A measurement of the rate of charm production in W decays

28 September 2000

Physics Letters B 490 Ž2000. 71–86 www.elsevier.nlrlocaternpe

A measurement of the rate of charm production in W decays OPAL Collaboration c ˚ G. Abbiendi b, K. Ackerstaff h , C. Ainsley e, P.F. Akesson , G. Alexander v, 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 , n,8 S. Bethke af , O. Biebel af , I.J. Bloodworth a , O. Boeriu j, P. Bock k , J. Bohme , ¨ b ae h a D. Bonacorsi , M. Boutemeur , S. Braibant , P. Bright-Thomas , 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 , h , D.I. Futyan p, P. Gagnon l , F. Fiedler h , I. Fleck j, M. Ford e, A. Frey h , A. Furtjes ¨ d y c J.W. Gary , G. Gaycken , C. Geich-Gimbel , G. Giacomelli b, P. Giacomelli h , D. Glenzinski i , J. Goldberg u , C. Grandi b, K. Graham z , E. Gross x , J. Grunhaus v, c M. Gruwe´ y, P.O. Gunther , 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, y K.R. Hossain ab, R. Howard aa , P. Huntemeyer , P. Igo-Kemenes k , K. Ishii w, ¨ t q r F.R. Jacob , A. Jawahery , H. Jeremie , 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. PII: S 0 3 7 0 - 2 6 9 3 Ž 0 0 . 0 0 9 7 1 - 0

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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 , h,10 S. Orito w, G. Pasztor , 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 , j,5 S. Soldner-Rembold , S. Spagnolo t , M. Sproston t , A. Stahl c , K. Stephens p, ¨ ae K. Stoll j, D. Strom s , R. Strohmer , 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, UK 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, UK 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, Canada h 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, USA j 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 b

f

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n

w

Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germany o UniÕersity College London, London WC1E 6BT, UK p Department of Physics, Schuster Laboratory, The UniÕersity, Manchester M13 9PL, UK q 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, UK u Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel v Department of Physics and Astronomy, Tel AÕiÕ UniÕersity, Tel AÕiÕ 69978, Israel 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, Israel y UniÕersitat ¨ Hamburgr DESY, 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, Canada aa UniÕersity of British Columbia, Department of Physics, VancouÕer, BC V6T 1Z1, Canada ab UniÕersity of Alberta, Department of Physics, Edmonton, AB T6G 2J1, Canada ac 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, Hungary ae Ludwigs-Maximilians-UniÕersitat Sektion Physik, Am Coulombwall 1, D-85748 Garching, Germany ¨ Munchen, ¨ af Max-Planck-Institute fur Ring 6, 80805 Munchen, Germany ¨ Physik, Fohring ¨ ¨ Received 24 July 2000; accepted 11 August 2000 K. Winter

Abstract

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Using data recorded at centre-of-mass energies around 183 and 189 GeV with the OPAL detector at LEP, the Ž fundamental coupling of the charm quark to the W boson has been studied. The ratio R W c X.rG ŽW hadrons. c 'G W has been measured from jet properties, lifetime information, and leptons produced in charm decays. A value compatible with Ž . Ž . the Standard Model expectation of 0.5 is obtained: R W c s 0.481 " 0.042 stat. " 0.032 syst. . By combining this result with measurements of the W boson total width and hadronic branching ratio, the magnitude of the CKM matrix element < Vcs < is determined to be < Vcs < s 0.969 " 0.058. q 2000 Elsevier Science B.V. All rights reserved.

E-mail address: [email protected] ŽOPAL Collaboration.. 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. 1

G. Abbiendi et al.r Physics Letters B 490 (2000) 71–86

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1. Introduction Since 1997 the LEP eqey collider has been operated at energies above the threshold for W-pair production. This offers a unique opportunity to study the hadronic decays of W bosons in a clean environment and to investigate the coupling strength of W bosons to different quark flavours. The fraction of W bosons decaying hadronically to different quark flavours is proportional to the sum of the squared magnitudes of the corresponding elements of the Cabibbo–Kobayashi–Maskawa ŽCKM. matrix w1x. A measurement of the production rates of different flavours therefore gives access to the individual CKM matrix elements. In eqey WqWy events, the only heavy quark commonly produced is the charm quark. The production of bottom quarks is in fact highly suppressed due to the small magnitude of < Vub < and < Vcb < and the large mass of the top quark, the weak partner of the bottom quark. This allows for a direct measurement of the production fraction of charm in W decays without a separation of charm and bottom quarks. The magnitude of the CKM matrix element Vcs can then be derived from the charm production rate, using the knowledge of the other CKM matrix elements. So far direct measurements of < Vcs < have limited precision compared to the other CKM matrix elements important in W decays, i.e. < Vud <, < Vus <, and < Vcd <. The most recent evaluation of the magnitude of Vcs from exclusive charm semi-electronic decays yields < Vcs < s 1.04 " 0.16 w2x. In the analysis presented here, a value of the partial decay width R cW ' G ŽW c X.rG ŽW hadrons. is extracted from the properties of final state particles in W decays. Charm hadron identification is based upon jet properties, lifetime information, and semileptonic decay products in WqWy qqqq and Wq Wy qq l n l events. The measured value of R cW is then used to determine < Vcs <.

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2. Data and Monte Carlo samples The data used for this analysis were recorded at LEP by the OPAL detector w3x at centre-of-mass energies around 183 GeV in 1997 and 189 GeV in

1998. OPAL14 is a multipurpose high energy physics detector incorporating excellent charged and neutral particle detection and measurement capabilities. The integrated luminosities used for the analysis amount to 56.5 pby1 Ž180.2 pby1 . at luminosity-weighted mean centre-of-mass energies of 182.7 GeV Ž188.6 GeV.. In addition, 2.1 pby1 Ž3.1 pby1 . of calibration data were collected at 's ; MZ in 1997 Ž1998. and have been used for fine tuning of the Monte Carlo simulation. To determine the selection criteria and tagging efficiencies, Monte Carlo samples were generated using the KORALW 1.42 w4x program, which utilizes JETSET 7.4 w5x for fragmentation, followed by a full simulation of the OPAL detector w6x. The centre-ofmass energies were set to 's s 183 and 189 GeV with a W mass of M W s 80.33 GeV. Additional samples with different centre-of-mass energies and W masses were used to estimate the sensitivity to these parameters. Further samples generated with PYTHIA w7x, HERWIG w8x, and EXCALIBUR w9x were used to determine the model dependence of the measurement. The dominant background sources for this analysis are Z 0rg qq events and four-fermion final states which are not from WqWy decays. Background samples were generated using the PYTHIA, HERWIG, EXCALIBUR, and GRC4F w10x generators. More details on the treatment of the backgrounds can be found in Refs. w11,12x.

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3. Event selection The WW event selections are the same as those used for the OPAL WW production cross-section measurements at 's s 183 GeV w11x and 189 GeV w12x. Events not selected as Wq Wy l q n l l Xy n l X candidates are passed to the Wq Wy qq l n l selec-

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

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Table 1 Number of selected WW candidate events and those expected from the main background sources for the selection at 183 and 189 GeV. The ‘qqqq’ background source refers to processes excluding doubly resonant W-pair production at tree level ŽCC03 diagrams.. The entry labeled ‘Wene’ refers to events where a singly produced W decays hadronically. The errors are the systematic errors on the background contributions, as evaluated in Refs. w11,12x 183 GeV

189 GeV

Type

qq l n

qqqq

qq l n

qqqq

selected events

350

432

1235

1532

Z 0 rg qq qqqq qq l q l y Wene

15.4 " 1.6 0.5 " 0.6 10.2 " 1.2 6.2 " 1.7

77.4 " 8.5 12.4 " 2.8 4.1 " 0.3 0"1

45.5 " 5.6 2.5 " 0.6 27.6 " 2.7 23.3 " 4.1

240.0 " 15.9 70.3 " 12.3 8.6 " 1.4 0"1

total background

32.4 " 2.7

93.9 " 9.0

98.9 " 7.5

318.9 " 20.2

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tion procedure and may be classified as qqene , qq mnm , or qqtnt candidates. The Wq Wy qqqq selection is applied to events that fail the preceding selections. It has been checked that the event selection introduces a negligible bias in the flavour composition. In this analysis, the small fraction of selected singly produced W bosons ŽWene . which decay hadronically to a charm quark is considered as signal. Since the identification of charm mesons relies heavily on lifetime and lepton information, the relevant parts of the detector were required to be operational while the data were recorded. Thus, in addition to the requirements which were already applied in Refs. w11,12x, it was required that the silicon microvertex detector and the muon chambers were fully operational. After all cuts, a total of 350 Ž1235. Wq Wy qq l n l candidates and 432 Ž1532. Wq Wy qqqq candidates were selected at 183 GeV Ž189 GeV.. A breakdown of the different background contributions is given in Table 1. The expected number of background events is calculated from the background cross-sections given in Refs. w11,12x; the errors correspond to the systematic errors quoted in these references.

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4. Measurement of R cW After the event selection, the hadronic part Žwhich excludes the identified lepton. of a qq l n event is

forced into two jets using the Durham algorithm w13x, while qqqq events are forced into four jets. Subsequently, a relative likelihood discriminant is calculated for each jet to separate jets originating from charm quarks and jets from u, d, and s quarks. This discriminant relies on jet and event shape properties, lifetime information, and lepton identification as described in the remaining parts of this section. The resulting likelihood distribution is fitted to obtain the relative fractions of uds and charm jets. In qq l n l events the two jets can be uniquely assigned to the decay of one W boson, while for qqqq events the four jets have to be grouped into pairs that are assumed to originate from the decay of one W boson. The jet pairing is chosen using a kinematic fit to find the jet combination which is most compatible with the production of two on-shell W bosons with a mass of 80.33 GeV. After the jet pairing has been performed in qq l n l and qqqq events, the jet energies are calculated in a kinematic fit, imposing energy-momentum conservation and equality of the masses of both W candidates. If the kinematic fit fails, the jet energies of each jet pair are scaled so that their sum equals the beam energy. The choice of the jet pairing influences the result of the present analysis only through the values of the jet angle u jet in the di-jet rest frame and the di-jet angle u W in the laboratory frame, both of which are calculated from the jet momenta determined by the kinematic fit. These two angles are employed in the likelihood functions as described in Sections 4.2 and

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4.3. It has been checked in the W mass measurement analysis w14,15x and in an analysis concerned with properties of hadronically decaying W bosons w16x that jet properties relevant for the jet pairing algorithm and the kinematic fit are well modelled in the Monte Carlo simulation. 4.1. Secondary Õertex tag Weakly decaying charm hadrons have lifetimes between 0.2 and 1 ps w2x, leading to typical decay lengths of a few hundred microns to a few millimetres at LEP2 energies. These relatively long-lived particles produce secondary decay vertices which are significantly displaced from the primary event vertex. The primary vertex in an event is found by fitting all charged tracks to a common point in space w17x. Its determination is improved by using the average beam position as a constraint with RMS values of 150 mm in x, dominated by the width of the beam, about 20 mm in y, and less than 1 cm in z. In the search for charm decay products, tracks in the central detector and clusters in the electromagnetic calorimeter within a given jet are considered. Tracks used to find secondary vertices must fulfill the quality criteria used in the WW cross-section analyses w11,12x. Additionally, the tracks are required to have a momentum larger than 0.75 GeV, a signed distance of closest approach to the primary vertex in the rf plane Ž2D-impact parameter. 0 cm - d 0 - 0.3 cm, and an error on the impact parameter, sd 0 , smaller than 0.1 cm. From the tracks which fulfill these criteria, the tracks which are most likely to originate from the decay products of a charm hadron are identified via an iterative procedure.Particles from charm hadron decays tend to havea large momentum and a large rapidity y s 12 ln Ž Ž E q p I . Ž E y p I . . Žwhere p I is the particle’s momentum component parallel to the jet direction and E is its energy. compared to fragmentation tracks, and their combined invariant mass should be compatible with a charm hadron mass. Therefore for each track and electromagnetic cluster which is not associated to any track, the rapidity y is calculated assuming the charged pion mass for tracks and zero mass for unassociated clusters. The track or cluster

with the lowest rapidity is removed from the sample and the invariant mass of the remaining tracks and clusters is calculated. This procedure is repeated until the mass of the remaining group of tracks and clusters falls below 2.5 GeV. This procedure selects preferentially tracks from the decay of charm hadrons w18x. All selected tracks in the jet are fitted to a common vertex in three dimensions. Tracks which contribute more than 4 to the x 2 of this fit are removed and the fit is repeated. The procedure is stopped when all tracks pass the x 2 requirement. At least two tracks are required to remain in the fit for the secondary vertex finding to be successful. Once tracks are associated to a secondary vertex, the distance L between the primary and the secondary vertex and its error sL are computed. The decay length significance of a secondary vertex, LrsL , is required to be positive Ži.e. LrsL ) 0., where L is given a positive sign if the secondary vertex is displaced from the primary vertex along the direction of the jet momentum. Jets containing a good secondary vertex are then used to tag charm decay products by means of an artificial neural network ŽANN. w19x to enhance the charm purity at a given efficiency. The nine ANN input variables are: the decay length significance LrsL of the secondary vertex; the primary vertex joint probability Žfor a definition, see Ref. w20x.; EvertexrE beam , where Evertex is the sum of the energy of all the tracks assigned to the secondary vertex and E beam is the beam energy; the distance of closest approach to the primary event vertex in rf z Ž3D. of the pseudo-particle formed from all the tracks in the secondary vertex; the normalised weighted average Žweighted by the measured error. of all the track 2D-impact parameters within the secondary vertex; the highest momentum of the charged particles in the secondary vertex; the invariant mass of the vertex; the largest track 3D-impact parameter in the secondary vertex; and the second largest track 3D-impact parameter in the secondary vertex. The same vertex ANN is used for Wq Wy qqqq and Wq Wy qq l n l events. The distributions of the two most discriminating input variables for the vertex ANN are shown in Fig. 1. Typically, charm hadrons have secondary vertices which are displaced from the primary vertex and charged tracks associ-

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Fig. 1. Distributions of the most sensitive input variables of the vertex ANN at 's s 183–189 GeV: Ža. decay length significance LrsL and Žb. primary vertex joint probability. Points with error bars represent the data Ž183 and 189 GeV samples combined.. Histograms represent the Monte Carlo expectation.

ated with charm particles have a lower probability to come from the primary vertex. Fig. 2a shows a comparison of the ANN output between data and Monte Carlo for 's s 183–189 GeV. The simulation of the OPAL tracking detectors w6x requires a detailed understanding of the track-finding efficiency and resolution. This is achieved by tuning the Monte Carlo simulation with the calibration data taken at the Z 0 resonance. Fig. 3a shows the distribution of LrsL for secondary vertices. The effect of a 5%

variation of the tracking resolution used to assess the systematic uncertainty is also depicted. 4.2. Lepton tag About 20% of all charm hadrons decay semileptonically and produce an electron or a muon in the final state. Because of the relatively large mass and hard fragmentation of the charm quark compared to light quarks, this lepton is expected to have a larger

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Fig. 2. Distributions of Ža. the vertex ANN output and Žb. the likelihood output of the lepton tag at 's s 183–189 GeV. Points with error bars represent the data Ž183 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.

momentum than leptons from other sources Žexcept the small contribution from semileptonic bottom decays in background events.. Therefore, identified electrons and muons can be used as tags for charm hadrons in W boson decays. In a first step, the leptons are identified using ANN algorithms. The electron ANN described in

Refs. w21,22x is used. Its most important input variables are the specific ionization in the central jet chamber Žd Erd x . of the electron candidate track and the ratio of the associated energy deposited in the electromagnetic calorimeter to the momentum of this track Ž Erp .. Photon conversions are rejected from the sample using another dedicated ANN

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Fig. 3. Comparison of discriminating variables between calibration data taken at the Z 0 resonance and Monte Carlo prediction. Points with error bars represent data from the Z 0 calibration runs. Histograms show the expectation from the Monte Carlo simulation. Ža. Decay length significance LrsL for data and Monte Carlo. The dotted line shows the effect of the "5% variation of the tracking resolution used to assess the systematic uncertainty on the vertex tag. Žb. Erp and Žc. 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 dotted lines show how the variation of the detection Žmis.identification and resolution for electron candidates affects the Erp and d Erd x distributions.

w21,22x. The muon ANN w23x is based on information from the tracking detectors Žincluding d Erd x ., the hadronic calorimeter, and the muon chambers. The lepton candidates have to be well contained in the detector Ž
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is done using the method described in Ref. w24x. The following input variables are used both for electrons and for muons: the output of the electron or muon ANN; the magnitude of the cosine of the polar angle of the lepton candidate
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tion uses the product of the charge of the lepton tagged in the charm decay and the charge of the lepton from the leptonically decaying W. Finally, for electron candidates, the likelihood discriminant employs the output of the conversion finder ANN to suppress electrons from photon conversions. In Fig. 2b the likelihood output of the lepton tag is shown for data and Monte Carlo at 's s 183–189 GeV. In this analysis precise modelling of the lepton identification is important. The lepton reconstruction efficiencies in the Monte Carlo simulation were tuned to match the values obtained from data collected at the Z 0 resonance. Figs. 3b,c show the Erp and normalised d Erd x distributions of electron candidates. Reasonable agreement between data and Monte Carlo simulation is observed. The variables used for muon identification are also well described in the simulation.

4.3. Combined tag For each jet, the vertex ANN and the lepton likelihood discriminant are merged into a single quantity by an additional likelihood function. This combined likelihood discriminant uses two additional variables: the cosine of the jet angle cos u jet in the rest frame of the W boson with respect to the W momentum direction and the likelihood output of the WW event selection w11,12x. The jet angle in the di-jet rest frame helps to separate jets originating from up-type and down-type quarks. Due to the polarisation of the W bosons and the V y A nature of the weak interaction, up-type quarks tend to be produced preferentially in the backward direction with respect to the W flight direction, while downtype quarks are found more often in the forward direction. The likelihood output of the WW event

Fig. 4. Ža. Output of the combined likelihood used to tag charm hadrons at 183–189 GeV. Points with error bars represent the data Ž183 and 189 GeV samples combined.. Histograms represent the results of the fits described in Section 4.4. Žb. Efficiency and purity computed after the WW selection as a function of a cut on the combined likelihood output.

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Table 2 Tagging efficiencies Žin %. 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 for qq l n and qqqq events. The errors are statistical only Tagging efficiency Ž%.

eW eW eW eW

183 GeV

™u ™d ™s ™c

189 GeV

qq l n

qqqq

qq l n

qqqq

4.3 " 0.5 3.1 " 0.4 3.2 " 0.4 18.1 " 0.6

3.8 " 0.3 3.0 " 0.2 3.0 " 0.2 15.8 " 0.4

4.9 " 0.5 3.2 " 0.4 3.3 " 0.4 18.9 " 0.6

4.4 " 0.3 3.1 " 0.2 3.1 " 0.2 16.7 " 0.4

6.0 " 2.7

4.7 " 1.0

8.0 " 2.1

5.4 " 0.8

e bgd

™

selection suppresses false tags from background events, especially from Z 0rg bb events. In Fig. 4a the combined likelihood output is shown, illustrating the discriminating power between charm and light flavoured jets. The efficiency and purity for a particular cut on the combined likelihood output are also depicted in Fig. 4b. Table 2 lists the tagging efficiencies for jets in WW and background events that result from a cut on the likelihood output at the optimal value of 0.7. The tagging efficiencies at 189 GeV are slightly higher due to the extra boost of the W bosons. These values are not directly used to derive R cW, but are quoted to give an impression of the performance of the charm tag.

with i: Bin index in the combined likelihood distribution; n i : Number of jets in the i th bin; N: Number of bins in the combined likelihood distribution; Pci : Probability for a charm jet to appear in the i th bin ŽW c X pdf.; i Puds : Probability for a uds jet to appear in the i th bin ŽW light flavour pdf.; Fbkg : Fraction of background jets; i P bkg : Probability for a non-WW jet to appear in th the i bin Žnon-WW background pdf.. The result of the fit for R cW is:

4.4. Determination of R cW

R cW s 0.493 " 0.090 at 183 GeV

To extract R cW from the data, a binned maximum likelihood fit is performed to the combined likelihood distributions. Template histograms for the charm, light-flavoured, and non-WW background components are produced from the main Monte Carlo samples. They are referred to as the probability density functions Žpdf. for the various components. Using this fitting method improves the statistical sensitivity of the measurement compared to simply counting the number of jets that pass a cut on the likelihood output. The function used to fit the data Žsee Fig. 4a. is:

and

N

½

yln L s y Ý n i ln Ž 1 y Fbkg . is1 i = Ž 12 R cW Pci q 1 y 12 R cW Puds . i qFbkg P bkg ,

5

Ž 1.

™ ™

R cW s 0.478 " 0.047 at 189 GeV. where the errors are statistical only. The x 2rŽdegree 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 R cW were taken from a Monte Carlo simulation, the analysis depends on the proper modelling of the data distributions in the simulation. The sources of systematic error are listed in Table 3 and are discussed below. Unless otherwise noted, all changes were applied to signal and background Monte Carlo samples.

G. Abbiendi et al.r Physics Letters B 490 (2000) 71–86

82

Table 3 Summary of the experimental systematic errors, statistical errors, and central values from the binned maximum likelihood fit on RW c at 183 GeV and 189 GeV

D RW c

Source of systematic error

183 GeV

189 GeV

hadronisation model centre-of-mass energy mass of the W boson charm fragmentation function background cross-section background composition charm hadron fractions light quark composition vertex reconstruction charm hadron lifetimes charm decay multiplicity lepton identification lepton energy spectrum l. branching ratio BrŽc

0.011 0.007 0.004 0.007 0.006 0.010 0.006 0.007 0.016 0.003 0.010 0.012 0.003 0.006

0.012 0.005 0.003 0.007 0.005 0.009 0.007 0.005 0.017 0.002 0.010 0.014 0.003 0.006

total systematic error

0.032

0.032

statistical error

0.090

0.047

value of RW c

0.493

0.478

™

v

v

v

v

v

v

v

Hadronisation model: The PYTHIA Monte Carlo sample, which uses the Lund string fragmentation as implemented in JETSET w5x, was compared to a sample generated with HERWIG w8x, which uses cluster fragmentation. The samples differ in their parton showering and hadronisation. W mass and centre-of-mass energy: As the jet pairing depends on the W mass, M W , and the centre-of-mass energy, 's , the analysis was repeated with different W masses and at different centre-of-mass energies. The W mass was varied by 100 MeV, which covers both the experimental uncertainty and the differences between the current world average mass w2x and the value used in the Monte Carlo. The centre-of-mass energy was varied by the difference between the luminosityweighted centre-of-mass energies in data and the value of 's used in the main Monte Carlo samples. Charm fragmentation: At 's s MZ , the mean scaled energy of weakly decaying charm hadrons was found to be ² x D Ž MZ .: s 0.484 " 0.008 w25x.

v

No measurements of this quantity exist for W decays, but it is expected to be similar to that in Z decays. The changes in the charm fragmentation due to QCD effects were taken from JETSETw5x. To assess the systematic uncertainty, ² x D Ž M W .: was varied by the experimental uncertainty obtained on ² x D Ž MZ .:, i.e. 0.008. The fragmentation schemes of Peterson w26x, Collins and Spiller w27x, Kartvelishvili w28x and the Lund group w29x were used to assess a possible discrepancy on the shape of the fragmentation function. The largest variation was assigned as the systematic error. Background cross-section: In the fit for extracting R cW, the fraction of background was varied according to the error on the expected fraction of background events from Refs. w11,12x. Background composition: The various background sources have different probabilities to fake a charm jet. The background composition was varied within the uncertainties given in Table 1. Charm hadron fractions: The fractions of the weakly decaying charm hadrons were varied within their experimental errors according to Ref. w25x. Light quark composition: The shape of the reference histogram for light-flavoured quarks depends on the relative fractions of the u, d, and s jets. The quark flavour fractions were varied according to the actual errors on the CKM matrix w2x so that the error covers the effect of assumptions concerning the CKM matrix elements on the uds template histogram. The number of bottom hadrons from W bosons was also doubled to ensure that the measured R cW was insensitive to the bottom fraction in W decays. Vertex reconstruction: The correct modelling of the detector resolution in the Monte Carlo simulation is of paramount importance for the description of the probability to find a secondary vertex. This was checked by comparing the track parameters between calibration data collected at 's ; MZ and Monte Carlo simulation. The sensitivity to the vertex reconstruction was assessed by degrading or improving the tracking resolution in the Monte Carlo. It was found that changing the track parameters resolution by "5% covers the range of the observed differences between data and Monte Carlo Žsee Fig. 3a. in the vertex ANN input and output distributions.

G. Abbiendi et al.r Physics Letters B 490 (2000) 71–86 v

v

v

v

Charm hadron lifetimes: The lifetimes of the weakly decaying charm hadrons were varied within their experimental errors according to Ref. w2x. Charm decay multiplicity: The performance of the secondary vertex finder depends on the multiplicity of the final state of the charm hadrons. The relative abundance of 1, 2, 3, 4, 5, and 6 prong charm decays was changed in the Monte Carlo within their experimental errors w30x. Similarly, the relative abundance of neutral pions was varied in the Monte Carlo within the experimental errors w30x. Lepton identification: The modelling of the input variables of the ANN for electron identification has been intensively studied at LEP1 w22x, while the performance of the muon tagging ANN has been investigated using various control samples of calibration data collected at the Z 0 resonance during each year of LEP2 w23x. The relative error of the efficiency to identify a genuine electron Žmuon. has been estimated to be 4% Ž3%., and the relative error on the probability to wrongly identify a hadron as a lepton has been evaluated to be around 16% Ž10%. for electrons Žmuons. w22,23x. By studying the d Erd x distributions for electron candidates in calibration data taken at the Z 0 mass in 1997 and 1998, it was found that a shift of the mean d Erd x of 0.04 keVrcm Ž0.3%. and a scaling by 1% of the d Erd x resolution in data was needed to correct a slight discrepancy between Monte Carlo and data. This effect was also taken into account in the assignment of the uncertainty on the electron tagging efficiency. The Žmis.identification probabilities for electrons and muons were varied by reweighting the Monte Carlo events and the largest resulting change in R cW was taken as the systematic error. It was verified that the variation of efficiencies and d Erd x resolution was sufficient to describe the possible differences between data and Monte Carlo Žsee Figs. 3b,c.. Lepton energy spectrum from semileptonic charm decays: The energy spectrum of the lepton in the rest frame of the weakly decaying charm hadron was reweighted from the spectrum implemented in JETSET to the ISGW w31x and ACCMM w32x models; the parameters pf and m s of the ACCMM model were varied in the range recommended in Ref. w25x.

v

™

83

Branching ratio Br(c l ): The branching fraction for inclusive charm decays to leptons was varied within the range BrŽc l . s 0.098 " 0.005 w25x by reweighting the Monte Carlo events.

™

The size of the systematic errors is very similar for the samples at 183 and 189 GeV. The dominant systematic errors are those associated with the vertex reconstruction and lepton identification.

5. Results The result of the charm tag analysis is R cW s 0.493 " 0.090 Ž stat. . " 0.032 Ž syst. . at 183 GeV and R cW s 0.478 " 0.047 Ž stat. . " 0.032 Ž syst. . at 189 GeV. The combined value of R cW obtained at 's s 183 and 189 GeV is R cW s 0.481 " 0.042 Ž stat. . " 0.032 Ž syst. . , where the systematic uncertainties are treated as being fully correlated.

6. Extraction of < Vcs < It is possible to extract < Vcs < from R cW using the relation R cW < Vcd < 2 q < Vcs < 2 q < Vcb < 2

s

< Vud < 2 q < Vus < 2 q < Vub < 2 q < Vcd < 2 q < Vcs < 2 q < Vcb < 2

,

Ž 2. which leads to

(

< Vcs < s

RW c 1y RW c

Ž < Vud < 2 q < Vus < 2 q < Vub < 2 . y < Vcd < 2 y < Vcb < 2 .

Ž 3.

G. Abbiendi et al.r Physics Letters B 490 (2000) 71–86

84

Table 4 Values of the CKM matrix elements used in the calculation of < Vcs < from RW w x c . The values are taken from Ref. 2 CKM matrix element

Value

< Vud < < Vus < < Vub
0.9735"0.0008 0.2196"0.0023 0.090"0.025 0.224"0.016 0.0402"0.0019

together with the measurement of R cW presented in this letter, one gets

G ŽW

™ c X. s 698 " 61 Ž stat..

"46 Ž syst. . " 18 Ž ext. . MeV,

™

where the last error is due to the uncertainties on the external parameters GtotW and Br ŽW hadrons.. This corresponds to < Vcd < 2 q < Vcs < 2 q < Vcb < 2 s 0.990 " 0.087 Ž stat. . " 0.065 Ž syst. .

Using the values of the other CKM matrix elements listed in Table 4, one gets < Vcs < s 0.93 " 0.08 Ž stat. . " 0.06 Ž syst. . " 0.004 Ž CKM. , where the last error is due to the uncertainty on the CKM matrix elements used in the calculation. A more precise value for < Vcs < can be obtained based on the Standard Model prediction of the decay width of the W boson to final states containing charm quarks:

G ŽW

™ c X. s

3 CG F M W

6'2 p

2

Ž < Vcd <

2

q < Vcs < q < Vcb <

2

.,

Ž 4. 3 with CG F M W 6'2 ps Ž705 " 4. MeV w2x and the color factor C given by w2x

ž

Cs3 1q

as Ž M W .

y12.77

p

q 1.409

a s3 Ž M W . p

™ G Ž W ™ c X. s R

3

/

a s2 Ž M W .

.

Ž 5.

Using the PDG 0.6848 " 0.0059 and15

15

™ hadrons. G . Ž 6. values Br ŽW ™ hadrons. s G s Ž2.12 " 0.05. GeV w2x W tot

Br Ž W

W tot

The most precise measurements of GtotW are determined from the quantity R s s Žpp WqX .PBr ŽW en . . In Ref. w33x, the s Žpp

™ ™ ™ Z qX.PBr ŽZ ™ e 0

0

Subtracting the off-diagonal CKM matrix elements, using the values listed in Table 4, results in < Vcs < s 0.969 " 0.045 Ž stat. . " 0.034 Ž syst. . " 0.013 Ž ext. . " 0.004 Ž CKM. , where the last error is due to the uncertainties on the CKM matrix elements used in the calculation. The determination of < Vcs < from Eqs. Ž4. and Ž6. only involves the CKM matrix elements for the transition W c X and well measured parameters such as GtotW and Br ŽW hadrons.. It is therefore more precise than the method which relies on Eq. Ž3.. Both results of < Vcs < presented here are compatible with the direct determination from D semi-electronic decays which yields < Vcs < s 1.04 " 0.16 w2x.

™ ™

7. Summary

p2

G ŽW c X. can be evaluated from R cW using the relation W c

" 0.026 Ž ext. . .

q y.

e

coupling of the W boson to light quarks is needed as input; however, direct measurements of the corresponding CKM matrix elements are so precise that it introduces a negligible uncertainty on GtotW.

Using data taken with the OPAL detector at LEP at centre-of-mass energies of 183 and 189 GeV, the ratio R cW s G ŽW c X.rG ŽW hadrons. has been measured using a technique based on jet properties, lifetime information, and leptons from charm decays. The combined result is

™

™

R cW s 0.481 " 0.042 Ž stat. . " 0.032 Ž syst. . , in agreement with the Standard Model expectation of 0.5. This result is consistent with the Standard Model prediction that the W boson couples to up and charm quarks with equal strength and it is in agreement with the recent measurements of DELPHI w34x and ALEPH w35x. Using the results from direct measurements of the other CKM matrix elements, < Vcs < can be calculated from R cW , yielding < Vcs < s 0.93 " 0.10. A more pre-

G. Abbiendi et al.r Physics Letters B 490 (2000) 71–86

™

cise value for < Vcs < can be derived from the measurements of R cW , Br ŽW hadrons., and GtotW : < Vcs < s 0.969 " 0.058.

This can be compared to a more indirect determination of < Vcs < by OPAL from the ratio of the W decay widths to qq and l n l , which yields < Vcs < s 1.014 " 0.029 Žstat.. " 0.014 Žsyst.. w12x under the assumption that the W boson couples with equal strength to quarks and leptons. It should be noted that the ratio Br ŽW qq.rBr ŽW l n l . is not used in the analysis presented here, so that these are independent determinations of < Vcs <.

™

™

Acknowledgements We particularly wish to thank the SL Division for the efficient operation of the LEP accelerator at all energies and for their continuing close cooperation with our experimental group. We thank our colleagues from CEA, DAPNIArSPP, CE-Saclay for their efforts over the years on the time-of-flight and trigger systems which we continue to use. In addition to the support staff at our own institutions we are pleased to acknowledge the Department of Energy, USA, National Science Foundation, USA, Particle Physics and Astronomy Research Council, UK, Natural Sciences and Engineering Research Council, Canada, Israel Science Foundation, administered by the Israel Academy of Science and Humanities, Minerva Gesellschaft, Benoziyo Center for High Energy Physics, Japanese Ministry of Education, Science and Culture Žthe Monbusho. and a grant under the Monbusho International Science Research Program, Japanese Society for the Promotion of Science ŽJSPS., German Israeli Bi-national Science Foundation ŽGIF., Bundesministerium fur ¨ Bildung und Forschung, Germany, National Research Council of Canada, Research Corporation, USA, Hungarian Foundation for Scientific Research, OTKA T029328, T023793 and OTKA F-023259.

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