Combined Forward-Backward Asymmetry Measurements in Top-Antitop Quark Production at the Tevatron

Combined Forward-Backward Asymmetry Measurements in Top-Antitop Quark

Production at the Tevatron

T. Aaltonen†_,21 _{V.M. Abazov}‡_,13 _{B. Abbott}‡_,115 _{B.S. Acharya}‡_,79_{M. Adams} ‡_,97 _{T. Adams}‡_,96 _{J.P. Agnew}‡_,93

G.D. Alexeev‡_,13 _{G. Alkhazov}‡_,87_{A. Alton}‡kk_,31_{S. Amerio} †bbb_,39_{D. Amidei} †_,31 _{A. Anastassov}†w_,15 _{A. Annovi} †_,17_{J. Antos}†_,12 _{G. Apollinari}†_,15_{J.A. Appel} †_,15 _{T. Arisawa}†_,51 _{A. Artikov}†_,13 _{J. Asaadi}†_,47_{W. Ashmanskas} †_,15 _{A. Askew}‡_,96_{S. Atkins} ‡_,105 _{B. Auerbach}†_,2 _{K. Augsten} ‡_,61 _{A. Aurisano}†_,47 _{V. Aushev}‡_,90 _{Y. Aushev}‡_,90

C. Avila‡_,59 _{F. Azfar}†_,38 _{F. Badaud}‡_,64_{W. Badgett}†_,15 _{T. Bae}†_,25 _{L. Bagby}‡_,15 _{B. Baldin}‡_,15 _{D.V. Bandurin} ‡_,122_{S. Banerjee}‡_,79_{A. Barbaro-Galtieri} †_,26 _{E. Barberis}‡_,106_{P. Baringer} ‡_,104 _{V.E. Barnes}†_,43_{B.A. Barnett}†_,23

P. Barria†ddd_,41 _{J.F. Bartlett}‡_,15 _{P. Bartos}†_,12_{U. Bassler} ‡_,69 _{M. Bauce}†bbb_,39 _{V. Bazterra}‡_,97_{A. Bean}‡_,104

F. Bedeschi†_,41 _{M. Begalli}‡_,56 _{S. Behari}†_,15_{L. Bellantoni} ‡_,15 _{G. Bellettini}†ccc_,41 _{J. Bellinger}†_,53 _{D. Benjamin} †_,14 _{A. Beretvas}†_,15 _{S.B. Beri}‡_,77_{G. Bernardi}‡_,68_{R. Bernhard}‡_,73_{I. Bertram}‡_,91_{M. Besan¸con}‡_,69_{R. Beuselinck}

‡_,92_{P.C. Bhat} ‡_,15 _{S. Bhatia}‡_,107_{V. Bhatnagar} ‡_,77 _{A. Bhatti}†_,45 _{K.R. Bland}†_,5 _{G. Blazey}‡_,98 _{S. Blessing}‡_,96

K. Bloom ‡,108_{B. Blumenfeld}†_,23 _{A. Bocci}†_,14_{A. Bodek}†_,44 _{A. Boehnlein}‡_,15_{D. Boline} ‡_,112 _{E.E. Boos}‡_,85

G. Borissov‡_,91 _{D. Bortoletto}†_,43 _{M. Borysova}‡vv_,90 _{J. Boudreau}†_,42 _{A. Boveia}†_,11 _{A. Brandt}‡_,119 _{O. Brandt} ‡_,74 _{L. Brigliadori}†aaa_,6_{M. Brochmann}‡_,123 _{R. Brock}‡_,32_{C. Bromberg}†_,32_{A. Bross}‡_,15_{D. Brown}‡_,68 _{E. Brucken}

†_,21 _{X.B. Bu}‡_,15 _{J. Budagov}†_,13 _{H.S. Budd}†_,44 _{M. Buehler}‡_,15_{V. Buescher}‡_,75_{V. Bunichev}‡_,85_{S. Burdin}‡ll_,91

K. Burkett †_,15 _{G. Busetto}†bbb_,39 _{P. Bussey}†_,19_{C.P. Buszello}‡_,89_{P. Butti}†ccc_,41 _{A. Buzatu}†_,19 _{A. Calamba}†_,10

E. Camacho-P´erez‡_,82_{S. Camarda}†_,4_{M. Campanelli}†_,28_{F. Canelli} †ee_,11 _{B. Carls}†_,22_{D. Carlsmith} †_,53_{R. Carosi} †_,41 _{S. Carrillo}†l_,16 _{B. Casal}†j_,9 _{M. Casarsa} †_,48 _{B.C.K. Casey} ‡_,15 _{H. Castilla-Valdez}‡_,82 _{A. Castro}†aaa_,6

P. Catastini†,20_{S. Caughron} ‡_,32 _{D. Cauz}†iiijjj_,48 _{V. Cavaliere}†_,22 _{A. Cerri}†e_,26_{L. Cerrito}†r_,28 _{S. Chakrabarti} ‡_,112_{K.M. Chan}‡_,102 _{A. Chandra}‡_,121 _{A. Chapelain}‡_,69_{E. Chapon} ‡_,69 _{G. Chen}‡_,104 _{Y.C. Chen}†_,1_{M. Chertok} †_,7_{G. Chiarelli}†_,41 _{G. Chlachidze}†_,15 _{K. Cho} †_,25 _{S.W. Cho}‡_,81_{S. Choi} ‡_,81 _{D. Chokheli}†_,13_{B. Choudhary} ‡_,78

S. Cihangir‡_,15,∗ _{D. Claes} ‡_,108 _{A. Clark}†_,18 _{C. Clarke}†_,52 _{J. Clutter}‡_,104 _{M.E. Convery} †_,15 _{J. Conway} †_,7 _{M. Cooke}‡uu_,15 _{W.E. Cooper} ‡_,15 _{M. Corbo}†z_,15 _{M. Corcoran}‡_,121,∗ _{M. Cordelli}†_,17 _{F. Couderc} ‡_,69

M.-C. Cousinou‡_,66 _{C.A. Cox}†_,7 _{D.J. Cox}†_,7 _{M. Cremonesi}†_,41 _{D. Cruz}†_,47_{J. Cuevas} †y_,9 _{R. Culbertson}†_,15

J. Cuth‡_,75 _{D. Cutts}‡_,118_{A. Das} ‡_,120 _{N. d’Ascenzo}†v_,15 _{M. Datta}†hh_,15 _{G. Davies}‡_,92 _{P. de Barbaro}†_,44

S.J. de Jong‡_,83, 84 _{E. De La Cruz-Burelo} ‡_,82 _{F. D´eliot}‡_,69_{R. Demina}‡_,44 _{L. Demortier}†_,45 _{M. Deninno}†_,6

D. Denisov‡_,15 _{S.P. Denisov}‡_,86 _{M. D’Errico}†bbb_,39 _{S. Desai}‡_,15 _{C. Deterre}‡mm_,93 _{K. DeVaughan}‡_,108 _{F. Devoto} †_,21 _{A. Di Canto}†ccc_,41 _{B. Di Ruzza}†p_,15 _{H.T. Diehl}‡_,15 _{M. Diesburg} ‡_,15 _{P.F. Ding}‡_,93 _{J.R. Dittmann}†_,5

A. Dominguez ‡_,108 _{S. Donati}†ccc_,41 _{M. D’Onofrio}†_,27 _{M. Dorigo}†kkk_,48_{A. Driutti} †iiijjj_,48 _{A. Drutskoy}‡_,33

A. Dubey ‡_,78 _{L.V. Dudko}‡_,85 _{A. Duperrin}‡_,66_{S. Dutt}‡_,77_{M. Eads}‡_,98 _{K. Ebina}†_,51_{R. Edgar} †_,31 _{D. Edmunds} ‡_,32 _{A. Elagin} †_,11 _{J. Ellison} ‡_,95 _{V.D. Elvira}‡_,15 _{Y. Enari}‡_,68 _{R. Erbacher} †_,7 _{S. Errede} †_,22 _{B. Esham}†_,22

H. Evans‡_,100 _{A. Evdokimov}‡_,97 _{V.N. Evdokimov}‡_,86 _{S. Farrington}†_,38 _{A. Faur´e}‡_,69_{L. Feng} ‡_,98 _{T. Ferbel}‡_,44

J.P. Fern´andez Ramos†_,29 _{F. Fiedler}‡_,75_{R. Field}†_,16_{F. Filthaut}‡_,83, 84 _{W. Fisher}‡_,32 _{H.E. Fisk}‡_,15 _{G. Flanagan} †t_,15 _{R. Forrest}†_,7 _{M. Fortner}‡_,98 _{H. Fox}‡_,91 _{J. Franc}‡_,61 _{M. Franklin}†_,20 _{J.C. Freeman}†_,15 _{H. Frisch}†_,11

S. Fuess‡_,15_{Y. Funakoshi} †_,51 _{C. Galloni}†ccc_,41_{P.H. Garbincius} ‡_,15 _{A. Garcia-Bellido}‡_,44 _{J.A. Garc´ıa-Gonz´alez} ‡_,82 _{A.F. Garfinkel} †_,43 _{P. Garosi}†ddd_,41 _{V. Gavrilov} ‡_,33 _{W. Geng}‡_,66, 32 _{C.E. Gerber}‡_,97 _{H. Gerberich}†_,22

E. Gerchtein†_,15 _{Y. Gershtein}‡_,109 _{S. Giagu}†_,46 _{V. Giakoumopoulou}†_,3 _{K. Gibson}†_,42_{C.M. Ginsburg} †_,15

G. Ginther‡_,15 _{N. Giokaris}†_,3,∗ _{P. Giromini}†_,17 _{V. Glagolev} †_,13 _{D. Glenzinski}†_,15_{O. Gogota} ‡_,90 _{M. Gold}†_,34

D. Goldin†_,47 _{A. Golossanov}†_,15 _{G. Golovanov} ‡_,13 _{G. Gomez}†_,9 _{G. Gomez-Ceballos}†_,30 _{M. Goncharov}†_,30

O. Gonz´alez L´opez†_,29 _{I. Gorelov} †_,34 _{A.T. Goshaw}†_,14 _{K. Goulianos}†_,45 _{E. Gramellini}†_,6 _{P.D. Grannis} ‡_,112

S. Greder‡_,70_{H. Greenlee}‡_,15 _{G. Grenier}‡_,71_{Ph. Gris}‡_,64_{J.-F. Grivaz}‡_,67_{A. Grohsjean} ‡mm_,69 _{C. Grosso-Pilcher} †_,11 _{S. Gr¨unendahl}‡_,15_{M.W. Gr¨unewald}‡_,80 _{T. Guillemin}‡_,67 _{J. Guimaraes da Costa}†_,20 _{G. Gutierrez}‡_,15

P. Gutierrez‡_,115 _{S.R. Hahn}†_,15 _{J. Haley}‡_,116_{J.Y. Han}†_,44 _{L. Han}‡_,58 _{F. Happacher}†_,17 _{K. Hara}†_,49 _{K. Harder}

‡_,93 _{M. Hare}†_,50 _{A. Harel}‡_,44 _{R.F. Harr} †_,52 _{T. Harrington-Taber}†m_,15_{K. Hatakeyama}†_,5 _{J.M. Hauptman}‡_,103

C. Hays†_,38_{J. Hays}‡_,92_{T. Head}‡_,93 _{T. Hebbeker} ‡_,72 _{D. Hedin}‡_,98 _{H. Hegab} ‡_,116 _{J. Heinrich}†_,40_{A.P. Heinson} ‡_,95 _{U. Heintz}‡_,118 _{C. Hensel}‡_,55 _{I. Heredia-De La Cruz} ‡nn_,82_{M. Herndon}†_,53_{K. Herner} ‡_,15 _{G. Hesketh}‡pp_,93

M.D. Hildreth‡_,102 _{R. Hirosky}‡_,122 _{T. Hoang}‡_,96 _{J.D. Hobbs}‡_,112 _{A. Hocker}†_,15_{B. Hoeneisen} ‡_,63 _{J. Hogan}‡_,121

M. Hohlfeld‡,75 _{J.L. Holzbauer} ‡_,107 _{Z. Hong}†w_,47 _{W. Hopkins}†f_,15 _{S. Hou}†_,1_{I. Howley} ‡_,119 _{Z. Hubacek}‡_,61, 69

R.E. Hughes†_,35_{U. Husemann}†_,54_{M. Hussein} †cc_,32 _{J. Huston}†_,32 _{V. Hynek}‡_,61_{I. Iashvili}‡_,111 _{Y. Ilchenko}‡_,120

R. Illingworth‡_,15 _{G. Introzzi}†f f f ggg_,41 _{M. Iori}†hhh_,46_{A.S. Ito}‡_,15 _{A. Ivanov}†o_,7 _{S. Jabeen}‡ww_,15 _{M. Jaffr´e}‡_,67

E. James†_,15_{D. Jang} †_,10_{A. Jayasinghe}‡_,115 _{B. Jayatilaka}†_,15_{E.J. Jeon}†_,25_{M.S. Jeong}‡_,81 _{R. Jesik}‡_,92_{P. Jiang} ‡_,58,∗ _{S. Jindariani}†_,15 _{K. Johns} ‡_,94 _{E. Johnson}‡_,32 _{M. Johnson}‡_,15 _{A. Jonckheere}‡_,15_{M. Jones}†_,43_{P. Jonsson}

‡_,92 _{K.K. Joo}†_,25 _{J. Joshi}‡_,95 _{S.Y. Jun}†_,10 _{A.W. Jung}‡yy_,15 _{T.R. Junk}†_,15 _{A. Juste}‡_,88 _{E. Kajfasz}‡_,66

M. Kambeitz†_,24_{T. Kamon}†_,25, 47 _{P.E. Karchin}†_,52 _{D. Karmanov}‡_,85 _{A. Kasmi}†_,5_{Y. Kato}†n_,37_{I. Katsanos}‡_,108

M. Kaur‡,77 _{R. Kehoe}‡_,120_{S. Kermiche} ‡_,66 _{W. Ketchum}†ii_,11 _{J. Keung}†_,40 _{N. Khalatyan}‡_,15_{A. Khanov} ‡_,116

A. Kharchilava‡_,111_{Y.N. Kharzheev}‡_,13 _{B. Kilminster}†ee_,15 _{D.H. Kim}†_,25_{H.S. Kim}†bb_,15 _{J.E. Kim}†_,25_{M.J. Kim} †_,17_{S.H. Kim} †_,49 _{S.B. Kim}†_,25_{Y.J. Kim}†_,25 _{Y.K. Kim}†_,11 _{N. Kimura}†_,51 _{M. Kirby} †_,15 _{I. Kiselevich} ‡_,33

J.M. Kohli‡_,77_{K. Kondo}†_,51,∗ _{D.J. Kong}†_,25_{J. Konigsberg} †_,16 _{A.V. Kotwal}†_,14 _{A.V. Kozelov}‡_,86_{J. Kraus}‡_,107

M. Kreps†_,24 _{J. Kroll}†_,40 _{M. Kruse}†_,14_{T. Kuhr} †_,24 _{A. Kumar}‡_,111 _{A. Kupco}‡_,62 _{M. Kurata} †_,49 _{T. Kurˇca}‡_,71

V.A. Kuzmin‡_,85_{A.T. Laasanen}†_,43_{S. Lammel}†_,15_{S. Lammers}‡_,100 _{M. Lancaster}†_,28_{K. Lannon}†x_,35 _{G. Latino} †ddd_,41 _{P. Lebrun}‡_,71 _{H.S. Lee}‡_,81_{H.S. Lee} †_,25 _{J.S. Lee}†_,25 _{S.W. Lee}‡_,103 _{W.M. Lee}‡_,15 _{X. Lei}‡_,94 _{J. Lellouch} ‡_,68 _{S. Leo}†_,22 _{S. Leone}†_,41 _{J.D. Lewis}†_,15 _{D. Li}‡_,68_{H. Li}‡_,122_{L. Li}‡_,95_{Q.Z. Li}‡_,15 _{J.K. Lim}‡_,81 _{A. Limosani} †s_,14_{D. Lincoln}‡_,15_{J. Linnemann}‡_,32 _{V.V. Lipaev}‡_,86,∗ _{E. Lipeles}†_,40 _{R. Lipton}‡_,15 _{A. Lister}†a_,18 _{H. Liu}‡_,120

Q. Liu †_,43 _{T. Liu} †_,15 _{Y. Liu}‡_,58 _{A. Lobodenko} ‡_,87 _{S. Lockwitz}†_,54 _{A. Loginov} †_,54 _{M. Lokajicek} ‡_,62

R. Lopes de Sa‡_,15_{D. Lucchesi} †bbb_,39 _{A. Luc`a} †_,17, 15 _{J. Lueck}†_,24 _{P. Lujan}†_,26 _{P. Lukens}†_,15_{R. Luna-Garcia} ‡qq_,82_{G. Lungu}†_,45 _{A.L. Lyon}‡_,15 _{J. Lys}†_,26,∗ _{R. Lysak} †d_,12 _{A.K.A. Maciel}‡_,55 _{R. Madar}‡_,73 _{R. Madrak}

†_,15 _{P. Maestro}†ddd_,41 _{R. Maga˜na-Villalba}‡_,82 _{S. Malik} †_,45 _{S. Malik} ‡_,108 _{V.L. Malyshev} ‡_,13 _{G. Manca} †b_,27 _{A. Manousakis-Katsikakis}†_,3 _{J. Mansour} ‡_,74 _{L. Marchese}†jj_,6 _{F. Margaroli}†_,46 _{P. Marino} †eee_,41

J. Mart´ınez-Ortega ‡,82 _{K. Matera}†_,22 _{M.E. Mattson}†_,52 _{A. Mazzacane} †_,15 _{P. Mazzanti}†_,6 _{R. McCarthy} ‡_,112

C.L. McGivern ‡_,93 _{R. McNulty}†i_,27 _{A. Mehta}†_,27 _{P. Mehtala}†_,21 _{M.M. Meijer}‡_,83, 84 _{A. Melnitchouk}‡_,15

D. Menezes‡_,98_{P.G. Mercadante} ‡_,57 _{M. Merkin}‡_,85_{C. Mesropian}†_,45 _{A. Meyer}‡_,72 _{J. Meyer}‡ss_,74_{T. Miao}†_,15

F. Miconi‡_,70 _{D. Mietlicki}†_,31_{A. Mitra} †_,1 _{H. Miyake}†_,49_{S. Moed}†_,15_{N. Moggi}†_,6 _{N.K. Mondal}‡_,79 _{C.S. Moon} †z_,15 _{R. Moore}†f f gg_,15 _{M.J. Morello}†eee_,41 _{A. Mukherjee}†_,15_{M. Mulhearn}‡_,122_{Th. Muller} †_,24 _{P. Murat}†_,15

M. Mussini†aaa_,6 _{J. Nachtman}†m_,15 _{Y. Nagai} †_,49 _{J. Naganoma}†_,51_{E. Nagy} ‡_,66 _{I. Nakano}†_,36 _{A. Napier}†_,50

M. Narain ‡_,118 _{R. Nayyar}‡_,94 _{H.A. Neal}‡_,31_{J.P. Negret}‡_,59_{J. Nett} †_,47 _{P. Neustroev} ‡_,87 _{H.T. Nguyen}‡_,122

T. Nigmanov†,42_{L. Nodulman}†_,2 _{S.Y. Noh}†_,25_{O. Norniella} †_,22 _{T. Nunnemann}‡_,76_{L. Oakes}†_,38 _{S.H. Oh}†_,14

Y.D. Oh†_,25_{T. Okusawa}†_,37 _{R. Orava}†_,21 _{J. Orduna}‡_,118 _{L. Ortolan}†_,4 _{N. Osman}‡_,66_{C. Pagliarone}†_,48 _{A. Pal} ‡_,119 _{E. Palencia}†e_,9 _{P. Palni}†_,34 _{V. Papadimitriou}†_,15 _{N. Parashar}‡_,101 _{V. Parihar}‡_,118 _{S.K. Park}‡_,81 _{W. Parker} †_,53 _{R. Partridge}‡oo_,118_{N. Parua}‡_,100_{A. Patwa}‡tt_,113 _{G. Pauletta}†iiijjj_,48_{M. Paulini}†_,10_{C. Paus}†_,30 _{B. Penning} ‡_,92 _{M. Perfilov}‡_,85_{Y. Peters}‡_,93 _{K. Petridis}‡_,93_{G. Petrillo}‡_,44_{P. P´etroff}‡_,67_{T.J. Phillips}†_,14_{G. Piacentino} †q_,15

E. Pianori†_,40 _{J. Pilot}†_,7 _{K. Pitts}†_,22 _{C. Plager}†_,8 _{M.-A. Pleier} ‡_,113 _{V.M. Podstavkov}‡_,15_{L. Pondrom} †_,53

A.V. Popov‡_,86 _{S. Poprocki}†f_,15 _{K. Potamianos}†_,26 _{A. Pranko}†_,26_{M. Prewitt}‡_,121_{D. Price}‡_,93 _{N. Prokopenko} ‡_,86_{F. Prokoshin}†aa_,13 _{F. Ptohos}†g_,17_{G. Punzi} †ccc_,41 _{J. Qian}‡_,31_{A. Quadt}‡_,74_{B. Quinn} ‡_,107 _{P.N. Ratoff}‡_,91

I. Razumov‡_,86_{I. Redondo Fern´andez}†_,29 _{P. Renton}†_,38 _{M. Rescigno}†_,46 _{F. Rimondi}†_,6,∗ _{I. Ripp-Baudot}‡_,70

L. Ristori†_,41, 15 _{F. Rizatdinova} ‡_,116 _{A. Robson}†_,19_{T. Rodriguez} †_,40 _{S. Rolli}†h_,50 _{M. Rominsky}‡_,15 _{M. Ronzani} †ccc_,41 _{R. Roser}†_,15 _{J.L. Rosner}†_,11 _{A. Ross}‡_,91 _{C. Royon}‡_,62_{P. Rubinov} ‡_,15 _{R. Ruchti}‡_,102 _{F. Ruffini}†ddd_,41

A. Ruiz†_,9_{J. Russ}†_,10 _{V. Rusu}†_,15 _{G. Sajot}‡_,65 _{W.K. Sakumoto} †_,44 _{Y. Sakurai}†_,51 _{A. S´anchez-Hern´andez}‡_,82

M.P. Sanders‡_,76 _{L. Santi}†iiijjj_,48 _{A.S. Santos}‡rr_,55 _{K. Sato}†_,49 _{G. Savage}‡_,15 _{V. Saveliev}†v_,15_{M. Savitskyi}‡_,90

A. Savoy-Navarro †z_,15 _{L. Sawyer}‡_,105 _{T. Scanlon}‡_,92_{R.D. Schamberger} ‡_,112 _{Y. Scheglov}‡_,87 _{H. Schellman} ‡_,117, 99 _{P. Schlabach}†_,15 _{E.E. Schmidt}†_,15_{M. Schott}‡_,75_{C. Schwanenberger} ‡_,93 _{T. Schwarz}†_,31_{R. Schwienhorst}

‡_,32 _{L. Scodellaro}†_,9 _{F. Scuri} †_,41 _{S. Seidel}†_,34 _{Y. Seiya}†_,37 _{J. Sekaric} ‡_,104 _{A. Semenov}†_,13 _{H. Severini}‡_,115

F. Sforza†ccc_,41_{E. Shabalina} ‡_,74 _{S.Z. Shalhout}†_,7 _{V. Shary} ‡_,69 _{S. Shaw}‡_,93 _{A.A. Shchukin}‡_,86_{T. Shears}†_,27

P.F. Shepard †_,42_{M. Shimojima} †u_,49 _{O. Shkola} ‡_,90 _{M. Shochet}†_,11 _{I. Shreyber-Tecker} †_,33_{V. Simak} ‡_,61

J. Snow‡_,114 _{S. Snyder}‡_,113_{S. S¨oldner-Rembold}‡_,93 _{H. Song}†_,42 _{L. Sonnenschein}‡_,72_{V. Sorin} †_,4 _{K. Soustruznik} ‡_,60_{R. St. Denis} †_,19,∗ _{M. Stancari}†_,15 _{J. Stark} ‡_,65 _{N. Stefaniuk} ‡_,90 _{D. Stentz}†w_,15 _{D.A. Stoyanova} ‡_,86

M. Strauss‡_,115 _{J. Strologas}†_,34 _{Y. Sudo}†_,49 _{A. Sukhanov} †_,15 _{I. Suslov} †_,13 _{L. Suter}‡_,93 _{P. Svoisky}‡_,122

K. Takemasa †_,49 _{Y. Takeuchi}†_,49 _{J. Tang}†_,11 _{M. Tecchio}†_,31 _{P.K. Teng} †_,1 _{J. Thom}†f_,15 _{E. Thomson} †_,40

V. Thukral†,47 _{M. Titov}‡_,69 _{D. Toback}†_,47 _{S. Tokar}†_,12 _{V.V. Tokmenin}‡_,13 _{K. Tollefson}†_,32_{T. Tomura}†_,49

D. Tonelli†e_,15 _{S. Torre}†_,17 _{D. Torretta}†_,15 _{P. Totaro}†_,39 _{M. Trovato}†eee_,41 _{Y.-T. Tsai}‡_,44 _{D. Tsybychev}‡_,112

B. Tuchming‡_,69 _{C. Tully}‡_,110_{F. Ukegawa}†_,49 _{S. Uozumi}†_,25 _{L. Uvarov}‡_,87 _{S. Uvarov}‡_,87 _{S. Uzunyan}‡_,98

R. Van Kooten‡_,100 _{W.M. van Leeuwen}‡_,83_{N. Varelas}‡_,97 _{E.W. Varnes}‡_,94 _{I.A. Vasilyev}‡_,86 _{F. V´azquez}†l_,16

G. Velev †_,15 _{C. Vellidis}†_,15 _{A.Y. Verkheev}‡_,13 _{C. Vernieri}†eee_,41 _{L.S. Vertogradov}‡_,13 _{M. Verzocchi}‡_,15

M. Vesterinen‡_,93 _{M. Vidal}†_,43 _{D. Vilanova}‡_,69 _{R. Vilar}†_,9_{J. Viz´an}†dd_,9 _{M. Vogel}†_,34_{P. Vokac}‡_,61_{G. Volpi}†_,17

P. Wagner†_,40 _{H.D. Wahl}‡_,96 _{R. Wallny}†j_,15 _{M.H.L.S. Wang}‡_,15_{S.M. Wang}†_,1 _{J. Warchol} ‡_,102 _{D. Waters}†_,28

G. Watts ‡,123 _{M. Wayne}‡_,102 _{J. Weichert}‡_,75 _{L. Welty-Rieger}‡_,99 _{W.C. Wester III}†_,15 _{D. Whiteson}†c_,40

A.B. Wicklund†_,2 _{S. Wilbur}†_,7 _{H.H. Williams}†_,40 _{M.R.J. Williams}‡xx_,100_{G.W. Wilson}‡_,104 _{J.S. Wilson}†_,31

P. Wilson†_,15 _{B.L. Winer}†_,35 _{P. Wittich}†f_,15 _{M. Wobisch}‡_,105 _{S. Wolbers} †_,15 _{H. Wolfmeister}†_,35_{D.R. Wood} ‡_,106 _{T. Wright}†_,31 _{X. Wu}†_,18 _{Z. Wu}†_,5_{T.R. Wyatt}‡_,93_{Y. Xie} ‡_,15 _{R. Yamada}‡_,15 _{K. Yamamoto}†_,37 _{D. Yamato}

†_,37 _{S. Yang}‡_,58 _{T. Yang}†_,15_{U.K. Yang} †_,25 _{Y.C. Yang}†_,25 _{W.-M. Yao}†_,26 _{T. Yasuda} ‡_,15 _{Y.A. Yatsunenko}‡_,13

W. Ye‡_,112_{Z. Ye}‡_,15 _{G.P. Yeh}†_,15 _{K. Yi}†m_,15 _{H. Yin}‡_,15 _{K. Yip}‡_,113 _{J. Yoh}†_,15 _{K. Yorita}†_,51_{T. Yoshida} †k_,37

S.W. Youn‡_,15 _{G.B. Yu}†_,14 _{I. Yu}†_,25 _{J.M. Yu}‡_,31 _{A.M. Zanetti}†_,48_{Y. Zeng}†_,14_{J. Zennamo}‡_,111 _{T.G. Zhao}‡_,93

B. Zhou‡,31 _{C. Zhou}†_,14 _{J. Zhu}‡_,31_{M. Zielinski} ‡_,44 _{D. Zieminska}‡_,100 _{L. Zivkovic}‡zz_,68 _{and S. Zucchelli} †aaa6

(CDF Collaboration)†

(D0 Collaboration)‡

1

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

2

Argonne National Laboratory, Argonne, Illinois 60439, USA

3

University of Athens, 157 71 Athens, Greece

4_{Institut de Fisica d’Altes Energies, ICREA, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain} 5_{Baylor University, Waco, Texas 76798, USA}

6_{Istituto Nazionale di Fisica Nucleare Bologna,} aaa_{University of Bologna, I-40127 Bologna, Italy} 7_{University of California, Davis, Davis, California 95616, USA}

8_{University of California, Los Angeles, Los Angeles, California 90024, USA} 9_{Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain}

10_{Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA} 11_{Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA}

12_{Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia} 13_{Joint Institute for Nuclear Research, RU-141980 Dubna, Russia}

14

Duke University, Durham, North Carolina 27708, USA

15

Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

16

University of Florida, Gainesville, Florida 32611, USA

17

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

18

University of Geneva, CH-1211 Geneva 4, Switzerland

19

Glasgow University, Glasgow G12 8QQ, United Kingdom

20

Harvard University, Cambridge, Massachusetts 02138, USA

21

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

22

University of Illinois, Urbana, Illinois 61801, USA

23

The Johns Hopkins University, Baltimore, Maryland 21218, USA

24

Institut f¨ur Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany

25

Center 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; Ewha Womans University, Seoul, 120-750, Korea

26

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

27

University of Liverpool, Liverpool L69 7ZE, United Kingdom

28

University College London, London WC1E 6BT, United Kingdom

29

Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

30

31

University of Michigan, Ann Arbor, Michigan 48109, USA

32_{Michigan State University, East Lansing, Michigan 48824, USA}

33_{Institute for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia} 34

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

35

The Ohio State University, Columbus, Ohio 43210, USA

36_{Okayama University, Okayama 700-8530, Japan} 37

Osaka City University, Osaka 558-8585, Japan

38

University of Oxford, Oxford OX1 3RH, United Kingdom

39_{Istituto Nazionale di Fisica Nucleare, Sezione di Padova,} bbb_{University of Padova, I-35131 Padova, Italy} 40

University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

41

Istituto Nazionale di Fisica Nucleare Pisa, cccUniversity of Pisa,

ddd_{University of Siena,} eee_{Scuola Normale Superiore,}

I-56127 Pisa, Italy, f f f_{INFN Pavia, I-27100 Pavia,}

Italy, gggUniversity of Pavia, I-27100 Pavia, Italy

42

University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

43_{Purdue University, West Lafayette, Indiana 47907, USA} 44

University of Rochester, Rochester, New York 14627, USA

45

The Rockefeller University, New York, New York 10065, USA

46_{Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1,} hhh

Sapienza Universit`a di Roma, I-00185 Roma, Italy

47

Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA

48_{Istituto Nazionale di Fisica Nucleare Trieste,} iii_{Gruppo Collegato di Udine,} jjj

University of Udine, I-33100 Udine, Italy, kkkUniversity of Trieste, I-34127 Trieste, Italy

49

University of Tsukuba, Tsukuba, Ibaraki 305, Japan

50_{Tufts University, Medford, Massachusetts 02155, USA} 51

Waseda University, Tokyo 169, Japan

52

Wayne State University, Detroit, Michigan 48201, USA

53_{University of Wisconsin-Madison, Madison, Wisconsin 53706, USA} 54

Yale University, New Haven, Connecticut 06520, USA

55

LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, RJ 22290, Brazil

56_{Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ 20550, Brazil} 57_{Universidade Federal do ABC, Santo Andr´e, SP 09210, Brazil} 58

University of Science and Technology of China, Hefei 230026, People’s Republic of China

59

Universidad de los Andes, Bogot´a, 111711, Colombia

60_{Charles University, Faculty of Mathematics and Physics,}

Center for Particle Physics, 116 36 Prague 1, Czech Republic

61

Czech Technical University in Prague, 116 36 Prague 6, Czech Republic

62_{Institute of Physics, Academy of Sciences of the Czech Republic, 182 21 Prague, Czech Republic} 63_{Universidad San Francisco de Quito, Quito 170157, Ecuador}

64

LPC, Universit´e Blaise Pascal, CNRS/IN2P3, Clermont, F-63178 Aubi`ere Cedex, France

65

LPSC, Universit´e Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National Polytechnique de Grenoble, F-38026 Grenoble Cedex, France

66

CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, F-13288 Marseille Cedex 09, France

67

LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, F-91898 Orsay Cedex, France

68_{LPNHE, Universit´es Paris VI and VII, CNRS/IN2P3, F-75005 Paris, France} 69

CEA Saclay, Irfu, SPP, F-91191 Gif-Sur-Yvette Cedex, France

70

IPHC, Universit´e de Strasbourg, CNRS/IN2P3, F-67037 Strasbourg, France

71_{IPNL, Universit´e Lyon 1, CNRS/IN2P3, F-69622 Villeurbanne Cedex,}

France and Universit´e de Lyon, F-69361 Lyon CEDEX 07, France

72

III. Physikalisches Institut A, RWTH Aachen University, 52056 Aachen, Germany

73

Physikalisches Institut, Universit¨at Freiburg, 79085 Freiburg, Germany

74_{II. Physikalisches Institut, Georg-August-Universit¨at G¨ottingen, 37073 G¨ottingen, Germany} 75

Institut f¨ur Physik, Universit¨at Mainz, 55099 Mainz, Germany

76

Ludwig-Maximilians-Universit¨at M¨unchen, 80539 M¨unchen, Germany

77_{Panjab University, Chandigarh 160014, India} 78

Delhi University, Delhi-110 007, India

79

Tata Institute of Fundamental Research, Mumbai-400 005, India

80_{University College Dublin, Dublin 4, Ireland}

81_{Korea Detector Laboratory, Korea University, Seoul, 02841, Korea} 82

CINVESTAV, Mexico City 07360, Mexico

83

Nikhef, Science Park, 1098 XG Amsterdam, the Netherlands

84_{Radboud University Nijmegen, 6525 AJ Nijmegen, the Netherlands} 85

86

Institute for High Energy Physics, Protvino, Moscow region 142281, Russia

87_{Petersburg Nuclear Physics Institute, St. Petersburg 188300, Russia} 88_{Instituci´o Catalana de Recerca i Estudis Avan¸cats (ICREA) and Institut}

de F´ısica d’Altes Energies (IFAE), 08193 Bellaterra (Barcelona), Spain

89_{Uppsala University, 751 05 Uppsala, Sweden}

90_{Taras Shevchenko National University of Kyiv, Kiev, 01601, Ukraine} 91

Lancaster University, Lancaster LA1 4YB, United Kingdom

92

Imperial College London, London SW7 2AZ, United Kingdom

93_{The University of Manchester, Manchester M13 9PL, United Kingdom} 94

University of Arizona, Tucson, Arizona 85721, USA

95

University of California Riverside, Riverside, California 92521, USA

96_{Florida State University, Tallahassee, Florida 32306, USA} 97

University of Illinois at Chicago, Chicago, Illinois 60607, USA

98

Northern Illinois University, DeKalb, Illinois 60115, USA

99_{Northwestern University, Evanston, Illinois 60208, USA} 100

Indiana University, Bloomington, Indiana 47405, USA

101

Purdue University Calumet, Hammond, Indiana 46323, USA

102_{University of Notre Dame, Notre Dame, Indiana 46556, USA} 103_{Iowa State University, Ames, Iowa 50011, USA} 104

University of Kansas, Lawrence, Kansas 66045, USA

105

Louisiana Tech University, Ruston, Louisiana 71272, USA

106_{Northeastern University, Boston, Massachusetts 02115, USA} 107

University of Mississippi, University, Mississippi 38677, USA

108

University of Nebraska, Lincoln, Nebraska 68588, USA

109_{Rutgers University, Piscataway, New Jersey 08855, USA} 110

Princeton University, Princeton, New Jersey 08544, USA

111

State University of New York, Buffalo, New York 14260, USA

112_{State University of New York, Stony Brook, New York 11794, USA} 113

Brookhaven National Laboratory, Upton, New York 11973, USA

114

Langston University, Langston, Oklahoma 73050, USA

115_{University of Oklahoma, Norman, Oklahoma 73019, USA} 116_{Oklahoma State University, Stillwater, Oklahoma 74078, USA}

117

Oregon State University, Corvallis, Oregon 97331, USA

118

Brown University, Providence, Rhode Island 02912, USA

119_{University of Texas, Arlington, Texas 76019, USA} 120

Southern Methodist University, Dallas, Texas 75275, USA

121

Rice University, Houston, Texas 77005, USA

122_{University of Virginia, Charlottesville, Virginia 22904, USA} 123

University of Washington, Seattle, Washington 98195, USA (Dated: September 13, 2017)

The CDF and D0 experiments at the Fermilab Tevatron have measured the asymmetry between yields of forward- and backward-produced top and antitop quarks based on their rapidity difference and the asymmetry between their decay leptons. These measurements use the full data sets collected in proton-antiproton collisions at a center-of-mass energy of√s = 1.96 TeV. We report the results of combinations of the inclusive asymmetries and their differential dependencies on relevant kinematic quantities. The combined inclusive asymmetry is At¯t

FB= 0.128 ± 0.025. The combined inclusive and

differential asymmetries are consistent with recent standard model predictions.

PACS numbers: 14.65.Ha, 12.38.Qk, 11.30.Er, 13.85.-t

The production of top and antitop quark (t¯t) pairs at the Tevatron proton-antiproton (p¯p) collider at Fermi-lab is dominated by the q ¯q annihilation process, which can lead to asymmetries, At¯t

FB, in the number of top

quarks produced within the hemisphere centered on the beam proton (forward) relative to those that are pro-duced within the antiproton hemisphere (backward). In the standard model (SM), no forward-backward asymme-tries are expected at leading order in perturbative quan-tum chromodynamics (QCD). However, contributions to the asymmetry from interference of leading order and

higher-order amplitudes, and smaller offsetting contribu-tions from the interference of initial- and final-state ra-diation, combine to yield a non-zero asymmetry [1–5]. Compared to older predictions [6] of the inclusive asym-metry at next-to-leading order (NLO) QCD, the latest higher-order corrections in QCD and electroweak theory (EW) are almost of the same size as the inclusive predic-tion at NLO QCD. Measurements of the inclusive asym-metries and their dependence on kinematic quantities of top quarks and their decay leptons are used to probe the production mechanism. Beyond-the-SM (BSM)

interac-tions [7] can significantly alter the dynamics, even such that differential asymmetries can be strikingly changed while inclusive asymmetries are only marginally affected. Inclusive and differential measurements [8, 9] by the CDF [10] and D0 [11] Collaborations in 2011 were only marginally consistent with each other, and with then-existing SM predictions [6]. Both collabo-rations have since completed measurements using the full Tevatron Run II pp collision data, corresponding to integrated luminosities between 9 and 10 fb−1. Assuming SM t and ¯t decays, they have measured asymmetries using events containing a single charged lepton (`+jets), where one W boson from a top quark decays to a charged lepton and a neutrino and the other decays to a quark and an antiquark that evolve into jets, and in events containing two charged leptons (``) where both W bosons decay leptonically. Both collaborations have measured inclusive and differential asymmetries as functions of kinematic quantities of the top quarks and their decay leptons. More refined analysis techniques have been employed since the initial measurements. In the `+jets channel, CDF performed a detailed investigation of the inclusive and differential t¯t asymmetries [12], and D0 used a novel partial event reconstruction for the inclusive and differential measure-ment of At¯t

FB [13]. In the `` channel, CDF used several

kinematic distributions to minimize the expected total uncertainty [14], while D0 carried out a simultaneous measurement of At¯t

FBand the top quark polarization [15].

We present the combinations of the final CDF and D0 measurements and compare them with current SM cal-culations [16]. Careful assessment of the correlations of systematic uncertainties between analysis channels and experiments is required for comparing the data with pre-dictions.

For reconstructed top and antitop quarks, At¯t FB is de-fined by At¯t FB= N (∆yt¯t> 0)− N(∆yt¯t< 0) N (∆yt¯t> 0) + N (∆yt¯t< 0) , (1)

where ∆yt¯t = yt− y¯t is the rapidity difference [17]

be-tween the t and ¯t quark, and N is the signal yield in a particular configuration. Typically, measurements of t¯t forward-backward asymmetries require reconstruction of top and antitop quarks using all available informa-tion associated with the final-state particles [18]. Back-ground contributions are subtracted from the yield of t¯t candidates, thereby providing the t¯t signal. The latter is corrected for detector effects, so as to unfold from the reconstructed t and ¯t quarks to the parton level.

The asymmetry in t and ¯t quark production also leads to asymmetries in their decay leptons which, while smaller in magnitude, do not need unfolding, but must be corrected for acceptance effects. The single-lepton

asym-metry is defined by A` FB= N (q`η`> 0)− N(q`η`< 0) N (q`η`> 0) + N (q`η`< 0) , (2)

where q` is the sign of the electric charge and η` the

pseudorapidity of the lepton in the laboratory frame. For the `` channel, the dilepton asymmetry is defined as

A`` FB=

N (∆η > 0)_{− N(∆η < 0)}

N (∆η > 0) + N (∆η < 0) , (3) where ∆η = η`+ − η<sub>`</sub>− is the pseudorapidity difference between the positive- and negative-charge lepton. The asymmetries obtained using top quarks and leptons are correlated, as a positive rapidity difference between a t and a ¯t quark is likely to produce a positive pseudora-pidity difference between a positive- and negative-charge decay lepton.

Inclusive and differential measurements of At¯t FB at the

Tevatron were reported in Refs. [12, 13] for the `+jets channel and in Refs. [14, 15] for the `` channel. Mea-surements of A`

FB for the `+jets channel are given in

Refs. [19, 20] and in Refs. [21, 22] for the `` channel. Measurements of A``

FB are reported in Refs. [21,22].

We combine the following CDF and D0 results using the best linear unbiased estimator (BLUE) [23–25]: the inclusive asymmetries At¯t FB, A ` FB, and A `` FB, each

extrap-olated to the full phase space relying on corresponding Monte Carlo simulations, and the differential asymme-try of At¯t

FB as a function of the invariant mass of the

t¯t system (mt¯t). For combinations of inclusive

asymme-tries the input uncertainties are symmetrized, while they are treated as asymmetric in the case of the combina-tion of the asymmetry as a funccombina-tion of mt¯t. A mutually

compatible classification of all systematic uncertainties is not available for At¯t

FB as a function of|∆yt¯t|. Hence,

we provide results of a simultaneous least-squares fit to determine the slope parameter of the asymmetry in the CDF and D0 data, assuming a linear dependence. A sim-ilar fit is also provided for At¯t

FB as a function of mt¯t. The

CDF and D0 differential asymmetries, A`

FBas a function

of q`η` and A``FB as a function of ∆η are not combined,

but are displayed together for ease of comparison. Predictions of inclusive and differential At¯t

FB

distribu-tions at next-to-next-to-leading order (NNLO) QCD cal-culations are available from Ref. [1]. The contribution from EW NLO corrections to the NLO QCD asymmetries are not negligible [3]. Hence, we compare the measure-ments to the latest NNLO QCD + NLO EW inclusive and differential At¯t

FB calculations [1, 26]. The combined

inclusive-lepton asymmetries A`

FBand A ``

FBare compared

to the NLO QCD + NLO EW predictions of Ref. [3]. To accommodate correlations among analysis channels and between experiments, we classify systematic uncer-tainties into the following categories:

(i) Background modeling: The uncertainties in the dis-tribution and normalization of the background are

assumed to be uncorrelated since the backgrounds are estimated differently in different analyses, and in the two experiments.

(ii) Signal modeling: The uncertainties in modeling the signal, parton showering [27], initial- and final-state radiation [28], and color connections [29] are taken to be fully correlated among analysis channels and experiments because they all rely on the same as-sumptions.

(iii) Detector modeling: The uncertainties in jet-energy scale [30] and the modeling of the detector are fully correlated within each experiment and uncorrelated between the two experiments.

(iv) Method: The uncertainties in the methods used to correct for detector acceptance, efficiency, and po-tential biases in the reconstruction of top quark kinematic properties are mostly taken to be uncor-related between experiments and analysis channels. However, the uncertainties on the phase-space cor-rection procedures for the leptonic asymmetry in the D0 `+jets [13] and `` [15] analyses are estimated using the same methods and are therefore corre-lated with each other but are uncorrecorre-lated with the CDF results.

(v) PDF: The uncertainties in parton-density distribu-tion funcdistribu-tions (PDF) and the pileup in energy from overlapping p¯p interactions are treated as fully cor-related between the analysis channels and the two experiments, because they characterize the same potential systematic biases.

The combined inclusive asymmetry is At¯t

FB = 0.128±

0.021(stat)±0.014(syst), consistent with the NNLO QCD + NLO EW prediction of 0.095_{± 0.007 [}2] within 1.3 standard deviations (SD). The combination has a χ2 _of

1.7 for 3 degrees of freedom (dof). BLUE also provides the weights in the combination for the CDF `+jets, D0 `+jets, CDF ``, and D0 `` results, which are 0.25, 0.64, 0.01, and 0.11, respectively.

The CDF and D0 differential At¯t

FB asymmetries as a

function of mt¯tare measured only for the `+jets channel.

We combine the D0 bins in the range of 350 < mt¯t< 550

GeV/c2 _{to provide uniform, 100 GeV/c}2_{-wide, bins for}

the combination. For the two measurements we use co-variance matrices [31] that take into account the bin-to-bin correlations from the unfolding of differential dis-tributions. The correlations in systematic uncertainties among channels and experiments for each mt¯t bin are

assumed to be equal to those in the inclusive measure-ments. However, the uncorrelated background uncertain-ties for the differential asymmetries are subdivided into two separate components, one for the overall normaliza-tion and one for the differential distribunormaliza-tion (shape) of the background. According to the different experimental

methodologies, these are treated as correlated between bins for the CDF measurement and as uncorrelated for the D0 measurement. We verify that changing the cor-relations of systematic uncertainties between−1 and +1 has negligible impact on the combined result because the statistical uncertainties dominate.

350 450 550 650 mt¯tGeV/c2 − 0. 4 − 0. 2 0. 0 0. 2 0. 4 0. 6 A t¯t FB D0 ` + jets, 9.7 fb−1 CDF ` + jets, 9.4 fb−1 Tevatron combination, ≤ 9.7 fb−1 αm_t¯t= (9.71 ± 3.28) × 10−4GeV−1c2 NNLO QCD + NLO EW [Czakon et al.]

Figure 1. Results for At¯t

FB vs. mt¯t for the individual CDF

and D0 measurements and for their combination. The inputs to the combination are displaced at different abscissa values within each mt¯tbin for ease of visibility. The inner error bar

indicates the statistical uncertainty, while the outer error bar corresponds to the total uncertainty including the systematic uncertainty added in quadrature. The value of the combined data point for the mass region of 550 − 650 GeV/c2 _is

dis-cussed in Ref. [31] in more detail. The linear dependence of the combined result is given by the solid black line together with the 1 SD total uncertainty of the two-parameter fit given by the shaded gray area. The dashed orange line shows the NNLO QCD + NLO EW prediction of Refs. [1,2,26], while the shaded orange area reflects its 1 SD uncertainty.

The combined At¯t

FB values, and their statistical and

systematic uncertainties for each category, are given in TableI, which also reports the probabilities for the CDF and D0 inputs to agree with each other in each mass bin. Overall, the differential combination has a χ2 _of

5.2 for 4 dof. The correlations in the total uncertainties between mt¯t bins are given in Ref. [31]. The values of

At¯t

FB as a function of mt¯t for each experiment and their

combination are shown in Fig.1, together with the NNLO QCD + NLO EW predictions [26].

The counter-intuitive value of the combined asymme-try in the 550− 650 GeV/c2 _{mass bin is due to the}

spe-cific pattern of the CDF and D0 bin-to-bin correlations stemming from different choices in the regularized matrix unfolding. The opposite correlations observed between the 600 GeV/c2 _{and the 700 GeV/c}2 _{mass bins in the}

CDF (large and positive) and D0 (small and negative) measurements give rise to a combined asymmetry in the 600 GeV/c2 _{bin that is smaller than that found in either}

measurement [31].

To reduce the correlations between the slope and the intercept, we use a linear fit of the form At¯t

FB(mt¯t) =

αmt¯t(mt¯t− 450 GeV/c

2_{) + β}

mt¯t. The linear fit yields a slope of αmt¯t = (9.71± 3.28) × 10

−4 _GeV−1_c2 _with

an intercept at a mt¯t value of 450 GeV/c2 of βmt¯t = 0.131± 0.034. The fit has a χ2 _{of 0.3 for 2 dof. The}

values predicted at NNLO QCD + NLO EW are αSM mt¯t = 5.11+0.42

−0.64

× 10−4 _GeV−1_c2 _{and an intercept of β}SM mt¯t = 0.087+0.005−0.006. The predicted dependence is determined by

a linear fit to the binned prediction from Ref. [26]. The NNLO QCD + NLO EW predictions of the differential At¯t

FBand of the slope parameters agree with the combined

experimental results to within 1.3 SD.

The differential t¯t asymmetry as a function of _|∆yt¯t|

is available from CDF for both the `+jets and `` chan-nels, and from D0 for the `+jets channel. The choice of binning differs for these measurements. We per-form a simultaneous least-squares fit to a linear func-tion At¯t

FB(|∆yt¯t|) = α∆yt¯t|∆yt¯t| for all available measure-ments, employing a combined 10_{× 10 covariance matrix} Cij. We define χ2(|∆yt¯t|) =

P

ij[yi−fi(|∆yt¯t|)] Cij−1[yj−

fj(|∆yt¯t|)], with yi and yj representing the bin i and j

of each of the three measurements, and fi(|∆yt¯t|) and

fj(|∆yt¯t|) representing the expectations from a linear

function. The definition of the asymmetry ensures that At¯t

FB= 0 at ∆yt¯t= 0. The correlations of the systematic

uncertainties among analysis channels and experiments are assumed to be equal to those in the At¯t

FBvs. mt¯t

mea-surements. Figure 2shows the individual measurements and the result of the linear fit. The linear dependence for the combination is measured to be α∆y_t¯t = 0.187± 0.038

with a χ2 _{of 10.9 for 9 dof. A fit to the binned NNLO}

QCD + NLO EW predictions of Ref. [1,2,26] gives the slope αSM

∆yt¯t = 0.129

+0.006

−0.012. The prediction and the

com-bined result differ by 1.5 SD.

The combined fit to the CDF and D0 inclusive single-lepton asymmetries gives A`

FB = 0.073± 0.016(stat) ±

0.012(syst). The fit has a χ2 _{of 2.2 for 3 dof, and the}

result is consistent with the NLO QCD + NLO EW pre-diction of 0.038± 0.003 [3] to within 1.6 SD. The weights of the CDF `+jets, D0 `+jets, CDF `` and D0 `` re-sults in the fit are 0.40, 0.27, 0.11, and 0.23, respectively. The individual CDF and D0 measurements of A`

FB as a

function of q`η` are shown in Fig.3.

The combined fit to the CDF and D0 inclusive A``

FB measurements yields A ``

FB = 0.108± 0.043(stat) ±

0.016(syst). The fit has a χ2 _{of 0.2 for 1 dof, and the}

result is consistent with the NLO QCD + NLO EW pre-diction of 0.048_{± 0.004 [}3] to within 1.3 SD. The weights of the CDF and D0 `` results in the fit are 0.32 and 0.68, respectively. The individual CDF and D0 measurements of A``

FB as a function of ∆η are shown in Fig.4.

In summary, we report combinations of the measure-ments of top-antitop quark forward-backward

asymme-0.0 0.4 0.8 1.2 1.6 2.0 |∆yt¯t| − 0. 4− 0. 2 0. 0 0. 2 0. 4 0. 6 0. 8 A t¯t FB

Tevatron combination:α∆yt¯t=0.187 ± 0.038

NNLO QCD + NLO EW [Czakon et al.]

D0 ` + jets, 9.7 fb−1 CDF ` + jets, 9.4 fb−1 CDF ``, 9.1 fb−1

Figure 2. Measurements of the differential asymmetries At¯FBt

vs. |∆yt¯t| with data points displayed at the

distribution-weighted center of the bins. The inner error bar indicates the statistical uncertainty, while the outer error bar corresponds to the total uncertainty, including the systematic uncertainty added in quadrature. The combined linear dependence for all the experimental results is given by the solid black line, with the 1 SD total uncertainty on the one-parameter fit given by the shaded gray area. The dashed orange line shows the NNLO QCD + NLO EW prediction [1,2,26], while the shaded orange area reflects its 1 SD uncertainty.

0.0 0.4 0.8 1.2 1.6 |q`η`| − 0. 3 − 0. 2 − 0. 1 0. 0 0. 1 0. 2 A ` FB <sub>D0 ` + jets, 9.7 fb</sub>−1 CDF ` + jets, 9.4 fb−1 D0 ``, 9.7 fb−1 CDF ``, 9.1 fb−1 NLO SM [Bernreuther and Si; Hong et al.]

Figure 3. Comparison of the differential asymmetries A`FBas

a function of |q`η`|. Each error bar represents the total

exper-imental uncertainty. The dashed orange line shows the NLO SM prediction [3,32], while the shaded orange area shows its 1 SD uncertainty.

tries performed in a pp collision sample corresponding to 9_{−10 fb}−1 _{collected by the CDF and D0 experiments at}

the Tevatron. Both the inclusive and differential mea-surements favor somewhat larger positive asymmetries than the predictions. The resulting combined inclusive asymmetry is At¯t

pre-Table I. Combined differential At¯t

FBvalues in bins of mt¯t, with the probability (Prob) for the CDF and D0 inputs to agree with

each other, with statistical (Stat), systematic (Tot syst), and total uncertainties. The systematic uncertainties are broken down into uncertainties in the distribution of the background (Bkd distr), background normalization (Bkd norm), signal modeling (Signal), detector modeling (Det), measurement method (Meth), and parton distribution function (PDF).

mt¯t (GeV/c2) At¯FBt Prob

Uncertainty

Total Stat Meth Signal PDF Det Bkd distr Bkd norm Tot syst 350–450 0.081 95% 0.037 0.031 0.009 0.012 0.004 0.007 0.010 0.003 0.020 450–550 0.195 22% 0.048 0.042 0.010 0.016 0.007 0.006 0.007 0.006 0.023 550–650 0.258 98% 0.093 0.063 0.008 0.062 0.017 0.017 0.006 0.008 0.068 > 650 0.319 8% 0.147 0.123 0.018 0.065 0.021 0.026 0.019 0.019 0.080 0.0 0.4 0.8 1.2 1.6 |∆η| − 0. 6 − 0. 4 − 0. 2 0. 0 0. 2 0. 4 A `` FB D0 ``, 9.7 fb−1 CDF ``, 9.1 fb−1 NLO SM [Bernreuther and Si; Hong et al.]

Figure 4. Comparison of the differential asymmetries A``FBas

a function of |∆η|. Each error bar represents the total exper-imental uncertainty. The dashed orange line shows the NLO SM prediction [3,32], while the shaded orange area shows its 1 SD uncertainty.

diction at NNLO QCD + NLO EW of 0.095_{± 0.007. All} three inclusive observables agree with the existing SM predictions to within 1.6 standard deviations. The dif-ferential asymmetries as a function of mt¯tand ∆yt¯tagree

to within 1.5 standard deviations. We conclude that the measurements and their combinations, shown in Fig. 5, are consistent with each other and with the SM predic-tions. The reported consistency is the result of an intense effort of refining the experimental and theoretical under-standing, which started in 2010, when significant depar-tures of the first Tevatron measurements [8,9] from the predictions suggested potential contributions from BSM dynamics.

This document was prepared by the CDF and D0 col-laborations using the resources of the Fermi National Ac-celerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), act-ing under Contract No. DE-AC02-07CH11359.

We thank the staffs at Fermilab and collaborating in-stitutions, and acknowledge support from the Depart-ment of Energy and the National Science Foundation (U.S.A.), the Australian Research Council (Australia), the National Council for the Development of Science and Technology and the Carlos Chagas Filho Founda-tion for the Support of Research in the State of Rio de Janeiro (Brazil), the Natural Sciences and Engineering Research Council (Canada), the China Academy of Sci-ences, the National Natural Science Foundation of China, and the National Science Council of the Republic of China (China), the Administrative Department of Sci-ence, Technology and Innovation (Colombia), the Min-istry of Education, Youth and Sports (Czech Repub-lic), the Academy of Finland, the Alternative Energies and Atomic Energy Commission and the National Center for Scientific Research/National Institute of Nuclear and Particle Physics (France), the Bundesministerium f¨ur Bildung und Forschung (Federal Ministry of Education and Research) and the Deutsche Forschungsgemeinschaft (German Research Foundation) (Germany), the Depart-ment of Atomic Energy and DepartDepart-ment of Science and Technology (India), the Science Foundation Ireland (Ire-land), the National Institute for Nuclear Physics (Italy), the Ministry of Education, Culture, Sports, Science and Technology (Japan), the Korean World Class University Program and the National Research Foundation of Korea (Korea), the National Council of Science and Technology (Mexico), the Foundation for Fundamental Research on Matter (Netherlands), the Ministry of Education and Sci-ence of the Russian Federation, the National Research Center Kurchatov Institute of the Russian Federation, and the Russian Foundation for Basic Research (Rus-sia), the Slovak R&D Agency (Slovakia), the Ministry of Science and Innovation, and the Consolider-Ingenio 2010 Program (Spain), the Swedish Research Council (Swe-den), the Swiss National Science Foundation (Switzer-land), the Ministry of Education and Science of Ukraine (Ukraine), the Science and Technology Facilities Coun-cil and The Royal Society (United Kingdom), the A. P. Sloan Foundation (U.S.A.), and the European Union

−15 0 15 30 Asymmetry [%] t¯t∆y Asymmetry At¯t FB
CDF ` + jets, 9.4 fb−1 PRD 87, 092002 (2013) 16.4 ± 4.7 CDF ``, 9.1 fb−1 PRD 93, 112005 (2016) 12 ± 13 D0 ` + jets, 9.7 fb−1 PRD 90, 072011 (2014) 10.6 ± 3.0 D0 ``, 9.7 fb−1 PRD 92, 052007 (2015) 17.5 ± 6.3 Tevatron combination 12.8 ± 2.5 Lepton qη Asymmetry A` FB
CDF ` + jets, 9.4 fb−1 PRD 88, 072003 (2013) 10.5 ± 3.2 2.9 CDF ``, 9.1 fb−1 PRL 113, 042001 (2014) 7.2 ± 6.0 D0 ` + jets, 9.7 fb−1 PRD 90, 072001 (2014) 5.0 ± 3.4 3.7 D0 ``, 9.7 fb−1 PRD 88, 112002 (2013) 4.4 ± 3.9 Tevatron combination 7.3 ± 2.0 Lepton∆η Asymmetry A`` FB
CDF ``, 9.1 fb−1 PRL 113, 042001 (2014) 7.6 ± 8.2 D0 ``, 9.7 fb−1 PRD 88, 112002 (2013) 12.3 ± 5.6 Tevatron combination 10.8 ± 4.6

NNLO QCD + NLO EW [Czakon et al.] NLO SM [Bernreuther and Si]

Figure 5. Summary of inclusive forward-backward asymme-tries in t¯t events in percents at the Tevatron.

community Marie Curie Fellowship Contract No. 302103.

∗

Deceased

†

With visitors froma_{University of British Columbia,}

Van-couver, BC V6T 1Z1, Canada, bIstituto Nazionale di Fisica Nucleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy, c_{University of California Irvine, Irvine,}

CA 92697, USA,d_{Institute of Physics, Academy of}

Sci-ences of the Czech Republic, 182 21, Czech Republic,

e

CERN, CH-1211 Geneva, Switzerland, fCornell Uni-versity, Ithaca, NY 14853, USA, g_{University of Cyprus,}

Nicosia CY-1678, Cyprus, hOffice of Science, U.S. De-partment of Energy, Washington, DC 20585, USA,

i_{University College Dublin, Dublin 4, Ireland,} j_ETH,

8092 Z¨urich, Switzerland, kUniversity of Fukui, Fukui

City, Fukui Prefecture, Japan 910-0017, lUniversidad Iberoamericana, Lomas de Santa Fe, M´exico, C.P. 01219, Distrito Federal, m_{University of Iowa, Iowa City, IA}

52242, USA, nKinki University, Higashi-Osaka City, Japan 577-8502, o_{Kansas State University, Manhattan,}

KS 66506, USA,p_{Brookhaven National Laboratory,}

Up-ton, NY 11973, USA,qIstituto Nazionale di Fisica Nu-cleare, Sezione di Lecce, Via Arnesano, I-73100 Lecce, Italy, r_{Queen Mary, University of London, London, E1}

4NS, United Kingdom, sUniversity of Melbourne, Vic-toria 3010, Australia, tMuons, Inc., Batavia, IL 60510, USA, u_{Nagasaki Institute of Applied Science, Nagasaki}

851-0193, Japan, vNational Research Nuclear Univer-sity, Moscow 115409, Russia, wNorthwestern Univer-sity, Evanston, IL 60208, USA, x_{University of Notre}

Dame, Notre Dame, IN 46556, USA, yUniversidad de Oviedo, E-33007 Oviedo, Spain, zCNRS-IN2P3, Paris, F-75205 France, aa_{Universidad Tecnica Federico Santa}

Maria, 110v Valparaiso, Chile,bb_{Sejong University, Seoul}

143-747, Korea, ccThe University of Jordan, Amman 11942, Jordan,ddUniversite catholique de Louvain, 1348 Louvain-La-Neuve, Belgium,ee_{University of Z¨urich, 8006}

Z¨urich, Switzerland, f fMassachusetts General Hospital, Boston, MA 02114 USA, ggHarvard Medical School, Boston, MA 02114 USA,hh_{Hampton University,}

Hamp-ton, VA 23668, USA,iiLos Alamos National Laboratory, Los Alamos, NM 87544, USA,jjUniversit`a degli Studi di Napoli Federico II, I-80138 Napoli, Italy

‡

With visitors fromkkAugustana University, Sioux Falls, SD 57197, USA,llThe University of Liverpool, Liverpool L69 3BX, UK, mm_{Deutsches Elektronen-Synchrotron}

(DESY), Notkestrase 85, Germany,nn_{Consejo Nacional}

de Ciencia y Tecnologia (Conacyt), M-03940 Mexico City, Mexico, ooSLAC, Menlo Park, CA 94025, USA,

pp_{University College London, London WC1E 6BT, UK,} qq

Centro de Investigacion en Computacion - IPN, CP 07738 Mexico City, Mexico, rrUniversidade Estadual Paulista, S˜ao Paulo, SP 01140, Brazil,ss_Karlsruher

In-stitut f¨ur Technologie (KIT) - Steinbuch Centre for Com-puting (SCC), D-76128 Karlsruher, Germany, ttOffice of Science, U.S. Department of Energy, Washington, D.C. 20585, USA, uuAmerican Association for the Ad-vancement of Science, Washington, D.C. 20005, USA,

vv_{National Academy of Science of Ukraine (NASU)}

- Kiev Institute for Nuclear Research (KINR), Kyiv 03680, Ukraine,wwUniversity of Maryland, College Park, MD 20742, USA, xxEuropean Organization for Nuclear Research (CERN), CH-1211 Gen´eve 23, Switzerland,

yy

Purdue University, West Lafayette, IN 47907, USA,

zz

Institute of Physics, Belgrade, CS-11080 Belgrade, Ser-bia

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