Mass Dependent Afb in T-tbar Production

8/3/2019 Mass Dependent Afb in T-tbar Production

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Fermilab-Pub-10-525-E

Evidence for a Mass Dependent Forward-Backward Asymmetry

in Top Quark Pair Production

T. Aaltonen,21 B. Alvarez Gonzalezv,9 S. Amerio,41 D. Amidei,32 A. Anastassov,36 A. Annovi,17 J. Antos,12

G. Apollinari,15 J.A. Appel,15 A. Apresyan,46 T. Arisawa,56 A. Artikov,13 J. Asaadi,51 W. Ashmanskas,15

B. Auerbach,59 A. Aurisano,51 F. Azfar,40 W. Badgett,15 A. Barbaro-Galtieri,26 V.E. Barnes,46 B.A. Barnett,23

P. Barriacc,44 P. Bartos,12 M. Bauceaa,41 G. Bauer,30 F. Bedeschi,44 D. Beecher,28 S. Behari,23 G. Bellettinibb,44J. Bellinger,58 D. Benjamin,14 A. Beretvas,15 A. Bhatti,48 M. Binkley,15 D. Biselloaa,41 I. Bizjakgg ,28 K.R. Bland,5

B. Blumenfeld,23 A. Bocci,14 A. Bodek,47 D. Bortoletto,46 J. Boudreau,45 A. Boveia,11 B. Braua,15 L. Brigliadoriz,6

A. Brisuda,12 C. Bromberg,33 E. Brucken,21 M. Bucciantoniobb,44 J. Budagov,13 H.S. Budd,47 S. Budd,22

K. Burkett,15 G. Busettoaa,41 P. Bussey,19 A. Buzatu,31 C. Calancha,29 S. Camarda,4 M. Campanelli,33

M. Campbell,32 F. Canelli12,15 A. Canepa,43 B. Carls,22 D. Carlsmith,58 R. Carosi,44 S. Carrillok,16 S. Carron,15

B. Casal,9 M. Casarsa,15 A. Castroz,6 P. Catastini,15 D. Cauz,52 V. Cavalierecc,44 M. Cavalli-Sforza,4 A. Cerrif,26

L. Cerritoq,28 Y.C. Chen,1 M. Chertok,7 G. Chiarelli,44 G. Chlachidze,15 F. Chlebana,15 K. Cho,25

D. Chokheli,13 J.P. Chou,20 W.H. Chung,58 Y.S. Chung,47 C.I. Ciobanu,42 M.A. Cioccicc,44 A. Clark,18

G. Compostellaaa,41 M.E. Convery,15 J. Conway,7 M.Corbo,42 M. Cordelli,17 C.A. Cox,7 D.J. Cox,7 F. Cresciolibb,44

C. Cuenca Almenar,59 J. Cuevasv,9 R. Culbertson,15 D. Dagenhart,15 N. dAscenzot,42 M. Datta,15 P. de Barbaro,47

S. De Cecco,49 G. De Lorenzo,4 M. DellOrsobb,44 C. Deluca,4 L. Demortier,48 J. Dengc,14 M. Deninno,6

F. Devoto,21

M. dErricoaa

,41

A. Di Cantobb

,44

B. Di Ruzza,44

J.R. Dittmann,5

M. DOnofrio,27

S. Donatibb

,44

P. Dong,15 M. Dorigo,52 T. Dorigo,41 K. Ebina,56 A. Elagin,51 A. Eppig,32 R. Erbacher,7 D. Errede,22 S. Errede,22

N. Ershaidaty,42 R. Eusebi,51 H.C. Fang,26 S. Farrington,40 M. Feindt,24 J.P. Fernandez,29 C. Ferrazzadd,44

R. Field,16 G. Flanaganr,46 R. Forrest,7 M.J. Frank,5 M. Franklin,20 J.C. Freeman,15 Y. Funakoshi,56

I. Furic,16 M. Gallinaro,48 J. Galyardt,10 J.E. Garcia,18 A.F. Garfinkel,46 P. Garosicc,44 H. Gerberich,22

E. Gerchtein,15 S. Giaguee,49 V. Giakoumopoulou,3 P. Giannetti,44 K. Gibson,45 C.M. Ginsburg,15 N. Giokaris,3

P. Giromini,17 M. Giunta,44 G. Giurgiu,23 V. Glagolev,13 D. Glenzinski,15 M. Gold,35 D. Goldin,51

N. Goldschmidt,16 A. Golossanov,15 G. Gomez,9 G. Gomez-Ceballos,30 M. Goncharov,30 O. Gonzalez,29

I. Gorelov,35 A.T. Goshaw,14 K. Goulianos,48 A. Gresele,41 S. Grinstein,4 C. Grosso-Pilcher,11 R.C. Group,55

J. Guimaraes da Costa,20 Z. Gunay-Unalan,33 C. Haber,26 S.R. Hahn,15 E. Halkiadakis,50 A. Hamaguchi,39

J.Y. Han,47 F. Happacher,17 K. Hara,53 D. Hare,50 M. Hare,54 R.F. Harr,57 K. Hatakeyama,5 C. Hays,40 M. Heck,24

J. Heinrich,43 M. Herndon,58 S. Hewamanage,5 D. Hidas,50 A. Hocker,15 W. Hopkinsg,15 D. Horn,24 S. Hou,1

R.E. Hughes,

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M. Hurwitz,

11

U. Husemann,

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N. Hussain,

31

M. Hussein,

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J. Huston,

33

G. Introzzi,

44

M. Iori

ee

,

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A. Ivanovo,7 E. James,15 D. Jang,10 B. Jayatilaka,14 E.J. Jeon,25 M.K. Jha,6 S. Jindariani,15 W. Johnson,7

M. Jones,46 K.K. Joo,25 S.Y. Jun,10 T.R. Junk,15 T. Kamon,51 P.E. Karchin,57 Y. Katon,39 W. Ketchum,11

J. Keung,43 V. Khotilovich,51 B. Kilminster,15 D.H. Kim,25 H.S. Kim,25 H.W. Kim,25 J.E. Kim,25 M.J. Kim,17

S.B. Kim,25 S.H. Kim,53 Y.K. Kim,11 N. Kimura,56 M. Kirby,15 S. Klimenko,16 K. Kondo,56 D.J. Kong,25

J. Konigsberg,16 A.V. Kotwal,14 M. Kreps,24 J. Kroll,43 D. Krop,11 N. Krumnackl,5 M. Kruse,14 V. Krutelyovd,51

T. Kuhr,24 M. Kurata,53 S. Kwang,11 A.T. Laasanen,46 S. Lami,44 S. Lammel,15 M. Lancaster,28 R.L. Lander,7

K. Lannonu,37 A. Lath,50 G. Latinocc,44 I. Lazzizzera,41 T. LeCompte,2 E. Lee,51 H.S. Lee,11 J.S. Lee,25

S.W. Leew,51 S. Leobb,44 S. Leone,44 J.D. Lewis,15 C.-J. Lin,26 J. Linacre,40 M. Lindgren,15 E. Lipeles,43 A. Lister,18

D.O. Litvintsev,15 C. Liu,45 Q. Liu,46 T. Liu,15 S. Lockwitz,59 N.S. Lockyer,43 A. Loginov,59 D. Lucchesiaa,41

J. Lueck,24 P. Lujan,26 P. Lukens,15 G. Lungu,48 J. Lys,26 R. Lysak,12 R. Madrak,15 K. Maeshima,15 K. Makhoul,30

P. Maksimovic,23 S. Malik,48 G. Mancab,27 A. Manousakis-Katsikakis,3 F. Margaroli,46 C. Marino,24 M. Martnez,4

R. Martnez-Ballarn,29 P. Mastrandrea,49 M. Mathis,23 M.E. Mattson,57 P. Mazzanti,6 K.S. McFarland,47

P. McIntyre,51 R. McNultyi,27 A. Mehta,27 P. Mehtala,21 A. Menzione,44 C. Mesropian,48 T. Miao,15

D. Mietlicki,32 A. Mitra,1 H. Miyake,53 S. Moed,20 N. Moggi,6 M.N. Mondragonk,15 C.S. Moon,25

R. Moore,15 M.J. Morello,15 J. Morlock,24 P. Movilla Fernandez,15 A. Mukherjee,15 Th. Muller,24 P. Murat,15

M. Mussiniz,6 J. Nachtmanm,15 Y. Nagai,53 J. Naganoma,56 I. Nakano,38 A. Napier,54 J. Nett,58 C. Neu,55

M.S. Neubauer,22 J. Nielsene,26 L. Nodulman,2 O. Norniella,22 E. Nurse,28 L. Oakes,40 S.H. Oh,14 Y.D. Oh,25

I. Oksuzian,55 T. Okusawa,39 R. Orava,21 L. Ortolan,4 S. Pagan Grisoaa,41 C. Pagliarone,52 E. Palenciaf,9

V. Papadimitriou,15 A.A. Paramonov,2 J. Patrick,15 G. Paulettaff,52 M. Paulini,10 C. Paus,30 D.E. Pellett,7

A. Penzo,52 T.J. Phillips,14 G. Piacentino,44 E. Pianori,43 J. Pilot,37 K. Pitts,22 C. Plager,8 L. Pondrom,58

K. Potamianos,46 O. Poukhov,13 F. Prokoshinx,13 A. Pronko,15 F. Ptohosh,17 E. Pueschel,10 G. Punzibb,44

arXiv:1101.0

034v1

[hep-ex]30

Dec2010


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J. Pursley,58 A. Rahaman,45 V. Ramakrishnan,58 N. Ranjan,46 I. Redondo,29 P. Renton,40 M. Rescigno,49

F. Rimondiz,6 L. Ristori45,15 A. Robson,19 T. Rodrigo,9 T. Rodriguez,43 E. Rogers,22 S. Rolli,54 R. Roser,15

M. Rossi,52 F. Rubbo,15 F. Ruffinicc,44 A. Ruiz,9 J. Russ,10 V. Rusu,15 A. Safonov,51 W.K. Sakumoto,47

Y. Sakurai,56 L. Santiff,52 L. Sartori,44 K. Sato,53 V. Savelievt,42 A. Savoy-Navarro,42 P. Schlabach,15

A. Schmidt,24 E.E. Schmidt,15 M.P. Schmidt,59 M. Schmitt,36 T. Schwarz,7 L. Scodellaro,9 A. Scribanocc,44

F. Scuri,44 A. Sedov,46 S. Seidel,35 Y. Seiya,39 A. Semenov,13 F. Sforzabb,44 A. Sfyrla,22 S.Z. Shalhout,7

T. Shears,27 P.F. Shepard,45 M. Shimojimas,53 S. Shiraishi,11 M. Shochet,11 I. Shreyber,34 A. Simonenko,13

P. Sinervo,31 A. Sissakian,13 K. Sliwa,54 J.R. Smith,7 F.D. Snider,15 A. Soha,15 S. Somalwar,50 V. Sorin,4

P. Squillacioti,15 M. Stancari,15 M. Stanitzki,59 R. St. Denis,19 B. Stelzer,31 O. Stelzer-Chilton,31 D. Stentz,36

J. Strologas,35 G.L. Strycker,32 Y. Sudo,53 A. Sukhanov,16 I. Suslov,13 K. Takemasa,53 Y. Takeuchi,53 J. Tang,11

M. Tecchio,32 P.K. Teng,1 J. Thomg,15 J. Thome,10 G.A. Thompson,22 E. Thomson,43 P. Ttito-Guzman,29

S. Tkaczyk,15 D. Toback,51 S. Tokar,12 K. Tollefson,33 T. Tomura,53 D. Tonelli,15 S. Torre,17 D. Torretta,15

P. Totaroff,52 M. Trovatodd,44 Y. Tu,43 F. Ukegawa,53 S. Uozumi,25 A. Varganov,32 F. Vazquezk,16 G. Velev,15

C. Vellidis,3 M. Vidal,29 I. Vila,9 R. Vilar,9 M. Vogel,35 G. Volpibb,44 P. Wagner,43 R.L. Wagner,15 T. Wakisaka,39

R. Wallny,8 S.M. Wang,1 A. Warburton,31 D. Waters,28 M. Weinberger,51 W.C. Wester III,15 B. Whitehouse,54

D. Whitesonc,43 A.B. Wicklund,2 E. Wicklund,15 S. Wilbur,11 F. Wick,24 H.H. Williams,43 J.S. Wilson,37

P. Wilson,15 B.L. Winer,37 P. Wittichg,15 S. Wolbers,15 H. Wolfe,37 T. Wright,32 X. Wu,18 Z. Wu,5 K. Yamamoto,39

J. Yamaoka,14 T. Yang,15 U.K. Yangp,11 Y.C. Yang,25 W.-M. Yao,26 G.P. Yeh,15 K. Yim,15 J. Yoh,15 K. Yorita,56

T. Yoshidaj ,39 G.B. Yu,14 I. Yu,25 S.S. Yu,15 J.C. Yun,15 A. Zanetti,52 Y. Zeng,14 and S. Zucchelliz6

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

2Argonne National Laboratory, Argonne, Illinois 60439, USA3University of Athens, 157 71 Athens, Greece

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

6Istituto Nazionale di Fisica Nucleare Bologna, zUniversity of Bologna, I-40127 Bologna, Italy7University of California, Davis, Davis, California 95616, USA

8University of California, Los Angeles, Los Angeles, California 90024, USA9Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

10Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA11Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

12Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia13Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

14

Duke University, Durham, North Carolina 27708, USA15Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA16University of Florida, Gainesville, Florida 32611, USA

17Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy18University of Geneva, CH-1211 Geneva 4, Switzerland

19Glasgow University, Glasgow G12 8QQ, United Kingdom20Harvard University, Cambridge, Massachusetts 02138, USA21Division of High Energy Physics, Department of Physics,

University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland22University of Il linois, Urbana, Il linois 61801, USA

23The Johns Hopkins University, Baltimore, Maryland 21218, USA24Institut fur Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany

25Center for High Energy Physics: Kyungpook National University,Daegu 702-701, Korea; Seoul National University, Seoul 151-742,

Korea; Sungkyunkwan University, Suwon 440-746,Korea; Korea Institute of Science and Technology Information,

Daejeon 305-806, Korea; Chonnam National University, Gwangju 500-757,Korea; Chonbuk National University, Jeonju 561-756, Korea

26Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA27University of Liverpool, Liverpool L69 7ZE, United Kingdom

28University College London, London WC1E 6BT, United Kingdom29Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

30Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA31Institute of Particle Physics: McGill University, Montreal, Quebec,

Canada H3A 2T8; Simon Fraser University, Burnaby, British Columbia,


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Canada V5A 1S6; University of Toronto, Toronto, Ontario,Canada M5S 1A7; and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3

32University of Michigan, Ann Arbor, Michigan 48109, USA33Michigan State University, East Lansing, Michigan 48824, USA

34Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia35University of New Mexico, Albuquerque, New Mexico 87131, USA

36Northwestern University, Evanston, Illinois 60208, USA37The Ohio State University, Columbus, Ohio 43210, USA

38Okayama University, Okayama 700-8530, Japan39Osaka City University, Osaka 588, Japan

40University of Oxford, Oxford OX1 3RH, United Kingdom41Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, aaUniversity of Padova, I-35131 Padova, Italy

42LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

44Istituto Nazionale di Fisica Nucleare Pisa, bbUniversity of Pisa,ccUniversity of Siena and ddScuola Normale Superiore, I-56127 Pisa, Italy

45University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA46Purdue University, West Lafayette, Indiana 47907, USA

47University of Rochester, Rochester, New York 14627, USA48The Rockefeller University, New York, New York 10065, USA

49Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1,eeSapienza Universita di Roma, I-00185 Roma, Italy

50Rutgers University, Piscataway, New Jersey 08855, USA51Texas A&M University, College Station, Texas 77843, USA

52Istituto Nazionale di Fisica Nucleare Trieste/Udine,I-34100 Trieste, ffUniversity of Trieste/Udine, I-33100 Udine, Italy

53University of Tsukuba, Tsukuba, Ibaraki 305, Japan54Tufts University, Medford, Massachusetts 02155, USA55University of Virginia, Charlottesville, VA 22906, USA

56Waseda University, Tokyo 169, Japan57Wayne State University, Detroit, Michigan 48201, USA

58University of Wisconsin, Madison, Wisconsin 53706, USA59Yale University, New Haven, Connecticut 06520, USA

We present a new measurement of the inclusive forward-backward tt production asymmetry andits rapidity and mass dependence. The measurements are performed with data corresponding toan integrated luminosity of 5.3 fb1 of pp collisions at

s = 1.96 TeV, recorded with the CDF

II Detector at the Fermilab Tevatron. Significant inclusive asymmetries are observed in both thelaboratory frame and the tt rest frame, and in both cases are found to be consistent with CPconservation under interchange of t and t. In the tt rest frame, the asymmetry is observed toincrease with the tt rapidity difference, y, and with the invariant mass Mtt of the tt system. Fullycorrected parton-level asymmetries are derived in two regions of each variable, and the asymmetryis found to be most significant at large y and Mtt. For Mtt 450 GeV/c2, the parton-levelasymmetry in the tt rest frame is Att = 0.475 0.114 compared to a next-to-leading order QCDprediction of 0.088 0.013.

PACS numbers: 11.30.Er, 12.38.Qk, 14.65.Ha

Deceased

With visitors from aUniversity of Massachusetts Amherst,Amherst, Massachusetts 01003, bIstituto Nazionale di Fisica Nu-cleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy,cUniversity of California Irvine, Irvine, CA 92697, dUniversity ofCalifornia Santa Barbara, Santa Barbara, CA 93106 eUniversityof California Santa Cruz, Santa Cruz, CA 95064, fCERN,CH-1211 Geneva, Switzerland, gCornell University, Ithaca, NY 14853,hUniversity of Cyprus, Nicosia CY-1678, Cyprus, iUniversity Col-lege Dublin, Dublin 4, Ireland, jUniversity of Fukui, Fukui City,Fukui Prefecture, Japan 910-0017, kUniversidad Iberoamericana,Mexico D.F., Mexico, lIowa State University, Ames, IA 50011,mUniversity of Iowa, Iowa City, IA 52242, nKinki University,

Higashi-Osaka City, Japan 577-8502,

o

Kansas State University,Manhattan, KS 66506, pUniversity of Manchester, Manchester M139PL, England, qQueen Mary, University of London, London, E14NS, England, rMuons, Inc., Batavia, IL 60510, sNagasaki In-stitute of Applied Science, Nagasaki, Japan, tNational ResearchNuclear University, Moscow, Russia, uUniversity of Notre Dame,Notre Dame, IN 46556, vUniversidad de Oviedo, E-33007 Oviedo,Spain, wTexas Tech University, Lubbock, TX 79609, xUniversidadTecnica Federico Santa Maria, 110v Valparaiso, Chile, yYarmoukUniversity, Irbid 211-63, Jordan, ggOn leave from J. Stefan Insti-tute, Ljubljana, Slovenia.


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I. INTRODUCTION

Top quark pair production in pp collisions is a sensi-tive probe of quantum chromodynamics at high energy.At lowest order in the standard model (SM), quark pairproduction is symmetric under charge conjugation. Atnext-to-leading order (NLO) the interference of processes

that differ under charge conjugation leads to a smallforward-backward asymmetry of order 0.06 0.01 in thett rest frame [13]. An analogous effect is predicted atorder 3 in QED and is confirmed in measurements ofe+e + [4]. Study of the NLO QCD asymmetryin inclusive jet events is hampered by the difficulty ofmeasuring the jet charge. In pair produced top quarkswith one semi-leptonic decay, the top can be tagged ac-cording to the well-measured lepton charge, enabling aprobe of the NLO QCD effect and a test of charge con-

jugation symmetry in strong interactions at high energy.

The CDF and D0 experiments have made initial mea-surements of the tt asymmetry in pp collisions at

s =

1.96 TeV at the Fermilab Tevatron [5, 6]. In the CP-invariant pp system, the NLO QCD effect appears as acharge dependent forward-backward asymmetry of thetop quark direction with respect to the proton direc-tion. Using data samples corresponding to 1.9 fb1

and 0.9 fb1 respectively, CDF and D0 report pos-itive asymmetries that are consistent with the QCDprediction within large experimental uncertainties. Anumber of theoretical papers suggest interesting newphysics mechanisms including axigluons, diquarks, newweak bosons, and extra-dimensions that can all pro-duce forward-backward tt asymmetries [7, 8]. The modelbuilding must accommodate the observed consistency of

the tt cross-section and total invariant mass distributionwith the SM QCD prediction [9, 10].

We report here on a new study of the forward-backward asymmetry in pp collisions at

s = 1.96 TeV,

using data corresponding to an integrated luminosity of5.3 fb1 recorded with the CDF II Detector. We studyevents with the lepton+jets topology, where either thet or t has decayed semileptonically. The asymmetriesare measured in two variables: yh, the rapidity of thehadronically decaying top quark, corresponding to thetop rapidity in the laboratory (lab) frame, and y, thedifference of the rapidities of the leptonic and hadronictop systems, which measures the top quark rapidity inthe tt rest frame. We show that t and t asymmetries areconsistent with CP conservation, and combine them tomeasure the total asymmetry in the sample. We measurethe inclusive asymmetries, and the functional dependenceof the tt frame asymmetry on y and on the total invari-ant mass of the tt system, Mtt. We apply correctionsfor backgrounds, acceptance, and resolution to calculateparton level measures of the inclusive asymmetry in boththe lab and tt rest frames, and in two regions of y andMtt in the tt frame.

II. DETECTION, EVENT SELECTION AND

RECONSTRUCTION

CDF II is a general purpose, azimuthally andforward-backward symmetric magnetic spectrometerwith calorimetry and muon detectors [11]. Charged parti-cle trajectories are measured with a silicon-microstrip de-tector backed by a large open-cell drift chamber in a 1.4 T

solenoidal magnetic field. Electromagnetic and hadroniccalorimeters located outside the solenoid provide jet andmissing energy reconstruction. Outside the calorimeterare multilayer proportional chambers and plastic scintil-lator hodoscopes that provide muon identification in thepseudorapidity region | | 1.0. We use a cylindricalcoordinate system with origin at the detector center andz-axis along the proton direction [12].

This measurement uses tt candidate events in the lep-ton+jets topology, where one top quark decays semilep-tonically (t lb) and the other hadronically (t qqb)[13]. We detect the lepton and four jets from top quarkdecays and quark hadronization, and an inferred neu-

trino based on the presence of missing energy. The de-tector is triggered by a high transverse momentum elec-tron(muon) in the central portion of the detector withET(pT) > 20 GeV(GeV/c) and || < 1.0. We require fouror more hadronic jets with ET > 20 GeV and || < 2.0,and a large amount of missing transverse energy, ET 20GeV, consistent with the presence of an undetected neu-trino. The jets are reconstructed using a cone algorithmwith R =

2 + 2 < 0.4, and calorimeter signals

are corrected for detector inefficiencies and for the en-ergy scale factor. The SECVTX algorithm [14] is usedto find displaced b-decay vertices using the tracks withinthe jet cones, and at least one jet must contain such a

b-tag. Jets with b-tags are restricted to || < 1.0.A total of 1260 events pass this selection. The size ofthe non-tt background processes in the lepton+jets+b-tag selection is derived in precision measurements of thett production cross-section [9]. The estimated back-ground in our sample 283.3 91.2 events. The pre-dominant backgrounds are from QCD-induced W+multi-parton events containing either b-tagged heavy-flavor jetsor errantly tagged light-flavor jets. These are mod-eled using a simulation sample derived from the alp-gen generator [15] and a data driven technique thatderives tagging efficiencies, mis-tagging rates and sam-ple normalizations from direct measurement. A back-ground component from QCD multi-jet events with fake

leptons and mis-measured ET is modeled using multi-jetevents with lepton candidates that are rejected by ourcuts. Other small backgrounds from electroweak pro-cesses (WW, WZ, single-top) are reliably estimated us-ing Monte Carlo generators. Further details on the sam-ple selection and background modeling can be found inRef. [9].

The reconstruction (reco) of the tt kinematics uses themeasured momenta of the lepton, the ET, and the fourleading jets in the event. The jet-parton assignment and


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calculation of the tt four-vectors uses a simple 2-basedfit of the lepton and jet kinematics to the tt hypoth-esis, allowing the jet energies to float within their ex-pected uncertainties, and applying the constraints thatMW = 80.4 GeV/c

2, Mt = 172.5 GeV/c2, and b-tagged

jets are associated with b-partons. This algorithm is wellunderstood in the context of precision top mass measure-ments, where the fit is performed without the top mass

constraint [16], and other top physics studies that use thetop mass constraint [10]. We study the reconstructed topquark rapidity and the difference in the reconstructed topand anti-top rapidities, from which we derive the forward-backward asymmetries in the pp (laboratory) rest frameand in the tt rest frame.

The validity of the analysis is checked at all stepsby comparison to a standard prediction made using thepythia [17] tt model, the CDF lepton+jets+b-tag back-ground model, and a full simulation of the CDF-II de-tector. We use pythia 6.2.16 with CTEQ5L parton dis-tribution functions [18] and Mt = 172.5 GeV/c

2. Thebackground model developed in concert with the preci-

sion cross-section studies provides good measures of boththe normalizations and shapes of the non-tt processes [9].The veracity of the combined pythia plus backgroundmodel, and in particular, its reliability for the estimationof systematic uncertainties, is well verified in many othertop-physics studies at CDF [5, 9, 10, 16, 31].

Note that because pythia does not include the NLOQCD charge asymmetry, the standard pythia predic-tion is not the SM prediction for the forward-backwardasymmetry. Studies with the mc@nlo generator [19] (seeSec. IV B) predict that the magnitude of reconstructedQCD asymmetry in our sample is smaller than the cur-rent experimental resolution. Symmetric pythia is thusa good approximation for SM tt and provides an unbi-

ased control sample for many of our studies. We will com-pare our measurements to the SM predictions ofmc@nlowhen appropriate.

III. RAPIDITY VARIABLES AND

ASYMMETRY DEFINITIONS

In the lepton+jets decay topology of the tt pair, thereis a leptonic decay, t W b lb, and a hadronic de-cay t W b qqb. The complications of the centrallepton acceptance and the reconstruction of the neutrinofrom the

ET create a difference in the reconstruction res-

olution for the two different kinds of decay. In order tocontrol effects of this kind, our treatment of top rapidityvariables maintains the distinction between the leptonicand hadronic decay systems, with the t and t assignmentsfollowing in accordance with the lepton charge.

The most direct measurement of the top direction withrespect to the beamline is the rapidity of the hadronic topsystem in the lab frame, yh, which has acceptance out to|| = 2.0 and good directional precision. In events witha negative (positive) lepton, yh is the lab rapidity of the

t quark, yppt (t quark, ypp

t). If CP is a good symmetry,

the distributions of yppt

and yppt are reflections of eachother, and we can combine both samples, weighting withthe lepton charge, to use qyh as the rapidity of the tquark in the lab frame, yppt .

A frame independent measurement is available in therapidity difference of the leptonic and hadronic systemsylh = yl

yh. After multiplication by the lepton charge

q, this variable measures the difference between the topand antitop rapidities: qylh = q(yl yh) = yt yt =y. The rapidity difference y is independent of the ttsystem longitudinal motion and is simply related to thetop quark rapidity in the tt rest frame: yttt =

12

y. Sincethe rapidity preserves the sign of the production angle,an asymmetry in y is identical to the asymmetry in thetop quark production angle in the tt rest frame.

With N as the number of events with a given rapidity,we define the total tt frame asymmetry:

Att =N(y > 0) N(y < 0)

N(y > 0) + N(y < 0)

(1)

=N(yttt > 0) N(yttt < 0)N(yttt > 0) + N(y

ttt < 0)

and the total laboratory frame asymmetry, assuming CPinvariance:

App =N(qyh > 0) N(qyh < 0)N(qyh > 0) + N(qyh < 0) (2)

=N(yppt > 0) N(yppt < 0)N(yppt > 0) + N(y

ppt < 0)

Since yh and ylh are identified with either a t or an tby the sign of the lepton in the event, they are the pri-mary variables for defining the charge dependence of theasymmetries and testing for CP invariance. We definethe forward-backward charge asymmetry in the tt restframe to be:

Alh =N(ylh > 0) N(ylh < 0)N(ylh > 0) + N(ylh < 0)

(3)

and in the laboratory frame to be:

Ah =N(yh > 0) N(yh < 0)N(yh > 0) + N(yh < 0)

(4)

where the superscript refers to the sign of the leptoncharge q.


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TABLE I: Summary of rapidity variables and asymmetries.

definitionyh rapidity of hadronic top system in labyl rapidity of leptonic top system in labylh rapidity difference yl yhy tt rapidity difference: yt yt = q(yl yh)yppt top quark rapidity in laboratory frame: qyhyttt top quark rapidity in tt rest frame:

1

2y

Ah asymmetry in yhAlh asymmetry in ylhApp laboratory frame asymmetry in yppt (both charges)

Att tt frame asymmetry in yttt (both charges)

The laboratory and tt frame present trade-offs for theasymmetry measurement. The laboratory frame is exper-imentally simple: the direction of the three-jet hadronictop decay in the detector is well-resolved, with uncer-tainty dominated by a Gaussian width yh 0.034, andfree from the complications of the neutrino reconstruc-tion [20]. The yh distribution is thus the simplest way to

test for the presence of an asymmetry. However, as thelaboratory frame includes an uncontrolled longitudinalboost from the rest frame of the primary qq interaction,the information on the fundamental production asymme-try is diluted.

Because the momentum scale of initial state radia-tion is small compared to Mtt, the qq frame is well ap-proximated by the tt rest frame. We measure the ttframe rapidity in an experimentally robust way usingthe difference of two rapidities in the detector frame,y = q(yl yh). But the inclusion of yl and the poorlyresolved neutrino reconstruction degrades the precision:

the Gaussian part of the tt frame resolution has widthy 0.100 and significant non-Gaussian tails. The ttframe has an advantage in interpretation, but a disad-vantage in resolution.

The frame dependent resolution has to be consideredagainst a possible frame dependence in the size of theasymmetry. In the case of the QCD charge asymmetry,our NLO models (see Table III) suggest that the recon-structed asymmetry is reduced by a factor of 0.6 0.7in the transition from the tt to laboratory frame. Thisroughly balances the resolution difference to give compa-

rable sensitivities to the inclusive QCD asymmetries inthe two frames. Asymmetries generated by other pro-cesses may produce a different ratio between the twoframes, possibly with a y or Mtt dependence, and amore precise measurement of the ratio could help to il-luminate the underlying physics. We will return to thisissue in Sec. VIII E.

A summary of the rapidity variable and asymmetrydefinitions used in this paper is given in Table I.

IV. PHYSICS MODELS AND EXPECTATIONS

We briefly describe the theoretical basis for the QCDasymmetry at NLO, the calculation of the theoreticalasymmetry using the MCFM program [22], and use ofthe mc@nlo event generator in creating a simulatedNLO sample for input to our analysis. We also de-

scribe a simple chiral color-octet model, executed in mad-graph [23], that we use to understand the response ofour analysis to a large tt asymmetry.

A. NLO QCD Theory and MCFM

The NLO QCD asymmetry arises in the interferenceofqq processes that behave differently under charge con-

jugation. The gg initial state does not contribute to theasymmetry, but does dilute the average value.

Early, pre-top, treatments of the QCD charge asym-

metry discussed measurement of generic heavy quarksin hadron collisions [24]. More recent treatments havefocused on the particular case of the top quark at theTevatron and at the LHC [13].

The asymmetry gets a positive contribution from inter-ference of the tree-level and box diagrams, as in the upperdiagrams in Fig. 1 and a negative contribution from theinterference of initial and final state radiation in tt + jet(ttj) final states, as in the lower diagrams. The totalinclusive asymmetry is the sum of these opposing contri-butions. An intuitive picture of the first effect is that theQCD Coulomb field of an incoming light quark repels thet quark to larger rapidities, while attracting the t quarkto smaller rapidities, thus creating a positive asymmetry

at large , as defined by the quark direction [21]. Thesecond effect can be pictured in terms of color-flow: whena forward gluon is radiated by the incoming quark, thelarge acceleration of the color charge biases the top quarktowards the backward direction.

Predictions for the NLO QCD asymmetry are derivedusing version 5.7 ofmcfm with CTEQ6.1(NLO) [18] andMt = 172.5 GeV/c2. The forward-backward asymmetryin the tt rest frame is found to be Att = 0.058 0.009.In the laboratory frame the top quark rapidities are


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FIG. 1: Interfering qq tt (above) and qq ttj (below) amplitudes.

broadened by the varying boost of the tt system alongthe beamline, and the asymmetry is diluted to App =0.038

0.006. Our mcfm predictions are in accord with

other recent calculations [13]. These predictions are fortop quarks as they emerge from the qq collision, beforeany modifications by detector acceptance and resolution.We will call this the parton-level. Based on our own stud-ies of scale dependence in mcfm and also the studies inthe references above, we assign a 15% relative uncertaintyto all NLO mcfm predictions.

An NLO calculation for inclusive tt production is anLO calculation for the production of a tt + jet final state,and thus an LO calculation for the asymmetry in finalstates containing an extra jet. A new NLO calculationfor ttj production (and thus for the asymmetry) suggeststhat the negative asymmetry in this final state is greatlyreduced from leading-order [25]. This new result for thettj asymmetry can be incorporated into an analysis ofthe asymmetry for inclusive tt production only within thecontext of a full NNLO calculation oftt production. Suchcalculations are underway but are not complete. Thresh-old resummation calculations indicate that the inclusiveasymmetry at NNLO should not differ greatly from thatpredicted at NLO [1, 21]. In this paper, we compareto the NLO predictions for tt production. We include a15% scale dependence uncertainty, but note that there isan overall unknown systematic uncertainty on the theo-retical prediction pending the completion of the NNLO

calculation.

In the near-threshold form of the cross section [1] thett frame asymmetry can be seen to increase with the topquark production angle and velocity (), and these arethus key variables for understanding the source of theasymmetry. In this analysis, the proxies for these vari-ables are the top quark rapidities and the mass Mtt ofthe tt system. Measurements of the rapidity and massdependence of Att are described in Sections VI and VII.

B. NLO QCD Simulation with MC@NLO

We use the event generator mc@nlo to create a sim-ulated sample that includes the QCD asymmetry as pre-dicted by the standard model at NLO. In addition toincluding the asymmetric processes this generator prop-erly estimates the amount ofgg, and thus the dilution ofthe asymmetry from these symmetric processes.

Some naming conventions for the data-to-simulationcomparison are given in Table II. All Monte Carlo (MC)generators will have the same conventions: the truth in-formation is the parton level; the pure top signal aftersimulation, selection, and reconstruction is the tt level,and the full prediction including backgrounds is tt + bkglevel. The reconstructed lepton+jets sample is the data.

Subtracting the backgrounds from the data yields thereconstructed tt signal-level. Correcting the data for ac-ceptance and resolution produces a measurement at theparton-level.

TABLE II: Naming conventions for data and simulation sam-ples.

sample level definition comparable todata data reco l+jetsdata signal data minus bkg tt in datadata parton corrected signal tt at creationMC tt+bkg reco tt + bkg dataMC tt reco tt no bkg data signal

MC parton truth level data parton

The mc@nlo predictions for the asymmetries at var-ious levels of simulation are shown in Table III. Theuncertainties include the Monte Carlo statistics and theNLO theoretical uncertainty. The parton-level mc@nloasymmetries are consistent with mcfm, as expected. Af-ter CDF detector simulation, event selection, and recon-struction, the asymmetries in the mc@nlo tt signal are


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TABLE III: NLO QCD asymmetries in two frames. Uncertainties includes MC statistics and scale dependence.

model level App Att App/Att

mcfm parton 0.038 0.006 0.058 0.009 0.66 0.10mc@nlo parton 0.032 0.005 0.052 0.008 0.62 0.09mc@nlo tt 0.018 0.005 0.024 0.005 0.75 0.11mc@nlo tt+bkg 0.001 0.003 0.017 0.004 0.06 0.01

h-yl

y-3 -2 -1 0 1 2 3

Events

0

50

100

150

200

250

300

350

400

450

dltay_not_qdltay_t_lhad[0][0][3][0][1][0]C

Entris1.92287+07

an -0.003806

0.7698

data

+ bkgttbkg

0.028= 0.008dataA

0.003= -0.003+bkgtt

A

0.002= -0.002tt

A

0.008= -0.009bkgA

hy

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Events

0

50

100

150

200

250

300

350

400

rcon_hadTo_raidity [0][0][3][0][1][0]C

Entris1.92287+07

an -0.00161

0.5558

data

+ bkgttbkg

0.028= 0.005data

A

0.003= -0.006+bkgtt

A

0.002= -0.002tt

A

0.008= -0.019bkgA

FIG. 2: Rapidity distributions in data compared to predictions. The legend tt + bkg implies totals in those bins are the sumof the tt and background components. The asymmetries in the data and the predicted tt signal, background, and combinationare shown in legends on top right of plots, using the conventions of Table II.

significantly reduced. In the laboratory frame, the ex-pected asymmetry at the reconstructed tt+bkg level is

consistent with zero.We will see in Sec. V that the statistical error on App

and Att in the current dataset is 0.028. Table III showsthat, even after background subtraction, the central val-ues of the expected asymmetries are smaller than theexperimental resolution. This motivates the continueduse of symmetric pythia as our default tt model (as dis-cussed in Sec. II), but we will also consider the mc@nlopredictions in several specific studies.

C. Generic Color-Octet with madevent

It is important that we test our measurement proce-dures in the regime of the observed asymmetries. Wehave used madgraph and the model of Ref. [8] to createasymmetric test samples that can be used as input to ouranalysis [26]. A massive axial color-octet G mixes withthe gluon to give a production cross section including poleand interference terms linear in cos(), where is thet production angle in the tt rest frame. In these modelsthe asymmetry is an explicit function of the productionangle and q2, again illustrating the importance of the y

and Mtt dependence for understanding the source of theasymmetry.

We tuned the octet mass MG to put the pole out ofrange and the couplings to give inclusive parton levelasymmetries in rough agreement with the data, App =0.110 and Att = 0.157, while minimizing the effect onthe tt cross section and Mtt distribution (see Appendix).After madgraph generation, partons are showered withpythia and the sample is passed through the completeCDF-II detector simulation. We call this sample OctetA.

A second sample, OctetB, has the same couplings andlower MG, to give inclusive parton level asymmetriesApp = 0.205 and Att = 0.282, with slight ( 5%) in-creases in the tt cross section and in the high M

tt

tail.We consider that OctetA is a better model for under-standing the experimental response, but we will appealto both models in order to span an asymmetry rangeextending beyond the experimental values.

We emphasize that our use of the Octet models is tostudy sensitivities and systematic effects in the presenceof large asymmetries, and should not be construed astests of physics hypothesis. More detail on these samplescan be found in the Appendix.


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h-yl

y-3 -2 -1 0 1 2 3

Events

0

50

100

150

200

250

dl t ay_not _qdl t ay_t _l had[ 0] [ 0][ 3] [1] [ 1][ 0] C

Entris 9615115

a n 0 . 00 3 2

0.7666

data (negative)

+ bkgtt

bkg

0.039= -0.048data

A

0.004= 0.008+bkgtt

A

0.003= 0.011tt

A

0.012= -0.004bkgA

h-yl

y-3 -2 -1 0 1 2 3

Events

0

50

100

150

200

250

dl t ay_not _qdl t ay_t _l had[ 0] [ 0] [ 3] [2] [ 1][ 0] C

Entris 9613620

a n - 0 . 0 1 1 03

0.7731

data (positive)

+ bkgtt

bkg

0.040= 0.067data

A

0.004= -0.015+bkgtt

A

0.003= -0.015tt

A

0.012= -0.014bkgA

hy

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Events

0

50

100

150

200

250

rcon_hadTo_rai di t y [0] [ 0] [3] [ 1][ 1] [0] C

Entris 9615115

a n - 0 . 0 1 3 99

0.5552

data (negative)

+ bkgtt

bkg

0.039= 0.076data

A

0.004= -0.024+bkgtt

A

0.003= -0.011tt

A

0.012= -0.073bkgA

hy

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Events

0

50

100

150

200

250

rcon_hadTo_r ai di t y[ 0] [0] [ 3][ 2] [1] [ 0] C

Entris 9613620

a n 0 . 0 1 1 3 3

0.556

data (positive)

+ bkgtt

bkg

0.040= -0.070dataA

0.004= 0.013+bkgtt

A

0.003= 0.006tt

A

0.012= 0.035bkgA

FIG. 3: Distributions of ylh (top) and yh (bottom) for events with negative leptons (left) and positive leptons (right).

V. MEASUREMENT OF THE INCLUSIVE

ASYMMETRIES

We now turn to the rapidity distributions in the data.The inclusive distributions of the ylh and yh variablesare shown in Fig. 2, compared to the standard pythiatt + background prediction. These distributions containthe full sample of both lepton signs and should be sym-metric. The legend on the top right shows the asym-metries in all components. The data agrees well withtt+bkg prediction in both variables, and, in particular,

the asymmetries are consistent with zero.A forward-backward asymmetry becomes apparent

when the sample is separated by charge. The top rowof Fig. 3 shows the y distributions for events with neg-ative leptons (left) and positive leptons(right). We findA+lh = 0.067 0.040 and Alh = 0.048 0.039, wherethe uncertainties are statistical only. With limited sig-nificance, the asymmetries are equal in magnitude andopposite in sign.

The bottom plots of Fig. 3 shows the yh distribu-

tions for events with negative leptons (left) and pos-itive leptons (right). An indication of asymmetry isalso observed in this figure: t quarks are dominant inthe forward (proton) direction and the t quarks in thebackward (p) direction. The measured asymmetries areA+h = 0.070 0.040 and Ah = 0.076 0.039, againequal and opposite within uncertainties.

The sign reversal of the asymmetry under interchangeof the lepton charge (or, in our formalism, under inter-change of t and t) is consistent with CP conservation.With larger samples and improved precision, the com-parison of the charge separated distributions will pro-vide a strict test of CP conservation in tt production. Ifwe assume CP conservation we can calculate the totalasymmetry in each frame using Eqs. (1) and (2). Thedistributions of these variables are shown in Fig. 4. Theasymmetry in the tt frame is Att = 0.057 0.028, and inthe laboratory frame is App = 0.073 0.028, where bothuncertainties are statistical.


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t- y

ty = y

-3 -2 -1 0 1 2 3

Events

0

50

100

150

200

250

300

350

400

450

dl t a_q_rai di t y_t _l had[ 0] [ 0] [3] [ 0] [1] [ 0] C

Entris1 . 9 2 2 8 7 +0 7

a n - 0 . 0 0 7 18 7

0.7698

data

+ bkgttbkg

0.028= 0.057data

A

0.003= -0.011+bkgtt

A

0.002= -0.013tt

A

0.008= -0.005bkgA

t

= yh

-qy-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Events

0

50

100

150

200

250

300

350

400

rcon_qt oh_rai di t y [ 0] [0] [ 3] [0] [ 1] [ 0]C

Entris1 . 9 2 2 8 7 +0 7

a n - 0 . 0 1 2 6 8

0.5556

data

+ bkgttbkg

0.028= 0.073dataA

0.003= -0.019+bkgtt

A

0.002= -0.009tt

A

0.008= -0.054bkg

fbA

FIG. 4: y and yppt distributions in data vs prediction.

A. The Parton-Level Asymmetry

In order to compare our results to theoretical predic-tions we must correct the data for backgrounds, for in-complete detector acceptance, and for the finite rapidityresolution of the reconstruction.

We derive the signal level tt distributions by sub-tracting the expected background from the reconstructeddata. This correction is most important in the laboratoryframe, where, as shown on the right in Fig. 4, the back-grounds show a significant negative asymmetry originat-ing in the W production asymmetry in W+jets events.

The reliability of the background model is verified in

the subset of the lepton+jets selection that has no b-tagged jets. This anti-tag sample is background en-riched, with S:B 0.3, and is also fully modeled in ouranalysis. The predicted tt and lab frame asymmetriesin the anti-tag data sample are in excellent agreementwith observation, as shown in Table IV. The absence ofasymmetry in this background enriched sample, and theconsistency between prediction and observation, suggestthat the asymmetry in the b-tagged sample is correlatedwith the tt signal and not the backgrounds.

TABLE IV: Asymmetries in the anti-tag sample of the dataand tt + bkg level prediction.

selection Att App

anti-tag data 0.033 0.018 0.016 0.018anti-tag prediction 0.010 0.007 0.023 0.007

Acceptance and resolution corrections are made witha simple linear unfolding of the y and yppt distribu-tions using the technique described in Ref. [5]. Let thebinned parton-level rapidity distributions be representedby the vector n. The n distribution is modified by the

acceptance and then by the smearing in the reconstruc-tion. These transformations can be expressed as matri-ces transforming the distribution vector from the partonlevel to our reconstructed signal: nsignal = SAnparton.

The matrices A and S are derived from pythia sam-ples by comparing distributions at the Monte Carlo truthlevel to the same distributions after reconstruction. Theacceptance matrix A is diagonal. The smearing matrixS measures the bin-to-bin migration arising from the fi-nite resolution of reconstructing the events in the tt hy-pothesis. To measure the parton-level value, we subtractbackgrounds to recover the signal from the data, and theninvert the transformation:

nparton = A1S1(ndata nbkg) (5)

With the assumption of the A and S response as com-puted with pythia, this technique gives a model inde-pendent measure of the parton-level asymmetry. Theresult was found to be robust and the uncertainty mini-mized when the distributions are separated into four binswith bin edges at 0.0, and |y| = 1.0 or |yppt | = 0.5[5, 2729].

The measurement is affected by uncertainties in ourmodels for the amount and shape of the backgrounds,the amount of initial state and final state radiation (ISRand FSR) in pythia, the jet energy scale (JES) of thecalorimeter, the parton distribution functions (PDF),and the color reconnection in the final state. These ad-ditional systematic uncertainties are studied by repeat-ing the analysis with reasonable variations in the modelparameters. We also test the result of substituting theother LO generators herwig and alpgen for pythiain the model for the matrix unfold. The effect of thesemodel variations on the parton-level asymmetry is small,as seen in Table V.


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t- y

ty = y

-3 -2 -1 0 1 2 3

Events

0

100

200

300

400

500

600

700

8000.028Data reco A = 0.057

0.036Signal A = 0.075tt

0.072Parton A = 0.158tt

0.002Pythia A = -0.011tt

t t r_ i n

E n tr i 1 2

n . 5 55

. 5

pp

t= y

h-qy

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Events

0

100

200

300

400

500

600

t t r_ i n

E n tr i 1 2

n . 5 55

. 5

t t r_ i n

E n tr i 1 2

n . 5 55

. 5

0.028Data reco A = 0.073

0.036Signal A = 0.110tt

0.050Parton A = 0.150tt

0.002Pythia A = -0.007tt

FIG. 5: Four-bin representation of rapidity distributions for all correction levels. Solid histogram is the pythia tt model.

TABLE V: Systematic uncertainties on parton-level asymme-tries in both frames.

effect App Att

background magnitude 0.015 0.011background shape 0.014 0.007ISR/FSR 0.010 0.001JES 0.003 0.007PDF 0.005 0.005color reconnection 0.001 0.004LO MC generator 0.005 0.005total 0.024 0.017

It is possible that the corrections in the presence ofa large asymmetry would differ from the corrections de-rived from the symmetric pythia. We have studied thispossibility by applying the pythia- based response cor-rections to the OctetA model, which has an asymmetrylike the data and a resemblance to the data in all otherrespects. We find that the bias in the corrected inclusiveasymmetries is small, roughly 0.02, and we take this asevidence that the technique is essentially robust againstperturbations of this kind. Since we have no reason toprefer the prediction of this or any other model, we donot include a modeling uncertainty. Our inclusive results

assume the corrections and uncertainties calculated withthe standard pythia model.

Fig. 5 shows the y and yppt distributions at all of thecorrection levels in the four-bin representation. The ef-fect of the background subtraction is clear. The tt signal(squares) derived from the background subtracted datacan be directly compared with the pythia signal pre-diction, and continues to show the asymmetries. Thecorrected distribution at the parton-level (triangles) canalso be compared to the symmetric pythia prediction.

TABLE VI: Summary of inclusive asymmetries. Uncertaintiesinclude statistical, systematic, and theoretical uncertainties.

sample level Att App

data data 0.057 0.028 0.073 0.028mc@nlo tt+bkg 0.017 0.004 0.001 0.003data signal 0.075 0.037 0.110 0.039mc@nlo tt 0.024 0.005 0.018 0.005data parton 0.158 0.074 0.150 0.055mcfm parton 0.058 0.009 0.038 0.006

Table VI summarizes the measured asymmetries forthe different levels of correction. It is interesting thatat the data-level in the laboratory frame we compare toa model prediction that is consistent with zero. Whenthe backgrounds are subtracted from the reconstructeddata we can calculate the asymmetry for a pure tt sam-ple at the signal level, and compare directly to mc@nlott. The signal uncertainty here includes the uncertaintyon the background correction. Correcting for acceptanceand reconstruction resolution yields the tt parton-levelasymmetry, where the uncertainty includes the effectslisted in Table V. The parton-level asymmetry may bedirectly compared with the standard model prediction ofmcfm.

The experimentally simple laboratory frame asymme-try exceeds the prediction by more than two standarddeviations at all correction levels. The tt frame asymme-tries are similar in magnitude to the laboratory frame,but less significant because of the larger uncertainties.The ratio of the parton-level asymmetries in the twoframes is App/Att = 0.95 0.41, where the error is cor-rected for the expected correlation across frames in theNLO QCD assumption. This measured ratio is consis-tent with the expected SM NLO value of 0.6, but the


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uncertainty is large.

B. Cross-Checks of the Inclusive Asymmetry

Table VII shows the asymmetries in the data when thesample is separated according to the lepton flavor and thenumber ofb-tagged jets in the event. All of our simulated

models predict asymmetries that are independent of thelepton type. Within the large errors, the data are con-sistent with this expectation.

The b-tagged sample contains 281 events with two b-tags. This double-tag sample is small, but has mini-mal backgrounds and robust jet-parton assignment. Thedouble-tag sample is a special category of tt decays whereboth the b and b jet have | | 1.0, but all of our simu-lation models predict similar asymmetries in single tagsand double-tags. In the data the results are consistentacross single and double-tags, albeit with reduced agree-ment in App. We will discuss the double-tag consistencyin the laboratory frame in more detail in Sec. VIII E.

TABLE VII: Measured asymmetries at the data-level for dif-ferent lepton and b-tag selections.

selection Att App

inclusive 0.057 0.028 0.073 0.028electrons 0.026 0.037 0.053 0.037muons 0.105 0.043 0.099 0.043single b-tags 0.058 0.031 0.095 0.032double b-tags 0.053 0.059 0.004 0.060

VI. RAPIDITY DEPENDENCE OF THE

ASYMMETRY IN THE tt REST FRAME

In Sec. IV we discussed the importance of measur-ing the rapidity and Mtt dependence of the asymme-try. The correlated dependence on both variables wouldbe most powerful, but, given the modest statistical pre-cision of our current dataset, we begin with separatemeasurements of each. In this section we show how ay-dependence may be calculated from the results ofSec. V A. The Mtt-dependence (as well as the correla-tion of Mtt and y) will be discussed in the sectionsfollowing.

In the standard model at NLO the tt frame asymme-try increases linearly with y, as seen in Fig. 6. Theslope is significant, with the asymmetry reaching valuesof roughly 20% at large y.

The y dependence of the asymmetry in our binneddata can be calculated in each bin i of positive y as

Att(yi) =N(yi) N(yi)N(yi) + N(yi) (6)

E nt rie s 0

Me an 0

RMS 0

y0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Asy

mmetry

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

E nt rie s 0

Me an 0

RMS 0

FIG. 6: y-dependence of Att according to mcfm.

FIG. 7: Parton level asymmetries at small and large y com-pared to SM prediction ofmcfm. The shaded bands representthe total uncertainty in each bin. The negative going uncer-tainty for y < 1.0 is suppressed.

A parton-level measurement of Att(yi) in two bins

of high and low y is available from the corrected ydistribution in Fig. 5. We calculate the asymmetry sep-arately for the low rapidity difference inner bin pair|y| < 1.0 and the large rapidity difference outer bin pair|y| 1.0. The systematic uncertainties in the bin-by-bin comparison are evaluated using the same techniquesas in the inclusive measurement. Uncertainty in the back-ground shape and normalization assumptions cause a sig-nificant systematic uncertainty in the high y bin.

The y-dependent asymmetries are shown in Table


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TABLE VIII: The tt frame asymmetry Att at small and largerapidity difference, compared to the SM prediction ofmcfm.

sample level |y| < 1.0 |y| 1.0data data 0.021 0.031 0.208 0.062data parton 0.026 0.104 0.056 0.611 0.210 0.147mcfm parton 0.039 0.006 0.123 0.018

VIII. For the parton-level data, the first uncertainty isstatistical and the second is systematic. The uncertaintyon the mcfm prediction is dominated by the NLO theoryuncertainty. For |y| 1.0, the small data-level asym-metry maps into a small parton-level value with largeerror. In the large y region the parton-level asymme-try is Att(|y| > 1.0) = 0.611 0.270 (statistical andsystematic errors added in quadrature) compared to themcfm prediction of 0.123 0.018. Fig. 7 displays theparton level comparison of asymmetries in data in thetwo y regions.

VII. MASS DEPENDENCE OF THE

ASYMMETRY IN THE tt REST FRAME

(GeV/c )tt

M300 400 500 600 700 800

Asymmetry

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

2

FIG. 8: Mtt-dependence of Att according to mcfm.

We now turn to the dependence of the asymmetryon the tt invariant mass Mtt. The NLO QCD asym-metry also has a strong Mtt dependence, as shown inFig. 8. We generally expect the Mtt dependence to con-tain characteristic information on the fundamental asym-metry mechanism.

In this analysis, the value of Mtt is derived from thesame reconstruction used to compute the top quark ra-pidities. The Mtt distribution in our sample, shown inFig. 9, is agreement with the standard prediction. Otherrecent studies of the top pair mass spectrum, including

)2

(GeV/ctt

M300 400 500 600 700 800 900

)2

Events/(15GeV/c

1

10

210

data

+ bkgttbackground

FIG. 9: Event distribution as a function of the total invariantmass Mtt.

the parton-level differential cross section d/dMtt, showgood agreement with the standard model [10, 30, 31].

Since the mass dependent behavior is usually describedin the tt rest frame we focus on the asymmetry in rapiditydifference y as a function ofMtt. The laboratory frameasymmetry derived with yh is discussed in Sec. VIII.

The underlying 2-dimensional distribution of y

vs.Mtt is shown on the left in Fig. 10. We expectthese variables to obey the simple kinematic relation-ship Mtt = 2mT cosh(y), where mT is the transversemass of the tt system, and we see this in both the dataand the prediction. It is clear that the prior measure-ment at large y captures only part of the region atlarge Mtt. Consequently, the separate measurements ofthe y- and Mtt-dependence of the asymmetry providecomplementary information.

Because cosh(y) is symmetric, this kinematic correla-tion is independent of the Mtt-dependence of any asym-metry in y. Because of the independence of mT,themeasurement at large |y| > 1.0 captures only part ofthe region at large Mtt. The separate measurementstherefore provide complementary information.

A mass dependent asymmetry Att(Mtt,i) is found bydividing the yMtt plane into bins of mass Mtt,i andcalculating the asymmetry in each:

Att(Mtt,i) =N(y > 0, Mtt,i N(y < 0, Mtt,i)N(y > 0, Mtt,i) + N(y < 0, Mtt,i)

(7)

We use 50 GeV/c2 bins ofMtt below 600 GeV/c2, and


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ttM

350 400 450 500 550 600 650 700 750 800

(M)

tt

A

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6data

+ bkgtNLO t

M (GeV/c )tt2

FIG. 10: Left: The yMtt plane. Each dot represents one event, while the intensity of the shading shows approximatelythe event probability in the standard pythia based prediction.Right: The tt frame asymmetry in the data in bins of invariantmass Mtt, compared to the prediction ofmc@nlo tt + backgrounds. The last bin includes all events with Mtt 700GeV/c2.

ttM

350 400 450 500 550 600 650 700 750 800

(M)

tt

A

-0.4

-0.2

0

0.2

0.4

0.6

data (+ lepton)

data ( - lepton)

M (GeV/c )tt2

FIG. 11: The tt frame asymmetries in bins of invariant massMtt when the data is partitioned by lepton charge.

100 GeV/c2 bins above that. The Mtt-dependent asym-metry in y is shown on the right in Fig. 10 and Ta-ble IX, compared to the prediction ofmc@nlo in combi-nation with the standard background. The uncertaintiesin the plot are the statistical errors only; in the table themc@nlo uncertainty contains both the statistical andtheoretical component. In the bulk of the data at lowmass the asymmetry is consistent with zero, while at highmass the asymmetry is consistently above the prediction.Fig. 11 shows that when the data are separated by leptoncharge, the asymmetries in the two independent samplesbehave in approximately opposite fashion.

TABLE IX: The data-level asymmetry Att in bins ofMtt com-pared to the prediction ofmc@nlo + backgrounds.

bin-center Att

(GeV/c2) N events data mc@nlo375 532 -0.019 0.043 0.003 0.006425 322 -0.012 0.056 0.026 0.008475 190 0.158 0.072 0.013 0.010525 95 0.305 0.097 0.019 0.013575 58 0.138 0.130 0.063 0.020650 34 0.471 0.151 0.051 0.020750 29 0.103 0.185 0.091 0.022

A. Asymmetries at High and Low Mass

The large statistical errors in the Att(Mtt,i) distribu-tion of Fig. 10 do not allow any conclusion on the func-tional dependence. In order to make a quantitative mea-surement ofAtt(Mtt) in a simple, statistically meaningfulway, we use a compact representation of Att(Mtt,i) into

just two Mtt bins, below and above a given mass bound-ary.

The boundary between the low and high mass regionsis chosen based on a study of the color-octet samples de-scribed in the Appendix. These samples have Att(Mtt,i)distributions that are comparable to the data and reason-able for modeling the sensitivity in that variable. We findthat the significance of the asymmetry at high mass ismaximized when the bin division is at Mtt = 450 GeV/c

2,and therefore adopt this cut.

Fig. 12 shows the y distributions when the datais divided into two regions, below and above Mtt =450 GeV/c2. At low mass the asymmetry is consis-tent with zero. At high mass, the rapidity difference is


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t- Y

tY = Y

-3 -2 -1 0 1 2 3

Events

/0.6

0

100

200

300

400

500

dataA = -0.016+/-0.034

+ bkgttA = -0.0087+/-0.034

bkg

A = 0.00073+/-0.069

t- Y

tY = Y

-3 -2 -1 0 1 2 3

Events

/0.6

0

20

40

60

80

100

120

140

160

dataA = 0.21+/-0.049

+ bkgttA = -0.017+/-0.05

bkg

A = -0.024+/-0.11

FIG. 12: Top: The distribution of y at low mass (left) and high mass (right).

t- Y

tY = Y

-3 -2 -1 0 1 2 3

Events

/0.6

0

10

20

30

40

50

60

70

data (negative lepton)A = -0.21+/-0.071

+ bkgttA = 0.015+/-0.07

bkg

A = 0.019+/-0.16

t- Y

tY = Y

-3 -2 -1 0 1 2 3

Events

/0.6

0

10

20

30

40

50

60

70

80

90

100data (positive lepton)A = 0.21+/-0.066

+ bkgttA = -0.02+/-0.072

bkg

A = -0.028+/-0.16

FIG. 13: The distribution of y at high mass for events with negative leptons (left) and positive leptons (right).

TABLE X: Charged and total asymmetries at the data-level, for all, low, and high Mtt.

selection all Mtt Mtt < 450 GeV/c2 Mtt 450 GeV/c2

reco data 0.0570.028 -0.0160.034 0.2100.049mc@nlo 0.0170.004 0.0120.006 0.0300.007

A+lh 0.0670.040 -0.0130.050 0.2100.066Alh -0.048

0.039 0.020

0.047 -0.210

0.071

broader, as expected from the kinematics, and an asym-metry is apparent. The top two lines of Table X comparethe high and low mass asymmetries with the mc@nloprediction. The uncertainty on the prediction combinesthe statistical and the theoretical uncertainties. At highmass the reconstructed asymmetry Att = 0.210 0.049(stat) is more than three standard deviations above the

prediction.

The high mass y distributions for the two separatelepton charges are shown in Fig. 13, and the asymmetriesin those distributions are summarized in the bottom partof Table X. Under the interchange of lepton charge, or,equivalently, under the interchange of t and t, the asym-metry at high mass is approximately reversed. This is


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TABLE XI: Tests of the combined mass and rapidity correction procedure. True, reconstructed, and fully corrected asymmetriesas found in the two mass regions. Uncertainties on predictions are statistical errors in the MC samples; at truth level these arenegligible.

Sample Att level Mtt < 450 GeV/c2 Mtt 450 GeV/c2

pythia MC truth 0.002 0.001reconstructed 0.011 0.006 0.013 0.008corrected 0.001 0.018 0.006 0.014

mc@nlo MC truth 0.043 0.070

reconstructed 0.015 0.006 0.043 0.009corrected 0.066 0.014 0.086 0.011

Octet A MC truth 0.081 0.276reconstructed 0.024 0.035 0.183 0.010corrected 0.054 0.022 0.308 0.016

Octet B MC truth 0.150 0.466reconstructed 0.078 0.036 0.310 0.009corrected 0.187 0.024 0.476 0.015

consistent with CP conservation, and also a strong argu-ment against a false asymmetry arising in event selectionor tt reconstruction, as neither the event selection norreconstruction make reference to the lepton charge.

The results here suggest that the modest inclusiveasymmetry in the tt rest frame originates with a largeasymmetry in a small population at high Mtt.

B. The Mass Dependent Asymmetry at the

Parton-Level

In the measurement of the inclusive asymmetry weused a simple matrix technique to correct the rapiditydistributions for acceptance and resolution and derive

parton-level asymmetries that could be compared withtheory. We do this now for the mass dependent asymme-try in the tt frame. We divide the data into two bins iny, forward and backward, and two bins in mass, aboveand below 450 GeV/c2 and re-apply the well tested 4 4unfold machinery of the inclusive analysis. The proce-dure yields fully corrected, model-independent asymme-tries that can be compared with theoretical predictions.

We represent the four bins of the parton-level dis-tribution of y and Mtt by a single vector n =[nLF, nLB, nHF, nHB ] where, for example, nLF is thenumber of forward events at low mass. As in the in-clusive case, we know that the true n distribution ismodified by matrices representing the acceptance and

then by the smearing in the reconstruction, so thatnsignal = SAnparton. To measure the parton-level value,we subtract backgrounds to recover the signal from thedata, and then invert the transformation as in Eq. (5).

As before, the matrices A and S are derived fromPythia Monte Carlo samples by comparing truth distri-butions to the same distributions after reconstruction.The bin-to-bin migration measured in the smearing ma-trix now includes the cross-terms between high and lowmass and forward and backward y. The most signifi-

cant migration is caused by mis-reconstructions that un-derestimate Mtt and smear the shape of the Mtt spectrumtowards lower masses.

TABLE XII: Systematic asymmetry uncertainties in the two-mass bin unfold

Source Mtt < 450 GeV/c2 Mtt 450 GeV/c2

background size 0.017 0.032background shape 0.003 0.003JES 0.005 0.012ISR/FSR 0.012 0.008color reconnection 0.009 0.004PDF 0.018 0.004physics model 0.035 0.035total 0.047 0.049

The accuracy of the procedure is first tested againstsimulated control samples using pythia and [email protected] pythia test uses a tt sample that is independent ofthe one used to create the response matrices. The toppart of Table XI shows that the correction procedure isunbiased when operating on the symmetric pythia in-put. The mc@nlo sample allows us to study the accu-racy of the correction in measuring the NLO QCD effect.A small possible bias of 0.02 is insignificant comparedto the statistical uncertainty in the present data set.

Next, we use the color-octet samples to test how wellthe correction derived from symmetric pythia can re-cover large parton-level asymmetries. The bottom halfof Table XI shows that the correction procedure recov-ers both the high and low mass asymmetries to withina few percent of the true values. The corrections in theOctet sample show a possible 0.02 0.03 bias that ismarginally significant compared to the statistical preci-sion of the test. Because the Octet samples match thedata well in the two key distributions y and Mtt (seeAppendix) we expect that this is a representative mea-sure of possible model dependence in the correction, and


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we assign a systematic uncertainty of 0.035 for this effect.

Additional systematic uncertainties are evaluated ina manner similar to the inclusive case. These uncertain-ties are estimated by repeating the analysis while varyingthe model assumptions within their known uncertaintiesfor background normalization and shape, the amount ofinitial- and final-state radiation (ISR/FSR) in pythia,the calorimeter jet energy scale (JES), the model of fi-

nal state color connection, and parton distribution func-tions (PDF). Table XII shows the expected size of allsystematic uncertainties. The physics model dependencedominates.

TABLE XIII: Asymmetry Att at high and low mass comparedto prediction.

selection Mtt < 450 GeV/c2 Mtt 450 GeV/c2

data 0.016 0.034 0.210 0.049tt+bkg +0.012 0.006 0.030 0.007(mc@nlo)data signal

0.022

0.039

0.017 0.266

0.053

0.032

tt +0.015 0.006 0.043 0.009(mc@nlo)data parton 0.116 0.146 0.047 0.475 0.101 0.049mcfm +0.040 0.006 0.088 0.013

Table XIII compares the low and high mass asymme-try to predictions for the data level, the background sub-tracted signal-level, and the fully corrected parton-level.The MC predictions include the 15% theoretical uncer-tainty. At low mass, within uncertainties, the asymmetryat all correction levels agrees with predictions consistent

with zero. At high mass, combining statistical and sys-tematic uncertainties in quadrature, the asymmetries atall levels exceed the predictions by more than three stan-dard deviations. The parton-level comparison is summa-rized in Fig. 14. For Mtt 450 GeV/c2, the parton-levelasymmetry at in the tt rest frame is Att = 0.475 0.114(stat+sys), compared with the MCFM prediction ofAtt = 0.088 0.013.

VIII. CROSS-CHECKS OF THE MASS

DEPENDENT ASYMMETRY

The large and unexpected asymmetry at high mass de-mands a broader study of related effects in the tt data.We look for anomalies that could be evidence of a falsepositive, along with correlations that could reveal moreabout a true positive. In order to avoid any assumptionsrelated to the background subtraction, we make compar-isons at the data level, appealing when necessary to thefull tt + bkg simulation models.

FIG. 14: Parton-level asymmetry in y at high and low masscompared to mcfm prediction. The shaded region represents

the total uncertainty in each bin.

2

0 10 20 30 40 50 60 70 80 90 100

Events

0

100

200

300

400

500

600

700

800

900

FIG. 15: Distribution of tt reconstruction 2. Black crossesare data, histogram is sig+bkg prediction.The last bin on theright contains all events with 2 > 100.

A. Lepton Type

All of our simulated models predict asymmetries thatare independent of the lepton type: pythia predictsasymmetries that are consistent with zero, and the Octetmodels predict asymmetries that are consistent with eachother. The data are shown in Table XIV. At high mass,both lepton types show positive asymmetries consistentwithin errors.


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TABLE XIV: Data level asymmetries Att for different event selections. In the case of no-b-fit, the tt reconstruction has beenrun without the constraint that b-tagged jets be associated with b-partons.

selection N events all Mtt Mtt < 450 GeV/c2 Mtt 450 GeV/c2

standard 1260 0.0570.028 -0.0160.034 0.2120.049electrons 735 0.0260.037 -0.0200.045 0.1200.063

muons 525 0.1050.043 -0.0120.054 0.3480.080data 2 < 3.0 338 0.030

0.054

0.033

0.065 0.180

0.099

data no-b-fit 1260 0.0620.028 0.006 0.034 0.190 0.050data single b-tag 979 0.0580.031 -0.0150.038 0.2240.056

data double b-tag 281 0.0530.059 -0.0230.076 0.1780.095data anti-tag 3019 0.0330.018 0.0290.021 0.0440.035pred anti-tag - 0.0100.007 0.0130.008 0.0010.014

pre-tag 4279 0.0400.015 0.0170.018 0.1000.029pre-tag no-b-fit 4279 0.0420.015 0.0230.018 0.0920.029

B. Reconstruction

It is conceivable that a reconstruction error could pro-

duce an asymmetry from symmetric inputs. The qual-ity of the reconstruction is summarized by a 2 thatmeasures the consistency of the solution with the tt hy-pothesis. The distribution of 2 in our sample, shown inFig. 15, is in very good agreement with the prediction,including a good match on the long tail. When the sam-ple is restricted to high quality fits with 2 3.0, we find338 events in which Att = 0.033 0.065 at low massand Att = 0.180 0.099 at high mass. Although thestatistical precision is diminished in this small sample,it suggests that the high mass asymmetry is present inthe best reconstructed events. Since the 2 requirementrejects a significant fraction of the background, it alsosuggests that the high mass asymmetry is not a back-ground related effect.

To test for possible reconstruction biases related to b-tagging, we re-run the reconstruction algorithm removingthe constraint that b-tag jets be matched to b partons.We find Att = 0.006 0.034 at low mass and Att =0.190 0.050 at high mass. When we further separatethe events by lepton charge, the ylh asymmetries areAlh = 0.190 0.074 and A+lh = 0.190 0.069. Thelarge forward-backward charge asymmetry at high massis seen to be independent of the use of b-jet identificationin the reconstruction.

C. B-Jet Identification

All of our simulated models predict asymmetries thatare independent of whether one or two jets are b-tagged.In single and double b-tagged samples pythia predictsasymmetries that are consistent with zero, and the Octetmodels predict asymmetries that are consistent with eachother. In the data, the two cases are consistent with eachother, although the statistical precision on the doubletagged sample is marginal.

In the background dominated anti-tags, the inclusiveand low mass samples have small asymmetries that agreewith the prediction. In the high mass anti-tag sample we

find A

tt

= 0.0440.035, consistent with either the modelprediction of zero or a slight excess due to the tt compo-nent there. Mixing backgrounds and tt in the expectedratio and assuming the tt component has an asymme-try of 0.266 (as in Table XIII), we find a total expectedasymmetry in the anti-tag sample of Att = 0.079 0.034in agreement with the data.

The lepton+jets sample with no b-tagging is the pre-tag sample. Our standard pythia + background modelpredicts pre-tag asymmetries consistent with zero for allmass categories. The asymmetries in the data are shownin Table XIV. At low mass the asymmetry in the pre-tagsis consistent with zero. At high mass, the pre-tag samplehas a significant asymmetry 0.100

0.029. If we assume

that tt signal at high mass has Att = 0.266 as in Ta-ble XIII and combine tt with our standard backgroundsin the expected pre-tag ratio, we predict a pre-tag asym-metry of Att = 0.111 0.028, in good agreement withthe data.

As a final check in the pre-tag sample, we repeat theexercise of running the reconstruction without the con-straint that b-tagged jets are used as b-partons. Theresults are shown in the bottom row of Table XIV. Theasymmetry at high mass is 0.092 0.029, a significanteffect in a sample that makes absolutely no reference tob-tagging.

D. Jet Multiplicity

In Sec. IV A we discussed the two components ofthe NLO QCD asymmetry: (1) radiative corrections toquark-antiquark production and (2) interference betweendifferent amplitudes contributing to the ttj final state.The two contributions have opposite signs. At NLO,the first is positive and dominant for the inclusive mea-surement, while the second is negative and subdominant.


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TABLE XV: mc@nlo predictions for Att in reconstructed tt signal (nobackgrounds) as a function ofMtt and jet multiplicity. The uncertaintiesreflect MC statistics only.


inclusive 0.024 0.004 0.015 0.005 0.043 0.0074-jet 0.048 0.005 0.033 0.006 0.078 0.0095-jet 0.035 0.007 0.032 0.009 0.040 0.012

TABLE XVI: Asymmetries Att in the data as a function of jet multiplicity.

selection N events all Mtt Mtt < 450 GeV/c2 Mtt 450 GeV/c2

inclusive 1260 0.0570.028 -0.0160.034 0.2120.0494-jet 939 0.0650.033 -0.0230.039 0.260.0575-jet 321 0.0340.056 0.00490.07 0.0860.093

TABLE XVII: Reconstruction level asymmetries App in the laboratory frame.


data reco 0.073

0.028 0.059

0.034 0.103

0.049mc@nlo 0.0010.003 -0.0080.005 0.0220.007

A+h -0.0700.040 -0.0280.050 -0.1480.066Ah 0.0760.039 0.0850.047 0.0530.072

single b-tags 0.0950.032 0.0790.034 0.1300.057double b-tags -0.0040.060 -0.0230.076 0.0280.097

Since only the second term produces ttj events, we ex-pect that the QCD asymmetry will be a function of the

jet multiplicity.

We have studied the jet multiplicity dependence of Att

in mc@nlo. We define 4-jet events as those with four

jets with ET 20 GeV and | | 2.0 and no other suchjets. We define 5-jet events as those with at least five jetswith ET > 20 GeV and | | 2.0. The mc@nlo predic-tion for the pure tt signal after reconstruction is shownin Table XV. The 5-jet asymmetries are negative, as ex-pected. The exclusive 4-jet sample shows asymmetriesthat are roughly double those in the inclusive sample.

As we discussed in Sec. IVA, the reliability of the NLOpicture has recently been called into question by NNLOcalculations of the ttj component [25], which reduce thenegative asymmetry there to close to zero. However,since no NNLO calculation exists for the exclusive 4-jet,inclusive, or mass dependent asymmetries, the mc@nlo

prediction in Table XV remains our comparison point.

The jet multiplicity dependence of the asymmetries inthe data is shown in Table XVI. Vetoing events with ex-tra jets does not produce a significant increase in theasymmetry. However, in the 5-jet sample, the high massasymmetry is consistent with zero. With a larger sampleand better precision it might be possible to use the jetmultiplicity to test whether the observed asymmetry isan amplified version of the QCD charge asymmetry or a

different effect altogether.

E. Frame Dependence

As in the inclusive analysis, it is interesting to compareAtt to App. In the NLO QCD effect, the frame depen-dence of the asymmetry (see Sec. IV A) persists at highmass. For Mtt 450 GeV/c2 our mc@nlo model pre-dicts the ratio of reconstructed asymmetries in the twoframes App/Att 0.74. The OctetA model predicts lessmass dependence, with a ratio of 0.90.

The lab frame data asymmetries above and belowMtt = 450 GeV/c

2 are shown in Table XVII. The varia-tion of the asymmetry across the 450 GeV/c2 mass edgeis not as distinct as in the tt frame, and the deviationfrom the mc@nlo prediction is not as significant. Withinthe large errors, the asymmetries in the two lepton charge

samples are consistent with CP invariance.Comparing Tables XVII and X, the ratio ofApp to Att

at high mass is 0.490.21, lower than both the mc@nloand Octet models. We have used pseudo-experimenttechniques to evaluate the statistical consistency of thisratio with the models, using a large number of simulatedexperiments that differ by Poisson fluctuations in the yand qyh distributions. A App/Att ratio of 0.49 or lessoccurs in 14% of pseudo-experiments with mc@nlo, butin < 1% of experiments with OctetA.


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Finally, we look at App as a function of the b-tag mul-tiplicity. We observed in Sec. VII that the inclusive App

is zero in the double b-tagged events. In Table XVII, wesee that this pattern persists at high mass, although thestatistical precision is poor. Appealing again to pseudo-experiments with Poisson fluctuations, we find that a ra-tio of double to single tag App as small as that in the dataoccurs in 6% of all pseudo-experiments with mc@nlo.

We conclude that the low value of App

in the double b-tagged sample is consistent with a statistical fluctuation.

IX. CONCLUSIONS

We have studied the forward-backward asymmetry oftop quark pairs produced in 1.96 TeV pp collisions atthe Fermilab Tevatron. In a sample of 1260 events inthe lepton+jet decay topology, we measure the parton-level inclusive asymmetry in both the laboratory and ttrest frame, and rapidity-dependent, and Mtt-dependentasymmetries in the tt rest frame. We compare to NLO

predictions for the small charge asymmetry of QCD.The laboratory frame measurement uses the rapidityof the hadronically decaying top system and combinesthe two lepton charge samples under the assumption ofCP conservation. This distribution shows a parton-levelforward backward asymmetry in the laboratory frame ofApp = 0.150 0.055 (stat+sys). This has less than 1%probability of representing a fluctuation from zero, andis two standard deviations above the predicted asymme-try from NLO QCD. We also study the frame-invariantdifference of the rapidities, y = yt yt, which is pro-portional to the top quark rapidity in the tt rest frame.Asymmetries in y are identical to those in the t pro-duction angle in the tt rest frame. We find a parton-levelasymmetry of Att = 0.158 0.075 (stat+sys), which issomewhat higher than, but not inconsistent with, theNLO QCD expectation of 0.058 0.009.

In the tt rest frame we measure fully corrected asym-metries at small and large y

Att(|y| < 1.0) = 0.026 0.118Att(|y| 1.0) = 0.611 0.256

to be compared with mcfm predictions of 0.039 0.006and 0.123 0.008 for these y regions respectively.

In the tt rest frame the asymmetry is a rising functionof the tt invariant mass Mtt, with parton level asymme-

tries

Att(Mtt < 450 GeV/c2) = 0.116 0.153

Att(Mtt 450 GeV/c2) = 0.475 0.114to be compared with mcfm predictions of 0.040 0.006and 0.088 0.013 for these Mtt regions respectively. Theasymmetry at high mass is 3.4 standard deviations abovethe NLO prediction for the charge asymmetry of QCD,however we are aware that the accuracy of these theo-retical predictions are under study. The separate results

at high mass and large y contain partially independentinformation on the asymmetry mechanism.

The asymmetries reverse sign under interchange of lep-ton charge in a manner consistent with CP conservation.The tt frame asymmetry for Mtt 450 GeV/c2 is foundto be robust against variations in tt reconstruction qual-ity and secondary vertex b-tagging. When the high-massdata is divided by the lepton flavor, the asymmetries

are larger in muonic events, but statistically compatibleacross species. Simple studies of the jet multiplicity andframe dependence of the asymmetry at high mass mayoffer the possibility of discriminating between the NLOQCD effect and other models for the asymmetry, but thestatistical power of these comparisons is currently insuf-ficient for any conclusion.

The measurements presented here suggest that themodest inclusive tt production asymmetry originatesfrom a significant effect at large rapidity difference yand total invariant mass Mtt. The predominantly qqcollisions of the Fermilab Tevatron are an ideal environ-ment for further examination of this effect, and additional

studies are in progress.We thank T. Tait, G. Sterman, W. Vogelsang, andA. Mitov for valuable conversations and assistance. Wethank the Fermilab staff and the technical staffs of theparticipating institutions for their vital contributions.This work was supported by the U.S. Department of En-ergy and National Science Foundation; the Italian Isti-tuto Nazionale di Fisica Nucleare; the Ministry of Educa-tion, Culture, Sports, Science and Technology of Japan;the Natural Sciences and Engineering Research Councilof Canada; the National Science Council of the Repub-lic of China; the Swiss National Science Foundation; theA.P. Sloan Foundation; the Bundesministerium fur Bil-dung und Forschung, Germany; the World Class Uni-

versity Program, the National Research Foundation ofKorea; the Science and Technology Facilities Council andthe Royal Society, UK; the Institut National de PhysiqueNucleaire et Physique des Particules/CNRS; the RussianFoundation for Basic Research; the Ministerio de Cien-cia e Innovacion, and Programa Consolider-Ingenio 2010,Spain; the Slovak R&D Agency; and the Academy of Fin-land.

X. APPENDIX: THE COLOR-OCTET MODELS

In the generic color-octet model of Ref. [8], the gluon-octet interference produces an asymmetric cos() termin the production cross section. The couplings of thetop and the light quarks to the massive gluon have op-posite sign, giving a positive asymmetry as seen in thedata. This was implemented in the madgraph frame-work, and the couplings and MG were tuned to reason-ably reproduce the asymmetries and Mtt distribution ofthe data [26]. The sample called OctetA, with couplingsgV = 0, gA(q) = 3/2, gA(t) = 3/2, and mass MG = 2.0TeV/c2, has parton level asymmetries ofApp = 0.110 and


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)2

(GeV/ctt

M300 400 500 600 700 800 900

)2

Events/(15GeV/c

10

210

310

octet A

+ bkgtt

t- Y

tY = Y

-3 -2 -1 0 1 2 3

Events

/0.6

0

2000

4000

6000

8000

10000

12000

14000

16000Octet A

A = 0.08+/-0.0058

+ Bkgtt

A = -0.013+/-0.0058

FIG. 16: The distributions of Mtt (left) and y (right) in the OctetA sample compared to pythia.

ttM

350 400 450 500 550 600 650 700 750 800

(M)

tt

A

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6Octet A

+ bkgtt

)2(GeV/ctt

Mtt

M350 400 450 500 550 600 650 700 750 800

(M)

tt

A

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6Octet B

+ bkgtt

)2(GeV/ctt

M

FIG. 17: The reconstructed M dependence of Att in the color-octet models. Left: OctetA. Right: OctetB.

TABLE XVIII: Att and significance (in units of standard deviation) in Octet samples for events with Mtt above the bin-edge.

OctetA OctetBbin-edge Att significance Att significance(GeV/c2)345 0.082 0.028 2.90 0.168 0.028 5.99400 0.128 0.036 3.55 0.235 0.035 6.74450 0.183 0.047 3.91 0.310 0.044 7.08500 0.215 0.060 3.60 0.369 0.054 6.81550 0.246 0.076 3.25 0.425 0.066 6.43600 0.290 0.097 2.97 0.460 0.081 5.70

Att = 0.157. The LO cross section for this sample is 6.1pb, in good agreement with the LO madgraph cross

section for standard model tt production at 6.0 pb.The sample is showered with pythia, run through the

CDF-II detector simulation, and then subjected to ourselection and reconstruction. The Mtt and y distribu-tions in OctetA are compared to the pythia versionsin Fig. 16. The Mtt distribution is a good match topythia, and we have checked that related transversevariables are also well-modeled. The rapidity distribu-tions after selection and reconstruction have asymmetriesApp = 0.073 0.006, Att = 0.079 0.006, which are rea-

sonable matches to the data.

The complementary OctetB sample has the same cou-

plings but MG = 1.8 TeV/c2, giving parton-level asym-metries App = 0.205 and Att = 0.282. The tt cross sec-tion increases by 5% and the reconstructed mass distri-bution has a slight excess at the high mass relative topythia. The data level asymmetry Att = 0.16 0.006,significantly higher than the data.

These models both show the same approximate factorof 2 dilution between data-level and parton-level asym-metries that is seen in the data and in mc@nlo.

Since these models have relatively low-lying octet


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22

t- Y

tY = Y

-3 -2 -1 0 1 2 3

Events

/0.6

0

2000

4000

6000

8000

10000

12000Octet A

A = 0.024+/-0.0072

+ Bkgtt

A = -0.012+/-0.0071

t- Y

tY = Y

-3 -2 -1 0 1 2 3

Events

/0.6

0

500

1000

1500

2000

2500

3000

3500

4000

4500Octet A

A = 0.18+/-0.0097

+ Bkgtt

A = -0.016+/-0.01

FIG. 18: Top: The distribution of y at low mass (left) and high mass (right). The pythia baseline model is the filledhistogram and the Octet samples are the points.

TABLE XIX: Reconstructed asymmetry Att below and above Mtt = 450 GeV/c2 in Octet models.

sample all Mtt Mtt < 450 GeV/c2 Mtt

450 GeV/c2

OctetA 0.080 0.006 0.024 0.007 0.180 0.010OctetB 0.160 0.006 0.078 0.007 0.310 0.009

masses near 2 TeV/c2 we expect a significant Mtt-dependent asymmetry over our experimental range. TheAtt(Mtt,i) behavior for the two color-octet samples isshown in Fig. 17. Both show a smooth and significantrise of the asymmetry with increasing mass.

In Sec. VIIA we discussed a simple representation ofAtt(Mtt) with two regions of low and high Mtt. The ques-tion for that representation is how to choose the bound-

ary mass between high and low. Table XVIII showsthe asymmetry, uncertainty, and significance Att/Att athigh mass as a function of the mass thre

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