arX

iv:0

910.

0969

v1 [

hep-

ex]

6 O

ct 2

009

Measurements of the top-quark mass using charged particle tracking

T. Aaltonen,24 J. Adelman,14 T. Akimoto,56 B. Alvarez Gonzalezt,12 S. Amerioz,44 D. Amidei,35 A. Anastassov,39

A. Annovi,20 J. Antos,15 G. Apollinari,18 A. Apresyan,49 T. Arisawa,58 A. Artikov,16 W. Ashmanskas,18 A. Attal,4

A. Aurisano,54 F. Azfar,43 W. Badgett,18 A. Barbaro-Galtieri,29 V.E. Barnes,49 B.A. Barnett,26 P. Barriabb,47

V. Bartsch,31 G. Bauer,33 P.-H. Beauchemin,34 F. Bedeschi,47 D. Beecher,31 S. Behari,26 G. Bellettiniaa,47

J. Bellinger,60 D. Benjamin,17 A. Beretvas,18 J. Beringer,29 A. Bhatti,51 M. Binkley,18 D. Biselloz,44 I. Bizjakff ,31

R.E. Blair,2 C. Blocker,7 B. Blumenfeld,26 A. Bocci,17 A. Bodek,50 V. Boisvert,50 G. Bolla,49 D. Bortoletto,49

J. Boudreau,48 A. Boveia,11 B. Braua,11 A. Bridgeman,25 L. Brigliadoriy,6 C. Bromberg,36 E. Brubaker,14

J. Budagov,16 H.S. Budd,50 S. Budd,25 S. Burke,18 K. Burkett,18 G. Busettoz,44 P. Bussey,22 A. Buzatu,34

K. L. Byrum,2 S. Cabrerav,17 C. Calancha,32 M. Campanelli,36 M. Campbell,35 F. Canelli14,18 A. Canepa,46

B. Carls,25 D. Carlsmith,60 R. Carosi,47 S. Carrillon,19 S. Carron,34 B. Casal,12 M. Casarsa,18 A. Castroy,6

P. Catastinibb,47 D. Cauzee,55 V. Cavalierebb,47 M. Cavalli-Sforza,4 A. Cerri,29 L. Cerritop,31 S.H. Chang,28

Y.C. Chen,1 M. Chertok,8 G. Chiarelli,47 G. Chlachidze,18 F. Chlebana,18 K. Cho,28 D. Chokheli,16 J.P. Chou,23

G. Choudalakis,33 S.H. Chuang,53 K. Chung,13 W.H. Chung,60 Y.S. Chung,50 T. Chwalek,27 C.I. Ciobanu,45

M.A. Cioccibb,47 A. Clark,21 D. Clark,7 G. Compostella,44 M.E. Convery,18 J. Conway,8 M. Cordelli,20

G. Cortianaz,44 C.A. Cox,8 D.J. Cox,8 F. Crescioliaa,47 C. Cuenca Almenarv,8 J. Cuevast,12 R. Culbertson,18

J.C. Cully,35 D. Dagenhart,18 M. Datta,18 T. Davies,22 P. de Barbaro,50 S. De Cecco,52 A. Deisher,29

G. De Lorenzo,4 M. Dell’Orsoaa,47 C. Deluca,4 L. Demortier,51 J. Deng,17 M. Deninno,6 P.F. Derwent,18

A. Di Cantoaa,47 G.P. di Giovanni,45 C. Dionisidd,52 B. Di Ruzzaee,55 J.R. Dittmann,5 M. D’Onofrio,4

S. Donatiaa,47 P. Dong,9 J. Donini,44 T. Dorigo,44 S. Dube,53 J. Efron,40 A. Elagin,54 R. Erbacher,8 D. Errede,25

S. Errede,25 R. Eusebi,18 H.C. Fang,29 S. Farrington,43 W.T. Fedorko,14 R.G. Feild,61 M. Feindt,27 J.P. Fernandez,32

C. Ferrazzacc,47 R. Field,19 G. Flanagan,49 R. Forrest,8 M.J. Frank,5 M. Franklin,23 J.C. Freeman,18 I. Furic,19

M. Gallinaro,52 J. Galyardt,13 F. Garberson,11 J.E. Garcia,21 A.F. Garfinkel,49 P. Garosibb,47 K. Genser,18

H. Gerberich,25 D. Gerdes,35 A. Gessler,27 S. Giagudd,52 V. Giakoumopoulou,3 P. Giannetti,47 K. Gibson,48

J.L. Gimmell,50 C.M. Ginsburg,18 N. Giokaris,3 M. Giordaniee,55 P. Giromini,20 M. Giunta,47 G. Giurgiu,26

V. Glagolev,16 D. Glenzinski,18 M. Gold,38 N. Goldschmidt,19 A. Golossanov,18 G. Gomez,12 G. Gomez-Ceballos,33

M. Goncharov,33 O. Gonzalez,32 I. Gorelov,38 A.T. Goshaw,17 K. Goulianos,51 A. Greselez,44 S. Grinstein,23

C. Grosso-Pilcher,14 R.C. Group,18 U. Grundler,25 J. Guimaraes da Costa,23 Z. Gunay-Unalan,36 C. Haber,29

K. Hahn,33 S.R. Hahn,18 E. Halkiadakis,53 B.-Y. Han,50 J.Y. Han,50 F. Happacher,20 K. Hara,56 D. Hare,53

M. Hare,57 S. Harper,43 R.F. Harr,59 R.M. Harris,18 M. Hartz,48 K. Hatakeyama,51 C. Hays,43 M. Heck,27

A. Heijboer,46 J. Heinrich,46 C. Henderson,33 M. Herndon,60 J. Heuser,27 S. Hewamanage,5 D. Hidas,17

C.S. Hillc,11 D. Hirschbuehl,27 A. Hocker,18 S. Hou,1 M. Houlden,30 S.-C. Hsu,29 B.T. Huffman,43 R.E. Hughes,40

U. Husemann,61 M. Hussein,36 J. Huston,36 J. Incandela,11 G. Introzzi,47 M. Ioridd,52 A. Ivanov,8 E. James,18

D. Jang,13 B. Jayatilaka,17 E.J. Jeon,28 M.K. Jha,6 S. Jindariani,18 W. Johnson,8 M. Jones,49 K.K. Joo,28

S.Y. Jun,13 J.E. Jung,28 T.R. Junk,18 T. Kamon,54 D. Kar,19 P.E. Karchin,59 Y. Katol,42 R. Kephart,18

W. Ketchum,14 J. Keung,46 V. Khotilovich,54 B. Kilminster,18 D.H. Kim,28 H.S. Kim,28 H.W. Kim,28 J.E. Kim,28

M.J. Kim,20 S.B. Kim,28 S.H. Kim,56 Y.K. Kim,14 N. Kimura,56 L. Kirsch,7 S. Klimenko,19 B. Knuteson,33

B.R. Ko,17 S.A. Koay,11 K. Kondo,58 D.J. Kong,28 J. Konigsberg,19 A. Korytov,19 A.V. Kotwal,17 M. Kreps,27

J. Kroll,46 D. Krop,14 N. Krumnack,5 M. Kruse,17 V. Krutelyov,11 T. Kubo,56 T. Kuhr,27 N.P. Kulkarni,59

M. Kurata,56 S. Kwang,14 A.T. Laasanen,49 S. Lami,47 S. Lammel,18 M. Lancaster,31 R.L. Lander,8 K. Lannons,40

A. Lath,53 G. Latinobb,47 I. Lazzizzeraz,44 T. LeCompte,2 E. Lee,54 H.S. Lee,14 S.W. Leeu,54 S. Leone,47

J.D. Lewis,18 C.-S. Lin,29 J. Linacre,43 M. Lindgren,18 E. Lipeles,46 A. Lister,8 D.O. Litvintsev,18 C. Liu,48 T. Liu,18

N.S. Lockyer,46 A. Loginov,61 M. Loretiz,44 L. Lovas,15 D. Lucchesiz,44 C. Lucidd,52 J. Lueck,27 P. Lujan,29

P. Lukens,18 G. Lungu,51 L. Lyons,43 J. Lys,29 R. Lysak,15 D. MacQueen,34 R. Madrak,18 K. Maeshima,18

K. Makhoul,33 T. Maki,24 P. Maksimovic,26 S. Malde,43 S. Malik,31 G. Mancae,30 A. Manousakis-Katsikakis,3

F. Margaroli,49 C. Marino,27 C.P. Marino,25 A. Martin,61 V. Martink,22 M. Martınez,4 R. Martınez-Balların,32

T. Maruyama,56 P. Mastrandrea,52 T. Masubuchi,56 M. Mathis,26 M.E. Mattson,59 P. Mazzanti,6 K.S. McFarland,50

P. McIntyre,54 R. McNultyj ,30 A. Mehta,30 P. Mehtala,24 A. Menzione,47 P. Merkel,49 C. Mesropian,51 T. Miao,18

N. Miladinovic,7 R. Miller,36 C. Mills,23 M. Milnik,27 A. Mitra,1 G. Mitselmakher,19 H. Miyake,56 N. Moggi,6

C.S. Moon,28 R. Moore,18 M.J. Morello,47 J. Morlock,27 P. Movilla Fernandez,18 J. Mulmenstadt,29 A. Mukherjee,18

Th. Muller,27 R. Mumford,26 P. Murat,18 M. Mussiniy,6 J. Nachtmano,18 Y. Nagai,56 A. Nagano,56 J. Naganoma,56

K. Nakamura,56 I. Nakano,41 A. Napier,57 V. Necula,17 J. Nett,60 C. Neuw,46 M.S. Neubauer,25 S. Neubauer,27

J. Nielseng,29 L. Nodulman,2 M. Norman,10 O. Norniella,25 E. Nurse,31 L. Oakes,43 S.H. Oh,17 Y.D. Oh,28

2

I. Oksuzian,19 T. Okusawa,42 R. Orava,24 K. Osterberg,24 S. Pagan Grisoz,44 E. Palencia,18 V. Papadimitriou,18

A. Papaikonomou,27 A.A. Paramonov,14 B. Parks,40 S. Pashapour,34 J. Patrick,18 G. Paulettaee,55 M. Paulini,13

C. Paus,33 T. Peiffer,27 D.E. Pellett,8 A. Penzo,55 T.J. Phillips,17 G. Piacentino,47 E. Pianori,46 L. Pinera,19

K. Pitts,25 C. Plager,9 L. Pondrom,60 O. Poukhov∗,16 N. Pounder,43 F. Prakoshyn,16 A. Pronko,18 J. Proudfoot,2

F. Ptohosi,18 E. Pueschel,13 G. Punziaa,47 J. Pursley,60 J. Rademackerc,43 A. Rahaman,48 V. Ramakrishnan,60

N. Ranjan,49 I. Redondo,32 P. Renton,43 M. Renz,27 M. Rescigno,52 S. Richter,27 F. Rimondiy,6 L. Ristori,47

A. Robson,22 T. Rodrigo,12 T. Rodriguez,46 E. Rogers,25 S. Rolli,57 R. Roser,18 M. Rossi,55 R. Rossin,11

P. Roy,34 A. Ruiz,12 J. Russ,13 V. Rusu,18 B. Rutherford,18 H. Saarikko,24 A. Safonov,54 W.K. Sakumoto,50

O. Salto,4 L. Santiee,55 S. Sarkardd,52 L. Sartori,47 K. Sato,18 A. Savoy-Navarro,45 P. Schlabach,18 A. Schmidt,27

E.E. Schmidt,18 M.A. Schmidt,14 M.P. Schmidt∗,61 M. Schmitt,39 T. Schwarz,8 L. Scodellaro,12 A. Scribanobb,47

F. Scuri,47 A. Sedov,49 S. Seidel,38 Y. Seiya,42 A. Semenov,16 L. Sexton-Kennedy,18 F. Sforzaaa,47 A. Sfyrla,25

S.Z. Shalhout,59 T. Shears,30 P.F. Shepard,48 M. Shimojimar,56 S. Shiraishi,14 M. Shochet,14 Y. Shon,60

I. Shreyber,37 P. Sinervo,34 A. Sisakyan,16 A.J. Slaughter,18 J. Slaunwhite,40 K. Sliwa,57 J.R. Smith,8 F.D. Snider,18

R. Snihur,34 A. Soha,8 S. Somalwar,53 V. Sorin,36 T. Spreitzer,34 P. Squillaciotibb,47 M. Stanitzki,61 R. St. Denis,22

B. Stelzer,34 O. Stelzer-Chilton,34 D. Stentz,39 J. Strologas,38 G.L. Strycker,35 J.S. Suh,28 A. Sukhanov,19

I. Suslov,16 T. Suzuki,56 A. Taffardf ,25 R. Takashima,41 Y. Takeuchi,56 R. Tanaka,41 M. Tecchio,35 P.K. Teng,1

K. Terashi,51 J. Thomh,18 A.S. Thompson,22 G.A. Thompson,25 E. Thomson,46 P. Tipton,61 P. Ttito-Guzman,32

S. Tkaczyk,18 D. Toback,54 S. Tokar,15 K. Tollefson,36 T. Tomura,56 D. Tonelli,18 S. Torre,20 D. Torretta,18

P. Totaroee,55 S. Tourneur,45 M. Trovatocc,47 S.-Y. Tsai,1 Y. Tu,46 N. Turinibb,47 F. Ukegawa,56 S. Vallecorsa,21

N. van Remortelb,24 A. Varganov,35 E. Vatagacc,47 F. Vazquezn,19 G. Velev,18 C. Vellidis,3 M. Vidal,32 R. Vidal,18

I. Vila,12 R. Vilar,12 T. Vine,31 M. Vogel,38 I. Volobouevu,29 G. Volpiaa,47 P. Wagner,46 R.G. Wagner,2

R.L. Wagner,18 W. Wagnerx,27 J. Wagner-Kuhr,27 T. Wakisaka,42 R. Wallny,9 S.M. Wang,1 A. Warburton,34

D. Waters,31 M. Weinberger,54 J. Weinelt,27 W.C. Wester III,18 B. Whitehouse,57 D. Whitesonf ,46 A.B. Wicklund,2

E. Wicklund,18 S. Wilbur,14 G. Williams,34 H.H. Williams,46 P. Wilson,18 B.L. Winer,40 P. Wittichh,18

S. Wolbers,18 C. Wolfe,14 T. Wright,35 X. Wu,21 F. Wurthwein,10 S. Xie,33 A. Yagil,10 K. Yamamoto,42

J. Yamaoka,17 U.K. Yangq,14 Y.C. Yang,28 W.M. Yao,29 G.P. Yeh,18 K. Yio,18 J. Yoh,18 K. Yorita,58 T. Yoshidam,42

G.B. Yu,50 I. Yu,28 S.S. Yu,18 J.C. Yun,18 L. Zanellodd,52 A. Zanetti,55 X. Zhang,25 Y. Zhengd,9 and S. Zucchelliy,6

(CDF Collaboration†)1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

2Argonne National Laboratory, Argonne, Illinois 604393University of Athens, 157 71 Athens, Greece

4Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain5Baylor University, Waco, Texas 76798

6Istituto Nazionale di Fisica Nucleare Bologna, yUniversity of Bologna, I-40127 Bologna, Italy7Brandeis University, Waltham, Massachusetts 02254

8University of California, Davis, Davis, California 956169University of California, Los Angeles, Los Angeles, California 90024

10University of California, San Diego, La Jolla, California 9209311University of California, Santa Barbara, Santa Barbara, California 93106

12Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain13Carnegie Mellon University, Pittsburgh, PA 15213

14Enrico Fermi Institute, University of Chicago, Chicago, Illinois 6063715Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

16Joint Institute for Nuclear Research, RU-141980 Dubna, Russia17Duke University, Durham, North Carolina 27708

18Fermi National Accelerator Laboratory, Batavia, Illinois 6051019University of Florida, Gainesville, Florida 32611

20Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy21University of Geneva, CH-1211 Geneva 4, Switzerland

22Glasgow University, Glasgow G12 8QQ, United Kingdom23Harvard University, Cambridge, Massachusetts 02138

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 6180126The Johns Hopkins University, Baltimore, Maryland 21218

27Institut fur Experimentelle Kernphysik, Universitat Karlsruhe, 76128 Karlsruhe, Germany28Center for High Energy Physics: Kyungpook National University,Daegu 702-701, Korea; Seoul National University, Seoul 151-742,

3

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

29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 9472030University of Liverpool, Liverpool L69 7ZE, United Kingdom

31University College London, London WC1E 6BT, United Kingdom32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

33Massachusetts Institute of Technology, Cambridge, Massachusetts 0213934Institute of Particle Physics: McGill University, Montreal, Quebec,

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 2A335University of Michigan, Ann Arbor, Michigan 48109

36Michigan State University, East Lansing, Michigan 4882437Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

38University of New Mexico, Albuquerque, New Mexico 8713139Northwestern University, Evanston, Illinois 6020840The Ohio State University, Columbus, Ohio 43210

41Okayama University, Okayama 700-8530, Japan42Osaka City University, Osaka 588, Japan

43University of Oxford, Oxford OX1 3RH, United Kingdom44Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, zUniversity of Padova, I-35131 Padova, Italy

45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France46University of Pennsylvania, Philadelphia, Pennsylvania 19104

47Istituto Nazionale di Fisica Nucleare Pisa, aaUniversity of Pisa,bbUniversity of Siena and ccScuola Normale Superiore, I-56127 Pisa, Italy

48University of Pittsburgh, Pittsburgh, Pennsylvania 1526049Purdue University, West Lafayette, Indiana 47907

50University of Rochester, Rochester, New York 1462751The Rockefeller University, New York, New York 10021

52Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1,ddSapienza Universita di Roma, I-00185 Roma, Italy53Rutgers University, Piscataway, New Jersey 08855

54Texas A&M University, College Station, Texas 7784355Istituto Nazionale di Fisica Nucleare Trieste/Udine,

I-34100 Trieste, eeUniversity of Trieste/Udine, I-33100 Udine, Italy56University of Tsukuba, Tsukuba, Ibaraki 305, Japan

57Tufts University, Medford, Massachusetts 0215558Waseda University, Tokyo 169, Japan

59Wayne State University, Detroit, Michigan 4820160University of Wisconsin, Madison, Wisconsin 53706

61Yale University, New Haven, Connecticut 06520(Dated: October 6, 2009)

We present three measurements of the top-quark mass in the lepton plus jets channel with approx-imately 1.9 fb−1 of integrated luminosity collected with the CDF II detector using quantities withminimal dependence on the jet energy scale. One measurement exploits the transverse decay lengthof b-tagged jets to determine a top-quark mass of 166.9+9.5

−8.5 (stat)± 2.9 (syst) GeV/c2, and anotherthe transverse momentum of electrons and muons from W -boson decays to determine a top-quarkmass of 173.5+8.8

−8.9 (stat)±3.8 (syst) GeV/c2. These quantities are combined in a third, simultaneous

mass measurement to determine a top-quark mass of 170.7 ± 6.3 (stat) ± 2.6 (syst) GeV/c2.

PACS numbers: 12.15.-y, 13.85.-t, 14.60.-z, 14.65.Fy, 14.65.Ha

∗Deceased†With visitors from aUniversity of Massachusetts Amherst,Amherst, Massachusetts 01003, bUniversiteit Antwerpen, B-2610Antwerp, Belgium, cUniversity of Bristol, Bristol BS8 1TL,United Kingdom, dChinese Academy of Sciences, Beijing 100864,China, eIstituto Nazionale di Fisica Nucleare, Sezione di Cagliari,

09042 Monserrato (Cagliari), Italy, f University of CaliforniaIrvine, Irvine, CA 92697, gUniversity of California Santa Cruz,Santa Cruz, CA 95064, hCornell University, Ithaca, NY 14853,iUniversity of Cyprus, Nicosia CY-1678, Cyprus, jUniversity Col-lege Dublin, Dublin 4, Ireland, kUniversity of Edinburgh, Edin-burgh EH9 3JZ, United Kingdom, lUniversity of Fukui, Fukui

4

I. INTRODUCTION

An accurate knowledge of the top-quark mass is im-portant. Combined with other standard model param-eters, the top-quark mass can be used to constrain theexpected standard model Higgs mass. The most preciseconstraints place an upper bound on the Higgs mass of154 GeV/c2 [1] at the 95% confidence level. Further,since the top quark will be produced in copious quanti-ties at the LHC, its mass can serve as a benchmark forb-jet energy calibrations, which are otherwise difficult tostudy in data.

Historically, top-quark mass measurements have beenlimited by uncertainties in the simulation of jet energymeasurements. For example, in the CDF Run I measure-ment [2] the top-quark mass systematic uncertainty was4.9 GeV/c2, of which the contribution from the uncer-tainty on jet energy measurements was 4.4 GeV/c2. Incomparison, for a modern CDF Run II measurement [3],the systematic uncertainty is 1.2 GeV/c2, of which thecontribution from jet energy uncertainties is 0.7 GeV/c2.This dramatic improvement in the jet energy uncertaintyis made possible by exploiting the hadronic W -boson de-cay. By constraining the reconstructed W -boson massto agree between data and simulation, the average sim-ulated jet energy bias is determined and applied to alljets in the event. In this technique, widely used in RunII top-quark mass measurements, most of the jet energyuncertainty becomes a statistical uncertainty rather thana systematic uncertainty. The remaining systematic un-certainty results from the assumption that simulation isbiased by the same amount, on average, for the b-jets as itis for the W -boson jets that are used for the calibration.

While jet energy uncertainties are no longer as large asthey once were, they still represent a significant fractionof the total uncertainty on the top-quark mass. Further,this dramatic improvement in the world average mass res-olution depends upon the reliability of a single technique.Thus, it is desirable to develop independent methods tomeasure the top-quark mass as a cross-check. A noveltechnique has been proposed for measuring the top-quarkmass in a manner that is almost completely independentof the calorimeter using the measured transverse distance[4] that b-hadrons from the top quarks travel before de-

City, Fukui Prefecture, Japan 910-0017 mKinki University, Higashi-Osaka City, Japan 577-8502 nUniversidad Iberoamericana, Mex-ico D.F., Mexico, oUniversity of Iowa, Iowa City, IA 52242,pQueen Mary, University of London, London, E1 4NS, Eng-land, qUniversity of Manchester, Manchester M13 9PL, Eng-land, rNagasaki Institute of Applied Science, Nagasaki, Japan,sUniversity of Notre Dame, Notre Dame, IN 46556, tUniversityde Oviedo, E-33007 Oviedo, Spain, uTexas Tech University, Lub-bock, TX 79609, vIFIC(CSIC-Universitat de Valencia), 46071 Va-lencia, Spain, wUniversity of Virginia, Charlottesville, VA 22904,xBergische Universitat Wuppertal, 42097 Wuppertal, Germany,ffOn leave from J. Stefan Institute, Ljubljana, Slovenia,

caying (Lxy) [5]. The transverse momenta of the top-quark decay products depend approximately linearly onthe top-quark mass. In turn, this means that the lifetimeand decay length of the b-hadrons depend approximatelylinearly on the top-quark mass. When this measurementwas performed using 695 pb−1 of integrated luminosity[6], it became the first top-quark mass measurement tobe mostly independent of calorimeter-based uncertain-ties, however it was also very statistically limited. Be-sides tripling the integrated luminosity with respect tothe previous measurement, we also improve the statisti-cal resolution by incorporating more information aboutthe event. Similarly to b-hadrons, the transverse mo-menta (pT ) of leptons from W -boson decays also dependlinearly on the top-quark mass, and are mostly indepen-dent of the calorimeter jet energy scale. Since the mo-mentum of the leptons is mostly uncorrelated to that ofthe b-quarks, this is complementary information, and itis an ideal variable to add to the measurement, as hasbeen previously proposed [5] [7].

In this paper we present measurements of the top-quark mass using both the lepton transverse momentumand the mean decay length variables. Both measure-ments are performed upon the same events which pass anevent selection that is designed to isolate tt events wherethe W -boson from one top-quark decays to two quarkjets, and the other decays leptonically to an electron ora muon plus a neutrino (the lepton plus jets channel).This decay channel was chosen because it occurs moreoften than any other final state that can be isolated witha high signal purity. We compute the mean Lxy of theleading two b-tagged jets and the mean transverse mo-mentum of the leptons identified in the events. We mea-sure the top-quark mass through comparisons with themean Lxy and mean lepton pT from analysis simulations(“pseudoexperiments”) performed for a variety of top-quark mass hypotheses. To illustrate the dependence ofthese variables on the top-quark mass, the expected dis-tributions for tt signal events passing our event selectionare shown in Figure 1. It should be noted that our mea-surements are sensitive to very different event character-istics than typical mass measurements, and thus requireunique treatments. In particular, it is more important forus to correctly model the boost of the top quarks thanfor other measurements. Thus, we reweight our simu-lated signal events to a more accurate parton distribu-tion function. Further, the Lxy values that are measuredin our simulation are sensitive to a variety of possiblemodeling inaccuracies. We determine correction factorsto be applied to the simulated Lxy values by comparingthe Lxy measurements between data and simulation forbb events, parameterized as a function of the jet energies.

Our measurements will be mostly independent ofcalorimeter-based jet energy uncertainties. However,some small dependence will remain because a loose jetenergy cut is applied when selecting events, as will beexplained below. Further, this parameterization of theLxy correction as a function of jet energy introduces a jet

5

Lxy [cm]-0.5 0 0.5 1 1.5 2 2.5 30

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08 2 = 150 GeV/ctm

2 = 200 GeV/ctm

Entr

ies

/ (0

.05

cm)

(a)

Lepton p [GeV/c]0 20 40 60 80 100 120 140 160 180 200

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09 2 = 150 GeV/ctm

2 = 200 GeV/ctm

Frac

tio

n /

(4 G

eV/c

)

T

(b)

FIG. 1: Distributions of our measurement variables for simulated tt events after passing our event selection for top-quarkmasses separated by 50 GeV/c2. These distributions are normalized to unit area.

energy uncertainty to the measurement. In order to mini-mize this latter effect, we develop and apply an algorithmto measure jet energies for our Lxy correction parame-terization that is based upon charged particle tracking.

This paper is organized as follows. We first presentthe relevant parts of the CDF detector in Section II, andthe event selection used in this analysis in Section III.We then explain the procedures for determining the nor-malizations as well as the shapes of the Lxy and leptonpT distributions for our backgrounds. In Section V weexplain how we calibrate our signal distributions. In Sec-tion VI we present the procedures we apply to extractthe top-quark mass from our final Lxy and lepton mo-mentum distributions and present our results. Finally,in Section VII we explain in detail how our systematicuncertainties are estimated. We conclude with some pro-jections of the future potential for this type of measure-ment.

II. THE CDF II DETECTOR

We describe the most important parts of the CDF de-tector for this analysis. A more complete descriptioncan be found elsewhere [8]. The CDF detector consistsof cylindrically symmetric layers of hardware, each de-signed to perform specific functions. The CDF trackingsystem consists of a silicon tracker, inside of a wire driftchamber, immersed in a 1.4 T magnetic field producedby a superconducting solenoid. Calorimeters encircle thetracking system and consist of alternating layers of scin-tillator and absorber. The calorimeter system is split intoan inner calorimeter that is designed to absorb and mea-sure the energies of photons and electrons, and an outercalorimeter that is designed to absorb and measure theenergies of hadrons.

The wire drift chamber consists of 96 wire planesgrouped into eight superlayers covering the radial regionbetween 0.40 and 1.37 m from the beam axis, and less

than 1.0 in pseudorapidity. The superlayers alternatebetween axial and ±2◦ stereo angle to provide both axialand longitudinal hit information. The inner tracker con-sists of eight layers of double sided silicon, covering theradial range between 1.35 and 29 cm, and less than 2.0in pseudorapidity. Again, to provide longitudinal hit in-formation, some layers contain double-sided silicon thatcombines axially oriented strips with strips oriented ei-ther at 90◦ or 1.2◦ relative to the axial direction. Thesilicon tracker is vital for vertexing, providing a two-dimensional impact parameter resolution of about 40 µmfor isolated tracks with high transverse momentum, in-cluding uncertainties on both the track trajectory and thelocation of the collision vertex. The wire tracker is vitalfor the lepton measurements in this analysis, providinga transverse momentum resolution of about 5% for 50GeV/c muons. Leptons and b-jets are reliably identifiedout to a pseudorapidity of about 1.0, after which the ef-ficiency drops rapidly due to tracks falling outside of therange of full tracker coverage. Muon candidates are iden-tified by matching tracks in the inner tracking detectorwith track stubs in the outer muon drift chambers. Elec-tron candidates are identified by matching tracks in theinner tracking detector with showers in the electromag-netic calorimeter. An energy resolution of about 3% isachieved for electrons with 50 GeV of transverse energy.

The Tevatron proton-antiproton bunches cross one an-other at a rate of 2.5 MHz. During each crossing oneor more collisions are likely to occur. In order to reducethis flow of information to a manageable level and toselect collision events of interest to particular analyses,CDF employs a three level triggering system to sequen-tially reject events that are less relevant. The final eventstream is read out at a rate of roughly 100 Hz. Detailsof the triggering system are provided in [8].

6

III. EVENT SELECTION

In comparison to the previous publication using onlyLxy [6], we tighten the event selection in the analyses pre-sented here to reduce the systematic uncertainties. Thestatistical sensitivities of both the lepton momentum andthe decay length measurements depend linearly on thefraction of events in which top quarks are produced[9],and scale as the square root of the number of events se-lected. This tightened selection improves the former andworsens the latter, and has little impact on the final sta-tistical sensitivity.

The data used in this analysis were collected betweenMarch 2002 and May 2007, and correspond to an inte-grated luminosity of 1.9 fb−1. Events passing the fulltrigger and event selections described below are stud-ied to determine the expected event counts and un-certainties for each signal and background type. Topquarks almost always decay to Wb. Our selection crite-ria are designed to accept events where one W -bosondecays to an electron or muon plus neutrino and theother decays to two jets. We start from a triggeringstream that requires one electron (muon) to have trans-verse energy (momentum) greater than 18 GeV (GeV/c);these requirements will later be tightened slightly. Onceevents are accepted by the trigger, they are saved, re-constructed, and studied in greater detail. Calorime-ter towers are clustered together within a cone of radiusR =

√

(φtow − φjet)2 + (ηtow − ηjet)2 = 0.4 [10] to formjets. At least three jets must be found with |η| < 2.0,and transverse energy greater than 20 GeV after correct-ing for multiple interactions, calorimeter response, noise,and other non-uniformities. No attempt is made to cor-rect for interactions from spectator partons (“underlyingevent”) or out-of-cone effects [10], but systematic uncer-tainties are assigned for these effects. To account for theneutrino and suppress the QCD background, a quantitycalled the missing transverse energy is used, which is de-fined as the transverse component of the four-momentumvector that is needed to conserve momentum in the event[11]. The missing transverse energy in the event must begreater than 20 GeV. Additionally, an electron (muon)must be identified with transverse energy (momentum)greater than 20 GeV (GeV/c). Electrons are identifiedfrom a track pointing at a cluster in the calorimeter whichmatches the expected shape profile. Most of the energyof this cluster is required to be confined in the electro-magnetic calorimeter, the track momentum is requiredto agree with the measured calorimeter energy to withina factor of two, and if the track is consistent with theelectron having originated from a photon conversion, theelectron candidate is vetoed. Muons are formed fromtracks in the muon chambers which are matched to tracksfound in the inner tracking system. The calorimeter en-ergy deposits along the muon trajectory must be consis-tent with that of a minimum ionizing particle. Calorime-ter isolation is based upon the fraction of the lepton’senergy (fiso) in a cone of radius R=0.4 centered on the

lepton, excluding the energy in the calorimeters fromthe lepton itself. Both electrons and muons must sat-isfy fiso < 0.1. This cut eliminates most jets that aremistakenly identified as leptons (“fake leptons”) as wellas real leptons which result from b-hadron decays. Fur-ther, at least one collision vertex must be reconstructedfrom tracks in the event, and the track of the lepton mustpass within 3 cm along the beam axis of the highest mo-mentum vertex to minimize contamination from multipleinteractions and tracking errors. One electron or muon isrequired to pass these cuts, but to suppress events fromthe dilepton channel the event is vetoed if any other lep-tons are found passing a much looser set of cuts whichalso allow non-isolated and forward leptons. Finally, oneor more jets must be identified (tagged) as originatingfrom a b-quark, as explained below. In the case whereonly three jets pass our selection, two of them must betagged in order to reduce the large W+jets and non-WQCD backgrounds in this kinematic region.

Jets containing b-quarks are identified using a taggingalgorithm known as SecVtx [12], which relies upon thelong lifetime of hadrons originating from b-quarks. Thisalgorithm attempts to construct a secondary vertex us-ing tracks that are likely to have originated from a b-hadron decay. If a vertex can be found which is signifi-cantly displaced from the primary vertex, then the jet istagged. Specifically, the SecVtx algorithm selects tracksassociated with the jet that are displaced from the fit-ted primary collision vertex, and that are well resolvedin both the silicon and the outer tracking chamber. Asa first pass the algorithm uses relatively less stringentcuts on track selection, and attempts to fit at least threetracks into a displaced vertex. If no vertex is found thetracking requirements are tightened significantly and thealgorithm searches for a two-track vertex. Further cutsare applied to eliminate tracks that are likely to originatefrom material interactions or long lived strange particles.If a secondary vertex is found the jet is tagged as a b-jetif the transverse distance from the primary vertex pro-jected onto the jet direction (Lxy) and its uncertainty (σ)satisfy Lxy/σ > 7.5. It should be noted that charmeddaughters of the b-hadron are also likely to travel a signif-icant distance before decaying. The SecVtx algorithm isdeliberately designed to be loose enough to attach sometracks from these tertiary decays into one “pseudovertex”at a position that is averaged between two real vertices.Since the boosts of the charm hadrons depend on theboost of the b-hadron, this extra information does notdilute our mass resolution.

IV. SAMPLE COMPOSITION

For this analysis we will need to know the Lxy andlepton pT distributions for each of our signal and back-ground samples, as well as their relative normalizationsafter full event selection is enforced. Specifically, wenormalize our signal and background distributions us-

7

ing the results of a cross section measurement that wasperformed on the same data using identical event selec-tion. The procedures for this cross section measurementare briefly described in subsection IVA. The proceduresthat are used to determine our Lxy and lepton pT shapesfor the backgrounds are deferred to Section IVB.

A. Sample normalization

In this section we give a brief outline of how the crosssection measurement is performed to determine our sig-nal and background normalizations along with the asso-ciated uncertainties. Further information can be foundin the publications of similar cross section measurements[13] [14], or in the Ph.D. thesis [15] which explains thetechnique we apply in detail. For this measurement tech-nique we begin by determining the expected backgroundsassuming the expected standard model tt cross section.The tt cross section will then be revised and the back-grounds redetermined in an iterative manner until thenumber of expected events matches the observed eventcounts both before and after b-tagging.

First we determine the numbers of events for some ofthe rarest processes from simulation. Backgrounds mod-eled from simulation include single top production as wellas the electroweak diboson (WW , WZ, ZZ) and Z plusjets final states. The diboson events are simulated usingpythia version 6.216 [16]. The single top and Z plusjets samples are simulated using other programs (MadE-vent [17] for single top, and alpgen version 2.10 prime[18] for Z plus jets). Hadronic showers are simulatedusing pythia. For each sample, the event count is de-termined and scaled according to the theoretical crosssection, branching ratio, and detector and trigger accep-tances. The tt signal is also simulated using pythia. Itscross section is initially set equal to its standard modelexpectation. For all of these samples, EvtGen [19] is usedto determine the lifetimes and masses of the various b-hadron species within jets. A further scaling is appliedto correct the b-tagging efficiency modeling based upondata-driven studies [14].

Since fake leptons are difficult to simulate accurately,the non-W QCD contribution is determined from data.Missing transverse energy templates are made for tt, Wplus jet, and QCD distributions, and used in a fit to de-termine the QCD normalization. Templates for the fakeelectrons are filled from events where isolated electroncandidates are selected and required to have a calorimetershower profile that is consistent with QCD fakes ratherthan true electrons. For muons the standard cuts arekept except that the isolation cut is inverted to requiregreater than 20% isolation instead of less than 10%. Dif-ferent binnings, fit ranges, and cuts are applied and thedifferences in the results are taken as a systematic un-certainty. This fit is done separately in the tagged andpretagged cases.

The remainder of the observed pretagged events are

all taken to originate from W plus jets. The W plusjets sample is simulated using alpgen version 2.10prime [18], and the resulting partons are showered us-ing pythia. This sample is simulated in various bins ofjet multiplicity for the Wbb, Wcc, Wc, and W plus lightflavor final states. These samples are then weighted bytheir theoretical cross sections and combined. It is impor-tant to make sure that the proper number of heavy fla-vor jets are simulated before b-tagging is applied. Pythiashowering will double count heavy flavor production fromthe alpgen simulation, so this overlap must be removed.Further, since the samples are only generated at leadingorder, a correction is needed to reweight the heavy flavorfraction. This correction is taken from comparisons be-tween data and simulation in related samples with higherstatistics [14].

By construction, this procedure yields pretagged back-ground and signal normalizations that exactly match theobserved number of data events. After b-tagging, how-ever, fewer events were predicted than were observed,and this discrepancy is attributed to tt events. Thus, thesignal cross section was increased and the analysis wasrepeated in an iterative fashion. The tt cross section atwhich we found agreement was 8.2±0.7 pb (ignoring lumi-nosity uncertainties). The resulting event counts passingfull event selection and tagging requirements are shownin Table I, along with the number of jets in these eventswhich were b-tagged and included in our Lxy analysis.

TABLE I: Estimated signal and background contributions af-ter full event selection.

Source Events Recorded b-Tags

Wbb 25.4 ± 7.0 37.5 ± 9.7

Wcc or Wc 13.9 ± 4.6 15.9 ± 4.7

Wplus light flavor 16.9 ± 3.7 17.9 ± 3.7

non-WQCD 18.8 ± 12.7 20.2 ± 13.2

Electroweak 9.0 ± 0.4 11.3 ± 0.5

Single Top 8.4 ± 0.4 13.4 ± 0.7

tt 478.3 ± 40.3 659.3 ± 45.5

Total 570.8 ± 44.3 775.5 ± 50.2

B. Background Lxy and lepton pT shapes

The dominant backgrounds for our analysis are W plusheavy flavor (b and c jets), W plus light flavor mistags,and non-W QCD events. Along with single top and di-boson events, these distributions and the signal accountfor about 99% of events passing selection. The remainingevents come from the Z plus jets background, for whichthe related W plus jets background Lxy and lepton pT

distributions were used.Single top samples (with masses mt = 165, 170, 175,

and 180 GeV/c2) were generated in MadEvent and de-

8

cayed in pythia, in both the s- and t- channels. Resultsfor the s- and t- channels were combined, weighted ac-cording to their expected theoretical cross sections, andthe final decay length and lepton momentum distribu-tions were fit to Gaussian plus exponential distributions.The trends in the fit parameters were extrapolated toother mass points, and were used to generate new Lxyand lepton pT distributions for each mass hypothesis.The W plus jets background is selected in exactly thesame way as for the cross section measurement, as is thebackground for non-W QCD electrons. For non-W QCDbackground in the muon channel, instead of using non-isolated muons, we selected muon candidates with highenergy deposition in the calorimeter, or that were asso-ciated with tracks that were highly displaced from thecollision vertex. These cuts were chosen based on studiessuggesting that they produced a minimum of bias in thelepton pT distribution.

Our final Lxy and lepton pT distributions are shownin Figure 2 for events passing full selection. As cross-checks the same distributions in the background domi-nated one and two jet bins are shown in Figures 3 and4. These cross-check samples are used in evaluating thebackground based systematic uncertainty as described inSection VII.

V. CORRECTIONS TO THE SIGNAL

SIMULATION

Our tt events are simulated in pythia for various hy-pothetical top-quark mass values. A number of correc-tions are applied to the simulated results as discussedbelow. In Section VA we will discuss corrections thatare needed to account for simulated parton distributionfunction inaccuracies. It is also necessary to correct thesimulated Lxy measurements to match observations fromdata. An overview for this procedure is given in Sec-tion V B. We will parameterize the Lxy correction as afunction of the jet transverse energy as measured usingtracking. The procedure for this will be discussed in Sec-tion VC. We will summarize the complete decay lengthcalibration procedure in Section VD.

A. Parton distribution functions

For this analysis it is vital to have accurate models ofthe lepton and jet boosts. Since these quantities dependon the energy of the colliding partons, an accurate model-ing of parton distribution functions (PDFs) for particleswithin the proton is very important. The tt samples weregenerated using the leading order CTEQ5L parton distri-bution function [20]. One drawback of this PDF is that itunderestimates the rate of tt production by gluon fusion(5% in simulation observed versus about 15% expected[21]). Since gluon fusion produces events with slightlysmaller boosts on average, this will bias the analysis. In

addition, since the CTEQ5L PDF overestimates the frac-tion of the proton momentum carried by colliding quarks,the tt events produced within the quark-antiquark anni-hilation channel have artificially high boosts. To com-pensate for this effect, different parton distribution func-tions were studied. The Les Houches Accord PDF In-terface [22] was used to determine the probabilities foreach parton involved in the collision to have the gener-ated momentum for a given PDF. One can then reweightthe simulated events to construct distributions appropri-ate to a different PDF as explained in [23]. We use thisprescription to reweight all of our tt events to the next-to-leading order CTEQ6M [24] parton distribution functionfor gluon fusion and quark annihilation events separately.A further weighting is then applied to gluon fusion eventsto scale the gluon fusion fraction to the value expected forthe sample’s top-quark mass (20% for mt = 150 GeV/c2,10% for mt = 200 GeV/c2). These combined reweight-ings result in new distributions to be used in our massmeasurement and lead to a 1.7 GeV/c2 shift in the top-quark mass for the lepton pT analysis and a 0.9 GeV/c2

shift for the Lxy analysis, relative to the values obtainedusing CTEQ5L. A similar prescription is used to reweightto other PDFs and gluon fractions to evaluate systematicuncertainties, as will be explained in Section VII.

B. Lxy calibration strategy

A number of effects may bias the decay length mea-surement in simulation. Inaccuracies in the EvtGen [19]values for the hadron lifetime or in the simulated pro-duction fractions would have a direct impact. Similarly,inaccuracies in the pythia fragmentation model wouldlead to the wrong boost, and thus the wrong average de-cay length, of the b-hadrons. Entirely different problemsmay arise from any inaccuracies in the modeling of thetracking system, which could lead to biases in the vertex-ing results. Our approach is to calibrate the simulationdirectly to the data to compensate for all of these biasessimultaneously. Systematic uncertainties on this calibra-tion will be discussed in Section VII F. We select ourcalibration sample so that the tagged jets will be almostexclusively b-jets. We select dijet events where the jetsare required to open at a wide angle with ∆φ > 2.0. Bothjets must be b-tagged, and one of the jets must containa well resolved muon with at least 9.5 GeV/c transversemomentum. We also apply additional cuts to minimizeoverlap between jets which will be discussed later. Weestimate these samples to be about 95% bb, with the re-maining 5% coming from charm contamination, which isaccounted for as a small systematic uncertainty.

Since jets from bb events tend to have a much lowertransverse energy than those from tt events, the possibil-ity that a different calibration is needed for higher energyjets must be taken into account. To this end, we bin ourbb jets according to their energy, and derive the neededcorrection bin-by-bin, which we apply based on the mea-

9

Lxy [cm]-0.5 0 0.5 1 1.5 2 2.5 3 3.5

0

10

20

30

40

50

60

70

)-1

-0.5 0 0.5 1 1.5 2 2.5 3 3.50

10

20

30

40

50

60

70 = 8.2 pbσttbar,

Electroweak

Single Top

W+jet

QCD

data

Entr

ies

/ (0

.05

cm)

(a)

Lepton p [GeV / c]0 50 100 150 200 250 300

0

10

20

30

40

50

0 50 100 150 200 250 3000

10

20

30

40

50

= 8.2 pbσttbar,

Electroweak

Single Top

W+jet

QCD

data

T

Entr

ies

/ (4

GeV

/c)

(b)

FIG. 2: Signal, background, and data for the Lxy and lepton pT distributions passing full event selection under hypothesizedtop-quark masses that are close to the measured results. The left plot is for the Lxy measurement, using top-quark mass168 GeV/c2, and the right plot is for the lepton pT measurement, using top-quark mass 173 GeV/c2.

Lxy [cm]

-0.5 0 0.5 1 1.5 2 2.5 3 3.5

En

trie

s /

(0.0

5 c

m)

0

20

40

60

80

100

120

140

160

180

200

220

240

-0.5 0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120

140

160

180

200

220

240ttbar

Single Top

Electroweak

QCD

W+Jet

(a)

Lepton p [GeV/c]

0 20 40 60 80 100 120 140 160 180 200

En

trie

s /

(4 G

eV

/c)

0

50

100

150

200

250

300

0 20 40 60 80 100 120 140 160 180 2000

50

100

150

200

250

300 ttbar

Single Top

Electroweak

QCD

W+Jet

T

(b)

FIG. 3: Background prediction compared with data (black points) in the one-jet control region for Lxy (left) and lepton pT

(right).

sured energy of the tagged signal jet. Great care mustbe taken in doing this, however, as this kinematic basedcorrection directly introduces a jet energy scale uncer-tainty to the analysis. If, for example, the simulationunderestimates the energies of jets, then the average de-cay length in a given energy bin will be too high in thesimulation, throwing off the calibration. This is an un-avoidable uncertainty for any kind of calibration usingdijets. In fact, even if we could convince ourselves thatit was unnecessary to parameterize this decay length cal-ibration as a function of energy, a significant jet energyuncertainty would still be needed to cover the determi-nation of which jets pass selection in the simulation. Asour goal is to minimize the calorimeter jet energy uncer-

tainties, we choose to parameterize our calibration basedupon the energies of jets measured using tracking ratherthan the calorimetry.

C. Track-based jet energies

We develop a straightforward algorithm for computingthe track-based energy of a jet. We start with one ofour jets that has been clustered in the calorimeter in theusual manner. We select tracks that are within R = 0.4of the calorimeter jet direction in η−φ space. The tracksthemselves are required to be well resolved in both thewire tracking chamber and in the silicon, and they must

10

Lxy [cm]

-0.5 0 0.5 1 1.5 2 2.5 3 3.5

En

trie

s /

(0.0

5 c

m)

0

20

40

60

80

100

120

140

-0.5 0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120

140ttbar

Single Top

Electroweak

QCD

W+Jet

(a)

Lepton p [GeV/c]

0 20 40 60 80 100 120 140 160 180 200

En

trie

s /

(4 G

eV

/c)

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160ttbar

Single Top

Electroweak

QCD

W+Jet

T

(b)

FIG. 4: Background prediction compared with data (black points) in the two-jet control region for Lxy (left) and lepton pT

(right).

have a transverse momentum of at least 1 GeV/c. Wealso require that the tracks pass within 3 cm along thebeam axis of the fitted primary collision vertex. This cuteliminates about 85% of the contamination from multipleinteractions. We then take the total transverse compo-nent of the sum of our track four-vectors as our trackingtransverse energy. We make no attempt to correct for themissing neutral particles. Our goal is not to measure thetrue jet energy, but rather to measure a quantity that isproportional to the true energy (in this case, the chargedtransverse energy) in a manner that agrees well betweendata and simulation.

We calibrate the energies of our track jets with a simi-lar approach to the one used for calorimeter jets at CDF[10]. We select events where one photon and one jetare found back-to-back (∆φ > 3 radians), where no ex-tra jets in the event above 3 GeV in ET are allowed,and strict cuts on photon quality are applied to mini-mize fakes. Under such a selection, the transverse mo-mentum of the photon should reflect the true transversemomentum of the jet. As a first step we consider the ra-tio of the track-based transverse energy of the jet to themeasured transverse energy of the photon. The distri-bution of this ratio shows good agreement between dataand simulation as seen in Figure 5(a) for a particularrange of photon energies, and this agreement also holdsfor higher energy photons. The mean fraction of the pho-ton transverse energy that is carried in the track-based jettransverse energy is shown for a range of true jet trans-verse energies (determined by the energy of the photon)in Figure 5(b). The extent of the agreement betweendata and simulation is given by the ratio of these trendsand is shown in black in the same figure. A line is fittedto these ratios and represents the calibration that willbe applied to the track jet energies that we measure inour simulation. Specifically, for a given tagged jet in our

simulated bb or tt sample, we begin by measuring thecorrected transverse energy of the jet in the calorimeterand its associated track-based jet transverse energy. Wethen correct this track-based transverse energy accord-ing to its calorimeter-based transverse energy and thefitted function in Figure 5(b). Uncertainties in the simu-lation of the calorimeter-based jet energy measurementsare found to have a negligibly small impact on the correc-tion factor that is determined in this manner. There are,however, significant statistical uncertainties on the fittedfunction that translate into a systematic uncertainty onour results as will be explained in Section VII.

When applying this calibration to the simulated bb andtt samples, however, it is important to account for thefact that these events contain more jets than those in thephoton calibration sample, and tracks from other jetsmay fall into the jet cones and bias the measured trackjet energies upwards. If our decay length calibration pa-rameterization proves to have a trend over jet energy,then such biases in the tt sample will have a direct im-pact on the correction factor that is applied to a givenjet. On the other hand, in the bb samples there will onlybe a bias to the extent that pythia does not properlymodel the amount of jet overlap that is observed in data.We start by minimizing this problem as much as possibleby removing events where a second jet is close to the jetwe are studying and might contribute overlapping parti-cles in both data and simulation. For our bb events weveto events where either of our tagged jets is between∆R of 0.7 and 1.2 of any other jet with energy greaterthan 9 GeV. This cut was chosen to remove most eventsthat might have extra jets in a region that could overlapour primary jet without eliminating jets with energeticout-of-cone QCD radiation.

In the tt simulation, we do not veto events in thismanner. Instead, we develop a correction procedure to

11

pγTrack-based Jet E / T T

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.02

0.04

0.06

0.08

0.1Data

Pythia

Entr

ies

/ (0

.06)

(a)

Jet Et [GeV]40 60 80 100 120 140

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

/ ndf 2χ 0.3546 / 3

Intercept 0.012– 1.008

Slope 0.0003192– 0.0001595

/ ndf 2χ 0.3546 / 3

Intercept 0.012± 1.008

Slope 0.0003192± 0.0001595

Ratio

Pythia

Data

En

erg

yγ

Me

an

Fra

ctio

n

(b)

FIG. 5: (a): The distributions of track-based jet transverse energy divided by the photon pT for events with photon pT between30 GeV/c and 40 GeV/c. (b): The mean fraction of track-based jet transverse energy / photon pT for Pythia (red) and thedata (blue) as a function of the measured photon transverse momentum (assumed to be the true jet transverse energy). Theratio of these trends between data and simulation is fitted to a line which is then used to correct measured track jet energiesin the simulation.

remove the effects of tracks from other jets that over-lap our jet cones. We do this by plotting the track mo-mentum associated with b-tagged tt jets as a function ofthe ∆R between the track and the jet direction as mea-sured in the calorimeter. We plot distributions binned inthe generator-level pT for the parent b-hadron in our jet.The higher the energy of the b-hadron, the narrower the∆R distribution, as expected. We fit these distributionsto two components, a “primary” part, and an “overlap”part. The tracks originating from the b-hadron and asso-ciated fragmentation products (the primary jet) are mod-eled by a Gaussian multiplied by a Fermi function to forcethe momentum fraction to converge to zero at small ∆R.The contribution from underlying event, minimum bias,and other jets (overlap), turns out to be well modeled bya quadratic function in ∆R, multiplied by a Fermi func-tion to account for damping effects as tracks pass out ofthe active detector range. The fits are performed sepa-rately for each region of b-hadron pT . Examples of thesefits (along with cross-check fits for bb events) are shownin Figure 6. We then use these fit results to extract cor-rection factors, parameterized by the b-hadron’s pT , toremove the average amount of momentum from chargedparticles expected to fall inside the track jet cone fromother sources.

There are a number of approximations and assump-tions that have gone into these vetoes and corrections.For example, the fitting functions could be inappropri-ate, or the vetoes applied to the bb events might be inad-equate. If so, then using an alternate cone size to selecttrack jets will lead to a direct systematic shift. Thus, thesystematics for this procedure are evaluated by changingthe track jet cone size to 0.7, removing overlap accord-ing to the revised jet size, and repeating the analysis, as

explained in Section VII F. However, two other cross-checks are also performed to improve confidence in theprocedure. First, we have no physical motivation for us-ing a quadratic function as the base shape of our over-lap, so in one cross-check we repeat the analysis, mod-eling our overlap as though it were distributed perfectlyuniformly in η − φ space (a line times a Fermi functionin ∆R). There is, of course, no physical basis for us-ing this symmetric distribution either, since complicatedcorrelations between jets according to tt kinematics andsculpting from the jet clustering algorithm could renderthe shape asymmetric. This alternate shape is simplya cross-check that leads to an overestimated amount ofoverlap falling inside of the jet cone. When the analysis isrepeated with the alternate shape it leads to a top-quarkmass measurement result that is shifted by an amountthat is smaller than the systematic we will eventuallyassign for the overlap removal procedure. As a secondcross-check we look at the tagged jets that are selectedto be back-to-back with the muon jet in the bb sample.If the overlap fitting function is incorrect, then we wouldexpect the shape of the primary part of the fit to be bet-ter modeled in these bb events, since the overlap is abouta factor of four smaller than in tt events. These bb com-parison distributions are shown as the dashed curves inFigure 6. By far the worst agreement is seen in the low-est bin of hadron pT (shown on the left). In every otherbin of b-hadron momentum, the differences between thebb and tt results can barely be distinguished, as is thecase in the right hand plot. But since less than 8% of ttjets have hadron momenta that fall into the lowest bin,the systematic mass shifts caused by enforcing the alter-nate bb shapes in the primary distribution will be wellless than the systematic that we will end up claiming.

12

(a)

R Track from Jet∆0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

P W

eig

hte

d C

ou

nt

0

20

40

60

80

100

310×

(b)

FIG. 6: These plots show the charged jet momentum spread in ∆R for pythia tt events. Specifically, the ∆R of each trackrelative to the calorimeter jet direction is plotted as the black points for tagged tt jets, weighted by the track momentum. Theresults are then fit to determine the fractions of primary jet energy and overlap energy from other jets for tt. The solid bluecurves are the fit shapes for the primary and overlap fit components and the solid red curve is the full fit result. The dashedblue curve shows the expected primary distribution based upon fits in the bb sample. (a): results for b-hadron Pt less than20 GeV/c. This is the only kinematic range where there is any significant disagreement between the tt and bb results. Muchmore typical is (b): results for b-hadron Pt between 50 GeV/c and 60 GeV/c.

D. Final decay length calibration

With the track jets in hand we can evaluate the de-cay length calibration parameterization in the bb sampleas described above. The calorimeter is still used to se-lect jets and determine their direction, but we loosen thecalorimeter jet energy cut significantly, and exclude mostjets with energies near this cut by applying a track jettransverse energy cut. As a result, calorimeter drivenjet energy uncertainties will play a minimal role. Ad-ditionally, we apply the overlap vetoes and correctionsas described above. Since it is possible for a jet to passour tracking energy cuts while failing the calorimeter en-ergy selection, fluctuations within standard, calorimeter-based jet energy uncertainties can still cause events topass in and out of selection. However this is a small ef-fect which is only significant in the lowest energy trackjet bins, and thus leads to a small systematic uncertainty.Figure 7 shows the trends in the mean decay length fordata and simulation. The ratio of these trends gives usthe correction that should be applied to the measureddecay lengths in data, depending on the measured trackjet energy in the signal samples. The distribution of thetrack jet energies to which the calibration will be appliedis overlaid.

VI. MASS MEASUREMENT METHOD

Given our mean measured Lxy and lepton pT valuesfrom the data (associated with the distributions of Fig-

Track Jet p [GeV/c]20 30 40 50 60 70 80 90 100 110

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2 / ndf 2

χ 11.74 / 13

Intercept 0.021– 1.047

Slope 0.0006788– -0.0003671 Scale Factor

Data Mean Lxy [cm]

Pythia Mean Lxy [cm]

ttbar

T

<L

xy>

[cm

]

FIG. 7: The decay length calibration parameterization versustrack jet transverse energy is shown here. It is developed fromthe solid black data and simulated average decay lengths, theratio of which gives the Scale Factor points, which are then fitto determine the calibration. Also shown is the distributionof tt jets to which the calibration is applied. For the Lxy dataand simulation the vertical scale represents the mean decaylength in cm, while for their Scale Factor ratio and the ttdistribution this axis is unitless.

ure 2) we need to determine the associated top-quarkmasses and statistical uncertainties. We simulate exper-iments under a variety of hypothetical top-quark massesand use them to perform each of the measurements as

13

described below.

A. Single variable measurements

Pseudoexperiment events are drawn from the eventsthat are used to construct the signal and backgrounddistributions where the probability of each event is givenby its PDF weighting as discussed in Section V. Themean Lxy (pT ) of the tagged jets (leptons) in these eventswill be used to measure the mass. Samples of tt events aregenerated under 23 hypothetical top-quark mass valuesranging from 140 GeV/c2 to 220 GeV/c2, and the decaylength results are corrected according to the track jetenergies by the fit results of Figure 7.

Uncertainties from the background normalization aresmall and are wrapped into the pseudoexperiments. Atotal of 92.5±17.1 background events are expected, how-ever due to the iterative nature of the tt cross sectionevaluation, there is a small additional uncertainty on thebackground normalization of ±3.7 events based upon thetheoretical uncertainty on the input tt cross section, lead-ing to a total background count uncertainty of ±17.5. Foreach pseudoexperiment, the total number of backgroundevents is fluctuated according to a Gaussian with theabove mean and RMS to determine an expected back-ground normalization. The resulting number is thenfluctuated according to Poisson statistics to determinea background normalization for each pseudoexperiment.Given a fixed number of observed data events, the excessis taken to be signal. Further, for each pseudoexperimentthe Lxy calibration parameterization is fluctuated withinthe fitted statistical uncertainties shown in Figure 7.

The mean Lxy and lepton pT pseudoexperiment re-sults are Gaussian in shape and are fit to a Gaussian foreach hypothetical top-quark mass. Examples of these fitsare shown in Figure 8. To evaluate the top-quark massresults for the Lxy and lepton pT measurements, the cen-tral values of these Gaussians are plotted as a functionof top-quark mass and are fit to a quadratic polynomial.The mean Lxy and lepton pT values measured in data arethen converted to the measured top-quark mass valuesaccording to this polynomial. To extract the statisticaluncertainties, the central Lxy and lepton pT pseudoex-periment values are shifted up and down by the standarddeviation of these Gaussian fits. Then the difference be-tween the measured top-quark mass according to the un-shifted polynomial and the top-quark masses resultingfrom these one standard deviation shifts are taken to bethe asymmetric one sigma statistical uncertainties on themeasurements. The fitted polynomials are shown in Fig-ure 9. The mean Lxy and lepton pT values measured indata are also shown as the horizontal black lines, alongwith the projections that are used to determine the sta-tistical uncertainties.

B. Measurement using both variables

The pseudoexperiments from the single variable resultsare used to plot two-dimensional mean Lxy versus meanlepton pT distributions. The results for the two mostextreme mass hypotheses are overlaid in Figure 10(a).

The observed data produce a point on this two-dimensional plane. Given this point, our task is to de-termine the most likely value of the top-quark mass andthe associated statistical errors. To accomplish this, weevaluate a likelihood for each mass hypothesis accordingto the data. The likelihood is simply the probability thatif the true mass were the one in our hypothesis, the meanLxy and lepton pT results would fluctuate as far away orfarther than the results we see in the data point. Thisprobability is taken from pseudoexperiment results suchas those shown in Figure 10(a). Specifically, we evaluatea “distance” that our data point is from the expectedcentral value for our mass hypothesis, and take the like-lihood that the hypothetical mass is correct to be thefraction of pseudoexperiments which are “farther away”from the expected values than our data point.

For this approach to be meaningful, a reasonable def-inition of “distance” must be used. We choose our def-inition so that distances are equal for points along theequal probability contours of a two-dimensional Gaus-sian centered at the expected mean Lxy and lepton pT

values, with the expected standard deviations. Here, theexpected means and standard deviations are taken fromthe Gaussian fits to the mean Lxy and lepton pT pseu-doexperiment results that were described for the singlevariable measurements. Then, the “distance” from theexpected value is defined according to the metric in Equa-tion 1:

D =

√

(

δPt

σP t

)2

+

(

δLxy

σLxy

)2

(1)

Here, δPt (δLxy) is the difference between the meanlepton pT (Lxy) of the data and the fitted central valuefor the hypothesized top-quark mass, and σP t (σLxy) isthe fitted standard deviation of the mean lepton pT (Lxy)for the hypothesized top-quark mass. In principle thisapproach could be modified to account for a correlationbetween the two variables, but this is unnecessary as thecorrelations are empirically determined to be negligiblysmall.

Based on this equation, the fraction of pseudoexperi-ments for each hypothesis for which the distance metricis evaluated to be larger than that for the data is takenas the likelihood for the hypothesized mass. Finally, thelikelihood values for each mass point are plotted with sta-tistical uncertainties determined by adding in quadraturethe statistical uncertainties from the pseudoexperiments,and the statistical uncertainty due to the number of sim-ulated events from which they are drawn. We run enoughpseudoexperiments (4000) that the size of our simulated

14

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.80

50

100

150

200

250

300

350

/ ndf 2χ 12.07 / 29

Peak 6.8± 348.1

Mean 0.0003± 0.5883

Sigma 0.00020± 0.01715

Mean Lxy [cm]

Entr

ies

/ (0

.003

8 cm

)

(a)

40 45 50 55 60 65 70 750

50

100

150

200

250

300

350

400 / ndf 2

χ 38.79 / 28Peak 7.1± 370.1 Mean 0.02± 54.98 Sigma 0.014± 1.246

Mean Lepton p [GeV/c]T

Entr

ies

/ (0

.29

GeV

/c)

(b)

FIG. 8: Pseudoexperiment distributions and fit results for example hypothetical top-quark mass values. (a): Mean Lxypseudoexperiments for mt = 165 GeV/c2. (b): Mean lepton pT pseudoexperiments for mt = 173 GeV/c2. The results of thesefits will be used to construct Figure 9.

]2Top Mass [GeV / c

130 140 150 160 170 180 190 200 210 220

> [

cm]

xy<

L

0.52

0.54

0.56

0.58

0.6

0.62

0.64

0.66

0.68

(a)

]2Top Mass [GeV / c

130 140 150 160 170 180 190 200 210 220

<L

ep

ton

p >

[G

eV

/ c

]

50

52

54

56

58

60

62T

(b)

FIG. 9: The mean values of the Gaussian fits to the pseudoexperiment results from Figure 8 are fit to the quadratic polynomialsplotted here in red. The one sigma statistical uncertainties from these fits lead to the blue contours. The mean values from dataare shown as the horizontal black lines. These values are then translated into top-quark masses according to their intersectionswith the red polynomial, and into asymmetric statistical uncertainties according to their intersections with the blue polynomials.

tt samples is the primary limitation. These likelihoodsare fit to a Gaussian as shown in Figure 10(b). The meanof the Gaussian is taken to be the result of our combinedmeasurement with a statistical uncertainty given by theRMS of the fit.

C. Results

Data events passing event selection have a mean Lxyof 0.590 ± 0.017 cm and a mean lepton pT of 55.2 ±1.3 GeV/c. Based upon these values, the mass measure-ment with the decay length technique yields a result of

166.9+9.5−8.5 GeV/c2, and with the lepton transverse mo-

mentum technique yields a result of 173.5+8.8−8.9 GeV/c2,

where the errors are statistical only. For the simultane-ous measurement with both variables the fit to data isshown in Figure 10 and corresponds to a mass result of170.7± 6.3 GeV /c2.

Some sanity checks were run for each of the three top-quark mass measurements. For these checks, nineteenadditional top-quark mass samples were generated withtop-quark masses varying between 152 and 193 GeV/c2.Ten of these samples were blind (the masses were hiddenfrom the authors until after the measurements were fin-

15

<Lxy> [cm]0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

<L

ep

ton

p >

[G

eV

/c]

40

45

50

55

60

65

70

75T

(a)

]2Top Mass [GeV/c140 150 160 170 180 190 200 210 220

Lik

elih

oo

d

0

0.2

0.4

0.6

0.8

1

/ ndf 2χ 13.8 / 15Prob 0.5408Peak 0.02283± 0.8886 CV 0.1924± 170.7 Sigma 0.1235± 6.299

/ ndf 2χ 13.8 / 15Prob 0.5408Peak 0.02283± 0.8886 CV 0.1924± 170.7 Sigma 0.1235± 6.299

(b)

FIG. 10: (a): distribution of mean Lxy versus mean lepton pT from pseudoexperiments for extreme mass cases of 140 GeVand 220 GeV. (b): the pseudoexperiment results for the 23 mass points considered are used to determine the likelihood ofagreement with the data according to the metric of Equation 1, and the results are plotted and fitted here. The mean fit resultis taken as the measurement result, and the RMS represents our statistical uncertainty.

ished). Pseudoexperiments were thrown using these sam-ples, and the means of the measured top-quark mass re-sults proved to be consistent with expectations to withinthe statistical uncertainties, indicating the method is un-biased. Further, the pulls (defined as the difference be-tween each measured mass and the generated mass di-vided by the statistical uncertainty) of the pseudoexperi-ment results prove to have a width that is consistent with1.0, indicating that the estimated statistical uncertaintiesare reliable.

VII. SYSTEMATIC UNCERTAINTIES

Next we will discuss the systematic uncertainties forthis measurement, and the motivations for the proce-dures we apply. A list of our final systematic uncertain-ties can be found in Table VI.

A. Background uncertainty

As mentioned above, the uncertainty on the back-ground composition and shape is evaluated in the controlregions of the one- and two-jet bins, shown in Figures 3and 4. The differences between the observed and ex-pected means are shown in Table II. The largest dis-agreements are observed in the one-jet bin of Lxy, andin the two-jet bin for lepton pT . Since both of theseworst-case shifts are larger than their uncertainties, theyare taken as the uncertainties on the background meanresults and are scaled by the background fraction to de-termine the systematic errors.

TABLE II: Background shifts and uncertainties in the oneand two-jet control regions. The uncertainties account forboth statistical effects due to data limitations as well us un-certainties in the relative contributions from the individualbackgrounds from the cross section measurement.

Variable Shift

One-Jet Lxy −0.0131 ± 0.0082(cm)

One-Jet lepton pT 0.25 ± 1.25(GeV/c)

Two-Jet Lxy 0.0022 ± 0.0118(cm)

Two-Jet lepton pT −2.22 ± 1.05(GeV/c)

B. QCD radiation uncertainty

Uncertainties in the simulation of QCD radiation couldhave a significant impact on the results of an analysislike this which is dependent upon an accurate model-ing of the boost of the decay products of the tt system.Comparisons of the dilepton boost for Drell-Yan eventshave been made between data and simulation [23] andused to constrain inaccuracies in the modeling of initialstate radiation in quark-antiquark interactions. pythia

parameters were varied to conservatively bracket the pos-sible disagreement between data and simulated initialstate radiation, and analogous parameters were simulta-neously varied for the final state radiation by an equiv-alent amount. Signal events were generated with theseparameters shifted up and down, and these samples werecompared with each other and the nominal pythia sam-ple. Half of the largest mass shifts between any pair ofthese three samples was taken as the QCD radiation sys-tematic uncertainty.

16

C. Parton Distribution Function uncertainty

As described in Section V, for this analysis we reweightour events to match both the predictions of the next toleading order CTEQ6M parton distribution function, andthe expected gluon fusion top production fractions pre-dicted by theory. The advantage of using the CTEQ6MPDF is that it includes a prescription for estimating PDFuncertainties [24]. The degrees of freedom of the PDFcan be parameterized in 20 orthogonal sources of un-certainty that are commonly called eigenvectors. Foreach of these uncertainty sources there are two partondistribution functions, where the parameters associatedwith these eigenvectors are shifted up or down to covera 90% confidence interval. We reweight our top-quarkmass 175 GeV/c2 sample to each of these forty alter-nate PDFs, taking half the full mass shift for each pairas a systematic uncertainty, and adding them in quadra-ture. While these uncertainties are intended to representa 90% confidence interval, we conservatively use them asone sigma systematics instead. While we fix the fractionof tt events produced by gluon fusion interactions to theo-retical expectations, it should be noted that some of theseeigenvector variations are expected to change this frac-tion. Thus, we allow the gluon fractions to float aroundtheir expectations for purposes of determining systematicuncertainties on the PDF results.

One uncertainty that is not accounted for by theseeigenvectors is the uncertainty on the strong couplingconstant, αs(mZ) = 0.1176 ± 0.0020 [25]. To study theeffects of this uncertainty we reweight to the CTEQ6Aand CTEQ6B PDFs [26], which are two different series ofPDFs constructed with varying αs values in intervals of0.002. We average the mass shifts obtained when varyingthe PDFs, and arrive at an uncertainty that is roughlyhalf as large as the eigenvector uncertainty. We observeconsistency between the A and B series PDFs. We addthis uncertainty in quadrature to the eigenvector uncer-tainty to determine our full PDF systematic. As a finalcross-check to the results of the CTEQ Collaboration, wealso reweight to the MRST Collaboration’s NLO PDFMRST2004 [27]. We observe agreement well within ourstated eigenvector uncertainty when this result is com-pared with the corresponding CTEQ6A/B PDFs.

D. Generator uncertainty

In CDF top-quark mass analyses it is conventional tore-evaluate the top-quark mass using samples producedwith the herwig 6.510 generator [28], and take the shiftfrom the pythia mass result as a systematic uncertainty.Note that many of the differences between these gener-ators will double count our existing systematic uncer-tainties. The different fragmentation models betweenpythia and herwig will double count the decay lengthscale, jet energy, and QCD Radiation uncertainties. her-

wig also does not properly handle QED radiation off

of leptons from the W -boson decays, which is insteadinserted with the PHOTOS [29] program. Differencesin these approaches will double count our lepton energyscale uncertainty. The generators also have minor differ-ences in the applied top width (and herwig has a sharpcutoff preventing the presence of top quarks in the highand low mass tails), and only herwig properly handlesspin correlation between the two top quarks. Despite thedouble counted uncertainties, we follow the conventionof other analyses for consistency by taking the differ-ence between our pythia and herwig mass results asa generator systematic. For the Lxy and combined mea-surements the statistical uncertainty on our mass shift isgreater than the shift itself, so we take the uncertaintyon the shift as our systematic instead.

E. Lepton momentum uncertainty

The modeling of the lepton momentum in simulationis tested by fitting the invariant mass of Z’s in data andsimulation, separately for electrons and muons. A Breit-Wigner function is used to model the inherent Z width,which was convoluted with a Gaussian to account for de-tector resolution. Additionally, to model the kinematicreduction in the cross section for higher mass Z produc-tion this function is multiplied by a decaying exponential.When a function modeling a QCD background shape isincluded the fits return zero for its normalization as ex-pected due to the high purity achieved by the leptonselection. The fit distributions are shown in Figures 11and 12.

The centers of the Breit-Wigner fit results, shown inTable III, were compared between simulation and data.To evaluate the systematic, the mean lepton pT of thesignal was scaled by the ratio of the data and simulatedmeans for electrons and muons separately, and the shiftin the measured mass results was taken as a systematic(the statistical uncertainties on these fit results are negli-gible). Clearly, the disagreements in the electron resultsdominate this uncertainty.

TABLE III: Centers of the Breit-Wigner functions from thefits to the Z peaks shown in Figures 11 and 12

Sample Mass Peak (GeV/c2)

Muon Simulation 91.16

Muon Data 90.96

Electron Simulation 91.81

Electron Data 90.84

F. Decay length related uncertainties

The procedure for calibrating the decay length mea-surements in our signal sample is described in sec-

17

75 80 85 90 95 100 1050

200

400

600

800

1000

75 80 85 90 95 100 1050

200

400

600

800

1000

Ev

en

ts /

( 0

.16

7 G

eV/c

2)

Z mass [GeV/c2]

(a)

75 80 85 90 95 100 1050

500

1000

1500

2000

2500

Z mass [GeV/c2]75 80 85 90 95 100 105

Ev

en

ts /

( 0

.16

7 G

eV/c

2)

0

500

1000

1500

2000

2500

(b)

FIG. 11: (a): fit to the dilepton mass peak for electrons in data. (b): fit to the Z mass peak for electrons in simulation.

75 80 85 90 95 100 1050

200

400

600

800

1000

1200

1400

1600

Z mass [GeV/c2]75 80 85 90 95 100 105

0

200

400

600

800

1000

1200

1400

1600

Ev

en

ts /

( 0

.16

7 G

eV/c

2)

(a)

75 80 85 90 95 100 1050

1000

2000

3000

4000

5000

Z mass [GeV/c2]

75 80 85 90 95 100 105

Ev

en

ts /

( 0

.16

7 G

eV/c

2)

0

1000

2000

3000

4000

5000

(b)

FIG. 12: (a): fit to the dilepton mass peak for muons in data. (b): fit to the Z mass peak for muons in simulation.

tion VB. There are many uncertainties which must beconsidered for this calibration, some due to the modelingof b-jets, and others due to the track jet energy measure-ments that are used to parameterize the calibration.

The decay length calibration has a statistical limita-tion due to the data and pythia bb sample sizes. Thisuncertainty is folded directly into the pseudoexperimentsas explained in section VI, but its contribution is quitesmall. There are a number of uncertainties on the photonplus jet energy calibration technique. The energy scalecalibration curve has an associated statistical uncertaintywhich propagates through to a mass uncertainty. A sys-tematic uncertainty of 1% is taken on the measured en-ergy of the photon in the simulation, which correspondsto a 1% uncertainty on the measured track jet trans-verse momentum. Finally, as described in [10], about30% of the photon plus jets sample in data is composed

of QCD dijet production where one of the QCD jets fakesa very clean photon signature through a pion or lambdadecay. This contamination has been determined to havea momentum balance discrepancy compared to the pho-ton plus jets signal at the 1% level, and so an additional0.3% uncertainty is taken on the track jet momentum.Finally, after applying the procedures described in sec-tion V to minimize (in the case of bb) or correct (in thecase of tt) for jet overlap and underlying event effects,the mass is reevaluated using a cone size of ∆R = 0.7instead of 0.4 for the track jets. The resulting shift inthe mass results is taken as an additional systematic torepresent out-of-cone and jet overlap uncertainties.

Another track jet energy uncertainty arises in connec-tion with the simulation of the b-jets. If the EvtGendecay tables do not produce the correct distributions ofcharged particles then this will artificially bias any mea-

18

surements of the tracking energy of the b-jets. The DEL-PHI Collaboration has measured the charged decay mul-tiplicity of b-hadrons [30], excluding the decay productsof long lived light-flavor particles and of excited b-hadronto ground state b-hadron transitions, and determined anaverage of 4.97 ± 0.07. We evaluate this number at gen-erator level in our samples using the same exclusionsand arrive at a mean result of 5.05. This discrepancyis very slightly larger than the reported error at DEL-PHI, and it cannot be explained by uncertainties in theproduction fractions of different b-hadron types or on thesemileptonic decay rate. Under the assumption that ex-cess tracks will be distributed randomly in the b-hadronrest frame, this discrepancy should directly translate intoan equivalent discrepancy on the measured energy of thecomponent of the track jet originating from the b-hadrondecay. This leads to an additional 1.1% uncertainty onthe measured track jet energies.

In addition to jet energy effects, other uncertaintiesare considered in relation to the modeling of the physicsof the bb sample. It is important to minimize and un-derstand any charm contamination in this sample. Ourstudies demonstrate that the muon jets in the sampleare about 95% likely to be b-jets, and 5% likely to becharm jets. But they also suggest that the simulationslightly underestimates the number of charm jets. Thisrequires a minor correction of the decay length mea-sured in this calibration sample, and the charm fractionis then fluctuated within its fitted one sigma uncertain-ties. The small resulting mass shifts are then taken as asystematic uncertainty. Another small uncertainty arisesfrom the event selection on the muons in our leptonicbb sample. If the simulation does not properly modelthe measurement of the muon momentum then higheror lower energy muons (corresponding to higher or lowerdecay length vertices) will pass selection. While our Zpeak fits above suggest a very accurate modeling of iso-lated muons, we conservatively take a 1% uncertainty onthe muon momentum scale, and evaluate the mass shiftthat results from the new set of events passing selection.Finally, it is important to understand the uncertaintiesin pythia’s modeling of the b-quark fragmentation. Inpythia, the energy carried by the hadron after the frag-mentation process is modeled with the Bowler function.The D0 Collaboration has studied LEP and SLD dataand determined the pythia tune required to reproducetheir results [31] . Samples of tt events were generatedaccording to each of these tunes, and the resulting b-hadron energies were found to be about 2% higher thanunder the default pythia tune. As expected, this resultsin a proportionally larger mean decay length of our sig-nal b-hadrons. However, since this effect also occurs inthe bb samples, the effects almost exactly cancel one an-other out, illustrating the motivation for our calibrationprocedure. The fragmentation fluctuations do, however,produce the following minor fluctuations which are notcanceled out. When events are reweighted to the alter-nate fragmentation distributions, it causes small alter-

ations to the measured track jet energies and raises themuon energy distribution slightly. Accounting for all ofthese effects, the larger of the mass shifts between thedefault pythia sample, and the results after reweightingto the SLD or LEP results are taken as a fragmentationsystematic uncertainty .

A summary of calibration systematic uncertainties forthe decay length measurement is shown in Table IV.

TABLE IV: Calibration based top-quark mass uncertaintiesfor the decay length measurement.

Systematic [GeV/c2] Lxy Lepton pT Simultaneous

Photon Plus Jet Stats 0.7 0 0.3

Photon pT 1.4 0 0.6

Photon Background 0.4 0 0.2

Track Jet Cone Size 0.8 0 0.3

Ntrk from b-hadrons 1.6 0 0.7

cc Background 0.2 0 0.1

Semilep Muon Pt 0.3 0 0.1

Fragmentation 0.6 0 0.3

Total Calibration 2.5 0 1.1

G. Multiple interactions uncertainty

There are two respects in which other interactions dur-ing a beam crossing may result in a systematic bias.These extra interactions are simulated as overlaid mini-mum bias events, however this modeling may not be ac-curate, resulting in biased jet energies. These effects aredescribed in Section VII H for calorimeter-based jet mea-surements, and in Section VII F for the tracking basedjet measurements.

However another effect must be taken into account.The simulation is tuned to an older dataset correspond-ing to an integrated luminosity of 1.2 fb−1. The newer 0.7fb−1 of data included in the measurement were collectedat higher instantaneous luminosities with more interac-tions per bunch crossing than the earlier data. To studythis effect we generated a high luminosity tt sample withtop-quark mass 175 GeV/c2. We then segregated theevents according to the number of collision vertices thatare reconstructed in the event (which has been shownto be approximately proportional to the luminosity [10]).While there is no statistically significant trend over num-ber of vertices for the Lxy measurement, there is a sig-nificant dependence for the lepton transverse momentummeasurement as shown in Figure 13. For electrons, asmall part of this trend is due to particles from othercollisions falling into the electron cluster, however theprimary cause of this effect is the isolation requirementfor the leptons. Since we require the total calorimeterenergy found around the lepton to be less than 10% ofthe lepton momentum, low momentum leptons are more

19

likely to fail selection in high luminosity events, as illus-trated in Figure 13.

Like the simulation, we segregate the data based uponthe number of reconstructed collision vertices. As ex-pected, the data have about 15% more reconstructed col-lision vertices per event than the standard tt samples.The high luminosity simulated events are reweighted toreproduce the distribution of the number of reconstructedvertices in both the standard tt samples and the datain turn. These two reweighted results are equivalent toeach other within statistics for the Lxy measurement,however the lepton transverse momentum is significantlyhigher under the luminosity profile of the data. Thereare insufficient statistics at very high luminosities to reli-ably correct for this effect in all of the signal tt samples.Instead we take the differences between the associatedtop-quark mass results using the luminosity profiles ofthe data and the simulation for the high luminosity sam-ple as a systematic uncertainty for each measurement.We emphasize that this uncertainty is due to the sim-ple logistics of the luminosity profile that was used inthe simulation, and is not due to any irreducible physicseffect. For the decay length measurement the statisti-cal uncertainty due to the number of generated tt eventsis larger than the observed systematic shift, and so thisstatistical uncertainty is taken as our systematic instead.

H. Jet energy uncertainties

Our jet energy uncertainties can be broken down intotwo categories: those arising from the tracking energymeasurements which impact the Lxy calibration, andthose from the calorimeter measurements that are com-mon to all our analyses. None of the uncertainties rep-resent an uncertainty on the determination of a “true”jet energy. Rather, they represent uncertainties in themodeling of jet energy measurements in simulation. Inthis section we discuss our evaluation of these uncertain-ties and explain why they have minimal correlation withthe calorimeter-based uncertainties that are claimed byother top-quark mass analyses.

The dominant jet energy uncertainties in this analysisarise from the track jets. They are listed in Table IV asPhoton Plus Jet Stats, Photon pT , Photon Background,Track Jet Cone Size, and Ntrk from b-hadrons. Of these,the Photon pT (energy bias in the calibration photons)and Ntrk from b-hadrons (EvtGen decay multiplicity mis-modeling) categories are the largest contributions to thejet energy uncertainties. The fourth largest uncertaintyis due to the limited statistics in the photon plus jetsdata and will not present any difficulty in future highstatistics analyses.

The third largest uncertainty is due to the size of thecone used to construct our track-based jets. This un-certainty may have components from a wide variety ofphysical effects, but minimal correlation to the jet en-ergy scale uncertainties of other analyses. The most

significant component comes from an uncertainty in theoverlap of particles from other jets falling into the jetcone, for which no corresponding uncertainty is claimedfor calorimeter jets. The only systematic components forwhich there are any correlations to calorimeter-based un-certainties are the much smaller underlying event, multi-ple interaction uncertainties, and out-of-cone uncertain-ties. Most of the multiple interaction contributions arevetoed by the z-vertex matching requirement. As for theout-of-cone uncertainty, it should be minimal due to theapplication of the photon calibration procedure. It willonly contribute to the extent in which the simulationmodels out-of-cone effects in b-jets with a different levelof accuracy compared to the light flavor jets on whichthe calibration is performed. To summarize, of all ourtrack jet energy uncertainties, only a small part of the0.8 GeV/c2 (0.3 GeV/c2) systematic uncertainty on theLxy (combined) measurements that is due to the alteredcone size could have any correlation to the calorimeter-based jet energy scale uncertainties we are claiming, orthose of other analyses.

The calorimeter-based uncertainties are split into sixcategories, which are assumed to be independent of oneanother and are described in [10]. Since these are thesame categories into which the jet energy scale correc-tions are split, these uncertainties are sometimes calledjet energy scale uncertainties. As for the tracking baseduncertainties, their impact on the decay length measure-ment arises based on which jets pass our event selectionthresholds. These low energy jets which pass in and outof our sample as the jet energies are varied within uncer-tainties tend to have a small decay length, and thereforebias the average decay length of our sample. Unlike trackjets, however, for calorimeter jets this effect is presentin both our bb calibration and our main analysis sam-ples, and it largely cancels in the final mass determina-tion. Such cancellations are what motivated the choiceof the Lxy calibration procedure. To evaluate these un-certainties, we fluctuate the calorimeter energies of thejets within these six categories and reevaluate the miss-ing energy of the event, keeping track of which jets andevents pass selection. We take the resulting mass shiftsas calorimeter-based systematic uncertainties.

One concern that arose at this point is that we mayhave over-optimized our procedures to create the fortu-itous systematic cancellations described above. This con-cern would specifically pertain to our out-of-cone jet en-ergy uncertainty. The out-of-cone uncertainties are delib-erately fixed to be more conservative than the worst casescenario disagreements between pythia-data and her-

wig-data out-of-cone comparisons as explained in [10].But if the out-of-cone disagreement between simulationand data is different for the jets in our bb sample than forthe jets in our tt sample, then by chance the cancellationmay lead to an artificially small systematic result.

To investigate this possibility, we must understand dif-ferences between jets in the samples. If jets near the se-lection threshold were to have identical properties for the

20

#Z Vertices1 2 3 4 5 6 7

<L

ep

ton

p >

[G

eV

/c]

59

60

61

62

63

64

T

(a)

FIG. 13: Effects of luminosity on the mean lepton transverse momentum. These results are evaluated at generator level andplotted against the number of reconstructed collision vertices. The higher the luminosity is (as measured by the number ofvertices), the smaller is the number of low energy leptons that pass the isolation requirement.

bb and tt samples, then disagreements between data andsimulation would be identical for the samples and the re-sulting systematic cancellation resulting from assumingidentical out-of-cone uncertainties would be appropriate.Fortunately, the differences are small. For our purposes,the only relevant differences between the jets in our sam-ples are that the bb jets used in our decay length calibra-tion are required to contain muons, and that some of thetagged jets in our backgrounds are light flavor or charm.In all other respects the simulated jets we use near ourselection threshold are similar. There are two systematiccross-checks that we run to address these concerns. Theresults will be shown at the end of this section.

As explained in [10], the out-of-cone jet energy un-certainties are parameterized based upon the calorimeterenergy measurement. Since lower energy jets are broader,a lower jet energy corresponds to a larger out-of-cone un-certainty. Since the muon’s energy is mostly lost for jetsin the bb sample, it can be argued that we are overes-timating the out-of-cone uncertainty for these jets. Tocheck the impact this would have, we add the muon’s en-ergy back in and repeat our systematics evaluation. Asa second check, we consider the possibility that the mis-modeling of out-of-cone effects by the simulation couldbe different for heavy and light flavor jets. We check theshifts of the uncertainties which occur when we fluctu-ate the size of our out-of-cone uncertainties for charmand light flavor jets relative to b-jets within conservativeconstraints determined by jet shape studies. The fluctu-ations from these two cross-checks are taken as residualout-of-cone systematic uncertainties. We take our fullout-of-cone systematic as the quadrature sum of directand residual out-of-cone uncertainties. The results aresummarized in Table V. The systematic uncertaintiesfrom all effects that have been considered are shown in

Table VI.

TABLE V: Calorimeter Based Jet Energy Uncertainties. Theresidual uncertainties result from possible inaccuracies in thecancellation that occurs for our out-of-cone uncertainty.

Systematic [GeV/c2] Lxy Lepton pT Simultaneous

Eta Dependent 0.06 -0.08 -0.02

Multiple Interactions 0.17 -0.01 0.07

Calorimeter Response -0.14 -0.07 -0.09

Underlying Event 0.09 -0.06 0.01

Splash Out 0.15 -0.10 0.02

Base Out of Cone 0.18 -0.28 -0.06

Out of Cone Residual Uncertainties

bb Semileptonic 0.24 NA 0.24

W plus charm/LF 0.14 0.22 0.30

Final Out of Cone 0.33 0.36 0.24

Total Calorimeter JES 0.44 0.39 0.32

VIII. CONCLUSION

Using a data sample corresponding to an integratedluminosity of 1.9 fb−1, we measure a top-quark mass ofmt = 166.9+9.5

−8.5 (stat)±2.9 (syst) GeV/c2 using the mean

transverse decay length of b-jets, mt = 173.5+8.8−8.9 (stat)±

3.8 (syst) GeV/c2 using the mean transverse momen-tum of the leptons from W -boson decays, and mt =170.7±6.3 (stat)±2.6 (syst) GeV/c2 using both variablessimultaneously. To date, these results represent the mostprecise measurement of the top-quark mass using an algo-rithm that has minimal dependence on calorimeter-based

21

TABLE VI: Final Systematic Uncertainties. The Lxy Cali-bration systematic is the quadrature sum of the systematicssummarized in Table IV. The Calorimeter JES systematicis the quadrature sum of the systematics summarized in Ta-ble V.

Systematic [GeV/c2] Lxy Lepton pT Simultaneous

Background Shape 1.0 2.3 1.7

QCD Radiation 0.5 1.2 0.7

PDF 0.3 0.6 0.5

Generator 0.7 0.9 0.3

Lepton pT Scale 0 2.3 1.2

Lxy Calibration 2.5 0 1.1

Multiple Interactions 0.2 1.2 0.7

Calorimeter JES 0.4 0.4 0.3

Systematics Total 2.9 3.8 2.6

jet energy uncertainties. Because we have improved thesystematic uncertainty on this measurement by a factorof 3.3 compared to the previous measurement [6], the pre-cision remains limited by statistics and therefore couldimprove significantly by the end of Run II. In contrast, ifa measurement of this type were performed at the LHC,the systematic uncertainties would be the true limitationas the statistical uncertainties would be negligible.

While a prediction of the systematic uncertainties insuch a measurement at the LHC is beyond the scope ofthis paper, we can predict some of the improvements tothe systematics that can be made at the Tevatron. Ifthe simulated events were regenerated using the proper

luminosity profile, the multiple interactions uncertaintywould become negligibly small. Preliminary studies [32]have also suggested a method for calibrating the leptonmomentum which should improve our lepton pT scalesystematic by more than a factor of two. If both of theseanalysis improvements were implemented, the systematicuncertainties for these measurements at CDF would beexpected to drop to 3.0 GeV/c2 for the lepton trans-verse momentum measurement, and 2.3 GeV/c2 usingboth variables simultaneously. It appears that an evensmaller systematic uncertainty may be attainable by per-forming the lepton pT analysis in the dilepton channel[32].

We thank the Fermilab staff and the technical staffsof the participating institutions for their vital contribu-tions. This work was supported by the U.S. Departmentof Energy and National Science Foundation; the ItalianIstituto Nazionale di Fisica Nucleare; the Ministry ofEducation, Culture, Sports, Science and Technology ofJapan; the Natural Sciences and Engineering ResearchCouncil of Canada; the National Science Council of theRepublic of China; the Swiss National Science Founda-tion; the A.P. Sloan Foundation; the Bundesministeriumfur Bildung und Forschung, Germany; the Korean Sci-ence and Engineering Foundation and the Korean Re-search Foundation; the Science and Technology FacilitiesCouncil and the Royal Society, UK; the Institut Nationalde Physique Nucleaire et Physique des Particules/CNRS;the Russian Foundation for Basic Research; the Ministe-rio de Ciencia e Innovacion, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; and theAcademy of Finland.

[1] The ALEPH, CDF, D0, DELPHI, L3, OPAL, SLD Col-laborations, the LEP Electroweak Working Group, theTevatron Electroweak Working Group, and the SLDElectroweak and heavy flavour groups, hep-ex/0811.4682(2008).

[2] F. Abe et al., Phys. Rev. Lett. 80, 2767 (1998).[3] T. Aaltonen et al., Phys. Rev. D 79, 072001 (2009).[4] The CDF coordinate system is right handed, with z-axis

tangent to the Tevatron ring and pointing in the directionof the proton beam. The x and y coordinates are definedpointing outward and upward from the Tevatron ring,respectively. The azimuthal angle φ is measured relativeto the x axis in the transverse plane. The pseudorapidityη is measured from the proton direction and is typicallyexpressed as η = − ln(tan θ

2), where θ is the polar angle

with respect to the z-axis. Transverse momentum andenergy are defined as pT = p sin(θ) and ET = E sin(θ),respectively.

[5] C. S. Hill, J. R. Incandela, and J. M. Lamb, Phys. Rev.D 71, 054029 (2005).

[6] A. Abulencia et al., Phys. Rev. D 75, 071102 (2007).[7] N. Giokaris et al., JINR-E1-2005-104, July 2005.[8] A. Abulencia et al., J. Phys. G 34, 2457 (2007).

[9] The mean of our Lxy or lepton pT distributions can beexpressed as < s > fs+ < b > fb where < s > and < b >denote the means of the signal and background distribu-tions, and fs and fb represent the fractions of events thatcome from these distributions. Since < b > does not de-pend on the top quark mass while < s > depends roughlylinearly on the top-quark mass, the statistical resolutionof the measurement will depend linearly on fs.

[10] A. Bhatti et al., Nucl. Instrum. Methods A 566, 375(2006).

[11] More explicitly, the missing transverse energy is definedas |−

∑

iEi

T ~ni|, where the sum is over calorimeter towers

with transverse energy deposits, EiT , and ~ni is the unit

vector from the collision vertex to the tower in the planetransverse to the beam direction. Further corrections areapplied to account for muon tracks and to account forcalorimeter non-uniformity and non-linearities.

[12] A. Abulencia et al., Phys. Rev. D 71, 052003 (2005).[13] A. Abulencia et al., Phys. Rev. Lett. 97, 082004 (2006).[14] D. Acosta et al., Phys. Rev. D 71, 052003 (2005).[15] D. Sherman, Ph.D. Thesis, Harvard University (2007).[16] T. Sjostrand et al., Comput. Phys. Commun. 135, 238

(2001).

22

[17] F. Maltoni and T. Stelzer, J. High Energy Phys. 0302,027 (2003).

[18] M. L. Mangano et al., J. High Energy Phys. 0307, 001(2003).

[19] D. J. Lange, Nucl. Instrum. Methods A 462, 152 (2001).[20] H. L. Lai et al., Eur. Phys. J. C 12, 375 (2000).[21] J. Incandela et al., Prog. Part. Nucl. Phys. to be pub-

lished 2009, hep-ex/0904.2499.[22] M. R. Whalley et al., arXiv:hep-ph/0508110 (2005).[23] A. Abulencia et al., Phys. Rev. D 73, 032003 (2006).[24] J. Pumplin et al., J. High Energy Phys. 07, 012 (2002).[25] C. Amsler et al. (Particle Data Group), Phys. Lett. B

667, 1 (2008).[26] J. Pumplin et al., J. High Energy Phys. 02, 032 (2006).[27] A. D. Martin et al., Phys. Lett. B 605, 61 (2004).[28] G. Corcella et al., J. High Energy Phys. 0101, 010 (2001).[29] E. Barberio and Z. Was, Comput. Phys. Commun. 79,

291 (1994).[30] P. Abreu et al., Phys. Lett. B 425, 399 (1998).[31] W. Fedorko, Ph.D. thesis, University of Chicago,

FERMILAB-THESIS-2008-42 (2008).[32] The CDF Collaboration, CDF Conf. Note 9881 (2009).