measurements of the bs0 and lambdab0 lifetimes

30 April 1998

Ž .Physics Letters B 426 1998 161–179

Measurements of the B0 and L0 lifetimess b

OPAL Collaboration

K. Ackerstaff h, G. Alexander v, J. Allison p, N. Altekamp e,K.J. Anderson i, S. Anderson l, S. Arcelli b, S. Asai w, S.F. Ashby a,D. Axen ab, G. Azuelos r,1, A.H. Ball q, E. Barberio h, R.J. Barlow p,

R. Bartoldus c, J.R. Batley e, S. Baumann c, J. Bechtluft n, C. Beeston p,T. Behnke h, A.N. Bell a, K.W. Bell t, G. Bella v, S. Bentvelsen h, S. Bethke n,

S. Betts o, O. Biebel n, A. Biguzzi e, S.D. Bird p, V. Blobel z, I.J. Bloodworth a,J.E. Bloomer a, M. Bobinski j, P. Bock k, D. Bonacorsi b, M. Boutemeur ag,S. Braibant h, L. Brigliadori b, R.M. Brown t, H.J. Burckhart h, C. Burgard h,

R. Burgin j, P. Capiluppi b, R.K. Carnegie f, A.A. Carter m, J.R. Carter e,¨C.Y. Chang q, D.G. Charlton a,2, D. Chrisman d, P.E.L. Clarke o, I. Cohen v,

J.E. Conboy o, O.C. Cooke h, C. Couyoumtzelis m, R.L. Coxe i, M. Cuffiani b,S. Dado u, C. Dallapiccola q, G.M. Dallavalle b, R. Davis ac, S. De Jong l,

L.A. del Pozo d, K. Desch c, B. Dienes af,3, M.S. Dixit g, M. Doucet r,E. Duchovni y, G. Duckeck ag, I.P. Duerdoth p, D. Eatough p, J.E.G. Edwards p,

P.G. Estabrooks f, H.G. Evans i, M. Evans m, F. Fabbri b, A. Fanfani b,M. Fanti b, A.A. Faust ac, L. Feld h, F. Fiedler z, M. Fierro b, H.M. Fischer c,

I. Fleck h, R. Folman y, D.G. Fong q, M. Foucher q, A. Furtjes h, D.I. Futyan p,¨P. Gagnon g, J.W. Gary d, J. Gascon r, S.M. Gascon-Shotkin q, N.I. Geddes t,

C. Geich-Gimbel c, T. Geralis t, G. Giacomelli b, P. Giacomelli d, R. Giacomelli b,V. Gibson e, W.R. Gibson m, D.M. Gingrich ac,1, D. Glenzinski i, J. Goldberg u,

M.J. Goodrick e, W. Gorn d, C. Grandi b, E. Gross y, J. Grunhaus v,M. Gruwe h, C. Hajdu ae, G.G. Hanson l, M. Hansroul h, M. Hapke m,´

C.K. Hargrove g, P.A. Hart i, C. Hartmann c, M. Hauschild h, C.M. Hawkes e,R. Hawkings z, R.J. Hemingway f, M. Herndon q, G. Herten j, R.D. Heuer h,

1 And at TRIUMF, Vancouver, Canada V6T 2A3.2 And Royal Society University Research Fellow.3 And Department of Experimental Physics, Lajos Kossuth University, Debrecen, Hungary.

0370-2693r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved.Ž .PII S0370-2693 98 00289-5

( )K. Ackerstaff et al.rPhysics Letters B 426 1998 161–179162

M.D. Hildreth h, J.C. Hill e, S.J. Hillier a, P.R. Hobson x, A. Hocker i,R.J. Homer a, A.K. Honma aa,1, D. Horvath ae,4, K.R. Hossain ac,´

R. Howard ab, P. Huntemeyer z, D.E. Hutchcroft e, P. Igo-Kemenes k,¨D.C. Imrie x, M.R. Ingram p, K. Ishii w, A. Jawahery q, P.W. Jeffreys t, H. Jeremie r,M. Jimack a, A. Joly r, C.R. Jones e,G. Jones p, M. Jones f, U. Jost k, P. Jovanovic a,

T.R. Junk h, J. Kanzaki w, D. Karlen f, V. Kartvelishvili p, K. Kawagoe w,T. Kawamoto w, P.I. Kayal ac, R.K. Keeler aa, R.G. Kellogg q, B.W. Kennedy t,

J. Kirk ab, A. Klier y, S. Kluth h, T. Kobayashi w, M. Kobel j, D.S. Koetke f,T.P. Kokott c, M. Kolrep j, S. Komamiya w, T. Kress k, P. Krieger f,

J. von Krogh k, P. Kyberd m, G.D. Lafferty p, R. Lahmann q, W.P. Lai s,D. Lanske n, J. Lauber o, S.R. Lautenschlager ad, J.G. Layter d, D. Lazic u,

A.M. Lee ad, E. Lefebvre r, D. Lellouch y, J. Letts l, L. Levinson y,S.L. Lloyd m, F.K. Loebinger p, G.D. Long aa, M.J. Losty g, J. Ludwig j, D. Lui l,

A. Macchiolo b, A. Macpherson ac, M. Mannelli h, S. Marcellini b, C. Markopoulos m,C. Markus c, A.J. Martin m, J.P. Martin r, G. Martinez q, T. Mashimo w,

P. Mattig y, W.J. McDonald ac, J. McKenna ab, E.A. Mckigney o,¨T.J. McMahon a, R.A. McPherson h, F. Meijers h, S. Menke c, F.S. Merritt i,

H. Mes g, J. Meyer z, A. Michelini b, G. Mikenberg y, D.J. Miller o, A. Mincer u,5,R. Mir y, W. Mohr j, A. Montanari b, T. Mori w, U. Muller c, S. Mihara w,¨

K. Nagai y, I. Nakamura w, H.A. Neal h, B. Nellen c, R. Nisius h, S.W. O’Neale a,F.G. Oakham g, F. Odorici b, H.O. Ogren l, A. Oh z, N.J. Oldershaw p,

M.J. Oreglia i, S. Orito w, J. Palinkas af,3, G. Pasztor ae, J.R. Pater p,´ ´ ´G.N. Patrick t, J. Patt j, R. Perez-Ochoa h, S. Petzold z, P. Pfeifenschneider n,

J.E. Pilcher i, J. Pinfold ac, D.E. Plane h, P. Poffenberger aa, B. Poli b,A. Posthaus c, C. Rembser h, S. Robertson aa, S.A. Robins u, N. Rodning ac,

J.M. Roney aa, A. Rooke o, A.M. Rossi b, P. Routenburg ac, Y. Rozen u,K. Runge j, O. Runolfsson h, U. Ruppel n, D.R. Rust l, R. Rylko x, K. Sachs j,

T. Saeki w, W.M. Sang x, E.K.G. Sarkisyan v, C. Sbarra ab,A.D. Schaile ag, O. Schaile ag, F. Scharf c, P. Scharff-Hansen h, J. Schieck k,

P. Schleper k, B. Schmitt h, S. Schmitt k, A. Schoning h, M. Schroder h,¨ ¨H.C. Schultz-Coulon j, M. Schumacher c, C. Schwick h, W.G. Scott t, T.G. Shears p,

B.C. Shen d, C.H. Shepherd-Themistocleous h, P. Sherwood o,G.P. Siroli b, A. Sittler z, A. Skillman o, A. Skuja q, A.M. Smith h,G.A. Snow q, R. Sobie aa, S. Soldner-Rembold j, R.W. Springer ac,¨

M. Sproston t, K. Stephens p, J. Steuerer z, B. Stockhausen c, K. Stoll j,

4 And Institute of Nuclear Research, Debrecen, Hungary.5 And Department of Physics, New York University, NY 1003, USA.

( )K. Ackerstaff et al.rPhysics Letters B 426 1998 161–179 163

D. Strom s, R. Strohmer ag, P. Szymanski t, R. Tafirout r, S.D. Talbot a,¨S. Tanaka w, P. Taras r, S. Tarem u, R. Teuscher h, M. Thiergen j, M.A. Thomson h,

E. von Torne c, E. Torrence h, S. Towers f, I. Trigger r, Z. Trocsanyi af,¨ ´ ´E. Tsur v, A.S. Turcot i, M.F. Turner-Watson h, P. Utzat k, R. Van Kooten l,

M. Verzocchi j, P. Vikas r, E.H. Vokurka p, H. Voss c, F. Wackerle j, A. Wagner z,¨C.P. Ward e, D.R. Ward e, P.M. Watkins a, A.T. Watson a, N.K. Watson a,

P.S. Wells h, N. Wermes c, J.S. White aa, B. Wilkens j, G.W. Wilson z,J.A. Wilson a, T.R. Wyatt p, S. Yamashita w, G. Yekutieli y, V. Zacek r,

D. Zer-Zion h

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

c Physikalisches Institut, UniÕersitat Bonn, D-53115 Bonn, Germany¨d Department of Physics, UniÕersity of California, RiÕerside, CA 92521, USA

e CaÕendish Laboratory, Cambridge CB3 0HE, UKf Ottawa-Carleton Institute for Physics, Department of Physics, Carleton UniÕersity, Ottawa, Ont. K1S 5B6, Canada

g Centre for Research in Particle Physics, Carleton UniÕersity, Ottawa, Ont. K1S 5B6, Canadah CERN, European Organisation for Particle Physics, CH-1211 GeneÕa 23, Switzerland

i Enrico Fermi Institute and Department of Physics, UniÕersity of Chicago, Chicago, IL 60637, USAj Fakultat fur Physik, Albert Ludwigs UniÕersitat, D-79104 Freiburg, Germany¨ ¨ ¨

k Physikalisches Institut, UniÕersitat Heidelberg, D-69120 Heidelberg, Germany¨l Indiana UniÕersity, Department of Physics, Swain Hall West 117, Bloomington, IN 47405, USA

m Queen Mary and Westfield College, UniÕersity of London, London E1 4NS, UKn Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germany

o UniÕersity College London, London WC1E 6BT, UKp Department of Physics, Schuster Laboratory, The UniÕersity, Manchester M13 9PL, UK

q Department of Physics, UniÕersity of Maryland, College Park, MD 20742, USAr Laboratoire de Physique Nucleaire, UniÕersite de Montreal, Montreal, Que. H3C 3J7, Canada´ ´ ´ ´

s UniÕersity of Oregon, Department of Physics, Eugene OR 97403, USAt Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK

u Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israelv Department of Physics and Astronomy, Tel AÕiÕ UniÕersity, Tel AÕiÕ 69978, Israel

w International Centre for Elementary Particle Physics and Department of Physics, UniÕersity of Tokyo, Tokyo 113, Japanand Kobe UniÕersity, Kobe 657, Japan

x Brunel UniÕersity, Uxbridge, Middlesex UB8 3PH, UKy Particle Physics Department, Weizmann Institute of Science, RehoÕot 76100, Israel

z UniÕersitat HamburgrDESY, II Institut fur Experimental Physik, Notkestrasse 85, D-22607 Hamburg, Germany¨ ¨aa UniÕersity of Victoria, Department of Physics, P.O. Box 3055, Victoria, BC V8W 3P6, Canada

ab UniÕersity of British Columbia, Department of Physics, VancouÕer, BC V6T 1Z1, Canadaac UniÕersity of Alberta, Department of Physics, Edmonton, AB T6G 2J1, Canada

ad Duke UniÕersity, Dept of Physics, Durham, NC 27708-0305, USAae Research Institute for Particle and Nuclear Physics, P.O. Box 49, H-1525 Budapest, Hungary

af Institute of Nuclear Research, P.O. Box 51, H-4001 Debrecen, Hungaryag Ludwigs-Maximilians-UniÕersitat Munchen, Sektion Physik, Am Coulombwall 1, D-85748 Garching, Germany¨ ¨

Received 18 December 1997Editor: K. Winter

Abstract

This paper presents updated measurements of the lifetimes of the B0 meson and the L0 baryon using 4.4 millions b

hadronic Z0 decays recorded by the OPAL detector at LEP from 1990 to 1995. A sample of B0 decays is obtained usings


Dyllq combinations, where the Dy is fully reconstructed in the fpy, K )0 Ky and KyK0 decay channels and partiallys s Sy y0 q qreconstructed in the f ll n X decay mode. A sample of L decays is obtained using L ll combinations, where the L isb c c

fully reconstructed in its decay to a pKypq final state and partially reconstructed in the L llqn X decay channel. Fromy q 0 Ž 0. q0.16172"28 D ll combinations attributed to B decays, the measured lifetime is t B s1.50 "0.04 ps, where thes s s y0.15

errors are statistical and systematic, respectively. From the 129"25 Lqlly combinations attributed to L

0 decays, thec bŽ 0 . q0.24measured lifetime is t L s1.29 "0.06 ps, where the errors are statistical and systematic, respectively. q 1998b y0.22

Published by Elsevier Science B.V. All rights reserved.

1. Introduction

The lifetimes of b flavoured hadrons are related both to the strengths of the b quark couplings to c and uquarks, described by the CKM matrix elements V and V , respectively, and to the dynamics of b hadroncb ub

decays. The spectator model assumes that the light quarks in b and c hadrons do not affect the decay of theheavy quark, and thus predicts the lifetimes of all b hadrons to be equal. For charm hadrons this prediction isinaccurate; non-spectator effects, such as interference between different decay modes, result in a Dq lifetime

0 y w xapproximately 2.5 times that of the D and more than twice that of the D 1 . Models which attempt to accounts

for non-spectator effects predict that the differences among b hadron lifetimes are much smaller than those inw xthe charm system due to the larger mass of the b quark 2–4 . These models predict a difference in lifetime

q 0 0 0 w xbetween the B and B meson of several percent, and between the B and B meson of about 1% 3,4 . OPALsw x w x 05,6 , and other collaborations 7 , have published measurements of the B lifetime which are in agreement withs

these models.Non-spectator decays of B mesons proceeding via W-exchange are Cabibbo-allowed but are expected to be

suppressed, relative to spectator decays, by an amount depending on the ratio of the initial-state meson mass andŽ .the final-state quark masses helicity-suppression . This suppression does not occur for baryon decay, therefore

b baryon lifetimes are expected to be shorter than b meson lifetimes. This expectation is consistent with existingw x Ž 0 . Ž 0. w xlifetime measurements 1 for which t L rt B s0.73"0.06 1 . It is also supported by a recent theoreticalb

w x Ž 0 . Ž 0. w x Ž 3 .prediction 3 which yields t L rt B of about 0.9. Ref. 4 finds this ratio to be 0.98qOO 1rm .b b

Measurements of the average b baryon lifetime have been published based both on analyses of L lly and Lq llyc

w x w xcorrelations by OPAL 8,9 and other collaborations 10 . In both analyses, the dominant contribution isexpected to come from L

0 baryons, though both L lly and Lq lly combinations can arise from the decays ofb c

other b baryons. The composition of each sample depends on the b baryon production fractions, but the Lq llyc

correlations provide a purer sample of L0 baryons.b

This paper presents updated measurements of the B0 meson and L0 baryon lifetimes using Dyllq and L

q llys b s c

combinations reconstructed from the full OPAL hadronic data sample collected on or near the Z0 resonance.y q w x q y w xThese results supersede the previous OPAL measurements using D ll 5 and L ll 8 combinations. Thes c

decay channels used for these lifetime measurements are: 6

where ll is an electron or a muon. In each case, the proper decay time of the b hadron is determined on anevent-by-event basis using measured decay lengths and estimates of the b hadron energy.

6 In this paper, charge conjugate modes are always implied.


The following section provides a brief description of the OPAL detector. The remaining sections describe theselection of Dyllq and L

q lly candidates, the determination of the b hadron decay lengths, the estimation of thes c

b hadron boost, the lifetime fits, the results, and the systematic errors.

2. The OPAL detector

w xThe OPAL detector is described in detail in Ref. 11 . The central tracking system is composed of a precisionvertex drift chamber, a large volume jet chamber surrounded by a set of chambers which measure thez-coordinate 7 and, for the majority of the data used in this analysis, a high-precision silicon microvertexdetector. These detectors are located inside a solenoidal coil. The detectors outside the solenoid consist of atime-of-flight scintillator array and a lead glass electromagnetic calorimeter with a presampler, followed by ahadron calorimeter consisting of the instrumented return yoke of the magnet, and several layers of muonchambers. Charged particles are identified by their specific energy loss per unit length, d Erd x, in the jetchamber. Further information on the performance of the tracking and d Erd x measurements can be found in

w xRef. 12 .

3. Monte Carlo simulation

Monte Carlo simulation samples of inclusive hadronic Z0 decays and of the specific decay modes of interestare used to check the selection procedure and lifetime fit procedure. These samples were produced using the

w x w xJETSET 7.4 parton shower Monte Carlo generator 13 with the fragmentation function of Peterson et al. 14w xfor heavy quarks, and then passed through the full OPAL detector simulation package 15 . A special sample ofw xsimulated data was generated using a modified JETSET decay routine for b baryons 16 , where it is assumed

w xthat the polarization of the b quark is carried by the b baryon. An additional form factor 17 describing theenergy transfer from the b to c flavoured baryon was used in the generation of the polarized sample.

4. Candidate selection

This analysis uses data collected during the 1990–1995 LEP running periods at centre-of-mass energies0 w xwithin "3 GeV of the Z resonance. After the standard hadronic event selection 18 and detector performance

requirements, a sample of 4.4 million events is selected. Jets are defined using charged tracks and electromag-netic clusters not associated with a charged track. These are combined into jets using the scaled invariant mass

w xalgorithm with the E0 recombination scheme 19 using y s0.04.cut

Only charged tracks that are well-measured in the x-y plane are considered in this analysis. Well measuredw xtracks are defined according to standard track quality cuts 20 . Within a single jet, not all combinations of

accepted tracks with the appropriate charge combination are considered in the Dy and Lq searches. Instead, tos c

reduce the combinatorial background, the d Erd x probability, w , that the observed d Erd x is consistent withi

the assumed particle hypothesis, i, is required to be greater than 1%. More restrictive requirements are imposedon a channel-by-channel basis, as described in the following subsections.

7 The right-handed coordinate system is defined such that the z-axis follows the electron beam direction and the x-y plane isperpendicular to it with the x-axis lying approximately horizontally. The polar angle u is defined relative to the q z-axis, and the azimuthalangle f is defined relative to the q x-axis.


Leptons are identified as follows. Electron candidates with a momentum of at least 2 GeVrc are identifiedusing an artificial neural network based on twelve measured quantities from the electromagnetic calorimeter and

w xthe central tracking detector 21 . Between 1 and 2 GeVrc, electron candidates are required to have a d Erd xprobability of larger than 1% for the electron hypothesis and less than 1% for the proton hypothesis, because itis in this region that the electron and proton d Erd x bands cross. Electron candidates identified as arising from

w xphoton conversions are rejected 22 . Muons are identified by associating central detector tracks with trackw xsegments in the muon detectors and requiring a position match in two orthogonal coordinates 22 .

4.1. Selection of Dy candidatess

The Dy candidates are reconstructed in four modes:s

1. Dy™K ) 0 Ky in which the K ) 0 decays into a Kqpy.s

2. Dy™fpy where the f subsequently decays into KqKy.s

3. Dy™KyK 0 where the K 0 decays into pqpy.s S Syy y q y4. The D is partially reconstructed in D ™f ll n X where the f decays into K K .s s

yIn all modes except f ll n X, charged kaon candidates are required to have a momentum greater than2 GeVrc. Also, because of the potential for misidentifying a pion as a kaon, if the observed energy loss of akaon candidate is greater than the mean expected for a kaon, it must satisfy w )5%.K

In both the Dy™K ) 0 Ky and the Dy™fpy channels, if the observed energy losses of both kaons s

candidates are greater than the mean expected for a kaon, the product of the two d Erd x probabilities mustsatisfy w Pw )0.02. The momentum of the KqKypy combination is required to be greater than 9 GeVrcK1 K 2

for both channels.For the K ) 0 Ky mode, the invariant mass of the Kqpy combination is required to satisfy 0.845-m -Kp

0.945 GeVrc2. To reduce the possibility of mistaking a Dy™K ) 0py decay for the desired signal, themeasured d Erd x of the Ky candidate must be at least one standard deviation below the mean d Erd x that isexpected for a pion.

In the fpy mode, the observed f width is dominated by detector resolution and the KqKy mass isrequired to satisfy 1.005-m -1.035 GeVrc2. The momentum of the f candidate is required to be greaterKK

than 4.0 GeVrc.Differences between the angular distributions of Dy decays and those of random track combinations are useds

to suppress further the combinatorial background. The Dy is a spin-0 meson and the final states of both decaysŽ ) 0. Ž y y. ymodes consist of a spin-1 f or K meson and a spin-0 p or K meson. The D signal is expected to bes

uniform in cosu , where u is the angle in the rest frame of the Dy between the spin-0 meson direction and thep p s

Dy direction in the laboratory frame. However, the cosu distribution of random combinations peaks in thes p< < Ž . ) 0 yŽ y.forward and backward directions. It is therefore required that cosu -0.8 0.9 for the K K fp mode.p

The distribution of cosu , where u is the angle in the rest frame of the spin-1 meson between the direction ofÕ Õ

the final state kaon from the decay of the spin-1 meson and the Dy direction, is proportional to cos2u for Dys Õ s

decays. The cosu distribution of the random KqKypy combinations in the data is, however, approximatelyÕ

< <flat. Therefore it is required that cosu )0.4.Õ

For reconstruction of the Dy™KyK 0 channel, accepted charged kaons are combined with K 0 mesonss S Sq y w x q yreconstructed in their decays to p p as described in 23 . The p p mass is required to satisfy

0.475-m -0.525 GeVrc2. The background of K 0 particles from fragmentation is reduced by requiring thepp S

K 0 momentum to be greater than 3 GeVrc. To reject background from L decays where the proton isS

misidentified as a pion, K 0 candidates are rejected if 1.10-m -1.13 GeVrc2, where m is the invariantS pp pp

mass of the two tracks when the highest momentum track is assigned the proton mass. To improve further themass resolution of the Dy, a fit using kinematic and geometrical constraints is performed. The mass of the twos

0 0 w x ytracks forming the K is constrained to the known K mass 1 . Further constraints are applied to the D andS S s

K 0 , in which the directions of the vectors between their production and decay points are constrained to be theS

same as the reconstructed momentum vectors.


yyFor the D ™f ll n X selection, the purity of the kaons from the f decay is enhanced by applying additionals

pion rejection. This requires that the d Erd x probability for the pion hypothesis be less than 40% for trackswhose momenta are such that the mean d Erd x for pions is higher than that of kaons, and less than 1% for lowmomentum tracks where the mean d Erd x for kaons is higher than that of pions. Additionally, the product ofthe d Erd x probabilities for a pion hypothesis for the two kaon candidates must be less than 0.018. The f

candidate momentum is required to be greater than 4.6 GeVrc. The lepton candidate is required to have amomentum greater than 1 GeVrc for electrons and 2 GeVrc for muons. The invariant mass of the f lly

combination must be less than 1.9 GeVrc2.

4.2. Selection of Lq candidatesc

The Lq candidates are reconstructed in two modes; L

q™pKypq and Lq™L llq

n X. In the pKypqc c c

selection, the proton, kaon and pion momenta are required to be greater than 3, 2 and 1 GeVrc, respectively. Ifthe observed energy loss of the proton or kaon candidate is greater than the mean d Erd x expected for thatparticle, the corresponding d Erd x probability is required to be greater than 3%. The d Erd x probability of thepion hypothesis for the proton candidate is required to be less than 1%, which substantially reduces thecombinatorial background. The pKypq combination must have a momentum greater than 9 GeVrc. To reduce

q Ž q y. q q qthe possibility of mistaking the decay D ™f K K p for a L decay by misidentifying the K as as c

proton, candidates are rejected if the invariant mass of the pKy combination, when the proton candidate is2 w xassigned the kaon mass, is within 10 MeVrc of the nominal f mass 1 .

In the Lq™L llq

n X selection, L candidates are identified via the decay L™ppy. The selection procedurecw xis similar to the one used in Ref. 9 . The track with the larger momentum is assumed to be the proton and its

momentum is required to be larger than 3.0 GeVrc. The other track is required to have a momentum larger than0.8 GeVrc. The selection criteria for the lepton are the same as described in the previous section for theselection of Dy semileptonic decays. The invariant mass of the L llq combination is required to be less thans

2.2 GeVrc2.

4.3. Dyll q and Lqll y selection and decay length determinations c

Once a combination of tracks that satisfies the Dy or Lq candidate selection is found, a search is performeds c

to find a lepton from b hadron decay of opposite charge in the same jet. Lepton candidates are identified asdescribed in the introduction to Section 4. Both the electron and muon candidates are required to have amomentum greater than 2 GeVrc except in the Dy™KyK 0 mode where a higher momentum cut of 5 GeVrcs S

is used to improve the signal to background ratio. It is also required that the lepton candidate track be measuredprecisely by either the silicon microvertex detector or the vertex drift chamber.

To further suppress combinatorial background, requirements are made on the invariant mass and momentumof the Dyllq and L

q lly candidate combinations. KqKypyllq combinations are required to have a masss c

between 3.2 and 5.5 GeVrc2 and momentum larger than 17 GeVrc. KyK 0 llq combinations are accepted ifS

they have an invariant mass between 3.4 and 5.5 GeVrc2 and a momentum greater than 17 GeVrc. The f llyllq

mass is required to be less than 4.8 GeVrc2 and its momentum greater than 12 GeVrc. Also, for the f llyllq

mode, the invariant mass of the f and the llq must be greater than 2.1 GeVrc2. In conjunction with theinvariant mass cut on the f lly pair, this unambiguously separates the leptons from the B0 and Dy decays. Thes s

pKypqlly combination must have a mass between 3.5 and 5.5 GeVrc2 and momentum greater than17 GeVrc. In the L llqlly channel, combinations are accepted if the L llqlly invariant mass is greater than2.5 GeVrc2 and less than 5 GeVrc2 and the invariant mass of the L and lly is greater than 2.2 GeVrc2.Furthermore, the cosine of the opening angle between the lepton and the Dy or L

q candidate must be greaters c

than 0.4.


Fig. 1. Invariant mass distributions from the four Dy llq reconstruction channels. In each plot, the result of the fit described in the text iss

overlaid as a solid line. The mass ranges used in the decay length fit are shown by the vertical dotted lines.

0 Ž 0 . y Ž q.Three vertices – the beam spot, the B L decay vertex and the D L decay vertex – are reconstructeds b s c

in the x-y plane. The beam spot is measured using charged tracks with a technique that follows any significantw xshifts in the beam spot position during a LEP fill 24 . The intrinsic width of the beam spot in the y direction is

taken to be 8 mm. The width in the x direction is measured directly and found to vary between 100 mm and160 mm.

y Ž q. 0 Ž 0 .The D L vertex is fitted in the r-f plane using all the candidate tracks. The B L decay vertex iss c s by Ž q.formed by extrapolating the candidate D L momentum vector from its decay vertex to the intersection withs c

y Ž q. 0 Ž 0 .the lepton track. The D L decay length is the distance between these two decay vertices. The B Ls c s b0 Ž 0 .decay length is found by a fit between the beam spot and the reconstructed B L decay vertex using thes b

Fig. 2. Invariant mass distributions from the two Lq lly reconstruction channels. In each plot, the result of the fit described in the text isc

w q x yoverlaid as a solid line. Also indicated are the mass ranges used in the decay length fit. The hatched histogram for the L ll ll channelq yw xrepresents the wrong-sign-L combinations: Lll ll .


Table 1Results of the mass fits to all the signal channels. The second column shows the number of candidates in the signal peak. The estimatedfraction of combinatorial background is given in the third. The fourth column gives the signal peak width found by the fit or the constraintthat was used in the fit to the invariant mass distribution. The mass range used in the lifetime fit is given in the fifth column and the last

q y q yw x w xcolumn gives the number of candidates in this mass range. For the L ll ll channel the number of wrong-sign-L candidates, Lll ll , isincluded in brackets

Decay Signal Comb. Width Fit range Cands.Ž . Ž .channel candidates fraction MeV MeV for fit

)K K 101"21 0.46"0.06 28"5 y50–200 280fp 53"11 0.24"0.05 17"4 y50–200 114

y 0K K 8"5 0.39"0.19 22"14 y50–200 21SŽ .f ll 37"10 0.23"0.07 4 fixed y8–60 94

qyD ll total 199"26 509s

pKp 108"22 0.56"0.06 21"5 y50–200 522Ž .L ll 37"9 0.11"0.05 3.4"0.5 y8–80 69 41

yqL ll total 145"24 632c

y q Ž q y.direction of the candidate D ll L ll momentum vector as a constraint. The two-dimensional projections ofs c0 Ž 0 . y Ž q.the B L and D L decay lengths are converted into three dimensions using the polar angles that ares b s c

y q Ž q y. y Ž q. y qreconstructed from the momenta of the D ll L ll and D L . Typical decay lengths for the D lls c s c sŽ q y.L ll vertex are about 0.3 cm and the corresponding decay length errors range from about 0.03 cm for thec

yq y y y q 0K K p , f ll n and pK p modes, to about twice this level for the modes which include a L or K .S

Additional criteria are used to select Dyllq and Lq lly candidates suitable for precise decay lengths c

measurements. In channels in which a charm state is fully reconstructed the x 2 of the charm vertex fit isŽ . 0required to be less than 10 for 1 degree of freedom . Finally, the decay length error of the reconstructed Bs

Ž 0 .L candidate must be less than 0.2 cm.b

4.4. Results of Dyll q and Lqll y selectionss c

The invariant mass distributions obtained in each of the Dy decay modes are shown in Fig. 1. The equivalents

distributions for the reconstructed Lq decay modes are shown in Fig. 2. In each case, the fit result overlaid onc

the histogram is obtained from an unbinned maximum likelihood fit to the invariant mass distribution. Theresults of these fits are summarised in Table 1.

Each mass fit uses a Gaussian function to describe the signals and a linear parametrization of thecombinatorial background. In the KqKypy distributions, a second Gaussian is used to parametrize contribu-tions from the Cabibbo suppressed decay Dy™KqKypy. The mean of this Gaussian is fixed to the nominal

y 2 w x yD mass, 1869.3 MeVrc 1 , and the width is constrained to be the same as that of the D peak. Bys

integrating the tail of the peak due to the Dy™KqKypy decays in this Dy signal region, the contaminations

from this source is found to be negligible. No significant peaks are observed in the mass distributions fory y Ž q q. ) 0 y y y 0wrong-sign D ll L ll combinations in the fully reconstructed decay channels K K , fp , K K ands c S

y q w qx y 8pK p . The L ll ll combinations include a contribution from L baryons from fragmentation that can beq yw xestimated from the wrong-sign-L distribution, Lll ll . Studies using simulated data show that the wrong-sign-L

8 The bracketed particles are those that are assigned to be the decay products of a Lq. The invariant mass requirements on L llc

combinations described in Sections 4.2 and 4.3, result in a unique assignment of the two leptons.


q yw xdistribution provides a good representation of these L baryons from fragmentation. The Lll ll candidatesare shown in the plot as a shaded histogram.

y Ž q. w xFor each channel, the fitted mass is consistent with the nominal D L mass 1 and the fitted width iss c

consistent with the expected detector resolution. In total, 199"26 Dyllq candidates and 145"24 Lq lly

s cy q Ž q y. 0 Ž 0 .candidates are observed. The D ll L ll combinations used in the B L lifetime fits are selected froms c s b

regions around the identified invariant mass peaks, including a sufficient number of candidates away from themass peaks to allow an estimate of the lifetime characteristics of the combinatorial background. There are 509for the B0 lifetime fit and 632 for the L

0 lifetime fit.s b

4.5. Backgrounds to the B0 ™Dyll q and L0 ™Lqll y signals s b c

0 Ž 0 .Potential sources of backgrounds to the B L signal considered here include decays of other b hadronss by q Ž q y. y Ž q.that can yield a D ll L ll final state or other final states that are misidentified as a D L hadron. Others c s c

y Ž q.sources are D L hadrons combined with a hadron that has been misidentified as a lepton, and randoms cy Ž q.associations of D L hadrons with genuine leptons. Finally, there is purely combinatorial background. Thes c

various physics backgrounds, and the calculation of their contributions relative to that of the signal, arediscussed below.

4.5.1. Physics backgrounds to B0 ™Dyll qs s

The signal event samples include properly reconstructed Dyllq combinations that do not arise from B0s s

decay. Two decay modes of B0 and Bq mesons are considered:qyŽ . Ž .a B™D DX, D™ ll n X where D is any non-strange charm meson , ands

Ž . y qb B™D K ll n X, where K is any type of kaon.s0Ž .For the signal production and decay sequence, the production rate times branching fraction f b™B Ps

Ž 0 y q . w xBr B ™D ll n X s 0.85"0.23% is used 1 . Monte Carlo simulations are used to determine the selections s

efficiencies for background modes relative to that of the signal mode.q 0 w xFor the background, the probability for a bottom quark to form either a B or B meson is 0.378"0.022 1

each. For the B™DyK llqn X mode, the measured branching ratio is less than 0.009 at the 90% confidences

w xlevel 1 . Half of this limit is used as a central value in estimating the contribution of this channel, and the rangeŽ .from zero to 0.009 is taken as the uncertainty. For the other background mode, it is noted that Br B™D D ss

w x0.049"0.011 1 , which is then corrected using Monte Carlo simulation to include the additional contributionfrom B™D DX decays. The possibility that all the B™D X modes include an additional charm meson iss s

considered as a systematic error. The effect on the reconstruction efficiency of D mesons arising from orbitallyexcited D mesons is also taken into account. The total contribution from these two sources of backgrounds isestimated to be 11"4%.

4.5.2. Physics backgrounds to L0 ™Lqll yb c

The events in the Lq peak may include L

q lly combinations that do not arise from L0 decay. The decayc c b

y yq q 0modes considered are B ™L J X, J ™X ll n and Bu,d,s ™L X ll n . An estimate of the L signalu,d c c bc c

contamination from other b baryons is also given.As before, the reconstruction efficiencies for these background modes are calculated relative to the signal

mode from simulated event samples. For the production rate times branching fraction of the signal modes,y0 0 qŽ . Ž . w xf b™L PBr L ™L ll n X s1.35"0.26% 1 is used.b b c

yqTo estimate the background from the internal-W decay B™L J X, J ™X ll n , the measured inclusivec c cŽ . w x w x Žbranching ratio Br B™charmed-baryon X s6.4"1.1% 1 is combined with the measurement 25 Br B™

q y. Ž .L X rBr B™L X s0.19"0.13"0.04, where B refers only to B mesons containing a b quark. It is alsoc cqassumed that when a L is produced, a J is always produced. The average semileptonic branching ratio of thec cŽ .charged and neutral J assuming they are produced at equal rates is estimated to be 25"10%. This wasc


q w xobtained from the semileptonic branching ratio of the L , using the theoretical prediction of 26 and thecw xmeasured lifetimes of these baryons 1 . After accounting for the relative efficiency, this mode comprises

2.0"1.5% of the signal.yqThe contribution from the external-W decay, B™L X ll n , was estimated using the 90% confidence levelc

yŽ . w xlimit Br B ™p ll n X -0.16% 27 . It is conservatively assumed that this decay always proceeds through au,dyq q qŽ .L and that a L is equally likely to decay to a proton or a neutron. Thus, Br B™L ll n X -0.32% at thec c c

90% confidence level. The analogous decays of B0 mesons are also taken into account by assuming that theirsyq w xbranching fraction to L ll n X is the same as for B and using the hadronization fractions from 1 .c u,d

Accounting for the relative detection efficiency yields an upper limit for this mode corresponding to 5.7% of thesignal. Half of this is taken as the central value for this background and the entire range from zero to 5.7% isconsidered in estimating the systematic error.

Potential contamination of the Lq lly signal by decays of b baryons other than L

0 is also investigated. Thec bw xprinciple sources of this contamination are from decays of J and S . There is some evidence for the J 28 ,b b b

w x w xwhich is expected to decay weakly 29 . Theoretical predictions 29 for the S mass suggest that it is largeb

enough to allow strong decay to a L0 . Accepting this, any non-L0 in the signal comes from J decays.b b b

Semileptonic decays of J baryons to excited charm-strange baryons that decay subsequently to Lq, orb c

y yq qnon-resonant decays such as J ™L X ll n can contribute to the L ll sample. The level of these decays isb c c

estimated using the B meson system as a guide. The branching ratio for non-strange B decays to X llqn , where

X is not simply a D or D) meson, is found to be 3.7"1.3%. This value is obtained by subtractingŽ 0 y q . Ž 0 )y q . Ž 0 q . w xBr B ™D ll n and Br B ™D ll n from Br B ™X ll n using the values from Ref. 1 . The same rate

is assumed for the analogous J decays mentioned above and the conservative assumption is made that in theseb

decays a Lq is always produced. It is further assumed that 20% of the weakly decaying b baryons are J ,c b

0 w xbased on the relative rates of production of the corresponding light-flavoured baryons in Z decays 1 . Usingthe above branching ratio estimates and reconstruction efficiencies for the signal mode and the modes underconsideration here, the contribution to the L

q lly signal from the decays of the J is estimated to be about 1%c b

and is, therefore, neglected.q y yThe L ll ll sample can have additional contributions from the decay of J ™J ll n X followed byb c

q Ž q q . Ž q . ŽJ ™J ll n X with J™Lp . Assumptions about Br L ™LX ll n rBr J ™JX ll n and Br J ™c c c c. Ž q . w x w xJX rBr L ™LX are required to estimate this background if measurements of L ll 9,10 and J ll 28c

production are to be used. In the case of the former ratio, this cannot be trivially related to the ratio of lifetimesbecause of Pauli Interference effects between the two strange quarks that result from the decay of a J , butc

q w xwhich are not present in the analogous L decay 26 . The latter ratio is even harder to predict theoretically,cw xeven to the extent of whether one would expect it to be greater than or less than unity 30 . In estimating the

systematic error due to this source, the fraction of L llqlly candidates due to J decays is varied from 10% tob

50%. The L0 lifetime will also be quoted with a functional dependence on the level of J contamination in theb b

L llqlly sample, f q y, using the average J lifetime of 1.39q0.34 ps as measured from J ll correlationsJ r L ll ll b y0.28b

w x28 .

4.5.3. Other backgroundsy Ž q.The D L candidate may be a misidentified charm hadron if one or more tracks are assigned the wrongs c

particle type. This constitutes an additional source of background which is studied using simulated events. Fory Ž q.this background, it is found that the invariant mass distribution around the D L mass is similar to that ofs c

the combinatorial background. Such events are therefore considered to be included in the combinatorialbackground fraction.

y Ž q.The level of background from genuine D L particles which are combined with a hadron that iss c

misidentified as a lepton can be estimated by fitting the invariant mass spectrum of wrong-sign combinations inwhich the charm candidate and the lepton candidate have the same charge. This assumes that randomcombinations are equally likely to have right and wrong charge correlations. For each channel where the charm


hadron is fully reconstructed, the wrong sign signal is consistent with zero. This is in agreement with what hasw xbeen found in a related analysis that has greater statistical significance 31 . This background source is therefore

neglected.y Ž q.The background from random associations of a D L with genuine leptons is estimated using simulateds c

data. The contribution is less than one event to each of our samples and is neglected.In the two modes in which the charm hadron is partially reconstructed from a semileptonic decay channel,

q yy qD ™f ll n X and L ™L ll n X, there are additional backgrounds to consider. These include the accidentals cŽ .combination of a f L , generally produced in fragmentation, with two leptons which arise from a semileptonic

bottom hadron decay, followed by a semileptonic charm hadron decay. In the case of the Lq lly channel, thisc

background is estimated using the observed peak in the L invariant mass spectrum for the wrong signy qcombination formed by an ll from the bottom hadron decay, an ll from the charm hadron decay and a L

q yŽ . w xwhereas signal would be a L . Fitting the L invariant mass distribution for these wrong sign, Lll ll ,candidates, yields a contribution from this source of 9"5 events. The contribution from random associations ofa particle that is not from L

q decay with a L and a lepton from L0 decay is found to be negligible. For thec b

yyanalogous D decay into f ll nX, there is no wrong sign distribution available, and hence simulated events ares

used to estimate this contribution to be 2.5"0.5 candidates. The potential contribution of leptons from Jrc

Ž .decays, which are then combined with a f either from fragmentation or from a b hadron decay is alsoestimated using simulated events to be 0.5"0.3 candidates. Finally, the contribution from hadrons misidentifiedas leptons is estimated by selecting events in which the two leptons in these modes have the same sign and isfound to contribute 2"2 candidates.

The non-combinatorial background sources mentioned above are expected to contribute a total of 27"11events to the Dyllq signal and 16"7 events to the L

q lly signal. The background subtracted number of Dyllqs c s

signal candidates is therefore

N B0 ™Dyllqn X s 172"28 .Ž .s s

The background subtracted number of Lq lly signal candidates isc

y0 qN L ™L ll n X s 129"25 ,Ž .b c

where no correction has been made for possible J contamination.b

5. The B0 and L0 lifetime fits b

0 Ž 0 .To extract the B L lifetimes from the measured decay lengths, an unbinned maximum likelihood fit iss b

performed using a likelihood function that accounts for both the signal and background components of thew xsample. This fit is largely the same as has been used previously in similar OPAL measurements 5,8 .

5.1. Boost determination

0 Ž 0 . 0 Ž 0 .For the component of the likelihood function describing the B L signals, the B L lifetime must bes b s b

related to the observed decay lengths. Since neither channel is fully reconstructed, because at least the neutrinoproduced in the b hadron decay is not reconstructed, it is necessary to estimate the b hadron momentum, p .B

0 Ž 0 .The probability distribution of a given candidate having a particular B L momentum, BB, is estimated on ans b

event-by-event basis in one of two ways, depending on the decay channel.y q w xFor the semileptonic D decay mode and both L decay modes, the technique employed in Ref. 8 is used.s c

This relies on information from Monte Carlo simulation to estimate the probability distribution of b hadronenergy, given the observed momentum, pi , and invariant mass, mi of all the observed tracks in the candidateD DŽ q y y q y q y y q y. ii.e., K K ll ll , pK p ll or pp ll ll . Using a conversion factor, R'p rp , the relationship of theD B


Ž i . 0 Ž 0 .decay time, t, to the decay length L, can be expressed as tsLPRP m rp , where m is the B L mass.B D B s b

The distribution of R was determined using simulated data for the signal Lq decay modes and the semileptonicc

y w xD decay mode produced with the JETSET 7.4 Monte Carlo 13 , using the fragmentation function of Petersonsw xet al. 14 . For each decay mode, twelve R distributions were produced covering different ranges of the

y q Ž q y.momentum and invariant mass of the D ll L ll combination. These distributions are used in the lifetimes cŽ i i . i ifit to describe the probability, BB p Np ,m that a candidate with a measured p and m will have aB D D D D

0 Ž 0 .particular B L momentum.s by y w xFor the other D decay modes in which the D is fully reconstructed, an analytic approach is used 5,31 .s s

This approach is not applicable in the case of the L0 decays because of the possibility of large polarizationb

Ž i i .effects. The same momentum and invariant mass observables p and m as the other method are employed,D D

but an exact calculation is used, based on the kinematics of the B0 ™Dyllqn X decay rather than Monte Carlos s

Ž i i .simulation, to calculate the probability distribution BB p Np ,m . This approach is described in detail in Ref.B D Dw x31 .

5.2. Likelihood functional form

0 Ž 0 .The likelihood function for observing a particular decay length of a B L hadron may now bes by q Ž q y.parametrized in terms of the measurement error of the decay length, the D ll L ll invariant mass ands c

momentum, and the assumed lifetime. The functional form of the likelihood is given by the convolution of three0 Ž 0 .terms: an exponential whose mean is the B L lifetime, the boost distribution obtained from the values of thes b

y q Ž q y.observed D ll L ll mass and momentum, and a Gaussian resolution function with width equal to thes c

measured decay length error. This can be expressed as:

` maxpBB i i i i i i i iLL L Nt ,s , p ,m s d l d p GG L N l ,s BB p Np ,m PP lNt , p , 1Ž . Ž .Ž . Ž . Ž .H Hi B L D D B L B D D B B0 0

where pmax is the maximum possible energy that the b hadron can have. The function GG is a Gaussian functionB

that describes the probability to observe a decay length, Li, given a true decay length l and the measurementi 0 Ž 0 . iuncertainty s . BB is the probability of a particular B L momentum for an observed momentum, p andL s b D

i 0 Ž 0 .invariant mass, m of all tracks comprising the candidate. PP is the probability for a given B L to decay atD s b

a distance l from the eqey interaction point. This function is given by:

m ylPmB BPP lNt , p s exp , 2Ž . Ž .B B

t p t pB B B B

where t p rm is the mean decay length for a given momentum, p , mean lifetime, t , and mass, m , of theB B B B B B0 Ž 0 .B L .s b

Ž .As discussed previously, non-combinatorial physics backgrounds result from the decay of other b hadrons.The likelihood function describing these sources of background is therefore taken to have the same form as the

0 Ž 0 .B L signal, except that the b hadron lifetimes contributing to these background samples are fixed to thes bw xexclusive world average values 1 , weighted appropriately. The level of the contributions to this background are

set to fixed fractions of the signal, as determined in the previous section. The effects of the uncertainty in thesefractions on the lifetime are addressed as a systematic error. The likelihood function, LL D ll ŽL ll ., describing alli

y q Ž q y. 0 Ž 0 .sources of D ll L ll combinations – the B L signal as well as these physics backgrounds – is just as c s b

linear combination of LL B and the physics background contributions. For the semileptonic channels, theiŽ . y Ž q.lifetime distribution of the backgrounds which include a real f L not from a D L , is estimated from thes c

sideband, in the case of Dy, or the sideband and the wrong-sign distribution for the Lq mode. For the purposess c

of determining the lifetime properties of the background, these background sources are treated as combinatorial.y q Ž q y.The fit must also account for the combinatorial background present in the D ll L ll sample. Thes c

functional form used to parametrize this source of background is composed of a positive and a negative


exponential, each convolved with the same boost function and Gaussian resolution function as the signal. Thiscan be expressed as:

LL comb Li Ntq ,ty , fq ,s i , pi ,miŽ .i bg bg bg L D D

` maxpB i i i i q y qs d l d p GG L N l ,s BB p Np ,m PP LNt ,t , f , p , 3Ž .Ž .Ž . Ž .H H B L B D D bg bg bg bg B0 0

where

m ylPm m y yl PmŽ .B B B Bq y q q qPP lNt ,t , f , p s f exp q 1y f exp . 4Ž .Ž . Ž .bg bg bg bg B bg bgq q y y< < < <t p t p t p t pbg B bg B bg B bg B

The fraction of background with positive lifetime, fq , as well as the characteristic positive and negativebg

lifetimes of the background, tq and ty , are free parameters in the fit. This double-exponential shape isbg bg

motivated by considerations of event topologies that can lead to apparent negative decay lengths, even beforeresolution effects are considered. The background parameters are fitted separately for the hadronic and

y Ž q. Ž .semileptonic D L modes, since the lifetime properties of the real f L backgrounds may well be differents c

from the purely combinatorial background in the other decay modes.The background in the event sample is taken into account by simultaneously fitting for the signal and

background contributions. The probability that a candidate arises from combinatorial background, f comb, isi

determined as a function of the observed invariant mass of this candidate from the fits to the invariant massspectra shown in Figs. 1 and 2.

Thus, the full likelihood for candidate i is:

LL Li Nt ,s i , pi ,mi s 1y f comb PLL D ll ŽL ll . q f comb PLL comb . 5Ž .Ž . Ž .i B L D D i i i i

0 Ž 0 .In total, four parameters are free in the fit: the B L lifetime, and the parameters describing the combinatorials bŽ q q y .background f , t and t .bg bg bg

5.3. Lifetime fit results

y q Ž 0. q0.16The fit to the decay lengths of the 509 D ll combinations yields t B s1.50 ps, where the error iss s y0.15q y Ž 0 . q0.23 9statistical only. The fit to the 632 L ll candidates yields t L s1.26 ps. The results of these fits arec b y0.20

shown in Fig. 3 and Fig. 4. In each figure, the candidates are divided into two categories – signal region andsideband region – in order to show the behaviour of the fit when the candidate sample consists mostly of signalor mostly of combinatorial background. The signal region is defined as the mass region within two standard

Ž .deviations of the fitted invariant mass see Figs. 1 and 2 . The curves in these figures represent the sums of thedecay length probability distributions for each event. The figures indicate that the fitted functional forms provide

0 Ž 0 . 2 Ž .a good description of the data for both signal and background. For the B L fit, a total x of 5.2 9.6 iss bŽ .found for the sum of the signal and sideband decay length distributions for 12 11 bins that contain at least five

candidates. As was stated earlier, the fits are to unbinned data.

6. Checks of the method

Tests are performed on several samples of simulated events to check for biases in the selection and fittingprocedures. The first tests involve a simple Monte Carlo program which generates decay length data for the

9 In comparing these two measurements, note that the fractional errors do not scale directly with the number of events in the signalbecause of the larger combinatorial background in the pKypq lly mode, which is the statistically dominant mode for the L

0 lifetimeb

measurement.


Fig. 3. Top: The decay length distribution of Dy llq combinations with an invariant mass within the signal region. The unhatched areas

represents the contribution from combinatorial background, the hatched area is the contribution from sources of non-combinatorialbackground and the double-hatched region is due to signal from decays of a B0. Bottom: The similar decay length distribution for candidatess

with an invariant mass in the sideband region. The curves are the results of the fit described in the text.

y q Ž q y. 0 Ž 0 .signal D ll L ll decays and combinatorial background. For each signal candidate from a B L decay,s c s b0 Ž 0 .this simulation generates a B L decay time from an exponential distribution with the mean set to a knowns b

0 Ž 0 . 0value. The B L momenta are chosen from a spectrum based on the full Monte Carlo simulation. The Bs b sŽ 0 .L decay length is then calculated and combined with the momentum to give the true candidate decay time.b

This is then degraded by a resolution function. Physics backgrounds are generated through a similar procedure.

Fig. 4. Top: The decay length distribution of Lq lly combinations with an invariant mass within the signal region. The unhatched areac

Ž .represents the contribution from combinatorial background, the very small hatched region represents non-combinatorial background, notincluding any J contribution, and the double-hatched area is due to signal from decays of a L

0 . Bottom: The similar decay lengthb b

distribution for candidates with an invariant mass in the sideband region. The curves are the results of the fit described in the text.


0 Ž 0 .Many fits are conducted over wide ranges of B L lifetimes with different levels and parametrizations of thes b0 Ž 0 .backgrounds. The results of these studies show no biases in the fitted B L lifetime to a level of less thans b

0.5% and that the statistical precision of the fit to data is consistent with the sample size and composition.y q Ž q y.To verify that the D ll L ll selection does not bias the reconstructed sample, lifetime measurements ares c

made using simulated event samples in which large numbers of the decays of interest are produced. In thesetests it is found that the mean lifetime of the selected sample of candidates is consistent with the lifetime used togenerate the sample, indicating no bias in the selection procedure. Applying the lifetime fit to the selectedsamples similarly shows no evidence for a bias to within the statistical precision allowed by these samples. Thisprecision ranged from 2% for the KqKypy and pKypq channels to 4% for the other decay modes. Similarly,applying the selection and fitting procedure to a Monte Carlo simulation sample of 4 million hadronic Z0

0 Ž 0 .decays, the fitted B L lifetimes agree with the generated lifetimes to within the statistical power of thes b

sample.The lifetime fit is also applied to each decay channel individually. The resulting lifetimes of these separate

fits are consistent with each other and with the fit to the entire sample.

7. Evaluation of systematic errors

The sources of systematic error considered are those due to the level, parametrization and source of thebackground, the boost estimation method, possible polarization of b baryons, the beam spot determination andpossible tracking errors. These systematic errors are summarized in Table 2.

The uncertainty in the level of combinatorial background has two sources: the uncertainty due to the mass fitto the candidate invariant mass spectra and the statistical variation of the background under the invariant masspeak. Background fractions due to one standard deviation variations for these two cases are determined and usedin the lifetime fit. This produces variations in the B0 and L

0 lifetimes of "0.03 ps. The width of the sidebands b

region of the mass spectra, from which candidates are selected for use in the lifetime fit, is also varied yieldingcontributions to the systematic errors of "0.01 ps for the B0 and "0.03 ps for the L

0 lifetimes. Using as b

quadratic function to describe the mass distribution of the combinatorial background has a negligible effect onthe fitted lifetimes.

The effect of the uncertainty in the level of the non-combinatorial backgrounds to the B0 and L0 signal iss b

estimated by varying these background levels over the ranges described in Section 4.5. This produces a"0.01 ps variation in the B0 lifetime. The systematic shift due to a J contamination of 30"20% in the L

0s b b

sample necessitates a correction of q0.02"0.02 ps. The correction to the central value of the measuredlifetime as a function of J contamination is q0.08P f q y ps. All other non-combinatorial backgroundsb J r L ll llb

mentioned in Section 4.5 contribute an additional error of "0.01 ps to the L0 lifetime. The b hadron lifetimesb

Table 2Summary of systematic corrections and uncertainties on the B0 and L

0 lifetimess b

0 0Ž . Ž . Ž . Ž .Source t B correction ps t L correction pss b

Ž .background excl. J 0.00 "0.03 0.00 "0.05b

J background q0.02"0.02b

uncertainty in boost 0.00 "0.02 0.00 "0.02polarization q0.01 "0.02beam spot 0.00 "0.01 0.00 "0.01alignment errors 0.00 "0.01 0.00 "0.01

total "0.04 q0.03 "0.06


w xused for these backgrounds are also varied within their measured errors 1 . The resulting change in the fittedlifetimes is less than "0.01 ps.

The total systematic error associated with the description of the combinatorial and physics backgrounds isŽ . 0 Ž 0 .therefore "0.03 ps "0.05 ps for the measured B L lifetimes.s b

The effects of uncertainty in the b hadron fragmentation are estimated slightly differently for the two boostestimation methods employed. For the hadronic Dy decay modes, the estimated B0 energy spectrum used bys s

w xthe boost estimation procedure is varied within the measured limits of the average b hadron energy 32 .Similarly, in generating the Monte Carlo events used to estimate the b hadron boost for the two L

q decayc

modes and the f lly mode, the average b hadron energy was varied by the same amounts as used above. Thesevariations yield changes in the fitted lifetimes of "0.02 ps. The effect on the lifetime of varying the mass of the

0 2 2 w x 2L by "50 MeVrc about its central value of 5641 MeVrc 1 is "0.01 ps. The effect of a 2 MeVrcb

0 w x 0uncertainty in the mass of the B 1 results in a change of less than 0.01 ps in the measured B lifetime.s s

In the Monte Carlo events used for the boost estimate, the L0 was assumed to be unpolarized. However, inb

the Standard Model, b baryons can retain up to the full longitudinal polarization of y0.94 from the b quark. Avariation from 0 to y0.94 polarization produces a change of q0.06 ps. A recent measurement of the

w xpolarization 33 is used to correct the lifetime extracted using the decay length fit. This yields a correction ofq0.014q0.020 ps, where this error results from the precision of the polarization measurement. The effect of they0.014

choice of form factor used to describe the energy transfer from the L0 to the L

q has also been investigated.b cw xThe use of the alternative form factors of Ref. 17 produces a negligible change in the fitted lifetime.

The average interaction point of the LEP beams in OPAL is used as the estimate of the production vertex ofthe B0 and L

0 candidates. The mean coordinates of the beam spot are known to better than 25mm in the xs b

direction and 10 mm in y. The effective r.m.s. spread of the beam is known to a precision of better than 10 mmŽ 0. Ž 0 .in both directions. To test the sensitivity of t B and t L to the assumed position and size of the beam spot,s b

the coordinates of the beam spot are shifted by "25mm, and the spreads are changed by "10 mm. The largestŽ 0. Ž 0 .observed variation in t B and t L is 0.01 ps which is assigned as a systematic error to both measurements.s b

The effects of alignment and calibration uncertainties on the result are not studied directly but are estimatedw xfrom a detailed study of 3-prong t decays 24 , in which the uncertainty in the decay length due to these effects

is found to be less than 1.8% for the data taken during 1990 and 1991 and less than 0.4% for later data. ThisŽ 0. Ž 0 .corresponds to an uncertainty on t B and t L of 0.01 ps. The potential for incorrect estimation of the decays b

length error is addressed by allowing an additional parameter in the lifetime fit which is a scale factor on theestimated decay length error. This parameter is found to be consistent with unity. This procedure changes the B0

s

lifetime by less than 0.01 ps and the L0 lifetime by y0.02 ps.b

8. Conclusion

q y0 y 0 q y ) 0 y y y 0The decay channels B ™D ll n X and L ™L ll n X, where D decays to K K , fp , K K ors s b c s Sy qq y q 0f ll n X and L decays to pK p or L ll n X have been reconstructed. From almost 4.4 million hadronic Zc

events recorded by OPAL from 1990 to 1995, a total of 172"28 such candidates are attributed to B0 decayss

and 129"25 such candidates are attributed to L0 decays.b

The B0 lifetime is found to be:s

t B0 s1.50q0 .16 "0.04 ps,Ž .s y0.15

w xwhere the first error is statistical and the second systematic. As predicted by theoretical calculations 3,4 , this0 w xresult is consistent with the observed value for the B lifetime 1 . This is also in agreement with other

0 w x Ž 0.measurements of the B lifetime 6,7 . The above value of t B has been combined with the OPALs s0 y w x Ž 0.measurement of the B lifetime in which only a D candidate is reconstructed 6 which yields t B ss s s

q0.20Ž .q0.18Ž .1.72 stat syst ps. Taking the correlated statistical and systematic errors into account, the average ofy0.19 y0.17

these two measurements is found to be 1.57"0.14 ps.


The measured L0 lifetime, is:b

q0 .230q yt L s 1.27q0.08P f "0.06 ps ,Ž .Ž .b J r L ll llb y0 .20

where the dependence of the fitted L0 lifetime is given in terms of the fraction, f q y, of the L llqllyb J r L ll llb

candidates that are due to J decays, the first error is statistical and the second systematic. Assuming Jb b

contamination of 30"20%, the L0 lifetime is:b

t L0 s1.29q0 .24 "0.06 ps.Ž .b y0.22

The lifetime using the L llqlly sample alone is found to be 0.85q0 .53 q0.11 ps, when the J content is taken toy0.37y0.14 b

be 30"20%. For the pKypqlly sample alone, the J content is estimated to be only about 1% and thebq0.25 w xlifetime of this sample is 1.36 "0.06 ps. These are consistent with other recent measurements 9,10 whichy0.23

0 w xhave tended to be lower than the B meson lifetime in qualitative agreement with the predictions of 3,4 .

Acknowledgements

We particularly wish to thank the SL Division for the efficient operation of the LEP accelerator at allenergies and for their continuing close cooperation with our experimental group. We also thank I.I. Bigi,B. Melic, M. Neubert and M.B. Voloshin for their aid in understanding the present theoretical description ofcharmed baryon decays. We thank our colleagues from CEA, DAPNIArSPP, CE-Saclay for their efforts overthe years on the time-of-flight and trigger systems which we continue to use. In addition to the support staff atour own institutions we are pleased to acknowledge theØ Department of Energy, USA,Ø National Science Foundation, USA,Ø Particle Physics and Astronomy Research Council, UK,Ø Natural Sciences and Engineering Research Council, Canada,Ø Israel Science Foundation, administered by the Israel Academy of Science and Humanities,Ø Minerva Gesellschaft,Ø Benoziyo Center for High Energy Physics,

Ž .Ø Japanese Ministry of Education, Science and Culture the Monbusho and a grant under the MonbushoInternational Science Research Program,

Ž .Ø German Israeli Bi-national Science Foundation GIF ,Ø Bundesministerium fur Bildung, Wissenschaft, Forschung und Technologie, Germany,¨Ø National Research Council of Canada,Ø Research Corporation, USA,Ø Hungarian Foundation for Scientific Research, OTKA T-016660, T023793 and OTKA F-023259.

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