Advertisement

Topological cell clustering in the ATLAS calorimeters and its performance in LHC Run 1

  • G. Aad
  • B. Abbott
  • J. Abdallah
  • O. Abdinov
  • R. Aben
  • M. Abolins
  • O. S. AbouZeid
  • H. Abramowicz
  • H. Abreu
  • R. Abreu
  • Y. Abulaiti
  • B. S. Acharya
  • L. Adamczyk
  • D. L. Adams
  • J. Adelman
  • S. Adomeit
  • T. Adye
  • A. A. Affolder
  • T. Agatonovic-Jovin
  • J. Agricola
  • J. A. Aguilar-Saavedra
  • S. P. Ahlen
  • F. Ahmadov
  • G. Aielli
  • H. Akerstedt
  • T. P. A. Åkesson
  • A. V. Akimov
  • G. L. Alberghi
  • J. Albert
  • S. Albrand
  • M. J. Alconada Verzini
  • M. Aleksa
  • I. N. Aleksandrov
  • C. Alexa
  • G. Alexander
  • T. Alexopoulos
  • M. Alhroob
  • G. Alimonti
  • L. Alio
  • J. Alison
  • S. P. Alkire
  • B. M. M. Allbrooke
  • P. P. Allport
  • A. Aloisio
  • A. Alonso
  • F. Alonso
  • C. Alpigiani
  • A. Altheimer
  • B. Alvarez Gonzalez
  • D. Álvarez Piqueras
  • M. G. Alviggi
  • B. T. Amadio
  • K. Amako
  • Y. Amaral Coutinho
  • C. Amelung
  • D. Amidei
  • S. P. Amor Dos Santos
  • A. Amorim
  • S. Amoroso
  • N. Amram
  • G. Amundsen
  • C. Anastopoulos
  • L. S. Ancu
  • N. Andari
  • T. Andeen
  • C. F. Anders
  • G. Anders
  • J. K. Anders
  • K. J. Anderson
  • A. Andreazza
  • V. Andrei
  • S. Angelidakis
  • I. Angelozzi
  • P. Anger
  • A. Angerami
  • F. Anghinolfi
  • A. V. Anisenkov
  • N. Anjos
  • A. Annovi
  • M. Antonelli
  • A. Antonov
  • J. Antos
  • F. Anulli
  • M. Aoki
  • L. Aperio Bella
  • G. Arabidze
  • Y. Arai
  • J. P. Araque
  • A. T. H. Arce
  • F. A. Arduh
  • J.-F. Arguin
  • S. Argyropoulos
  • M. Arik
  • A. J. Armbruster
  • O. Arnaez
  • H. Arnold
  • M. Arratia
  • O. Arslan
  • A. Artamonov
  • G. Artoni
  • S. Artz
  • S. Asai
  • N. Asbah
  • A. Ashkenazi
  • B. Åsman
  • L. Asquith
  • K. Assamagan
  • R. Astalos
  • M. Atkinson
  • N. B. Atlay
  • K. Augsten
  • M. Aurousseau
  • G. Avolio
  • B. Axen
  • M. K. Ayoub
  • G. Azuelos
  • M. A. Baak
  • A. E. Baas
  • M. J. Baca
  • C. Bacci
  • H. Bachacou
  • K. Bachas
  • M. Backes
  • M. Backhaus
  • P. Bagiacchi
  • P. Bagnaia
  • Y. Bai
  • T. Bain
  • J. T. Baines
  • O. K. Baker
  • E. M. Baldin
  • P. Balek
  • T. Balestri
  • F. Balli
  • W. K. Balunas
  • E. Banas
  • Sw. Banerjee
  • A. A. E. Bannoura
  • L. Barak
  • E. L. Barberio
  • D. Barberis
  • M. Barbero
  • T. Barillari
  • M. Barisonzi
  • T. Barklow
  • N. Barlow
  • S. L. Barnes
  • B. M. Barnett
  • R. M. Barnett
  • Z. Barnovska
  • A. Baroncelli
  • G. Barone
  • A. J. Barr
  • F. Barreiro
  • J. Barreiro Guimarães da Costa
  • R. Bartoldus
  • A. E. Barton
  • P. Bartos
  • A. Basalaev
  • A. Bassalat
  • A. Basye
  • R. L. Bates
  • S. J. Batista
  • J. R. Batley
  • M. Battaglia
  • M. Bauce
  • F. Bauer
  • H. S. Bawa
  • J. B. Beacham
  • M. D. Beattie
  • T. Beau
  • P. H. Beauchemin
  • R. Beccherle
  • P. Bechtle
  • H. P. Beck
  • K. Becker
  • M. Becker
  • M. Beckingham
  • C. Becot
  • A. J. Beddall
  • A. Beddall
  • V. A. Bednyakov
  • C. P. Bee
  • L. J. Beemster
  • T. A. Beermann
  • M. Begel
  • J. K. Behr
  • C. Belanger-Champagne
  • W. H. Bell
  • G. Bella
  • L. Bellagamba
  • A. Bellerive
  • M. Bellomo
  • K. Belotskiy
  • O. Beltramello
  • O. Benary
  • D. Benchekroun
  • M. Bender
  • K. Bendtz
  • N. Benekos
  • Y. Benhammou
  • E. Benhar Noccioli
  • J. A. Benitez Garcia
  • D. P. Benjamin
  • J. R. Bensinger
  • S. Bentvelsen
  • L. Beresford
  • M. Beretta
  • D. Berge
  • E. Bergeaas Kuutmann
  • N. Berger
  • F. Berghaus
  • J. Beringer
  • C. Bernard
  • N. R. Bernard
  • C. Bernius
  • F. U. Bernlochner
  • T. Berry
  • P. Berta
  • C. Bertella
  • G. Bertoli
  • F. Bertolucci
  • C. Bertsche
  • D. Bertsche
  • M. I. Besana
  • G. J. Besjes
  • O. Bessidskaia Bylund
  • M. Bessner
  • N. Besson
  • C. Betancourt
  • S. Bethke
  • A. J. Bevan
  • W. Bhimji
  • R. M. Bianchi
  • L. Bianchini
  • M. Bianco
  • O. Biebel
  • D. Biedermann
  • N. V. Biesuz
  • M. Biglietti
  • J. Bilbao De Mendizabal
  • H. Bilokon
  • M. Bindi
  • S. Binet
  • A. Bingul
  • C. Bini
  • S. Biondi
  • D. M. Bjergaard
  • C. W. Black
  • J. E. Black
  • K. M. Black
  • D. Blackburn
  • R. E. Blair
  • J.-B. Blanchard
  • J. E. Blanco
  • T. Blazek
  • I. Bloch
  • C. Blocker
  • W. Blum
  • U. Blumenschein
  • S. Blunier
  • G. J. Bobbink
  • V. S. Bobrovnikov
  • S. S. Bocchetta
  • A. Bocci
  • C. Bock
  • M. Boehler
  • J. A. Bogaerts
  • D. Bogavac
  • A. G. Bogdanchikov
  • C. Bohm
  • V. Boisvert
  • T. Bold
  • V. Boldea
  • A. S. Boldyrev
  • M. Bomben
  • M. Bona
  • M. Boonekamp
  • A. Borisov
  • G. Borissov
  • S. Borroni
  • J. Bortfeldt
  • V. Bortolotto
  • K. Bos
  • D. Boscherini
  • M. Bosman
  • J. Boudreau
  • J. Bouffard
  • E. V. Bouhova-Thacker
  • D. Boumediene
  • C. Bourdarios
  • N. Bousson
  • S. K. Boutle
  • A. Boveia
  • J. Boyd
  • I. R. Boyko
  • I. Bozic
  • J. Bracinik
  • A. Brandt
  • G. Brandt
  • O. Brandt
  • U. Bratzler
  • B. Brau
  • J. E. Brau
  • H. M. Braun
  • W. D. Breaden Madden
  • K. Brendlinger
  • A. J. Brennan
  • L. Brenner
  • R. Brenner
  • S. Bressler
  • T. M. Bristow
  • D. Britton
  • D. Britzger
  • F. M. Brochu
  • I. Brock
  • R. Brock
  • J. Bronner
  • G. Brooijmans
  • T. Brooks
  • W. K. Brooks
  • J. Brosamer
  • E. Brost
  • P. A. Bruckman de Renstrom
  • D. Bruncko
  • R. Bruneliere
  • A. Bruni
  • G. Bruni
  • M. Bruschi
  • N. Bruscino
  • L. Bryngemark
  • T. Buanes
  • Q. Buat
  • P. Buchholz
  • A. G. Buckley
  • I. A. Budagov
  • F. Buehrer
  • L. Bugge
  • M. K. Bugge
  • O. Bulekov
  • D. Bullock
  • H. Burckhart
  • S. Burdin
  • C. D. Burgard
  • B. Burghgrave
  • S. Burke
  • I. Burmeister
  • E. Busato
  • D. Büscher
  • V. Büscher
  • P. Bussey
  • J. M. Butler
  • A. I. Butt
  • C. M. Buttar
  • J. M. Butterworth
  • P. Butti
  • W. Buttinger
  • A. Buzatu
  • A. R. Buzykaev
  • S. Cabrera Urbán
  • D. Caforio
  • V. M. Cairo
  • O. Cakir
  • N. Calace
  • P. Calafiura
  • A. Calandri
  • G. Calderini
  • P. Calfayan
  • L. P. Caloba
  • D. Calvet
  • S. Calvet
  • R. Camacho Toro
  • S. Camarda
  • P. Camarri
  • D. Cameron
  • R. Caminal Armadans
  • S. Campana
  • M. Campanelli
  • A. Campoverde
  • V. Canale
  • A. Canepa
  • M. Cano Bret
  • J. Cantero
  • R. Cantrill
  • T. Cao
  • M. D. M. Capeans Garrido
  • I. Caprini
  • M. Caprini
  • M. Capua
  • R. Caputo
  • R. M. Carbone
  • R. Cardarelli
  • F. Cardillo
  • T. Carli
  • G. Carlino
  • L. Carminati
  • S. Caron
  • E. Carquin
  • G. D. Carrillo-Montoya
  • J. R. Carter
  • J. Carvalho
  • D. Casadei
  • M. P. Casado
  • M. Casolino
  • D. W. Casper
  • E. Castaneda-Miranda
  • A. Castelli
  • V. Castillo Gimenez
  • N. F. Castro
  • P. Catastini
  • A. Catinaccio
  • J. R. Catmore
  • A. Cattai
  • J. Caudron
  • V. Cavaliere
  • D. Cavalli
  • M. Cavalli-Sforza
  • V. Cavasinni
  • F. Ceradini
  • L. Cerda Alberich
  • B. C. Cerio
  • K. Cerny
  • A. S. Cerqueira
  • A. Cerri
  • L. Cerrito
  • F. Cerutti
  • M. Cerv
  • A. Cervelli
  • S. A. Cetin
  • A. Chafaq
  • D. Chakraborty
  • I. Chalupkova
  • Y. L. Chan
  • P. Chang
  • J. D. Chapman
  • D. G. Charlton
  • C. C. Chau
  • C. A. Chavez Barajas
  • S. Che
  • S. Cheatham
  • A. Chegwidden
  • S. Chekanov
  • S. V. Chekulaev
  • G. A. Chelkov
  • M. A. Chelstowska
  • C. Chen
  • H. Chen
  • K. Chen
  • L. Chen
  • S. Chen
  • S. Chen
  • X. Chen
  • Y. Chen
  • H. C. Cheng
  • Y. Cheng
  • A. Cheplakov
  • E. Cheremushkina
  • R. Cherkaoui El Moursli
  • V. Chernyatin
  • E. Cheu
  • L. Chevalier
  • V. Chiarella
  • G. Chiarelli
  • G. Chiodini
  • A. S. Chisholm
  • R. T. Chislett
  • A. Chitan
  • M. V. Chizhov
  • K. Choi
  • S. Chouridou
  • B. K. B. Chow
  • V. Christodoulou
  • D. Chromek-Burckhart
  • J. Chudoba
  • A. J. Chuinard
  • J. J. Chwastowski
  • L. Chytka
  • G. Ciapetti
  • A. K. Ciftci
  • D. Cinca
  • V. Cindro
  • I. A. Cioara
  • A. Ciocio
  • F. Cirotto
  • Z. H. Citron
  • M. Ciubancan
  • A. Clark
  • B. L. Clark
  • P. J. Clark
  • R. N. Clarke
  • C. Clement
  • Y. Coadou
  • M. Cobal
  • A. Coccaro
  • J. Cochran
  • L. Coffey
  • J. G. Cogan
  • L. Colasurdo
  • B. Cole
  • S. Cole
  • A. P. Colijn
  • J. Collot
  • T. Colombo
  • G. Compostella
  • P. Conde Muiño
  • E. Coniavitis
  • S. H. Connell
  • I. A. Connelly
  • V. Consorti
  • S. Constantinescu
  • C. Conta
  • G. Conti
  • F. Conventi
  • M. Cooke
  • B. D. Cooper
  • A. M. Cooper-Sarkar
  • T. Cornelissen
  • M. Corradi
  • F. Corriveau
  • A. Corso-Radu
  • A. Cortes-Gonzalez
  • G. Cortiana
  • G. Costa
  • M. J. Costa
  • D. Costanzo
  • D. Côté
  • G. Cottin
  • G. Cowan
  • B. E. Cox
  • K. Cranmer
  • G. Cree
  • S. Crépé-Renaudin
  • F. Crescioli
  • W. A. Cribbs
  • M. Crispin Ortuzar
  • M. Cristinziani
  • V. Croft
  • G. Crosetti
  • T. Cuhadar Donszelmann
  • J. Cummings
  • M. Curatolo
  • J. Cúth
  • C. Cuthbert
  • H. Czirr
  • P. Czodrowski
  • S. D’Auria
  • M. D’Onofrio
  • M. J. Da Cunha Sargedas De Sousa
  • C. Da Via
  • W. Dabrowski
  • A. Dafinca
  • T. Dai
  • O. Dale
  • F. Dallaire
  • C. Dallapiccola
  • M. Dam
  • J. R. Dandoy
  • N. P. Dang
  • A. C. Daniells
  • M. Danninger
  • M. Dano Hoffmann
  • V. Dao
  • G. Darbo
  • S. Darmora
  • J. Dassoulas
  • A. Dattagupta
  • W. Davey
  • C. David
  • T. Davidek
  • E. Davies
  • M. Davies
  • P. Davison
  • Y. Davygora
  • E. Dawe
  • I. Dawson
  • R. K. Daya-Ishmukhametova
  • K. De
  • R. de Asmundis
  • A. De Benedetti
  • S. De Castro
  • S. De Cecco
  • N. De Groot
  • P. de Jong
  • H. De la Torre
  • F. De Lorenzi
  • D. De Pedis
  • A. De Salvo
  • U. De Sanctis
  • A. De Santo
  • J. B. De Vivie De Regie
  • W. J. Dearnaley
  • R. Debbe
  • C. Debenedetti
  • D. V. Dedovich
  • I. Deigaard
  • J. Del Peso
  • T. Del Prete
  • D. Delgove
  • F. Deliot
  • C. M. Delitzsch
  • M. Deliyergiyev
  • A. Dell’Acqua
  • L. Dell’Asta
  • M. Dell’Orso
  • M. Della Pietra
  • D. della Volpe
  • M. Delmastro
  • P. A. Delsart
  • C. Deluca
  • D. A. DeMarco
  • S. Demers
  • M. Demichev
  • A. Demilly
  • S. P. Denisov
  • D. Derendarz
  • J. E. Derkaoui
  • F. Derue
  • P. Dervan
  • K. Desch
  • C. Deterre
  • K. Dette
  • P. O. Deviveiros
  • A. Dewhurst
  • S. Dhaliwal
  • A. Di Ciaccio
  • L. Di Ciaccio
  • A. Di Domenico
  • C. Di Donato
  • A. Di Girolamo
  • B. Di Girolamo
  • A. Di Mattia
  • B. Di Micco
  • R. Di Nardo
  • A. Di Simone
  • R. Di Sipio
  • D. Di Valentino
  • C. Diaconu
  • M. Diamond
  • F. A. Dias
  • M. A. Diaz
  • E. B. Diehl
  • J. Dietrich
  • S. Diglio
  • A. Dimitrievska
  • J. Dingfelder
  • P. Dita
  • S. Dita
  • F. Dittus
  • F. Djama
  • T. Djobava
  • J. I. Djuvsland
  • M. A. B. do Vale
  • D. Dobos
  • M. Dobre
  • C. Doglioni
  • T. Dohmae
  • J. Dolejsi
  • Z. Dolezal
  • B. A. Dolgoshein
  • M. Donadelli
  • S. Donati
  • P. Dondero
  • J. Donini
  • J. Dopke
  • A. Doria
  • M. T. Dova
  • A. T. Doyle
  • E. Drechsler
  • M. Dris
  • Y. Du
  • E. Dubreuil
  • E. Duchovni
  • G. Duckeck
  • O. A. Ducu
  • D. Duda
  • A. Dudarev
  • L. Duflot
  • L. Duguid
  • M. Dührssen
  • M. Dunford
  • H. Duran Yildiz
  • M. Düren
  • A. Durglishvili
  • D. Duschinger
  • B. Dutta
  • M. Dyndal
  • C. Eckardt
  • K. M. Ecker
  • R. C. Edgar
  • W. Edson
  • N. C. Edwards
  • W. Ehrenfeld
  • T. Eifert
  • G. Eigen
  • K. Einsweiler
  • T. Ekelof
  • M. El Kacimi
  • M. Ellert
  • S. Elles
  • F. Ellinghaus
  • A. A. Elliot
  • N. Ellis
  • J. Elmsheuser
  • M. Elsing
  • D. Emeliyanov
  • Y. Enari
  • O. C. Endner
  • M. Endo
  • J. Erdmann
  • A. Ereditato
  • G. Ernis
  • J. Ernst
  • M. Ernst
  • S. Errede
  • E. Ertel
  • M. Escalier
  • H. Esch
  • C. Escobar
  • B. Esposito
  • A. I. Etienvre
  • E. Etzion
  • H. Evans
  • A. Ezhilov
  • L. Fabbri
  • G. Facini
  • R. M. Fakhrutdinov
  • S. Falciano
  • R. J. Falla
  • J. Faltova
  • Y. Fang
  • M. Fanti
  • A. Farbin
  • A. Farilla
  • T. Farooque
  • S. Farrell
  • S. M. Farrington
  • P. Farthouat
  • F. Fassi
  • P. Fassnacht
  • D. Fassouliotis
  • M. Faucci Giannelli
  • A. Favareto
  • L. Fayard
  • O. L. Fedin
  • W. Fedorko
  • S. Feigl
  • L. Feligioni
  • C. Feng
  • E. J. Feng
  • H. Feng
  • A. B. Fenyuk
  • L. Feremenga
  • P. Fernandez Martinez
  • S. Fernandez Perez
  • J. Ferrando
  • A. Ferrari
  • P. Ferrari
  • R. Ferrari
  • D. E. Ferreira de Lima
  • A. Ferrer
  • D. Ferrere
  • C. Ferretti
  • A. Ferretto Parodi
  • M. Fiascaris
  • F. Fiedler
  • A. Filipčič
  • M. Filipuzzi
  • F. Filthaut
  • M. Fincke-Keeler
  • K. D. Finelli
  • M. C. N. Fiolhais
  • L. Fiorini
  • A. Firan
  • A. Fischer
  • C. Fischer
  • J. Fischer
  • W. C. Fisher
  • N. Flaschel
  • I. Fleck
  • P. Fleischmann
  • G. T. Fletcher
  • G. Fletcher
  • R. R. M. Fletcher
  • T. Flick
  • A. Floderus
  • L. R. Flores Castillo
  • M. J. Flowerdew
  • A. Formica
  • A. Forti
  • D. Fournier
  • H. Fox
  • S. Fracchia
  • P. Francavilla
  • M. Franchini
  • D. Francis
  • L. Franconi
  • M. Franklin
  • M. Frate
  • M. Fraternali
  • D. Freeborn
  • S. T. French
  • S. M. Fressard-Batraneanu
  • F. Friedrich
  • D. Froidevaux
  • J. A. Frost
  • C. Fukunaga
  • E. Fullana Torregrosa
  • B. G. Fulsom
  • T. Fusayasu
  • J. Fuster
  • C. Gabaldon
  • O. Gabizon
  • A. Gabrielli
  • A. Gabrielli
  • G. P. Gach
  • S. Gadatsch
  • S. Gadomski
  • G. Gagliardi
  • P. Gagnon
  • C. Galea
  • B. Galhardo
  • E. J. Gallas
  • B. J. Gallop
  • P. Gallus
  • G. Galster
  • K. K. Gan
  • J. Gao
  • Y. Gao
  • Y. S. Gao
  • F. M. Garay Walls
  • F. Garberson
  • C. García
  • J. E. García Navarro
  • M. Garcia-Sciveres
  • R. W. Gardner
  • N. Garelli
  • V. Garonne
  • C. Gatti
  • A. Gaudiello
  • G. Gaudio
  • B. Gaur
  • L. Gauthier
  • P. Gauzzi
  • I. L. Gavrilenko
  • C. Gay
  • G. Gaycken
  • E. N. Gazis
  • P. Ge
  • Z. Gecse
  • C. N. P. Gee
  • Ch. Geich-Gimbel
  • M. P. Geisler
  • C. Gemme
  • M. H. Genest
  • C. Geng
  • S. Gentile
  • M. George
  • S. George
  • D. Gerbaudo
  • A. Gershon
  • S. Ghasemi
  • H. Ghazlane
  • B. Giacobbe
  • S. Giagu
  • V. Giangiobbe
  • P. Giannetti
  • B. Gibbard
  • S. M. Gibson
  • M. Gignac
  • M. Gilchriese
  • T. P. S. Gillam
  • D. Gillberg
  • G. Gilles
  • D. M. Gingrich
  • N. Giokaris
  • M. P. Giordani
  • F. M. Giorgi
  • F. M. Giorgi
  • P. F. Giraud
  • P. Giromini
  • D. Giugni
  • C. Giuliani
  • M. Giulini
  • B. K. Gjelsten
  • S. Gkaitatzis
  • I. Gkialas
  • E. L. Gkougkousis
  • L. K. Gladilin
  • C. Glasman
  • J. Glatzer
  • P. C. F. Glaysher
  • A. Glazov
  • M. Goblirsch-Kolb
  • J. R. Goddard
  • J. Godlewski
  • S. Goldfarb
  • T. Golling
  • D. Golubkov
  • A. Gomes
  • R. Gonçalo
  • J. Goncalves Pinto Firmino Da Costa
  • L. Gonella
  • S. González de la Hoz
  • G. Gonzalez Parra
  • S. Gonzalez-Sevilla
  • L. Goossens
  • P. A. Gorbounov
  • H. A. Gordon
  • I. Gorelov
  • B. Gorini
  • E. Gorini
  • A. Gorišek
  • E. Gornicki
  • A. T. Goshaw
  • C. Gössling
  • M. I. Gostkin
  • D. Goujdami
  • A. G. Goussiou
  • N. Govender
  • E. Gozani
  • H. M. X. Grabas
  • L. Graber
  • I. Grabowska-Bold
  • P. O. J. Gradin
  • P. Grafström
  • J. Gramling
  • E. Gramstad
  • S. Grancagnolo
  • V. Gratchev
  • H. M. Gray
  • E. Graziani
  • Z. D. Greenwood
  • C. Grefe
  • K. Gregersen
  • I. M. Gregor
  • P. Grenier
  • J. Griffiths
  • A. A. Grillo
  • K. Grimm
  • S. Grinstein
  • Ph. Gris
  • J.-F. Grivaz
  • S. Groh
  • J. P. Grohs
  • A. Grohsjean
  • E. Gross
  • J. Grosse-Knetter
  • G. C. Grossi
  • Z. J. Grout
  • L. Guan
  • J. Guenther
  • F. Guescini
  • D. Guest
  • O. Gueta
  • E. Guido
  • T. Guillemin
  • S. Guindon
  • U. Gul
  • C. Gumpert
  • J. Guo
  • Y. Guo
  • S. Gupta
  • G. Gustavino
  • P. Gutierrez
  • N. G. Gutierrez Ortiz
  • C. Gutschow
  • C. Guyot
  • C. Gwenlan
  • C. B. Gwilliam
  • A. Haas
  • C. Haber
  • H. K. Hadavand
  • N. Haddad
  • P. Haefner
  • S. Hageböck
  • Z. Hajduk
  • H. Hakobyan
  • M. Haleem
  • J. Haley
  • D. Hall
  • G. Halladjian
  • G. D. Hallewell
  • K. Hamacher
  • P. Hamal
  • K. Hamano
  • A. Hamilton
  • G. N. Hamity
  • P. G. Hamnett
  • L. Han
  • K. Hanagaki
  • K. Hanawa
  • M. Hance
  • B. Haney
  • P. Hanke
  • R. Hanna
  • J. B. Hansen
  • J. D. Hansen
  • M. C. Hansen
  • P. H. Hansen
  • K. Hara
  • A. S. Hard
  • T. Harenberg
  • F. Hariri
  • S. Harkusha
  • R. D. Harrington
  • P. F. Harrison
  • F. Hartjes
  • M. Hasegawa
  • Y. Hasegawa
  • A. Hasib
  • S. Hassani
  • S. Haug
  • R. Hauser
  • L. Hauswald
  • M. Havranek
  • C. M. Hawkes
  • R. J. Hawkings
  • A. D. Hawkins
  • T. Hayashi
  • D. Hayden
  • C. P. Hays
  • J. M. Hays
  • H. S. Hayward
  • S. J. Haywood
  • S. J. Head
  • T. Heck
  • V. Hedberg
  • L. Heelan
  • S. Heim
  • T. Heim
  • B. Heinemann
  • L. Heinrich
  • J. Hejbal
  • L. Helary
  • S. Hellman
  • C. Helsens
  • J. Henderson
  • R. C. W. Henderson
  • Y. Heng
  • C. Hengler
  • S. Henkelmann
  • A. Henrichs
  • A. M. Henriques Correia
  • S. Henrot-Versille
  • G. H. Herbert
  • Y. Hernández Jiménez
  • G. Herten
  • R. Hertenberger
  • L. Hervas
  • G. G. Hesketh
  • N. P. Hessey
  • J. W. Hetherly
  • R. Hickling
  • E. Higón-Rodriguez
  • E. Hill
  • J. C. Hill
  • K. H. Hiller
  • S. J. Hillier
  • I. Hinchliffe
  • E. Hines
  • R. R. Hinman
  • M. Hirose
  • D. Hirschbuehl
  • J. Hobbs
  • N. Hod
  • M. C. Hodgkinson
  • P. Hodgson
  • A. Hoecker
  • M. R. Hoeferkamp
  • F. Hoenig
  • M. Hohlfeld
  • D. Hohn
  • T. R. Holmes
  • M. Homann
  • T. M. Hong
  • W. H. Hopkins
  • Y. Horii
  • A. J. Horton
  • J.-Y. Hostachy
  • S. Hou
  • A. Hoummada
  • J. Howard
  • J. Howarth
  • M. Hrabovsky
  • I. Hristova
  • J. Hrivnac
  • T. Hryn’ova
  • A. Hrynevich
  • C. Hsu
  • P. J. Hsu
  • S.-C. Hsu
  • D. Hu
  • Q. Hu
  • X. Hu
  • Y. Huang
  • Z. Hubacek
  • F. Hubaut
  • F. Huegging
  • T. B. Huffman
  • E. W. Hughes
  • G. Hughes
  • M. Huhtinen
  • T. A. Hülsing
  • N. Huseynov
  • J. Huston
  • J. Huth
  • G. Iacobucci
  • G. Iakovidis
  • I. Ibragimov
  • L. Iconomidou-Fayard
  • E. Ideal
  • Z. Idrissi
  • P. Iengo
  • O. Igonkina
  • T. Iizawa
  • Y. Ikegami
  • M. Ikeno
  • Y. Ilchenko
  • D. Iliadis
  • N. Ilic
  • T. Ince
  • G. Introzzi
  • P. Ioannou
  • M. Iodice
  • K. Iordanidou
  • V. Ippolito
  • A. Irles Quiles
  • C. Isaksson
  • M. Ishino
  • M. Ishitsuka
  • R. Ishmukhametov
  • C. Issever
  • S. Istin
  • J. M. Iturbe Ponce
  • R. Iuppa
  • J. Ivarsson
  • W. Iwanski
  • H. Iwasaki
  • J. M. Izen
  • V. Izzo
  • S. Jabbar
  • B. Jackson
  • M. Jackson
  • P. Jackson
  • M. R. Jaekel
  • V. Jain
  • K. B. Jakobi
  • K. Jakobs
  • S. Jakobsen
  • T. Jakoubek
  • J. Jakubek
  • D. O. Jamin
  • D. K. Jana
  • E. Jansen
  • R. Jansky
  • J. Janssen
  • M. Janus
  • G. Jarlskog
  • N. Javadov
  • T. Javůrek
  • L. Jeanty
  • J. Jejelava
  • G.-Y. Jeng
  • D. Jennens
  • P. Jenni
  • J. Jentzsch
  • C. Jeske
  • S. Jézéquel
  • H. Ji
  • J. Jia
  • H. Jiang
  • Y. Jiang
  • S. Jiggins
  • J. Jimenez Pena
  • S. Jin
  • A. Jinaru
  • O. Jinnouchi
  • M. D. Joergensen
  • P. Johansson
  • K. A. Johns
  • W. J. Johnson
  • K. Jon-And
  • G. Jones
  • R. W. L. Jones
  • T. J. Jones
  • J. Jongmanns
  • P. M. Jorge
  • K. D. Joshi
  • J. Jovicevic
  • X. Ju
  • A. Juste Rozas
  • M. Kaci
  • A. Kaczmarska
  • M. Kado
  • H. Kagan
  • M. Kagan
  • S. J. Kahn
  • E. Kajomovitz
  • C. W. Kalderon
  • A. Kaluza
  • S. Kama
  • A. Kamenshchikov
  • N. Kanaya
  • S. Kaneti
  • V. A. Kantserov
  • J. Kanzaki
  • B. Kaplan
  • L. S. Kaplan
  • A. Kapliy
  • D. Kar
  • K. Karakostas
  • A. Karamaoun
  • N. Karastathis
  • M. J. Kareem
  • E. Karentzos
  • M. Karnevskiy
  • S. N. Karpov
  • Z. M. Karpova
  • K. Karthik
  • V. Kartvelishvili
  • A. N. Karyukhin
  • K. Kasahara
  • L. Kashif
  • R. D. Kass
  • A. Kastanas
  • Y. Kataoka
  • C. Kato
  • A. Katre
  • J. Katzy
  • K. Kawade
  • K. Kawagoe
  • T. Kawamoto
  • G. Kawamura
  • S. Kazama
  • V. F. Kazanin
  • R. Keeler
  • R. Kehoe
  • J. S. Keller
  • J. J. Kempster
  • H. Keoshkerian
  • O. Kepka
  • B. P. Kerševan
  • S. Kersten
  • R. A. Keyes
  • F. Khalil-zada
  • H. Khandanyan
  • A. Khanov
  • A. G. Kharlamov
  • T. J. Khoo
  • V. Khovanskiy
  • E. Khramov
  • J. Khubua
  • S. Kido
  • H. Y. Kim
  • S. H. Kim
  • Y. K. Kim
  • N. Kimura
  • O. M. Kind
  • B. T. King
  • M. King
  • S. B. King
  • J. Kirk
  • A. E. Kiryunin
  • T. Kishimoto
  • D. Kisielewska
  • F. Kiss
  • K. Kiuchi
  • O. Kivernyk
  • E. Kladiva
  • M. H. Klein
  • M. Klein
  • U. Klein
  • K. Kleinknecht
  • P. Klimek
  • A. Klimentov
  • R. Klingenberg
  • J. A. Klinger
  • T. Klioutchnikova
  • E.-E. Kluge
  • P. Kluit
  • S. Kluth
  • J. Knapik
  • E. Kneringer
  • E. B. F. G. Knoops
  • A. Knue
  • A. Kobayashi
  • D. Kobayashi
  • T. Kobayashi
  • M. Kobel
  • M. Kocian
  • P. Kodys
  • T. Koffas
  • E. Koffeman
  • L. A. Kogan
  • S. Kohlmann
  • Z. Kohout
  • T. Kohriki
  • T. Koi
  • H. Kolanoski
  • M. Kolb
  • I. Koletsou
  • A. A. Komar
  • Y. Komori
  • T. Kondo
  • N. Kondrashova
  • K. Köneke
  • A. C. König
  • T. Kono
  • R. Konoplich
  • N. Konstantinidis
  • R. Kopeliansky
  • S. Koperny
  • L. Köpke
  • A. K. Kopp
  • K. Korcyl
  • K. Kordas
  • A. Korn
  • A. A. Korol
  • I. Korolkov
  • E. V. Korolkova
  • O. Kortner
  • S. Kortner
  • T. Kosek
  • V. V. Kostyukhin
  • V. M. Kotov
  • A. Kotwal
  • A. Kourkoumeli-Charalampidi
  • C. Kourkoumelis
  • V. Kouskoura
  • A. Koutsman
  • R. Kowalewski
  • T. Z. Kowalski
  • W. Kozanecki
  • A. S. Kozhin
  • V. A. Kramarenko
  • G. Kramberger
  • D. Krasnopevtsev
  • M. W. Krasny
  • A. Krasznahorkay
  • J. K. Kraus
  • A. Kravchenko
  • S. Kreiss
  • M. Kretz
  • J. Kretzschmar
  • K. Kreutzfeldt
  • P. Krieger
  • K. Krizka
  • K. Kroeninger
  • H. Kroha
  • J. Kroll
  • J. Kroseberg
  • J. Krstic
  • U. Kruchonak
  • H. Krüger
  • N. Krumnack
  • A. Kruse
  • M. C. Kruse
  • M. Kruskal
  • T. Kubota
  • H. Kucuk
  • S. Kuday
  • S. Kuehn
  • A. Kugel
  • F. Kuger
  • A. Kuhl
  • T. Kuhl
  • V. Kukhtin
  • R. Kukla
  • Y. Kulchitsky
  • S. Kuleshov
  • M. Kuna
  • T. Kunigo
  • A. Kupco
  • H. Kurashige
  • Y. A. Kurochkin
  • V. Kus
  • E. S. Kuwertz
  • M. Kuze
  • J. Kvita
  • T. Kwan
  • D. Kyriazopoulos
  • A. La Rosa
  • J. L. La Rosa Navarro
  • L. La Rotonda
  • C. Lacasta
  • F. Lacava
  • J. Lacey
  • H. Lacker
  • D. Lacour
  • V. R. Lacuesta
  • E. Ladygin
  • R. Lafaye
  • B. Laforge
  • T. Lagouri
  • S. Lai
  • L. Lambourne
  • S. Lammers
  • C. L. Lampen
  • W. Lampl
  • E. Lançon
  • U. Landgraf
  • M. P. J. Landon
  • V. S. Lang
  • J. C. Lange
  • A. J. Lankford
  • F. Lanni
  • K. Lantzsch
  • A. Lanza
  • S. Laplace
  • C. Lapoire
  • J. F. Laporte
  • T. Lari
  • F. Lasagni Manghi
  • M. Lassnig
  • P. Laurelli
  • W. Lavrijsen
  • A. T. Law
  • P. Laycock
  • T. Lazovich
  • O. Le Dortz
  • E. Le Guirriec
  • E. Le Menedeu
  • M. LeBlanc
  • T. LeCompte
  • F. Ledroit-Guillon
  • C. A. Lee
  • S. C. Lee
  • L. Lee
  • G. Lefebvre
  • M. Lefebvre
  • F. Legger
  • C. Leggett
  • A. Lehan
  • G. Lehmann Miotto
  • X. Lei
  • W. A. Leight
  • A. Leisos
  • A. G. Leister
  • M. A. L. Leite
  • R. Leitner
  • D. Lellouch
  • B. Lemmer
  • K. J. C. Leney
  • T. Lenz
  • B. Lenzi
  • R. Leone
  • S. Leone
  • C. Leonidopoulos
  • S. Leontsinis
  • C. Leroy
  • C. G. Lester
  • M. Levchenko
  • J. Levêque
  • D. Levin
  • L. J. Levinson
  • M. Levy
  • A. Lewis
  • A. M. Leyko
  • M. Leyton
  • B. Li
  • H. Li
  • H. L. Li
  • L. Li
  • L. Li
  • S. Li
  • X. Li
  • Y. Li
  • Z. Liang
  • H. Liao
  • B. Liberti
  • A. Liblong
  • P. Lichard
  • K. Lie
  • J. Liebal
  • W. Liebig
  • C. Limbach
  • A. Limosani
  • S. C. Lin
  • T. H. Lin
  • F. Linde
  • B. E. Lindquist
  • J. T. Linnemann
  • E. Lipeles
  • A. Lipniacka
  • M. Lisovyi
  • T. M. Liss
  • D. Lissauer
  • A. Lister
  • A. M. Litke
  • B. Liu
  • D. Liu
  • H. Liu
  • J. Liu
  • J. B. Liu
  • K. Liu
  • L. Liu
  • M. Liu
  • M. Liu
  • Y. Liu
  • M. Livan
  • A. Lleres
  • J. Llorente Merino
  • S. L. Lloyd
  • F. Lo Sterzo
  • E. Lobodzinska
  • P. Loch
  • W. S. Lockman
  • F. K. Loebinger
  • A. E. Loevschall-Jensen
  • K. M. Loew
  • A. Loginov
  • T. Lohse
  • K. Lohwasser
  • M. Lokajicek
  • B. A. Long
  • J. D. Long
  • R. E. Long
  • K. A. Looper
  • L. Lopes
  • D. Lopez Mateos
  • B. Lopez Paredes
  • I. Lopez Paz
  • J. Lorenz
  • N. Lorenzo Martinez
  • M. Losada
  • P. J. Lösel
  • X. Lou
  • A. Lounis
  • J. Love
  • P. A. Love
  • H. Lu
  • N. Lu
  • H. J. Lubatti
  • C. Luci
  • A. Lucotte
  • C. Luedtke
  • F. Luehring
  • W. Lukas
  • L. Luminari
  • O. Lundberg
  • B. Lund-Jensen
  • D. Lynn
  • R. Lysak
  • E. Lytken
  • H. Ma
  • L. L. Ma
  • G. Maccarrone
  • A. Macchiolo
  • C. M. Macdonald
  • B. Maček
  • J. Machado Miguens
  • D. Macina
  • D. Madaffari
  • R. Madar
  • H. J. Maddocks
  • W. F. Mader
  • A. Madsen
  • J. Maeda
  • S. Maeland
  • T. Maeno
  • A. Maevskiy
  • E. Magradze
  • K. Mahboubi
  • J. Mahlstedt
  • C. Maiani
  • C. Maidantchik
  • A. A. Maier
  • T. Maier
  • A. Maio
  • S. Majewski
  • Y. Makida
  • N. Makovec
  • B. Malaescu
  • Pa. Malecki
  • V. P. Maleev
  • F. Malek
  • U. Mallik
  • D. Malon
  • C. Malone
  • S. Maltezos
  • V. M. Malyshev
  • S. Malyukov
  • J. Mamuzic
  • G. Mancini
  • B. Mandelli
  • L. Mandelli
  • I. Mandić
  • R. Mandrysch
  • J. Maneira
  • L. Manhaes de Andrade Filho
  • J. Manjarres Ramos
  • A. Mann
  • A. Manousakis-Katsikakis
  • B. Mansoulie
  • R. Mantifel
  • M. Mantoani
  • L. Mapelli
  • L. March
  • G. Marchiori
  • M. Marcisovsky
  • C. P. Marino
  • M. Marjanovic
  • D. E. Marley
  • F. Marroquim
  • S. P. Marsden
  • Z. Marshall
  • L. F. Marti
  • S. Marti-Garcia
  • B. Martin
  • T. A. Martin
  • V. J. Martin
  • B. Martin dit Latour
  • M. Martinez
  • S. Martin-Haugh
  • V. S. Martoiu
  • A. C. Martyniuk
  • M. Marx
  • F. Marzano
  • A. Marzin
  • L. Masetti
  • T. Mashimo
  • R. Mashinistov
  • J. Masik
  • A. L. Maslennikov
  • I. Massa
  • L. Massa
  • P. Mastrandrea
  • A. Mastroberardino
  • T. Masubuchi
  • P. Mättig
  • J. Mattmann
  • J. Maurer
  • S. J. Maxfield
  • D. A. Maximov
  • R. Mazini
  • S. M. Mazza
  • G. Mc Goldrick
  • S. P. Mc Kee
  • A. McCarn
  • R. L. McCarthy
  • T. G. McCarthy
  • N. A. McCubbin
  • K. W. McFarlane
  • J. A. Mcfayden
  • G. Mchedlidze
  • S. J. McMahon
  • R. A. McPherson
  • M. Medinnis
  • S. Meehan
  • S. Mehlhase
  • A. Mehta
  • K. Meier
  • C. Meineck
  • B. Meirose
  • B. R. Mellado Garcia
  • F. Meloni
  • A. Mengarelli
  • S. Menke
  • E. Meoni
  • K. M. Mercurio
  • S. Mergelmeyer
  • P. Mermod
  • L. Merola
  • C. Meroni
  • F. S. Merritt
  • A. Messina
  • J. Metcalfe
  • A. S. Mete
  • C. Meyer
  • C. Meyer
  • J.-P. Meyer
  • J. Meyer
  • H. Meyer Zu Theenhausen
  • R. P. Middleton
  • S. Miglioranzi
  • L. Mijović
  • G. Mikenberg
  • M. Mikestikova
  • M. Mikuž
  • M. Milesi
  • A. Milic
  • D. W. Miller
  • C. Mills
  • A. Milov
  • D. A. Milstead
  • A. A. Minaenko
  • Y. Minami
  • I. A. Minashvili
  • A. I. Mincer
  • B. Mindur
  • M. Mineev
  • Y. Ming
  • L. M. Mir
  • K. P. Mistry
  • T. Mitani
  • J. Mitrevski
  • V. A. Mitsou
  • A. Miucci
  • P. S. Miyagawa
  • J. U. Mjörnmark
  • T. Moa
  • K. Mochizuki
  • S. Mohapatra
  • W. Mohr
  • S. Molander
  • R. Moles-Valls
  • R. Monden
  • M. C. Mondragon
  • K. Mönig
  • C. Monini
  • J. Monk
  • E. Monnier
  • A. Montalbano
  • J. Montejo Berlingen
  • F. Monticelli
  • S. Monzani
  • R. W. Moore
  • N. Morange
  • D. Moreno
  • M. Moreno Llácer
  • P. Morettini
  • D. Mori
  • T. Mori
  • M. Morii
  • M. Morinaga
  • V. Morisbak
  • S. Moritz
  • A. K. Morley
  • G. Mornacchi
  • J. D. Morris
  • S. S. Mortensen
  • A. Morton
  • L. Morvaj
  • M. Mosidze
  • J. Moss
  • K. Motohashi
  • R. Mount
  • E. Mountricha
  • S. V. Mouraviev
  • E. J. W. Moyse
  • S. Muanza
  • R. D. Mudd
  • F. Mueller
  • J. Mueller
  • R. S. P. Mueller
  • T. Mueller
  • D. Muenstermann
  • P. Mullen
  • G. A. Mullier
  • F. J. Munoz Sanchez
  • J. A. Murillo Quijada
  • W. J. Murray
  • H. Musheghyan
  • E. Musto
  • A. G. Myagkov
  • M. Myska
  • B. P. Nachman
  • O. Nackenhorst
  • J. Nadal
  • K. Nagai
  • R. Nagai
  • Y. Nagai
  • K. Nagano
  • A. Nagarkar
  • Y. Nagasaka
  • K. Nagata
  • M. Nagel
  • E. Nagy
  • A. M. Nairz
  • Y. Nakahama
  • K. Nakamura
  • T. Nakamura
  • I. Nakano
  • H. Namasivayam
  • R. F. Naranjo Garcia
  • R. Narayan
  • D. I. Narrias Villar
  • T. Naumann
  • G. Navarro
  • R. Nayyar
  • H. A. Neal
  • P. Yu. Nechaeva
  • T. J. Neep
  • P. D. Nef
  • A. Negri
  • M. Negrini
  • S. Nektarijevic
  • C. Nellist
  • A. Nelson
  • S. Nemecek
  • P. Nemethy
  • A. A. Nepomuceno
  • M. Nessi
  • M. S. Neubauer
  • M. Neumann
  • R. M. Neves
  • P. Nevski
  • P. R. Newman
  • D. H. Nguyen
  • R. B. Nickerson
  • R. Nicolaidou
  • B. Nicquevert
  • J. Nielsen
  • N. Nikiforou
  • A. Nikiforov
  • V. Nikolaenko
  • I. Nikolic-Audit
  • K. Nikolopoulos
  • J. K. Nilsen
  • P. Nilsson
  • Y. Ninomiya
  • A. Nisati
  • R. Nisius
  • T. Nobe
  • L. Nodulman
  • M. Nomachi
  • I. Nomidis
  • T. Nooney
  • S. Norberg
  • M. Nordberg
  • O. Novgorodova
  • S. Nowak
  • M. Nozaki
  • L. Nozka
  • K. Ntekas
  • G. Nunes Hanninger
  • T. Nunnemann
  • E. Nurse
  • F. Nuti
  • F. O’grady
  • D. C. O’Neil
  • V. O’Shea
  • F. G. Oakham
  • H. Oberlack
  • T. Obermann
  • J. Ocariz
  • A. Ochi
  • I. Ochoa
  • J. P. Ochoa-Ricoux
  • S. Oda
  • S. Odaka
  • H. Ogren
  • A. Oh
  • S. H. Oh
  • C. C. Ohm
  • H. Ohman
  • H. Oide
  • W. Okamura
  • H. Okawa
  • Y. Okumura
  • T. Okuyama
  • A. Olariu
  • S. A. Olivares Pino
  • D. Oliveira Damazio
  • A. Olszewski
  • J. Olszowska
  • A. Onofre
  • K. Onogi
  • P. U. E. Onyisi
  • C. J. Oram
  • M. J. Oreglia
  • Y. Oren
  • D. Orestano
  • N. Orlando
  • C. Oropeza Barrera
  • R. S. Orr
  • B. Osculati
  • R. Ospanov
  • G. Otero y Garzon
  • H. Otono
  • M. Ouchrif
  • F. Ould-Saada
  • A. Ouraou
  • K. P. Oussoren
  • Q. Ouyang
  • A. Ovcharova
  • M. Owen
  • R. E. Owen
  • V. E. Ozcan
  • N. Ozturk
  • K. Pachal
  • A. Pacheco Pages
  • C. Padilla Aranda
  • M. Pagáčová
  • S. Pagan Griso
  • E. Paganis
  • F. Paige
  • P. Pais
  • K. Pajchel
  • G. Palacino
  • S. Palestini
  • M. Palka
  • D. Pallin
  • A. Palma
  • Y. B. Pan
  • E. St. Panagiotopoulou
  • C. E. Pandini
  • J. G. Panduro Vazquez
  • P. Pani
  • S. Panitkin
  • D. Pantea
  • L. Paolozzi
  • Th. D. Papadopoulou
  • K. Papageorgiou
  • A. Paramonov
  • D. Paredes Hernandez
  • M. A. Parker
  • K. A. Parker
  • F. Parodi
  • J. A. Parsons
  • U. Parzefall
  • E. Pasqualucci
  • S. Passaggio
  • F. Pastore
  • Fr. Pastore
  • G. Pásztor
  • S. Pataraia
  • N. D. Patel
  • J. R. Pater
  • T. Pauly
  • J. Pearce
  • B. Pearson
  • L. E. Pedersen
  • M. Pedersen
  • S. Pedraza Lopez
  • R. Pedro
  • S. V. Peleganchuk
  • D. Pelikan
  • O. Penc
  • C. Peng
  • H. Peng
  • B. Penning
  • J. Penwell
  • D. V. Perepelitsa
  • E. Perez Codina
  • M. T. Pérez García-Estañ
  • L. Perini
  • H. Pernegger
  • S. Perrella
  • R. Peschke
  • V. D. Peshekhonov
  • K. Peters
  • R. F. Y. Peters
  • B. A. Petersen
  • T. C. Petersen
  • E. Petit
  • A. Petridis
  • C. Petridou
  • P. Petroff
  • E. Petrolo
  • F. Petrucci
  • N. E. Pettersson
  • R. Pezoa
  • P. W. Phillips
  • G. Piacquadio
  • E. Pianori
  • A. Picazio
  • E. Piccaro
  • M. Piccinini
  • M. A. Pickering
  • R. Piegaia
  • D. T. Pignotti
  • J. E. Pilcher
  • A. D. Pilkington
  • A. W. J. Pin
  • J. Pina
  • M. Pinamonti
  • J. L. Pinfold
  • A. Pingel
  • S. Pires
  • H. Pirumov
  • M. Pitt
  • C. Pizio
  • L. Plazak
  • M.-A. Pleier
  • V. Pleskot
  • E. Plotnikova
  • P. Plucinski
  • D. Pluth
  • R. Poettgen
  • L. Poggioli
  • D. Pohl
  • G. Polesello
  • A. Poley
  • A. Policicchio
  • R. Polifka
  • A. Polini
  • C. S. Pollard
  • V. Polychronakos
  • K. Pommès
  • L. Pontecorvo
  • B. G. Pope
  • G. A. Popeneciu
  • D. S. Popovic
  • A. Poppleton
  • S. Pospisil
  • K. Potamianos
  • I. N. Potrap
  • C. J. Potter
  • C. T. Potter
  • G. Poulard
  • J. Poveda
  • V. Pozdnyakov
  • M. E. Pozo Astigarraga
  • P. Pralavorio
  • A. Pranko
  • S. Prasad
  • S. Prell
  • D. Price
  • L. E. Price
  • M. Primavera
  • S. Prince
  • M. Proissl
  • K. Prokofiev
  • F. Prokoshin
  • E. Protopapadaki
  • S. Protopopescu
  • J. Proudfoot
  • M. Przybycien
  • E. Ptacek
  • D. Puddu
  • E. Pueschel
  • D. Puldon
  • M. Purohit
  • P. Puzo
  • J. Qian
  • G. Qin
  • Y. Qin
  • A. Quadt
  • D. R. Quarrie
  • W. B. Quayle
  • M. Queitsch-Maitland
  • D. Quilty
  • S. Raddum
  • V. Radeka
  • V. Radescu
  • S. K. Radhakrishnan
  • P. Radloff
  • P. Rados
  • F. Ragusa
  • G. Rahal
  • S. Rajagopalan
  • M. Rammensee
  • C. Rangel-Smith
  • F. Rauscher
  • S. Rave
  • T. Ravenscroft
  • M. Raymond
  • A. L. Read
  • N. P. Readioff
  • D. M. Rebuzzi
  • A. Redelbach
  • G. Redlinger
  • R. Reece
  • K. Reeves
  • L. Rehnisch
  • J. Reichert
  • H. Reisin
  • C. Rembser
  • H. Ren
  • A. Renaud
  • M. Rescigno
  • S. Resconi
  • O. L. Rezanova
  • P. Reznicek
  • R. Rezvani
  • R. Richter
  • S. Richter
  • E. Richter-Was
  • O. Ricken
  • M. Ridel
  • P. Rieck
  • C. J. Riegel
  • J. Rieger
  • O. Rifki
  • M. Rijssenbeek
  • A. Rimoldi
  • L. Rinaldi
  • B. Ristić
  • E. Ritsch
  • I. Riu
  • F. Rizatdinova
  • E. Rizvi
  • S. H. Robertson
  • A. Robichaud-Veronneau
  • D. Robinson
  • J. E. M. Robinson
  • A. Robson
  • C. Roda
  • S. Roe
  • O. Røhne
  • A. Romaniouk
  • M. Romano
  • S. M. Romano Saez
  • E. Romero Adam
  • N. Rompotis
  • M. Ronzani
  • L. Roos
  • E. Ros
  • S. Rosati
  • K. Rosbach
  • P. Rose
  • O. Rosenthal
  • V. Rossetti
  • E. Rossi
  • L. P. Rossi
  • J. H. N. Rosten
  • R. Rosten
  • M. Rotaru
  • I. Roth
  • J. Rothberg
  • D. Rousseau
  • C. R. Royon
  • A. Rozanov
  • Y. Rozen
  • X. Ruan
  • F. Rubbo
  • I. Rubinskiy
  • V. I. Rud
  • C. Rudolph
  • M. S. Rudolph
  • F. Rühr
  • A. Ruiz-Martinez
  • Z. Rurikova
  • N. A. Rusakovich
  • A. Ruschke
  • H. L. Russell
  • J. P. Rutherfoord
  • N. Ruthmann
  • Y. F. Ryabov
  • M. Rybar
  • G. Rybkin
  • N. C. Ryder
  • A. Ryzhov
  • A. F. Saavedra
  • G. Sabato
  • S. Sacerdoti
  • A. Saddique
  • H. F.-W. Sadrozinski
  • R. Sadykov
  • F. Safai Tehrani
  • P. Saha
  • M. Sahinsoy
  • M. Saimpert
  • T. Saito
  • H. Sakamoto
  • Y. Sakurai
  • G. Salamanna
  • A. Salamon
  • J. E. Salazar Loyola
  • M. Saleem
  • D. Salek
  • P. H. Sales De Bruin
  • D. Salihagic
  • A. Salnikov
  • J. Salt
  • D. Salvatore
  • F. Salvatore
  • A. Salvucci
  • A. Salzburger
  • D. Sammel
  • D. Sampsonidis
  • A. Sanchez
  • J. Sánchez
  • V. Sanchez Martinez
  • H. Sandaker
  • R. L. Sandbach
  • H. G. Sander
  • M. P. Sanders
  • M. Sandhoff
  • C. Sandoval
  • R. Sandstroem
  • D. P. C. Sankey
  • M. Sannino
  • A. Sansoni
  • C. Santoni
  • R. Santonico
  • H. Santos
  • I. Santoyo Castillo
  • K. Sapp
  • A. Sapronov
  • J. G. Saraiva
  • B. Sarrazin
  • O. Sasaki
  • Y. Sasaki
  • K. Sato
  • G. Sauvage
  • E. Sauvan
  • G. Savage
  • P. Savard
  • C. Sawyer
  • L. Sawyer
  • J. Saxon
  • C. Sbarra
  • A. Sbrizzi
  • T. Scanlon
  • D. A. Scannicchio
  • M. Scarcella
  • V. Scarfone
  • J. Schaarschmidt
  • P. Schacht
  • D. Schaefer
  • R. Schaefer
  • J. Schaeffer
  • S. Schaepe
  • S. Schaetzel
  • U. Schäfer
  • A. C. Schaffer
  • D. Schaile
  • R. D. Schamberger
  • V. Scharf
  • V. A. Schegelsky
  • D. Scheirich
  • M. Schernau
  • C. Schiavi
  • C. Schillo
  • M. Schioppa
  • S. Schlenker
  • K. Schmieden
  • C. Schmitt
  • S. Schmitt
  • S. Schmitt
  • S. Schmitz
  • B. Schneider
  • Y. J. Schnellbach
  • U. Schnoor
  • L. Schoeffel
  • A. Schoening
  • B. D. Schoenrock
  • E. Schopf
  • A. L. S. Schorlemmer
  • M. Schott
  • D. Schouten
  • J. Schovancova
  • S. Schramm
  • M. Schreyer
  • N. Schuh
  • M. J. Schultens
  • H.-C. Schultz-Coulon
  • H. Schulz
  • M. Schumacher
  • B. A. Schumm
  • Ph. Schune
  • C. Schwanenberger
  • A. Schwartzman
  • T. A. Schwarz
  • Ph. Schwegler
  • H. Schweiger
  • Ph. Schwemling
  • R. Schwienhorst
  • J. Schwindling
  • T. Schwindt
  • E. Scifo
  • G. Sciolla
  • F. Scuri
  • F. Scutti
  • J. Searcy
  • G. Sedov
  • E. Sedykh
  • P. Seema
  • S. C. Seidel
  • A. Seiden
  • F. Seifert
  • J. M. Seixas
  • G. Sekhniaidze
  • K. Sekhon
  • S. J. Sekula
  • D. M. Seliverstov
  • N. Semprini-Cesari
  • C. Serfon
  • L. Serin
  • L. Serkin
  • T. Serre
  • M. Sessa
  • R. Seuster
  • H. Severini
  • T. Sfiligoj
  • F. Sforza
  • A. Sfyrla
  • E. Shabalina
  • M. Shamim
  • L. Y. Shan
  • R. Shang
  • J. T. Shank
  • M. Shapiro
  • P. B. Shatalov
  • K. Shaw
  • S. M. Shaw
  • A. Shcherbakova
  • C. Y. Shehu
  • P. Sherwood
  • L. Shi
  • S. Shimizu
  • C. O. Shimmin
  • M. Shimojima
  • M. Shiyakova
  • A. Shmeleva
  • D. Shoaleh Saadi
  • M. J. Shochet
  • S. Shojaii
  • S. Shrestha
  • E. Shulga
  • M. A. Shupe
  • P. Sicho
  • P. E. Sidebo
  • O. Sidiropoulou
  • D. Sidorov
  • A. Sidoti
  • F. Siegert
  • Dj. Sijacki
  • J. Silva
  • Y. Silver
  • S. B. Silverstein
  • V. Simak
  • O. Simard
  • Lj. Simic
  • S. Simion
  • E. Simioni
  • B. Simmons
  • D. Simon
  • M. Simon
  • P. Sinervo
  • N. B. Sinev
  • M. Sioli
  • G. Siragusa
  • A. N. Sisakyan
  • S. Yu. Sivoklokov
  • J. Sjölin
  • T. B. Sjursen
  • M. B. Skinner
  • H. P. Skottowe
  • P. Skubic
  • M. Slater
  • T. Slavicek
  • M. Slawinska
  • K. Sliwa
  • V. Smakhtin
  • B. H. Smart
  • L. Smestad
  • S. Yu. Smirnov
  • Y. Smirnov
  • L. N. Smirnova
  • O. Smirnova
  • M. N. K. Smith
  • R. W. Smith
  • M. Smizanska
  • K. Smolek
  • A. A. Snesarev
  • G. Snidero
  • S. Snyder
  • R. Sobie
  • F. Socher
  • A. Soffer
  • D. A. Soh
  • G. Sokhrannyi
  • C. A. Solans Sanchez
  • M. Solar
  • J. Solc
  • E. Yu. Soldatov
  • U. Soldevila
  • A. A. Solodkov
  • A. Soloshenko
  • O. V. Solovyanov
  • V. Solovyev
  • P. Sommer
  • H. Y. Song
  • N. Soni
  • A. Sood
  • A. Sopczak
  • B. Sopko
  • V. Sopko
  • V. Sorin
  • D. Sosa
  • M. Sosebee
  • C. L. Sotiropoulou
  • R. Soualah
  • A. M. Soukharev
  • D. South
  • B. C. Sowden
  • S. Spagnolo
  • M. Spalla
  • M. Spangenberg
  • F. Spanò
  • W. R. Spearman
  • D. Sperlich
  • F. Spettel
  • R. Spighi
  • G. Spigo
  • L. A. Spiller
  • M. Spousta
  • R. D. St. Denis
  • A. Stabile
  • S. Staerz
  • J. Stahlman
  • R. Stamen
  • S. Stamm
  • E. Stanecka
  • R. W. Stanek
  • C. Stanescu
  • M. Stanescu-Bellu
  • M. M. Stanitzki
  • S. Stapnes
  • E. A. Starchenko
  • J. Stark
  • P. Staroba
  • P. Starovoitov
  • R. Staszewski
  • P. Steinberg
  • B. Stelzer
  • H. J. Stelzer
  • O. Stelzer-Chilton
  • H. Stenzel
  • G. A. Stewart
  • J. A. Stillings
  • M. C. Stockton
  • M. Stoebe
  • G. Stoicea
  • P. Stolte
  • S. Stonjek
  • A. R. Stradling
  • A. Straessner
  • M. E. Stramaglia
  • J. Strandberg
  • S. Strandberg
  • A. Strandlie
  • E. Strauss
  • M. Strauss
  • P. Strizenec
  • R. Ströhmer
  • D. M. Strom
  • R. Stroynowski
  • A. Strubig
  • S. A. Stucci
  • B. Stugu
  • N. A. Styles
  • D. Su
  • J. Su
  • R. Subramaniam
  • A. Succurro
  • S. Suchek
  • Y. Sugaya
  • M. Suk
  • V. V. Sulin
  • S. Sultansoy
  • T. Sumida
  • S. Sun
  • X. Sun
  • J. E. Sundermann
  • K. Suruliz
  • G. Susinno
  • M. R. Sutton
  • S. Suzuki
  • M. Svatos
  • M. Swiatlowski
  • I. Sykora
  • T. Sykora
  • D. Ta
  • C. Taccini
  • K. Tackmann
  • J. Taenzer
  • A. Taffard
  • R. Tafirout
  • N. Taiblum
  • H. Takai
  • R. Takashima
  • H. Takeda
  • T. Takeshita
  • Y. Takubo
  • M. Talby
  • A. A. Talyshev
  • J. Y. C. Tam
  • K. G. Tan
  • J. Tanaka
  • R. Tanaka
  • S. Tanaka
  • B. B. Tannenwald
  • S. Tapia Araya
  • S. Tapprogge
  • S. Tarem
  • F. Tarrade
  • G. F. Tartarelli
  • P. Tas
  • M. Tasevsky
  • T. Tashiro
  • E. Tassi
  • A. Tavares Delgado
  • Y. Tayalati
  • A. C. Taylor
  • F. E. Taylor
  • G. N. Taylor
  • P. T. E. Taylor
  • W. Taylor
  • F. A. Teischinger
  • P. Teixeira-Dias
  • K. K. Temming
  • D. Temple
  • H. Ten Kate
  • P. K. Teng
  • J. J. Teoh
  • F. Tepel
  • S. Terada
  • K. Terashi
  • J. Terron
  • S. Terzo
  • M. Testa
  • R. J. Teuscher
  • T. Theveneaux-Pelzer
  • J. P. Thomas
  • J. Thomas-Wilsker
  • E. N. Thompson
  • P. D. Thompson
  • R. J. Thompson
  • A. S. Thompson
  • L. A. Thomsen
  • E. Thomson
  • M. Thomson
  • R. P. Thun
  • M. J. Tibbetts
  • R. E. Ticse Torres
  • V. O. Tikhomirov
  • Yu. A. Tikhonov
  • S. Timoshenko
  • E. Tiouchichine
  • P. Tipton
  • S. Tisserant
  • K. Todome
  • T. Todorov
  • S. Todorova-Nova
  • J. Tojo
  • S. Tokár
  • K. Tokushuku
  • K. Tollefson
  • E. Tolley
  • L. Tomlinson
  • M. Tomoto
  • L. Tompkins
  • K. Toms
  • E. Torrence
  • H. Torres
  • E. Torró Pastor
  • J. Toth
  • F. Touchard
  • D. R. Tovey
  • T. Trefzger
  • L. Tremblet
  • A. Tricoli
  • I. M. Trigger
  • S. Trincaz-Duvoid
  • M. F. Tripiana
  • W. Trischuk
  • B. Trocmé
  • C. Troncon
  • M. Trottier-McDonald
  • M. Trovatelli
  • L. Truong
  • M. Trzebinski
  • A. Trzupek
  • C. Tsarouchas
  • J. C.-L. Tseng
  • P. V. Tsiareshka
  • D. Tsionou
  • G. Tsipolitis
  • N. Tsirintanis
  • S. Tsiskaridze
  • V. Tsiskaridze
  • E. G. Tskhadadze
  • K. M. Tsui
  • I. I. Tsukerman
  • V. Tsulaia
  • S. Tsuno
  • D. Tsybychev
  • A. Tudorache
  • V. Tudorache
  • A. N. Tuna
  • S. A. Tupputi
  • S. Turchikhin
  • D. Turecek
  • R. Turra
  • A. J. Turvey
  • P. M. Tuts
  • A. Tykhonov
  • M. Tylmad
  • M. Tyndel
  • I. Ueda
  • R. Ueno
  • M. Ughetto
  • F. Ukegawa
  • G. Unal
  • A. Undrus
  • G. Unel
  • F. C. Ungaro
  • Y. Unno
  • C. Unverdorben
  • J. Urban
  • P. Urquijo
  • P. Urrejola
  • G. Usai
  • A. Usanova
  • L. Vacavant
  • V. Vacek
  • B. Vachon
  • C. Valderanis
  • N. Valencic
  • S. Valentinetti
  • A. Valero
  • L. Valery
  • S. Valkar
  • S. Vallecorsa
  • J. A. Valls Ferrer
  • W. Van Den Wollenberg
  • P. C. Van Der Deijl
  • R. van der Geer
  • H. van der Graaf
  • N. van Eldik
  • P. van Gemmeren
  • J. Van Nieuwkoop
  • I. van Vulpen
  • M. C. van Woerden
  • M. Vanadia
  • W. Vandelli
  • R. Vanguri
  • A. Vaniachine
  • F. Vannucci
  • G. Vardanyan
  • R. Vari
  • E. W. Varnes
  • T. Varol
  • D. Varouchas
  • A. Vartapetian
  • K. E. Varvell
  • F. Vazeille
  • T. Vazquez Schroeder
  • J. Veatch
  • L. M. Veloce
  • F. Veloso
  • T. Velz
  • S. Veneziano
  • A. Ventura
  • D. Ventura
  • M. Venturi
  • N. Venturi
  • A. Venturini
  • V. Vercesi
  • M. Verducci
  • W. Verkerke
  • J. C. Vermeulen
  • A. Vest
  • M. C. Vetterli
  • O. Viazlo
  • I. Vichou
  • T. Vickey
  • O. E. Vickey Boeriu
  • G. H. A. Viehhauser
  • S. Viel
  • R. Vigne
  • M. Villa
  • M. Villaplana Perez
  • E. Vilucchi
  • M. G. Vincter
  • V. B. Vinogradov
  • I. Vivarelli
  • S. Vlachos
  • D. Vladoiu
  • M. Vlasak
  • M. Vogel
  • P. Vokac
  • G. Volpi
  • M. Volpi
  • H. von der Schmitt
  • H. von Radziewski
  • E. von Toerne
  • V. Vorobel
  • K. Vorobev
  • M. Vos
  • R. Voss
  • J. H. Vossebeld
  • N. Vranjes
  • M. Vranjes Milosavljevic
  • V. Vrba
  • M. Vreeswijk
  • R. Vuillermet
  • I. Vukotic
  • Z. Vykydal
  • P. Wagner
  • W. Wagner
  • H. Wahlberg
  • S. Wahrmund
  • J. Wakabayashi
  • J. Walder
  • R. Walker
  • W. Walkowiak
  • C. Wang
  • F. Wang
  • H. Wang
  • H. Wang
  • J. Wang
  • J. Wang
  • K. Wang
  • R. Wang
  • S. M. Wang
  • T. Wang
  • T. Wang
  • X. Wang
  • C. Wanotayaroj
  • A. Warburton
  • C. P. Ward
  • D. R. Wardrope
  • A. Washbrook
  • C. Wasicki
  • P. M. Watkins
  • A. T. Watson
  • I. J. Watson
  • M. F. Watson
  • G. Watts
  • S. Watts
  • B. M. Waugh
  • S. Webb
  • M. S. Weber
  • S. W. Weber
  • J. S. Webster
  • A. R. Weidberg
  • B. Weinert
  • J. Weingarten
  • C. Weiser
  • H. Weits
  • P. S. Wells
  • T. Wenaus
  • T. Wengler
  • S. Wenig
  • N. Wermes
  • M. Werner
  • P. Werner
  • M. Wessels
  • J. Wetter
  • K. Whalen
  • A. M. Wharton
  • A. White
  • M. J. White
  • R. White
  • S. White
  • D. Whiteson
  • F. J. Wickens
  • W. Wiedenmann
  • M. Wielers
  • P. Wienemann
  • C. Wiglesworth
  • L. A. M. Wiik-Fuchs
  • A. Wildauer
  • H. G. Wilkens
  • H. H. Williams
  • S. Williams
  • C. Willis
  • S. Willocq
  • A. Wilson
  • J. A. Wilson
  • I. Wingerter-Seez
  • F. Winklmeier
  • B. T. Winter
  • M. Wittgen
  • J. Wittkowski
  • S. J. Wollstadt
  • M. W. Wolter
  • H. Wolters
  • B. K. Wosiek
  • J. Wotschack
  • M. J. Woudstra
  • K. W. Wozniak
  • M. Wu
  • M. Wu
  • S. L. Wu
  • X. Wu
  • Y. Wu
  • T. R. Wyatt
  • B. M. Wynne
  • S. Xella
  • D. Xu
  • L. Xu
  • B. Yabsley
  • S. Yacoob
  • R. Yakabe
  • M. Yamada
  • D. Yamaguchi
  • Y. Yamaguchi
  • A. Yamamoto
  • S. Yamamoto
  • T. Yamanaka
  • K. Yamauchi
  • Y. Yamazaki
  • Z. Yan
  • H. Yang
  • H. Yang
  • Y. Yang
  • W.-M. Yao
  • Y. C. Yap
  • Y. Yasu
  • E. Yatsenko
  • K. H. Yau Wong
  • J. Ye
  • S. Ye
  • I. Yeletskikh
  • A. L. Yen
  • E. Yildirim
  • K. Yorita
  • R. Yoshida
  • K. Yoshihara
  • C. Young
  • C. J. S. Young
  • S. Youssef
  • D. R. Yu
  • J. Yu
  • J. M. Yu
  • J. Yu
  • L. Yuan
  • S. P. Y. Yuen
  • A. Yurkewicz
  • I. Yusuff
  • B. Zabinski
  • R. Zaidan
  • A. M. Zaitsev
  • J. Zalieckas
  • A. Zaman
  • S. Zambito
  • L. Zanello
  • D. Zanzi
  • C. Zeitnitz
  • M. Zeman
  • A. Zemla
  • J. C. Zeng
  • Q. Zeng
  • K. Zengel
  • O. Zenin
  • T. Ženiš
  • D. Zerwas
  • D. Zhang
  • F. Zhang
  • G. Zhang
  • H. Zhang
  • J. Zhang
  • L. Zhang
  • R. Zhang
  • X. Zhang
  • Z. Zhang
  • X. Zhao
  • Y. Zhao
  • Z. Zhao
  • A. Zhemchugov
  • J. Zhong
  • B. Zhou
  • C. Zhou
  • L. Zhou
  • L. Zhou
  • M. Zhou
  • N. Zhou
  • C. G. Zhu
  • H. Zhu
  • J. Zhu
  • Y. Zhu
  • X. Zhuang
  • K. Zhukov
  • A. Zibell
  • D. Zieminska
  • N. I. Zimine
  • C. Zimmermann
  • S. Zimmermann
  • Z. Zinonos
  • M. Zinser
  • M. Ziolkowski
  • L. Živković
  • G. Zobernig
  • A. Zoccoli
  • M. zur Nedden
  • G. Zurzolo
  • L. Zwalinski
  • ATLAS Collaboration
Open Access
Regular Article - Experimental Physics

Abstract

The reconstruction of the signal from hadrons and jets emerging from the proton–proton collisions at the Large Hadron Collider (LHC) and entering the ATLAS calorimeters is based on a three-dimensional topological clustering of individual calorimeter cell signals. The cluster formation follows cell signal-significance patterns generated by electromagnetic and hadronic showers. In this, the clustering algorithm implicitly performs a topological noise suppression by removing cells with insignificant signals which are not in close proximity to cells with significant signals. The resulting topological cell clusters have shape and location information, which is exploited to apply a local energy calibration and corrections depending on the nature of the cluster. Topological cell clustering is established as a well-performing calorimeter signal definition for jet and missing transverse momentum reconstruction in ATLAS.

1 Introduction

The detectable final state emerging from the proton–proton collisions at the Large Hadron Collider (LHC) consists of particles and jets which are reconstructed with high precision for physics analyses. In the ATLAS experiment [1], clusters of topologically connected calorimeter cell signals (topo-clusters) are employed as a principal signal definition for use in the reconstruction of the (hadronic) part of the final state comprising isolated hadrons, jets and hadronically decaying \(\tau \)-leptons. In addition, topo-clusters are also used to represent the energy flow from softer particles, which is needed for the reconstruction of full-event observables such as the missing transverse momentum.

The algorithm building the topo-clusters explores the spatial distribution of the cell signals in all three dimensions to establish connections between neighbours in an attempt to reconstruct the energy and directions of the incoming particles. The signals from cells determined to be connected are summed, and are used together with the cell locations to calculate direction, location, and shapes of the resulting clusters. Calorimeter cells with insignificant signals found to not be connected to neighbouring cells with significant signals are considered noise and discarded from further jet, particle and missing transverse momentum reconstruction.

The topo-clusters, while well established in deep inelastic scattering experiments such as H1 [2] at HERA and in electron–positron collider experiments such as ALEPH [3] at LEP and BaBar [4] at PEP-II, are used here in an innovative implementation as fully calibrated three-dimensional objects representing the calorimeter signals in the complex final-state environment of hadron–hadron collisions. A similar application in this particular environment, previously developed by the D0 Collaboration, implements the topological clustering in the two dimensions spanned by pseudorapidity and the azimuthal angle, thus applying the noise-suppression strategy inherent in this algorithm for jet reconstruction [5]. Several features and aspects of the ATLAS topo-cluster algorithms and their validations have previously been presented in Refs. [6, 7, 8, 9].

Some of the complexity of the final state in hadron–hadron collisions is introduced by particles from the underlying event generated by radiation and multiple parton interactions in the two colliding hadrons producing the hard-scatter final state. Other detector signal contributions from the collision environment, especially important for higher intensity operations at the LHC, arise from pile-up generated by diffuse particle emissions produced by the additional proton–proton collisions occurring in the same bunch crossing as the hard-scatter interaction (in-time pile-up). Further pile-up influences on the signal are from signal remnants from the energy flow in other bunch crossings in the ATLAS calorimeters (out-of-time pile-up).

This paper first describes the ATLAS detector in Sect. 2, together with the datasets used for the performance evaluations. The motivations and basic implementation of the topo-cluster algorithm are presented in Sect. 3. The computation of additional variables associated with topo-clusters including geometric and signal moments is described in Sect. 4. The various signal corrections applied to topo-clusters in the context of the local hadronic calibration are presented in Sect. 5. Section 6 summarises the performance of the topo-cluster signal in the reconstruction of isolated hadrons and jets produced in the proton–proton collisions at LHC. Performance evaluations with and without pile-up are discussed in this section, together with results from the corresponding Monte Carlo (MC) simulations. The paper concludes with a summary and outlook in Sect. 7.

2 The ATLAS experiment

In this section the basic systems forming the ATLAS detector are described in Sect. 2.1, followed in Sect. 2.2 by a description of the datasets considered in this paper and the corresponding run conditions in data. The MC simulation setup for final-state generation and the simulation of the calorimeter response to the incident particles is described in Sect. 2.3.

2.1 The ATLAS detector

The ATLAS experiment features a multi-purpose detector system with a forward–backward symmetric cylindrical geometry. It provides nearly complete and hermetic coverage of the solid angle around the proton–proton collisions at the LHC. A detailed description of the ATLAS experiment can be found in Ref. [1].

2.1.1 The ATLAS detector systems

The detector closest to the proton–proton collision vertex is the inner tracking detector (ID). It has complete azimuthal coverage and spans the pseudorapidity1 region \(|\eta |<2.5\). It consists of a silicon pixel detector, a silicon micro-strip detector, and a straw-tube transition radiation tracking detector covering \(|\eta |<2\). The ID is immersed into a uniform axial magnetic field of \(2\,\text {T}\) provided by a thin superconducting solenoid magnet.
Fig. 1

Cutaway view on the ATLAS calorimeter system

The ATLAS calorimeter system is illustrated in Fig. 1. It comprises several calorimeters with various read-out granularities and with different technologies. The electromagnetic calorimeter (EM) surrounding the ID is a high-granularity liquid-argon sampling calorimeter (LAr), using lead as an absorber. It is divided into one barrel (EMB; \(|\eta |<1.475\)) and two end-cap (EMEC; \(1.375<|\eta |<3.2\)) regions.

The barrel and end-cap regions also feature pre-samplers mounted between the cryostat cold wall and the calorimeter modules. The barrel pre-sampler (PreSamplerB) covers \(|\eta | < 1.52\), while the end-cap pre-sampler (PreSamplerE) covers \(1.5< |\eta | < 1.8\).

The hadronic calorimeters are divided into three distinct sections. The most central section contains the central barrel region (\(|\eta |<0.8\)) and two extended barrel regions (\(0.8<|\eta |<1.7\)). These regions are instrumented with scintillator-tile/steel hadronic calorimeters (Tile). Each barrel region consists of 64 modules with individual azimuthal (\(\phi \)) coverages of \(\pi /32\) rad. The two hadronic end-cap calorimeters (HEC; \(1.5<|\eta |<3.2\)) feature liquid-argon/copper calorimeter modules. The two forward calorimeters (FCAL; \(3.1<|\eta |<4.9\)) are instrumented with liquid-argon/copper and liquid-argon/tungsten modules for electromagnetic and hadronic energy measurements, respectively.

The ATLAS calorimeters have a highly granular lateral and longitudinal segmentation. Including the pre-samplers, there are seven sampling layers in the combined central calorimeters (PreSamplerB, three in EMB and three in Tile) and eight sampling layers in the end-cap region (PreSamplerE, three in EMEC and four in HEC). The three FCal modules provide three sampling layers in the forward region. Altogether, the calorimeter system has about \(188\,000\) read-out channels. The EM calorimeters are between 24 radiation lengths (\(X_{0}\)) and \(27\,X_{0}\) deep. The combined depth of the calorimeters for hadronic energy measurements is more than 10 hadronic interaction lengths (\(\lambda \)) nearly everywhere across the full detector acceptance (\(|\eta | \le 4.9\)). The amount of inactive material in front of the calorimeters depends on \(\eta \). It varies from about \(2\,X_{0}\) at \(\eta = 0\) to about \(4\,X_{0}\) at \(|\eta | \approx 1.8\), when measured from the nominal interaction point in ATLAS to the first active sampling layer (including PreSamplerB and PreSamplerE). It can increase to more than \(6\,X_{0}\) in the transition region between central and end-cap calorimeters (\(|\eta | \approx 1.45\) and \(|\eta | \approx 1.7\)). The amount of inactive material for hadrons is approximately \(1\,\lambda \) across the full covered \(\eta \)-range, with spikes going up to more than \(2\,\lambda \) in transition regions and in regions with complex cryostat structures and beam line services (\(|\eta | \approx 4\)).

The absorption power of the ATLAS calorimeters and their segmentation allow for very precise energy-flow reconstruction based on the topo-clusters described in this paper, with considerable exploitation of the topo-cluster shapes for signal calibration purposes. For more details of the calorimeter read-out structures, absorption characteristics, inactive material distributions, and cell signal formation, see Ref. [1]. The segmentation of the read-out structure in the various calorimeter sampling layers, each named by a dedicated identifier (\(S_{\text {calo}}\)), is shown in Table 1.
Table 1

The read-out granularity of the ATLAS calorimeter system [1], given in terms of \(\Delta \eta \times \Delta \phi \) with the exception of the forward calorimeters, where it is given in linear measures \(\Delta x \times \Delta y\), due to the non-pointing read-out geometry of the FCAL. For comparison, the FCAL granularity is approximately \(\Delta \eta \times \Delta \phi = 0.15 \times 0.15 (0.3 \times 0.3)\) at \(\eta = 3.5(4.5)\). The total number of read-out cells, including both ends of the calorimeter system, with (without) pre-samplers is \(187\,652\) (178,308)

Calorimeter

Module sampling (\(S_{\text {calo}}\))

\(N_{\text {cells}}\)

\(\eta \)-coverage

\(\Delta \eta \times \Delta \phi \)

Electromagnetic calorimeters

EMB

109,568

\(|\eta |<1.52\)

 
 

PreSamplerB

7808

\(|\eta |<1.52\)

\(0.025\times \pi /32\)

 

EMB1

 

\(|\eta |<1.4\)

\(0.025/8\times \pi /32\)

   

\(1.4<|\eta |<1.475\)

\(0.025\times \pi /128\)

 

EMB2

 

\(|\eta |<1.4\)

\(0.025\times \pi /128\)

   

\(1.4<|\eta |<1.475\)

\(0.075\times \pi /128\)

 

EMB3

 

\(|\eta |<1.35\)

\(0.050\times \pi /128\)

 

EMEC

63,744

\(1.375< |\eta | < 3.2\)

 
 

PreSamplerE

1536

\(1.5<|\eta |<1.8\)

\(0.025\times \pi /32\)

 

EME1

 

\(1.375<|\eta |<1.425\)

\(0.050\times \pi /32\)

   

\(1.425<|\eta |<1.5\)

\(0.025\times \pi /32\)

   

\(1.5<|\eta |<1.8\)

\(0.025/8\times \pi /32\)

   

\(1.8<|\eta |<2.0\)

\(0.025/6\times \pi /32\)

   

\(2.0<|\eta |<2.4\)

\(0.025/4\times \pi /32\)

   

\(2.4<|\eta |<2.5\)

\(0.025\times \pi /32\)

   

\(2.5<|\eta |<3.2\)

\(0.1\times \pi /32\)

 

EME2

 

\(1.375<|\eta |<1.425\)

\(0.050\times \pi /128\)

   

\(1.425<|\eta |<2.5\)

\(0.025\times \pi /128\)

   

\(2.5<|\eta |<3.2\)

\(0.1\times \pi /128\)

 

EME3

 

\(1.5<|\eta |<2.5\)

\(0.050\times \pi /128\)

Hadronic calorimeters

Tile (barrel)

2880

\(|\eta |<1\)

 
 

TileBar0/1

  

\(0.1\times \pi /32\)

 

TileBar2

  

\(0.2 \times \pi /32\)

 

Tile (extended barrel)

2304

\(0.8< |\eta | < 1.7\)

 
 

TileExt0/1

  

\(0.1\times \pi /32\)

 

TileExt2

  

\(0.2\times \pi /32\)

 

HEC

5632

\(1.5<|\eta |<3.2\)

 
 

HEC0/1/2/3

 

\(1.5<|\eta |<2.5\)

\(0.1\times \pi /32\)

   

\(2.5<|\eta |<3.2\)

\(0.2\times \pi /16\)

Forward calorimeters

FCAL

3524

\(3.1<|\eta |<4.9\)

\(\Delta x \times \Delta y\)

 

FCAL0

 

\(3.1<|\eta |<3.15\)

\(1.5\,{\text {cm}}\times 1.3\,{\text {cm}}\)

   

\(3.15<|\eta |<4.3\)

\(3.0\,{\text {cm}}\times 2.6\,{\text {cm}}\)

   

\(4.3<|\eta |<4.83\)

\(1.5\,{\text {cm}}\times 1.3\,{\text {cm}}\)

 

FCAL1

 

\(3.2<|\eta |<3.24\)

\(1.7\,{\text {cm}}\times 2.1\,{\text {cm}}\)

   

\(3.24<|\eta |<4.5\)

\(3.3\,{\text {cm}}\times 4.2\,{\text {cm}}\)

   

\(4.5<|\eta |<4.81\)

\(1.7\,{\text {cm}}\times 2.1\,{\text {cm}}\)

 

FCAL2

 

\(3.29<|\eta |<3.32\)

\(2.7\,{\text {cm}}\times 2.4\,{\text {cm}}\)

   

\(3.32<|\eta |<4.6\)

\(5.4\,{\text {cm}}\times 4.7\,{\text {cm}}\)

   

\(4.6<|\eta |<4.75\)

\(2.7\,{\text {cm}}\times 2.4\,{\text {cm}}\)

The muon spectrometer surrounds the ATLAS calorimeters. A system of three large air-core toroids, a barrel and two end-caps with eight coils each, generates a magnetic field in the pseudorapidity range of \(|\eta | < 2.7\). The muon spectrometer measures the full momentum of muons based on their tracks reconstructed with three layers of precision tracking chambers in the toroidal field. It is also instrumented with separate trigger chambers.

2.1.2 The ATLAS trigger

The trigger system for the ATLAS detector in Run 1 consisted of a hardware-based Level 1 (L1) trigger and a software-based High Level Trigger (HLT) [10]. For the evaluation of the topo-cluster reconstruction performance, samples of minimum-bias (MB) triggered events, samples of events selected by jet triggers, and samples of events with hard objects such as muons, which are not triggered by the calorimeter, are useful.

The ATLAS MB trigger [11] used signals from a dedicated system of scintillators (MBTS [12]; \(2.1< |\eta | < 3.8\)) at L1 in 2010 and 2011 data-taking. Depending on the run period, it required one hit in either of the \(\eta \) hemispheres, or one hit in each \(\eta \) hemisphere. In 2012, the MB samples were triggered by a zero-bias trigger. This trigger unconditionally accepted events from bunch crossings occurring a fixed number of LHC cycles after a high-energy electron or photon was accepted by the L1 trigger. The L1 trigger rate for these hard objects scales linearly with luminosity, thus the collision environment generated by the luminosity-dependent additional proton–proton interactions discussed in Sect. 2.2.1 is well reflected in the MB samples.

For triggering on collision events with jets at L1, jets are first built from coarse-granularity calorimeter towers using a sliding-window algorithm (L1-jets). The events are accepted if they have L1-jets passing triggers based on (1) the transverse momentum (\(p_{\text {T}}\)) of individual L1-jets (single-jet triggers) or on (2) the detection of several such jets at increasing transverse momenta (multi-jet triggers). Those events accepted by L1 are then subjected to refined jet-trigger decisions based on jet \(p_{\text {T}}\) and multi-jet topology in the HLT, now using jets that are reconstructed from calorimeter cell signals with algorithms similar to the ones applied in the offline precision reconstruction [13].

A \(Z\) boson sample is collected from muon triggers at L1. Since the trigger rate and the reconstruction of the decay properties of the accepted \(Z \!\rightarrow \!\mu \mu \) events are basically unaffected by pile-up, this sample is not only unbiased in this respect but also with respect to other possible biases introduced by the ATLAS calorimeter signals.

2.2 Dataset

Fig. 2

The peak luminosities measured by the ATLAS online luminosity monitor system throughout the run years are shown in (a). The mean number of additional proton–proton interactions at the beginning of each LHC fill is shown in (b) for the same period in time

The data used for the evaluation of the topo-cluster reconstruction performance are selected from proton–proton collision events at a centre-of-mass energy of \(\sqrt{s} = 7\,{\text {TeV}}\), recorded with the ATLAS detector in 2010, and at \(\sqrt{s} = 8\,{\text {TeV}}\) in 2012. The overall amount of high-quality data recorded at those times corresponds to \(\sim \!45\,\text {pb}^{-1}\) in 2010, and \(\sim \!20.3\,\text {fb}^{-1}\) in 2012. Peak instantaneous luminosities reached in the first three years of LHC running (LHC Run 1) are shown in Fig. 2a. Some early data recorded during the very first proton–proton collisions in the LHC in 2009 are considered for the studies of the topo-cluster reconstruction performance as well. The corresponding events are extracted from approximately \(540\,000\) proton–proton collisions at \(\sqrt{s} = 900\,{\text {GeV}}\), recorded during stable beam conditions and corresponding to about \(12\,\text {mb}^{-1}\). Occasional references to 2011 run conditions, where protons collided in the LHC with \(\sqrt{s} = 7\,{\text {TeV}}\) and ATLAS collected data corresponding to \(\sim \!5.1\,\text {fb}^{-1}\), are provided to illustrate the evolution of the operational conditions during LHC Run 1 relevant to topo-cluster reconstruction. The specific choice of 2010 and 2012 data for the performance evaluations encompasses the most important scenarios with the lowest and highest luminosity operation, respectively.

2.2.1 Pile-up in data

One important aspect of the contribution from additional proton–proton interactions (pile-up) to the calorimeter signal in data is the sensitivity of the ATLAS liquid-argon calorimeters to this pile-up as a function of the instantaneous luminosity, and as a function of the signal history from previous bunch crossings.

In the initial phase of data-taking in 2010 the proton beam intensities at LHC were relatively low. The recorded events contain on average three additional proton–proton interactions, as shown in Fig. 2b. In addition, the initial bunch crossing interval of \(t_{\text {BX}} = 750\,{\text {ns}}\) was larger than the window of sensitivity of the LAr calorimeter, which is defined by the duration \(\tau _{\text {signal}}\) of the shaped signal, with \(\tau _{\text {signal}} \approx 600\,{\text {ns}}\), as depicted in Fig. 3 for the typical charge collection time of \(t_{\text {d}} = 450\,{\text {ns}}\) in this detector. In later data-taking periods in 2010 the bunch crossing interval was reduced to \(t_{\text {BX}} = 175\,{\text {ns}}\), which is within the sensitivity of the LAr calorimeter signal formation (\(t_{\text {BX}} < \tau _{\text {signal}}\)). Nevertheless, the still-low instantaneous luminosity reduced the amount of energy scattered into the calorimeter in the other bunch crossings to a negligible contribution with little effect on the signal history.
Fig. 3

The pulse shape in the ATLAS LAr calorimeters. The unipolar triangular pulse is the current pulse in the liquid argon generated by fast ionising particles. Its characteristic time is the drift time (charge collection time) \(t_{\text {d}}\), with \(t_{\text {d}} \approx 450\,{\text {ns}}\) in the example for the central EMB calorimeter shown here. The shaped pulse is superimposed, with a characteristic duration of \(\tau _{\text {signal}} \approx 600\,{\text {ns}}\). The full circles on the shaped pulse indicate the nominal bunch crossings at \(25\,{\text {ns}}\) intervals. The figure has been adapted from Ref. [14]

Throughout operations in 2011 and 2012, the proton beam intensities in the LHC were significantly increased, leading to the corresponding increases in the number of pile-up interactions per bunch crossing shown in Fig. 2(b). At the same time, \(t_{\text {BX}}\) was reduced to \(50\,{\text {ns}}\). These two changes in the run conditions introduced a sensitivity of the LAr calorimeter signal to the signal residuals from proton–proton interactions occurring in \(N_{\text {BX}}^{\text {PU}} \approx 12\) preceding bunch crossings at the LHC (out-of-time pile-up), in addition to pile-up interactions in the current bunch crossing (in-time pile-up). The out-of-time pile-up effect on the cell signal depends on \(N_{\text {BX}}^{\text {PU}} \approx \tau _{\text {signal}}/t_{\text {BX}}\) and the energy deposited in each of the \(N_{\text {BX}}^{\text {PU}}\) bunch crossings.

The bipolar shape of the LAr calorimeter signal shown in Fig. 3 reduces the overall effect of pile-up, because it features a net-zero integral over time. This leads to cancellation on average of in-time pile-up signal contributions by out-of-time pile-up signal residuals in any given calorimeter cell. By design of the shaping amplifier, and the choice of digitally sampling the shaped pulse amplitude in time with a frequency of \(40\,\text {MHz}\) in the read-out, the most efficient suppression is achieved for \(25\,{\text {ns}}\) bunch spacing in the LHC beams. It is fully effective in the limit where for each bunch crossing contributing to out-of-time pile-up about the same amount of energy is deposited in a given calorimeter cell. A small loss of efficiency is observed for \(50\,{\text {ns}}\) bunch spacing, due to the less frequent injection of energy by the fewer previous bunch crossings.

Approximately the first ten bunch crossings in each LHC bunch train at \(50\,{\text {ns}}\) bunch spacing are characterised by different out-of-time pile-up contributions from the collision history. This history gets filled with signal remnants from an increasing number of past bunch crossings with proton–proton interactions the larger the time difference between the bunch crossing and the beginning of the train becomes. The remaining bunch crossings in a train, about 26 of a total of 36 in 2011 and 62 of a total of 72 in 2012, have an out-of-time pile-up signal contribution which is stable within the bunch-to-bunch fluctuations in the beam intensity. In 2012 data a dedicated cell-by-cell correction is applied in the offline cell signal reconstruction to compensate for the corresponding variations in the out-of-time pile-up. Further details of the ATLAS liquid-argon calorimeter read-out and signal processing can be found in Ref. [15].

Even with a constant proton bunch intensity and apart from the bunch train effects, the efficiency of pile-up suppression by signal shaping is reduced by the large fluctuations in the number of additional interactions from bunch crossing to bunch crossing, and by the different energy-flow patterns of the individual collisions in the time window of sensitivity \(\tau _{\text {signal}}\) in the LAr calorimeters. Consequently, the signal shows a principal sensitivity to pile-up, even after shaping and digital filtering in the read-out. This is evident from the residual event-by-event deviation of the cell-signal baseline, which depends on the specific pile-up condition at the time of the triggered event, from the (average zero) baseline expected from the signal shaping. These baseline fluctuations can lead to relevant signal offsets once the noise suppression is applied, which is an important part of the calorimeter signal extraction strategy using topo-clusters presented in Sect. 3.

The Tile calorimeter shows very little sensitivity to pile-up since most of the associated (soft particle) energy flow is absorbed in the LAr calorimeters in front of it. Moreover, out-of-time pile-up is suppressed by a shorter signal collection time and a short pulse shaping time, reducing the sensitivity of the signal to only about three bunch crossings at \(50\,{\text {ns}}\) intervals [12].

2.2.2 Effect on calorimeter noise

Fig. 4

The energy-equivalent cell noise in the ATLAS calorimeters on the electromagnetic (EM) scale as a function of the direction \(\left| \eta \right| \) in the detector, for a the 2010 configuration with \(\mu = 0\), b the 2011 configuration with \(\mu = 8\) (both plots from Ref. [16]), and c the 2012 configuration with \(\mu = 30\). The various colours indicate the noise in the pre-sampler (PS) and the three layers of the LAr EM calorimeter, the three layers of the Tile calorimeter, the four layers of the hadronic end-cap (HEC) calorimeter, and the three modules of the forward (FCAL) calorimeter

In ATLAS operations prior to 2011 the cell noise was dominated by electronic noise. The short bunch crossing interval and higher instantaneous luminosity in 2011 and 2012 LHC running added additional and dominant noise contributions from the cell-signal baseline fluctuations introduced by pile-up, as discussed in Sect. 2.2.1. These fluctuations, even though not perfectly following a Gaussian distribution,2 can nevertheless be expressed as noise measured by the standard deviation of their distribution, taken from simulated MB events and scaled to the expected number of pile-up interactions. The cell noise thresholds steering the topo-cluster formation described in Sect. 3 thus needed to be increased from those used in 2010 to accommodate this pile-up-induced noise. This is done by adjusting the nominal energy-equivalent noise \(\sigma _{\text {noise}}\) according to
$$\begin{aligned} \sigma _{\text {noise}}= \left\{ \begin{array}{lr} \sigma _{\text {noise}}^{\text {electronic}}&{}\text {(2010 operations)}, \\ \sqrt{\left( \sigma _{\text {noise}}^{\text {electronic}}\right) ^{2} + \left( \sigma _{\text {noise}}^{\mathrm{pile-up}}\right) ^{2}} &{}\text {(2011 and 2012 operations)}. \end{array}\right. \end{aligned}$$
(1)
Here, \(\sigma _{\text {noise}}^{\text {electronic}}\) is the electronic noise, and \(\sigma _{\text {noise}}^{\mathrm{pile-up}}\) the noise from pile-up, corresponding to an average of eight additional proton–proton interactions per bunch crossing (\(\mu = 8\)) in 2011, and \(\mu = 30\) in 2012. These configurations are choices based on the expected average \(\langle \mu \rangle \) for the run year. They needed to be made before the respective data-taking started, to allow for a fast turn-around reconstruction of the collected data. As \(\mu \) changes with the decrease of the instantaneous luminosity \(L_{\text {inst}}\) through-out the LHC proton fill, \(\sigma _{\text {noise}}^{\mathrm{pile-up}}\) is only optimal for the small subset of data recorded when \(L_{\text {inst}}\) generated the nominal (a priori chosen) \(\mu \) pile-up interactions on average. LHC operations at lower \(\mu \) lead to slightly reduced calorimeter sensitivity to relevant small signals, as \(\sigma _{\text {noise}}^{\mathrm{pile-up}}\) is too large. For data-taking periods with higher than nominal \(\mu \) the noise suppression is not optimal, leading to more noise contributions to the topo-cluster signals.

The change of the total nominal noise \(\sigma _{\text {noise}}\) and its dependence on the calorimeter region in ATLAS can be seen by comparing Fig. 4a–c. In most calorimeter regions, the total noise rises significantly above the electronic noise with increasing pile-up activity, as expected. This increase is largest in the forward calorimeters, where \(\sigma _{\text {noise}}^{\mathrm{pile-up}}\gg \sigma _{\text {noise}}^{\text {electronic}}\) by more than one order of magnitude, already under 2011 run conditions.

2.3 Monte Carlo simulations

The energy and direction of particles produced in proton–proton collisions are simulated using various MC event generators. An overview of these generators for LHC physics can be found in Ref. [17]. The samples for comparisons to 2010 data are produced at \(\sqrt{s} = 7\,{\text {TeV}}\), while the MC samples for 2012 analyses are generated at \(\sqrt{s} = 8\,{\text {TeV}}\). Some configuration details for the inclusive jet and inclusive \(Z\) boson MC samples and the simulated MB samples are given below.

2.3.1 Monte Carlo simulations of signal samples

Simulated signal samples include inclusive jet-production, which is generated using Pythia [18] version 6.425 for 2010 analyses, and Pythia8 [19] version 8.160 for 2012 analysis. Both generators model the hard sub-process in the final states of the generated proton–proton collisions using a \(2\!\!\rightarrow \!\!2\) matrix element at leading order in the strong coupling \(\alpha _{\text {S}}\). Additional radiation is modelled in the leading-logarithmic (LL) approximation by \(p_{\text {T}}\)-ordered parton showers [20]. Multiple parton interactions (MPI) [21], as well as fragmentation and hadronisation based on the Lund string model [22], are also generated.

For comparisons with 2012 data, samples of \(Z\) bosons with \(Z \!\rightarrow \!\mu \mu \) are generated. The next-to-leading-order (NLO) POWHEG [23, 24] model is used, with the final-state partons showered by Pythia8 using the CT10 NLO parton distribution function (PDF) [25] and the ATLAS AU2 [26] set of tuned parton shower and other soft underlying event generation parameters. Pythia8 also provides the MPI, fragmentation and hadronisation for these events.

2.3.2 Minimum-bias samples and pile-up modelling

The MB samples for 2012 running conditions are generated using Pythia8 with the ATLAS AM2 [26] set of tuned soft interaction parameters and the MSTW2008LO PDF set [27]. A single, fully simulated event for that run year is built by overlaying a number \(N_{\text {PU}}\) of generated MB events onto one generated hard-scatter event. The actual \(N_{\text {PU}}\) is drawn from a Poisson distribution around the average number \(\langle \mu \rangle \) of additional proton–proton collisions per bunch crossing. The value of \(\langle \mu \rangle \) is measured by the experiment as an average over one luminosity block, which can last as long as two minutes, with its actual duration depending on the central data acquisition configuration at the time of the data-taking. The measurement of \(\langle \mu \rangle \) is mainly based on single \(\eta \)-hemisphere hit counting as well as counting coincidental hits in both \(\eta \)-hemispheres with the fast ATLAS luminosity detectors consisting of two small Cherenkov counter (LUCID; \(5.6< |\eta | < 6.0\)) and two sets of small diamond sensors forming two beam conditions monitors (BCM; \(|\eta | = 4.2\)). Details of these detectors and the measurement are given in Ref. [28]. The distribution of the measured \(\langle \mu \rangle \) over the whole run period is taken into account in the pile-up simulation.

The LHC bunch train structure with 72 proton bunches per train and \(50\,{\text {ns}}\) spacing between the bunches in 2012, is also modelled by organising the simulated collisions into four such trains. This allows the inclusion of out-of-time pile-up effects driven by the distance of the hard-scatter events from the beginning of the bunch train, as discussed in Sect. 2.2.1. A correction depending on the bunch position in the train is applied to data and MC simulations to mitigate these effects. Bunch-to-bunch intensity fluctuations in the LHC are not included in the MC modelling. These are corrected in the data by the correction depending on the position of the bunch in the train.

2.3.3 Minimum-bias overlay samples for 2012

In addition to the fully generated and simulated MC samples described earlier, samples with events mixing data and MC simulations are used to study the topo-cluster reconstruction performance. These samples are produced by overlaying one event from the MB samples collected by the zero-bias trigger described in Sect. 2.1.2 and a hard-scatter interaction from the MC generator [29, 30, 31]. The generated hard-scatter event is simulated using the detector simulation described in Sect. 2.1, but without any noise effects included. The recorded and simulated raw electronic signals are then overlaid prior to the digitisation step in the simulation. This results in modelling both the detector noise and the effect of pile-up from data with the correct experimental conditions on top of the simulated event. Theses samples are useful for detailed comparisons of topo-cluster signal features in 2012, as they do not depend on limitations in the soft-event modelling introduced by any of the generators.

2.3.4 Detector simulation

The Geant4 software toolkit [32] within the ATLAS simulation framework [33] propagates the stable particles3 produced by the event generators through the ATLAS detector and simulates their interactions with the detector material and the signal formation. Hadronic showers are simulated with the quark–gluon-string-plasma model employing a quark–gluon string model [34] at high energies and the Bertini intra-nuclear cascade model [35, 36, 37] at low energies (QGSP_BERT). There are differences between the detector simulation used in 2010 and in 2012. A newer version of Geant4 (version 9.4) is employed in 2012, together with a more detailed description of the LAr calorimeter absorber structure. These geometry changes introduce an increase of about 2% in the calorimeter response to pions with energies of less than \(10\,{\text {GeV}}\).

2.4 Hadronic final-state reconstruction in ATLAS

The fully reconstructed final state of the proton–proton collisions in ATLAS includes identified individual particles comprising electrons, photons, muons, and \(\tau \)-leptons, in addition to jets and missing transverse momentum (\(E_{\text {T}}^{\text {miss}}\)). Calorimeter signals contribute to all objects, except for muons. The topo-clusters introduced in detail in Sect. 3 are primarily used for the reconstruction of isolated hadrons, jets and \(E_{\text {T}}^{\text {miss}}\).

Jets are reconstructed using topo-clusters, with their energies either reconstructed on the basic (electromagnetic) scale presented in Sect. 3.2, or on the fully calibrated and corrected (hadronic) scale described in Sect. 5.

Additional refinement of the jet energy scale (JES) may include reconstructed charged-particle tracks from the ID. More details of jet reconstruction and calibration can be found in Refs. [16, 38].

Jets used in the studies presented here are reconstructed in data and MC simulations using the anti-\(k_{t}\) jet algorithm [39] as implemented in the FastJet package [40]. The jet size is defined by the radius parameter R in the jet algorithm, where both \(R = 0.4\) and \(R = 0.6\) are used. Full four-momentum recombination is used, restricting the input topo-cluster signals to be positive for a meaningful jet formation. The jets are fully calibrated and corrected after formation, including a correction for pile-up signal contributions. For 2012, the pile-up correction employs the reconstructed median transverse momentum density in the event and the area of the jet to subtract the \(p_{\text {T}}\) contribution from pile-up, following the suggestions in Ref. [41]. In addition, an MC simulation-based residual correction is applied [42].

3 Topological cluster formation and features

The collection of the calorimeter signals of a given collision event into clusters of topologically connected cell signals is an attempt to extract the significant signal from a background of electronic noise and other sources of fluctuations such as pile-up. This strategy is most effective in a highly granular calorimeter system such as the one employed by ATLAS. Finely segmented lateral read-out together with longitudinal sampling layers allows the resolution of energy-flow structures generating these spatial signal patterns, thus retaining only signals important for particle and jet reconstruction while efficiently removing insignificant signals induced by noise. The signal extraction is guided by reconstructing three-dimensional “energy blobs” from particle showers in the active calorimeter volume. Individual topo-clusters are not solely expected to contain the entire response to a single particle all of the time. Rather, depending on the incoming particle types, energies, spatial separations and cell signal formation, individual topo-clusters represent the full or fractional response to a single particle (full shower or shower fragment), the merged response of several particles, or a combination of merged full and partial showers.

3.1 Topo-cluster formation

The collection of calorimeter cell signals into topo-clusters follows spatial signal-significance patterns generated by particle showers. The basic observable controlling this cluster formation is the cell signal significance \(\varsigma _{\text {cell}}^{\,{{\text {EM}}}}\), which is defined as the ratio of the cell signal to the average (expected) noise \(\sigma _{\text {noise,cell}}^{\,{{\text {EM}}}}\) in this cell, as estimated for each run year according to Eq. (1) (with \( \sigma _{\text {noise,cell}}^{\,{{\text {EM}}}}= \sigma _{\text {noise}}\)),
$$\begin{aligned} \varsigma _{\text {cell}}^{\,{{\text {EM}}}}= \frac{E_{\text {cell}}^{{{\text {EM}}}}}{\sigma _{\text {noise,cell}}^{\,{{\text {EM}}}}} . \end{aligned}$$
(2)
Both the cell signal \(E_{\text {cell}}^{{{\text {EM}}}}\) and \(\sigma _{\text {noise,cell}}^{\,{{\text {EM}}}}\) are measured on the electromagnetic (EM) energy scale. This scale reconstructs the energy deposited by electrons and photons correctly but does not include any corrections for the loss of signal for hadrons due to the non-compensating character of the ATLAS calorimeters.
Topo-clusters are formed by a growing-volume algorithm starting from a calorimeter cell with a highly significant seed signal. The seeding, growth, and boundary features of topo-clusters are in this algorithm controlled by the three respective parameters \(\{S,N,P\}\), which define signal thresholds in terms of \(\sigma _{\text {noise,cell}}^{\,{{\text {EM}}}}\) and thus apply selections based on \(\varsigma _{\text {cell}}^{\,{{\text {EM}}}}\) from Eq. (2),
$$\begin{aligned} \left| E_{\text {cell}}^{{{\text {EM}}}}\right|> S \sigma _{\text {noise,cell}}^{\,{{\text {EM}}}}&\Rightarrow \left| \varsigma _{\text {cell}}^{\,{{\text {EM}}}}\right| > S&(\text {primary seed threshold, default} S = 4); \end{aligned}$$
(3)
$$\begin{aligned} \left| E_{\text {cell}}^{{{\text {EM}}}}\right|> N \sigma _{\text {noise,cell}}^{\,{{\text {EM}}}}&\Rightarrow \left| \varsigma _{\text {cell}}^{\,{{\text {EM}}}}\right| > N&(\text {threshold for growth control, default } N = 2); \end{aligned}$$
(4)
$$\begin{aligned} \left| E_{\text {cell}}^{{{\text {EM}}}}\right|> P \sigma _{\text {noise,cell}}^{\,{{\text {EM}}}}&\Rightarrow \left| \varsigma _{\text {cell}}^{\,{{\text {EM}}}}\right| > P&(\text {principal cell filter, default } P = 0). \end{aligned}$$
(5)
Useful configurations employ a \(S > N \ge P\) rule, as reflected in the default configuration for ATLAS indicated above. The default values are derived from optimisations of the response and the relative energy resolution for charged pions in test-beam experiments using ATLAS calorimeter prototypes [43].

3.1.1 Collecting cells into topo-clusters

Topo-cluster formation is a sequence of seed and collect steps, which are repeated until all topologically connected cells passing the criteria given in Eqs. (3) and (4) and their direct neighbours satisfying the condition in Eq. (5) are found. The algorithm starts by selecting all cells with signal significances \(\varsigma _{\text {cell}}^{\,{{\text {EM}}}}\) passing the threshold defined by S in Eq. (3) from calorimeter regions which are allowed to seed clusters.4 These seed cells are then ordered in decreasing \(\varsigma _{\text {cell}}^{\,{{\text {EM}}}}\).

Each seed cell forms a proto-cluster. The cells neighbouring a seed and satisfying Eqs. (4) or (5) are collected into the corresponding proto-cluster. Here neighbouring is generally defined as two calorimeter cells being directly adjacent in a given sampling layer, or, if in adjacent layers, having at least partial overlap in the \((\eta ,\phi )\) plane. This means that the cell collection for topo-clusters can span modules within the same calorimeter as well as calorimeter sub-detector transition regions. Should a neigbouring cell have a signal significance passing the threshold defined by the parameter N in Eq. (4), its neighbours are collected into the proto-cluster as well. If a particular neighbour is a seed cell passing the threshold S defined in Eq. (3), the two proto-clusters are merged. If a neighbouring cell is attached to two different proto-clusters and its signal significance is above the threshold defined by N, the two proto-clusters are merged. This procedure is iteratively applied to further neighbours until the last set of neighbouring cells with significances passing the threshold defined by P in Eq. (5), but not the one in Eq. (4), is collected. At this point the formation stops.
Fig. 5

Signal significance (\(\varsigma _{\text {cell}}^{\,{{\text {EM}}}}\)) distributions for all cells (blue/cyan) and for cells after the noise suppression in the topological cell clustering is applied (red/yellow), in selected sampling layers of the LAr calorimeters: a the first sampling of the central electromagnetic LAr calorimeter (EMB), b the first sampling of the electromagnetic LAr end-cap calorimeter (EMEC), c the first sampling of the hadronic LAr end-cap calorimeter (HEC), and d the first module of the LAr forward calorimeter (FCAL). The spectra are extracted from 2012 zero-bias data at \(\sqrt{s} = 8\,{\text {TeV}}\) with an average number of pile-up interactions \(\langle \mu \rangle = 28\). The dashed lines indicate \(S = \pm 4\), \(N = \pm 2\), and \(P = 0\)

The resulting proto-cluster is characterised by a core of cells with highly significant signals. This core is surrounded by an envelope of cells with less significant signals. The configuration optimised for ATLAS hadronic final-state reconstruction is \(S = 4\), \(N = 2\), and \(P = 0\), as indicated in Eqs. (3) to (5). This particular configuration with \(P = 0\) means that any cell neighbouring a cell with signal significance passing the threshold given by N in Eq. (4) is collected into a proto-cluster, independent of its signal. Using the correlations between energies in adjacent cells in this way allows the retention of cells with signals that are close to the noise levels while preserving the noise suppression feature of the clustering algorithm.

The implicit noise suppression implemented by the topo-cluster algorithm discussed above leads to significant improvements in various aspects of the calorimeter performance, such as the energy and spatial resolutions in the presence of pile-up. Contributions from large negative and positive signal fluctuations introduced by pile-up can survive in a given event, though, and thus contribute to the sensitivity to pile-up observed in e.g. the jet response [42], in addition to the cell-level effects mentioned in Sect. 2.2.1. Examples of the effect of this noise suppression on the cells contributing to zero-bias events recorded with ATLAS in 2012 are shown in the cell signal-significance spectra in Fig. 5a–d for four different LAr calorimeters in ATLAS.

3.1.2 Treatment of negative cell signals

Negative cell signals in the ATLAS calorimeters are the result of fluctuations introduced predominantly by pile-up and, to a lesser extent, by electronic noise, as discussed in Sects. 2.2.1 and 2.2.2. The thresholds in Eqs. (3)–(5) are applied in terms of the absolute value of \(\varsigma _{\text {cell}}^{\,{{\text {EM}}}}\). This means that not only large positive cell signals can seed a cluster, but also those with large negative signals. In addition, cells with negative signals can also contribute to the cluster growth control and are added to the envelope around the topo-cluster core.

The use of cells with \(E_{\text {cell}}^{{{\text {EM}}}}< 0\) as topo-cluster seeds provides a diagnostic tool for the amount of noise in the overall calorimeter signal for a given event. At the fixed noise value given in Eq. (1) and used in Eq. (3), the luminosity-dependent actual noise in the event is reflected in the number of topo-clusters reconstructed with negative seeds. This number serves as an estimator mainly for out-of-time pile-up.

Topo-clusters with negative seeds often have a total energy \(E_{\text {clus}}^{{{\text {EM}}}}< 0\) as well, especially when \(|\varsigma _{\text {cell}}^{\,{{\text {EM}}}}| \gg P\). This is due to the dominance of the negative seed and the correlation between this seed signal and signals in the neighbouring cells, which likely also have \(E_{\text {cell}}^{{{\text {EM}}}}< 0\). If a negative seed signal is generated by out-of-time pile-up, it is induced by a particle injected into the calorimeter more than \(100\,{\text {ns}}\) before the event. Its residual signal trace is scaled by the negative undershoot of the shaping function shown in Fig. 3. This particle also injected significant energy in the neighbouring cells at the same time, due to its electromagnetic or hadronic shower, which leads to \(E_{\text {cell}}^{{{\text {EM}}}}< 0\) in these cells at the time of the event. For the same reasons, topo-clusters from out-of-time pile-up seeded by \(E_{\text {cell}}^{{{\text {EM}}}}>0\) often yield \(E_{\text {clus}}^{{{\text {EM}}}}> 0\), because they are typically generated by particles injected in past bunch crossings closer in time (within \(100\,{\text {ns}}\)). The topo-clusters with \(E_{\text {clus}}^{{{\text {EM}}}}< 0\) can be used to provide an average global cancellation of contributions of clusters seeded by positive fluctuations in out-of-time pile-up in full event observables including \(E_{\text {T}}^{\text {miss}}\)  [44].

Clustering cells with \(E_{\text {cell}}^{{{\text {EM}}}}< 0\) in any topo-cluster, including those containing and seeded by large positive signals, improves noise suppression due to the local cancellation of random positive (upward) noise fluctuations by negative (downward) fluctuations within this cluster. Allowing only positive signals to contribute introduces a bias in the cluster signal, while the random cancellation partially suppresses this bias.

To reconstruct physics objects such as jets from topo-clusters, only those clusters with a net energy \(E_{\text {clus}}^{{{\text {EM}}}}> 0\) are considered. The expectation is that clusters with net negative energy have no contribution to the signal of the reconstructed object, as there is no correlation of the corresponding downward fluctuation mainly induced by the energy flow in previous bunch crossings with the final state that is triggered and reconstructed.

3.1.3 Cluster splitting

The proto-clusters built as described in Sect. 3.1.1 can be too large to provide a good measurement of the energy flow from the particles generated in the recorded event. This is true because spatial signal structures inside those clusters are not explicitly taken into account in the formation. In particular, local signal maxima indicate the presence of two or more particles injecting energy into the calorimeter in close proximity.

To avoid biases in jet-finding and to support detailed jet substructure analysis as well as a high-quality \(E_{\text {T}}^{\text {miss}}\) reconstruction, proto-clusters with two or more local maxima are split between the corresponding signal peaks in all three spatial dimensions. A local signal maximum is defined by \(E_{\text {cell}}^{{{\text {EM}}}}> 500\,\text {MeV}\), in addition to the topological requirements for this cell to have at least four neighbours and that none of the neighbours has a larger signal. Also, the location of cells providing local maxima is restricted to cells in the EM sampling layers EMB2, EMB3, EME2 and EME3, and to FCAL0. This means that for a proto-cluster located completely inside the electromagnetic calorimeters, or extending from the electromagnetic to the hadronic calorimeters, splitting is guided by the spatial cell signal distributions in the highly granular electromagnetic calorimeters. The cluster splitting is refined in an additional step, where signal maxima can be provided by cells from the thin EM sampling layers EMB1 and EME1 with a highly granular \(\eta \)-strip read-out geometry, all sampling layers in the hadronic calorimeters (HEC0 to HEC3, Tile0 to Tile2), and the hadronic forward calorimeter modules FCAL1 and FCAL2.5 The use of EMB1 and EME1 in the topo-cluster splitting improves the photon separation in \(\pi ^{0}\rightarrow \gamma \gamma \).
Fig. 6

Stages of topo-cluster formation in the first module (FCAL0) of the FCAL calorimeter for a simulated dijet event with at least one jet entering this calorimeter. Shown in a are cells with signal significance \(|\varsigma _{\text {cell}}^{\,{{\text {EM}}}}| > 4\) that can seed topo-clusters, in b cells with \(|\varsigma _{\text {cell}}^{\,{{\text {EM}}}}| > 2\) controlling the topo-cluster growth, and in c all clustered cells and the outline of topo-clusters and topo-cluster fragments in this module. All clusters shown in c which do not contain a seed cell from this module are seeded in other modules of the FCAL, or in other calorimeters surrounding it. Pile-up is not included in this simulation, but electronic noise is modelled. Cells not colour coded but inside a topo-cluster have a negative signal, while cells shaded grey are completely surrounded by clustered cells but not part of a topo-cluster themselves. The cell and cluster boundaries are displayed on a dimensionless grid using the polar angle \(\theta \) and the azimuthal angle \(\phi \). This view maintains the cell shapes and proportions. For the definition of the cell signal significance \(\varsigma _{\text {cell}}^{\,{{\text {EM}}}}\) see Eq. (2)

The cluster splitting algorithm can find cells which are neighbours to two or more signal maxima. In this case, the cell is assigned to the two highest-energy clusters after splitting of the original topo-cluster it is associated with. This means that each cell is only shared once at most, and, even then, is never shared between more than two clusters.

The sharing of its signal between the two clusters with respective energies \(E_{\text {clus},1}^{{{\text {EM}}}}\) and \(E_{\text {clus},2}^{{{\text {EM}}}}\) is expressed in terms of two geometrical weights \(w_{\text {cell},1}^{\text {geo}}\) and \(w_{\text {cell},2}^{\text {geo}}\). These weights are calculated from the distances of the cell to the centres of gravity of the two clusters (\(d_{1}\), \(d_{2}\)), measured in units of a typical electromagnetic shower size scale in the ATLAS calorimeters,6 and the cluster energies,
$$\begin{aligned} w_{\text {cell},1}^{\text {geo}}= & {} \dfrac{E_{\text {clus},1}^{{{\text {EM}}}}}{E_{\text {clus},1}^{{{\text {EM}}}} + r E_{\text {clus},2}^{{{\text {EM}}}}}, \end{aligned}$$
(6)
$$\begin{aligned} w_{\text {cell},2}^{\text {geo}}= & {} 1 - w_{\text {cell},1}^{\text {geo}}, \end{aligned}$$
(7)
$$\begin{aligned} r= & {} \exp (d_{1}-d_{2}). \end{aligned}$$
(8)
The geometrical weights reflect the splitting rule that each cell can only appear in two proto-clusters at most, as \(w_{\text {cell},1}^{\text {geo}} + w_{\text {cell},2}^{\text {geo}} = 1\). After splitting, the final proto-clusters are the topo-clusters used for further reconstruction of the recorded or simulated final state.
Figure 6 shows an example of topo-clusters generated by an MC simulated jet in the first module of the ATLAS forward calorimeter under 2010 run conditions (no pile-up). Possible seed cells, as defined in Eq. (3), are shown in Fig. 6a. Cells with signal significances above the threshold N specified in Eq. (4) are displayed in Fig. 6b. The cells from this module included in any topo-cluster are shown in Fig. 6c. This display shows the effectiveness of cluster splitting in tracing signal structures. Comparing Figs. 6a and c clearly shows the survival of cells with \(|\varsigma _{\text {cell}}^{\,{{\text {EM}}}}| < 2\) in the vicinity of more significant signals, even if those are not in the same module (or sampling layer).
Fig. 7

The number of reconstructed clusters for simulated charged and neutral single pions without actual pile-up added but with nominal pile-up noise used in the reconstruction. In a the distribution of the number of clusters \(N_{\text {clus}}\) is shown for neutral and charged pions injected into the ATLAS calorimeters at \(|\eta | = 0.3\) with an energy of \(E = 100\,{\text {GeV}}\), together with the \(N_{\text {clus}}\) distribution for empty events (topo-clusters generated by electronic noise only). The distributions are individually normalised to unity. The dependence of the average \(\langle N_{\text {clus}}\rangle \) on the generated \(\eta _{\text {gen}}\) is shown in b again for \(\pi ^{0}\), \(\pi ^{-}\) and empty events. The shaded area and the dashed lines indicate the spread (in terms of RMS) around the central value

3.1.4 Cluster multiplicities in electromagnetic and hadronic showers

One of the original motivations behind any cell clustering is to reconstruct single-particle showers with the highest possible precision in terms of energy and shape. The immediate expectation is that the clustering algorithm should be very efficient in reconstructing one cluster for each particle entering the calorimeter. While this view is appropriate for dense and highly compact electromagnetic showers with relatively small shower-to-shower fluctuations in their longitudinal (along the direction of flight of the incoming particle) and lateral (perpendicular to the direction of flight) extensions, hadronic showers are subject to much larger intrinsic fluctuations leading to large shower-to-shower variations in their shapes and compactness. Hadrons generated in inelastic interactions in the course of the hadronic shower can even travel significant distances and generate sub-showers outside the direct neighbourhood of the calorimeter cell containing the initial hadronic interaction. This means that topo-clusters can contain only a fraction of the hadronic shower.

The distributions of the topo-cluster multiplicity \(N_{\text {clus}}\) for single particles which primarily generate electromagnetic showers (\(\pi ^{0}\)) and hadronic showers (\(\pi ^{-}\)) in the central (barrel) calorimeter region are shown in Fig. 7a. The dependence of the average \(N_{\text {clus}}\) on the pseudorapidity \(\eta \) is displayed in Fig. 7b.

Neutral pions with \(E_{\pi ^{0}} = 100\,{\text {GeV}}\) injected into the detector at a fixed direction often generate only one topo-cluster from largely overlapping electromagnetic showers, as the angular distance between the two photons from \(\pi ^{0}\!\rightarrow \!\gamma \gamma \) is small. This is demonstrated by the \(N_{\text {clus}}\) distribution for topo-clusters generated by \(\pi ^{0}\) at \(|\eta | = 0.3\) in ATLAS in Fig. 7a peaking at \(N_{\text {clus}}= 1\), with a probability only slightly larger than the one for \(N_{\text {clus}}=2\). In the latter case the two topo-clusters from the \(\pi ^{0}\) are generated by (1) resolving the two photon-induced showers, (2) a possible residual imperfect signal collection and proto-cluster splitting in the topo-cluster algorithm, or by (3) accidental inclusion of additional topo-cluster(s) generated by electronic noise. While the particular reason for the second cluster depends on effects introduced by local features including the calorimeter read-out granularity and cell noise levels at a given direction \(\eta \), hypothesis (1) is found to be least likely as it is observed that the energy sharing between the two topo-clusters is typically very asymmetric. The leading topo-cluster generated by \(\pi ^{0}\) at \(100\,{\text {GeV}}\) contains very close to \(100\,\%\) of the total energy in this calorimeter region, indicating that the second and any further topo-clusters arise from hypotheses (2) and (3).

Figure 7b shows the average \(N_{\text {clus}}\) as a function of the generated particle direction \(\eta = \eta _{\text {gen}}\). Especially around transition regions at \(|\eta | \approx 1.4\) (central to end-cap calorimeters) and \(|\eta | \approx 3.2\) (end-cap to forward calorimeters), which both have reduced calorimetric coverage, \(N_{\text {clus}}\) can significantly increase due to reduction or loss of the core signal of the showers.

The number of clusters generated by \(\pi ^{-}\) with \(E = 100\,{\text {GeV}}\) injected at \(\eta = 0.3\) peaks at \(N_{\text {clus}}= 3\) and has a more significant tail to higher multiplicities, as shown in Fig. 7a. This is expected for hadronic showers, where the distance between two inelastic interactions with significant energy release is of the order of the nuclear interaction length \(\lambda _{\text {nucl}}\), typically \(\mathcal {O}(10\,{\text {cm}})\). This can lead to several well-separated topo-clusters. For example, at \(100\,{\text {GeV}}\) incident energy the leading topo-cluster generated by \(\pi ^{-}\) contains on average \(85\,{\text {GeV}}\), while the next-to-leading topo-cluster contains about \(10\,{\text {GeV}}\) on average. The remaining energy is distributed among one or more low-energy topo-clusters.

The wider hadronic shower spread introduces a higher sensitivity of \(N_{\text {clus}}\) to the calorimeter read-out granularities and transition regions, as can be seen in Fig. 7b. The transition regions at \(|\eta | \approx 0.8\text {--}1.0\), \(|\eta | \approx 1.4\) and \(|\eta | \approx 3.2\) affect the topo-cluster formation more than in the case of electromagnetic showers, not only in terms of the peak \(N_{\text {clus}}\) but also in terms of the range in \(\eta \). In particular the region around \(|\eta | \approx 0.8\text {--}1.0\) has a larger effect on \(N_{\text {clus}}\) for hadrons than for electromagnetic interacting particles, as this is the transition from the central to the extended Tile calorimeter introducing reduced calorimetric coverage for hadrons. The central electromagnetic calorimeter provides hermetic coverage here, without any effect on \(N_{\text {clus}}\). The sharp drop of \(N_{\text {clus}}\) for \(\pi ^{-}\) at \(|\eta | = 2.5\) corresponds to the reduction in calorimeter cell granularity by a factor of approximately four.

3.2 Cluster kinematics

The cluster kinematics are the result of the recombination of cell energies and directions. The presence of cells with \(E_{\text {cell}}^{{{\text {EM}}}}< 0\) requires a special recombination scheme to avoid directional biases.

The cluster directions are calculated as signal-weighted barycentres \((\eta _{\text {clus}},\phi _{\text {clus}})\). Using \(E_{\text {cell}}^{{{\text {EM}}}}< 0 \) in this scheme leads to distortion of these directions, even projecting them into the wrong hemispheres. Ignoring the contribution of cells with negative signals, on the other hand, biases the cluster directions with contributions from upward noise fluctuations. To avoid both effects, the cluster directions are calculated with absolute signal weights \(|E_{\text {cell}}^{{{\text {EM}}}}|\),
$$\begin{aligned} \eta _{\text {clus}}= & {} \dfrac{\sum _{i=1}^{N_{\text {cell}}} w_{\text {cell},i}^{\text {geo}} \cdot |E_{\text {cell},i}^{\text {EM}}|\cdot \eta _{\text {cell},i}}{\sum _{i=1}^{N_{\text {cell}}} w_{\text {cell},i}^{\text {geo}} \cdot |E_{\text {cell},i}^{\text {EM}}|} \end{aligned}$$
(9)
$$\begin{aligned} \phi _{\text {clus}}= & {} \dfrac{\sum _{i=1}^{N_{\text {cell}}} w_{\text {cell},i}^{\text {geo}} \cdot |E_{\text {cell},i}^{\text {EM}}|\cdot \phi _{\text {cell},i}}{\sum _{i=1}^{N_{\text {cell}}} w_{\text {cell},i}^{\text {geo}} \cdot |E_{\text {cell},i}^{\text {EM}}|} . \end{aligned}$$
(10)
Here \(N_{\text {cell}}\) is the number of cells in the cluster, and \(w_{\text {cell},i}^{\text {geo}}\) are the geometrical signal weights introduced by cluster splitting, as given in Eqs. (6)–(8) in Sect. 3.1.3. The direction of each cell is given by \((\eta _{\text {cell}},\phi _{\text {cell}})\), calculated from its location with respect to the centre of ATLAS at \((x=0,y=0,z=0)\) in the detector reference frame. The cluster directions are therefore reconstructed with respect to this nominal detector centre.
The total cluster signal amplitude \(E_{\text {clus}}^{{{\text {EM}}}}\) reflects the correct signal contributions from all cells,
$$\begin{aligned} E_{\text {clus}}^{{{\text {EM}}}}= \sum _{i=1}^{N_{\text {cell}}} w_{\text {cell},i}^{\text {geo}} E_{\text {cell},i}^{\text {EM}}, \end{aligned}$$
(11)
and is calculated using the signed cell signals \(E_{\text {cell},i}^{\text {EM}}\) and taking into account the geometrical signal weights. In general, all clusters with \(E_{\text {clus}}^{{{\text {EM}}}}> 0\) are used for the reconstruction of physics objects in the ATLAS calorimeters, including the very few ones seeded by cell signals \(E_{\text {cell}}^{{{\text {EM}}}}<0\).
Each topo-cluster is interpreted as a massless pseudo-particle in physics object reconstruction. The energy and momentum components on the EM scale are calculated from the basic reconstructed kinematic variables \((E_{\text {clus}}^{{{\text {EM}}}},\eta _{\text {clus}},\phi _{\text {clus}})\) as
$$\begin{aligned} \text {P}_{\text {clus}}^{\,{{\text {EM}}}}= E_{\text {clus}}^{{{\text {EM}}}}\cdot \left( 1,\sin \theta _{\text {clus}}\cos \phi _{\text {clus}},\sin \theta _{\text {clus}}\sin \phi _{\text {clus}},\cos \theta _{\text {clus}}\right) = \left( E_{\text {clus}}^{{{\text {EM}}}},\vec {p}_{\text {clus}}^{\,\text {EM}}\right) \end{aligned}$$
(12)
with terms involving \(\theta _{\text {clus}}\), the polar angle calculated from \(\eta _{\text {clus}}\), and \(\phi _{\text {clus}}\).

The massless pseudo-particle interpretation is appropriate as there is no physically meaningful cluster mass without a specific and valid particle hypothesis for the origin of the signal. Such a hypothesis seems to be impossible to obtain from the calorimeter signals alone, especially for hadrons or hadronically decaying particles, where particle identification often requires a measurement of the charge. A topo-cluster mass could in principle be reconstructed from the cell signals and their spatial distribution, but this observable is dominated by lateral shower spreading, which does not represent a physically meaningful mass. It is also highly affected by the settings for the noise thresholds, which control the lateral and longitudinal spread of the cluster in a given pile-up environment (see Sect. 3.1.1).

In addition, hadronic showers tend to be split more often into two or more topo-clusters, as discussed in Sect. 3.1.4 for single particles. Also, it is very likely in the proton–proton collision environment at the LHC that a given topo-cluster contains signals from several particles, especially when located inside a jet, as a mix of electromagnetic and hadronic showers or shower fragments. These issues make a physical particle hypothesis very unlikely, and any cluster mass measurement would be very hard to interpret or validate in relation to a “real” particle.

4 Topo-cluster moments

The shape of a topo-cluster and its internal signal distribution contain valuable information for signal characterisation with respect to its origin, and therefore cluster-based calibrations. The list of reconstructed observables (“cluster moments”) is long. In this section the focus is on moments used to evaluate the signal quality in data, to determine the cluster location and size, and to calibrate each cluster. The geometry relevant to some of the moments is depicted in Fig. 8. Moments which are useful for purely technical reasons, such as those related to the information about the true energy deposited in the calorimeter in MC simulations, are not discussed in this paper.

Most moments are defined at a given order n for a given calorimeter cell variable \(\upsilon _{\text {cell}}\) as
$$\begin{aligned} \langle \upsilon _{\text {cell}}^{\,n} \rangle = \dfrac{\sum _{\{i\,|E_{\text {cell},i}^{\text {EM}}>0\}} w_{\text {cell},i}^{\text {geo}} E_{\text {cell},i}^{\text {EM}} \upsilon _{\text {cell},i}^{\,n}}{\sum _{\{i\,|E_{\text {cell},i}^{\text {EM}} > 0\}} w_{\text {cell},i}^{\text {geo}} E_{\text {cell},i}^{\text {EM}}} . \end{aligned}$$
(13)
All moments use the EM scale cell signals \(E_{\text {cell}}^{{{\text {EM}}}}\), thus they do not depend on any refined calibration. The moment calculation is further restricted to in-time signals, meaning only cells with \(E_{\text {cell}}^{{{\text {EM}}}}> 0\) are considered. Even though higher-order moments can be reconstructed, only centroids (\(n = 1\)) and spreads (\(n = 2\)) are used.
Fig. 8

Schematic view of geometrical moments for topo-clusters

4.1 Geometrical moments

Each topo-cluster with at least three cells with \(E_{\text {cell}}^{{{\text {EM}}}}> 0\) has a full set of geometrical moments. Simple directional moments (barycentres in \((\eta ,\phi )\) space) and locations (centres of gravity) are available for all clusters. Not all geometrical moments can be evaluated in a meaningful way for all topo-clusters, mostly due to lack of relevant information in clusters with few cells. In this case, a default value specific to each of these moments is provided.

4.1.1 Location

The location of a topo-cluster is defined by its centre of gravity \(\vec {c}\) in three-dimensional space, as shown in Fig. 8. This centre is calculated from the first moments of the three Cartesian coordinates specifying the calorimeter cell centres, following the definition given in Eq. (13). These locations are provided in the nominal detector frame of reference defined by the interaction point (IP) being located at \((x=0,y=0,z=0)\).

In addition to the absolute location measured by the centre of gravity, the distance \(\lambda _{\text {clus}}\) of the centre of gravity from the calorimeter front face, determined along the shower axis (see below and Fig. 8), is calculated for each topo-cluster.

4.1.2 Directions

The direction of a topo-cluster is given by \((\eta _{\text {clus}},\phi _{\text {clus}})\), reconstructed as given in Eqs. (9) and (10). In addition, the first- and second-order directional moments using \(\eta _{\text {cell}}\) and \(\phi _{\text {cell}}\) are calculated using Eq. (13) with \(n =1\) and \(n =2 \), respectively.7 The reference for these direction measures is the IP discussed above.

The shower axis is a measure of the direction of flight of the incoming particle. It is defined by a principal value analysis of the energy-weighted spatial correlations between cells with \(E_{\text {cell}}^{{{\text {EM}}}}> 0\) with respect to the cluster centre in Cartesian coordinates,
$$\begin{aligned} C_{uv} = \dfrac{1}{\mathcal {W}} \sum _{\{i\,|E_{\text {cell},i}^{\text {EM}} > 0\}} \left( w_{\text {cell},i}^{\text {geo}}E_{\text {cell},i}^{\text {EM}}\right) ^{2} (u_{i} - \langle u \rangle )(v_{i} - \langle v \rangle ) , \end{aligned}$$
(14)
with all permutations of \(u,v \in \{x,y,z\}\). The normalisation \(\mathcal {W}\) is given by
$$\begin{aligned} \mathcal {W} = \sum _{\{i\,|E_{\text {cell},i}^{\text {EM}} > 0\}} \left( w_{\text {cell},i}^{\text {geo}}E_{\text {cell},i}^{\text {EM}}\right) ^{2} . \end{aligned}$$
(15)
The \(C_{uv}\) fill a symmetric \(3 \times 3\) matrix \(\mathbf{C} = \left[ C_{uv}\right] \). The eigenvector of \(\mathbf{C}\) closest to the direction \(\vec {c}\) from the IP to the centre of gravity of the topo-cluster is taken to be the shower axis \(\vec {s}\). If the angular distance \(\Delta \alpha \) between \(\vec {c}\) and \(\vec {s}\) is \(\Delta \alpha > 20^{\circ }\), \(\vec {c}\) is used as the shower axis. Figure 8 depicts the geometry of the two axis definitions for topo-clusters.

4.1.3 Extensions and sizes

The size of the topo-cluster is calculated with respect to the shower axis \(\vec {s}\) and the centre of gravity \(\vec {c}\). For this, cells are first located with reference to \(\vec {s}\) and \(\vec {c}\). The distances of a cell at \(\vec {x}_{i}\) to the shower axis and the centre of gravity are then given by
$$\begin{aligned} r_{i}&= | (\vec {x}_{i} - \vec {c}\,) \times \vec {s}\,|&\text {(radial distance to shower axis)}; \end{aligned}$$
(16)
$$\begin{aligned} \lambda _{i}&= (\vec {x}_{i} - \vec {c}\,) \cdot \vec {s}&\text {(longitudinal distance from shower centre of gravity)}. \end{aligned}$$
(17)
The first moment \(\langle \lambda \rangle \) calculated according to Eq. (13) with \(\upsilon _{\text {cell},i} = \lambda _{i}\) and \(n =1\) is \(\langle \lambda \rangle = 0\) by definition. The same equation is used for the first moment \(\langle r\rangle \) of \(r_{i}\) (\(\upsilon _{\text {cell},i} = r_{i}\), \(n = 1\)). The longitudinal and lateral extensions of a topo-cluster can then respectively be measured in terms of the second moments \(\langle \lambda^{2}\rangle \) and \(\langle r^{2}\rangle \), again using Eq. (13), but with \(n = 2\). Specifying cluster dimensions in this fashion describes a spheroid with two semi-axes of respective lengths \(\sqrt{\langle \lambda ^{2}\rangle }\) and \(\sqrt{\langle r^{2}\rangle }\).
As calorimeter technologies and granularities change as function of \(\eta \) in ATLAS, measures representing the lateral and longitudinal extension of topo-clusters in a more universal and normalised fashion are constructed. These measures are defined in terms of second moments with value ranges from 0 to 1,
$$\begin{aligned} \mathfrak {m}_{\text {lat}}^{2}&= \dfrac{\langle r^{2}\rangle _{\text {out}}}{\langle r^{2}\rangle _{\text {out}} + \langle r^{2}\rangle _{\text {core}}}&\text {normalised lateral energy dispersion (width measure)}; \end{aligned}$$
(18)
$$\begin{aligned} \mathfrak {m}_{\text {long}}^{2}&= \dfrac{\langle \lambda ^{2}\rangle _{\text {out}}}{\langle \lambda ^{2}\rangle _{\text {out}} + \langle \lambda ^{2}\rangle _{\text {core}}}&\text {normalised longitudinal energy dispersion (length measure)}. \end{aligned}$$
(19)
The \(\langle r^{2}\rangle _{\text {out}}\) term is calculated using Eq. (13) with \(n =2\) and \(\upsilon _{\text {cell},i} = r_{i}\), but with \(r_{i} = 0\) for the two most energetic cells in the cluster. The term \(\langle r^{2}\rangle _{\text {core}}\) is calculated with the same equation, but now with a fixed \(r_{i} = r_{\text {core}}\) for the two most energetic cells, and \(r_{i} = 0\) for the rest. The calculation of the corresponding terms \(\langle \lambda ^{2}\rangle _{\text {out}}\) and \(\langle \lambda ^{2}\rangle _{\text {core}}\) for \(\mathfrak {m}_{\text {long}}^{2}\) follows the same respective rules, now with \(\upsilon _{\text {cell},i} = \lambda _{i}\) in Eq. (13) and \(\lambda _{\text {core}}\) for the most energetic cells in \(\langle \lambda ^{2}\rangle _{\text {core}}\).8

The normalised moments \(\mathfrak {m}_{\text {long}}^{2}\) and \(\mathfrak {m}_{\text {lat}}^{2}\) do not directly provide a measure of spatial topo-cluster dimensions, rather they measure the energy dispersion in the cells belonging to the topo-cluster along the two principal cluster axes. Characteristic values are \(\mathfrak {m}_{\text {long}}^{2}\rightarrow 0\) (\(\mathfrak {m}_{\text {lat}}^{2}\rightarrow 0\)) indicating few highly energetic cells distributed in close proximity along the longitudinal (lateral) cluster extension, and \(\mathfrak {m}_{\text {long}}^{2}\rightarrow 1\) (\(\mathfrak {m}_{\text {lat}}^{2}\rightarrow 1\)) indicating a longitudinal (lateral) distribution of cells with more similar energies. Small values of \(\mathfrak {m}_{\text {long}}^{2}\) (\(\mathfrak {m}_{\text {lat}}^{2}\)) therefore mean short (narrow) topo-clusters, while larger values are indicative of long (wide) clusters.

The effective size of the topo-cluster in \((\eta ,\phi )\) space can in good approximation be estimated as9
$$\begin{aligned} \sigma _{\eta } \simeq \sigma _{\phi } \simeq \quad {{\mathrm{atan}}}\quad \left( \dfrac{\sqrt{\langle r^{2}\rangle }}{|\vec {c}\,|}\right) \times \cosh (\eta ). \end{aligned}$$
(20)
The fact that this approximation holds for both the cluster size in \(\eta \) (\(\sigma _{\eta }\)) and \(\phi \) (\(\sigma _{\phi }\)) is due to the particular granularity of the ATLAS calorimeters.

4.2 Signal moments

Topo-cluster moments related to the distribution of the cell signals inside the cluster are useful in determining the density and compactness of the underlying shower, the significance of the cluster signal itself, and the quality of the cluster reconstruction. These moments thus not only provide an important input to the calibrations and corrections discussed in Sect. 5, but also support data quality driven selections in the reconstruction of physics objects. Additional topo-cluster signal quality moments related to instantaneous, short term, and long term detector defects introducing signal efficiency losses are available but very technical in nature, and very specific to the ATLAS calorimeters. Their discussion is outside of the scope of this paper.

4.2.1 Signal significance

The significance of the topo-cluster signal is an important measure of the relevance of a given cluster contribution to the reconstruction of physics objects. Similar to the cell signal significance \(\varsigma _{\text {cell}}^{\,{{\text {EM}}}}\) given in Eq. (2) in Sect. 3.1, it is measured with respect to the total noise \(\sigma _{\text {noise,clus}}^{\,{{\text {EM}}}}\) in the topo-cluster. The definition of \(\sigma _{\text {noise,clus}}^{\,{{\text {EM}}}}\) assumes incoherent noise in the cells contributing to the topo-cluster,10
$$\begin{aligned} \sigma _{\text {noise,clus}}^{\,{{\text {EM}}}}= \sqrt{\sum _{i=1}^{N_{\text {cell}}} \left( \sigma _{\text {noise,cell},i}^{\,{{\text {EM}}}}\right) ^{2}}. \end{aligned}$$
(21)
Here \(N_{\text {cell}}\) is the number of cells forming the cluster, including the ones with \(E_{\text {cell}}^{{{\text {EM}}}}< 0\). As discussed in Sect. 2.2.2, the individual overall cell noise \(\sigma _{\text {noise,cell},i}^{\,{{\text {EM}}}}\) is set according to the nominal pile-up condition for a given data taking period. The topo-cluster signal significance \(\varsigma _{\text {clus}}^{\,\text {EM}}\) is then measured using \(\sigma _{\text {noise,clus}}^{\,{{\text {EM}}}}\) and \(E_{\text {clus}}^{{{\text {EM}}}}\),
$$\begin{aligned} \varsigma _{\text {clus}}^{\,\text {EM}}= \dfrac{E_{\text {clus}}^{{{\text {EM}}}}}{\sigma _{\text {noise,clus}}^{\,{{\text {EM}}}}} . \end{aligned}$$
(22)
In addition to \(\varsigma _{\text {clus}}^{\,\text {EM}}\), \(\varsigma _{\text {cell}}^{\,{{\text {EM}}}}\) of the cell with the highest significant signal (the original cluster seed) is available to further evaluate the topo-cluster. A highly significant seed is a strong indication of an important cluster signal, even if \(\varsigma _{\text {clus}}^{\,\text {EM}}\) may be reduced by inclusion of a larger number of less significant cell signals.

4.2.2 Signal density

The signal density of the topo-cluster is indicative of the nature of the underlying particle shower. It can be evaluated in two different approaches. First, \(E_{\text {clus}}^{{{\text {EM}}}}\) can be divided by the volume the cluster occupies in the calorimeter. This volume is the sum of volumes of all cells contributing to the cluster. The signal density reconstructed this way is subject to considerable instabilities introduced by signal fluctuations from noise, as large volume cells can be added with a very small signal due to those fluctuations.

The default for topo-cluster calibration is the second and more stable estimate of the topo-cluster signal density measured by the cell-energy-weighted first moment \(\rho _{\text {clus}}= \langle \rho _{\text {cell}}\rangle \) of the signal densities \(\rho _{\text {cell},i} = E_{\text {cell},i}^{\text {EM}}/V_{\text {cell},i}\) of cells \(i = 1 \ldots N_{\text {cell}}\) forming the cluster. Here \(V_{\text {cell},i}\) is the volume of cell i. The \(\rho _{\text {clus}}\) variable is calculated using Eq. (13) with \(\upsilon _{\text {cell},i} = \rho _{\text {cell},i}\) and \(n =1\). It is much less sensitive to the accidental inclusion of large volume cells with small signals into the cluster, and is used in the context of topo-cluster calibration. The corresponding second moment is calculated using Eq. (13) with \(n = 2\). It indicates the spread of cell energy densities in the topo-cluster, thus its compactness.

4.2.3 Signal timing

The topo-cluster signal timing is a sensitive estimator of its signal quality. It is particularly affected by large signal remnants from previous bunch crossings contributing to the cluster, or even exclusively forming it, and can thus be employed as a tag for topo-clusters indicating pile-up activity.

The reconstructed signal \(E_{\text {cell}}^{{{\text {EM}}}}\) in all calorimeter cells in ATLAS is derived from the reconstruction of the peak amplitude of the time-sampled analogue signal from the calorimeter shaping amplifiers. In the course of this reconstruction the signal peaking time \(t_{\text {cell}}\) with respect to the \(40\,\text {MHz}\) LHC bunch crossing clock is determined as well. The timing \(t_{\text {clus}}\) of a topo-cluster is then calculated from \(t_{\text {cell},i}\) of the clustered cells \(i = 1\ldots N_{\text {cell}}\) according to
$$\begin{aligned} t_{\text {clus}}= \dfrac{\sum _{\{i|\varsigma _{\text {cell},i}^{{{\text {EM}}}}>2\}} \left( w_{\text {cell},i}^{\text {geo}}E_{\text {cell},i}^{\text {EM}}\right) ^{2} t_{\text {cell},i}}{\sum _{\{i|\varsigma _{\text {cell},i}^{{{\text {EM}}}}>2\}} \left( w_{\text {cell},i}^{\text {geo}}E_{\text {cell},i}^{\text {EM}}\right) ^{2}}, \end{aligned}$$
(23)
where only cells with a signal significance \(\varsigma _{\text {cell},i}^{{{\text {EM}}}}\) sufficient to reconstruct \(E_{\text {cell},i}^{\text {EM}}\) and \(t_{\text {cell},i}\) are used (\(\varsigma _{\text {cell},i}^{{{\text {EM}}}} > 2\)). The particular weight of the contribution of \(t_{\text {cell},i}\) to \(t_{\text {clus}}\) in Eq. (23) is found to optimise the cluster timing resolution [6].

4.2.4 Signal composition

The signal distribution inside a topo-cluster is measured in terms of the energy sharing between the calorimeters contributing cells to the cluster, and other variables measuring the cell signal sharing. The energy sharing between the electromagnetic and hadronic calorimeters is expressed in terms of the signal ratio \(f_{\text {emc}}\), and can be used as one of the characteristic observables indicating an underlying electromagnetic shower. The signal fraction \(f_{\text {max}}\) carried by the most energetic cell in the cluster is a measure of its compactness. The signal fraction \(f_{\text {core}}\) of the summed signals from the highest energetic cell in each longitudinal calorimeter sampling layer contributing to the topo-cluster can be considered as a measure of its core signal strength. It is sensitive not only to the shower nature but also to specific features of individual hadronic showers. These fractions are calculated for each topo-cluster with \(E_{\text {clus}}^{{{\text {EM}}}}> 0\) as follows (EMC denotes the electromagnetic calorimeters11 in ATLAS),
$$\begin{aligned} f_{\text {emc}}&= \dfrac{1}{E_{\text {clus},\text {pos}}^{{{\text {EM}}}}}\sum _{\{i\,\in \,\mathrm{EMC};E_{\text {cell},i}^{\text {EM}} > 0\}} w_{\text {cell},i}^{\text {geo}}E_{\text {cell},i}^{\text {EM}}&(\mathrm{EMC{} signal fraction in cluster}); \end{aligned}$$
(24)
$$\begin{aligned} f_{\text {max}}&= \dfrac{1}{E_{\text {clus},\text {pos}}^{{{\text {EM}}}}}\max \left\{ w_{\text {cell},i}^{\text {geo}}E_{\text {cell},i}^{\text {EM}}\right\}&(\text {most energetic cell signal fraction in cluster}); \end{aligned}$$
(25)
$$\begin{aligned} f_{\text {core}}&= \dfrac{1}{E_{\text {clus},\text {pos}}^{{{\text {EM}}}}}\sum _{s\,\in \,\{\text {samplings}\}} \max _{i\,\in \,s}\left\{ w_{\text {cell},i}^{\text {geo}}E_{\text {cell},i}^{\text {EM}}\right\}&(\text {core signal fraction in cluster}). \end{aligned}$$
(26)
The index s steps through the set of calorimeter sampling layers with cells contributing to the topo-cluster. Only cells with \(E_{\text {cell}}^{{{\text {EM}}}}> 0\) are used in the calculation of these fractions. Correspondingly, they are normalised to \(E_{\text {clus},\text {pos}}^{{{\text {EM}}}}\) given by
$$\begin{aligned} E_{\text {clus},\text {pos}}^{{{\text {EM}}}} = \sum _{\{i|E_{\text {cell},i}^{\text {EM}}>0\}} w_{\text {cell},i}^{\text {geo}}E_{\text {cell},i}^{\text {EM}}. \end{aligned}$$
(27)
All these moments have a value range of [0,1].

One of the variables that can be considered for further evaluation of the relevance of the cluster signal in the presence of pile-up is the ratio of \(E_{\text {clus},\text {pos}}^{{{\text {EM}}}}\) to \(E_{\text {clus}}^{{{\text {EM}}}}\). It is sensitive to the negative energy content of a given topo-cluster which is largely injected by out-of-time pile-up dominated by the negative tail of the bipolar signal shaping function discussed in Sect. 3.1.2.

4.2.5 Topological isolation

The implicit noise suppression in the topological clustering algorithms leads to signal losses affecting the calorimeter response to particles, as further discussed in Sect. 5.4. As these signal losses appear at the boundary of the topo-cluster, corresponding corrections need to be sensitive to whether the lost signals may be included in another close-by cluster or if they are lost for good. This is particularly important for jets, where the topo-cluster density can be very high.

The degree of isolation is measured by the isolation moment \(f_{\text {iso}}\), with \(0 \le f_{\text {iso}} \le 1\). A topo-cluster with \(f_{\text {iso}} = 1\) is completely isolated, while a cluster with \(f_{\text {iso}} = 0\) is completely surrounded by others. The isolation measures the sampling layer energy (\(E_{s}^{{{\text {EM}}}}\))-weighted fraction of non-clustered neighbour cells on the outer perimeter of the topo-cluster. Here \(E_{s}^{{{\text {EM}}}}\) is defined as the sum of the energies \(E_{\text {cell}}^{{{\text {EM}}}}\) of all cells in a topo-cluster located in a given sampling layer s of the calorimeter.

The isolation moment is reconstructed by first counting the number of calorimeter cells \(N_{\text {cell},s}^{\text {noclus}}\) in sampling layer s neighbouring a topo-cluster but not collected into one themselves. Second, the ratio \(N_{\text {cell},s}^{\text {noclus}}/N_{\text {cell},s}^{\text {neighbour}}\) of this number to the number of all neighbouring cells (\(N_{\text {cell},s}^{\text {neighbour}}\)) for each s contributing to the cluster is calculated. The per-cluster \(E_{s}^{{{\text {EM}}}}\)-weighted average of these ratios from all included s is the isolation moment \(f_{\text {iso}}\),
$$\begin{aligned} f_{\text {iso}} = \dfrac{\sum _{s \in \{\text {samplings with }E_{s}^{{{\text {EM}}}}>0\}} E_{s}^{{{\text {EM}}}} N_{\text {cell},s}^{\text {noclus}}/N_{\text {cell},s}^{\text {neighbour}}}{\sum _{s \in \{\text {samplings with }E_{s}^{{{\text {EM}}}}>0\}} E_{s}^{{{\text {EM}}}}}. \end{aligned}$$
(28)

5 Local hadronic calibration and signal corrections

The motivation for the calibration scheme described in this section arises from the intention to provide a calorimeter signal for physics object reconstruction in ATLAS which is calibrated outside any particular assumption about the kind of object. This is of particular importance for final-state objects with a significant hadronic signal content, such as jets and, to a lesser degree, \(\tau \)-leptons. In addition to these discrete objects, the precise reconstruction of the missing transverse momentum requires well-calibrated hadronic signals even outside hard final-state objects, to e.g. avoid deterioration of the \(E_{\text {T}}^{\text {miss}}\) resolution due to highly fluctuating (fake) \(p_{\text {T}}\)-imbalances introduced by the non-linear hadronic response on the EM scale.

The topo-cluster moments provide information sensitive to the nature of the shower generating the cluster signal. This information can be explored to apply moment-dependent calibrations cluster-by-cluster, and thus correct for the effects of the non-compensating calorimeter response to hadrons, accidental signal losses due to the clustering strategy, and energy lost in inactive material in the vicinity of the topo-cluster. The calibration strategy discussed in some detail in the following is local because it attempts to calibrate highly localised and relatively small (in transverse momentum flow space) topo-clusters.12 As the local hadronic calibration includes cell signal weighting, the calibration based on topo-clusters is referred to as “local hadronic cell weighting” (LCW) calibration.

All calibrations and corrections are derived using MC simulations of single pions (charged and neutral) at various energies in all ATLAS calorimeter regions. This fully simulation-based approach requires good agreement between data and these MC simulations for the topo-cluster signals and moments used for any of the applied corrections in terms of distribution shapes and averages. Reconstructed observables which are not well-modelled by simulation are not considered. The data/MC comparisons for most used observables are shown in the context of the discussion of the methods using them.

5.1 General topo-cluster calibration strategy

The LCW calibration aims at the cluster-by-cluster reconstruction of the calorimeter signal on the appropriate (electromagnetic or hadronic) energy scale. In this, the cluster energy resolution is expected to improve by using other information in addition to the cluster signal in the calibration. The basic calorimeter signal inefficiencies that this calibration must address are given below.
  • Non-compensating calorimeter response: All calorimeters employed in ATLAS are non-compensating, meaning their signal for hadrons is smaller than the one for electrons and photons depositing the same energy (\(e/\pi >1\)). Applying corrections to the signal locally so that \(e/\pi \) approaches unity on average improves the linearity of the response as well as the resolution for jets built from a mix of electromagnetic and hadronic signals. It also improves the reconstruction of full event observables such as \(E_{\text {T}}^{\text {miss}}\), which combines signals from the whole calorimeter system and requires balanced electromagnetic and hadronic responses in and outside signals from (hard) particles and jets.

  • Signal losses due to clustering: The topo-cluster formation applies an intrinsic noise suppression, as discussed in detail in Sect. 3.1. Depending on the pile-up conditions and the corresponding noise thresholds, a significant amount of true signal can be lost this way, in particular at the margins of the topo-cluster. This requires corrections to allow for a more uniform and linear calorimeter response.

  • Signal losses due to energy lost in inactive material: This correction is needed to address the limitations in the signal acceptance in active calorimeter regions due to energy losses in nearby inactive material in front, between, and inside the calorimeter modules.

Fig. 9

Overview of the local hadronic cell-weighting (LCW) calibration scheme for topo-clusters. Following the topo-cluster formation, the likelihood for a cluster to be generated by electromagnetic energy deposit (\(\mathcal {P}_{\text {clus}}^{\,{{\text {EM}}}}\)) is calculated. After this, the sequence of calibration and corrections indicated in the schematics is executed, each yielding cell signal weights for the two possible interpretations of the cluster signals. These weights are indicated in the figure. They are then used together with \(\mathcal {P}_{\text {clus}}^{\,{{\text {EM}}}}\) to calculate the topo-cluster energy and barycentre from the contributing calorimeter cells, as described in the text

The corrections collected in the LCW calibration address these three main sources of signal inefficiency. The specifics of the calibrations and corrections applied to correct for these signal inefficiencies depend on the nature of the energy deposit – hadronic (HAD) or electromagnetic (EM). Therefore, the first step of the topo-cluster calibration procedure is to determine the probability \(0 \le \mathcal {P}_{\text {clus}}^{\,{{\text {EM}}}}\le 1\) that a given topo-cluster is generated by an electromagnetic shower. This approach provides straightforward dynamic scales (cluster-by-cluster) for the application of specific electromagnetic (\(\mathcal {P}_{\text {clus}}^{\,{{\text {EM}}}}\)) and hadronic (\(1-\mathcal {P}_{\text {clus}}^{\,{{\text {EM}}}}\)) calibrations and corrections. For topo-clusters with \(\mathcal {P}_{\text {clus}}^{\,{{\text {EM}}}}= 1\), it suppresses the application of a hadronic calibration mostly addressing the non-compensating response to hadrons, and applies the electromagnetic-signal-specific corrections for the losses introduced by clustering and inactive material mentioned above. Reversely, very hadronic topo-clusters with \(\mathcal {P}_{\text {clus}}^{\,{{\text {EM}}}}= 0\) receive the appropriate hadronic calibration and hadronic-signal-specific signal loss corrections.

The main differences in the hadronic and electromagnetic calibration of topo-clusters are the magnitudes of the applied corrections, which in the EM case are significantly smaller than for HAD. Applying an exclusive categorisation based on the probability distributions described in Sect. 5.2 can lead to inconsistent calibrations especially for low-energy or small (few cells only) clusters, as misclassification for these kinds of topo-clusters is more likely than for clusters with higher energies or larger sizes. To allow for smooth transitions and reduce the dependency on the classification, the signal weights \(w_{\text {cell}}^{\text {cal}}\) applied to cell signals in the topo-cluster at any of the calibration and correction steps are calculated as
$$\begin{aligned} w_{\text {cell}}^{\text {cal}}= \mathcal {P}_{\text {clus}}^{\,{{\text {EM}}}}\cdot w_{\text {cell}}^{\text {em-cal}}+ ( 1 - \mathcal {P}_{\text {clus}}^{\,{{\text {EM}}}})\cdot w_{\text {cell}}^{\text {had-cal}}. \end{aligned}$$
(29)
The weights \(w_{\text {cell}}^{\text {em-cal}}\) and \(w_{\text {cell}}^{\text {had-cal}}\) represent the factors applied by the EM or HAD calibration to the cell signal. The effective representation of all calibration steps in terms of these cell-level signal weights implements a consistent approach independent of the nature of the actual correction applied at any given step. As detailed in Sects. 5.35.5, the weights can depend on the cell signal itself, thus yielding a different weight for each cell. They can also represent cluster-level corrections generating the same weight for all cells, or a subset of cells, of the topo-cluster. This cell weighting scheme therefore provides not only the corrected overall cluster energy after each calibration step by weighted cell signal re-summation, but also the corresponding (possibly modified) cluster barycentre. Thus the cumulative effect on the topo-cluster energy and direction can be validated after each step. The steps of the general LCW calibration are schematically summarised in Fig. 9, and the individual steps are described in more detail below.

The EM calibrations and corrections and their respective parameters are determined with single-particle MC simulations of neutral pions for a large set of energies distributed uniformly in terms of \(\log (E)\) between \(200\,\text {MeV}\) and \(2\,{\text {TeV}}\), at various directions \(\eta \). The same energy and \(\eta \) phase space is used for the corresponding simulations of charged pions to determine the HAD calibrations and corrections. The signals in these simulations are reconstructed with thresholds corresponding to the nominal \(\sigma _{\text {noise}}^{\,{{\text {EM}}}}\) for a given run period, which reflects the pile-up conditions according to Eq. (1) in Sect. 2.2.2. Only electronic noise is added into the signal formation in the MC simulation, so that the derived calibrations and corrections effectively correct for signal losses introduced by the clustering itself. In particular, additional signal from pile-up and modifications of the true signal by out-of-time pile-up are not considered, as these are expected to cancel on average.

5.2 Cluster classification

Fig. 10

Distribution of the likelihood \(\mathcal {P}_{\text {clus}}^{\,{{\text {EM}}}}(\rho _{\text {clus}}/E_{\text {clus}}^{{{\text {EM}}}},\lambda _{\text {clus}})\) for reconstructed topo-clusters to originate from an electromagnetic shower as a function of the shower depth \(\lambda _{\text {clus}}\) and the normalised cluster signal density \(\rho _{\text {clus}}/E_{\text {clus}}^{{{\text {EM}}}}\), with \(\rho _{\text {clus}}= \langle \rho _{\text {cell}}\rangle \) being the energy-weighted average of \(\rho _{\text {cell}}\). The shown distribution is determined as described in the text, in a selected bin of the cluster energy \(E_{\text {clus}}^{{{\text {EM}}}}\) and the cluster direction \(\eta _{\text {clus}}\). The red line indicates the boundary of the \(\mathcal {P}_{\text {clus}}^{\,{{\text {EM}}}}> 50\,\)% selection, below which the topo-cluster is classified as mostly electromagnetic (“EM-like”) and above which it is classified as mostly hadronic (“HAD-like”). The small EM-like area at the edge of the HAD-like region stems from neutral pions showering late. These areas are typical in regions of the detector where the second layer of the EM calorimeter is thinner and substantial parts of the shower are deposited in its last layer. The larger volume of the cells in this last layer leads to the reduced energy density while the position at the back of the EM calorimeter means a larger \(\lambda _{\text {clus}}\)

As discussed in Sect. 4, most topo-clusters provide geometrical and signal moments sensitive to the nature of the shower producing the cluster signal. In particular, electromagnetic showers with their compact shower development, early starting point and relatively small intrinsic fluctuations can generate cluster characteristics very different from those generated by hadronic showers. The latter are in general subjected to larger shower-by-shower fluctuations in their development and can be located deeper into the calorimeter. I