Production of <em>ψ</em>(2S) mesons in <em>pp</em> collisions at 1.96 TeV

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Article

Reference

Production of ψ (2S) mesons in pp collisions at 1.96 TeV

CDF Collaboration

CLARK, Allan Geoffrey (Collab.), et al.

Abstract

We have measured the differential cross section for the inclusive production of ψ(2S) mesons decaying to μ+μ− that were produced in prompt or B-decay processes from pp collisions at 1.96 TeV. These measurements have been made using a data set from an integrated luminosity of 1.1 fb−1 collected by the CDF II detector at Fermilab. For events with transverse momentum pT(ψ(2S))>2 GeV/c and rapidity |y(ψ(2S))|

CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Production of ψ (2S) mesons in pp collisions at 1.96 TeV. Physical Review. D , 2009, vol. 80, no. 03, p. 031103

DOI : 10.1103/PhysRevD.80.031103

Available at:

http://archive-ouverte.unige.ch/unige:38626

Disclaimer: layout of this document may differ from the published version.

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Production of c ð2 S Þ mesons in p p collisions at 1.96 TeV

T. Aaltonen,²⁴J. Adelman,¹⁴T. Akimoto,⁵⁶B. A´ lvarez Gonza´lez,^12,uS. Amerio,^44b,44aD. Amidei,³⁵A. Anastassov,³⁹ A. Annovi,²⁰J. Antos,¹⁵G. Apollinari,¹⁸A. Apresyan,⁴⁹T. Arisawa,⁵⁸A. Artikov,¹⁶W. Ashmanskas,¹⁸A. Attal,⁴

A. Aurisano,⁵⁴F. Azfar,⁴³W. Badgett,¹⁸A. Barbaro-Galtieri,²⁹V. E. Barnes,⁴⁹B. A. Barnett,²⁶P. Barria,^47c,47a V. Bartsch,³¹G. Bauer,³³P.-H. Beauchemin,³⁴F. Bedeschi,^47aD. Beecher,³¹S. Behari,²⁶G. Bellettini,^47b,47aJ. Bellinger,⁶⁰

D. Benjamin,¹⁷A. Beretvas,¹⁸J. Beringer,²⁹A. Bhatti,⁵¹M. Binkley,¹⁸D. Bisello,^44b,44aI. Bizjak,^31,zR. E. Blair,² C. Blocker,⁷B. Blumenfeld,²⁶A. Bocci,¹⁷A. Bodek,⁵⁰V. Boisvert,⁵⁰G. Bolla,⁴⁹D. Bortoletto,⁴⁹J. Boudreau,⁴⁸ A. Boveia,¹¹B. Brau,^11,bA. Bridgeman,²⁵L. Brigliadori,^6b,a6aC. Bromberg,³⁶E. Brubaker,¹⁴J. Budagov,¹⁶H. S. Budd,⁵⁰

S. Budd,²⁵S. Burke,¹⁸K. Burkett,¹⁸G. Busetto,^44b,44aP. Bussey,²²A. Buzatu,³⁴K. L. Byrum,²S. Cabrera,^17,w C. Calancha,³²M. Campanelli,³⁶M. Campbell,³⁵F. Canelli,^14,18 A. Canepa,⁴⁶B. Carls,²⁵D. Carlsmith,⁶⁰R. Carosi,^47a S. Carrillo,^19,oS. Carron,³⁴B. Casal,¹²M. Casarsa,¹⁸A. Castro,^6b,a6aP. Catastini,^47c,47aD. Cauz,^55b,55aV. Cavaliere,^47c,47a M. Cavalli-Sforza,⁴A. Cerri,²⁹L. Cerrito,^31,qS. H. Chang,⁶²Y. C. Chen,¹M. Chertok,⁸G. Chiarelli,^47aG. Chlachidze,¹⁸ F. Chlebana,¹⁸K. Cho,⁶²D. Chokheli,¹⁶J. P. Chou,²³G. Choudalakis,³³S. H. Chuang,⁵³K. Chung,¹³W. H. Chung,⁶⁰

Y. S. Chung,⁵⁰T. Chwalek,²⁷C. I. Ciobanu,¹M. A. Ciocci,^47c,47aA. Clark,²¹D. Clark,⁷G. Compostella,^44a M. E. Convery,¹⁸J. Conway,⁸M. Cordelli,²⁰G. Cortiana,^44b,44aC. A. Cox,⁸D. J. Cox,⁸F. Crescioli,^47b,47a C. Cuenca Almenar,^8,wJ. Cuevas,^12,uR. Culbertson,¹⁸J. C. Cully,³⁵D. Dagenhart,¹⁸M. Datta,¹⁸T. Davies,²² P. de Barbaro,⁵⁰S. De Cecco,^52aA. Deisher,²⁹G. De Lorenzo,⁴M. Dell’Orso,^47b,47aC. Deluca,⁴L. Demortier,⁵¹J. Deng,¹⁷

M. Deninno,^a6aP. F. Derwent,¹⁸A. Di Canto,^47b,47aG. P. di Giovanni,¹C. Dionisi,^52b,52aB. Di Ruzza,^55b,55a J. R. Dittmann,⁵M. D’Onofrio,⁴S. Donati,^47b,47aP. Dong,⁹J. Donini,^44aT. Dorigo,^44aS. Dube,⁵³J. Efron,⁴⁰A. Elagin,⁵⁴

R. Erbacher,⁸D. Errede,²⁵S. Errede,²⁵R. Eusebi,¹⁸H. C. Fang,²⁹S. Farrington,⁴³W. T. Fedorko,¹⁴R. G. Feild,⁶¹ M. Feindt,²⁷J. P. Fernandez,³²C. Ferrazza,^47d,47aR. Field,¹⁹G. Flanagan,⁴⁹R. Forrest,⁸M. J. Frank,⁵M. Franklin,²³ J. C. Freeman,¹⁸I. Furic,¹⁹M. Gallinaro,^52aJ. Galyardt,¹³F. Garberson,¹¹J. E. Garcia,²¹A. F. Garfinkel,⁴⁹P. Garosi,^47c,47a K. Genser,¹⁸H. Gerberich,²⁵D. Gerdes,³⁵A. Gessler,²⁷S. Giagu,^52b,52aV. Giakoumopoulou,³P. Giannetti,^47aK. Gibson,⁴⁸

J. L. Gimmell,⁵⁰C. M. Ginsburg,¹⁸N. Giokaris,³M. Giordani,^55b,55aP. Giromini,²⁰M. Giunta,^47aG. Giurgiu,²⁶ V. Glagolev,¹⁶D. Glenzinski,¹⁸M. Gold,³⁸N. Goldschmidt,¹⁹A. Golossanov,¹⁸G. Gomez,¹²G. Gomez-Ceballos,³³

M. Goncharov,³³O. Gonza´lez,³²I. Gorelov,³⁸A. T. Goshaw,¹⁷K. Goulianos,⁵¹A. Gresele,^44b,44aS. Grinstein,²³ C. Grosso-Pilcher,¹⁴R. C. Group,¹⁸U. Grundler,²⁵J. Guimaraes da Costa,²³Z. Gunay-Unalan,³⁶C. Haber,²⁹K. Hahn,³³

S. R. Hahn,¹⁸E. Halkiadakis,⁵³B.-Y. Han,⁵⁰J. Y. Han,⁵⁰F. Happacher,²⁰K. Hara,⁵⁶D. Hare,⁵³M. Hare,⁵⁷S. Harper,⁴³ R. F. Harr,⁵⁹R. M. Harris,¹⁸M. Hartz,⁴⁸K. Hatakeyama,⁵¹C. Hays,⁴³M. Heck,²⁷A. Heijboer,⁴⁶J. Heinrich,⁴⁶ C. Henderson,³³M. Herndon,⁶⁰J. Heuser,²⁷S. Hewamanage,⁵D. Hidas,¹⁷C. S. Hill,^11,dD. Hirschbuehl,²⁷A. Hocker,¹⁸

S. Hou,¹M. Houlden,³⁰S.-C. Hsu,²⁹B. T. Huffman,⁴³R. E. Hughes,⁴⁰U. Husemann,⁶¹M. Hussein,³⁶J. Huston,³⁶ J. Incandela,¹¹G. Introzzi,^47aM. Iori,^52b,52aA. Ivanov,⁸E. James,¹⁸D. Jang,¹³B. Jayatilaka,¹⁷E. J. Jeon,⁶²M. K. Jha,^a6a

S. Jindariani,¹⁸W. Johnson,⁸M. Jones,⁴⁹K. K. Joo,⁶²S. Y. Jun,¹³J. E. Jung,⁶²T. R. Junk,¹⁸T. Kamon,⁵⁴D. Kar,¹⁹ P. E. Karchin,⁵⁹Y. Kato,^42,nR. Kephart,¹⁸W. Ketchum,¹⁴J. Keung,⁴⁶V. Khotilovich,⁵⁴B. Kilminster,¹⁸D. H. Kim,⁶²

H. S. Kim,⁶²H. W. Kim,⁶²J. E. Kim,⁶²M. J. Kim,²⁰S. B. Kim,⁶²S. H. Kim,⁵⁶Y. K. Kim,¹⁴N. Kimura,⁵⁶L. Kirsch,⁷ S. Klimenko,¹⁹B. Knuteson,³³B. R. Ko,¹⁷K. Kondo,⁵⁸D. J. Kong,⁶²J. Konigsberg,¹⁹A. Korytov,¹⁹A. V. Kotwal,¹⁷ M. Kreps,²⁷J. Kroll,⁴⁶D. Krop,¹⁴N. Krumnack,⁵M. Kruse,¹⁷V. Krutelyov,¹¹T. Kubo,⁵⁶T. Kuhr,²⁷N. P. Kulkarni,⁵⁹

M. Kurata,⁵⁶S. Kwang,¹⁴A. T. Laasanen,⁴⁹S. Lami,^47aS. Lammel,¹⁸M. Lancaster,³¹R. L. Lander,⁸K. Lannon,^40,t A. Lath,⁵³G. Latino,^47c,47aI. Lazzizzera,^44b,44aT. LeCompte,²E. Lee,⁵⁴H. S. Lee,¹⁴S. W. Lee,^54,vS. Leone,^47a J. D. Lewis,¹⁸C.-S. Lin,²⁹J. Linacre,⁴³M. Lindgren,¹⁸E. Lipeles,⁴⁶A. Lister,⁸D. O. Litvintsev,¹⁸C. Liu,⁴⁸T. Liu,¹⁸

N. S. Lockyer,⁴⁶A. Loginov,⁶¹M. Loreti,^44b,44aL. Lovas,¹⁵D. Lucchesi,^44b,44aC. Luci,^52b,52aJ. Lueck,²⁷P. Lujan,²⁹ P. Lukens,¹⁸G. Lungu,⁵¹L. Lyons,⁴³J. Lys,²⁹R. Lysak,¹⁵D. MacQueen,³⁴R. Madrak,¹⁸K. Maeshima,¹⁸K. Makhoul,³³

T. Maki,²⁴P. Maksimovic,²⁶S. Malde,⁴³S. Malik,³¹G. Manca,^30,fA. Manousakis-Katsikakis,³F. Margaroli,⁴⁹ C. Marino,²⁷C. P. Marino,²⁵A. Martin,⁶¹V. Martin,^22,lM. Martıńez,⁴R. Martıńez-Ballarıń,³²T. Maruyama,⁵⁶ P. Mastrandrea,^52aT. Masubuchi,⁵⁶M. Mathis,²⁶M. E. Mattson,⁵⁹P. Mazzanti,â6aK. S. McFarland,⁵⁰P. McIntyre,⁵⁴ R. McNulty,^30,kA. Mehta,³⁰P. Mehtala,²⁴A. Menzione,^47aP. Merkel,⁴⁹C. Mesropian,⁵¹T. Miao,¹⁸N. Miladinovic,⁷ R. Miller,³⁶C. Mills,²³M. Milnik,²⁷A. Mitra,¹G. Mitselmakher,¹⁹H. Miyake,⁵⁶N. Moggi,â6aM. N. Mondragon,^18,o C. S. Moon,⁶²R. Moore,¹⁸M. J. Morello,^47aJ. Morlock,²⁷P. Movilla Fernandez,¹⁸J. Mu¨lmensta¨dt,²⁹A. Mukherjee,¹⁸

Th. Muller,²⁷R. Mumford,²⁶P. Murat,¹⁸M. Mussini,^6b,a6aJ. Nachtman,^18,pY. Nagai,⁵⁶A. Nagano,⁵⁶J. Naganoma,⁵⁶ K. Nakamura,⁵⁶I. Nakano,⁴¹A. Napier,⁵⁷V. Necula,¹⁷J. Nett,⁶⁰C. Neu,^46,xM. S. Neubauer,²⁵S. Neubauer,²⁷

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J. Nielsen,^29,hL. Nodulman,²M. Norman,¹⁰O. Norniella,²⁵E. Nurse,³¹L. Oakes,⁴³S. H. Oh,¹⁷Y. D. Oh,⁶²I. Oksuzian,¹⁹ T. Okusawa,⁴²R. Orava,²⁴K. Osterberg,²⁴S. Pagan Griso,^44b,44aE. Palencia,¹⁸V. Papadimitriou,¹⁸A. Papaikonomou,²⁷

A. A. Paramonov,¹⁴B. Parks,⁴⁰S. Pashapour,³⁴J. Patrick,¹⁸G. Pauletta,^55b,55aM. Paulini,¹³C. Paus,³³T. Peiffer,²⁷ D. E. Pellett,⁸A. Penzo,^55aT. J. Phillips,¹⁷G. Piacentino,^47aE. Pianori,⁴⁶L. Pinera,¹⁹K. Pitts,²⁵C. Plager,⁹L. Pondrom,⁶⁰

O. Poukhov,^16,aN. Pounder,⁴³F. Prakoshyn,¹⁶A. Pronko,¹⁸J. Proudfoot,²F. Ptohos,^18,jE. Pueschel,¹³G. Punzi,^47b,47a J. Pursley,⁶⁰J. Rademacker,^43,dA. Rahaman,⁴⁸V. Ramakrishnan,⁶⁰N. Ranjan,⁴⁹I. Redondo,³²P. Renton,⁴³M. Renz,²⁷

M. Rescigno,^52aS. Richter,²⁷F. Rimondi,^6b,a6aL. Ristori,^47aA. Robson,²²T. Rodrigo,¹²T. Rodriguez,⁴⁶E. Rogers,²⁵ S. Rolli,⁵⁷R. Roser,¹⁸M. Rossi,^55aR. Rossin,¹¹P. Roy,³⁴A. Ruiz,¹²J. Russ,¹³V. Rusu,¹⁸B. Rutherford,¹⁸H. Saarikko,²⁴ A. Safonov,⁵⁴W. K. Sakumoto,⁵⁰O. Salto´,⁴L. Santi,^55b,55aS. Sarkar,^52b,55aL. Sartori,^47aK. Sato,¹⁸A. Savoy-Navarro,¹

P. Schlabach,¹⁸A. Schmidt,²⁷E. E. Schmidt,¹⁸M. A. Schmidt,¹⁴M. P. Schmidt,^61,aM. Schmitt,³⁹T. Schwarz,⁸ L. Scodellaro,¹²A. Scribano,^47c,47aF. Scuri,^47aA. Sedov,⁴⁹S. Seidel,³⁸Y. Seiya,⁴²A. Semenov,¹⁶L. Sexton-Kennedy,¹⁸ F. Sforza,^47b,47aA. Sfyrla,²⁵S. Z. Shalhout,⁵⁹T. Shears,³⁰P. F. Shepard,⁴⁸M. Shimojima,^56,sS. Shiraishi,¹⁴M. Shochet,¹⁴

Y. Shon,⁶⁰I. Shreyber,³⁷P. Sinervo,³⁴A. Sisakyan,¹⁶A. J. Slaughter,¹⁸J. Slaunwhite,⁴⁰K. Sliwa,⁵⁷J. R. Smith,⁸ F. D. Snider,¹⁸R. Snihur,³⁴A. Soha,⁸S. Somalwar,⁵³V. Sorin,³⁶T. Spreitzer,³⁴P. Squillacioti,^47c,47aM. Stanitzki,⁶¹ R. St. Denis,²²B. Stelzer,³⁴O. Stelzer-Chilton,³⁴D. Stentz,³⁹J. Strologas,³⁸G. L. Strycker,³⁵J. S. Suh,⁶²A. Sukhanov,¹⁹

I. Suslov,¹⁶T. Suzuki,⁵⁶A. Taffard,^25,gR. Takashima,⁴¹Y. Takeuchi,⁵⁶R. Tanaka,⁴¹M. Tecchio,³⁵P. K. Teng,¹ K. Terashi,⁵¹J. Thom,^18,iA. S. Thompson,²²G. A. Thompson,²⁵E. Thomson,⁴⁶P. Tipton,⁶¹P. Ttito-Guzma´n,³² S. Tkaczyk,¹⁸D. Toback,⁵⁴S. Tokar,¹⁵K. Tollefson,³⁶T. Tomura,⁵⁶D. Tonelli,¹⁸S. Torre,²⁰D. Torretta,¹⁸P. Totaro,^55b,55a S. Tourneur,¹M. Trovato,^47d,47aS.-Y. Tsai,¹Y. Tu,⁴⁶N. Turini,^47c,47aF. Ukegawa,⁵⁶S. Vallecorsa,²¹N. van Remortel,^24,c

A. Varganov,³⁵E. Vataga,^47d,47aF. Va´zquez,^19,oG. Velev,¹⁸C. Vellidis,³M. Vidal,³²R. Vidal,¹⁸I. Vila,¹²R. Vilar,¹² T. Vine,³¹M. Vogel,³⁸I. Volobouev,^29,vG. Volpi,^47b,47aP. Wagner,⁴⁶R. G. Wagner,²R. L. Wagner,¹⁸W. Wagner,^27,y J. Wagner-Kuhr,²⁷T. Wakisaka,⁴²R. Wallny,⁹S. M. Wang,¹A. Warburton,³⁴D. Waters,³¹M. Weinberger,⁵⁴J. Weinelt,²⁷

W. C. Wester III,¹⁸B. Whitehouse,⁵⁷D. Whiteson,^46,gA. B. Wicklund,²E. Wicklund,¹⁸S. Wilbur,¹⁴G. Williams,³⁴ H. H. Williams,⁴⁶P. Wilson,¹⁸B. L. Winer,⁴⁰P. Wittich,^18,iS. Wolbers,¹⁸C. Wolfe,¹⁴T. Wright,³⁵X. Wu,²¹ F. Wu¨rthwein,¹⁰S. Xie,³³A. Yagil,¹⁰K. Yamamoto,⁴²J. Yamaoka,¹⁷U. K. Yang,^14,rY. C. Yang,⁶²W. M. Yao,²⁹G. P. Yeh,¹⁸ K. Yi,^18,pJ. Yoh,¹⁸K. Yorita,⁵⁸T. Yoshida,^42,mG. B. Yu,⁵⁰I. Yu,⁶²S. S. Yu,¹⁸J. C. Yun,¹⁸L. Zanello,^52b,52aA. Zanetti,^55a

X. Zhang,²⁵Y. Zheng,^9,eand S. Zucchelli^6b,a6a (CDF Collaboration)

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

2Argonne National Laboratory, Argonne, Illinois 60439, USA

3University of Athens, 157 71 Athens, Greece

4Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

5Baylor University, Waco, Texas 76798, USA

a6aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy

6bUniversity of Bologna, I-40127 Bologna, Italy

7Brandeis University, Waltham, Massachusetts 02254, USA

8University of California, Davis, Davis, California 95616, USA

9University of California, Los Angeles, Los Angeles, California 90024, USA

10University of California, San Diego, La Jolla, California 92093, USA

11University of California, Santa Barbara, Santa Barbara, California 93106, USA

12Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

13Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

14Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

15Comenius University, 842 48 Bratislava, Slovakia;

Institute of Experimental Physics, 040 01 Kosice, Slovakia

16Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

17Duke University, Durham, North Carolina 27708, USA

18Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

19University of Florida, Gainesville, Florida 32611, USA

20Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

21University of Geneva, CH-1211 Geneva 4, Switzerland

22Glasgow University, Glasgow G12 8QQ, United Kingdom

23Harvard University, Cambridge, Massachusetts 02138, USA

T. AALTONENet al. PHYSICAL REVIEW D80,031103(R) (2009)

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24Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

25University of Illinois, Urbana, Illinois 61801, USA

26The Johns Hopkins University, Baltimore, Maryland 21218, USA

27Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

28Center for High Energy Physics: Kyungpook National University, Daegu 702-701, Korea;

Seoul National University, Seoul 151-742, Korea;

Sungkyunkwan University, Suwon 440-746, Korea;

Korea Institute of Science and Technology Information, Daejeon, 305-806, Korea;

Chonnam National University, Gwangju, 500-757, Korea;

Chonbuk National University, Jeonju 561-756, Korea

29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

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, USA

34Institute of Particle Physics: McGill University, Montre´al, Que´bec, Canada H3A 2T8;

Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6;

University of Toronto, Toronto, Ontario, Canada M5S 1A7;

and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3

35University of Michigan, Ann Arbor, Michigan 48109, USA

36Michigan State University, East Lansing, Michigan 48824, USA

37Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

38University of New Mexico, Albuquerque, New Mexico 87131, USA

39Northwestern University, Evanston, Illinois 60208, USA

40The Ohio State University, Columbus, Ohio 43210, USA

41Okayama University, Okayama 700-8530, Japan

42Osaka City University, Osaka 588, Japan

43University of Oxford, Oxford OX1 3RH, United Kingdom

44aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

44bUniversity of Padova, I-35131 Padova, Italy

1LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

46University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

47aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy

47bUniversity of Pisa, I-56127 Pisa, Italy

47cUniversity of Siena, I-56127 Pisa, Italy

47dScuola Normale Superiore, I-56127 Pisa, Italy

48University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

49Purdue University, West Lafayette, Indiana 47907, USA

50University of Rochester, Rochester, New York 14627, USA

51The Rockefeller University, New York, New York 10021, USA

52aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy

52bSapienza Universita` di Roma, I-00185 Roma, Italy

53Rutgers University, Piscataway, New Jersey 08855, USA

54Texas A&M University, College Station, Texas 77843, USA

55aIstituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, Italy

55bUniversity of Trieste/Udine, I-33100 Udine, Italy

56University of Tsukuba, Tsukuba, Ibaraki 305, Japan

57Tufts University, Medford, Massachusetts 02155, USA

58Waseda University, Tokyo 169, Japan

59Wayne State University, Detroit, Michigan 48201, USA

60University of Wisconsin, Madison, Wisconsin 53706, USA

61Yale University, New Haven, Connecticut 06520, USA

62Center for High Energy Physics: Kyungpook National University, Daegu 702-701, Korea;

Seoul National University, Seoul 151-742, Korea;

Sungkyunkwan University, Suwon 440-746, Korea;

Korea Institute of Science and Technology Information, Daejeon, 305-806, Korea;

Chonnam National University, Gwangju, 500-757, Korea (Received 14 May 2009; published 6 August 2009)

PRODUCTION OF cð2SÞMESONS INpp. . . PHYSICAL REVIEW D80,031103(R) (2009)

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We have measured the differential cross section for the inclusive production ofcð2SÞmesons decaying to^þ that were produced in prompt orB-decay processes from pp collisions at 1.96 TeV. These measurements have been made using a data set from an integrated luminosity of1:1 fb¹collected by the CDF II detector at Fermilab. For events with transverse momentump_Tðcð2SÞÞ>2 GeV=cand rapidity jyðcð2SÞÞj<0:6 we measure the integrated inclusive cross section ðpp!cð2SÞXÞ Brðcð2SÞ ! ^þÞto be3:290:04ðstatÞ 0:32ðsystÞnb.

DOI:10.1103/PhysRevD.80.031103 PACS numbers: 14.40.Gx, 13.85.Ni, 13.20.Gd

The mechanism for producing heavy vector mesons in pp collisions is not well understood. The experimental measurement of promptJ=c ^and cð2SÞproduction cross sections by CDF in Tevatron run I [1] showed that the measured cross sections were 1 to 2 orders of magnitude larger than expected from the leading order color-singlet models. Theoretical efforts to improve the calculations added color octet contributions that increased the predicted cross sections, e.g., in the nonrelativistic QCD (NRQCD) model [2]. Recently there have been other approaches that do not directly introduce a color octet amplitude; rather, they incorporate the effects of multiple gluon processes during the production process, e.g., the k_T-factorization formalism [3] and the gluon tower model [4].

The NRQCD model with parametrized production matrix elements adjusted to data can successfully account for the Tevatron prompt cð2SÞ cross section measurements, but it makes an unequivocal prediction of increasing transverse polarization of vector mesons as their transverse momentum p_T from production increases [2]. A recent polarization measurement at CDF [5] contradicts the NRQCD model prediction.

Experimentally, the extraction of directJ=c ^production information is complicated by significant feed-down from decays of promptly produced higher-mass charmonium

states ðc;cð2SÞÞ toJ=c mesons. This is not a problem for direct cð2SÞproduction because there are no reported charmonium states with significant hadronic production cross sections that decay to the cð2SÞ. Consequently the cð2SÞprovides an ideal testing ground for studying charmonium hadroproduction mechanisms. In this paper we present a measurement of thep_T dependence of thecð2SÞ production cross section over the cð2SÞ transverse momentum range 2< p_Tðcð2SÞÞ<30 GeV=cwith rapidity jyðcð2SÞÞj<0:6. This measurement greatly increases the statistical power of the data in the perturbative regime (m_T _QCD), facilitating comparison with theory.

We use data taken using the CDF II detector at the Fermilab Tevatron at 1.96 TeV [6]. The integrated luminosity of the data sample is1:1 fb¹. The CDF II detector, described in detail elsewhere [7], includes a tracking system in a solenoidal 1.4 T magnetic field. Electromagnetic and hadronic calorimeters backed by muon detectors sur- round the tracker. The essential detector elements for this analysis are the silicon strip tracking detector (SVX II), the central drift chamber (COT), and the central muon system (CMU and CMP). The CMU is a four-layer planar drift chamber system outside the CDF magnet coil and calo- rimeter steel (5 interaction lengths). The CMP is another muon chamber system behind the CMU, shielded by an

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additional 0.6 m of iron in the flux return yoke. In this analysis, we use only information provided by the central sector of the detector, with pseudorapidityjj<0:6.

Muon candidates are identified by a first-level hardware- based trigger that reconstructs a charged track in four axial layers of the COT [8]. The trigger then projects the track into the CMU/CMP system and matches the projected trajectory to a collection of three or four hits in the CMU muon system within a search window around the extrapo- lated track [9]. The dimuon trigger requires two opposite- sign muon candidates each havingp_T >1:5 GeV=c.

The cð2SÞ !^þ candidates were reconstructed from muon pairs. The cð2SÞ events may originate from the primary interaction (prompt) or from decays of B hadrons (B decay). In off-line reconstruction, each muon had to have at least three hits in therstrips of SVX II in order to guarantee good vertex information to separate prompt and B-decay candidates. The minimum muonp_Tis2 GeV=c. If the CMU candidate has matching hits in the CMP chambers [7], the trackp_T requirement is raised to3 GeV=cto account for the extra iron traversed.

The cð2SÞmass and proper time distributions are used in a joint unbinned maximum likelihood fit to extract the prompt and B-decay signals in bins of p_T for cð2SÞ candidates. The mass component separates signal from background, while the proper time component separates prompt cð2SÞ events from those produced by B decays.

The mass signal probability distribution function is the sum of a Gaussian plus an asymmetric function (CBF) [10]

given by

CBF ¼ 8<

:

Ae^ððMm⁰^Þ²⁼²²^Þ ^Mm ⁰>; A ðⁿÞⁿ_ðMm^e^ð0 ²^=2Þ

þⁿÞⁿ Mm₀

;

wherem₀ is a fit parameter for the invariant mass peak,M is the dimuon invariant mass of each event, A is the normalization constant, the asymmetry parameter is the relative fraction of mass parton distribution function (PDF) due to the symmetric Gaussian term, and empirical parametersandndescribe the tails of the function:

P^mass_s ¼ ffiffiffiffiffiffiffiffiffiffiffiffi 2²

p e^ðMm^o^Þ²⁼²²þ ð1ÞCBFðn; ; Þ: CBF parametersandnand the asymmetry parameter are fixed by a fit to all data over the entirep_Trange, using thep_T dependence of the width parameteras given by simulation and fixing the absolute width in the highestp_T bin from this global fit. Thevalues are the same in the explicit Gaussian and in the CBF term. The results of the global fit fixto 0.834, meaning that the signal mass PDF is dominated by a symmetric single Gaussian function. The background mass PDF term is linear in mass.

The proper decay lengthct is used to identify prompt andB-decay contributions to the mass signal. Herect¼ L_xy=ðpT=MÞ, where L_xy is the transverse decay length

projected onto thecð2SÞmomentum. The prompt component is described by a double Gaussian function centered at zero (P^ct_p). The long-lived component is an exponential (P^ct_long). Because the cð2SÞ events from B decay come fromB_h!cð2SÞX, they do not have aB-hadron lifetime distribution. We use the effective lifetime of the B-decay signal as a fit parameter. Because it is defined in thecð2SÞ rest frame, it is the same in all p_T bins. Finally, the background in thectdistribution is described by the sum of a prompt double Gaussian (P^ct_pb) plus three exponentials, each convolved with a Gaussian resolution function: one symmetric about zero (P^ct_sym), one for positivectonly (P^ct_þ), and one for negativectonly (P^ct). The likelihood function is

L¼f_sP^mass_s ½f_pP^ct_p þ ð1f_pÞP^ct_long

þ ð1f_sÞP^mass_bkg½f_symP^ct_symþf_þP^ct_þþfP^ct

þ ð1f_symf_þfÞP^ct_pb: (1) The population fractions include f_s, the cð2SÞ signal fraction from the total number of candidates in the fit, f_p, the fraction of prompt cð2SÞ, f_sym, the fraction of symmetric long-lived background, f_þ, the fraction of positive-ct long-lived background, and f, the fraction of negative-ctlong-lived background.

The fit parameters are the width of the overall Gaussian in P^mass_s , the parameters of the double Gaussians for the prompt signal and backgroundctdensity distributions, the lifetime of the overall long-lived signal, the five data fractionsf_ifrom Eq. (1), and the parameters of the long- lived background functions in eachp_T bin. The fit projections in mass and proper time for 5:5< p_T <6:0 GeV=c are shown in Fig.1. Projecting the likelihood fits onto the mass distribution in eachp_T bin gives² probabilities in the range½0:4–100%. The fitted yields in eachp_T bin are summarized in Table I. Signal events are classified as prompt or long lived by the fit parameter f_p. For each cð2SÞp_T bin we know the total number of eventsN. The fit returns the signal fractionf_sand its uncertainty_f_s. The

2) m (GeV/

c

3.5 3.55 3.6 3.65 3.7 3.75 3.8 2Entries / 3 MeV/ c

0 200 400 600

(a)

ct (cm)

−0.2 −0.1 0 0.1 0.2 0.3

mµEntries / 40

1 10 102 103 104 (b)

FIG. 1 (color online). The projections on the invariant mass (a) and the proper decay length (b) for5:5< p_T<6:0 GeV=c. The fitted curve for total signal plus background is overlaid on the data points. The prompt (solid lines) and long-lived (dashed lines) proper time signal curves are shown separately.

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signal yield is S¼f_sN; ²_S¼ ð_f_s NÞ²þNf²_s. Analogous equations hold for the prompt yield P¼f_p Sand theB-decay yieldB¼ ð1f_sÞ S. The correlation between the signal fraction and the prompt fraction is considered in the uncertainty of the prompt andB-decay yield. The number of prompt andB-decay events are also listed in TableI.

We have checked the p_T dependence of all the fit parameters. The variation is smooth and shows no indications of rapid changes of the background functions at anyp_T. The prompt fraction decreases approximately linearly in the interval2< p_T<30 GeV=c.

The differential cross section is evaluated using the expression

dðcð2SÞÞ

dp_T ¼ Nðcð2SÞÞ A"_recoR

Ldtp_T: (2) Here ^dð_dp^c^ð2SÞÞ

T is the average cross section for cð2SÞ production in the givenp_T bin integrated over rapidity in the range jyj 0:6, Nðcð2SÞÞ is the number of cð2SÞ events determined by the fit, A is the geometric acceptance combined with the CDF dimuon trigger efficiency,

"_reco is the reconstruction efficiency, R

Ldt is the integrated luminosity of the data set, andp_T is the width of

the p_T bin. The acceptance and reconstruction efficiency are determined as follows.

The geometric acceptance is calculated by a Monte Carlo simulation (MC) method, using cð2SÞ ! ^þ decays generated uniformly for 1< p_T<

40 GeV=c, jyj<1, and 02. The cð2SÞdecays are handled by EVTGEN [11], allowing us to specify the decay polarization as transverse, longitudinal, or unpolar- ized. We generate independent MC sets for these three options. Tracking proceeds from the large-radius detectors inward, and matching silicon hits are added to COT tracks.

This makes the geometric acceptance insensitive to dis- placements of thecð2SÞdecay point on the scale of 1 mm, typical ofB-hadron flight paths in CDF. Therefore we use the same MC samples for calculating the geometric acceptance for both prompt andB-decay events. The systematic uncertainty for this assumption is negligible.

The MC events are passed through the CDF II GEANT- based simulation [12] and the standard CDF reconstruction. Events that pass the geometric selection are accepted based on each event’s dimuon trigger efficiency, derived from CDF data for muon pairs havingjyj 0:6with each muon havingp_T 2 GeV=c[13]. Variations with run and luminosity are included in the measurements. The prompt MC sample was analyzed with the likelihood fitter to check TABLE I. Event yields from the unbinned maximum likelihood fit and prompt event fraction.

Transverse momenta are inGeV=c. The uncertainties are statistical only.

pT hpTi Signal Prompt Prompt fraction Bdecay

2.0–2.5 2.3 196199 170196 0:8670:019 26039

2.5–3.0 2.8 5025157 4241152 0:8440:011 78558

3.0–3.5 3.2 7003177 5955170 0:8500:009 104864

3.5–4.0 3.8 6902171 5754166 0:8340:009 114863

4.0–4.5 4.2 7060160 5778153 0:8180:008 128260

4.5–5.0 4.7 6612147 5376141 0:8130:008 123657

5.0–5.5 5.2 5519133 4462127 0:8090:009 105752

5.5–6.0 5.7 5236121 4213114 0:8050:009 102350

6.0–6.5 6.2 4663111 3636108 0:7800:011 102751

6.5–7.0 6.7 396199 310594 0:7840:011 85745

7.0–7.5 7.2 317387 240881 0:7590:012 76541

7.5–8.0 7.7 273578 206673 0:7560:013 66837

8.0–8.5 8.2 220969 158962 0:7200:014 61935

8.5–9.0 8.7 180462 126156 0:6990:016 54332

9.0–9.5 9.2 141855 98749 0:6960:019 43029

9.5–10.0 9.7 117050 80045 0:6840:021 36927

10.0–11.0 10.5 169260 113454 0:6700:018 55833

11.0–12.0 11.5 120651 81045 0:6720:021 39528

12.0–13.0 12.5 78841 51136 0:6480:026 27723

13.0–14.0 13.5 56035 33130 0:5910:032 22921

14.0–15.0 14.5 41029 24025 0:5860:036 17017

15.0–17.5 16.1 51936 28430 0:5470:036 23522

17.5–20.0 18.6 24226 12922 0:5350:058 11215

20.0–25.0 22.1 20225 11722 0:5770:063 8614

25.0–30.0 27.1 7417 4514 0:6090:106 299

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forp_T variations in prompt selection efficiency. None were seen.

DeterminingA is sensitive to the cð2SÞ polarization parameter , which defines the muon decay angular distribution in the vector meson rest frame:dN=dcos¼1þ cos². The polar angle is measured from the vector meson’s direction in the laboratory frame.

We have previously measured thecð2SÞpolarization in threep_T bins for prompt events and the average polarization inB-decay events [5]. With 15% probability a² fit shows that the three measured points are consistent with

¼0. We use this as a basis to make the assumption that the polarization parameter is constant over thep_T range of the data. Averaging the three measured points gives an average parameter ¼0:010:13, which is used to de- termineA and its polarization-dependent systematic uncertainty. The prompt acceptance A varies from 2% at p_T ¼3 GeV=cto 20% atp_T ¼23 GeV=c.

For B-decay events we use the same procedure. The polarization dependence is calculated using the measured B-decay polarization _eff ¼0:360:250:03 [5]. The B-decay acceptance varies from 1.5% atp_T ¼3 GeV=cto 19% atp_T ¼23 GeV=c. Since the polarization is different for the prompt andB-decay events, a weighted average of

the acceptances in each p_T bin is used for the inclusive differential cross section.

The reconstruction efficiency is the product of tracking and muon selection efficiencies measured in CDF data, including the tracking efficiencies for the COT (0:996 0:009), SVX II (0:9580:006), and the dimuon tracking and selection efficiency (0:8750:019). Combining all the factors and adding the uncertainties in quadrature gives

"_reco¼0:8050:038.

Because the instantaneous CDF trigger rate might ex- ceed our data handling capacity, the dimuon trigger, like many others, is prescaled. The integrated luminosity for the data sample has to be reduced by the luminosity-dependent dimuon trigger prescale factor to calculate the cross section. This is done on a run-by-run basis and has negligible statistical or systematic uncertainty. The 1:1 fb¹ sample luminosity is reduced to 0:95 fb¹ for this trigger. The resulting inclusive cross sections for prompt and B-decay production are listed in TableII. The prompt andB-decay data are plotted versusp_T in Fig.2(a). Data from the run I CDF measurement [1] are also included in Fig.2(b).

The major systematic uncertainties on these results are due to the systematic uncertainty in the luminosity determination (6%) [14] and the polarization uncertainty in the

TABLE II. The differential cross section (pb=GeV=c) times the dimuon branching fraction as a function ofp_Tforjyj 0:6. For the B-decay measurement the symbol Br includes the branching fraction forbquark inclusive decay tocð2SÞX as well as the dimuon branching fraction ofcð2SÞ.

p_T(GeV=c) Inclusive_dp^d

TBr(pb=GeV=c) Prompt_dp^d

TBr(pb=GeV=c) Bdecay_dp^d

TBr(pb=GeV=c)

2.0–2.5 114458132 95354113 1912845

2.5–3.0 115336112 9463495 2071532

3.0–3.5 103726102 8562487 1811130

3.5–4.0 7791973 6301861 149823

4.0–4.5 6111460 4831349 128621

4.5–5.0 4901148 3831039 107518

5.0–5.5 316829 248723 68310

5.5–6.0 262624 204619 5838

6.0–6.5 189517 143413 4626

6.5–7.0 146413 111310 3525

7.0–7.5 105:42:99:5 77:12:67:1 28:31:53:8

7.5–8.0 81:92:37:4 59:82:15:5 22:11:22:9

8.0–8.5 60:91:95:5 42:11:73:9 18:81:12:5

8.5–9.0 45:41:64:0 30:51:32:7 14:90:91:8

9.0–9.5 32:31:32:8 21:81:11:9 10:50:71:2

9.5–10.0 25:91:12:2 17:21:01:5 8:70:60:9

10.0–11.0 17:70:61:5 11:40:541:0 6:30:40:7

11.0–12.0 11:960:51:1 7:720:430:69 4:240:300:51

12.0–13.0 7:330:390:64 4:560:330:40 2:770:230:31

13.0–14.0 5:030:320:44 2:850:260:24 2:180:200:24

14.0–15.0 3:420:250:29 1:930:200:16 1:490:150:15

15.0–17.5 1:610:110:14 0:850:090:07 0:760:070:08

17.5–20.0 0:680:070:06 0:350:060:03 0:330:050:03

20.0–25.0 0:270:030:02 0:150:030:01 0:120:020:01

25.0–30.0 0:0890:0200:007 0:0530:0170:004 0:0360:0110:003

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acceptance calculation (9% at low p_T, 2% at high p_T).

Other systematic uncertainties arise fromp_T variations in the trigger (<3%) and reconstruction efficiencies (4.7%).

Systematic uncertainties due to the mass shape parametrization, fitting function parametrization, and prompt fraction determination are all less than 1%. The data in Fig.2 have both statistical and systematic uncertainties included.

The integrated cross sections are calculated by summing the differential cross sections acrossp_T bins. The systematic uncertainty on the integrated cross section is calculated

by assuming that all sources of uncertainty are fully correlated among p_T bins, with the exception of the trigger efficiency uncertainty, which is uncorrelated among p_T bins. After calculating the uncertainty on the integrated cross section from each source, the total uncertainty is calculated by summing the individual contributions in quadrature.

The integrated inclusive differential cross section for p_T>2 GeV=candjyj<0:6is measured to be

p_Tðcð2SÞÞ>2 GeV=c ðpp !cð2SÞXÞ Brðcð2SÞ !þÞ ¼3:290:04ðstatÞ 0:32ðsystÞ nb:

For comparison to the run I measurement, we limit thep_Trange top_T>5 GeV=c. Then the measured integrated inclusive cross section is

p_Tðcð2SÞÞ>5 GeV=c ðpp !cð2SÞXÞ Brðcð2SÞ !^þÞ ¼0:690:01ðstatÞ 0:06ðsystÞ nb:

At 1.8 TeV the integrated inclusive cross section for p_T>5 GeV=c and pseudorapidity <0:6 was 0:57 0:04^þ0:08_0:09 nb [1]. The increase is ð2119Þ%, compared to a theoretical prediction ofð148Þ%based on changes in the parton energy distribution at the higher collision energy [15]. The uncertainty on the experimental ratio is dominated by the run I measurement due to its much lower statistics.

Promptcð2SÞproduction has a harderp_Tspectrum than that forJ=c production [7]. We compute the ratioRof the two differential cross sections evaluated at the same p_T range for each vector meson. Thep_Tbinning is matched to the J=c measurements of Ref. [7]. Since both measurements use the CDF apparatus, most systematic uncertainties cancel in the ratio. The luminosity uncertainty is fully correlated and is shown explicitly in the error bars in Fig.3(a). The increase in the ratio at largerp_T reflects the slope difference. Even though it neglects any feed- down contributions toJ=c prompt production, the model of Ref. [4] predicts thep_Tdependence of this behavior, as

shown by the dashed line in Fig.3(a). The model prediction is normalized to these data in the p_T bin covering 8–9 GeV=c. This same behavior is seen in the ratio of cross sections for production from B decay, also shown in Fig.3(a). The ratio of these two ratios is independent of p_T, as shown in Fig.3(b). There is no theoretical motiva- tion for this relation.

In conclusion, we have measured thep_T dependence of the cross section forcð2SÞproduction inpp production at 1.96 TeV. These data have at least an order of magnitude more events than the run I measurements and show more precisely the trends seen in those data. The increase in the inclusive cross section at the higher energy of run II (1.96 TeV) compared to run I (1.8 TeV) agrees with expectations based on the increase in parton energy distribution.

These data extend the cð2SÞ differential cross section measurement up to30 GeV=c. They are an important input

(GeV/ ) c pT

0 5 10 15 20 25 30

BR (nb/(GeV/ )) c×T/dPσd

10−5

10−4

10−3

10−2

10−1

1

Run II Prompt Run II B decay

(a)

(GeV/ ) c pT

0 5 10 15 20 25 30

BR (nb/(GeV/ )) c×T/dPσd

10−6

10−5

10−4

10−3

10−2

10−1

1 Run II Prompt

Run I Prompt

× 0.1 Run II B decay

× 0.1 Run I B decay

(b)

FIG. 2 (color online). (a) Prompt and B-decay production cross section distributions versus p_T for these data. (b) The same data with the run I points included. We ignore differences between rapidity and pseudorapidity for this comparison. The B-decay points have been scaled down by a factor of 10 for clarity of display.

(GeV/ ) c pT

0 2 4 6 8 10 12 14 16 18 20

R

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Rp Rb Khoze et al

(a)

(GeV/ ) c pT

2 4 6 8 10 12 14

p/RbR

0 0.5 1 1.5 2 2.5

(b)

FIG. 3 (color online). (a) The differential cross section ratio of cð2SÞ to J=c as a function of vector meson p_T for prompt events (Rp) andB-decay events (Rb). The main error bar on each point is the quadrature sum of the statistical and uncorrelated systematic uncertainties for that p_T bin. The extensions to the error bars show the correlated uncertainty from the luminosity.

The dashed line is calculated using the prompt ratio predicted from Ref. [4] normalized to data for the p_T bin covering 8–9 GeV=c. (b) The ratio of B decay to prompt ratiosRb=Rp

as a function of vector mesonp_T. The fit to a constant gives a² of 13 for 14 degrees of freedom.

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for an update of the matrix elements in the NRQCD factorization approach [2]. In the gluon tower model [4], the prompt hadroproduction ofJ=c^, cð2SÞ, andstates has been calculated. The uncertainties of their calculation are rather large but their cross section prediction with adjusted parameters describes the published Tevatron data. In addition, their mechanism predicts a longitudinal polarization ofJ=c at large transverse momentum which agrees qualitatively with the recent Tevatron measurement [5]. We hope that in future calculations with this and other models the uncertainties can be reduced in order to make a meaningful comparison to these new cross section data. A successful description of both the cross section data and polarization measurements in the perturbative p_T region would demonstrate a good understanding of the charmonium hadroproduction mechanisms.

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 the 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 fu¨r Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Science and Technology Facilities Council and the Royal Society, U.K.; the Institut National de Physique Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Ministerio de Ciencia e Innovacio´n, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; and the Academy of Finland.

[1] F. Abeet al.(CDF Collaboration), Phys. Rev. Lett.79, 572 (1997).

[2] G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev. D 51, 1125 (1995); 55, 5853(E) (1997); E. Braaten and S. Fleming, Phys. Rev. Lett.74, 3327 (1995). A discussion of recent developments in heavy quarkonium theory can be found in P. Artoisenet et al., Phys. Rev. Lett. 101, 152001 (2008). See also a recent review of this same work by J. P. Lansberg, Eur. Phys. J. C61, 693 (2009).

[3] S. P. Baranov, Phys. Rev. D66, 114003 (2002).

[4] V. A. Khoze, A. D. Martin, M. G. Ryskin, and W. J.

Stirling, Eur. Phys. J. C39, 163 (2005).

[5] A. Abulenciaet al.(CDF Collaboration), Phys. Rev. Lett.

99, 132001 (2007).

[6] The CDF coordinate system hasz^along the proton direction,x^horizontal pointing outward from the Tevatron ring, andy^ vertical. ðÞis the polar (azimuthal) angle measured with respect toz^andis the pseudorapidity defined

aslnðtanð=2ÞÞ. The transverse momentum of a particle is denoted aspT¼psin.

[7] D. Acosta et al.(CDF Collaboration), Phys. Rev. D71, 032001 (2005).

[8] E. J. Thomson et al., IEEE Trans. Nucl. Sci. 49, 1063 (2002).

[9] R. Downing et al., Nucl. Instrum. Methods Phys. Res., Sect. A570, 36 (2007).

[10] J. Gaisser, Report No. SLAC-0255, 1982.

[11] D. J. Lange, Nucl. Instrum. Methods Phys. Res., Sect. A 462, 152 (2001).

[12] E. Gerchtein and M. Paulini, arXiv:physics/0306031.

[13] D. Acostaet al.(CDF Collaboration), Phys. Rev. Lett.93, 032001 (2004).

[14] S. Klimenko, J. Konigsberg, and T. M. Liss, Report No. FERMILAB-N-741, 2003.

[15] K. Anikeevet al., arXiv:hep-ph/0201071.