28 September 2000

Ž .Physics Letters B 490 2000 71–86www.elsevier.nlrlocaternpe

A measurement of the rate of charm production in W decays

OPAL Collaboration

b h e ˚ c vG. Abbiendi , K. Ackerstaff , C. Ainsley , P.F. Akesson , G. Alexander ,J. Allison p, K.J. Anderson i, S. Arcelli q, S. Asai w, S.F. Ashby a, D. Axen aa,

G. Azuelos r,1, I. Bailey z, A.H. Ball h, E. Barberio h, R.J. Barlow p, S. Baumann c,T. Behnke y, K.W. Bell t, G. Bella v, A. Bellerive i, G. Benelli b, S. Bentvelsen h,S. Bethke af, O. Biebel af, I.J. Bloodworth a, O. Boeriu j, P. Bock k, J. Bohme n,8,¨

D. Bonacorsi b, M. Boutemeur ae, S. Braibant h, P. Bright-Thomas a, L. Brigliadori b,R.M. Brown t, H.J. Burckhart h, J. Cammin c, P. Capiluppi b, R.K. Carnegie f,A.A. Carter m, J.R. Carter e, C.Y. Chang q, D.G. Charlton a,2, P.E.L. Clarke o,

E. Clay o, I. Cohen v, O.C. Cooke h, J. Couchman o, C. Couyoumtzelis m, R.L. Coxe i,A. Csilling o,10, M. Cuffiani b, S. Dado u, G.M. Dallavalle b, S. Dallison p,

A. de Roeck h, E. de Wolf h, P. Dervan o, K. Desch y, B. Dienes ad,8, M.S. Dixit g,M. Donkers f, J. Dubbert ae, E. Duchovni x, G. Duckeck ae, I.P. Duerdoth p,P.G. Estabrooks f, E. Etzion v, F. Fabbri b, M. Fanti b, L. Feld j, P. Ferrari l,

F. Fiedler h, I. Fleck j, M. Ford e, A. Frey h, A. Furtjes h, D.I. Futyan p, P. Gagnon l,¨J.W. Gary d, G. Gaycken y, C. Geich-Gimbel c, G. Giacomelli b, P. Giacomelli h,

D. Glenzinski i, J. Goldberg u, C. Grandi b, K. Graham z, E. Gross x, J. Grunhaus v,M. Gruwe y, P.O. Gunther c, C. Hajdu ac, G.G. Hanson l, M. Hansroul h, M. Hapke m,´ ¨

K. Harder y, A. Harel u, M. Harin-Dirac d, A. Hauke c, M. Hauschild h, C.M. Hawkes a,R. Hawkings h, R.J. Hemingway f, C. Hensel y, G. Herten j, R.D. Heuer y, J.C. Hill e,

A. Hocker i, K. Hoffman h, R.J. Homer a, A.K. Honma h, D. Horvath ac,3,´K.R. Hossain ab, R. Howard aa, P. Huntemeyer y, P. Igo-Kemenes k, K. Ishii w,¨

F.R. Jacob t, A. Jawahery q, H. Jeremie r, C.R. Jones e, P. Jovanovic a, T.R. Junk f,N. Kanaya w, J. Kanzaki w, G. Karapetian r, D. Karlen f, V. Kartvelishvili p,

K. Kawagoe w, T. Kawamoto w, R.K. Keeler z, R.G. Kellogg q, B.W. Kennedy t,D.H. Kim s, K. Klein k, A. Klier x, S. Kluth af, T. Kobayashi w, M. Kobel c,T.P. Kokott c, S. Komamiya w, R.V. Kowalewski z, T. Kress d, P. Krieger f,

J. von Krogh k, T. Kuhl c, M. Kupper x, P. Kyberd m, G.D. Lafferty p, H. Landsman u,

0370-2693r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0370-2693 00 00971-0

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–8672

D. Lanske n, I. Lawson z, J.G. Layter d, A. Leins ae, D. Lellouch x, J. Letts l,L. Levinson x, R. Liebisch k, J. Lillich j, B. List h, C. Littlewood e, A.W. Lloyd a,S.L. Lloyd m, F.K. Loebinger p, G.D. Long z, M.J. Losty g, J. Lu aa, J. Ludwig j,

A. Macchiolo r, A. Macpherson ab,13, W. Mader c, S. Marcellini b, T.E. Marchant p,A.J. Martin m, J.P. Martin r, G. Martinez q, T. Mashimo w, P. Mattig x,¨

W.J. McDonald ab, J. McKenna aa, T.J. McMahon a, R.A. McPherson z, F. Meijers h,P. Mendez-Lorenzo ae, W. Menges y, F.S. Merritt i, H. Mes g, A. Michelini b,

S. Mihara w, G. Mikenberg x, D.J. Miller o, W. Mohr j, A. Montanari b,T. Mori w, K. Nagai h, I. Nakamura w, H.A. Neal l,6, R. Nisius h, S.W. O’Neale a,F.G. Oakham g, F. Odorici b, H.O. Ogren l, A. Oh h, A. Okpara k, M.J. Oreglia i,

S. Orito w, G. Pasztor h,10, J.R. Pater p, G.N. Patrick t, J. Patt j,´P. Pfeifenschneider n,9, J.E. Pilcher i, J. Pinfold ab, D.E. Plane h, B. Poli b,

J. Polok h, O. Pooth h, M. Przybycien h,4, A. Quadt h, C. Rembser h, P. Renkel x,´H. Rick d, N. Rodning ab, J.M. Roney z, S. Rosati c, K. Roscoe p, A.M. Rossi b,

Y. Rozen u, K. Runge j, O. Runolfsson h, D.R. Rust l, K. Sachs f, T. Saeki w,O. Sahr ae, E.K.G. Sarkisyan v, C. Sbarra z, A.D. Schaile ae, O. Schaile ae,

P. Scharff-Hansen h, M. Schroder h, M. Schumacher y, C. Schwick h, W.G. Scott t,¨R. Seuster n,8, T.G. Shears h,11, B.C. Shen d, C.H. Shepherd-Themistocleous e,

P. Sherwood o, G.P. Siroli b, A. Skuja q, A.M. Smith h, G.A. Snow q, R. Sobie z,S. Soldner-Rembold j,5, S. Spagnolo t, M. Sproston t, A. Stahl c, K. Stephens p,¨K. Stoll j, D. Strom s, R. Strohmer ae, L. Stumpf z, B. Surrow h, S.D. Talbot a,¨

S. Tarem u, R.J. Taylor o, R. Teuscher i, M. Thiergen j, J. Thomas o,M.A. Thomson h, E. Torrence i, S. Towers f, D. Toya w, T. Trefzger ae, I. Trigger h,

Z. Trocsanyi ad,7, E. Tsur v, M.F. Turner-Watson a, I. Ueda w, P. Vannerem j,´ ´M. Verzocchi h, H. Voss h, J. Vossebeld h, D. Waller f, C.P. Ward e,

D.R. Ward e, P.M. Watkins a, A.T. Watson a, N.K. Watson a, P.S. Wells h,T. Wengler h, N. Wermes c, D. Wetterling k, J.S. White f, G.W. Wilson p,J.A. Wilson a, T.R. Wyatt p, S. Yamashita w, V. Zacek r, D. Zer-Zion h,12

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 Nuclear Research, 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, UK

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–86 73

n Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germanyo UniÕersity College London, London WC1E 6BT, UK

p Department of Physics, Schuster Laboratory, The UniÕersity, Manchester M13 9PL, UKq Department of Physics, UniÕersity of Maryland, College Park, MD 20742, USA

r Laboratoire de Physique Nucleaire, UniÕersite de Montreal, Montreal, Que. H3C 3J7, Canada´ ´ ´ ´s UniÕersity of Oregon, Department of Physics, Eugene, OR 97403, USA

t CLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UKu 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 113-0033,and Kobe UniÕersity, Kobe 657-8501, Japan

x Particle Physics Department, Weizmann Institute of Science, RehoÕot 76100, Israely UniÕersitat HamburgrDESY, II Institut fur Experimental Physik, Notkestrasse 85, D-22607 Hamburg, Germany¨ ¨

z UniÕersity of Victoria, Department of Physics, P.O. Box 3055, Victoria, BC V8W 3P6, Canadaaa UniÕersity of British Columbia, Department of Physics, VancouÕer, BC V6T 1Z1, Canada

ab UniÕersity of Alberta, Department of Physics, Edmonton, AB T6G 2J1, Canadaac Research Institute for Particle and Nuclear Physics, P.O. Box 49, H-1525 Budapest, Hungary

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

af Max-Planck-Institute fur Physik, Fohring Ring 6, 80805 Munchen, Germany¨ ¨ ¨

Received 24 July 2000; accepted 11 August 2000K. Winter

Abstract

Using data recorded at centre-of-mass energies around 183 and 189 GeV with the OPAL detector at LEP, theW Ž . Ž .fundamental coupling of the charm quark to the W boson has been studied. The ratio R 'G W™c X rG W™hadronsc

has been measured from jet properties, lifetime information, and leptons produced in charm decays. A value compatible withW Ž . Ž .the Standard Model expectation of 0.5 is obtained: R s0.481"0.042 stat. "0.032 syst. . By combining this result withc

< <measurements of the W boson total width and hadronic branching ratio, the magnitude of the CKM matrix element V iscs< <determined to be V s0.969"0.058. q 2000 Elsevier Science B.V. All rights reserved.cs

Ž .E-mail address: mette.stuwe@cern.ch OPAL Collaboration .1 And at TRIUMF, Vancouver, Canada V6T 2A3.2 And Royal Society University Research Fellow.3 And Institute of Nuclear Research, Debrecen, Hungary.4 And University of Mining and Metallurgy, Cracow.5 And Heisenberg Fellow.6 Now at Yale University, Department of Physics, New Haven, CT, USA.7 And Department of Experimental Physics, Lajos Kossuth University, Debrecen, Hungary.8 And MPI Munchen.¨9 Now at MPI fur Physik, 80805 Munchen.¨ ¨

10 And Research Institute for Particle and Nuclear Physics, Budapest, Hungary.11 Now at University of Liverpool, Department of Physics, Liverpool L69 3BX, UK.12 And University of California, Riverside, High Energy Physics Group, Riverside, CA 92521, USA.13 And CERN, EP Div, 1211 Geneva 23.

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–8674

1. Introduction

Since 1997 the LEP eqey collider has beenoperated at energies above the threshold for W-pairproduction. This offers a unique opportunity to studythe hadronic decays of W bosons in a clean environ-ment and to investigate the coupling strength of Wbosons to different quark flavours. The fraction of Wbosons decaying hadronically to different quarkflavours is proportional to the sum of the squaredmagnitudes of the corresponding elements of the

Ž . w xCabibbo–Kobayashi–Maskawa CKM matrix 1 . Ameasurement of the production rates of differentflavours therefore gives access to the individual CKMmatrix elements.

In eqey™WqWy events, the only heavy quark

commonly produced is the charm quark. The produc-tion of bottom quarks is in fact highly suppressed

< < < <due to the small magnitude of V and V and theub cb

large mass of the top quark, the weak partner of thebottom quark. This allows for a direct measurementof the production fraction of charm in W decayswithout a separation of charm and bottom quarks.The magnitude of the CKM matrix element V cancs

then be derived from the charm production rate,using the knowledge of the other CKM matrix ele-

< <ments. So far direct measurements of V havecs

limited precision compared to the other CKM matrix< < < <elements important in W decays, i.e. V , V , andud us

< <V . The most recent evaluation of the magnitude ofcd

V from exclusive charm semi-electronic decayscs< < w xyields V s1.04"0.16 2 .cs

In the analysis presented here, a value of theW Ž . Žpartial decay width R 'G W™c X rG W™c

.hadrons is extracted from the properties of finalstate particles in W decays. Charm hadron identifica-tion is based upon jet properties, lifetime informa-tion, and semileptonic decay products in WqWy

™

q yqqqq and W W ™qq ll n events. The measuredllW < <value of R is then used to determine V .c cs

2. Data and Monte Carlo samples

The data used for this analysis were recorded atw xLEP by the OPAL detector 3 at centre-of-mass

energies around 183 GeV in 1997 and 189 GeV in

1998. OPAL14 is a multipurpose high energy physicsdetector incorporating excellent charged and neutralparticle detection and measurement capabilities. Theintegrated luminosities used for the analysis amount

y1 Ž y1 .to 56.5 pb 180.2 pb at luminosity-weightedŽmean centre-of-mass energies of 182.7 GeV 188.6

. y1 Ž y1 .GeV . In addition, 2.1 pb 3.1 pb of calibration' Ž .data were collected at s ;M in 1997 1998 andZ

have been used for fine tuning of the Monte Carlosimulation.

To determine the selection criteria and taggingefficiencies, Monte Carlo samples were generated

w xusing the KORALW 1.42 4 program, which utilizesw xJETSET 7.4 5 for fragmentation, followed by a full

w xsimulation of the OPAL detector 6 . The centre-of-'mass energies were set to s s183 and 189 GeV

with a W mass of M s80.33 GeV. AdditionalW

samples with different centre-of-mass energies andW masses were used to estimate the sensitivity tothese parameters. Further samples generated with

w x w x w xPYTHIA 7 , HERWIG 8 , and EXCALIBUR 9 were usedto determine the model dependence of the measure-ment.

The dominant background sources for this analy-0sis are Z rg™qq events and four-fermion final

states which are not from WqWy decays. Back-ground samples were generated using the PYTHIA,

w xHERWIG, EXCALIBUR, and GRC4F 10 generators. Moredetails on the treatment of the backgrounds can be

w xfound in Refs. 11,12 .

3. Event selection

The WW event selections are the same as thoseused for the OPAL WW production cross-section

' w xmeasurements at s s183 GeV 11 and 189 GeVXyqq y

Xw x12 . Events not selected as W W ™ ll n ll nll llq ycandidates are passed to the W W ™qq ll n selec-ll

14 The OPAL coordinate system is defined such that the z-axisis parallel to and in the direction of the ey beam, the x-axis liesin the plane of the accelerator pointing towards the centre of theLEP ring, and the y-axis is normal to the plane of the acceleratorand has its positive direction defined to yield a right-handedcoordinate system. The azimuthal angle, f, and the polar angle,u , are the conventional spherical coordinates.

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–86 75

Table 1Number of selected WW candidate events and those expected from the main background sources for the selection at 183 and 189 GeV. The

Ž .‘qqqq’ background source refers to processes excluding doubly resonant W-pair production at tree level CC03 diagrams . The entry labeled‘Wen ’ refers to events where a singly produced W decays hadronically. The errors are the systematic errors on the backgrounde

w xcontributions, as evaluated in Refs. 11,12

183 GeV 189 GeV

Type qq ll n qqqq qq ll n qqqq

selected events 350 432 1235 1532

0Z rg™qq 15.4"1.6 77.4"8.5 45.5"5.6 240.0"15.9qqqq 0.5"0.6 12.4"2.8 2.5"0.6 70.3"12.3

q yqq ll ll 10.2"1.2 4.1"0.3 27.6"2.7 8.6"1.4Wen 6.2"1.7 0"1 23.3"4.1 0"1e

total background 32.4"2.7 93.9"9.0 98.9"7.5 318.9"20.2

tion procedure and may be classified as qqen ,eq yqq mn , or qqtn candidates. The W W ™qqqqm t

selection is applied to events that fail the precedingselections. It has been checked that the event selec-tion introduces a negligible bias in the flavour com-position. In this analysis, the small fraction of

Ž .selected singly produced W bosons Wen whiche

decay hadronically to a charm quark is considered assignal.

Since the identification of charm mesons reliesheavily on lifetime and lepton information, the rele-vant parts of the detector were required to be opera-tional while the data were recorded. Thus, in addi-tion to the requirements which were already applied

w xin Refs. 11,12 , it was required that the siliconmicrovertex detector and the muon chambers were

Ž .fully operational. After all cuts, a total of 350 1235q y Ž .W W ™ qq ll n candidates and 432 1532llq yW W ™qqqq candidates were selected at 183 GeV

Ž .189 GeV . A breakdown of the different backgroundcontributions is given in Table 1. The expectednumber of background events is calculated from the

w xbackground cross-sections given in Refs. 11,12 ; theerrors correspond to the systematic errors quoted inthese references.

4. Measurement of R Wc

ŽAfter the event selection, the hadronic part which.excludes the identified lepton of a qq ll n event is

w xforced into two jets using the Durham algorithm 13 ,while qqqq events are forced into four jets. Subse-quently, a relative likelihood discriminant is calcu-lated for each jet to separate jets originating fromcharm quarks and jets from u, d, and s quarks. Thisdiscriminant relies on jet and event shape properties,lifetime information, and lepton identification as de-scribed in the remaining parts of this section. Theresulting likelihood distribution is fitted to obtain therelative fractions of uds and charm jets.

In qq ll n events the two jets can be uniquelyll

assigned to the decay of one W boson, while forqqqq events the four jets have to be grouped intopairs that are assumed to originate from the decay ofone W boson. The jet pairing is chosen using akinematic fit to find the jet combination which ismost compatible with the production of two on-shellW bosons with a mass of 80.33 GeV. After the jetpairing has been performed in qq ll n and qqqqll

events, the jet energies are calculated in a kinematicfit, imposing energy-momentum conservation andequality of the masses of both W candidates. If thekinematic fit fails, the jet energies of each jet pair arescaled so that their sum equals the beam energy. Thechoice of the jet pairing influences the result of thepresent analysis only through the values of the jetangle u in the di-jet rest frame and the di-jet anglejet

u in the laboratory frame, both of which areW

calculated from the jet momenta determined by thekinematic fit. These two angles are employed in thelikelihood functions as described in Sections 4.2 and

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–8676

4.3. It has been checked in the W mass measurementw xanalysis 14,15 and in an analysis concerned with

w xproperties of hadronically decaying W bosons 16that jet properties relevant for the jet pairing algo-rithm and the kinematic fit are well modelled in theMonte Carlo simulation.

4.1. Secondary Õertex tag

Weakly decaying charm hadrons have lifetimesw xbetween 0.2 and 1 ps 2 , leading to typical decay

lengths of a few hundred microns to a few millime-tres at LEP2 energies. These relatively long-livedparticles produce secondary decay vertices which aresignificantly displaced from the primary event ver-tex. The primary vertex in an event is found byfitting all charged tracks to a common point in spacew x17 . Its determination is improved by using theaverage beam position as a constraint with RMSvalues of 150 mm in x, dominated by the widthof the beam, about 20 mm in y, and less than1 cm in z.

In the search for charm decay products, tracks inthe central detector and clusters in the electromag-netic calorimeter within a given jet are considered.Tracks used to find secondary vertices must fulfillthe quality criteria used in the WW cross-section

w xanalyses 11,12 . Additionally, the tracks are re-quired to have a momentum larger than 0.75 GeV, asigned distance of closest approach to the primary

Ž .vertex in the rf plane 2D-impact parameter 0 cm-d -0.3 cm, and an error on the impact para-0

meter, s , smaller than 0.1 cm. From the tracksd0

which fulfill these criteria, the tracks which are mostlikely to originate from the decay products of acharm hadron are identified via an iterative pro-cedure.Particles from charm hadron decays tendto havea large momentum and a large rapidity y

1 Žs ln Eqp Eyp where p is the parti-Ž . Ž .Ž .I I I2

cle’s momentum component parallel to the jet direc-.tion and E is its energy compared to fragmentation

tracks, and their combined invariant mass should becompatible with a charm hadron mass. Therefore foreach track and electromagnetic cluster which is notassociated to any track, the rapidity y is calculatedassuming the charged pion mass for tracks and zeromass for unassociated clusters. The track or cluster

with the lowest rapidity is removed from the sampleand the invariant mass of the remaining tracks andclusters is calculated. This procedure is repeateduntil the mass of the remaining group of tracks andclusters falls below 2.5 GeV. This procedure selectspreferentially tracks from the decay of charm hadronsw x18 .

All selected tracks in the jet are fitted to a com-mon vertex in three dimensions. Tracks which con-tribute more than 4 to the x 2 of this fit are removedand the fit is repeated. The procedure is stoppedwhen all tracks pass the x 2 requirement. At leasttwo tracks are required to remain in the fit for thesecondary vertex finding to be successful. Oncetracks are associated to a secondary vertex, the dis-tance L between the primary and the secondaryvertex and its error s are computed. The decayL

length significance of a secondary vertex, Lrs , isLŽ .required to be positive i.e. Lrs )0 , where L isL

given a positive sign if the secondary vertex isdisplaced from the primary vertex along the directionof the jet momentum.

Jets containing a good secondary vertex are thenused to tag charm decay products by means of an

Ž . w xartificial neural network ANN 19 to enhance thecharm purity at a given efficiency. The nine ANNinput variables are: the decay length significanceLrs of the secondary vertex; the primary vertexL

Ž w x.joint probability for a definition, see Ref. 20 ;E rE , where E is the sum of the energyvertex beam vertex

of all the tracks assigned to the secondary vertex andE is the beam energy; the distance of closestbeam

Ž .approach to the primary event vertex in rf z 3D ofthe pseudo-particle formed from all the tracks in thesecondary vertex; the normalised weighted averageŽ .weighted by the measured error of all the track2D-impact parameters within the secondary vertex;the highest momentum of the charged particles in thesecondary vertex; the invariant mass of the vertex;the largest track 3D-impact parameter in the sec-ondary vertex; and the second largest track 3D-im-pact parameter in the secondary vertex.

q yThe same vertex ANN is used for W W ™qqqqq yand W W ™qq ll n events. The distributions ofll

the two most discriminating input variables for thevertex ANN are shown in Fig. 1. Typically, charmhadrons have secondary vertices which are displacedfrom the primary vertex and charged tracks associ-

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–86 77

' Ž .Fig. 1. Distributions of the most sensitive input variables of the vertex ANN at s s183–189 GeV: a decay length significance Lrs andLŽ . Ž .b primary vertex joint probability. Points with error bars represent the data 183 and 189 GeV samples combined . Histograms representthe Monte Carlo expectation.

ated with charm particles have a lower probability tocome from the primary vertex. Fig. 2a shows acomparison of the ANN output between data and

'Monte Carlo for s s183–189 GeV. The simulationw xof the OPAL tracking detectors 6 requires a de-

tailed understanding of the track-finding efficiencyand resolution. This is achieved by tuning the MonteCarlo simulation with the calibration data taken atthe Z0 resonance. Fig. 3a shows the distribution ofLrs for secondary vertices. The effect of a 5%L

variation of the tracking resolution used to assess thesystematic uncertainty is also depicted.

4.2. Lepton tag

About 20% of all charm hadrons decay semilep-tonically and produce an electron or a muon in thefinal state. Because of the relatively large mass andhard fragmentation of the charm quark compared tolight quarks, this lepton is expected to have a larger

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–8678

'Ž . Ž .Fig. 2. Distributions of a the vertex ANN output and b the likelihood output of the lepton tag at s s183–189 GeV. Points with errorŽ .bars represent the data 183 and 189 GeV samples combined . Histograms show the results of the fits to the combined likelihood described

in Section 4.4. If no vertex or lepton tag information is available, the corresponding variable is assigned the value of zero.

Žmomentum than leptons from other sources exceptthe small contribution from semileptonic bottom de-

.cays in background events . Therefore, identifiedelectrons and muons can be used as tags for charmhadrons in W boson decays.

In a first step, the leptons are identified usingANN algorithms. The electron ANN described in

w xRefs. 21,22 is used. Its most important input vari-ables are the specific ionization in the central jet

Ž .chamber d Erd x of the electron candidate trackand the ratio of the associated energy deposited inthe electromagnetic calorimeter to the momentum of

Ž .this track Erp . Photon conversions are rejectedfrom the sample using another dedicated ANN

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–86 79

Fig. 3. Comparison of discriminating variables between calibration data taken at the Z0 resonance and Monte Carlo prediction. Points with0 Ž .error bars represent data from the Z calibration runs. Histograms show the expectation from the Monte Carlo simulation. a Decay length

significance Lrs for data and Monte Carlo. The dotted line shows the effect of the "5% variation of the tracking resolution used toLŽ . Ž .assess the systematic uncertainty on the vertex tag. b Erp and c normalised d Erd x for electron candidates from data and Monte Carlo.

In these plots, electrons must satisfy the pre-selection described in the text and have an electron ANN output greater than 0.5. The dottedŽ .lines show how the variation of the detection mis identification and resolution for electron candidates affects the Erp and d Erd x

distributions.

w x w x21,22 . The muon ANN 23 is based on informationŽ .from the tracking detectors including d Erd x , the

hadronic calorimeter, and the muon chambers. Thelepton candidates have to be well contained in the

Ž < <detector cosu -0.9, where u is the polar anglell lly .with respect to the e beam direction and are

required to have momentum p )2 GeV.ll

The most energetic lepton candidate in each jet isused to calculate a relative likelihood discriminantwith the goal of separating leptons in charm decaysfrom leptons from other sources. Dedicated likeli-hood functions are set up for electrons and muons in

q y q yW W ™qqqq and W W ™qq ll n events, usingll

additional variables that describe properties of thelepton within a jet and enhance the separation ofcharm jets from uds jets. The likelihood calculation

w xis done using the method described in Ref. 24 . Thefollowing input variables are used both for electronsand for muons: the output of the electron or muonANN; the magnitude of the cosine of the polar angle

< <of the lepton candidate cosu ; and the magnitude ofll

the momentum of the lepton candidate p .ll

In qqqq events, where the charge of the decayingW boson is not known, the likelihood function alsouses the product of the lepton charge and the cosineof the W production angle, Q cosu , where u isll W W

defined as the polar angle of the sum of momenta ofboth jets of the pair that contains the lepton. Thisquantity makes use of the strong forward–backwardasymmetry of the produced W bosons.

In qq ll n events, where the charge of the W bosondecaying leptonically is known, the likelihood func-

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–8680

tion uses the product of the charge of the leptontagged in the charm decay and the charge of thelepton from the leptonically decaying W. Finally, forelectron candidates, the likelihood discriminant em-ploys the output of the conversion finder ANN tosuppress electrons from photon conversions.

In Fig. 2b the likelihood output of the lepton tag'is shown for data and Monte Carlo at s s183–189

GeV. In this analysis precise modelling of the leptonidentification is important. The lepton reconstructionefficiencies in the Monte Carlo simulation were tunedto match the values obtained from data collected atthe Z0 resonance. Figs. 3b,c show the Erp andnormalised d Erd x distributions of electron candi-dates. Reasonable agreement between data and MonteCarlo simulation is observed. The variables used formuon identification are also well described in thesimulation.

4.3. Combined tag

For each jet, the vertex ANN and the leptonlikelihood discriminant are merged into a singlequantity by an additional likelihood function. Thiscombined likelihood discriminant uses two addi-tional variables: the cosine of the jet angle cosu injet

the rest frame of the W boson with respect to the Wmomentum direction and the likelihood output of the

w xWW event selection 11,12 . The jet angle in thedi-jet rest frame helps to separate jets originatingfrom up-type and down-type quarks. Due to thepolarisation of the W bosons and the VyA nature ofthe weak interaction, up-type quarks tend to beproduced preferentially in the backward directionwith respect to the W flight direction, while down-type quarks are found more often in the forwarddirection. The likelihood output of the WW event

Ž . ŽFig. 4. a Output of the combined likelihood used to tag charm hadrons at 183–189 GeV. Points with error bars represent the data 183 and. Ž .189 GeV samples combined . Histograms represent the results of the fits described in Section 4.4. b Efficiency and purity computed after

the WW selection as a function of a cut on the combined likelihood output.

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–86 81

Table 2Ž .Tagging efficiencies in % after the WW selection from Monte Carlo simulation for u, d, s, and c jets in WW events and for jets from

background events, for a cut on the combined likelihood of 0.7. The values are shown separately for events at 183 and 189 GeV and forqq ll n and qqqq events. The errors are statistical only

Tagging 183 GeV 189 GeVŽ .efficiency % qq ll n qqqq qq ll n qqqq

e 4.3"0.5 3.8"0.3 4.9"0.5 4.4"0.3W™ u

e 3.1"0.4 3.0"0.2 3.2"0.4 3.1"0.2W™ d

e 3.2"0.4 3.0"0.2 3.3"0.4 3.1"0.2W™ s

e 18.1"0.6 15.8"0.4 18.9"0.6 16.7"0.4W™ c

e 6.0"2.7 4.7"1.0 8.0"2.1 5.4"0.8bgd

selection suppresses false tags from background0events, especially from Z rg™bb events.

In Fig. 4a the combined likelihood output isshown, illustrating the discriminating power betweencharm and light flavoured jets. The efficiency andpurity for a particular cut on the combined likelihoodoutput are also depicted in Fig. 4b. Table 2 lists thetagging efficiencies for jets in WW and backgroundevents that result from a cut on the likelihood outputat the optimal value of 0.7. The tagging efficienciesat 189 GeV are slightly higher due to the extra boostof the W bosons. These values are not directly usedto derive RW, but are quoted to give an impressionc

of the performance of the charm tag.

4.4. Determination of RWc

To extract RW from the data, a binned maximumc

likelihood fit is performed to the combined likeli-hood distributions. Template histograms for thecharm, light-flavoured, and non-WW backgroundcomponents are produced from the main Monte Carlosamples. They are referred to as the probability

Ž .density functions pdf for the various components.Using this fitting method improves the statisticalsensitivity of the measurement compared to simplycounting the number of jets that pass a cut on thelikelihood output. The function used to fit the dataŽ .see Fig. 4a is:

N

yln LLsy n ln 1yFŽ .½Ý i bkgis1

= 1 1W i W iR PP q 1y R PPŽ .c c c uds2 2

qF PP i , 1Ž .5bkg bkg

withi: Bin index in the combined likelihood distribu-

tion;n : Number of jets in the i th bin;i

N: Number of bins in the combined likelihooddistribution;

PP i: Probability for a charm jet to appear in the i thcŽ .bin W™c X pdf ;

PP i : Probability for a uds jet to appear in the i thudsŽ .bin W™ light flavour pdf ;

F : Fraction of background jets;bkg

PP i : Probability for a non-WW jet to appear inbkgth Ž .the i bin non-WW background pdf .

The result of the fit for RW is:c

RW s0.493"0.090 at 183 GeVc

and

RW s0.478"0.047 at 189 GeV.c

2 Žwhere the errors are statistical only. The x r degree.of freedom of the fits are 17.2r24 at 183 GeV and

35.4r24 at 189 GeV.

4.5. Systematic uncertainties

Since the reference histograms, the efficiencies,and the background for the calculation of RW werec

taken from a Monte Carlo simulation, the analysisdepends on the proper modelling of the data distribu-tions in the simulation. The sources of systematicerror are listed in Table 3 and are discussed below.Unless otherwise noted, all changes were applied tosignal and background Monte Carlo samples.

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–8682

Table 3Summary of the experimental systematic errors, statistical errors,and central values from the binned maximum likelihood fit on RW

c

at 183GeV and 189GeVWSource of D Rc

systematic error 183 GeV 189 GeV

hadronisation model 0.011 0.012centre-of-mass energy 0.007 0.005mass of the W boson 0.004 0.003charm fragmentation function 0.007 0.007background cross-section 0.006 0.005background composition 0.010 0.009charm hadron fractions 0.006 0.007light quark composition 0.007 0.005vertex reconstruction 0.016 0.017charm hadron lifetimes 0.003 0.002charm decay multiplicity 0.010 0.010lepton identification 0.012 0.014lepton energy spectrum 0.003 0.003

Ž .branching ratio Br c™ ll 0.006 0.006

total systematic error 0.032 0.032

statistical error 0.090 0.047

Wvalue of R 0.493 0.478c

v Hadronisation model: The PYTHIA Monte Carlosample, which uses the Lund string fragmentation

w xas implemented in JETSET 5 , was compared to aw xsample generated with HERWIG 8 , which uses

cluster fragmentation. The samples differ in theirparton showering and hadronisation.

v W mass and centre-of-mass energy: As the jetpairing depends on the W mass, M , and theW'centre-of-mass energy, s , the analysis was re-peated with different W masses and at differentcentre-of-mass energies. The W mass was variedby 100 MeV, which covers both the experimentaluncertainty and the differences between the current

w xworld average mass 2 and the value used in theMonte Carlo. The centre-of-mass energy was var-ied by the difference between the luminosity-weighted centre-of-mass energies in data and the

'value of s used in the main Monte Carlo sam-ples.

v 'Charm fragmentation: At s sM , the meanZ

scaled energy of weakly decaying charm hadrons² Ž .: w xwas found to be x M s0.484"0.008 25 .D Z

No measurements of this quantity exist for Wdecays, but it is expected to be similar to that in Zdecays. The changes in the charm fragmentation

w xdue to QCD effects were taken from JETSET 5 . To² Ž .:assess the systematic uncertainty, x M wasD W

varied by the experimental uncertainty obtained on² Ž .:x M , i.e. 0.008. The fragmentation schemesD Z

w x w xof Peterson 26 , Collins and Spiller 27 , Kartvel-w x w xishvili 28 and the Lund group 29 were used to

assess a possible discrepancy on the shape of thefragmentation function. The largest variation wasassigned as the systematic error.

v Background cross-section: In the fit for extractingRW, the fraction of background was varied accord-c

ing to the error on the expected fraction of back-w xground events from Refs. 11,12 .

v Background composition: The various backgroundsources have different probabilities to fake a charmjet. The background composition was varied withinthe uncertainties given in Table 1.

v Charm hadron fractions: The fractions of theweakly decaying charm hadrons were varied within

w xtheir experimental errors according to Ref. 25 .v Light quark composition: The shape of the refer-

ence histogram for light-flavoured quarks dependson the relative fractions of the u, d, and s jets. Thequark flavour fractions were varied according to

w xthe actual errors on the CKM matrix 2 so that theerror covers the effect of assumptions concerningthe CKM matrix elements on the uds templatehistogram. The number of bottom hadrons from Wbosons was also doubled to ensure that the mea-sured RW was insensitive to the bottom fraction inc

W decays.v Vertex reconstruction: The correct modelling of

the detector resolution in the Monte Carlo simula-tion is of paramount importance for the descriptionof the probability to find a secondary vertex. Thiswas checked by comparing the track parameters

'between calibration data collected at s ;M andZ

Monte Carlo simulation. The sensitivity to thevertex reconstruction was assessed by degrading orimproving the tracking resolution in the MonteCarlo. It was found that changing the track param-eters resolution by "5% covers the range of theobserved differences between data and Monte CarloŽ .see Fig. 3a in the vertex ANN input and outputdistributions.

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–86 83

v Charm hadron lifetimes: The lifetimes of theweakly decaying charm hadrons were varied within

w xtheir experimental errors according to Ref. 2 .v Charm decay multiplicity: The performance of the

secondary vertex finder depends on the multiplic-ity of the final state of the charm hadrons. Therelative abundance of 1, 2, 3, 4, 5, and 6 prongcharm decays was changed in the Monte Carlo

w xwithin their experimental errors 30 . Similarly, therelative abundance of neutral pions was varied inthe Monte Carlo within the experimental errorsw x30 .

v Lepton identification: The modelling of the inputvariables of the ANN for electron identification

w xhas been intensively studied at LEP1 22 , whilethe performance of the muon tagging ANN hasbeen investigated using various control samples ofcalibration data collected at the Z0 resonance dur-

w xing each year of LEP2 23 . The relative error ofŽ .the efficiency to identify a genuine electron muon

Ž .has been estimated to be 4% 3% , and the relativeerror on the probability to wrongly identify ahadron as a lepton has been evaluated to be around

Ž . Ž . w x16% 10% for electrons muons 22,23 . Bystudying the d Erd x distributions for electron can-didates in calibration data taken at the Z0 mass in1997 and 1998, it was found that a shift of the

Ž .mean d Erd x of 0.04 keVrcm 0.3% and ascaling by 1% of the d Erd x resolution in datawas needed to correct a slight discrepancy betweenMonte Carlo and data. This effect was also takeninto account in the assignment of the uncertainty

Ž .on the electron tagging efficiency. The mis identi-fication probabilities for electrons and muons werevaried by reweighting the Monte Carlo events andthe largest resulting change in RW was taken asc

the systematic error. It was verified that the varia-tion of efficiencies and d Erd x resolution wassufficient to describe the possible differences be-

Ž .tween data and Monte Carlo see Figs. 3b,c .v Lepton energy spectrum from semileptonic charm

decays: The energy spectrum of the lepton in therest frame of the weakly decaying charm hadronwas reweighted from the spectrum implemented in

w x w xJETSET to the ISGW 31 and ACCMM 32 mod-els; the parameters p and m of the ACCMMf s

model were varied in the range recommended inw xRef. 25 .

v ( )Branching ratio Br c™ ll : The branching frac-tion for inclusive charm decays to leptons was

Ž .varied within the range Br c™ ll s0.098"0.005w x25 by reweighting the Monte Carlo events.

The size of the systematic errors is very similar forthe samples at 183 and 189 GeV. The dominantsystematic errors are those associated with the vertexreconstruction and lepton identification.

5. Results

The result of the charm tag analysis is

RW s0.493"0.090 stat. "0.032 syst.Ž . Ž .c

at 183 GeV

and

RW s0.478"0.047 stat. "0.032 syst.Ž . Ž .c

at 189 GeV.W 'The combined value of R obtained at s s183 andc

189 GeV is

RW s0.481"0.042 stat. "0.032 syst. ,Ž . Ž .c

where the systematic uncertainties are treated asbeing fully correlated.

< <6. Extraction of Vcs

< < WIt is possible to extract V from R using thecs c

relation

RWc

< < 2 < < 2 < < 2V q V q Vcd cs cbs ,2 2 2 2 2 2< < < < < < < < < < < <V q V q V q V q V q Vud us ub cd cs cb

2Ž .

which leads to

WRc 2 2 2 2 2< < < < < < < < < < < <V s V q V q V y V y V .Ž .cs ud us ub cd cb( W1y Rc

3Ž .

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–8684

Table 4Values of the CKM matrix elements used in the calculation of< < W w xV from R . The values are taken from Ref. 2cs c

CKM matrix element Value

< <V 0.9735"0.0008ud< <V 0.2196"0.0023us< < < <V r V 0.090"0.025ub cb< <V 0.224"0.016cd< <V 0.0402"0.0019cb

Using the values of the other CKM matrix elementslisted in Table 4, one gets

< <V s0.93"0.08 stat.Ž .cs

"0.06 syst. "0.004 CKM ,Ž . Ž .where the last error is due to the uncertainty on theCKM matrix elements used in the calculation.

< <A more precise value for V can be obtainedcs

based on the Standard Model prediction of the decaywidth of the W boson to final states containingcharm quarks:

CG M 3F W 2 2 2< < < < < <G W™c X s V q V q V ,Ž . Ž .cd cs cb'6 2 p

4Ž .3 ' Ž . w xwith CG M 6 2 ps 705"4 MeV 2 and theF W

w xcolor factor C given by 2

a M a 2 MŽ . Ž .s W s WCs3 1q q1.409 2ž p p

a 3 MŽ .s Wy12.77 . 5Ž .3 /p

Ž . WG W™c X can be evaluated from R using thec

relation

G W™c X sRW Br W™hadrons G W . 6Ž . Ž . Ž .c tot

Ž .Using the PDG values Br W™ hadrons s15 W Ž . w x0.6848"0.0059 and G s 2.12"0.05 GeV 2tot

15 The most precise measurements of G W are determined fromtotŽ . Ž .s pp™WqX PBr W™en w xthe quantity RRs . In Ref. 33 , the

0 0 q yŽ . Ž .s pp™Z qX PBr Z ™e e

coupling of the W boson to light quarks is needed as input;however, direct measurements of the corresponding CKM matrixelements are so precise that it introduces a negligible uncertaintyon G W.tot

together with the measurement of RW presented inc

this letter, one gets

G W™c X s 698"61 stat.Ž . Ž ."46 syst. "18 ext. MeV,Ž . Ž .

where the last error is due to the uncertainties on theW Ž .external parameters G and Br W™hadrons . Thistot

corresponds to

< < 2 < < 2 < < 2V q V q V s0.990"0.087 stat.Ž .cd cs cb

"0.065 syst.Ž ."0.026 ext. .Ž .

Subtracting the off-diagonal CKM matrix elements,using the values listed in Table 4, results in

< <V s0.969"0.045 stat. "0.034 syst.Ž . Ž .cs

"0.013 ext. "0.004 CKM ,Ž . Ž .where the last error is due to the uncertainties on theCKM matrix elements used in the calculation. The

< < Ž . Ž .determination of V from Eqs. 4 and 6 onlycs

involves the CKM matrix elements for the transitionW™c X and well measured parameters such as G W

totŽ .and Br W™hadrons . It is therefore more precise

Ž .than the method which relies on Eq. 3 . Both results< <of V presented here are compatible with the directcs

determination from D semi-electronic decays which< < w xyields V s1.04"0.16 2 .cs

7. Summary

Using data taken with the OPAL detector at LEPat centre-of-mass energies of 183 and 189 GeV, the

W Ž . Ž .ratio R s G W™ c X rG W™ hadrons hasc

been measured using a technique based on jet prop-erties, lifetime information, and leptons from charmdecays. The combined result is

RW s0.481"0.042 stat. "0.032 syst. ,Ž . Ž .c

in agreement with the Standard Model expectation of0.5. This result is consistent with the Standard Modelprediction that the W boson couples to up and charmquarks with equal strength and it is in agreement

w xwith the recent measurements of DELPHI 34 andw xALEPH 35 .

Using the results from direct measurements of the< <other CKM matrix elements, V can be calculatedcs

W < <from R , yielding V s0.93"0.10. A more pre-c cs

( )G. Abbiendi et al.rPhysics Letters B 490 2000 71–86 85

< <cise value for V can be derived from the measure-csW Ž . Wments of R , Br W™hadrons , and G :c tot

< <V s0.969"0.058.cs

This can be compared to a more indirect determina-< <tion of V by OPAL from the ratio of the W decaycs

< <widths to qq and ll n , which yields V s1.014"ll csŽ . Ž . w x0.029 stat. "0.014 syst. 12 under the assumption

that the W boson couples with equal strength toquarks and leptons. It should be noted that the ratio

Ž . Ž .Br W™qq rBr W™ ll n is not used in the anal-ll

ysis presented here, so that these are independent< <determinations of V .cs

Acknowledgements

We particularly wish to thank the SL Division forthe efficient operation of the LEP accelerator at allenergies and for their continuing close cooperationwith our experimental group. We thank our col-leagues from CEA, DAPNIArSPP, CE-Saclay fortheir efforts over the years on the time-of-flight andtrigger systems which we continue to use. In additionto the support staff at our own institutions we arepleased to acknowledge the Department of Energy,USA, National Science Foundation, USA, ParticlePhysics and Astronomy Research Council, UK, Nat-ural Sciences and Engineering Research Council,Canada, Israel Science Foundation, administered bythe Israel Academy of Science and Humanities, Min-erva Gesellschaft, Benoziyo Center for High EnergyPhysics, Japanese Ministry of Education, Science

Ž .and Culture the Monbusho and a grant under theMonbusho International Science Research Program,Japanese Society for the Promotion of ScienceŽ .JSPS , German Israeli Bi-national Science Founda-

Ž .tion GIF , Bundesministerium fur Bildung und¨Forschung, Germany, National Research Council ofCanada, Research Corporation, USA, HungarianFoundation for Scientific Research, OTKA T-029328, T023793 and OTKA F-023259.

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