Measurement of J/ψ and ψ (2S) Polarization in pp Collisions at
CLARK, Allan Geoffrey (Collab.), et al.
We have measured the polarization of J/ψ and ψ(2S) mesons produced in pp¯ collisions at s√=1.8TeV, using data collected at the Collider Detector at Fermilab during 1992–1995. The polarization of promptly produced J/ψ [ψ(2S)] mesons is isolated from those produced in B-hadron decay, and measured over the kinematic range 4 [5.5]
CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Measurement of J/ψ and ψ (2S) Polarization in pp Collisions at √s=1.8TeV. Physical Review Letters , 2000, vol. 85, no. 14, p.
DOI : 10.1103/PhysRevLett.85.2886
Disclaimer: layout of this document may differ from the published version.
1 / 1
Measurement of J 兾兾兾 c and c 共共共 2S 兲兲兲 Polarization in pp Collisions at p p p
s 5 1.8 TeV
T. Affolder,21H. Akimoto,43 A. Akopian,36 M. G. Albrow,10 P. Amaral,7S. R. Amendolia,32D. Amidei,24K. Anikeev,22 J. Antos,1G. Apollinari,10T. Arisawa,43 T. Asakawa,41W. Ashmanskas,7M. Atac,10 F. Azfar,29 P. Azzi-Bacchetta,30
N. Bacchetta,30 M. W. Bailey,26 S. Bailey,14 P. de Barbaro,35 A. Barbaro-Galtieri,21 V. E. Barnes,34 B. A. Barnett,17 M. Barone,12 G. Bauer,22 F. Bedeschi,32 S. Belforte,40 G. Bellettini,32 J. Bellinger,44 D. Benjamin,9J. Bensinger,4
A. Beretvas,10 J. P. Berge,10J. Berryhill,7B. Bevensee,31 A. Bhatti,36 M. Binkley,10 D. Bisello,30 R. E. Blair,2 C. Blocker,4K. Bloom,24B. Blumenfeld,17 S. R. Blusk,35A. Bocci,32A. Bodek,35 W. Bokhari,31 G. Bolla,34 Y. Bonushkin,5D. Bortoletto,34 J. Boudreau,33 A. Brandl,26 S. van den Brink,17 C. Bromberg,25 M. Brozovic,9
N. Bruner,26E. Buckley-Geer,10J. Budagov,8H. S. Budd,35 K. Burkett,14G. Busetto,30 A. Byon-Wagner,10 K. L. Byrum,2P. Calafiura,21M. Campbell,24 W. Carithers,21 J. Carlson,24 D. Carlsmith,44 J. Cassada,35A. Castro,30 D. Cauz,40A. Cerri,32 A. W. Chan,1P. S. Chang,1P. T. Chang,1J. Chapman,24C. Chen,31 Y. C. Chen,1M.-T. Cheng,1
M. Chertok,38 G. Chiarelli,32 I. Chirikov-Zorin,8G. Chlachidze,8F. Chlebana,10 L. Christofek,16M. L. Chu,1 C. I. Ciobanu,27 A. G. Clark,13A. Connolly,21J. Conway,37 J. Cooper,10 M. Cordelli,12J. Cranshaw,39 D. Cronin-Hennessy,9R. Cropp,23R. Culbertson,7D. Dagenhart,42 F. DeJongh,10 S. Dell’Agnello,12M. Dell’Orso,32
R. Demina,10 L. Demortier,36M. Deninno,3P. F. Derwent,10 T. Devlin,37 J. R. Dittmann,10 S. Donati,32J. Done,38 T. Dorigo,14 N. Eddy,16 K. Einsweiler,21 J. E. Elias,10 E. Engels, Jr.,33 W. Erdmann,10 D. Errede,16 S. Errede,16 Q. Fan,35R. G. Feild,45C. Ferretti,32 R. D. Field,11 I. Fiori,3B. Flaugher,10G. W. Foster,10M. Franklin,14J. Freeman,10
J. Friedman,22 Y. Fukui,20 I. Furic,22S. Galeotti,32M. Gallinaro,36 T. Gao,31 M. Garcia-Sciveres,21 A. F. Garfinkel,34 P. Gatti,30C. Gay,45 S. Geer,10 D. W. Gerdes,24P. Giannetti,32P. Giromini,12 V. Glagolev,8M. Gold,26 J. Goldstein,10 A. Gordon,14A. T. Goshaw,9Y. Gotra,33K. Goulianos,36 C. Green,34 L. Groer,37C. Grosso-Pilcher,7M. Guenther,34 G. Guillian,24 J. Guimaraes da Costa,14R. S. Guo,1R. M. Haas,11 C. Haber,21E. Hafen,22S. R. Hahn,10 C. Hall,14
T. Handa,15 R. Handler,44W. Hao,39 F. Happacher,12 K. Hara,41 A. D. Hardman,34R. M. Harris,10F. Hartmann,18 K. Hatakeyama,36J. Hauser,5J. Heinrich,31 A. Heiss,18 M. Herndon,17 B. Hinrichsen,23 K. D. Hoffman,34C. Holck,31 R. Hollebeek,31 L. Holloway,16 R. Hughes,27 J. Huston,25J. Huth,14 H. Ikeda,41 J. Incandela,10 G. Introzzi,32 J. Iwai,43
Y. Iwata,15E. James,24H. Jensen,10M. Jones,31U. Joshi,10 H. Kambara,13 T. Kamon,38T. Kaneko,41 K. Karr,42 H. Kasha,45 Y. Kato,28 T. A. Keaffaber,34K. Kelley,22 M. Kelly,24R. D. Kennedy,10 R. Kephart,10 D. Khazins,9 T. Kikuchi,41 B. Kilminster,35 M. Kirby,9M. Kirk,9B. J. Kim,19 D. H. Kim,19 H. S. Kim,16M. J. Kim,19 S. H. Kim,41
Y. K. Kim,21 L. Kirsch,4S. Klimenko,11 P. Koehn,27A. Köngeter,18K. Kondo,43 J. Konigsberg,11 K. Kordas,23 A. Korn,22 A. Korytov,11 E. Kovacs,2J. Kroll,31M. Kruse,35 S. E. Kuhlmann,2K. Kurino,45 T. Kuwabara,41 A. T. Laasanen,34N. Lai,7S. Lami,36 S. Lammel,10 J. I. Lamoureux,4M. Lancaster,21 G. Latino,32T. LeCompte,2 A. M. Lee IV,9K. Lee,39 S. Leone,32J. D. Lewis,10M. Lindgren,5T. M. Liss,16J. B. Liu,35 Y. C. Liu,1N. Lockyer,31
J. Loken,29 M. Loreti,30D. Lucchesi,30P. Lukens,10S. Lusin,44 L. Lyons,29 J. Lys,21R. Madrak,14 K. Maeshima,10 P. Maksimovic,14L. Malferrari,3M. Mangano,32 M. Mariotti,30G. Martignon,30 A. Martin,45 J. A. J. Matthews,26
J. Mayer,23 P. Mazzanti,3K. S. McFarland,35 P. McIntyre,38 E. McKigney,31 M. Menguzzato,30A. Menzione,32 C. Mesropian,36T. Miao,10 R. Miller,25 J. S. Miller,24 H. Minato,41S. Miscetti,12M. Mishina,20 G. Mitselmakher,11
N. Moggi,3E. Moore,26R. Moore,24 Y. Morita,20 M. Mulhearn,22 A. Mukherjee,10T. Muller,18 A. Munar,32 P. Murat,10 S. Murgia,25M. Musy,40J. Nachtman,5S. Nahn,45 H. Nakada,41 T. Nakaya,7I. Nakano,15 C. Nelson,10
D. Neuberger,18 C. Newman-Holmes,10C.-Y. P. Ngan,22 P. Nicolaidi,40H. Niu,4L. Nodulman,2A. Nomerotski,11 S. H. Oh,9T. Ohmoto,15 T. Ohsugi,15R. Oishi,41 T. Okusawa,28 J. Olsen,44 W. Orejudos,21 C. Pagliarone,32 F. Palmonari,32 R. Paoletti,32 V. Papadimitriou,39 S. P. Pappas,45D. Partos,4J. Patrick,10G. Pauletta,40 M. Paulini,21
C. Paus,22L. Pescara,30 T. J. Phillips,9G. Piacentino,32 K. T. Pitts,16R. Plunkett,10 A. Pompos,34 L. Pondrom,44 G. Pope,33M. Popovic,23F. Prokoshin,8J. Proudfoot,2F. Ptohos,12 O. Pukhov,8G. Punzi,32 K. Ragan,23A. Rakitine,22
D. Reher,21 A. Reichold,29 W. Riegler,14A. Ribon,30F. Rimondi,3L. Ristori,32W. J. Robertson,9A. Robinson,23 T. Rodrigo,6S. Rolli,42 L. Rosenson,22R. Roser,10 R. Rossin,30 A. Safonov,36W. K. Sakumoto,35D. Saltzberg,5 A. Sansoni,12 L. Santi,40H. Sato,41 P. Savard,23 P. Schlabach,10E. E. Schmidt,10M. P. Schmidt,45 M. Schmitt,14 L. Scodellaro,30 A. Scott,5A. Scribano,32 S. Segler,10 S. Seidel,26 Y. Seiya,41 A. Semenov,8F. Semeria,3T. Shah,22
M. D. Shapiro,21 P. F. Shepard,33 T. Shibayama,41M. Shimojima,41M. Shochet,7J. Siegrist,21G. Signorelli,32 A. Sill,39 P. Sinervo,23 P. Singh,16 A. J. Slaughter,45K. Sliwa,42C. Smith,17F. D. Snider,10A. Solodsky,36J. Spalding,10
T. Speer,13 P. Sphicas,22 F. Spinella,32 M. Spiropulu,14 L. Spiegel,10J. Steele,44 A. Stefanini,32 J. Strologas,16 F. Strumia,13 D. Stuart,10 K. Sumorok,22 T. Suzuki,41 T. Takano,28 R. Takashima,15 K. Takikawa,41P. Tamburello,9 2886 0031-9007兾00兾85(14)兾2886(6)$15.00 © 2000 The American Physical Society
M. Tanaka,41B. Tannenbaum,5W. Taylor,23M. Tecchio,24 P. K. Teng,1K. Terashi,41 S. Tether,22 D. Theriot,10 R. Thurman-Keup,2P. Tipton,35 S. Tkaczyk,10 K. Tollefson,35A. Tollestrup,40 H. Toyoda,28 W. Trischuk,23 J. F. de Troconiz,14 J. Tseng,22N. Turini,32 F. Ukegawa,41T. Vaiciulis,35J. Valls,37 S. Vejcik III,10G. Velev,10
R. Vidal,10R. Vilar,6I. Volobouev,21D. Vucinic,22R. G. Wagner,2R. L. Wagner,10J. Wahl,7N. B. Wallace,37 A. M. Walsh,37 C. Wang,9C. H. Wang,1M. J. Wang,1T. Watanabe,41 D. Waters,29T. Watts,37 R. Webb,38H. Wenzel,18
W. C. Wester III,10 A. B. Wicklund,2E. Wicklund,10 H. H. Williams,31 P. Wilson,10 B. L. Winer,27D. Winn,24 S. Wolbers,10 D. Wolinski,24J. Wolinski,25 S. Wolinski,24S. Worm,26 X. Wu,43J. Wyss,32A. Yagil,10 W. Yao,21G. P. Yeh,10 P. Yeh,1J. Yoh,10 C. Yosef,25 T. Yoshida,28I. Yu,19 S. Yu,31Z. Yu,45 A. Zanetti,40
F. Zetti,21 and S. Zucchelli3 (CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439
3Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
4Brandeis University, Waltham, Massachusetts 02254
5University of California at Los Angeles, Los Angeles, California 90024
6Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
7Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637
8Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
9Duke University, Durham, North Carolina 27708
10Fermi National Accelerator Laboratory, Batavia, Illinois 60510
11University of Florida, Gainesville, Florida 32611
12Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
13University of Geneva, CH-1211 Geneva 4, Switzerland
14Harvard University, Cambridge, Massachusetts 02138
15Hiroshima University, Higashi-Hiroshima 724, Japan
16University of Illinois, Urbana, Illinois 61801
17The Johns Hopkins University, Baltimore, Maryland 21218
18Institut f ür Experimentelle Kernphysik, Universität Karlsruhe, 76128 Karlsruhe, Germany
19Korean Hadron Collider Laboratory: Kyungpook National University, Taegu 702-701, Seoul National University, Seoul 151-742
and SungKyunKwan University, Suwon 440-746, Korea
20High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
21Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720
22Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
23Institute of Particle Physics: McGill University, Montreal H3A 2T8 and University of Toronto, Toronto, Canada M5S 1A7
24University of Michigan, Ann Arbor, Michigan 48109
25Michigan State University, East Lansing, Michigan 48824
26University of New Mexico, Albuquerque, New Mexico 87131
27The Ohio State University, Columbus, Ohio 43210
28Osaka City University, Osaka 588, Japan
29University of Oxford, Oxford OX1 3RH, United Kingdom
30Universita di Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova, I-35131 Padova, Italy
31University of Pennsylvania, Philadelphia, Pennsylvania 19104
32Istituto Nazionale di Fisica Nucleare, University and Scuola Normale Superiore of Pisa, I-56100 Pisa, Italy
33University of Pittsburgh, Pittsburgh, Pennsylvania 15260
34Purdue University, West Lafayette, Indiana 47907
35University of Rochester, Rochester, New York 14627
36Rockefeller University, New York, New York 10021
37Rutgers University, Piscataway, New Jersey 08855
38Texas A&M University, College Station, Texas 77843
39Texas Tech University, Lubbock, Texas 79409
40Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy
41University of Tsukuba, Tsukuba, Ibaraki 305, Japan
42Tufts University, Medford, Massachusetts 02155
43Waseda University, Tokyo 169, Japan
44University of Wisconsin, Madison, Wisconsin 53706
45Yale University, New Haven, Connecticut 06520 (Received 25 April 2000)
We have measured the polarization of J兾c and c共2S兲 mesons produced inpp collisions at p s苷 1.8TeV, using data collected at the Collider Detector at Fermilab during 1992 – 1995. The polarization of promptly produced J兾c 关c共2S兲兴 mesons is isolated from those produced in B-hadron decay, and measured over the kinematic range 4关5.5兴,PT ,20GeV兾candjyj,0.6. ForPT *12GeV兾cwe do not observe significant polarization in the prompt component.
PACS numbers: 13.85.Qk, 13.20.Gd, 13.88. + e, 14.40.Gx
The production of heavy quarkonia states, cc andbb, provides a useful system for the study of quantum chro- modynamics (QCD), as it involves both perturbative and nonperturbative energy scales. In pp collisions, charmo- nium production occurs through three mechanisms: direct production, the decay of heavier charmonia, and the decay ofb-flavored hadrons. The first two mechanisms are col- lectively known as “prompt” because they are observed to occur at thepp interaction point.
The Collider Detector at Fermilab (CDF) Collaboration previously reported results on the production of J兾c and c共2S兲 mesons [1,2]. The measured cross sections for di- rect production were on the order of 50 times larger than predicted by the color singlet model . However, calcu- lations based on the nonrelativistic QCD (NRQCD) factor- ization formalism [4,5] are able to account for the observed cross sections by including color octet production mecha- nisms. This leads to the prediction that directly produced c mesons will be increasingly transversely polarized at highPT [5 – 7]. [In this Letter we usec to denote either J兾c orc共2S兲mesons.] This is because the production of cmesons withPT ¿ Mc is dominated by gluon fragmen- tation. It is predicted that the gluon’s transverse polariza- tion is preserved as theccpair evolves into a bound state c meson. On the other hand, the color evaporation model predicts an absence of polarization . In this Letter, we report on measurements of the polarization of promptly producedc mesons at CDF. Our analysis also yields as a by-product the effective polarization of thecmesons pro- duced inB-hadron decays.
CDF is a multipurpose detector designed to study high energy pp collisions produced by the Fermilab Tevatron . The CDF coordinate system is defined with the z axis along the proton beam direction. The polar angleu is defined relative to the z axis, r is the perpendicular radius from this axis, and f is the azimuthal angle.
Pseudorapidity is defined as h ⬅2ln关tan共u兾2兲兴. Three charged-particle tracking detectors immersed in a 1.4 T solenoidal magnetic field surround the beam line. This tracking system is contained within a calorimeter, while drift chambers outside the calorimeter identify muon candidates.
The innermost tracking device is a 4-layer silicon mi- crostrip detector (SVX) located at radii between 2.9 and 7.9 cm from the beam axis. The SVX is surrounded by a set of time projection chambers extending out to a radius of 22 cm. An 84-layer cylindrical drift cham- ber (CTC) measures the particle trajectories in the region between 30 and 132 cm from the beam. This tracking
system has high efficiency for detecting charged particles with momentum transverse to the beamPT .0.4GeV兾c and jhj&1.1. Together, the CTC and SVX measure charged-particle transverse momenta with a precision of sPT兾PT 苷0.007 ©0.001PT (with PT in GeV兾c). The impact parameter resolution is sd 苷共13140兾PT兲mm for tracks with SVX and CTC information.
The central muon detection system consists of four layers of planar drift chambers separated from the in- teraction point by five interaction lengths of material.
This system detects muons with PT *1.4GeV兾c and jhj&0.6. Dimuon candidates used in this analysis are collected using a 3-level m1m2 trigger. The first-level trigger requires that two candidates be observed in the muon chambers. For each muon candidate the first-level trigger efficiency rises from ⬃40% at PT 苷1.5GeV兾c to⬃93%for muons withPT .3.0GeV兾c. The second- level trigger requires one or more charged particle tracks in the CTC, reconstructed using the central fast tracker (CFT).
The CFT performs a partial reconstruction of all charged tracks withPTabove⬃2 GeV兾c. Muon candidates found by the first-level trigger are required to match a CFT track within 15± in azimuth. The third-level trigger performs three-dimensional track reconstruction and accepts dimuon masses in a broad window around the J兾c and c共2S兲 masses.
The data used in this study correspond to an integrated luminosity of110pb21 and were collected between 1992 and 1995. Following the online data collection, additional requirements are made offline to identify the signals and to reduce the backgrounds. To identify muon candidates and reduce the rate from sources such as p兾K meson decay-in-flight, we require that each track observed in the muon chambers be associated with a matching CTC track.
These matches are required to pass a maximumx2cut of 9 and 12 (for 1 degree of freedom) in thefandzviews, respectively. Also, we require PT greater than about 2GeV兾c for each muon candidate. This requirement ensures that the muon trigger and reconstruction efficien- cies are well understood, to avoid biases in the decay angular distributions of the charmonia states studied below.
The measurement of the polarization of c mesons is made by analyzing their decays to m1m2 in the helicity basis, in which the spin quantization axis lies along thec direction in theppcenter-of-mass (laboratory) frame. We defineuⴱas the angle between the m1 direction in thec rest frame and thec direction in the laboratory frame. The normalized angular distributionI共cosuⴱ兲is given by
2共a 13兲共11 acos2uⴱ兲. (1) Unpolarizedc mesons havea 苷 0, whereas a 苷11or 21 corresponds to fully transverse or longitudinal polar- izations, respectively. Experimentally, the acceptance is severely reduced as jcosuⴱjapproaches 1, due to the PT
cuts on the muons. Our method for determiningais to fit the observed distributions of cosuⴱto distributions derived from simulated c ! m1m2 decays. The Monte Carlo simulation accounts for the geometric and kinematic ac- ceptance of the detector as well as the reconstruction effi- ciency as a function of cosuⴱ.
In order to extract the polarization parameter a for promptly produced c mesons, we separate the prompt component from theB-decay component using the proper decay length of each event. Forc candidates with one or both muons reconstructed in the SVX (the SVX sample), we define a vector point from theppcollision point to the c decay vertex. The transverse decay length Lxy is then defined as the projection of this vector onto the c trans- verse momentum. The proper decay lengthctis related to the transverse decay length by ct 苷共McLxy兲兾共Fcorrc PTc兲, whereMc is thec mass. HereFcorrc is a correction factor obtained from Monte Carlo studies , which accounts for the fact that we are using thec PT instead of the B hadron PT. Prompt events have ct consistent with zero, whereasBdecays have an exponentialct distribution; the detector resolution smears thectdistribution. We fit thect distribution to obtain the relative fractions of prompt and B-decay production. Details of this fitting procedure are given in . The measured fraction ofJ兾cmesons which come fromB-hadron decay increases from共13.0 60.3兲% at PTJ兾c 苷4GeV兾c to 共4062兲% at 20GeV兾c. For c共2S兲mesons, an increase from共2162兲%to共356 4兲% is seen in the range from 5.5 to20GeV兾c.
The proper decay length measurement allows us to divide the data into two samples: a short-lived sample dominated by prompt production and a long-lived sample dominated byBdecays. The short-lived sample is defined by 20.1#ct # 0.013关0.01兴cm, and the long-lived sample by 0.013关0.01兴#ct # 0.3cm, for the J兾c 关c共2S兲兴analyses, respectively. The boundary between the twoct regions has been optimized separately for theJ兾c and c共2S兲 samples, to maximize the purity of prompt decays in the short-lived sample andBdecays in the long- lived sample. Depending on PTc, the prompt fraction in the short-lived sample ranges from 85% [86%] to 96%
[95%], and theB-decay fraction in the long-lived sample ranges from 83% [86%] to 98% [91%], forJ兾c 关c共2S兲兴, respectively.
TheJ兾cpolarization is measured in sevenPTbins, cov- ering a range of4 20 GeV兾c. Using a 3 standard devia- tion mass window around theJ兾c peak, our data sample consists of 180 000 signal J兾c events, with a signal-to- background ratio of about 13. TheJ兾c sample is divided
into three subsamples: the short-lived and long-lived SVX samples described above, and a third sample (the CTC sample) in which neither muon has SVX information and noctmeasurement is made. In eachPTJ兾c bin, we measure the prompt polarization共aP兲and the effective polarization ofJ兾c mesons fromB-hadron decays共aB兲. (We refer to aB as “effective” because uⴱ is defined by using the lab frame, not theB-hadron rest frame — in effect this dilutes any polarization from theB decay toward zero.) We find that it is not feasible to make separate polarization mea- surements for direct J兾c production and for production fromxcandc共2S兲decays. The latter sources account for 共3666兲% of the prompt component, with only a small PTJ兾c dependence .
TheJ兾cpolarization is measured by fitting cosuⴱdistri- butions in data to a set of Monte Carlo templates . The templates are generated by processing simulated samples ofJ兾c !m1m2decays with a detector and trigger simu- lation. The polarization is obtained using ax2 fit of the data to a weighted sum of transversely polarized and longi- tudinally polarized templates. The fitted weights yield the polarization. Two transverse /longitudinal template pairs are generated, using measured prompt andB-decayPJT兾c spectra . The cosuⴱdistribution of background events is modeled in the fit using sidebands around theJ兾c mass peak. The fit is performed simultaneously on the SVX short-lived, SVX long-lived, and CTC samples, with two fit parameters: aP andaB. To account for the mixture of prompt andB-decay components in each sample, the rela- tive fractions of prompt andB-decay templates in each are fixed in the fit using the results of the lifetime fit. The B-decay fraction in the CTC sample is assumed to be the
FIG. 1. TheJ兾c polarization fit to cosuⴱ distributions in the 12 15GeV兾c bin. Points: sideband-subtracted data in the SVX short-lived, SVX long-lived, and CTC samples. Dashed lines: fit.
TABLE I. Fit results forJ兾c polarization, with statistical and systematic uncertainties.
PT bin MeanPT
共GeV兾c兲 共GeV兾c兲 aP aB
4 – 5 4.5 0.3060.12 60.12 20.4960.4160.13
5 – 6 5.5 0.0160.10 60.07 20.1860.3360.07
6 – 8 6.9 0.17860.07260.036 0.1060.2060.04
8 – 10 8.8 0.32360.09460.019 20.0660.2060.02
10 – 12 10.8 0.2660.14 60.02 20.1960.2360.02
12 – 15 13.2 0.1160.17 60.01 0.1160.310.28 60.02
15 – 20 16.7 20.2960.23 60.03 20.1660.380.33 60.05
same as in the SVX sample, because the two samples differ primarily in thez position of the primary vertex. Within each PTJ兾c bin, a small correction is applied to the PTJ兾c distributions of the Monte Carlo samples so that they match with those in the data. As an example, the fit in the PT
range,12 15GeV兾c, is shown in Fig. 1.
Three sources of systematic uncertainty are evaluated:
the trigger efficiency, the fitted prompt andB-decay frac- tions, and thePJT兾cspectra used in making the Monte Carlo templates. Except in the lowest PT bins, the systematic uncertainties are much smaller than the statistical uncer- tainties. Our fit results are listed in Table I, andaP is com- pared with a theoretical NRQCD prediction  in Fig. 2.
The measurement of thec共2S兲polarization is made in threePT bins covering5.5 20.0GeV兾c. Both muons are
FIG. 2. (a) The fitted polarization of promptJ兾c mesons for jyJ兾cj,0.6. Full error bars denote statistical and systematic uncertainties added in quadrature; ticks denote statistical errors alone. The shaded band shows a NRQCD factorization pre- diction  which includes the contribution fromxc andc共2S兲 decays. (b) The fitted polarization of prompt c共2S兲 mesons for jyc共2S兲j,0.6. Error bars denote statistical and system- atic uncertainties added in quadrature. Shaded bands show two NRQCD factorization predictions [6,7].
required to be reconstructed in the SVX. The resulting dimuon mass distribution is fitted with a Gaussian signal and a linear background. We find a total of 18556 65 signalc共2S兲 events, with a signal-to-background ratio of about 1 in a 3 standard deviation mass window around the c共2S兲mass.
As discussed above, the sample in eachPTbin is further divided into two subsamples based on thectdistribution.
Because the statistics are lower than in theJ兾c case, we use ten bins injcosuⴱj. The number of signal events in eachjcosuⴱjbin is obtained by fitting its mass distribution.
The resultingjcosuⴱjdistributions in the two ct subsam- ples are fitted simultaneously to the predicted number of events to extract the c共2S兲 polarizations for prompt and B-decay production. The number of predicted events in eachjcosuⴱjbin is derived by weighting the normalized angular distributionI共cosuⴱ兲with the detector acceptance . We use the measured prompt andB-decayPTc共2S兲dis- tributions  to calculate the acceptance. As in theJ兾c case, there is a small correlation between the measured PTc共2S兲 distributions and the polarization. A correction is
FIG. 3. Fits to jcosuⴱj distributions in the short-lived c共2S兲 data sample, in the threePTbins. Points: data. Dashed lines: fit.
The acceptance extends farther out injcosuⴱjasPT increases.
TABLE II. Fit results forc共2S兲polarization, with statistical and systematic uncertainties.
PT bin MeanPT
共GeV兾c兲 共GeV兾c兲 aP aB
5.5 – 7.0 6.2 20.0860.6360.02 20.2661.2660.04
7.0 – 9.0 7.9 0.5060.7660.04 21.6860.5560.12
9.0 – 20.0 11.6 20.5460.4860.04 0.2760.8160.06
applied iteratively in the fits to account for this depen- dence. Figure 3 shows the observed angular distributions with their polarization fits for the short-lived sample in the three PTc共2S兲 bins.
Three sources of systematic uncertainty are considered:
the uncertainty in the event yield from the mass fits in the jcosuⴱj bins, the uncertainty due to the error on the fitted prompt and B-decay fractions, and the uncertainty on thejcosuⴱjacceptance from the Monte Carlo modeling of the PTc共2S兲 distributions. The uncertainty due to the trigger efficiency is negligible in the PcT共2S兲 range used.
The systematic uncertainties are much smaller than the statistical uncertainties. The fitted values of aP and aB
as a function of PcT共2S兲 are listed in Table II, andaP is shown in Fig. 2 with the NRQCD predictions [6,7].
In conclusion, we have measured the polarization of J兾c and c共2S兲 mesons produced in 1.8 TeV pp colli- sions. The polarization fromBdecays is generally consis- tent with zero, as expected. In both the J兾c andc共2S兲 cases, we do not observe increasing prompt transverse polarization at PT *12GeV兾c. Our measurements are limited by statistics, especially for thec共2S兲, but they ap- pear to indicate that no large transverse prompt polariza- tion is present at high PT, in disagreement with NRQCD factorization predictions.
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, Sports and Culture of Japan, the Natural Sciences and Engineering Research Council of Canada, the Na-
tional Science Council of the Republic of China, the Swiss National Science Foundation, the A. P. Sloan Foundation, and the Bundesministerium für Bildung und Forschung, Germany.
 The CDF Collaboration, F. Abeet al.,Phys. Rev. Lett.79, 572 (1997).
 The CDF Collaboration, F. Abeet al.,Phys. Rev. Lett.79, 578 (1997).
 M. Cacciari and M. Greco, Phys. Rev. Lett. 73, 1586 (1994); E. Braaten et al., Phys. Lett. B333, 548 (1994);
D. P. Roy and K. Sridhar, Phys. Lett. B339,141 (1994).
 G. Bodwin, E. Braaten, and G. Lepage, Phys. Rev. D51, 1125 (1995);55,5853(E) (1997); E. Braaten and S. Flem- ing, Phys. Rev. Lett. 74,3327 (1995); M. Cacciari et al., Phys. Lett. B 356, 553 (1995); E. Braaten and Y. Chen, Phys. Rev. D54,3216 (1996); P. Cho and A. K. Leibovich, Phys. Rev. D53,150 (1996);ibid.53,6203 (1996).
 P. Cho and M. Wise, Phys. Lett. B346,129 (1995).
 M. Beneke and M. Krämer, Phys. Rev. D55,5269 (1997).
 E. Braaten, B. Kniehl, and J. Lee, hep-ph / 9911436.
 J. Amundsonet al.,Phys. Lett. B390,323 (1997).
 The CDF Collaboration, F. Abeet al.,Nucl. Instrum. Meth- ods Phys. Res., Sect. A 271, 387 (1998); The CDF Col- laboration, F. Abe et al., Phys. Rev. D 52, 4784 (1995);
P. Azziet al.,Nucl. Instrum. Methods Phys. Res., Sect. A 360,137 (1995).
 The CDF Collaboration, F. Abe et al., Phys. Rev. D 57, 5382 (1998).
 R. Cropp, Ph.D. thesis, University of Toronto, 2000.
 C.-Y. P. Ngan, Ph.D. thesis, Massachusetts Institute of Technology, 2000.