First Measurement of the W Boson Mass in Run II of the Tevatron
aa r X i v : . [ h e p - e x ] N ov First Measurement of the W Boson Massin 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, A. Annovi, J. Antos, M. Aoki, G. Apollinari, T. Arisawa, A. Artikov, W. Ashmanskas, A. Attal, A. Aurisano, F. Azfar, P. Azzi-Bacchetta, P. Azzurri, N. Bacchetta, W. Badgett, A. Barbaro-Galtieri, V.E. Barnes, B.A. Barnett, S. Baroiant, V. Bartsch, G. Bauer, P.-H. Beauchemin, F. Bedeschi, S. Behari, G. Bellettini, J. Bellinger, A. Belloni, D. Benjamin, A. Beretvas, J. Beringer, T. Berry, A. Bhatti, M. Binkley, D. Bisello, I. Bizjak, R.E. Blair, C. Blocker, B. Blumenfeld, A. Bocci, A. Bodek, V. Boisvert, G. Bolla, A. Bolshov, D. Bortoletto, J. Boudreau, A. Boveia, B. Brau, L. Brigliadori, C. Bromberg, E. Brubaker, J. Budagov, H.S. Budd, S. Budd, K. Burkett, G. Busetto, P. Bussey, A. Buzatu, K. L. Byrum, S. Cabrera q , M. Campanelli, M. Campbell, F. Canelli, A. Canepa, S. Carrillo i , D. Carlsmith, R. Carosi, S. Carron, B. Casal, M. Casarsa, A. Castro, P. Catastini, D. Cauz, M. Cavalli-Sforza, A. Cerri, L. Cerrito m , S.H. Chang, Y.C. Chen, M. Chertok, G. Chiarelli, G. Chlachidze, F. Chlebana, I. Cho, K. Cho, D. Chokheli, J.P. Chou, G. Choudalakis, S.H. Chuang, K. Chung, W.H. Chung, Y.S. Chung, M. Cilijak, C.I. Ciobanu, M.A. Ciocci, A. Clark, D. Clark, M. Coca, G. Compostella, M.E. Convery, J. Conway, B. Cooper, K. Copic, M. Cordelli, G. Cortiana, F. Crescioli, C. Cuenca Almenar q , J. Cuevas l , R. Culbertson, J.C. Cully, S. DaRonco, M. Datta, S. D’Auria, T. Davies, D. Dagenhart, P. de Barbaro, S. De Cecco, A. Deisher, G. De Lentdecker c , G. De Lorenzo, M. Dell’Orso, F. Delli Paoli, L. Demortier, J. Deng, M. Deninno, D. De Pedis, P.F. Derwent, G.P. Di Giovanni, C. Dionisi, B. Di Ruzza, J.R. Dittmann, M. D’Onofrio, C. D¨orr, S. Donati, P. Dong, J. Donini, T. Dorigo, S. Dube, J. Efron, R. Erbacher, D. Errede, S. Errede, R. Eusebi, H.C. Fang, S. Farrington, I. Fedorko, W.T. Fedorko, R.G. Feild, M. Feindt, J.P. Fernandez, R. Field, G. Flanagan, R. Forrest, S. Forrester, M. Franklin, J.C. Freeman, I. Furic, M. Gallinaro, J. Galyardt, J.E. Garcia, F. Garberson, A.F. Garfinkel, C. Gay, H. Gerberich, D. Gerdes, S. Giagu, P. Giannetti, K. Gibson, J.L. Gimmell, C. Ginsburg, N. Giokaris a , M. Giordani, P. Giromini, M. Giunta, G. Giurgiu, V. Glagolev, D. Glenzinski, M. Gold, N. Goldschmidt, J. Goldstein b , A. Golossanov, G. Gomez, G. Gomez-Ceballos, M. Goncharov, O. Gonz´alez, I. Gorelov, A.T. Goshaw, K. Goulianos, A. Gresele, S. Grinstein, C. Grosso-Pilcher, R.C. Group, U. Grundler, J. Guimaraes da Costa, Z. Gunay-Unalan, C. Haber, K. Hahn, S.R. Hahn, E. Halkiadakis, A. Hamilton, B.-Y. Han, J.Y. Han, R. Handler, F. Happacher, K. Hara, D. Hare, M. Hare, S. Harper, R.F. Harr, R.M. Harris, M. Hartz, K. Hatakeyama, J. Hauser, C. Hays, M. Heck, A. Heijboer, B. Heinemann, J. Heinrich, C. Henderson, M. Herndon, J. Heuser, D. Hidas, C.S. Hill b , D. Hirschbuehl, A. Hocker, A. Holloway, S. Hou, M. Houlden, S.-C. Hsu, B.T. Huffman, R.E. Hughes, U. Husemann, J. Huston, J. Incandela, G. Introzzi, M. Iori, A. Ivanov, B. Iyutin, E. James, D. Jang, B. Jayatilaka, D. Jeans, E.J. Jeon, S. Jindariani, W. Johnson, M. Jones, K.K. Joo, S.Y. Jun, J.E. Jung, T.R. Junk, T. Kamon, P.E. Karchin, Y. Kato, Y. Kemp, R. Kephart, U. Kerzel, V. Khotilovich, B. Kilminster, D.H. Kim, H.S. Kim, J.E. Kim, M.J. Kim, S.B. Kim, S.H. Kim, Y.K. Kim, N. Kimura, L. Kirsch, S. Klimenko, M. Klute, B. Knuteson, B.R. Ko, K. Kondo, D.J. Kong, J. Konigsberg, A. Korytov, A.V. Kotwal, A.C. Kraan, J. Kraus, M. Kreps, J. Kroll, N. Krumnack, M. Kruse, V. Krutelyov, T. Kubo, S. E. Kuhlmann, T. Kuhr, N.P. Kulkarni, Y. Kusakabe, S. Kwang, A.T. Laasanen, S. Lai, S. Lami, S. Lammel, M. Lancaster, R.L. Lander, K. Lannon, A. Lath, G. Latino, I. Lazzizzera, T. LeCompte, J. Lee, J. Lee, Y.J. Lee, S.W. Lee o , R. Lef`evre, N. Leonardo, S. Leone, S. Levy, J.D. Lewis, C. Lin, C.S. Lin, M. Lindgren, E. Lipeles, T.M. Liss, A. Lister, D.O. Litvintsev, T. Liu, N.S. Lockyer, A. Loginov, M. Loreti, R.-S. Lu, D. Lucchesi, P. Lujan, P. Lukens, G. Lungu, L. Lyons, J. Lys, R. Lysak, E. Lytken, P. Mack, D. MacQueen, R. Madrak, K. Maeshima, K. Makhoul, T. Maki, P. Maksimovic, S. Malde, S. Malik, G. Manca, A. Manousakis a , F. Margaroli, R. Marginean, C. Marino, C.P. Marino, A. Martin, M. Martin, V. Martin g , M. Mart´ınez, R. Mart´ınez-Ballar´ın, T. Maruyama, P. Mastrandrea, T. Masubuchi, H. Matsunaga, M.E. Mattson, R. Mazini, P. Mazzanti, K.S. McFarland, P. McIntyre, R. McNulty f , A. Mehta, P. Mehtala, S. Menzemer h , A. Menzione, P. Merkel, C. Mesropian, A. Messina, T. Miao, N. Miladinovic, J. Miles, R. Miller, C. Mills, M. Milnik, A. Mitra, G. Mitselmakher, A. Miyamoto, S. Moed, N. Moggi, B. Mohr, C.S. Moon, R. Moore, M. Morello, P. Movilla Fernandez, J. M¨ulmenst¨adt, A. Mukherjee, Th. Muller, R. Mumford, P. Murat, M. Mussini, J. Nachtman, A. Nagano, J. Naganoma, K. Nakamura, I. Nakano, A. Napier, V. Necula, C. Neu, M.S. Neubauer, J. Nielsen n , L. Nodulman, O. Norniella, E. Nurse, S.H. Oh, Y.D. Oh, I. Oksuzian, T. Okusawa, R. Oldeman, R. Orava, K. Osterberg, C. Pagliarone, E. Palencia, V. Papadimitriou, A. Papaikonomou, A.A. Paramonov, B. Parks, S. Pashapour, J. Patrick, G. Pauletta, M. Paulini, C. Paus, D.E. Pellett, A. Penzo, T.J. Phillips, G. Piacentino, J. Piedra, L. Pinera, K. Pitts, C. Plager, L. Pondrom, X. Portell, O. Poukhov, N. Pounder, F. Prakoshyn, A. Pronko, J. Proudfoot, F. Ptohos e , G. Punzi, J. Pursley, J. Rademacker b , A. Rahaman, V. Ramakrishnan, N. Ranjan, I. Redondo, B. Reisert, V. Rekovic, P. Renton, M. Rescigno, S. Richter, F. Rimondi, L. Ristori, A. Robson, T. Rodrigo, E. Rogers, S. Rolli, R. Roser, M. Rossi, R. Rossin, P. Roy, A. Ruiz, J. Russ, V. Rusu, H. Saarikko, A. Safonov, W.K. Sakumoto, G. Salamanna, O. Salt´o, L. Santi, S. Sarkar, L. Sartori, K. Sato, P. Savard, A. Savoy-Navarro, T. Scheidle, P. Schlabach, E.E. Schmidt, M.P. Schmidt, M. Schmitt, T. Schwarz, L. Scodellaro, A.L. Scott, A. Scribano, F. Scuri, A. Sedov, S. Seidel, Y. Seiya, A. Semenov, L. Sexton-Kennedy, A. Sfyrla, S.Z. Shalhout, M.D. Shapiro, T. Shears, P.F. Shepard, D. Sherman, M. Shimojima k , M. Shochet, Y. Shon, I. Shreyber, A. Sidoti, P. Sinervo, A. Sisakyan, A.J. Slaughter, J. Slaunwhite, K. Sliwa, J.R. Smith, F.D. Snider, R. Snihur, M. Soderberg, A. Soha, S. Somalwar, V. Sorin, J. Spalding, F. Spinella, T. Spreitzer, P. Squillacioti, M. Stanitzki, A. Staveris-Polykalas, R. St. Denis, B. Stelzer, O. Stelzer-Chilton, D. Stentz, J. Strologas, D. Stuart, J.S. Suh, A. Sukhanov, H. Sun, I. Suslov, T. Suzuki, A. Taffard p , R. Takashima, Y. Takeuchi, R. Tanaka, M. Tecchio, P.K. Teng, K. Terashi, J. Thom d , A.S. Thompson, E. Thomson, P. Tipton, V. Tiwari, S. Tkaczyk, D. Toback, S. Tokar, K. Tollefson, T. Tomura, D. Tonelli, S. Torre, D. Torretta, S. Tourneur, W. Trischuk, S. Tsuno, Y. Tu, N. Turini, F. Ukegawa, S. Uozumi, S. Vallecorsa, N. van Remortel, A. Varganov, E. Vataga, F. Vazquez i , G. Velev, C. Vellidis a , G. Veramendi, V. Veszpremi, M. Vidal, R. Vidal, I. Vila, R. Vilar, T. Vine, M. Vogel, I. Vollrath, I. Volobouev o , G. Volpi, F. W¨urthwein, P. Wagner, R.G. Wagner, R.L. Wagner, J. Wagner, W. Wagner, R. Wallny, S.M. Wang, A. Warburton, D. Waters, M. Weinberger, W.C. Wester III, B. Whitehouse, D. Whiteson p , A.B. Wicklund, E. Wicklund, G. Williams, H.H. Williams, P. Wilson, B.L. Winer, P. Wittich d , S. Wolbers, C. Wolfe, T. Wright, X. Wu, S.M. Wynne, A. Yagil, K. Yamamoto, J. Yamaoka, T. Yamashita, C. Yang, U.K. Yang j , Y.C. Yang, W.M. Yao, G.P. Yeh, J. Yoh, K. Yorita, T. Yoshida, G.B. Yu, I. Yu, S.S. Yu, J.C. Yun, L. Zanello, A. Zanetti, I. Zaw, X. Zhang, J. Zhou, and S. Zucchelli (CDF Collaboration ∗ ) Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China Argonne National Laboratory, Argonne, Illinois 60439 Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain Baylor University, Waco, Texas 76798 Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy Brandeis University, Waltham, Massachusetts 02254 University of California, Davis, Davis, California 95616 University of California, Los Angeles, Los Angeles, California 90024 University of California, San Diego, La Jolla, California 92093 University of California, Santa Barbara, Santa Barbara, California 93106 Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain Carnegie Mellon University, Pittsburgh, PA 15213 Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637 Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia Joint Institute for Nuclear Research, RU-141980 Dubna, Russia Duke University, Durham, North Carolina 27708 Fermi National Accelerator Laboratory, Batavia, Illinois 60510 University of Florida, Gainesville, Florida 32611 Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy University of Geneva, CH-1211 Geneva 4, Switzerland Glasgow University, Glasgow G12 8QQ, United Kingdom Harvard University, Cambridge, Massachusetts 02138 Division of High Energy Physics, Department of Physics,University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland University of Illinois, Urbana, Illinois 61801 The Johns Hopkins University, Baltimore, Maryland 21218 Institut f¨ur Experimentelle Kernphysik, Universit¨at Karlsruhe, 76128 Karlsruhe, Germany High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan 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 Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720 University of Liverpool, Liverpool L69 7ZE, United Kingdom University College London, London WC1E 6BT, United Kingdom Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Institute of Particle Physics: McGill University, Montr´eal,Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7 University of Michigan, Ann Arbor, Michigan 48109 Michigan State University, East Lansing, Michigan 48824 University of New Mexico, Albuquerque, New Mexico 87131 Northwestern University, Evanston, Illinois 60208 The Ohio State University, Columbus, Ohio 43210 Okayama University, Okayama 700-8530, Japan Osaka City University, Osaka 588, Japan University of Oxford, Oxford OX1 3RH, United Kingdom University of Padova, Istituto Nazionale di Fisica Nucleare,Sezione di Padova-Trento, I-35131 Padova, Italy LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France University of Pennsylvania, Philadelphia, Pennsylvania 19104 Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa,Siena and Scuola Normale Superiore, I-56127 Pisa, Italy University of Pittsburgh, Pittsburgh, Pennsylvania 15260 Purdue University, West Lafayette, Indiana 47907 University of Rochester, Rochester, New York 14627 The Rockefeller University, New York, New York 10021 Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1,University of Rome “La Sapienza,” I-00185 Roma, Italy Rutgers University, Piscataway, New Jersey 08855 Texas A&M University, College Station, Texas 77843 Istituto Nazionale di Fisica Nucleare, University of Trieste/ Udine, Italy University of Tsukuba, Tsukuba, Ibaraki 305, Japan Tufts University, Medford, Massachusetts 02155 Waseda University, Tokyo 169, Japan Wayne State University, Detroit, Michigan 48201 University of Wisconsin, Madison, Wisconsin 53706 Yale University, New Haven, Connecticut 06520
We present a measurement of the W boson mass using 200 pb − of 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 M W = (80413 ± stat ± syst =80413 ±
48) MeV/ c . 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 ∗ With visitors from a 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 CornellUniversity, 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 King-dom, h University of Heidelberg, D-69120 Heidelberg, Germany, i Universidad Iberoamericana, Mexico D.F., Mexico, j Universityof Manchester, Manchester M13 9PL, England, k Nagasaki Insti-tute of Applied Science, Nagasaki, Japan, l University de Oviedo,E-33007 Oviedo, Spain, m University of London, Queen Mary Col-
The standard model (SM) invokes the Higgs mecha-nism of spontaneous symmetry breaking to generate massfor 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- lege, London, E1 4NS, England, n University of California SantaCruz, Santa Cruz, CA 95064, o Texas Tech University, Lubbock,TX 79409, p University of California, Irvine, Irvine, CA 92697, q IFIC(CSIC-Universitat de Valencia), 46071 Valencia, Spain. son masses and the electromagnetic and weak gauge cou-plings. The prediction for the W boson mass M W interms of the precisely measured Z boson mass M Z , theFermi decay constant G F extracted from the muon life-time measurement, and the electromagnetic coupling α at the scale M Z , is given in the “on-shell” scheme by [1] M W = ¯ h c πα √ G F − c W )(1 − ∆ r ) , where c W = M W /M Z and ∆ r is the quantum-loop cor-rection. A precise measurement of M W provides a mea-surement of ∆ r . In the SM the contributions to ∆ r aredominated by the top quark and the Higgs boson loops,such that M W in conjunction with the top quark massconstrains the mass m H of the undiscovered Higgs boson.An m H constraint inconsistent with direct searches canindicate the presence of new physics, such as contribu-tions to ∆ r from supersymmetric particles [2].The W boson mass [1] has been measured most pre-cisely by the LEP [3, 4] and Tevatron [5] experiments,with the world-average M W = (80392 ±
29) MeV/ c [4].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 p T [6].The W → ℓν decays, characterized by a high- p T chargedlepton ( ℓ = e or µ ) and neutrino, can be selected withhigh purity and provide precise mass information.This analysis [7, 8] uses 200 pb − collected by theCDF II detector [7] in p ¯ p collisions at √ s = 1 .
96 TeVat the Tevatron. CDF II is a magnetic spectrometer sur-rounded by calorimeters and muon detectors. We use thecentral drift chamber (COT) [9], the central calorime-ter [10] with embedded wire chambers [11] at the electro-magnetic (EM) shower maximum, and the muon detec-tors [12] for identification of muons and electrons with | η | < p T > c [6], and matching muon chamber hits(EM calorimeter cluster with E T >
18 GeV).In the analysis, we select muons with a COT trackmatched to muon chamber hits and passing quality re-quirements, track p T >
30 GeV/ c , and a minimum-ionization signal in the calorimeter. Cosmic rays arerejected using COT hit timing [13]. We select elec-trons with track p T >
18 GeV/ c , EM cluster E T >
30 GeV [6, 7], and passing quality requirements on theCOT track and the track-cluster matching. Additionalrequirements are based on the ratio of the calorimeterenergy E to track momentum p ( E/pc < E Had /E EM < .
1, and the transverse shower profile [7].A veto on the presence of a second lepton suppresses Z boson background, with negligible loss of W bosonevents. Control samples of Z boson events require twooppositely charged leptons with the above criteria.The ~p T of the hadronic recoil ( ~u ) equals the vectorsum ~u = Σ i E i sin( θ i )ˆ n i /c over calorimeter towers [10], with energy E i , polar angle θ i , and transverse direc-tions specified by unit vectors ˆ n i . Energy associatedwith the charged lepton(s) is not included. We impose ~p T balance to infer the neutrino’s transverse momentum p νT ≡ | − ~p ℓT − ~u | [6] and the W transverse mass m T = q p ℓT p νT − ~p ℓT · ~p νT ) /c . We require p νT >
30 GeV/ c and | ~u | <
15 GeV/ c to obtain a W candidate sample ofhigh purity, whose m T and lepton p T distributions arestrongly correlated with M W . The sample consists of63964 W → eν and 51128 W → µν candidates.The W boson mass is extracted by performing binnedmaximum likelihood fits to the distributions of m T , p ℓT and p νT . We generate 800 templates as functions of M W between 80 GeV/ c and 81 GeV/ c using a custom MonteCarlo (MC) simulation [7] of boson production and de-cay, and of the detector response to the lepton(s) andhadronic recoil. The custom MC optimizes computingspeed and control of systematic uncertainties. The kine-matics of W and Z boson decays are obtained from the resbos [14] program. We tune the non-perturbativeform factor in resbos , which describes the boson p T spectrum at low p T , on the dilepton p T distributionsin the Z boson data. Single photons (FSR) radiatedfrom the final-state leptons are generated according tothe wgrad program [15]. The FSR photon energies areincreased by 10% (with an absolute uncertainty of 5%)to account for additional energy loss due to two-photonradiation [16]. wgrad is also used to estimate the initial-state QED radiation. We use the CTEQ6M [17] set ofparton distribution functions and their uncertainties.The custom MC performs a hit-level simulation ofthe 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 aregenerated and propagated to the calorimeter. COT hitsare generated according to the resolution ( ≈ µ m) andefficiencies 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- p T cosmic ray muons. Each muon’scomplete trajectory is fit to a single helix [13]. The fitsdetermine the relative locations of the sense wires, includ-ing gravitational and electrostatic displacements, with aprecision of a few microns. We constrain remaining mis-alignments, which cause a bias in the track curvature, bycomparing h E/pc i 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 (cid:10) /p ℓT ( µ ) (cid:11) to mea-sure any non-linearity due to mismodelling of the ion-ization energy loss and other smaller effects, and inbins of h cot θ ( µ ) i to measure the magnetic field non-uniformity. To account for the observed momentumnon-linearity, a downward 6% correction to the pre-dicted ionization energy loss is applied in the simula-
70 80 90 100 1100100200 /dof = 34 / 38 c ee fi Z ee m c c (GeV/ ) E ve n t s / ( . G e V / )
70 80 90 100 1100200400 /dof = 33 / 30 c mm fi Z mm m c c (GeV/ ) E ve n t s / ( . G e V / ) 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. tion to make the measured J/ψ mass independent of (cid:10) /p ℓT ( µ ) (cid:11) . The calibration derived from the J/ψ andΥ data yields M Z = (91184 ± stat ) MeV/ c (Fig. 1)from the Z → µµ data, consistent with the world aver-age [1, 4] of (91188 ±
2) MeV/ c . The systematic uncer-tainties due to QED radiative corrections and magneticfield non-uniformity dominate the total uncertainty of0.02% on the combined momentum scale, derived fromthe J/ψ,
Υ and Z boson mass fits.We simulate the electron cluster by merging theenergies of the primary electron and the proximatebremsstrahlung photons and conversion electrons. Thedistributions of electron and photon energy loss in thesolenoid coil, and leakage into the hadronic calorimeter,are determined using geant [18] as a function of E T .The fractional energy resolution is given by the quadra-ture sum of a sampling term (13.5%/ p E T / GeV) and aconstant term κ = (0 . ± . κ γ = (8 . ± . κ γ term contributes ≈ .
3% in quadrature to the effective constant term for theinclusive electron sample. The distribution of the under-lying event energy [7] in the cluster is simulated. We tune κ on the width of the E/pc peak (Fig. 2) of the W bosonsample, and κ γ on the width of the Z → ee mass peakwhen both electrons are radiative ( E/pc > . E/pc peak in bins of electron E T to determine the elec-tron energy scale and non-linearity. The position ofthe E/pc peak is sensitive to the number of radiationlengths X ( ≈ X by comparing the fraction of /dof = 17 / 16 c ) n e fi E/pc (W E ve n t s / . FIG. 2: The distribution of
E/pc for the W → eν data(points) and the best-fit simulation (histogram) including thesmall jet background (shaded). The arrows indicate the fit-ting range used for the electron energy calibration. The jetbackground, which is barely visible on this scale, contributesa negligible uncertainty in the calibrations of the electron en-ergy scale and the amount of radiative material. 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 M Z = (91190 ± stat )MeV/ c (Fig. 1), consistent with the world average [1, 4].For maximum precision, the energy scales from the WE/pc fit and the Z → ee mass fit are combined usingthe Best Linear Unbiased Estimate (BLUE) method [19],with a resulting uncertainty that is mostly statistical.The recoil ~u excludes towers in which the lepton(s) de-posit energy. The underlying event energy in these towersis measured from the nearby towers in W boson data, in-cluding its dependence on η ℓ and ~u . The resolution of ~u has jet-like and underlying event components, with thelatter modelled using data triggered on inelastic ¯ pp inter-actions. The recoil parameterizations are tuned on themean and r.m.s. of the ~p T imbalance between the dilep-ton ~p T and ~u in Z → ℓℓ events. The lepton identificationefficiency is measured as a function of u || = ~u · ~p ℓT /p ℓT ) c (GeV/ ) n e fi (Wu -15 -10 -5 0 5 10 15 ) c E ve n t s / ( G e V / c (GeV/ ) nmfi |u| (W ) c E ve n t s / ( G e V / FIG. 3: Left: The u || distribution for the electron channeldata (points) and simulation (histogram). Right: The | ~u | distribution for the muon channel. The mean and r.m.s. ofthe histograms agree between data and simulation, within thestatistical precisions of ≈ using the Z → ℓℓ data, in order to model its effect on the p ℓT and p νT distributions. Cross-checks of the recoil modelusing the W boson data show good agreement (Fig. 3). Distribution W boson mass (MeV/ c ) χ /dof m T ( e, ν ) 80493 ± stat ± syst p ℓT ( e ) 80451 ± stat ± syst p νT ( e ) 80473 ± stat ± syst m T ( µ, ν ) 80349 ± stat ± syst p ℓT ( µ ) 80321 ± stat ± syst p νT ( µ ) 80396 ± stat ± syst M W . The fit win-dows are 65 −
90 GeV/ c for the m T fit and 32 −
48 GeV/ c forthe p ℓT and p νT fits. The χ of the fit is computed using theexpected statistical errors on the data points. Backgrounds in the W boson candidate samples arisefrom misidentified jets containing high- p T tracks and EMclusters, Z → ℓℓ where a lepton is not reconstructed andmimics a neutrino, W → τ ν , π/K decays in flight (DIF),and cosmic rays. Jet, DIF, and cosmic ray backgroundsare estimated from the data to be less than 0.5% com-bined. The W → τ ν background is 0 .
9% (0 . Z → ℓℓ background is 6.6% (0.24%) in the muon(electron) channel, as estimated using a detailed geant -based detector simulation. The background shapes areobtained using simulation and data-derived distributions. Systematic W → eν W → µν Common p T ( W ) model 3 3 3QED radiation 11 12 11Parton distributions 11 11 11Lepton energy scale 30 17 17Lepton energy resolution 9 3 0Recoil energy scale 9 9 9Recoil energy resolution 7 7 7 u || efficiency 3 1 0Lepton removal 8 5 5Backgrounds 8 9 0Total systematic 39 27 26Total uncertainty 62 60 26TABLE II: Systematic and total uncertainties in MeV/ c forthe m T fits, which are the most precise. The last columnshows the correlated uncertainties. Table I shows the fit results from the m T (Fig. 4), p ℓT ,and p νT distributions. These fits are partially uncorre-lated and have different systematic uncertainties, thusproviding an important cross-check. The fit values werehidden during analysis by adding an unknown offset inthe range [-100, 100] MeV/ c . The systematic uncertain-ties (Table II) were evaluated by fitting MC events topropagate the analysis parameter uncertainties to M W .
60 70 80 90 100050010001500 /dof = 59 / 48 c T m nm fi W c c (GeV/ ) E ve n t s / ( . G e V / )
60 70 80 90 100050010001500 /dof = 86 / 48 c T m n e fi W c c (GeV/ ) E ve n t s / ( . G e V / ) FIG. 4: The m T distribution of the data (points) andthe best-fit simulation template (histogram) including back-grounds (shaded), for muons (top) and electrons (bottom).The arrows indicate the fitting range. The χ /dof for the elec-tron channel distribution receives large contributions from afew bins near 65 GeV/ c , which do not bias the mass fit. The consistency of the fit results (Table I) obtainedfrom the different distributions shows that the W bo-son production, decay, and the hadronic recoil are well-modeled. The statistical correlations (evaluated usingensembles of MC events) between the m T and p ℓT ( p νT )fit values is 69% (68%), and between the p ℓT and p νT fit values is 27%. We numerically combine (using theBLUE method) the six individually fitted M W values,including their correlations, to obtain M W = (80413 ± stat ± syst ) MeV/ c , with χ / dof = 4 . /
5. The m T , p ℓT and p νT fits in the electron (muon) channel contributeweights of 32.3% (47.7%), 8.9% (3.4%) and 6.8% (0.9%)respectively. This establishes an a-priori procedure toincorporate the information from individual fits. Themuon (electron) channel alone yields M W = (80352 ± c ( M W = (80477 ±
62) MeV/ c ) with χ / dof =1 . / . / m T ( p ℓT , p νT ) fit results from the muonand electron channels are consistent with a probability of7% (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. We mea-sure M W = (80413 ±
48) MeV/ c , the most precise sin-gle measurement to date, and we update the world av-erage [4] to M W = (80398 ±
25) MeV/ c . This analysissignificantly improves in precision over previous Tevatronmeasurements, not only through the increased integratedluminosity but also through improved analysis techniquesand understanding of systematic uncertainties. As manysimulation parameters are constrained by data controlsamples, their uncertainties are statistical in nature andare expected to be reduced with more data. Inclusion ofour result in the global electroweak fit [4, 7] reduces thepredicted mass of the SM Higgs boson by 6 GeV/ c anddecreases its range to m H = 76 +33 − GeV/ c .We thank the Fermilab staff and the technical staffs ofthe 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 Councilof Canada; the National Science Council of the Repub-lic of China; the Swiss National Science Foundation; theA.P. Sloan Foundation; the Bundesministerium f¨ur Bil-dung und Forschung, Germany; the Korean Science andEngineering Foundation and the Korean Research Foun-dation; the Science and Technology Facilities Council andthe Royal Society, UK; the Institut National de PhysiqueNucleaire et Physique des Particules/CNRS; the RussianFoundation for Basic Research; the Comisi´on Intermin-isterial de Ciencia y Tecnolog´ıa, Spain; the EuropeanCommunity’s Human Potential Programme; the Euro-pean Commission under the Marie Curie Programme; theSlovak R&D Agency; and the Academy of Finland. [1] W.-M. Yao et al. , J. Phys. G , 1 (2006).[2] S. Heinemeyer et al. , J. High Energy Phys. , 052(2006).[3] S. Schael et al. (ALEPH Collaboration), Eur. Phys. J. C , 309 (2006); G. Abbiendi et al. (OPAL Collaboration),Eur. Phys. J. C , 307 (2006); P. Achard et al. (L3 Col-laboration), Eur. Phys. J. C , 569 (2006); J. Abdallah et al. (DELPHI Collaboration), to be submitted to Eur.Phys. J. C.[4] LEP Collaborations and LEP Electroweak WorkingGroup, CERN-PH-EP/2006-042, and references therein.[5] T. Affolder et al. (CDF Collaboration), Phys. Rev. D ,052001 (2001); V. M. Abazov et al. (DØ Collaboration),Phys. Rev. D , 012001 (2002); B. Abbott et al. (DØCollaboration), Phys. Rev. D , 092006 (2000); B. Ab-bott et al. (DØ Collaboration), Phys. Rev. D , 092003(1998); V. M. Abazov et al. (CDF and DØ Collabora-tions), Phys. Rev. D , 092008 (2004).[6] Pseudorapidity is defined as η = − ln[tan( θ/ θ is the polar angle from the beam axis. Energy (momen-tum) transverse to the beam is denoted as E T ( p T ).[7] T. Aaltonen et al. (CDF Collaboration), submitted forpublication in Phys. Rev. D; hep-ex/0708.3642.[8] O. Stelzer-Chilton, Ph.D. thesis, University of Toronto,2005; I. Vollrath, Ph.D. thesis, ibid , 2006. [9] T. Affolder et al. , Nucl. Instrum. Methods Phys. Res. A , 249 (2004).[10] F. Abe et al. (CDF Collaboration), Nucl. Instrum. Meth-ods Phys. Res. A , 387 (1988).[11] A. Byon-Wagner et al. , IEEE Trans. Nucl. Sci. , 2567(2002).[12] G. Ascoli et al. , Nucl. Instrum. Methods Phys. Res. A , 33 (1988).[13] A. V. Kotwal, H. K. Gerberich, and C. Hays, Nucl. In-strum. Methods Phys. Res. A , 110 (2003).[14] C. Balazs and C.-P. Yuan, Phys. Rev. D , 5558 (1997);G. A. Ladinsky and C.-P. Yuan, Phys. Rev. D , R4239(1994); F. Landry, R. Brock, P. M. Nadolsky and C.-P.Yuan, Phys. Rev. D , 073016 (2003).[15] U. Baur, S. Keller, and D. Wackeroth, Phys. Rev. D ,013002 (1998).[16] C.M. Carloni Calame, G. Montagna, O. Nicrosini, andM. Treccani, Phys. Rev. D. , 037301 (2004).[17] J. Pumplin et al. , J. High Energy Phys. , 012 (2002).[18] R. Brun and F. Carminati, CERN Program Library LongWriteup, W5013, 1993 (unpublished), version 3.15.[19] L. Lyons, D. Gibaut, and P. Clifford, Nucl. Instrum.Methods Phys. Res. A270