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Measurement of the top quark mass in the \(t\bar{t}\rightarrow \) lepton+jets channel from \(\sqrt{s}=8\) TeV ATLAS data and combination with previous results

  • M. Aaboud
  • G. Aad
  • B. Abbott
  • O. Abdinov
  • B. Abeloos
  • D. K. Abhayasinghe
  • S. H. Abidi
  • O. S. AbouZeid
  • N. L. Abraham
  • H. Abramowicz
  • H. Abreu
  • Y. Abulaiti
  • B. S. Acharya
  • S. Adachi
  • L. Adam
  • L. Adamczyk
  • J. Adelman
  • M. Adersberger
  • A. Adiguzel
  • T. Adye
  • A. A. Affolder
  • Y. Afik
  • C. Agheorghiesei
  • J. A. Aguilar-Saavedra
  • F. Ahmadov
  • G. Aielli
  • S. Akatsuka
  • T. P. A. Åkesson
  • E. Akilli
  • A. V. Akimov
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  • J. Albert
  • P. Albicocco
  • M. J. Alconada Verzini
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  • M. Aleksa
  • I. N. Aleksandrov
  • C. Alexa
  • T. Alexopoulos
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  • G. Alimonti
  • J. Alison
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  • M. I. Alstaty
  • B. Alvarez Gonzalez
  • D. Álvarez Piqueras
  • M. G. Alviggi
  • B. T. Amadio
  • Y. Amaral Coutinho
  • A. Ambler
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  • S. Amoroso
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  • R. El Kosseifi
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  • J. Erdmann
  • A. Ereditato
  • S. Errede
  • M. Escalier
  • C. Escobar
  • O. Estrada Pastor
  • A. I. Etienvre
  • E. Etzion
  • H. Evans
  • A. Ezhilov
  • M. Ezzi
  • F. Fabbri
  • L. Fabbri
  • V. Fabiani
  • G. Facini
  • R. M. Faisca Rodrigues Pereira
  • R. M. Fakhrutdinov
  • S. Falciano
  • P. J. Falke
  • S. Falke
  • J. Faltova
  • Y. Fang
  • M. Fanti
  • A. Farbin
  • A. Farilla
  • E. M. Farina
  • T. Farooque
  • S. Farrell
  • S. M. Farrington
  • P. Farthouat
  • F. Fassi
  • P. Fassnacht
  • D. Fassouliotis
  • M. Faucci Giannelli
  • A. Favareto
  • W. J. Fawcett
  • L. Fayard
  • O. L. Fedin
  • W. Fedorko
  • M. Feickert
  • S. Feigl
  • L. Feligioni
  • C. Feng
  • E. J. Feng
  • M. Feng
  • M. J. Fenton
  • A. B. Fenyuk
  • L. Feremenga
  • J. Ferrando
  • A. Ferrari
  • P. Ferrari
  • R. Ferrari
  • D. E. Ferreira de Lima
  • A. Ferrer
  • D. Ferrere
  • C. Ferretti
  • F. Fiedler
  • A. Filipčič
  • F. Filthaut
  • K. D. Finelli
  • M. C. N. Fiolhais
  • L. Fiorini
  • C. Fischer
  • W. C. Fisher
  • N. Flaschel
  • I. Fleck
  • P. Fleischmann
  • R. R. M. Fletcher
  • T. Flick
  • B. M. Flierl
  • L. M. Flores
  • L. R. Flores Castillo
  • F. M. Follega
  • N. Fomin
  • G. T. Forcolin
  • A. Formica
  • F. A. Förster
  • A. C. Forti
  • A. G. Foster
  • D. Fournier
  • H. Fox
  • S. Fracchia
  • P. Francavilla
  • M. Franchini
  • S. Franchino
  • D. Francis
  • L. Franconi
  • M. Franklin
  • M. Frate
  • M. Fraternali
  • A. N. Fray
  • D. Freeborn
  • S. M. Fressard-Batraneanu
  • B. Freund
  • W. S. Freund
  • E. M. Freundlich
  • D. C. Frizzell
  • D. Froidevaux
  • J. A. Frost
  • C. Fukunaga
  • E. Fullana Torregrosa
  • T. Fusayasu
  • J. Fuster
  • O. Gabizon
  • A. Gabrielli
  • A. Gabrielli
  • G. P. Gach
  • S. Gadatsch
  • P. Gadow
  • G. Gagliardi
  • L. G. Gagnon
  • C. Galea
  • B. Galhardo
  • E. J. Gallas
  • B. J. Gallop
  • P. Gallus
  • G. Galster
  • R. Gamboa Goni
  • K. K. Gan
  • S. Ganguly
  • J. Gao
  • Y. Gao
  • Y. S. Gao
  • C. García
  • J. E. García Navarro
  • J. A. García Pascual
  • M. Garcia-Sciveres
  • R. W. Gardner
  • N. Garelli
  • S. Gargiulo
  • V. Garonne
  • K. Gasnikova
  • A. Gaudiello
  • G. Gaudio
  • I. L. Gavrilenko
  • A. Gavrilyuk
  • C. Gay
  • G. Gaycken
  • E. N. Gazis
  • C. N. P. Gee
  • J. Geisen
  • M. Geisen
  • M. P. Geisler
  • K. Gellerstedt
  • C. Gemme
  • M. H. Genest
  • C. Geng
  • S. Gentile
  • S. George
  • D. Gerbaudo
  • G. Gessner
  • S. Ghasemi
  • M. Ghasemi Bostanabad
  • M. Ghneimat
  • B. Giacobbe
  • S. Giagu
  • N. Giangiacomi
  • P. Giannetti
  • A. Giannini
  • S. M. Gibson
  • M. Gignac
  • D. Gillberg
  • G. Gilles
  • D. M. Gingrich
  • M. P. Giordani
  • F. M. Giorgi
  • P. F. Giraud
  • P. Giromini
  • G. Giugliarelli
  • D. Giugni
  • F. Giuli
  • M. Giulini
  • S. Gkaitatzis
  • I. Gkialas
  • E. L. Gkougkousis
  • P. Gkountoumis
  • L. K. Gladilin
  • C. Glasman
  • J. Glatzer
  • P. C. F. Glaysher
  • A. Glazov
  • M. Goblirsch-Kolb
  • J. Godlewski
  • S. Goldfarb
  • T. Golling
  • D. Golubkov
  • A. Gomes
  • R. Goncalves Gama
  • R. Gonçalo
  • G. Gonella
  • L. Gonella
  • A. Gongadze
  • F. Gonnella
  • J. L. Gonski
  • S. González de la Hoz
  • S. Gonzalez-Sevilla
  • L. Goossens
  • P. A. Gorbounov
  • H. A. Gordon
  • B. Gorini
  • E. Gorini
  • A. Gorišek
  • A. T. Goshaw
  • C. Gössling
  • M. I. Gostkin
  • C. A. Gottardo
  • C. R. Goudet
  • D. Goujdami
  • A. G. Goussiou
  • N. Govender
  • C. Goy
  • E. Gozani
  • I. Grabowska-Bold
  • P. O. J. Gradin
  • E. C. Graham
  • J. Gramling
  • E. Gramstad
  • S. Grancagnolo
  • V. Gratchev
  • P. M. Gravila
  • F. G. Gravili
  • C. Gray
  • H. M. Gray
  • Z. D. Greenwood
  • C. Grefe
  • K. Gregersen
  • I. M. Gregor
  • P. Grenier
  • K. Grevtsov
  • N. A. Grieser
  • J. Griffiths
  • A. A. Grillo
  • K. Grimm
  • S. Grinstein
  • Ph. Gris
  • J.-F. Grivaz
  • S. Groh
  • E. Gross
  • J. Grosse-Knetter
  • G. C. Grossi
  • Z. J. Grout
  • C. Grud
  • A. Grummer
  • L. Guan
  • W. Guan
  • J. Guenther
  • A. Guerguichon
  • F. Guescini
  • D. Guest
  • R. Gugel
  • B. Gui
  • T. Guillemin
  • S. Guindon
  • U. Gul
  • C. Gumpert
  • J. Guo
  • W. Guo
  • Y. Guo
  • Z. Guo
  • R. Gupta
  • S. Gurbuz
  • G. Gustavino
  • B. J. Gutelman
  • P. Gutierrez
  • C. Gutschow
  • C. Guyot
  • M. P. Guzik
  • C. Gwenlan
  • C. B. Gwilliam
  • A. Haas
  • C. Haber
  • H. K. Hadavand
  • N. Haddad
  • A. Hadef
  • S. Hageböck
  • M. Hagihara
  • H. Hakobyan
  • M. Haleem
  • J. Haley
  • G. Halladjian
  • G. D. Hallewell
  • K. Hamacher
  • P. Hamal
  • K. Hamano
  • A. Hamilton
  • G. N. Hamity
  • K. Han
  • L. Han
  • S. Han
  • K. Hanagaki
  • M. Hance
  • D. M. Handl
  • B. Haney
  • R. Hankache
  • P. Hanke
  • E. Hansen
  • J. B. Hansen
  • J. D. Hansen
  • M. C. Hansen
  • P. H. Hansen
  • K. Hara
  • A. S. Hard
  • T. Harenberg
  • S. Harkusha
  • P. F. Harrison
  • N. M. Hartmann
  • Y. Hasegawa
  • A. Hasib
  • S. Hassani
  • S. Haug
  • R. Hauser
  • L. Hauswald
  • L. B. Havener
  • M. Havranek
  • C. M. Hawkes
  • R. J. Hawkings
  • D. Hayden
  • C. Hayes
  • C. P. Hays
  • J. M. Hays
  • H. S. Hayward
  • S. J. Haywood
  • M. P. Heath
  • V. Hedberg
  • L. Heelan
  • S. Heer
  • K. K. Heidegger
  • J. Heilman
  • S. Heim
  • T. Heim
  • B. Heinemann
  • J. J. Heinrich
  • L. Heinrich
  • C. Heinz
  • J. Hejbal
  • L. Helary
  • A. Held
  • S. Hellesund
  • C. M. Helling
  • S. Hellman
  • C. Helsens
  • R. C. W. Henderson
  • Y. Heng
  • S. Henkelmann
  • A. M. Henriques Correia
  • G. H. Herbert
  • H. Herde
  • V. Herget
  • Y. Hernández Jiménez
  • H. Herr
  • M. G. Herrmann
  • T. Herrmann
  • G. Herten
  • R. Hertenberger
  • L. Hervas
  • T. C. Herwig
  • G. G. Hesketh
  • N. P. Hessey
  • A. Higashida
  • S. Higashino
  • E. Higón-Rodriguez
  • K. Hildebrand
  • E. Hill
  • J. C. Hill
  • K. K. Hill
  • K. H. Hiller
  • S. J. Hillier
  • M. Hils
  • I. Hinchliffe
  • M. Hirose
  • D. Hirschbuehl
  • B. Hiti
  • O. Hladik
  • D. R. Hlaluku
  • X. Hoad
  • J. Hobbs
  • N. Hod
  • M. C. Hodgkinson
  • A. Hoecker
  • M. R. Hoeferkamp
  • F. Hoenig
  • D. Hohn
  • D. Hohov
  • T. R. Holmes
  • M. Holzbock
  • M. Homann
  • B. H. Hommels
  • S. Honda
  • T. Honda
  • T. M. Hong
  • A. Hönle
  • B. H. Hooberman
  • W. H. Hopkins
  • Y. Horii
  • P. Horn
  • A. J. Horton
  • L. A. Horyn
  • J-Y. Hostachy
  • A. Hostiuc
  • S. Hou
  • A. Hoummada
  • J. Howarth
  • J. Hoya
  • M. Hrabovsky
  • I. Hristova
  • J. Hrivnac
  • A. Hrynevich
  • T. Hryn’ova
  • P. J. Hsu
  • S.-C. Hsu
  • Q. Hu
  • S. Hu
  • Y. Huang
  • Z. Hubacek
  • F. Hubaut
  • M. Huebner
  • F. Huegging
  • T. B. Huffman
  • M. Huhtinen
  • R. F. H. Hunter
  • P. Huo
  • A. M. Hupe
  • N. Huseynov
  • J. Huston
  • J. Huth
  • R. Hyneman
  • G. Iacobucci
  • G. Iakovidis
  • I. Ibragimov
  • L. Iconomidou-Fayard
  • Z. Idrissi
  • P. Iengo
  • R. Ignazzi
  • O. Igonkina
  • R. Iguchi
  • T. Iizawa
  • Y. Ikegami
  • M. Ikeno
  • D. Iliadis
  • N. Ilic
  • F. Iltzsche
  • G. Introzzi
  • M. Iodice
  • K. Iordanidou
  • V. Ippolito
  • M. F. Isacson
  • N. Ishijima
  • M. Ishino
  • M. Ishitsuka
  • W. Islam
  • C. Issever
  • S. Istin
  • F. Ito
  • J. M. Iturbe Ponce
  • R. Iuppa
  • A. Ivina
  • H. Iwasaki
  • J. M. Izen
  • V. Izzo
  • P. Jacka
  • P. Jackson
  • R. M. Jacobs
  • V. Jain
  • G. Jäkel
  • K. B. Jakobi
  • K. Jakobs
  • S. Jakobsen
  • T. Jakoubek
  • D. O. Jamin
  • R. Jansky
  • J. Janssen
  • M. Janus
  • P. A. Janus
  • G. Jarlskog
  • N. Javadov
  • T. Javůrek
  • M. Javurkova
  • F. Jeanneau
  • L. Jeanty
  • J. Jejelava
  • A. Jelinskas
  • P. Jenni
  • J. Jeong
  • N. Jeong
  • S. Jézéquel
  • H. Ji
  • J. Jia
  • H. Jiang
  • Y. Jiang
  • Z. Jiang
  • S. Jiggins
  • F. A. Jimenez Morales
  • J. Jimenez Pena
  • S. Jin
  • A. Jinaru
  • O. Jinnouchi
  • H. Jivan
  • P. Johansson
  • K. A. Johns
  • C. A. Johnson
  • W. J. Johnson
  • K. Jon-And
  • R. W. L. Jones
  • S. D. Jones
  • S. Jones
  • T. J. Jones
  • J. Jongmanns
  • P. M. Jorge
  • J. Jovicevic
  • X. Ju
  • J. J. Junggeburth
  • A. Juste Rozas
  • A. Kaczmarska
  • M. Kado
  • H. Kagan
  • M. Kagan
  • T. Kaji
  • E. Kajomovitz
  • C. W. Kalderon
  • A. Kaluza
  • S. Kama
  • A. Kamenshchikov
  • L. Kanjir
  • Y. Kano
  • V. A. Kantserov
  • J. Kanzaki
  • B. Kaplan
  • L. S. Kaplan
  • D. Kar
  • M. J. Kareem
  • E. Karentzos
  • S. N. Karpov
  • Z. M. Karpova
  • V. Kartvelishvili
  • A. N. Karyukhin
  • L. Kashif
  • R. D. Kass
  • A. Kastanas
  • Y. Kataoka
  • C. Kato
  • J. Katzy
  • K. Kawade
  • K. Kawagoe
  • T. Kawamoto
  • G. Kawamura
  • E. F. Kay
  • V. F. Kazanin
  • R. Keeler
  • R. Kehoe
  • J. S. Keller
  • E. Kellermann
  • J. J. Kempster
  • J. Kendrick
  • O. Kepka
  • S. Kersten
  • B. P. Kerševan
  • S. Ketabchi Haghighat
  • R. A. Keyes
  • M. Khader
  • F. Khalil-Zada
  • A. Khanov
  • A. G. Kharlamov
  • T. Kharlamova
  • E. E. Khoda
  • A. Khodinov
  • T. J. Khoo
  • E. Khramov
  • J. Khubua
  • S. Kido
  • M. Kiehn
  • C. R. Kilby
  • Y. K. Kim
  • N. Kimura
  • O. M. Kind
  • B. T. King
  • D. Kirchmeier
  • J. Kirk
  • A. E. Kiryunin
  • T. Kishimoto
  • D. Kisielewska
  • V. Kitali
  • O. Kivernyk
  • E. Kladiva
  • T. Klapdor-Kleingrothaus
  • M. H. Klein
  • M. Klein
  • U. Klein
  • K. Kleinknecht
  • P. Klimek
  • A. Klimentov
  • T. Klingl
  • T. Klioutchnikova
  • F. F. Klitzner
  • P. Kluit
  • S. Kluth
  • E. Kneringer
  • E. B. F. G. Knoops
  • A. Knue
  • A. Kobayashi
  • D. Kobayashi
  • T. Kobayashi
  • M. Kobel
  • M. Kocian
  • P. Kodys
  • P. T. Koenig
  • T. Koffas
  • E. Koffeman
  • N. M. Köhler
  • T. Koi
  • M. Kolb
  • I. Koletsou
  • T. Kondo
  • N. Kondrashova
  • K. Köneke
  • A. C. König
  • T. Kono
  • R. Konoplich
  • V. Konstantinides
  • N. Konstantinidis
  • B. Konya
  • R. Kopeliansky
  • S. Koperny
  • K. Korcyl
  • K. Kordas
  • G. Koren
  • A. Korn
  • I. Korolkov
  • E. V. Korolkova
  • N. Korotkova
  • O. Kortner
  • S. Kortner
  • T. Kosek
  • V. V. Kostyukhin
  • A. Kotwal
  • A. Koulouris
  • A. Kourkoumeli-Charalampidi
  • C. Kourkoumelis
  • E. Kourlitis
  • V. Kouskoura
  • A. B. Kowalewska
  • R. Kowalewski
  • T. Z. Kowalski
  • C. Kozakai
  • W. Kozanecki
  • A. S. Kozhin
  • V. A. Kramarenko
  • G. Kramberger
  • D. Krasnopevtsev
  • M. W. Krasny
  • A. Krasznahorkay
  • D. Krauss
  • J. A. Kremer
  • J. Kretzschmar
  • P. Krieger
  • K. Krizka
  • K. Kroeninger
  • H. Kroha
  • J. Kroll
  • J. Kroll
  • J. Krstic
  • U. Kruchonak
  • H. Krüger
  • N. Krumnack
  • M. C. Kruse
  • T. Kubota
  • S. Kuday
  • J. T. Kuechler
  • S. Kuehn
  • A. Kugel
  • F. Kuger
  • T. Kuhl
  • V. Kukhtin
  • R. Kukla
  • Y. Kulchitsky
  • S. Kuleshov
  • Y. P. Kulinich
  • M. Kuna
  • T. Kunigo
  • A. Kupco
  • T. Kupfer
  • O. Kuprash
  • H. Kurashige
  • L. L. Kurchaninov
  • Y. A. Kurochkin
  • A. Kurova
  • M. G. Kurth
  • E. S. Kuwertz
  • M. Kuze
  • J. Kvita
  • T. Kwan
  • A. La Rosa
  • J. L. La Rosa Navarro
  • L. La Rotonda
  • F. La Ruffa
  • C. Lacasta
  • F. Lacava
  • J. Lacey
  • D. P. J. Lack
  • H. Lacker
  • D. Lacour
  • E. Ladygin
  • R. Lafaye
  • B. Laforge
  • T. Lagouri
  • S. Lai
  • S. Lammers
  • W. Lampl
  • E. Lançon
  • U. Landgraf
  • M. P. J. Landon
  • M. C. Lanfermann
  • V. S. Lang
  • J. C. Lange
  • R. J. Langenberg
  • A. J. Lankford
  • F. Lanni
  • K. Lantzsch
  • A. Lanza
  • A. Lapertosa
  • S. Laplace
  • J. F. Laporte
  • T. Lari
  • F. Lasagni Manghi
  • M. Lassnig
  • T. S. Lau
  • A. Laudrain
  • M. Lavorgna
  • M. Lazzaroni
  • B. Le
  • O. Le Dortz
  • E. Le Guirriec
  • E. P. Le Quilleuc
  • M. LeBlanc
  • T. LeCompte
  • F. Ledroit-Guillon
  • C. A. Lee
  • G. R. Lee
  • L. Lee
  • S. C. Lee
  • B. Lefebvre
  • M. Lefebvre
  • F. Legger
  • C. Leggett
  • K. Lehmann
  • N. Lehmann
  • G. Lehmann Miotto
  • W. A. Leight
  • A. Leisos
  • M. A. L. Leite
  • R. Leitner
  • D. Lellouch
  • K. J. C. Leney
  • T. Lenz
  • B. Lenzi
  • R. Leone
  • S. Leone
  • C. Leonidopoulos
  • G. Lerner
  • C. Leroy
  • R. Les
  • A. A. J. Lesage
  • C. G. Lester
  • M. Levchenko
  • J. Levêque
  • D. Levin
  • L. J. Levinson
  • D. Lewis
  • B. Li
  • B. Li
  • C-Q. Li
  • H. Li
  • H. Li
  • L. Li
  • M. Li
  • Q. Li
  • Q. Y. Li
  • S. Li
  • X. Li
  • Y. Li
  • Z. Liang
  • B. Liberti
  • A. Liblong
  • K. Lie
  • S. Liem
  • A. Limosani
  • C. Y. Lin
  • K. Lin
  • T. H. Lin
  • R. A. Linck
  • J. H. Lindon
  • B. E. Lindquist
  • A. L. Lionti
  • E. Lipeles
  • A. Lipniacka
  • M. Lisovyi
  • T. M. Liss
  • A. Lister
  • A. M. Litke
  • J. D. Little
  • B. Liu
  • B. L Liu
  • H. B. Liu
  • H. Liu
  • J. B. Liu
  • J. K. K. Liu
  • K. Liu
  • M. Liu
  • P. Liu
  • Y. Liu
  • Y. L. Liu
  • Y. W. Liu
  • M. Livan
  • A. Lleres
  • J. Llorente Merino
  • S. L. Lloyd
  • C. Y. Lo
  • F. Lo Sterzo
  • E. M. Lobodzinska
  • P. Loch
  • T. Lohse
  • K. Lohwasser
  • M. Lokajicek
  • J. D. Long
  • R. E. Long
  • L. Longo
  • K. A. Looper
  • J. A. Lopez
  • I. Lopez Paz
  • A. Lopez Solis
  • J. Lorenz
  • N. Lorenzo Martinez
  • M. Losada
  • P. J. Lösel
  • A. Lösle
  • X. Lou
  • X. Lou
  • A. Lounis
  • J. Love
  • P. A. Love
  • J. J. Lozano Bahilo
  • H. Lu
  • M. Lu
  • Y. J. Lu
  • H. J. Lubatti
  • C. Luci
  • A. Lucotte
  • C. Luedtke
  • F. Luehring
  • I. Luise
  • L. Luminari
  • B. Lund-Jensen
  • M. S. Lutz
  • P. M. Luzi
  • D. Lynn
  • R. Lysak
  • E. Lytken
  • F. Lyu
  • V. Lyubushkin
  • T. Lyubushkina
  • H. Ma
  • L. L. Ma
  • Y. Ma
  • G. Maccarrone
  • A. Macchiolo
  • C. M. Macdonald
  • J. Machado Miguens
  • D. Madaffari
  • R. Madar
  • W. F. Mader
  • A. Madsen
  • N. Madysa
  • J. Maeda
  • K. Maekawa
  • S. Maeland
  • T. Maeno
  • M. Maerker
  • A. S. Maevskiy
  • V. Magerl
  • D. J. Mahon
  • C. Maidantchik
  • T. Maier
  • A. Maio
  • O. Majersky
  • S. Majewski
  • Y. Makida
  • N. Makovec
  • B. Malaescu
  • Pa. Malecki
  • V. P. Maleev
  • F. Malek
  • U. Mallik
  • D. Malon
  • C. Malone
  • S. Maltezos
  • S. Malyukov
  • J. Mamuzic
  • G. Mancini
  • I. Mandić
  • J. Maneira
  • L. Manhaes de Andrade Filho
  • J. Manjarres Ramos
  • K. H. Mankinen
  • A. Mann
  • A. Manousos
  • B. Mansoulie
  • J. D. Mansour
  • M. Mantoani
  • S. Manzoni
  • A. Marantis
  • G. Marceca
  • L. March
  • L. Marchese
  • G. Marchiori
  • M. Marcisovsky
  • C. Marcon
  • C. A. Marin Tobon
  • M. Marjanovic
  • D. E. Marley
  • F. Marroquim
  • Z. Marshall
  • M. U. F Martensson
  • S. Marti-Garcia
  • C. B. Martin
  • T. A. Martin
  • V. J. Martin
  • B. Martin dit Latour
  • M. Martinez
  • V. I. Martinez Outschoorn
  • S. Martin-Haugh
  • V. S. Martoiu
  • A. C. Martyniuk
  • A. Marzin
  • L. Masetti
  • T. Mashimo
  • R. Mashinistov
  • J. Masik
  • A. L. Maslennikov
  • L. H. Mason
  • L. Massa
  • P. Massarotti
  • P. Mastrandrea
  • A. Mastroberardino
  • T. Masubuchi
  • P. Mättig
  • J. Maurer
  • B. Maček
  • S. J. Maxfield
  • D. A. Maximov
  • R. Mazini
  • I. Maznas
  • S. M. Mazza
  • G. Mc Goldrick
  • S. P. Mc Kee
  • A. McCarn
  • T. G. McCarthy
  • L. I. McClymont
  • W. P. McCormack
  • E. F. McDonald
  • J. A. Mcfayden
  • G. Mchedlidze
  • M. A. McKay
  • K. D. McLean
  • S. J. McMahon
  • P. C. McNamara
  • C. J. McNicol
  • R. A. McPherson
  • J. E. Mdhluli
  • Z. A. Meadows
  • S. Meehan
  • T. M. Megy
  • S. Mehlhase
  • A. Mehta
  • T. Meideck
  • B. Meirose
  • D. Melini
  • B. R. Mellado Garcia
  • J. D. Mellenthin
  • M. Melo
  • F. Meloni
  • A. Melzer
  • S. B. Menary
  • E. D. Mendes Gouveia
  • L. Meng
  • X. T. Meng
  • A. Mengarelli
  • S. Menke
  • E. Meoni
  • S. Mergelmeyer
  • S. A. M. Merkt
  • C. Merlassino
  • P. Mermod
  • L. Merola
  • C. Meroni
  • F. S. Merritt
  • A. Messina
  • J. Metcalfe
  • A. S. Mete
  • C. Meyer
  • J. Meyer
  • J-P. Meyer
  • H. Meyer Zu Theenhausen
  • F. Miano
  • R. P. Middleton
  • L. Mijović
  • G. Mikenberg
  • M. Mikestikova
  • M. Mikuž
  • M. Milesi
  • A. Milic
  • D. A. Millar
  • D. W. Miller
  • A. Milov
  • D. A. Milstead
  • A. A. Minaenko
  • M. Miñano Moya
  • I. A. Minashvili
  • A. I. Mincer
  • B. Mindur
  • M. Mineev
  • Y. Minegishi
  • Y. Ming
  • L. M. Mir
  • A. Mirto
  • K. P. Mistry
  • T. Mitani
  • J. Mitrevski
  • V. A. Mitsou
  • M. Mittal
  • A. Miucci
  • P. S. Miyagawa
  • A. Mizukami
  • J. U. Mjörnmark
  • T. Mkrtchyan
  • M. Mlynarikova
  • T. Moa
  • K. Mochizuki
  • P. Mogg
  • S. Mohapatra
  • S. Molander
  • R. Moles-Valls
  • M. C. Mondragon
  • K. Mönig
  • J. Monk
  • E. Monnier
  • A. Montalbano
  • J. Montejo Berlingen
  • F. Monticelli
  • S. Monzani
  • N. Morange
  • D. Moreno
  • M. Moreno Llácer
  • P. Morettini
  • M. Morgenstern
  • S. Morgenstern
  • D. Mori
  • M. Morii
  • M. Morinaga
  • V. Morisbak
  • A. K. Morley
  • G. Mornacchi
  • A. P. Morris
  • J. D. Morris
  • L. Morvaj
  • P. Moschovakos
  • M. Mosidze
  • H. J. Moss
  • J. Moss
  • K. Motohashi
  • R. Mount
  • E. Mountricha
  • E. J. W. Moyse
  • S. Muanza
  • F. Mueller
  • J. Mueller
  • R. S. P. Mueller
  • D. Muenstermann
  • G. A. Mullier
  • F. J. Munoz Sanchez
  • P. Murin
  • W. J. Murray
  • A. Murrone
  • M. Muškinja
  • C. Mwewa
  • A. G. Myagkov
  • J. Myers
  • M. Myska
  • B. P. Nachman
  • O. Nackenhorst
  • K. Nagai
  • K. Nagano
  • Y. Nagasaka
  • M. Nagel
  • E. Nagy
  • A. M. Nairz
  • Y. Nakahama
  • K. Nakamura
  • T. Nakamura
  • I. Nakano
  • H. Nanjo
  • F. Napolitano
  • R. F. Naranjo Garcia
  • R. Narayan
  • D. I. Narrias Villar
  • I. Naryshkin
  • T. Naumann
  • G. Navarro
  • R. Nayyar
  • H. A. Neal
  • P. Y. Nechaeva
  • T. J. Neep
  • A. Negri
  • M. Negrini
  • S. Nektarijevic
  • C. Nellist
  • M. E. Nelson
  • S. Nemecek
  • P. Nemethy
  • M. Nessi
  • M. S. Neubauer
  • M. Neumann
  • P. R. Newman
  • T. Y. Ng
  • Y. S. Ng
  • H. D. N. Nguyen
  • T. Nguyen Manh
  • E. Nibigira
  • R. B. Nickerson
  • R. Nicolaidou
  • D. S. Nielsen
  • J. Nielsen
  • N. Nikiforou
  • V. Nikolaenko
  • I. Nikolic-Audit
  • K. Nikolopoulos
  • P. Nilsson
  • Y. Ninomiya
  • A. Nisati
  • N. Nishu
  • R. Nisius
  • I. Nitsche
  • T. Nitta
  • T. Nobe
  • Y. Noguchi
  • M. Nomachi
  • I. Nomidis
  • M. A. Nomura
  • T. Nooney
  • M. Nordberg
  • N. Norjoharuddeen
  • T. Novak
  • O. Novgorodova
  • R. Novotny
  • L. Nozka
  • K. Ntekas
  • E. Nurse
  • F. Nuti
  • F. G. Oakham
  • H. Oberlack
  • J. Ocariz
  • A. Ochi
  • I. Ochoa
  • J. P. Ochoa-Ricoux
  • K. O’Connor
  • S. Oda
  • S. Odaka
  • S. Oerdek
  • A. Oh
  • S. H. Oh
  • C. C. Ohm
  • H. Oide
  • M. L. Ojeda
  • H. Okawa
  • Y. Okazaki
  • Y. Okumura
  • T. Okuyama
  • A. Olariu
  • L. F. Oleiro Seabra
  • S. A. Olivares Pino
  • D. Oliveira Damazio
  • J. L. Oliver
  • M. J. R. Olsson
  • A. Olszewski
  • J. Olszowska
  • D. C. O’Neil
  • A. Onofre
  • K. Onogi
  • P. U. E. Onyisi
  • H. Oppen
  • M. J. Oreglia
  • G. E. Orellana
  • Y. Oren
  • D. Orestano
  • E. C. Orgill
  • N. Orlando
  • A. A. O’Rourke
  • R. S. Orr
  • B. Osculati
  • V. O’Shea
  • R. Ospanov
  • G. Otero y Garzon
  • H. Otono
  • M. Ouchrif
  • F. Ould-Saada
  • A. Ouraou
  • Q. Ouyang
  • M. Owen
  • R. E. Owen
  • V. E. Ozcan
  • N. Ozturk
  • J. Pacalt
  • H. A. Pacey
  • K. Pachal
  • A. Pacheco Pages
  • L. Pacheco Rodriguez
  • C. Padilla Aranda
  • S. Pagan Griso
  • M. Paganini
  • G. Palacino
  • S. Palazzo
  • S. Palestini
  • M. Palka
  • D. Pallin
  • I. Panagoulias
  • C. E. Pandini
  • J. G. Panduro Vazquez
  • P. Pani
  • G. Panizzo
  • L. Paolozzi
  • T. D. Papadopoulou
  • K. Papageorgiou
  • A. Paramonov
  • D. Paredes Hernandez
  • S. R. Paredes Saenz
  • B. Parida
  • T. H. Park
  • A. J. Parker
  • K. A. Parker
  • M. A. Parker
  • F. Parodi
  • J. A. Parsons
  • U. Parzefall
  • V. R. Pascuzzi
  • J. M. P. Pasner
  • E. Pasqualucci
  • S. Passaggio
  • F. Pastore
  • P. Pasuwan
  • S. Pataraia
  • J. R. Pater
  • A. Pathak
  • T. Pauly
  • B. Pearson
  • M. Pedersen
  • L. Pedraza Diaz
  • R. Pedro
  • S. V. Peleganchuk
  • O. Penc
  • C. Peng
  • H. Peng
  • B. S. Peralva
  • M. M. Perego
  • A. P. Pereira Peixoto
  • D. V. Perepelitsa
  • F. Peri
  • L. Perini
  • H. Pernegger
  • S. Perrella
  • V. D. Peshekhonov
  • K. Peters
  • R. F. Y. Peters
  • B. A. Petersen
  • T. C. Petersen
  • E. Petit
  • A. Petridis
  • C. Petridou
  • P. Petroff
  • M. Petrov
  • F. Petrucci
  • M. Pettee
  • N. E. Pettersson
  • A. Peyaud
  • R. Pezoa
  • T. Pham
  • F. H. Phillips
  • P. W. Phillips
  • M. W. Phipps
  • G. Piacquadio
  • E. Pianori
  • A. Picazio
  • M. A. Pickering
  • R. H. Pickles
  • R. Piegaia
  • J. E. Pilcher
  • A. D. Pilkington
  • M. Pinamonti
  • J. L. Pinfold
  • M. Pitt
  • L. Pizzimento
  • M.-A. Pleier
  • V. Pleskot
  • E. Plotnikova
  • D. Pluth
  • P. Podberezko
  • R. Poettgen
  • R. Poggi
  • L. Poggioli
  • I. Pogrebnyak
  • D. Pohl
  • I. Pokharel
  • G. Polesello
  • A. Poley
  • A. Policicchio
  • R. Polifka
  • A. Polini
  • C. S. Pollard
  • V. Polychronakos
  • D. Ponomarenko
  • L. Pontecorvo
  • G. A. Popeneciu
  • D. M. Portillo Quintero
  • S. Pospisil
  • K. Potamianos
  • I. N. Potrap
  • C. J. Potter
  • H. Potti
  • T. Poulsen
  • J. Poveda
  • T. D. Powell
  • M. E. Pozo Astigarraga
  • P. Pralavorio
  • S. Prell
  • D. Price
  • M. Primavera
  • S. Prince
  • N. Proklova
  • K. Prokofiev
  • F. Prokoshin
  • S. Protopopescu
  • J. Proudfoot
  • M. Przybycien
  • A. Puri
  • P. Puzo
  • J. Qian
  • Y. Qin
  • A. Quadt
  • M. Queitsch-Maitland
  • A. Qureshi
  • P. Rados
  • F. Ragusa
  • G. Rahal
  • J. A. Raine
  • S. Rajagopalan
  • A. Ramirez Morales
  • T. Rashid
  • S. Raspopov
  • M. G. Ratti
  • D. M. Rauch
  • F. Rauscher
  • S. Rave
  • B. Ravina
  • I. Ravinovich
  • J. H. Rawling
  • M. Raymond
  • A. L. Read
  • N. P. Readioff
  • M. Reale
  • D. M. Rebuzzi
  • A. Redelbach
  • G. Redlinger
  • R. Reece
  • R. G. Reed
  • K. Reeves
  • L. Rehnisch
  • J. Reichert
  • D. Reikher
  • A. Reiss
  • C. Rembser
  • H. Ren
  • M. Rescigno
  • S. Resconi
  • E. D. Resseguie
  • S. Rettie
  • E. Reynolds
  • O. L. Rezanova
  • P. Reznicek
  • E. Ricci
  • R. Richter
  • S. Richter
  • E. Richter-Was
  • O. Ricken
  • M. Ridel
  • P. Rieck
  • C. J. Riegel
  • O. Rifki
  • M. Rijssenbeek
  • A. Rimoldi
  • M. Rimoldi
  • L. Rinaldi
  • G. Ripellino
  • B. Ristić
  • E. Ritsch
  • I. Riu
  • J. C. Rivera Vergara
  • F. Rizatdinova
  • E. Rizvi
  • C. Rizzi
  • R. T. Roberts
  • S. H. Robertson
  • D. Robinson
  • J. E. M. Robinson
  • A. Robson
  • E. Rocco
  • C. Roda
  • Y. Rodina
  • S. Rodriguez Bosca
  • A. Rodriguez Perez
  • D. Rodriguez Rodriguez
  • A. M. Rodríguez Vera
  • S. Roe
  • C. S. Rogan
  • O. Røhne
  • R. Röhrig
  • C. P. A. Roland
  • J. Roloff
  • A. Romaniouk
  • M. Romano
  • N. Rompotis
  • M. Ronzani
  • L. Roos
  • S. Rosati
  • K. Rosbach
  • N-A. Rosien
  • B. J. Rosser
  • E. Rossi
  • E. Rossi
  • E. Rossi
  • L. P. Rossi
  • L. Rossini
  • J. H. N. Rosten
  • R. Rosten
  • M. Rotaru
  • J. Rothberg
  • D. Rousseau
  • D. Roy
  • A. Rozanov
  • Y. Rozen
  • X. Ruan
  • F. Rubbo
  • F. Rühr
  • A. Ruiz-Martinez
  • Z. Rurikova
  • N. A. Rusakovich
  • H. L. Russell
  • J. P. Rutherfoord
  • E. M. Rüttinger
  • Y. F. Ryabov
  • M. Rybar
  • G. Rybkin
  • S. Ryu
  • A. Ryzhov
  • G. F. Rzehorz
  • P. Sabatini
  • G. Sabato
  • S. Sacerdoti
  • H. F-W. Sadrozinski
  • R. Sadykov
  • F. Safai Tehrani
  • P. Saha
  • M. Sahinsoy
  • A. Sahu
  • M. Saimpert
  • M. Saito
  • T. Saito
  • H. Sakamoto
  • A. Sakharov
  • D. Salamani
  • G. Salamanna
  • J. E. Salazar Loyola
  • P. H. Sales De Bruin
  • D. Salihagic
  • A. Salnikov
  • J. Salt
  • D. Salvatore
  • F. Salvatore
  • A. Salvucci
  • A. Salzburger
  • J. Samarati
  • D. Sammel
  • D. Sampsonidis
  • D. Sampsonidou
  • J. Sánchez
  • A. Sanchez Pineda
  • H. Sandaker
  • C. O. Sander
  • M. Sandhoff
  • C. Sandoval
  • D. P. C. Sankey
  • M. Sannino
  • Y. Sano
  • A. Sansoni
  • C. Santoni
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  • ATLAS CollaborationEmail author
Open Access
Regular Article - Experimental Physics

Abstract

The top quark mass is measured using a template method in the \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) channel (lepton is e or \(\mu \)) using ATLAS data recorded in 2012 at the LHC. The data were taken at a proton–proton centre-of-mass energy of \({\sqrt{s}} =8\) \(\text {TeV}\) and correspond to an integrated luminosity of \(20.2\)  fb\(^{-1}\). The \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) channel is characterized by the presence of a charged lepton, a neutrino and four jets, two of which originate from bottom quarks (b). Exploiting a three-dimensional template technique, the top quark mass is determined together with a global jet energy scale factor and a relative b-to-light-jet energy scale factor. The mass of the top quark is measured to be \(m_{\mathrm {top}} =172.08 \,\pm \,0.39 \,\mathrm {(stat)}\,\pm \,0.82 \,\mathrm {(syst)} \) \(\text {GeV}\). A combination with previous ATLAS \(m_{\mathrm {top}}\) measurements gives \(m_{\mathrm {top}} = 172.69 \,\pm \,0.25 \,\mathrm {(stat)}\,\pm \,0.41 \,\mathrm {(syst)} \) \(\text {GeV}\).

1 Introduction

The mass of the top quark \(m_{\mathrm {top}}\) is an important parameter of the Standard Model (SM). Precise measurements of \(m_{\mathrm {top}}\) provide crucial information for global fits of electroweak parameters [1, 2, 3] which help to assess the internal consistency of the SM and probe its extensions. In addition, the value of \(m_{\mathrm {top}}\) affects the stability of the SM Higgs potential, which has cosmological implications [4, 5, 6].

Many measurements of \(m_{\mathrm {top}}\) in each \(t\bar{t}\) decay channel were performed by the Tevatron and LHC collaborations. The most precise measurements per experiment in the \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) channel are \(m_{\mathrm {top}} =172.85\,\pm \,0.71\,\mathrm {(stat)}\,\pm \,0.84\,\mathrm {(syst)} \) \(\text {GeV}\) by CDF [7], \(m_{\mathrm {top}} =174.98\,\pm \,0.58\,\mathrm {(stat)}\,\pm \,0.49\,\mathrm {(syst)} \) \(\text {GeV}\) by D0 [8], \(m_{\mathrm {top}} =172.33\,\pm \,0.75\,\mathrm {(stat)}\,\pm \,1.03\,\mathrm {(syst)} \) \(\text {GeV}\) by ATLAS [9] and \(m_{\mathrm {top}} =172.35\,\pm \,0.16\,\mathrm {(stat)}\,\pm \,0.48\,\mathrm {(syst)} \) \(\text {GeV}\) by CMS [10]. Combinations are performed, by either the individual experiments, or by several Tevatron and LHC experiments [11]. In these combinations, selections of measurements from all \(t\bar{t}\) decay channels are used. The latest combinations per experiment are \(m_{\mathrm {top}} =173.16\,\pm \,0.57\,\mathrm {(stat)}\,\pm \,0.74\,\mathrm {(syst)} \) \(\text {GeV}\) by CDF [12], \(m_{\mathrm {top}} =174.95\,\pm \,0.40\,\mathrm {(stat)}\,\pm \,0.64\,\mathrm {(syst)} \) \(\text {GeV}\) by D0 [13], \(m_{\mathrm {top}} =172.84\,\pm \,0.34\,\mathrm {(stat)}\,\pm \,0.61\,\mathrm {(syst)} \) \(\text {GeV}\) by ATLAS [14] and \(m_{\mathrm {top}} =172.44\,\pm \,0.13\,\mathrm {(stat)}\,\pm \,0.47\,\mathrm {(syst)} \) \(\text {GeV}\) by CMS [10].

In this paper, an ATLAS measurement of \(m_{\mathrm {top}}\) in the \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) channel is presented. The result is obtained from \(pp\) collision data recorded in 2012 at a centre-of-mass energy of \({\sqrt{s}} =8\) \(\text {TeV}\) with an integrated luminosity of about \(20.2 \) \(\mathrm {fb}^{-1} \). The analysis exploits the decay \(t\bar{t} \rightarrow W^{+} W^{-} b\bar{b} \rightarrow \ell \nu q\bar{q}^\prime b\bar{b} \), which occurs when one \(W\) boson decays into a charged lepton (\(\ell \) is e or \(\mu \) including \(\tau \rightarrow e,\mu \) decays) and a neutrino (\(\nu \)), and the other into a pair of quarks. In the analysis presented here, \(m_{\mathrm {top}}\) is obtained from the combined sample of events selected in the electron+jets and muon+jets final states. Single-top-quark events with the same reconstructed final states contain information about the top quark mass and are therefore included as signal events.

The measurement uses a template method, where simulated distributions are constructed for a chosen quantity sensitive to the physics parameter under study using a number of discrete values of that parameter. These templates are fitted to functions that interpolate between different input values of the physics parameter while fixing all other parameters of the functions. In the final step, an unbinned likelihood fit to the observed data distribution is used to obtain the value of the physics parameter that best describes the data. In this procedure, the experimental distributions are constructed such that fits to them yield unbiased estimators of the physics parameter used as input in the signal Monte Carlo (MC) samples. Consequently, the top quark mass determined in this way corresponds to the mass definition used in the MC simulation. Because of various steps in the event simulation, the mass measured in this way does not necessarily directly coincide with mass definitions within a given renormalization scheme, e.g. the top quark pole mass. Evaluating these differences is a topic of theoretical investigations [15, 16, 17, 18, 19].

The measurement exploits the three-dimensional template fit technique presented in Ref. [9]. To reduce the uncertainty in \(m_{\mathrm {top}}\) stemming from the uncertainties in the jet energy scale (\(\mathrm {JES}\)) and the additional \(b\text {-jet}\) energy scale (\(\mathrm {bJES}\)), \(m_{\mathrm {top}}\) is measured together with the jet energy scale factor (\(\mathrm {JSF}\)) and the relative b-to-light-jet energy scale factor (\(\mathrm {bJSF}\)). Given the larger data sample than used in Ref. [9], the analysis is optimized to reject combinatorial background arising from incorrect matching of the observed jets to the daughters arising from the top quark decays, thereby achieving a better balance of the statistical and systematic uncertainties and reducing the total uncertainty. Given this new measurement, an update of the ATLAS combination of \(m_{\mathrm {top}}\) measurements is also presented.

This document is organized as follows. After a short description of the ATLAS detector in Sect. 2, the data and simulation samples are discussed in Sect. 3. Details of the event selection are given in Sect. 4, followed by the description of the reconstruction of the three observables used in the template fit in Sect. 5. The optimization of the event selection using a multivariate analysis approach is presented in Sect. 6. The template fits are introduced in Sect. 7. The evaluation of the systematic uncertainties and their statistical uncertainties are discussed in Sect. 8, and the measurement of \(m_{\mathrm {top}}\) is given in Sect. 9. The combination of this measurement with previous ATLAS results is discussed in Sect. 10 and compared with measurements of other experiments. The summary and conclusions are given in Sect. 11. Additional information about the optimization of the event selection and on specific uncertainties in the new measurement of \(m_{\mathrm {top}}\) in the \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) channel are given in Appendix A, while Appendix B contains information about various combinations performed, together with comparisons with results from other experiments.

2 The ATLAS experiment

The ATLAS experiment [20] at the LHC is a multipurpose particle detector with a forward–backward symmetric cylindrical geometry and a near \(4\pi \) coverage in the solid angle.1 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 inner tracking detector covers the pseudorapidity range \(|\eta | < 2.5\). It consists of silicon pixel, silicon microstrip, and transition radiation tracking detectors. Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic (EM) energy measurements with high granularity. A hadronic (steel/scintillator-tile) calorimeter covers the central pseudorapidity range (\(|\eta | < 1.7\)). The endcap and forward regions are instrumented with LAr calorimeters for both the EM and hadronic energy measurements up to \(|\eta | = 4.9\). The muon spectrometer surrounds the calorimeters and is based on three large air-core toroid superconducting magnets with eight coils each. Its bending power is 2.0 to 7.5 T m. It includes a system of precision tracking chambers and fast detectors for triggering.

A three-level trigger system was used to select events. The first-level trigger is implemented in hardware and used a subset of the detector information to reduce the accepted rate to at most 75 kHz. This is followed by two software-based trigger levels that together reduced the accepted event rate to 400 Hz on average depending on the data-taking conditions during 2012.

3 Data and simulation samples

The analysis is based on \(pp\) collision data recorded by the ATLAS detector in 2012 at a centre-of-mass energy of \({\sqrt{s}} =8\) \(\text {TeV}\). The integrated luminosity is \(20.2 \) \(\mathrm {fb}^{-1} \) with an uncertainty of \(1.9\%\)  [21]. The modelling of top quark pair (\(t\bar{t}\)) and single-top-quark signal events, as well as most background processes, relies on MC simulations. For the simulation of \(t\bar{t}\) and single-top-quark events, the Powheg-Box v1 [22, 23, 24] program was used. Within this framework, the simulations of the \(t\bar{t}\)  [25] and single-top-quark production in the s- and t-channels [26] and the Wt-channel [27] used matrix elements at next-to-leading order (NLO) in the strong coupling constant \(\alpha _{\text {S}}\) with the NLO CT10 [28] parton distribution function (PDF) set and the \(h_{\mathrm {damp}}\) parameter2 set to infinity. Using \(m_{\mathrm {top}}\) and the top quark transverse momentum \(p_{\text {T}}\) for the underlying leading-order Feynman diagram, the dynamic factorization and renormalization scales were set to \(\sqrt{m_{\mathrm {top}} ^2 + p_{\text {T}} ^2}\). The Pythia  (v6.425) program [29] with the P2011C [30] set of tuned parameters (tune) and the corresponding CTEQ6L1 PDFs [31] provided the parton shower, hadronization and underlying-event modelling.

For \(m_{\mathrm {top}}\) hypothesis testing, the \(t\bar{t}\) and single-top-quark event samples were generated with five different assumed values of \(m_{\mathrm {top}}\) in the range from 167.5 to 177.5 \(\text {GeV}\) in steps of 2.5 \(\text {GeV}\). The integrated luminosity of the simulated \(t\bar{t}\) sample with \(m_{\mathrm {top}} =172.5\) \(\text {GeV}\) is about 360 \(\mathrm {fb}^{-1} \). Each of these MC samples is normalized according to the best available cross-section calculations. For \(m_{\mathrm {top}} =172.5\) \(\text {GeV}\), the \(t\bar{t}\) cross-section is \(\sigma _{t\bar{t}}=253^{+13}_{-15}\) \(\mathrm {pb} \), calculated at next-to-next-to-leading order (NNLO) with next-to-next-to-leading logarithmic soft gluon terms [32, 33, 34, 35, 36] with the Top++ 2.0 program [37]. The PDF- and \(\alpha _{\text {S}}\)-induced uncertainties in this cross-section were calculated using the PDF4LHC prescription [38] with the MSTW2008 \(68\%\) CL NNLO PDF [39, 40], CT10 NNLO PDF [28, 41] and NNPDF2.3 5f FFN PDF [42] and were added in quadrature with the uncertainties obtained from the variation of the factorization and renormalization scales by factors of 0.5 and 2.0. The cross-sections for single-top-quark production were calculated at NLO and are \(\sigma _\mathrm {t}=87.8\,^{+3.4}_{-1.9}\) \(\mathrm {pb} \) [43], \(\sigma _{Wt}=22.4\,\pm \,1.5\) \(\mathrm {pb} \) [44] and \(\sigma _\mathrm {s}=5.6\,\pm \,0.2\) \(\mathrm {pb} \) [45] in the t-, the Wt- and the s-channels, respectively.

The Alpgen  (v2.13) program [46] interfaced to the Pythia6 program was used for the simulation of the production of \(W^{\pm }\) or \(Z\) bosons in association with jets. The CTEQ6L1 PDFs and the corresponding AUET2 tune [47] were used for the matrix element and parton shower settings. The \(W\)+jets and \(Z\)+jets events containing heavy-flavour (HF) quarks (Wbb+jets, Zbb+jets, Wcc+jets, Zcc+jets, and Wc+jets) were generated separately using leading-order (LO) matrix elements with massive bottom and charm quark s. Double-counting of HF quarks in the matrix element and the parton shower evolution was avoided via a HF overlap-removal procedure that used the \(\Delta R\) between the additional heavy quarks as the criterion. If the \(\Delta R\) was smaller than 0.4, the parton shower prediction was taken, while for larger values, the matrix element prediction was used. The \(Z\)+jets sample is normalized to the inclusive NNLO calculation [48]. Due to the large uncertainties in the overall \(W\)+jets normalization and the flavour composition, both are estimated using data-driven techniques as described in Sect. 4.2. Diboson production processes (WW, WZ and ZZ) were simulated using the Alpgen program with CTEQ6L1 PDFs interfaced to the Herwig  (v6.520) [49] and Jimmy  (v4.31) [50] programs. The samples are normalized to their predicted cross-sections at NLO [51].

All samples were simulated taking into account the effects of multiple soft \(pp\) interactions (pile-up) that are present in the 2012 data. These interactions were modelled by overlaying simulated hits from events with exactly one inelastic collision per bunch crossing with hits from minimum-bias events produced with the Pythia  (v8.160) program [52] using the A2 tune [53] and the MSTW2008 LO PDF. The number of additional interactions is Poisson-distributed around the mean number of inelastic \(pp\) interactions per bunch crossing \(\mu \). For a given simulated hard-scatter event, the value of \(\mu \) depends on the instantaneous luminosity and the inelastic \(pp\) cross-section, taken to be 73 mb [21]. Finally, the simulation sample is reweighted such as to match the pile-up observed in data.

A simulation [54] of the ATLAS detector response based on Geant4  [55] was performed on the MC events. This simulation is referred to as full simulation. The events were then processed through the same reconstruction software as the data. A number of samples used to assess systematic uncertainties were produced bypassing the highly computing-intensive full Geant4 simulation of the calorimeters. They were produced with a faster version of the simulation [56], which retained the full simulation of the tracking but used a parameterized calorimeter response based on resolution functions measured in full simulation samples. This simulation is referred to as fast simulation.

4 Object reconstruction, background estimation and event preselection

The reconstructed objects resulting from the top quark pair decay are electron and muon candidates, jets and missing transverse momentum (\(E_{\text {T}}^{\text {miss}}\)). In the simulated events, corrections are applied to these objects based on detailed data-to-simulation comparisons for many different processes, so as to match their performance in data.

4.1 Object reconstruction

Electron candidates [57] are required to have a transverse energy of \(E_{\text {T}} >25\) \(\text {GeV}\) and a pseudorapidity of the corresponding EM cluster of \(\vert \eta _\mathrm {cluster} \vert < 2.47\) with the transition region \(1.37<\vert \eta _\mathrm {cluster} \vert <1.52\) between the barrel and the endcap calorimeters excluded. Muon candidates [58] are required to have transverse momentum \(p_{\text {T}} >25\) \(\text {GeV}\) and \(\vert \eta \vert <2.5\). To reduce the contamination by leptons from HF decays inside jets or from photon conversions, referred to collectively as non-prompt (NP) leptons, strict isolation criteria are applied to the amount of activity in the vicinity of the lepton candidate [57, 58, 59].

Jets are built from topological clusters of calorimeter cells [60] with the anti-\(k_{t}\) jet clustering algorithm [61] using a radius parameter of \(R=0.4\). The clusters and jets are calibrated using the local cluster weighting (LCW) and the global sequential calibration (GSC) algorithms, respectively [62, 63, 64]. The subtraction of the contributions from pile-up is performed via the jet area method [65]. Jets are calibrated using an energy- and \(\eta \)-dependent simulation-based scheme with in situ corrections based on data [63]. Jets originating from pile-up interactions are identified via their jet vertex fraction (JVF), which is the \(p_{\text {T}}\) fraction of associated tracks stemming from the primary vertex. The requirement \(\mathrm {JVF}>0.5\) is applied solely to jets with \(p_{\text {T}} <50\) \(\text {GeV}\) and \(|\eta | <2.4\) [65]. Finally, jets are required to satisfy \(p_{\text {T}} >25\) \(\text {GeV}\) and \(|\eta | <2.5\).

Muons reconstructed within a \(\Delta R =0.4\) cone around the axis of a jet with \(p_{\text {T}} >25\) \(\text {GeV}\) are excluded from the analysis. In addition, the closest jet within a \(\Delta R =0.2\) cone around an electron candidate is removed, and then electrons within a \(\Delta R =0.4\) cone around any of the remaining jets are discarded.

The identification of jets containing reconstructed b-hadrons, called \(b\text {-tagging}\), is used for event reconstruction and background suppression. In the following, irrespective of their origin, jets tagged by the \(b\text {-tagging}\) algorithm are referred to as \(b\text {-tagged}\) jets, whereas those not tagged are referred to as untagged jets. Similarly, whether they are tagged or not, jets containing b-hadrons in simulation are referred to as \(b\text {-jets}\) and those containing only lighter-flavour hadrons from udcs-quarks, or originating from gluons, are collectively referred to as light-jets. The working point of the neural-network-based MV1 \(b\text {-tagging}\) algorithm [66] corresponds to an average \(b\text {-tagging}\) efficiency of 70\(\%\) for \(b\text {-jet}\) s in simulated \(t\bar{t}\) events and rejection factors of 5 for jets containing a c-hadron and 140 for jets containing only lighter-flavour hadrons. To match the \(b\text {-tagging}\) performance in the data, \(p_{\text {T}}\)- and \(\eta \)-dependent scale factors, obtained from dijet and \(t\bar{t} \rightarrow \mathrm {dilepton}\) events, are applied to MC jets depending on their generated quark flavour, as described in Refs. [66, 67, 68].

The missing transverse momentum \(E_{\text {T}}^{\text {miss}}\) is the absolute value of the vector \(\overrightarrow{E_\mathrm {T}}^\mathrm {miss} \) calculated from the negative vectorial sum of all transverse momenta. The vectorial sum takes into account all energy deposits in the calorimeters projected onto the transverse plane. The clusters are corrected using the calibrations that belong to the associated physics object. Muons are included in the calculation of the \(E_{\text {T}}^{\text {miss}}\) using their momentum reconstructed in the inner tracking detectors [69].

4.2 Background estimation

The contribution of events falsely reconstructed as \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) events due to the presence of objects misidentified as leptons (fake leptons) and NP leptons originating from HF decays, is estimated from data using the matrix-method [70]. The technique employed uses \(\eta \)- and \(p_{\text {T}}\)-dependent efficiencies for NP/fake-leptons and prompt-leptons. They are measured in a background-enhanced control region with low \(E_{\text {T}}^{\text {miss}}\) and from events with dilepton masses around the \(Z\) boson peak [71], respectively. For the \(W\)+jets background, the overall normalization is estimated from data. The estimate is based on the charge-asymmetry method [72], relying on the fact that at the LHC more \(W^{+}\) than \(W^{-}\) bosons are produced. In addition, a data-driven estimate of the \(Wb\bar{b}\), \(Wc\bar{c}\), Wc and W+light-jet fractions is performed in events with exactly two jets and at least one b-tagged jet. Further details are given in Ref. [73]. The \(Z\)+jets and diboson background processes are normalized to their predicted cross-sections as described in Sect. 3.

4.3 Event preselection

Triggering of events is based solely on the presence of a single electron or muon, and no information from the hadronic final state is used. A logical OR of two triggers is used for each of the \(t\bar{t} \rightarrow \mathrm {electron+jets}\) and \(t\bar{t} \rightarrow \mathrm {muon+jets}\) channels. The triggers with the lower thresholds of 24 \(\text {GeV}\) for electrons or muons select isolated leptons. The triggers with the higher thresholds of 60 \(\text {GeV}\) for electrons and 36 \(\text {GeV}\) for muons do not include an isolation requirement. The further selection requirements closely follow those in Ref. [9] and are
  • Events are required to have at least one primary vertex with at least five associated tracks. Each track needs to have a minimum \(p_{\text {T}}\) of 0.4 \(\text {GeV}\). For events with more than one primary vertex, the one with the largest \(\sum p_\mathrm{T}^2\) is chosen as the vertex from the hard scattering.

  • The event must contain exactly one reconstructed charged lepton, with \(E_{\text {T}} > 25\) \(\text {GeV}\) for electrons and \(p_{\text {T}} > 25\) \(\text {GeV}\) for muons, that matches the charged lepton that fired the corresponding lepton trigger.

  • In the \(t\bar{t} \rightarrow \mathrm {muon+jets}\) channel, \(E_{\text {T}}^{\text {miss}} >20\) \(\text {GeV}\) and \(E_{\text {T}}^{\text {miss}} +m_{\mathrm {T}}^{W} >60\) \(\text {GeV}\) are required.3

  • In the \(t\bar{t} \rightarrow \mathrm {electron+jets}\) channel, more stringent requirements on \(E_{\text {T}}^{\text {miss}}\) and \(m_{\mathrm {T}}^{W}\) are applied because of the higher level of NP/fake-lepton background. The requirements are \(E_{\text {T}}^{\text {miss}} > 30\) \(\text {GeV}\) and \(m_{\mathrm {T}}^{W} >30\) \(\text {GeV}\).

  • The presence of at least four jets with \(p_{\text {T}} >25\) \(\text {GeV}\) and \(\vert \eta \vert <2.5\) is required.

  • The presence of exactly two \(b\text {-tagged}\) jets is required.

The resulting event sample is statistically independent of the ones used for the measurement of \(m_{\mathrm {top}}\) in the \(t\bar{t} \rightarrow \mathrm {dilepton}\) and \(t\bar{t} \rightarrow \mathrm {all\,jets}\) channels at \({\sqrt{s}} =8\) \(\text {TeV}\) [14, 74]. The observed number of events in the data after this preselection and the expected numbers of signal and background events corresponding to the same integrated luminosity as the data are given in Table 1. For all predictions, the uncertainties are estimated as the sum in quadrature of the statistical uncertainty, the uncertainty in the integrated luminosity and all systematic uncertainties assigned to the measurement of \(m_{\mathrm {top}}\) listed in Sect. 8, except for the PDF and pile-up uncertainties, which are small. The normalization uncertainties listed below are included for the predictions shown in this section, but due to their small effect on the measured top quark mass they are not included in the final measurement.
For the signal, the \(5.7\%\) uncertainty in the \(t\bar{t}\) cross-section introduced in Sect. 3 and a \(6.0\%\) uncertainty in the single-top-quark cross-section are used. The latter uncertainty is obtained from the cross-section uncertainties given in Sect. 3 and the fractions of the various single-top-quark production processes after the selection requirements. The background uncertainties contain uncertainties of \(48\%\) in the normalization of the diboson and \(Z\)+jets production processes. These uncertainties are calculated using Berends–Giele scaling [75]. Assuming a top quark mass of \(m_{\mathrm {top}} =172.5\) \(\text {GeV}\), the predicted number of events is consistent within uncertainties with the number observed in the data.
Table 1

The observed numbers of events in data after the event preselection and the \(\mathrm {BDT}\) selection (see Sect. 6). In addition, the expected numbers of signal events for \(m_{\mathrm {top}} =172.5\) \(\text {GeV}\) and background events corresponding to the same integrated luminosity as the data are given. The uncertainties in the predicted number of events take into account the statistical and systematic sources explained in Sect. 4.3. Two significant digits are used for the uncertainties in the predicted events

Selection

Preselection

\(\mathrm {BDT}\) selection

Data

96105

38054

\(t\bar{t}\) signal

85000 ± 10000

36100 ± 5500

Single-top-quark signal

4220 ± 360

883 ± 85

NP/fake leptons (data-driven)

700 ± 700

9.2 ± 9.2

\(W\)+jets (data-driven)

2800 ± 700

300 ± 100

\(Z\)+jets

430 ± 230

58 ± 33

WW / WZ / ZZ

63 ± 32

7.0 ± 5.2

Signal+background

93000 ± 10000

37300 ± 5500

Expected background fraction

0.043 ± 0.012

0.010 ± 0.003

Data/(signal+background)

1.03 ± 0.12

1.02 ± 0.15

5 Reconstruction of the three observables

As in Ref. [9], a full kinematic reconstruction of the event is done with a likelihood fit using the KLFitter package [76, 77]. The KLFitter algorithm relates the measured kinematics of the reconstructed objects to the leading-order representation of the \(t\bar{t}\) system decay using \(t\bar{t} \rightarrow \ell \nu b_\mathrm {lep} \,q_1 q_2 b_\mathrm {had} \). In this procedure, the measured jets correspond to the quark decay products of the \(W\) boson, \(q_1\) and \(q_2\), and to the \(b\text {-quarks}\), \(b_\mathrm {lep}\) and \(b_\mathrm {had}\), produced in the semi-leptonic and hadronic top quark decays, respectively.

The event likelihood is the product of Breit–Wigner (BW) distributions for the \(W\) bosons and top quarks and transfer functions (TFs) for the energies of the reconstructed objects that are input to KLFitter. The W boson BW distributions use the world combined values of the W boson mass and decay width from Ref. [3]. A common mass parameter \(m_{\mathrm {top}} ^{\mathrm {reco}}\) is used for the BW distributions describing the semi-leptonically and hadronically decaying top quarks and is fitted event-by-event. The top quark width varies with \(m_{\mathrm {top}} ^{\mathrm {reco}}\) according to the SM prediction [3]. The TFs are derived from the Powheg+Pythia \(t\bar{t}\) signal MC simulation sample at an input mass of \(m_{\mathrm {top}} =172.5\) \(\text {GeV}\). They represent the experimental resolutions in terms of the probability that the observed energy at reconstruction level is produced by a given parton-level object for the leading-order decay topology and in the fit constrain the variations of the reconstructed objects.

The input objects to the event likelihood are the reconstructed charged lepton, the missing transverse momentum and up to six jets. These are the two \(b\text {-tagged}\) jets and the four untagged jets with the highest \(p_{\text {T}}\). The x- and y-components of the missing transverse momentum are starting values for the neutrino transverse-momentum components, and its longitudinal component \(p_{\nu ,z}\) is a free parameter in the kinematic likelihood fit. Its starting value is computed from the \(W\rightarrow \ell \nu \) mass constraint. If there are no real solutions for \(p_{\nu ,z}\), a starting value of zero is used. If there are two real solutions, the one giving the largest likelihood value is taken.

Maximizing the event-by-event likelihood as a function of \(m_{\mathrm {top}} ^{\mathrm {reco}}\) establishes the best assignment of reconstructed jets to partons from the \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) decay. The maximization is performed by testing all possibilities for assigning \(b\text {-tagged}\) jets to \(b\text {-quark}\) positions and untagged jets to light-quark positions. With the above settings of the reconstruction algorithm, compared with the settings4 used in Ref. [9], a larger fraction of correct assignments of reconstructed jets to partons from the \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) decay is achieved. The performance of the reconstruction algorithm is discussed in Sect. 6.

The value of \(m_{\mathrm {top}} ^{\mathrm {reco}}\) obtained from the kinematic likelihood fit is used as the observable primarily sensitive to the underlying \(m_{\mathrm {top}}\). The invariant mass of the hadronically decaying \(W\) boson \(m_{W}^{\mathrm {reco}}\), which is sensitive to the \(\mathrm {JES}\), is calculated from the assigned jets of the chosen permutation. Finally, an observable called \(R_{bq}^{\mathrm {reco}}\), designed to be sensitive to the \(\mathrm {bJES}\), is computed as the scalar sum of the transverse momenta of the two \(b\text {-tagged}\) jets divided by the scalar sum of the transverse momenta of the two jets associated with the hadronic \(W\) boson decay:
$$\begin{aligned} R_{bq}^{\mathrm {reco}}&= \frac{p_\mathrm {T}^{b_\mathrm{had}} + p_\mathrm {T}^{b_\mathrm{lep}}}{p_\mathrm {T}^{q_1} + p_\mathrm {T}^{q_2}}. \end{aligned}$$
The values of \(m_{W}^{\mathrm {reco}}\) and \(R_{bq}^{\mathrm {reco}}\) are computed from the jet four-vectors as given by the jet reconstruction instead of using the values obtained in the kinematic likelihood fit. This ensures the maximum sensitivity to the jet calibration for light-jets and \(b\text {-jets}\).
Some distributions of the observed event kinematics after the event preselection and for the best permutation are shown in Fig. 1. Given the good description of the observed number of events by the prediction shown in Sect. 4.3 and that the measurement of \(m_{\mathrm {top}}\) is mostly sensitive to the shape of the distributions, the comparison of the data with the predictions is based solely on the distributions normalized to the number of events observed in data. The systematic uncertainty assigned to each bin is calculated from the sum in quadrature of all systematic uncertainties discussed in Sect. 4.3. Within uncertainties, the predictions agree with the observed distributions in Fig. 1, which shows the transverse momentum of the lepton, the average transverse momentum of the jets, the transverse momentum of the hadronically decaying top quark \(p_{\mathrm {T, had}}\), the transverse momentum of the \(t\bar{t}\) system, the logarithm of the event likelihood of the best permutation and the distance \(\Delta R\) of the two untagged jets \(q_1\) and \(q_2\) assigned to the hadronically decaying \(W\) boson. The distributions of transverse momenta predicted by the simulation, e.g. the \(p_{\mathrm {T, had}}\) distribution shown in Fig. 1c, show a slightly different trend than observed in data, with the data being softer. This difference is fully covered by the uncertainties. This trend was also observed in Ref. [14] for the \(p_{\mathrm {T}, \ell b}\) distribution in the \(t\bar{t} \rightarrow \mathrm {dilepton}\) channel and in the measurement of the differential \(t\bar{t}\) cross-section in the lepton+jets channel [78].
Fig. 1

Distributions for the events passing the preselection. The data are shown together with the signal-plus-background prediction, normalized to the number of events observed in the data. The hatched area is the uncertainty in the prediction as described in the text. The rightmost bin contains all entries with values above the lower edge of this bin, similarly the leftmost bin contains all entries with values below the upper edge of this bin. a shows the transverse momentum of the lepton, b shows the average transverse momentum of the jets, c shows the transverse momentum of the hadronically decaying top quark, d shows the transverse momentum of the \(t\bar{t}\) system, e shows the logarithm of the event likelihood of the best permutation and f shows the distance \(\Delta R\) of the two untagged jets \(q_1\) and \(q_2\) from the hadronically decaying \(W\) boson

In anticipation of the template parameterization described in Sect. 7, the following restrictions on the three observables are applied: \(125 \le m_{\mathrm {top}} ^{\mathrm {reco}} \le 200~\text {GeV}\), \(55 \le m_{W}^{\mathrm {reco}} \le 110~\text {GeV}\), and \(0.3 \le R_{bq}^{\mathrm {reco}} \le 3\). Since in this analysis only the best permutation is considered, events that do not pass these requirements are rejected. This removes events in the tails of the three distributions, which are typically poorly reconstructed with small likelihood values and do not contain significant information about \(m_{\mathrm {top}}\). The resulting templates have simpler shapes, which are easier to model analytically with fewer parameters. The preselection with these additional requirements is referred to as the standard selection to distinguish it from the boosted decision tree (BDT) optimization for the smallest total uncertainty in \(m_{\mathrm {top}}\), discussed in the next section.

6 Multivariate analysis and BDT event selection

For the measurement of \(m_{\mathrm {top}}\), the event selection is refined enriching the fraction of events with correct assignments of reconstruction-level objects to their generator-level counterparts which should be better measured and therefore lead to smaller uncertainties. The optimization of the selection is based on the multivariate BDT algorithm implemented in the TMVA package [79]. The reconstruction-level objects are matched to the closest parton-level object within a \(\Delta R\) of 0.1 for electrons and muons and 0.3 for jets. A matched object is defined as a reconstruction-level object that falls within the relevant \(\Delta R\) of any parton-level object of that type, and a correct match means that this generator-level object is the one it originated from. Due to acceptance losses and reconstruction inefficiencies, not all reconstruction-level objects can successfully be matched to their parton-level counterparts. If any object cannot be unambiguously matched, the corresponding event is referred to as unmatched. The efficiency for correctly matched events \(\epsilon _{\mathrm {cm}}\) is the fraction of correctly matched events among all the matched events, and the selection purity \(\pi _{\mathrm {cm}}\) is the fraction of correctly matched events among all selected events, regardless of whether they could be matched or not.

The BDT algorithm is exploited to enrich the event sample in events that have correct jet-to-parton matching by reducing the remainder, i.e. the sum of incorrectly matched and unmatched events. Using the preselection, the BDT algorithm is trained on the simulated \(t\bar{t}\) signal sample with \(m_{\mathrm {top}} =172.5\) \(\text {GeV}\). Many variables were studied and only those with a separation5 larger than \(0.1\%\) are used in the training. The 13 variables chosen for the final training are given in Table 2. For all input variables to the BDT algorithm, good agreement between the MC predictions and the data is found, as shown in Fig. 1e, f for the examples of the likelihood of the chosen permutation and the opening angle \(\Delta R\) of the two untagged jets associated with the \(W\) boson decay. These two variables also have the largest separation for the correctly matched events and the remainder. The corresponding distributions for the two event classes are shown in Fig. 2a, b. These figures show a clear separation of the correctly matched events and the remainder. Half the simulation sample is used to train the algorithm and the other half to assess its performance. The significant difference between the distributions of the output value \(r_{\mathrm {BDT}}\) of the BDT classifier between the two classes of events in Fig. 2c shows their efficient separation by the BDT algorithm. In addition, reasonable agreement is found for the \(r_{\mathrm {BDT}}\) distributions in the statistically independent test and training samples. The \(r_{\mathrm {BDT}}\) distributions in simulation and data in Fig. 2d agree within the experimental uncertainties. The above findings justify the application of the BDT approach to the data.
Table 2

The input variables to the BDT algorithm sorted by their separation

Separation (%)

Description

31

Logarithm of the event likelihood of the best permutation, \(\ln L\)

13

\(\Delta R\) of the two untagged jets \(q_1\) and \(q_2\) from the hadronically decaying \(W\) boson, \(\Delta R (q,q)\)

5.0

\(p_{\text {T}}\) of the hadronically decaying \(W\) boson

4.3

\(p_{\text {T}}\) of the hadronically decaying top quark

4.2

Relative event probability of the best permutation

2.0

\(p_{\text {T}}\) of the reconstructed \(t\bar{t}\) system

1.7

\(p_{\text {T}}\) of the semi-leptonically decaying top quark

1.2

Transverse mass of the leptonically decaying \(W\) boson

0.3

\(p_{\text {T}}\) of the leptonically decaying \(W\) boson

0.3

Number of jets

0.2

\(\Delta R\) of the reconstructed \(b\text {-tagged}\) jets

0.2

Missing transverse momentum

0.1

\(p_{\text {T}}\) of the lepton

Fig. 2

Input and results of the BDT training on \(t\bar{t}\) signal events for the preselection. a shows the logarithm of the event likelihood of the best permutation (\(\ln L\)) for the correctly matched events and the remainder. Similarly, b shows the distribution of the \(\Delta R\) between the two untagged jets assigned to the \(W\) boson decay. c shows the distribution of the BDT output (\(r_{\mathrm {BDT}}\)) for the two classes of events for both the training (histograms) and test samples (points with statistical uncertainties). The compatibility in terms of the \(\chi ^2\) probability is also listed. The distributions peaking at around \(r_{\mathrm {BDT}} =0.1\) are for the correctly matched events, the ones to the left are for incorrectly or unmatched events. The ratio figure shows the difference between the number of events in the training and test samples divided by the statistical uncertainty in this difference. Finally, d shows the comparison of the \(r_{\mathrm {BDT}}\) distributions observed in data and MC simulation. The hatched area includes the uncertainties as detailed in the text. The uncertainty bars correspond to the statistical uncertainties in the data

Fig. 3

Various classes of \(m_{\mathrm {top}}\) uncertainties as a function of the minimum requirement on the BDT output \(r_{\mathrm {BDT}}\) and for the standard selection. The total uncertainty (solid line) is the sum in quadrature of the statistical (dotted line) and total systematic uncertainty (short dash-dotted line). The total systematic uncertainty consists of the total experimental (dashed line) and total signal-modelling uncertainty (long dash-dotted line). The uncertainties in the background estimate are included in the total experimental uncertainty. The minimum requirement on \(r_{\mathrm {BDT}}\) defining the \(\mathrm {BDT}\) selection is indicated by the vertical black dashed line. All uncertainties are included except for the method and the pile-up uncertainties

The full \(m_{\mathrm {top}}\) analysis detailed in Sect. 8 is performed, except for the evaluation of the small method and pile-up uncertainties described in Sect. 8, for several minimum requirements on \(r_{\mathrm {BDT}}\) in the range of \([-0.10, 0.05]\) in steps of 0.05 to find the point with smallest total uncertainty. The total uncertainty in \(m_{\mathrm {top}}\) together with the various classes of uncertainty sources as a function of \(r_{\mathrm {BDT}}\) evaluated in the \(\mathrm {BDT}\) optimization are shown in Fig. 3. The minimum requirement \(r_{\mathrm {BDT}} =-0.05\) provides the smallest total uncertainty in \(m_{\mathrm {top}}\). The resulting numbers of events for this BDT selection are given in Table 1. Compared with the preselection, \(\epsilon _{\mathrm {cm}}\) is increased from \(0.71\) to \(0.82\), albeit at the expense of a significant reduction in the number of selected events. The purity \(\pi _{\mathrm {cm}}\) is increased from \(0.28\) to \(0.41\). In addition, the intrinsic resolution in \(m_{\mathrm {top}}\) of the remaining event sample is improved, i.e. the statistical uncertainty in \(m_{\mathrm {top}}\) in Fig. 3 is almost constant as a function of \(r_{\mathrm {BDT}}\); in particular, it does not scale with the square root of the number of events retained. For the signal sample with \(m_{\mathrm {top}} =172.5\) \(\text {GeV}\), the template fit functions for the standard selection and the \(\mathrm {BDT}\) selection, together with their ratios, are shown in Fig. 12 in Appendix A. The shape of the signal modelling uncertainty derives from a sum of contributions with different shapes. The curves from the signal Monte Carlo generator and colour reconnection uncertainties decrease, the one from the underlying event uncertainty is flat, the one from the initial- and final-state QCD radiation has a valley similar to the sum of all contributions, and finally the one from the hadronization uncertainty rises.

Some distributions of the observed event kinematics after the \(\mathrm {BDT}\) selection are shown in Fig. 4. Good agreement between the MC predictions and the data is found, as seen for the preselection in Fig. 1. The examples shown are the observed \(W\) boson transverse mass for the semi-leptonically decaying top quark in Fig. 4a and the three observables of the \(m_{\mathrm {top}}\) analysis (within the ranges of the template fit) in Fig. 4b–d. The sharp edge observed at 30 \(\text {GeV}\) in Fig. 4a originates from the different selection requirements for the \(W\) boson transverse mass in the electron+jets and muon+jets final states.
Fig. 4

Distributions for the events passing the BDT selection. The data are shown, together with the signal-plus-background prediction normalized to the number of events observed in the data. The hatched area is the uncertainty in the prediction described in the text. The rightmost bin contains all entries with values above the lower edge of this bin, similarly the leftmost bin contains all entries with values below the upper edge of this bin. a shows the \(W\) boson transverse mass for the semi-leptonic top quark decay. The remaining figures show the three observables used for the determination of \(m_{\mathrm {top}}\), where b shows the reconstructed top quark mass \(m_{\mathrm {top}} ^{\mathrm {reco}}\), c shows the reconstructed invariant mass of the \(W\) boson \(m_{W}^{\mathrm {reco}}\) and d shows the reconstructed ratio of jet transverse momenta \(R_{bq}^{\mathrm {reco}}\). The three distributions are shown within the ranges of the template fit

7 Template fit

This analysis uses a three-dimensional template fit technique which determines \(m_{\mathrm {top}}\) together with the jet energy scale factors \(\mathrm {JSF}\) and \(\mathrm {bJSF}\). The aim of the multi-dimensional fit to the data is to measure \(m_{\mathrm {top}}\) and, at the same time, to absorb the mean differences between the jet energy scales observed in data and MC simulated events into jet energy scale factors. By using \(\mathrm {JSF}\) and \(\mathrm {bJSF}\), most of the uncertainties in \(m_{\mathrm {top}}\) induced by \(\mathrm {JES}\) and \(\mathrm {bJES}\) uncertainties are transformed into additional statistical components caused by the higher dimensionality of the fit. This method reduces the total uncertainty in \(m_{\mathrm {top}}\) only for sufficiently large data samples. In this case, the sum in quadrature of the additional statistical uncertainty in \(m_{\mathrm {top}}\) due to the \(\mathrm {JSF}\)  (or \(\mathrm {bJSF}\)) fit and the residual \(\mathrm {JES}\)-induced (or \(\mathrm {bJES}\)-induced) systematic uncertainty is smaller than the original \(\mathrm {JES}\)-induced (or \(\mathrm {bJES}\)-induced) uncertainty in \(m_{\mathrm {top}}\). This situation was already realized for the \({\sqrt{s}} =7\) \(\text {TeV}\) data analysis [9] and is even more advantageous for the much larger data sample of the \({\sqrt{s}} =8\) \(\text {TeV}\) data analysis. Since \(\mathrm {JSF}\) and \(\mathrm {bJSF}\) are global factors, they do not completely absorb the \(\mathrm {JES}\) and \(\mathrm {bJES}\) uncertainties which have \(p_{\text {T}}\)- and \(\eta \)-dependent components.

For simultaneously determining \(m_{\mathrm {top}}\), \(\mathrm {JSF}\) and \(\mathrm {bJSF}\), templates are constructed from the MC samples. Templates of \(m_{\mathrm {top}} ^{\mathrm {reco}}\) are constructed with several input \(m_{\mathrm {top}}\) values used in the range 167.5–177.5 \(\text {GeV}\) and for the sample at \(m_{\mathrm {top}} =172.5\) \(\text {GeV}\) also with independent input values for \(\mathrm {JSF}\) and \(\mathrm {bJSF}\) in the range 0.96–1.04 in steps of 0.02. Statistically independent MC samples are used for different input values of \(m_{\mathrm {top}}\). The templates with different values of \(\mathrm {JSF}\) and \(\mathrm {bJSF}\) are constructed by scaling the energies of the jets appropriately. In this procedure, \(\mathrm {JSF}\) is applied to all jets, while \(\mathrm {bJSF}\) is solely applied to \(b\text {-jets}\) according to the generated quark flavour. The scaling is performed after the various correction steps of the jet calibration but before the event selection. This procedure results in different events passing the \(\mathrm {BDT}\) selection from one energy scale variation to another. However, many events are in all samples, resulting in a large statistical correlation of the samples with different jet scale factors. Similarly, templates of \(m_{W}^{\mathrm {reco}}\) and \(R_{bq}^{\mathrm {reco}}\) are constructed with the above listed input values of \(m_{\mathrm {top}}\), \(\mathrm {JSF}\) and \(\mathrm {bJSF}\).

Independent signal templates are derived for the three observables for all \(m_{\mathrm {top}}\)-dependent samples, consisting of the \(t\bar{t}\) signal events and single-top-quark production events. This procedure is adopted because single-top-quark production carries information about the top quark mass, and in this way, \(m_{\mathrm {top}}\)-independent background templates can be used. The signal templates are simultaneously fitted to the sum of a Gaussian and two Landau functions for \(m_{\mathrm {top}} ^{\mathrm {reco}}\), to the sum of two Gaussian functions for \(m_{W}^{\mathrm {reco}}\) and to the sum of two Gaussian and one Landau function for \(R_{bq}^{\mathrm {reco}}\). This set of functions leads to an unbiased estimate of \(m_{\mathrm {top}}\), but is not unique. For the background, the \(m_{\mathrm {top}} ^{\mathrm {reco}}\) distribution is fitted to a Landau function, while both the \(m_{W}^{\mathrm {reco}}\) and the \(R_{bq}^{\mathrm {reco}}\) distributions are fitted to the sum of two Gaussian functions.

In Fig. 5a–c, the sensitivity of \(m_{\mathrm {top}} ^{\mathrm {reco}}\) to the fit parameters \(m_{\mathrm {top}}\), \(\mathrm {JSF}\) and \(\mathrm {bJSF}\) is shown by the superposition of the signal templates and their fits for three input values per varied parameter. In a similar way, the sensitivity of \(m_{W}^{\mathrm {reco}}\) to \(\mathrm {JSF}\) is shown in Fig. 5d. The dependences of \(m_{W}^{\mathrm {reco}}\) on the input values of \(m_{\mathrm {top}}\) and \(\mathrm {bJSF}\) are negligible and are not shown. Consequently, to increase the size of the simulation sample, the fit is performed on the sum of the \(m_{W}^{\mathrm {reco}}\) distributions of the samples with different input top quark masses. Finally, the sensitivity of \(R_{bq}^{\mathrm {reco}}\) to the input values of \(m_{\mathrm {top}}\) and \(\mathrm {bJSF}\) is shown in Fig. 5e, f. The dependence of \(R_{bq}^{\mathrm {reco}}\) on \(\mathrm {JSF}\)  (not shown) is much weaker than the dependence on \(\mathrm {bJSF}\).
Fig. 5

Template parameterizations for signal events, composed of \(t\bar{t}\) and single-top-quark production events. ac show the sensitivity of \(m_{\mathrm {top}} ^{\mathrm {reco}}\) to \(m_{\mathrm {top}}\), \(\mathrm {JSF}\) and \(\mathrm {bJSF}\), d shows the sensitivity of \(m_{W}^{\mathrm {reco}}\) to \(\mathrm {JSF}\) and e, f show the sensitivity of \(R_{bq}^{\mathrm {reco}}\) to \(m_{\mathrm {top}}\) and \(\mathrm {bJSF}\). Each template is overlaid with the corresponding probability density function from the combined fit to all templates described in the text. The ratios shown are calculated relative to the probability density function of the central sample with \(m_{\mathrm {top}} = 172.5\) \(\text {GeV}\), \(\mathrm {JSF} = 1\) and \(\mathrm {bJSF} = 1\)

For the signal, the parameters of the fitting functions for \(m_{\mathrm {top}} ^{\mathrm {reco}}\) depend linearly on \(m_{\mathrm {top}}\), \(\mathrm {JSF}\) and \(\mathrm {bJSF}\). The parameters of the fitting functions for \(m_{W}^{\mathrm {reco}}\) depend linearly on \(\mathrm {JSF}\). Finally, the parameters of the fitting functions for \(R_{bq}^{\mathrm {reco}}\) depend linearly on \(m_{\mathrm {top}}\), \(\mathrm {JSF}\) and \(\mathrm {bJSF}\). For the background, the dependences of the parameters of the fitting functions are identical to those for the signal, except that they do not depend on \(m_{\mathrm {top}}\) and that those for \(R_{bq}^{\mathrm {reco}}\) do not depend on \(\mathrm {JSF}\).

Signal and background probability density functions \(P_{\mathrm {top}}^{\mathrm {sig}}\) and \(P_{\mathrm {top}}^{\mathrm {bkg}}\) for the \(m_{\mathrm {top}} ^{\mathrm {reco}}\), \(m_{W}^{\mathrm {reco}}\) and \(R_{bq}^{\mathrm {reco}}\) distributions are used in an unbinned likelihood fit to the data for all events, \(i=1,\dots N\). The likelihood function maximized is
$$\begin{aligned}&L _\mathrm {shape}^{\ell \mathrm {+jets}}(m_{\mathrm {top}}, \mathrm {JSF}, \mathrm {bJSF}, f_{\mathrm {bkg}}) \nonumber \\&\quad =\prod _{i=1}^{N} P_{\mathrm {top}} (m_{\mathrm {top}} ^{\mathrm {reco}, i} \,\vert \,m_{\mathrm {top}}, \mathrm {JSF}, \mathrm {bJSF}, f_{\mathrm {bkg}}) \nonumber \\&\qquad \times \,P_{W} (m_{W}^{\mathrm {reco}, i} \,\vert \,\mathrm {JSF}, f_{\mathrm {bkg}}) \nonumber \\&\qquad \times \,P_{R_{bq}} (R_{bq}^{\mathrm {reco}, i} \,\vert \,m_{\mathrm {top}}, \mathrm {JSF}, \mathrm {bJSF}, f_{\mathrm {bkg}}), \end{aligned}$$
(1)
with
$$\begin{aligned}&P_{\mathrm {top}} (m_{\mathrm {top}} ^{\mathrm {reco}, i} \,\vert \,m_{\mathrm {top}}, \mathrm {JSF}, \mathrm {bJSF}, f_{\mathrm {bkg}}) \\&\quad = (1-f_{\mathrm {bkg}})\cdot P_{\mathrm {top}}^{\mathrm {sig}} (m_{\mathrm {top}} ^{\mathrm {reco}, i} \,\vert \,m_{\mathrm {top}}, \mathrm {JSF}, \mathrm {bJSF}) \\&\qquad +f_{\mathrm {bkg}} \cdot P_{\mathrm {top}}^{\mathrm {bkg}} (m_{\mathrm {top}} ^{\mathrm {reco}, i} \,\vert \,\mathrm {JSF}, \mathrm {bJSF}), \\&P_{W} (m_{W}^{\mathrm {reco}, i} \,\vert \,\mathrm {JSF}, f_{\mathrm {bkg}}) \\&\quad = (1-f_{\mathrm {bkg}})\cdot P_{W}^{\mathrm {sig}} (m_{W}^{\mathrm {reco}, i} \,\vert \,\mathrm {JSF}) \\&\qquad +f_{\mathrm {bkg}} \cdot P_{W}^{\mathrm {bkg}} (m_{W}^{\mathrm {reco}, i} \,\vert \,\mathrm {JSF}),\quad \text {and} \\&P_{R_{bq}} (R_{bq}^{\mathrm {reco}, i} \,\vert \,m_{\mathrm {top}}, \mathrm {JSF}, \mathrm {bJSF}, f_{\mathrm {bkg}})\\&\quad = (1-f_{\mathrm {bkg}})\cdot P_{R_{bq}}^{\mathrm {sig}} (R_{bq}^{\mathrm {reco}, i} \,\vert \,m_{\mathrm {top}}, \mathrm {JSF}, \mathrm {bJSF}) \\&\qquad +f_{\mathrm {bkg}} \cdot P_{R_{bq}}^{\mathrm {bkg}} (R_{bq}^{\mathrm {reco}, i} \,\vert \, \mathrm {bJSF}) \end{aligned}$$
where the fraction of background events is denoted by \(f_{\mathrm {bkg}}\). The parameters determined by the fit are \(m_{\mathrm {top}}\), \(\mathrm {JSF}\) and \(\mathrm {bJSF}\), while \(f_{\mathrm {bkg}}\) is fixed to its expectation shown in Table 1. It was verified that the correlations between \(m_{\mathrm {top}} ^{\mathrm {reco}}\), \(m_{W}^{\mathrm {reco}}\) and \(R_{bq}^{\mathrm {reco}}\) of \(\rho (m_{\mathrm {top}} ^{\mathrm {reco}}, m_{W}^{\mathrm {reco}})= 0.05 \), \(\rho (m_{\mathrm {top}} ^{\mathrm {reco}}, R_{bq}^{\mathrm {reco}})= 0.18 \), and \(\rho (m_{W}^{\mathrm {reco}}, R_{bq}^{\mathrm {reco}})= -0.13 \), are small enough that formulating the likelihood in Eq. (1) as a product of three one-dimensional likelihoods does not bias the result.
Pseudo-experiments are used to verify the internal consistency of the fitting procedure and to obtain the expected statistical uncertainty for the data. For each set of parameter values, \(500\) pseudo-experiments are performed, each corresponding to the integrated luminosity of the data. To retain the correlation of the three observables for the three-dimensional fit, individual events are used. Because this exceeds the number of available MC events, results are corrected for oversampling [80]. The results of pseudo-experiments for different input values of \(m_{\mathrm {top}}\) are obtained from statistically independent samples, while the results for different \(\mathrm {JSF}\) and \(\mathrm {bJSF}\) are obtained from statistically correlated samples as explained above. For each fitted quantity and each variation of input parameters, the residual, i.e. the difference between the input value and the value obtained by the fit, is compatible with zero. The three expected statistical uncertainties are
$$\begin{aligned} \sigma _{\mathrm {stat}} (m_{\mathrm {top}})&= 0.389 \pm 0.004 ~\text {GeV}, \\ \sigma _{\mathrm {stat}} (\mathrm {JSF})&= 0.00115 \pm 0.00001,\quad \text {and}\\ \sigma _{\mathrm {stat}} (\mathrm {bJSF})&= 0.0046 \pm 0.0001, \end{aligned}$$
where the values quoted are the mean and RMS of the distribution of the statistical uncertainties in the fitted quantities from pseudo-experiments. The widths of the pull distributions are below unity for \(m_{\mathrm {top}}\) and the two jet scale factors, which results in an overestimation of the uncertainty in \(m_{\mathrm {top}}\) of up to 7\(\%\). Since this leads to a conservative estimate of the uncertainty in \(m_{\mathrm {top}}\), no attempts to mitigate this feature are made.

8 Uncertainties affecting the \(\mathbf {m_{\mathrm {top}}}\) determination

Table 3

Systematic uncertainties in \(m_{\mathrm {top}}\). The measured values of \(m_{\mathrm {top}}\) are given together with the statistical and systematic uncertainties in \(\text {GeV}\) for the standard and the BDT event selections. For comparison, the result in the \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) channel at \({\sqrt{s}} =7\) \(\text {TeV}\) from Ref. [9] is also listed. For each systematic uncertainty listed, the first value corresponds to the uncertainty in \(m_{\mathrm {top}}\), and the second to the statistical precision in this uncertainty. An integer value of zero means that the corresponding uncertainty is negligible and therefore not evaluated. Statistical uncertainties quoted as 0.00 are smaller than 0.005. The statistical uncertainty in the total systematic uncertainty is calculated from uncertainty propagation. The last line refers to the sum in quadrature of the statistical and systematic uncertainties

 

\({\sqrt{s}} =7\) \(\text {TeV}\)

\({\sqrt{s}} =8\) \(\text {TeV}\)

Event selection

Standard

Standard

BDT

\(m_{\mathrm {top}}\) result [\(\text {GeV}\)]

\(172.33\)

\(171.90\)

\(172.08\)

Statistics

\(0.75\)

\(0.38\)

\(0.39\)

   – Stat. comp. (\(m_{\mathrm {top}}\))

\(0.23\)

\(0.12\)

\(0.11\)

   – Stat. comp. (\(\mathrm {JSF}\))

\(0.25\)

\(0.11\)

\(0.11\)

   – Stat. comp. (\(\mathrm {bJSF}\))

\(0.67\)

\(0.34\)

\(0.35\)

Method

0.11 ± 0.10

0.04 ± 0.11

0.13 ± 0.11

Signal Monte Carlo generator

0.22 ± 0.21

0.50 ± 0.17

0.16 ± 0.17

Hadronization

0.18 ± 0.12

0.05 ± 0.10

0.15 ± 0.10

Initial- and final-state QCD radiation

0.32 ± 0.06

0.28 ± 0.11

0.08 ± 0.11

Underlying event

0.15 ± 0.07

0.08 ± 0.15

0.08 ± 0.15

Colour reconnection

0.11 ± 0.07

0.37 ± 0.15

0.19 ± 0.15

Parton distribution function

0.25 ± 0.00

0.08 ± 0.00

0.09 ± 0.00

Background normalization

0.10 ± 0.00

0.04 ± 0.00

0.08 ± 0.00

W+jets shape

0.29 ± 0.00

0.05 ± 0.00

0.11 ± 0.00

Fake leptons shape

0.05 ± 0.00

0

0

Jet energy scale

0.58 ± 0.11

0.63 ± 0.02

0.54 ± 0.02

Relative b-to-light-jet energy scale

0.06 ± 0.03

0.05 ± 0.01

0.03 ± 0.01

Jet energy resolution

0.22 ± 0.11

0.23 ± 0.03

0.20 ± 0.04

Jet reconstruction efficiency

0.12 ± 0.00

0.04 ± 0.01

0.02 ± 0.01

Jet vertex fraction

0.01 ± 0.00

0.13 ± 0.01

0.09 ± 0.01

\(b\text {-tagging}\)

0.50 ± 0.00

0.37 ± 0.00

0.38 ± 0.00

Leptons

0.04 ± 0.00

0.16 ± 0.01

0.16 ± 0.01

Missing transverse momentum

0.15 ± 0.04

0.08 ± 0.01

0.05 ± 0.01

Pile-up

0.02 ± 0.01

0.14 ± 0.01

0.15 ± 0.01

Total systematic uncertainty

\(1.04\) ± \(0.08\)

\(1.07\) ± \(0.10\)

\(0.82\) ± \(0.06\)

Total

\(1.28\) ± \(0.08\)

\(1.13\) ± \(0.10\)

\(0.91\) ± \(0.06\)

This section focuses on the treatment of uncertainty sources of a systematic nature. The same systematic uncertainty sources as in Ref. [9] are investigated. If possible, the corresponding uncertainty in \(m_{\mathrm {top}}\) is evaluated by varying the respective quantities by \(\pm 1 \sigma \) from their default values, constructing the corresponding event sample and measuring the average \(m_{\mathrm {top}}\) change relative to the result from the nominal MC sample with \(500\) pseudo-experiments each, drawn from the full MC sample. In the absence of a \(\pm 1 \sigma \) variation, e.g. for the evaluation of the uncertainty induced by the choice of signal MC generator, the full observed difference is assigned as a symmetric systematic uncertainty and further treated as a variation equivalent to a \(\pm 1 \sigma \) variation. Wherever a \(\pm 1 \sigma \) variation can be performed, half the observed difference between the \(+1\sigma \) and \(-1\sigma \) variation in \(m_{\mathrm {top}}\) is assigned as an uncertainty if the \(m_{\mathrm {top}}\) values obtained from the variations lie on opposite sides of the nominal result. If they lie on the same side, the maximum observed difference is taken as a symmetric systematic uncertainty. Since the systematic uncertainties are derived from simulation or data samples with limited numbers of events, all systematic uncertainties have a corresponding statistical uncertainty, which is calculated taking into account the statistical correlation of the considered samples, as explained in Sect. 8.5. The statistical uncertainty in the total systematic uncertainty is dominated by the limited sizes of the simulation samples. The resulting systematic uncertainties are given in Table 3 independent of their statistical significance. Further information is given in Tables 8, 9, 10, 11 and 12 in Appendix A. This approach follows the suggestion in Ref. [81] and relies on the fact that, given a large enough number of considered uncertainty sources, statistical fluctuations average out.6 The uncertainty sources are designed to be uncorrelated with each other, and thus the total uncertainty is taken as the sum in quadrature of uncertainties from all sources. The individual uncertainties are compared in Table 3 for three cases: the standard selection for the \({\sqrt{s}} =7\) \(\text {TeV}\) [9] and 8 \(\text {TeV}\) data and the \(\mathrm {BDT}\) selection for \({\sqrt{s}} =8\) \(\text {TeV}\) data. Many uncertainties in \(m_{\mathrm {top}}\) obtained with the standard selection at the two centre-of-mass energies agree within their statistical uncertainties such that the resulting total systematic uncertainties are almost identical. Consequently, repeating the \({\sqrt{s}} =7\) \(\text {TeV}\) analysis on \({\sqrt{s}} =8\) \(\text {TeV}\) data would have only improved the statistical precision. The picture changes when comparing the uncertainties in \({\sqrt{s}} =8\) \(\text {TeV}\) data for the standard selection and the \(\mathrm {BDT}\) selection. In general, the experimental uncertainties change only slightly, with the largest reduction observed for the JES uncertainty. In contrast, a large improvement comes from the reduced uncertainties in the modelling of the \(t\bar{t}\) signal processes as shown in Table 3. This, together with the improved intrinsic resolution in \(m_{\mathrm {top}}\), more than compensates for the small loss in precision caused by the increased statistical uncertainty. The individual sources of systematic uncertainties and the evaluation of their effect on \(m_{\mathrm {top}}\) are described in the following.

8.1 Statistics and method calibration

Uncertainties related to statistical effects and the method calibration are discussed here.

Statistical: The quoted statistical uncertainty consists of three parts: a purely statistical component in \(m_{\mathrm {top}}\) and the contributions stemming from the simultaneous determination of \(\mathrm {JSF}\) and \(\mathrm {bJSF}\). The purely statistical component in \(m_{\mathrm {top}}\) is obtained from a one-dimensional template method exploiting only the \(m_{\mathrm {top}} ^{\mathrm {reco}}\) observable, while fixing the values of \(\mathrm {JSF}\) and \(\mathrm {bJSF}\) to the results of the three-dimensional analysis. The contribution to the statistical uncertainty in the fitted parameters due to the simultaneous fit of \(m_{\mathrm {top}}\) and \(\mathrm {JSF}\) is estimated as the difference in quadrature between the statistical uncertainty in a two-dimensional fit to \(m_{\mathrm {top}} ^{\mathrm {reco}}\) and \(m_{W}^{\mathrm {reco}}\) while fixing the value of \(\mathrm {bJSF}\) and the one-dimensional fit to the data described above. Analogously, the contribution of the statistical uncertainty due to the simultaneous fit of \(m_{\mathrm {top}}\) together with \(\mathrm {JSF}\) and \(\mathrm {bJSF}\) is defined as the difference in quadrature between the statistical uncertainties obtained in the three-dimensional and the two-dimensional fits to the data. This separation allows a comparison of the statistical sensitivities of the \(m_{\mathrm {top}}\) estimator used in this analysis, to those of analyses exploiting a different number of observables in the fit. In addition, the sensitivity of the estimators to the global jet energy scale factors can be compared directly. These uncertainties are treated as uncorrelated uncertainties in \(m_{\mathrm {top}}\) combinations. Together with the systematic uncertainty in the residual jet energy scale uncertainties discussed below, they directly replace the uncertainty in \(m_{\mathrm {top}}\) from the jet energy scale variations present without the in situ determination.

Method: The residual difference between fitted and generated \(m_{\mathrm {top}}\) when analysing a template from a MC sample reflects the potential bias of the method. Consequently, the largest observed fitted \(m_{\mathrm {top}}\) residual and the largest observed statistical uncertainty in this quantity, in any of the five signal samples with different assumed values of \(m_{\mathrm {top}}\), is assigned as the method calibration uncertainty and its corresponding statistical uncertainty, respectively. This also covers effects from limited numbers of simulated events in the templates and potential deficiencies in the template parameterizations.

8.2 Modelling of signal processes

The modelling of \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) events incorporates a number of processes that have to be accurately described, resulting in systematic effects, ranging from the \(t\bar{t}\) production to the hadronization of the showered objects.

Thanks to the restrictive event-selection requirements, the contribution of non-\(t\bar{t}\) processes, comprising the single-top-quark process and the various background processes, is very low. The systematic uncertainty in \(m_{\mathrm {top}}\) from the uncertainty in the single-top-quark normalization is estimated from the corresponding uncertainty in the theoretical cross-section given in Sect. 3. The resulting systematic uncertainty is small compared with the systematic uncertainty in the \(t\bar{t}\) production and is consequently neglected. For the modelling of the signal processes, the consequence of including single-top-quark variations in the uncertainty evaluation was investigated for various uncertainty sources and found to be negligible. Therefore, the single-top-quark variations are not included in the determination of the signal event uncertainties.

Signal Monte Carlo generator: The full observed difference in fitted \(m_{\mathrm {top}}\) between the event samples produced with the Powheg-Box and MC@NLO  [82, 83] programs is quoted as a systematic uncertainty. For the renormalization and factorization scales the Powheg-Box sample uses the function given in Sect. 3, while the MC@NLO sample uses \(\mu _\mathrm {R, F} =\sqrt{m_{\mathrm {top}} ^2 + 0.5 (p_{\mathrm{T},t}^2 + p_{\mathrm{T}, \bar{t}}^2)}\). Both samples are generated with a top quark mass of \(m_{\mathrm {top}} =172.5\) \(\text {GeV}\) with the CT10 PDFs in the matrix-element calculation and use the Herwig and Jimmy programs with the ATLAS AUET2 tune [47].

Hadronization: To cover the choice of parton shower and hadronization models, samples produced with the Powheg-Box program are showered with either the Pythia6 program using the P2011C tune or the Herwig and Jimmy programs using the ATLAS AUET2 tune. This includes different approaches in shower modelling, such as using a \(p_{\text {T}}\)-ordered parton showering in the Pythia program or angular-ordered parton showering in the Herwig program, the different parton shower matching scales, as well as fragmentation functions and hadronization models, such as choosing the Lund string model [84, 85] implemented in the Pythia program or the cluster fragmentation model [86] used in the Herwig program. The full observed difference between the samples is quoted as a systematic uncertainty.

As shown in Fig. 1, the distributions of transverse momenta in data are slightly softer than those in the Powheg+Pythia MC simulation samples. Similarly to what was observed in the \(t\bar{t} \rightarrow \mathrm {dilepton}\) channel for the \(p_{\mathrm {T}, \ell b}\) distribution, in the \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) channel the Powheg+Herwig sample is much closer to the data for several distributions of transverse momenta. The \(p_{\mathrm {T, had}}\) distribution is much better described by the Powheg+Herwig sample as was also observed in Ref. [78]. In addition, but to a lesser extent, the MC@NLO sample used to assess the signal Monte Carlo generator uncertainty and the samples to assess the initial- and final-state QCD radiation uncertainty discussed next also lead to a softer distribution in simulation. Given this, the observed difference in the \(p_{\mathrm {T, had}}\) distribution is covered by a combination of the signal-modelling uncertainties given in Table 3.

Despite the fact that the \(\mathrm {JES}\) and \(\mathrm {bJES}\) are estimated independently using dijet and other non-\(t\bar{t}\) samples [63], some double-counting of hadronization-uncertainty-induced uncertainties in the \(\mathrm {JES}\) and \(m_{\mathrm {top}}\) cannot be excluded. This was investigated closely for the ATLAS top quark mass measurement in the \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) channel at \({\sqrt{s}} =7\) \(\text {TeV}\). The results in Ref. [87] revealed that the amount of double-counting of \(\mathrm {JES}\) and hadronization effects for the \(t\bar{t} \rightarrow \mathrm {lepton+jets}\) channel is small.

Initial- and final-state QCD radiation (ISR/FSR): ISR/FSR leads to a higher jet multiplicity and different jet energies than the hard process, which affects the distributions of the three observables. The uncertainties due to ISR/FSR modelling are estimated with samples generated with the Powheg-Box program interfaced to the Pythia6 program for which the parameters of the generation are varied to span the ranges compatible with the results of measurements of \(t\bar{t}\) production in association with jets [88, 89, 90]. This uncertainty is evaluated by comparing two dedicated samples that differ in several parameters, namely the QCD scale \(\Lambda _\mathrm {QCD}\), the transverse momentum scale for space-like parton-shower evolution \(Q^2_\mathrm {max}\), the \(h_{\mathrm {damp}}\) parameter [91] and the P2012 RadLo and RadHi tunes [30]. In Ref. [90], it was shown that a number of final-state distributions are better accounted for by the Powheg+Pythia samples with \(h_{\mathrm {damp}} =m_{\mathrm {top}} \). Therefore, these samples are used for evaluating this uncertainty, taking half the observed difference between the up variation and the down variation sample. Because the parameterizations for the template fit to data are obtained from Powheg+Pythia samples using \(h_{\mathrm {damp}} =\infty \), it was verified that, considering the method uncertainty quoted in Table 3, applying the same functions to the \(h_{\mathrm {damp}} =m_{\mathrm {top}} \) samples leads to a result compatible with the input top quark mass.

Underlying event: To reduce statistical fluctuations in the evaluation of this systematic uncertainty, the difference in underlying-event modelling is assessed by comparing a pair of Powheg-Box samples based on the same partonic events generated with the CT10 PDFs. A sample with the P2012 tune is compared with a sample with the P2012 mpiHi tune [30], with both tunes using the same CTEQ6L1 PDFs [92] for parton showering and hadronization. The Perugia 2012 mpiHi tune provides more semi-hard multiple parton interactions and is used for this comparison with identical colour reconnection parameters in both tunes. The full observed difference is assigned as a systematic uncertainty.

Colour reconnection: This systematic uncertainty is estimated using a pair of samples with the same partonic events as for the underlying-event uncertainty evaluation but with the P2012 tune and the P2012 loCR tune [30] for parton showering and hadronization. The full observed difference is assigned as a systematic uncertainty.

Parton distribution function (PDF): The PDF systematic uncertainty is the sum in quadrature of three contributions. These are the sum in quadrature of the differences in fitted \(m_{\mathrm {top}}\) for the 26 eigenvector variations of the CT10 PDF and two differences in \(m_{\mathrm {top}}\) obtained from reweighting the central CT10 PDF set to the MSTW2008 PDF [39] and the NNPDF2.3 PDF [42].

8.3 Modelling of background processes

Uncertainties in the modelling of the background processes are taken into account by variations of the corresponding normalizations and shapes of the distributions.

Background normalization: The normalizations are varied for the data-driven background estimates according to their uncertainties. For the negligible contribution from diboson production, no normalization uncertainty is evaluated.

Background shape: For the \(W\)+jets background, the shape uncertainty is evaluated from the variation of the heavy-flavour fractions. The corresponding uncertainty is small. Given the very small contribution from \(Z\)+jets, diboson and NP/fake-lepton backgrounds, no shape uncertainty is evaluated for these background sources.

8.4 Detector modelling

The level of understanding of the detector response and of the particle interactions therein is reflected in numerous systematic uncertainties.

Jet energy scale (JES): The \(\mathrm {JES}\) is measured with a relative precision of about \(1\%\) to \(4\%\), typically falling with increasing jet \(p_{\text {T}}\) and rising with increasing jet \(\vert \eta \vert \) [93, 94]. The total \(\mathrm {JES}\) uncertainty consists of more than 60 subcomponents originating from the various steps in the jet calibration. The number of these nuisance parameters is reduced with a matrix diagonalization of the full \(\mathrm {JES}\) covariance matrix including all nuisance parameters for a given category of the \(\mathrm {JES}\) uncertainty components.

The analyses of \({\sqrt{s}} =7\) \(\text {TeV}\) and \({\sqrt{s}} =8\) \(\text {TeV}\) data make use of the EM+JES and LCW+GSC [93] jet calibrations, respectively. The two calibrations feature different sets of nuisance parameters, and the LCW+GSC calibration generally has smaller uncertainties than the EM+JES calibration. While the pile-up correction for the jet calibration for \({\sqrt{s}} =7\) \(\text {TeV}\) data only depends on the number of primary vertices (\(n_\mathrm {vtx}\)) and the mean number of interactions per bunch crossing (\(\mu \)), a pile-up subtraction method based on jet area is introduced for the \({\sqrt{s}} =8\) \(\text {TeV}\) data. Terms to account for uncertainties in the pile-up estimation are added. They depend on the jet \(p_{\text {T}}\) and the local transverse momentum density. In addition, the punch-through uncertainty, i.e. an uncertainty for jets that penetrate through to the muon spectrometer, is added. The final reduced number of nuisance parameters for the \({\sqrt{s}} =8\) \(\text {TeV}\) analysis is 25. The JES-uncertainty-induced uncertainty in \(m_{\mathrm {top}}\) is the dominant systematic uncertainty for all results shown in Table 3. When only a one-dimensional fit to \(m_{\mathrm {top}} ^{\mathrm {reco}}\) or a two-dimensional fit to \(m_{\mathrm {top}} ^{\mathrm {reco}}\) and \(m_{W}^{\mathrm {reco}}\) is done, this uncertainty is \(0.99\)  \(\text {GeV}\) or \(0.74\)  \(\text {GeV}\), respectively.

Relative b-to-light-jet energy scale (bJES): The \(\mathrm {bJES}\) uncertainty is an additional uncertainty for the remaining differences between \(b\text {-jets}\) and light-jets after the global \(\mathrm {JES}\) is applied, and therefore the corresponding uncertainty is uncorrelated with th