Production of Xc1 and Xc2 in pp(overbar) collisions at (square root)s = 1.8 TeV

Production of

x

and

x

in

pp

Collisions at

p

p

p

s

5

1

.

8 TeV

T. Affolder,23 _{H. Akimoto,}45_{A. Akopian,}38 _{M. G. Albrow,}11 _{P. Amaral,}8_{S. R. Amendolia,}34_{D. Amidei,}26 K. Anikeev,24_{J. Antos,}1_{G. Apollinari,}11_{T. Arisawa,}45_{T. Asakawa,}43_{W. Ashmanskas,}8_{F. Azfar,}31_{P. Azzi-Bacchetta,}32

N. Bacchetta,32 M. W. Bailey,28S. Bailey,16 P. de Barbaro,37 A. Barbaro-Galtieri,23 V. E. Barnes,36 B. A. Barnett,19 S. Baroiant,5_{M. Barone,}13_{G. Bauer,}24 _{F. Bedeschi,}34 _{S. Belforte,}42_{W. H. Bell,}15 _{G. Bellettini,}34_{J. Bellinger,}46 D. Benjamin,10 J. Bensinger,4A. Beretvas,11J. P. Berge,11J. Berryhill,8B. Bevensee,33 A. Bhatti,38M. Binkley,11

D. Bisello,32 _{M. Bishai,}11_{R. E. Blair,}2_{C. Blocker,}4_{K. Bloom,}26 _{B. Blumenfeld,}19 _{S. R. Blusk,}37_{A. Bocci,}34 A. Bodek,37 W. Bokhari,33 G. Bolla,36Y. Bonushkin,6D. Bortoletto,36 J. Boudreau,35A. Brandl,28S. van den Brink,19 C. Bromberg,27 _{M. Brozovic,}10_{N. Bruner,}28 _{E. Buckley-Geer,}11_{J. Budagov,}9_{H. S. Budd,}37 _{K. Burkett,}16_{G. Busetto,}32

A. Byon-Wagner,11 _{K. L. Byrum,}2_{P. Calafiura,}23 _{M. Campbell,}26 _{W. Carithers,}23 _{J. Carlson,}26 _{D. Carlsmith,}46 W. Caskey,5J. Cassada,37 A. Castro,32 D. Cauz,42A. Cerri,34 A. W. Chan,1P. S. Chang,1P. T. Chang,1J. Chapman,26 C. Chen,33_{Y. C. Chen,}1_{M.-T. Cheng,}1_{M. Chertok,}40 _{G. Chiarelli,}34 _{I. Chirikov-Zorin,}9_{G. Chlachidze,}9_{F. Chlebana,}11

L. Christofek,18M. L. Chu,1Y. S. Chung,37C. I. Ciobanu,29 A. G. Clark,14 A. Connolly,23J. Conway,39 M. Cordelli,13 J. Cranshaw,41_{D. Cronin-Hennessy,}10 _{R. Cropp,}25_{R. Culbertson,}11 _{D. Dagenhart,}44 _{S. D’Auria,}15_{F. DeJongh,}11

S. Dell’Agnello,13M. Dell’Orso,34 L. Demortier,38 M. Deninno,3P. F. Derwent,11T. Devlin,39J. R. Dittmann,11 S. Donati,34_{J. Done,}40_{T. Dorigo,}16_{N. Eddy,}18 _{K. Einsweiler,}23 _{J. E. Elias,}11 _{E. Engels, Jr.,}35 _{R. Erbacher,}11 D. Errede,18 _{S. Errede,}18_{Q. Fan,}37 _{R. G. Feild,}47 _{J. P. Fernandez,}11 _{C. Ferretti,}34_{R. D. Field,}12 _{I. Fiori,}3_{B. Flaugher,}11 G. W. Foster,11M. Franklin,16J. Freeman,11J. Friedman,24Y. Fukui,22I. Furic,24S. Galeotti,34M. Gallinaro,38T. Gao,33 M. Garcia-Sciveres,23_{A. F. Garfinkel,}36_{P. Gatti,}32_{C. Gay,}47_{D. W. Gerdes,}26 _{P. Giannetti,}34 _{P. Giromini,}13_{V. Glagolev,}9

D. Glenzinski,11 M. Gold,28J. Goldstein,11A. Gordon,16I. Gorelov,28 A. T. Goshaw,10Y. Gotra,35K. Goulianos,38 C. Green,36 _{G. Grim,}5_{P. Gris,}11 _{L. Groer,}39_{C. Grosso-Pilcher,}8_{M. Guenther,}36_{G. Guillian,}26_{J. Guimaraes da Costa,}16

R. M. Haas,12C. Haber,23 E. Hafen,24S. R. Hahn,11C. Hall,16 T. Handa,17 R. Handler,46W. Hao,41 F. Happacher,13 K. Hara,43 _{A. D. Hardman,}36 _{R. M. Harris,}11 _{F. Hartmann,}20_{K. Hatakeyama,}38 _{J. Hauser,}6_{J. Heinrich,}33 _{A. Heiss,}20

M. Herndon,19 _{C. Hill,}5_{K. D. Hoffman,}36 _{C. Holck,}33 _{R. Hollebeek,}33 _{L. Holloway,}18 _{R. Hughes,}29 _{J. Huston,}27 J. Huth,16H. Ikeda,43J. Incandela,11G. Introzzi,34J. Iwai,45Y. Iwata,17E. James,26H. Jensen,11M. Jones,33U. Joshi,11 H. Kambara,14 _{T. Kamon,}40_{T. Kaneko,}43 _{K. Karr,}44_{H. Kasha,}47 _{Y. Kato,}30 _{T. A. Keaffaber,}36 _{K. Kelley,}24_{M. Kelly,}26

R. D. Kennedy,11R. Kephart,11 D. Khazins,10 T. Kikuchi,43 B. Kilminster,37 B. J. Kim,21 D. H. Kim,21H. S. Kim,18 M. J. Kim,21 _{S. H. Kim,}43_{Y. K. Kim,}23_{M. Kirby,}10 _{M. Kirk,}4_{L. Kirsch,}4_{S. Klimenko,}12 _{P. Koehn,}29_{A. Köngeter,}20

K. Kondo,45 J. Konigsberg,12K. Kordas,25 A. Korn,24 A. Korytov,12E. Kovacs,2J. Kroll,33 M. Kruse,37 S. E. Kuhlmann,2_{K. Kurino,}17 _{T. Kuwabara,}43_{A. T. Laasanen,}36 _{N. Lai,}8_{S. Lami,}38_{S. Lammel,}11_{J. I. Lamoureux,}4

J. Lancaster,10 _{M. Lancaster,}23_{R. Lander,}5_{G. Latino,}34_{T. LeCompte,}2_{A. M. Lee IV,}10 _{K. Lee,}41 _{S. Leone,}34 J. D. Lewis,11M. Lindgren,6T. M. Liss,18J. B. Liu,37Y. C. Liu,1N. Lockyer,33J. Loken,31M. Loreti,32 D. Lucchesi,32

P. Lukens,11_{S. Lusin,}46 _{L. Lyons,}31 _{J. Lys,}23 _{R. Madrak,}16 _{K. Maeshima,}11 _{P. Maksimovic,}16_{L. Malferrari,}3 M. Mangano,34M. Mariotti,32 G. Martignon,32 A. Martin,47 J. A. J. Matthews,28 J. Mayer,25P. Mazzanti,3 K. S. McFarland,37_{P. McIntyre,}40_{E. McKigney,}33 _{M. Menguzzato,}32_{A. Menzione,}34_{C. Mesropian,}38 _{A. Meyer,}11

T. Miao,11 R. Miller,27 J. S. Miller,26 H. Minato,43 S. Miscetti,13 M. Mishina,22G. Mitselmakher,12N. Moggi,3 E. Moore,28 _{R. Moore,}26_{Y. Morita,}22_{T. Moulik,}24_{M. Mulhearn,}24_{A. Mukherjee,}11 _{T. Muller,}20_{A. Munar,}34 P. Murat,11 _{S. Murgia,}27_{J. Nachtman,}6_{S. Nahn,}47 _{H. Nakada,}43_{T. Nakaya,}8_{I. Nakano,}17 _{C. Nelson,}11 _{T. Nelson,}11

C. Neu,29 D. Neuberger,20 C. Newman-Holmes,11C.-Y. P. Ngan,24 H. Niu,4L. Nodulman,2A. Nomerotski,12 S. H. Oh,10_{T. Ohmoto,}17_{T. Ohsugi,}17_{R. Oishi,}43 _{T. Okusawa,}30_{J. Olsen,}46_{W. Orejudos,}23_{C. Pagliarone,}34 F. Palmonari,34 R. Paoletti,34V. Papadimitriou,41S. P. Pappas,47 D. Partos,4J. Patrick,11 G. Pauletta,42M. Paulini,23,*

C. Paus,24 _{L. Pescara,}32 _{T. J. Phillips,}10 _{G. Piacentino,}34_{K. T. Pitts,}18 _{A. Pompos,}36 _{L. Pondrom,}46 _{G. Pope,}35 M. Popovic,25 F. Prokoshin,9J. Proudfoot,2F. Ptohos,13O. Pukhov,9G. Punzi,34K. Ragan,25A. Rakitine,24D. Reher,23

A. Reichold,31_{A. Ribon,}32 _{W. Riegler,}16 _{F. Rimondi,}3_{L. Ristori,}34 _{M. Riveline,}25_{W. J. Robertson,}10 _{A. Robinson,}25 T. Rodrigo,7_{S. Rolli,}44_{L. Rosenson,}24_{R. Roser,}11 _{R. Rossin,}32_{A. Roy,}24 _{A. Safonov,}38_{R. St. Denis,}15 W. K. Sakumoto,37D. Saltzberg,6C. Sanchez,29 A. Sansoni,13L. Santi,42 H. Sato,43P. Savard,25P. Schlabach,11 E. E. Schmidt,11_{M. P. Schmidt,}47_{M. Schmitt,}16_{L. Scodellaro,}32 _{A. Scott,}6_{A. Scribano,}34 _{S. Segler,}11 _{S. Seidel,}28 Y. Seiya,43 A. Semenov,9F. Semeria,3T. Shah,24 M. D. Shapiro,23P. F. Shepard,35 T. Shibayama,43 M. Shimojima,43 M. Shochet,8_{J. Siegrist,}23 _{G. Signorelli,}34 _{A. Sill,}41 _{P. Sinervo,}25_{P. Singh,}18 _{A. J. Slaughter,}47_{K. Sliwa,}44_{C. Smith,}19

J. Steele,46_{A. Stefanini,}34_{J. Strologas,}18 _{F. Strumia,}14 _{D. Stuart,}11_{K. Sumorok,}24_{T. Suzuki,}43_{T. Takano,}30 R. Takashima,17K. Takikawa,43 P. Tamburello,10 M. Tanaka,43 B. Tannenbaum,6W. Taylor,25 M. Tecchio,26 R. Tesarek,11 _{P. K. Teng,}1_{K. Terashi,}38 _{S. Tether,}24 _{A. S. Thompson,}15 _{R. Thurman-Keup,}2_{P. Tipton,}37 _{S. Tkaczyk,}11 K. Tollefson,37 A. Tollestrup,11H. Toyoda,30W. Trischuk,25 J. F. de Troconiz,16 J. Tseng,24N. Turini,34F. Ukegawa,43 T. Vaiciulis,37 J. Valls,39 S. Vejcik III,11 G. Velev,11 R. Vidal,11R. Vilar,7I. Volobouev,23D. Vucinic,24R. G. Wagner,2

R. L. Wagner,11 _{J. Wahl,}8_{N. B. Wallace,}39 _{A. M. Walsh,}39 _{C. Wang,}10_{M. J. Wang,}1_{T. Watanabe,}43 _{D. Waters,}31 T. Watts,39 R. Webb,40H. Wenzel,20W. C. Wester III,11 A. B. Wicklund,2E. Wicklund,11 T. Wilkes,5H. H. Williams,33 P. Wilson,11 _{B. L. Winer,}29 _{D. Winn,}26_{S. Wolbers,}11 _{D. Wolinski,}26 _{J. Wolinski,}27_{S. Wolinski,}26_{S. Worm,}28 _{X. Wu,}14

J. Wyss,34 A. Yagil,11 W. Yao,23 G. P. Yeh,11 P. Yeh,1J. Yoh,11C. Yosef,27 T. Yoshida,30 I. Yu,21 S. Yu,33 Z. Yu,47 A. Zanetti,42 _{F. Zetti,}23 _{and S. Zucchelli}3

(CDF Collaboration)

1_{Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China}

2_{Argonne National Laboratory, Argonne, Illinois 60439}

3_{Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy}

4_{Brandeis University, Waltham, Massachusetts 02254}

5_{University of California at Davis, Davis, California 95616} 6_{University of California at Los Angeles, Los Angeles, California 90024} 7_{Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain}

8_{Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637}

9_{Joint Institute for Nuclear Research, RU-141980 Dubna, Russia}

10_{Duke University, Durham, North Carolina 27708}

11_{Fermi National Accelerator Laboratory, Batavia, Illinois 60510} 12_{University of Florida, Gainesville, Florida 32611}

13_{Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy}

14_{University of Geneva, CH-1211 Geneva 4, Switzerland}

15_{Glasgow University, Glasgow G12 8QQ, United Kingdom}

16_{Harvard University, Cambridge, Massachusetts 02138}

17_{Hiroshima University, Higashi-Hiroshima 724, Japan}

18_{University of Illinois, Urbana, Illinois 61801}

19_{The Johns Hopkins University, Baltimore, Maryland 21218}

20_{Institut für Experimentelle Kernphysik, Universität Karlsruhe, 76128 Karlsruhe, Germany}

21_{Center for High Energy Physics, Kyungpook National University, Taegu 702-701, Korea,}

Seoul National University, Seoul 151-742, Korea,

and SungKyunKwan University, Suwon 440-746, Korea

22_{High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan}

23_{Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720}

24_{Massachusetts Institute of Technology, Cambridge, Massachusetts 02139}

25_{Institute of Particle Physics, McGill University, Montreal H3A 2T8, Canada,}

and University of Toronto, Toronto M5S 1A7, Canada

26_{University of Michigan, Ann Arbor, Michigan 48109}

27_{Michigan State University, East Lansing, Michigan 48824}

28_{University of New Mexico, Albuquerque, New Mexico 87131}

29_{The Ohio State University, Columbus, Ohio 43210}

30_{Osaka City University, Osaka 588, Japan}

31_{University of Oxford, Oxford OX1 3RH, United Kingdom}

32_{Universita di Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova, I-35131 Padova, Italy} 33_{University of Pennsylvania, Philadelphia, Pennsylvania 19104}

34_{Istituto Nazionale di Fisica Nucleare, University and Scuola Normale Superiore of Pisa, I-56100 Pisa, Italy} 35_{University of Pittsburgh, Pittsburgh, Pennsylvania 15260}

36_{Purdue University, West Lafayette, Indiana 47907} 37_{University of Rochester, Rochester, New York 14627}

38_{Rockefeller University, New York, New York 10021}

39_{Rutgers University, Piscataway, New Jersey 08855}

40_{Texas A&M University, College Station, Texas 77843}

41_{Texas Tech University, Lubbock, Texas 79409}

42_{Istituto Nazionale di Fisica Nucleare, University of Trieste, Udine, Italy} 43_{University of Tsukuba, Tsukuba, Ibaraki 305, Japan}

45_{Waseda University, Tokyo 169, Japan}

46_{University of Wisconsin, Madison, Wisconsin 53706}

47_{Yale University, New Haven, Connecticut 06520}

(Received 30 October 2000)

We have measured the ratio of prompt production rates of the charmonium states xc1 andxc2 in

110pb21_{ofpp collisions at}p_{s苷1.8TeV. The photon from their decay intoJ兾cg is reconstructed} through conversion intoe1_e2_{pairs. The energy resolution this technique provides makes the resolution}

of the two states possible. We find the ratio of production cross sections sxc2

sxc1 苷0.9660.27共stat兲6 0.11共syst兲for events withpT共J兾c兲.4.0GeV兾c,jh共J兾c兲j,0.6, andpT共g兲.1.0GeV兾c.

DOI: 10.1103/PhysRevLett.86.3963 PACS numbers: 13.85.Ni, 14.40.Gx

The production of charmonium inpp collisions occurs promptly, or through the decay of hadrons containing theb

quark. Prompt charmonium production can be easily sepa-rated from B hadron decay backgrounds using the life-time distributions. The cross section of prompt J兾c’s can be described by calculations based on the nonrelativis-tic QCD factorization formalism [1,2] that includes both color singlet and color octet contributions [3,4]. However, these QCD calculations of charmonium production predict a large transverse polarization of theJ兾candc共2S兲which is not seen in the data [5]. This discrepancy between the experimental observations and theoretical understanding of prompt charmonium production heightens the importance of exploring such processes as completely as possible.

In this paper, we contribute to the study of the char-monium system by measuring the relative cross sections of the xc1 and xc2 promptly produced in pp collisions atps 苷1.8TeV using the Collider Detector at Fermilab (CDF). Knowledge of this ratio is needed for any model that calculatesJ兾cproduction through radiativexcdecay,

and can be an important standard for comparing production models. We study the processpp ! xcJX,xcJ !J兾cg,

J兾c ! m1m2, wherexcJis taken to representxc1orxc2. The final state photons are reconstructed through conver-sion intoe1e2pairs, which provide excellent energy reso-lution for the photons fromxcJ decay. The resultingJ兾cg

mass resolution allows us to distinguish the xc1andxc2, and thereby perform the measurement using110pb21of data taken during the 1992–1995 operation of the Teva-tron. The low efficiency of the photon conversion process precludes a refinement of previous measurement of the to-talxcJ cross section [4].

The CDF detector has been described in detail elsewhere [6]. Charged particles emerging from the pp interaction point are detected in a silicon vertex detector (SVX), a time projection chamber (VTX), and a central tracking chamber (CTC). These tracking detectors are located in a 1.4 Tesla solenoidal field. Our coordinate system defines the z

axis to be the proton beam direction, withf andr being the azimuthal angle and transverse distance, respectively. The CTC, an 84 layer drift chamber, covers the pseudo-rapidity intervaljhj,1(whereh ⬅2ln关tan共u兾2兲兴 and u is the angle with respect to the proton beam direc-tion) and provides information in both the r 2z and

r 2 f views. The efficiency for track reconstruction

in the CTC cuts off for tracks with pT ,0.2GeV兾c,

rises over the range 0.2GeV兾c,pT ,0.4GeV兾c, and

reaches 艐93% for tracks with pT .0.4GeV兾c, where

pT is the track transverse momentum. The SVX extends

over approximately 60% of the interaction region. This de-tector provides track impact parameter measurements for the muons fromJ兾cdecay in ther 2 fview with a reso-lution of共13140兾pT兲mm, where pT is in GeV兾c. The

combined momentum resolution of the tracking chambers is dpT兾pT 苷关共0.0009pT兲2 1共0.0066兲2兴1兾2, wherepT is

in GeV兾c. The beam pipe, SVX, VTX, and inner support cylinder of the CTC contribute to an average thickness of

6.02 60.33% radiation lengths of material [7], as mea-sured perpendicular to the beam line.

Muons from the decay J兾c !m1_m2 _{are identified} by drift chambers located outside the electromagnetic and hadron calorimeters. The central muon chambers used in this analysis cover the regionjhj,0.6, and are used in a three level trigger system to require a pair of muons in the event. The first trigger level identifies muon candidates by requiring a coincidence between two radially aligned muon chambers. Two such coincidences are required for this trig-ger. The second dimuon trigger level combines the muon candidates with information from the fast track processor in the CTC. For the first 19.4 pb21 of data collected, a single match between a muon chamber coincidence and a CTC track withpT .2.8GeV兾cwas required. For the

re-mainder of the data, this trigger required two such matches with trackpT .2.0GeV兾c. The final level of the trigger

was performed in software, and required events to contain oppositely charged muon candidate pairs with an invariant mass within approximately300MeV兾c2of the world av-erageJ兾c mass of3096.9MeV兾c2_[8].

The J兾c !m1_m2 _{candidates are selected by} requir-ing events that satisfy all trigger requirements after offline reconstruction, and have pT共J兾c兲. 4.0GeV兾c. A

si-multaneous mass and vertex constrained fit is performed on the muon tracks, where the dimuon mass is constrained to theJ兾c mass. We find⬃151 000events have a good fit to the J兾c mass. A subset of⬃88 000events have both decay muons measured within the SVX, which provides vertex resolution sufficient for determining the fraction of events due toB hadron decay.

event. Pairs of oppositely charged tracks are chosen with cos共ue2e兲 .0.995, where ue2e is the opening angle

between the tracks at the point of intersection. These pairs have their track parameters recalculated by using a least squares fit, with constraints consistent with the photon conversion hypothesis. Specifically, the two tracks are constrained to be parallel at their point of intersection, and the momentum of the pair is constrained to pass through the dimuon vertex. The radial distance from the dimuon vertex to the intersection point is required to be 1.0 cm or more in order to reduce the background due to particles originating from the primary vertex. Also, we require

pT共g兲 .1.0GeV兾c and pT共e6兲 .0.4GeV兾c. A final

fit on all four particle trajectories is then performed that simultaneously constrains the muon momenta to form the world average J兾c mass [8] and the g momentum to point to the dimuon vertex.

Relative acceptance and reconstruction efficiencies for

J兾cg final states of different invariant mass have been studied with simulated events generated with a pT共xcJ兲

distribution that was tuned to match the distribution of events seen in the data [4]. Monte Carlo generatedxcJ !

J兾cg events are used as input to the detector and trigger simulations, to provide a measure of our acceptance for thexcJ states. The larger mass of thexc2 gives a higher efficiency at lowpT共xcJ兲than for thexc1; this difference vanishes for pT共xcJ兲

M共xcJ兲 ¿1. The overall efficiency ratio is

found to beexc1

exc2 苷0.85 60.014, where the uncertainty is

due to the simulated event sample size and uncertainty in thepT共xcJ兲distribution used in the simulation.

Systematic effects that might change the reconstruction efficiency ratio exc1

exc2 would have to affect one spin state

dif-ferently from the other. The decay angle distribution is one such possibility, and an estimate of our sensitivity to differ-ences between the two states is made by convoluting a dis-tribution of the form 11 am2_gcos2共um2_g兲, where am2_g is a constant and um2_g is the angle between the photon andm2 measured in theJ兾cg rest frame, with the effi-ciency distribution. The results of this calculation indicate that values ofam2_g over the range21to 11correspond to a variation in thexcJ reconstruction efficiency of67%.

We have taken half of this variation as the systematic un-certainty on the relative efficiency ratioexc1

exc2 due to possible

decay angle distributions.

Any differences in the production of the two states asso-ciated with the polarization orpT共xcJ兲distributions would

require different production mechanisms for the xc1 and xc2, and is therefore considered to be unlikely. The data are too sparse to provide much guidance. Therefore, we have assigned no systematic uncertainty onexc1

exc2 due to

pos-sible differences in thexc1andxc2production kinematics. The predominantxcJ background is due to photons

re-sulting from the decay ofp0,h, andK_s0mesons produced in association with the J兾c. To model this background, charged tracks that originate from the J兾c vertex in the

data are used to define the momentum of simulatedp0_,h, andK0

s’s produced in the ratio 4:2:1, respectively, as was

done in [4]. The simulated decay of these particles pro-vides a photon spectrum that, taken with the J兾c, yields aJ兾cg mass spectrum whose shape is used to model the background under the xcJ states. Our sensitivity to the

p0:h:K_s0ratio is negligible since the background variation is small over the range ofJ兾cg mass combinations used in this analysis.

Although the production of hc共1P兲 mesons is poorly

established [8], we nonetheless consider it a second source of background to thexc1, due to its mass (3526 6

0.24 MeV兾c2) and the partial reconstruction, hc !

J兾cp0_,p0_{!gg. A Monte Carlo simulation ofh}

c

pro-duction and decay, along with reconstruction of only one final state photon, provided a J兾cg mass spectrum for this background component. We find the overallhc

accep-tance with respect to thexc1to be e_hc

exc1 苷0.523 60.005.

The cross sections for hc and xc1 are predicted to be comparable [10], and the hc branching ratio to J兾cp0

is predicted to be 0.5–1.0% [11]. Taken together, these predictions and our efficiency suggest that the number of hc events in our data should be 0.01– 0.02 times the

number of xc1 events.

The decay of hadrons containing b quarks provides another background to prompt xcJ production. We use

the decay length measured in the SVX to discriminate between xc events produced promptly and through B

decay processes. Since anyJ兾cg combination that origi-nates fromBdecay provides only a partial reconstruction of the B hadron, the proper decay length is not directly measurable. We therefore use the effective decay length leff 苷 Lxy

M共J兾c兲

pT共J兾c兲Fcorr关pT共Jc兲兴 whereM共J兾c兲andpT共J兾c兲

are the mass and transverse momentum, respectively, of theJ兾c,Lxy is the measured displacement of the dimuon

vertex in the direction of its transverse momentum, and

Fcorr关pT共Jc兲兴 is a correction factor between the B and

J兾c momentum, which is obtained by Monte Carlo simulation of Bhadron decay [9].

The J兾cg mass spectrum is shown in Fig. 1. Thexc1 andxc2are clearly resolved, although no evidence for the xc0is seen in this distribution. The effective decay length distribution for events measured in the SVX is shown in Fig. 2. The mass and decay length distributions are fit simultaneously using the maximum likelihood method to obtain the number ofxcJ events due to prompt production.

The likelihood function used is given by

L 苷 N

Y

i苷1

关f₁i_Fx1 1f₂i_Fx2 1共12 f1 2f2兲Fbcki 兴, (1)

where f1, f2 are the fractions of the events in the xc1, xc2 signals, Fxi1, F

i

x2 are the products of the mass and

effective decay length distributions for the signals,Fbcki is

FIG. 1. TheJ兾cg mass spectrum. The background estimate is indicated by the shaded area, and the solid line histogram shows the result of the likelihood fit for thexcJsignals.

The function representing the signal shape consists of two Gaussians whose characteristic width is given by the measured mass uncertainty for each event, times a scale factor. The mass is allowed to vary in the fit, but the differ-ence in mass between the two signals is constrained to the

FIG. 2. TheJ兾cgeffective decay length spectrum for events measured in the SVX. (A) The decay length distribution for can-didates having 3350MeV兾c2 _{,M共J兾cg兲,3470MeV兾c}2 and 3590MeV兾c2_{,M共J兾cg兲,3710MeV兾c}2_{. (B) The} decay length distribution for the xc1, 3492MeV兾c2 ,

M共J兾cg兲,3528MeV兾c2_{. (C) The decay length distribution} for the xc2, 3538MeV兾c2,M共J兾cg兲,3574MeV兾c2.

The fit to the data points is shown in each distribution. The shaded functions in (B,C) indicate the effective decay length distribution due to background sources.

known xc1兾xc2 mass difference of 46MeV兾c2 [8]. The background function shape was determined by the Monte Carlo method described above, and its normalization was allowed to vary in the fit.

The decay length distributions used for both signals and the background consist of a sum of prompt and B de-cay components. The prompt contribution is a Gaussian centered at the beam position, with a characteristic width that is given by the decay length uncertainty calculated for each event. The B decay contribution is a convolu-tion between an exponential distribuconvolu-tion with a character-istic decay length and the decay length uncertainty for each event. The relative contribution between the prompt andB

decay components is allowed to vary for each signal and the background independently. The characteristic proper decay length is constrained to 470mm, the average de-cay length forBhadron mixtures [8], for both signals and background. Although all events were subjected to the same likelihood fit, only the events measured in the SVX have the decay length resolution to contribute significantly to separating the prompt andBdecay components.

The fit gives118.7 613.5 total xcJ events, and a xc1 mass of 3508.3 60.7MeV兾c2. The ratio of events be-tween the xc1and xc2 is measured to be

Nxc2

Nxc1 苷0.63 6 0.15 for the full data sample, where NxcJ is the number

of events obtained for each xcJ. Decays of B hadrons

are found to contribute共865%兲,共186 9%兲, and共256

3%兲 to the xc1, xc2, and background, respectively. The ratio of events in the prompt subset of the data is then

Nxc2 Nxc1

12fb2

12fb1 苷0.56 60.16, where NxcJ is the number of

events measured, and fbJ are the fractions of events due

to B decay. Variation of the characteristic decay length by650mm corresponded to a change in the prompt yield ratio of less than 1023, so no systematic uncertainty has been attributed to the choice of decay length used in the fit. Variation of the hc contribution to the background by

60.01Nxc1produced a60.4%change in the measurement

of the prompt event ratio, which is used as a systematic uncertainty.

The ratio of prompt cross sections for thexc1 andxc2 is given by

sxc2

sx_c1 苷

Nxc2共12fb2兲exc1B共xc1 !J兾cg兲

Nxc1共12fb1兲exc2B共xc2 !J兾cg兲 , (2) where sxcJ is the production cross section, excJ is the

reconstruction acceptance and efficiency, and B共xcJ !

J兾cg兲is the branching ratio into theJ兾cg final state for each of thexcJ states.

The ratio of decay branching ratios is B共xc1!J兾cg兲 B_共xc2!J兾cg兲 苷

27.361.6%

13.561.1% 苷共2.02 60.20兲, assuming the two values are uncorrelated [8]. Consequently, we are left with a relative systematic uncertainty on the ratio of cross sections of 610%due to the branching ratio uncertainties.

un-TABLE I. Systematic uncertainties for the relative rate ofxcJ

production.

Effect Uncertainty

Possiblehc background 10.4%,20

Efficiency ratio uncertainty 61.4%

Decay angular distribution 63.5%

Branching ratios 610%

Total 611%

certainties are combined in quadrature to give the total systematic uncertainty on the cross section ratio. Our final result on the relative rate of prompt production is then

sx_c2 sxc1

苷 0.966 0.27共stat兲 60.11共syst兲. (3)

Previous measurements of thexc2兾xc1ratio have been at fixed target experiments [12], operating at lower energies than those obtained at the Tevatron. Despite significant theoretical efforts to understand charmonium production in that environment [13,14], the comparison between this result and those is not straightforward. The present mea-surement provides a similar constraint on theoretical un-derstanding of charmonium production at the Tevatron. This result appears to prefer an approximately equal pro-duction of the twoxcJ states, although it is consistent with

the expectation that the cross sections are proportional to

共2J 11兲 at highpt共xcJ兲[14]. A recent NRQCD

predic-tion for the cross secpredic-tion ratio is1.160.2[15], in good agreement with this measurement.

We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions. This work was supported by the U.S. Department of En-ergy and National Science Foundation, the Italian Istituto Nazionale di Fisica Nucleare, the Ministry of Education,

Science and Culture of Japan, the Natural Sciences and En-gineering Research Council of Canada, the National Sci-ence Council of the Republic of China, and the A. P. Sloan Foundation.

*Present address: Carnegie Mellon University, Pittsburgh, Pennsylvania 15213.

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