Polarizations of J/ψ and ψ(2S) Mesons Produced in pp Collisions at
s = 1.96 TeV
A. Abulencia,24 J. Adelman,13 T. Affolder,10 T. Akimoto,55 M.G. Albrow,17 S. Amerio,43 D. Amidei,35
A. Anastassov,52 K. Anikeev,17 A. Annovi,19 J. Antos,14 M. Aoki,55 G. Apollinari,17 T. Arisawa,57 A. Artikov,15
W. Ashmanskas,17 A. Attal,3 A. Aurisano,42 F. Azfar,42 P. Azzi-Bacchetta,43 P. Azzurri,46 N. Bacchetta,43
W. Badgett,17 A. Barbaro-Galtieri,29 V.E. Barnes,48 B.A. Barnett,25 S. Baroiant,7 V. Bartsch,31 G. Bauer,33
P.-H. Beauchemin,34 F. Bedeschi,46 S. Behari,25 G. Bellettini,46 J. Bellinger,59 A. Belloni,33 D. Benjamin,16
A. Beretvas,17 J. Beringer,29 T. Berry,30 A. Bhatti,50 M. Binkley,17 D. Bisello,43 I. Bizjak,31 R.E. Blair,2
C. Blocker,6 B. Blumenfeld,25 A. Bocci,16 A. Bodek,49 V. Boisvert,49 G. Bolla,48 A. Bolshov,33 D. Bortoletto,48
J. Boudreau,47 A. Boveia,10 B. Brau,10 L. Brigliadori,5 C. Bromberg,36 E. Brubaker,13 J. Budagov,15 H.S. Budd,49
S. Budd,24 K. Burkett,17 G. Busetto,43 P. Bussey,21 A. Buzatu,34 K. L. Byrum,2 S. Cabreraq,16 M. Campanelli,20
M. Campbell,35 F. Canelli,17 A. Canepa,45 S. Carilloi,18 D. Carlsmith,59 R. Carosi,46 S. Carron,34 B. Casal,11
M. Casarsa,54 A. Castro,5 P. Catastini,46 D. Cauz,54 M. Cavalli-Sforza,3 A. Cerri,29 L. Cerritom,31 S.H. Chang,28
Y.C. Chen,1 M. Chertok,7 G. Chiarelli,46 G. Chlachidze,17 F. Chlebana,17 I. Cho,28 K. Cho,28 D. Chokheli,15
J.P. Chou,22 G. Choudalakis,33 S.H. Chuang,52 K. Chung,12 W.H. Chung,59 Y.S. Chung,49 M. Cilijak,46
C.I. Ciobanu,24 M.A. Ciocci,46 A. Clark,20 D. Clark,6 M. Coca,16 G. Compostella,43 M.E. Convery,50 J. Conway,7
B. Cooper,31 K. Copic,35 M. Cordelli,19 G. Cortiana,43 F. Crescioli,46 C. Cuenca Almenarq,7 J. Cuevasl,11
R. Culbertson,17 J.C. Cully,35 S. DaRonco,43 M. Datta,17 S. D’Auria,21 T. Davies,21 D. Dagenhart,17
P. de Barbaro,49 S. De Cecco,51 A. Deisher,29 G. De Lentdeckerc,49 G. De Lorenzo,3 M. Dell’Orso,46 F. Delli Paoli,43
L. Demortier,50 J. Deng,16 M. Deninno,5 D. De Pedis,51 P.F. Derwent,17 G.P. Di Giovanni,44 C. Dionisi,51
B. Di Ruzza,54 J.R. Dittmann,4 M. D’Onofrio,3 C. Dörr,26 S. Donati,46 P. Dong,8 J. Donini,43 T. Dorigo,43
S. Dube,52 J. Efron,39 R. Erbacher,7 D. Errede,24 S. Errede,24 R. Eusebi,17 H.C. Fang,29 S. Farrington,30
I. Fedorko,46 W.T. Fedorko,13 R.G. Feild,60 M. Feindt,26 J.P. Fernandez,32 R. Field,18 G. Flanagan,48 R. Forrest,7
S. Forrester,7 M. Franklin,22 J.C. Freeman,29 I. Furic,13 M. Gallinaro,50 J. Galyardt,12 J.E. Garcia,46
F. Garberson,10 A.F. Garfinkel,48 C. Gay,60 H. Gerberich,24 D. Gerdes,35 S. Giagu,51 P. Giannetti,46 K. Gibson,47
J.L. Gimmell,49 C. Ginsburg,17 N. Giokarisa,15 M. Giordani,54 P. Giromini,19 M. Giunta,46 G. Giurgiu,25
V. Glagolev,15 D. Glenzinski,17 M. Gold,37 N. Goldschmidt,18 J. Goldsteinb,42 A. Golossanov,17 G. Gomez,11
G. Gomez-Ceballos,33 M. Goncharov,53 O. González,32 I. Gorelov,37 A.T. Goshaw,16 K. Goulianos,50 A. Gresele,43
S. Grinstein,22 C. Grosso-Pilcher,13 R.C. Group,17 U. Grundler,24 J. Guimaraes da Costa,22 Z. Gunay-Unalan,36
C. Haber,29 K. Hahn,33 S.R. Hahn,17 E. Halkiadakis,52 A. Hamilton,20 B.-Y. Han,49 J.Y. Han,49 R. Handler,59
F. Happacher,19 K. Hara,55 D. Hare,52 M. Hare,56 S. Harper,42 R.F. Harr,58 R.M. Harris,17 M. Hartz,47
K. Hatakeyama,50 J. Hauser,8 C. Hays,42 M. Heck,26 A. Heijboer,45 B. Heinemann,29 J. Heinrich,45 C. Henderson,33
M. Herndon,59 J. Heuser,26 D. Hidas,16 C.S. Hillb,10 D. Hirschbuehl,26 A. Hocker,17 A. Holloway,22 S. Hou,1
M. Houlden,30 S.-C. Hsu,9 B.T. Huffman,42 R.E. Hughes,39 U. Husemann,60 J. Huston,36 J. Incandela,10
G. Introzzi,46 M. Iori,51 A. Ivanov,7 B. Iyutin,33 E. James,17 D. Jang,52 B. Jayatilaka,16 D. Jeans,51 E.J. Jeon,28
S. Jindariani,18 W. Johnson,7 M. Jones,48 K.K. Joo,28 S.Y. Jun,12 J.E. Jung,28 T.R. Junk,24 T. Kamon,53
P.E. Karchin,58 Y. Kato,41 Y. Kemp,26 R. Kephart,17 U. Kerzel,26 V. Khotilovich,53 B. Kilminster,39 D.H. Kim,28
H.S. Kim,28 J.E. Kim,28 M.J. Kim,17 S.B. Kim,28 S.H. Kim,55 Y.K. Kim,13 N. Kimura,55 L. Kirsch,6 S. Klimenko,18
M. Klute,33 B. Knuteson,33 B.R. Ko,16 K. Kondo,57 D.J. Kong,28 J. Konigsberg,18 A. Korytov,18 A.V. Kotwal,16
A.C. Kraan,45 J. Kraus,24 M. Kreps,26 J. Kroll,45 N. Krumnack,4 M. Kruse,16 V. Krutelyov,10 T. Kubo,55
S. E. Kuhlmann,2 T. Kuhr,26 N.P. Kulkarni,58 Y. Kusakabe,57 S. Kwang,13 A.T. Laasanen,48 S. Lai,34 S. Lami,46
S. Lammel,17 M. Lancaster,31 R.L. Lander,7 K. Lannon,39 A. Lath,52 G. Latino,46 I. Lazzizzera,43 T. LeCompte,2
J. Lee,49 J. Lee,28 Y.J. Lee,28 S.W. Leeo,53 R. Lefèvre,20 N. Leonardo,33 S. Leone,46 S. Levy,13 J.D. Lewis,17
C. Lin,60 C.S. Lin,17 M. Lindgren,17 E. Lipeles,9 A. Lister,7 D.O. Litvintsev,17 T. Liu,17 N.S. Lockyer,45
A. Loginov,60 M. Loreti,43 R.-S. Lu,1 D. Lucchesi,43 P. Lujan,29 P. Lukens,17 G. Lungu,18 L. Lyons,42 J. Lys,29
R. Lysak,14 E. Lytken,48 P. Mack,26 D. MacQueen,34 R. Madrak,17 K. Maeshima,17 K. Makhoul,33 T. Maki,23
P. Maksimovic,25 S. Malde,42 S. Malik,31 G. Manca,30 F. Margaroli,5 R. Marginean,17 C. Marino,26
C.P. Marino,24 A. Martin,60 M. Martin,25 V. Marting,21 M. Mart́ınez,3 R. Mart́ınez-Ballaŕın,32 T. Maruyama,55
P. Mastrandrea,51 T. Masubuchi,55 H. Matsunaga,55 M.E. Mattson,58 R. Mazini,34 P. Mazzanti,5 K.S. McFarland,49
P. McIntyre,53 R. McNultyf ,30 A. Mehta,30 P. Mehtala,23 S. Menzemerh,11 A. Menzione,46 P. Merkel,48
C. Mesropian,50 A. Messina,36 T. Miao,17 N. Miladinovic,6 J. Miles,33 R. Miller,36 C. Mills,10 M. Milnik,26
A. Mitra,1 G. Mitselmakher,18 A. Miyamoto,27 S. Moed,20 N. Moggi,5 B. Mohr,8 C.S. Moon,28 R. Moore,17
http://arxiv.org/abs/0704.0638v2
M. Morello,46 P. Movilla Fernandez,29 J. Mülmenstädt,29 A. Mukherjee,17 Th. Muller,26 R. Mumford,25
P. Murat,17 M. Mussini,5 J. Nachtman,17 A. Nagano,55 J. Naganoma,57 K. Nakamura,55 I. Nakano,40 A. Napier,56
V. Necula,16 C. Neu,45 M.S. Neubauer,9 J. Nielsenn,29 L. Nodulman,2 O. Norniella,3 E. Nurse,31 S.H. Oh,16
Y.D. Oh,28 I. Oksuzian,18 T. Okusawa,41 R. Oldeman,30 R. Orava,23 K. Osterberg,23 C. Pagliarone,46
E. Palencia,11 V. Papadimitriou,17 A. Papaikonomou,26 A.A. Paramonov,13 B. Parks,39 S. Pashapour,34
J. Patrick,17 G. Pauletta,54 M. Paulini,12 C. Paus,33 D.E. Pellett,7 A. Penzo,54 T.J. Phillips,16 G. Piacentino,46
J. Piedra,44 L. Pinera,18 K. Pitts,24 C. Plager,8 L. Pondrom,59 X. Portell,3 O. Poukhov,15 N. Pounder,42
F. Prakoshyn,15 A. Pronko,17 J. Proudfoot,2 F. Ptohose,19 G. Punzi,46 J. Pursley,25 J. Rademackerb,42
A. Rahaman,47 V. Ramakrishnan,59 N. Ranjan,48 I. Redondo,32 B. Reisert,17 V. Rekovic,37 P. Renton,42
M. Rescigno,51 S. Richter,26 F. Rimondi,5 L. Ristori,46 A. Robson,21 T. Rodrigo,11 E. Rogers,24 S. Rolli,56
R. Roser,17 M. Rossi,54 R. Rossin,10 P. Roy,34 A. Ruiz,11 J. Russ,12 V. Rusu,13 H. Saarikko,23 A. Safonov,53
W.K. Sakumoto,49 G. Salamanna,51 O. Saltó,3 L. Santi,54 S. Sarkar,51 L. Sartori,46 K. Sato,17 P. Savard,34
A. Savoy-Navarro,44 T. Scheidle,26 P. Schlabach,17 E.E. Schmidt,17 M.P. Schmidt,60 M. Schmitt,38 T. Schwarz,7
L. Scodellaro,11 A.L. Scott,10 A. Scribano,46 F. Scuri,46 A. Sedov,48 S. Seidel,37 Y. Seiya,41 A. Semenov,15
L. Sexton-Kennedy,17 A. Sfyrla,20 S.Z. Shalhout,58 M.D. Shapiro,29 T. Shears,30 P.F. Shepard,47 D. Sherman,22
M. Shimojimak,55 M. Shochet,13 Y. Shon,59 I. Shreyber,20 A. Sidoti,46 P. Sinervo,34 A. Sisakyan,15 A.J. Slaughter,17
J. Slaunwhite,39 K. Sliwa,56 J.R. Smith,7 F.D. Snider,17 R. Snihur,34 M. Soderberg,35 A. Soha,7 S. Somalwar,52
V. Sorin,36 J. Spalding,17 F. Spinella,46 T. Spreitzer,34 P. Squillacioti,46 M. Stanitzki,60 A. Staveris-Polykalas,46
R. St. Denis,21 B. Stelzer,8 O. Stelzer-Chilton,42 D. Stentz,38 J. Strologas,37 D. Stuart,10 J.S. Suh,28 A. Sukhanov,18
H. Sun,56 I. Suslov,15 T. Suzuki,55 A. Taffardp,24 R. Takashima,40 Y. Takeuchi,55 R. Tanaka,40 M. Tecchio,35
P.K. Teng,1 K. Terashi,50 J. Thomd,17 A.S. Thompson,21 E. Thomson,45 P. Tipton,60 V. Tiwari,12 S. Tkaczyk,17
D. Toback,53 S. Tokar,14 K. Tollefson,36 T. Tomura,55 D. Tonelli,46 S. Torre,19 D. Torretta,17 S. Tourneur,44
W. Trischuk,34 R. Tsuchiya,57 S. Tsuno,40 Y. Tu,45 N. Turini,46 F. Ukegawa,55 S. Uozumi,55 S. Vallecorsa,20
N. van Remortel,23 A. Varganov,35 E. Vataga,37 F. Vazquezi,18 G. Velev,17 G. Veramendi,24 V. Veszpremi,48
M. Vidal,32 R. Vidal,17 I. Vila,11 R. Vilar,11 T. Vine,31 I. Vollrath,34 I. Volobouevo,29 G. Volpi,46 F. Würthwein,9
P. Wagner,53 R.G. Wagner,2 R.L. Wagner,17 J. Wagner,26 W. Wagner,26 R. Wallny,8 S.M. Wang,1 A. Warburton,34
D. Waters,31 M. Weinberger,53 W.C. Wester III,17 B. Whitehouse,56 D. Whiteson,45 A.B. Wicklund,2
E. Wicklund,17 G. Williams,34 H.H. Williams,45 P. Wilson,17 B.L. Winer,39 P. Wittichd,17 S. Wolbers,17
C. Wolfe,13 T. Wright,35 X. Wu,20 S.M. Wynne,30 A. Yagil,9 K. Yamamoto,41 J. Yamaoka,52 T. Yamashita,40
C. Yang,60 U.K. Yangj,13 Y.C. Yang,28 W.M. Yao,29 G.P. Yeh,17 J. Yoh,17 K. Yorita,13 T. Yoshida,41 G.B. Yu,49
I. Yu,28 S.S. Yu,17 J.C. Yun,17 L. Zanello,51 A. Zanetti,54 I. Zaw,22 X. Zhang,24 J. Zhou,52 and S. Zucchelli5
(CDF Collaboration∗)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439
3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain
4Baylor University, Waco, Texas 76798
5Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
6Brandeis University, Waltham, Massachusetts 02254
7University of California, Davis, Davis, California 95616
8University of California, Los Angeles, Los Angeles, California 90024
9University of California, San Diego, La Jolla, California 92093
10University of California, Santa Barbara, Santa Barbara, California 93106
11Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
12Carnegie Mellon University, Pittsburgh, PA 15213
13Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637
14Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia
15Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
16Duke University, Durham, North Carolina 27708
∗ With visitors from aUniversity of Athens, bUniversity of Bristol, cUniversity Libre de Bruxelles, dCornell University, eUniversity
of Cyprus, fUniversity of Dublin, gUniversity of Edinburgh, hUniversity of Heidelberg, iUniversidad Iberoamericana, jUniversity of
Manchester, kNagasaki Institute of Applied Science, lUniversity de Oviedo, mUniversity of London, Queen Mary College, nUniversity
of California Santa Cruz, oTexas Tech University, pUniversity of California Irvine, and qIFIC(CSIC-Universitat de Valencia).
17Fermi National Accelerator Laboratory, Batavia, Illinois 60510
18University of Florida, Gainesville, Florida 32611
19Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
20University of Geneva, CH-1211 Geneva 4, Switzerland
21Glasgow University, Glasgow G12 8QQ, United Kingdom
22Harvard University, Cambridge, Massachusetts 02138
23Division of High Energy Physics, Department of Physics,
University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland
24University of Illinois, Urbana, Illinois 61801
25The Johns Hopkins University, Baltimore, Maryland 21218
26Institut für Experimentelle Kernphysik, Universität Karlsruhe, 76128 Karlsruhe, Germany
27High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
28Center for High Energy Physics: Kyungpook National University,
Taegu 702-701, Korea; Seoul National University, Seoul 151-742,
Korea; SungKyunKwan University, Suwon 440-746, Korea
29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720
30University of Liverpool, Liverpool L69 7ZE, United Kingdom
31University College London, London WC1E 6BT, United Kingdom
32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain
33Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
34Institute of Particle Physics: McGill University, Montréal,
Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7
35University of Michigan, Ann Arbor, Michigan 48109
36Michigan State University, East Lansing, Michigan 48824
37University of New Mexico, Albuquerque, New Mexico 87131
38Northwestern University, Evanston, Illinois 60208
39The Ohio State University, Columbus, Ohio 43210
40Okayama University, Okayama 700-8530, Japan
41Osaka City University, Osaka 588, Japan
42University of Oxford, Oxford OX1 3RH, United Kingdom
43University of Padova, Istituto Nazionale di Fisica Nucleare,
Sezione di Padova-Trento, I-35131 Padova, Italy
44LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France
45University of Pennsylvania, Philadelphia, Pennsylvania 19104
46Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa,
Siena and Scuola Normale Superiore, I-56127 Pisa, Italy
47University of Pittsburgh, Pittsburgh, Pennsylvania 15260
48Purdue University, West Lafayette, Indiana 47907
49University of Rochester, Rochester, New York 14627
50The Rockefeller University, New York, New York 10021
51Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1,
University of Rome “La Sapienza,” I-00185 Roma, Italy
52Rutgers University, Piscataway, New Jersey 08855
53Texas A&M University, College Station, Texas 77843
54Istituto Nazionale di Fisica Nucleare, University of Trieste/ Udine, Italy
55University of Tsukuba, Tsukuba, Ibaraki 305, Japan
56Tufts University, Medford, Massachusetts 02155
57Waseda University, Tokyo 169, Japan
58Wayne State University, Detroit, Michigan 48201
59University of Wisconsin, Madison, Wisconsin 53706
60Yale University, New Haven, Connecticut 06520
We have measured the polarizations of J/ψ and ψ(2S) mesons as functions of their transverse
momentum pT when they are produced promptly in the rapidity range |y| < 0.6 with pT ≥ 5 GeV/c.
The analysis is performed using a data sample with an integrated luminosity of about 800 pb−1
collected by the CDF II detector. For both vector mesons, we find that the polarizations become
increasingly longitudinal as pT increases from 5 to 30 GeV/c. These results are compared to the pre-
dictions of nonrelativistic quantum chromodynamics and other contemporary models. The effective
polarizations of J/ψ and ψ(2S) mesons from B-hadron decays are also reported.
PACS numbers: 13.88.+e, 13.20.Gd, 14.40.Lb
An effective field theory, nonrelativistic quantum chromodynamics (NRQCD) [1], provides a rigorous formalism for
calculating the production rates of charmonium (cc) states. NRQCD explains the direct production cross sections
for J/ψ and ψ(2S) mesons observed at the Tevatron [2, 3] and predicts their increasingly transverse polarizations
as pT increases, where pT is the meson’s momentum component perpendicular to the colliding beam direction [4].
The first polarization measurements at the Tevatron [5] did not show such a trend. This Letter reports on J/ψ and
ψ(2S) polarization measurements with a larger data sample than previously available. This allows the extension of
the measurement to a higher pT region and makes a more stringent test of the NRQCD prediction.
The NRQCD cross section calculation for cc production separates the long-distance nonperturbative contributions
from the short-distance perturbative behavior. The former is treated as an expansion of the matrix elements in powers
of the nonrelativistic charm-quark velocity. This expansion can be computed by lattice simulations, but currently the
expansion coefficients are treated as universal parameters, which are adjusted to match the cross section measurements
at the Tevatron [2, 3]. The calculation also applies to cc production in ep collisions, but HERA measurements of J/ψ
polarization tend to disagree with the NRQCD prediction [6]. These difficulties have led some authors to explore
alternative power expansions of the long-distance interactions for the cc system [7]. There are also new QCD-inspired
models, the gluon tower model [8] and the kT -factorization model [9], that accomodate vector-meson cross sections at
both HERA and the Tevatron and predict the vector-meson polarizations as functions of pT . These authors emphasize
that measuring the vector-meson polarizations as functions of pT is a crucial test of NRQCD.
The CDF II detector is described in detail elsewhere [3, 10]. In this analysis, the essential features are a muon system
covering the central region of pseudorapidity, |η| < 0.6, and the tracking system, immersed in the 1.4 T solenoidal
magnetic field and composed of a silicon microstrip detector and a cylindrical drift chamber called the central outer
tracker (COT). The data used here correspond to an integrated luminosity of about 800 pb−1 and were recorded
between June 2004 and February 2006 by a dimuon trigger, which requires two opposite-charge muon candidates,
each having pT > 1.5 GeV/c.
Decays of vector mesons V (either J/ψ or ψ(2S)) → µ+µ− are selected from dimuon events for which each track
has segments reconstructed in both the COT and the silicon microstrip detector. The pT of each muon is required
to exceed 1.75 GeV/c in order to guarantee a well-measured trigger efficiency. The muon track pair is required to
be consistent with originating from a common vertex and to have an invariant mass M within the range 2.8 (3.4) <
M < 3.4 (3.9) GeV/c2 to be considered as a J/ψ (ψ(2S)) candidate. To have a reasonable polarization sensitivity,
the vector-meson candidates are required to have pT ≥ 5 GeV/c in the rapidity range |y (≡ 12 ln
E+p||
E−p||
)| < 0.6, where
E is the energy and p|| is the momentum parallel to the beam direction of the dimuon system. Events are separated
into a signal region and sideband regions, as indicated in Fig. 1. The fit to the data uses a double (single) Gaussian
for the J/ψ (ψ(2S)) signal and a linear background shape. The fits are used only to define signal and background
regions. The signal regions are within 3σV of the fitted mass peaks MV , where σV is the width obtained in the fit
to the invariant mass distribution. Both the background distribution and the quantity of background events under
the signal peak are estimated by events from the lower and upper mass sidebands. The sideband regions are 7σJ/ψ
(4σψ(2S)) away from the signal region for J/ψ (ψ(2S)).
For each candidate, we compute ct =MLxy/pT , where t is the proper decay time and Lxy is the transverse distance
between the beam line and the decay vertex in the plane normal to the beam direction. The ct distributions of the
selected dimuon events are shown in Fig. 2. The ct distribution of prompt events is a Gaussian distribution centered
at zero due to finite tracking resolution. For J/ψ, the prompt events are due to direct production or the decays of
heavier charmonium states such as χc and ψ(2S); for ψ(2S), the prompt events are almost entirely due to direct
production since heavier charmonium states rarely decay to ψ(2S) [11]. Both the J/ψ and the ψ(2S) samples contain
significant numbers of events originating from long-lived B-hadron decays, as can be seen from the event excess at
positive ct. We have measured the fraction of B → J/ψ + X events in the J/ψ sample and found agreement with
other results [3]. We select prompt events by requiring the sum of the squared impact parameter significances of the
positively and negatively charged muon tracks S ≡ ( d
)2 + (
)2 ≤ 8. The impact parameter d0 is the distance
of closest approach of the track to the beam line in the transverse plane. Vector-meson candidates from B-hadron
decays are selected by requiring S > 16 and ct > 0.03 cm. This requirement retains a negligible fraction of prompt
events in the B sample.
To measure the polarizations of prompt J/ψ and ψ(2S) mesons as functions of pT , the J/ψ events are analyzed in
six pT bins and the ψ(2S) events in three bins, shown in Table I. We determine the fraction of B-decay background
remaining in prompt samples fbkd by subtracting the number of negative ct events from the number of positive ct
events. Only a negligible fraction (< 0.2%) of B decays produce vector-meson events with negative ct. For both
vector mesons, fbkd increases with pT , as listed in Table I. The prompt polarization from the fitting algorithm is
corrected for this contamination.
M (GeV/c
2.8 2.9 3 3.1 3.2 3.3 3.4
M (GeV/c
3.4 3.5 3.6 3.7 3.8 3.9
FIG. 1: Invariant mass distributions for (a) J/ψ and (b) ψ(2S) candidates. The curves are fits to the data. The solid (dashed)
lines indicate the signal (sideband) regions.
ct (cm)
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
510 (a)
ct (cm)
-0.2 -0.1 0 0.1 0.2
410 (b)
FIG. 2: Sideband-subtracted ct distributions for (a) J/ψ and (b) ψ(2S) events. The prompt Gaussian peak, positive excess
from B-hadron decays, and negative tail from mismeasured events are shown. The dotted line is the reflection of the negative
ct histogram about zero.
The polarization information is contained in the distribution of the muon decay angle θ∗, the angle of the µ+ in the
rest frame of vector meson with respect to the vector-meson boost direction in the laboratory system. The decay angle
distribution depends on the polarization parameter α:
d cos θ∗
∝ 1 + α cos2θ∗ (−1 ≤ α ≤ 1). For fully transverse
(longitudinal) polarization, α = +1 (−1). Intermediate values of α indicate a mixture of transverse and longitudinal
polarization.
A template method is used to account for acceptance and efficiency. Two sets of cos θ∗ distributions for fully
polarized decays of J/ψ and ψ(2S) events, one longitudinal (L) and the other transverse (T ), are produced with the
CDF simulation program using the efficiency-corrected pT spectra measured from data [3, 12]. We use the muon
trigger efficiency measured using data as a function of track parameters (pT , η, φ) to account for detector non-
uniformities. The parametrized efficiency is used as a filter on all simulated muons. Events that pass reconstruction
represent the behavior of fully polarized vector-meson decays in the detector.
The fitting algorithm [5] uses two binned cos θ∗ distributions for each pT bin, one made by NS events from the
signal region (signal plus background) and the other made by NB events from the sideband regions (background).
The χ2 minimization is done simultaneously for both cos θ∗ distributions. The fitting algorithm includes an individual
background term for each cos θ∗ bin, normalized to NB. Simulation shows that the cos θ
∗ resolution at all decay
angles over the entire pT range is much smaller than the bin width of 0.05 (0.10 for ψ(2S)) used here. The data, fit,
and template distributions for the worst fit (9% probability) in the J/ψ data are shown in Fig. 3.
*θcos 
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
 (GeV/c) <  9T p≤ 7 
FIG. 3: cos θ∗ distribution of data (points) and polarization fit for the worst χ2 probability bin in the J/ψ data. The dotted
(dashed) line is the template for fully L (T) polarization. The fit describes the overall trend of the data well.
All systematic uncertainties are much smaller than the statistical uncertainties. Varying the pT spectrum used in
the simulation by 1σ changed the polarization parameter for J/ψ at most by 0.002. A systematic uncertainty of 0.007
was estimated by the change in the polarization parameter when a modification was made on all trigger efficiencies
by ±1σ. For ψ(2S), the dominant systematic uncertainty came from the yield estimate because of the radiative tail
and the large background. The total systematic uncertainties shown in Table I were taken to be the quadrature
sum of these individual uncertainties. Other possible sources of systematic uncertainties - signal definition and cos θ∗
binning - were determined to be negligible. Corrections to prompt polarization from B-decay contamination were
small, so that uncertainties on B-decay polarization measurements also had negligible effect. No φ-dependence of the
polarizations was observed.
The polarization of J/ψ mesons from inclusive Bu and Bd decays was measured by the BABAR collaboration [13].
In this analysis, the B-hadron direction is unknown, so we define θ∗ with respect to the J/ψ direction in the laboratory
system. The resulting polarization is somewhat diluted. As discussed in Ref. [3], CDF uses a Monte Carlo procedure to
adapt the BABAR measurement to predict the effective J/ψ polarization parameter. For the J/ψ events with 5 ≤ pT <
30 GeV/c, the CDF model for Bu and Bd decays gives αeff = −0.145± 0.009, independent of pT . We have measured
the polarization of vector mesons from B-hadron decays. For J/ψ, we find αeff = −0.106±0.033 (stat)±0.007 (syst).
At this level of accuracy, a polarization contribution by J/ψ mesons from Bs and b-baryon decays cannot be separated
from the effective polarization due to those from Bu and Bd decays. We also report the first measurement of the
ψ(2S) polarization from B-hadron decays: αeff = 0.36± 0.25 (stat)± 0.03 (syst).
The polarization parameters for both prompt vector mesons corrected for fbkd using our experimental results on αeff
are listed as functions of pT in Table I and are plotted in Fig. 4. The polarization parameters for J/ψ are negative
over the entire pT range of measurement and become increasingly negative (favoring longitudinal polarization) as
pT increases. For ψ(2S), the central value of the polarization parameter is positive at small pT , but, given the
uncertainties, its behavior is consistent with the trend shown in the measurement of the J/ψ polarization.
The polarization behavior measured previously with 110 pb−1 [5] is not consistent with the results presented here.
This is a differential measurement, and the muon efficiencies in this analysis are true dimuon efficiencies. In Ref. [5],
they are the product of independent single muon efficiencies. The efficiency for muons with pT < 4 GeV/c is crucial for
good polarization sensitivity. In this analysis, the muon efficiency varies smoothly from 99% to 97% over this range.
In the analysis of Ref. [5], it varied from 93% to 40% with significant jumps between individual data points. Data
from periods of drift chamber aging were omitted from this analysis because the polarization results were inconsistent
with the remainder of the data. Studies such as this were not done in the analysis of Ref. [5]. The systematics of the
polarization measurement are much better understood in this analysis.
These polarization measurements for the charmed vector mesons extend to a pT regime where perturbative QCD
should be applicable. The results are compared to the predictions of NRQCD and the kT -factorization model in Fig. 4.
The prediction of the kT -factorization model is presented for pT < 20 GeV/c and does not include the contribution
pT (GeV/c) <pT > (GeV/c) fbkd(%) α χ
2/d.o.f
J/ψ 5−6 5.5 2.8± 0.2 −0.004± 0.029± 0.009 15.5/21
6−7 6.5 3.4± 0.2 −0.015± 0.028± 0.010 24.1/23
7−9 7.8 4.1± 0.2 −0.077± 0.023± 0.013 35.1/25
9−12 10.1 5.7± 0.3 −0.094± 0.028± 0.007 34.0/29
12−17 13.7 6.7± 0.6 −0.140± 0.043± 0.007 35.0/31
17−30 20.0 13.6± 1.4 −0.187± 0.090± 0.007 33.9/35
ψ(2S) 5−7 5.9 1.6± 0.9 +0.314± 0.242± 0.028 13.1/11
7−10 8.2 4.9± 1.2 −0.013± 0.201± 0.035 18.5/13
10−30 12.6 8.6± 1.8 −0.374± 0.222± 0.062 26.9/17
TABLE I: Polarization parameter α for prompt production in each pT bin. The first (second) uncertainty is statistical (sys-
tematic). <pT > is the average transverse momentum.
 (GeV/c)Tp
5 10 15 20 25 30
CDF Data
NRQCD
-factorizationTk
 (GeV/c)Tp
5 10 15 20 25 30
CDF Data
NRQCD
-factorizationTk
FIG. 4: Prompt polarizations as functions of pT : (a) J/ψ and (b) ψ(2S). The band (line) is the prediction from NRQCD [4]
(the kT -factorization model [9]).
from the decays of heavier charmonium states for J/ψ production. The polarizations for prompt production of
both vector mesons become increasingly longitudinal as pT increases beyond 10 GeV/c. This behavior is in strong
disagreement with the NRQCD prediction of large transverse polarization at high pT . It is striking that the NRQCD
calculation and the other models reproduce the measured J/ψ and ψ(2S) cross sections at the Tevatron, but fail to
describe the polarization at high pT . This indicates that there is some important aspect of the production mechanism
that is not yet understood.
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 Energy and National Science Foundation; the Italian Istituto
Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the
Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of
China; the Swiss National Science Foundation; the A.P. Sloan Foundation; the Bundesministerium für Bildung und
Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the
Particle Physics and Astronomy Research Council and the Royal Society, UK; the Institut National de Physique
Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Comisión Interministerial
de Ciencia y Tecnoloǵıa, Spain; the European Community’s Human Potential Programme; the Slovak R&D Agency;
and the Academy of Finland.
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	References

  We have measured the polarizations of $\jpsi$ and $\psiprime$ mesons as
functions of their transverse momentum $\pt$ when they are produced promptly in
the rapidity range $|y|<0.6$ with $\pt \geq 5 \pgev$. The analysis is performed
using a data sample with an integrated luminosity of about $800 \ipb$ collected
by the CDF II detector. For both vector mesons, we find that the polarizations
become increasingly longitudinal as $\pt$ increases from 5 to $30 \pgev$. These
results are compared to the predictions of nonrelativistic quantum
chromodynamics and other contemporary models. The effective polarizations of
$\jpsi$ and $\psiprime$ mesons from $B$-hadron decays are also reported.

Polarizations of J/ψ and ψ(2S) Mesons Produced in pp Collisions at
s = 1.96 TeV
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P. de Barbaro,49 S. De Cecco,51 A. Deisher,29 G. De Lentdeckerc,49 G. De Lorenzo,3 M. Dell’Orso,46 F. Delli Paoli,43
L. Demortier,50 J. Deng,16 M. Deninno,5 D. De Pedis,51 P.F. Derwent,17 G.P. Di Giovanni,44 C. Dionisi,51
B. Di Ruzza,54 J.R. Dittmann,4 M. D’Onofrio,3 C. Dörr,26 S. Donati,46 P. Dong,8 J. Donini,43 T. Dorigo,43
S. Dube,52 J. Efron,39 R. Erbacher,7 D. Errede,24 S. Errede,24 R. Eusebi,17 H.C. Fang,29 S. Farrington,30
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(CDF Collaboration∗)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439
3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain
4Baylor University, Waco, Texas 76798
5Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
6Brandeis University, Waltham, Massachusetts 02254
7University of California, Davis, Davis, California 95616
8University of California, Los Angeles, Los Angeles, California 90024
9University of California, San Diego, La Jolla, California 92093
10University of California, Santa Barbara, Santa Barbara, California 93106
11Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
12Carnegie Mellon University, Pittsburgh, PA 15213
13Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637
14Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia
15Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
16Duke University, Durham, North Carolina 27708
∗ With visitors from aUniversity of Athens, bUniversity of Bristol, cUniversity Libre de Bruxelles, dCornell University, eUniversity
of Cyprus, fUniversity of Dublin, gUniversity of Edinburgh, hUniversity of Heidelberg, iUniversidad Iberoamericana, jUniversity of
Manchester, kNagasaki Institute of Applied Science, lUniversity de Oviedo, mUniversity of London, Queen Mary College, nUniversity
of California Santa Cruz, oTexas Tech University, pUniversity of California Irvine, and qIFIC(CSIC-Universitat de Valencia).
17Fermi National Accelerator Laboratory, Batavia, Illinois 60510
18University of Florida, Gainesville, Florida 32611
19Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
20University of Geneva, CH-1211 Geneva 4, Switzerland
21Glasgow University, Glasgow G12 8QQ, United Kingdom
22Harvard University, Cambridge, Massachusetts 02138
23Division of High Energy Physics, Department of Physics,
University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland
24University of Illinois, Urbana, Illinois 61801
25The Johns Hopkins University, Baltimore, Maryland 21218
26Institut für Experimentelle Kernphysik, Universität Karlsruhe, 76128 Karlsruhe, Germany
27High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
28Center for High Energy Physics: Kyungpook National University,
Taegu 702-701, Korea; Seoul National University, Seoul 151-742,
Korea; SungKyunKwan University, Suwon 440-746, Korea
29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720
30University of Liverpool, Liverpool L69 7ZE, United Kingdom
31University College London, London WC1E 6BT, United Kingdom
32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain
33Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
34Institute of Particle Physics: McGill University, Montréal,
Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7
35University of Michigan, Ann Arbor, Michigan 48109
36Michigan State University, East Lansing, Michigan 48824
37University of New Mexico, Albuquerque, New Mexico 87131
38Northwestern University, Evanston, Illinois 60208
39The Ohio State University, Columbus, Ohio 43210
40Okayama University, Okayama 700-8530, Japan
41Osaka City University, Osaka 588, Japan
42University of Oxford, Oxford OX1 3RH, United Kingdom
43University of Padova, Istituto Nazionale di Fisica Nucleare,
Sezione di Padova-Trento, I-35131 Padova, Italy
44LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France
45University of Pennsylvania, Philadelphia, Pennsylvania 19104
46Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa,
Siena and Scuola Normale Superiore, I-56127 Pisa, Italy
47University of Pittsburgh, Pittsburgh, Pennsylvania 15260
48Purdue University, West Lafayette, Indiana 47907
49University of Rochester, Rochester, New York 14627
50The Rockefeller University, New York, New York 10021
51Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1,
University of Rome “La Sapienza,” I-00185 Roma, Italy
52Rutgers University, Piscataway, New Jersey 08855
53Texas A&M University, College Station, Texas 77843
54Istituto Nazionale di Fisica Nucleare, University of Trieste/ Udine, Italy
55University of Tsukuba, Tsukuba, Ibaraki 305, Japan
56Tufts University, Medford, Massachusetts 02155
57Waseda University, Tokyo 169, Japan
58Wayne State University, Detroit, Michigan 48201
59University of Wisconsin, Madison, Wisconsin 53706
60Yale University, New Haven, Connecticut 06520
We have measured the polarizations of J/ψ and ψ(2S) mesons as functions of their transverse
momentum pT when they are produced promptly in the rapidity range |y| < 0.6 with pT ≥ 5 GeV/c.
The analysis is performed using a data sample with an integrated luminosity of about 800 pb−1
collected by the CDF II detector. For both vector mesons, we find that the polarizations become
increasingly longitudinal as pT increases from 5 to 30 GeV/c. These results are compared to the pre-
dictions of nonrelativistic quantum chromodynamics and other contemporary models. The effective
polarizations of J/ψ and ψ(2S) mesons from B-hadron decays are also reported.
PACS numbers: 13.88.+e, 13.20.Gd, 14.40.Lb
An effective field theory, nonrelativistic quantum chromodynamics (NRQCD) [1], provides a rigorous formalism for
calculating the production rates of charmonium (cc) states. NRQCD explains the direct production cross sections
for J/ψ and ψ(2S) mesons observed at the Tevatron [2, 3] and predicts their increasingly transverse polarizations
as pT increases, where pT is the meson’s momentum component perpendicular to the colliding beam direction [4].
The first polarization measurements at the Tevatron [5] did not show such a trend. This Letter reports on J/ψ and
ψ(2S) polarization measurements with a larger data sample than previously available. This allows the extension of
the measurement to a higher pT region and makes a more stringent test of the NRQCD prediction.
The NRQCD cross section calculation for cc production separates the long-distance nonperturbative contributions
from the short-distance perturbative behavior. The former is treated as an expansion of the matrix elements in powers
of the nonrelativistic charm-quark velocity. This expansion can be computed by lattice simulations, but currently the
expansion coefficients are treated as universal parameters, which are adjusted to match the cross section measurements
at the Tevatron [2, 3]. The calculation also applies to cc production in ep collisions, but HERA measurements of J/ψ
polarization tend to disagree with the NRQCD prediction [6]. These difficulties have led some authors to explore
alternative power expansions of the long-distance interactions for the cc system [7]. There are also new QCD-inspired
models, the gluon tower model [8] and the kT -factorization model [9], that accomodate vector-meson cross sections at
both HERA and the Tevatron and predict the vector-meson polarizations as functions of pT . These authors emphasize
that measuring the vector-meson polarizations as functions of pT is a crucial test of NRQCD.
The CDF II detector is described in detail elsewhere [3, 10]. In this analysis, the essential features are a muon system
covering the central region of pseudorapidity, |η| < 0.6, and the tracking system, immersed in the 1.4 T solenoidal
magnetic field and composed of a silicon microstrip detector and a cylindrical drift chamber called the central outer
tracker (COT). The data used here correspond to an integrated luminosity of about 800 pb−1 and were recorded
between June 2004 and February 2006 by a dimuon trigger, which requires two opposite-charge muon candidates,
each having pT > 1.5 GeV/c.
Decays of vector mesons V (either J/ψ or ψ(2S)) → µ+µ− are selected from dimuon events for which each track
has segments reconstructed in both the COT and the silicon microstrip detector. The pT of each muon is required
to exceed 1.75 GeV/c in order to guarantee a well-measured trigger efficiency. The muon track pair is required to
be consistent with originating from a common vertex and to have an invariant mass M within the range 2.8 (3.4) <
M < 3.4 (3.9) GeV/c2 to be considered as a J/ψ (ψ(2S)) candidate. To have a reasonable polarization sensitivity,
the vector-meson candidates are required to have pT ≥ 5 GeV/c in the rapidity range |y (≡ 12 ln
E+p||
E−p||
)| < 0.6, where
E is the energy and p|| is the momentum parallel to the beam direction of the dimuon system. Events are separated
into a signal region and sideband regions, as indicated in Fig. 1. The fit to the data uses a double (single) Gaussian
for the J/ψ (ψ(2S)) signal and a linear background shape. The fits are used only to define signal and background
regions. The signal regions are within 3σV of the fitted mass peaks MV , where σV is the width obtained in the fit
to the invariant mass distribution. Both the background distribution and the quantity of background events under
the signal peak are estimated by events from the lower and upper mass sidebands. The sideband regions are 7σJ/ψ
(4σψ(2S)) away from the signal region for J/ψ (ψ(2S)).
For each candidate, we compute ct =MLxy/pT , where t is the proper decay time and Lxy is the transverse distance
between the beam line and the decay vertex in the plane normal to the beam direction. The ct distributions of the
selected dimuon events are shown in Fig. 2. The ct distribution of prompt events is a Gaussian distribution centered
at zero due to finite tracking resolution. For J/ψ, the prompt events are due to direct production or the decays of
heavier charmonium states such as χc and ψ(2S); for ψ(2S), the prompt events are almost entirely due to direct
production since heavier charmonium states rarely decay to ψ(2S) [11]. Both the J/ψ and the ψ(2S) samples contain
significant numbers of events originating from long-lived B-hadron decays, as can be seen from the event excess at
positive ct. We have measured the fraction of B → J/ψ + X events in the J/ψ sample and found agreement with
other results [3]. We select prompt events by requiring the sum of the squared impact parameter significances of the
positively and negatively charged muon tracks S ≡ ( d
)2 + (
)2 ≤ 8. The impact parameter d0 is the distance
of closest approach of the track to the beam line in the transverse plane. Vector-meson candidates from B-hadron
decays are selected by requiring S > 16 and ct > 0.03 cm. This requirement retains a negligible fraction of prompt
events in the B sample.
To measure the polarizations of prompt J/ψ and ψ(2S) mesons as functions of pT , the J/ψ events are analyzed in
six pT bins and the ψ(2S) events in three bins, shown in Table I. We determine the fraction of B-decay background
remaining in prompt samples fbkd by subtracting the number of negative ct events from the number of positive ct
events. Only a negligible fraction (< 0.2%) of B decays produce vector-meson events with negative ct. For both
vector mesons, fbkd increases with pT , as listed in Table I. The prompt polarization from the fitting algorithm is
corrected for this contamination.
M (GeV/c
2.8 2.9 3 3.1 3.2 3.3 3.4
M (GeV/c
3.4 3.5 3.6 3.7 3.8 3.9
FIG. 1: Invariant mass distributions for (a) J/ψ and (b) ψ(2S) candidates. The curves are fits to the data. The solid (dashed)
lines indicate the signal (sideband) regions.
ct (cm)
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
510 (a)
ct (cm)
-0.2 -0.1 0 0.1 0.2
410 (b)
FIG. 2: Sideband-subtracted ct distributions for (a) J/ψ and (b) ψ(2S) events. The prompt Gaussian peak, positive excess
from B-hadron decays, and negative tail from mismeasured events are shown. The dotted line is the reflection of the negative
ct histogram about zero.
The polarization information is contained in the distribution of the muon decay angle θ∗, the angle of the µ+ in the
rest frame of vector meson with respect to the vector-meson boost direction in the laboratory system. The decay angle
distribution depends on the polarization parameter α:
d cos θ∗
∝ 1 + α cos2θ∗ (−1 ≤ α ≤ 1). For fully transverse
(longitudinal) polarization, α = +1 (−1). Intermediate values of α indicate a mixture of transverse and longitudinal
polarization.
A template method is used to account for acceptance and efficiency. Two sets of cos θ∗ distributions for fully
polarized decays of J/ψ and ψ(2S) events, one longitudinal (L) and the other transverse (T ), are produced with the
CDF simulation program using the efficiency-corrected pT spectra measured from data [3, 12]. We use the muon
trigger efficiency measured using data as a function of track parameters (pT , η, φ) to account for detector non-
uniformities. The parametrized efficiency is used as a filter on all simulated muons. Events that pass reconstruction
represent the behavior of fully polarized vector-meson decays in the detector.
The fitting algorithm [5] uses two binned cos θ∗ distributions for each pT bin, one made by NS events from the
signal region (signal plus background) and the other made by NB events from the sideband regions (background).
The χ2 minimization is done simultaneously for both cos θ∗ distributions. The fitting algorithm includes an individual
background term for each cos θ∗ bin, normalized to NB. Simulation shows that the cos θ
∗ resolution at all decay
angles over the entire pT range is much smaller than the bin width of 0.05 (0.10 for ψ(2S)) used here. The data, fit,
and template distributions for the worst fit (9% probability) in the J/ψ data are shown in Fig. 3.
*θcos 
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
 (GeV/c) <  9T p≤ 7 
FIG. 3: cos θ∗ distribution of data (points) and polarization fit for the worst χ2 probability bin in the J/ψ data. The dotted
(dashed) line is the template for fully L (T) polarization. The fit describes the overall trend of the data well.
All systematic uncertainties are much smaller than the statistical uncertainties. Varying the pT spectrum used in
the simulation by 1σ changed the polarization parameter for J/ψ at most by 0.002. A systematic uncertainty of 0.007
was estimated by the change in the polarization parameter when a modification was made on all trigger efficiencies
by ±1σ. For ψ(2S), the dominant systematic uncertainty came from the yield estimate because of the radiative tail
and the large background. The total systematic uncertainties shown in Table I were taken to be the quadrature
sum of these individual uncertainties. Other possible sources of systematic uncertainties - signal definition and cos θ∗
binning - were determined to be negligible. Corrections to prompt polarization from B-decay contamination were
small, so that uncertainties on B-decay polarization measurements also had negligible effect. No φ-dependence of the
polarizations was observed.
The polarization of J/ψ mesons from inclusive Bu and Bd decays was measured by the BABAR collaboration [13].
In this analysis, the B-hadron direction is unknown, so we define θ∗ with respect to the J/ψ direction in the laboratory
system. The resulting polarization is somewhat diluted. As discussed in Ref. [3], CDF uses a Monte Carlo procedure to
adapt the BABAR measurement to predict the effective J/ψ polarization parameter. For the J/ψ events with 5 ≤ pT <
30 GeV/c, the CDF model for Bu and Bd decays gives αeff = −0.145± 0.009, independent of pT . We have measured
the polarization of vector mesons from B-hadron decays. For J/ψ, we find αeff = −0.106±0.033 (stat)±0.007 (syst).
At this level of accuracy, a polarization contribution by J/ψ mesons from Bs and b-baryon decays cannot be separated
from the effective polarization due to those from Bu and Bd decays. We also report the first measurement of the
ψ(2S) polarization from B-hadron decays: αeff = 0.36± 0.25 (stat)± 0.03 (syst).
The polarization parameters for both prompt vector mesons corrected for fbkd using our experimental results on αeff
are listed as functions of pT in Table I and are plotted in Fig. 4. The polarization parameters for J/ψ are negative
over the entire pT range of measurement and become increasingly negative (favoring longitudinal polarization) as
pT increases. For ψ(2S), the central value of the polarization parameter is positive at small pT , but, given the
uncertainties, its behavior is consistent with the trend shown in the measurement of the J/ψ polarization.
The polarization behavior measured previously with 110 pb−1 [5] is not consistent with the results presented here.
This is a differential measurement, and the muon efficiencies in this analysis are true dimuon efficiencies. In Ref. [5],
they are the product of independent single muon efficiencies. The efficiency for muons with pT < 4 GeV/c is crucial for
good polarization sensitivity. In this analysis, the muon efficiency varies smoothly from 99% to 97% over this range.
In the analysis of Ref. [5], it varied from 93% to 40% with significant jumps between individual data points. Data
from periods of drift chamber aging were omitted from this analysis because the polarization results were inconsistent
with the remainder of the data. Studies such as this were not done in the analysis of Ref. [5]. The systematics of the
polarization measurement are much better understood in this analysis.
These polarization measurements for the charmed vector mesons extend to a pT regime where perturbative QCD
should be applicable. The results are compared to the predictions of NRQCD and the kT -factorization model in Fig. 4.
The prediction of the kT -factorization model is presented for pT < 20 GeV/c and does not include the contribution
pT (GeV/c) <pT > (GeV/c) fbkd(%) α χ
2/d.o.f
J/ψ 5−6 5.5 2.8± 0.2 −0.004± 0.029± 0.009 15.5/21
6−7 6.5 3.4± 0.2 −0.015± 0.028± 0.010 24.1/23
7−9 7.8 4.1± 0.2 −0.077± 0.023± 0.013 35.1/25
9−12 10.1 5.7± 0.3 −0.094± 0.028± 0.007 34.0/29
12−17 13.7 6.7± 0.6 −0.140± 0.043± 0.007 35.0/31
17−30 20.0 13.6± 1.4 −0.187± 0.090± 0.007 33.9/35
ψ(2S) 5−7 5.9 1.6± 0.9 +0.314± 0.242± 0.028 13.1/11
7−10 8.2 4.9± 1.2 −0.013± 0.201± 0.035 18.5/13
10−30 12.6 8.6± 1.8 −0.374± 0.222± 0.062 26.9/17
TABLE I: Polarization parameter α for prompt production in each pT bin. The first (second) uncertainty is statistical (sys-
tematic). <pT > is the average transverse momentum.
 (GeV/c)Tp
5 10 15 20 25 30
CDF Data
NRQCD
-factorizationTk
 (GeV/c)Tp
5 10 15 20 25 30
CDF Data
NRQCD
-factorizationTk
FIG. 4: Prompt polarizations as functions of pT : (a) J/ψ and (b) ψ(2S). The band (line) is the prediction from NRQCD [4]
(the kT -factorization model [9]).
from the decays of heavier charmonium states for J/ψ production. The polarizations for prompt production of
both vector mesons become increasingly longitudinal as pT increases beyond 10 GeV/c. This behavior is in strong
disagreement with the NRQCD prediction of large transverse polarization at high pT . It is striking that the NRQCD
calculation and the other models reproduce the measured J/ψ and ψ(2S) cross sections at the Tevatron, but fail to
describe the polarization at high pT . This indicates that there is some important aspect of the production mechanism
that is not yet understood.
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 Energy and National Science Foundation; the Italian Istituto
Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the
Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of
China; the Swiss National Science Foundation; the A.P. Sloan Foundation; the Bundesministerium für Bildung und
Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the
Particle Physics and Astronomy Research Council and the Royal Society, UK; the Institut National de Physique
Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Comisión Interministerial
de Ciencia y Tecnoloǵıa, Spain; the European Community’s Human Potential Programme; the Slovak R&D Agency;
and the Academy of Finland.
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