First Measurement of the W Boson Mass in Run II of the Tevatron

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First Measurement of the W Boson Mass in Run II of

the Tevatron

T. Aaltonen, A. Abulencia, J. Adelman, T. Affolder, T. Akimoto, M.G.

Albrow, S. Amerio, D. Amidei, A. Anastassov, K. Anikeev, et al.

To cite this version:

in Run II of the Tevatron

T. Aaltonen,23 _{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,}53 _{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. Carrillo}i_,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. Cerrito}m_,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. Cuevas}l_,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 Lentdecker}c_,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. D¨orr,}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. Giokaris}a_,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. Goldstein}b_,42 _{A. Golossanov,}17

G. Gomez,11 _{G. Gomez-Ceballos,}33_{M. Goncharov,}53_{O. Gonz´alez,}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. Hill}b_,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. Lee}o_,53 _{R. Lef`evre,}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_{T.M. Liss,}24_{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 _{A. Manousakis}a_,15 _{F. Margaroli,}5 _{R. Marginean,}17

C. Marino,26 _{C.P. Marino,}24 _{A. Martin,}60 _{M. Martin,}25 _{V. Martin}g_,21 _{M. Mart´ınez,}3 _{R. Mart´ınez-Ballar´ın,}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. McNulty}f_,30 _{A. Mehta,}30 _{P. Mehtala,}23 _{S. Menzemer}h_,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

2 R. Moore,17_{M. Morello,}46_{P. Movilla Fernandez,}29 _{J. M¨ulmenst¨adt,}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. Nielsen}n_,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. Ptohos}e_,19 _{G. Punzi,}46 _{J. Pursley,}25 _{J. Rademacker}b_,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. Salt´o,}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. Taffard}p_,24 _{R. Takashima,}40 _{Y. Takeuchi,}55_{R. Tanaka,}40 _{M. Tecchio,}35

P.K. Teng,1 _{K. Terashi,}50 _{J. Thom}d_,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_{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. Vazquez}i_,18 _{G. Velev,}17 _{C. Vellidis}a_,46 _{G. Veramendi,}24_{V. Veszpremi,}48_{M. Vidal,}32

R. Vidal,17 _{I. Vila,}11 _{R. Vilar,}11_{T. Vine,}31 _{M. Vogel,}37 _{I. Vollrath,}34 _{I. Volobouev}o_,29 _{G. Volpi,}46 _{F. W¨urthwein,}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}p_,45 _{A.B. Wicklund,}2

E. Wicklund,17 _{G. Williams,}34 _{H.H. Williams,}45 _{P. Wilson,}17 _{B.L. Winer,}39 _{P. Wittich}d_,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. Yang}j_,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. Zucchelli}5

(CDF Collaboration)

1_{Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China} 2_{Argonne National Laboratory, Argonne, Illinois 60439}

3_{Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain} 4_{Baylor University, Waco, Texas 76798}

5_{Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy} 6_{Brandeis University, Waltham, Massachusetts 02254}

7_{University of California, Davis, Davis, California 95616} 8_{University of California, Los Angeles, Los Angeles, California 90024}

9_{University of California, San Diego, La Jolla, California 92093} 10_{University of California, Santa Barbara, Santa Barbara, California 93106} 11_{Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain}

12_{Carnegie Mellon University, Pittsburgh, PA 15213}

13_{Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637}

14_{Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia} 15_{Joint Institute for Nuclear Research, RU-141980 Dubna, Russia}

16_{Duke University, Durham, North Carolina 27708} 17_{Fermi National Accelerator Laboratory, Batavia, Illinois 60510}

18_{University of Florida, Gainesville, Florida 32611}

19_{Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy} 20_{University of Geneva, CH-1211 Geneva 4, Switzerland}

21_{Glasgow University, Glasgow G12 8QQ, United Kingdom} 22_{Harvard University, Cambridge, Massachusetts 02138} 23_{Division of High Energy Physics, Department of Physics,}

University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

25_{The Johns Hopkins University, Baltimore, Maryland 21218}

26_{Institut f¨ur Experimentelle Kernphysik, Universit¨at Karlsruhe, 76128 Karlsruhe, Germany} 27_{High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan}

28_{Center for High Energy Physics: Kyungpook National University,}

Taegu 702-701, Korea; Seoul National University, Seoul 151-742, Korea; SungKyunKwan University, Suwon 440-746, Korea

29_{Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720} 30_{University of Liverpool, Liverpool L69 7ZE, United Kingdom}

31_{University College London, London WC1E 6BT, United Kingdom}

32_{Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain} 33_{Massachusetts Institute of Technology, Cambridge, Massachusetts 02139}

34_{Institute of Particle Physics: McGill University, Montr´eal,}

Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7

35_{University of Michigan, Ann Arbor, Michigan 48109} 36_{Michigan State University, East Lansing, Michigan 48824} 37_{University of New Mexico, Albuquerque, New Mexico 87131}

38_{Northwestern University, Evanston, Illinois 60208} 39_{The Ohio State University, Columbus, Ohio 43210}

40_{Okayama University, Okayama 700-8530, Japan} 41_{Osaka City University, Osaka 588, Japan} 42_{University of Oxford, Oxford OX1 3RH, United Kingdom} 43_{University of Padova, Istituto Nazionale di Fisica Nucleare,}

Sezione di Padova-Trento, I-35131 Padova, Italy

44_{LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France} 45_{University of Pennsylvania, Philadelphia, Pennsylvania 19104}

46_{Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa,}

Siena and Scuola Normale Superiore, I-56127 Pisa, Italy

47_{University of Pittsburgh, Pittsburgh, Pennsylvania 15260} 48_{Purdue University, West Lafayette, Indiana 47907} 49_{University of Rochester, Rochester, New York 14627} 50_{The Rockefeller University, New York, New York 10021} 51_{Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1,}

University of Rome “La Sapienza,” I-00185 Roma, Italy

52_{Rutgers University, Piscataway, New Jersey 08855} 53_{Texas A&M University, College Station, Texas 77843}

54_{Istituto Nazionale di Fisica Nucleare, University of Trieste/ Udine, Italy} 55_{University of Tsukuba, Tsukuba, Ibaraki 305, Japan}

56_{Tufts University, Medford, Massachusetts 02155} 57_{Waseda University, Tokyo 169, Japan} 58_{Wayne State University, Detroit, Michigan 48201} 59_{University of Wisconsin, Madison, Wisconsin 53706}

60_{Yale University, New Haven, Connecticut 06520}

We present a measurement of the W boson mass using 200 pb−1of data collected in p¯p collisions at √_{s = 1.96 TeV by the CDF II detector at Run II of the Fermilab Tevatron. With a sample of 63964} W → eν candidates and 51128 W → µν candidates, we measure MW = (80413 ± 34stat± 34syst=

80413 ± 48) MeV/c2_{. This is the most precise single measurement of the W boson mass to date.}

PACS numbers: 13.38.Be, 14.70.Fm, 12.15.Ji, 13.85.Qk

The standard model (SM) [2] invokes the Higgs mecha-nism of spontaneous symmetry breaking to generate mass for the W and Z bosons, which mediate the weak force. The SU (2) × U(1) symmetry of the electroweak inter-action predicts the relation between the W and Z bo-son masses and the electromagnetic and weak gauge cou-plings. The prediction for the W boson mass MW in

terms of the precisely measured Z boson mass MZ, the

Fermi decay constant GF extracted from the muon

life-time measurement, and the electromagnetic coupling α

at the scale MZ, is given in the “on-shell” scheme by [3]

M2 W = ¯ h3 c πα √ 2GF 1 (1 − c2 W)(1 − ∆r) , (1) where cW = MW/MZ and ∆r is the quantum-loop

cor-rection. A precise measurement of MW provides a

mea-surement of ∆r. In the SM the contributions to ∆r are dominated by the top quark and the Higgs boson loops, such that MW in conjunction with the top quark mass

constrains the mass mHof the undiscovered Higgs boson.

An mH constraint inconsistent with direct searches can

contribu-4 tions to ∆r from supersymmetric particles [4].

The W boson mass [3] has been measured most pre-cisely by the LEP [5, 6] and Tevatron [7] experiments, with the world-average MW = (80392 ± 29) MeV/c2 [6].

At the Tevatron, W bosons are mainly produced in quark (q′_{) anti-quark (¯q) annihilation q}′_{q → W + X. Here X¯}

includes the QCD radiation that forms the “hadronic re-coil” balancing the boson’s transverse momentum pT [8].

The W → ℓν decays, characterized by a high-pT charged

lepton (ℓ = e or µ) and neutrino, can be selected with high purity and provide precise mass information.

This analysis [9, 10] uses 200 pb−1 _{collected by the}

CDF II detector [9] in p¯p collisions at √s = 1.96 TeV at the Tevatron. CDF II is a magnetic spectrometer surrounded by calorimeters and muon detectors. We use the central drift chamber (COT) [11], the central calorimeter [12] with embedded wire chambers [13] at the electromagnetic (EM) shower maximum, and the muon detectors [14] for identification of muons and electrons with |η| < 1 [8] and measurement of their four-momenta. The muon (electron) trigger requires a COT track with pT > 18(9) GeV/c [8], and matching muon chamber hits

(EM calorimeter cluster with ET > 18 GeV).

In the analysis, we select muons with a COT track matched to muon chamber hits and passing quality re-quirements, track pT > 30 GeV/c , and a

minimum-ionization signal in the calorimeter. Cosmic rays are rejected using COT hit timing [15]. We select elec-trons with track pT > 18 GeV/c , EM cluster ET >

30 GeV [8, 9], and passing quality requirements on the COT track and the track-cluster matching. Additional requirements are based on the ratio of the calorimeter energy E to track momentum p (E/pc < 2), the ratio of energies detected in the hadronic and EM calorimeters EHad/EEM < 0.1, and the transverse shower profile [9].

A veto on the presence of a second lepton suppresses Z boson background, with negligible loss of W boson events. Control samples of Z boson events require two oppositely charged leptons with the above criteria.

The ~pT of the hadronic recoil (~u) is computed as the

vector sum ~u = ΣiEisin(θi)ˆni/c over calorimeter

tow-ers [12], with energy Ei, polar angle θi, and transverse

directions specified by unit vectors ˆni. Energy associated

with the charged lepton(s) is not included. We impose ~

pT balance to infer the neutrino’s transverse momentum

pν

T ≡ | − ~pTℓ− ~u| [8] and the W transverse mass mT =

q 2 ( pℓ

T pνT− ~pTℓ· ~pTν)/c. We require pνT > 30 GeV/c

and |~u| < 15 GeV/c to obtain a W candidate sample of high purity, whose mT and lepton pT distributions are

strongly correlated with the W boson mass. Our final sample consists of 63964 W → eν candidates and 51128 W → µν candidates.

The W boson mass is extracted by performing binned maximum likelihood fits to the distributions of mT, pℓT

and pν

T. We generate 800 templates as functions of MW

between 80 GeV/c2_{and 81 GeV/c}2_{using a custom Monte}

Carlo (MC) simulation [9] of W boson production and

de-cay, and of the detector response to the charged lepton and hadronic recoil. The custom MC optimizes comput-ing speed and control of systematic uncertainties. The kinematics of W and Z boson decays are obtained from the resbos [16] program. resbos calculates the differ-ential production cross section d4_σ

dQ dy dqT dΩ , where Q, y,

and qT are the boson invariant mass, rapidity, and pT

respectively, and dΩ is the solid angle element in the de-cay lepton direction. The non-perturbative form factor which describes the qT spectrum at low qT is tuned on

the dilepton pT distributions in the Z boson data. Single

photons (FSR) radiated from the final-state leptons are generated according to the wgrad program [17]. The FSR photon energies are increased by 10% (with an ab-solute uncertainty of 5%) to account for additional energy loss due to two-photon radiation [18]. wgrad is also used to estimate the uncertainty due to QED radiation from the initial state (ISR) and interference between ISR and FSR. We use the CTEQ6M [19] set of parton distribution functions and their uncertainties.

The custom MC performs a hit-level simulation of the lepton track. A fine-grained model of passive ma-terial properties is used to calculate ionization and ra-diative energy loss and multiple Coulomb scattering. Bremsstrahlung photons and conversion electrons are generated and propagated to the calorimeter. COT hits are generated according to the resolution (≈ 150 µm) and efficiencies measured from muon tracks in Υ, W , and Z boson decays. A helix fit (with optional beam constraint) is performed to simulate the reconstructed track.

The alignment of the COT is performed using a high-purity sample of high-pT cosmic ray muons. Each muon’s

complete trajectory is fit to a single helix [15]. The fits determine the relative locations of the sense wires, includ-ing gravitational and electrostatic displacements, with a precision of a few microns. We constrain remaining mis-alignments, which cause a bias in the track curvature, by comparing hE/pci for electrons and positrons.

The tracker momentum scale is measured by template-fitting the J/ψ → µµ and Υ → µµ mass peaks. The J/ψ fits are performed in bins of 1/pℓ

T(µ)

to mea-sure any non-linearity due to mismodelling of the ioniza-tion energy loss and other smaller effects, and in bins of hcot θ(µ)i to measure the magnetic field non-uniformity. To account for the observed momentum non-linearity, a 6% correction to the predicted ionization energy loss is applied to make the measured J/ψ mass independent of 1/pℓ

T(µ). Applying the calibration derived from the

J/ψ and Υ data to the Z → µµ data, we measure MZ = (91184 ± 43stat) MeV/c2(Fig. 1), consistent with

the world average [3, 6] of (91188 ± 2) MeV/c2_{. The}

sys-tematic uncertainties due to QED radiative corrections and magnetic field non-uniformity dominate the total un-certainty of 0.02% on the combined momentum scale, de-rived from the J/ψ, Υ and Z boson mass fits.

70 80 90 100 110 0 200 400 /dof = 33 / 30 2 χ µ µ → Z µ µ m _c2 2 c (GeV/ ) Events / (0.5 GeV/ ) 70 80 90 100 110 0 100 200 /dof = 34 / 38 2 χ ee → Z ee m _c2 2 c (GeV/ ) Events / (0.5 GeV/ )

FIG. 1: The Z → µµ (top) and Z → ee (bottom) mass fits, showing the data (points) and the simulation (histogram). The arrows indicate the fitting range.

distributions of electron and photon energy loss in the solenoid coil, and leakage into the hadronic calorimeter, are determined using geant [20] as a function of ET.

The fractional energy resolution is given by the quadra-ture sum of a sampling term (13.5%/pET/GeV) and a

constant term κ = (0.89 ± 0.15)% applied to the cluster energy, and an additional constant term κγ = (8.3±2.2)%

applied only to the energies of bremsstrahlung photons and conversion electrons. The κγ term contributes ≈

1.3% in quadrature to the effective constant term for the inclusive electron sample. The distribution of the under-lying event energy [21] in the cluster is simulated. We tune κ on the width of the E/pc peak (Fig. 2) of the W boson sample, and κγ on the width of the Z → ee mass

peak when both electrons are radiative (E/pc > 1.06). Given the tracker momentum calibration, we fit the E/pc peak in bins of electron ET to determine the

elec-tron energy scale and non-linearity. The position of the E/pc peak is sensitive to the number of radiation lengths x0(≈19%), due to bremsstrahlung upstream of the COT.

We constrain x0 by comparing the fraction of electrons

with high E/pc between data and simulation. Applying the E/pc-based energy calibration, we fit the Z → ee mass peak and measure MZ = (91190 ± 67stat) MeV/c2

(Fig. 1), consistent with the world average [3, 6]. For maximum precision, the energy scales from the E/pc fit and the Z → ee mass fit are combined using the Best Linear Unbiased Estimate (BLUE) method [22], with a resulting uncertainty that is predominantly statistical.

The recoil ~u excludes towers in which the lepton(s) de-posit energy. The underlying event energy in these towers

1 1.5 0 2000 4000 /dof = 17 / 16 2 χ ) ν e → E/pc (W Events/0.01

FIG. 2: The distribution of E/pc for the W → eν data (points) and the best-fit simulation (histogram) including the small jet background (shaded). The arrows indicate the fit-ting range used for the electron energy calibration.

is measured from the nearby towers in W boson data, in-cluding its dependence on ηℓ _{and ~u. The resolution of ~u}

has jet-like and underlying event components, with the latter modelled using data triggered on inelastic ¯pp inter-actions. The recoil parameterizations are tuned on the mean and r.m.s. of the ~pT imbalance between the

dilep-ton ~pT and ~u in Z → ℓℓ events. The lepton identification

efficiency is measured as a function of u|| = ~u · ~pTℓ/pTℓ

using the Z → ℓℓ data, in order to model its effect on the pℓ

T and pνT distributions. Cross-checks of the recoil model

using the W boson data show good agreement (Fig. 3). Backgrounds in the W boson candidate samples arise from misidentified jets containing high-pT tracks and EM

clusters, Z → ℓℓ where one of the leptons is not recon-structed and mimics a neutrino, W → τν, kaon and pion decays in flight (DIF), and cosmic rays (the latter two in the muon channel only). Jet, DIF, and cosmic ray back-grounds are estimated from the data to be less than 0.5% combined. The W → τν background is 0.9% (0.9%), and the Z → ℓℓ background is 6.6% (0.24%) in the muon (electron) channel, as estimated using a detailed

geant-) c (GeV/ ) ν e → (W u -15 -10 -5 0 5 10 15 ) c Events / (2 GeV/ 0 5000 10000 15000 ) c (GeV/ ) ν µ → |u| (W 0 5 10 15 ) c Events / (GeV/ 0 5000

FIG. 3: Left: The u|| distribution for the electron channel

6

Distribution W boson mass (MeV/c2_{) χ}2_/dof

mT(e, ν) 80493 ± 48stat± 39syst 86/48

pℓ

T(e) 80451 ± 58stat± 45syst 63/62

pν

T(e) 80473 ± 57stat± 54syst 63/62

mT(µ, ν) 80349 ± 54stat± 27syst 59/48

pℓ

T(µ) 80321 ± 66stat± 40syst 72/62

pν

T(µ) 80396 ± 66stat± 46syst 44/62

TABLE I: Fit results and uncertainties for MW. The fit

win-dows are 65 −90 GeV/c2_{for the m}

Tfit and 32 −48 GeV/c for

the pℓ

T and pνT fits. The χ2 of the fit is computed using the

expected statistical errors on the data points.

based detector simulation. The background shapes are obtained using simulation and data-derived distributions.

60 70 80 90 100 0 500 1000 /dof = 59 / 48 2 χ T m ν µ → W 2 c 2 c (GeV/ ) Events / (0.5 GeV/ ) 60 70 80 90 100 0 500 1000 1500 /dof = 86 / 48 2 χ T m ν e → W 2 c 2 c (GeV/ ) Events / (0.5 GeV/ )

FIG. 4: The mTdistribution of the data (points) and the

best-fit simulation template (histogram) including backgrounds (shaded), for muons (top) and electrons (bottom). The ar-rows indicate the fitting range. The χ2_{/dof for the electron}

channel distribution receives large contributions from a few bins near 65 GeV/c2_{, which do not bias the mass fit.}

Table I shows the fit results from the mT (Fig. 4), pℓT,

and pν

T distributions. These fits are partially

uncorre-lated and have different systematic uncertainties, thus providing an important cross-check. The fit values were hidden by adding an unknown offset in the range [-100, 100] MeV/c2 _{until the analysis was finalized. The}

sys-Systematic W → eν W → µν Common pT(W ) model 3 3 3

QED radiation 11 12 11 Parton distributions 11 11 11 Lepton energy scale 30 17 17 Lepton energy resolution 9 3 0

Recoil energy scale 9 9 9 Recoil energy resolution 7 7 7 u||efficiency 3 1 0

Lepton removal 8 5 5 Backgrounds 8 9 0 Total systematic 39 27 26 Total uncertainty 62 60 26 TABLE II: Systematic uncertainties in MeV/c2 _{for the m}

T

fits, which are the most precise. The last column shows the correlated uncertainties. The last row shows the combined statistical and systematic uncertainty.

tematic uncertainties (Table II) were evaluated by fitting MC events to propagate the previously discussed analysis parameter uncertainties to MW.

The consistency of the fit results (Table I) obtained from the different distributions shows that the W bo-son production, decay, and the hadronic recoil are well-modeled. The statistical correlations (evaluated using ensembles of MC events) between the mT and pℓT (pνT) fit

values is 69% (68%), and between the pℓ

T and pνT fit values

is 27%. We combine (using the BLUE method) the six W boson mass fits including all correlations to obtain MW =

(80413 ± 34stat± 34syst) MeV/c2, with χ2/dof = 4.8/5.

The mT, pℓT and pνT fits contribute weights of 80%, 12%

and 8% respectively. The muon (electron) channel alone yields MW = (80352 ± 60) MeV/c2(MW = (80477 ± 62)

MeV/c2_{) with χ}2_{/dof = 1.4/2 (0.8/2). The m}

T (pℓT, pνT)

fit results from the muon and electron channels are con-sistent with a probability of 7% (18%, 43%), taking into account their correlations.

In conclusion, we report the first measurement of the W boson mass from Run II of the Tevatron, using 200 pb−1_{and the muon and electron decay channels. We}

measure MW = (80413 ± 48) MeV/c2, the most precise

single measurement to date, and we update the world av-erage [6] to MW = (80398 ± 25) MeV/c2. This analysis

significantly improves in precision over previous Tevatron measurements, not only through the increased integrated luminosity but also through improved analysis techniques and understanding of systematic uncertainties. As many simulation parameters are constrained by data control samples, their uncertainties are statistical in nature and are expected to be reduced with more data. Inclusion of our result in the global electroweak fit [9] reduces the predicted mass of the SM Higgs boson by 6 GeV/c2 _and

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 Isti-tuto Nazionale di Fisica Nucleare; the Ministry of Educa-tion, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Repub-lic of China; the Swiss National Science Foundation; the A.P. Sloan Foundation; the Bundesministerium f¨ur

Bil-dung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foun-dation; the Science and Technology Facilities Council and the Royal Society, UK; the Institut National de Physique Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Comisi´on Intermin-isterial de Ciencia y Tecnolog´ıa, Spain; the European Community’s Human Potential Programme; the Euro-pean Commission under the Marie Curie Programme; the Slovak R&D Agency; and the Academy of Finland.

[1] With visitors froma_{University of Athens, 15784 Athens,}

Greece, b_{University of Bristol, Bristol BS8 1TL,}

United Kingdom, c_{University Libre de Bruxelles,}

B-1050 Brussels, Belgium, d_{Cornell University, Ithaca,}

NY 14853, e_{University of Cyprus, Nicosia CY-1678,}

Cyprus, f_{University College Dublin, Dublin 4, Ireland,} g_{University of Edinburgh, Edinburgh EH9 3JZ, United}

Kingdom, h_{University of Heidelberg, D-69120}

Heidel-berg, Germany, i_{Universidad Iberoamericana, Mexico}

D.F., Mexico, j_{University of Manchester, Manchester}

M13 9PL, England, k_{Nagasaki Institute of Applied}

Sci-ence, Nagasaki, Japan, l_{University de Oviedo, E-33007}

Oviedo, Spain,m_{University of London, Queen Mary}

Col-lege, London, E1 4NS, England,n_{University of California}

Santa Cruz, Santa Cruz, CA 95064, o_{Texas Tech}

Uni-versity, Lubbock, TX 79409, p_{University of California,}

Irvine, Irvine, CA 92697,q_{IFIC(CSIC-Universitat de}

Va-lencia), 46071 Valencia, Spain.

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