, E. Gross26,J. Grunhaus23, M. Gruwe8, C. Hajdu32, G.G. Hanson12, M. Hansroul8, M. Hapke13, C.K. Hargrove7, P.A. Hart9, C. Hartmann3,M. Hauschild8, C.M. Hawkes5, R. Hawkings8, R.J. Hemingway6, M. Herndon17, G. Herten10, R.D. Heuer8, M.D. Hildreth8,J.C. Hill5, S.J. Hillier1, T. Hilse10, P.R. Hobson25, R.J. Homer1, A.K. Honma28,a, D. Horvath32,c, R. Howard29, R.E. Hughes-Jones16, D.E. Hutchcroft5, P. Igo-Kemenes11, D.C. Imrie25, M.R. Ingram16, K. Ishii24, A. Jawahery17, P.W. Jeffreys20,H. Jeremie18, M. Jimack1, A. Joly18, C.R. Jones5, G. Jones16, M. Jones6, R.W.L. Jones8, U. Jost11, P. Jovanovic1,T.R. Junk8, D. Karlen6, K. Kawagoe24, T. Kawamoto24, R.K. Keeler28, R.G. Kellogg17, B.W. Kennedy20, B.J. King8,J. Kirk29, S. Kluth8, T. Kobayashi24, M. Kobel10, D.S. Koetke6, T.P. Kokott3, M. Kolrep10, S. Komamiya24, T. Kress11,P. Krieger6, J. von Krogh11, P. Kyberd13, G.D. Lafferty16, H. Lafoux21, R. Lahmann17, W.P. Lai19, D. Lanske14, J. Lauber15,S.R. Lautenschlager31, J.G. Layter4, D. Lazic22, A.M. Lee31, E. Lefebvre18, D. Lellouch26, J. Letts2, L. Levinson26, C. Lewis15,S.L. Lloyd13, F.K. Loebinger16, G.D. Long17, M.J. Losty7, J. Ludwig10, A. Malik21, M. Mannelli8, S. Marcellini2, C. Markus3,A.J. Martin13, J.P. Martin18, G. Martinez17, T. Mashimo24, W. Matthews25, P. Mattig3, W.J. McDonald30, J. McKenna29,E.A. Mckigney15, T.J. McMahon1, A.I. McNab13, R.A. McPherson8, F. Meijers8, S. Menke3, F.S. Merritt9, H. Mes7,J. Meyer27, A. Michelini2, G. Mikenberg26, D.J. Miller15, R. Mir26, W. Mohr10, A. Montanari2, T. Mori24, M. Morii 24,U. Muller3, K. Nagai26, I. Nakamura24, H.A. Neal8, B. Nellen3, B. Nijjhar16, R. Nisius8, S.W. O’Neale1, F.G. Oakham7,F. Odorici2, H.O. Ogren12, N.J. Oldershaw16, T. Omori24, M.J. Oreglia9, S. Orito24, J. Palinkas33,d, G. Pasztor32, J.R. Pater16,G.N. Patrick20, J. Patt10, M.J. Pearce1, S. Petzold27, P. Pfeifenschneider14, J.E. Pilcher9, J. Pinfold30, D.E. Plane8,P. Poffenberger28, B. Poli2, A. Posthaus3, H. Przysiezniak30, D.L. Rees1, D. Rigby1, S. Robertson28, S.A. Robins13,N. Rodning30, J.M. Roney28, A. Rooke15, E. Ros8, A.M. Rossi2, M. Rosvick28, P. Routenburg30, Y. Rozen22, K. Runge10,O. Runolfsson8, U. Ruppel14, D.R. Rust12, R. Rylko25, K. Sachs10, E.K.G. Sarkisyan23, M. Sasaki24, C. Sbarra2, A.D. Schaile34,O. Schaile34, F. Scharf3, P. Scharff-Hansen8, P.. Schenk27, B. Schmitt8, S. Schmitt11, M. Schroder8, H.C. Schultz-Coulon10,M. Schulz8, M. Schumacher3, P. Schutz3, W.G. Scott20, T.G. Shears16, B.C. Shen4, C.H. Shepherd-Themistocleous8,P. Sherwood15, G.P. Siroli2, A. Sittler27, A. Skillman15, A. Skuja17, A.M. Smith8, T.J. Smith28, G.A. Snow17, R. Sobie28,S. Soldner-Rembold10, R.W. Springer30, M. Sproston20, A. Stahl3, M. Steiert11, K. Stephens16, J. Steuerer27, B. Stockhausen3,D. Strom19, F. Strumia8, P. Szymanski20, R. Tafirout18, S.D. Talbot1, S. Tanaka24, P. Taras18, S. Tarem22, M. Thiergen10,M.A. Thomson8, E. von Torne3, S. Towers6, I. Trigger18, T. Tsukamoto24, E. Tsur23, A.S. Turcot9, M.F. Turner-Watson8,P. Utzat11, R. Van Kooten12, G. Vasseur21, M. Verzocchi10, P. Vikas18, M. Vincter28, E.H. Vokurka16, F. Wackerle10,A. Wagner27, C.P. Ward5, D.R. Ward5, J..J. Ward15, P.M. Watkins1, A.T. Watson1, N.K. Watson7, P.S. Wells8, N. Wermes3,J.S. White28, B.. Wilkens10, G.W. Wilson27, J.A. Wilson1, G. Wolf26, S. Wotton5, T.R. Wyatt16, S. Yamashita24, G. Yekutieli26,V. Zacek18

1 School of Physics and Space Research, University of Birmingham, Birmingham B15 2TT, UK2 Dipartimento di Fisica dell’ Universita di Bologna and INFN, I-40126 Bologna, Italy3 Physikalisches Institut, Universitat Bonn, D-53115 Bonn, Germany4 Department of Physics, University of California, Riverside CA 92521, USA5 Cavendish Laboratory, Cambridge CB3 0HE, UK6 Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada7 Centre for Research in Particle Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada8 CERN, European Organisation for Particle Physics, CH-1211 Geneva 23, Switzerland

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9 Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago IL 60637, USA10 Fakultat fur Physik, Albert Ludwigs Universitat, D-79104 Freiburg, Germany11 Physikalisches Institut, Universitat Heidelberg, D-69120 Heidelberg, Germany12 Indiana University, Department of Physics, Swain Hall West 117, Bloomington IN 47405, USA13 Queen Mary and Westfield College, University of London, London E1 4NS, UK14 Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germany15 University College London, London WC1E 6BT, UK16 Department of Physics, Schuster Laboratory, The University, Manchester M13 9PL, UK17 Department of Physics, University of Maryland, College Park, MD 20742, USA18 Laboratoire de Physique Nucleaire, Universite de Montreal, Montreal, Quebec H3C 3J7, Canada19 University of Oregon, Department of Physics, Eugene OR 97403, USA20 Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK21 CEA, DAPNIA/SPP, CE-Saclay, F-91191 Gif-sur-Yvette, France22 Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel23 Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel24 International Centre for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo 113, and Kobe University, Kobe 657, Japan25 Brunel University, Uxbridge, Middlesex UB8 3PH, UK26 Particle Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel27 Universitat Hamburg/DESY, II Institut fur Experimental Physik, Notkestrasse 85, D-22607 Hamburg, Germany28 University of Victoria, Department of Physics, P O Box 3055, Victoria BC V8W 3P6, Canada29 University of British Columbia, Department of Physics, Vancouver BC V6T 1Z1, Canada30 University of Alberta, Department of Physics, Edmonton AB T6G 2J1, Canada31 Duke University, Dept of Physics, Durham, NC 27708-0305, USA32 Research Institute for Particle and Nuclear Physics, H-1525 Budapest, P O Box 49, Hungary33 Institute of Nuclear Research, H-4001 Debrecen, P O Box 51, Hungary34 Ludwigs-Maximilians-Universitat Munchen, Sektion Physik, Am Coulombwall 1, D-85748 Garching, Germany

Received: 21 November 1996

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Abstract. We present the first measurement of the ratioRΛ` defined asRΛ` = BR(Λb → Λ`X)/BR(Λb → ΛX)whereΛb denotes all weakly decaying b baryons and` repre-sents the average of electrons and muons. Using all hadronicZ0 decay events collected with the OPAL detector near theZ0 resonance, we measureRΛ` = (7.0± 1.2± 0.7)%.We also measuref (b→ Λb) · BR(Λb → ΛX) = (3.93± 0.46± 0.37)%,f (b→ B) · BR(B→ ΛX) = (1.94± 0.28± 0.24)%, andBR(b → ΛX) = (5.87± 0.46± 0.48)%.In all cases, the uncertainties shown are statistical and sys-tematic, respectively.

1 Introduction

Recent measurements have shown that there is a largerthan expected lifetime difference between b baryons andB mesons. The average b baryon lifetime is 1.14± 0.08ps [1] whereas the B0 lifetime is 1.56± 0.06 ps [1]. Thelifetime difference is expected to arise due to decay am-plitudes that directly involve the light quarks (the so-called“non-spectator amplitudes”). So far, however, no theoreticalcalculation has been able to account for a difference in thelifetime ratio smaller than approximately 0.9 [2, 3], com-pared to the measured value of 0.731±0.058. Since lifetimes

a and at TRIUMF, Vancouver, Canada V6T 2A3b and Royal Society University Research Fellowc and Institute of Nuclear Research, Debrecen, Hungaryd and Department of Experimental Physics, Lajos Kossuth University, De-brecen, Hungary

and branching fractions are related, an independent way toprobe the effects of non-spectator diagrams is to measure thesemileptonic branching fractions for the different b hadrons.

Recent calculations which include higher-order perturba-tive corrections [4, 5] adequately reproduce the experimen-tal results for the B meson semileptonic branching ratio,BRB

SL. These corrections also predict a value fornc con-sistent with data [5], wherenc is the average number ofcharmed hadrons produced per B decay. So far, no theoreti-cal prediction has been published for the inclusive b baryonsemileptonic branching fraction. Calculations exist for exclu-sive channels, such as BR(Λ0

b → Λc`ν) where a predictionhas been made for ground state b baryons within the rela-tivistic quark model [6], placing the semileptonic decay ratefor Λ0

b → Λceν at (5.1× 1010) s−1. Using the measuredΛ0b

lifetime [1], one obtains the exclusive semileptonic branch-ing fraction (5.8± 0.4)%. The error shown reflects only theexperimental uncertainty on theΛ0

b lifetime.Given the observed difference in lifetimes between B

mesons and b baryons, the semileptonic branching fractionof b baryons is expected to be significantly smaller thanfor B mesons. The semileptonic branching fraction for Bmesons has been measured at theΥ (4S) resonance to beBRB

SL = (10.43±0.24)% [1]. Using the results from [1] ob-tained above the B meson production threshold, one obtainsBRb

SL = (11.13± 0.29)%. In a more recent measurement,the L3 collaboration reports BRbSL = (10.68± 0.46)% [7]also consistent with the world average. The b superscriptindicates that the high-energy data correspond to a mixtureof B±, B0, Bs and b baryons as opposed to B± and B0 onlyas at theΥ (4S) resonance. The production fractions of thedifferent b hadron species near the Z0 resonance is evaluatedto be (37.8± 2.2)% each for B± and B0, (11.2± 1.9)% forBs, and (13.2± 4.1)% for b baryons [1].

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An estimate of the semileptonic branching fraction of bbaryons can be obtained by scaling the measured semilep-tonic B meson and generic b hadron branching fractionsby the lifetime ratios [1]. AssumingΓsl, the semileptonicwidth, to be the same for all b hadrons [5], and given thatthe semileptonic branching ratio isΓsl/Γtotal, one obtains:

BR(Λb → `X) =τΛb

τB· BRB

SL = (7.5± 0.6)%, (1)

BR(Λb → `X) =τΛb

τb· BRb

SL = (8.2± 0.6)% (2)

whereΛb denotes the admixture of all weakly decaying bbaryons produced near the Z0 resonance, represents theaverage of electrons and muons, and b refers to all b hadrons.

This paper describes the measurement of the ratio

RΛ` =BR(Λb → Λ`X)BR(Λb → ΛX)

. (3)

If non-spectator amplitudes were negligible for all b hadrons,then RΛ`= BR(Λb → `X)= BR(B → `X). The extent towhich RΛ` and BR(B→ `X) differ depends on the mag-nitude of the non-spectator diagrams in b hadron decays.

Most of this paper concerns the evaluation ofBR(Λb → ΛX), the denominator in the calculation ofRΛ`.We present a new method which allows the separation ofΛb → ΛX events from the main sources of background byimposing more restrictions on the nature of “X”, the rest ofthe decay products found with theΛ. We require the pres-ence of aΛ and another baryon1 in the event, and fit the two-dimensional distribution of the momentum spectra of thesetwo baryons to extract the fraction of these events comingfrom Λb → ΛX and B→ ΛX events. These fractions arelater used in calculating bothf (b → Λb) · BR(Λb → ΛX)andf (b→ B)·BR(B→ ΛX). The method used to determineBR(Λb → Λ`X) in the numerator ofRΛ` has been describedelsewhere [8, 9] and will only be mentioned briefly here.

2 The OPAL detector and Monte Carlo samples

The OPAL detector is described in [10]. The central trackingsystem is composed of a high-precision silicon microver-tex detector, a precision vertex drift chamber, and a largevolume jet chamber surrounded by a set of chambers thatmeasure thez-coordinate2 (z-chambers). These detectors arelocated inside a solenoid. The detectors outside the solenoidconsist of a time-of-flight scintillator array and a lead glasselectromagnetic calorimeter with a presampler, followed bya hadron calorimeter, consisting of the instrumented returnyoke of the magnet, and several layers of muon chambers.Charged particles are identified by their specific energy loss,dE/dx, in the jet chamber. Further information on the per-formance of the tracking and dE/dx measurements can befound in [11].

1 Charge conjugation is implied throughout this paper2 The coordinate system is defined such that thez-axis follows the elec-

tron beam direction and thex-axis pointing towards the centre of the LEPring. The polar angleθ is defined relative to the +z-axis, and the azimuthalangleφ is defined relative to the +x-axis

Three independent sets of Monte Carlo events are com-bined for this analysis. These events correspond to the simu-lation of a total of 6.5 million inclusive multihadronic Z0 de-cays and two million heavy flavour hadronic decays (bb andcc). The two multihadronic samples were produced using theJETSET 7.3 (2.5× 106 events) and JETSET 7.4 (4.0× 106

events) Monte Carlo generators [12] respectively, with thefragmentation function of Peterson et al. [13] for heavyquarks. The heavy flavour Monte Carlo events were gen-erated using the JETSET 7.4 version with an updated de-cay table forΛc decays. All simulated events were passedthrough the full OPAL detector simulation package [14].

3 Event selection and method

This analysis uses data with centre-of-mass energies within3 GeV of the Z0 peak collected during the 1991-1995 run-ning period when the silicon microvertex detector was oper-ational. Standard hadronic event selection [15] and detectorperformance requirements select a sample of 3.84 millionevents. Each event is divided into two hemispheres by theplane perpendicular to the thrust axis. The thrust of the eventis required to be greater than 0.8, and the polar angle of thethrust axis,θth, must satisfy| cosθth| < 0.75, ensuring thatthe event is contained within the central barrel region. Jetfinding is done using a cone algorithm [16], with the mini-mum energy for a jet set to 5.0 GeV and the cone radius setto 550 mrad.

Lifetime tagging of b-flavoured events is used to reducecontamination from other quark flavours. Hemispheres weretagged as containing candidate b hadrons (“b-tagged”) usingsecondary vertices reconstructed from charged tracks withthe algorithm described in [17]. Properties of such sec-ondary vertices were used as inputs to a neural network al-gorithm that was trained to select Z0 → bb events. The neu-ral network has seven input parameters, the most importantof which are the decay length, its uncertainty and the vertexmultiplicity. Based on Monte Carlo studies, we estimate theb-tagging efficiency per event to be 0.442± 0.004 with apurity of (93.7 ± 0.5)% where the errors are from MonteCarlo statistics. The b-tagging neural network performancewas compared between data and Monte Carlo using a doubletag technique. The small observed difference is taken intoaccount by assigning an additional systematic uncertainty,as discussed in Sect. 6.8.

The difficulty in the evaluation of the ratioRΛ` =BR(Λb → Λ`X)/BR(Λb → ΛX) comes from the evaluationof the denominator, when attempting to distinguishΛ’s com-ing from Λb decays (which we will refer to as the directΛ’s) from the different sources of background in b-flavouredevents. We proceed as follow: If either hemisphere is taggedas containing a primary b flavour quark and one of the hemi-spheres contains both aΛ and an anti-baryon (p or Λ), thathemisphere is considered to be a candidate to contain the de-cayΛb → ΛX. The anti-baryon is expected to be producedwith theΛb in order to locally conserve baryon number. Thisassumption of jet hadronisation with local conservation ofbaryon number [18] has been verified experimentally [19].This baryon, which will be referred to as the companionbaryon, is required to be identified in order to discriminate

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against sources of background. The shapes of the momentumdistributions for the directΛ and the companion baryon aredifferent forΛb events and all other b-flavoured events. TheB meson decays produce directΛ’s with a momentum spec-trum similar to those found inΛb events, whereas fragmenta-tion Λ’s are produced with a softer momentum spectrum. Byitself, theΛ momentum spectrum is only useful to differenti-ate between b hadron decays and fragmentation events. It ispossible to separateΛb → ΛX events from B→ ΛX eventsusing the momentum spectrum of the companion baryon. ForΛb events, the companion baryon is produced during frag-mentation when the b quark hadronises to form the b baryon.Hence, the companion baryon has a softer momentum spec-trum than for B→ ΛX events, where the companion baryonis also a B meson decay product. Both baryons coming fromB meson decays receive a strong boost and have harder mo-mentum spectra than fragmentation particles.

To determine the fraction of candidate events comingfrom Λb → ΛX decays, we perform a maximum likelihoodfit to the two-dimensionalΛ and companion baryon mo-mentum spectra. This fraction times the number of selectedcandidates of b-flavoured events containing a directΛ anda companion baryon gives the number ofΛb → ΛX eventsneeded for the denominator ofRΛ`.

Finally, for the numerator ofRΛ`, b-tagged events con-taining a Λ and a prompt lepton (eithere or µ) are se-lected without the companion baryon requirement. The ratioof branching ratios is extracted by comparing the number ofselected b-tagged events containing aΛ-` pair to the fractionof events found with aΛ and a companion baryon which isattributed toΛb → ΛX decays, as estimated by the fit de-scribed above.

3.1Λ selection

TheΛ particle is reconstructed via itsΛ→ pπ− decay [20].Pairs of oppositely charged tracks are fitted to a common ver-tex. The track with the larger momentum is assumed to bethe proton. The measurement of the ionization energy loss,dE/dx, is used for particle identification. Both the proton andthe pion must have a dE/dx measurement compatible withthat expected for that particle type. For protons, this require-ment discriminates against background from K0

s → π+π−decays. The invariant mass of these candidates is required tobe between 1.110 and 1.121 GeV/c2. In order to enhance theselection of directΛ’s coming fromΛb → ΛX decays andreduce the contribution ofΛ candidates coming from frag-mentation [8], a minimum momentum requirement of 4.5GeV/c is made. A maximum momentum cut is also appliedat 15 GeV/c to restrict the analysis to the well populated re-gion which will later be used for the fit. The fakeΛ fractionin the data is estimated using both Monte Carlo studies andthe Λ invariant mass distribution outside the signal region.This fraction is found to be (5.9 ± 0.2)% once all selec-tion criteria for theΛ and companion baryon are applied, asdescribed next.

3.2 Companion baryon selection

The companion baryon can be either aΛ, in which casethe same mass selection criteria as above are applied, oran anti-proton. If aΛΛ pair of candidates is found in thesame hemisphere, the higher momentum one is assumed tocome from theΛb decay. All companionΛ’s with momen-tum less than 12 GeV/c are considered. Protons are selectedusing dE/dx measurement information. The proton candi-date tracks must have at least one hit in either the siliconmicrovertex or central vertex chamber, and a sufficient num-ber of hits in the jet chamber for the ionization loss mea-surement. For these tracks, the measured dE/dx is comparedwith that expected for a given mass hypothesis. The proba-bility that they are consistent with being protons is requiredto be greater than 1%. The dE/dx probability according to aGaussian distribution for the pion hypothesis for the protoncandidate must also be less than 1%. Only tracks with mo-mentum in the 0.33−1.4 GeV/c or 3.0−12 GeV/c ranges areretained to exclude the region where the dE/dx informationcannot be used to discriminate between pions and protons.Proton tracks with momenta greater than 3 GeV/c are fur-thermore required not to be identified as a lepton using thelepton identification criteria described in the next section.

When two proton candidates are found in the same hemi-sphere, the track with the higher dE/dx proton probabilityis retained. Most companion baryons are proton candidates(88.5±0.3)%. From the Monte Carlo sample, it is estimatedthat (80.6± 0.4)% of these are true protons. The remainderof the companions areΛ candidates with an estimated pu-rity of (90.7±0.8)%. The overall companion baryon samplepurity is (81.8± 0.4)%. All errors are statistical only.

3.3 Lepton identification

Electron candidates are identified using an artificial neu-ral network based on twelve measured quantities from theelectromagnetic calorimeter and the central tracking detec-tor [21]. The most significant input parameters are the ratioof the energy deposited in the electromagnetic calorimeter tothe track momentum, the specific energy loss per unit lengthin the central tracking chambers and the shape of the energycluster in the calorimeter. Muons are identified by associat-ing central detector tracks with track segments in the muondetectors and requiring a position match in two orthogonalcoordinates [22]. Electron candidates identified as arisingfrom photon conversions are rejected [21]. Electron andmuon candidates are required to have momenta greater than2 GeV/c and 3 GeV/c, respectively.

Prompt lepton candidates are used to identify semilep-tonic b baryon decays in the hemisphere containing theΛ.Cascade leptons (b→ c → `) are rejected from the sampleby requiringpcomb≡

√(p/10)2 + p2

t > 1.2 GeV/c, wherepis the lepton momentum andpt is the transverse momentumof the lepton relative to the axis of the jet containing it [23].This jet axis is calculated including the lepton track. Further-more, the invariant mass of theΛ-lepton pair is required tobe larger than 2.2 GeV/c2 [8] to removeΛc → Λ`X events.Using Monte Carlo simulated events, we estimate the aver-

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age selection efficiency forΛ` in Λb → Λ`X events to be0.040± 0.002.

4 Signal and background estimation

The methods used to evaluate the respective backgrounds inΛb → Λ`X andΛb → ΛX events are described below.

4.1 Background sources forΛb → Λ`X

Right-sign pairs are formed byΛ` and Λ ¯ combinations.Λ baryons originating from the fragmentation process ratherthan directly from heavy hadron decays combined with lep-tons from semileptonic c- or b-hadron decays are found tobe the largest sources of background and populate right-signand wrong-sign combinations roughly equally. Hence, thenumber of wrong-sign charge candidates is used to estimatethe background in the right-signΛb → Λ`X sample. How-ever, in the framework of string fragmentation and the “pop-corn” model [18] as implemented in the JETSET MonteCarlo program, it is expected that this background con-tributes differently to the right-sign and wrong-sign samples.A correction factor is evaluated using the Monte Carlo sam-ple and is applied to the data. This correction factor is simi-lar to the one described in a previous analysis [9] althoughslightly different since the two analyses were performed withdifferent selection criteria. The number ofΛb → Λ`X eventsis obtained by subtracting from the number of right-signevents the number of wrong-sign events divided by the cor-rection factor of 0.91± 0.07 to account for the imbalancein sign-correlation in the background. The systematic un-certainty quoted includes a contribution accounting for dif-ferences obtained with the different Monte Carlo generatorsdescribed in Sect. 2.

4.2 Background sources forΛb → ΛX

The background contribution in theΛb → ΛX sample ismuch more difficult to estimate. We use the Monte Carloto predict the shape of the signal as well as the backgroundsand fit for these backgrounds in the data. The Monte Carloevents are selected using the same criteria as for data, exceptthat the b-flavour tagging requirement is removed. Instead,bb events are selected using information stored at generation.This selection is done to reduce the statistical uncertaintiesin the Monte Carlo studies and does not influence the shapeof theΛ and companion baryon momentum spectra, as wasverified by comparing theΛ momentum spectra for taggedand non-tagged events.

The Monte Carlo events are divided into three categoriesrepresentingΛb → ΛX events and the two dominant back-grounds.

– The Λb → ΛX sample is formed with Monte Carloevents containing aΛ with subsequent decay to pπ, anda reconstructed companion baryon (Λ or p).

– The second sample contains B→ ΛX events having aΛin the final state and a reconstructed companion baryon.

– The third sample contains all other background sources.The biggest contribution (86%) comes fromΛ’s pro-duced in the fragmentation process in bb, cc and lighterquark flavour events. Other types of backgrounds are in-cluded, such as fakeΛ’s from combinatorial background.

Events are classified in either of the first two categoriesregardless of the true origin of the reconstructed companionbaryon as long as the directΛ is a genuine decay productof a b hadron. This ensures that all directΛ’s coming fromb hadron decays are in one of the first two samples. Therelative number of selected light flavours, cc and bb events inthe last sample is adjusted to reflect the flavour compositionin the data after the b-tagging requirements are applied.

Using the Monte Carlo simulation, we estimate the frac-tion of events containing primary cc quarks in the final sam-ple after b-tagging to be (4.3± 0.4)%. Contamination fromlighter flavours after the b-tagging accounts for (2.0±0.3)%of the total selected events. These are statistical errors.

4.3 Background separation method

As mentioned in Sect. 3, all b hadron decays produce directΛ’s with a similar momentum spectrum, whereas fragmenta-tion Λ’s are produced with a softer momentum spectrum. Byitself, theΛ momentum spectrum only helps in separating bhadron decays from fragmentation events. This is illustratedin the left column of Fig. 1 for Monte Carlo events.

To separateΛb → ΛX events from B→ ΛX events,we use the distinctive momentum spectra of the compan-ion baryon. ForΛb events, the companion baryon is pro-duced during fragmentation, and hence has a softer spectrum,whereas for B→ ΛX events, both the companion baryonand the directΛ are B meson decay products. This resultsin a strong boost, giving them a harder momentum spectrathan fragmentation particles. This behaviour is shown in theright column of Fig. 1. The jointΛ and companion baryonmomentum spectra allow the separation ofΛb → ΛX eventsfrom both types of background events.

4.4 Extracting theΛb → ΛX fraction

The fraction ofΛb → ΛX events in the denominator of (3)is extracted from the data by performing a binned maximumlikelihood fit to the two-dimensional momentum distributionof theΛ and the companion baryon. This momentum spaceis divided into 36 bins (6 bins of equal size for each axis).Three parameters are evaluated by the fit:fΛb, the signalfraction Λb → ΛX, fB, the fraction of events coming fromB → ΛX decays, andffrag, the fraction coming from frag-mentation and misidentifiedΛ’s. The data are assumed tobe a mixture of these three types of events such that theexpected number of events in bini, Ni, normalised to thetotal number of selected data eventsndata, is given by:

Ni =(fΛb

N iΛb

NΛb

+ fBN iB

NB+ ffrag

N if

Nf

)· ndata (4)

whereN iΛb/NΛb

, N iB/NB andN i

f/Nf represent the frac-tions of Monte Carlo events in bini from Λb, B, and frag-mentation plus other background events, respectively. These

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Fig. 1. TheΛ (left column) and the companion baryon (right column) mo-mentum spectra for baryons coming fromΛb decays(a,b), B meson decays(c,d) and from other background events(e,f) are shown for Monte Carloevents. The gap in the momentum spectrum of the companion baryon comesfrom the proton momentum cut. The hatched areas represent events wherethe companion baryon is misidentified. The “other backgrounds” sampleincludes baryons from fragmentation mostly in bb events, as well as fakeΛ’s. The spectra shown are obtained after detector simulation and applyingall selection criteria

fractions describe the shape of the two-dimensional momen-tum distributions for each of the three categories of events.The probabilityPi thatni data events are observed in biniwhenNi are expected is calculated using a Poisson distri-bution function:

Pi =Nnii e−Ni

ni!. (5)

Finally, the negative log likelihood, calculated from theproduct of the probabilitiesPi over all bins, is minimised:

− ln L = ndata −∑i

(ni lnNi) + constant. (6)

4.5 Testing theΛb → ΛX estimation method with MonteCarlo

This fitting method does not assume that the compositionof the data and Monte Carlo samples is the same. It canalso properly distinguish events containingΛb and B mesonsdecaying into aΛ, despite some dilution effect due to theselection of a random track instead of the true companionin about 25% ofΛb and B meson events. The separationpower is tested using Monte Carlo events. The Monte Carlosample is divided into three independent sets correspondingto the different generator versions described in Sect. 2. Foreach test, one sample is substituted for ‘data’ and anothersample is used as the reference Monte Carlo. Each sampleis compared to the two other Monte Carlo samples and the

Table 1. The true composition and the measured fractions from the fittingprocedure for two test Monte Carlo samples. The composition of the ref-erence Monte Carlo sample is given in the first column. The uncertaintiesshown are uncorrelated. The first one reflects the limited sample size ofthe test sample whereas the second one accounts for the limited number ofevents in the reference sample. Theχ2/d.o.f. are 25.5 for 32 d.o.f and 36.6for 31 d.o.f for the first and second tests, respectively. An empty bin in thesecond test sample was combined with an adjacent bin before performingthe fit, reducing the number of degrees of freedom by one. These valuesof χ2 are only indicators of the goodness-of-fit and are not used in theoptimisation process

Test 1reference true fitted

Λb 27.5% 24.6% (27.1± 2.4± 2.5)%B mesons 30.8% 30.7% (30.4± 1.9± 1.9)%

other background 41.7% 44.7% (42.4± 2.4± 2.5)%

Test 2reference true fitted

Λb 27.5% 38.3% (42.4± 3.6± 2.8)%B mesons 30.8% 7.8% (7.6± 2.4± 2.0)%

other background 41.7% 53.9% (50.0± 3.6± 2.9)%

fitting method is used to evaluate the sample composition,that is, the fit returns the values offΛb, fB andffrag describedin (4). The reference Monte Carlo provides the shape of themomentum distributions also described in (4). For each ofthe six possible tests, the fit estimates the true compositionof the test sample to within about 1.5 standard deviations,where the uncertainty is calculated by adding in quadraturethe uncorrelated uncertainties due to the limited size of thetest sample and the reference sample. Two typical resultsare shown in Table 1. Note that in the case of test 2, the fitproperly predicts the true test sample composition, despite avery different sample composition in the reference sample.

The fitting procedure also yields consistent results whenthe event selection criteria forΛ’s are modified. The fit isrepeated after varying the minimum momentum requirementfor Λ’s. The fit gives good agreement with the true compo-sition of the Monte Carlo samples in the range of 4.0 to 5.5GeV/c. As the required minimumΛ momentum increases,so does the correlation between theΛb → ΛX and the frag-mentation background. Beyond 5.5 GeV/c, the correlationbetweenfΛb and ffrag becomes too large and the methodloses reliability. The fitting method is not very sensitive tothe number of bins used for the fit. The good agreement be-tween fit and true compositions of these test samples underthese different changes supports the reliability of the fittingprocedure.

The fitting procedure exhibits proper statistical behaviour,as was checked using 1000 variations of the original MonteCarlo momentum distributions. These tests checked the errorestimate and that no bias or systematic shift was introducedby the fitting procedure.

5 Results from the analysis of the data sample

5.1 TheΛb → ΛX sample

The numbers ofΛb → ΛX events selected in the data and inthe Monte Carlo samples are shown in Table 2. The resultsof the fit arefΛb = 0.360± 0.046, fB = 0.192± 0.032 and

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Table 2. Numbers of selected events in the data and the Monte Carlosamples. The fragmentation sample contains events withΛ’s produced byfragmentation in bb, cc and lighter flavour events, as well as fakeΛ’s

# of eventsData 1595

all Monte Carlo events 12181Λb 3440

B mesons 3169fragmentation and other backgrounds 5572

fragmentation and other backgrounds 5572fragmentation in bb 4115fragmentation in cc 501

fragmentation in uds 234fakeΛ’s 722

ffrag = 0.448± 0.047, where the statistical uncertainties areshown. The correlation coefficient betweenfΛb andffrag isfairly large (−0.67). There is much less correlation betweenfΛb andfB (−0.30), and betweenfB andffrag (−0.30). Theχ2 is 36.8 for 32 degrees of freedom.

In about 25% of all b hadron events, a random track isselected for companion instead of the baryon produced tolocally conserve baryon number. This contamination affectsthe discrimination power of the fitting procedure by alter-ing the spectrum of true companion baryons for B mesons.Two thirds of these random tracks have momenta below 2.5GeV/c. We check that selecting a random track instead ofthe true companion baryon has no effect on the fit result.To do this, we set the minimum momentum requirement forcompanion baryons to be 2.5 GeV/c. The fractions resultingfrom the fit change by the same amount as the true fractionsin Monte Carlo for the same minimum momentum cut. Thisshows that the analysis selects incorrect companion baryontracks in a similar proportion in data and Monte Carlo, andthat these random tracks have no significant influence on thefit results.

5.2 TheΛb → Λ`X sample

To estimate the number ofΛb → Λ`X events in the data, allb-tagged events having a prompt lepton and aΛ with mo-mentum greater than 4.5 GeV/c are retained.3 No companionbaryon is required for this sample since requiring a promptlepton is sufficient to selectΛb → Λ`X events [8, 9].In the data, 298 events are selected, 215 of which havethe right-sign lepton charge and baryon number correla-tion, and 83 have the wrong-sign. Of these events, 133 con-tained an electron, and 165 a muon. After correcting for theright-sign wrong-sign imbalance as described in Sect. 4.1,the number ofΛb → Λ`X events in the data is found tobe 144.9 ± 17.3 ± 11.1 (64.8 ± 11.5 ± 5.0 electrons and80.3 ± 12.8 ± 6.1 muons). The second uncertainty comesfrom the estimate of the correction factor.

3 The b-tagging requirement is imposed on these events to maintainuniformity when selectingΛb → ΛX andΛb → Λ`X events. Monte Carlosimulation studies showed that the b-tagging requirement does not distorttheΛ momentum spectrum

6 Corrections and sources of systematic uncertainties

The most important contributions to the systematic uncer-tainty for RΛ`=BR(Λb → Λ`X)/BR(Λb → ΛX) are associ-ated with the estimate of theΛb fraction in theΛ X sample.The uncertainty arises from the proper Monte Carlo simu-lation of theΛ and the companion baryon spectra, and thelimited number of Monte Carlo events used for the fittingprocedure. In the next three sections, we compare data andMonte Carlo for each spectrum used in the extraction of thefraction ofΛb events.

Throughout this section, unless otherwise specified, thesystematic uncertainty is taken to be the size of the excursionfrom the central value when the studied parameter is allowedto vary within some limits. In the case where a significantdifference between Monte Carlo and data is observed, a cor-rection is applied. The final values for the systematic uncer-tainties and shifts due to corrections are listed in Table 3.An additional source of systematic uncertainty that does notcontribute to the calculation ofRΛ` but is needed to evaluatef (b→ Λb) ·BR(Λb → ΛX) andf (b→ B) ·BR(B→ ΛX) isgiven in the last subsection.

6.1Λ spectrum fromΛb decays

To check that the Monte Carlo properly simulates theΛ mo-mentum spectrum ofΛb → ΛX baryon decays as shownin Fig. 1a, we compare the spectrum ofΛ’s produced inΛb semileptonic decay between data and Monte Carlo sim-ulation. The Monte CarloΛ momentum spectrum fromΛb → ΛX decays is compared to that ofΛ’s coming fromΛb → Λ`X decays to ensure that the test is meaningful.Figure 2a shows that the Monte Carlo predicts no measur-able difference between theΛ spectrum inΛb → Λ`X andΛb → ΛX events.

The Λb → Λ`X events are selected as described inSect. 3.3, except that b-tagging is not imposed and the min-imum Λ momentum is reduced to 4 GeV/c in order toincrease statistics. The spectrum from wrong-sign lepton-baryon combinations is subtracted from the right-sign spec-trum to form the “direct” spectrum shown in Fig. 2b for dataand Monte Carlo. The measured meanΛ momentum in datais (7.32± 0.13) GeV/c compared to (7.59± 0.09) GeV/c inMonte Carlo after the wrong-sign subtraction. Theχ2 in Λ`events between Monte Carlo and data is measured to be 14.5for 17 d.o.f. in Fig. 2b. The observed difference in the meanΛ momentum inΛ` events between Monte Carlo and data iscorrected by scaling theΛ momenta for Monte Carlo eventsin theΛb → ΛX sample by 0.95. This slightly improves theoverall agreement between Monte Carlo and data. When thefit is redone with this modified Monte CarloΛ momentumspectrum, the value offΛb changes from 0.360 to 0.401.This is taken into account by including a correction to thefitted fraction of +0.041. An uncertainty in theΛ momen-tum scale factor of±0.02 is assumed, corresponding to onestandard deviation in the measured average momentum forΛ’s coming fromΛb decays in data. When the fit is redonewith a scale factor varying between 0.93 and 0.97, the fit-ting procedure evaluatesfΛb to be between 0.385 and 0.426,which results in an uncertainty infΛb of ±0.021. This cor-rection also takes into account possible differences in the

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Fig. 2. a) Two types of events from the Monte Carlo simulation are com-pared: The directΛ’s produced in theΛb → Λ`X decays (dashed line)compared toΛ’s from Λb → ΛX decays (solid line). b) The momentumspectrum of directΛ’s produced in semileptonicΛb → Λ`X events fordata (points) and Monte Carlo (already shown ina) (hatched histogram)after wrong-sign subtraction

Λ momentum spectra between data and Monte Carlo com-ing from incorrect modelling of the relative population ofexcited b baryon states.

In addition to the test shown in Fig. 2a, we also useMonte Carlo events to determine the effect of theΛb de-cay multiplicity on theΛ momentum spectrum since thatcould lead to differences in the momentum spectrum ofΛ’sfrom semileptonicΛb decays compared to allΛb events. Weexamine allΛb decays and compare the averageΛ momen-tum in hadronic and semileptonic decays, looking for a dif-ference in average momenta. The average momentum for aΛ from Λb → Λπππ is measured to be about 0.97 times thatfrom a semileptonic decay, well within the range of varia-tion investigated. Hence, no further correction or systematicuncertainty is applied.

The momentum spectrum of theΛb decay productsdepends both on the model used to simulate the decayand on theΛb polarisation. We use two additional MonteCarlo samples to check the dependence of theΛ spec-trum on the decay model andΛb polarisation. A first set ofΛb → Λ`X events4 is selected from a separate Monte Carlosample [9] where the b baryon decay is simulated using adifferent decay model [24]. In this model, the momentumdistribution of the b baryon decay products depends stronglyon the form factors used to describe the energy transfer fromthe b baryon to the c baryon. The particular choice of formfactors [25] used in generating these events results in asofter momentum spectrum for the c baryon and therefore asofterΛ spectrum. A second set of Monte Carlo events was

4 Form factors and polarisation have been simulated only in semileptonicdecays

Fig. 3. The momentum spectrum ofΛ’s selected with a prompt anti-leptonin b-tagged events. The points represent the data and the histograms showthe spectra for Monte Carlo events after they were normalised to the numberof data events. The hatched histogram corresponds to contamination frommisreconstructedΛ’s

generated using the same decay model and adding maximumpolarisation to theΛb baryons.

In each case, theΛ momentum spectrum for these MonteCarlo events is compared with the spectrum found forsemileptonicΛb events in the data, shown in Fig. 2. Thedifferences observed are within the limits allowed for theuncertainty in the shape of theΛ spectrum inΛb decays.Hence, no additional correction or systematic uncertainty isneeded to account for the effects of decay model or polari-sation.

6.2 Fragmentation spectrum

This section describes studies that check the Monte Carlospectra for baryons created in the fragmentation process,such as those shown in Figs. 1b, e and f. We use two dif-ferent methods: the first one is a direct but low statisticstechnique, whereas the second is an indirect approach withthe advantage of high statistics.

To test the spectrum shown in Fig. 1b (baryons pro-duced from fragmentation in aΛb event), we look for acompanion baryon in semileptonicΛb events and comparethe data directly to the Monte Carlo after subtracting thewrong-signΛ-lepton combinations from the right-sign com-binations. According to Monte Carlo studies, (95± 1)% ofΛ’s found in a wrong-signΛ-lepton combination are fromfragmentation. Of those events coming from fragmentation,(82± 3)% contain a properly identified companion baryon.Only 130 events are found in the data sample containingboth aΛ-lepton pair with the wrong sign combination anda companion baryon even after removing the b-tagging re-quirement. Given these statistical limitations, we can onlyinfer that there is no gross problem in the Monte Carlo sim-ulation of the fragmentation spectrum displayed in Figs. 1b, e and f.

For a second but more indirect check of the fragmen-tation baryon momentum simulation, the shape of the mo-mentum spectrum for baryons coming from fragmentationis extracted from the data and compared with Monte Carloevents. These baryons are either created during the frag-mentation process in bb events or are produced to con-serve baryon number inΛb production. Such events are se-lected by requiring that either hemisphere satisfies the b-tagging requirements described earlier. Each hemisphere is

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Fig. 4. Comparison of the momentum spectrum in data (points) and MonteCarlo (histograms) for a sample of protons selected with a prompt anti-lepton in b-tagged events and after rejecting tracks consistent with being akaon. The spectra are shown for two different ranges:a) 0.33-1.4 GeV/c(anti-protons only) andb) 3.0-12 GeV/c. Thehatched histogramshows thelevel of contamination from misidentified particles

then searched for a prompt lepton (as defined in Sect. 3.3)and an anti-baryon (eitherΛ or p). In the Monte Carlo simu-lation, (83.8±0.2)% of these prompt leptons originate from ab quark decay. Only events with the wrong-sign combination(i.e. a lepton and an anti-baryon pair) are retained in order topreferentially select baryons produced in the fragmentationand to reject baryons coming directly from b hadron decay.Using the Monte Carlo, we estimate that (91.8± 0.5)% ofthe trueΛ’s so selected are baryons coming from the frag-mentation process. The spectrum of theseΛ’s is shown inFig. 3, where the hatched region represents the misidentifiedparticles.

For the proton sample, the simpler selection5 require-ments imposed for this test lead to higher background con-tamination by misidentified kaons. By rejecting kaons us-ing a more stringent dE/dx requirement than required forthe main analysis, we can select a purer sample of pro-tons. The momentum spectrum of these proton candidatesis shown in Fig. 4 for two separate momentum ranges.Only anti-protons are shown in Fig. 4a to reduce contri-butions from secondary interactions which produce mainlyprotons below 1 GeV/c. We estimate that (98.1± 0.2)% ofthe protons shown in Fig. 4a and (92.4 ± 1.2)% of thoseshown in b are baryons created during the fragmentationprocess. A systematic uncertainty from this source is as-cribed by modifying the fragmentation spectrum for MonteCarlo events and refitting the data. ForΛ’s, the mean mo-mentum in the data is ¯pdata = (2.80± 0.06) GeV/c com-pared to ¯pMC = (2.98± 0.03) GeV/c in the Monte Carlo. InFig. 4a, the mean momentum for anti-protons from the data

5 No directΛ is required for this sample, as was the case when selectingcompanion protons for the main analysis

is pdata = (0.913± 0.008) GeV/c whereas for Monte Carloevents, ¯pMC = (0.935± 0.004) GeV/c, when including allbackground contaminants. Above 3 GeV/c in Fig. 4b, weobtain pdata = (5.80± 0.13) GeV/c and pMC = (5.91± 0.08)GeV/c. The small observed difference in the average protonmomentum is corrected for in the Monte Carlo by apply-ing a multiplicative factor of 0.976 to the momentum ofall baryons coming from fragmentation. When refitting withthese modified momenta, we observe a shift of the centralvalue forfΛb of −0.005. An uncertainty of±0.010 is takenon the correction factor, which leads to a systematic uncer-tainty of ±0.003 on fΛb. The shifts and uncertainties areshown in Table 3 for the three fit parameters.

6.3Λ’s coming from B meson decays

We compare the momentum spectrum ofΛ’s coming from Bmeson decays in the simulated sample (such as those shownin Fig. 1c and d) to the spectrum for B→ ΛX events mea-sured by the CLEO collaboration [26]. At theΥ (4S) reso-nance, B mesons are essentially produced at rest. We use theshape of the distribution forxp, the fraction of the maximummomentum carried by theΛ, as defined by CLEO. The max-imum momentum is determined by the difference betweenthe beam energy at theΥ (4S) resonance and the mass oftheΛ. We reweight the Monte Carlo events to simulate thexp distribution observed by CLEO. There is very little dif-ference in the average momentum ofΛ’s (1.6%) betweenweighted and unweighted events for theΛ momentum dis-tribution. We estimate the systematic uncertainty by usingthe weighted events to perform the fit. There is no effect onthe fitted value forfΛb and a small change forfB andffrag,hence the small contributions to the systematic uncertaintiesshown in Table 3.

6.4 Protons coming from B meson decays

For companion protons produced in the B→ ΛX decays,we do not have a direct way of comparing the Monte Carlosimulation with the data. Based on the good agreement withdata found for companionΛ’s in these decays and the gen-eral agreement of our Monte Carlo simulation for the mo-mentum spectrum of all protons found in b-tagged eventscontaining a prompt lepton, we estimate the contribution tothe systematic uncertainty by modifying the momentum ofcompanion protons by a multiplicative factor ranging from0.95 to 1.05 and refitting. The corresponding variations inthe estimate of the sample composition are shown in Table 3.

6.5 The b hadron momentum spectrum

TheΛ and companion baryon momenta are also modified toevaluate the effects of a slightly different b hadron momen-tum spectrum on the fit results. The average b hadron mo-mentum has been measured by OPAL [9] to be (33.9±0.2)GeV/c, compared to 33.7 GeV/c in the Monte Carlo sim-ulation. Accordingly, variations in the momentum of theΛ’s coming from b hadron decays (B mesons andΛb’s)

432

by ±0.6% were investigated. The fit is repeated with thesemodified momenta, giving a contribution of±0.003 to thesystematic uncertainty from this source. This uncertainty canbe expected to account for possible differences in the baryonspectra between data and Monte Carlo simulation due to theparametrisation of the fragmentation process.

6.6 Background in theΛ sample

The background in theΛ sample is compared between dataand Monte Carlo using the sidebands of the (p-π) invariantmass distribution. A fakeΛ fraction of (5.9±0.2)% is foundin theΛb → ΛX region for Monte Carlo, in agreement withthe rate of (5.9±1.1)% observed in the data. We evaluate thecontribution to the systematic uncertainty by adding back-ground events to the Monte Carlo sample so as to raise thefakeΛ rate to 7%, corresponding to one standard deviationin the fake rate measured in data. When refitting, the valueof fΛb changes from 0.360 to 0.358. The difference is takento be the size of the systematic uncertainty, that is±0.002.

6.7 Finite Monte Carlo sample size

The finite Monte Carlo sample size introduces an additionaluncertainty in the fit result. This systematic uncertainty isevaluated separately using a set of 1000 “toy” Monte Carlosamples. The number of Monte Carlo events found in eachmomentum bin is allowed to fluctuate around the initial cen-tral value according to Poisson statistics. Each sample is usedto fit the data sample. The spread in the distribution of re-sults for fΛb for these 1000 separate trials is a measure ofthe systematic uncertainty introduced in the fit due to thelimited number of Monte Carlo statistics. An uncertainty onfΛb of ±0.019 is assigned for the systematic uncertainty andis shown, with all other sources, in Table 3.

6.8 b-flavour tagging

Systematic uncertainties for b-tagging account for the un-certainty in the evaluation of the efficiency using a finiteMonte Carlo sample and for the difference observed betweendata and Monte Carlo, which is obtained using a double-tag technique [17]. The b-tagging requirement has an ef-ficiency of 0.406± 0.008 in retainingΛb → ΛX events inthe Monte Carlo, where the error is purely statistical. ForΛb → Λ`X events, one can obtain a clean sample withoutimposing the b-tagging requirement using the wrong-signbackground subtraction [8, 9]. Hence, the efficiency can bemeasured in both the data and the Monte Carlo simulationfor Λb → Λ`X events. The efficiency forΛb → Λ`X eventsis measured to be 0.383± 0.032 for Monte Carlo and0.426± 0.067 for data. Applying the b-tagging require-ments to a larger sample of Monte CarloΛb events revealsthat the b-tagging efficiency is slightly less for semileptonicΛb events than for allΛb events. The reduced efficiency forsemileptonic events is explained by the lower track multi-plicity at theΛb decay vertex because of the invisible neu-trino. An additional systematic uncertainty of 0.015 is added

in quadrature to account for a small difference in b-taggingefficiency observed between data and Monte Carlo whenusing double tags. In this case, the b-tagging efficiency forΛb → ΛX events is 0.406± 0.017 and 0.383± 0.035 forΛb → Λ`X events. For B→ ΛX events, we estimate theefficiency from the Monte Carlo to be 0.455±0.019, includ-ing all systematic uncertainties. The b-tagging efficiency isslightly less forΛb → ΛX events than for other bb eventsdue to the shorterΛb lifetime and a lower track multiplicityat theΛb decay vertex since tracks from theΛ decay prod-ucts do not contribute to the b vertex reconstruction. Allb-tagging efficiencies given above are efficiencies per eventwhen one hemisphere contains the specified type of eventsand the other hemisphere contains any type of b decay.

6.9Λ finding efficiencies

To evaluatef (b → Λb) · BR(Λb → ΛX) and f (b → B) ·BR(B → ΛX), the systematic uncertainty on theΛ findingefficiency is also needed, which is evaluated by comparingdata with Monte Carlo. We obtain theΛ finding efficiencyfrom the number ofΛ’s retained in the signal region afterapplying the dE/dx selection criteria for the proton and pionafter background subtraction, which is the dominant effect.The background is evaluated using the side-bands of theΛ invariant mass distribution. A similar comparison is doneafter degrading the tracking resolution in the Monte Carlosimulation. We assign an uncertainty of±2% to account forboth of these effects.

6.10 Summary of systematic uncertainties

After making the corrections for systematic shifts listed inTable 3, and including all systematic errors, the compositionof the data sample selected with a directΛ and a companionbaryon is:

fΛb = 0.396± 0.046± 0.031,

fB = 0.219± 0.032± 0.024, and

ffrag = 0.385± 0.047± 0.034.

Using these fractions, we can adequately reproduce the shapeof the momentum distributions observed in data forΛ’s andthe companion baryons. This can be seen in Fig. 5 wherewe have superimposed the momentum distributions from thethree types of Monte Carlo events used to perform the fit.

To verify that no correlations in the two-dimensional dis-tributions have been neglected, we also examine theΛ mo-mentum in the data for low and high-momentum compan-ion baryons separately. Again, good agreement between thespectra in data and the total Monte Carlo prediction supportsthe reliability of this technique.

7 Calculation of the ratio of branching ratios

To calculate the ratio of branching ratios, the respective se-lection efficiencies forΛe andΛµ (εΛe andεΛµ), and the ef-ficiency to find both theΛ and the companion baryon (εΛp),need to be included. The ratioRΛ` is given by:

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Table 3. Contributions from different sources to the systematic uncertainties in the estimate offΛb,fB andffrag. The shifts correspond to the corrections applied to the Monte Carlo when a significantdifference is found between data and Monte Carlo

Source fΛb shift δ fΛb fB shift δ fB ffrag shift δ ffrag

Λ’s from Λb decays +0.041 ±0.021 +0.006 ±0.002 −0.047 ±0.023fragmentation simulation −0.005 ±0.003 +0.021 ±0.010 −0.016 ±0.009Λ’s from B→ ΛX ±0.000 ±0.011 ±0.011protons in B→ ΛX ±0.012 ±0.014 ±0.003b hadron momentum ±0.003 ±0.006 ±0.007fakeΛ rate in data ±0.002 ±0.002 ±0.005

Monte Carlo sample size ±0.019 ±0.012 ±0.019total contribution +0.036 ±0.031 +0.027 ±0.024 −0.063 ±0.034

Fig. 5. Results of the fit where the contributions from the three types ofMonte Carlo events are compared with data for theΛ and companionbaryon momentum spectra. These values ofχ2 are calculated includingonly statistical errors. These are only indicators of the goodness-of-fit andare not used in the optimisation process

RΛ` =BR(Λb → Λ`X)BR(Λb → ΛX)

=12

(NΛe

εΛe+NΛµ

εΛµ

)· εΛp

fΛb N

·εΛb−tag

εΛ`b−tag

. (7)

NΛe (NΛµ) is obtained by subtracting the wrong-signΛe(Λµ) from the right-sign combinations found in data andcorrecting for the background imbalance. The numeratorin RΛ` is obtained from the average ofNΛe and NΛµ,weighted by their respective efficiencies. The number of se-lectedΛb → ΛX events is given by theΛb fractionfΛb fromthe fit times the number of selected events,N . The b-taggingefficiencies for events withΛb → ΛX and Λb → Λ`X de-cays (as discussed in Sect. 6.8) are given byεΛb−tag andεΛ`b−tag,respectively. Monte Carlo predictsεΛe = 0.0386± 0.0015andεΛµ = 0.0423±0.0016. This includes theΛ finding andlepton identification efficiencies. For the denominator,εΛp is0.0242±0.0004 for theΛ and companion finding efficienciescombined. All uncertainties are statistical and are estimatedfrom the Monte Carlo.

Table 4. Results for the 1991-95 data sample including all corrections andsystematic uncertainties. The numbers ofΛ` have been corrected for thebackground imbalance described in Sect. 4.1 and the systematic uncertain-ties come from that correction factor. The correction factor accounting fordifferences in proton finding efficiencies in the data has been absorbed inεΛp

NΛe 64.8± 11.5 (stat.)± 5.0 (syst.)NΛµ 80.3± 12.8 (stat.)± 6.2 (syst.)N 1595± 40 (stat.)fΛb 0.396± 0.046 (stat.)± 0.031 (syst.)εΛe 0.0386± 0.0018 (syst.)εΛµ 0.0423± 0.0020 (syst.)εΛp 0.0233± 0.0007 (syst.)εΛb−tag 0.406± 0.017 (syst.)εΛ`b−tag 0.383± 0.035 (syst.)

RΛ` (7.0± 1.2 (stat.)± 0.7 (syst.))%

Table 5. Effect of the minimum momentum cut on the central value forRΛ`. The errors shown are the statistical uncertainties related to the datasample size and are partly correlated

minimumΛ momentum cut RΛ`

4.00 GeV/c (8.1± 1.4)%4.25 GeV/c (8.0± 1.4)%4.50 GeV/c (7.0± 1.2)%4.75 GeV/c (7.2± 1.3)%5.00 GeV/c (6.3± 1.1)%5.25 GeV/c (6.8± 1.3)%5.50 GeV/c (6.8± 1.3)%

Only factors not common to the numerator and denom-inator need to be considered in evaluating the systematicuncertainty. These are uncertainties related to lepton iden-tification for the numerator, and companion baryon findingfor the denominator. They reflect differences in observed ef-ficiencies between Monte Carlo and data. For electron iden-tification using a neural network, the systematic uncertaintyon the electron finding efficiency is evaluated to be 2.5%using electrons coming from photo conversions [21]. Formuons, the uncertainty is 3.0% [27]. About 87% of thecompanion baryons are protons identified using dE/dx infor-mation. A difference in efficiency between data and MonteCarlo is observed when the dE/dx information is used toidentify protons coming fromΛ decays. The efficiency is(3.42± 0.05)% higher in the Monte Carlo than in data. Acorrection of−3.42% is applied toεΛp with a systematicuncertainty equivalent to half the correction itself. The re-sulting efficiencies and their uncertainties are summarised inTable 4.

No systematic uncertainty is attributed to the estimationof theΛ finding efficiency. This is because theΛ momentum

434

Table 6.Results for different data subsamples: Using data from 1991-93 versus data from 1994-95;using exclusivelyΛ or Λ in the denominator of (7); or using electrons and muons separately in thenumerator. HereNΛb→Λ` X denotes the sum of the electron and muon channels, and∆NΛb→Λ` X,the statistical error. The imbalance in the number ofΛ and Λ found reflects the fact that morecompanion protons than companion anti-protons are found, due to secondary interactions with thedetector material. All results are consistent with each other, as well as with the full data set

for denominator: for numerator:all data 1991-93 1994-95 Λ only Λ only e only µ only

NΛb→Λ` X 145.1 61.6 83.5 145.1 145.1 64.8 80.3∆NΛb→Λ` X ±17.3 ±11.0 ±13.3 ±17.3 ±17.3 ±11.5 ±12.8

NΛ 1595 698 897 706 889 1595 1595fΛb from fit 0.396 0.358 0.431 0.350 0.436 0.396 0.396∆ fΛb (stat.) ±0.046 ±0.068 ±0.062 ±0.067 ±0.064 ±0.046 ±0.046

RΛ` 7.0% 7.5% 6.6% 8.1% 6.2% 6.6% 7.4%stat. error ±1.2% ±2.0% ±1.4% ±1.9% ±1.2% ±1.4% ±1.5%

Table 7. All quantities and their uncertainties needed for the evaluation ofthe product branching ratios

fΛb 0.396± 0.046± 0.031fB 0.219± 0.032± 0.024ffrag 0.385± 0.047± 0.034N 1595± 40Nhad 3840074± 1960Rb 0.2209± 0.0021εΛp 0.0233± 0.0008(syst.)εΛb−tag 0.406± 0.017(syst.)εB

b−tag 0.455± 0.019(syst.)

distribution is very similar forΛb → ΛX and Λb → Λ`Xevents, both in data and Monte Carlo. Hence this factor can-cels out when taking the ratio.

This leads to a value of

RΛ` =BR(Λb → Λ`X)BR(Λb → ΛX)

= (7.0± 1.2 (stat.)± 0.7 (syst.))%

for the ratio of branching ratios averaging over electrons andmuons.

8 Further consistency checks

The effect of changing the minimumΛ momentum require-ment on the measured value forRΛ` is investigated overthe range of reliability of the fitting procedure. We in-crease the minimumΛ momentum cutpcut in steps of 0.25GeV/c and recalculateRΛ` each time. All results are con-sistent with each other, although the values obtained forpcut < 4.5 GeV/c show a larger deviation. Further inves-tigation reveals that these are consistent with being causedby small statistical fluctuations in the evaluation of the de-nominator forRΛ`. Similar fluctuations were also observedwith Monte Carlo. Aspcut is lowered, the sample com-position changes since more background events are intro-duced, modifying the overall correlations between the fitvariables. The different values obtained forRΛ` seen in Ta-ble 5 have an r.m.s. value of 0.6%, which is well within thestatistical error of this measurement. The 4.5 GeV/c mini-mum Λ momentum requirement optimises the suppressionof contributions from fragmentation and other backgrounds,without causing an increase in the overall statistical uncer-tainty. Three uncorrelated and statistically independent sub-samples are used to further check our result for the ratio

RΛ`=BR(Λb → Λ`X)/BR(Λb → ΛX) for consistency. In thefirst test, the data are divided into two subsamples corre-sponding to the 1991-93 and 1994-95 data samples. In thesecond test, the sample of all selectedΛb → ΛX candidatesin the data is divided between events containing aΛ versusevents containing aΛ in the denominator while the originalfull sample is used in the numerator. In the third test, thedata are divided in the numerator into the separate electronand muon samples, keeping the original full sample in thedenominator. For each of these subsamples, the ratioRΛ` iscalculated. All results are found to be statistically consistentwith each other and with the full data sample as can be seenin Table 6.

A separate cross-check is made using this measurementto derivef (b→ Λb) ·BR(Λb → Λ`νX). We measure (2.57±0.23)× 10−3, to be compared to (2.91± 0.23± 0.25)×10−3 obtained in a previous analysis [9]. The uncertaintyshown is statistical only. The systematic uncertainty wouldbe of similar size. The statistical and systematic uncertaintiesof the two measurements are only partly correlated sincedifferent selection criteria as well as different Monte Carlosimulations and data samples are used for these analyses.

9 Related measurements and conclusions

We have presented the first measurement ofRΛ`=BR(Λb → Λ`X)/BR(Λb → ΛX) whereΛb denotes inclusiveb baryons. The measured value is:

RΛ` = (7.0± 1.2± 0.7)%,

significantly lower than BRBSL = (10.43± 0.24)% [1], thesemileptonic branching fraction for B0 and B± mesons mea-sured at theΥ (4S) resonance, as well as significantly lowerthan BRbSL = (11.13± 0.29)% [1] for the average b hadronsemileptonic branching ratio measured at high energy. Thisindicates that non-spectator amplitudes play a significant rolein b hadron decays, as can be inferred from the differenceobserved between the measured B0 lifetime and the b baryonlifetime [1].

It is interesting to note that for B denoting both B0 andB± mesons, and b denoting all b hadrons formed at the Z0

resonance

RΛ`

BR(B→ `X)= 0.67± 0.13 and

τΛb

τB= 0.72± 0.05; (8)

435

RΛ`

BR(b→ `X)= 0.63± 0.13 and

τΛb

τb= 0.74± 0.05 (9)

all have very similar values. This indicates that the non-spectator effects responsible for the observed lifetime differ-ences in b hadrons mainly influence the total decay widthsbut not the semileptonic decay widths, in accordance withtheoretical expectations [5].

From this analysis, we can extract other interesting quan-tities, provided we include an additional contribution to thesystematic uncertainty for theΛ selection efficiency, as de-scribed in Sect. 6.9. We obtain the product branching frac-tion:

f (b→ Λb) · BR(Λb → ΛX) =fΛb · NεΛp

· 12 Rb Nhad

and (10)

f (b→ B) · BR(B→ ΛX) =fB NεΛp

· 12 Rb Nhad

(11)

wheref (b → Λb) is the fraction of b quarks formingΛb’s(all weakly decaying b baryons found near the Z0 resonance),andf (b→ B), the fraction of b quarks forming B0, B± andBs mesons.N represents the number of selected events con-taining a directΛ and a companion baryon,Rb is the frac-tion of hadronic Z0 decays into bb quarks [28], andNhadthe number of hadronic Z0 decays passing our selection cri-teria [15]. The extra factor of two accounts for the presenceof two hemispheres per event. All relevant quantities andtheir systematic uncertainties are summarised in Table 7.The results are:

f (b→ Λb) · BR(Λb → ΛX) = (3.93± 0.46± 0.37)% and

f (b→ B) · BR(B→ ΛX) = (1.94± 0.28± 0.24)%.

We obtain the inclusive b hadron branching ratio using (fΛb +fB = 1−ffrag) to evaluate the inclusive fraction of b hadronsdecaying intoΛ’s.

BR(b → ΛX) = (5.87± 0.46± 0.48)%,

to be compared with (5.9±0.7±0.9)% from DELPHI [29].The b represents an admixture of B0, B±, Bs and Λb asproduced near the Z0 resonance. Assumingf (b→ Λb) to be0.132± 0.041 [1], we obtain

BR(Λb → ΛX) = (29.8± 3.5± 2.3± 9.2)%.

This can be compared with the world average (17+9−6 ±

5)% [1]. Both results are evaluated using the same as-sumption forf (b → Λb). The last uncertainty reflects theuncertainty fromf (b → Λb). Assuming f (b → B) =0.868± 0.041 [1] yields

BR(B→ ΛX) = (2.2± 0.3± 0.2± 0.1)%

where the last error comes from the uncertainty onf (b →B). In this case, B represents all B mesons, i.e. an admixtureof B0, B± and Bs. This result can be compared with thecombined results obtained at theΥ (4S) resonance [1] of(4.0± 0.5)% which includes only B0 and B± decays.

Acknowledgements.We particularly wish to thank the SL Division for theefficient operation of the LEP accelerator and for their continuing closecooperation with our experimental group. In addition to the support staff

at our own institutions we are pleased to acknowledge the Departmentof Energy, USA, National Science Foundation, USA, Particle Physics andAstronomy Research Council, UK, Natural Sciences and Engineering Re-search Council, Canada, Israel Science Foundation, administered by the Is-rael Academy of Science and Humanities, Minerva Gesellschaft, JapaneseMinistry of Education, Science and Culture (the Monbusho) and a grantunder the Monbusho International Science Research Program, German Is-raeli Bi-national Science Foundation (GIF), Direction des Sciences de laMatiere du Commissariata l’Energie Atomique, France, Bundesministeriumfur Bildung, Wissenschaft, Forschung und Technologie, Germany, NationalResearch Council of Canada, Hungarian Foundation for Scientific Research,OTKA T-016660, and OTKA F-015089.

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