Z. Phys. C 76, 425–440 (1997) ZEITSCHRIFTFUR PHYSIK Cc© Springer-Verlag 1997

Production of P-wave charm and charm-strange mesonsin hadronic Z 0 decaysThe OPAL Collaboration

K. Ackerstaff8, G. Alexander23, J. Allison16, N. Altekamp5, K.J. Anderson9, S. Anderson12, S. Arcelli2, S. Asai24, D. Axen29,G. Azuelos18,a, A.H. Ball17, E. Barberio8, R.J. Barlow16, R. Bartoldus3, J.R. Batley5, S. Baumann3, J. Bechtluft14, C. Beeston16,T. Behnke8, A.N. Bell1, K.W. Bell20, G. Bella23, S. Bentvelsen8, P. Berlich10, S. Bethke14, O. Biebel14, A. Biguzzi5,S.D. Bird16, V. Blobel27, I.J. Bloodworth1, J.E. Bloomer1, M. Bobinski10, P. Bock11, D. Bonacorsi2, M. Boutemeur34,B.T. Bouwens12, S. Braibant12, L. Brigliadori2, R.M. Brown20, H.J. Burckhart8, C. Burgard8, R. Burgin10, P. Capiluppi2,R.K. Carnegie6, A.A. Carter13, J.R. Carter5, C.Y. Chang17, D.G. Charlton1,b, D. Chrisman4, P.E.L. Clarke15, I. Cohen23,J.E. Conboy15, O.C. Cooke16, M. Cuffiani2, S. Dado22, C. Dallapiccola17, G.M. Dallavalle2, S. De Jong12, L.A. del Pozo4,K. Desch3, M.S. Dixit7, E. do Couto e Silva12, M. Doucet18, E. Duchovni26, G. Duckeck34, I.P. Duerdoth16, D. Eatough16,J.E.G. Edwards16, P.G. Estabrooks6, H.G. Evans9, M. Evans13, F. Fabbri2, M. Fanti2, A.A. Faust30, F. Fiedler27, M. Fierro2,H.M. Fischer3, I. Fleck8, R. Folman26, D.G. Fong17, M. Foucher17, A. Furtjes8, D.I. Futyan16, P. Gagnon7, J.W. Gary4,J. Gascon18, S.M. Gascon-Shotkin17, N.I. Geddes20, C. Geich-Gimbel3, T. Geralis20, G. Giacomelli2, P. Giacomelli4,R. Giacomelli2, V. Gibson5, W.R. Gibson13, D.M. Gingrich30,a, D. Glenzinski9, J. Goldberg22, M.J. Goodrick5, W. Gorn4,C. Grandi2, E. Gross26, J. Grunhaus23, M. Gruwe8, C. Hajdu32, G.G. Hanson12, M. Hansroul8, M. Hapke13, C.K. Hargrove7,P.A. Hart9, C. Hartmann3, M. Hauschild8, C.M. Hawkes5, R. Hawkings27, R.J. Hemingway6, M. Herndon17, G. Herten10,R.D. Heuer8, M.D. Hildreth8, J.C. Hill5, S.J. Hillier1, T. Hilse10, P.R. Hobson25, R.J. Homer1, A.K. Honma28,a, D. Horvath32,c,R. Howard29, D.E. Hutchcroft5, P. Igo-Kemenes11, D.C. Imrie25, M.R. Ingram16, K. Ishii24, A. Jawahery17, P.W. Jeffreys20,H. Jeremie18, M. Jimack1, A. Joly18, C.R. Jones5, G. Jones16, M. Jones6, U. Jost11, P. Jovanovic1, T.R. Junk8, D. Karlen6,V. Kartvelishvili16, K. Kawagoe24, T. Kawamoto24, R.K. Keeler28, R.G. Kellogg17, B.W. Kennedy20, J. Kirk29, A. Klier26,S. Kluth8, T. Kobayashi24, M. Kobel10, D.S. Koetke6, T.P. Kokott3, M. Kolrep10, S. Komamiya24, T. Kress11, P. Krieger6,J. von Krogh11, P. Kyberd13, G.D. Lafferty16, R. Lahmann17, W.P. Lai19, D. Lanske14, J. Lauber15, S.R. Lautenschlager31,J.G. Layter4, D. Lazic22, A.M. Lee31, E. Lefebvre18, D. Lellouch26, J. Letts12, L. Levinson26, S.L. Lloyd13, F.K. Loebinger16,G.D. Long28, M.J. Losty7, J. Ludwig10, A. Macchiolo2, A. Macpherson30, M. Mannelli8, S. Marcellini2, C. Markus3,A.J. Martin13, J.P. Martin18, G. Martinez17, T. Mashimo24, P. Mattig3, W.J. McDonald30, J. McKenna29, E.A. Mckigney15,T.J. McMahon1, R.A. McPherson8, F. Meijers8, S. Menke3, F.S. Merritt9, H. Mes7, J. Meyer27, A. Michelini2, G. Mikenberg26,D.J. Miller15, A. Mincer22,e, R. Mir26, W. Mohr10, A. Montanari2, T. Mori24, M. Morii 24, U. Muller3, K. Nagai26, I. Nakamura24,H.A. Neal8, B. Nellen3, R. Nisius8, S.W. O’Neale1, F.G. Oakham7, F. Odorici2, H.O. Ogren12, N.J. Oldershaw16, M.J. Oreglia9,S. Orito24, J. Palinkas33,d, G. Pasztor32, J.R. Pater16, G.N. Patrick20, J. Patt10, M.J. Pearce1, S. Petzold27, P. Pfeifenschneider14,J.E. Pilcher9, J. Pinfold30, D.E. Plane8, P. Poffenberger28, B. Poli2, A. Posthaus3, H. Przysiezniak30, D.L. Rees1, D. Rigby1,S. Robertson28, S.A. Robins22, N. Rodning30, J.M. Roney28, A. Rooke15, E. Ros8, A.M. Rossi2, M. Rosvick28, P. Routenburg30,Y. Rozen22, K. Runge10, O. Runolfsson8, U. Ruppel14, D.R. Rust12, R. Rylko25, K. Sachs10, T. Saeki24, E.K.G. Sarkisyan23,C. Sbarra29, A.D. Schaile34, O. Schaile34, F. Scharf3, P. Scharff-Hansen8, P. Schenk34, J. Schieck11, P. Schleper11, B. Schmitt8,S. Schmitt11, A. Schoning8, M. Schroder8, H.C. Schultz-Coulon10, M. Schulz8, M. Schumacher3, C. Schwick8, W.G. Scott20,T.G. Shears16, B.C. Shen4, C.H. Shepherd-Themistocleous8, P. Sherwood15, G.P. Siroli2, A. Sittler27, A. Skillman15,A. Skuja17, A.M. Smith8, G.A. Snow17, R. Sobie28, S. Soldner-Rembold10, R.W. Springer30, M. Sproston20, K. Stephens16,J. Steuerer27, B. Stockhausen3, K. Stoll10, D. Strom19, P. Szymanski20, R. Tafirout18, S.D. Talbot1, S. Tanaka24, P. Taras18,S. Tarem22, R. Teuscher8, M. Thiergen10, M.A. Thomson8, E. von Torne3, S. Towers6, I. Trigger18, E. Tsur23, A.S. Turcot9,M.F. Turner-Watson8, P. Utzat11, R. Van Kooten12, M. Verzocchi10, P. Vikas18, E.H. Vokurka16, H. Voss3, F. Wackerle10,A. Wagner27, C.P. Ward5, D.R. Ward5, P.M. Watkins1, A.T. Watson1, N.K. Watson1, P.S. Wells8, N. Wermes3, J.S. White28,B. Wilkens10, G.W. Wilson27, J.A. Wilson1, G. Wolf26, T.R. Wyatt16, S. Yamashita24, G. Yekutieli26, V. Zacek18, D. Zer-Zion8

1School of Physics and Space Research, University of Birmingham, Birmingham B15 2TT, UK2Dipartimento di Fisica dell’ Universita di Bologna and INFN, I-40126 Bologna, Italy3Physikalisches Institut, Universitat Bonn, D-53115 Bonn, Germany4Department of Physics, University of California, Riverside CA 92521, USA5Cavendish Laboratory, Cambridge CB3 0HE, UK6 Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada7Centre for Research in Particle Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada8CERN, European Organisation for Particle Physics, CH-1211 Geneva 23, Switzerland9Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago IL 60637, USA10Fakultat fur Physik, Albert Ludwigs Universitat, D-79104 Freiburg, Germany

426

11Physikalisches Institut, Universitat Heidelberg, D-69120 Heidelberg, Germany12Indiana University, Department of Physics, Swain Hall West 117, Bloomington IN 47405, USA13Queen Mary and Westfield College, University of London, London E1 4NS, UK14Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germany15University College London, London WC1E 6BT, UK16Department of Physics, Schuster Laboratory, The University, Manchester M13 9PL, UK17Department of Physics, University of Maryland, College Park, MD 20742, USA18Laboratoire de Physique Nucleaire, Universite de Montreal, Montreal, Quebec H3C 3J7, Canada19University of Oregon, Department of Physics, Eugene OR 97403, USA20Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK22Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel23Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel24International Centre for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo 113, and Kobe University, Kobe 657, Japan25Brunel University, Uxbridge, Middlesex UB8 3PH, UK26Particle Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel27Universitat Hamburg/DESY, II Institut fur Experimental Physik, Notkestrasse 85, D-22607 Hamburg, Germany28University of Victoria, Department of Physics, P O Box 3055, Victoria BC V8W 3P6, Canada29University of British Columbia, Department of Physics, Vancouver BC V6T 1Z1, Canada30University of Alberta, Department of Physics, Edmonton AB T6G 2J1, Canada31Duke University, Dept of Physics, Durham, NC 27708-0305, USA32Research Institute for Particle and Nuclear Physics, H-1525 Budapest, P O Box 49, Hungary33Institute of Nuclear Research, H-4001 Debrecen, P O Box 51, Hungary34Ludwigs-Maximilians-Universitat Munchen, Sektion Physik, Am Coulombwall 1, D-85748 Garching, Germany

Received: 4 April 1997

426

Abstract. Results are presented on the production of ex-cited charm and excited charm-strange mesons in hadronicZ0 decays. The results are obtained from approximately 4.3million hadronic Z0 decays, collected on or near the Z0 res-onance using the OPAL detector at LEP. The D0

1(2420) andD∗0

2 (2460) mesons are reconstructed in the D∗+π− final stateand their separate production rates in charm fragmentationand in weak decays of b-hadrons are determined. Assumingthat the decay widths of these mesons are saturated by theallowed D∗π and Dπ final states, the charm hadronizationfractions and the inclusive branching ratios of b-hadrons tothese neutral P-wave charm mesons are determined to be

f (c → D01) = 0.021± 0.007(stat)± 0.003(syst),

f (c → D∗02 ) = 0.052± 0.022(stat)± 0.013(syst),

f (b → D01) = 0.050± 0.014(stat)± 0.006(syst),

f (b → D∗02 ) = 0.047± 0.024(stat)± 0.013(syst).

We also present the first observation at LEP of the D+s1(2536)

meson which is reconstructed in both the D∗+K0S and D∗0K+

final states. After correcting for the expected contributionfrom bb events, assuming that the D∗K channels saturatethe available final states, these results are used to derive thecharm hadronization fractionf (c → D+

s1):

f (c → D +s1) = 0.016± 0.004(stat)± 0.003(syst).

a and at TRIUMF, Vancouver, Canada V6T 2A3b and Royal Society University Research Fellowc and Institute of Nuclear Research, Debrecen, Hungaryd and Department of Experimental Physics, Lajos Kossuth University, De-brecen, Hungarye and Depart of Physics, New York University, NY 1003, USA

1 Introduction

In a cq meson system withL = 0, whereL is the orbital an-gular momentum, for each light anti-quark flavour,q, thereare two possible meson spin states: spin-0 and spin-1. Thesecorrespond, respectively, to the pseudoscalar and vector cqground-state mesons. ForL = 1, four cq meson states arepredicted; a triplet of states and a singlet state coming, re-spectively, from the vector addition of one unit of orbitalangular momentum to the spin-1 or spin-0 cq system. Heavyquark spin symmetry [1] suggests that the properties of theseP-wave (L = 1) mesons are determined mainly by the totalangular momentum of the light quark,jq = L+ sq, wheresqrepresents the spin of the light quark. Thus, in the heavy-quark limit, the four states are grouped into two doubletsaccording to whetherjq = 3

2 or 12.

Based on the measured masses of the states which havebeen experimentally observed, and on theoretical predictionsfor the masses of unobserved states, it is commonly assumedthat the decays of theL = 1 excited charm and charm-strangemesons are dominated by two-body decays to D(∗)π andD(∗)K, respectively. In this case, conservation of spin-paritydictates both the allowed decay channels for the individualstates and the allowed partial waves [1,2]. The members ofthe jq = 1

2 doublet decay through S-waves and are thereforeexpected to have widths of order 100− 200 MeV/c2. Thestates in thejq = 3

2 doublet, the D01(2420) and the D∗02 (2460),

can decay only through D-waves. They are therefore rathernarrow, with widths of order 20 MeV/c2.

The six narrow states (jq = 32), corresponding to the

three species of light anti-quark, have all been observed ex-perimentally by the ARGUS [3–6] and CLEO [7–9] col-laborations. Some of these states have also been observedat fixed target experiments [10, 11], in bubble chamber ex-periments [12] and at LEP [13, 14]. The properties of thesestates [15] are summarized in Table 1. OPAL [16] and otherLEP experiments [17, 18] have also provided evidence forP-wave B and Bs meson production in hadronic Z0 decays.

427

Table 1.Summary of the measured properties of the six narrowL = 1 charmmesons [15]. The last column shows the two-body final states allowed byspin-parity and isospin conservation

L = 1 State Mass (MeV/c2) Width Γ (MeV/c2) Final StatesD0

1 2422.2± 1.8 18.9 +−

4.63.5 D∗π

D∗02 2458.9± 2.0 23± 5 D∗π, Dπ

D +1 2427± 5 28± 8 D∗π

D∗+2 2459± 4 25+

−87 D∗π, Dπ

D+s1 2535.35± 0.34 < 2.3 (90% CL) D∗K

D∗+s2 2573.5± 1.7 15+

−54 D∗K, DK

In Z0 decays, D∗∗0 mesons1 are produced both in charmfragmentation and as the decay products of b-flavouredhadrons. As these processes are physically distinct, it isdesirable to determine these two contributions to the totalD∗∗0 production rate separately. Measurements of the pro-duction of these states in Z0 → cc events provides usefulinformation about heavy-quark fragmentation since they areproduced earlier in the fragmentation and decay chain thanare the lighter D∗ and D mesons. Also, the observation ofboth members of ajq = 3

2 doublet allows spin-counting as-sumptions about particle production to be tested. Similarly,measurement ofL = 1 charm-strange meson production ratesrelative to their non-strange counterparts provides a test ofassumptions about strange-quark suppression effects in thefragmentation process.

This paper describes measurements made with the OPALdetector at LEP. Section 2 provides a brief discussion of thedetector as well as the data and Monte Carlo samples used.Section 3 describes measurements of the production rates forthe D0

1(2420) and D∗02 (2460) mesons in charm and bottom-

enriched samples of hadronic Z0 decays. These states arereconstructed through their decay2 D∗∗0 → D∗+(2010)π−.Section 4 presents a measurement of the D+

s1 production ratein Z0 → cc events. This state is observed in both the D∗0K+

and the D∗+K0S final states. This measurement represents the

first observation of this state at LEP.

2 The OPAL detector and data sample

A complete description of the OPAL detector can be foundelsewhere [19]. However, aspects of the detector which areparticularly pertinent to this analysis are briefly describedhere. The tracking of charged particles is performed by alarge central jet chamber, a precision vertex drift chamberand chambers which measure thez-coordinate of tracks asthey leave the jet chamber3. These detectors are located in-side a uniform solenoidal field of 0.435 T. The jet cham-ber also provides measurements of the ionization energyloss (dE/dx) of charged particles. This information is usedfor charged-particle identification. In 1991, a high-precisionsilicon microvertex detector [20], providing two layers ofsilicon strip readout in theφ plane, was installed arounda beryllium-composite beam pipe. This was upgraded in

1 In this paper, the symbol D∗∗0 represents an arbitrary mixture of thetwo states, D01(2420) and D∗0

2 (2460)2 Charge conjugation is implied throughout this paper3 The right-handed coordinate system used by OPAL has thez-axis along

the electron beam and they-axis pointing up. The polar angleθ and theazimuthal angleφ are defined with respect to thez- andx-axes, respectively

1993 [21] with a new silicon detector which provides bothφ and z information. For Z0 → µ+µ− events, the detectorachieves impact parameter resolutions of 15µm in r−φ andfrom 20− 50µm in z, depending on the polar angleθ.

The solenoid coil is surrounded by an assembly of time-of-flight scintillators and an electromagnetic calorimeter con-sisting of lead-glass blocks instrumented with a presampler.These are located inside the iron return yoke of the mag-net which is instrumented to serve as a hadronic calorimeterand is itself surrounded by several layers of muon cham-bers. A similar configuration of subdetectors is present inthe end-cap regions of the detector.

This analysis makes use of approximately 4.3 millionhadronic Z0 decays recorded by OPAL in the region ofthe Z0 resonance, between 1990 and 1995. The selection ofhadronic Z0 decays used in this analysis has been describedelsewhere [22]. For simulation studies, approximately 6 mil-lion five-flavour hadronic Monte Carlo events were gener-ated, 2 million using JETSET 7.3 [23] and 4 million withJETSET 7.4 [24]. All Monte Carlo samples described in thispaper were passed through a full simulation of the OPAL de-tector [25] and processed using the same reconstruction andselection algorithms used to process the raw data recordedwith the detector. The D0 and B meson lifetimes used wereτ (D0) = 0.415 ps andτ (B) = 1.60 ps, consistent with cur-rent world averages [15]. The fragmentation of heavy quarkswas simulated using Peterson fragmentation parameters [26]tuned to reproduce measured values for the mean scaledenergies of heavy mesons,〈xE(B)〉 = 0.695± 0.010 [27],〈xE(D+)〉 = 0.483+

−0.0070.011 and〈xE(D0)〉 = 0.487+

−0.0170.018 [28].

While JETSET can generate the full multiplet of heavyP-wave states, the wideJP = 1+ and 0+ resonances wereomitted. Since theoretical predictions for their natural widthsare of order 100-200 MeV/c2, these states are not expectedto produce observable resonant structure in this analysis. Theresonance parameters of the narrow P-wave charm mesonswere set to values consistent with those compiled in 1996by the Particle Data Group [15]. The ratio of the branchingratios for D∗+

s2 (2573) decays to D∗K and DK final states wasset to 1/9, consistent with the CLEO limit [9]

Br(D∗+s2 (2573)→ D∗K)

Br(D∗+s2 (2573)→ DK)

< 0.33 at 90% C.L. (1)

and with theoretical predictions of 0.1 to 0.14 [29].Two additional samples of Z0 → cc events contain-

ing D+s1 mesons were generated using JETSET 7.4. Ap-

proximately 8000 and 4000 events were generated with D+s1

mesons decaying to the D∗0K+ and D∗+K0S final states, re-

spectively. These samples were used to study the mass reso-lution and efficiency for D+s1 reconstruction in each of thesefinal states.

3 D01 and D∗0

2 production

In this analysis, the D01 and D∗02 states were reconstructed in

the decay sequence

D∗∗0 - D∗(2010)+π−

�- D0π+

�- K−π+ (2)

428

since the D∗+ can be cleanly reconstructed through the decaychain D∗+ → D0π+. The criteria for the selection of high-quality charged tracks and the D∗+ reconstruction methodwere identical to those used previously by OPAL [30].Only D∗+ candidates having a scaled energy,xE(D∗+) ≡ED∗+/Ebeam, greater than 0.2 were accepted. Here,ED∗+ andEbeam are the D∗+ and beam energies, respectively. The in-variant mass of each K−π+ combination was required tobe within the range 1.79 < M (K−π+) < 1.94 GeV/c2

and the mass-difference between the reconstructed D0π+

combination and the D0 was required to be in the range142< ∆M (D0π+) < 149 MeV/c2. The remaining D∗+ se-lection criteria differed slightly for the accepted regions ofxE(D∗+) above and below 0.5, since the combinatorial back-ground is largest at low energies. The pseudoscalar nature ofthe D0 was used to reduce random K−π+ combinations byrequiring that| cosθ∗| < 0.8 (0.9) whenxE(D∗+) < (>)0.5.Here,θ∗ is the angle between the K− and the D0 boost di-rection, calculated in the D0 rest frame. The K− purity wasenhanced by exploiting the particle identification capabili-ties of the OPAL jet chamber. Tracks were assigned dE/dxweights,wx, according to the assumed particle species,x,the measured energy loss per unit length, and the corre-sponding uncertainty. These weights were signed accord-ing to whether the measured energy loss was greater orless than that expected for the assumed particle type. Inthe selection of D∗+ candidates, the symmetric requirement|wK(K−)| > 0.1 was imposed on kaon track candidatesfor D∗+ mesons withxE < 0.5. No cut was applied forxE > 0.5.

Finally, D∗∗0 candidates were formed by selecting D∗+π−combinations, where the momentum of the pion candidatewas required to exceed 2 GeV/c. This momentum cut wasmade in order to suppress pion candidates produced in quarkfragmentation. These have a much softer momentum spec-trum than the pions from D∗∗0 decays.

The contributions to the inclusive D∗∗0 rate were sepa-rated into the bb and cc components by using lifetime andenergy information. In Z0 → cc events, D∗∗0 mesons areproduced near the beginning of the fragmentation chain andthus have a significantly harderxE spectrum than those pro-duced in the decays of b-flavoured hadrons. Furthermore, be-cause of the longer b-hadron lifetime, D0 mesons producedin b-hadron decays will decay, on average, further from theprimary vertex than those produced in charm fragmentation.These differences were exploited to obtain D∗∗0 sampleswhich were enriched in each flavour. Each flavour-enrichedsample, however, contained some residual contribution fromthe other. In order to properly account for this impurity, therates in charm and bottom events were determined simulta-neously.

In order to measure the individual production rates forthe D0

1 and D∗02 , the D∗∗0 signal must also be separated into

contributions from these two states. This could be achievedsimply by parameterizing the signal as the sum of two Breit-Wigners convoluted with the experimental mass resolution,with the mass and width of the D0

1 and D∗02 components

fixed to their nominal values [15]. In this analysis, however,additional information from the angular distribution of theD∗∗0 decay products is also used. The narrowJP = 1+ and2+ L = 1 states have distinct distributions of cosα, whereα

is defined as the angle between theπ− from the D∗∗0 decayand theπ+ from the D∗+ decay, in the rest frame of the D∗+.In the heavy-quark limit discussed earlier, these are of theform 1 + 3 cos2α for the D0

1 and sin2α for the D∗02 states,

regardless of any spin alignment of the initial state [2].Although the D0

1 meson could be a mixture ofjq = 32

(narrow) andjq = 12 (broad) states, it has been experimen-

tally observed to decay with a cosα distribution consistentwith the form expected for an unmixed state [4,8,11]. There-fore, the angular distributions quoted above were includedin a maximum likelihood fit in order to provide additionalseparation power between the two signal components andbetween signal and background, which is expected to havea cosα distribution which is approximately isotropic.

The selection of the flavour-enriched samples is de-scribed below in Sects. 3.1 and 3.2. Section 3.3 describesthe fit procedure used to simultaneously extract the D∗∗0

rates in charm and bottom events. The treatment of system-atic errors is described in Sect. 3.4. The final results arepresented in Sect. 3.5 and are discussed further in Sect. 3.6.

3.1 The c-enriched sample

The sample enriched in Z0 → cc → D∗∗0X was obtainedby requiringxE(D∗∗0) > 0.5. Additional suppression of bbevents was achieved by requiringcτ (D0) < 0.03 cm wherecτ = MD0`xy/pxy is the apparent proper time of the D0

decay, computed usingMD0, the D0 mass [15], its decaylength `xy, and its momentumpxy, measured in the planetransverse to the beam axis.

The reconstruction efficiency and purity of the selectionwere studied using Monte Carlo. After all selection criteriawere applied, the efficiency was (18.7 ± 0.8)% for D∗∗0

mesons produced in charm fragmentation withxE > 0.5.Accounting for the region of scaled energy below the cut,this corresponds to a selection efficiency, for all D∗∗0 →D∗+π− decays in charm events, of about 12%. Less than2% of all such decays produced in b-events are acceptedby these selection criteria. The charm-purity of the selectedsample was 67%, with 20% of the D∗+π− candidates comingfrom bb events and the remainder from light-quark events.

Figure 1a shows the mass-difference distribution ob-tained using this selection. A clear enhancement is visiblein the mass region of the excited charm states. The massresolution is about 7 MeV/c2, so this enhancement is ratherbroad relative to the width of a single D∗∗0 state. This isdue to overlapping contributions from the two narrow states.Figure 1b shows the effect of requiring that the helicity an-gle in the decay satisfies| cosα| > 0.7. As expected, basedon the angular distributions discussed above, this suppressesboth the background and the D∗0

2 signal relative to the D01component.

The fit procedure and results, as well as the determinationof the rate, corrected for the background from bb events, isdescribed in Sect. 3.3. This requires not only knowledge ofthe D∗∗0 production rate in bottom events but also of thefraction of these in the D01 state, since there is no reasonto expect this fraction to be the same in charm and bottomevents.

429

0

10

20

30

40

50

60

70

80

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

(a)

M(D*+π-)-M(D*+) (GeV/c2)

Ent

ries

/ 10

MeV

/c2

OPAL

0

5

10

15

20

25

30

35

40

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1M(D*+π-)-M(D*+) (GeV/c2)

Ent

ries

/ 10

MeV

/c2

|cos α| > 0.7

(b) OPAL

Fig. 1. M (D∗+π−)−M (D∗+) distribution for the charm-enriched samplewith a no restriction on the helicity angle andb for | cosα| > 0.7 In eachcase, theshaded distributionshows the expected contribution from bottom-flavoured events, determined from the simultaneous fit. Overlaid as asolidline is the fit result. The fit result shown inb is not the result of a separatefit but is obtained by integrating the likelihood function from the fit to thefull distribution over the region| cosα| > 0.7. In each case, thedashedline indicates the background component of the fit result

3.2 The b-enriched sample

A sample of D∗∗0 → D∗+π− decays produced mainly fromdecays of b-hadrons was obtained by reconstructing b-decayvertices in events containing D∗+ candidates. Once a D∗+

candidate was found, the b-vertex reconstruction algorithmassigned tracks to the primary Z0 decay vertex, the candi-date b-decay vertex, or to a subset of tracks unassociatedwith either vertex. Track assignment hypotheses were testedby fitting the primary vertex and the B→ D∗+X vertextopology. This procedure includes a fit of the two-track D0

vertex. The decay length of the D0 candidate with respectto the b-decay vertex was included as a free parameter butits flight vector was constrained by momentum conservationto point back to the b-vertex. Since the algorithm for the b-enrichment depends strongly on vertexing, this analysis wasperformed using only data taken while the silicon microver-tex chamber was operational. This is true for approximately86% of the OPAL hadronic data sample.

The algorithm first grouped tracks in the event into jetsusing a cone-based algorithm [31]. This jet-finding schemedefines the 4-momentum of a jet as the sum of the 4-momenta of the constituent tracks. Tracks within a cone ofhalf-angleR = 0.7 radians were assigned to a single jet ifthe resulting jet energy,ε, exceeded 10 GeV.

An initial primary vertex for the event was determinedusing an iterativeχ2 minimization method which includedthe average LEP beamspot position, measured by OPAL [32],as a constraint. This initial primary-vertex estimate used allhigh-quality tracks except those forming the D∗+ candidate.Based on their contribution to theχ2 of the fit, tracks incon-

0

20

40

60

80

100

120

-10 -5 0 5 10 15 20 25

Monte Carlo

Data

Non b background

S/σS

b-ve

rtex

can

dida

tes

/ 106 e

vent

s

OPAL

Fig. 2. Decay length significance distribution for the b hadron from theb → D∗+X decay. Theopen histogramshows the distribution obtainedfrom Monte Carlo. Thepoints with error barsare from analysis of theOPAL data. Thehatched histogramshows the expected contributions fromcharm and light-flavour events, from Monte Carlo. Thearrow indicates thecut of S/σS > 2 used in the selection

sistent with the vertex position were removed. This proce-dure was repeated until all remaining tracks were consistentwith the vertex position. An initial b-vertex was formed us-ing a similar algorithm applied to those tracks in the D∗+

jet which were not consistent with the primary vertex posi-tion. Tracks inconsistent with this b-vertex candidate wereiteratively removed. This vertex fit was performed in two orthree dimensions, depending on whether tracks hadz-hits inthe silicon detector.

The track assignments to the primary vertex and the b-vertex candidate were then optimized by fitting all verticesin which one track was moved from the primary vertex to theb-vertex, orvice versa. The track reassignment which gavethe largest reduction inχ2

total = χ2prim + χ2

sec was retainedand the procedure was iterated until no further reassignmentcould reduceχ2

total. In bb events, typically about two trackswere reassigned by this procedure.

Finally, to improve the efficiency for assigning a D∗∗0

decay pion to the b-vertex, tracks assigned to the primaryvertex were reassigned to the b-vertex if this did not increasetheχ2

total by more than 1.5. Thus, tracks produced with lowtransverse momentum with respect to the jet axis could beassigned to the b-vertex, even if they were also consistentwith production at the primary vertex.

Displaced vertices were selected by requiringS/σS > 2andL/σL > −2, where,S andL are the decay lengths ofthe b-vertex with respect to the primary and the D0 vertexwith respect to the b-vertex, respectively. The quantitiesσSandσL are the corresponding uncertainties. TheS/σS andL/σL distributions for data and Monte Carlo are shown inFigs. 2 and 3 and indicate that the modelling of the vertexreconstruction in the Monte Carlo is adequate. These distri-

430

0

50

100

150

200

250

300

350

400

-10 -5 0 5 10 15 20 25

Monte Carlo

Data

Non b background

L/σL

b-ve

rtex

can

dida

tes

/ 106 e

vent

s

OPAL

Fig. 3. Decay length significance distribution for the D0 from the b→D∗+X,D∗+ → D0π+ decay sequence. Theopen histogramshows the dis-tribution obtained from Monte Carlo. Thepoints with error barsare fromanalysis of the OPAL data. Thehatched histogramshows the expected pop-ulation from charm and light flavour events and thearrow indicates the cutof L/σL > −2 used in the selection

butions are similar for the two and three-dimensional ver-tex reconstructions. Further comparisons of the agreementbetween data and Monte Carlo were made by examiningthe reconstructed b-vertex multiplicities and the relative fre-quency with which tracks identified as leptons were assignedto b-vertices. These comparisons provided qualitative checksthat the b-decay multiplicity is modelled properly and thatleptons from semileptonic b-decays are indeed preferentiallyassigned to the appropriate b-vertices. The agreement in bothcases provided additional support for the adequacy of theMonte Carlo simulation. However, due to the different mo-mentum spectra of leptons from semileptonic b-decays andπ− mesons from D∗∗0 → D∗+π− decays, it was not possi-ble to use this as an independent, quantitative determinationof the D∗∗0 reconstruction efficiency.

The D∗∗0 candidates were reconstructed by combiningthe D∗+ candidate with pion candidates selected from thetracks assigned to the corresponding b-vertex. Backgroundsresulting from false secondary vertices reconstructed incharm or light-flavour events are small since these verticesare typically of lower multiplicity than those reconstructedin bb events.

The efficiency for reconstructing D∗∗0 → D∗+π− decaysin bb events was (6.3± 0.8)% for xE > 0.2. In the MonteCarlo, about 15% of D∗∗0 mesons produced in bb decayshavexE < 0.2. The efficiency for reconstructing a D∗∗0 →D∗+π− decay in a bb event, averaged over allxE values,was therefore about 5.5%. The corresponding efficiency forselecting a D∗∗0 from a cc event, with this selection, wasabout 0.7%. These efficiencies were obtained from MonteCarlo.

0

10

20

30

40

50

60

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

OPAL(a)

M(D*+π-)-M(D*+) (GeV/c2)

Ent

ries

/ 10

MeV

/c2

0

5

10

15

20

25

30

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

|cos α| > 0.7

(b) OPAL

M(D*+π-)-M(D*+) (GeV/c2)

Ent

ries

/ 10

MeV

/c2

Fig. 4.M (D∗+π−)−M (D∗+) distribution for the bottom-enriched samplewith a no restriction on the helicity angle andb for | cosα| > 0.7. In eachcase, theshaded histogramshows the expected contribution from charmfragmentation, determined from the simultaneous fit. Overlaid as asolidline is the fit result. The fit result shown inb is not the result of a separatefit but is obtained by integrating the likelihood function from the fit to thefull distribution over the region| cosα| > 0.7. In each case, thedashedline indicates the background component of the fit result

The mass-difference distribution of D∗+π− combinationsin the b-enriched sample is shown in Fig. 4a. Figure 4bshows the effect of imposing the requirement| cosα| > 0.7.The effect of this cut is consistent with that expected for theangular distributions described earlier. The fit procedure isdescribed in the next section.

3.3 Fitting procedures

The rates of D∗∗0 production in bb and cc events were deter-mined by simultaneously fitting the distributions shown inFigs. 1a and 4a. The rates were extracted from an unbinnedlikelihood fit in which both mass-difference and helicity an-gle information were used to discriminate between the twoD∗∗0 states and the background.

The likelihood functions used to fit the charm and bottomdistributions were

Lcc =∏i

((f cc

c f cc1 + fbb

c fbb1 )s1(xi, αi)

+(f ccc (1− f cc

1 ) + fbbc (1− fbb

1 ))s2(xi, αi)

+(1− f ccc − fbb

c )bc(xi, αi))

(3)

Lbb =∏i

((fbb

b fbb1 + f cc

b f cc1 )s1(xi, αi)

+(fbbb (1− fbb

1 ) + f ccb (1− f cc

1 ))s2(xi, αi)

+(1− fbbb − f cc

b )bb(xi, αi))

(4)

431

wherexi andαi represent the mass-difference and the he-licity angle for the ith D∗+π− combination, respectively.The functionss1(xi, αi) and s2(xi, αi) represent the mass-difference and helicity-angle distributions of the D0

1 and D∗02 ,

respectively. They are the same in both likelihood func-tions. The functionsbc(xi, αi) and bb(xi, αi) parameterizethe background in the charm and b-enriched distributions,respectively. Each of the signal and background functions isthe product of two functions, describing the mass-differenceand helicity-angle distributions respectively,e.g. s1(xi, αi)= sx1 (xi) · sα1 (αi). The mass-difference distributions for thesignals consist of Breit-Wigner distributions convoluted withthe mass resolution,σxi (typically 7 MeV/c2), on an event-by-event basis. The resonance parameters for the D0

1 andD∗0

2 were fixed to the world average values [15]. The mass-difference distribution for the background was parameterizedby a function of the formbxq (x) ∝ e−Bq(x−mπ)(x −mπ)Cq

wheremπ is theπ± mass andBq andCq are free parameters,defined separately for the two flavours (q = c, b).

The signal and background functions for each mass-difference parameterization were multiplied by functions de-scribing the corresponding helicity-angle distribution:

sα1 (α) = 1 + 3 cos2α D01 state

sα2 (α) = 1− cos2α D∗02 state

bαq (α) = 1 +βq cosα + γq cos2α background(5)

whereβq and γq are parameters which describe the effec-tive helicity structure of the background for each flavour-enriched sample, q.

In (3), the parameterf ccc is the fraction of D∗+π− can-

didates coming from D∗∗0 production in cc events. The pa-rameterf cc

1 specifies the fraction of this signal due to the D01

state. Likewise,fbbb andfbb

1 in (4) are the D∗∗0 signal frac-tion and the fraction of this signal due to the D0

1 state, for bb

events. The parametersfbbc andf cc

b represent the fractions ofthe reconstructed D∗∗0 signals in c and b-enriched samplescoming from D∗∗0 decays in bb and cc events, respectively,where

fbbc = fbb

bNbε

bbc

Ncεbbb

, (6)

and similarly for f ccb . Here,Nb and Nc are the numbers

of D∗+π− combinations accepted in each flavour-enrichedsample andεbb

b and εbbc are the efficiencies for accepting a

D∗∗0 from a bb event in the bottom and charm-enriched se-lections, respectively, corrected for unmeasuredxE regions.Since D∗∗0 production in charm events is observed only forxE > 0.5, it is necessary to perform such a correction toestimate the expected background in the b-enriched sample.Both the efficiencies and the corrections were obtained fromMonte Carlo.

The fit was performed with 12 freely varying parameters:f cc

c , f cc1 , fbb

b and fbb1 , which specified the D∗∗0 production

rates and D01 signal fractions in cc and bb events, andBq, Cq,βq and γq, specified separately for q = c, b, which definedthe shapes and helicity structures of the backgrounds in thetwo flavour-enriched samples.

The results of the fits to the charm and bottom-enrichedmass-difference distributions, shown in Figs. 1a and 4a, yield

D∗∗0 signals of 147± 37 events and 106± 24 events, re-spectively. Figures 1b and 4b show the mass-difference dis-tributions obtained with the requirement that| cosα| > 0.7.The fit results shown in these figures are not independent ofthose shown in Figs. 1a and 4a, but were obtained from thefit to the full distribution by integrating it over this rangeof cosα. The background and the D∗0

2 signal are suppressedwith respect to the D01 signal. This behaviour is expectedfrom the helicity-angle distributions assumed for the D0

1, D∗02

and background components in the fit. The level of the back-ground for | cosα| > 0.7 is also seen to be described wellin both the bb and cc distributions.

The mean multiplicity of D∗∗0 → D∗+π− decays pro-duced in Z0 → cc events, forxE(D∗∗0) > 0.5, is obtainedfrom f cc

c using

nZ0→cc→D∗∗0(xE>0.5) · Br(D∗∗0 → D∗+π−) (7)

=Nccf

ccc

NMHε′cc· 1

Br(D∗+ → D0π+)Br(D0 → K−π+).

Here,NMH is the number of hadronic events analysed andε′cc is the efficiency for reconstructing the D∗∗0 decay, de-termined only for the accepted region of scaled energy,xE > 0.5. A similar expression relates the fractionfbb

b to themean multiplicity of D∗∗0 → D∗+π− decays withxE > 0.2in bb events. The efficiencies are taken from Monte Carlostudies.

Correcting for the efficiencies and branching ratios, whichwere taken to be Br(D∗+ → D0π+) · Br(D0 → K−π+) =(2.616± 0.089)% [15], yields the following measurementsof the mean multiplicity for D∗∗0 production in Z0 → cc andZ0 → bb events:

rcc ≡ nZ0→cc→D∗∗0(xE>0.5) · Br(D∗∗0 → D∗+π−)

=(5.4 +

−1.41.3

)× 10−3 (8)

rbb ≡ nZ0→bb→D∗∗0(xE>0.2) · Br(D∗∗0 → D∗+π−)

=(16.1 +

−3.73.6

)× 10−3. (9)

The fractions of these signals due to the D01 state, in cc and

bb events were

f cc1 = 0.56± 0.15 (10)

and

fbb1 = 0.77 +

−0.160.14. (11)

The quoted errors are statistical only. The correlation coeffi-cient between the measured rates,rbb andrcc, was−0.308.The correlation coefficients betweenrcc andf cc

1 and between

rbb and fbb1 were−0.089 and−0.419, respectively. These

correlations are accounted for in Sect. 5 where these num-bers are used to derive other results. Finally, we note thatthe quoted results are all consistent with the correspondingresults obtained from a fit in which the helicity informationis not used. The inclusion of the helicity information yieldsimproved statistical errors.

3.4 Treatment of systematic errors

Contributions to the systematic uncertainties in the measuredrates have been investigated in detail. The dominant sources

432

are from uncertainties in the reconstruction efficiency, otheraspects of Monte Carlo modelling, and inputs to the fit. Allcontributions are discussed below and summarized in Ta-ble 2.

The contribution to the systematic error coming from un-certainties on the measured D0

1 and D∗02 resonance parame-

ters was estimated by varying them within their one standarddeviation errors. The changes in the measured quantities re-sulting when each resonance parameter was varied individ-ually were added in quadrature. Also, the mass-differenceresolution was scaled by factors ranging between 0.75 to1.25 to estimate the effect of imperfect determination of thetrack-parameter error matrices.

The D∗∗0 production rates in cc and bb events were de-termined for different ranges of scaled energy. Calculatingthe efficiencies with which opposite-flavour decays populatethe flavour-enriched mass-difference distributions requiredextrapolation into unmeasuredxE regions. The D∗∗0 rate incc events was determined only forxE > 0.5, but this ratewas extrapolated to lower values of scaled energy in orderto estimate the fraction of the D∗∗0 signal in the b-enrichedsample that was actually due to charm events. Likewise, thefraction of the D∗∗0 signal in bb events havingxE > 0.5was used to estimate the signal fraction in the c-enrichedsample which was actually due to bottom events. Both ofthese extrapolations were performed using the Monte Carlo.This introduces a dependence on the fragmentation parame-ters used. The central values used for the Peterson fragmen-tation parameters [26] wereεc = 0.031 andεb = 0.0038,tuned to reproduce the mean scaled energy of B and Dhadrons [27, 28]. The uncertainties in these measurements(see Sect. 2) motivated variation of these parameters overthe ranges 0.018< εc < 0.044 and 0.0018< εb < 0.0068.The corresponding variations in the final result were used toestimate the size of the associated systematic effects.

Systematic uncertainties due to the lifetimes of B0 andB+ mesons used in the Monte Carlo were studied by reweight-ing the reconstruction efficiencies with these lifetimes variedby ±5%, a range similar to the precision of current worldaverages [15]. The D0 lifetime has been measured to within1%. Variation of its lifetime within this uncertainty had anegligible effect on the final result. Effects due to imper-fect tracking resolution, which could influence the vertexreconstruction and flavour separation, were estimated withMonte Carlo by redetermining the efficiencies with the res-olutions of the track angles and impact parameters changedby ±10%.

The minimum momentum requirement applied to theπ−from the D∗∗0 decay limits the acceptance to decays in whichtheπ− is emitted preferentially in the forward direction. Inthe case of the charm-enriched sample, the minimum mo-mentum cut corresponds approximately to a requirement ofcosθπ > −0.6. For the b-enriched sample, the acceptanceis approximately limited to cosθπ > −0.3. Here,θπ is thedecay angle of theπ− in the rest frame of the D∗∗0.

The limited cosθπ acceptance introduces two sourcesof systematic uncertainty since spin-alignment effects canproduce a non-uniform distribution in cosθπ. This non-uniformity takes different forms depending on the D∗∗0 spin-alignment, but can be parameterized in terms of even powersof cosθπ, since odd powers are forbidden by parity con-

servation. The Monte Carlo samples were generated withan isotropic distribution, so the efficiencies might requirereweighting to correct for the unmeasured region. To in-vestigate this effect, the cosθπ distribution was obtained bydetermining the D∗∗0 rate in bins of cosθπ. This distributionwas fitted with the function 1 +a cos2 θπ wherea was deter-mined to be 0.0± 1.0 for the charm-enriched and 0.8± 1.1for the bottom-enriched samples. These values are consistentwith zero, providing no evidence for non-isotropic distribu-tions in cosθπ. Nevertheless, variation of these parametersby their fitted uncertainties was used to assign a system-atic error to account for possible non-uniform distributionsarising from D∗∗0 spin-alignment. Due to limited statistics,decay angle distributions with fourth powers of cosθπ werenot considered. Although such contributions are allowed forindividual helicity states of D∗0

2 mesons, a mixture of sev-eral states reduces this effect. Thus, the polynomial form ofcosθπ studied was considered adequate for the purpose ofestimating systematic uncertainties.

The second source of uncertainty introduced by the lim-ited cosθπ acceptance arises due to the fact that a restrictedrange of cosθπ can modify the expected cosα distributionof D0

1 decays, as discussed in [8]. The systematic error asso-ciated with this effect was estimated by calculating the cosαdistribution for a limited cosθπ acceptance, as a function ofthe D0

1 spin-alignment. Because of parity invariance, this canbe specified in terms of a single spin density matrix element,which was varied between 0 and 1.

The systematic uncertainty associated with the assump-tion of a 1 + 3 cos2α form for the D0

1 helicity-angle distribu-tion was estimated by refitting using the function 1+B cos2αwhere the value ofB was varied between 1.81 and 4.14. Thisrange corresponds to the uncertainty on a CLEO [8] mea-surement ofB, derived from a fit to the D01 helicity-angledistribution.

Finally, contributions to the systematic error were as-signed for uncertainties related to limited Monte Carlo statis-tics and imperfect knowledge of the D∗+ → D0π+ andD0 → K−π+ branching ratios.

As a cross-check, the selection criteria most sensitive toMonte Carlo modelling were varied to assess the stability ofthese results. The following modifications were made to theselection:

– The minimum momentum cut imposed on theπ− wasvaried from 1.5 to 2.5 GeV/c.

– The maximum proper time (cτ ) for D0 decays in thecharm sample was varied from 0.01 to 0.05 cm.

– TheS/σS cut was varied between 0 and 4 standard de-viations.

– The L/σL cut was varied between−4 and 0 standarddeviations.

In all cases, the variations in the D∗∗0 production rates andD0

1 signal fractions were consistent with being statistical innature. Since there was no evidence for systematic effectsnot already accounted for, no additional systematic errorswere assigned.

Finally, because the charm and bottom enhanced sam-ples are not mutually exclusive, a study was performed todetermine the fraction of the signals common to both selec-tions. This study indicated that 11±4 D∗∗0 → D∗+π− decays

433

Table 2. Summary of systematic uncertainties for the D∗∗0 production rates and D01 signal frac-tions. The ratesrcc andrbb are defined in (8) and (9) respectively

Source ∆rcc × 10−3 ∆rbb × 10−3 ∆fcc1 ∆fbb

1Resonance parameters + 0.21

−0.21+ 1.0−0.9

+ 0.023−0.022

+ 0.038−0.040

Resolution scale + 0.15−0.23

+ 0.6−0.6

+ 0.021−0.024

+ 0.007−0.000

Fragmentation parameters + 0.15−0.08

+ 0.1−0.0

+ 0.006−0.004

+ 0.000−0.001

B lifetime + 0.03−0.00

+ 0.3−0.3

+ 0.001−0.001

+ 0.000−0.000

Track resolution + 0.04−0.00

+ 0.9−0.6

+ 0.004−0.004

+ 0.001−0.005

cosθπ acceptance (efficiency) + 0.34−0.65

+ 0.6−0.7

+ 0.004−0.006

+ 0.001−0.001

cosθπ acceptance (D01 spin-alignment) + 0.06−0.23

+ 0.3−0.2

+ 0.008−0.014

+ 0.009−0.004

D01 helicity (1+B cos2α) + 0.03

−0.15+ 0.1−0.1

+ 0.000−0.005

+ 0.012−0.010

Monte Carlo statistics + 0.23−0.23

+ 1.0−1.0 — —

Br(D∗+ → D0π+) · Br(D0 → K−π+) + 0.20−0.20

+ 0.6−0.6 — —

Total + 0.55−0.82

+ 2.0−1.8

+ 0.033−0.036

+ 0.039−0.041

were common to the two samples. This is consistent with thenumber expected from the the measured rates and the MonteCarlo efficiencies for decays passing both selections.

3.5 Results

Accounting for the systematic errors discussed in the pre-vious section, the results presented at the end of Sect. 3.3become:

nZ0→cc→D∗∗0(xE>0.5) · Br(D∗∗0 → D∗+π−)

=(5.4 + 1.4

−1.3+ 0.6−0.8

)× 10−3 (12)

nZ0→bb→D∗∗0(xE>0.2) · Br(D∗∗0 → D∗+π−)

=(16.1 + 3.7

−3.6+ 2.0−1.8

)× 10−3 (13)

and

f cc1 = 0.56± 0.15 + 0.03

−0.04 (14)

fbb1 = 0.77 + 0.16

−0.14 ± 0.04. (15)

where the errors are statistical and systematic, respectively.

3.6 Calculation off (c → D∗∗0) andf (b → D∗∗0)

The rates expressed in (12) and (13) were extrapolated to thefull range ofxE using factors determined from the MonteCarlo. The fragmentation parameters used were tuned to re-produce the meanxE values of B+/0 and D+/0 mesons,as described in Sect. 3.4. Assuming quark fragmentation toD∗∗0 and b-hadron states to be independent ofxE , this yields

2 · Γcc

Γhad· f (c → D∗∗0) · Br(D∗∗0 → D∗+π−)

=(8.4 + 2.2

−2.1+ 0.9−1.3

+ 0.4−0.5

)× 10−3 (16)

2 · Γbb

Γhad· f (b → D∗∗0) · Br(D∗∗0 → D∗+π−)

=(18.3 + 4.2

−4.1+ 2.3−2.1

+ 0.4−0.5

)× 10−3. (17)

Here,f (c → D∗∗0) is the fraction of charm quarks produc-ing a D∗∗0 in fragmentation andf (b → D∗∗0) is the inclusivebranching fraction, at the Z0, of b-hadrons into D∗∗0X. The

second systematic error indicates the uncertainty on the ex-trapolation, including a contribution from the use of differ-ent fragmentation models [33]. In each case the fragmenta-tion model parameters used were those obtained from fits toOPAL results on the production of weakly-decaying bottomand charm hadrons in hadronic Z0 decays [27, 28].

The fraction of charm quarks which fragment to form ei-ther a D0

1 or a D∗02 was determined using the values from (14)

and (16). Assuming that the decay widths of these mesonsare saturated by the allowed D∗π and Dπ final states, thevalue of Br(D0

1 → D∗+π−) is constrained to be 0.65 byphase-space and isospin symmetry. Isospin considerationsalong with measurements of Br(D∗0

2 → D+π−)/Br(D∗02 →

D∗+π−) = (2.3 ± 0.6) [15] yield Br(D∗02 → D∗+π−) =

(0.21± 0.04). Using these values, we estimate the charmhadronization factors,f (c → D0

1) and f (c → D∗02 ), defined

as the fractions of charm quarks producing these states infragmentation. This yields

f (c → D01) = 0.021± 0.007± 0.003 (18)

f (c → D∗02 ) = 0.052± 0.022± 0.013, (19)

where the standard model expectation [34]Γcc/Γhad = 0.172has been used. Hence, the fraction of charm quarks produc-ing neutral narrow P-wave charm mesons is determined tobe

f (c → D∗∗0) = 0.073± 0.023± 0.014 (20)

where the appropriate correlations have been accounted for.The corresponding fractions can also be calculated for theproduction of these states in b-events using the standardmodel value ofΓbb/Γhad = 0.216 [34]:

f (b → D01) = 0.050± 0.014± 0.006 (21)

f (b → D∗02 ) = 0.047± 0.024± 0.013. (22)

From these values we obtain the inclusive branching ratioof b-hadrons to D∗∗0 mesons:

f (b → D∗∗0) = 0.097± 0.035± 0.017. (23)

These results are discussed further in Sect. 5.

4 D+s1(2536) production in charm fragmentation

The D+s1 corresponds to theJP = 1+ state of thejq = 3

2doublet of cs mesons discussed in the introduction. As such,

434

the only allowed final states for its decay are D∗+K0 andD∗0K+. The very narrow width of this state (Γ < 2.3 MeV/c2

at 90% CL [15]) is attributed to its proximity to thresholdfor both of these final states. The narrow width of this statemakes it easier to observe than itsJP = 2+ partner. Thatstate, the D∗+

s2 (2573), has a natural width of 15+ 5−4 MeV/c2

and lies well above the threshold of both final states that areavailable.

The D+s1 can be reconstructed in both final states. Re-

construction of the D∗0K+ final state involves either the re-construction of theπ0 or γ from the D∗0 decay or the useof a partial reconstruction which does not require detectionof the neutral particle. The analysis presented here uses apartial reconstruction technique introduced by the ARGUScollaboration [6].

Reconstruction of the D+s1 in the D∗+K0S decay mode pro-

vides the best signal to background ratio since it can exploitthe clean, well-understood signals obtainable for the D∗+

and K0S mesons. However, for the single D0 decay channel

used in this analysis, this reconstruction suffers from a smallproduct of efficiency and branching ratios. With the availablestatistics, this means that the expected signal in this channelis quite small, relative to that obtainable in the D∗0K+ finalstate.

While isospin invariance requires that the matrix ele-ments for decays to the two final states be the same, thelargerQ-value for the D∗0K+ final state, relative to D∗+K0,results in a 12% increase in the momentum of the final stateparticles, in the D+s1 rest frame. This can result in up to a75% kinematic enhancement of the branching ratio to theD∗0K+ final state, relative to D∗+K0. This number comesfrom the expectation that the relative enhancement is givenby

R ≡ Br(D+s1 → D∗0K+)

Br(D+s1 → D∗+K0)

=

(qD∗0K+

qD∗+K0S

)2L+1

≈ 1.75 (24)

whereq represents the momentum of the final state particlesin the D+

s1 rest frame. The factor of 1.75 comes from theassumption of a pure D-wave decay,i.e. L=2 in the aboveexpression. CLEO has measuredR=1.1± 0.3 [7] while theratio of the two ARGUS results [5, 6] yieldsR=1.4± 0.6.

In this analysis, both final states were reconstructed. Sec-tion 4.1 describes the analysis of the D∗0K+ final state. Sec-tion 4.2 describes D+s1 reconstruction in the D∗+K0

S final state.A calculation of the total rate for D+s1 production in Z0 → ccevents is presented in Sect. 4.3.

4.1 Analysis of theD∗0K+ final state

The analysis of this final state utilized a partial reconstructionof the decay sequence

D+s1(2536)- D∗0K+

�- D0(π0, γ)�- K−π+ (25)

in which theπ0 or γ from the D∗0 decay was not identi-fied. The lowQ-value for the D∗0 decay means that non-observation of the neutral particle does not greatly affect

the mass reconstruction. A peak arising from this decay se-quence should be observable in the invariant-mass distribu-tion of D0K+ combinations. The presence of an unobservedneutral particle simply shifts the peak to a lower mass andslightly degrades the mass resolution. Instead of looking ata D0K+ invariant-mass distribution, we examined the mass-difference distribution

∆M (D0K+) ≡M (D0K+) −M (D0) (26)

in which a peak arising from the decay sequence (25) shouldhave a central value which does not depend on whether theneutral particle has been reconstructed. Use of the mass-difference technique also results in a better signal resolutionthan can be achieved using the invariant-mass distribution.

The D0 → K−π+ candidates were selected from oppo-sitely charged pairs of tracks, each with momentum greaterthan 6 GeV/c. The invariant mass of each combinationwas required to be within the range 1.79 < M (K−π+) <1.94 GeV/c2 and the scaled energy,xE ≡ ED0/Ebeam, wasrequired to exceed 0.45. In order to suppress combinatorialbackground, we required| cosθ∗| < 0.9. Here,θ∗ is the D0

decay angle, defined as the angle between the kaon and theD0 boost vector in its rest frame. Additional suppression ofcombinatorial background due to particles produced at theprimary vertex was achieved using lifetime information. Thedecay length of the reconstructed K−π+ vertex was requiredto be displaced with respect to the primary vertex by atleast 0.5 standard deviations. D0 mesons from D∗+ → D0π+

decays were suppressed by rejecting D0 candidates if com-bination with anyπ+ candidate in the event yielded a mass-difference,∆M (D0π+) = M (D0π+) − M (D0), which wasless than 0.16 GeV/c2.

The dE/dx information from the OPAL jet chamber wasused to enhance the purity of the kaon sample. Kaon can-didates were rejected if their measured energy loss yieldeda signed weight in the range−0.05 < wK(K) < 0.15. Thisasymmetric window preferentially rejects pions since thesedeposit more dE/dx than do kaons of the same momentum,above 600 MeV/c. Pion candidates were required to sat-isfy |wπ(π)| > 0.01. Finally, to rejectD0 → K+π− decayswhere theπ− and K+ were incorrectly identified as K− andπ+, the weights were required to satisfy|wK(K−)wπ(π+)| >|wπ(K−)wK(π+)|.

To partially reconstruct D+s1 → D∗0K+ decays, D0 can-didates were combined with positively charged kaon candi-dates. The kaons were required to satisfy−0.05< wK(K) <0.15 and to have momenta greater than 5.5 GeV/c. Com-bined with thexE requirement on the D0 candidate, thisimposed an effective cut on the scaled energy of the D0K+

of xE > 0.57. Because of the missing neutral particle in theD∗0 decay, this corresponds closely to selecting D+

s1 decayswith xE > 0.6. The Monte Carlo simulation yields an effi-ciency of (9.0± 0.7)% for selecting D+s1 → D∗0K+ decayswith xE > 0.6.

This selection was applied to 6 million hadronic MonteCarlo events. The resulting mass-difference distribution isshown in Fig. 5a. The hatched peak near threshold indicatesthe contribution from true D+s1 → D∗0K+ decays. Beforedetector resolution effects are considered, the D0K+ mass-difference resulting from a D+s1 → D∗0K+ decay depends onthe angle at which the unobservedπ0 or γ is emitted, in

435

0

5

10

15

20

25

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8M(D0K+)-M(D0) (GeV/c2)

Ent

ries

/ 5 M

eV/c

2

Monte Carlo(a)

0

5

10

15

20

25

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8M(D0K+)-M(D0) (GeV/c2)

Ent

ries

/ 5 M

eV/c

2

OPAL(b)

Fig. 5. Mass-difference distributions in the D0K+ channel froma OPALMonte Carlo andb the OPAL hadronic data sample. Thesolid curvesarethe result of the fit described in the text, while thedashed curvesshow thefitted background component. Ina, thehatched distributionunder the fittedpeak indicates the contribution from D+

s1→ D∗0K+ decays, while thecross-hatched distributionat higher mass-differences shows the contribution fromD∗+

s2 → D0K+

the rest frame of the D∗0. An approximately uniform distri-bution of this decay angle leads to D0K+ mass differencesuniformly distributed between the allowed kinematic limits.Thus, the form of the D+s1 signal in this channel consistedof two uniform distributions, weighted by the D∗0 → D0π0

and D∗0 → D0γ branching ratios, and convoluted with theexpected detector resolution, determined from Monte Carlostudies. The curve overlaid on Fig. 5a is the result of an un-binned likelihood fit in which the signal was parameterizedin this way. In this fit, the background shape was describedby the functional formb(x) ∝ e−B(x−mK )(x−mK)C , wheremK is the charged kaon mass andB andC are free param-eters.

The fitted number of D+s1 decays reconstructed in theMonte Carlo was 28.5± 8.1, consistent with the 27 eventswhich were actually present. Although the width of the sig-nal was fixed by the kinematics and detector resolution, itsposition was freely varied. The fitted mass-difference was525.7 ± 2.1 MeV/c2, consistent with the generated valueof 528.3 MeV/c2. Allowing the width to vary yielded aGaussian width of 6.0 ± 2.2 MeV/c2, consistent with theexpectation of 7± 1 MeV/c2 derived from the high statis-tics D+

s1 → D∗0K+ Monte Carlo sample.Figure 5a also shows the entries from direct D∗+

s2 →D0K+ decays. Since the partial reconstruction selects onlyD0K+, such decays produce a cluster of events near a mass-difference of 700 MeV/c2. This state has a natural width of15 MeV/c2 . This, and the fact that the resolution is some-what poorer at higher mass-differences, means that this con-tribution to the mass-difference distribution is much broaderthan that of the D+s1. Based on the level of signal to back-ground observed in the Monte Carlo analysis one does not

Table 3. Summary of systematic uncertainties for the rate determined fromthe D+

s1→ D∗0K+ channel

Source Uncertainty×10−3

Background parameterization + 0.10−0.04

Signal parameterization + 0.09−0.12

Tracking resolution + 0.04−0.04

dE/dx modelling + 0.03−0.03

Monte Carlo b/c efficiency + 0.03−0.04

Monte Carlo D∗0 ε · Br + 0.02−0.02

Monte Carlo statistics + 0.15−0.15

Br(D0 → K−π+) + 0.06−0.06

Total ±0.22

expect that a contribution from this state would be observ-able above background in the analysis of the OPAL data.

The D0K+ mass-difference distribution obtained from theanalysis of OPAL data is shown in Fig. 5b. With the massesof the D+

s1 and D∗0 fixed to world average values [15] andthe resolution fixed to the value obtained from Monte Carlo,the fit yields a signal of 28.7± 8.3 events. Parameterizationof the signal as a single Gaussian, with both the mass andwidth allowed to vary, yielded a mass-difference of 527.3±2.2 MeV/c2 and a width of 5.6± 2.2 MeV/c2, consistentwith expectations.

Using the efficiency described above and accounting forthe D0 → K−π+ branching ratio [15], the 28.7± 8.3 eventsobserved correspond to a mean multiplicity, per hadronic Z0

decay of

nZ0→D+s1(xE>0.6) · Br(D+

s1 → D∗0K+)

= (1.9± 0.5 ± 0.2 ) × 10−3. (27)

The quoted systematic uncertainty was determined by vary-ing the choice of signal and background parameterizations,accounting for Monte Carlo statistics, the uncertainty on theD0 and D∗0 branching fractions and the uncertainty in thefraction of D+

s1 candidates from bb and cc events. Thesecontributions are discussed below and summarized in Ta-ble 3.

The fit to the Monte Carlo distribution was found to re-produce the number of D+s1 decays, indicating that the back-ground shape had been described adequately. Nevertheless,the effects of different background functions were consid-ered as potential sources of systematic uncertainty. The otherbackground parameterizations used were the Weibull func-tion, b(x) ∝ ((x − mK)/B)C−1 exp(−((x − mK)/B)C), asecond-order polynomial multiplied by a square-root thresh-old function, and a flat background above 0.51 GeV/c2, withno threshold description.

Contributions due to the signal parameterization werealso investigated. Possible effects due to an improperly de-termined mass resolution were estimated by varying the res-olution, obtained from Monte Carlo, by±25%. The fit wasalso repeated with the signal parameterized by a Gaussianwith the mass and width left free to vary.

Systematic uncertainties on the reconstruction efficiencyarising from improperly modelled tracking resolution wereestimated with Monte Carlo by redetermining the efficiencieswith the resolutions of the track angles and impact parame-ters changed by±10%.

436

The use of asymmetric kaon dE/dx cuts can intro-duce systematic effects if the dE/dx is improperly mod-elled in the Monte Carlo. Such effects were studied usinghigh-statistics samples of D∗+ → (K−π+)π+ decays in boththe data and Monte Carlo. Using the D0 selection describedabove, the relative efficiencies for the charged kaons to passthe dE/dx requirements were obtained. Good agreementwas observed between data and Monte Carlo. The statisticaluncertainty on this relative efficiency was used to assign acontribution to the systematic error.

In the accepted region ofxE(D+s1) > 0.6 there is a

small residual contribution from D+s1 mesons produced in bbevents. The systematic uncertainty associated with slightlydifferent reconstruction efficiencies for D∗∗0 mesons from bband cc events was estimated by varying the b-contributionby ±50%.

Finally, D+s1 decay sequences which proceed via D∗0 →

D0γ and D∗0 → D0π0 also have slightly different reconstruc-tion efficiencies. The systematic uncertainty attributable tothis effect was estimated by folding the small efficiency dif-ference together with the uncertainties on the D∗0 branchingfractions. The remaining contributions are from the uncer-tainty on the reconstruction efficiency due to limited MonteCarlo statistics, and from the uncertainty on the D0 → K−π+

branching ratio [15].The stability of this measurement was checked by vary-

ing the cuts used to select the D0K+ combinations. The fol-lowing cuts were modified:

– The minimumxD0 requirement was varied from 0.40 to0.55.

– The minimum K+ momentum was varied from 4.0 to6.5 GeV/c.

– The minimum K− and π+ momenta were varied from5.0 to 8.0 GeV/c.

– dE/dx weights for kaon identification were varied from±0.05 to±0.15.

– The minimum D0 decay length significance was variedfrom 0 to 1.

The changes in the measured rate introduced by variations ofthe selection criteria were consistent with the expected sizeof statistical fluctuations. Since there was no evidence forsystematic effects not already accounted for, no additionalsystematic errors were assigned.

4.2 Analysis of theD∗+K0 final state

The full decay chain used for the analysis of this channelwas

D+s1(2536)- D∗+K0

S

�- D0π+ (28)�- K−π+

with D∗+ candidates reconstructed using the selection de-scribed for the D∗∗0 analysis in Sect. 3. For this analy-sis, selected D∗+ candidates were required to have a mass-difference in the range 143< ∆M (D0π+) < 148 MeV/c2

in order to improve the signal to background ratio. Ac-cepted D∗+ candidates were combined with K0

S mesons re-

constructed through their decays toπ+π−, where the charac-teristic displaced vertex allows one to obtain a clean sample.For this decay channel it was essential to maintain a highreconstruction efficiency. For this reason, the cuts used toselect K0

S → π+π− decays were relaxed from those used inother OPAL analyses [35]. The point of intersection of theπ+ and π− was required to have a radial separation fromthe interaction point,Rint, in the range 1< Rint < 150 cm.The angle between the vector joining the primary vertex tothe point of intersection and the summed momentum vec-tor of the π candidate tracks, computed at this point, wasrequired to be less than 2 degrees. Good determination ofthe K0

S momentum was ensured by requiring that each trackhave either a minimum number of hits in thez-chambers,or that its endpoint be constrained to thez-coordinate of theend of the sensitive region of a jet chamber wire near theend-plate. No requirements were imposed on the transverseimpact parameters of the tracks with respect to the primaryvertex and only loose restrictions were imposed on the trackseparation inz at the point of intersection in therφ plane.The invariant mass of theπ+π− pair was required to be inthe range 0.45< M (π+π−) < 0.54 GeV/c2, which is widecompared with the intrinsic K0S mass resolution. This reducesthe systematic uncertainties associated with tails in the massdistribution.

Accepted D∗+K0S combinations were required to satisfy

xE > 0.6. In this energy region, the efficiency for recon-structing the D+s1 → D∗+K0

S decay was determined to be(10.6± 1.0)% using Monte Carlo. Monte Carlo studies alsoshowed that an improved mass-difference resolution couldbe obtained by considering the mass-difference calculatedusing

∆M (D∗+K0S) = M (D∗+K0

S) −M (D∗+) −M (K0S) +Mnominal

K0S

(29)

where the nominal K0S mass [15] was added to reproducethe usual mass-difference scale. For the D∗+K0

S selection justdescribed, this yielded a resolution of 3.7± 0.4 MeV/c2.

The mass-difference distribution obtained from the OPALhadronic Monte Carlo sample is shown in Fig. 6a. Over-laid as a hatched distribution is the contribution from trueD+

s1 → D∗+K0S decays. The Monte Carlo distribution indi-

cates that a signal from D+s1 → D∗+K0S decays should be

seen near threshold. Although the Monte Carlo included thedecay mode D∗+

s2 → D∗+K0S, this channel is phase-space sup-

pressed relative to the DK final state. No D∗+s2 → D∗+K0

Sdecays were reconstructed in the Monte Carlo sample.

Overlaid as a solid line is the result of an unbinned like-lihood fit to the distribution. In this fit, the D+s1 signal wasparameterized as a Gaussian with mass-difference fixed tothe expected value [15] and width fixed to the resolutionobtained from Monte Carlo studies. The background wasparameterized byb(x) ∝ e−B(x−mK0)(x−mK0)C wheremK0

is the K0 mass andB andC are free parameters. The fittednumber of events in the Monte Carlo sample was 6.0+ 2.8

−2.3,consistent with the true value of 7.

The mass-difference distribution obtained from analysisof the OPAL data sample is shown in Fig. 6b. Overlaid as asolid line is the result of a fit to the distribution with the samefit procedure described for the Monte Carlo analysis. How-

437

0

1

2

3

4

5

6

7

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8M(D*+K0

S)-M(D*+) (GeV/c2)

Ent

ries

/ 5 M

eV/c

2Monte Carlo(a)

0

1

2

3

4

5

6

7

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8M(D*+K0

S)-M(D*+) (GeV/c2)

Ent

ries

/ 5 M

eV/c

2

OPAL(b)

Fig. 6. Mass-difference distributions in the D∗+K0S channel froma OPAL

Monte Carlo andb the OPAL hadronic data sample. Thesolid curvesarethe result of the fit described in the text, while thedashed curvesshowthe fitted background component. Thehatched distributionin a shows thecontribution from D+

s1 decays

ever, because no events were observed at mass-differencesbelow the signal, the threshold behaviour may not be ade-quately described by a freely varying background function.For this reason, the background was constrained to the shapedetermined from the fit to the distribution obtained from theMonte Carlo. Different background treatments were studiedto estimate the systematic uncertainties. The fitted numberof D+

s1 decays observed in OPAL data wasN (D+s1) = 5.9+ 2.8

−2.3

which corresponds to a mean multiplicity per hadronic Z0

decay of

nZ0→D+s1(xE>0.6) · Br(D+

s1 → D∗+K0)

=(1.0 + 0.5

−0.4 ± 0.1)× 10−3. (30)

The contributions to the quoted systematic error are dis-cussed below and summarized in Table 4.

The systematic uncertainty associated with the back-ground parameterization in the likelihood fit was estimatedby refitting the mass-difference distribution with the uncon-strained background function and with a polynomial multi-plied by a square-root threshold factor.

Effects associated with the signal parameterization wereinvestigated by varying the mass-difference resolution by±25%. The corresponding systematic error was found to benegligible.

Systematic uncertainties on the reconstruction efficiencyarising due to improperly modelled tracking resolution wereestimated with Monte Carlo by redetermining the efficiencieswith the impact parameter and angle resolutions changed by±10%.

The uncertainty resulting from different efficiencies forreconstructing D+s1 decays in bb and cc events was deter-mined by varying the bb fraction by±50% and was foundto be negligible. The remaining uncertainties are due to fi-

Table 4. Summary of systematic uncertainties for the rate determined fromthe D+

s1→ D∗+K0S channel

Source Uncertainty×10−3

Background parameterization + 0.05−0.02

Signal parameterization < + 0.005−0.005

Tracking resolution + 0.03−0.02

Monte Carlo b/c efficiency < + 0.005−0.005

Monte Carlo statistics + 0.09−0.09

Br(D∗+ → D0π+) · Br(D0 → K−π+) + 0.04−0.04

Total + 0.11−0.10

nite Monte Carlo statistics and uncertainties on the D∗+ andD0 branching ratios.

The stability of this measurement was checked by vary-ing the cuts used to select the D∗+K0

S combinations. Thefollowing cuts were modified:

– The width of the mass-difference window used to selectD∗+ candidates was varied between 4 and 6 MeV/c2.

– The width of theπ+π− mass window used to select K0S

candidates was varied between 50 and 130 MeV/c2.– The requirement that the K0

S tracks have hits in thez-chambers or the jet-chamber end-plate was removed.

The changes in the measured rate introduced by variations ofthe selection criteria were consistent with the expected sizeof statistical fluctuations. Since there was no evidence forsystematic effects not already accounted for, no additionalsystematic errors were assigned.

Since the two rates, (27) and (30), are measured for thesame region ofxE(D+

s1), taking the ratio of the two resultsyields a measurement of the ratio of branching ratios:

R ≡ Br(D+s1 → D∗0K+)

Br(D+s1 → D∗+K0)

= 1.9 + 1.1−0.9 ± 0.4. (31)

This is consistent with previous measurements [5, 7] andwith the theoretical expectation discussed in Sect. 4.

4.3 Calculation off (c → D +s1(2536))

Assuming that the decay width of the D+s1 is saturated by the

D∗K final states, the mean multiplicity for the production ofthis state in hadronic Z0 decays, forxE > 0.6, is the sumof the two measured values shown in (27) and (30):

nZ0→D+s1(xE>0.6) =

(2.9 + 0.7

−0.6 ± 0.2)× 10−3. (32)

As stated in Sect. 4.1, Monte Carlo studies indicated thatthe D+

s1 signal withxE > 0.6 has a small contribution frombb events. The expected contributions are about four eventsin the D∗0K+ channel and one event in the D∗+K0

S analysis.Because of their inherent model dependence, these numberswere allowed to vary by±50% when making the corre-sponding subtraction4. Assuming the production of this state

4 The OPAL Monte Carlo is believed to describe the production of thisstate in bb events to a level of precision consistent with the quoted 50%error on this correction, though there are no published measurements ofthis rate. The dominant contribution to this uncertainty comes from poorknowledge of the Bs → Ds1X inclusive branching ratio. The equivalent ratein the non-strange system was measured in Sect. 3. The measured rate of D0

1

438

in charm fragmentation to be well modelled, one can thenuse Monte Carlo to extrapolate the result to the entirexErange. The systematic error associated with this procedurewas estimated by varyingεc over a range of values consis-tent with OPAL measurements [28] of the meanxE of D0

and D+ mesons produced in charm fragmentation. This wasdone in the manner described in Sect. 3.4 for the D∗∗0 anal-ysis. Performing this extrapolation and writing the correctedrate in terms of the charm hadronization factor,f (c → D+

s1),defined as the fraction of charm quarks producing a D+

s1 statein fragmentation, we obtain

2 · Γcc

Γhad· f (c → D+

s1(2536))

=(5.6 + 1.5

−1.3 ± 0.6 ± 0.8)× 10−3 (33)

where the second systematic error accounts for the combineduncertainties of the correction for the b-contribution and theextrapolation to the full range ofxE . The latter contributionincludes the uncertainty arising from the use of differentfragmentation models [33]. UsingΓcc/Γhad = 0.172 [34] thiscorresponds to the hadronization fraction

f (c → D+s1) = 0.016± 0.004± 0.003. (34)

5 Discussion

The measured D∗∗0 production rates in charm quark frag-mentation can be compared with predictions made usingsimplified assumptions about fragmentation. Based on fits tothe production rates of light-flavoured hadrons, predictionshave been made for the average production rates of heavyflavoured hadrons [36]. These includef (c → (D1 +D∗2)u,d) =0.170 andf (c → Ds1 + D∗s2) = 0.028. Assuming isospinsymmetry, the former impliesf (c → D∗∗0) = 0.085 whichagrees well with the measured rate shown in (20). The ratiof (c → D0

1)/f (c → D∗02 ) is calculated from the measured

value off cc1 yielding

f (c → D01)

f (c → D∗02 )

= 0.40± 0.25± 0.10, (35)

where correlations in the systematic uncertainties have beentaken into account. This value is consistent with the simplespin-counting prediction of 3/5.

A prediction for the combined rate of D+s1 and D∗+

s2 pro-duction was presented in [36]. The approximate degeneracyin the D+

s1 and D∗+s2 masses allows predictions for the indi-

vidual production rates to be estimated using spin-countingarguments in the context of this model. This results in thepredictionf (c → D+

s1) = 0.011 which is consistent with the

mesons in bb events, given in (17), is consistent with the corresponding ratein the OPAL Monte Carlo to within half a standard deviation. The decaysof Bs → Ds1X are modelled analogously to the B→ D1X decays in thenon-strange system, with equivalent branching ratios. The rate in the OPALMonte Carlo corresponds tof (b→ Ds1) = 0.0129. Additional studies wereperformed to examine the size of possible contributions from b-decays inwhich a Ds1 is produced in the decay of the virtual W. These contributionsare small, well within the assigned systematic error, unless the B→ D(∗)Ds1two-body branching ratios are large. The additional contribution from suchdecays would be about 1.3(1.0) events for each percent of B→ DDs1(2536)(B → D∗Ds1(2536)) branching ratio

measurement given in (34). This is a test of strange-quarksuppression.

OPAL has also observed the production of P-wave Bmesons in hadronic Z0 decays [16] and has measured therelative branching fractions:

Γ (Z0 → b → B∗∗0 → B(∗)+π−)

Γ (Z0 → b → B+)= 0.18± 0.04 (36)

and

Γ (Z0 → b → B∗∗0s → B(∗)+K−)

Γ (Z0 → b → B+)= 0.026± 0.008. (37)

Measurements of the former quantity have also been pub-lished by the DELPHI [17] and ALEPH [18] collaborations,in each case yielding results consistent with the OPAL mea-surement.

Assuming that the B0s1 and B∗0s2 states are produced

in a ratio of 3/5 (from spin-statistics), that Br(B∗∗0s →

B(∗)+K−) = 1/2 and Br(B∗∗0 → B(∗)+π−) = 2/3 (fromisospin invariance), and that B0 and B+ mesons are pro-duced at equal rates in b-quark fragmentation, then usingf (b → B+) = 0.378± 0.022 [15], we obtain

f (b → B∗∗0) = 0.10± 0.02 (38)

and

f (b → B0s1) = 0.007± 0.002. (39)

These values are similar to the corresponding fractions forthe production of excited charm and charm-strange mesonsin charm fragmentation.

Measurements of P-wave meson production in the light-quark sector have been performed by OPAL [37] and DEL-PHI [38]. However, since the relative mass-differences be-tween the P-wave states and the corresponding pseudoscalarand vector ground-state mesons are much larger in the light-quark sector than for B or D mesons, it is difficult to drawconclusions from direct comparisons of the relative produc-tion rates.

6 Conclusions

We have measured the mean multiplicities for production ofD0

1(2420) and D∗02 (2460) mesons in Z0 decays. The measured

values are

nZ0→cc→D∗∗0(xE>0.5) · Br(D∗∗0 → D∗+π−)

=(5.4 + 1.4

−1.3+ 0.6−0.8

)× 10−3 (40)

nZ0→bb→D∗∗0(xE>0.2) · Br(D∗∗0 → D∗+π−)

=(16.1 + 3.7

−3.6+ 2.0−1.8

)× 10−3. (41)

The fraction of the D∗∗0 signal due to the D01 state wasdetermined to be

f cc1 = 0.56± 0.15 + 0.03

−0.04 (42)

and

fbb1 = 0.77 + 0.16

−0.14 ± 0.04, (43)

for D∗∗0 production in cc and bb events, respectively.

439

Extrapolating the mean multiplicity measurements in ccevents to the full region ofxE(D∗∗0), using the quoted valueof f cc

1 , and assuming that the decay widths of these mesonsare saturated by the allowed D∗π and Dπ final states, weestimate the fractions of charm quarks producing these statesin fragmentation to be

f (c → D01) = 0.021± 0.007± 0.003 (44)

and

f (c → D∗02 ) = 0.052± 0.022± 0.013 (45)

where the systematic uncertainty includes the model depen-dence introduced by the extrapolation of the measured ratesto the full range ofxE . The combination of these resultsyields

f (c → D∗∗0) = 0.073± 0.023± 0.014. (46)

The corresponding fractions of b-hadron decays producingthese states are

f (b → D01) = 0.050± 0.014± 0.006, (47)

f (b → D∗02 ) = 0.047± 0.024± 0.013, (48)

and

f (b → D∗∗0) = 0.097± 0.035± 0.017. (49)

The D+s1(2536) meson has been observed in both the

D∗0K+ and D∗+K0S final states. We obtain

nZ0→D+s1(xE>0.6) · Br(D+

s1 → D∗0K+)

= (1.9± 0.5 ± 0.2 ) × 10−3 (50)

nZ0→D+s1(xE>0.6) · Br(D+

s1 → D∗+K0)

=(1.0 + 0.5

−0.4 ± 0.1)× 10−3. (51)

Assuming that these two channels saturate the available D+s1

final states, the measured mean multiplicity for productionof this state in hadronic Z0 decays is therefore

nZ0→D+s1(xE>0.6) =

(2.9 + 0.7

−0.6 ± 0.2)× 10−3 (52)

for the quoted region ofxE . The ratio of branching ratiosfor the two final states is

R ≡ Br(D+s1 → D∗0K+)

Br(D+s1 → D∗+K0)

= 1.9 + 1.1−0.9 ± 0.4. (53)

Using Monte Carlo to correct for small contributions from bbevents and for extrapolation of the mean-multiplicity mea-surement to the full region ofxE , we obtain an estimate forthe fraction of charm quarks producing D+

s1 mesons:

f (c → D+s1) = 0.016± 0.004± 0.003. (54)

All production fractions are found to be similar in mag-nitude to the corresponding production fractions in the b-quark sector. The results obtained in this analysis are con-sistent with predictions based on current understanding ofthe heavy-quark fragmentation process.

Acknowledgements.We particularly wish to thank the SL Division for theefficient operation of the LEP accelerator and for their continuing close co-operation with our experimental group. We thank our colleagues from CEA,DAPNIA/SPP, 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 theDepartment 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 Scienceand Humanities,Minerva Gesellschaft,Benoziyo Center for High Energy Physics,Japanese Ministry of Education, Science and Culture (the Monbusho) anda grant under the Monbusho International Science Research Program,German Israeli Bi-national Science Foundation (GIF),Direction des Sciences de la Matiere du Commissariata l’Energie Atom-ique, France,Bundesministerium fur Bildung, Wissenschaft, Forschung und Technologie,Germany,National Research Council of Canada,Hungarian Foundation for Scientific Research, OTKA T-016660, T023793and OTKA F-023259.

References

1. N. Isgur and M. B. Wise, Phys. Rev. Lett.66 (1991) 11302. J. L. Rosner, Comments Nucl. Part. Phys.16 (1986) 1093. ARGUS Collaboration, H. Albrecht, et al., Phys. Rev. Lett.56 (1986)

549, Phys. Lett.B221 (1989) 422, Phys. Lett.B231 (1989) 208, Z.Phys.C69 (1996) 405

4. ARGUS Collaboration, H. Albrecht, et al., Phys. Lett.B232 (1989)398

5. ARGUS Collaboration, H. Albrecht, et al., Phys. Lett.B230 (1989)162

6. ARGUS Collaboration, H. Albrecht, et al., Phys. Lett.B297 (1992)425

7. CLEO Collaboration, P. Avery, et al., Phys. Rev.D41 (1990) 774,Phys. Lett.B303 (1993) 377, Phys. Lett.B340 (1994) 194

8. CLEO Collaboration, P. Avery, et al., Phys. Lett.B331 (1994) 2369. CLEO Collaboration, Y. Kubota, et al., Phys. Rev. Lett.72 (1994)

197210. E691 Collaboration, J.C. Anjos, et al., Phys. Rev. Lett.62 (1989) 171711. E687 Collaboration, P.L. Frabetti, et al., Phys. Rev. Lett.72 (1994)

32412. BEBC Collaboration, A.E. Asratian, et al., Z. Phys.C61 (1994) 56313. OPAL Collaboration, R. Akers, et al., Z. Phys.C67 (1995) 5714. ALEPH Collaboration, D. Buskulic, et al., Phys. Lett.B345 (1994)

103; Z. Phys.C62 (1994) 1, Z. Phys.C73 (1997) 60115. Particle Data Group, R.M. Barnett, et al., Phys. Rev.D54 (1996) 116. OPAL Collaboration, R. Akers, et al., Z. Phys.C66 (1995) 1917. DELPHI Collaboration, P. Abreu, et al., Phys. Lett.B345 (1995) 59818. ALEPH Collaboration, D. Abbaneo, et al., Z. Phys.C69 (1996) 39319. OPAL Collaboration, K. Ahmet et al., Nucl. Instrum. MethodsA305

(1991) 27520. P.P. Allport, et al., Nucl. Instrum. MethodsA324 (1993) 3421. P.P. Allport, et al., Nucl. Instrum. MethodsA346 (1994) 47622. OPAL Collaboration, G. Alexanderet al., Z. Phys.C52 (1991) 17523. T. Sjostrand, Comp. Phys. Comm.39 (1986) 347;

T. Sjostrand and M. Bengtsson, Comp. Phys. Comm.43 (1987) 367;T. Sjostrand, CERN-TH 6488/92

24. T. Sjostrand, JETSET 7.4 Manual, CERN-TH 7112/9325. J. Allison, et al., Nucl. Instrum. MethodsA317 (1992) 4726. C. Peterson, et al., Phys. Rev.D27 (1983) 10527. OPAL Collaboration, G. Alexander, et al., Phys. Lett.B364 (1995) 9328. OPAL Collaboration, G. Alexander, et al., Z. Phys.C72 (1996) 129. S.Godfrey and R. Kokoski, Phys Rev.D43 (1991) 1679.

The quoted values have been recalculated using experimentally ob-served masses

30. OPAL Collaboration, R. Akers, et al., Z. Phys.C67 (1995) 2731. CDF Collaboration, F. Abeet al., Phys. Rev.D45 (1992) 144832. OPAL Collaboration, P.D. Acton, et al., Phys. Lett.B273 (1991)

355

440

33. P. Collins and T. Spiller, J. Phys.G11 (1985) 1289;V.G. Kartvelishvili, A.K. Likhoded and V.A. Petrov, Phys. Lett.B78(1978) 615;B. Andersson, G. Gustafson and B. Soderberg, Z. Phys.C20 (1983)317

34. The current world average values [15] forRc andRb are consistentwith Standard Model predictions Accounting for the experimental un-certainties would introduce only a negligible contribution to the sys-tematic error

35. OPAL Collaboration, R. Akers, et al., Z. Phys.C67 (1995) 38936. Yi-Jin Pei, Z. Phys.C72 (1996) 3937. OPAL Collaboration, R. Akers, et al., Z. Phys.C68 (1995) 138. DELPHI Collaboration, P. Abreu, et al., CERN-PPE/96-77, Submitted

to Z. PhysikC, Phys. Lett.B379 (1996) 309, Z. Phys.C65 (1995) 587