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Combined performance studies for electrons at the 2004 ATLAS combined test-beam

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2010 JINST 5 P11006(http://iopscience.iop.org/1748-0221/5/11/P11006)
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P UBLISHED BY IOP P UBLISHING FOR SISSAR ECEIVED: September 6, 2010
ACCEPTED: November 1, 2010
P UBLISHED: November 25, 2010

Combined performance studies for electrons at the2004 ATLAS combined test-beam

1 Deceased
2 Now at SUNY, Stony Brook, United States of America
3 Now at Université de Genève, Switzerland
4 Now at DESY, Zeuthen, Germany
5 Now at INFN Genova and Università di Genova, Italy
6 Now at CERN
7 Now at University of Helsinki, Finland
8 Now at Joint Institute for Nuclear Research, Dubna, Russia

c 2010 IOP Publishing Ltd and SISSA

doi:10.1088/1748-0221/5/11/P11006

2010 JINST 5 P11006

E. Abat,k,1 J.M. Abdallah, f T.N. Addy,ag P. Adragna,cc M. Aharrouche,ba
A. Ahmad,cm,2 T.P.A. Akesson,ay M. Aleksa,s C. Alexa,n K. Anderson,tA. Andreazza,be,b f F. Anghinolfi,s A. Antonaki,e G. Arabidze,e E. Arik,k T. Atkinson,bd
J. Baines,c f O.K. Baker,dd D. Banfi,be,b f S. Baron,s A.J. Barr,bs R. Beccherle,a j
H.P. Beck,i B. Belhorma,aw P.J. Bell,bb,3 D. Benchekroun,q D.P. Benjamin,acK. Benslama,cg E. Bergeaas Kuutmann,cp,4 J. Bernabeu,cz H. Bertelsen,v S. Binet,bq
C. Biscarat,ad V. Boldea,n V.G. Bondarenko,bk M. Boonekamp,c j M. Bosman, f
C. Bourdarios,bq Z. Broklova,ca D. Burckhart Chromek,s V. Bychkov,an J. Callahan,ai
D. Calvet,u M. Canneri,bw M. Capeáns Garrido,s M. Caprini,n L. Cardiel Sas,s T. Carli,sL. Carminati,be,b f J. Carvalho, p,by M. Cascella,bw M.V. Castillo,cz A. Catinaccio,sD. Cauz,ak D. Cavalli,be M. Cavalli Sforza, f V. Cavasinni,bw S.A. Cetin,k H. Chen, j
R. Cherkaoui,cd L. Chevalier,c j F. Chevallier,aw S. Chouridou,cx M. Ciobotaru,cv
M. Citterio,be A. Clark,ae B. Cleland,bx M. Cobal,ak E. Cogneras,i P. Conde Muino,by
M. Consonni,be,b f S. Constantinescu,n T. Cornelissen,s,5 S. Correard,w
A. Corso Radu,s G. Costa,be M.J. Costa,cz D. Costanzo,cl S. Cuneo,a j P. Cwetanski,ai
D. Da Silva,ch M. Dam,v M. Dameri,a j H.O. Danielsson,s D. Dannheim,s G. Darbo,a j
T. Davidek,ca K. De,d P.O. Defay,u B. Dekhissi,ax J. Del Peso,az T. Del Prete,bw
M. Delmastro,s F. Derue,av L. Di Ciaccio,ar B. Di Girolamo,s S. Dita,n F. Dittus,sF. Djama,w T. Djobava,cs D. Dobos,aa,6 M. Dobson,s B.A. Dolgoshein,bk A. Dotti,bw
G. Drake,b Z. Drasal,ca N. Dressnandt,bu C. Driouchi,v J. Drohan,cw W.L. Ebenstein,ac
P. Eerola,ay,7 I. Efthymiopoulos,s K. Egorov,ai T.F. Eifert,s K. Einsweiler,hM. El Kacimi,as M. Elsing,s D. Emelyanov,c f ,8 C. Escobar,cz A.I. Etienvre,c j A. Fabich,s9 Now at Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
10 Corresponding author, robert.froeschl@cern.ch
11 Now at Yale University, New Haven, U.S.A.
12 Now at Université de Genève, Switzerland
13 Now at SLAC, Stanford, U.S.A.
14 Now at Georg-August-Universitaet, Goettingen, Germany
15 Now at Versicherungskammer Bayern, Munich, Germany
16 Now at Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
17 Now at Université Pierre et Marie Curie (Paris 6) and Université Denis Diderot (Paris-7), France
18 Now at Laboratoire de Physique de Particules (LAPP), Annecy-le-Vieux, France
19 Now at University of Pittsburgh, U.S.A.
20 Now at Physikalisches Institut der Universitaet Bonn, Germany
21 Now at Universität Heidelberg, Germany
22 Now at IPHC, Universit’e de Strasbourg, CNRS/IN2P3, Strasbourg, France

2010 JINST 5 P11006

K. Facius,v A.I. Fakhr-Edine,o M. Fanti,be,b f A. Farbin,d P. Farthouat,sD. Fassouliotis,e L. Fayard,bq R. Febbraro,u O.L. Fedin,bv A. Fenyuk,cb
D. Fergusson,h P. Ferrari,s,9 R. Ferrari,bt B.C. Ferreira,ch A. Ferrer,cz D. Ferrere,ae
G. Filippini,u T. Flick,dc D. Fournier,bq P. Francavilla,bw D. Francis,s R. Froeschl,s,10
D. Froidevaux,s E. Fullana,b S. Gadomski,ae G. Gagliardi,a j P. Gagnon,ai M. Gallas,sB.J. Gallop,c f S. Gameiro,s K.K. Gan,bp R. Garcia,az C. Garcia,cz I.L. Gavrilenko,b j
C. Gemme,a j P. Gerlach,dc N. Ghodbane,u V. Giakoumopoulou,e V. Giangiobbe,bw
N. Giokaris,e G. Glonti,an T. Goettfert,bm T. Golling,h,11 N. Gollub,s A. Gomes,at,au,byM.D. Gomez,ae S. Gonzalez-Sevilla,cz,12 M.J. Goodrick,r G. Gorfine,bo B. Gorini,sD. Goujdami,o K-J. Grahn,aq P. Grenier,u,13 N. Grigalashvili,an Y. Grishkevich,bl
J. Grosse-Knetter,l,14 M. Gruwe,s C. Guicheney,u A. Gupta,t C. Haeberli,iR. Haertel,bm,15 Z. Hajduk,y H. Hakobyan,de M. Hance,bu J.D. Hansen,v P.H. Hansen,v
K. Hara,cu A. Harvey Jr.,ag R.J. Hawkings,s F.E.W. Heinemann,bs
A. Henriques Correia,s T. Henss,dc L. Hervas,s E. Higon,cz J.C. Hill,r J. Hoffman,zJ.Y. Hostachy,aw I. Hruska,ca F. Hubaut,w F. Huegging,l W. Hulsbergen,s,16
M. Hurwitz,t L. Iconomidou-Fayard,bq E. Jansen,ce I. Jen-La Plante,t
P.D.C. Johansson,cl K. Jon-And,cp M. Joos,s S. Jorgensen, f J. Joseph,hA. Kaczmarska,y,17 M. Kado,bq A. Karyukhin,cb M. Kataoka,s,18 F. Kayumov,b j
A. Kazarov,bv P.T. Keener,bu G.D. Kekelidze,an N. Kerschen,cl S. Kersten,dc
A. Khomich,bc G. Khoriauli,an E. Khramov,an A. Khristachev,bv J. Khubua,an
T.H. Kittelmann,v,19 R. Klingenberg,aa E.B. Klinkby,ac P. Kodys,ca T. Koffas,sS. Kolos,cv S.P. Konovalov,b j N. Konstantinidis,cw S. Kopikov,cb I. Korolkov, f
V. Kostyukhin,a j,20 S. Kovalenko,bv T.Z. Kowalski,x K. Krüger,s,21 V. Kramarenko,bl
L.G. Kudin,bv Y. Kulchitsky,bi C. Lacasta,cz R. Lafaye,ar B. Laforge,av W. Lampl,cF. Lanni, j S. Laplace,ar T. Lari,be A-C. Le Bihan,s,22 M. Lechowski,bq
F. Ledroit-Guillon,aw G. Lehmann,s R. Leitner,ca D. Lelas,bq C.G. Lester,r Z. Liang,zP. Lichard,s W. Liebig,bo A. Lipniacka,g M. Lokajicek,bz L. Louchard,u K.F. Lourerio,bp
A. Lucotte,aw F. Luehring,ai B. Lund-Jensen,aq B. Lundberg,ay H. Ma, j

23 Now at Laboratoire de Physique Subatomique et de Cosmologie CNRS/IN2P3, Grenoble, France
24 Now at CERN
25 Now at Harvard University, Cambridge, U.S.A.
26 Now at ICEPP, Tokyo, Japan
27 Now at P.N. Lebedev Institute of Physics, Moscow, Russia
28 Now at University of South Carolina, Columbia, U.S.A.
29 Now at UT Dallas
30 Now at IFAE, Barcelona, Spain
31 Now at CERN
32 Now at CERN

2010 JINST 5 P11006

R. Mackeprang,v A. Maio,at,au,by V.P. Maleev,bv F. Malek,aw L. Mandelli,be J. Maneira,by
M. Mangin-Brinet,ae,23 A. Manousakis,e L. Mapelli,s C. Marques,by S.Marti i Garcia,cz
F. Martin,bu M. Mathes,l M. Mazzanti,be K.W. McFarlane,ag R. McPherson,daG. Mchedlidze,cs S. Mehlhase,ah C. Meirosu,s Z. Meng,ck C. Meroni,be V. Mialkovski,an
B. Mikulec,ae,24 D. Milstead,cp I. Minashvili,an B. Mindur,x V.A. Mitsou,cz S. Moed,ae,25
E. Monnier,w G. Moorhead,bd P. Morettini,a j S.V. Morozov,bk M. Mosidze,cs
S.V. Mouraviev,b j E.W.J. Moyse,s A. Munar,bu A. Myagkov,cb A.V. Nadtochi,bv
K. Nakamura,cu,26 P. Nechaeva,a j,27 A. Negri,bt S. Nemecek,bz M. Nessi,sS.Y. Nesterov,bv F.M. Newcomer,bu I. Nikitine,cb K. Nikolaev,an I. Nikolic-Audit,av
H. Ogren,ai S.H. Oh,ac S.B. Oleshko,bv J. Olszowska,y A. Onofre,bg,by
C. Padilla Aranda,s S. Paganis,cl D. Pallin,u D. Pantea,n V. Paolone,bx F. Parodi,a j
J. Parsons,bn S. Parzhitskiy,an E. Pasqualucci,ci S.M. Passmored,s J. Pater,bb
S. Patrichev,bv M. Peez,az V. Perez Reale,bn L. Perini,be,b f V.D. Peshekhonov,an
J. Petersen,s T.C. Petersen,v R. Petti, j,28 P.W. Phillips,c f J. Pina,at,au,by B. Pinto,byF. Podlyski,u L. Poggioli,bq A. Poppleton,s J. Poveda,db P. Pralavorio,w L. Pribyl,sM.J. Price,s D. Prieur,c f C. Puigdengoles, f P. Puzo,bq O. Røhne,br F. Ragusa,be,b f
S. Rajagopalan, j K. Reeves,dc,29 I. Reisinger,aa C. Rembser,sP.A. Bruckman de Renstrom,bs P. Reznicek,ca M. Ridel,av P. Risso,a j I. Riu,ae,30
D. Robinson,r C. Roda,bw S. Roe,s O. Rohne,br A. Romaniouk,bk D. Rousseau,bq
A. Rozanov,w A. Ruiz,cz N. Rusakovich,an D. Rust,ai Y.F. Ryabov,bv V. Ryjov,sO. Salto, f B. Salvachua,b A. Salzburger,al,31 H. Sandaker,g C. Santamarina Rios,sL. Santi,ak C. Santoni,u J.G. Saraiva,at,au,by F. Sarri,bw G. Sauvage,ar L.P. Says,uM. Schaefer,aw V.A. Schegelsky,bv C. Schiavi,a j J. Schieck,bm G. Schlager,sJ. Schlereth,b C. Schmitt,ba J. Schultes,dc P. Schwemling,av J. Schwindling,c j
J.M. Seixas,ch D.M. Seliverstov,bv L. Serin,bq A. Sfyrla,ae,32 N. Shalanda,bh C. Shaw,a f
T. Shin,ag A. Shmeleva,b j J. Silva,by S. Simion,bq M. Simonyan,ar J.E. Sloper,s
S.Yu. Smirnov,bk L. Smirnova,bl C. Solans,cz A. Solodkov,cb O. Solovianov,cb
I. Soloviev,bv V.V. Sosnovtsev,bk F. Spanò,bn P. Speckmayer,s S. Stancu,cv R. Stanek,b
E. Starchenko,cb A. Straessner,ab S.I. Suchkov,bk M. Suk,ca R. Szczygiel,x
F. Tarrade, j F. Tartarelli,be P. Tas,ca Y. Tayalati,u F. Tegenfeldt,am R. Teuscher,ct
M. Thioye,cq V.O. Tikhomirov,b j C.J.W.P. Timmermans,ce S. Tisserant,w B. Toczek,xa University of Alberta, Department of Physics, Centre for Particle Physics,

Edmonton, AB T6G 2G7, Canada
Argonne National Laboratory, High Energy Physics Division,
9700 S. Cass Avenue, Argonne IL 60439, United States of Americac University of Arizona, Department of Physics, Tucson, AZ 85721, United States of America
d University of Texas at Arlington, Department of Physics,
Box 19059, Arlington, TX 76019, United States of America
e University of Athens, Nuclear & Particle Physics Department of Physics, Panepistimiopouli Zografou, GR
15771 Athens, GreecefInstitut de Fisica d’Altes Energies, IFAE, Universitat Autònoma de Barcelona, Edifici Cn, ES - 08193
Bellaterra (Barcelona) Spaing University of Bergen, Department for Physics and Technology, Allegaten 55, NO - 5007 Bergen, Norwayh Lawrence Berkeley National Laboratory and University of California, Physics Division, MS50B-6227, 1
Cyclotron Road, Berkeley, CA 94720, United States of America
i University of Bern, Laboratory for High Energy Physics, Sidlerstrasse 5, CH - 3012 Bern, Switzerland
j Brookhaven National Laboratory, Physics Department, Bldg. 510A, Upton,
NY 11973, United States of AmericakBogazici University, Faculty of Sciences, Department of Physics, TR - 80815 Bebek-Istanbul, TurkeylPhysikalisches Institut der Universitaet Bonn, Nussallee 12, D - 53115 Bonn, Germanym
Comenius University, Faculty of Mathematics Physics & Informatics, Mlynska dolina F2, SK - 84248
Bratislava, Slovak Republicn National Institute of Physics and Nuclear Engineering (Bucharest -IFIN-HH), P.O. Box MG-6, R-077125
Bucharest, Romania
o Université Cadi Ayyad, Marrakech, Morocco
p Department of Physics, University of Coimbra, P-3004-516 Coimbra, Portugal
q Université Hassan II, Faculté des Sciences Ain Chock, B.P. 5366, MA - Casablanca, Moroccor Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, United
Kingdoms European Laboratory for Particle Physics (CERN), CH-1211 Geneva 23, Switzerlandt University of Chicago, Enrico Fermi Institute,
5640 S. Ellis Avenue, Chicago, IL 60637, United States of Americab

33 Now at LAL-Orsay, France
34 Now at Universität Mainz, Mainz, Germany
35 Now at Georg-August-Universitaet, Goettingen, Germany

2010 JINST 5 P11006

L. Tremblet,s C. Troncon,be P. Tsiareshka,bi M. Tyndel,c f M.Karagoez. Unel,bs
G. Unal,s G. Unel,ai G. Usai,t R. Van Berg,bu A. Valero,cz S. Valkar,ca J.A. Valls,cz
W. Vandelli,s F. Vannucci,av A. Vartapetian,d V.I. Vassilakopoulos,ag L. Vasilyeva,b j
F. Vazeille,u F. Vernocchi,a j Y. Vetter-Cole,z I. Vichou,cy V. Vinogradov,an J. Virzi,hI. Vivarelli,bw J.B.de. Vivie,w,33 M. Volpi, f T. Vu Anh,ae,34 C. Wang,ac M. Warren,cw
J. Weber,aa M. Weber,c f A.R. Weidberg,bs J. Weingarten,l,35 P.S. Wells,s P. Werner,sS. Wheeler,a M. Wiessmann,bm H. Wilkens,s H.H. Williams,bu I. Wingerter-Seez,arY. Yasu,ap A. Zaitsev,cb A. Zenin,cb T. Zenis,m Z. Zenonos,bw H. Zhang,w A. Zhelezkobk
and N. Zhoubn

u Laboratoire de Physique Corpusculaire (LPC), IN2P3-CNRS, Université Blaise-Pascal Clermont-Ferrand,

FR - 63177 Aubiere, France
Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK - 2100 Kobenhavn 0, Denmarkw
Université Méditerranée, Centre de Physique des Particules de Marseille,
CNRS/IN2P3, F-13288 Marseille, Francex Faculty of Physics and Applied Computer Science of the AGH-University of Science and Technology,(FPACS, AGH-UST), al. Mickiewicza 30, PL-30059 Cracow, Polandy The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego
152, PL - 31342 Krakow PolandzSouthern Methodist University, Physics Department, 106 Fondren Science Building, Dallas, TX 752750175, United States of America
aa Universitaet Dortmund, Experimentelle Physik IV, DE - 44221 Dortmund, Germany
ab Technical University Dresden, Institut fuer Kern- und Teilchenphysik,
Zellescher Weg 19, D-01069 Dresden, Germany
ac Duke University, Department of Physics Durham, NC 27708, United States of America
ad Centre de Calcul CNRS/IN2P3, Lyon, France
ae Université de Genève, Section de Physique, 24 rue Ernest Ansermet, CH - 1211 Genève 4, Switzerlanda f University of Glasgow, Department of Physics and Astronomy, UK - Glasgow G12 8QQ, United Kingdom
ag Hampton University, Department of Physics, Hampton, VA 23668, United States of America
ah Institute of Physics, Humboldt University, Berlin, Newtonstrasse 15, D-12489 Berlin, Germany
ai Indiana University, Department of Physics,
Swain Hall West 117, Bloomington, IN 47405-7105, United States of America
a j INFN Genova and Università di Genova, Dipartimento di Fisica,
via Dodecaneso 33, IT - 16146 Genova, Italyak INFN Gruppo Collegato di Udine and Università di Udine, Dipartimento di Fisica, via delle Scienze 208,
IT - 33100 Udine;
INFN Gruppo Collegato di Udine and ICTP, Strada Costiera 11, IT - 34014 Trieste, ItalyalInstitut fuer Astro- und Teilchenphysik, Technikerstrasse 25, A - 6020 Innsbruck, Austria
am
Iowa State University, Department of Physics and Astronomy, Ames High Energy Physics Group, Ames,
IA 50011-3160, United States of America
an Joint Institute for Nuclear Research, JINR Dubna, RU - 141 980 Moscow Region, Russia
ao Institut fuer Prozessdatenverarbeitung und Elektronik, Karlsruher Institut fuer Technologie, Campus Nord,
Hermann-v.Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen
ap KEK, High Energy Accelerator Research Organization,
1-1 Oho Tsukuba-shi, Ibaraki-ken 305-0801, Japanaq
Royal Institute of Technology (KTH), Physics Department, SE - 106 91 Stockholm, SwedenarLaboratoire de Physique de Particules (LAPP), Université de Savoie, CNRS/IN2P3,
Annecy-le-Vieux Cedex, France
as Laboratoire de Physique de Particules (LAPP), Université de Savoie, CNRS/IN2P3, Annecy-le-Vieux
Cedex, France and Université Cadi Ayyad, Marrakech, Morocco
at Departamento de Fisica, Faculdade de Ciéncias, Universidade de Lisboa, P-1749-016 Lisboa, Portugal
au Centro de Fı́sica Nuclear da Universidade de Lisboa, P-1649-003 Lisboa, Portugal
av Université Pierre et Marie Curie (Paris 6) and Université Denis Diderot (Paris-7), Laboratoire de Physique
Nucléaire et de Hautes Energies, CNRS/IN2P3,
Tour 33 4 place Jussieu, FR - 75252 Paris Cedex 05, Francev

2010 JINST 5 P11006

aw Laboratoire de Physique Subatomique et de Cosmologie CNRS/IN2P3, Université Joseph Fourier INPG,

53 avenue des Martyrs, FR - 38026 Grenoble Cedex, France
Laboratoire de Physique Théorique et de Physique des Particules, Université Mohammed Premier,Oujda, Morocco
ay Lunds universitet, Naturvetenskapliga fakulteten, Fysiska institutionen,Box 118, SE - 221 00, Lund, Sweden
az Universidad Autonoma de Madrid, Facultad de Ciencias, Departamento de Fisica Teorica,
ES - 28049 Madrid, Spainba Universität Mainz, Institut für Physik, Staudinger Weg 7, DE 55099, GermanybbSchool of Physics and Astronomy, University of Manchester, UK - Manchester M13 9PL, United Kingdom
bc
Universitaet Mannheim, Lehrstuhl fuer Informatik V, B6, 23-29, DE - 68131 Mannheim, Germany
bd
School of Physics, University of Melbourne, AU - Parkvill, Victoria 3010, Australia
be INFN Sezione di Milano, via Celoria 16, IT - 20133 Milano, Italyb f Università di Milano, Dipartimento di Fisica, via Celoria 16, IT - 20133 Milano, Italybg Departamento de Fisica, Universidade do Minho, P-4710-057 Braga, Portugal
bh B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Independence Avenue 68,
Minsk 220072, Republic of Belarusbi B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Independence Avenue 68,
Minsk 220072, Republic of Belarus and Joint Institute for Nuclear Research, JINR Dubna, RU - 141 980
Moscow Region, Russia
bj
P.N. Lebedev Institute of Physics, Academy of Sciences, Leninsky pr. 53, RU - 117 924, Moscow, Russia
bk Moscow Engineering & Physics Institute (MEPhI), Kashirskoe Shosse 31, RU - 115409 Moscow, Russia
bl Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics, RU - 119 991 GSP-1
Moscow Lenskiegory 1-2, Russia
bm Max-Planck-Institut für Physik, (Werner-Heisenberg-Institut),Föhringer Ring 6, 80805 München, Germany
bn Columbia University, Nevis Laboratory, 136 So. Broadway, Irvington, NY 10533, United States of America
bo Nikhef National Institute for Subatomic Physics, Kruislaan 409,
P.O. Box 41882, NL - 1009 DB Amsterdam, Netherlands
bp Ohio State University, 191 West WoodruAve, Columbus, OH 43210-1117, United States of America
bq LAL, Université Paris-Sud, IN2P3/CNRS, Orsay, France
br University of Oslo, Department of Physics, P.O. Box 1048, Blindern T, NO - 0316 Oslo, Norway
bs Department of Physics, Oxford University, Denys Wilkinson Building,
Keble Road, Oxford OX1 3RH, United Kingdom
bt Università di Pavia, Dipartimento di Fisica Nucleare e Teorica and INFN Pavia,
Via Bassi 6 IT-27100 Pavia, Italybu University of Pennsylvania, Department of Physics, High Energy Physics, 209 S. 33rd Street Philadelphia,
PA 19104, United States of America
bv Petersburg Nuclear Physics Institute, RU - 188 300 Gatchina, Russia
bw Universitad́i Pisa, Dipartimento di Fisica E. Fermi and INFN Pisa,
Largo B.Pontecorvo 3, IT - 56127 Pisa, Italybx University of Pittsburgh, Department of Physics and Astronomy, 3941 O’Hara Street, Pittsburgh, PA
15260, United States of America
by Laboratorio de Instrumentacao e Fisica Experimental de Particulas - LIP, and SIM/Univ. de Lisboa,
Avenida Elias Garcia 14-1, PT - 1000-149, Lisboa, Portugalax

2010 JINST 5 P11006

bz Academy of Sciences of the Czech Republic, Institute of Physics and Institute for Computer Science, Na

Slovance 2, CZ - 18221 Praha 8, Czech RepublicCharles University in Prague, Faculty of Mathematics and Physics, Institute of Particle and Nuclear
Physics, V Holesovickach 2, CZ - 18000 Praha 8, Czech Republic
cb Institute for High Energy Physics (IHEP), Federal Agency of Atom. Energy, Moscow Region, RU - 142
284 Protvino, Russia
cc Queen Mary, University of London, Mile End Road, E1 4NS, London, United Kingdom
cd Université Mohammed V, Faculté des Sciences, BP 1014, MO - Rabat, Moroccoce Radboud University Nijmegen/NIKHEF, Dept. of Exp. High Energy Physics, Toernooiveld 1, NL - 6525
ED Nijmegen, Netherlands
cf
Rutherford Appleton Laboratory, Science and Technology Facilities Council, Harwell Science and Innovation Campus, Didcot OX11 0QX, United Kingdom
cg University of Regina, Physics Department, Canada
ch Universidade Federal do Rio De Janeiro, Instituto de Fisica, Caixa Postal 68528, Ilha do Fundao, BR 21945-970 Rio de Janeiro, Brazil
ci Università La Sapienza, Dipartimento di Fisica and INFN Roma I,
Piazzale A. Moro 2, IT- 00185 Roma, Italy
c j Commissariàt a l’Enegie Atomique (CEA), DSM/DAPNIA, Centre d’Etudes de Saclay,
91191 Gif-sur-Yvette, France
ck Insitute of Physics, Academia Sinica, TW - Taipei 11529, Taiwan and Shandong University, School ofPhysics, Jinan, Shandong 250100, P. R. China
cl University of Sheffield, Department of Physics & Astronomy,
Hounseld Road, Sheffield S3 7RH, United Kingdom
cm Insitute of Physics, Academia Sinica, TW - Taipei 11529, Taiwan
cn SLAC National Accelerator Laboratory, Stanford, California 94309, United States of America
co University of South Carolina, Columbia, United States of America
cp
Stockholm University, Department of Physics and The Oskar Klein Centre, SE - 106 91 Stockholm, Swedencq
Department of Physics and Astronomy, Stony Brook, NY 11794-3800, United States of America
crInsitute of Physics, Academia Sinica, TW - Taipei 11529, Taiwan and Sun Yat-sen University, School ofphysics and engineering, Guangzhou 510275, P. R. China
cs Tbilisi State University, High Energy Physics Institute, University St. 9, GE - 380086 Tbilisi, Georgia
ct University of Toronto, Department of Physics, 60 Saint George Street, Toronto M5S 1A7, Ontario, Canada
cu University of Tsukuba, Institute of Pure and Applied Sciences,1-1-1 Tennoudai, Tsukuba-shi, JP - Ibaraki 305-8571, Japan
cv University of California, Department of Physics & Astronomy, Irvine,
CA 92697-4575, United States of Americacw
University College London, Department of Physics and Astronomy,
Gower Street, London WC1E 6BT, United Kingdom
cx University of California Santa Cruz, Santa Cruz Institute for Particle Physics (SCIPP), Santa Cruz, CA
95064, United States of America
cy University of Illinois, Department of Physics,
1110 West Green Street, Urbana, Illinois 61801 United States of America
cz Instituto de Fı́sica Corpuscular (IFIC), Centro Mixto UVEG-CSIC, Apdo. 22085, ES-46071 Valencia;
Dept. Fı̈sica At., Mol. y Nuclear, Univ. of Valencia and Instituto de Microelectrónica de Barcelona(IMB-CNM-CSIC), 08193 Bellaterra, Barcelona, Spainca2010 JINST 5 P11006

da University of Victoria, Department of Physics and Astronomy,

P.O. Box 3055, Victoria B.C., V8W 3P6, Canada
University of Wisconsin, Department of Physics,
1150 University Avenue, WI 53706 Madison, Wisconsin, United States of America
dc Bergische Universitaet, Fachbereich C, Physik,
Postfach 100127, Gauss-Strasse 20, DE-42097 Wuppertal, Germany
dd Yale University, Department of Physics,
PO Box 208121, New Haven, CT06520-8121, United States of America
de Yerevan Physics Institute, Alikhanian Brothers Street 2, AM - 375036 Yrevan, Armeniadb

A BSTRACT: In 2004 at the ATLAS (A Toroidal LHC ApparatuS) combined test beam, one slice of
the ATLAS barrel detector (including an Inner Detector set-up and the Liquid Argon calorimeter)
was exposed to particles from the H8 SPS beam line at CERN. It was the first occasion to test the
combined electron performance of ATLAS. This paper presents results obtained for the momentum
measurement p with the Inner Detector and for the performance of the electron measurement with
the LAr calorimeter (energy E linearity and resolution) in the presence of a magnetic field in the
Inner Detector for momenta ranging from 20 GeV/c to 100 GeV/c. Furthermore the particle identification capabilities of the Transition Radiation Tracker, Bremsstrahlungs-recovery algorithms
relying on the LAr calorimeter and results obtained for the E/p ratio and a way how to extract
scale parameters will be discussed.
K EYWORDS : Particle tracking detectors; Transition radiation detectors; Calorimeters; Large detector systems for particle and astroparticle physics–1–

2010 JINST 5 P11006

E-mail: robert.froeschl@cern.ch

Contents
Introduction

1

2

Setup
2.1 Sub-detectors geometry and granularity
2.2 Read-out electronics, data acquisition and reconstruction software
2.3 Beam lines set-up and instrumentation

3
3
6
7

3

Energy measurement with the Liquid Argon calorimeter8
3.1 Data samples
8
3.2 Event selection
8
3.2.1 Particle identification
8
3.2.2 Beam quality
9
3.2.3 Detector imperfections
11
3.2.4 Quality of reconstructed objects
12
3.3 Energy measurement12
3.3.1 Electronic calibration
12
3.3.2 Cluster building
13
3.4 Monte Carlo simulation and comparison to data
13
3.4.1 Monte Carlo simulation of the Combined Test Beam 2004
14
3.4.2 Energy response
15
3.4.3 Shower development
17
3.4.4 Systematic uncertainties
20
3.5 The Calibration Hits Method
21
3.5.1 General strategy for the computation of representative values for distributions 22
3.5.2 Estimation of the energy deposited upstream of the accordion
22
3.5.3 Estimation of the energy deposited in the accordion
24
3.5.4 Estimation of the energy deposited downstream of the accordion
26
3.5.5 Iterative procedure27
3.6 Linearity and resolution
29

4

Momentum measurement with the Inner Detector
4.1 Track reconstruction
4.2 Monte Carlo simulation and comparison with data

32
33
33

5

Particle identification with the Transition Radiation Tracker
5.1 Introduction to particle identification with the Transition Radiation Tracker
5.2 The combined test beam data
5.2.1 Data samples
5.2.2 Data quality
5.2.3 Electron and pion samples

34
34
35
35
36
36

–i–

2010 JINST 5 P11006

1

5.3

5.4

Particle identification methods
5.3.1 The high threshold method
5.3.2 The time-over-threshold method
5.3.3 Combined method
Measurement of the high threshold onset
5.4.1 Procedure and error evaluation
5.4.2 Results

37
37
38
39
40
40
41

Bremsstrahlungs recovery using the Liquid Argon calorimeter
6.1 Results with combined test beam data

42
43

7

Intercalibration with E/p
7.1 Modeling the detector response functions
7.2 Scale factor extraction procedure
7.3 Estimation of systematic errors
7.4 Results

47
48
52
53
53

8

Conclusions

56

1

Introduction

The Large Hadron Collider (LHC) collides 7 TeV proton beams, extending the available centreof-mass energy by about an order of magnitude over that of existing colliders. Together with its
high collision rate, corresponding to an expected integrated luminosity of 10–100 fb−1 /year, theseenergies will allow for the production of particles with high masses or high transverse momenta
or other processes with low production cross-sections. The LHC will search for effects of new
interactions at very short distances and for new particles beyond the Standard Model of particle
physics (SM).
An excellent knowledge of the electron energy and momentum and of the photon energy in alarge energy range is needed for precision measurements within and beyond the SM and to resolve
possible narrow resonances of new particles over a large background. Therefore good energy resolution and linearity are needed for energies ranging from a few GeV up to a few TeV. An excellent
and uniform measurement of the photon and electron energy is necessary for the potential discoveryof the Higgs boson in the decay channels H → γγ or H → ZZ∗ → 4e. In addition good e/π separation capabilities are needed to suppress the background from QCD (quantum chromodynamics)
jets1 faking an electron signal by the required factor of 10−5 .
In order to test the performance of the ATLAS (A Toroidal LHC ApparatuS) subdetectors inconditions similar to those expected at LHC, a Combined Test-Beam (CTB) campaign was set up
1 A jet is an ensemble of hadrons and other particles produced by the hadronization of a quark or gluon emitted in anarrow cone.

–1–

2010 JINST 5 P11006

6

in 2004 where a full slice of the barrel detectors2 was exposed to particles (electrons, pions, muons,
protons and photons) of momenta ranging from 1 GeV/c to 350 GeV/c. The most important goalsof this campaign were• to test the detector performance in a combined set-up with final or close to final electronics
and TDAQ (Trigger and Data Acquisition) infrastructure;• to develop and test reconstruction and calibration software similar to that used by ATLAS;• to perform combined studies in a set-up very close to ATLAS (e.g. combined calorimetry,
inner tracker and calorimetry).
This paper presents results combining the performance of various ATLAS subdetectors,
namely the Pixel detector, the Semiconductor Tracker (SCT), the Transition Radiation Tracker(TRT) and the electromagnetic calorimeter.
The Pixel detector [1] is a silicon detector providing discrete spacepoints that are used for highresolution tracking. The SCT detector [2] consists of silicon strips providing stereo pairs to thetracking algorithms. The TRT [3–5] is a straw tube tracker with electron identification capabilities
mainly through detection of transition radiation photons created in a radiator between the straws.
In this way electrons can be distinguished from hadrons, mostly pions. The Pixel detector together
with the SCT detector and the TRT compose the ATLAS Inner Detector.
The electromagnetic calorimeter of the ATLAS detector [6–9], is a lead and liquid argon (LAr)sampling calorimeter with accordion shaped absorbers, and has been designed to fulfill the above
mentioned requirements [10, 11]. The used LAr calorimeter module will be described in moredetail in section 2. Its performance has been measured in many test-beam campaigns, the resultson linearity, uniformity and resolution for the LAr barrel calorimeter have been published in [12]and [13] for “close-to-ideal” conditions, with very little material upstream the calorimeter, withno other ATLAS detectors being operated simultaneously (potential sources of coherent noise)
and without any magnetic field. The electron performance of the LAr barrel calorimeter at the
CTB, including linearity, uniformity, and resolution with different amounts of material upstream
the calorimeter and momenta ranging from 1 GeV to 250 GeV/c without magnetic field in the Inner
Detector has been published in [14]. This paper presents results obtained for the electromagnetic
performance of the LAr calorimeter (linearity and resolution) in the presence of a magnetic field in
the Inner Detector.
After a description of the setup at the CTB (section 2), results obtained for the electromagnetic performance of the LAr calorimeter (linearity and resolution) in the presence of a magnetic
field in the Inner Detector (section 3) and for the momentum measurement with the Inner Detector(section 4) are presented. Furthermore the e/π separation performance of the Transition Radiation Tracker is discussed in section 5. A bremstrahlungs-recovery algorithm relying on the LAr
calorimeter is presented in section 6 and results obtained for the E/p ratio, i.e. the ratio of the
2 The barrel detectors constitute the central part of the ATLAS detector, i.e. around the plane through the interaction

point and perpendicular to the beam axis.

–2–2010 JINST 5 P11006• to validate the description of the data by Monte-Carlo (MC) simulations to prepare for thesimulation of ATLAS data;

y

x

z

Inclination of cryostat = 11.25o

Figure 1. Schematic view of the H8 CTB set-up, including the inner detector components and the LAr andTile calorimeters.

energy measured by the electromagnetic calorimeter and the momentum measured by the Inner
Detector, and a way how to extract scale parameters are discussed in section 7.

2

Setup

During the 2004 CTB campaign all ATLAS sub-detectors (barrel wedge) collected data with partsof their detectors in the H8 beam line of the CERN Super Proton Synchrotron (SPS) (see section 2.3). The detectors were installed in the beam line with relative positions as close as technically possible to the real ATLAS geometry: the distance between sub-detectors, the pointing
geometry, and the magnetic field orientation have been preserved where permitted, although the
distance between the Inner Detector and the calorimeters is much larger than in ATLAS (figure 1,
figure 2, length scale in figure 4). A detailed description of the whole set-up can be found in [15].
2.1

Sub-detectors geometry and granularity

The ATLAS combined set-up at the 2004 CTB included:• Six modules of the Pixel detector (2 modules for each of the three pixel layers: B, 1 and 2 asdefined for the ATLAS detector) [1];• Eight modules of the Semiconductor Tracker (SCT) detector (2 modules per layer, as in the
ATLAS detector) [2];• Two barrel wedges of the Transition Radiation Tracker (TRT) [3] corresponding to 1/16 of
one barrel wheel;• One module of the LAr electromagnetic barrel calorimeter (EMB) corresponding to 1/16 of
one barrel wheel [16];–3–2010 JINST 5 P11006

2860 mm

H8 beam• Three long barrel modules and three extended barrel modules3 of the hadronic Tile Calorimeter [17];• Muon spectrometer: three stations of barrel Monitored Drift Tube (MDT) chambers andthree stations of MDT endcap chambers4 [18].
The Inner Detector (ID) consists of three different subdetectors, namely Pixel, SCT and TRT.
The CTB coordinate system is chosen to be right-handed, with the Z-axis along the beam direction
and the Y-axis pointing vertically towards the sky as depicted in figure 1. The Pixel and SCT
modules were located inside a MBPS magnet (MBPSID). This magnet is one meter long, and isoften used at CERN as bending magnet for the accelerators. It provided a field along the x direction,
deviating the particles in φ (angle in the z-y plane), as in the ATLAS detector. It is mainly operated
with a -850 A current, providing an integrated field of ∼ 1.4 Tm. In such a field the deviation for
a 10 GeV/c electron is about 4 cm at the exit of the magnet, and ∼ 11 cm at the front face of the
3 The three extended barrel modules were only present at the beginning of the data taking period.
4 During parts of the test-beam campaign an additional barrel muon chamber was placed directly downstream of the

Tile Calorimeter set-up (before the beam dump).

–4–

2010 JINST 5 P11006

Figure 2. The ATLAS 2004 CTB set-up. The beam is coming from the left side. From left to right are locatedthe inner detector components including a magnet, the LAr cryostat with the Tile Calorimeter modules rightbehind. The muon set-up is located on the right outside of the scope of the picture.

5 In ATLAS, the TRT detector is inside the solenoidal field.
6 These three layers are also called the accordion part of the calorimeter.
7 The pseudorapidity η is defined as η = − ln tan θ .
2–5–2010 JINST 5 P11006

electromagnetic barrel module; in ATLAS, a 10 GeV/c electron produced at the vertex is deviatedby ∼ 13 cm. Even though the set-up could not be identical as the ATLAS set-up, the configuration
provided a good enough approximation for many studies. The TRT modules were located outside
the magnet due to space limitations.5 The origin of the global reference frame is located at theentrance of the MBPSID magnet.
A Pixel module consists of a single silicon wafer with an array of 50 µ m×400 µ m pixels thatare readout by 16 chips. In the CTB setup, six Pixel modules are used and distributed by pairs inthree layers and two sectors. The distance along the beam axis between the different layers andthe location of the modules within each layer coincides with the arrangement of the modules in
ATLAS. The active area of each module is z×y = 60.8×16.4 mm2 . Each module is positioned at
an angle of about 20o with a superposition of the two modules in each layer of about 200 µ m.
The SCT detector consists of silicon microstrip sensor modules with 80 µ m pitch. Each module has two sets of sensors glued back-to-back around a central TPG (Thermo-Pyrolithic Graphite)spine with a relative rotation of 40 mrad with respect to each other to give the required capability
for a 3D space point reconstruction. The SCT has a single module type design for the barrel region,plus three types for the end-caps (namely outer, middle and inner according to their position in theend-cap wheels). Though the CTB was meant to reproduce a slice of the ATLAS barrel, eight SCT
end-cap outer modules were used in the final setup. As in the pixels case, two SCT modules areused in each of the four layers and distributed in two sectors. The SCT module location is similar
to the one that may be encountered in ATLAS, but the modules were mounted perpendicular to thebeam axis. The four SCT layers cover an area of z×y = 120.0×60.0 mm2 . There is a 4 mm overlap
between the two modules in each layer. Because of hardware problems, the front side of the lower
SCT module in the third layer was not functioning.
The TRT setup is made of two barrel wedges. Each wedge is equivalent to 1/16 of the circumference of a cylinder, with inner radius of 558 mm and outer radius of 1080 mm and overall length
along the Z-axis of 1425.5 mm. For some of the runs, the Pixel and SCT detector were exposed
to a magnetic field. The magnetic field profile has also been measured and its non uniformity has
been also considered in the software and the track reconstruction has been carried out taking into
account its effects.
The alignment of the Inner Detector components has been done with charged-hadron beams
with beam momenta between 5 and 180 GeV/c [19]. The RMS for the residuals was 10 µ m for the
Pixel modules and 25 µ m for the SCT modules.
The electromagnetic LAr calorimeter module was built for the ATLAS CTB, using absorbers,
electrodes, motherboards, connectors and cables left from the production of the 32 ATLAS electromagnetic barrel modules. An extensive description of the electromagnetic barrel calorimeter and its
modules can be found in [16]. The electromagnetic barrel is a lead/LAr sampling calorimeter andis longitudinally segmented into three layers6 (strip, middle and back layer), each having different
longitudinal thickness and transverse segmentation into read-out cells with the following granularity (see figure 3): the strip layer is finely segmented in pseudorapidity7 η with a granularity of
0.025/8 η -units, but has only four subdivisions in φ per module and hence a granularity of 2π /64;

Cells in Layer 3∆ϕ×∆η = 0.0245×0.05
Trigger Towe∆η = 0 r
.1

2X0

47

0m

m

η=0

16X0
TriggeTow r∆ϕ = 0er
.0

m
15
00
m

1.7X0
∆ϕ=0.0245x36.8m 4mx
=147.3 4mm

ϕSquare cells in
Layer 2∆ϕ = 0.0245∆η = 0.025
m/8 =4∆η = 0 .69 mm.0031
Strip cells in Layer 1

37.5m

η

Figure 3. Sketch of a barrel module of the electromagnetic LAr calorimeter. The accordion structure andthe granularity in η and ϕ of the cells of each of the three layers is shown.

the middle layer has a segmentation of 0.025 in η and 2π /256 in φ ; the back layer has the same φ
granularity as the middle one, but is twice as coarse in η (0.05). A thin presampler (PS) detector
is mounted in front of the LAr calorimeter module: the PS is segmented in η with a granularity of∼ 0.025 (as the middle layer), and has a granularity of 2π /64 in φ (as the strip layer). Between the
PS and the strip layer readout-out cables and signal collection boards are installed.
The cryostat containing the module of the electromagnetic calorimeter is installed on a movable support table which can rotate in θ (angle in the x-z plane) and translate in x. It was therefore
possible to move different pseudorapidity regions into the particle beam, but it was not possible torotate in azimuth φ .
2.2

Read-out electronics, data acquisition and reconstruction software

The Front-End Boards (FEB) and back-end electronics used for the CTB campaign were the final prototypes of the boards built to equip the LAr calorimeters installed in ATLAS. A detailed
description of these boards is available in dedicated publications for the front-end board [20], calibration board [21], controller and tower builder boards [22], and the Read-Out Driver (ROD) andback-end system [23]. Further explanations on the LAr read-out system used for the CTB can befound in [24]. Similarly to the detector set-up and read-out, the Data-Acquisition system (TDAQ)
software in operation for the CTB data taking was an early version of the packages developed for–6–2010 JINST 5 P11006

982

4.3X0

Figure 4. Outline of the beam line instrumentation. [15]. The straight line represents the high energy beamline that was used for the data analyzed in this paper. The acronyms are explained in the text.

2.3

Beam lines set-up and instrumentation

The CERN H8 beam line provides hadrons, electrons or muons with momenta from 1 GeV/c to350 GeV/c. The H8 beam is created by extracting 400 GeV/c protons from the SPS towards theNorth Area experimental zone. From the primary target (T4, beryllium up to 300 mm in length),
the secondary beam had momenta between 9 GeV/c to 350 GeV/c. We call this the High Energy(HE) beam line. A secondary filter target (8 or 16 mm of lead for an electron beam) was introduced
to produce a “pure” electron beam. The beam can also be diverted onto an additional target (T48)
further downstream, close to the experiment to provide momenta from 1 GeV/c to 9 GeV/c. Thisis called the Very Low Energy (VLE) beam line.
Figure 4 shows the beam line instrumentation for the HE and the VLE beam lines [15]. ThreeČerenkov counters were used on the H8 beam line, CHRV1 was furthest upstream, and the othertwo were placed about 1 m upstream of the last bending magnet of the VLE spectrometer (CHRV2),
one on HE beam line for momenta > 9 GeV/c and the other one on the path of the particles in the
VLE beam line. Five beam chambers (BC-2, BC-1, BC0, BC1, and BC2) were used to define thebeam profile. A beam stop was inserted after the first bending magnet of the VLE spectrometer andthe scintillator SMV behind served as a muon veto. The scintillators S1, S2 and S3 were used forthe main trigger, SMH (scintillator with a hole of diameter 3.4 cm) was used in anti-coincidence toveto the muon halo of the beam.
The beam momentum measurement at the CTB is described in detail in [14]. The absolute energy scale of the electromagnetic LAr barrel calorimeter has been determined by means of selected
electron runs (not listed in table 1) with a nominal beam momentum of 180 GeV/c and withoutmagnetic field in the MBPS magnet. This scale has been used for the entire CTB. It depends on
the LAr temperature which was measured to be 89.7 ± 0.1 K. A comparison between the measured visible energy in a 3 × 3 cluster (see section 3.3.2 for a description of the clustering) and–7–

2010 JINST 5 P11006

ATLAS [25].
Previous stand-alone test-beam campaigns had been monitored and analysed using specificsoftware. For this campaign, the C++ reconstruction software in the Athena framework, up to then
only used for Monte Carlo simulation based studies [26], has been adapted to process the datafrom the 2004 CTB. The experience from the 2004 CTB has been invaluable in the development of
ATLAS software used in data recording of events from cosmic rays hitting the detector since 2006
and in LHC collisions.

Table 1. Run number, nominal beam momentum, estimated average beam momentum, beam spread, nominal η impact position, current in the MBPS magnet that provides the field for the inner detector and the total
number of events taken for the data samples before and after cuts and the number of events after cuts for theMonte Carlo simulation used in this analysis.
Run number
21023992102400
21024132102452

pnominalbeam( GeV/c)
100
50
20
80

σ (pbeam )( GeV/c)
0.24
0.12
0.05
0.19

η nominal
0.45
0.45
0.45
0.45

MBPS current
(A)
-850
-850
-850
-850

Events Data
20000020000070000
200000

Events Data
(after cuts)
19075
19723
6583
8180

Events MC(after cuts)
55665
56151
41600
57473

the simulated one yielded the absolute energy scale of the calorimeter that is used throughout thispaper. Details on the runs used and the method applied to extract the energy scale are describedin [14]. The uncertainty on the obtained absolute energy scale has been estimated to be 0.7 %. It
accounts for the HE spectrometer current error for these runs (∼ 0.04 %); the absolute scale for the
CTB (25%/pbeam ⊕ 0.5 % = 0.52 % for pbeam = 180 GeV/c) and the detector response uniformity(< 0.4 %, uniformity, see [14] for details). These three components have been added in quadrature.

3

Energy measurement with the Liquid Argon calorimeter

After a brief description of the data samples (section 3.1) and the event selection (section 3.2), theway the energy deposited in a single calorimeter cell is measured and how clusters are formed outof these cells is recapitulated in section 3.3 . This is followed by a comparison of the Monte Carlosimulation to data (section 3.4). Finally a Monte Carlo simulation based calibration procedure forthe cluster energy is presented in section 3.5 and applied to data in section 3.6 in order to extract
the linearity and resolution for the liquid argon calorimeter in the presence of a magnetic field in
the Inner Detector.
3.1

Data samples

The data samples that were taken during the CTB 2004 and used for the analysis in this paper are
listed in table 1. The average beam momentum, denoted < pbeam >, and the beam spread, denotedσ (pbeam ), were computed for each run using the collimator settings and the currents from the beam
momentum selection spectrometer as described in [14].
3.2

Event selection

This section describes the event selection procedure for the CTB 2004. Section 3.2.1 is devoted toparticle identification for electrons, section 3.2.2 describes the requirements concerning the beam
quality and section 3.2.3 deals with detector imperfections. Finally section 3.2.4 discusses thequality requirements for reconstructed electron-like objects.
3.2.1

Particle identification

The purpose of the procedures described in this subsection is to select only events for the analysis
that are triggered from an electron from the beam entering the calorimeter. Requirements concern-–8–2010 JINST 5 P11006< pbeam >( GeV/c)
99.80 ± 0.11
50.29 ± 0.10
20.16 ± 0.09
80.0 ± 0.10

ing measurement variables from the beam line instrumentation present only in the data samples
are only applied there. Requirements that involve measurement variables from the calorimetersor the inner detector are applied both to the data and to the simulation samples in order to avoid
introducing any bias. When cuts were used only on data, it is explicitly stated.
The following requirements have to be met for an event to be accepted:
1. Less than 700 MeV is deposited in the first tile calorimeter layer. The purpose of this requirement is to reject pions.

3. There must be at least 20 hits in the TRT. The purpose of this requirement is to be sure tohave a good track in the TRT.
4. TRT High Level Hit Probability8 > 0.15: The purpose of this requirement is to reject pions
and muons . This requirement is applied only to the data samples, since the TRT High Level
Hit Probability is not correctly modeled in the simulation, and only electrons have been
simulated.
5. Trigger from the trigger scintillators S1∧S2: This requirement guarantees that only beam
particle triggered events are considered and not random triggers that were injected to measurepedestal levels. Since the trigger scintillators are not simulated, the requirement is applied
only to the data samples.
6. Muon halo veto scintillator (SMH) < 460 ADC: The purpose of this requirement is to rejectmuons. Since the muon halo veto scintillator is not simulated, the requirement is applied
only to the data samples.
7. Cherenkov counter CHRV2,HE > 650 ADC: The purpose of this requirement is to rejectpions for the run at 20 GeV/c nominal beam momentum. Since the cherenkov counter is not
simulated, the requirement is applied only to the data samples.
3.2.2

Beam quality

Two additional cuts are applied to the data to ensure that only particles from the central part of thebeam and no particles from the beam halo are used.
1. The x values measured by the beam chambers BC-1 and BC0 are linearly correlated since
the setup is rigid and there is no magnetic field in the flight path between these two beamchambers. The same is true for y values. The left figures of figure 5 show the distributions
for x and y. A line is fitted to each of the distributions and the orthogonal distances (∆xBC-1
and ∆yBC-1 ) are shown in the right figures of figure 5. Gaussians are fitted to the orthogonal distance distributions and 3 times the σ of a Gaussian is defined as the largest allowed
absolute orthogonal distance. The x and y distributions and the corresponding orthogonal
distance distributions with these cuts applied are shown in figure 6.
8 The TRT High Level Hit probability is explained in section 5.

–9–2010 JINST 5 P11006

2. Less than one percent of the energy deposited in the calorimeters is deposited in the tile
calorimeter. The purpose of this requirement is to reject pions.

dN (mm−1)d∆ xBC−1

xBC−1 (mm)

50
40
30
20

105

Constant 8.484e+04 ± 296
Mean−2.983± 0.002
Sigma
0.6624 ± 0.0014

104
103

10
0

102

−10
−20

10

−30
−50
−20 −15 −10 −5

0

5

1
−60

10 15 20

−40

−20

0

20

60

(mm−1)

4

Constant1.717e+04 ± 83
Mean
45.53 ± 0.01
Sigma
2.154 ± 0.008

BC−1

(mm)

10

dN
d∆ y

−20

y

BC−1

−10

40

∆ xBC−1 (mm)x BC0 (mm)

−30

103

−40
102

−50
−60

10

−70
−80
−20 −15 −10 −5

105

10 15 20
y
(mm)
BC0

0

10 20 30 40 50 60 70 80
∆y
(mm)
BC−1

Figure 5. Beam chambers BC-1 vs. BC0 x (top left) and y (bottom left) measurements with fitted line.
Distribution of the orthogonal distances (∆xBC-1 and ∆yBC-1 ) from this line for x (top right) and y (bottom
right) values together with a Gaussian fitted to the core of the distribution.

Table 2. Allowed ranges for the x and y values (denoted BC1x and BC1y ) of beam chamber BC1 for all beam
momenta.
pnominal( GeV/c)
beam
20
50
80
100

(min,max) BC1x (mm)(−15, +7)(−15, +5)(−5, +7)(−15, +7)

(min,max) BC1y (mm)(−13, +12)(−15, +15)(−10, +10)(−15, +15)

2. The x and y values (denoted BC1x and BC1y ) of beam chamber BC1 are restricted to ranges
where the total visible energy in the electromagnetic calorimeter is flat with respect to BC1x
and BC1y . The intervals used are given in table 2.

– 10 –

2010 JINST 5 P11006−40

dN (mm−1)d∆ xBC−1

xBC−1 (mm)

20
15
10

Constant
2929 ± 12.3
Mean
−3.03 ± 0.00
Sigma
0.4961 ± 0.0014

103

5
102

0
−5
−10

10
5

10 15 20

−4.5 −4 −3.5 −3 −2.5 −2 −1.5

x BC0 (mm)∆ xBC−1 (mm)(mm−1)

0Constant 2624 ± 12.3
Mean
45.49 ± 0.01
Sigma
1.92 ± 0.01

BC−1

−30
−35

dN
d∆ y

y

BC−1

(mm)

−20
−20 −15 −10 −5

−40

103

−45
102

−50
−55
−60
−20 −15 −10 −5

10
0

5

10 15 20
y
(mm)
BC0

40

42

44

46

48

50
∆y

BC−1

52
(mm)

Figure 6. Beam chambers BC-1 vs. BC0 x (top left) and y (bottom left) measurements with fitted line with
3σ cut applied. Distribution of the orthogonal distances (∆xBC-1 and ∆yBC-1 ) from this line for x (top right)
and y (bottom right) values together with a Gaussian fitted to the core of the distribution.

3.2.3

Detector imperfections

This subsection describes the procedures to discard events that have been affected by detector
imperfections.
Coherent noise in the presampler. In order to reject events with coherent noise in the presampler
layer of the LAr calorimeter, the distribution of the presampler cell energies of all cells outside theregion where the beam hits the calorimeter is considered, i.e. |ηcell − ηbeam | > 0.2. If there is nocoherent noise present, this distribution is a Gaussian with mean equal to 0 and an rms equal to theaverage noise of the cells. Let n+
PS denote the number of presampler cells with positive energy andn+ −n−

PSPS> 0.6.
n−−
PS the number of presampler cells with negative energy. An event is rejected if n+
PS +nPS
Since the coherent noise is not simulated this cut is only applied to the data samples. Less than
0.2% of the events are rejected by this cut.

– 11 –

2010 JINST 5 P11006−15

Shaper problem. The four cells at 0 < ϕcell < 0.1, ηcell = 0.3875 in the middle layer of the
LAr calorimeter suffered from an unstable signal shaper. The stochastic distortion of the signal
shape introduced a variation of the order of 3% for the gain values. Although the effect on thereconstructed cluster energy is ≪ 1%, all events with clusters that contain any of these cells are
discarded. In order not to introduce a bias, this cut is applied both to the data samples and to thesimulation samples.
3.2.4

Quality of reconstructed objects

Track to cluster matching. A track9 in the Inner Detector can be extrapolated to the LAr
calorimeter and the η and ϕ coordinates of this extrapolation, denoted ηTrack and ϕTrack are compared with the η and ϕ coordinates computed for the clusters in the calorimeter, denoted ηClusterand ϕCluster . In order for a track to be matched to a cluster the following two conditions are imposed• |ϕTrack − ϕCluster | < 0.05 rad,• |ηTrack − ηCluster | < 0.01.
An event is accepted for the analysis if there is at least one matched track-cluster combination.
Track quality. At least 2 hits in the Pixel detector for the matched track are required. Thisrequirement ensures an acceptable track quality.
3.3

Energy measurement

The calibration of the energy measurement of the LAr calorimeter consists of two consecutive
steps. First the raw signal (in ADC counts) for each cell is converted into the deposited energy inthe cell. This step is denoted as electronic calibration and briefly discussed in section 3.3.1. During
the second step clusters are formed out of calorimeter cells and an estimate of the initial energyof the impinging particle associated with the cluster is computed. The cluster formation algorithm
is briefly described in section 3.3.2 and section 3.5 is devoted to a Monte Carlo simulation based
procedure for computing the estimate for the initial energy of the particle.
3.3.1

Electronic calibration

A very detailed discussion of the electronic calibration and cell energy reconstruction for the LAr
EMB calorimeter is given in [24].
The signals that are induced by the drifting electrons in the liquid argon gaps of the calorimeterare amplified, shaped and then digitized at a sampling rate of 40 MHz in one of the three available
gain channels. Since the particles in the testbeam (unlike in the LHC) do not arrive in phase withthe 40 MHz clock, the phase is measured for each event by a scintillator in the beam line. Thismeasured event phase is then used to select the correct set of optimal filtering constants. The sets
9 The track reconstruction for the CTB 2004 is described in section 4.1.

– 12 –

2010 JINST 5 P11006

The purpose of the requirements described in this subsection is to select events that have a reconstructed electron-like object. This object consists of a cluster in the electromagnetic calorimeterand a track in the Inner Detector that is geometrically matched to the cluster.

of optimal filtering constants had been prepared previously for all different event phases (1 set per
1 ns). In the CTB 2004 setup six samples are digitized. From these six samples five samples siclosest to the signal peak are chosen and the signal amplitude ADC peak is computed by the Optimal
Filtering Method [27]5ADC peak = ∑ ai (si − p) ,

(3.1)

i=1

Ecell = FDAC→µ A Fµ A→MeV

1
Phys∑ Ri ADCpeak ,

M
i=1,2
MCal



i

(3.2)

where the factors Ri model the electronic gain with a second order polynomial, converting the
ADC peak amplitude into the equivalent current units (DAC). The constant factor MPhys /MCal takes
the difference between the amplitudes of a calibration and an ionization signal of the same current
for the electronic gain into account [28–31]. The constants FDAC→µ A and Fµ A→MeV finally transformthe current (DAC) into energy (MeV). The details of the computation and validation of all thecalibration constants used in eq. (3.1) and eq. (3.2) are described in [24].
The extraction of the Fµ A→MeV conversion factor determines the absolute energy scale of thecalorimeter and is extracted by comparing the energy response in selected runs with MC simulations (see more detailed description in section 2.3 and [14]).
3.3.2

Cluster building

In order to reduce the noise contribution to the energy measurement, a finite number of cells isused to calculate the energy. The process of choosing which cells are used is called cluster building. Several methods exist [32], e.g. topological clustering and sliding window clustering. In theanalysis here the standard ATLAS clustering [32] is used. For electrons, this means that in order
to find the seed position for the cluster, a window of 5 × 5 middle cells (η × ϕ extension) is slid
across the calorimeter and the energy content in these 25 middle cells is computed. The position of
the central cell of the 5 × 5 window with the highest energy content is then used as seed position
for the cluster. This seed position is propagated to the other layers of the calorimeter. For eachlayer, the cells contained in windows centered at the given seed position for the layer belong to thecluster. The size of the window is different for the various layers, e.g. for the middle layer the sizeis 3 × 7.
A 3 × 3 cluster has been used to extract the absolute energy scale of the electromagnetic LArbarrel calorimeter from selected electron runs (not listed in table 1) with a nominal beam momentum of 180 GeV/c and without magnetic field in the MBPS magnet. Details can be found in [14].
3.4Monte Carlo simulation and comparison to data

After a description of the Monte Carlo simulation setup in section 3.4.1, the results of the Monte
Carlo simulation are compared to data taken in the CTB 2004. This comparison is performed for the– 13 –

2010 JINST 5 P11006

where ai are the optimal filtering coefficients that are computed from the predicted ionization pulses
obtained using the technique described in [28] and p is the pedestal value which is the mean of thesignal values generated by the electronic noise that is measured in dedicated calibration runs.
From the signal amplitude ADC peak the cell energy Ecell is computed byenergy response for the different layers of the calorimeter (subsection 3.4.2) and the developmentof the electromagnetic shower (section 3.4.3).
Since the calibration procedure (section 3.5) relies on Monte Carlo simulation a sufficiently
good agreement between the Monte Carlo simulation and the data is necessary to achieve the required level of accuracy for the electron energy measurement. For the required linearity of 0.5%
the agreement between the Monte Carlo simulation and the data for the sum of the visible energiesof all cells in a cluster also has to be at the level of 0.5%.
3.4.1

Monte Carlo simulation of the Combined Test Beam 2004

10 The sum of the energies of all cells of a given layer is denoted as its layer energy.
11 Each middle cell has 8 adjacent strip cells.

– 14 –

2010 JINST 5 P11006

The response of the detector setup of the Combined Test Beam 2004 to the various beam particles
is simulated using the GEANT4 toolkit [33]. GEANT4 uses Monte Carlo methods to simulate thephysics processes when particles pass through matter. The QGSP-EMV physics list was used toparameterize these physics processes. The details of the geometric description of the Combined
Test Beam 2004 in GEANT4 are described in [34]. The simulated energy deposits are reconstructedwith the same software as the data. This is all done inside the ATLAS offline software framework
ATHENA, release 12.0.95.
The far upstream material (section 2) is taken into account by introducing a piece of aluminum with the equivalent thickness of 15% of a radiation length placed directly downstream of
the GEANT4 particle generator. All particles that emerge from the far upstream material are recordedin the simulation and are used to model the effect of the beam line acceptance (section 3.4.1).
One effect that is not modeled in the simulation is the cross talk between strip and middle layers. This cross talk has been measured by analyzing the response of the various cells to calibration
pulses [35, 36]. A cross-talk of Xmi→st = 0.05 % from the middle layer to the strip layer and of
Xst→mi = 0.15 % from the strip layer to the middle layer have been obtained (peak-to-peak values).
They are accounted for after the energy reconstruction by redistributing 8 · Xmi→st · EMiddle from the
middle layer energy10 to the strip layer energy11 and Xst→mi · EStrips from the strip layer energy to
the middle layer energy.
The simulated electron momentum that is used in the Monte Carlo simulation is the nominal
for the given run (table 1). Since the average beam momentum < pbeam >beam momentum pnominal
beam
all energies in the Monte Carlo simulais not identical to the nominal beam momentum pnominal
beam
nominaltion are scaled by < pbeam > /pbeam . This is justified because the nonlinearities of the detector
response are negligible for such scaling factors very close to unity for the investigated beam momentum range. The beam spread σ (pbeam ) for the given run (table 1) was also not simulated andtherefore has to be subtracted for the Monte Carlo simulation to data comparison of the resolution.
The beam profiles change with the beam energy due to modifications in the beam optics.
Consequently, in order to guarantee the best agreement between data and MC, the beam profiles
have been matched run-by-run: in the “standalone period” and the “calorimeter and TRT period”
the MC beam profiles are generated as wide flat distributions in the (η , φ ) plane, whereas in the“fully combined period” they are generated to match the profiles measured in the SCT and Pixel
detectors. For all periods the events are then re-weighted in order to obtain the best match between
the (η , φ ) distributions obtained in MC and in the data in the calorimeter.

Weight (%)

100
90
80
70
60
50

30
20
10
0
20

30

40

50

60

70

80

90

100

~
E / Enominal(%)
beam
Figure 7. Beam line acceptance weight function.

Beam line acceptance. Particles which loose a significant amount of energy in the beam line will
have a smaller probability to reach the trigger scintillators. Since the beam line was not modeledin the Monte Carlo simulation, a weighting scheme is employed to simulate the acceptance ofthe beam line. In the simulation a detector is placed directly after the far upstream material (seesection 2 and section 3.4.1). For each event the ratio of the energy of the most energetic particle
nominal , is used to compute aẼ measured by this detector and the nominal beam energy, i.e. Ẽ/Ebeam
weight from the weighting curve shown in figure 7. This weight is attributed to all measurement
variables of the event. The weighting curve has been obtained by a dedicated beam line simulation
beforehand [37]. The application of the beam line acceptance weight has no significant impact on
the calorimeter measurements, but is needed for a correct description of the tail of the momentum
measurement in the inner detector (see figure 8).
3.4.2

Energy response

The Monte Carlo simulation to data comparisons for a beam momentum of 50 GeV/c for the reconstructed presampler layer energies EPS , for the reconstructed strip layer energies Estrips , for thereconstructed middle layer energies EMiddle and for the reconstructed back layer energies EBack areshown in figure 9. The agreement concerning the shapes of the distributions is good in general.
The Monte Carlo simulation to data comparisons of the visible energy EVis which is the sumof all layer energies is presented in figure 10 for all beam momenta. The shape agreement isbest at pbeam = 20 GeV/c and deteriorates with increasing beam momentum. One cause for thisdiscrepancy is the fact that the beam spread σ (pbeam ) for the given run (table 1) was not simulated
and the impact of the beam spread is larger for higher beam momenta since the relative resolution– 15 –

2010 JINST 5 P11006

40

Data
0.1
Simulation
Simulation without Acceptance

0.08

0.06

0.04

0.02

0
0.04

0.05

0.06

0.07

0.08

0.09
-1
1
p (c GeV )Figure 8. The distribution of 1/p measured with the silicon detector (3 pixel layers and 4 SCT layers)
for a beam momentum of pbeam = 20 GeV/c. The solid circles are the data, the shaded area represents thesimulation including the beam acceptance, the dashed line the simulation without the beam acceptance. The
remaining discrepancy between the Monte Carlo simulation including the beam acceptance and the data
comes from a slight misalignment of the Inner Detector.

improves whereas the relative beam spread is constant with beam momentum. In addition, the tails
towards lower energies are larger in data than in the Monte Carlo simulation. The same behaviour
has been found for runs of the CTB 2004 without magnetic field [14, 38]. The reason for thisis that the beam line is not modeled in the Monte Carlo simulation and the beam line acceptanceweighting does only approximate the effect of the beam line. In order to quantify this effect,
the visible energy EVis distributions are fitted with Crystal Ball functions12 and the tail fraction
is defined as the fraction of events with a visible energy EVis below the mean µEVis of the fitted
Crystal Ball function minus two standard deviations σEVis of the fitted Crystal Ball function. The
tail fraction for Monte Carlo simulation and data is shown in table 3 for all beam momenta. Notethat for a Gaussian distribution the tail fraction would be 2.3%.
The ratio of the peak µE data for the data and the peak µE MC for the Monte Carlo simulation isVisVisshown in figure 11 for all beam momenta. The deviation of µE data /µE MC from 1 is compatible with
calib
calib
the energy scale uncertainty and the error bars. The main contributions to the error bars are thebeam momentum uncertainty (data only) and the statistical errors.

12 The definition of the Crystal Ball function is given in section 7.1, eq. (7.5).

– 16 –

2010 JINST 5 P11006

normalized number of events

0.12

1 d N (Gev-1)
N dEStrips

1 d N (Gev-1)
N dEPS

0.12

0.1

0.08

0.14

0.12

0.1

0.08
0.06
0.06
0.04
0.04
0.02

0
-1

0.02

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0

4

0

5

10

15

20

30

1 d N (Gev-1)
N dEBack(b) Strip layer

0.14

0.12

0.1

0.18
0.16
0.14
0.12
0.1

0.08

0.08

0.06

0.06
0.04
0.04
0.02

0

0

0.02
5

10

15

20

25

30

35

40

45

0
-0.2

50

0

0.2

0.4

0.6

EMiddle (GeV)

0.8

1EBack (GeV)(c) Middle layer(d) Back layer

Figure 9. Energy deposit in all layers for pbeam = 50 GeV/c. Shaded area: Monte Carlo simulation; dots:
data.
Table 3. Tail fraction (defined in the text) for Monte Carlo simulation and data for all beam momenta.

pnominalbeam( GeV/c)
20
50
80
100

3.4.3

Tail fraction
Data (%)
16.0(6)16.0(3)16.2(5)14.4(3)

Tail fraction
Monte Carlo simulation (%)
10.8(2)11.9(2)8.5(1)
6.4(1)

Shower development

For the comparison of the longitudinal shower development two quantities are studied. Since inboth quantities reconstructed energies appear in the numerator as well as in the denominator, they
are independent of the global energy scale. The first quantity is the shower depth Xmean defined as
the energy weighted average layer depth of all accordion layers by
Xmean =

EStrips XStrips + EMiddle XMiddle + EBack XBack,
EStrips + EMiddle + EBack– 17 –(3.3)

2010 JINST 5 P11006(a) Presampler
1 d N (Gev-1)
N dEMiddle

25

EStrips (GeV)

EPS (GeV)

1 d N (Gev-1)
N dEVis1 d N (Gev-1)
N dEVis

0.1

0.08

0.22
0.2
0.18
0.16
0.14

0.06

0.12

0.04

0.08

0.1

0.06
0.04

0.02

0.02
0
14

15

16

17

18

19

20

21

0

22

38

40

42

44

46

48

50

52

EVis (GeV)

1 d N (Gev-1)
N dEVis1 d N (Gev-1)
N dEVis(b) pbeam = 50 GeV/c

0.25

0.2

0.25

0.2

0.15

0.15

0.1

0.1

0.05

0.05

65

70

75

80

0
85

85

90

95

100

EVis (GeV)

105

110

EVis (GeV)(c) pbeam = 80 GeV/c(d) pbeam = 100 GeV/c

Figure 10. Total LAr EM calorimeter response EVis (sum of the accordion compartments plus presampler
layer) for all beam momenta. Shaded area: Monte Carlo simulation; dots: data.
Table 4. LAr EMB layer boundaries and average depth at the beam impact point (η = 0.442, ϕ = 0).

Layer
Presampler
StripsMiddleBackstart (X )Xlayer
0
1.50
2.18
6.41
25.02

stop

Xlayer (X0 )
1.78
6.41
25.02
26.78

Xlayer (X0 )
1.64
4.29
15.71
25.90

where XStrips , XMiddle , XBack denote the average depth of the corresponding layer in units of radiation lengths (X0 ) given in table 4. The Monte Carlo simulation to data comparison is shown infigure 12(a) for pbeam = 50 GeV/c. Again there is sufficiently good agreement, although the simulated showers tend to be shorter with respect to the data.
The second quantity for the longitudinal shower development is the ratio Estrips /Emiddle of theenergies of the strip and middle layers. This ratio is very sensitive to the amount of material in frontof the calorimeter. Therefore it can be used to assess the level of accuracy of the material description in the simulation. The Monte Carlo simulation to data comparison is shown in figure 12(b)for pbeam = 50 GeV/c. The shape agreement is good. Again, the showers start earlier in the Monte– 18 –

2010 JINST 5 P11006(a) pbeam = 20 GeV/c

054

EVis (GeV)

EVis

EVis

1.015

µ data/ µ MC

1.02

1.01
1.005

1

0.99
0.985
0.98
10

20

30

40

50

60

70

80

90

100

pbeam (GeV/c)dN
1
N d(EStrips/EMiddle)dN1(X -1)N d ShowerDepth 0

Figure 11. Ratio of the peak µE data of the visible energy EVis for the data and the peak µE MC of the visible
Vis
Vis
energy EVis for the Monte Carlo simulation for all beam momenta. The shaded band representes the energy
scale uncertainty for the data.

0.14

0.12

0.1

0.1

0.08

0.06

0.08

0.06

0.04

0.04
0.02
0.02

0

8

9

10

11

12

13

14

15

0

16

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

EStrips
EMiddleShowerDepth (X 0)(b) Estrips /Emiddle(a) Shower depth

Figure 12. Shower depth (left) and the ratio between the energy deposit in the strips layer and in the middle
layer (right) for pbeam = 50 GeV/c. Shaded area: Monte Carlo simulation; dots: data.

Carlo simulation than in data confirming the interpretation of the shower depth distribution in figure 12(a). The Monte Carlo simulation to data comparison for the mean of Estrips /Emiddle for all
beam momenta (figure 13) shows that the simulated showers tend to get shorter with respect to thedata with increasing beam momentum.

– 19 –

2010 JINST 5 P11006

0.995

data

MC

EStrips
EStrips< data > / < MC >EMiddleEMiddle

1.05
1.04
1.03
1.02
1.01
1

0.98
0.97
0.96
0.95
10

20

30

40

50

60

70

80

90

100

pbeam (GeV/c)

FigureRatio
 13.
 between the energy deposit in the strips layer and in the middle
 of the mean oftheMCratio
data
Estrips
Estripslayer E data
for the Monte Carlo simulation for all beam momenta.
for the data and E MC
middle3.4.4

middleSystematic uncertainties

The level of accuracy of the Monte Carlo simulation description of the electromagnetic shower
development in the LAr calorimeter is affected by uncertainties associated with the geometrical
set-up and detector description (thickness of the lead absorbers, the depth of the first layer, theexact amount of material in front of the strip compartment, cables, electronics, the thickness ofthe cryostat and the amount of LAr in front of the presampler). Similar uncertainties will be anissue for the ATLAS detector at the LHC. Therefore, it is important to investigate them in thecontrolled test-beam environment. However, the uncertainties associated with the description of
the combined test beam set-up itself will not be present in ATLAS. In order to understand the true
systematic effects relevant to ATLAS, the combined test beam set-up-related uncertainties must be
understood and a procedure developed to isolate them.
The dominant contributions of the total systematic uncertainty are• Uncertainties in the knowledge of the beam momentum. Although the absolute beam momentum may include large errors, the relative momentum shifts between different nominal
beam momenta are considerably smaller and depend on changes in beam conditions (collimator apertures, magnet currents, etc). Their total contribution is generally relatively small
at the level of 0.1 % (0.2 % for a beam momentum of 20 GeV/c and below) [14].
• Simulation uncertainties in the description of the electromagnetic shower development by
the simulation. Comparisons between GEANT4.8 and GEANT4.7 showed small differences– 20 –

2010 JINST 5 P11006

0.99

at the level of 1% in the lateral and longitudinal shower development because G EANT 4.8
features an improved description of multiple Coulomb scattering.

– Cross-talk in the strip compartment– MPhys /MCal in the strip compartment (see subsection 3.3.1)– Cross-talk between the strip and middle compartments– Depth of the strip section (boundary between middle and strip compartment)– Lead absorber thickness– Monte Carlo simulation description of the presampler response– Upstream material in the beam line
– Material in front of the presampler– Dead material between the presampler and the strip compartment– Simulation of charge collection– Monte Carlo simulation description of lateral and longitudinal shower shape
A detailed description of the systematic uncertainties can be found in [14].
3.5

The Calibration Hits Method

In the LAr calorimeter only energy deposits inside the active material of the calorimeter are measured. This implies that certain energy deposits are not measured directly. These are
1. Energy deposited outside the electromagnetic calorimeter: In the Monte Carlo simulation
this energy is split into 3 contributions:true• EupstreamPS: Energy deposited upstream of the presampler, see section 3.5.2.

true• EPS−Acc: Energy deposited between the presampler and the accordion, see section 3.5.2.
true: Energy deposited downstream of the accordion, see section 3.5.4.
• Edownstream

2. Energy deposited inside the electromagnetic calorimeter, but outside of the reconstructedcluster: In order to minimize the noise contribution and to be able to measure the energies ofseveral particles simultaneously, clusters of finite size are used for the energy measurement.
However, the energy deposits in the calorimeter cells outside the cluster are not taken directly
into account and therefore have to be estimated, see section 3.5.3.

– 21 –

2010 JINST 5 P11006• Uncertainties in the Monte Carlo simulation description of the beam line and the descriptionof the cryostat and the calorimeter. The impact of these contributions on the uncertaintyof the reconstructed energy is smaller than 0.4 %. However, in terms of linearity, the listed
effects have a much larger impact at lower energies than at higher energies; their impact
on the linearity for momenta > 20 GeV/c is estimated to be less than 0.1 %. Most of themcome from the limited precision of the measurement of some parameters like the beam-line
geometry, detector geometry, cross-talk, etc. These uncertainties — except uncertainties ofthe beam-line description — will also be present for ATLAS and are therefore listed below:

3. Energy deposited inside the reconstructed cluster in the inactive material: Because the LAr
EMB calorimeter is a sampling calorimeter and the development and energy deposition of
the electromagnetic cascade for an electron is a stochastic process, the ratio of the energy
deposits in the active and passive material inside the cluster varies event-by-event and also as
a function of the beam momentum. At 0th order this ratio is approximated by a single factor,
the sampling fraction, which is already applied at the cell reconstruction level. Higher ordercorrections are presented in subsection 3.5.3.

EAcc = EStrips + EMiddle + EBack ,(3.4)

or the shower depth Xmean . Therefore quantities for the different energy deposits are defined foreach event. These quantities are binned with respect to the measurable quantity that is used toparameterize the energy deposits. For each bin a representative value is computed. Finally a fit tothese extracted representative values is made in order to obtain the desired parameterization for theestimate.
The performance of the Calibration Hits Method for the Combined Test Beam 2004 for runs
without magnetic field in the Inner Detector has already been discussed in [14, 38]. Therefore,
the impact of the presence of the magnetic field in the Inner Detector on the performance of theCalibration Hits Method will be emphasized.
3.5.1

General strategy for the computation of representative values for distributions

The calibration of the electron energy is performed with respect to the peak position of the calibrated cluster energy. The reason for this choice is to minimize the effect of event selection cutsfor physics analyses. These cuts mostly affect events in the tails of the various distributions and thedependence of peak values on these tails is the small. In order to be consistent, the peak positionof a distribution is used to characterize its representative value throughout this section.
3.5.2

Estimation of the energy deposited upstream of the accordion

The energy deposited upstream of the accordion consists of the energy deposited upstream of thetruetrue and the energy deposited bepresampler EupstreamPS, the energy deposited in the presampler EPS
true
tween the presampler and the accordion EPS−Acc. For a given beam momentum the sum of these entrue
ergies, denoted EupstreamAcc
is estimated as a function of the measured presampler energy EPS . Fortruebins of EPS covering the whole energy range of presampler energy measurements, the EupstreamAcc
distributions are accumulated.
For each bin a fit with a Gaussian is performed around the peak and the mean of the Gaussian
trueĒupstreamAcc is attributed to the measured presampler energy corresponding to the center of the bin.
The resulting profile is plotted in figure 14 for pbeam = 50 GeV/c.

– 22 –

2010 JINST 5 P11006

These energy deposits are recorded as additional hits in the simulation, therefore the name Calibration Hits Method.
The idea of this calibration procedure is to estimate these different kinds of energy deposits
by means of Monte Carlo simulations and correlate them to measurable quantities, namely themeasured cluster presampler energy EPS , the measured cluster accordion energy EAcc which is thesum of the strips, middle and back layer cluster energies,

EupstreamAcc (GeV)

true

2.5

2

1.5

0.5
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

EPS (GeV)ba (GeV)

Figure 14. Energy deposited upstream of the accordion as a function of the reconstructed presampler energy
for pbeam = 50 GeV/c. The error bars are within the disks.

1.1

0.45

0.445

1.08

0.44
1.06
0.435
1.04
0.43

1.02

0.425

20

30

40

50

60

70

80

90

100

20

pbeam (GeV/c)

30

40

50

60

70

80

90

100

pbeam (GeV/c)

Figure 15. Offset (left) and slope (right) of the estimation of the energy deposited upstream of the accordion(eq. (3.5) and eq. (3.6)).

For each beam momentum a straight line is fitted. The obtained offsets ā(pbeam ) and slopesb̄(pbeam ) are shown in figure 15. For the runs at the Combined Test Beam 2004 without magnetic
field in the Inner Detector the offsets ā(pbeam ) are a monotonously rising function of pbeam [38].
With magnetic field in the Inner Detector, the tracks of the particles with lower momentum arebent more strongly resulting in a smaller impact angle. This leads to an increase of the lengths ofthe tracks in the cryostat and therefore to an increase of ā(pbeam ). As a consequence, the obtained
offsets ā(pbeam ) are a nearly constant function of pbeam within the errors.

– 23 –

2010 JINST 5 P11006

1

Next, the offset as a function of the beam momentum is parameterized by fittingâ(pbeam ) = a0 + a1 log pbeam ,(3.5)

b̂(pbeam ) = b0 + b1 log pbeam ,(3.6)

and the slope by fitting
in units of GeV c−1 for the logarithms. These are the same parameterizations that have

estim
EupstreamAcc(EPS , pbeam ) = â(pbeam ) + b̂(pbeam ) EPS .

(3.7)

In order to determine the particle energy without prior knowledge of the beam momentum, an
iterative procedure is applied, see subsection 3.5.5.
3.5.3

Estimation of the energy deposited in the accordion

true deposited in the accordion can be estimated either as a function of the shower
The energy EAcc
depth or as a function of the beam momentum.
For each event the ratio d of the energy deposited in the accordion and the measured accordion
energy (equation (3.4)) is defined by
E true(3.8)
d = Acc .
EAcc

Beam momentum parameterization. For each beam momentum a Gaussian is fitted to the d¯ beam ) is extracted
distribution for the specific beam momentum and the mean of this Gaussian d(p¯and shown in figure 16. Then d(pbeam ) is approximated by fitting
ˆ beam ) = d0 + d1 log pbeam + d2 (log pbeam )2 ,
d(p

(3.9)

with pbeam in units of GeV c−1 for the logarithms. The fitted values are d0 = 1.262516(15), d1 =0.107626(8) and d2 = 0.011840(1).
The values for d¯ are close to one since a coarse sampling fraction correction is applied at thecell energy reconstruction (Fµ A→MeV , see section 3.3.1). It increases with decreasing beam momentum because of two effects: The sampling fraction slightly decreases with decreasing beam
momentum [39] and this is not taken into account by the coarse sampling fraction correction mentioned above. In addition, since the electrons are stronger deflected by the magnetic field withdecreasing beam momentum, the emitted bremsstrahlung is more likely to be not contained in thecluster which increases the fraction of energy deposited outside the cluster with decreasing beam
momentum.
For a given event at a given beam momentum the energy deposited in the accordion is estimated byestimˆ beam ) EAcc .
EAcc(EAcc , pbeam ) = d(p(3.10)In order to determine the particle energy without prior knowledge of the beam momentum, an
iterative procedure is applied, see subsection 3.5.5.

– 24 –

2010 JINST 5 P11006

with pbeam
also been used for the runs without magnetic field in the Inner Detector. The slope is very wellparameterized and the differences for the offset are at the level of 20 MeV. The fitted values are
a0 = 0.45(1) GeV, a1 = −0.003(3) GeV, b0 = 0.89(2) GeV and b1 = 0.43(5) GeV.
Then for a given event at a given beam momentum the energy deposited upstream of theaccordion is estimated by

d

1.1
1.09
1.08
1.07
1.06
1.05

1.03
1.02
1.01
1

20

30

40

50

60

70

80

90

100

pbeam (GeV/c)¯ beam ) of the Gaussian fitted to the d distribution (eq. (3.8)) for all beam momenta andFigure 16. Mean d(pˆ beam ). The error bars are within the disks.
its parameterization d(pShower depth parameterization. The idea of this parameterization is to correct for sampling
fraction fluctuations event by event by relating the sampling fraction to the shower depth. Analysesof CTB 2004 data have shown that this method works very well without magnetic field upstreamof the calorimeter [14].
For bins of the measured shower depth Xmean covering the whole shower depth range, the ddistributions are accumulated. For each bin a fit with a Gaussian is performed and the mean of the¯ mean ) is attributed to the measured shower depth corresponding to the center of theGaussian d(Xbin. The resulting profiles for all beam momenta are shown in figure 17.
¯ mean ) as a function of the shower depth
Figure 17 demonstrates that the parameterization of d(Xdoes not remove the dependence on the beam momentum. This is contrary to what has been found
for the Combined Test Beam 2004 for runs without magnetic field in the Inner Detector [14, 38].
The reason for this discrepancy is that in the presence of the magnetic field the energy deposited
inside the electromagnetic calorimeter but outside of the reconstructed cluster relative to the energyof the particle depends on the beam momentum. In figure 18 the mean d¯5x11 (pbeam ) dependence
for clusters of 5 × 11 instead of 3 × 7 middle cells (section 3.3.2) is shown for all beam momenta.
These clusters are large enough to contain the whole shower in the calorimeter. The fact that there is
no beam momentum dependence for the 5 × 11 clusters indicates that the 3 × 7 cluster size together¯ mean ) on the beam momentum. Therefore
with the magnetic field generates the dependence of d(Xthis parameterization is not used for the linearity and resolution measurements in section 3.6.
The same effect is also visible in ATLAS Monte Carlo simulation, although the effect there is– 25 –

2010 JINST 5 P11006

1.04

d

1.1

pbeam= 20 GeV/c
1.09

pbeam= 50 GeV/cpbeam= 80 GeV/cpbeam= 100 GeV/c

1.08
1.07
1.06
1.05

1.03
1.02
1.01
1
8

9

10

11

12

13

14

15

16

Xmean (X )0

¯ beam ) of the Gaussian fitted to the d distribution (equation (3.8)) as a function of the
Figure 17. Mean d(pshower depth Xmean for all beam momenta.

so small that the shower depth parameterization is used by default for the electron energy calibration [40]. The reason why this effect is much smaller for the ATLAS detector is that the geometriclayout of the CTB 2004 is a bit different from ATLAS, in particular the distances between the innerdetector components and the LAr EMB calorimeter are larger for the CTB 2004 setup.
3.5.4

Estimation of the energy deposited downstream of the accordion

true
deposited downstream of the accordion can be estimated either as a function
The energy Edownstreamof the shower depth or as a function of the beam momentum.

Beam momentum parameterization. For each beam momentum a Gaussian is fitted to the
true
true
(pbeam ) is obtained and shown
distribution and the mean of the Gaussian Ēdownstream
Edownstream
true
in figure 19. Then Ēdownstream (pbeam ) is approximated by fitting
estim(pbeam ) = λ0 pbeam + λ1 p2beam .
Edownstream(3.11)

The fitted values are λ0 = 9(4) 10−4 c and λ1 = 2.3(7) 10−6 c2 GeV−1 .
In order to determine the particle energy without prior knowledge of the beam momentum, an
iterative procedure is applied, see section 3.5.5.
Shower depth parameterization. For each event the ratio of the energy deposited downstreamof the accordion and the measured accordion energy which is the sum of the measured strips,– 26 –

2010 JINST 5 P11006

1.04

d5x111.03

pbeam= 20 GeV/c
1.025

pbeam= 50 GeV/c

1.02

pbeam= 80 GeV/cpbeam= 100 GeV/c

1.015
1.01

1
0.995
0.99
8

9

10

11

12

13

14

15

16

Xmean (X )0

Figure 18. Mean d¯5x11 (pbeam ) of the Gaussian fitted to the d distribution (equation (3.8)) for 5 × 11 clusters
as a function of the shower depth Xmean for all beam momenta.

middle and back layer energies is defined by

λ=

true
Edownstream.
EAcc(3.12)For bins of the measured shower depth Xmean covering the whole shower depth range, theλ distributions are accumulated. For each bin a fit with a Gaussian is performed and the mean of
the Gaussian λ̄ (Xmean ) is attributed to the measured shower depth corresponding to the center ofthe bin. The resulting profiles for all beam momenta are plotted in figure 20.
Figure 20 shows that the parameterization of the ratio of energy deposited downstream of theaccordion and the measured accordion energy does not completely remove the dependence on the
beam momentum. The remaining differences are at the half permille level.
For the reasons shown in section 3.5.3, this parameterization is not used for the linearity andresolution measurements in section 3.6.
3.5.5

Iterative procedure

An iterative procedure is applied to compute the calibrated cluster energy. Starting value for theestimate for the calibrated cluster energy is the visible energy. In each iteration step the estimatedcalibrated cluster energy from the previous step together with
E 2 = p2 c2 + m2 c4– 27 –(3.13)

2010 JINST 5 P11006

1.005

true

Edownstream (GeV)

0.35
0.3
0.25
0.2

0.1
0.05
0

20

30

40

50

60

70

80

90

100

pbeam (GeV/c)

Figure 19. Mean of the energy deposited downstream of the accordion for all beam momenta and its paramestim
eterization Edownstream(pbeam ) (eq. (3.11)).

is used to estimate the proper beam/particle momentum to select the new estimation coefficients.
Here the knowledge that electrons have been selected from the beam is used to justify the neglectof the rest mass term contribution to the particle energy.13 The selected estimation coefficients arethen used to compute a new estimate for the calibrated cluster energy.
Beam momentum parameterization. Using the beam momentum parameterizations for the enestim deposited in the accordion and the energy E estim
ergy EAcc
downstream deposited downstream of theaccordion, the iterative procedure is given by:0
ECalib= EPS + EAcc
E0
p0 = Calib
c
..
.
estim
estim
k
= EupstreamAcc(EPS , pk−1 ) + EAcc
(EAcc , pk−1 )ECalibestim(pk−1 )
+ Edownstream

ˆ k−1 ) EAcc
= â(pk−1 ) + b̂(pk−1 ) EPS + d(pestim(pk−1 ) k > 0+ Edownstream

pk =13 The rest mass of an electron is mkECalibck>0e = 511 keV/c. The investigated beam momenta are > 10 GeV/c.

– 28 –(3.14)

2010 JINST 5 P11006

0.15

λ

0.01

p
0.009

p
p

0.008

p
0.007

= 20 GeV/cbeam= 50 GeV/cbeam= 80 GeV/c

beam= 100 GeV/c

beam

0.006
0.005

0.003
0.002
0.001
0

8

9

10

11

12

13

14

15

16

Xmean (X 0)
Figure 20. Mean λ̄ (pbeam ) of the Gaussian fitted to the λ distribution (equation (3.12)) as a function of theshower depth Xmean for all beam momenta.
kis the k-th estimation ofwhere pk is the k-th estimation of the particle momentum and ECalib
k−1
k−1
k−1
estim
the particle energy. EupstreamAcc (EPS , p ) = â(p ) + b̂(p ) EPS is used to estimate the energy
estim (Ek−1 ) = d(pˆ k−1 ) EAcc to estimate the energy
deposited upstream of the accordion and EAcc
Acc , pdeposited in the accordion.
This iteration procedure is executed until the relative difference between the two consecutive
k−1k− ECalib| is smaller than 10−6 . On average 3 iterations are required to meet thisECalib values |ECalibtermination condition.

3.6

Linearity and resolution

The calibrated cluster energies are computed using the iteration scheme for the beam momentum
parameterization (eq. (3.14)). The Monte Carlo simulation to data comparison is shown in figure 21
for all beam momenta. The shape agreement for calibrated cluster energy distributions is similar tothe shape agreement for the visible energy distributions described in section 3.4.2. This means thatthe shape agreement is best at pbeam = 20 GeV/c and deteriorates with increasing beam momentum
due to the beam spread that has not been simulated and due to low energy tails larger in data than in
the Monte Carlo simulation. These low energy tails are mainly due to the fact that a priori the beam
particles are simulated without taking into account any losses along the beam line. The correction
introduced in section 3.4.1 only describes this effect in an approximate manner.
The calibrated cluster energy distributions are fitted with Crystal Ball functions14 and the mean
14 The definition of the Crystal Ball function is given in section 7.1, eq. (7.5).

– 29 –

2010 JINST 5 P11006

0.004

1 d N (Gev-1)
N dECalib

1 d N (Gev-1)
N dECalib

0.1

0.08

0.22
0.2
0.18
0.16
0.14

0.06

0.12

0.04

0.08

0.1

0.06
0.04

0.02

0.02
0
14

15

16

17

18

19

20

21

0

22

38

40

42

44

46

48

50

ECalib (GeV)

1 d N (Gev-1)
N dECalib

1 d N (Gev-1)
N dECalib

0.2

0.25

0.2

0.15

0.15

0.1

0.1

0.05

0.05

70

75

80

0
85

85

90

95

100

ECalib (GeV)

105

110

ECalib (GeV)(c) pbeam = 80 GeV/c(d) pbeam = 100 GeV/c

Figure 21. Calibrated energy for all beam momenta. Shaded area: Monte Carlo simulation; dots: data.

µEcalib and the sigma σECalib of these Crystal Ball functions divided by Ebeam = pbeam · c are plottedin figure 22 and figure 23 to assess the linearity and resolution.
In figure 22 the deviation of µEcalib /Ebeam from 1 is within the energy scale uncertainty andthe error bars. The main contributions to the errors bars are the beam momentum uncertainty (dataonly) and the statistical errors. The square root of the mean squared deviation of µEcalib /Ebeam from
1 is 0.1% for the Monte Carlo simulation and 0.6% for the data. For the data this is within theenergy scale uncertainty. Adjusting the energy scale, the linearity defined as the unbiased estimateof the standard deviation of µEcalib /Ebeam is 0.1% for the Monte Carlo simulation and 0.28% for thedata. This is within the estimated systematic uncertainties discussed in section 3.4.4. Therefore thelinearity at the CTB 2004 is understood at the level of the estimated systematic uncertainties.
The resolution shown in figure 23 is described byσECalib (Ebeam )
b
a
⊕
=√
⊕c
Ebeam
Ebeam Ebeam(3.15)

where the first term in the quadratic sum is the stochastic term, the second the noise term andthe third the local constant term. Since the beam spread σ (pbeam ) (table 1) was not simulated,
it have been subtracted quadratically for every measurement point for Data in figure 23 before.
In addition, since the noise of the read-out electronics was measured regularly during the whole– 30 –

2010 JINST 5 P11006(b) pbeam = 50 GeV/c

0.25

65

54

ECalib (GeV)(a) pbeam = 20 GeV/c

052

EbeamECalib

µ

1.02

Data

1.015

Monte Carlo simulation

1.01
1.005

1

0.99
0.985
0.98
10

20

30

40

50

60

70

80

90

100

pbeam (GeV/c)

Figure 22. Linearity for Monte Carlo simulation and data. The shaded band representes the energy scale
uncertainty for the data.

CTB 2004 data taking period by taking dedicated calibration runs, the noise values for the 3x7
clusters have also been subtracted quadratically for every measurement point for Data in figure 23
before. They have been computed for each run by averaging the noise values for the clusters over
events that have been triggered randomly. The noise value of a given cluster was computed as thequadratic sum of the noise values of all cells in the cluster in their chosen read out gain for the
given event. The noise value of a given cell in a given read out gain was taken from the previously
mentioned calibration runs. The noise values are shown in table 5. The noise increases slightly
with increasing beam momentum because more cells are read out in medium gain than in high gain
due to the higher energy deposits and because the noise for the medium gain is higher than forthe high gain. The reason for this difference in the noise values of a cell for the various gains isthat the noise is first amplified with different gain factors but then digitized with a constant ADC
resolution. Afterwards the gain dependent FDAC→µ A · Fµ A→MeV factor (see section 3.3.1) is applied
to adjust the mean values of the noise distributions for the different gains. The net result of thisprocedure on the standard deviation of the noise distribution of a given cell which is the noise valueof the given cell is the small gain dependence.
The error bars for the resolution shown in figure 23 are dominated by the systematic errorof the fit of the calibrated cluster energy distributions from figure 21. The error bars have been
estimated to be the difference of the standard deviations obtained with three different models: A
Gaussian fitted to the peak part of the distribution, a Crystal Ball function fitted to the distribution
and an exponential function convoluted with a Gaussian (defined by equation (7.3)) fitted to the
distribution.

– 31 –

2010 JINST 5 P11006

0.995

Table 5. Noise values for the 3x7 clusters for all beam momenta.

Calib

σE

( GeV/c)pnominal
beam
100
50
20
80

0.05

Noise ( MeV)
209.7
207.4
207.4
207.9

σE

= (10.0±0.1)%GeV / E⊕ 0.2%
Ebeam
σE
1/2
beam
Calib
MC
= (9.9±0.1)%GeV / E⊕ 0.2%
Ebeam
Data

0.045
0.04

1/2

Calib

beam

0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
10

20

30

40

50

60

70

80

90

100

pbeam (GeV/c)

Figure 23. Relative energy resolution for Monte Carlo simulation and data for all beam momenta after
subtraction of the beam spread and the noise. The error bars are dominated by the systematic error of the fitof the calibrated cluster energy distributions and are explained in the text.

The fit to extract a is done with b = 0 and c = 0.2% whose value is known from previous test
beams. The value for a extracted by the fit is (9.9 ± 0.1)% GeV1/2 for Monte Carlo simulationand (10.0 ± 0.1)% GeV1/2 for data which is compatible with previous test beam results withoutmagnetic field. It is the first measurement of a for the ATLAS LAr calorimeter with particles
traversing a magnetic field similar as for ATLAS data taking at the LHC. However, the resolution
for beam momenta of 50 GeV/c and 80 GeV/c is too small in the Monte Carlo simulation.

4

Momentum measurement with the Inner Detector

This section presents the performance of the momentum measurement for electrons with the
ATLAS Inner Detector in the ATLAS Combined Test Beam 2004. The track reconstruction is– 32 –

2010 JINST 5 P11006

Ebeam

Run number
21023992102400
21024132102452

described in section 4.1. This is followed by a comparison of the Monte Carlo simulation to data
(section 4.2). The data samples and the event selection were the same as in section 3.
4.1

Track reconstruction

pX
σ1/pT (pT ) = σ1/pT (∞) 1 ⊕ T
pT



,

(4.1)

where σ1/pT (∞) is the asymptotic resolution expected at infinite momentum and pXT is a constantrepresenting the value of pT , for which the contribution of the intrinsic and multiple-scatteringterms to the resolution are equal. Therefore the inverse momentum 1/p measured by the Inner
Detector is used in section 4.2 to assess the quality of the description of the data by the Monte
Carlo simulation. It is normalized to the beam momentum pbeam , i.e. pbeam /p is shown.
4.2

Monte Carlo simulation and comparison with data

The ratio pbeam /p of the beam momentum and the momentum measured by the Inner Detector isshown in figure 24 for all beam momenta and compared to Monte Carlo simulation.
The agreement of the description of the tails of the distribution is sufficiently good, but thescale agreement is not better than a few percent because of residual misalignment between thevarious Inner Detector components that could not be resolved [42].

– 33 –

2010 JINST 5 P11006

The track reconstruction algorithms for the CTB 2004 have been implemented in the CTB-Tracking(‘Cosmics + TestBeam’) package. This package provides a pattern recognition that works without avertex constraint which is an ideal approach for the testbeam and is also needed for other situations,e.g. reconstructing cosmic or beam halo events. Details can be found in [41].
Tracks in the Inner Detector are reconstructed in three consecutive steps. In the pre-processing
step, the raw data from the Pixel and SCT detectors are converted into clusters and the SCT clusters
are then transformed into space-points. Furthermore, the TRT raw timing information is, based ona calibration obtained from data, first corrected for an offset with respect to the expected timeof a signal for particles passing through the middle of the straw, and then the remaining delaycaused by drift time is converted into a drift radius. At the track-finding step track candidates are
identified using different tracking strategies. Fake tracks among these track candidates are rejectedby applying quality cuts, e.g. on the number of associated clusters or the number of holes per
track (a hole is defined as a silicon sensor crossed by a track without generating any associatedcluster). The remaining track candidates are the reconstructed tracks for the given event. The trackparameters are determined by global χ 2 minimization of the residuals (i.e. the difference between
the measurement position and the position as predicted by the track), and their errors. During thefinal post-processing stage photon conversions and secondary vertices are reconstructed. At the
CTB this final step is of minor importance except for photon conversion studies.
In a homogeneous magnetic field the sagitta of a curved track is directly proportional to 1/p
and without bremsstrahlung events would be distributed like a Gaussian. The resolution of theinverse transverse momentum 1/pT (which is equal to the inverse momentum in the CTB) can be
expressed as a function of pT :

1 dN
N pbeamd p

1 dN
N pbeam
d p

0.25

0.14

0.12
0.2
0.1
0.15
0.08

0.06

0.1

0.04
0.05
0.02

0

0

0.5

1

1.5

2

2.5

0

3

0

0.5

1

1.5

2

2.5

pbeam
p

1 dN
N pbeamd p(b) pbeam = 50 GeV/c

0.12

0.1

0.09
0.08
0.07

0.08
0.06
0.05

0.06

0.04
0.04

0.03
0.02

0.02
0.01
0

0

0.5

1

1.5

2

2.5

0

3

0

0.5

1

1.5

2

2.5

pbeam
p

3

pbeam
p

(c) pbeam = 80 GeV/c(d) pbeam = 100 GeV/c

Figure 24. Ratio pbeam /p of the beam momentum and the momentum measured by the Inner Detector forvarious beam momenta. Shaded area: Monte Carlo simulation; dots: data.

5

Particle identification with the Transition Radiation Tracker

This section presents the electron identification (ePID) with the TRT. After a short introduction
to particle identification with the TRT in section 5.1, the data samples used for this analysis are
discussed in section 5.2. Section 5.3 presents methods used for ePID in the TRT, and finally themeasurement of the transition radiation onset from data is discussed in section 5.4.
5.1

Introduction to particle identification with the Transition Radiation Tracker

The TRT is a straw tube tracker with ePID capabilities mainly through detection of transition
radiation photons created in the radiator between the straws. The detector is situated in front of
the EM calorimeter and is described in detail in [3].
The output of the TRT is 27 bits per straw — 24 low threshold (LT) bits and 3 high threshold(HT) bit spanning 75ns. An illustration of a regular pulse along with its resulting bit output isshown in figure 25.
The number of HT hits are mainly the result of transition radiation (TR) photons, created
when charged particles with high gamma factors pass the radiator material15 between the straws.
15 Material with rapidly changing dielectric constant (filt structure), creating TR through interference.

– 34 –

2010 JINST 5 P11006(a) pbeam = 20 GeV/c
1 dN
N pbeam
d p

3

pbeam
p

Pulse height|0 0 0 0 0 0 0 1|1 1 1 1 1 1 1 0|0 0 0 0 0 0 0 0| LT bits0
10
HT bits

High Threshold (HT) at 6 keV|{z}Time-over-Threshold (ToT)Time (bits)
1 bit = 3.125 ns

Figure 25. Example of a regular TRT pulse including its LT and HT bit response.

At the energies of the final state particles at LHC, essentially only electrons have such high gamma
factors, and thus a HT hit signifies an electron.
The number of LT hits refers to the number of straw hits assigned to a specific track. In
principle some straws could be crossed without a LT hit, but this fraction is very low, and will nothave any significant influence on the results. For each LT hit, the number of bits set between thefirst bin (leading edge) and the last bin (trailing edge) yields the Time-over-Threshold (ToT). Sinceelectrons ionize more than pions given a certain path length in the straw, a longer ToT signifies
an electron. However, since the difference in dE/dx between electrons and pions vanishes at highenergy, the ToT variable is expected to give better separation at low energy.
The separation between electrons and hadrons, mostly pions16 presented in the following isbased primarily on the HT information while the ToT information provides secondary separation
most notably at lower energies. The optimization has been done to maximize the pion rejection(defined as Rπ = 1/επ , where επ is the pion efficiency) at 90% electron efficiency.
The algorithm should also be efficient at finding (possibly soft) electrons in jets for b-quark
tagging, which again requires good e/π separation. Here the TRT plays a central role.
5.2
5.2.1

The combined test beam data
Data samples

In order to get the best knowledge of the energy sensitivity of the e/π separation, the whole beam
momentum range from 2 to 180 GeV/c was used. For each beam momentum, only runs without
B-field and without additional material were used, though the results were not much affected by
B-field and material. In addition, muon runs at 150 and 350 GeV/c were added to the data set
16 Here and in the following, “pions” will be used as a generic word for “hadrons”.

– 35 –

2010 JINST 5 P11006

11111111 Low Threshold (LT) at 300 eV00000000
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111

Table 6. Table showing all used runs, with their run-number, beam momentum in GeV/c, B-field in T ,average number of LT hits, number of events Nrun , number of events after selection Ncuts and numbers ofpions, electrons, and muons (Nπ , Ne , Nµ ).
pnominal
beam ( GeV/c)
2
3
5
9
20
50
80
100
150
150
180
350
350
350

B(T )
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.16
0.16
0.00
0.16
0.16
1.40

hLT hitsi
36.38±0.03
37.17±0.03
37.41±0.03
37.44±0.02
32.83±0.02
33.75±0.02
34.38±0.02
33.89±0.02
36.10±0.02
35.78±0.02
33.95±0.02
35.42±0.01
34.57±0.02
34.57±0.02

Nrun
50000
50000
50000
50000
50000
50000
50000
40000
27219
29486
50000
50000
30494
46416

Ncuts
25105
26873
32316
39649
41500
39815
39156
32031
24683
26922
44097
48589
29543
45098

Nπ
3178
5547
12092
14134
2378
6105
6989
8017
414
2919
20683
61
47
62

Ne
15755
16684
14190
8369
31817
27254
24891
16520
0
0
6090
0
0
0

Nµ
157
0
0
113
271
12
33
509
21590
21300
2439
46029
27932
42671

for the measurement of the TR onset (see section 5.4). These runs had non-zero B-field. During
the data taking period two TRT geometry configurations were used, coinciding with the choice ofbeam momentum, such that at low beam energy (2, 3, 5, and 9 GeV/c) the lower three modules of
the TRT were centered to the beam, while at high beam energy (20, 50, 80, 100, and 180 GeV/c)the three upper ones were aligned.
The complete list of runs used in this analysis, including their beam momentum pbeam in
GeV/c, B-field in T , material status M, average number of LT hits, number of events in file Nfile andafter cuts Ncuts , and estimated statistics for each particle sample is presented in table 6.
5.2.2

Data quality

To ensure single high quality TRT tracks with no interference from other effects, events wererequired to have exactly one global track (i.e. a track seen and matched between the Pixel detector,
the SCT, and the TRT) with at least 20 hits in the TRT. In addition a quality assurance is applied toeach TRT straw, requiring that at least 100 identified electrons and pions passed through that straw,
that the probability for an electron to make a HT hit (pHTe ) is at least 50% higher than the same forHTa pion (pπ ), and that the latter is below 12.5% to avoid noisy straws. Straws that do not pass thesecuts (6.1%) are removed from the track, and the requirement of at least 20 hits on track is repeated,excluding about 2% of the tracks.
5.2.3

Electron and pion samples

To obtain large clean samples of electrons and pions separately, a Cherenkov counter17 and the
ATLAS calorimeters were used for discrimination.
17 This detector is only part of the CTB setup, not of the ATLAS detector.

– 36 –

2010 JINST 5 P11006

Run
21021152102098
2102097
21021032102397210241021024542102398
2102433
2102434
2102461210273021027312102728

Table 7. Electron and pion contaminations for the non-TRT separation requirements at beam momenta of 2,
3, 5, 9, 20, 50, 80, 100, and 180 GeV/c, respectively. An entry of 0.1 × 10−6 indicates that the contamination
is at or below this level.
pnominal( GeV/c)beam
e contamination in π sample (10−6)
π contamination in e sample (10−6)

2
8.4
17.1

3
2.1
9.5

5
0.2
4.1

9
0.1
0.1

20
0.1
0.1

50
0.1
1.4

80
0.1
1.9

100
0.1
1.9

180
0.1
0.2

5.3

Particle identification methods

5.3.1

The high threshold method

The occurrence of a HT hit in a straw signifies transition radiation (TR), which, in the given momentum range, is essentially only emitted by electrons . However, HT hits can also be producedby other particles, mostly because of Landau fluctuations in the dE/dx and/or δ -rays (atomic electrons knocked out), which as a result decreases the separation. Given knowledge of the electron
and pion HT hit probabilities, peHT,i and pπHT,i , these can be used to calculate the probability for a
track to originate from an electron as follows:peHT =∏i peHT,ij∑ ∏i pHT,i

,

(5.1)

j = e, π

where the product of probabilities is normalised to the probability of all possible particle types (inthis analysis only pions and electrons). It has been checked that each straw can be considered an
independent detector, and thus there is no correlation between straws.
The electron and pion HT hit probabilities used in the likelihood have been determined as
averages for each straw and at each beam momentum. This method includes the variations withdepth into the TRT observed. Also variations with distance from the track to the anode have been
determined, but these are not used in the likelihood, as they are purely geometrical, and do notprovide additional separation. An example of the HT distribution of likelihoods at 9 GeV/c isshown in figure 26.

– 37 –

2010 JINST 5 P11006

The fraction of energy deposited in the first sampling and the entire cluster in the Liquid Argon
calorimeter, provides very good separation. Additional information is provided by the Cherenkov
counter at lower beam momenta (2-20 GeV/c) and the energy fraction in the Tile calorimeter athigher beam momenta (20-180 GeV/c). Finally, the muon system provides a muon tag, such that
also clean samples of muons are available for the TR onset analysis.
The selections were obtained through an iterative process, where each variable is consideredin turn, while applying the separating requirements to all the other detectors. This optimisation
was performed at all beam energies, as most separation requirements are momentum dependent.
For the study of the TRT ePID, reasonably large samples (> 1000 events) are needed, while at thesame time good purities (< 0.2% contamination) are maintained. Generally, contaminations weremuch smaller, see table 7. It was checked that possible correlations would not affect the results
significantly.

Fraction of events

1

E = 9 GeVElectrons
Pions

10−1

10−2

−3

10

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Electron probability from HT information

Figure 26. Distribution of likelihoods obtained from the HT information for electrons (solid) and pions(dashed) at 9 GeV/c.

Finally, the distribution of HT hits on the track (i.e. whether they occur randomly distributed
or not) has been considered using the Wald-Wolfowitz run test [43]. No significant deviations fromindependent behavior was found.
5.3.2

The time-over-threshold method

In addition to the HT information, one can consider taking the ToT information into account as
well, and especially at low momenta this is expected to increase the separation.
The ToT is very dependent on the distance r from the track to the anode (this is the information
used by the tracking algorithms), and thus this geometrical effect has to be taken into account when
considering the ToT for ePID. Also, while the ToT momentum dependence is not very pronounced
for electrons, it does change with momentum for pions due to the stronger momentum dependenceof dE/dx for pions. The larger the momentum, the closer dE/dx for pions gets to dE/dx ofelectrons, which thus in turn diminishes the separation between the two, using ToT information.
Given the ToT and the distance from the track to the anode r, a likelihood ratio similar to thatof the HT is calculated as follows:
peToT =

∏i,noHT peToT,ij∑ ∏i,noHT pToT,i

,

(5.2)

j = e, π

wherein the product of probabilities is normalised to the probability of all possible particle types(pions and electrons). The probabilities peToT and pπToT are determined as a function of ToT and r
for each beam momentum averaged over all straws (to increase statistics).
Anticipating the combination of the HT and ToT information, the HT hits are excluded fromthe ToT likelihood to minimize the correlation between the two. It has been checked that theToT information of the straws with HT hits do not carry any significant additional separation.
An example of the distribution of likelihoods obtained with the ToT method not using HT hits at
9 GeV/c is shown in figure 27.

– 38 –

2010 JINST 5 P11006

0Fraction of events

10−1

Electrons

E = 9 GeV

Pions

10−2

10−3
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Electron probability from ToT information

1
90% electron efficiency

Pion Efficiency

Figure 27. Distribution of likelihoods obtained from the ToT information for electrons (solid) and pions(dashed) at 9 GeV/c.

10−1

Time−over−threshold

10−2

High−threshold

E = 9 GeV
0.84

0.86

0.88

Combined
0.9

0.92

0.94

0.96

0.98

1

Electron Efficiency

Figure 28. π -efficiency versus e-efficiency for ToT methods at 9 GeV/c.

5.3.3

Combined method

Having obtained separating methods using both the HT and the ToT information, a combination ofthese is considered to achieve the best pion rejection possible. It was checked that the correlation
between the two were below 20% at all energies, and therefore the two variables are combined asfollows:
peall =

peHT peToT

j
j
pToT
∑ pHT

.

(5.3)

j = e, πThe e/π separation performance resulting from this combination can be seen along with theseparate HT and ToT performances in figure 28 at 9 GeV/c, which shows the π -efficiency as afunction of e-efficiency. As can be seen from the figure, the HT information provides the bulk of
the separation, while the ToT information gives a significant addition, as also seen in the combined
performance, which is most performant.

– 39 –

2010 JINST 5 P11006

0Pion efficiency (at 90% electron eff.)

1

10−1

10−2

Time−over−threshold
High−threshold
Combined

10102
Energy (GeV)

Figure 29. π -efficiency at 90% e-efficiency as a function of beam energy.

The algorithms for e/π separation were applied at all beam momenta, and using the pion
efficiency at 90% electron efficiency (indicated by a vertical dashed black line in figure 28) as a
figure of merit, the separation as a function of beam energy is shown in figure 29. As can be seen,
the optimal e/π separation for the TRT is in the range 3-30 GeV/c, where it rejects more than 97%
of pions while retaining 90% of electrons. The rejection is less outside this range, but still quite
significant. The reason for this structure is related to the onset of TR for pions and electrons (seesection 5.4). At low beam momentum the TR emittance of electrons has not reached its maximum
yet, and at high beam momentum pions start to emit TR as well.
5.4

Measurement of the high threshold onset

Using the data and selection described in previous sections along with 5 muon runs at 150 and
350 GeV/c (see table 6), the TR dependence on the γ factor was measured. Since the TRT barrel
radiator material is irregular, reliable calculations of the TR build-up are hard and need verification
and/or tuning from data.
5.4.1

Procedure and error evaluation

For each run and particle type (π , e, µ ) the HT probability was determined along with its (almost
negligible) statistical error. These values were then combined into an average for each beam momentum and particle type, using the RMS between runs as a measure of the uncertainty due tovariations in running conditions. The systematic error from the straw quality requirement is determined by applying two alternative selections, and the RMS of the variation is considered asystematic error.
At low γ factors (< 500), the HT probabilities are expected to be near constant (and low), sincethese probabilities are the result of the Landau tail of the dE/dx. However, due to the two different
geometry configurations at low and high energy (see section 5.2), the HT probability changes anda correction has to be made. The correction is calculated by comparing the average HT probability(from 5 values) for pions and muons at low beam momenta (2-9 GeV/c) with that (from 3 values) at
π +µhigh beam momenta (20-50 GeV/c), where no change is expected. The averages hpHT (low E)i =– 40 –

2010 JINST 5 P11006

1

ATLAS TRT barrel
Combined test beam data, 2004

Electrons
Muons
Pions

γ −factor
10

102

103

1

10

102

Pion momentum (GeV) Muon momentum (GeV)

105

104

102

10

Electron momentum (GeV)

Figure 30. HT Probability as a function of γ factor for electrons (squares), muons (triangles) and pions(circles) in the beam energy range 2-350 GeV/c. The curve is a fit with a generic function, and the fit
residuals are shown in the top plot, where the two dashed lines represent ±0.005.
π +µ

π +µ

0.0402 and hpHT (high E)i = 0.0350 compared to the overall average of hpHT (all E)i = 0.0383
yield corrections of -0.0020 and 0.0033 at low and high beam momenta, respectively. Half of thecorrections are used as a systematic error.
5.4.2

Results

The final values and their uncertainties are fitted with a generic function of log10 γ consisting of afirst degree polynomial and a sigmoid function:
pHT (γ ) = c0 + c1 log10 γ +c2
1.0 + exp(−(log10 γ − c3 )/c4 )(5.4)

with γ ∈ [1, 500000]. The result, along with the data points and the fitted function, can be seen in
figure 30.
As figure 30 shows, the fit describes the data well. In γ regions in figure 30 where the values
for the different particle types overlap, the HT probability does not seem to depend on the particle
type, but only on the γ factor, as expected.
While the HT onset starts at about γ ∼ 1000, it does not reach its maximum until γ ∼ 15000.
Likewise, even at high beam momenta pions do not emit much TR, and can thus be separated
from electrons up to momenta of 150-200 GeV/c. Finally, and perhaps most importantly, thismeasurement enables a precise tuning of the TRT simulation.

– 41 –

2010 JINST 5 P11006

High−threshold probability

0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0

6

Bremsstrahlungs recovery using the Liquid Argon calorimeter

A common problem for a tracking detector in a magnetic field is that for electrons the emissionof bremsstrahlung during the passage through the tracker might lead to an underestimation of theinitial momentum of the electron.
The purpose of the presented algorithm, denoted bremsstrahlungs recovery, is to correct for
momentum underestimation for electrons due to bremsstrahlung in the ATLAS Inner Detector using the electromagnetic calorimeter. At momenta lower than 20 GeV/c, the momentum underestimation can be corrected using only the Inner Detector hit pattern. Examples are DNA (Dynamic
Noise Adjustment) [44] which is a Kalman fitter where the noise is adjusted to take the effects frombremsstrahlung emission into account and the Gaussian-Sum filter [45] where the Bethe-Heitler
distribution of the bremsstrahlungs loss is modeled by a weighted sum of Gaussian distributions.
At higher momenta, as the electron trajectory curvature is less pronounced, the combination of the
Inner Detector information with that of the electromagnetic calorimeter is needed to correct the
momentum underestimation.
The idea behind the bremsstrahlungs recovery with the electromagnetic calorimeter is basedon the following: In the simplest case of single photon emission, the barycenter of the cluster ofthe photon and the one of the electron after bremsstrahlung in the calorimeter coincides with theposition of the ideal electron without any bremsstrahlung activity. This is illustrated in figure 31.
This observation holds true also for any number of photons as long as the energy deposits from thephotons and electrons are fully reconstructed by the calorimeter cluster.
In ATLAS, given the standard size of the electromagnetic cluster (∆η × ∆φ = 3 × 7 in the LAr
middle cell unit), most of the time the energy deposits for the photon and electron are collected in
the same reconstructed cluster. In the standard ATLAS electron reconstruction a cluster and a trackthat geometrically matches this cluster are grouped together into an electron candidate object,
therefore only one single cluster can be provided to the bremsstrahlungs recovery algorithm. In a
dedicated electron reconstruction for the combined test-beam which allows more than one cluster
to be associated with a track, the barycenter of the clusters can be used in the bremsstrahlung
recovery algorithm.

– 42 –

2010 JINST 5 P11006

Figure 31. Sketch of an event with large bremsstrahlung emission. The solid line is the track of the electron, the dashed line the emitted bremsstrahlung photon and the dotted line the track of the electron if nobremsstrahlung had been emitted. The electromagnetic showers in the calorimeter are also shown. They
are usually reconstructed in a single cluster except for large bremsstrahlung emission. The energy-weighted
barycenter of the photon-electron system is the same as that of an electron without bremsstrahlung emission.

Events

Events3000
Monte Carlo simulation

2500

3000
Monte Carlo simulation

2500

Data

Data

2000

2000

1500

1500

1000

1000

500

500

0
-0.02

-0.01

0

0.01

0.02

0.03
ϕ

track

0.04
-ϕ

cluster

0
-0.02

0.05

-0.01

0

0.01

0.02

0.03
ϕ

(rad)

0.04
-ϕ

cluster

0.05
(rad)

(b) pbeam = 50 GeV/c

Figure 32. Distributions of XBrem = ϕtrack − ϕcluster , i.e. the distance in ϕ between the extrapolated track andthe calorimeter cluster, for various beam momenta.

In the CTB the Transition Radiation Tracker (TRT) is placed outside the magnet unlike in
the ATLAS configuration. Therefore in the CTB only bremsstrahlung occurrences in the precision
layers (Pixels and SCT) lead to momentum underestimation. The alignment between the electromagnetic calorimeter and the Inner Detector was crucial for this step and had to be adjusted
following a dedicated study using pion tracks, i.e. particle tracks with negligible bremsstrahlung
activity. In addition, while the Pixels and SCT modules alignment is final, the TRT has not been
completely aligned. Consequently, only the tracks reconstructed exclusively from Pixel and SCT
hits will be considered in this analysis.
Given a reconstructed track and cluster, the bremsstrahlungs recovery is implemented in thefollowing way: A track hit is chosen as a hypothetical point of bremsstrahlung emission. Then the
track hits in the track hit collection that are closer to the interaction vertex than the hypotheticalpoint of bremsstrahlung emission are refitted. This refitted track is extrapolated to the calorimeterand its distance to the cluster is computed. This distance is minimized by varying the chosen hypothetical point of bremsstrahlung emission yielding the computed point of bremsstrahlung emission.
Note that this stage the cluster position, itself a point in the three dimensional space, is used only
as a reference to the refitted track extrapolation but not in the refitting procedure itself. If the computed point of bremsstrahlung emission is found to be either in the Pixel layers or in the first SCT
layer, an additional step in the track fitting procedure is carried out in order to improve the tracking
resolution: This additional track refit is performed on the combination of the hit collection of the
track part close to the interaction vertex and the cluster position. Finally, the refitted track associated with the computed point of bremsstrahlung emission is used to estimate the inverse momentumof the initial electron.
6.1

Results with combined test beam data

The data samples used in the analysis are from run 2102446 for pbeam = 20 GeV/c and from run
2102400 for pbeam = 50 GeV/c.
The performance of the bremsstrahlungs recovery algorithm is investigated for different samples of events. First, samples of events with large bremsstrahlung emission are discussed. Next,– 43 –

2010 JINST 5 P11006(a) pbeam = 20 GeV/ctrack

MC Standard reconstruction
Data Standard reconstruction

500

EventsEvents600

MC Brem recovery

300
MC Standard reconstruction
Data Standard reconstruction

250

MC Brem recovery

Data Brem recovery

Data Brem recovery

400

200

300

150

200

100

100

50

0

0.04

0.06

0.08

0.1

0.12

0
0.01

0.14

0.02

0.03

0.04

0.05

1/pT (c/GeV)

0.06

1/pT (c/GeV)(b) pbeam = 50 GeV/c

Figure 33. Distributions of reconstructed and corrected 1/pT for large XBrem events for various beam momenta.

the performance is evaluated on samples of events with more than one reconstructed cluster in thecalorimeter. Finally, the performance of the bremsstrahlungs recovery algorithm is discussed forall events.
The detailed comparisons with CTB data necessitates a measure of bremsstrahlung activity
applicable to both, data and Monte Carlo simulation. A natural quantity is the distance in ϕ between
the extrapolated track and the calorimeter cluster, denoted XBrem = ϕtrack − ϕcluster . The cluster
position is relatively stable under bremsstrahlung (it usually collects most of the energy of thephoton and electron showers) while the track curvature becomes more pronounced in the case ofenergy loss due to bremsstrahlung. A larger XBrem means larger bremsstrahlung activity in the Inner
Detector. Figure 32 shows the distribution of XBrem for pbeam = 20 GeV/c and pbeam = 50 GeV/cwith the characteristic long asymmetric tails due to bremsstrahlung.
In order to investigate the impact of the bremsstrahlungs recovery algorithm on events withlarge bremsstrahlung emission, the 12% of events with largest XBrem are selected and denoted large
XBrem events. For pbeam = 20 GeV/c the corresponding cut is XBrem ≥ 10 mrad and for pbeam =50 GeV/c the corresponding cut is XBrem ≥ 5 mrad. Figure 33 shows the distributions of 1/pT
before and after bremsstrahlungs recovery for large XBrem events.
For large XBrem events the position of the peak of the reconstructed 1/pT distribution using
the standard reconstruction is closely related to the XBrem cut. The magnet used in the combined
test-beam had a bending power of 1.52 Tm. Without bremsstrahlung, a pbeam = 50 GeV/c electronis bent in ϕ by 9.1 mrad after crossing the Inner Detector. For an XBrem value of 5 mrad andassuming that the cluster collects all the energy which means that the ϕcluster is the same as withoutbremsstrahlung, ϕtrack is actually 14.1 mrad. This corresponds to a reconstructed 1/pT of about
0.03 GeV−1 c as shown by the peak in the reconstructed 1/pT distribution for pbeam =50 GeV/c forthe standard reconstruction in figure 33(b). With bremsstrahlung recovery, the 1/pT peak is around0.02 GeV−1 c as expected.
For a low momentum beam like pbeam = 20 GeV/c, if the bremsstrahlung occurs strongly andearly enough, the electron will be sufficiently bent by the magnetic field so that its cluster and thatof the photon are reconstructed separately in the calorimeter. Figure 34 shows the distribution of– 44 –

2010 JINST 5 P11006(a) pbeam = 20 GeV/c

Events

600
MC Standard reconstruction
Data Standard reconstruction

500

MC Brem recovery
Data Brem recovery

400
300

100
0

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1/pT (c/GeV)

1600
Standard reconstruction

1400

Brem recovery (single cluster)

1200

EventsEventsFigure 34. Distributions of reconstructed and corrected 1/pT for pbeam = 20 GeV/c for events with at least
2 reconstructed clusters.

103Standard reconstruction
Brem recovery (single cluster)Brem recovery (multiple cluster)Brem recovery (multiple cluster)

102

1000
800

10

600
400
200
0

1
0.04

0.06

0.08

0.1

0.12

0.14

0.04

0.06

0.08

0.1

1/pT (c/GeV)

0.12

0.14
1/pT (c/GeV)(a)(b) log scale

Figure 35. Distributions of 1/pT for the standard reconstruction, for the reconstruction with bremsstrahlungs
recovery using a single cluster and for the reconstruction with bremsstrahlungs recovery using a combinationof multiple clusters for Monte Carlo simulation for pbeam = 20 GeV/c.

1/pT before and after bremsstrahlungs recovery for events having at least two reconstructed 3 × 7
clusters for pbeam = 20 GeV/c. The reconstructed 1/pT exhibits a double-peak structure. The
small peak around 0.05 GeV−1 c represents events that do not have significant bremsstrahlung andthe second cluster is made essentially of noise. The fraction of these events is quite small, about– 45 –

2010 JINST 5 P11006

200

Events

Events

7000
Standard reconstruction

6000

Brem recovery (single cluster)Standard reconstruction
Brem recovery (single cluster)

103

Brem recovery (multiple cluster)

5000

Brem recovery (multiple cluster)

4000
102

3000
2000

10

1000
0

0.04

0.06

0.08

0.1

0.12

0.14

0.04

0.06

0.08

0.1

1/pT (c/GeV)

0.12

0.14
1/pT (c/GeV)(b) log scale

1400

EventsEventsFigure 36. Distributions of 1/pT for the standard reconstruction, for the reconstruction with bremsstrahlungs
recovery using a single cluster and for the reconstruction with bremsstrahlungs recovery using a combinationof multiple clusters for data for pbeam = 20 GeV/c.

Standard reconstruction

1200

Brem recovery (single cluster)

103Standard reconstruction
Brem recovery (single cluster)Brem recovery (multiple cluster)Brem recovery (multiple cluster)

1000
800

102

600
400
10

200
0
0.01

0.02

0.03

0.04

0.05

0.06

0.01

0.02

0.03

0.04

1/pT (c/GeV)

0.05

0.06

1/pT (c/GeV)(a)(b) log scale

Figure 37. Distributions of 1/pT for the standard reconstruction, for the reconstruction with bremsstrahlungs
recovery using a single cluster and for the reconstruction with bremsstrahlungs recovery using a combinationof multiple clusters for Monte Carlo simulation for pbeam = 50 GeV/c.
Table 8. Tail fractions of 1/pT before and after the bremsstrahlung correction using a single cluster or a
combination of multiple clusters. The quoted errors are statistical only.
pnominalbeam( GeV/c)20 GeV/c
50 GeV/c

SampleData
Monte Carlo
Data
Monte Carlo

Tail fraction
Standard reconstruction
0.090 ± 0.001
0.098 ± 0.001
0.091 ± 0.001
0.097 ± 0.001

Tail fraction
Brem recovery (single cluster)
0.078 ± 0.001
0.093 ± 0.001
0.034 ± 0.000
0.031 ± 0.000

Tail fraction
Brem recovery (multiple clusters)
0.012 ± 0.000
0.015 ± 0.000
0.034 ± 0.000
0.028 ± 0.000

300 events in 40, 000 events in total. The much broader peak around 0.09 GeV−1 c represents eventswith bremsstrahlung carrying around 50% of the original electron energy. It can be seen clearly– 46 –

2010 JINST 5 P11006(a)Events

Events

3000

Standard reconstruction
Brem recovery (single cluster)Standard reconstruction
Brem recovery (single cluster)
3

2500

10

Brem recovery (multiple cluster)Brem recovery (multiple cluster)

2000
1500
102
1000
500
0
0.01

0.02

0.03

0.04

0.05

0.06

0.01

0.02

0.03

0.04

1/pT (c/GeV)

0.05

0.06

1/pT (c/GeV)(b) log scale

Figure 38. Distributions of 1/pT for the standard reconstruction, for the reconstruction with bremsstrahlungs
recovery using a single cluster and for the reconstruction with bremsstrahlungs recovery using a combinationof multiple clusters for data for pbeam = 50 GeV/c.

that the correction permits to recover the original electron energy.
Overall, in both cases of large XBrem and multiple cluster events, there is a good agreement to
the level of 1 − 2% between the data and the Monte Carlo simulation.
Figure 35, figure 36, figure 37 and figure 38 show the distribution of 1/pT before and after
bremsstrahlungs recovery for all electrons. The bremsstrahlungs recovery is performed by using
the single ∆η × ∆φ = 3 × 7 cluster matching to the original track and by combining multiple 3 ×
7 clusters. These figures show that the bremsstrahlungs recovery reduces the tails of the 1/pT
distributions significantly, for the Monte Carlo simulation as well as for the data. In addition, forpbeam = 20 GeV/c the combination of multiple calorimeter clusters decreases the tails comparedto the single cluster method because for events with large bremsstrahlung emission the energy
deposition for the photon may not be sufficiently contained in the single cluster associated with theelectron. Therefore the position of the single cluster is far from the barycenter of the combinationof the cluster of the photon and the one of the electron yielding a performance of the single cluster
method comparable to the standard reconstruction for events with large bremsstrahlung emission.
In order to quantify the recovery power, a new figure of merit, the tail fraction, is introduced.
It is defined as the fraction of events with 1/pT above twice the nominal beam momentum value,i.e. > 2/pnominal
T,beam . The tail fractions before and after the bremsstrahlung correction using single ormultiple 3 × 7 clusters for pbeam = 20 GeV/c and pbeam = 50 GeV/c are summarized in table 8
demonstrating the improvements due to the bremsstrahlungs recovery algorithm.

7Intercalibration with E/p

This section presents a method to intercalibrate the energy scale of the electromagnetic calorimeterand the momentum scale of the Inner Detector. The intercalibration is performed by investigating the ratio E/p for electrons, i.e. the ratio of the energy E measured by the electromagnetic
calorimeter and the momentum p measured by the Inner Detector.

– 47 –

2010 JINST 5 P11006(a)1. Derive parameterizations for the E/pbeam and pbeam /p distributions. For this step, the knowledge of the beam momentum is necessary.
2. E/p is modeled by convoluting E/pbeam and pbeam /p. This can be done by treating E/pbeam
and pbeam /p as independent random variables or by taking their correlation into account.
The knowledge of the beam momentum is used for the description of the correlation. It
has been shown that for ATLAS, where single momentum datasets will not be available,
the correlations for the corresponding pT distributions can be extracted using Monte Carlosimulations and successfully applied to data [47].
3. The parameterization for E/p is fitted to the observed E/p distribution. All parameters
except a relative scale parameter are kept fixed to their values obtained in step 1.
The modeling of the E/p distribution is described in section 7.1. The details of the relative
scale extraction procedure are described in section 7.2 and results for combined test beam data andMonte Carlo simulation are shown in section 7.4.
7.1

Modeling the detector response functions

One way of modeling the E/pbeam distribution is to parameterize the energy loss in front of thecalorimeter and fold it with a generic Gaussian detector resolution. One can make the following– 48 –

2010 JINST 5 P11006

Ideally the ratio E/p is expected to be 1 (in units of c) for relativistic electrons measured by
the Inner Detector and the electromagnetic calorimeter. However, due to the fact that each of thedetectors has its intrinsic measurement resolution, in reality the ratio E/p will be a distribution that
depends strongly on the detector response functions (and their correlation) of the Inner Detector
and the electromagnetic calorimeter.
The key concept of this intercalibration method is to extract information for the detector response functions, such as e.g. their scale, of the electromagnetic calorimeter, i.e. E/pbeam , and of
the Inner Detector, i.e. pbeam /p, from a fit to the E/p distribution. In order to be able to achievethis, the E/p distribution has to be parameterized through the two individual detector response
functions E/pbeam and pbeam /p. Since E/pbeam and pbeam /p describe not necessarily uncorrelated
random variables, their correlation also has to be taken into account for the E/p parameterization.
Since the knowledge of the true momentum of the particles, i.e. pbeam , is necessary to obtain adescription of this correlation and this knowledge will not be available for ATLAS, the correlationis computed for Monte Carlo simulation.
The E/p parameterization is fitted to the observed E/p distribution and since it is built upon
the individual detector response functions, the fit parameters obtained from the E/p fit reflect theproperties of the individual response functions. This section is devoted to the extraction of therelative scale of the two individual response functions. Since in ATLAS the momentum scale ofthe Inner Detector is determined by the magnetic field that has been measured very precisely [46],the relative scale can be used to transform the momentum scale into the absolute energy scale ofthe electromagnetic calorimeter.
For each beam momentum pbeam the intercalibration is done in the following steps:

exponential ansatz to model the beam energy minus the energy lost upstream of the calorimeternormalized to the beam energyfe (ε ; τE , E0 ) :=

ε
1
τE E0
, ε < E0eτE E0 (eτE − 1)

(7.1)

where E0 is a scale parameter and τE describes the tail towards lower energies.
Next the generic detector resolution (without upstream material) can be modeled with a Gaussian with standard deviation σE :
2

(7.2)

Convoluting eq. (7.1) and eq. (7.2) to get the energy response of the calorimeter leads toE(ε ; τE , E0 , σE ) =
=

R E0
0

fe (x; τE , E0 ) D(ε − x; σE ) dx

2 
2ε E0 τE +σE




2 2
ε E0 τE +σE 2
ε E0 τE −E0 2 τE +σE 2√
Erf √2E
e 2E0 τE−Erf
τ σ
2E0 τE σE
0 E E 
12 e τE −1 E0 τE

(7.3)
,

where Erf(x) denotes the Gaussian error function defined by
Erf(x) =Z x
02

e−t dt.

(7.4)

The parameters τE , E0 , σE depend on the beam momentum pbeam and denote the tail, the scale andthe width of the distribution. The position of the peak of the distribution E(ε ; τE , E0 , σE ), denotedµe is a function of the parameters τE , E0 , σE , i.e. µe = µe (τE , E0 , σE ).
This parameterization is capable of describing the effect of additional material in front of
the electromagnetic calorimeter. Since additional material should not affect the intrinsic detector
resolution, only the parameter τE should change. For a beam momentum of 20 GeV/c additional
material equivalent to 10% of a radiation length was placed between the Pixel detector and the SCT
and additional 20% between the SCT and the TRT. The E/pbeam distribution without (solid line)
and with (dashed line) this additional material in the Inner Detector is shown in figure 39 together
with the corresponding fits with the convolution model. The obtained parameters are given intable 9. The two values of E0 (with and without additional material) are compatible within theerror bars, whereas µe is as expected slightly lower for the run with additional material. Thereis some correlation between the resolution σE and the tail parameter τE . The difference of theresolution σE for the different material description is of the order of 3 standard deviations, but the
tail parameter τE is approximately 7.5 standard deviations larger for the geometry description withadditional material demonstrating the sensitivity of this parameter to additional material in frontof the electromagnetic calorimeter. It has been shown in Monte Carlo simulations for the ATLAS
detector that the tail parameter τE can be extracted from the E/p distribution [47].
Although the convolution model describes the E/pbeam distributions at pbeam = 20 GeV/c very
well, the Crystal Ball model presented below describes the E/pbeam distributions far better at beam

– 49 –

2010 JINST 5 P11006

−x
1
2
e 2σE
D(x; σE ) := √2πσE

(c-1)
1 dN
N d E/p

beam

p
8

p

= 20 GeV/c, additional material

beam= 20 GeV/c

beam

6

4

0
0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

E/pbeam (c)Figure 39. The E/pbeam distribution for a beam momentum of pbeam = 20 GeV/c fitted with the convolution
model (equation (7.3)) without (solid line) and with (dashed line) additional material in the Inner Detector.

Table 9. The parameter values for the convolution model (eq. (7.3)) obtained from a fit to the E/pbeam
distribution for a beam momentum of pbeam = 20 GeV/c without (nominal) and with additional material in
the Inner Detector.
material
nominaladditionalτE (10−2)4.84(6)
5.78(11)σE (10−2)2.66(7)2.32(9)E01.0275(4)1.0267(7)µe (τE , E0 , σE )1.0013(5)1.0003(7)momenta above 20 GeV/c. The Crystal Ball model is therefore used for the combined test beam
2004 for E/pbeam distributions for the sake of consistency (see figure 21).
The Crystal Ball function [48], named after the Crystal Ball Collaboration, is a probability
density function commonly used to model various processes in high energy physics. It consists ofa Gaussian core part and a power-law low-end tail below a certain threshold. These two parts arespliced together (via the coefficients A and B) in such a way that the function and its first derivative
are both continuous. The Crystal Ball function fCB is given byfCB (x; α , n, µ , σ ) = N ·(µ)) for x−σ µ > −αexp(− (x−2σ 2A · (B − x−σ µ )−n for x−σ µ ≤ −α2– 50 –(7.5)

2010 JINST 5 P11006

2

where
!

n n
|α |2
A=
· exp −|α |2n− |α | .
B=
|α |


(7.6)

N is a normalization factor and α , n, µ and σ are parameters.
The model for the E/pbeam distribution, denoted E(ε ; αε , nε , µε , σε ), is given byE(ε ; αε , nε , µε , σε ) = c fCB (ε ; αε , nε , µε σε ),(7.7)

fmirror (x; α , n, µ , σ ) = fCB (µ − (x − µ ); α , n, µ , σ ) = fCB (2µ − x; α , n, µ , σ )(7.8)

with the Crystal Ball function defined in eq. (7.5) and eq. (7.6).
The model for the pbeam /p distribution, denoted Q(q; αq , nq , µq , σq ), is given byQ(q; αq , nq , µq , σq ) = fmirror (q; αq , nq , µq , σq ),(7.9)

where q = pbeam /p.
Treating the measurement variables ε and q as random variables, the distribution R of the
product r = ε · q, which describes the ratio E/p, is given by
Z ∞
r 1
,w
dw,
(7.10)
f(E,Q)
R(r) =
w
w−∞

where f(E,Q) (ε , q) denotes the joint distribution of ε and q. Using the parameterizations
E(ε ; αε , nε , µε , σε ) and Q(q; αq , nq , µq , σq ) for ε (eq. (7.7)) and q (eq. (7.9)) and the fact that E(ε )and Q(q) are always positive, the joint distribution can be rewritten asf(E,Q) (ε , q; αε , nε , µε , σε , αq , nq , µq , σq ) =E(ε ; αε , nε , µε , σε ) · Q(q; αq , nq , µq , σq ) ·C(ε , q), (7.11)

where C(ε , q) describes the correlation between ε and q. No correlation would be equivalent toC(ε , q) = 1. Inserting eq. (7.11) into eq. (7.10) leads toR(r; αε , nε , µε , σε , αq , nq , µq , σq ) =
Z ∞

1
r
r
E( ; αε , nε , µε , σε ) Q(w; αq , nq , µq , σq )C( , w) dw (7.12)
w
w
w
−∞

Two ways of dealing with the correlation between ε and q are considered in the following.

No correlation. It is assumed that there is no correlation between ε and q, i.e. ε and q are independent random variables. For the modeling this means C(ε , q) = 1 in equation (7.12). Thisshould be the case for high energy electrons where the impact of bremsstrahlung on the momentum
measurement is small. Later it will be shown that the correlation between ε and q has to be taken
into account in order to achieve a precision for the relative scale at the 0.5% level.

– 51 –

2010 JINST 5 P11006

where ε = E/pbeam . The parameters αε , nε , µε , σε depend on the beam momentum pbeam .
The pbeam /p distribution also is modeled using a Crystal Ball function that is mirrored at x = µwhich ispbeam/p

pbeam/p

2.2

2

10

1.8

2.2

2

10

1.8

1.6

1.6

1.4

1.4

1

1
1.2

1.2

1

1

0.8
0.75

10
0.8

0.85

0.9

0.95

1

1.05

-1

10-1

0.8

1.1

0.75

0.8

0.85

0.9

0.95

1

E/pbeam (c)

1.05

1.1

E/pbeam (c)(b) pbeam = 100 GeV/c

Figure 40. The joint distribution f(E,Q) (ε , q) (eq. (7.10)) for CTB data for pbeam = 20 GeV/c and pbeam =100 GeV/c.

Correlation obtained from Monte Carlo simulation. The continous function C(ε , q) in
eq. (7.11) can be approximated by discrete values for bins in ε and q. C(ε , q) is determined fromMonte Carlo simulations by performing the divisionC(ε , q) =f(E,Q) (ε , q)E(ε ) Q(q)(7.13)

bin-wise. In order to be able to compute C(ε , q) the knowledge of the beam momentum is necessary, but since the computation is performed bin-wise it is independent of the choice of theparameterizations for E(ε ) and Q(q).
The joint distributions f(E,Q) (ε , q) of ε and q for CTB data are shown for pbeam = 20 GeV/cand for pbeam = 100 GeV/c in figure 40, the correlation function C(ε , q) extracted from Monte
Carlo simulations together with its projection onto the E/pbeam axis for pbeam = 20 GeV/c in figure 41 and for pbeam = 100 GeV/c in figure 42. For pbeam = 20 GeV/c the correlation factor C(ε , q)derived from Monte Carlo simulation shows a gradient in the upper-left direction in the parameter
space resulting in a slope in the projection onto the E/pbeam axis in figure 41(a). This gradient becomes smaller for pbeam = 50 GeV/c and vanishes for pbeam = 80 GeV/c and pbeam = 100 GeV/cmaking the projection onto the E/pbeam axis in figure 42(a) constant within errors.
7.2

Scale factor extraction procedure

This procedure is applied for each beam momentum pbeam separately. The parameters α̂ε , n̂ε , µ̂ε , σ̂εare obtained by fitting the Crystal Ball parameterization E(ε ; αε , nε , µε , σε ) (eq. (7.7)) to theE/pbeam distribution. The parameters α̂q , n̂q , µ̂q , σ̂q are computed by fitting the mirror Crystal
Ball parameterization Q(q; αq , nq , µq , σq ) (eq. (7.9)) to the pbeam /p distribution. Then the scaleparameter µ̄ε for the E/pbeam distribution is calculated by fitting R(r; α̂ε , n̂ε , µ̄ε , σ̂ε , α̂q , n̂q , µ̂q , σ̂q )(eq. (7.12)) to the E/p distribution. In this fit only the µ̄ε parameter is allowed to vary. The otherparameters α̂ε , n̂ε , σ̂ε , α̂q , n̂q , µ̂q , σ̂q are fixed to the values obtained by the E/pbeam and pbeam /pfits, respectively. The relative scale factor is then defined by the ratio µ̄ε /µ̂ε .

– 52 –

2010 JINST 5 P11006(a) pbeam = 20 GeV/c

pbeam/p

2.5

2.2

2

2
1.8

1.6

1.5

1.4
1
1.2

1

0.5

0.8
0
0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

0.75

0.8

0.85

0.9

0.95

1

E/pbeam (c)

1.05

1.1

E/pbeam (c)(b) C(ε , q) for pbeam = 20 GeV/cpbeam/pFigure 41. Correlation factor C(ε , q) (eq. (7.13)) derived from Monte Carlo simulation (41(b)) and its
projection onto the E/pbeam axis (41(a)) for pbeam = 20 GeV/c.

1.6
1.4

2.2

2

1.2

1.8

1

1.6

0.8
1.4
0.6
1.2
0.4
1
0.2
0.8

0
0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

0.75

E/pbeam (c)

0.8

0.85

0.9

0.95

1

1.05

1.1

E/pbeam (c)(a) Projection of C(ε , q) for pbeam = 100 GeV/c(b) C(ε , q) for pbeam = 100 GeV/c

Figure 42. Correlation factor C(ε , q) (eq. (7.13)) derived from Monte Carlo simulation (42(b)) and its
projection onto the E/pbeam axis (42(a)) for pbeam = 100 GeV/c.

This procedure is based on the assumption that the relative scale factor is close to 1 and therefore the effect of the scaling of the parameters α̂ε , n̂ε , σ̂ε is negligible. Otherwise they would haveto be scaled accordingly.
7.3

Estimation of systematic errors

The procedure to extract the relative scale factor between the energy scale of the electromagnetic
calorimeter and the momentum scale of the inner detector has been validated using a dedicatedMonte Carlo simulation. The systematic error due to the scale extraction procedure is found to be
below 1 permil [47].
7.4

Results

The E/pbeam distribution with the fitted E(ε ; α̂ε , n̂ε , µ̂ε , σ̂ε ) model, the pbeam /p distribution with the fitted Q(q; α̂q , n̂q , µ̂q , σ̂q ) model and the E/pbeam distribution fitted with– 53 –

2010 JINST 5 P11006(a) Projection of C(ε , q) for pbeam = 20 GeV/c

1 dN
N pbeam
d p

(c-1)
1 dN
N d E/p

beam

0.16
0.14

0.25

0.2

0.12
0.1

0.15
0.08
0.1

0.06
0.04

0.05
0.02
0

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

0

1.1

0

0.5

1

1.5

2

2.5

1 d N (c-1)
N d E/p

1 d N (c-1)
N d E/p

0.25

0.3

0.25

0.2

0.2

0.15

0.15

0.1

0.1

0.05

0.05

0

0

0.5

1

1.5

2

2.5

0

3

E/p (c)

0

0.5

1

1.5

2

2.5

3

E/p (c)Figure 43. Monte Carlo simulation: The E/pbeam distribution with the fitted E(ε ; α̂ε , n̂ε , µ̂ε , σ̂ε ) model(top left), the pbeam /p distribution with the fitted Q(q; α̂q , n̂q , µ̂q , σ̂q ) model (top right) and the E/p distribution fitted with R(r; α̂ε , n̂ε , µ̄ε , σ̂ε , α̂q , n̂q , µ̂q , σ̂q ) without (bottom left) and with (bottom right) Monte Carlosimulation correlation modeling for Monte Carlo simulation for pbeam = 20 GeV/c.

R(r; α̂ε , n̂ε , µ̄ε , σ̂ε , α̂q , n̂q , µ̂q , σ̂q ) without and with Monte Carlo simulation correlation modelingare shown in figure 43 (Monte Carlo simulation) and figure 44 (data) for pbeam =20 GeV/c. The
number of events after all cuts is given in table 1.
Figures 43 and 44 show that for pbeam = 20 GeV/c the modeling of the correlation between
ε and q is needed to improve the description of the shape of the E/p distributions. The E/p
distribution for data for pbeam = 20 GeV/c is not perfectly described by applying the correlation
obtained from the Monte Carlo simulation implying that the correlation is larger in data than in theMonte Carlo simulation.
The relative scale factor µ̄ε /µ̂ε without and with Monte Carlo simulation correlation modelingis shown in figure 45 for all beam momenta. A value of 1 is expected for all beam momenta. For
pbeam = 80 GeV/c and higher the modeling of the correlation between ε and q does not improve therelative scale factor. For pbeam = 50 GeV/c and specially for pbeam = 20 GeV/c the modeling of
the correlation between ε and q brings the relative scale factor down to the 2 respectively 5 permill
level. Within the available statistics, the uncertainties on the relative scale factor are comparablewith the expectation from the dedicated validation Monte Carlo simulation model.
This demonstrates that for the CTB 2004 a Monte Carlo simulation correlation modeling canbe used to extract the relative scale factor µ̄ε /µ̂ε from the data and therefore a similar approach– 54 –

2010 JINST 5 P11006

0.3

3

pbeam
p

E/pbeam (c)1 dN
N pbeam
d p

(c-1)
1 dN
N d E/p

beam

0.16
0.14

0.25

0.2

0.12
0.1

0.15
0.08
0.1

0.06
0.04

0.05
0.02
0

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

0

1.1

0

0.5

1

1.5

2

2.5

1 d N (c-1)
N d E/p

1 d N (c-1)
N d E/p

0.25

0.3

0.25

0.2

0.2

0.15

0.15

0.1

0.1

0.05

0.05

0

0

0.5

1

1.5

2

2.5

0

3

0

0.5

1

1.5

2

2.5

E/p (c)3

E/p (c)1.02µε / µεµε / µεFigure 44. CTB data: The E/pbeam distribution with the fitted E(ε ; α̂ε , n̂ε , µ̂ε , σ̂ε ) model (top left), thepbeam /p distribution with the fitted Q(q; α̂q , n̂q , µ̂q , σ̂q ) model (top right) and the E/p distribution fittedwith R(r; α̂ε , n̂ε , µ̄ε , σ̂ε , α̂q , n̂q , µ̂q , σ̂q ) without (bottom left) and with (bottom right) Monte Carlo simulation
correlation modeling for CTB data for pbeam = 20 GeV/c.

Data
1.015

1.02

Data
1.015

MC

MC

1.01

1.01

1.005

1.005

1

1

0.995

0.995

0.99
10

20

30

40

50

60

70

80

90

0.99
10

100

20

30

40

50

60

70

pbeam (GeV/c)

80

90

100

pbeam (GeV/c)(a) without correlation(b) with correlation

Figure 45. The relative scale factor µ̄ε /µ̂ε extracted from the E/p distributions without (figure 45(a)) andwith (figure 45(b)) correlation weighting for Monte Carlo simulation and data for all beam momenta.

will be used for ATLAS. The description of the correlation should be easier for ATLAS since thematerial distribution upstream of the electromagnetic calorimeter is much better understood for
ATLAS than for the CTB 2004 due to the presence of the far upstream material at the CTB 2004.

– 55 –

2010 JINST 5 P11006

0.3

3

pbeam
p

E/pbeam (c)8Conclusions

The combined performance for electrons of a barrel segment of the ATLAS detector has been
evaluated in the 2004 combined test-beam in conditions close to those expected in ATLAS. Readout electronics and data acquisition were early versions of those used in ATLAS.
It has been shown that the Monte Carlo simulation describes well all important distributions ofmeasured variables for the Inner Detector and the LAr calorimeter with the presence of a magnetic
field in the Inner Detector.

A probability based approach for the particle identification with the Transition Radiation
Tracker has been applied for both High Threshold (HT) hits and Time-over-Threshold (ToT) information. For HT information, the probability based particle identification gives a pion rejection
factor of 9 to 40 depending on the particle momentum at 90% electron efficiency. This is an improvement of 13% to 30% compared to using only the number of HT hits as separation criteria.
Furthermore, including the ToT information increases the rejection power to 25 to 70, mostly at
low momenta as expected. In addition, the onset of transition radiation has been measured in adata-driven way using the variety of momenta and particle types at the 2004 combined test-beamwhich is crucial for tuning the Monte Carlo simulation of the transition radiation.
The bremsstrahlung recovery algorithm using the calorimeter has been investigated using
Monte Carlo simulation for the 2004 combined test-beam setup. It has been demonstrated thatthe correction algorithm is able to recover the initial electron momentum, even in extreme situations where the photon and electron clusters are reconstructed separately in the calorimeter, byremoving the bremsstrahlung tail in the 1/pT distribution. A detailed comparison of performancewith 2004 combined test-beam data shows an agreement with the Monte Carlo simulation at thelevel of 1–2%.
It has been demonstrated that the E/p parameterization based on a Monte Carlo simulation
correlation modeling can be used to extract the electromagnetic scale from data with a precision of
better than 0.5% with the available statistics.
These combined performance studies at the 2004 combined test-beam give strong evidence
that the performance of the ATLAS detector for electrons will be within the requirements imposedby the ATLAS physics program.

– 56 –

2010 JINST 5 P11006

The calibration of the energy measurement for electrons with the presence of a magnetic fieldhas been investigated and the differences with respect to the calibration without magnetic field havebeen analyzed. The parameterization of the energy deposit in the calorimeter as a function of theshower depth cannot be used at the 2004 combined test-beam due to the larger out-of-cluster energy
deposits at lower beam momenta which stem from the larger distances between the Inner Detector
and the calorimeter set-up. The linearity obtained is 0.28% for the momentum range of 20 to
100 GeV/c which is within the estimated systematic uncertainties coming from statistics and fromthe beam energies. The stochastic term of the energy resolution is (10.0 ± 0.1)% GeV1/2 , with anaverage electronic noise term of about 208 MeV. This is compatible with previous test beam results
without magnetic field and fulfills the physics requirements for the ATLAS LAr calorimeter. The
2004 combined test-beam showed that the calibration procedure of the ATLAS electromagnetic
calorimeter for electrons works as expected in very realistic conditions.

Acknowledgments
We are grateful to our colleagues from the accelerator department for the support in running the H8beam line. We are indebted to our technicians and engineers for their contribution to the construction, testing and the operation of the detector modules, cooling systems and electronics. Those of
us from non-member states wish to thank CERN for its hospitality.

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[18] F. Bauer et al., Large-scale production of monitored drift tube chambers for the ATLAS muon
spectrometer, Nucl. Instrum. Meth. A 518 (2004) 69.
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