
==== Front
Nature
Nature
Nature
0028-0836
1476-4687
Nature Publishing Group UK London

39294352
7824
10.1038/s41586-024-07824-z
Article
Observation of quantum entanglement with top quarks at the ATLAS detector
The ATLAS CollaborationAad G. 1
Abbott B. 2
Abeling K. 3
Abicht N. J. 4
Abidi S. H. 5
Aboulhorma A. 6
Abramowicz H. 7
Abreu H. 8
Abulaiti Y. 9
Acharya B. S. 101112
Bourdarios C. Adam 13
Adamczyk L. 14
Addepalli S. V. 15
Addison M. J. 16
Adelman J. 17
Adiguzel A. 18
Adye T. 19
Affolder A. A. 20
Afik Y. 21
Agaras M. N. 22
Agarwala J. 2324
Aggarwal A. 25
Agheorghiesei C. 26
Ahmad A. 27
Ahmadov F. 28
Ahmed W. S. 29
Ahuja S. 30
Ai X. 31
Aielli G. 3233
Aikot A. 34
Tamlihat M. Ait 6
Aitbenchikh B. 35
Aizenberg I. 36
Akbiyik M. 25
Åkesson T. P. A. 37
Akimov A. V.
Akiyama D. 38
Akolkar N. N. 39
Aktas S. 40
Khoury K. Al 41
Alberghi G. L. 42
Albert J. 43
Albicocco P. 44
Albouy G. L. 45
Alderweireldt S. 46
Alegria Z. L. 47
Aleksa M. 27
Aleksandrov I. N.
Alexa C. 48
Alexopoulos T. 49
Alfonsi F. 42
Algren M. 50
Alhroob M. 2
Ali B. 51
Ali H. M. J. 52
Ali S. 53
Alibocus S. W. 54
Aliev M. 55
Alimonti G. 56
Alkakhi W. 3
Allaire C. 57
Allbrooke B. M. M. 58
Allen J. F. 46
Flores C. A. Allendes 59
Allport P. P. 60
Aloisio A. 6162
Alonso F. 63
Alpigiani C. 64
Estevez M. Alvarez 65
Fernandez A. Alvarez 25
Cardoso M. Alves 50
Alviggi M. G. 6162
Aly M. 16
Coutinho Y. Amaral 66
Ambler A. 29
Amelung C. 27
Amerl M. 16
Ames C. G. 67
Amidei D. 68
Dos Santos S. P. Amor 69
Amos K. R. 34
Ananiev V. 70
Anastopoulos C. 71
Andeen T. 72
Anders J. K. 27
Andrean S. Y. 7374
Andreazza A. 5675
Angelidakis S. 76
Angerami A. 4177
Anisenkov A. V.
Annovi A. 78
Antel C. 50
Anthony M. T. 71
Antipov E. 79
Antonelli M. 44
Anulli F. 80
Aoki M. 81
Aoki T. 82
Pozo J. A. Aparisi 34
Aparo M. A. 58
Bella L. Aperio 83
Appelt C. 84
Apyan A. 15
Val S. J. Arbiol 85
Arcangeletti C. 44
Arce A. T. H. 86
Arena E. 54
Arguin J-F. 87
Argyropoulos S. 88
Arling J.-H. 83
Arnaez O. 13
Arnold H. 89
Artoni G. 8090
Asada H. 91
Asai K. 92
Asai S. 82
Asbah N. A. 93
Assamagan K. 5
Astalos R. 94
Atashi S. 95
Atkin R. J. 96
Atkinson M. 97
Atmani H. 98
Atmasiddha P. A. 99
Augsten K. 51
Auricchio S. 6162
Auriol A. D. 60
Austrup V. A. 16
Avolio G. 27
Axiotis K. 50
Azuelos G. 87100
Babal D. 101
Bachacou H. 102
Bachas K. 103104
Bachiu A. 105
Backman F. 7374
Badea A. 21
Baer T. M. 68
Bagnaia P. 8090
Bahmani M. 84
Bahner D. 88
Bailey A. J. 34
Bailey V. R. 97
Baines J. T. 19
Baines L. 106
Baker O. K. 107
Bakos E. 108
Gupta D. Bakshi 109
Balakrishnan V. 2
Balasubramanian R. 89
Baldin E. M.
Balek P. 14
Ballabene E. 42110
Balli F. 102
Baltes L. M. 111
Balunas W. K. 112
Balz J. 25
Banas E. 85
Bandieramonte M. 113
Bandyopadhyay A. 39
Bansal S. 39
Barak L. 7
Barakat M. 83
Barberio E. L. 114
Barberis D. 115116
Barbero M. 1
Barel M. Z. 89
Barends K. N. 96
Barillari T. 117
Barisits M-S. 27
Barklow T. 118
Baron P. 119
Moreno D. A. Baron 16
Baroncelli A. 120
Barone G. 5
Barr A. J. 121
Barr J. D. 122
Barreiro F. 65
da Costa J. Barreiro Guimarães 123
Barron U. 7
Teixeira M. G. Barros 69
Barsov S.
Bartels F. 111
Bartoldus R. 118
Barton A. E. 52
Bartos P. 94
Basan A. 25
Baselga M. 4
Bassalat A. 57124
Basso M. J. 100
Basson C. R. 16
Bates R. L. 125
Batlamous S. 6
Batley J. R. 112
Batool B. 126
Battaglia M. 20
Battulga D. 84
Bauce M. 8090
Bauer M. 27
Bauer P. 39
Hurrell L. T. Bazzano 127
Beacham J. B. 86
Beau T. 128
Beaucamp J. Y. 63
Beauchemin P. H. 129
Bechtle P. 39
Beck H. P. 130131
Becker K. 132
Beddall A. J. 133
Bednyakov V. A.
Bee C. P. 79
Beemster L. J. 108
Beermann T. A. 27
Begalli M. 134
Begel M. 5
Behera A. 79
Behr J. K. 83
Beirer J. F. 27
Beisiegel F. 39
Belfkir M. 135
Bella G. 7
Bellagamba L. 42
Bellerive A. 105
Bellos P. 60
Beloborodov K.
Benchekroun D. 35
Bendebba F. 35
Benhammou Y. 7
Beresford L. 83
Beretta M. 44
Kuutmann E. Bergeaas 136
Berger N. 13
Bergmann B. 51
Beringer J. 137
Bernardi G. 138
Bernius C. 118
Bernlochner F. U. 39
Bernon F. 127
Guardia A. Berrocal 22
Berry T. 30
Berta P. 139
Berthold A. 140
Bertram I. A. 52
Bethke S. 117
Betti A. 8090
Bevan A. J. 106
Bhalla N. K. 88
Bhamjee M. 55
Bhatta S. 79
Bhattacharya D. S. 141
Bhattarai P. 118
Bhide K. D. 88
Bhopatkar V. S. 47
Bianchi R. M. 113
Bianco G. 42110
Biebel O. 67
Bielski R. 142
Biglietti M. 143
Billingsley C. S. 144
Bindi M. 3
Bingul A. 145
Bini C. 8090
Biondini A. 54
Birch-sykes C. J. 16
Bird G. A. 19112
Birman M. 36
Biros M. 139
Biryukov S. 58
Bisanz T. 4
Bisceglie E. 146147
Biswal J. P. 19
Biswas D. 126
Bjørke K. 70
Bloch I. 83
Blue A. 125
Blumenschein U. 106
Blumenthal J. 25
Bobbink G. J. 89
Bobrovnikov V. S.
Boehler M. 88
Boehm B. 141
Bogavac D. 27
Bogdanchikov A. G.
Bohm C. 73
Boisvert V. 30
Bokan P. 27
Bold T. 14
Bomben M. 138
Bona M. 106
Boonekamp M. 102
Booth C. D. 30
Borbély A. G. 125
Bordulev I. S.
Borecka-Bielska H. M. 87
Borissov G. 52
Bortoletto D. 121
Boscherini D. 42
Bosman M. 22
Bossio Sola J. D. 27
Bouaouda K. 35
Bouchhar N. 34
Boudreau J. 113
Bouhova-Thacker E. V. 52
Boumediene D. 148
Bouquet R. 43
Boveia A. 149
Boyd J. 27
Boye D. 5
Boyko I. R.
Bracinik J. 60
Brahimi N. 150
Brandt G. 151
Brandt O. 112
Braren F. 83
Brau B. 152
Brau J. E. 142
Brener R. 36
Brenner L. 89
Brenner R. 136
Bressler S. 36
Britton D. 125
Britzger D. 117
Brock I. 39
http://orcid.org/0000-0002-4556-9212
Brock R. 153
Brooijmans G. 41
Brooks W. K. 59
Brost E. 5
Brown L. M. 43
Bruce L. E. 93
Bruckler T. L. 121
de Renstrom P. A. Bruckman 85
Brüers B. 83
Bruni A. 42
Bruni G. 42
Bruschi M. 42
Bruscino N. 8090
Buanes T. 154
Buat Q. 64
Buchin D. 117
Buckley A. G. 125
Bulekov O.
Bullard B. A. 118
Burdin S. 54
Burgard C. D. 4
Burger A. M. 27
Burghgrave B. 109
Burlayenko O. 88
Burr J. T. P. 112
Burton C. D. 72
Burzynski J. C. 155
Busch E. L. 41
Büscher V. 25
Bussey P. J. 125
Butler J. M. 156
Buttar C. M. 125
Butterworth J. M. 122
Buttinger W. 19
Vazquez C. J. Buxo 153
Buzykaev A. R.
Urbán S. Cabrera 34
Cadamuro L. 57
Caforio D. 157
Cai H. 113
Cai Y. 123158
Cai Y. 159
Cairo V. M. M. 27
Cakir O. 160
Calace N. 27
Calafiura P. 137
Calderini G. 128
Calfayan P. 161
Callea G. 125
Caloba L. P. 66
Calvet D. 148
Calvet S. 148
Calvetti M. 78162
Toro R. Camacho 128
Camarda S. 27
Munoz D. Camarero 15
Camarri P. 3233
Camerlingo M. T. 6162
Cameron D. 27
Camincher C. 43
Campanelli M. 122
Camplani A. 163
Canale V. 6162
Cantero J. 34
Cao Y. 97
Capocasa F. 15
Capua M. 146147
Carbone A. 5675
Cardarelli R. 32
Cardenas J. C. J. 109
Cardillo F. 34
Carducci G. 146147
Carli T. 27
Carlino G. 61
Carlotto J. I. 22
Carlson B. T. 113164
Carlson E. M. 43100
Carminati L. 5675
Carnelli A. 102
Carnesale M. 8090
Caron S. 165
Carquin E. 59
Carrá S. 56
Carratta G. 42110
Carroll A. M. 142
Carter J. W. S. 166
Carter T. M. 46
Casado M. P. 22167
Caspar M. 83
Castillo F. L. 13
Garcia L. Castillo 22
Gimenez V. Castillo 34
Castro N. F. 69168
Catinaccio A. 27
Catmore J. R. 70
Cavaliere T. 13
Cavaliere V. 5
Cavalli N. 42110
Cavasinni V. 78162
Cekmecelioglu Y. C. 83
Celebi E. 40
Celli F. 121
Centonze M. S. 169170
Cepaitis V. 50
Cerny K. 119
Cerqueira A. S. 171
Cerri A. 58
Cerrito L. 3233
Cerutti F. 137
Cervato B. 126
Cervelli A. 42
Cesarini G. 44
Cetin S. A. 133
Chakraborty D. 17
Chan J. 137
Chan W. Y. 82
Chapman J. D. 112
Chapon E. 102
Chargeishvili B. 172
Charlton D. G. 60
Chatterjee M. 130
Chauhan C. 139
Che Y. 159
Chekanov S. 173
Chekulaev S. V. 100
Chelkov G. A.
Chen A. 68
Chen B. 7
Chen B. 43
Chen H. 159
Chen H. 5
Chen J. 174
Chen J. 155
Chen M. 121
Chen S. 82
Chen S. J. 159
Chen X. 102174
Chen X. 175176
Chen Y. 120
Cheng C. L. 177
Cheng H. C. 178
Cheong S. 118
Cheplakov A.
Cheremushkina E. 83
Cherepanova E. 89
El Moursli R. Cherkaoui 6
Cheu E. 179
Cheung K. 180
Chevalier L. 102
Chiarella V. 44
Chiarelli G. 78
Chiedde N. 1
Chiodini G. 169
Chisholm A. S. 60
Chitan A. 48
Chitishvili M. 34
Chizhov M. V.
Choi K. 72
Chou Y. 64
Chow E. Y. S. 165
Chu K. L. 36
Chu M. C. 178
Chu X. 123158
Chudoba J. 181
Chwastowski J. J. 85
Cieri D. 117
Ciesla K. M. 14
Cindro V. 182
Ciocio A. 137
Cirotto F. 6162
Citron Z. H. 36183
Citterio M. 56
Ciubotaru D. A. 48
Clark A. 50
Clark P. J. 46
Clarry C. 166
Columbie J. M. Clavijo 83
Clawson S. E. 83
Clement C. 7374
Clercx J. 83
Coadou Y. 1
Cobal M. 10184
Coccaro A. 116
Barrue R. F. Coelho 69
De Sa R. Coelho Lopes 152
Coelli S. 56
Cole B. 41
Collot J. 45
Muiño P. Conde 69185
Connell M. P. 55
Connell S. H. 55
Connelly I. A. 125
Conroy E. I. 121
Conventi F. 61186
Cooke H. G. 60
Cooper-Sarkar A. M. 121
Choi A. Cordeiro Oudot 128
Corpe L. D. 148
Corradi M. 8090
Corriveau F. 29187
Cortes-Gonzalez A. 84
Costa M. J. 34
Costanza F. 13
Costanzo D. 71
Cote B. M. 149
Cowan G. 30
Cranmer K. 177
Cremonini D. 42110
Crépé-Renaudin S. 45
Crescioli F. 128
Cristinziani M. 126
Cristoforetti M. 188189
Croft V. 89
Crosby J. E. 47
Crosetti G. 146147
Cueto A. 65
Donszelmann T. Cuhadar 95
Cui H. 123158
Cui Z. 179
Cunningham W. R. 125
Curcio F. 146147
Czodrowski P. 27
Czurylo M. M. 190
Da Cunha Sargedas De Sousa M. J. 115116
Pinto J. V. Da Fonseca 66
Da Via C. 16
Dabrowski W. 14
Dado T. 4
Dahbi S. 191
Dai T. 68
Dal Santo D. 130
Dallapiccola C. 152
Dam M. 163
D’amen G. 5
D’Amico V. 67
Damp J. 25
Dandoy J. R. 105
Danninger M. 155
Dao V. 27
Darbo G. 116
Darmora S. 173
Das S. J. 5192
D’Auria S. 5675
David C. 96
Davidek T. 139
Davis-Purcell B. 105
Dawson I. 106
Day-hall H. A. 51
De K. 109
De Asmundis R. 61
De Biase N. 83
De Castro S. 42110
De Groot N. 165
de Jong P. 89
De la Torre H. 17
De Maria A. 159
De Salvo A. 80
De Sanctis U. 3233
De Santis F. 169170
De Santo A. 58
De Regie J. B. De Vivie 45
Dedovich D. V.
Degens J. 89
Deiana A. M. 144
Del Corso F. 42110
Del Peso J. 65
Del Rio F. 111
Delagrange L. 128
Deliot F. 102
Delitzsch C. M. 4
Della Pietra M. 6162
Della Volpe D. 50
Dell’Acqua A. 27
Dell’Asta L. 5675
Delmastro M. 13
Delsart P. A. 45
Demers S. 107
Demichev M.
Denisov S. P.
D’Eramo L. 148
Derendarz D. 85
Derue F. 128
Dervan P. 54
Desch K. 39
Deutsch C. 39
Di Bello F. A. 115116
Di Ciaccio A. 3233
Di Ciaccio L. 13
Di Domenico A. 8090
Di Donato C. 6162
Di Girolamo A. 27
Di Gregorio G. 27
Di Luca A. 188189
Di Micco B. 143193
Di Nardo R. 143193
Diamantopoulou M. 105
Dias F. A. 89
Do Vale T. Dias 155
Diaz M. A. 194195
Capriles F. G. Diaz 39
Didenko M. 34
Diehl E. B. 68
Diehl L. 88
Cornell S. Díez 83
Pardos C. Diez 126
Dimitriadi C. 39136
Dimitrievska A. 137
Dingfelder J. 39
Dinu I-M. 48
Dittmeier S. J. 190
Dittus F. 27
Djama F. 1
Djobava T. 172
Doglioni C. 1637
Dohnalova A. 94
Dolejsi J. 139
Dolezal Z. 139
Dona K. M. 21
Donadelli M. 196
Dong B. 153
Donini J. 148
D’Onofrio A. 6162
D’Onofrio M. 54
Dopke J. 19
Doria A. 61
Fernandes N. Dos Santos 69
Dougan P. 16
Dova M. T. 63
Doyle A. T. 125
Draguet M. A. 121
Dreyer E. 36
Drivas-koulouris I. 49
Drnevich M. 9
Drozdova M. 50
Du D. 120
du Pree T. A. 89
Dubinin F.
Dubovsky M. 94
Duchovni E. 36
Duckeck G. 67
Ducu O. A. 48
Duda D. 46
Dudarev A. 27
Duden E. R. 15
D’uffizi M. 16
Duflot L. 57
Dührssen M. 27
Dumitriu A. E. 48
Dunford M. 111
Dungs S. 4
Dunne K. 7374
Duperrin A. 1
Yildiz H. Duran 160
Düren M. 157
Durglishvili A. 172
Dwyer B. L. 17
Dyckes G. I. 137
Dyndal M. 14
Dziedzic B. S. 85
Earnshaw Z. O. 58
Eberwein G. H. 121
Eckerova B. 94
Eggebrecht S. 3
De Souza E. Egidio Purcino 128
Ehrke L. F. 50
Eigen G. 154
Einsweiler K. 137
Ekelof T. 136
Ekman P. A. 37
El Farkh S. 197
El Ghazali Y. 197
El Jarrari H. 27
El Moussaouy A. 87
Ellajosyula V. 136
Ellert M. 136
Ellinghaus F. 151
Ellis N. 27
Elmsheuser J. 5
Elsing M. 27
Emeliyanov D. 19
Enari Y. 82
Ene I. 137
Epari S. 22
Erland P. A. 85
Errenst M. 151
Escalier M. 57
Escobar C. 34
Etzion E. 7
Evans G. 69
Evans H. 161
Evans L. S. 30
Evans M. O. 58
Ezhilov A.
Ezzarqtouni S. 35
Fabbri F. 125
Fabbri L. 42110
Facini G. 122
Fadeyev V. 20
Fakhrutdinov R. M.
Fakoudis D. 25
Falciano S. 80
Falda Ulhoa Coelho L. F. 27
Falke P. J. 39
Faltova J. 139
Fan C. 97
Fan Y. 123
Fang Y. 123158
Fanti M. 5675
Faraj M. 1011
Farazpay Z. 198
Farbin A. 109
Farilla A. 143
Farooque T. 153
Farrington S. M. 46
Fassi F. 6
Fassouliotis D. 76
Giannelli M. Faucci 3233
Fawcett W. J. 112
Fayard L. 57
Federic P. 139
Federicova P. 181
Fedin O. L.
Fedotov G.
Feickert M. 177
Feligioni L. 1
Fellers D. E. 142
Feng C. 199
Feng M. 175
Feng Z. 89
Fenton M. J. 95
Ferencz L. 83
Ferguson R. A. M. 52
Luengo S. I. Fernandez 59
Martinez P. Fernandez 22
Fernoux M. J. V. 1
Ferrando J. 52
Ferrari A. 136
Ferrari P. 89165
Ferrari R. 23
Ferrere D. 50
Ferretti C. 68
Fiedler F. 25
Fiedler P. 51
Filipčič A. 182
Filmer E. K. 200
Filthaut F. 165
Fiolhais M. C. N. 69201202
Fiorini L. 34
Fisher W. C. 153
Fitschen T. 16
Fitzhugh P. M. 102
Fleck I. 126
Fleischmann P. 68
Flick T. 151
Flores M. 203
Castillo L. R. Flores 178
De Acedo L. Flores Sanz 27
Follega F. M. 188189
Fomin N. 154
Foo J. H. 166
Formica A. 102
Forti A. C. 16
Fortin E. 27
Fortman A. W. 137
Foti M. G. 137
Fountas L. 76204
Fournier D. 57
Fox H. 52
Francavilla P. 78162
Francescato S. 93
Franchellucci S. 50
Franchini M. 42110
Franchino S. 111
Francis D. 27
Franco L. 165
Lima V. Franco 27
Franconi L. 83
Franklin M. 93
Frattari G. 15
Freegard A. C. 106
Freund W. S. 66
Frid Y. Y. 7
Friend J. 125
Fritzsche N. 140
Froch A. 88
Froidevaux D. 27
Frost J. A. 121
Fu Y. 120
Garrido S. Fuenzalida 59
Fujimoto M. 1
Fung K. Y. 178
De Simas Filho E. Furtado 66
Furukawa M. 82
Fuster J. 34
Gabrielli A. 42110
Gabrielli A. 166
Gadow P. 27
Gagliardi G. 115116
Gagnon L. G. 137
Gallas E. J. 121
Gallop B. J. 19
Gan K. K. 149
Ganguly S. 82
Gao Y. 46
Walls F. M. Garay 194195
Garcia B. 5
García C. 34
Alonso A. Garcia 89
Caffaro A. G. Garcia 107
Navarro J. E. García 34
Garcia-Sciveres M. 137
Gardner G. L. 99
Gardner R. W. 21
Garelli N. 129
Garg D. 205
Garg R. B. 118206
Gargan J. M. 46
Garner C. A. 166
Garvey C. M. 96
Gaspar P. 66
Gassmann V. K. 129
Gaudio G. 23
Gautam V. 22
Gauzzi P. 8090
Gavrilenko I. L.
Gavrilyuk A.
Gay C. 207
Gaycken G. 83
Gazis E. N. 49
Geanta A. A. 48
Gee C. M. 20
Gekow A. 149
Gemme C. 116
Genest M. H. 45
Gentile S. 8090
Gentry A. D. 208
George S. 30
George W. F. 60
Geralis T. 209
Gessinger-Befurt P. 27
Geyik M. E. 151
Ghani M. 132
Ghneimat M. 126
Ghorbanian K. 106
Ghosal A. 126
Ghosh A. 95
Ghosh A. 179
Giacobbe B. 42
Giagu S. 8090
Giani T. 89
Giannetti P. 78
Giannini A. 120
Gibson S. M. 30
Gignac M. 20
Gil D. T. 210
Gilbert A. K. 14
Gilbert B. J. 41
Gillberg D. 105
Gilles G. 89
Ginabat L. 128
Gingrich D. M. 100211
Giordani M. P. 10184
Giraud P. F. 102
Giugliarelli G. 10184
Giugni D. 56
Giuli F. 27
Gkialas I. 76204
Gladilin L. K.
Glasman C. 65
Gledhill G. R. 142
Glemža G. 83
Glisic M. 142
Gnesi I. 147212
Go Y. 5
Goblirsch-Kolb M. 27
Gocke B. 4
Godin D. 87
Gokturk B. 40
Goldfarb S. 114
Golling T. 50
Gololo M. G. D. 191
Golubkov D.
Gombas J. P. 153
Gomes A. 69213
Da Silva G. Gomes 126
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Gonçalo R. 69201
Gonella L. 60
Gongadze A. 214
Gonnella F. 60
Gonski J. L. 41
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de la Hoz S. González 34
Lopez R. Gonzalez 54
Renteria C. Gonzalez 137
Rodrigues M. V. Gonzalez 83
Suarez R. Gonzalez 136
Gonzalez-Sevilla S. 50
Rodriguez G. R. Gonzalvo 34
Goossens L. 27
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Yin P. 41
Yorita K. 38
Younas S. 48
Young C. J. S. 27
Young C. 118
Yu C. 123158
Yu Y. 120
Yuan M. 68
Yuan R. 199
Yue L. 122
Zaazoua M. 120
Zabinski B. 85
Zaid E. 46
Zak Z. K. 85
Zakareishvili T. 34
Zakharchuk N. 105
Zambito S. 50
Saa J. A. Zamora 195235
Zang J. 82
Zanzi D. 88
Zaplatilek O. 51
Zeitnitz C. 151
Zeng H. 123
Zeng J. C. 97
Zenger D. T. Jr 15
Zenin O.
Ženiš T. 94
Zenz S. 106
Zerradi S. 35
Zerwas D. 57
Zhai M. 123158
Zhang D. F. 71
Zhang J. 199
Zhang J. 173
Zhang K. 123158
Zhang L. 159
Zhang P. 123158
Zhang R. 177
Zhang S. 68
Zhang S. 144
Zhang T. 82
Zhang X. 174
Zhang X. 199
Zhang Y. 138174
Zhang Y. 122
Zhang Y. 159
Zhang Z. 137
Zhang Z. 57
Zhao H. 64
Zhao T. 199
Zhao Y. 20
Zhao Z. 120
Zhemchugov A.
Zheng J. 159
Zheng K. 97
Zheng X. 120
Zheng Z. 118
Zhong D. 97
Zhou B. 68
Zhou H. 179
Zhou N. 174
Zhou Y. 159
Zhou Y. 179
Zhu C. G. 199
Zhu J. 68
Zhu Y. 174
Zhu Y. 120
Zhuang X. 123
Zhukov K.
Zimine N. I.
Zinsser J. 190
Ziolkowski M. 126
Živković L. 108
Zoccoli A. 42110
Zoch K. 93
Zorbas T. G. 71
Zormpa O. 209
Zou W. 41
Zwalinski L. 27
atlas.publications@cern.ch

1
1 https://ror.org/035xkbk20 grid.5399.6 0000 0001 2176 4817 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
2 https://ror.org/02aqsxs83 grid.266900.b 0000 0004 0447 0018 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK USA
3 https://ror.org/01y9bpm73 grid.7450.6 0000 0001 2364 4210 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany
4 https://ror.org/01k97gp34 grid.5675.1 0000 0001 0416 9637 Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
5 https://ror.org/02ex6cf31 grid.202665.5 0000 0001 2188 4229 Physics Department, Brookhaven National Laboratory, Upton, NY USA
6 https://ror.org/00r8w8f84 grid.31143.34 0000 0001 2168 4024 Faculté des sciences, Université Mohammed V, Rabat, Morocco
7 https://ror.org/04mhzgx49 grid.12136.37 0000 0004 1937 0546 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel
8 https://ror.org/03qryx823 grid.6451.6 0000 0001 2110 2151 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel
9 https://ror.org/0190ak572 grid.137628.9 0000 0004 1936 8753 Department of Physics, New York University, New York, NY USA
10 grid.470223.0 0000 0004 1760 7175 INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy
11 https://ror.org/009gyvm78 grid.419330.c 0000 0001 2184 9917 ICTP, Trieste, Italy
12 https://ror.org/0220mzb33 grid.13097.3c 0000 0001 2322 6764 Department of Physics, King’s College London, London, UK
13 https://ror.org/04gqg1a07 grid.5388.6 0000 0001 2193 5487 LAPP, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France
14 grid.9922.0 0000 0000 9174 1488 Faculty of Physics and Applied Computer Science, AGH University of Krakow, Krakow, Poland
15 https://ror.org/05abbep66 grid.253264.4 0000 0004 1936 9473 Department of Physics, Brandeis University, Waltham, MA USA
16 https://ror.org/027m9bs27 grid.5379.8 0000 0001 2166 2407 School of Physics and Astronomy, University of Manchester, Manchester, UK
17 https://ror.org/012wxa772 grid.261128.e 0000 0000 9003 8934 Department of Physics, Northern Illinois University, DeKalb, IL USA
18 https://ror.org/03a5qrr21 grid.9601.e 0000 0001 2166 6619 Department of Physics, Istanbul University, Istanbul, Türkiye
19 https://ror.org/03gq8fr08 grid.76978.37 0000 0001 2296 6998 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK
20 https://ror.org/03s65by71 grid.205975.c 0000 0001 0740 6917 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA USA
21 https://ror.org/024mw5h28 grid.170205.1 0000 0004 1936 7822 Enrico Fermi Institute, University of Chicago, Chicago, IL USA
22 https://ror.org/01sdrjx85 grid.435462.2 0000 0004 5930 4594 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain
23 https://ror.org/01st30669 grid.470213.3 INFN Sezione di Pavia, Pavia, Italy
24 https://ror.org/00s6t1f81 grid.8982.b 0000 0004 1762 5736 Dipartimento di Fisica, Università di Pavia, Pavia, Italy
25 grid.5802.f 0000 0001 1941 7111 Institut für Physik, Universität Mainz, Mainz, Germany
26 https://ror.org/022kvet57 grid.8168.7 0000 0004 1937 1784 Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania
27 grid.9132.9 0000 0001 2156 142X CERN, Geneva, Switzerland
28 https://ror.org/013rnrt24 grid.435347.2 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan
29 https://ror.org/01pxwe438 grid.14709.3b 0000 0004 1936 8649 Department of Physics, McGill University, Montreal, Quebec Canada
30 https://ror.org/04g2vpn86 grid.4970.a 0000 0001 2188 881X Department of Physics, Royal Holloway University of London, Egham, UK
31 https://ror.org/04ypx8c21 grid.207374.5 0000 0001 2189 3846 School of Physics and Microelectronics, Zhengzhou University, Zhengzhou, China
32 https://ror.org/025rrx658 grid.470219.9 INFN Sezione di Roma Tor Vergata, Rome, Italy
33 grid.6530.0 0000 0001 2300 0941 Dipartimento di Fisica, Università di Roma Tor Vergata, Roma, Italy
34 https://ror.org/017xch102 grid.470047.0 0000 0001 2178 9889 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain
35 https://ror.org/001q4kn48 grid.412148.a 0000 0001 2180 2473 Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies – Université Hassan II, Casablanca, Morocco
36 https://ror.org/0316ej306 grid.13992.30 0000 0004 0604 7563 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel
37 https://ror.org/012a77v79 grid.4514.4 0000 0001 0930 2361 Fysiska Institutionen, Lunds Universitet, Lund, Sweden
38 https://ror.org/00ntfnx83 grid.5290.e 0000 0004 1936 9975 Waseda University, Tokyo, Japan
39 grid.10388.32 0000 0001 2240 3300 Physikalisches Institut, Universität Bonn, Bonn, Germany
40 https://ror.org/03z9tma90 grid.11220.30 0000 0001 2253 9056 Department of Physics, Bogazici University, Istanbul, Türkiye
41 https://ror.org/00hj8s172 grid.21729.3f 0000 0004 1936 8729 Nevis Laboratory, Columbia University, Irvington, NY USA
42 https://ror.org/04j0x0h93 grid.470193.8 0000 0004 8343 7610 INFN Sezione di Bologna, Bologna, Italy
43 https://ror.org/04s5mat29 grid.143640.4 0000 0004 1936 9465 Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia Canada
44 https://ror.org/049jf1a25 grid.463190.9 0000 0004 0648 0236 INFN e Laboratori Nazionali di Frascati, Frascati, Italy
45 grid.5676.2 0000000417654326 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France
46 https://ror.org/01nrxwf90 grid.4305.2 0000 0004 1936 7988 SUPA - School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK
47 https://ror.org/01g9vbr38 grid.65519.3e 0000 0001 0721 7331 Department of Physics, Oklahoma State University, Stillwater, OK USA
48 https://ror.org/00d3pnh21 grid.443874.8 0000 0000 9463 5349 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania
49 https://ror.org/03cx6bg69 grid.4241.3 0000 0001 2185 9808 Physics Department, National Technical University of Athens, Zografou, Greece
50 https://ror.org/01swzsf04 grid.8591.5 0000 0001 2175 2154 Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland
51 https://ror.org/03kqpb082 grid.6652.7 0000 0001 2173 8213 Czech Technical University in Prague, Prague, Czech Republic
52 https://ror.org/04f2nsd36 grid.9835.7 0000 0000 8190 6402 Physics Department, Lancaster University, Lancaster, UK
53 grid.28665.3f 0000 0001 2287 1366 Institute of Physics, Academia Sinica, Taipei, Taiwan
54 https://ror.org/04xs57h96 grid.10025.36 0000 0004 1936 8470 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK
55 https://ror.org/04z6c2n17 grid.412988.e 0000 0001 0109 131X Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa
56 https://ror.org/04w4m6z96 grid.470206.7 INFN Sezione di Milano, Milan, Italy
57 grid.503243.3 IJCLab, Université Paris-Saclay, Orsay, France
58 https://ror.org/00ayhx656 grid.12082.39 0000 0004 1936 7590 Department of Physics and Astronomy, University of Sussex, Brighton, UK
59 https://ror.org/05510vn56 grid.12148.3e 0000 0001 1958 645X Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile
60 https://ror.org/03angcq70 grid.6572.6 0000 0004 1936 7486 School of Physics and Astronomy, University of Birmingham, Birmingham, UK
61 https://ror.org/015kcdd40 grid.470211.1 0000 0004 8343 7696 INFN Sezione di Napoli, Napoli, Italy
62 grid.4691.a 0000 0001 0790 385X Dipartimento di Fisica, Università di Napoli, Napoli, Italy
63 https://ror.org/01pmtm379 grid.450288.3 0000 0004 0452 5277 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina
64 https://ror.org/00cvxb145 grid.34477.33 0000 0001 2298 6657 Department of Physics, University of Washington, Seattle, WA USA
65 https://ror.org/01cby8j38 grid.5515.4 0000 0001 1957 8126 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain
66 grid.8536.8 0000 0001 2294 473X Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil
67 https://ror.org/05591te55 grid.5252.0 0000 0004 1936 973X Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany
68 https://ror.org/00jmfr291 grid.214458.e 0000 0004 1936 7347 Department of Physics, University of Michigan, Ann Arbor, MI USA
69 https://ror.org/01hys1667 grid.420929.4 Laboratório de Instrumentação e Física Experimental de Partículas - LIP, Lisboa, Portugal
70 https://ror.org/01xtthb56 grid.5510.1 0000 0004 1936 8921 Department of Physics, University of Oslo, Oslo, Norway
71 https://ror.org/05krs5044 grid.11835.3e 0000 0004 1936 9262 Department of Physics and Astronomy, University of Sheffield, Sheffield, UK
72 https://ror.org/00hj54h04 grid.89336.37 0000 0004 1936 9924 Department of Physics, University of Texas at Austin, Austin, TX USA
73 https://ror.org/05f0yaq80 grid.10548.38 0000 0004 1936 9377 Department of Physics, Stockholm University, Stockholm, Sweden
74 grid.10548.38 0000 0004 1936 9377 Oskar Klein Centre, Stockholm, Sweden
75 grid.4708.b 0000 0004 1757 2822 Dipartimento di Fisica, Università di Milano, Milano, Italy
76 https://ror.org/04gnjpq42 grid.5216.0 0000 0001 2155 0800 Physics Department, National and Kapodistrian University of Athens, Athens, Greece
77 https://ror.org/041nk4h53 grid.250008.f 0000 0001 2160 9702 Lawrence Livermore National Laboratory, Livermore CA, USA
78 https://ror.org/05symbg58 grid.470216.6 INFN Sezione di Pisa, Pisa, Italy
79 https://ror.org/05qghxh33 grid.36425.36 0000 0001 2216 9681 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY USA
80 https://ror.org/05eva6s33 grid.470218.8 INFN Sezione di Roma, Rome, Italy
81 https://ror.org/01g5y5k24 grid.410794.f 0000 0001 2155 959X KEK, High Energy Accelerator Research Organization, Tsukuba, Japan
82 https://ror.org/057zh3y96 grid.26999.3d 0000 0001 2169 1048 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan
83 https://ror.org/01js2sh04 grid.7683.a 0000 0004 0492 0453 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany
84 https://ror.org/01hcx6992 grid.7468.d 0000 0001 2248 7639 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany
85 https://ror.org/01n78t774 grid.418860.3 0000 0001 0942 8941 Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland
86 https://ror.org/00py81415 grid.26009.3d 0000 0004 1936 7961 Department of Physics, Duke University, Durham, NC USA
87 https://ror.org/0161xgx34 grid.14848.31 0000 0001 2104 2136 Group of Particle Physics, University of Montreal, Montreal, Quebec Canada
88 https://ror.org/0245cg223 grid.5963.9 0000 0004 0491 7203 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany
89 https://ror.org/00f9tz983 grid.420012.5 0000 0004 0646 2193 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands
90 https://ror.org/02be6w209 grid.7841.a Dipartimento di Fisica, Sapienza Università di Roma, Roma, Italy
91 grid.27476.30 0000 0001 0943 978X Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan
92 grid.412314.1 0000 0001 2192 178X Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan
93 https://ror.org/03vek6s52 grid.38142.3c 0000 0004 1936 754X Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA USA
94 grid.7634.6 0000000109409708 Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia
95 https://ror.org/04gyf1771 grid.266093.8 0000 0001 0668 7243 Department of Physics and Astronomy, University of California Irvine, Irvine, CA USA
96 https://ror.org/03p74gp79 grid.7836.a 0000 0004 1937 1151 Department of Physics, University of Cape Town, Cape Town, South Africa
97 https://ror.org/047426m28 grid.35403.31 0000 0004 1936 9991 Department of Physics, University of Illinois, Urbana, IL USA
98 https://ror.org/03xc55g68 grid.501615.6 0000 0004 6007 5493 Institute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir, Morocco
99 https://ror.org/00b30xv10 grid.25879.31 0000 0004 1936 8972 Department of Physics, University of Pennsylvania, Philadelphia, PA USA
100 https://ror.org/03kgj4539 grid.232474.4 0000 0001 0705 9791 TRIUMF, Vancouver, British Columbia Canada
101 grid.435184.f 0000 0004 0488 9791 Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Košice, Slovak Republic
102 https://ror.org/03xjwb503 grid.460789.4 0000 0004 4910 6535 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
103 https://ror.org/02j61yw88 grid.4793.9 0000 0001 0945 7005 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece
104 https://ror.org/04v4g9h31 grid.410558.d 0000 0001 0035 6670 Department of Physics, University of Thessaly, Thessaly, Greece
105 https://ror.org/02qtvee93 grid.34428.39 0000 0004 1936 893X Department of Physics, Carleton University, Ottawa, Ontario Canada
106 https://ror.org/026zzn846 grid.4868.2 0000 0001 2171 1133 School of Physics and Astronomy, Queen Mary University of London, London, UK
107 https://ror.org/03v76x132 grid.47100.32 0000 0004 1936 8710 Department of Physics, Yale University, New Haven, CT USA
108 https://ror.org/02qsmb048 grid.7149.b 0000 0001 2166 9385 Institute of Physics, University of Belgrade, Belgrade, Serbia
109 https://ror.org/019kgqr73 grid.267315.4 0000 0001 2181 9515 Department of Physics, University of Texas at Arlington, Arlington, TX USA
110 https://ror.org/01111rn36 grid.6292.f 0000 0004 1757 1758 Dipartimento di Fisica e Astronomia A. Righi, Università di Bologna, Bologna, Italy
111 https://ror.org/038t36y30 grid.7700.0 0000 0001 2190 4373 Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
112 https://ror.org/013meh722 grid.5335.0 0000 0001 2188 5934 Cavendish Laboratory, University of Cambridge, Cambridge, UK
113 https://ror.org/01an3r305 grid.21925.3d 0000 0004 1936 9000 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA USA
114 https://ror.org/01ej9dk98 grid.1008.9 0000 0001 2179 088X School of Physics, University of Melbourne, Melbourne Victoria, Australia
115 https://ror.org/0107c5v14 grid.5606.5 0000 0001 2151 3065 Dipartimento di Fisica, Università di Genova, Genova, Italy
116 https://ror.org/02v89pq06 grid.470205.4 INFN Sezione di Genova, Genova, Italy
117 grid.435824.c 0000 0001 2375 0603 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany
118 https://ror.org/05gzmn429 grid.445003.6 0000 0001 0725 7771 SLAC National Accelerator Laboratory, Stanford, CA USA
119 grid.10979.36 0000 0001 1245 3953 Joint Laboratory of Optics, Palacký University, Olomouc, Czech Republic
120 https://ror.org/04c4dkn09 grid.59053.3a 0000 0001 2167 9639 Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China
121 https://ror.org/052gg0110 grid.4991.5 0000 0004 1936 8948 Department of Physics, Oxford University, Oxford, UK
122 https://ror.org/02jx3x895 grid.83440.3b 0000 0001 2190 1201 Department of Physics and Astronomy, University College London, London, UK
123 grid.9227.e 0000000119573309 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China
124 https://ror.org/0046mja08 grid.11942.3f 0000 0004 0631 5695 An-Najah National University, Nablus, Palestine
125 https://ror.org/00vtgdb53 grid.8756.c 0000 0001 2193 314X SUPA - School of Physics and Astronomy, University of Glasgow, Glasgow, UK
126 https://ror.org/02azyry73 grid.5836.8 0000 0001 2242 8751 Department Physik, Universität Siegen, Siegen, Germany
127 grid.531657.3 Facultad de Ciencias Exactas y Naturales, Departamento de Física, Universidad de Buenos Aires, y CONICET, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
128 grid.433124.3 0000 0001 0664 3574 LPNHE, Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, France
129 https://ror.org/05wvpxv85 grid.429997.8 0000 0004 1936 7531 Department of Physics and Astronomy, Tufts University, Medford, MA USA
130 https://ror.org/02k7v4d05 grid.5734.5 0000 0001 0726 5157 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland
131 https://ror.org/022fs9h90 grid.8534.a 0000 0004 0478 1713 Department of Physics, University of Fribourg, Fribourg, Switzerland
132 https://ror.org/01a77tt86 grid.7372.1 0000 0000 8809 1613 Department of Physics, University of Warwick, Coventry, UK
133 https://ror.org/03081nz23 grid.508740.e 0000 0004 5936 1556 Istinye University, Sariyer, Istanbul, Türkiye
134 https://ror.org/0198v2949 grid.412211.5 0000 0004 4687 5267 Rio de Janeiro State University, Rio de Janeiro, Brazil
135 https://ror.org/01km6p862 grid.43519.3a 0000 0001 2193 6666 United Arab Emirates University, Al Ain, United Arab Emirates
136 https://ror.org/048a87296 grid.8993.b 0000 0004 1936 9457 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden
137 grid.184769.5 0000 0001 2231 4551 Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA USA
138 https://ror.org/05f82e368 grid.508487.6 0000 0004 7885 7602 APC, Université Paris Cité, CNRS/IN2P3, Paris, France
139 https://ror.org/024d6js02 grid.4491.8 0000 0004 1937 116X Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic
140 https://ror.org/042aqky30 grid.4488.0 0000 0001 2111 7257 Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany
141 https://ror.org/00fbnyb24 grid.8379.5 0000 0001 1958 8658 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany
142 https://ror.org/0293rh119 grid.170202.6 0000 0004 1936 8008 Institute for Fundamental Science, University of Oregon, Eugene, OR USA
143 grid.470220.3 INFN Sezione di Roma Tre, Rome, Italy
144 https://ror.org/042tdr378 grid.263864.d 0000 0004 1936 7929 Physics Department, Southern Methodist University, Dallas, TX USA
145 https://ror.org/020vvc407 grid.411549.c 0000 0001 0704 9315 Department of Physics Engineering, Gaziantep University, Gaziantep, Türkiye
146 https://ror.org/02rc97e94 grid.7778.f 0000 0004 1937 0319 Dipartimento di Fisica, Università della Calabria, Rende, Italy
147 grid.6045.7 0000 0004 1757 5281 Laboratori Nazionali di Frascati, INFN Gruppo Collegato di Cosenza, Frascati, Italy
148 https://ror.org/01a8ajp46 grid.494717.8 0000 0001 2173 2882 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France
149 https://ror.org/00rs6vg23 grid.261331.4 0000 0001 2285 7943 Ohio State University, Columbus, OH USA
150 grid.16821.3c 0000 0004 0368 8293 Tsung-Dao Lee Institute, Shanghai, China
151 https://ror.org/00613ak93 grid.7787.f 0000 0001 2364 5811 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany
152 grid.266683.f 0000 0001 2166 5835 Department of Physics, University of Massachusetts, Amherst, MA USA
153 https://ror.org/05hs6h993 grid.17088.36 0000 0001 2195 6501 Department of Physics and Astronomy, Michigan State University, East Lansing, MI USA
154 https://ror.org/03zga2b32 grid.7914.b 0000 0004 1936 7443 Department for Physics and Technology, University of Bergen, Bergen, Norway
155 https://ror.org/0213rcc28 grid.61971.38 0000 0004 1936 7494 Department of Physics, Simon Fraser University, Burnaby, British Columbia Canada
156 https://ror.org/05qwgg493 grid.189504.1 0000 0004 1936 7558 Department of Physics, Boston University, Boston, MA USA
157 https://ror.org/033eqas34 grid.8664.c 0000 0001 2165 8627 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany
158 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 University of Chinese Academy of Science (UCAS), Beijing, China
159 https://ror.org/01rxvg760 grid.41156.37 0000 0001 2314 964X Department of Physics, Nanjing University, Nanjing, China
160 https://ror.org/01wntqw50 grid.7256.6 0000 0001 0940 9118 Department of Physics, Ankara University, Ankara, Türkiye
161 grid.411377.7 0000 0001 0790 959X Department of Physics, Indiana University, Bloomington, IN USA
162 https://ror.org/03ad39j10 grid.5395.a 0000 0004 1757 3729 Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy
163 https://ror.org/035b05819 grid.5254.6 0000 0001 0674 042X Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
164 https://ror.org/00xhcz327 grid.268217.8 0000 0000 8538 5456 Department of Physics, Westmont College, Santa Barbara, CA USA
165 grid.5590.9 0000000122931605 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University/Nikhef, Nijmegen, The Netherlands
166 https://ror.org/03dbr7087 grid.17063.33 0000 0001 2157 2938 Department of Physics, University of Toronto, Toronto, Ontario Canada
167 grid.7080.f 0000 0001 2296 0625 Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain
168 https://ror.org/037wpkx04 grid.10328.38 0000 0001 2159 175X Departamento de Física, Universidade do Minho, Braga, Portugal
169 https://ror.org/00qrf6g60 grid.470680.d 0000 0004 1761 7699 INFN Sezione di Lecce, Lecce, Italy
170 https://ror.org/03fc1k060 grid.9906.6 0000 0001 2289 7785 Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy
171 https://ror.org/04yqw9c44 grid.411198.4 0000 0001 2170 9332 Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil
172 https://ror.org/05fd1hd85 grid.26193.3f 0000 0001 2034 6082 High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia
173 https://ror.org/05gvnxz63 grid.187073.a 0000 0001 1939 4845 High Energy Physics Division, Argonne National Laboratory, Argonne, IL USA
174 https://ror.org/0220qvk04 grid.16821.3c 0000 0004 0368 8293 School of Physics and Astronomy, Shanghai Jiao Tong University, Key Laboratory for Particle Astrophysics and Cosmology (MOE), SKLPPC, Shanghai, China
175 https://ror.org/03cve4549 grid.12527.33 0000 0001 0662 3178 Physics Department, Tsinghua University, Beijing, China
176 https://ror.org/03jn38r85 grid.495569.2 The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China
177 https://ror.org/01y2jtd41 grid.14003.36 0000 0001 2167 3675 Department of Physics, University of Wisconsin, Madison, WI USA
178 grid.10784.3a 0000 0004 1937 0482 Department of Physics, Chinese University of Hong Kong, Shatin, Hong Kong
179 https://ror.org/03m2x1q45 grid.134563.6 0000 0001 2168 186X Department of Physics, University of Arizona, Tucson, AZ USA
180 https://ror.org/00zdnkx70 grid.38348.34 0000 0004 0532 0580 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
181 https://ror.org/02yhj4v17 grid.424881.3 0000 0004 0634 148X Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic
182 grid.8954.0 0000 0001 0721 6013 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia
183 https://ror.org/05tkyf982 grid.7489.2 0000 0004 1937 0511 Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel
184 grid.5390.f 0000 0001 2113 062X Dipartimento Politecnico di ngegneria e Architettura, Università di Udine, Udine, Italy
185 grid.9983.b 0000 0001 2181 4263 Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
186 grid.17682.3a 0000 0001 0111 3566 Università di Napoli Parthenope, Napoli, Italy
187 https://ror.org/014er3x17 grid.421197.8 Institute of Particle Physics (IPP), Victoria British Columbia, Canada
188 grid.470224.7 INFN-TIFPA, Povo, Italy
189 https://ror.org/05trd4x28 grid.11696.39 0000 0004 1937 0351 Università degli Studi di Trento, Trento, Italy
190 https://ror.org/038t36y30 grid.7700.0 0000 0001 2190 4373 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
191 https://ror.org/03rp50x72 grid.11951.3d 0000 0004 1937 1135 School of Physics, University of the Witwatersrand, Johannesburg, South Africa
192 https://ror.org/02ttsq026 grid.266190.a 0000 0000 9621 4564 Department of Physics, University of Colorado Boulder, Boulder CO, USA
193 https://ror.org/05vf0dg29 grid.8509.4 0000 0001 2162 2106 Dipartimento di Matematica e Fisica, Università Roma Tre, Roma, Italy
194 https://ror.org/04teye511 grid.7870.8 0000 0001 2157 0406 Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile
195 https://ror.org/00rbe2516 Millennium Institute for Subatomic physics at high energy frontier (SAPHIR), Santiago, Chile
196 https://ror.org/036rp1748 grid.11899.38 0000 0004 1937 0722 Instituto de Física, Universidade de São Paulo, São Paulo, Brazil
197 https://ror.org/02wj89n04 grid.412150.3 0000 0004 0648 5985 Faculté des Sciences, Université Ibn-Tofail, Kénitra, Morocco
198 https://ror.org/04q9esz89 grid.259237.8 0000 0001 2150 6076 Louisiana Tech University, Ruston, LA USA
199 https://ror.org/0207yh398 grid.27255.37 0000 0004 1761 1174 Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China
200 https://ror.org/00892tw58 grid.1010.0 0000 0004 1936 7304 Department of Physics, University of Adelaide, Adelaide South Australia, Australia
201 https://ror.org/04z8k9a98 grid.8051.c 0000 0000 9511 4342 Departamento de Física, Universidade de Coimbra, Coimbra, Portugal
202 grid.212340.6 0000000122985718 Borough of Manhattan Community College, City University of New York, New York, NY USA
203 https://ror.org/03tbh6y23 grid.11134.36 0000 0004 0636 6193 National Institute of Physics, University of the Philippines Diliman, Quezon City, Philippines
204 https://ror.org/03zsp3p94 grid.7144.6 0000 0004 0622 2931 Department of Financial and Management Engineering, University of the Aegean, Chios, Greece
205 https://ror.org/036jqmy94 grid.214572.7 0000 0004 1936 8294 University of Iowa, Iowa City, IA USA
206 https://ror.org/00f54p054 grid.168010.e 0000 0004 1936 8956 Department of Physics, Stanford University, Stanford, CA USA
207 https://ror.org/03rmrcq20 grid.17091.3e 0000 0001 2288 9830 Department of Physics, University of British Columbia, Vancouver, British Columbia Canada
208 grid.266832.b 0000 0001 2188 8502 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM USA
209 https://ror.org/038jp4m40 grid.6083.d 0000 0004 0635 6999 National Centre for Scientific Research ‘Demokritos’, Agia Paraskevi, Greece
210 https://ror.org/03bqmcz70 grid.5522.0 0000 0001 2337 4740 Marian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland
211 https://ror.org/0160cpw27 grid.17089.37 Department of Physics, University of Alberta, Edmonton, Alberta Canada
212 grid.449962.4 Centro Studi e Ricerche Enrico Fermi, Rome, Italy
213 https://ror.org/01c27hj86 grid.9983.b 0000 0001 2181 4263 Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal
214 https://ror.org/00te3t702 grid.213876.9 0000 0004 1936 738X University of Georgia, Tbilisi, Georgia
215 https://ror.org/0583a0t97 grid.14004.31 0000 0001 2182 0073 West University in Timisoara, Timisoara, Romania
216 grid.253561.6 0000 0001 0806 2909 California State University, Los Angeles, CA USA
217 https://ror.org/0371hy230 grid.425902.8 0000 0000 9601 989X Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain
218 https://ror.org/02956yf07 grid.20515.33 0000 0001 2369 4728 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan
219 https://ror.org/0244rem06 grid.263518.b 0000 0001 1507 4692 Department of Physics, Shinshu University, Nagano, Japan
220 https://ror.org/0112mx960 grid.32197.3e 0000 0001 2179 2105 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan
221 https://ror.org/04rswrd78 grid.34421.30 0000 0004 1936 7312 Department of Physics and Astronomy, Iowa State University, Ames, IA USA
222 grid.6936.a 0000000123222966 Technical University of Munich, Munich, Germany
223 https://ror.org/035t8zc32 grid.136593.b 0000 0004 0373 3971 Graduate School of Science, Osaka University, Osaka, Japan
224 National University of Science and Technology Politechnica, Bucharest, Romania
225 https://ror.org/02zhqgq86 grid.194645.b 0000 0001 2174 2757 Department of Physics, University of Hong Kong, Pok Fu Lam, Hong Kong
226 https://ror.org/025mx2575 grid.32140.34 0000 0001 0744 4075 Physics Department, Yeditepe University, Istanbul, Türkiye
227 https://ror.org/049emcs32 grid.267323.1 0000 0001 2151 7939 Physics Department, University of Texas at Dallas, Richardson, TX USA
228 https://ror.org/05fd1hd85 grid.26193.3f 0000 0001 2034 6082 E. Andronikashvili Institute of Physics, Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia
229 https://ror.org/051qn8h41 grid.428923.6 0000 0000 9489 2441 Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia
230 https://ror.org/04xe01d27 grid.412182.c 0000 0001 2179 0636 Instituto de Alta Investigación, Universidad de Tarapacá, Arica, Chile
231 https://ror.org/05fq50484 grid.21100.32 0000 0004 1936 9430 Department of Physics and Astronomy, York University, Toronto, Ontario Canada
232 https://ror.org/02kpeqv85 grid.258799.8 0000 0004 0372 2033 Faculty of Science, Kyoto University, Kyoto, Japan
233 https://ror.org/054pv6659 grid.5771.4 0000 0001 2151 8122 Universität Innsbruck, Department of Astro and Particle Physics, Innsbruck, Austria
234 Center for Interdisciplinary Research and Innovation (CIRI-AUTH), Thessaloniki, Greece
235 https://ror.org/01qq57711 grid.412848.3 0000 0001 2156 804X Department of Physics, Universidad Andres Bello, Santiago, Chile
236 https://ror.org/03tgsfw79 grid.31432.37 0000 0001 1092 3077 Graduate School of Science, Kobe University, Kobe, Japan
237 https://ror.org/02kq26x23 grid.55939.33 0000 0004 0622 2659 Hellenic Open University, Patras, Greece
238 https://ror.org/026vcq606 grid.5037.1 0000 0001 2158 1746 Department of Physics, Royal Institute of Technology, Stockholm, Sweden
239 https://ror.org/02v51f717 grid.11135.37 0000 0001 2256 9319 Center for High Energy Physics, Peking University, Beijing, China
240 grid.24515.37 0000 0004 1937 1450 Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Kowloon, Hong Kong China
241 https://ror.org/0064kty71 grid.12981.33 0000 0001 2360 039X School of Science, Shenzhen Campus of Sun Yat-sen University, Guangzhou, China
242 grid.424142.5 0000 0004 1803 4225 Centro Nacional de Microelectrónica (IMB-CNM-CSIC), Barcelona, Spain
243 grid.9983.b 0000 0001 2181 4263 Centro de Física Nuclear da Universidade de Lisboa, Lisboa, Portugal
244 https://ror.org/05bk57929 grid.11956.3a 0000 0001 2214 904X Department of Physics, Stellenbosch University, Stellenbosch, South Africa
245 grid.508721.9 0000 0001 2353 1689 L2IT, Université de Toulouse, CNRS/IN2P3UPS, Toulouse, France
246 grid.253564.3 0000 0001 2169 6543 Department of Physics, California State University, Sacramento, CA USA
247 https://ror.org/02p0gd045 grid.4795.f 0000 0001 2157 7667 Departamento de Física de Materiales, Universidad Complutense de Madrid, Madrid, Spain
248 https://ror.org/014hpw227 grid.440783.c 0000 0001 2219 7324 Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia
249 https://ror.org/00e5k0821 grid.440573.1 0000 0004 1755 5934 New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
250 https://ror.org/0384j8v12 grid.1013.3 0000 0004 1936 834X School of Physics, University of Sydney, Sydney, New South Wales Australia
251 https://ror.org/00g30e956 grid.9026.d 0000 0001 2287 2617 Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany
252 https://ror.org/00p4k0j84 grid.177174.3 0000 0001 2242 4849 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan
253 grid.410890.4 0000 0004 1772 8348 LPMR, Faculté des Sciences, Université Mohamed Premier, Oujda, Morocco
254 https://ror.org/01cg9ws23 grid.5120.6 0000 0001 2159 8361 Transilvania University of Brasov, Brasov, Romania
255 https://ror.org/05v0gvx94 grid.435410.7 0000 0004 0634 1551 National Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj-Napoca, Romania
256 https://ror.org/059yx9a68 grid.10689.36 0000 0004 9129 0751 Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia
257 https://ror.org/00engpz63 grid.412789.1 0000 0004 4686 5317 University of Sharjah, Sharjah, United Arab Emirates
258 grid.425050.6 0000 0004 0519 4756 Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Sofia, Bulgaria
259 https://ror.org/03j3dbz94 grid.265158.d 0000 0004 1936 8235 Washington College, Chestertown, MD USA
260 https://ror.org/01ht74751 grid.19208.32 0000 0001 0161 9268 Instituto de Investigación Multidisciplinario en Ciencia y Tecnología, y Departamento de Física, Universidad de La Serena, La Serena, Chile
261 https://ror.org/03ewx7v96 grid.412749.d 0000 0000 9058 8063 Division of Physics, TOBB University of Economics and Technology, Ankara, Türkiye
262 grid.425564.4 0000 0004 0587 3863 Institute of Physics and Technology, Mongolian Academy of Sciences, Ulaanbaatar, Mongolia
263 grid.47840.3f 0000 0001 2181 7878 University of California, Berkeley, CA USA
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Entanglement is a key feature of quantum mechanics1–3, with applications in fields such as metrology, cryptography, quantum information and quantum computation4–8. It has been observed in a wide variety of systems and length scales, ranging from the microscopic9–13 to the macroscopic14–16. However, entanglement remains largely unexplored at the highest accessible energy scales. Here we report the highest-energy observation of entanglement, in top–antitop quark events produced at the Large Hadron Collider, using a proton–proton collision dataset with a centre-of-mass energy of √s = 13 TeV and an integrated luminosity of 140 inverse femtobarns (fb)−1 recorded with the ATLAS experiment. Spin entanglement is detected from the measurement of a single observable D, inferred from the angle between the charged leptons in their parent top- and antitop-quark rest frames. The observable is measured in a narrow interval around the top–antitop quark production threshold, at which the entanglement detection is expected to be significant. It is reported in a fiducial phase space defined with stable particles to minimize the uncertainties that stem from the limitations of the Monte Carlo event generators and the parton shower model in modelling top-quark pair production. The entanglement marker is measured to be D = −0.537 ± 0.002 (stat.) ± 0.019 (syst.) for 340GeV<mtt¯<380GeV. The observed result is more than five standard deviations from a scenario without entanglement and hence constitutes the first observation of entanglement in a pair of quarks and the highest-energy observation of entanglement so far.

Entanglement was observed in top–antitop quark events by the ATLAS experiment produced at the Large Hadron Collider at CERN using a proton–proton collision dataset with a centre-of-mass energy of √s  = 13 TeV and an integrated luminosity of 140 fb−1.

Subject terms

Experimental particle physics
Particle physics
issue-copyright-statement© Springer Nature Limited 2024
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Particle colliders, such as the Large Hadron Collider (LHC) at CERN, probe fundamental particles and their interactions at the highest energies accessible in a laboratory, exceeded only by astrophysical sources. Beyond the fundamental interest of exploring quantum entanglement in a new setting, this observation demonstrates the potential of using high-energy colliders, such as the LHC, as tools for testing our fundamental understanding of quantum mechanics. Hadron colliders offer a truly relativistic environment and provide a rich variety of fundamental interactions, rarely considered for experiments in quantum information. Relativistic effects are expected to play a critical part in quantum information17 and the measurement described here illustrates the potential for new approaches to explore these effects and other foundational problems in quantum mechanics using colliders.

Recently, the heaviest fundamental particle known to exist, the top quark, was proposed as a new laboratory to study quantum entanglement and quantum information18,19. In this Article, the spin correlation between the top quark and antitop quark is used to probe the effects of quantum entanglement, in proton–proton (pp) collision events recorded with the ATLAS detector with a centre-of-mass energy of 13 TeV. Entanglement is observed with a significance of more than five standard deviations for the first time in pairs of quarks.

If two particles are entangled, the quantum state of one particle cannot be described independently of the other. The simplest example of an entangled system involves a pair of quantum bits (qubits); pieces of quantum information about two particles in the same quantum state that exist in superposition. The spin quantum number of a fundamental fermion, a particle that can take spin values of ±1/2, is one of the simplest and most fundamental examples of a qubit. Among the fundamental fermions of the standard model of particle physics, the top quark is uniquely suited for high-energy spin measurements because of its unique properties: its immense mass gives it a lifetime (about 10−25 s) notably shorter than the timescale needed for the quantum numbers of a quark to be shrouded by hadronization (around 10−24 s) and spin decorrelation (approximately 10−21 s) effects20. As a result, its spin information is transferred to its decay products. This unique feature provides an opportunity to study a pseudo-bare quark, free of the colour-confinement properties of the strong force that shrouds other quarks.

Quarks are most commonly produced in hadron collider experiments as matter–antimatter pairs. A pair of top–antitop quarks (tt¯) is a two-qubit system in which the spin quantum state is described by the spin density matrix ρ:ρ=14I4+ ∑iBi+σi⊗I2+Bi−I2⊗σi+ ∑i,jCijσi⊗σj.

The first term in the linear sum is a normalization constant, where In is the n × n identity matrix. The second term describes the intrinsic polarization of the top and the antitop quarks, where σi are the corresponding Pauli matrices and the real numbers Bi± characterize the spin polarization of each particle. The third term describes the spin correlation between the particles, encoded by the spin correlation matrix Cij. In all expressions, an orthogonal coordinate system is represented by the indices i, j = 1, 2, 3.

At hadron colliders, tt¯ pairs are produced mainly by the strong interaction and thus have no intrinsic polarization (that is, Bi±≃0) because of parity conservation and time invariance in quantum chromodynamics (QCD)21. However, the spins of these pairs are expected to be correlated, and this correlation has already been observed by both the ATLAS and CMS experiments at the LHC22–26. Entanglement in top-quark pairs can be observed by an increase in the strength of their spin correlations.

Owing to their short lifetime, top quarks cannot be detected directly in experiments. In the standard model, the top quarks decay almost exclusively into a bottom quark and a W boson, and the W boson subsequently decays into either a pair of lighter quarks or a charged lepton and a neutrino. In this measurement, only W bosons decaying into leptons are considered because charged leptons, especially electrons and muons, are readily detected with high precision at collider experiments. To a good approximation, the degree to which the leptons carry the spin information of their parent top quarks is 100% because of the maximally parity-violating nature of the electro-weak charged current. The angular direction of each of these leptons is correlated with the direction of the spin of their parent top quark or antitop quark in such a way that the normalized differential cross-section (σ) of the process may be written as271σdσdΩ+dΩ−=1+B+⋅q^+−B−⋅q^−−q^+⋅C⋅q^−(4π)2,

where q^+ is the antilepton direction in the rest frame of its parent top quark and q^− is the lepton direction in the rest frame of its parent antitop quark; and Ω+ is the solid angle associated with the antilepton and Ω− is the solid angle associated with the lepton. The vectors B± determine the top-quark and antitop-quark polarizations, whereas the matrix C contains their spin correlations. These terms are the same as those that appear in the general form for ρ. As the information about the polarizations and spin correlations of the short-lived top quarks is transferred to the decay leptons, their values can be extracted from a measurement of angular observables associated with these leptons, allowing us to reconstruct the tt¯ spin quantum state.

The experiments at the LHC ring, such as ATLAS, are the only ones currently taking data that are able to produce and study the properties of the top quark. At the LHC, tt¯ pairs are produced mainly by gluon–gluon fusion. When they are produced close to their production threshold, that is, when their invariant mass mtt¯ is close to twice the mass of the top quark (mtt¯~2⋅mt~350  GeV), approximately 80% of the production cross-section of tt¯ pairs arises from a spin-singlet state28–30, which is maximally entangled. After averaging over all possible top-quark directions, entanglement only survives close to the threshold because of the rotational invariance of the spin-singlet. This invariance implies that the trace (the sum of all of the diagonal elements) of the correlation matrix C, in which each diagonal element corresponds to the spin correlation in a particular direction, is a good entanglement witness. It is an observable that can signal the presence of entanglement, with tr(C) + 1 < 0 as a sufficient condition for entanglement18. It can be understood as a violation of a Cauchy–Schwarz inequality, a notable entanglement criterion in fields such as quantum optics, condensed matter or analogue gravity31–34.

It is more convenient to define an entanglement marker by using D = tr[C]/3 (ref. 18), which can be experimentally measured asD=−3⟨cosφ⟩,

where ⟨cos φ⟩ is the average value of the cosine of the angle (dot product) between the charged-lepton directions after they have been subjected to Lorentz boosting into the tt¯ rest frame and then the rest frames of their parent top-quark and antitop-quark, which can be measured experimentally in an ensemble dataset. The existence of an entangled state is demonstrated if the measurement satisfies D < −1/3, derived from the Peres–Horodecki criterion35,36 and is independent of the order of the calculation. It should be noted that the CMS collaboration has already measured D = −0.237 ± 0.011 (ref. 26) inclusively, showing no signal of entanglement.

The standard model is a quantum theory, and entanglement is implicitly present in its predictions. Nevertheless, a demonstration of spin entanglement in tt¯ pairs is challenging because of the inability to control the internal degrees of freedom in the initial state19. Currently, entanglement can be detected only with the help of a dedicated analysis in a restricted phase space such as the one presented here.

The ATLAS detector and event samples

The ATLAS experiment37–39 at the LHC is a multipurpose particle detector with a forward–backward symmetric cylindrical geometry and a solid-angle coverage of almost 4π. It is used to record particles produced in LHC collisions through a combination of particle position and energy measurements. The coordinate system is defined in the section ‘Object identification in the ATLAS detector’. It consists of an inner-tracking detector surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field, electromagnetic and hadronic calorimeters, and a muon spectrometer. The muon spectrometer surrounds the calorimeters and is based on three large superconducting air-core toroidal magnets with eight coils each providing a field integral of between 2.0 T m and 6.0 T m across the detector. An extensive software suite40 is used in data simulation, the reconstruction and analysis of real and simulated data, detector operations, and the trigger and data acquisition systems of the experiment. The complete dataset of pp collision events with a centre-of-mass energy of √s = 13 TeV collected with the ATLAS experiment during 2015–2018 is used, corresponding to an integrated luminosity of 140 fb−1. This analysis focuses on the data sample recorded using single-electron or single-muon triggers41.

A unique feature of particle physics is that very precise simulations of the standard model can be realized through the use of Monte Carlo event generators. These simulations replicate real collisions and their resultant particles on an event-by-event basis, and these events can be passed through sophisticated simulations of the ATLAS detector to produce simulated data. Comparing these simulated events with those recorded by the detector is one way to test the predictions of the standard model. Another is to use the simulated data to model how the ATLAS detector responds to a particular physics process, such as the pair production of top quarks, and to use these data to create corrections to undo the effect of the detector response on real data and then to compare these corrected data with theoretical predictions. This measurement uses the latter strategy.

Three distinct types of real and simulated data are used, each with associated physics objects. Detector level refers to real data before they have been corrected for detector effects and simulated data after they have been passed through simulation of the ATLAS detector. Parton level refers to simulated Monte Carlo events in which the particles arise from the fundamental interaction being simulated, such as quarks and bosons, or to real collision data that have been corrected to this level. Particle level refers to simulated data with physics objects that are built only from the stable particles that remain after the decay of the particles that exist at parton level, that is, particles that live long enough to interact with the detector, or to real data that have been corrected to this level. This measurement relies on the selection and reconstruction of muons, electrons, quarks and gluons as hadronic jets, neutrinos as missing transverse momentum (pTmiss), W bosons and top quarks. These objects are each reconstructed at the detector level, particle level and parton level. Details of how these objects are reconstructed in ATLAS and Monte Carlo simulations are provided in the section ‘Object identification in the ATLAS detector’.

Monte Carlo event simulations are used to model the tt¯ signal and the expected standard model background processes. The production of tt¯ events was modelled using the POWHEG BOX v.2 heavy-quark (hvq) (refs. 42–45) generator at next-to-leading order (NLO) precision in QCD and the events were interfaced to either PYTHIA 8.230 (ref. 46) or HERWIG 7.2.1 (refs. 47,48) to model the parton shower and hadronization. The decays of the top quarks, including their spin correlations, were modelled at leading-order (LO) precision in QCD. An additional sample that generates tt¯ events at full NLO accuracy in production and decay was generated using the POWHEG BOX RES (bb4ℓ) (refs. 49,50) generator, interfaced to PYTHIA. Further details of the setup and tuning of these generators are provided in the section ‘Monte Carlo simulation’. An important difference between PYTHIA and HERWIG is that the former uses a pT-ordered shower, whereas the latter uses an angular-ordered shower (see section ‘Parton shower and hadronization effects’). Another important consideration is that full information on the spin density matrix is not passed to the parton shower programs and, therefore, is not fully preserved during the shower.

The standard model background processes that contribute to the analysis are the production of a single top quark with a W boson (tW), pair production of top quarks with an additional boson tt¯+X (X = H, W, Z) and the production of dileptonic events from either one or two massive gauge bosons (W and Z bosons). The generators for the hard-scatter processes and the showering are listed in the section ‘Monte Carlo simulation’. The procedure for identifying and reconstructing detector-level objects is the same for data and Monte Carlo events.

Analysis procedure

Only events taken during stable-beam conditions, and for which all relevant components of the detector were operational, are considered. To be selected, events must have exactly one electron and one muon with opposite-sign electric charges. A minimum of two jets is required, and at least one of them must be identified to originate from a b-hadron (b-tagged).

The background contribution of events with reconstructed objects that are misidentified as leptons, referred to as the ‘fake-lepton’ background, is estimated using a combination of Monte Carlo prediction and correction based on data. This data-driven correction is obtained from a control region dominated by fake leptons. It is defined by using the same selection criteria as above, except that the two leptons must have the same-sign electric charges. The difference between the numbers of observed events and predicted events in this region is taken as a scale factor and applied to the predicted fake-lepton events in the signal region.

Events that pass the event selection are separated into three analysis regions, based on the detector-level, particle-level or parton-level mtt¯, depending on the region. The signal region is constructed to be dominated by events that are as close to the production threshold as the resolution of the reconstruction method will allow, as this is the region in which the entanglement of the top quarks is expected to be maximized.

The optimal mass window for the signal region was determined to be 340<mtt¯<380GeV. Two additional validation regions are defined to validate the method used for the measurement. First, a region is defined close to the limit in which entanglement is not expected to be observable, and also with sizeable dilution from mis-reconstructed events from non-entangled regions, by requiring 380<mtt¯<500GeV. Second, a region in which no signal of entanglement is expected is defined with mtt¯>500GeV. Each of the regions has a tt¯-event purity of more than 90%. The dominant sources of background processes arise from tW and fake-lepton, accounting for 56% and 27% of the background in the signal region, respectively. The remaining 17% of background events arise from tt¯+X and the production of dileptonic events from either one or two massive gauge bosons. The distribution of cos φ in the signal region and the detector-level Ddetector value, built from the cos φ at the reconstructed detector level and after background subtraction, are shown in Fig. 1a,b.Fig. 1 Detector-level results.

a, The cos φ observable in the signal region at the detector level. b, The entanglement marker D, calculated from the detector-level distributions, from three different Monte Carlo generators; the POWHEG + PYTHIA and POWHEG + HERWIG heavy-quark models, labelled Pow+Py (hvq) and Pow+H7 (hvq), respectively, and the POWHEG + PYTHIA bb4ℓ model, labelled Pow + Py (bb4ℓ), are shown after background processes are subtracted. The uncertainty band shows the uncertainties from all sources added in quadrature. The ratios of the predictions to the data are shown at the bottom of a and b. The quoted value for D for the bb4ℓ model also includes subtraction of the single-top-quark background.

To compare the data with calculations and correct for detector effects, we must also define an event selection using the ‘truth’ information in the Monte Carlo event record. This selection uses particle-level objects to match as closely as possible the selection at the detector level and is called a fiducial particle-level selection. Particle-level events are required to contain exactly one electron and one muon with opposite-sign electric charges and at least two particle-level jets, one of which must contain a b-hadron. The cos φ distribution is then constructed from the particle-level top quarks and charged leptons in the same manner as at the detector level.

The response of the detector, the event selections and the top-quark reconstruction distort the shape of the cos φ distribution. The observed distribution is corrected for these effects with a simple method: a simulation-based calibration curve that connects any value at the detector level to the corresponding value at the particle level. We correct the data for detector effects by using a unique calibration curve built for each signal and validation region based on the expected signal model, after subtracting the expected contribution from background processes. Owing to the limited resolution of the reconstructed mass of the tt¯ system, some events that truly belong to the validation regions can enter the signal region at the detector level. These events are treated as detector effects.

To build these curves, Monte Carlo event samples are created with alternative values of D by reweighting the events, following the procedure described in the section ‘Reweighting the cos φ distribution’. The calibration curve corrects the value Ddetector measured at the detector level to a corresponding value Dparticle at the particle level. To construct the calibration curve, several hypotheses for different values of D, denoted by Dparticle′ with a corresponding Ddetector′ value, are created corresponding to the changes in the expected value of entanglement.

The pairs of Ddetector′ and Dparticle′ are plotted in Fig. 2a. A straight line interpolates between the points. With this calibration curve, any value for Ddetector can be calibrated to the particle level.Fig. 2 Summary of results.

a, Calibration curve for the dependence between the particle-level value of D and the detector-level value of D in the signal region. The yellow band represents the statistical uncertainty, and the grey band represents the total uncertainty obtained by adding the statistical and systematic uncertainties in quadrature. The measured values and expected values from POWHEG + PYTHIA 8 (hvq) are marked with black and red circles, respectively, and the entanglement limit is shown as a dashed line. b, The particle-level D results in the signal and validation regions compared with various Monte Carlo models. The entanglement limit shown is a conversion from its parton-level value of D = −1/3 to the corresponding value at the particle level, and the uncertainties that are considered for the band are described in the text.

Three categories of uncertainties are included in the calibration curves: uncertainties in modelling tt¯ production and decay, uncertainties in modelling the backgrounds and detector-related uncertainties for both the tt¯ signal and the standard model background processes. Each source of systematic uncertainty can result in a different calibration curve because it changes the shape of the cos φ distribution at the particle level and/or detector level. For each source of systematic uncertainty, the data are corrected using this new calibration curve, and the resultant deviation from the data corrected by the nominal curve is taken as the systematic uncertainty of the data due to that source. Systematic uncertainties from all sources are summed in quadrature to determine the final uncertainty in the result.

For all of the detector-related uncertainties, the particle-level quantity is not affected and only detector-level values change. For signal modelling uncertainties, the effects at the particle level propagate to the detector level, resulting in shifts in both. Uncertainties in modelling the background processes affect how much background is subtracted from the expected or observed data and can, therefore, cause changes in the calibration curve. These uncertainties are treated as fully correlated between the signal and background (that is, if a source of systematic uncertainty is expected to affect both the signal and background processes, this is estimated simultaneously and not separately).

A summary of the different sources of systematic uncertainty and their impact on the result is given in Table 1. The size of each systematic uncertainty depends on the value of D and is given in Table 1 for the standard model prediction, calculated with POWHEG + PYTHIA. The systematic uncertainties considered in the analysis are described in detail in the section ‘Systematic uncertainties’.Table 1 Summary of uncertainties

Source of uncertainty	ΔDobserved (D = −0.537)	ΔDobserved (%)	ΔDexpected (D = −0.470)	ΔDexpected (%)	
Signal modelling	0.017	3.2	0.015	3.2	
Electrons	0.002	0.4	0.002	0.4	
Muons	0.001	0.2	0.001	0.1	
Jets	0.004	0.7	0.004	0.8	
b-Tagging	0.002	0.4	0.002	0.4	
Pile-up	<0.001	<0.1	<0.001	<0.1	
ETmiss	0.002	0.4	0.002	0.4	
Backgrounds	0.005	0.9	0.005	1.1	
Total statistical uncertainty	0.002	0.3	0.002	0.4	
Total systematic uncertainty	0.019	3.5	0.017	3.6	
Total uncertainty	0.019	3.5	0.017	3.6	
A summary of the effect of the groups of uncertainties at the expected standard model value of Dexpected = −0.470, corresponding to the POWHEG + PYTHIA modelling, and the observed value Dobserved = −0.537, both in the signal region. ETmiss denotes the magnitude of the missing transverse momentum. The total systematic uncertainty is calculated as the sum in quadrature of the individual groups of systematic uncertainties.

To compare the particle-level result with the parton-level entanglement limit D < −1/3, the limit must be folded to the particle level. A second calibration curve is constructed to relate the value of Dparton to the corresponding Dparticle. The definitions of parton-level top quarks and leptons in the Monte Carlo generator follow ref. 24 and correspond approximately to those of stable top quarks and leptons in a fixed-order calculation. Only systematic uncertainties related to the modelling of the tt¯ production and decay process are considered while building this calibration curve. The migration of the parton-level events from the signal region into the validation regions at the particle level and vice versa is very small.

The calibration procedure is performed in the signal region and the two validation regions to correct the data to a fiducial phase space at the particle level, as described in the previous section. All systematic uncertainties are included in the three regions. The observed (expected) results areD=−0.537±0.002(stat.)±0.019(syst.)(−0.470±0.002(stat.)±0.017(syst.)),

in the signal region of 340<mtt¯<380GeV andD=−0.265±0.001(stat.)±0.019(syst.)(−0.258±0.001(stat.)±0.019(syst.)),

D=−0.093±0.001(stat.)±0.021(syst.)(−0.103±0.001(stat.)±0.021(syst.)),

in the validation regions of 380<mtt¯<500GeV and mtt¯>500GeV, respectively. The expected values are those predicted by POWHEG + PYTHIA. The calibration curve for the signal region and a summary of the results in all regions are presented in Fig. 2.

The observed values of the entanglement marker D are compared with the entanglement limit in Fig. 2b. The parton-level bound D = −1/3 is converted to a particle-level bound by folding the limit to particle level to better highlight the differences between the predictions using different parton shower orderings. For POWHEG + PYTHIA, this yields −0.322 ± 0.009, in which the uncertainty includes all uncertainties in the POWHEG + PYTHIA model except the parton shower uncertainty (for more details of these uncertainties, see section ‘Systematic uncertainties’). Similarly, for POWHEG + HERWIG, with an angular-ordered parton shower, a value of −0.27 is obtained. No uncertainties are assigned in this case because it is merely used as an alternative model.

Discussion

In both of the validation regions, with no entanglement signal, the measurements are found to agree with the predictions from different Monte Carlo setups within the uncertainties. This serves as a consistency check to validate the method used for the measurement.

Although the different models yield different predictions, the current precision of the measurements in the validation regions does not allow us to rule out any of the Monte Carlo setups that were used. It is important to note that close to the threshold, non-relativistic QCD processes, such as Coulomb bound state effects, affect the production of tt¯ events28 and are not accounted for in the Monte Carlo generators. The main impact of these effects is to change the line shape of the mtt¯ spectrum. The impact of these missing effects was tested by introducing them with an ad hoc reweighting of the Monte Carlo based on theoretical predictions, and the effect was found to be 0.5%. Other systematic uncertainties on the top-quark decay (1.6%) and top-quark mass (0.7%) also similarly change the line shape within our experimental resolution and have a much larger impact. Therefore, the ad hoc reweighting is not included by default in the measurement because including it would not change the sensitivity of the result within the precision quoted.

In the signal region, the POWHEG + PYTHIA and POWHEG+ HERWIG generators yield different predictions. The size of the observed difference is consistent with changing the method of shower ordering and is discussed in detail in the section ‘Parton shower and hadronization effects’.

In the signal region, the observed and expected significances with respect to the entanglement limit are well beyond five standard deviations, independently of the Monte Carlo model used to correct the entanglement limit to account for the fiducial phase space of the measurement. This is shown in Fig. 2b, in which the hypothesis of no entanglement is shown. The observed result in the region with 340GeV<mtt¯<380GeV establishes the formation of entangled tt¯ states. This constitutes the first observation of entanglement in a quark–antiquark pair.

Apart from the fundamental interest in testing quantum entanglement in a new environment, this measurement in top quarks paves the way to use high-energy colliders, such as the LHC, as a laboratory to study quantum information and foundational problems in quantum mechanics. From a quantum information perspective, high-energy colliders are particularly interesting because of their relativistic nature and the richness of the interactions and symmetries that can be probed there. Furthermore, highly demanding measurements, such as measuring quantum discord and reconstructing the steering ellipsoid, can be naturally implemented at the LHC because of the vast number of available tt¯ events51. From a high-energy physics perspective, borrowing concepts from quantum information theory inspires new approaches and observables that can be used to search for physics beyond the standard model52–55.

Methods

Object identification in the ATLAS detector

ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the interaction point to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, ϕ) are used in the transverse plane, where ϕ is the azimuth angle around the z-axis. The pseudorapidity is defined in terms of the polar angle θ as η = −ln tan(θ/2). Angular distance is measured in units of ΔR≡(Δη)2+(Δϕ)2.

Reconstructed (detector-level) objects are defined as follows. Electron candidates are required to satisfy the ‘tight’ likelihood-based identification requirement as well as calorimeter- and track-based isolation criteria56 and have pseudorapidity ∣η∣ < 1.37 or 1.52 < ∣η∣ < 2.47. Muon candidates are required to satisfy the ‘medium’ identification requirement as well as track-based isolation criteria57–59 and have ∣η∣ < 2.5. Electrons and muons must have a minimum transverse momentum (pT) of 25–28 GeV, depending on the data-taking period. Showers of particles (jets) that arise from the hadronization of quarks and gluons60 are reconstructed from particle-flow objects61, using the anti-kt algorithm62,63 with a radius parameter R = 0.4, a pT threshold of 25 GeV and a ∣η∣ < 2.5 requirement. Objects can fulfil the criteria for both jet and lepton selections, necessitating the implementation of an overlap removal procedure. This way, objects are associated with a singular hypothesis. First, any electron candidates that share a track with a muon candidate are removed. Subsequently, jets within ΔR = 0.2 of an electron are removed, and afterwards, electrons within a region 0.2 < ΔR < 0.4 around any remaining jet are rejected. Jets that have fewer than three tracks and are within ΔR = 0.2 of a muon candidate are removed, and muons within ΔR = 0.4 of any remaining jet are discarded. A Jet-Vertex-Tagger (JVT) requirement is applied to jets with pT < 60 GeV and ∣η∣ < 2.4 to suppress jets originating from additional interactions in the same or neighbouring bunch crossings (pile-up)64. Jets are tagged as containing b-hadrons using the DL1r tagger65 with a b-tagging efficiency of 85%. Missing transverse momentum (pTmiss) (refs. 66,67) is determined from the imbalance in the transverse momenta of all reconstructed objects.

To measure D, the top quarks must be reconstructed from their measured decay products. In the tt¯ dileptonic decay, apart from charged leptons and jets, there are two neutrinos that are not measured by the detector. Several methods are available to reconstruct the top quarks from the detector-level charged leptons, jets and pTmiss. The main method used in this work is the Ellipse method68, which is a geometric approach to analytically calculate the neutrino momenta. This method yields at least one real solution in 85% of events. We always choose the solution with the lowest top-quark pair invariant mass, to populate the region that is close to the threshold. If this method fails (for example, the resultant solutions are all complex), the Neutrino Weighting method69 is used. The Neutrino Weighting method assigns a weight to each possible solution by assessing the compatibility of the neutrino momenta and the pTmiss in the event, after scanning possible values of the pseudorapidities of the neutrinos. In this analysis, the Neutrino Weighting method is only used in a small fraction of events (about 5%). Furthermore, in ref. 24, it was used in all events and the performance was found to be the same between samples that include and exclude spin correlation. If both methods fail, a simple pairing of each lepton with its closest b-tagged jet is used as proxies for the top- and antitop-quark, and no attempt is made to reconstruct the neutrinos. If a second b-tagged jet is not present in the event, the leading (highest) pT untagged jet is used instead. In all cases, a W boson mass of 80.4 GeV and a top-quark mass of 172.5 GeV are used as input parameters.

In simulated events, parton-level objects are taken directly from the Monte Carlo history information and are required to have a status code of 1, indicating that they are the fundamental particles (partons) of the interaction. Top quarks are required to be partons that decay to a W boson and a b quark, whereas charged leptons are required to be the immediate decay parton from the W boson from the top quark. Particle-level objects are reconstructed using simulated stable particles in the Monte Carlo simulation before their reconstruction in the detector but after hadronization. A particle is defined as stable if it has a mean lifetime greater than 30 ps, within the pseudorapidity acceptance of the detector. The selection criteria for the particle-level objects are chosen to correspond as closely as possible to the criteria applied to the detector-level objects. Electrons, muons and neutrinos are required to come from the electroweak decay of a top quark and are discarded if they arise from the decay of a hadron or a τ-lepton. Electrons and muons are then ‘dressed’ by summing their four momenta with any prompt photons within ΔR = 0.1. Electrons and muons must also be well separated from jet activity. If they lie within ΔR < 0.4 from a jet, they are removed from the event. Leptons are also required to have pT > 10 GeV and ∣η∣ < 2.5, and at least one lepton must have pT > 25 GeV. Jets are built by clustering all stable particles, using the anti-kt algorithm with a radius parameter of R = 0.4 and are tagged as containing b-hadrons if they have at least one ghost-matched b-hadron70,71 with pT > 5 GeV. Jets are also required to have pT > 25 GeV and ∣η∣ < 2.5. Each W boson is reconstructed by combining an available electron and electron neutrino or muon and muon neutrino. The top quark and antitop quark are reconstructed by pairing the two leading b-tagged jets, or the b-tagged jet and the highest-pT untagged jet in events with only one b-tag, with the reconstructed W bosons. Both potential jet–lepton combinations are formed and the one that minimizes ∣mt − m(W1 + b1/2)∣ + ∣mt − m(W2 + b2/1)∣ is taken as the correct pairing, where mt denotes the mass of the top quark, b1/2 denotes the two jets selected for the reconstruction, W1/2 refers to the reconstructed W bosons and m is the invariant mass of the objects in brackets.

Monte Carlo simulation

The production of tt¯ events was modelled using the POWHEG BOX v.2 heavy-quark (hvq) (refs. 42–45) event generator. This generator uses matrix elements calculated at next-to-leading-order (NLO) precision in a strong coupling constant power expansion in QCD with the NNPDF3.0NLO (ref. 72) parton distribution function (PDF) set and the hdamp parameter set to 1.5mt (ref. 73). The hdamp parameter is a resummation damping factor and one of the parameters that control the matching of POWHEG matrix elements to the parton shower and thus effectively regulates the high-pT radiation against which the system recoils. The decays of the top quarks, including their spin correlations, were modelled at leading-order (LO) precision in QCD. As an alternative, the POWHEG BOX RES (refs. 49,50) event generator, developed to treat decaying resonances within the POWHEG BOX framework and including off-shell and non-resonant effects in the matrix element calculation, was used to produce an additional event sample, labelled as bb4ℓ in the following. Although bb4ℓ is the higher-precision Monte Carlo sample, it cannot be compared directly with the data after they are corrected for detector effects as it is not possible to remove its off-shell component in a formally correct way. However, the effect of using this model was tested approximately and was found to not significantly change the conclusions of the measurement.

In the bb4ℓ event sample, spin correlations are calculated at NLO, and full NLO accuracy in tt¯ production and decays is attained. To model the parton shower, hadronization and underlying event, the events from both POWHEG BOX v.2 and POWHEG BOX RES were interfaced to PYTHIA 8.230 (ref. 46), with parameters set according to the A14 set of tuned parameters74 and using the NNPDF2.3LO set of PDFs75. Similarly, the events from POWHEG BOX v.2 (hvq) were also interfaced with HERWIG 7.2.1 (refs. 47,48), using the HERWIG 7.2.1 default set of tuned parameters. The decays of bottom and charm hadrons were performed by Evtgen 1.6.0 (ref. 76). The spin information from the matrix element calculation is not passed to the parton shower programs and, therefore, is not fully preserved during the shower.

All simulated event samples include pile-up interactions, and the events are reweighted to reproduce the observed distribution of the average number of collisions per bunch crossing.

Reweighting the cos φ distribution

To construct the calibration curve, templates for alternative scenarios with different degrees of entanglement, and therefore with different values of D, must be extracted. The degree of entanglement is intrinsic in the calculations of the Monte Carlo event generators. However, the effects of entanglement can be directly accessed using D, measured from the average of the cos φ distribution in the event. Therefore, an event-by-event reweighting based on D is used to vary the degree of entanglement. Although the measurement uses detector-level and particle-level objects, the observable D is changed at the parton level, at which it is directly related to the entanglement between the top and antitop spins. Therefore, each event is reweighted according to its parton-level values of mtt¯ and cos φ, as described below.

The entanglement marker D is extracted at the parton level from the cos φ distribution by using either the mean of the distribution D = −3 · ⟨cos φ⟩ or the slope of the normalized differential cross-section (1/σ)dσ/dcosφ=(1/2)(1−Dcosφ).

For simplicity, the analysis always uses the mean of the distribution, although the two methods are equivalent. Thus, for the purpose of reweighting, we must change the slope of the cos φ distribution at the parton level. Each event is reweighted according to this slope, which in turn changes the distributions at the particle level and detector level.

The observable D depends on the invariant mass of the tt¯ system, mtt¯. To perform the reweighting, the differential value of D per mass unit as a function of mtt¯, DΩ(mtt¯), has to be calculated. This is achieved by fitting a third-order polynomial of the formDΩ(mtt¯)=x0+x1⋅mtt¯−1+x2⋅mtt¯−2+x3⋅mtt¯−3,

where x0, x1, x2 and x3 are constants. This parametrization was found to describe well the value of DΩ(mtt¯), in good agreement with the Monte Carlo prediction. The values of the parameters of DΩ(mtt¯) depend on the Monte Carlo event generator and have to be calculated for the nominal sample and for the effect of each of the tt¯ theory systematic uncertainties, as they change the parton-level cos φ values and thus DΩ(mtt¯).

The reweighting method is a simple scaling of the cos φ distribution according to the desired new value of D. This is done by assigning a weight w to each event at parton level asw=1−DΩ(mtt¯)⋅X⋅cosφ1−DΩ(mtt¯)⋅cosφ,

with X as the scaling hypothesis of D. If, for example, X=1.2, it means that D is scaled up by 20% relative to its nominal value. To build the calibration curve, four alternative values of D are considered, with X=0.4,0.6,0.8,1.2, in addition to the nominal value without reweighting (X=1.0). It is important to note that these X values change D across the entire mtt¯ spectrum. In Extended Data Fig. 1, the parton-level distribution of D is shown in the signal region before and after reweighting.

Background modelling

Simulated data in the form of Monte Carlo samples were produced using either the full ATLAS detector simulation77 based on the GEANT4 framework78 or, for the estimation of some of the systematic uncertainties, a faster simulation with parameterized showers in the calorimeters79. The effect of pile-up was modelled by overlaying each hard-scattering event with inelastic pp collisions generated with PYTHIA 8.186 (ref. 80) using the NNPDF2.3LO set of PDFs75 and the A3 set of tuned parameters81. Except for the events simulated with SHERPA, the EVTGEN program was used to simulate bottom and charm hadron decays. If not mentioned otherwise, the top-quark mass was set to mt = 172.5 GeV. All event samples that were interfaced with PYTHIA used the A14 set of tuned parameters74 and the NNPDF2.3LO PDF set.

Single-top quark tW associated production was modelled using the POWHEG BOX v.2 (refs. 43–45,82) event generator, which provides matrix elements at NLO in the strong coupling constant αs in the five-flavour scheme with the NNPDF3.0NLO (ref. 72) PDF set. The functional form of the renormalization and factorization scales was set to the default scale, which is equal to the top-quark mass. The diagram-removal scheme83 was used to handle the interference with tt¯ production73. The inclusive cross-section was corrected to the theoretical prediction calculated at NLO in QCD with next-to-next-leading-logarithm (NNLL) soft-gluon corrections84,85. For pp collisions at a centre-of-mass energy of √s = 13 TeV, this cross-section corresponds to σ(tW)NLO+NNLL = 71.7 ± 3.8 pb. The uncertainty in the cross-section due to the PDF was estimated using the MSTW2008NNLO 90%CL (refs. 86,87) PDF set and was added in quadrature to the effect of the scale uncertainty.

Samples of diboson final states (VV), where V denotes a W or Z boson, were simulated with the SHERPA 2.2.2 (ref. 88) event generator, including off-shell effects and Higgs boson contributions, where appropriate. Fully leptonic final states and semileptonic final states, in which one boson decays leptonically and the other hadronically, were generated using matrix elements at NLO accuracy in QCD for up to one additional parton and at LO accuracy for up to three additional parton emissions. Samples for the loop-induced processes gg → VV were generated using LO-accurate matrix elements for up to one additional parton emission for both the cases of fully leptonic and semileptonic final states. The matrix element calculations were matched and merged with the SHERPA parton shower based on Catani–Seymour dipole factorization89,90 using the MEPS@NLO prescription91–94. The virtual QCD corrections were provided by the OPENLOOPS library95–97. The NNPDF3.0NNLO set of PDFs was used72, along with the dedicated set of tuned parton-shower parameters developed by the SHERPA authors.

The production of V + jets events was simulated with the SHERPA 2.2.11 (ref. 88) event generator using NLO matrix elements for up to two partons, and LO matrix elements for up to five partons, calculated with the Comix (ref. 89) and OPENLOOPS 2 (refs. 95–98) libraries. They were matched with the SHERPA parton shower90 using the MEPS@NLO prescription91–94. The set of tuned parameters developed by the SHERPA authors was used, along with the NNPDF3.0NNLO set of PDFs72.

The production of tt¯V events was modelled using the MADGRAPH5_AMC@NLO 2.3.3 (ref. 99) event generator, which provides matrix elements at NLO in the strong coupling constant αs with the NNPDF3.0NLO (ref. 72) PDFs. The functional form of the renormalization and factorization scales was set to 0.5×∑imi2+pT,i2, where the sum runs over all the particles generated from the matrix element calculation. Top quarks were decayed at LO using MADSPIN (refs. 100,101) to preserve spin correlations. The events were interfaced with PYTHIA 8.210 (ref. 46) for the simulation of parton showering and hadronization. The cross-sections were calculated at NLO QCD and NLO EW accuracy using MADGRAPH5_AMC@NLO as reported in ref. 102. For tt¯ℓℓ events, the cross-section was scaled by an off-shell correction estimated at one-loop level in αs.

The production of tt¯H events was modelled using the POWHEG BOX v.2 (refs. 42–45,103) event generator, which provides matrix elements at NLO in the strong coupling constant αs in the five-flavour scheme with the NNPDF3.0NLO (ref. 72) PDF set. The functional form of the renormalization and factorization scales was set to mT(t)⋅mT(t¯)⋅mT(H)3. The events were interfaced with PYTHIA 8.230. The cross-section was calculated at NLO QCD and NLO EW accuracy using MADGRAPH5_AMC@NLO as reported in ref. 102. The predicted value at √s = 13 TeV is 507−50+35fb, for which the uncertainties were estimated from variations of both αs and the renormalization and factorization scales.

The background from non-prompt or fake leptons was modelled using simulated Monte Carlo events to describe the shape of the kinematic distributions. Monte Carlo event generator information is used to distinguish events with prompt leptons from events with non-prompt or fake leptons. The normalization of this background was obtained from data by using a dedicated control region. This control region uses the same basic event selection as the signal and validation regions, the only difference being that the electric charges of the electron and muon must have the same sign. Within this control region, the number of simulated prompt-lepton events is subtracted from the observed number of data events. The number of events remaining is then divided by the number of simulated fake-lepton events, resulting in a normalization factor of 1.4. This scale factor is then applied to the simulated fake-lepton events in the signal and validation regions.

Systematic uncertainties

The systematic uncertainties can be divided into three separate categories: signal modelling uncertainties, which stem from the theory prediction of tt¯ production; object systematic uncertainties, which arise from the uncertainty in the detector response to objects used in the analysis; and background modelling systematic uncertainties, which are related to the theory prediction of the standard model backgrounds. All systematic uncertainties, grouped according to their sources, are described in the following sections. The signal modelling uncertainties were found to dominate the overall uncertainty of this measurement.

For each source of systematic uncertainty, a new calibration curve is created and the simulated (or observed) data are corrected, resulting in a shifted corrected result. In most cases, the systematic uncertainty is taken to be the difference between the nominal expected and observed result and the systematically shifted result. In cases in which a systematic shift only affects the background model (for example, background cross-section uncertainties), the systematically shifted background sample is subtracted from the data instead before the calibration is performed. In cases in which the systematic uncertainty is one-sided, the uncertainty is symmetrized. In cases in which the uncertainties are asymmetric, the larger of the two variations is symmetrized. The signal modelling uncertainties dominate the measurement, and their estimated sizes are presented in Extended Data Table 1.

Signal modelling uncertainties

Signal modelling uncertainties are those related to the choice of POWHEG BOX + PYTHIA as the nominal Monte Carlo setup as well as those affecting the theoretical calculation itself. These systematic uncertainties are considered in two forms: alternative event generators and weights. For the alternative-generator uncertainties, the difference between the calibrated values of D is taken as the systematic uncertainty. For the systematic uncertainties involving weights, the difference between the calibrated D values for the nominal sample and the weight-shifted sample is taken as the uncertainty. These uncertainties follow the description in ref. 104 and are enumerated as follows:pThard setting: the region of phase space that is vetoed in the showering when matched to a parton shower is varied by changing the internal pThard parameter of POWHEG BOX from 0 to 1, as described in ref. 105.

Top-quark decay: the uncertainty in the modelling of the decay of the top quarks and of the mtt¯ line shape is estimated by comparing the nominal decay in POWHEG BOX with the decays modelled with MADSPIN (refs. 100,101). The effect of this uncertainty is to shift the mtt¯ line shape to lower or higher values that alter the degree of entanglement entering the signal region. Thus, this is one of the most impactful sources of systematic uncertainty.

NNLO QCD + NLO EW reweighting: the uncertainty due to missing higher-order corrections is estimated by reweighting the pT of the top quarks, the pT of the tt¯ system and the mtt¯ spectra at parton level to match the predicted NNLO QCD and NLO EW differential cross-sections106,107.

Parton shower and hadronization: this uncertainty is estimated by comparing two different parton-shower and hadronization algorithms, PYTHIA and HERWIG, interfaced with the same matrix element event generator (POWHEG BOX).

Recoil scheme: the nominal sample uses a recoil scheme in which the partons recoil against b-quarks. This recoil scheme changes the modelling of the second and subsequent gluon emissions from quarks produced by coloured resonance decays, such as the b-quark in a top-quark decay, and therefore affects how the momentum is rearranged between the W boson and the b-quark. An alternative sample is produced in which the recoil is set to be against the top quark itself for the second and subsequent emissions108.

Scale uncertainties: the renormalization and factorization scales are raised and lowered by a factor of 2 in the nominal POWHEG setup, including simultaneous variations in the same direction. The envelope of results from all of these variations is taken as the final uncertainty.

Initial-state radiation: The uncertainty due to initial-state radiation is estimated by choosing the Var3c up/down variations of the A14 tune as described in ref. 109.

Final-state radiation: the impact of final-state radiation is evaluated by doubling or halving the renormalization scale for emissions from the parton shower.

PDF: the systematic uncertainty due to the choice of PDF is assessed using the PDF4LHC15 eigenvector decomposition110. The full difference between the results from the nominal PDF and the varied PDF is taken and symmetrized for each of the 30 eigenvectors. The quadrature sum of all result variations is provided in Extended Data Table 1.

hdamp setting: the hdamp parameter is a resummation damping factor and one of the parameters that control the matching of POWHEG BOX matrix elements to the parton shower and thus effectively regulates the high-pT radiation against which the tt¯ system recoils. The systematic uncertainty due to the chosen value of the hdamp parameter is assessed by comparing the nominal POWHEG+ PYTHIA result with one in which the hdamp parameter is increased by a factor of two.

Top-quark mass: the effect of the top-quark mass uncertainty is examined by comparing the nominal sample with alternative samples that use mt = 172 GeV or 173 GeV in the simulation.

Object systematic uncertainties

Systematic uncertainties that originate from the uncertainty in the detector response to the objects used in the analysis are estimated.Electrons: The systematic uncertainties considered for electrons arise mainly from uncertainties in their trigger, reconstruction, identification and isolation efficiencies and are estimated using tag-and-probe measurements in Z and J/ψ decays56,111. Electron-related systematic uncertainties have a negligible impact on the final measurement, with a total contribution of about 0.2%.

Muons: The systematic uncertainties considered for muons arise from uncertainties in their trigger, identification and isolation efficiencies, and their energy scale and resolution, and are estimated using tag-and-probe measurements in Z and J/ψ decays57–59. Muon-related systematic uncertainties have a negligible impact on the final measurement, with a total contribution of about 0.3%.

Jets: The systematic uncertainties associated with jets are separated into those related to the jet-energy scale and resolution (JES and JER)60 and those related to the JVT algorithm64. The JES uncertainty consists of 31 individual components and the JER uncertainty consists of 13 individual components that are added in quadrature with the JVT uncertainty to obtain the total jet uncertainty. The largest contribution from a single source is 0.2%.

b-Tagging: The estimation of these uncertainties is described in ref. 112. A total of 17 independent systematic variations are considered: 9 related to b-hadrons, 4 related to c-hadrons, and 4 related to light-jet misidentification. Furthermore, two high-pT extrapolation uncertainties are taken into account. The largest contribution from a single systematic variation is 0.4%.

ETmiss: All object-based uncertainties are fully correlated with the reconstruction of the ETmiss object of the event, the magnitude of the pTmiss vector. However, there are some uncertainties specific to the reconstruction of ETmiss that concern soft tracks not matched to leptons or jets. These uncertainties are divided into parallel and perpendicular response components as well as a scale uncertainty66. These have a negligible effect on the measurement.

Pile-up: The effect of pile-up was modelled by overlaying the simulated hard-scattering events with inelastic pp events. To assess the systematic uncertainty due to pile-up, the reweighting performed to match simulation to data is varied within its uncertainty64. The resulting uncertainty has an effect of less than 0.1%.

Luminosity: The luminosity uncertainty only changes the normalization of the signal and background samples. The value of D is calculated from the normalized cos φ distribution and, therefore, is not affected by varying the sample normalization. However, the total expected statistical uncertainty can be affected by the luminosity uncertainty. This analysis uses the latest integrated luminosity estimate of 140.1 ± 1.2 fb−1 (ref. 113). Its uncertainty affects the measurement by less than 0.1%.

Background modelling systematic uncertainties

Background events are a relatively small source of uncertainty in this measurement because the event selection and top-quark reconstruction, especially the mtt¯ constraint, tend to suppress them. The uncertainties and their sources are listed in the following:Single top quark: two uncertainties are considered for the single-top quark background: a cross-section uncertainty of 5.3% based on the NNLO cross-section uncertainty85 and an uncertainty for the choice of schemes used to remove higher-order diagrams that overlap with the tt¯ process. For the latter, the nominal POWHEG + PYTHIA sample, generated with the diagram-removal scheme83, was compared with an alternative sample generated using the diagram-subtraction scheme73,83. The cross-section uncertainty has a 0.4% effect on the measurement, whereas the choice of diagram scheme has less than 0.1% effect on the measurement.

tt¯+X: a normalization uncertainty is considered for each of the tt¯+X backgrounds: a cross-section uncertainty of 1−12%+10% for tt¯+Z and 1−12%+13% for tt¯+W. Both are based on the NLO cross-section uncertainty derived from the renormalization and factorization scale variations and PDF uncertainties in the matrix element calculation. These uncertainties have a negligible effect on the measurement because the tt¯+X processes make a very small contribution to the signal region.

Diboson: a normalization uncertainty of  ±10% is considered for the diboson process to account for the difference between the NLO precision of the Sherpa event generator and the precision of the theoretical cross-sections calculated to NNLO in QCD with NLO EW corrections. This simple K-factor approach is taken, rather than a more elaborate prescription, because the diboson background is small and the phase space selected by the analysis (mtt¯<380 GeV) is unlikely to be sensitive to shape effects in the EW corrections, typically observed in high-pT tails. This uncertainty has less than 0.1% effect on the measurement.

Z → ττ: a conservative cross-section uncertainty of ±20% is applied to the Z → ττ background to account for the uncertainty in the cross-section prediction (which is much smaller than this variation) as well as to account for some mismodelling of the rate of associated heavy-flavor production, which is typically seen in ee and μμ dileptonic tt¯ analyses and was estimated to be a 5% (3%) effect in previous iterations of this analysis that included the ee (μμ) channel. This assumption is conservative as it is not possible to isolate a pure Z → ττ control region in which to estimate this effect, and therefore additional lepton-flavor-related effects present in the ee and μμ channels are also being included. This uncertainty has a noticeable impact on the final measurement, becoming the largest background-related uncertainty. It becomes large, despite this background being relatively small, because the reconstruction-level Z→ττcosφ distribution is quite flat and, therefore, subtracting even a relatively small amount of Z → ττ background can noticeably affect the mean of the overall cos φ distribution and therefore the D observable. This uncertainty has an impact of 0.8% on the measurement.

Fake and non-prompt leptons: a normalization uncertainty of ±50% is assigned to account for the uncertainty in the total yield of fake or non-prompt leptons in the signal region compared with the same-sign control region to ensure adequate coverage for our understanding of the rates of these types of events. It is a conservative uncertainty based on the observed level of data and Monte Carlo agreement in the same-sign region. The uncertainty has only a 0.1% effect on the final measurement.

Most of the systematic uncertainties that are considered are inconsequential to the measurement, and the dominant systematic uncertainties arise mostly from the signal modelling. These findings are true for the validation regions as well.

Parton shower and hadronization effects

The studies described in the following were performed to gain a more detailed understanding of why the different parton-shower and hadronization algorithms yield different values for the entanglement- and spin-correlation-related observables. The nominal Monte Carlo sample was produced with the NLO matrix element implemented in POWHEG BOX (hvq). The four momenta produced with POWHEG BOX were interfaced with either PYTHIA or HERWIG for the parton shower, hadronization and underlying-event model.

At the parton level, the two predictions are nearly identical, whereas at the stable-particle and detector levels, the two predictions show larger differences in the shape of the cos φ distributions. A parton-level measurement would, therefore, suffer from the ambiguity in cos φ, whereas the particle-level measurement presented in this paper does not. An extensive suite of studies was performed to understand the origin of this difference.

Apart from using different parameter-tuning strategies, there are two main differences between the two parton-shower algorithms: their hadronization model and the shower ordering. Whereas PYTHIA is based on the Lund string model and uses a pT-ordered dipole shower114–116, the HERWIG samples used in this study are based on a cluster model and use an angular-ordered shower as the default117.

A comparison between Monte Carlo simulations with different hadronization models was performed. For one study, Sherpa was used with either a string or a cluster model for hadronization. For the other study, HERWIG 7 was used, again comparing the effects of using either a string or a cluster model. Changing the hadronization model has shown in both cases to have a negligible effect on the cos φ distribution, both when not placing a cut on mtt¯ and when using a smaller part of phase space close to the signal region of the analysis, with mtt¯<380GeV. Instead, most of the differences seem to originate from the different orderings in the parton shower. To illustrate this, different event generator setups were used for simulation and the corresponding cos φ distributions were compared at particle level. The cos φ distributions for the POWHEG + PYTHIA and POWHEG + HERWIG samples used in the analysis are shown in Extended Data Fig. 2a, together with distributions for two different setups of HERWIG 7 in Extended Data Fig. 2b. In these setups, HERWIG 7 was used both for the production of the tt¯ events and for the parton shower, hadronization and underlying event. The samples were produced at LO, using either a dipole shower or an angular-ordered shower. All distributions are normalized to unity. A difference of up to 6% is observed when examining the ratio of POWHEG + HERWIG to POWHEG + PYTHIA distributions. The same behaviour is observed when comparing the two different showering orders for HERWIG.

The similarities between the samples used in this analysis and the HERWIG samples with different showering orders imply that the ordering of the shower is the main cause of the observed differences. It has to be noted, however, that POWHEG does not pass the spin correlation information to the parton shower algorithms, whereas this is done in the LO HERWIG setup used to study these hadronization effects.

These findings lead to the conclusion that performing the measurement at the particle level is more attractive because the difference in the predictions while extrapolating from the parton to particle level can be isolated and not taken as full systematic uncertainty. In the validation regions, the level of agreement between either POWHEG + PYTHIA or POWHEG + HERWIG and the data are similar. As the measurement is performed at the stable-particle level, the parton-level prediction for the entanglement limit was folded to the particle level as well, using a special calibration curve for this step. The prediction for the entanglement limit with POWHEG + HERWIG is further away from the data measurement than the one for POWHEG + PYTHIA. This difference is not symmetrized. All uncertainties in the POWHEG + PYTHIA prediction itself are folded to the particle level as well and are included in the grey uncertainty band in Fig. 2b.

The procedure used in Monte Carlo event generators to combine the matrix element with a parton-shower algorithm requires special attention in future higher-precision quantum information studies at the LHC.

Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41586-024-07824-z.

Supplementary information

Peer Review file

Extended data figures and tables

Extended Data Fig. 1 Example of reweighting technique.

Example of the nominal cosφ distribution and the results of applying the reweighting technique with X=0.4,0.6,0.8,1.2 in the signal region at parton level. The lower panel shows the ratio of each D value after reweighting (‘Pred.’) to the nominal D value (‘Nom.’).

Extended Data Fig. 2 Parton shower generator studies.

Comparison between cosφ distributions in the signal region with mtt¯<380 GeV for different Monte Carlo event generator setups at stable-particle level. Figure (a) compares events simulated with POWHEG BOX which are interfaced with either PYTHIA (red line, pT-ordered dipole shower) or HERWIG (blue line, angular-ordered shower) while figure (b) compares events simulated with HERWIG using either a dipole-ordered shower (red line) or an angular-ordered shower (blue line).

Extended Data Table 1 Summary of modelling uncertainties

Relative sizes of the signal modelling uncertainties at the standard model expectation point Dparticle = −0.47 for the nominal POWHEG BOX sample.

Extended data

is available for this paper at 10.1038/s41586-024-07824-z.

Supplementary information

The online version contains supplementary material available at 10.1038/s41586-024-07824-z.

Acknowledgements

We thank CERN for the very successful operation of the LHC and its injectors, as well as the support staff at CERN and at our institutions worldwide without whom ATLAS could not be operated efficiently. The crucial computing support from all WLCG partners is acknowledged, in particular, from CERN, the ATLAS Tier-1 facilities at TRIUMF/SFU (Canada), NDGF (Denmark, Norway and Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (the Netherlands), PIC (Spain), RAL (UK) and BNL (USA), the tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors to computing resources are listed in ref. 120. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC, China; Minciencias, Colombia; MEYS CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRI, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, the Netherlands; RCN, Norway; MEiN, Poland; FCT, Portugal; MNE/IFA, Romania; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taipei; TENMAK, Türkiye; STFC, UK; DOE and NSF, USA. Individual groups and members have received support from BCKDF, CANARIE, CRC and DRAC, Canada; CERN-CZ, PRIMUS 21/SCI/017 and UNCE SCI/013, Czech Republic; COST, ERC, ERDF, Horizon 2020, ICSC-NextGenerationEU and Marie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex, Investissements d’Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and MINERVA, Israel; Norwegian Financial Mechanism 2014–2021, Norway; NCN and NAWA, Poland; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, UK. Moreover, individual members wish to acknowledge support from CERN: European Organization for Nuclear Research (CERN PJAS); Chile: Agencia Nacional de Investigación y Desarrollo (FONDECYT 1190886, FONDECYT 1210400, FONDECYT 1230812 and FONDECYT 1230987); China: National Natural Science Foundation of China (NSFC - 12175119, NSFC 12275265, NSFC-12075060); Czech Republic: PRIMUS Research Programme (PRIMUS/21/SCI/017); European Union: European Research Council (ERC - 948254), Horizon 2020 Framework Programme (MUCCA - CHIST-ERA-19-XAI-00), European Union, Future Artificial Intelligence Research (FAIR-NextGenerationEU PE00000013), Italian Center for High Performance Computing, Big Data and Quantum Computing (ICSC, NextGenerationEU), Marie Sklodowska–Curie Actions (EU H2020 MSC IF grant no. 101033496); France: Agence Nationale de la Recherche (ANR-20-CE31-0013, ANR-21-CE31-0013 and ANR-21-CE31-0022), Investissements d’Avenir Idex (ANR-11-LABX-0012), Investissements d’Avenir Labex (ANR-11-LABX-0012); Germany: Baden–Württemberg Stiftung (BW Stiftung-Postdoc Eliteprogramme), Deutsche Forschungsgemeinschaft (DFG - 469666862, DFG - CR 312/5-1); Italy: Istituto Nazionale di Fisica Nucleare (FELLINI G.A. no. 754496, ICSC, NextGenerationEU); Japan: Japan Society for the Promotion of Science (JSPS KAKENHI JP21H05085, JSPS KAKENHI JP22H01227, JSPS KAKENHI JP22H04944 and JSPS KAKENHI JP22KK0227); the Netherlands: The Netherlands Organisation for Scientific Research (NWO Veni 2020 - VI.Veni.202.179); Norway: Research Council of Norway (RCN-314472); Poland: Polish National Agency for Academic Exchange (PPN/PPO/2020/1/00002/U/00001), Polish National Science Centre (NCN 2021/42/E/ST2/00350, NCN OPUS no. 2022/47/B/ST2/03059, NCN UMO-2019/34/E/ST2/00393, UMO-2020/37/B/ST2/01043, UMO-2021/40/C/ST2/00187); Slovenia: Slovenian Research Agency (ARIS grant J1-3010); Spain: BBVA Foundation (LEO22-1-603), Generalitat Valenciana (Artemisa, FEDER, IDIFEDER/2018/048), La Caixa Banking Foundation (LCF/BQ/PI20/11760025), Ministry of Science and Innovation (MCIN and NextGenEU PCI2022-135018-2, MICIN and FEDER PID2021-125273NB, RYC2019-028510-I, RYC2020-030254-I, RYC2021-031273-I and RYC2022-038164-I), PROMETEO and GenT Programmes Generalitat Valenciana (CIDEGENT/2019/023, CIDEGENT/2019/027); Sweden: Swedish Research Council (VR 2018-00482, VR 2022-03845, VR 2022-04683 and VR grant 2021-03651), Knut and Alice Wallenberg Foundation (KAW 2017.0100, KAW 2018.0157, KAW 2018.0458 and KAW 2019.0447); Switzerland: Swiss National Science Foundation (SNSF - PCEFP2_194658); UK: Leverhulme Trust (Leverhulme Trust RPG-2020-004); USA: US Department of Energy (ECA DE-AC02-76SF00515), Neubauer Family Foundation.

Author contributions

All authors have contributed to the publication, being variously involved in the design and the construction of the detectors, in writing the software, calibrating subsystems, operating the detectors and acquiring data and finally analysing the processed data. The ATLAS Collaboration members discussed and approved the scientific results. This Article was prepared by a subgroup of authors appointed by the ATLAS Collaboration and subjected to an internal collaboration-wide review process. All authors reviewed and approved the final version of the paper.

Peer review

Peer review information

Nature thanks Martin Hentschinski, Kazuki Sakurai and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Data availability

Raw data were generated by the ATLAS experiment. Derived data supporting the findings of this study are available from the ATLAS Collaboration upon request.

Code availability

The ATLAS data reduction software is available at Zenodo (https://doi.org/10.5281/zenodo.4772550) (ref. 118). Statistical modelling and analysis are based on the ROOT software and its embedded RooFit and RooStats modules, available at Zenodo (10.5281/zenodo.3895852) (ref. 119). Code to configure these statistical tools and to process their output is available upon request.

Competing interests

The authors declare no competing interests.

Faculty of Physics, University of Bucharest, Bucharest, Romania

iThemba Labs, Western Cape, South Africa

University of South Africa, Department of Physics, Pretoria, South Africa

University of Zululand, KwaDlangezwa, South Africa

Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech, Morocco

Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, Spain

Faculty of Physics, Sofia University, ‘St. Kliment Ohridski’, Sofia, Bulgaria

Affiliated with an international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland

Affiliated with an institute covered by a cooperation agreement with CERN, Geneva, Switzerland

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Deceased: N. D. Hehir, M. Lokajicek, B. Lund-Jensen, S. Yu. Sivoklokov

A list of authors and their affiliations appears online
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