Model-Independent and Quasi-Model-Independent Search for New Physics at CDF

T. Aaltonen,23 A. Abulencia,24 J. Adelman,13 T. Akimoto,54 M.G. Albrow,17 B. Álvarez González,11 S. Amerio,42

D. Amidei,34 A. Anastassov,51 A. Annovi,19 J. Antos,14 G. Apollinari,17 A. Apresyan,47 T. Arisawa,56 A. Artikov,15
W. Ashmanskas,17 A. Aurisano,52 F. Azfar,41 P. Azzi-Bacchetta,42 P. Azzurri,45 N. Bacchetta,42 W. Badgett,17
V.E. Barnes,47 B.A. Barnett,25 S. Baroiant,7 V. Bartsch,30 G. Bauer,32 P.-H. Beauchemin,33 F. Bedeschi,45
P. Bednar,14 S. Behari,25 G. Bellettini,45 J. Bellinger,58 A. Belloni,32 D. Benjamin,16 A. Beretvas,17 T. Berry,29
A. Bhatti,49 M. Binkley,17 D. Bisello,42 I. Bizjak,30 R.E. Blair,2 C. Blocker,6 B. Blumenfeld,25 A. Bocci,16
A. Bodek,48 V. Boisvert,48 G. Bolla,47 A. Bolshov,32 D. Bortoletto,47 J. Boudreau,46 A. Boveia,10 B. Brau,10
L. Brigliadori,5 C. Bromberg,35 E. Brubaker,13 J. Budagov,15 H.S. Budd,48 S. Budd,24 K. Burkett,17 G. Busetto,42
P. Bussey,21 A. Buzatu,33 K. L. Byrum,2 S. Cabrerar ,16 M. Campanelli,35 M. Campbell,34 F. Canelli,17
A. Canepa,44 D. Carlsmith,58 R. Carosi,45 S. Carrillol ,18 S. Carron,33 B. Casal,11 M. Casarsa,17 A. Castro,5
P. Catastini,45 D. Cauz,53 A. Cerri,28 L. Cerritop ,30 S.H. Chang,27 Y.C. Chen,1 M. Chertok,7 G. Chiarelli,45
arXiv:0712.1311v2 [hep-ex] 13 Jul 2008

G. Chlachidze,17 F. Chlebana,17 K. Cho,27 D. Chokheli,15 J.P. Chou,22 G. Choudalakis,32 S.H. Chuang,51

K. Chung,12 W.H. Chung,58 Y.S. Chung,48 C.I. Ciobanu,24 M.A. Ciocci,45 A. Clark,20 D. Clark,6 G. Compostella,42
M.E. Convery,17 J. Conway,7 B. Cooper,30 K. Copic,34 M. Cordelli,19 G. Cortiana,42 F. Crescioli,45
C. Cuenca Almenarr ,7 J. Cuevaso ,11 R. Culbertson,17 J.C. Cully,34 D. Dagenhart,17 M. Datta,17 T. Davies,21
P. de Barbaro,48 S. De Cecco,50 A. Deisher,28 G. De Lentdeckerd,48 M. Dell’Orso,45 L. Demortier,49 J. Deng,16
M. Deninno,5 D. De Pedis,50 P.F. Derwent,17 G.P. Di Giovanni,43 C. Dionisi,50 B. Di Ruzza,53 J.R. Dittmann,4
S. Donati,45 P. Dong,8 J. Donini,42 T. Dorigo,42 S. Dube,51 J. Efron,38 R. Erbacher,7 D. Errede,24 S. Errede,24
R. Eusebi,17 H.C. Fang,28 S. Farrington,29 W.T. Fedorko,13 R.G. Feild,59 M. Feindt,26 J.P. Fernandez,31
C. Ferrazza,45 R. Field,18 G. Flanagan,47 R. Forrest,7 S. Forrester,7 M. Franklin,22 J.C. Freeman,28 I. Furic,18
M. Gallinaro,49 J. Galyardt,12 F. Garberson,10 J.E. Garcia,45 A.F. Garfinkel,47 H. Gerberich,24 D. Gerdes,34
S. Giagu,50 P. Giannetti,45 K. Gibson,46 J.L. Gimmell,48 C. Ginsburg,17 N. Giokarisa ,15 M. Giordani,53
P. Giromini,19 M. Giunta,45 V. Glagolev,15 D. Glenzinski,17 M. Gold,36 N. Goldschmidt,18 J. Goldsteinc ,41
A. Golossanov,17 G. Gomez,11 G. Gomez-Ceballos,32 M. Goncharov,52 O. González,31 I. Gorelov,36
A.T. Goshaw,16 K. Goulianos,49 A. Gresele,42 S. Grinstein,22 C. Grosso-Pilcher,13 R.C. Group,17 U. Grundler,24
J. Guimaraes da Costa,22 Z. Gunay-Unalan,35 K. Hahn,32 S.R. Hahn,17 E. Halkiadakis,51 A. Hamilton,20
B.-Y. Han,48 J.Y. Han,48 R. Handler,58 F. Happacher,19 K. Hara,54 D. Hare,51 M. Hare,55 S. Harper,41 R.F. Harr,57
R.M. Harris,17 M. Hartz,46 K. Hatakeyama,49 J. Hauser,8 C. Hays,41 M. Heck,26 A. Heijboer,44 J. Heinrich,44
C. Henderson,32 M. Herndon,58 J. Heuser,26 S. Hewamanage,4 D. Hidas,16 C.S. Hillc ,10 D. Hirschbuehl,26
A. Hocker,17 S. Hou,1 M. Houlden,29 S.-C. Hsu,9 B.T. Huffman,41 R.E. Hughes,38 U. Husemann,59 J. Huston,35
J. Incandela,10 G. Introzzi,45 M. Iori,50 A. Ivanov,7 B. Iyutin,32 E. James,17 B. Jayatilaka,16 D. Jeans,50 E.J. Jeon,27
S. Jindariani,18 W. Johnson,7 M. Jones,47 K.K. Joo,27 S.Y. Jun,12 J.E. Jung,27 T.R. Junk,24 T. Kamon,52 D. Kar,18
P.E. Karchin,57 Y. Kato,40 R. Kephart,17 U. Kerzel,26 V. Khotilovich,52 B. Kilminster,38 D.H. Kim,27 H.S. Kim,27
J.E. Kim,27 M.J. Kim,17 S.B. Kim,27 S.H. Kim,54 Y.K. Kim,13 N. Kimura,54 L. Kirsch,6 S. Klimenko,18 M. Klute,32
B. Knuteson,32 B.R. Ko,16 S.A. Koay,10 K. Kondo,56 D.J. Kong,27 J. Konigsberg,18 A. Korytov,18 A.V. Kotwal,16
J. Kraus,24 M. Kreps,26 J. Kroll,44 N. Krumnack,4 M. Kruse,16 V. Krutelyov,10 T. Kubo,54 S. E. Kuhlmann,2
T. Kuhr,26 N.P. Kulkarni,57 Y. Kusakabe,56 S. Kwang,13 A.T. Laasanen,47 S. Lai,33 S. Lami,45 M. Lancaster,30
R.L. Lander,7 K. Lannon,38 A. Lath,51 G. Latino,45 I. Lazzizzera,42 T. LeCompte,2 J. Lee,48 J. Lee,27 Y.J. Lee,27
S.W. Leeq ,52 R. Lefèvre,20 N. Leonardo,32 S. Leone,45 S. Levy,13 J.D. Lewis,17 C. Lin,59 M. Lindgren,17
E. Lipeles,9 A. Lister,7 D.O. Litvintsev,17 T. Liu,17 N.S. Lockyer,44 A. Loginov,59 M. Loreti,42 L. Lovas,14
R.-S. Lu,1 D. Lucchesi,42 J. Lueck,26 C. Luci,50 P. Lujan,28 P. Lukens,17 G. Lungu,18 L. Lyons,41 R. Lysak,14
E. Lytken,47 P. Mack,26 D. MacQueen,33 R. Madrak,17 K. Maeshima,17 K. Makhoul,32 T. Maki,23 P. Maksimovic,25
S. Malde,41 S. Malik,30 A. Manousakisa,15 F. Margaroli,47 C. Marino,26 C.P. Marino,24 A. Martin,59 M. Martin,25
V. Martinj ,21 R. Martı́nez-Balları́n,31 T. Maruyama,54 P. Mastrandrea,50 T. Masubuchi,54 M.E. Mattson,57
P. Mazzanti,5 K.S. McFarland,48 P. McIntyre,52 R. McNultyi ,29 A. Mehta,29 P. Mehtala,23 S. Menzemerk ,11
A. Menzione,45 P. Merkel,47 C. Mesropian,49 A. Messina,35 T. Miao,17 N. Miladinovic,6 J. Miles,32 R. Miller,35
C. Mills,22 M. Milnik,26 A. Mitra,1 G. Mitselmakher,18 H. Miyake,54 S. Moed,20 N. Moggi,5 C.S. Moon,27
R. Moore,17 M. Morello,45 P. Movilla Fernandez,28 S. Mrenna,17 J. Mülmenstädt,28 A. Mukherjee,17 Th. Muller,26
R. Mumford,25 P. Murat,17 M. Mussini,5 J. Nachtman,17 Y. Nagai,54 A. Nagano,54 J. Naganoma,56 K. Nakamura,54
I. Nakano,39 A. Napier,55 V. Necula,16 C. Neu,44 M.S. Neubauer,24 L. Nodulman,2 M. Norman,9 O. Norniella,24
E. Nurse,30 S.H. Oh,16 Y.D. Oh,27 I. Oksuzian,18 T. Okusawa,40 R. Orava,23 K. Osterberg,23 S. Pagan Griso,42
C. Pagliarone,45 E. Palencia,17 V. Papadimitriou,17 A. Papaikonomou,26 A.A. Paramonov,13 B. Parks,38
2

S. Pashapour,33 J. Patrick,17 G. Pauletta,53 M. Paulini,12 C. Paus,32 D.E. Pellett,7 A. Penzo,53 T.J. Phillips,16
G. Piacentino,45 J. Piedra,43 L. Pinera,18 K. Pitts,24 C. Plager,8 L. Pondrom,58 O. Poukhov,15 N. Pounder,41
F. Prakoshyn,15 A. Pronko,17 J. Proudfoot,2 F. Ptohosh,17 G. Punzi,45 J. Pursley,58 J. Rademackerc,41
A. Rahaman,46 V. Ramakrishnan,58 N. Ranjan,47 I. Redondo,31 B. Reisert,17 V. Rekovic,36 P. Renton,41
M. Rescigno,50 S. Richter,26 F. Rimondi,5 L. Ristori,45 A. Robson,21 T. Rodrigo,11 E. Rogers,24 R. Roser,17
M. Rossi,53 R. Rossin,10 P. Roy,33 A. Ruiz,11 J. Russ,12 V. Rusu,17 H. Saarikko,23 A. Safonov,52 W.K. Sakumoto,48
G. Salamanna,50 L. Santi,53 S. Sarkar,50 L. Sartori,45 K. Sato,17 A. Savoy-Navarro,43 T. Scheidle,26 P. Schlabach,17
E.E. Schmidt,17 M.P. Schmidt,59 M. Schmitt,37 T. Schwarz,7 L. Scodellaro,11 A.L. Scott,10 A. Scribano,45
F. Scuri,45 A. Sedov,47 S. Seidel,36 Y. Seiya,40 A. Semenov,15 L. Sexton-Kennedy,17 A. Sfyrla,20 S.Z. Shalhout,57
T. Shears,29 P.F. Shepard,46 D. Sherman,22 M. Shimojiman ,54 M. Shochet,13 Y. Shon,58 I. Shreyber,20 A. Sidoti,45
A. Sisakyan,15 A.J. Slaughter,17 J. Slaunwhite,38 K. Sliwa,55 J.R. Smith,7 F.D. Snider,17 R. Snihur,33
M. Soderberg,34 A. Soha,7 S. Somalwar,51 V. Sorin,35 J. Spalding,17 F. Spinella,45 T. Spreitzer,33 P. Squillacioti,45
M. Stanitzki,59 R. St. Denis,21 B. Stelzer,8 O. Stelzer-Chilton,41 D. Stentz,37 J. Strologas,36 D. Stuart,10 J.S. Suh,27
A. Sukhanov,18 H. Sun,55 I. Suslov,15 T. Suzuki,54 A. Taffarde ,24 R. Takashima,39 Y. Takeuchi,54 R. Tanaka,39
M. Tecchio,34 P.K. Teng,1 K. Terashi,49 J. Thomg ,17 A.S. Thompson,21 G.A. Thompson,24 E. Thomson,44
P. Tipton,59 V. Tiwari,12 S. Tkaczyk,17 D. Toback,52 S. Tokar,14 K. Tollefson,35 T. Tomura,54 D. Tonelli,17
S. Torre,19 D. Torretta,17 S. Tourneur,43 Y. Tu,44 N. Turini,45 F. Ukegawa,54 S. Uozumi,54 S. Vallecorsa,20
N. van Remortel,23 A. Varganov,34 E. Vataga,36 F. Vázquezl ,18 G. Velev,17 C. Vellidisa ,45 V. Veszpremi,47
M. Vidal,31 R. Vidal,17 I. Vila,11 R. Vilar,11 T. Vine,30 M. Vogel,36 G. Volpi,45 F. Würthwein,9 P. Wagner,44
R.G. Wagner,2 R.L. Wagner,17 J. Wagner,26 W. Wagner,26 R. Wallny,8 S.M. Wang,1 A. Warburton,33 D. Waters,30
M. Weinberger,52 W.C. Wester III,17 B. Whitehouse,55 D. Whitesone ,44 A.B. Wicklund,2 E. Wicklund,17
G. Williams,33 H.H. Williams,44 P. Wilson,17 B.L. Winer,38 P. Wittichg ,17 S. Wolbers,17 C. Wolfe,13 T. Wright,34
X. Wu,20 S.M. Wynne,29 S. Xie,32 A. Yagil,9 K. Yamamoto,40 J. Yamaoka,51 T. Yamashita,39 C. Yang,59
U.K. Yangm ,13 Y.C. Yang,27 W.M. Yao,28 G.P. Yeh,17 J. Yoh,17 K. Yorita,13 T. Yoshida,40 G.B. Yu,48 I. Yu,27
S.S. Yu,17 J.C. Yun,17 L. Zanello,50 A. Zanetti,53 I. Zaw,22 X. Zhang,24 Y. Zhengb ,8 and S. Zucchelli5
(CDF Collaboration∗)
1
Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2
Argonne National Laboratory, Argonne, Illinois 60439
3
Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain
4
Baylor University, Waco, Texas 76798
5
Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
6
Brandeis University, Waltham, Massachusetts 02254
7
University of California, Davis, Davis, California 95616
8
University of California, Los Angeles, Los Angeles, California 90024
9
University of California, San Diego, La Jolla, California 92093
10
University of California, Santa Barbara, Santa Barbara, California 93106
11
Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
12
Carnegie Mellon University, Pittsburgh, PA 15213
13
Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637
14
Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia
15
Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
16
Duke University, Durham, North Carolina 27708
17
Fermi National Accelerator Laboratory, Batavia, Illinois 60510
18
University of Florida, Gainesville, Florida 32611
19
Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
20
University of Geneva, CH-1211 Geneva 4, Switzerland
21
Glasgow University, Glasgow G12 8QQ, United Kingdom
22
Harvard University, Cambridge, Massachusetts 02138
23
Division of High Energy Physics, Department of Physics,
University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland
24
University of Illinois, Urbana, Illinois 61801
25
The Johns Hopkins University, Baltimore, Maryland 21218
26
Institut für Experimentelle Kernphysik, Universität Karlsruhe, 76128 Karlsruhe, Germany
27
Center for High Energy Physics: Kyungpook National University,
Taegu 702-701, Korea; Seoul National University, Seoul 151-742,
Korea; SungKyunKwan University, Suwon 440-746,
Korea; Korea Institute of Science and Technology Information, Daejeon,
305-806, Korea; Chonnam National University, Gwangju, 500-757, Korea
 3

28
Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720
29
University of Liverpool, Liverpool L69 7ZE, United Kingdom
30
University College London, London WC1E 6BT, United Kingdom
31
Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain
32
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
33
Institute of Particle Physics: McGill University, Montréal,
Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7
34
University of Michigan, Ann Arbor, Michigan 48109
35
Michigan State University, East Lansing, Michigan 48824
36
University of New Mexico, Albuquerque, New Mexico 87131
37
Northwestern University, Evanston, Illinois 60208
38
The Ohio State University, Columbus, Ohio 43210
39
Okayama University, Okayama 700-8530, Japan
40
Osaka City University, Osaka 588, Japan
41
University of Oxford, Oxford OX1 3RH, United Kingdom
42
University of Padova, Istituto Nazionale di Fisica Nucleare,
Sezione di Padova-Trento, I-35131 Padova, Italy
43
LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France
44
University of Pennsylvania, Philadelphia, Pennsylvania 19104
45
Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa,
Siena and Scuola Normale Superiore, I-56127 Pisa, Italy
46
University of Pittsburgh, Pittsburgh, Pennsylvania 15260
47
Purdue University, West Lafayette, Indiana 47907
48
University of Rochester, Rochester, New York 14627
49
The Rockefeller University, New York, New York 10021
50
Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1,
University of Rome “La Sapienza,” I-00185 Roma, Italy
51
Rutgers University, Piscataway, New Jersey 08855
52
Texas A&M University, College Station, Texas 77843
53
Istituto Nazionale di Fisica Nucleare, University of Trieste/ Udine, Italy
54
University of Tsukuba, Tsukuba, Ibaraki 305, Japan
55
Tufts University, Medford, Massachusetts 02155
56
Waseda University, Tokyo 169, Japan
57
Wayne State University, Detroit, Michigan 48201
58
University of Wisconsin, Madison, Wisconsin 53706
59
Yale University, New Haven, Connecticut 06520
Data collected in Run II of the Fermilab Tevatron are searched for indications of new electroweak
scale physics. Rather than focusing on particular new physics scenarios, CDF data are analyzed
for discrepancies with respect to the standard model prediction. A model-independent approach
(Vista) considers the gross features of the data, and is sensitive to new large cross section physics.
A quasi-model-independent approach (Sleuth) searches for a significant excess of events with large
summed transverse momentum, and is particularly sensitive to new electroweak scale physics that
appears predominantly in one final state. This global search
√ for new physics in over three hundred
exclusive final states in 927 pb−1 of pp̄ collisions at s = 1.96 TeV reveals no such significant
indication of physics beyond the standard model.

∗ With visitors from a University of Athens, 15784 Athens, Greece,

b Chinese Academy of Sciences, Beijing 100864, China, c University
University, Lubbock, TX 79409, r IFIC(CSIC-Universitat de Valen-
of Bristol, Bristol BS8 1TL, United Kingdom, d University Libre
cia), 46071 Valencia, Spain.
de Bruxelles, B-1050 Brussels, Belgium, e University of California,
Irvine, Irvine, CA 92697, f University of California Santa Cruz,
Santa Cruz, CA 95064, g Cornell University, Ithaca, NY 14853,
h University of Cyprus, Nicosia CY-1678, Cyprus, i University Col-

lege Dublin, Dublin 4, Ireland, j University of Edinburgh, Edin-

burgh EH9 3JZ, United Kingdom, k University of Heidelberg, D-
69120 Heidelberg, Germany, l Universidad Iberoamericana, Mexico
D.F., Mexico, m University of Manchester, Manchester M13 9PL,
England, n Nagasaki Institute of Applied Science, Nagasaki, Japan,
o University de Oviedo, E-33007 Oviedo, Spain, p Queen Mary’s Col-

lege, University of London, London, E1 4NS, England, q Texas Tech

4

Contents I. INTRODUCTION

I. Introduction 4 In the past thirty years of frontier energy collider

physics, the only objects discovered were those for which
II. Strategy 4 the predictions were definite. The W and Z bosons (dis-
covered at CERN in 1983 [1, 2, 3, 4]) and the top quark
III. Vista 5 (discovered at Fermilab in 1995 [5, 6]) were well known
A. CDF II detector 5 objects long before their discoveries, with all quantum
B. Object identification 6 numbers but mass uniquely specified. The present situa-
C. Event selection 6 tion is qualitatively different, with plausible predictions
D. Event generation 7 for physics lying beyond the standard model running the
E. Detector simulation 8 gamut of possible experimental signatures.
F. Correction model 8 Searches for physics beyond the standard model typi-
G. Results 13 cally begin with a particular model. A region is selected
in the data where the model’s expected contribution is
IV. Sleuth 15 enhanced, and the extent to which the data (dis)favor
A. Algorithm 15 the model is determined by comparing the prediction to
1. Final states 15 data.
2. Variable 16 The state of the theoretical landscape and the vastness
3. Regions 16 of most model spaces suggests the utility of searching in
4. Output 17 a different space altogether. The experimental space, de-
B. Sensitivity 17 fined by the isolated and energetic objects observed in
1. Known standard model processes 17 frontier energy collisions, forms a natural space to con-
2. Specific models of new physics 19 sider.
C. Results 21 This article describes a systematic and model-
independent look (Vista) at gross features of the data,
V. Conclusions 23 and a quasi-model-independent search (Sleuth) for new
physics at high transverse momentum. These global al-
Acknowledgments 23 gorithms provide a complementary approach to searches
optimized for more specific new physics scenarios.
A. Vista correction model details 24
1. Fake rate physics 24
2. Additional background sources 29 II. STRATEGY
a. Cosmic ray and beam halo muons 29
b. Multiple interactions 31
The search for new physics described in this article is
c. Intrinsic kT 31
designed with the intention of maximizing the chance for
3. Global fit 32
discovery, and not excluding model parameter space if no
a. χ2k 32
discrepancy is found. Discrepancies between data and a
b. χ2constraints 32
complete standard model background estimate are iden-
c. Covariance matrix 33 tified in a global sample of high transverse momentum
4. Correction factor values 33 (high-pT ) collision events. Three statistics are employed
a. k-factors 33 to identify and quantify disagreement: populations of ex-
b. Identification efficiencies 36 clusive final states defined by the objects the events con-
c. Fake rates 36 tain, shapes of kinematic distributions, and excesses on
d. Trigger efficiencies 37 the tail of summed scalar transverse momentum distri-
e. Energy scales 37 butions.
The Vista [51] algorithm provides a global study of the
B. Sleuth details 37 standard model prediction and CDF detector response in
1. Partitioning 37 the bulk of the high-pT data; an algorithm called Sleuth
2. Minimum number of events 37 complements this with a search for possibly small cross
section physics in the high-pT tails. The purpose of these
References 38
algorithms is to identify discrepancies worthy of further
consideration.
A claim of discovery requires convincing arguments
that the observed discrepancy between data and stan-
dard model prediction

1. is not a statistical fluctuation,

 5

2. is not due to a mismodeling of the detector re- This search for new physics terminates when one of
sponse, and two conditions are satisfied: either a compelling case for
new physics is made, or there remain no statistically sig-
3. is not due to an inadequate implementation of the nificant discrepancies on which a new physics case can
standard model prediction, be made. In the former case, to quantitatively assess
the significance of the potential discovery, a full treat-
and therefore must be due to new underlying physics. ment of systematic uncertainties must be implemented.
Any observed discrepancy is subject to scrutiny, and ex- In the latter case, it is sufficient to demonstrate that all
planations are sought in terms of the above points. observed effects are not in significant disagreement with
The Vista and Sleuth algorithms provide a means for an appropriate global Standard Model description.
making the above three arguments, with a high threshold
placed on the statistical significance of a discrepancy in
order to minimize the chance of a false discovery claim. III. VISTA
As described later, this threshold is the requirement that
the false discovery rate is less than 0.001, after taking into
This section describes Vista: object identification,
account the total number of final states, distributions, or
event selection, estimation of standard model back-
regions being examined.
grounds, simulation of the CDF detector response, de-
This analysis employs a correction model implement- velopment of a correction model, and results.
ing specific hypotheses to account for mismodeling of de-
tector response and imperfect implementation of stan-
dard model prediction. Achieving this on the entire high-
pT dataset requires a framework for quickly implement- A. CDF II detector
ing and testing modifications to the correction model.
The specific details of the correction model are intention- CDF II is a general purpose detector [7, 8] designed
ally kept as simple as possible in the interest of trans- to detect particles produced in pp̄ collisions. The detec-
parency in the event of a possible new physics claim. tor has a cylindrical layout centered on the accelerator
Vista’s toolkit includes a global comparison of data to beamline.
the standard model prediction, with a check of thousands CDF uses a cylindrical coordinate system with the z-
of kinematic distributions and an easily adjusted correc- axis along the axis of the colliding beams. The variable θ
tion model allowing a quick fit for values of associated is the polar angle relative to the incoming proton beam,
correction factors. and the variable φ is the azimuthal angle about the beam
The traditional notions of signal and control regions axis. The pseudorapidity of a particle trajectory is de-
are modified. Without prejudice as to where new physics fined as η = − ln(tan(θ/2)). It is also useful to define
may appear, all regions of the data are treated as both detector pseudorapidity ηdet , denoting a particle’s pseu-
signal and control. This analysis is not blind, but rather dorapidity in a coordinate system in which the origin lies
seeks to identify and understand discrepancies between at the center of the CDF detector rather than at the event
data and the standard model prediction. With the goal vertex. The transverse momentum pT is the component
of discovery, emphasis is placed on examining discrep- of the momentum projected on a plane perpendicular to
ancies, focusing on outliers rather than global goodness the beam axis.
of fit. Individual discrepancies that are not statistically Charged particle tracks are reconstructed in a 3.1 m
significant are generally not pursued. long open cell drift chamber that performs up to 96 mea-
Vista and Sleuth are employed simultaneously, surements of the track position in the radial region from
rather than sequentially. An effect highlighted by 0.4 m to 1.4 m. Between the beam pipe and this tracking
Sleuth prompts additional investigation of the discrep- chamber are multiple layers of silicon microstrip detec-
ancy, usually resulting in a specific hypothesis explaining tors, enabling high precision determination of the impact
the discrepancy in terms of a detector effect or adjust- parameter of a track relative to the primary event vertex.
ment to the standard model prediction that is then fed The tracking detectors are immersed in a uniform 1.4 T
back and tested for global consistency using Vista. solenoidal magnetic field.
Forming hypotheses for the cause of specific discrepan- Outside the solenoid, calorimeter modules are arranged
cies, implementing those hypotheses to assess their wider in a projective tower geometry to provide energy mea-
consequences, and testing global agreement after the im- surements for both charged and neutral particles. Pro-
plementation are emphasized as the crucial activities for portional chambers are embedded in the electromagnetic
the investigator throughout the process of data analysis. calorimeters to measure the transverse profile of electro-
This process is constrained by the requirement that all magnetic showers at a depth corresponding to the shower
adjustments be physically motivated. The investigation maximum for electrons. The outermost part of the de-
and resolution of discrepancies highlighted by the algo- tector consists of a series of drift chambers used to detect
rithms is the defining characteristic of this global analy- and identify muons, minimum ionizing particles that typ-
sis [52]. ically pass through the calorimeter.
6

A set of forward gas Čerenkov detectors is used to small summed scalar transverse momentum containing
measure the average number of inelastic pp̄ collisions per only jets.
Tevatron bunch crossing, and hence determine the lumi- A secondary vertex b-tagging algorithm is used to iden-
nosity acquired. A three level trigger and data acqui- tify jets likely resulting from the fragmentation of a bot-
sition system selects the most interesting collisions for tom quark (b) produced in the hard scattering [14].
offline analysis. Momentum visible in the detector but not clustered
Here and below the word “central” is used to describe into an electron, muon, tau, photon, jet, or b-tagged jet
objects with |ηdet | < 1.0; “plug” is used to describe ob- is referred to as unclustered momentum (uncl).
jects with 1.0 < |ηdet | < 2.5. Missing momentum ( /p) is calculated as the negative
vector sum of the 4-vectors of all identified objects and
unclustered momentum. An event is said to contain a /p
B. Object identification object if the transverse momentum of this object exceeds
17 GeV, and if additional quality criteria discriminating
Energetic and isolated electrons, muons, taus, photons, against fake missing momentum due to jet mismeasure-
jets, and b-tagged jets with |ηdet | < 2.5 and pT > 17 GeV ment are satisfied [53].
are identified according to standard criteria. The same
criteria are used for all events. The isolation criteria
employed vary according to object, but roughly require C. Event selection
less thanp2 GeV of extra energy flow within a cone of
∆R = ∆η 2 + ∆φ2 = 0.4 in η–φ space around each Events containing an energetic and isolated electron,
object. muon, tau, photon, or jet are selected. A set of three
Standard CDF criteria [9] are used to identify electrons level online triggers requires:
(e± ) in the central and plug regions of the CDF detector.
Electrons are characterized by a narrow shower in the • a central electron candidate with pT > 18 GeV
passing level 3, with an associated track having
central or plug electromagnetic calorimeter and a match-
pT > 8 GeV and an electromagnetic energy clus-
ing isolated track in the central gas tracking chamber or
ter with pT > 16 GeV at levels 1 and 2; or
a matching plug track in the silicon detector.
Standard CDF muons (µ± ) are identified using three • a central muon candidate with pT > 18 GeV pass-
separate subdetectors in the regions |ηdet | < 0.6, 0.6 < ing level 3, with an associated track having pT >
|ηdet | < 1.0, and 1.0 < |ηdet | < 1.5 [9]. Muons are 15 GeV and muon chamber track segments at levels
characterized by a track in the central tracking cham- 1 and 2; or
ber matched to a track segment in the central muon de-
tectors, with energy consistent with minimum ionizing • a central or plug photon candidate with pT >
deposition in the electromagnetic and hadronic calorime- 25 GeV passing level 3, with hadronic to electro-
ters along the muon trajectory. magnetic energy less than 1:8 and with energy sur-
Narrow central jets with a single charged track are rounding the photon to the photon’s energy less
identified as tau leptons (τ ± ) that have decayed hadron- than 1:7 at levels 1 and 2; or
ically [10]. Taus are distinguished from electrons by re-
quiring a substantial fraction of their energy to be de- • a central or plug jet with pT > 20 GeV passing level
posited in the hadron calorimeter; taus are distinguished 3, with 15 GeV of transverse momentum required
from muons by requiring no track segment in the muon at levels 1 and 2, with corresponding prescales of
detector coinciding with the extrapolated track of the 50 and 25, respectively; or
tau. Track and calorimeter isolation requirements are
• a central or plug jet with pT > 100 GeV passing
imposed.
level 3, with energy clusters of 20 GeV and 90 GeV
Standard CDF criteria requiring the presence of a nar-
required at levels 1 and 2; or
row electromagnetic cluster with no associated tracks are
used to identify photons (γ) in the central and plug re- • a central electron candidate with pT > 4 GeV and
gions of the CDF detector [11]. a central muon candidate with pT > 4 GeV pass-
Jets (j) are reconstructed using the JetClu [12] clus- ing level 3, with a muon segment, electromagnetic
tering algorithm with a cone of size ∆R = 0.4, unless the cluster, and two tracks with pT > 4 GeV required
event contains one or more jets with pT > 200 GeV and at levels 1 and 2; or
no leptons or photons, in which case cones of ∆R = 0.7
are used. Jet energies are appropriately corrected to the • a central electron or muon candidate with pT >
parton level [13]. Since uncertainties in the standard 4 GeV and a plug electron candidate with pT >
model prediction grow with increasing jet multiplicity, 8 GeV, requiring a central muon segment and track
up to the four largest pT jets are used to characterize the or central electromagnetic energy cluster and track
event; any reconstructed jets with pT -ordered ranking of at levels 1 and 2, together with an isolated plug
five or greater are neglected, except in final states with electromagnetic energy cluster; or
 7

• two central or plug electromagnetic clusters with possibly with other objects present. Explicit online trig-
pT > 18 GeV passing level 3, with hadronic to elec- gers feeding this offline selection are required. The pT
tromagnetic energy less than 1:8 at levels 1 and 2; thresholds for these criteria are chosen to be sufficiently
or above the online trigger turn-on curves that trigger effi-
ciencies can be treated as roughly independent of object
• two central tau candidates with pT > 10 GeV pT .
passing level 3, each with an associated track hav- Good run criteria are imposed, requiring the operation
ing pT > 10 GeV and a calorimeter cluster with of all major subdetectors. To reduce contributions from
pT > 5 GeV at levels 1 and 2. cosmic rays and events from beam halo, standard CDF
cosmic ray and beam halo filters are applied [15].
Events satisfying one or more of these online triggers
These selections result in a sample of roughly two mil-
are recorded for further study. Offline event selection for
lion high-pT data events in an integrated luminosity of
this analysis uses a variety of further filters. Single object
927 pb−1 .
requirements keep events containing:

• a central electron with pT > 25 GeV, or

D. Event generation
• a plug electron with pT > 40 GeV, or
Standard model backgrounds are estimated by gener-
• a central muon with pT > 25 GeV, or ating a large sample of Monte Carlo events, using the
Pythia [16], MadEvent [17], and Herwig [18] gener-
• a central photon with pT > 60 GeV, or
ators. MadEvent performs an exact leading order ma-
• a central jet or b-tagged jet with pT > 200 GeV, or trix element calculation, and provides 4-vector informa-
tion corresponding to the outgoing legs of the underlying
• a central jet or b-tagged jet with pT > 40 GeV Feynman diagrams, together with color flow information.
(prescaled by a factor of roughly 104 ), Pythia 6.218 is used to handle showering and fragmen-
tation. The CTEQ5L [19] parton distribution functions
possibly with other objects present. Multiple object cri- are used.
teria select events containing: QCD jets. QCD dijet and multijet production are es-
timated using Pythia. Samples are generated with Tune
• two electromagnetic objects (electron or photon) A [20] with lower cuts on p̂T , the transverse momentum
with |η| < 2.5 and pT > 25 GeV, or of the scattered partons in the center of momentum frame
of the incoming partons, of 0, 10, 18, 40, 60, 90, 120, 150,
• two taus with |η| < 1.0 and pT > 17 GeV, or
200, 300, and 400 GeV. These samples are combined to
• a central electron or muon with pT > 17 GeV and provide a complete estimation of QCD jet production,
a central or plug electron, central muon, or central using the sample with greatest statistics in each range of
tau with pT > 17 GeV, or p̂T .
γ+jets. The estimation of QCD single prompt pho-
• a central photon with pT > 40 GeV and a central ton production comes from Pythia. Five samples are
electron or muon with pT > 17 GeV, or generated with Tune A corresponding to lower cuts on
p̂T of 8, 12, 22, 45, and 80 GeV. These samples are com-
• a central or plug photon with pT > 40 GeV and a bined to provide a complete estimation of single prompt
central tau with pT > 40 GeV, or photon production in association with one or more jets,
placing cuts on p̂T to avoid double counting.
• a central photon with pT > 40 GeV and a central γγ+jets. QCD diphoton production is estimated us-
b-jet with pT > 25 GeV, or ing Pythia.
V +jets. The estimation of V +jets processes (with V
• a central jet or b-tagged jet with pT > 40 GeV and
denoting W or Z), where the W or Z decays to first or
a central tau with pT > 17 GeV (prescaled by a
second generation leptons, comes from MadEvent, with
factor of roughly 103 ), or
Pythia employed for showering. Tune AW [20] is used
• a central or plug photon with pT > 40 GeV and within Pythia for these samples. The CKKW matching
two central taus with pT > 17 GeV, or prescription [21] with a matching scale of 15 GeV is used
to combine these samples and avoid double counting. Ad-
• a central or plug photon with pT > 40 GeV and ditional statistics are generated on the high-pT tails using
two central b-tagged jets with pT > 25 GeV, or the MLM matching prescription [22]. The factorization
scale is set to the vector boson mass; the renormalization
• a central or plug photon with pT > 40 GeV, a cen- scale for each vertex is set to the pT of the jet. W +4 jets
tral tau with pT > 25 GeV, and a central b-tagged are generated inclusively in the number of jets; Z+3 jets
jet with pT > 25 GeV, are generated inclusively in the number of jets.
8

V V +jets. The estimation of W W , W Z, and ZZ pro- events in this analysis.

duction with zero or more jets comes from Pythia.
V γ+jets. The estimation of W γ and Zγ production
comes from MadEvent, with showering provided by E. Detector simulation
Pythia. These samples are inclusive in the number of
jets. The response of the CDF detector is simulated using
W (→ τ ν)+jets. Estimation of W → τ ν with zero or a geant-based detector simulation (CdfSim) [25], with
more jets comes from Pythia. gflash [26] used to simulate shower development in the
Z(→ τ τ )+jets. Estimation of Z → τ τ with zero or calorimeter.
more jets comes from Pythia. In pp̄ collisions there is an ordering of frequency with
tt̄. Top quark pair production is estimated using which objects of different types are produced: many more
Herwig assuming a top quark mass of 175 GeV and jets (j) are produced than b-jets (b) or photons (γ), and
NNLO cross section of 6.77 ± 0.42 pb [23]. many more of these are produced than charged leptons
Remaining processes, including for example Z(→ ν ν̄)γ (e, µ, τ ). The CDF detectors and reconstruction algo-
and Z(→ ℓ+ ℓ− )bb̄, are generated by systematically rithms have been designed such that the probability of
looping over possible final state partons, using Mad- misreconstructing a frequently produced object as an in-
Graph [24] to determine all relevant diagrams, and us- frequently produced object is small. The fraction of cen-
ing MadEvent to perform a Monte Carlo integration tral jets that CdfSim misreconstructs as photons, elec-
over the final state phase space and to generate events. trons, and muons is ∼ 10−3 , ∼ 10−4 , and ∼ 10−5 , respec-
The MLM matching prescription is employed to combine tively. Due to these small numbers, the use of CdfSim
samples with different numbers of final state jets. to model these fake processes would require generating
A higher statistics estimate of the high-p samples with prohibitively large statistics. Instead, the
P T tails is ob-
tained by computing the thresholds in pT correspond- modeling of a frequently produced object faking a less
frequently produced object (specifically: j faking b, γ, e,
P
ing to the top 10% and 1% of each process, where pT
denotes the scalar summed transverse momentum of all µ, or τ ; or b or γ faking e, µ, or τ ) is obtained by the ap-
identified objects in an event. Roughly ten times as many plication of a misidentification probability, a particular
events are generated for the top 10%, and roughly one type of correction factor in the Vista correction model,
hundred times as many events are generated for the top described in the next section.
1%. In Monte Carlo samples passed through CdfSim, re-
Cosmic rays. Backgrounds from cosmic ray or beam constructed leptons and photons are required to match to
halo muons that interact with the hadronic or electro- a corresponding generator level object. This procedure
magnetic calorimeters, producing objects that look like a removes reconstructed leptons or photons that arise from
photon or jet, are estimated using a sample of data events a misreconstructed quark or gluon jet.
containing fewer than three reconstructed tracks. This
procedure is described in more detail in Appendix A 2 a.
Minimum bias. Minimum bias events are overlaid ac- F. Correction model
cording to run-dependent instantaneous luminosity in
some of the Monte Carlo samples, including those used Unfortunately some numbers that cannot be deter-
for inclusive W and Z production. In all samples not mined from first principles enter the comparison between
containing overlaid minimum bias events, including those data and the standard model prediction. These numbers
used to estimate QCD dijet production, additional un- are referred to as “correction factors” in the Vista cor-
clustered momentum is added to events to mimic the rection model. This correction model is applied to gen-
effect of the majority of multiple interactions, in which erated Monte Carlo events to obtain the standard model
a soft dijet event accompanies the rare hard scattering prediction across all final states.
of interest. A random number is drawn from a Gaussian Correction factors must be obtained from the data
centered at 0 with width 1.5 GeV for each of the x and y themselves. These factors may be thought of as Bayesian
components of the added unclustered momentum. Back- nuisance parameters. The actual values of the correction
grounds due to two rare hard scatterings occurring in the factors are not directly of interest. Of interest is the
same bunch crossing are estimated by forming overlaps comparison of data to standard model prediction, with
of events, as described in Appendix A 2 b. correction factors adjusted to whatever they need to be,
Each generated standard model event is assigned a consistent with external constraints, to bring the stan-
weight, calculated as the cross section for the process dard model into closest agreement with the data.
(in units of picobarns) divided by the number of events The traditional prescription for determining these cor-
generated for that process, representing the number of rection factors is to measure them in a control region in
such events expected in a data sample corresponding to which no signal is expected. This procedure encounters
an integrated luminosity of 1 pb−1 . When multiplied by difficulty when the entire high-pT data sample is consid-
the integrated luminosity of the data sample used in this ered to be a signal region. The approach adopted instead
analysis, the weight gives the predicted number of such is to ask whether a consistent set of correction factors
 9

Code Category Explanation Value Error Error(%)

0001 luminosity CDF integrated luminosity 927 20 2.2
0002 k-factor cosmic γ 0.69 0.05 7.3
0003 k-factor cosmic j 0.446 0.014 3.1
0004 k-factor 1γ1j 0.95 0.04 4.2
0005 k-factor 1γ2j 1.2 0.05 4.1
0006 k-factor 1γ3j 1.48 0.07 4.7
0007 k-factor 1γ4j+ 1.97 0.16 8.1
0008 k-factor 2γ0j 1.81 0.08 4.4
0009 k-factor 2γ1j 3.42 0.24 7.0
0010 k-factor 2γ2j+ 1.3 0.16 12.3
0011 k-factor W 0j 1.453 0.027 1.9
0012 k-factor W 1j 1.06 0.03 2.8
0013 k-factor W 2j 1.02 0.03 2.9
0014 k-factor W 3j+ 0.76 0.05 6.6
0015 k-factor Z0j 1.419 0.024 1.7
0016 k-factor Z1j 1.18 0.04 3.4
0017 k-factor Z2j+ 1.03 0.05 4.8
0018 k-factor 2j, p̂T < 150 0.96 0.022 2.3
0019 k-factor 2j, 150 < p̂T 1.256 0.028 2.2
0020 k-factor 3j, p̂T < 150 0.921 0.021 2.3
0021 k-factor 3j, 150 < p̂T 1.36 0.03 2.4
0022 k-factor 4j, p̂T < 150 0.989 0.025 2.5
0023 k-factor 4j, 150 < p̂T 1.7 0.04 2.3
0024 k-factor 5j+ 1.25 0.05 4.0
0025 ID eff p(e → e) central 0.986 0.006 0.6
0026 ID eff p(e → e) plug 0.933 0.009 1.0
0027 ID eff p(µ → µ), |η| < 0.6 0.845 0.008 0.9
0028 ID eff p(µ → µ), 0.6 < |η| 0.915 0.011 1.2
0029 ID eff p(γ → γ) central 0.974 0.018 1.8
0030 ID eff p(γ → γ) plug 0.913 0.018 2.0
0031 ID eff p(b → b) central 1 0.04 4.0
0032 fake rate p(e → γ) plug 0.045 0.012 27.0
0033 fake rate p(q → e) central 9.71×10−5 1.9×10−6 2.0
0034 fake rate p(q → e) plug 0.000876 1.8×10−5 2.1
0035 fake rate p(q → µ) 1.157×10−5 2.7×10−7 2.3
0036 fake rate p(j → b) 0.01684 0.00027 1.6
0037 fake rate p(q → τ ), pT < 60 0.00341 0.00012 3.5
0038 fake rate p(q → τ ), 60 < pT 0.00038 4×10−5 10.5
0039 fake rate p(q → γ) central 0.000265 1.5×10−5 5.7
0040 fake rate p(q → γ) plug 0.00159 0.00013 8.2
0041 trigger p(e → trig) central, pT > 25 0.976 0.007 0.7
0042 trigger p(e → trig) plug, pT > 25 0.835 0.015 1.8
0043 trigger p(µ → trig) |η| < 0.6, pT > 25 0.917 0.007 0.8
0044 trigger p(µ → trig) 0.6 < |η| < 1.0, pT > 25 0.96 0.01 1.0

TABLE I: The 44 correction factors introduced in the Vista correction model. The leftmost column (Code) shows correction
factor codes. The second column (Category) shows correction factor categories. The third column (Explanation) provides a
short description. The correction factor best fit value (Value) is given in the fourth column. The correction factor error (Error)
resulting from the fit is shown in the fifth column. The fractional error (Error(%)) is listed in the sixth column. All values
are dimensionless with the exception of code 0001 (luminosity), which has units of pb−1 . The values and uncertainties of these
correction factors are valid within the context of this correction model.
10

can be chosen so that the standard model prediction is details relegated to Appendix A 3.
in agreement with the CDF high-pT data. Events are first partitioned into final states according
The correction model is obtained by an iterative pro- to the number and types of objects present. Each final
cedure informed by observed inadequacies in modeling. state is then subdivided into bins according to each ob-
The process of correction model improvement, motivated ject’s detector pseudorapidity (ηdet ) and transverse mo-
by observed discrepancies, may allow a real signal to be mentum (pT ), as described in Appendix A 3 a.
artificially suppressed. If adjusting correction factor val- Generated Monte Carlo events, adjusted by the cor-
ues within allowed bounds removes a signal, then the rection model, provide the standard model prediction for
case for the signal disappears, since it can be explained each bin. The standard model prediction in each bin is
in terms of known physics. This is true in any analysis. therefore a function of the correction factor values. A
The stronger the constraints on the correction model, the figure of merit is defined to quantify global agreement
more difficult it is to artificially suppress a real signal. By between the data and the standard model prediction,
requiring a consistent interpretation of hundreds of final and correction factor values are chosen to maximize this
states, Vista is less likely to mistakenly explain away agreement, consistent with external experimental con-
new physics than if it had more limited scope. straints.
The 44 correction factors currently included in the Letting ~s represent a vector of correction factors, for
Vista correction model are shown in Table I. These the k th bin
factors can be classified into two categories: theoretical (Data[k] − SM[k])2
and experimental. A more detailed description of each χ2k (~s) = p 2 , (1)
individual correction factor is provided in Appendix A 4. SM[k] + δSM[k]2
Theoretical correction factors reflect the practical dif- where Data[k] is the number of data events observed in
ficulty of calculating accurately within the framework the k th bin, SM[k] is the number of events predicted by
of the standard model. These factors take the form the standard model in the k th bin, δSM[k] is the Monte
of k-factors, so-called “knowledge factors,” represent- Carlo statistical uncertainty on p the standard model pre-
ing the ratio of the unavailable all order cross section diction in the k th bin [54], and SM[k] is the statistical
to the calculable leading order cross section. Twenty-
uncertainty on the expected data in the k th bin. The
three k-factors are used for standard model processes in-
standard model prediction SM[k] in the k th bin is a func-
cluding QCD multijet production, W+jets, Z+jets, and
tion of ~s.
(di)photon+jets production.
Relevant information external to the Vista high-pT
Experimental correction factors include the integrated data sample provides additional constraints in this global
luminosity of the data, efficiencies associated with trig- fit. The CDF luminosity counters measure the inte-
gering on electrons and muons, efficiencies associated grated luminosity of the sample described in this ar-
with the correct identification of physics objects, and ticle to be 902 pb−1 ± 6% by measuring the fraction
fake rates associated with the mistaken identification of of bunch crossings in which zero inelastic collisions oc-
physics objects. Obtaining an adequate description of cur [27]. The integrated luminosity of the sample mea-
object misidentification has required an understanding sured by the luminosity counters enters in the form of
of the underlying physical mechanisms by which objects a Gaussian constraint on the luminosity correction fac-
are misreconstructed, as described in Appendix A 1. tor. Higher order theoretical calculations exist for some
In the interest of simplicity, correction factors repre- standard model processes, providing constraints on cor-
senting k-factors, efficiencies, and fake rates are generally responding k-factors, and some CDF experimental cor-
taken to be constants, independent of kinematic quanti- rection factors are also constrained from external infor-
ties such as object pT , with only five exceptions. The pT mation. In total, 26 of the 44 correction factors are con-
dependence of three fake rates is too large to be treated strained. The specific constraints employed are provided
as approximately constant: the jet faking electron rate in Appendix A 3 b.
p(j → e) in the plug region of the CDF detector; the jet The overall function to be minimized takes the form
faking b-tagged jet rate p(j → b), which increases steadily !
with increasing pT ; and the jet faking tau rate p(j → τ ), X
χ2 (~s) = χ2k (~s) + χ2constraints (~s), (2)
which decreases steadily with increasing pT . Two other
k∈bins
fake rates possess geometrical features in η–φ due to the
construction of the CDF detector: the jet faking electron where the sum in the first term is over bins in the CDF
rate p(j → e) in the central region, because of the fidu- high-pT data sample with χ2k (~s) defined in Eq. 1, and the
cial tower geometry of the electromagnetic calorimeter; second term is the contribution from explicit constraints.
and the jet faking muon rate p(j → µ), due to the non- Minimization of χ2 (~s) in Eq. 2 as a function of the
trivial fiducial geometry of the muon chambers. After vector of correction factors ~s results in a set of correction
determining appropriate functional forms, a single over- factor values ~s0 providing the best global agreement be-
all multiplicative correction factor is used. tween the data and the standard model prediction. The
Correction factor values are obtained from a global fit best fit correction factor values are shown in Table I, to-
to the data. The procedure is outlined here, with further gether with absolute and fractional uncertainties. The
 11

determined uncertainties are not used explicitly in the

subsequent analysis, but rather provide information used Entries 344
implicitly to assist in appropriate adjustment to the cor- 90 Underflow 0
Overflow 0
rection model in light of observed discrepancies. The 80
uncertainties are verified by subdividing the data into
70

Vista Final States

thirds, performing separate fits on each third, and not-
ing that the correction factor values obtained with each 60
subset are consistent within quoted uncertainties. Fur- 50
ther details on the correlation matrix and other technical
40
aspects of this global fit can be found in Appendix A 3 c.
30
Although the correction factors are determined from a
global fit, in practice the determination of many correc- 20
tion factors’ values are dominated by one recognizable 10
subsample. The rate p(j → e) for a jet to fake an elec-
tron is determined largely by the number of events in the 0
-6 -4 -2 0 2 4 6
ej final state, since the largest contribution to this final σ
state is from dijet events with one jet misreconstructed
as an electron. Similarly, the rates p(j → b) and p(j → τ )
Entries 16486
for a jet to fake a b-tagged jet and tau lepton are deter- Entries
Underflow 164860
mined largely by the number of events in the bj and τ j 2500
Overflow 0

final states, respectively. The determination of the fake

Vista Distributions
rate p(j → γ), photon efficiency p(γ → γ), and k-factors
2000
for prompt photon production and prompt diphoton pro-
duction are dominated by the γj, γjj, and γγ final states.
Additional knowledge incorporated in the determination 1500
of fake rates is described in Appendix A 1.

overflow
1000
The global fit χ2 per number of bins is 288.1/133+27.9,
where the last term is the contribution to the χ2 from the
imposed constraints. A χ2 per degree of freedom larger 500
than unity is expected, since the limited set of correction
factors in this correction model is not expected to provide 0
-10 -8 -6 -4 -2 0 2 4 6 8 10
a complete description of all features of the data. Em- σ
phasis is placed on individual outlying discrepancies that
may motivate a new physics claim, rather than overall FIG. 1: Distribution of observed discrepancy between data
goodness of fit. and the standard model prediction, measured in units of stan-
Corrections to object identification efficiencies are typ- dard deviation (σ), shown as the solid (green) histogram, be-
ically less than 10%; fake rates are consistent with an fore accounting for the trials factor. The upper pane shows
understanding of the underlying physical mechanisms re- the distribution of discrepancies between the total number
of events observed and predicted in the 344 populated fi-
sponsible; k-factors range from slightly less than unity to
nal states considered. Negative values on the horizontal axis
greater than two for some processes with multiple jets. correspond to a deficit of data compared to standard model
All values obtained are physically reasonable. Further prediction; positive values indicate an excess of data com-
analysis is provided in Appendix A 4. pared to standard model prediction. The lower pane shows
With the details of the correction model in place, the the distribution of discrepancies between the observed and
complete standard model prediction can be obtained. For predicted shapes in 16,486 kinematic distributions. Distribu-
tions in which the shapes of data and standard model predic-
each Monte Carlo event after detector simulation, the
tion are in relative disagreement correspond to large positive
event weight is multiplied by the value of the luminosity σ. The solid (black) curves indicate expected distributions,
correction factor and the k-factor for the relevant stan- if the data were truly drawn from the standard model back-
dard model process. The single Monte Carlo event can ground. Interest is focused on the entries in the tails of the
be misreconstructed in a number of ways, producing a upper distribution and the high tail of the lower distribution.
set of Monte Carlo events derived from the original, with The final state entering the upper histogram at −4.03σ is the
weights multiplied by the probability of each misrecon- Vista 3j τ final state, which heads Table II. Most of the dis-
struction. The weight of each resulting event is multiplied tributions entering the lower histogram with > 4σ derive from
by the probability the event satisfies trigger criteria. The the 3j ∆R(j2 , j3 ) discrepancy, discussed in the text.
resulting standard model prediction, corrected as just de-
scribed, is referred to as “the standard model prediction”
throughout the rest of this paper, with “corrected” im-
plied in all cases.
12

Final State Data Background σ Final State Data Background Final State Data Background
3jτ ± 71 113.7 ± 3.6 −2.3 2jµ± 9513 9362.3 ± 166.8 e± /
pτ ± 20 18.7 ± 1.9
5j 1661 1902.9 ± 50.8 −1.7 2e± j 13 9.8 ± 2.2 e± γp/ 141 144.2 ± 6
2jτ ± 233 296.5 ± 5.6 −1.6 2e± e∓ 12 4.8 ± 1.2 e± µ∓ /
p 54 42.6 ± 2.7
2j2τ ± 6 27 ± 4.6 −1.4 2e± 23 36.1 ± 3.8 e± µ± /
p 13 10.9 ± 1.3
be± j 2015.4 ± 28.7 335.8 ± 7 e± µ∓ 127.6 ± 4.2
P
2207 +1.4 2b, low pT 327 153
35436 37294.6 ± 524.3 −1.1 e± j
P
pT 173.1 ± 7.1 386880 392614 ± 5031.8
P
3j, high 2b, high pT 187
e± 3jp/ 1751.6 ± 42 33.5 ± 5.5 e± j2γ 15.9 ± 2.9
P
1954 +1.1 2b3j, high pT 28 14
be± 2j 695.3 ± 13.3 326.3 ± 8.4 e± jτ ± 79.3 ± 2.9
P
798 +1.1 2b2j, low pT 355 79
/, low 967.5 ± 38.4 −0.8 e± jτ ∓
P
pT 80.2 ± 5 148.8 ± 7.6
P
3jp 811 2b2j, high pT 56 162
e± µ± 26 11.6 ± 1.5 +0.8 2b2jγ 16 15.4 ± 3.6 e± jp
/ 58648 57391.7 ± 661.6
e± γ 636 551.2 ± 11.2 +0.7 2bγ 37 31.7 ± 4.8 e± jγp
/ 52 76.2 ± 9
e± 3j 28656 27281.5 ± 405.2 +0.6 393.8 ± 9.1 e± jµ∓ / 13.1 ± 1.7
P
2bj, low pT 415 p 22
b5j 131 95 ± 4.7 +0.5 195.8 ± 8.3 e± jµ∓ 26.8 ± 2.3
P
2bj, high pT 161 28
j2τ ± 50 85.6 ± 8.2 −0.4 /, low 23.2 ± 2.6 e± e∓ 4j 113.5 ± 5.9
P
2bjp pT 28 103
jτ ± τ ∓ 74 125 ± 13.6 −0.4 2bjγ 25 24.7 ± 4.3 e± e∓ 3j 456 473 ± 14.6
/, low 29.5 ± 4.6 −0.4 2be± 2jp e± e∓ 2jp
P
bp pT 10 / 15 12.3 ± 1.6 / 30 39 ± 4.6
e± jγ 286 369.4 ± 21.1 −0.3 2be± 2j 30 30.5 ± 2.5 e± e∓ 2j 2149 2152 ± 40.1
e± jp
/τ ∓ 29 14.2 ± 1.8 +0.2 2be± j 28 29.1 ± 2.8 e± e∓ τ ± 14 11.1 ± 2
96502 92437.3 ± 1354.5 +0.1 2be± e± e∓ /
P
2j, high pT 48 45.2 ± 3.7 p 491 487.9 ± 12
be± 3j 356 298.6 ± 7.7 +0.1 τ±τ∓ 498 428.5 ± 22.7 e± e∓ γ 127 132.3 ± 4.2
8j 11 6.1 ± 2.5 γτ ± 177 204.4 ± 5.4 e± e∓ j 10726 10669.3 ± 123.5
7j 57 35.6 ± 4.9 γp
/ 1952 1945.8 ± 77.1 e± e∓ jp
/ 157 144 ± 11.2
6j 335 298.4 ± 14.7 µ± τ ± 18 19.8 ± 2.3 e± e∓ jγ 26 45.6 ± 4.7
39665 40898.8 ± 649.2 µ± τ ∓ 151 179.1 ± 4.7 e± e∓ 58344 58575.6 ± 603.9
P
4j, low pT
8403.7 ± 144.7 µ± /
p 321351 320500 ± 3475.5 b6j 24 15.5 ± 2.3
P
4j, high pT 8241
µ± /
pτ ∓ 25.8 ± 2.7 9.2 ± 1.8
P
4j2γ 38 57.5 ± 11 22 b4j, low pT 13
4jτ ± µ± γ 285.5 ± 5.9 499.2 ± 12.4
P
20 36.9 ± 2.4 269 b4j, high pT 464
µ± γp/ 282.2 ± 6.6 5285 ± 72.4
P
/, low 525.2 ± 34.5 269 b3j, low pT 5354
P
4jp pT 516
µ± µ∓ / 61.4 ± 3.5
P
/
4jγp 28 53.8 ± 11 p 49 b3j, high pT 1639 1558.9 ± 24.1
µ± µ∓ γ 29.9 ± 2.6
P
4jγ 3693 3827.2 ± 112.1 32 /, low
b3jp pT 111 116.8 ± 11.2
4jµ± 576 568.2 ± 26.1 µ± µ∓ 10648 10845.6 ± 96 b3jγ 182 194.1 ± 8.8
4jµ± /
p 232 224.7 ± 8.5 j2γ 2196 2200.3 ± 35.2 b3jµ± /
p 37 34.1 ± 2
4jµ± µ∓ 17 20.1 ± 2.5 j2γp/ 38 27.3 ± 3.2 b3jµ± 47 52.2 ± 3
3γ 13 24.2 ± 3 jτ ± 563 585.7 ± 10.2 b2γ 15 14.6 ± 2.1
/, low 4209.1 ± 56.1 8576.2 ± 97.9
P
pT
P
pT
P
3j, low pT 75894 75939.2 ± 1043.9 jp 4183 b2j, low 8812
48743 ± 546.3 4646.2 ± 57.7
P
3j2γ 145 178.1 ± 7.4 jγ 49052 b2j, high pT 4691
jγτ ± 104 ± 4.1 /, low 209.2 ± 8.3
P
pT
P
/, high
3jp pT 20 30.9 ± 14.4 106 b2jp 198
3jγτ ± 13 11 ± 2 /
jγp 913 965.2 ± 41.5 b2jγ 429 425.1 ± 13.1
/
3jγp 83 102.9 ± 11.1 jµ± 33462 34026.7 ± 510.1 b2jµ± /
p 46 40.1 ± 2.7
3jγ 11424 11506.4 ± 190.6 jµ± τ ∓ 29 37.5 ± 4.5 b2jµ± 56 60.6 ± 3.4
3jµ± /
p 1114 1118.7 ± 27.1 jµ± /
pτ ∓ 10 9.6 ± 2.1 bτ ± 19 19.9 ± 2.2
3jµ± µ∓ 61 84.5 ± 9.2 jµ± /
p 45728 46316.4 ± 568.2 bγ 976 1034.8 ± 15.6
3jµ± 2132 2168.7 ± 64.2 jµ± γp/ 78 69.8 ± 9.9 /
bγp 18 16.7 ± 3.1
9.3 ± 1.9 jµ± γ 70 98.4 ± 12.1 bµ± 303 263.5 ± 7.9
P
3bj, low pT 14
2τ ± 316 290.8 ± 24.2 jµ± µ∓ 1977 2093.3 ± 74.7 bµ± /
p 204 218.1 ± 6.4
e± 4j 6661.9 ± 147.2 9275.7 ± 87.8
P
/
2γp 161 176 ± 9.1 7144 bj, low pT 9060
e± 4jp
/ 363 ± 9.9 7030.8 ± 74
P
2γ 8482 8349.1 ± 84.1 403 bj, high pT 7236
93408 92789.5 ± 1138.2 e± 3jτ ∓ 7.6 ± 1.6 17.6 ± 3.3
P
2j, low pT 11 bj2γ 13
2j2γ 645 612.6 ± 18.8 e± 3jγ 27 21.7 ± 3.4 bjτ ± 13 12.9 ± 1.8
2jτ ± τ ∓ e± 2γ 74.5 ± 5
P
15 25 ± 3.5 47 /, low
bjp pT 53 60.4 ± 19.9
/, low 106 ± 7.8 e± 2j 126665 122457 ± 1672.6 989.4 ± 20.6
P
2jp pT 74 bjγ 937
/, high 37.7 ± 100.2 e± 2jτ ∓ 37.3 ± 3.9 / 30.5 ± 4
P
2jp pT 43 53 bjγp 34
2jγ 33684 33259.9 ± 397.6 e± 2jτ ± 20 24.7 ± 2.3 bjµ± /
p 104 112.6 ± 4.4
2jγτ ± 48 41.4 ± 3.4 e± 2jp
/ 12451 12130.1 ± 159.4 bjµ± 173 141.4 ± 4.8
/
2jγp 403 425.2 ± 29.7 e± 2jγ 101 88.9 ± 6.1 be± 3jp
/ 68 52.2 ± 2.2
2jµ± /
p 7287 7320.5 ± 118.9 e± τ ∓ 609 555.9 ± 10.2 be± 2jp
/ 87 65 ± 3.3
2jµ± γp/ 13 12.6 ± 2.7 e± τ ± 225 211.2 ± 4.7 be± /
p 330 347.2 ± 6.9
2jµ± γ 41 35.7 ± 6.1 e± /
p 476424 479572 ± 5361.2 be± jp
/ 211 176.6 ± 5
2jµ± µ∓ 374 394.2 ± 24.8 e± /
pτ ∓ 48 35 ± 2.7 be± e∓ j 22 34.6 ± 2.6

TABLE II: A subset of the Vista comparison between Tevatron Run II data and standard model prediction, showing the twenty
most discrepant final states and all final states populated with ten or more data events. Events are partitioned into exclusive
final states based on standard CDF object identification
P criteria. FinalP
states are labeled in this table according to the number
and types of objects present, and whether (high pT ) or not (low pT ) the summed scalar transverse momentum of all
objects in the events exceeds 400 GeV, for final states not containing leptons or photons. Final states are ordered according to
decreasing discrepancy between the total number of events expected, taking into account the error from Monte Carlo statistics
and the total number observed in the data. Final states exhibiting mild discrepancies are shown together with the significance
of the discrepancy in units of standard deviations (σ) after accounting for a trials factor corresponding to the number of final
states considered. Final states that do not exhibit even mild discrepancies are listed below the horizontal line in inverted
alphabetical order. Only Monte Carlo statistical uncertainties on the background prediction are included.
 13

into units of standard deviations by solving for σ such

R∞ x2
that σ √12π e− 2 dx = p [55]. A final state exhibiting
a population discrepancy greater than 3σ after the trials
factor is thus accounted for is considered significant.
Many kinematic distributions are considered in each
final state, including the transverse momentum, pseudo-
rapidity, detector pseudorapidity, and azimuthal angle of
all objects, masses of individual jets and b-jets, invari-
ant masses of all object combinations, transverse masses
of object combinations including /p, angular separation
∆φ and ∆R of all object pairs, and several other more
specialized variables. A Kolmogorov-Smirnov (KS) test
is used to quantify the difference in shape of each kine-
matic distribution between data and standard model pre-
diction. As with populations, a trials factor is assessed
to account for the 16,486 distributions examined, and the
resulting probability is converted into units of standard
FIG. 2: The invariant mass of the tau lepton and two leading
jets in the final state consisting of three jets and one positively
deviations. A distribution with KS statistic greater than
or negatively charged tau. (The Vista final state naming 0.02 and probability corresponding to greater than 3σ
convention gives the tau lepton a positive charge.) Data are after assessing the trials factor is considered significant.
shown as filled (black) circles, with the standard model pre- Table II shows a subset of the Vista comparison of
diction shown as the shaded (red) histogram. This is the most data to standard model prediction. Shown are all final
discrepant kinematic distribution in the final state exhibiting states containing ten or more data events, with the most
the largest population discrepancy. discrepant final states in population heading the list. Af-
ter accounting for the trials factor, no final state has a
statistically significant (> 3σ) population discrepancy.
G. Results The most discrepant final state (3j τ ± ) contains 71 data
events and 113.7 ± 3.6 events expected from the standard
Data and standard model events are partitioned into model. The Poisson probability for 113.7 ± 3.6 expected
exclusive final states. This partitioning is orthogonal, events to result in 71 or fewer events observed in this
with each event ending up in one and only one final state. final state is 2.8 × 10−5 , corresponding to an entry at
Data are compared to standard model prediction in each −4.03σ in Fig. 1. The probability for one or more of the
final state, considering the total number of events ob- 344 populated final states considered to display disagree-
served and predicted, and the shapes of relevant kine- ment in population corresponding to a probability less
matic distributions. than 2.8 × 10−5 is 1%. The 3j τ ± population discrepancy
In a data driven search, it is crucial to explicitly ac- is thus not statistically significant. The most discrepant
count for the trials factor, quantifying the number of kinematic distribution in this final state is the invariant
places an interesting signal could appear. Fluctuations mass of the tau lepton and the two highest transverse
at the level of three or more standard deviations are ex- momentum jets, shown in Fig. 2.
pected to appear simply because a large number of re- The six final states with largest population discrepancy
gions are considered. A reasonably rigorous accounting are 3j τ , 5j, 2j τ , 2j 2τ , b e j, and the low-pT 3j final
of this trials factor is possible as long as the measures state, with b e j being the only one of these six to exhibit
of interest and the regions to which these measures are an excess of data. The 3j τ , 2j τ , and 2j 2τ final states
applied are specified a priori, as is done here. In this appear to reflect an incomplete understanding of the rate
analysis a discrepancy at the level of 3σ or greater after of jets faking taus (p(j → τ )) as a function of the number
accounting for the trials factor (typically corresponding of jets in the event, at the level of ∼ 30% difference be-
to a discrepancy at the level of 5σ or greater before ac- tween the total number of observed and predicted events
counting for the trials factor) is considered “significant.” in the most populated of these final states. The value of
Discrepancy in the total number of events in a fi- p(j → τ ) is primarily determined by the j τ final state. In-
nal state (fs) is measured by the Poisson probability terestingly, although the underlying physical mechanism
pfs that the number of predicted events would fluctu- for p(j → e) is very similar to that for p(j → τ ), as dis-
ate up to or above (or down to or below) the number of cussed in Appendix A 1, a significant dependence on the
events observed. To account for the trials factor due presence of additional jets is not observed for p(j → e).
to the 344 Vista final states examined, the quantity The 5j discrepancy results from a tension with the e 4j
p = 1 − (1 − pfs )344 is calculated for each final state. final state, whose dominant contribution comes from 5j
The result is the probability p of observing a discrepancy production convoluted with p(j → e). The low-pT 3j dis-
corresponding to a probability less than pfs in the total crepancy results from a tension with the e 2j final state,
sample studied. This probability p can then be converted whose dominant contribution comes from 3j production
14

∑p
CDF Run II Data
bj T > 400 GeV Other
MadEvent W(→eν) jj : 0%
Pythia γ j : 0.2%
Pythia bj : 15.8%
1000 Pythia jj : 83.9%

Number of Events
500

0
50 100
M(j) (GeV)
FIG.
P 4: The jet mass distribution in the bj final state with
FIG. 3: A shape discrepancy highlighted by Vista in the fi- pT > 400 GeV. The 3j ∆R(j2 , j3 ) discrepancy illustrated
nal state consisting of exactly three reconstructed jets with in Fig. 3 manifests itself also by producing jets more massive
|η| < 2.5 and pT > 17 GeV, and with one of the jets satis- in data than predicted by Pythia’s showering algorithm. The
fying |η| < 1 and pT > 40 GeV. This distribution illustrates mass of a jet is determined by treating energy deposited in
the effect underlying most of the Vista shape discrepancies. each calorimeter tower as a massless 4-vector, summing the
Filled (black) circles show CDF data, with the shaded (red) 4-vectors of all towers within the jet, and computing the mass
histogram showing the prediction of Pythia. The discrep- of the resulting (massive) 4-vector.
ancy is clearly statistically significant, with statistical error
bars smaller than the size of the data points. The vertical
axis shows the number of events per bin, withpthe horizon-
tal axis showing the angular separation (∆R = ∆η 2 + δφ2 )
between the second and third jets, where the jets are ordered
according to decreasing transverse momentum. In the region
∆R(j2 , j3 ) & 2, populated primarily by initial state radiation,
the standard model prediction can to some extent be adjusted.
The region ∆R(j2 , j3 ) . 2 is dominated by final state radi-
ation, the description of which is constrained by data from
LEP 1.

convoluted with p(j → e). The b e j final state is pre-

dominantly 3j production convoluted with p(j → b) and
p(j → e); this discrepancy also arises from a tension with
the low-pT 3j and e 2j final states. The b e j final state is
the Vista final state in which the largest excess of data
over standard model prediction is seen. The fraction of
hypothetical similar CDF experiments that would pro-
duce a Vista normalization excess as significant as the FIG. 5: The distribution of ∆R between the jet and b-tagged
jet in the final state b e j. The primary standard model con-
excess observed in this final state is 8%. The 5j, b e j,
tribution to this final state is QCD three jet production with
and low-pT 3j discrepancies correspond to a difference of one jet misreconstructed as an electron. The similarity to the
∼ 10% between the total number of observed and pre- 3j ∆R(j2 , j3 ) discrepancy illustrated in Fig. 3 in the region
dicted events in these final states. ∆R(j, b) < 2 is clear. Less clear is the underlying explana-
Figure 1 summarizes in a histogram the measured dis- tion for the difference with respect to Fig. 3 in the region
crepancies between data and the standard model predic- ∆R(j, b) > 2.
tion for CDF high-pT final state populations and kine-
matic distributions. Values in this figure represent in-
dividual discrepancies, and do not account for the trials tributed to modeling parton radiation, deriving from the
factor associated with examining many possibilities. 3j ∆R(j2 , j3 ) discrepancy shown in Fig. 3, with 186 of
Of the 16,484 kinematic distributions considered, 384 these 312 shape discrepancies pointing out that individ-
distributions are found to correspond to a discrepancy ual jet masses are larger in data than in the prediction, as
greater than 3σ after accounting for the trials factor, en- shown in Fig. 4. A careful reading of the literature reveals
tering with a KS probability of roughly 5σ or greater in that the same effect was observed (but not emphasized)
Fig. 1. Of these 384 discrepant distributions, 312 are at- by both CDF [28, 29] and DØ [30] in Tevatron Run I. The
 15

3j ∆R(j2 , j3 ) and jet mass discrepancies appear to be two of this research program involves the systematic search
different views of a single underlying discrepancy, noting for such physics using an algorithm called Sleuth [32].
that two sufficiently nearby distinct jets correspond to a Sleuth is quasi model independent, where “quasi” refers
pattern of calorimetric energy deposits similar to a single to the assumption that the first sign of new physics will
massive jet. The underlying 3j ∆R(j2 , j3 ) discrepancy is appear as an excess of events in some final
P state at large
manifest in many other final states. The final state b e j, summed scalar transverse momentum ( pT ).
arising primarily from QCD production of three jets with The Sleuth algorithm used by CDF in Tevatron Run
one misreconstructed as an electron, shows a similar dis- II is essentially that developed by DØ in Tevatron Run
crepancy in ∆R(j, b) in Fig. 5. I [33, 34, 35], and subsequently improved by H1 in HERA
While these discrepancies are clearly statistically sig- Run I [36], with small modifications.
nificant, basing a new physics claim around them is diffi- Sleuth’s definition of interest relies on the following
cult. In the kinematic regime of the discrepancy, different assumptions.
algorithms to match exact leading order calculations with
a parton shower lead to different predictions [31]. Newer 1. The data can be categorized into exclusive final
predictions have not been systematically compared to states in such a way that any signature of new
LEP 1 data, which provide constraints on parton show- physics is apt to appear predominantly in one of
ering reflected in Pythia’s tuning. Further investigation these final states.
into obtaining an adequate QCD-based description of this
discrepancy continues. 2. New physics will appear with P objects at high
summed transverse momentum ( pT ) relative to
An additional 59 discrepant distributions reflect an
standard model and instrumental background.
inadequate modeling of the overall transverse boost of
the system. The overall transverse boost of the primary 3. New physics will appear as an excess of data over
physics objects in the event is attributed to two sources: standard model and instrumental background.
the intrinsic Fermi motion of the colliding partons within
the proton, and soft or collinear radiation of the collid-
ing partons as they approach collision. Together these A. Algorithm
effects are here referred to as “intrinsic kT ,” representing
an overall momentum kick to the hard scattering. Fur-
ther discussion appears in Appendix A 2 c. The Sleuth algorithm consists of three steps, follow-
The remaining 13 discrepant distributions are seen to ing the above three assumptions.
be due to the coarseness of the Vista correction model.
Most of these discrepancies, which are at the level of
10% or less when expressed as (data − theory)/theory, 1. Final states
arise from modeling most fake rates as independent of
transverse momentum. In the first step of the algorithm, all events are placed
In summary, this global analysis of the bulk features into exclusive final states as in Vista, with the following
of the high-pT data has not yielded a discrepancy mo- modifications.
tivating a new physics claim. There are no statistically
significant population discrepancies in the 344 populated • Jets are identified as pairs, rather than individu-
final states considered, and although there are several ally, to reduce the total number of final states and
statistically significant discrepancies among the 16,486 to keep signal events with one additional radiated
kinematic distributions investigated, the nature of these gluon within the same final state. Final state names
discrepancies makes it difficult to use them to support a include “n jj” if n jet pairs are identified, with pos-
new physics claim. sibly one unpaired jet assumed to have originated
This global analysis of course cannot conclude with from a radiated gluon.
certainty that there is no new physics hiding in the CDF
data. The Vista population and shape statistics may be • The present understanding of quark flavor suggests
insensitive to a small excess of events appearing at large that b quarks should be produced in pairs. Bottom
P
pT in a highly populated final state. For such signals quarks are identified as pairs, rather than individu-
another algorithm is required. ally, to increase the robustness of identification and
to reduce the total number of final states. Final
state names include “n bb” if n b pairs are identi-
fied.
IV. SLEUTH
• Final states related through global charge conjuga-
Taking a broad view of all proposed models that might tion are considered to be equivalent. Thus e+ e− γ
extend the standard model, a profound commonality is is a different final state than e+ e+ γ, but e+ e+ γ
noted: nearly all predict an excess of events at high pT , and e− e− γ together make up a single Sleuth final
concentrated in a particular final state. The second stage state.
16

• Final states related through global interchange of • In each final state, the regions
P considered are the
the first and second generation are considered to be one dimensional intervals in pT extending from
equivalent. Thus e+ / pγ and µ+ /pγ together make each data point up to infinity. A region is required
up a single Sleuth final state. The decision to to contain at least three data events, as described
consider third generation objects (b quarks and τ in Appendix B.
leptons) differently from first and second generation
objects reflects theoretical prejudice that the third
generation may be special, and the experimental • In a particular finalP state, the data point with the
ability (in the case of b quarks) and experimental dth largest
Pvalue of pT defines an interval in the
challenge (in the case of τ leptons) in the identifi- variable pT extending from this data point up
cation of third generation objects. to infinity. This semi-infinite interval contains d
data events. The standard model prediction in this
The symbol ℓ is used to denote electron or muon. The interval, estimated from the Vista comparison de-
symbol W is used in naming final states containing one scribed above, integrates to b predicted events. In
electron or muon, significant missing momentum, and this final state, the interest of the dth region is de-
perhaps other non-leptonic objects. Thus the final states fined as the Poisson probability pd = ∞
P bi −b
i=d i! e
e+ /pγ, e− /pγ, µ+ /
pγ, and µ− /
pγ are combined into the that the standard model background b would fluc-
Sleuth final state W γ. A table showing the relation- tuate up to or above the observed number of data
ship between Vista and Sleuth final states is provided events d in this region. The most interesting region
in Appendix B 1. in this final state is the one with smallest Poisson
probability.
2. Variable
• For this final state, pseudo experiments are gener-
The second step of the algorithm considers a single ated, with pseudo data pulled from the standard
variable in each exclusive final state: the summedP
scalar model background. For each pseudo experiment,
transverse momentum of all objects in the event ( pT ). the interest of the most interesting region is calcu-
Assuming momentum conservation in the plane trans- lated. An ensemble of pseudo experiments deter-
verse to the axis of the colliding beams, mines the fraction P of pseudo experiments in this
−−→ final state in which the most interesting region is
p~i + uncl + ~/
X
p = ~0, (3) more interesting than the most interesting region
i in this final state observed in the data. If there is
where the sum over i represents a sum over all identified no new physics in this final state, P is expected to
objects in the event, the ith object has momentum ~pi , be a random number pulled from a uniform distri-
−−→ bution in the unit interval. If there is new physics
uncl denotes the vector sum of all momentum visible in
the detector but not clustered into an identified object, in this final state, P is expected to be small.
~/
p denotes the missing momentum, and the equation is a
two-component vector equality for the components of the • Looping over all final states, P is computed for each
momentum along the two spatial directions transverse to final state. The minimum of these values is denoted
the axis of the colliding beams. The Sleuth variable
P Pmin . The most interesting region in the final state
pT is then defined by with smallest P is denoted R.
−−→  
pi | + uncl + ~/
X X
pT ≡ |~ p , (4)
   
i • The interest of the most interesting region R in
where only the momentum components transverse to the theQmost interesting final state is defined by P̃ =
axis of the colliding beams are considered when comput- 1− a (1−p̂a ), where the product is over all Sleuth
ing magnitudes. final states a, and p̂a is the lesser of Pmin and the
probability for the total number of events predicted
by the standard model in the final state a to fluc-
3. Regions tuate up to or above three data events. The quan-
tity P̃ represents the fraction of hypothetical sim-
The algorithm’s third step involves searching for re- ilar CDF experiments that would produce a final
gions in which more events are seen in the data than state with P < Pmin . The range of P̃ is the unit
expected from standard model and instrumental back- interval. If the data are distributed according to
ground. This search is performed in the variable space standard model prediction, P̃ is expected to be a
defined in the second step of the algorithm, for each of random number pulled from a uniform distribution
the exclusive final states defined in the first step. in the unit interval. If new physics is present, P̃ is
The steps of the search can be sketched as follows. expected to be small.
 17

Number of pseudo-experiments
4. Output
100
The output of the algorithm is the most interesting re-
gion R observed in the data, and a number P̃ quantifying
the interest of R. A reasonable threshold for discovery is
P̃ . 0.001, which corresponds loosely to a local 5σ effect
after the trials factor is accounted for. 50
Although no integration over systematic errors is per-
formed in computing P̃, systematic uncertainties do af-
fect the final Sleuth result. If Sleuth highlights a dis-
crepancy in a particular final state, explanations in terms
of a correction to the background estimate are consid- 0
0 0.5 1
ered. This process necessarily requires physics judge- ~
P
ment. A reasonable explanation of a Sleuth discrep-
ancy in terms of an inadequacy in the modeling of the
detector response or standard model prediction that is

Number of pseudo-experiments
consistent with external information is fed back into the 100
Vista correction model and tested for global consistency.
In this way, plausible explanations for discrepancies ob-
served by Sleuth are incorporated into the Vista cor-
rection model. This iteration continues until either all
reasonable explanations for a significant Sleuth discrep-
50
ancy are exhausted, resulting in a possible new physics
claim, or no significant Sleuth discrepancy remains.

B. Sensitivity
0
-4 -2 0 2 4
~
Two important questions must be asked: P in units of σ

• Will Sleuth find nothing if there is nothing to be FIG. 6: Distribution of 103 P̃ values from 103 CDF pseudo ex-
found? periments, in which pseudo data are pulled from the standard
model prediction. The distribution of P̃ is shown in the unit
interval (upper), with one entry for each of the CDF pseudo
• Will Sleuth find something if there is something
experiments. The distribution of P̃ translated into units of
to be found? standard deviations is also shown (lower). The distribution
of P̃ from pseudo experiments is consistent with flat (upper),
If there is nothing to be found, Sleuth will find noth- and consistent with a Gaussian when translated into units of
ing 999 times out of 1000, given a uniform distribution of standard deviations (lower), as expected.
P̃ and a discovery threshold of P̃ . 0.001. The uniform
distribution of P̃ in the absence of new physics is illus-
trated in Fig. 6, using values of P̃ obtained in pseudo ex-
1. Known standard model processes
periments with pseudo data generated from the standard
model prediction. Sleuth will of course return spuri-
ous signals if provided improperly modeled backgrounds. Consideration of specific standard model processes can
The algorithm directly addresses the issue of whether an provide intuition for Sleuth’s sensitivity to new physics.
observed hint is due to a statistical fluctuation. Sleuth This section tests Sleuth’s sensitivity to the production
itself is unable to address systematic mismeasurement or of top quark pairs, W boson pairs, single top, and the
incorrect modeling, but quite useful in bringing these to Higgs boson.
attention. a. Top quark pairs. Top quark pair production re-
The answer to the second question depends to what de- sults in two b jets and two W bosons, each of which may
gree the new physics satisfies the three assumptions on decay leptonically or hadronically. The W branching ra-
which Sleuth is based: new physics will appear predom- tios are such that this signal predominantly populates
inantly in one final state, at high summed scalar trans- the Sleuth final state W bb̄jj, where “W ” denotes an
verse momentum, and as an excess of data over standard electron or muon and significant missing momentum. Al-
model prediction. Sleuth’s sensitivity to any particular though the final states ℓ+ ℓ− /pbb̄ were important in verify-
new phenomenon depends on the extent to which this ing the top quark pair production hypothesis in the initial
new phenomenon satisfies these assumptions. observation by CDF [5] and DØ [6] in 1995, most of the
18

FIG. 7: (Top left) The Sleuth final state bb̄ℓ+ ℓ′− / p, consisting of events with one electron and one muon of opposite sign,
missing momentum, and two or three jets, one or two of which are b-tagged. Data corresponding to 927 pb−1 are shown as
filled (black) circles; the standard model prediction is shown as the (red) shaded histogram. (Top right) The same final state
with tt̄ subtracted from the standard model prediction. (Bottom row) The Sleuth final state W bb̄jj, with the standard model
tt̄ contribution included (lower left) and removed (lower right). Significant discrepancies far surpassing Sleuth’s discovery
threshold are observed in these final states with tt̄ removed from the standard model background estimate. If the top quark
had not been predicted, Sleuth would have discovered it.

statistical power came from the final state W bb̄jj. The quark pair production, this process is removed from the
all hadronic decay final state bb̄ 4j has only convincingly standard model prediction, and the values of the Vista
been seen after integrating substantial Run II luminos- correction factors are re-obtained from a global fit as-
ity [37]. Sleuth’s first assumption that new physics will suming ignorance of tt̄ production. Sleuth easily dis-
appear predominantly in one final state is thus reason- covers tt̄ production in 927 pb−1 in the final states
ably well satisfied. Since the top quark has a mass of bb̄ℓ+ ℓ′− /p and W bb̄jj, shown in Fig. 7. Sleuth finds
170.9 ± 1.8 GeV [38], the production
P of two such objects Pbb̄ℓ+ ℓ′− p/ < 1.5 × 10−8 and PW bb̄jj < 8.3 × 10−7 , far
leads to a signal at large pT relative to the standard surpassing the discovery threshold of P̃ . 0.001.
model background of W bosons produced in association
with jets, satisfying Sleuth’s second and third assump- The test is repeated as a function of assumed inte-
tions. Sleuth is expected to perform reasonably well on grated luminosity, and Sleuth is found to highlight the
this example. top quark signal at an integrated luminosity of roughly
To quantitatively test Sleuth’s sensitivity to top 80 ± 60 pb−1 , where the large variation arises from sta-
 19

l + l’- pT P = 0.035 l + l’- pT

Dibosons subtracted from background
P < 1.4e-06
10
Number of Events

CDF Run II data 10

Number of Events
CDF Run II data
Pythia WW : 45% 8 SM= 56 Pythia Z(→ττ) : 51% SM= 30
25 Pythia Z(→ττ) : 27% d= 77 MadEvent W(→µ ν) γ : 13%
8
d= 77
MadEvent W(→µ ν) γ : 6.6% 25
6 MadEvent W(→µ ν) j : 7.6%
MadEvent W(→µ ν) j : 4.1% Pythia Z(→µµ ) : 6.2%
6
Other 4 Other 4
20 20
2 2

0 0
100 200 300 100 200 300
15 15

10 10

5 5

0 0
0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350

71 ∑ p (GeV)
T 71 ∑pT
(GeV)

FIG. 8: (Left) The final state ℓ+ ℓ′ /

−
p, consisting of events with an electron and muon of opposite sign and missing transverse
momentum, in 927 pb−1 of CDF data. (Right) The same final state with standard model W W , W Z, and ZZ contributions
subtracted, and with the Vista correction factors re-fit in the absence of these contributions. Sleuth finds the final state
ℓ+ ℓ′ /
−
p to contain a discrepancy surpassing the discovery threshold of P̃ < 0.001 with the processes W W , W Z, and ZZ
removed from the standard model background.

P
tistical fluctuations in the tt̄ signal events. Weaker con- it does not appear at particularly large pT relative
straints on the Vista correction factors at lower inte- to other standard model processes. Since the standard
grated luminosity marginally increase the integrated lu- model Higgs boson poorly satisfies Sleuth’s first and
minosity required to claim a discovery. second assumptions, a targeted search for this specific
b. W boson pairs. The sensitivity to standard signal is expected to outperform Sleuth.
model W W production is tested by removing this pro-
cess from the standard model background prediction and
allowing the Vista correction factors to be re-fit. In
2. Specific models of new physics
927 pb−1 of Tevatron Run II data, Sleuth identifies an
excess in the final state ℓ+ ℓ′ − /
p, consisting of an electron
and muon of opposite sign and missing momentum. This To build intuition for Sleuth’s sensitivity to new
excess corresponds to P̃ < 2 × 10−4 , sufficient for the physics signals, several sensitivity tests are conducted for
discovery of W W , as shown in Fig. 8. a variety of new physics possibilities. Some of the new
c. Single top. Single top quarks are produced physics models chosen have already been considered by
weakly, and predominantly decay to populate the more specialized analyses within CDF, making possible
Sleuth final state W bb̄, satisfying Sleuth’s first as- a comparison between Sleuth’s sensitivity and the sen-
sumption. Single top production will appear as an ex- sitivity of these previous analyses.
cess of events, satisfying Sleuth’s third assumption. Sleuth’s sensitivity can be compared to that of a ded-
Sleuth’s second assumption is not well satisfied for icated search by determining the minimum new physics
this example, since single top production does not lie at cross section σmin required for a discovery by each. The
discovery for Sleuth occurs when P̃ < 0.001. In most
P
large pT relative to other standard model processes.
Sleuth is thus expected to be outperformed by a tar- Sleuth regions satisfying the discovery threshold of
geted search in this example. P̃ < 0.001, the probability for the predicted number of
d. Higgs boson. Assuming a standard model Higgs events to fluctuate up to or above the number of events
boson of mass mh = 115 GeV, the dominant observable observed corresponds to greater than 5σ. The discov-
production mechanism is pp̄ → W h and pp̄ → Zh, popu- ery for the dedicated search occurs when the observed
lating the final states W bb̄, ℓ+ ℓ− bb̄, and /
p bb̄. The signal excess of data corresponds to a 5σ effect. Smaller σmin
is thus spread over three Sleuth final states. Events in corresponds to greater sensitivity.
the last of these ( /
p bb̄) do not pass the Vista event selec- The sensitivity tests are performed by first generating
tion, which does not use / p as a trigger object. Sleuth’s pseudo data from the standard model background pre-
first assumption is thus poorly satisfied for this exam- diction. Signal events for the new physics model are gen-
ple. The standard model Higgs boson signal will appear erated, passed through the chain of CDF detector simu-
as an excess, but as in the case of single top production lation and event reconstruction, and consecutively added
20

Model Description Sensitivity

1 GMSB, Λ = 82.6 GeV, tan β = 15,

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
µ > 0, with one messenger of M = σ min (pb)
2Λ.

2 Z ′ → ℓ+ ℓ− , mZ ′ = 250 GeV, with

standard model couplings to lep- 1 1.2 1.4 1.6 1.8
σmin (pb)
tons.

3 Z ′ → q q̄, mZ ′ = 700 GeV,

with standard model couplings to 3 3.5 4 4.5 5 5.5
σmin (pb)
quarks.

4 Z ′ → q q̄, mZ ′ = 1 TeV, with stan-

dard model couplings to quarks. 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1
σmin (pb)

5 Z ′ → tt̄, mZ ′ = 500 GeV, with

standard model couplings to tt̄. 0 1 2 3 4 5 6
σmin (pb)

TABLE III: Summary of Sleuth’s sensitivity to several new physics models, expressed in terms of the minimum production
cross section needed for discovery with 927 pb−1 . Where available, a comparison is made to the sensitivity of a dedicated
search for this model. The solid (red) box represents Sleuth’s sensitivity, and the open (white) box represents the sensitivity
of the dedicated analysis. Systematic uncertainties are not included in the sensitivity calculation. The width of each box shows
typical variation under fluctuation of data statistics. In Models 3 and 4, there is no targeted analysis available for comparison.
Sleuth is seen to perform comparably to the targeted analyses on models satisfying the assumptions on which Sleuth is
based.

to the pseudo data until Sleuth finds P̃ < 0.001. The tions on which Sleuth P is based. For models in which
number of signal events needed to trigger discovery is Sleuth’s simple use of pT can be improved upon by
used to calculate σmin . optimizing for a specific feature, a targeted search may
For each dedicated analysis to which Sleuth is com- be expected to achieve greater sensitivity. One of the im-
pared, the number of standard model events expected portant features of Sleuth is that it not only performs
in 927 pb−1 within the region targeted is used to calcu- reasonably well, but that it does so broadly. In Model
late the number of signal events required in that region 1, a search for a particular model point in a gauge medi-
to produce a discrepancy corresponding to 5σ. Using ated supersymmetry breaking (GMSB) scenario, Sleuth
the signal efficiency determined in the dedicated analysis, gains an advantage by exploiting a final state not consid-
σmin is calculated. The effect of systematic uncertainties ered in the targeted analysis [39]. In Model 2, a search for
are removed from the dedicated analyses, and are not a Z ′ decaying to lepton pairs, the targeted analysis [40]
included for Sleuth. The inclusion of systematic uncer- exploits the narrow resonance in the e+ e− invariant mass.
tainties will reduce the sensitivity of both Sleuth and In Models 3 and 4, which are searches for a hadronically
the dedicated analysis to the extent that the systematic decaying Z ′ of different masses, there is no targeted anal-
parameters are allowed to vary. Vista and Sleuth have ysis against which to compare. In Model 5, a search for
the advantage of using a large data set to constrain them. a Z ′ → tt̄ resonance, the signal appears at large summed
The results of five such sensitivity tests are summa- scalar transverse momentum in a particular final state,
rized in Table III. Sleuth is seen to perform comparably resulting in comparable sensitivity between Sleuth and
to targeted analyses on models satisfying the assump- the targeted analysis [41].
 21

Entries 72
as discussed below.
25 The final state j /p, consisting of events with one recon-
structed jet and significant missing transverse momen-
Number of final states

20
tum, is the second final state identified by Sleuth. The
primary background is due to non-collision processes, in-
cluding cosmic rays and beam halo backgrounds, whose
15
estimation is discussed in Appendix A 2 a. Since the
hadronic energy is not required to be deposited in time
10
with the beam crossing, Sleuth’s analysis of this final
state is sensitive to particles with a lifetime between 1 ns
5 and 1 µs that lodge temporarily in the hadronic calorime-
ter, complementing Ref. [42].
+ + +
0
0 0.2 0.4 0.6 0.8 1 The final states ℓ+ ℓ′ /pjj, ℓ+ ℓ′ /p, and ℓ+ ℓ′ all con-
P ′
tain an electron (ℓ) and muon (ℓ ) with identical recon-
FIG. 9: The distribution of P in the data, with one entry for structed charge (either both positive or both negative).
each final state considered by Sleuth. The final states with and without missing transverse mo-
mentum are qualitatively different in terms of the stan-
dard model processes contributing to the background es-
−
timate, with the final state ℓ+ ℓ′ composed mostly of di-
C. Results
jets where one jet is misreconstructed as an electron and
a second jet is misreconstructed as a muon; Z → τ + τ − ,
The distribution of P for the final states considered where one tau decays to a muon and the other to a lead-
by Sleuth in the data is shown in Fig. 9. The concav- ing π 0 , one of the two photons from which converts while
ity of this distribution reflects the degree to which the traveling through the silicon support structure to result
correction model described in Sec. III F has been tuned. in an electron reconstructed with the same sign as the
A crude correction model tends to produce a distribu- muon, as described in Appendix A 1; and Z → µ+ µ− ,
tion that is concave upwards, as seen in this figure, while in which a photon is produced, converts, and is misre-
an overly tuned correction model produces a distribution constructed as an electron. The final states containing
that is concave downwards, with more final states than missing transverse momentum are dominated by the pro-
expected having P near the midpoint of the unit interval. duction of W (→ µν) in association with one or more
The most interesting final states identified by Sleuth jets, with one of the jets misreconstructed as an elec-
are shown in Fig. 10, together with a quantitative mea- tron. The muon is significantly more likely than the
sure (P) of the interest of the most interesting region in electron to have been produced in the hard interaction,
each final state, determined as described in Sec. IV A 3. since the fake rate p(j → µ) is roughly an order of mag-
The legends of Fig. 10 show the primary contributing nitude smaller than the fake rate p(j → e), as observed
−
standard model processes in each of these final states, in Table I. The final state ℓ+ ℓ′ /pjj, which contains two
together with the fractional contribution of each. The or three reconstructed jets in addition to the electron,
top six final states, which correspond to entries in the muon, and missing transverse momentum, also has some
leftmost bin in Fig. 9. span a range of populations, rel- contribution from W Z and top quark pair production.
evant physics objects, and important background contri- The final state τ /p contains one reconstructed tau, sig-
butions. nificant missing transverse momentum, and one recon-
The final state bb̄, consisting of two or three recon- structed jet with pT > 200 GeV. This final state in prin-
structed jets, one or two of which are b-tagged, heads ciple also contains events with one reconstructed tau, sig-
the list. These events enter the analysis by satisfying nificant missing transverse momentum, and zero recon-
the Vista offline selection requiring one or more jets or structed jets, but such events do not satisfy the offline
b-jets with pT > 200 GeV. The definition of Sleuth’s selection criteria described in Sec. III C. Roughly half
of the background is non-collision, in which two differ-
P
pT variable is such
P that all events in this final state
consequently have pT > 400 GeV. Sleuth chooses the ent cosmic ray muons (presumably from the same cosmic
pT > 469 GeV, which includes nearly 104 data ray shower) leave two distinct energy deposits in the CDF
P
region
events. The standard model prediction in this region hadronic calorimeter, one with pT > 200 GeV, and one
is sensitive to the b-tagging efficiency p(b → b) and the with a single associated track from a pp̄ collision occur-
fake rate p(j → b), which have few strong constraints on ring during the same bunch crossing. Less than a single
their values for jets with pT > 200 GeV other than those event is predicted from this non-collision source (using
imposed by other Vista kinematic distributions within techniques described in Appendix A 2 a) over the past
this and a few other related final states. For this region five years of Tevatron running.
Sleuth finds Pbb̄ = 0.0055, which is unfortunately not In these CDF data, Sleuth finds P̃ = 0.46. The frac-
statistically significant after accounting for the trials fac- tion of hypothetical similar CDF experiments (assuming
tor associated with looking in many different final states, a fixed standard model prediction, detector simulation,
22

bb P = 0.0055 j pT P = 0.0092
240

Number of Events
CDF Run II data
Number of Events
CDF Run II data 2000 600 220
Pythia jj : 82% 1800 SM= 9540 Non-collision : 88% 200 SM= 1030
Pythia bj : 18% 1600 d= 9900 Pythia jj : 9.3% 180 d= 1150
3500 MadEvent Z(→νν) j : 0.89% 160
Pythia γ j : 0.2% 1400
140
Herwig tt : 0.11% 1200
500 MadEvent W(→µ ν) j : 0.76% 120
Other 1000 Other 100
3000 800 80
600 60
400 40
2500 200 400 20
0 0
600 800 1000 1200 1000 2000 3000

2000 300

1500
200
1000
100
500

0 0
400 500 600 700 800 900 1000 1100 1200 1300 500 1000 1500 2000 2500 3000

469 ∑
p (GeV)
T 679 ∑p (GeV)
T

+ + + +
l l’ pT jj P = 0.011 l l’ pT P = 0.016
3.5
Number of Events

Number of Events
CDF Run II data CDF Run II data 6
2.5 MadEvent W(→µ ν) jjj : 23% 3 SM= 0.71 9 MadEvent W(→µ ν) γ : 27% 5 SM= 6.9
MadEvent W(→µ ν) jj : 21% 2.5 d= 4 MadEvent W(→µ ν) j : 14% d= 16
Pythia WZ : 14% Pythia Z(→µµ ) : 13% 4
Herwig tt : 9.9% 2 8 MadEvent W(→µ ν) jj : 9.5%
3
Other 1.5 Other
2
1 7 2

0.5 1
6
0 0
1.5 200 250 300 150 200 250
5

4
1
3

0.5 2

0 0
0 100 200 300 400 500 600 0 50 100 150 200 250 300 350

168 ∑ p (GeV)
T 117 ∑p T
(GeV)

τ pT P = 0.016 l l’ + +
P = 0.021
10
Number of Events

Number of Events

CDF Run II data 4.5 CDF Run II data

2.5 cosmic : 49% 4 SM= 1.2 18 Pythia jj : 29% SM= 16
8
Pythia Z(→ττ) : 30% 3.5 d= 5 Pythia Z(→ττ) : 18% d= 29
Herwig tt : 7.1% 3 Pythia Z(→µµ ) : 15%
MadEvent W(→µ ν) jj : 6.7% 16 MadEvent W(→µ ν) jj : 11%
6
2.5
Other 2 Other 4
2 14
1.5
1 2
0.5 12
0 0
1.5 450 500 550 100 150
10

8
1
6

0.5 4

0 0
400 500 600 700 800 900 1000 1100 0 20 40 60 80 100 120 140 160 180 200

416 ∑ p (GeV)
T 57 ∑p T
(GeV)

FIG. 10: The most interesting final states identified by Sleuth. The region chosen by Sleuth, extending up to infinity, is
shown by the (blue) arrow just below the horizontal axis. Data are shown as filled (black) circles, and the standard model
prediction is shown as the shaded (red) histogram. The Sleuth final state is labeled in the upper left corner of each panel, with
ℓ denoting e or µ, and ℓ+ ℓ′+ denoting an electron and muon with the same electric charge. The number at upper right in each
panel shows P, the fraction of hypothetical similar experiments in which something at least as interesting as the region shown
would be seen in this final state. The inset in each panel shows an enlargement of the region selected by Sleuth, together with
the number of events (SM) predicted by the standard model in this region, and the number of data events (d) observed in this
region.
 23

and correction model) that would exhibit a final state and compared with data in 344 populated exclusive final
with P smaller than the smallest P observed in the CDF states and 16,486 relevant kinematic distributions, most
Run II data is approximately 46%. The actual value ob- of which have not been previously considered. Considera-
tained for P̃ is not of particular interest, except to note tion of exclusive final state populations yields no statisti-
that this value is significantly greater than the thresh- cally significant (> 3σ) discrepancy after the trials factor
old of . 0.001 required to claim an effect of statistical is accounted for. Quantifying the difference in shape of
significance. Sleuth has not revealed a discrepancy of kinematic distributions using the Kolmogorov-Smirnov
sufficient statistical significance to justify a new physics statistic, significant discrepancies are observed between
claim. data and standard model prediction. These discrepan-
Systematics are incorporated into Sleuth in the form cies are believed to arise from mismodeling of the parton
of the flexibility in the Vista correction model, as de- shower and intrinsic kT , and represent observables for
scribed previously. This flexibility is significantly more which a QCD-based understanding is highly motivated.
important in practice than the uncertainties on particular None of the shape discrepancies highlighted motivates a
correction factor values obtained from the fit, although new physics claim.
the latter are easier to discuss. The relative importance A further systematic
P search (Sleuth) for regions of
of correction factor value uncertainties on Sleuth’s re- excess on the high- pT tails of exclusive final states has
sult depends on the number ofPpredicted standard model been performed, representing a quasi-model-independent
events (b) in Sleuth’s high pT tail. The uncertain- search for new electroweak scale physics. Most of the ex-
ties on the correction factors of Table I are such that clusive final states searched with Sleuth have not been
the appropriate addition in quadrature gives a typical considered by previous Tevatron analyses. A measure of
uncertainty of ≈ 10% on the total background predic- interest rigorously accounting for the trials factor asso-
tion in each
√ final state. Using σsys ≈ 10% × b and ciated with looking in many regions with few events is
σstat ≈ b, the relative importance of systematic un- defined, and used to quantify the most interesting region
certainty and statistical √ uncertainty is estimated to be observed P in the CDF Run II data. No region of excess on
σsys /σstat = 10% × b/ b. The importance of system- the high- pT tail of any of the Sleuth exclusive final
atic and states surpasses the discovery threshold.
P statistical uncertainties are thus comparable for
high pT tails containing b ∼ 100 predicted events. The Although this global analysis of course cannot prove
effect of systematic uncertainties is provided in this ap- that no new physics is hiding in these data, this broad
proximation rather than through a rigorous integration search of the Tevatron Run II data represents one of the
over these uncertainties as nuisance parameters due to single most encompassing tests of the particle physics
the high computational cost of performing the integra- standard model at the energy frontier.
tion. This estimate of systematic uncertainty is valid only
within the particular correction model resulting in the list
of correction factors shown in Table I; additional changes Acknowledgments
to the correction model may result in larger variation.
The inclusion of additional systematic uncertainties does Tim Stelzer and Fabio Maltoni have provided partic-
not qualitatively change the conclusion that Sleuth has ularly valuable assistance in the estimation of standard
not revealed a discrepancy of sufficient statistical signifi- model backgrounds. Sergey Alekhin provided helpful cor-
cance to justify a new physics claim. respondence in understanding the theoretical uncertain-
Due to the large number of final states considered, ties on W and Z production imposed as constraints on
there are regions (such as those shown in Fig. 10) in which the Vista correction factor fit. Sascha Caron provided
the probability for the standard model prediction to fluc- insight gained from the general search at H1. Torbjörn
tuate up to or above the number of events observed in Sjöstrand assisted in the understanding of Pythia’s
the data corresponds to a significance exceeding 3σ if the treatment of parton showering applied to the Vista 3j
appropriate trials factor is not accounted for. A doubling ∆R(j2 , j3 ) discrepancy.
of data may therefore result in discovery. In particular, We thank the Fermilab staff and the technical staffs
although the excesses in Fig. 10 are currently consistent of the participating institutions for their vital contribu-
with simple statistical fluctuations, if any of them are tions. This work was supported by the U.S. Department
genuinely due to new physics, Sleuth will find they pass of Energy and National Science Foundation; the Italian
the discovery threshold of P̃ < 0.001 with roughly a dou- Istituto Nazionale di Fisica Nucleare; the Ministry of
bling of data. Education, Culture, Sports, Science and Technology of
Japan; the Natural Sciences and Engineering Research
Council of Canada; the National Science Council of the
V. CONCLUSIONS Republic of China; the Swiss National Science Founda-
tion; the A.P. Sloan Foundation; the Bundesministerium
A broad search for new physics (Vista) has been per- für Bildung und Forschung, Germany; the Korean Sci-
formed in 927 pb−1 of CDF Run II data. A complete ence and Engineering Foundation and the Korean Re-
standard model background estimate has been obtained search Foundation; the Science and Technology Facilities
 24

e+ e− µ+ µ− τ+ τ− γ j b tor fit, including the construction of the χ2 function that

+
e 62228 33 0 0 182 0 2435 28140 0 is minimized and the resulting covariance matrix. Ap-
e− 24 62324 0 0 0 192 2455 28023 1 pendix A 4 discusses the values of the correction factors
µ +
0 0 50491 0 6 0 0 606 0 that are obtained.
µ− 0 1 0 50294 0 6 0 577 0
γ 1393 1327 0 0 1 1 67679 21468 0
1. Fake rate physics
π 0 1204 1228 0 0 5 8 58010 33370 0
π+ 266 0 115 0 41887 6 95 54189 37
− The following facts begin to build a unified understand-
π 1 361 0 88 13 41355 148 54692 44
ing of fake rates for electrons, muons, taus, and photons.
K+ 156 1 273 0 42725 7 37 52317 24 This understanding is woven throughout the Vista cor-
K− 1 248 0 165 28 41562 115 53917 22 rection model, and significantly informs and constrains
B+ 100 0 77 1 100 10 40 66062 25861 the Vista correction process. Explicit constraints de-
B− 2 85 3 68 11 99 45 66414 25621 rived from these studies are provided in Appendix A 3.
B 0
88 27 87 17 77 32 21 65866 25046 The underlying physical mechanisms for these fakes lead
B¯0 17 79 11 71 41 77 21 66034 25103 to simple and well justified relations among them.
D+ 126 6 62 0 1485 67 207 79596 11620 Table IV shows the response of the CDF detector sim-
D− 4 134 3 74 64 1400 234 79977 11554
ulation, reconstruction, and object identification algo-
rithms to single particles. Using a single particle gun, 105
D0 60 13 27 2 312 1053 248 88821 5487
particles of each type shown at the left of the table are
D̄0 15 46 5 28 1027 253 237 89025 5480 shot with pT = 25 GeV into the CDF detector, uniformly
KL0 1 4 0 0 71 60 202 96089 26 distributed in θ and in φ. The resulting reconstructed ob-
KS0 26 31 2 1 170 525 9715 76196 0 ject types are shown at the top of the table, labeling the
τ + 1711 13 1449 0 4167 2 673 50866 607 columns. The first four entries on the diagonal at upper
τ− 12 1716 0 1474 6 3940 621 51125 580 left show the efficiency for reconstructing electrons and
u 8 10 1 0 446 31 247 94074 26 muons [56]. The fraction of electrons misidentified as
d 3 4 0 0 64 308 191 94322 22 photons, shown in the top row, seventh column, is seen
to be roughly equal to the fraction of photons identified
g 2 0 0 0 17 14 12 81865 99
as electrons or positrons, shown in the fifth row, first and
TABLE IV: Central single particle misidentification matrix. second columns, and measures the number of radiation
Using a single particle gun, 105 particles of each type shown lengths in the innermost regions of the CDF tracker. The
at the left of the table are shot with pT = 25 GeV into the cen- fraction of B mesons identified as electrons or muons, pri-
tral CDF detector, uniformly distributed in θ and in φ. The marily through semileptonic decay, are shown in the four
resulting reconstructed object types are shown at the top of left columns, eleventh through fourteenth rows. Other
the table, labeling the table columns. Thus the rightmost ele- entries provide similarly useful information, most easily
ment of this matrix in the fourth row from the bottom shows comprehensible from simple physics.
p(τ − → b), the number of negatively charged tau leptons (out
The transverse momenta of the objects reconstructed
of 105 ) reconstructed as a b-tagged jet.
from single particles are displayed in Fig. 11. The rel-
ative resolutions for the measurement of electron and
muon momenta are shown in the first four histograms
Council and the Royal Society, UK; the Institut National on the diagonal at upper left. The histograms in the
de Physique Nucleaire et Physique des Particules/CNRS; left column, sixth through eighth rows, show that sin-
the Russian Foundation for Basic Research; the Comisión gle neutral pions misreconstructed as electrons have their
Interministerial de Ciencia y Tecnologı́a, Spain; the Eu- momenta well measured, while single charged pions mis-
ropean Community’s Human Potential Programme; the reconstructed as electrons have their momenta system-
Slovak R&D Agency; and the Academy of Finland. atically undermeasured, as discussed below. The his-
togram in the top row, second column from the right,
shows that electrons misreconstructed as jets have their
APPENDIX A: VISTA CORRECTION MODEL energies systematically overmeasured. Other histograms
DETAILS in Fig. 11 contain similarly relevant information, easily
overlooked without the benefit of this study, but under-
This appendix contains details of the Vista correc- standable from basic physics considerations once the ef-
tion model. Appendix A 1 covers the physical mecha- fect has been brought to attention.
nisms underlying fake rates. Appendix A 2 contains in- Here and below p(q → X) denotes a quark fragmenting
formation about additional background sources, includ- to X carrying nearly all of the parent quark’s energy, and
ing backgrounds from cosmic rays and beam halo, mul- p(j → X) denotes a parent quark or gluon being misre-
tiple interactions, and the effects of intrinsic kT . Ap- constructed in the detector as X.
pendix A 3 contains details of the Vista correction fac- The probability for a light quark jet to be misrecon-
 25

e+ e- µ+ µ- τ+ τ- γ j b structed as an e+ can be written

e+
p(j → e+ ) = p(q → γ) p(γ → e+ ) +
p(q → π 0 ) p(π 0 → e+ ) +
e-
p(q → π + ) p(π + → e+ ) +
µ+
p(q → K + ) p(K + → e+ ). (A1)

A similar equation holds for a light quark jet faking an

µ-
e− .
γ
The probability for a light quark jet to be misrecon-
structed as a µ+ can be written
π0
p(j → µ+ ) = p(q → π + ) p(π + → µ+ ) +
π+ p(q → K + ) p(K + → µ+ ). (A2)

π- Here p(π → µ) denotes pion decay-in-flight, and p(K → µ)

denotes kaon decay-in-flight; other processes contribute
K+ negligibly. A similar equation holds for a light quark jet
faking a µ− .
K- The only non-negligible underlying physical mecha-
nisms for a jet to fake a photon are for the parent quark
B+ or gluon to fragment into a photon or a neutral pion, car-
rying nearly all the energy of the parent quark or gluon.
B- Thus

B0 p(j → γ) = p(q → π 0 ) p(π 0 → γ) +

p(q → γ) p(γ → γ). (A3)
B0
Up and down quarks and gluons fragment nearly
D+ equally to each species of pion; hence
D- 1
p(q → π) = p(q → π + ) = p(q → π − )
3
D0 = p(q → π 0 ), (A4)
D0 where p(q → π) denotes fragmentation into any pion car-
rying nearly all of the parent quark’s energy. Fragmenta-
K0L
tion into each type of kaon also occurs with equal prob-
ability; hence
K0S
1
τ+
p(q → K) = p(q → K + ) = p(q → K − )
4
= p(q → K 0 ) = p(q → K¯0 ), (A5)
τ-

where p(q → K) denotes fragmentation into any kaon car-

u
rying nearly all of the parent quark’s energy.
Pythia contains a parameter that sets the number
d
of string fragmentation kaons relative to the number of
fragmentation pions. The default value of this parame-
g
ter, which has been tuned to LEP I data, is 0.3; for every
1 up quark and every 1 down quark, 0.3 strange quarks
FIG. 11: Transverse momentum distribution of reconstructed are produced. Strange particles are produced perturba-
objects (labeling columns) arising from single particles (la- tively in the hard interaction itself, and in perturbative
beling rows) with pT = 25 GeV shot from a single particle radiation, at a ratio larger than 0.3:1:1. This leads to the
gun into the central CDF detector. The area under each his- inequality
togram is equal to the number of events in the corresponding
misidentification matrix element of Table IV, with the verti- p(q → K)
cal axis of each histogram scaled to the peak of each distribu- 0.3 . < 1, (A6)
p(q → π)
tion. A different vertical scale is used for each histogram, and
histograms with fewer than ten events are not shown. The where p(q → K) and p(q → π) are as defined above.
horizontal axis ranges from 0 to 50 GeV.
26

FIG. 12: A few of the most discrepant distributions in the final states ej and jµ, which are greatly affected by the fake
rates p(j → e) and p(j → µ), respectively. These distributions are among the 13 significantly discrepant distributions identified
as resulting from coarseness of the correction model employed. The vertical axis shows the number of events; the horizontal
axes show the transverse momentum and pseudorapidity of the lepton. Filled (black) circles show CDF data, and the shaded
(red) histogram shows the standard model prediction. Events enter the ej final state either on a central electron trigger with
pT > 25 GeV, or on a plug electron trigger with pT > 40 GeV. The fake rate p(j → e) is significantly larger in the plug region
than in the central region of the CDF detector. Muons are identified with separate detectors covering the regions |η| < 0.6 and
0.6 < |η| < 1.0.

The probability for a jet to be misreconstructed as a data, Pythia predicts the probability for a quark jet to
tau lepton can be written fake a one-prong tau to be roughly four times the proba-
bility for a gluon jet to fake a one-prong tau. This differ-
p(j → τ + ) = p(j → τ1+ ) + p(j → τ3+ ), (A7) ence in fragmentation is incorporated into Vista’s treat-
ment of jets faking electrons, muons, taus, and photons.
where p(j → τ1+ ) denotes the probability for a jet to fake The Vista correction model includes such correction fac-
a 1-prong tau, and p(j → τ3+ ) denotes the probability for tors as the probability for a jet with a parent quark to
a jet to fake a 3-prong tau. For 1-prong taus, fake an electron (0033 and 0034) and the probability for
p(j → τ1+ ) = p(q → π + ) p(π + → τ + ) + a jet with a parent quark to fake a muon (0035); the
probability for a jet with a parent gluon to fake an elec-
p(q → K + ) p(K + → τ + ). (A8) tron or muon is then obtained by dividing the values of
these fitted correction factors by four.
Similar equations hold for negatively charged taus.
Figure 14 shows the probability for a quark (or gluon) The physical mechanism underlying the process
to fake a one-prong tau, as a function of transverse mo- whereby an incident photon or neutral pion is misrecon-
mentum. Using fragmentation functions tuned on LEP 1 structed as an electron is a conversion in the material
 27

FIG. 13: A few of the most discrepant distributions in the final states jτ and jγ, which are greatly affected by the fake rates
p(j → τ ) and p(j → γ), respectively. The vertical axis shows the number of events; the horizontal axes show the transverse
momentum and pseudorapidity of the tau lepton and photon. Filled (black) circles show CDF data, and the shaded (red)
histogram shows the standard model prediction. The distributions in the jγ final state are among the 13 significantly discrepant
distributions identified as resulting from coarseness of the correction model employed.

serving as the support structure of the silicon vertex de- tive to the K − cross section by roughly a factor of two.
tector. This process produces exactly as many e+ as e− , The physical process primarily responsible for π ± →
leading to e± is inelastic charge exchange
1
p(γ → e) = p(γ → e+ ) = p(γ → e− ) π− p → π0 n
2
1 π+ n → π0 p (A10)
p(π 0 → e) = p(π 0 → e+ ) = p(π 0 → e− ), (A9)
2 occurring within the electromagnetic calorimeter. The
where e is an electron or positron. charged pion leaves the “electron’s” track in the CDF
From Fig. 11, the average pT of electrons reconstructed tracking chamber, and the π 0 produces the “electron’s”
from 25 GeV incident photons is 23.9 ± 1.4 GeV. The av- electromagnetic shower. No true electron appears at all
erage pT of electrons reconstructed from incident 25 GeV in this process, except as secondaries in the electromag-
neutral pions is 23.7 ± 1.3 GeV. netic shower originating from the π 0 .
The charge asymmetry between p(K + → e+ ) and The average pT of reconstructed “electrons” originat-
p(K − → e− ) in Table IV arises because K − can capture ing from a single charged pion is 18.8 ± 2.2 GeV, indi-
on a nucleon, producing a single hyperon. Conservation cating that the misreconstructed “electron” in this case
of baryon number and strangeness prevents K + from cap- is measured to have on average only 75% of the total en-
turing on a nucleon, reducing the K + cross section rela- ergy of the parent quark or gluon. This is expected, since
28

through the calorimeter is Lcal ≈ 2 meters, leading to

p(decays within calorimeter) ≈ 0.00025. Summing the
contributions from decay within the tracking volume
and decay within the calorimeter volume, p(π + → µ+ ) ≈
0.00125.
The primary physical mechanism by which a jet fakes a
photon is for the parent quark or gluon to fragment into a
leading π 0 carrying nearly all the momentum. The highly
boosted π 0 decays within the beam pipe to two photons
that are sufficiently collinear to appear in the preshower,
electromagnetic calorimeter, and shower maximum de-
tector as a single photon. Thus
p(j → γ) = p(q → π 0 )p(π 0 → γ). (A14)
An immediate corollary is that the misreconstructed
“photon” carries the energy of the parent quark or gluon,
and is well measured.
Typical jets are measured with poorer energy resolu-
FIG. 14: The probability for a generated parton to be mis- tion than jets that have faked electrons, muons, or pho-
reconstructed as a one-prong τ , as a function of the parton’s
tons.
generated pT . Filled (red) circles show the probability for a
jet arising from a parent quark to be misreconstructed as a
Since p(q → π 0 ) ≫ p(q → γ), it follows from Eq. A4 and
one-prong tau. Filled (blue) triangles show the probability Table IV that the conversion contribution to p(j → e) is
for a jet arising from a parent gluon to be misreconstructed ≈ 75%, and the charge exchange contribution is ≈ 25%:
as a one-prong tau. 0.75
=( p(q → γ) p(γ → e+ )+
0.25
the recoiling nucleon from the charge exchange process p(q → π 0 ) p(π 0 → e+ ) ) /
carries some of the incident pion’s momentum. ( p(q → π + ) p(π + → e+ )+
An additional small loss in energy for a jet misrecon- p(q → K + ) p(K + → e+ ) ). (A15)
structed as an electron, photon, or muon is expected since
the leading π + , K + , π 0 , or γ takes only some fraction of
the parent quark’s energy. The number of e+ j events in data is 0.9 times the
The cross sections for π − p → π 0 n and π + n → π 0 p, number of e− j events. This charge asymmetry arises
proceeding through the isospin I conserving and I3 inde- from p(K + → e+ ) and p(K − → e− ) in Table IV. Quanti-
pendent strong interaction, are roughly equal. The cor- tatively,
responding particles in the two reactions are related by p(j → e+ ) 0.9 + 0.2 p(K + → e+ )/p(K → e)
interchanging the signs of their z-components of isospin. = , (A16)
p(j → e− ) 0.9 + 0.2 p(K − → e− )/p(K → e)
The probability for a 25 GeV π + to decay to a µ+ can
be written where 0.9 is the sum of 0.75 from Eq. A15 and
0.15 ≈ 0.25 × 0.6 from Eq. A6, and 0.2 is twice
p(π + → µ+ ) = p(decays within tracker) + 1 − 0.9. From p(K + → e+ ) and p(K − → e− )
p(decays within calorimeter). (A11) in Table IV, p(K + → e+ )/p(K → e) = 1/3
− −
and p(K → e )/p(K → e) = 2/3, predicting
The probability for the pion to decay within the tracking p(j → e+ )/p(j → e− ) = 0.935, in reasonable agree-
volume is ment with the ratio of the observed number of events in
the e+ j and e− j final states.
p(decays within tracker) = 1 − e−Rtracker /γ(cτ ), (A12) The number of j µ+ events observed in CDF Run
II is 1.1 times the number of j µ− events observed.
where γ = 25 GeV / 140 MeV = 180 is the pion’s This charge asymmetry arises from p(K + → µ+ ) and
Lorentz boost, the proper decay length of the charged p(K − → µ− ) in Table IV.
pion is (cτ ) = 7.8 meters, and the radius of the The physical mechanism by which a prompt photon
CDF tracking volume is Rtracker = 1.5 meters, giving fakes a tau lepton is for the photon to convert, producing
p(decays within tracker) = 0.001. The probability for an electron or positron carrying most of the photon’s
the pion to decay within the calorimeter volume is energy, which is then misreconstructed as a tau. The
p(decays within calorimeter) ≈ λI /γ(cτ ), (A13) probability for this to occur is equal for positively and
negatively charged taus,
where λI ≈ 0.4 meters is the nuclear interaction length 1
for charged pions on lead or iron and the path length p(γ → τ ) = p(γ → τ + ) = p(γ → τ − ), (A17)
2
 29

and is related to previously defined quantities by Isolated and energetic electrons and muons arising from
1 parent b quarks in this way are modeled as having pT
p(γ → τ ) = p(γ → e) p(e → τ ), (A18) equal to the parent b quark pT , multiplied by a random
p(e → e) number uniformly distributed between 0 and 1.
where p(γ → e) denotes the fraction of produced photons
that are reconstructed as electrons, p(e → e) denotes the
fraction of produced electrons that are reconstructed as 2. Additional background sources
electrons, and hence p(γ → e)/p(e → e) is the fraction of
produced photons that pair produce a single leading elec- This appendix provides additional details on the esti-
tron. mation of the standard model prediction.
Note p(e → γ) ≈ p(γ → e) from Table IV, as expected,
with value of ≈ 0.03 determined by the amount of mate-
rial in the inner detectors and the tightness of isolation a. Cosmic ray and beam halo muons
criteria. A hard bremsstrahlung followed by a conver-
sion is responsible for electrons to be reconstructed with There are four dominant categories of events caused by
opposite sign; hence cosmic ray muons penetrating the detector: µ /p, µ+ µ− ,
p(e± → e∓ ) = p(e+ → e− ) = p(e− → e+ ) γ /p, and j /p. There is negligible contribution from cosmic
ray secondaries of any particle type other than muons.
≈ 12 p(e± → γ)p(γ → e∓ ), (A19)
A cosmic ray muon penetrating the CDF detector
where the factor of 1/2 comes because the material al- whose trajectory passes within 1 mm of the beam line
ready traversed by the e± will not be traversed again by and within −60 < z < 60 cm of the origin may be recon-
the γ. In particular, track curvature mismeasurement is structed as two outgoing muons. In this case the cosmic
not responsible for erroneous sign determination in the ray event is partitioned into the final state µ+ µ− . If
central region of the CDF detector. one of the tracks is missed, the cosmic ray event is parti-
From knowledge of the underlying physical mecha- tioned into the final state µ /p. The standard CDF cosmic
nisms by which jets fake electrons, muons, taus, and ray filter, which makes use of drift time information in
photons, the simple use of a reconstructed jet as a lep- the central tracking chamber, is used to reduce these two
ton or photon with an appropriate fake rate applied to categories of cosmic ray events.
the weight of the event needs slight modification to cor- CDF data events with exactly one track (correspond-
rectly handle the fact that a jet that has faked a lep- ing to one muon) and events with exactly two tracks (cor-
ton or photon generally is measured more accurately responding to two muons) are used to estimate the cosmic
than a hadronic jet. Rather than using the momentum ray muon contribution to the final states µ /p and µ+ µ−
of the reconstructed jet, the momentum of the parent after the cosmic ray filter. This sample of events is used
quark or gluon is determined by adding up all Monte as the standard model background process cosmic µ.
Carlo particle level objects within a cone of ∆R = 0.4 The cosmic µ sample does not contribute to the events
about the reconstructed jet. In misreconstructing a jet passing the analysis offline trigger, whose cleanup cuts
in an event, the momentum of the corresponding par- require the presence of three or more tracks. Roughly
ent quark or gluon is used rather than the momentum 100 events are expected from cosmic ray muons in the
of the reconstructed jet. A jet that fakes a photon categories µ+ /p and µ+ µ− . The sample cosmic µ is ne-
then has momentum equal to the momentum of the par- glected from the background estimate, since there is no
ent quark or gluon plus a fractional correction equal to discrepancy that demands its inclusion.
0.01×(parent pT −25 GeV)/(25 GeV) to account for leak- The remaining two categories are γ /p and j /p, result-
age out
√ of the √cone of ∆R = 0.4, and a further smearing ing from a cosmic ray muon that penetrates the CDF
of 0.2 GeV× parent pT , reflecting the electromagnetic electromagnetic or hadronic calorimeter and undergoes
resolution of the CDF detector. The momenta of jets that a hard bremsstrahlung in one calorimeter cell. Such an
fake photons are multiplied by an overall factor of 1.12, interaction can mimic a single photon or a single jet, re-
and jets that fake electrons, muons, or taus are multi- spectively. The reconstruction algorithm infers the pres-
plied by an overall factor of 0.95. These numbers are ence of significant missing energy balancing the “photon”
determined by the ℓ / p, ℓj, and γj final states. The distri- or “jet.” If this cosmic ray interaction occurs during a
butions most sensitive to these numbers are the missing bunch crossing in which there is a pp̄ interaction produc-
energy and the jet pT . ing three or more tracks, the event will be partitioned
A b quark fragmenting into a leading b hadron that into the final state γ /p or j /p.
then decays leptonically or semileptonically results in an CDF data events with fewer than three tracks are
electron or muon that shares the pT of the parent b quark used to estimate the cosmic ray muon contribution to
with the associated neutrino. If all hadronic decay prod- the final states γ /p and j /p. These samples of events are
ucts are soft, the distribution of the momentum fraction used as standard model background processes cosmic γ
carried by the charged lepton can be obtained by con- and cosmic j for the modeling of this background, cor-
sidering the decay of a scalar to two massless fermions. responding to offline triggers requiring a photon with
30

∑p
CDF Run II Data CDF Run II Data
γ pT Other j pT T > 400 GeV Other
Pythia W(→eν) : 1.8% MadEvent W(→µν) j : 0.7%
600 MadEvent Z(→νν) γ : 2.3% MadEvent Z(→νν) j : 0.8%
Pythia jj : 10.4% Pythia jj : 8.9%
Non-collision : 81.7% 1000 Non-collision : 88.5%
Number of Events

Number of Events
400

500
200

0 0
100 200 300 200 400 600 800
γ pT (GeV) j p T (GeV)

∑p
CDF Run II Data CDF Run II Data
γ pT Other j pT T > 400 GeV Other
Pythia W(→eν) : 1.8% MadEvent W(→µν) j : 0.7%
MadEvent Z(→νν) γ : 2.3% MadEvent Z(→νν) j : 0.8%
Pythia jj : 10.4% Pythia jj : 8.9%
Non-collision : 81.7%
300 Non-collision : 88.5%
Number of Events

Number of Events
100
200

50
100

0 0
-2 0 2 -2 0 2
γ φ (radians) j φ (radians)
FIG. 15: The distribution of transverse momentum and azimuthal angle for photons and jets in the γ / p and j /
p final states,
dominated by cosmic ray and beam halo muons. The vertical axis shows the number of events in each bin. Data are shown
as filled (black) circles; the standard model prediction is shown as the shaded (red) histogram. Here the “standard model”
prediction includes contributions from cosmic ray and beam halo muons, estimated using events containing fewer than three
reconstructed tracks. The contribution from cosmic ray muons is flat in φ, while the contribution from beam halo is localized
to φ = 0. The only degrees of freedom for the background to these final states are the cosmic γ and cosmic j correction factors,
whose values are determined from the global Vista fit and provided in Table I.

pT > 60 GeV, or a jet with pT > 40 GeV (prescaled) or luminosity.

pT > 200 GeV (unprescaled), respectively. These sam- The cosmic ray muon contribution to the final states
ples do not contribute to the events passing the anal- γ /p and j /p is uniform as a function of the CDF azimuthal
ysis offline trigger, whose cleanup cuts require three or angle φ. Consider the CDF detector to be a thick cylin-
more tracks. The contribution of these events is adjusted drical shell, and consider two arbitrary infinitesimal vol-
with correction factors that are listed as cosmic γ and ume elements at different locations in the material of
cosmic j “k-factors” in Table I, but which are more prop- the shell. Since the two volume elements have simi-
erly understood as reflecting the number of bunch cross- lar overburdens, the number of cosmic ray muons with
ings with zero pp̄ interactions (resulting in zero recon- E & 20 GeV penetrating the first volume element is very
structed tracks) relative to the number of bunch cross- nearly the same as the number of cosmic ray muons with
ings with one or more interactions (resulting in three or E & 20 GeV penetrating the second volume element.
more reconstructed tracks). Since the number of bunch Since the material of the CDF calorimeters is uniform
crossings with no inelastic pp̄ interactions is used to de- as a function of CDF azimuthal angle φ, it follows that
termine the CDF instantaneous luminosity, these cosmic the cosmic ray muon contribution to the final states γ /p
correction factors can be viewed as containing direct in- and j /p should also be uniform as a function of φ. In
formation about the luminosity-averaged instantaneous particular, it is noted that the φ dependence of this con-
 31

tribution depends solely on the material distribution of c. Intrinsic kT

CDF calorimeter, which is uniform in φ, and has no
dependence on the distribution of the horizon angle of Significant discrepancy is observed in many final states
the muons from cosmic rays streaking through the atmo- containing two objects o1 and o2 in the variables
sphere. ∆φ(o1,o2), uncl pT , and /pT . These discrepancies are
The final states γ /
p and j /
p are also populated by beam ascribed to the sum of two effects: (1) an intrinsic Fermi
halo muons, traveling horizontally through the CDF de- motion of the colliding partons within the proton and
tector in time with a bunch. A beam halo muon can anti-proton, and (2) soft radiation along the beam axis.
undergo a hard bremsstrahlung in the electromagnetic The sum of these two effects appears to be larger in Na-
or hadronic calorimeters, producing an energy deposit ture than predicted by Pythia with the parameter tunes
that can be reconstructed as a photon or jet, respectively. used for the generation of the samples employed in this
These beam halo muons tend to lie in the plane and out- analysis. This discrepancy is well known from previous
side of the Tevatron ring, thus horizontally penetrating studies at the Tevatron and elsewhere, and affects this
the CDF detector along ẑ at y = 0, x > 0, and hence analysis similarly to other Tevatron analyses.
φ = 0. The W and Z electroweak samples used in this analysis
Figure 15 shows the γ / p and j /p final states, in which have been generated with an adjusted Pythia parameter
events come primarily from cosmic ray and beam halo that increases the intrinsic kT . For all other generated
muons. standard model events, the net effect of the Fermi motion
of the colliding partons and the soft non-perturbative ra-
diation is hypothesized to be described by an overall “ef-
b. Multiple interactions fective intrinsic kT ,” and the center of mass of each event
is given a transverse kick. Specifically, for every event of
invariant Pmass m and generated summed transverse mo-
In order to estimate event overlaps, consider an inter-
mentum pT , a random number kT is pulled from the
esting event observed in final state C, which looks like an
probability distribution
overlap of two events in the final states A and B. An ex-
ample is C=e+e-4j, A=e+e- and B=4j. It is desired to p(kT ) ∝ (kT < m/5)× [ 54 g(kT ; µ = 0, σ1 ) +
estimate how many C events are expected from the over- 1
lap of A and B events, given the observed frequencies of 5 g(kT ; µ = 0, σ2 )], (A24)
A and B. where (kT < m/5) evaluates to unity if true and zero if
Let L(t) be the instantaneous luminosity as a function false; g(kT ; µ, σ) is a Gaussian function of kT withP cen-
of time t; let ter at µ and width σ; σ1 = 2.55 GeV + 0.0085 pT
Z is the width of the coreP of the double Gaussian; and
L= L(t)dt = 927 pb−1 (A20) σ2 = 5.25 GeV + 0.0175 pT is the width of the sec-
RunII ond, wider Gaussian. The event is then  boosted to an
inertial frame traveling with speed β~  = kT /m with re-
 
denote the total integrated luminosity; and let
spect to the lab frame, in a direction transverse to the
beam axis, where m is the invariant mass of all recon-
R
L(t)L(t)dt
L̄ = RunII
R ≈ 1032 cm−2 s−1 (A21) structed objects in the event, along an azimuthal angle
RunII
L(t)dt
pulled randomly from a uniform distribution between 0
be the luminosity-averaged instantaneous luminosity. and 2π. The momenta of identified objects are recalcu-
Denote by t0 the time interval of 396 ns between suc- lated in the lab frame. Sixty percent of the recoil kick
cessive bunch crossings. The total number of effective is assigned to unclustered momentum in the event. The
bunch crossings X is then remaining forty percent of the recoil kick is assumed to
disappear down the beam pipe, and contributes to the
L missing transverse momentum in the event. This picture,
X= ≈ 2.3 × 1013 . (A22) and the particular parameter values that accompany this
L̄t0
story, are determined primarily by the uncl pT and /pT
Letting A and B denote the number of observed events in distributions in highly populated two-object final states,
final states A and B, it follows that the number of events including the low-pT 2j final state, the high-pT 2j final
in the final state C expected from overlap of A and B is state, and the final states jγ, e+ e− , and µ+ µ− .
Under the hypothesis described, reasonable although
AB imperfect agreement with observation is obtained. The
C= . (A23) result of this analysis supports the conclusions of previous
X
studies indicating that the effective intrinsic kT needed to
Overlap events are included in the Vista background match observation is quite large relative to naive expec-
estimate, although their contribution is generally negli- tation. That the data appear to require such a large ef-
gible. fective intrinsic kT may be pointing out the need for some
32

basic improvement to our understanding of this physics. probabilityPassesTrigger[(k1 , k2 )] represents the proba-
bility that an event produced with energy clusters in the
detector regions labeled by k1 that are identified as ob-
3. Global fit jects labeled by k2 would pass the trigger.
The quantity SM0 [(k1 , k2 ′ )][l] is obtained by generating
This section describes the construction of the global some number nl (say 104 ) of Monte Carlo events corre-
χ2 used in the Vista global fit. sponding to the process l. The event generator provides
a cross section σl for this process l. The weight of each of
these Monte Carlo events is equal to σl /nl . Passing these
a. χ2k events through the CDF simulation and reconstruction,
the sum of the weights of these events falling into the bin
(k1 , k2 ′ ) is SM0 [(k1 , k2 ′ )][l].
The bins in the CDF high-pT data sample are labeled
by the index k = (k1 , k2 ), where each value of k1 rep-
resents a phrase such as “this bin contains events with
b. χ2constraints
three objects: one with 17 < pT < 25 GeV and |η| < 0.6,
one with 40 < pT < 60 GeV and 0.6 < |η| < 1.0, and
one with 25 < pT < 40 GeV and 1.0 < |η|,” and each The term χ2constraints (~s) in Eq. 2 reflects constraints on
value of k2 represents a phrase such as “this bin contains the values of the correction factors determined by data
events with three objects: an electron, muon, and jet, other than those in the global high-pT sample. These
respectively.” The reason for splitting k into k1 and k2 constraints include k-factors taken from theoretical cal-
is that a jet can fake an electron (mixing the contents of culations and numbers from the CDF literature when use
k2 ), but an object with |η| < 0.6 cannot fake an object is made of CDF data external to the Vista high-pT sam-
with 0.6 < |η| < 1.0 (no mixing of k1 ). The term corre- ple. The constraints imposed are:
sponding to the k th bin takes the form of Eq. 1, where • The luminosity (0001) is constrained to be within
Data[k] is the number of data events observed in the k th 6% of the value measured by the CDF Čerenkov
bin, SM[k] is the number of events predicted by the stan- luminosity counters.
dard model in the k th bin, δSM[k] is the Monte Carlo
statistical uncertainty
p on the standard model prediction • The fake rate p(q → γ) (0039) is constrained to be
in the k th bin, and SM[k] is the statistical uncertainty 2.6 × 10−4 ± 1.5 × 10−5, from the single particle gun
on the prediction in the k th bin. To legitimize the use study of Appendix A 1.
of Gaussian errors, only bins containing eight or more
data events are considered. The standard model predic- • The fake rate p(e → γ) (0032) plus the efficiency
tion SM[k] for the k th bin can be written in terms of the p(e → e) (0026) for electrons in the plug is con-
introduced correction factors as strained to be within 1% of unity.
• Noting p(q → γ) corresponds to correction factor
SM[k] = SM[(k1 , k2 )] = 0039, p(q → π ± ) = 2 p(q → π 0 ), and p(q → π 0 ) =
P P
k ′ ∈objectLists
2 l∈processes p(q → γ)/p(π 0 → γ), and taking p(π 0 → γ) = 0.6
( L dt) · (kFactor[l]) · (SM0 [(k1 , k2 ′ )][l]) ·
R and p(π ± → τ ) = 0.415 from the single parti-
cle gun study of Appendix A 1, the fake rate
(probabilityToBeSoMisreconstructed[(k1 , k2 ′ )][k2 ]) · p(q → τ ) (0038) is constrained to p(q → τ ) =
(probabilityPassesTrigger[(k1 , k2 )]), (A25) p(q → π ± )p(π ± → τ ) ± 10%.
where SM[k] is the standard model prediction for the • The k-factors for dijet production (0018 and 0019)
k th bin; the index k is the Cartesian product of are constrained to 1.10 ± 0.05 and 1.33 ± 0.05 in
the two indices k1 and k2 introduced above, label- the kinematic regions p̂T < 150 GeV and p̂T >
ing the regions of the detector in which there are 150 GeV, respectively, where p̂T is the transverse
energy clusters and the identified objects correspond- momentum of the scattered partons in the 2 → 2
ing to those clusters, respectively; the index k2 ′ is process in the colliding parton center of momentum
a dummy summation index; the index l labels stan- frame.
dard model background processes, such as dijet pro-
duction or W +1 jet production; SM0 [(k1 , k2 ′ )][l] is the • The inclusive k-factor for γ + N jets (0004–0007) is
initial number of standard model events predicted in constrained to 1.25 ± 0.15 [43, 44].
bin (k1 , k2 ′ ) from the process labeled by the index • The inclusive k-factor for γγ + N jets (0008–0010)
l; probabilityToBeMisreconstructedThus[(k1 , k2 ′ )][k2 ] is is constrained to 2.0 ± 0.15 [45].
the probability that an event produced with en-
ergy clusters in the detector regions labeled by k1 • The inclusive k-factors for W and Z production
that are identified as objects labeled by k2 ′ would (0011–0014 and 0015–0017) are subject to a 2-
be mistaken as having objects labeled by k2 ; and dimensional Gaussian constraint, with mean at the
 33

NNLO/LO theoretical values [46], and a covari- model prediction to data. The correction factors consid-
ance matrix that encapsulates the highly corre- ered are numbers that can in principle be calculated a
lated theoretical uncertainties, as discussed in Ap- priori, but whose calculation is in practice not feasible.
pendix A 4. These correction factors divide naturally into two classes,
the first of which reflects the difficulty of calculating the
• Trigger efficiency correction factors are constrained standard model prediction to all orders, and the second
to be less than unity. of which reflects the difficulty of understanding from first
principles the response of the experimental apparatus.
• All correction factors are constrained to be positive.
The theoretical correction factors considered are of two
types. The difficulty of calculating the standard model
c. Covariance matrix
prediction for many processes to all orders in perturba-
tion theory is handled through the introduction of k-
factors, representing the ratio of the true all orders pre-
This section describes the correction factor covariance diction to the prediction at lowest order in perturbation
matrix Σ. The inverse of the covariance matrix is ob- theory. Uncertainties in the distribution of partons in-
tained from side the colliding proton and anti-proton as a function of
1 ∂ 2 χ2 (~s) 
 parton momentum are in principle handled through the
−1
Σij = , (A26) introduction of correction factors associated with parton
2 ∂si ∂sj ~s0
distribution functions, but there are currently no discrep-
ancies to motivate this.
where χ2 (~s) is defined by Eq. 2 as a function of the correc-
Experimental correction factors correspond to num-
tion factor vector ~s, vector elements si and sj are the ith
bers describing the response of the CDF detector that are
and j th correction factors, and ~s0 is the vector of correc-
precisely calculable in principle, but that are in practice
tion factors that minimizes χ2 (~s). Numerical estimation
best constrained by the high-pT data themselves. These
of the right hand side of Eq. A26 is achieved by calcu-
correction factors take the form of the integrated lumi-
lating χ2 at ~s0 and at positions slightly displaced from
nosity, object identification efficiencies, object misiden-
~s0 in the direction of the ith and j th correction factors,
tification probabilities, trigger efficiencies, and energy
denoted by the unit vectors î and ĵ. Approximating the
scales.
second partial derivative

∂ 2 χ2  χ2 (~s0 + î δsi + ĵ δsj ) − χ2 (~s0 + ĵ δsj )


= − a. k-factors
∂sj ∂si ~s0
 δsj δsi
χ2 (~s0 + î δsi ) − χ2 (~s0 ) For nearly all standard model processes, k-factors are
δsj δsi used as an overall multiplicative constant, rather than be-
ing considered to be a function of one or more kinematic
leads to variables. The spirit of the approach is to introduce as
few correction factors as possible, and to only introduce
Σ−1
ij = [χ2 (~s0 + δsi î + δsj ĵ) correction factors motivated by specific discrepancies.
−χ2 (~s0 + δsi î) 0001. The integrated luminosity of the analysis sam-
ple has a close relationship with the theoretically deter-
−χ2 (~s0 + δsj ĵ)
mined values of inclusive W and Z production at the
+χ2 (~s0 )]/(2δsi δsj ), (A27) Tevatron. Figure 16 shows the variation in calculated in-
clusive W and Z k-factors under changes in the assumed
for appropriately small steps δsi and δsj away from the parton distribution functions. Each point represents a
minimum. The covariance matrix Σ is calculated by in- different W and Z inclusive cross section determined us-
verting Σ−1 . The diagonal element Σii is the variance ing modified parton distribution functions. The use of
σi2 of the ith correction factor, and the correlation ρij be- 16 bases to reflect systematic uncertainties results in 32
tween the ith and j th correction factors is ρij = Σij /σi σj . black dots in Fig. 16. The uncertainties in the W and
The variances of each correction factor, corresponding to Z cross sections due to variations in the renormalization
the diagonal elements of the covariance matrix, are shown and factorization scales are nearly 100% correlated; vary-
in Table I. The correlation matrix obtained is shown in ing these scales affects both the W and Z inclusive cross
Table V. sections in the same way. The uncertainties in the parton
distribution functions and the choice of renormalization
and factorization scales represent the dominant contribu-
4. Correction factor values tions to the theoretical uncertainty in the total inclusive
W and Z cross section calculations at the Tevatron. The
This section provides notes on the values of the Vista term in χ2constraints that reflects our knowledge of the the-
correction factors obtained from a global fit of standard oretical prediction of the inclusive W and Z cross sections
 34
0001 0002 0003 0004 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014 0015 0016 0017 0018 0019 0020 0021 0022 0023 0024 0025 0026 0027 0028 0029 0030 0031 0032 0033 0034 0035 0036 0037 0038 0039 0040 0041 0042 0043 0044
0001 1 -.32 -.7 -.56 -.53 -.45 -.26 -.36 -.21 -.14 -.87 -.77 -.51 -.28 -.82 -.55 -.31 -.95 -.96 -.94 -.94 -.88 -.88 -.62 -.54 -.17 -.46 -.37 -.09 -.1 0 -.24 +.08 +.17 +.08 -.01 -.04 +.01 +.02 -.02 -.22 -.21 -.13 -.11
0002 -.32 1 +.21 +.37 +.38 +.33 +.2 +.34 +.18 +.12 +.28 +.25 +.17 +.09 +.27 +.18 +.1 +.3 +.31 +.31 +.3 +.28 +.28 +.2 +.18 +.06 +.15 +.12 -.31 +.02 0 +.08 -.14 -.06 -.03 0 +.01 -.03 -.07 -.07 +.07 +.07 +.04 +.04
0003 -.7 +.21 1 +.39 +.37 +.31 +.18 +.25 +.14 +.1 +.61 +.53 +.35 +.2 +.57 +.38 +.21 +.66 +.66 +.66 +.65 +.61 +.61 +.43 +.38 +.12 +.32 +.26 +.06 +.07 -.01 +.17 -.05 -.12 -.06 +.01 +.03 -.01 -.01 +.01 +.15 +.14 +.09 +.08
0004 -.56 +.37 +.39 1 +.9 +.77 +.48 +.61 +.33 +.23 +.49 +.43 +.29 +.16 +.46 +.32 +.18 +.5 +.53 +.53 +.52 +.49 +.49 +.35 +.3 +.1 +.25 +.2 -.46 +.03 0 +.13 -.44 -.09 -.03 -.01 +.02 -.32 -.62 -.17 +.11 +.11 +.07 +.06
0005 -.53 +.38 +.37 +.9 1 +.75 +.46 +.62 +.31 +.21 +.46 +.41 +.27 +.15 +.44 +.3 +.17 +.5 +.51 +.48 +.5 +.47 +.46 +.33 +.29 +.1 +.24 +.19 -.49 +.03 -.02 +.12 -.43 -.09 -.04 0 +.02 -.29 -.57 -.16 +.11 +.1 +.07 +.06
0006 -.45 +.33 +.31 +.77 +.75 1 +.4 +.54 +.29 +.13 +.4 +.35 +.24 +.13 +.38 +.26 +.14 +.43 +.44 +.42 +.42 +.35 +.4 +.28 +.25 +.09 +.2 +.16 -.45 +.02 -.01 +.1 -.36 -.07 -.04 0 +.01 -.24 -.46 -.14 +.09 +.09 +.06 +.05
0007 -.26 +.2 +.18 +.48 +.46 +.4 1 +.34 +.18 +.09 +.23 +.2 +.13 +.08 +.22 +.15 +.08 +.24 +.25 +.25 +.24 +.21 +.22 +.02 +.14 +.05 +.12 +.09 -.29 +.01 -.02 +.06 -.23 -.04 -.02 +.01 +.01 -.15 -.3 -.09 +.05 +.05 +.03 +.03
0008 -.36 +.34 +.25 +.61 +.62 +.54 +.34 1 +.37 +.28 +.32 +.28 +.19 +.1 +.3 +.22 +.12 +.34 +.34 +.34 +.33 +.31 +.31 +.22 +.18 +.06 +.16 +.12 -.61 -.03 0 +.11 -.29 -.06 -.03 0 +.01 -.09 -.17 -.28 +.07 +.07 +.04 +.04
0009 -.21 +.18 +.14 +.33 +.31 +.29 +.18 +.37 1 +.06 +.19 +.17 +.11 +.06 +.2 +.06 +.11 +.2 +.2 +.19 +.19 +.18 +.18 +.13 +.08 +.03 +.07 +.06 -.31 +.05 0 +.06 -.15 -.03 -.01 0 +.01 -.04 -.08 -.29 +.04 +.04 +.03 +.02
0010 -.14 +.12 +.1 +.23 +.21 +.13 +.09 +.28 +.06 1 +.13 +.11 +.08 +.06 +.13 +.11 -.03 +.13 +.14 +.13 +.13 +.12 +.12 +.09 +.05 -.01 +.05 +.04 -.19 +.06 0 +.07 -.1 -.03 -.01 0 +.01 -.04 -.07 -.26 +.03 +.04 +.01 +.01
0011 -.87 +.28 +.61 +.49 +.46 +.4 +.23 +.32 +.19 +.13 1 +.85 +.58 +.32 +.89 +.61 +.33 +.83 +.84 +.82 +.82 +.76 +.77 +.54 +.25 +.09 +.16 +.15 +.07 +.07 0 +.12 +.1 +.04 +.02 0 +.01 -.01 -.02 +.01 -.13 -.04 -.11 -.09
0012 -.77 +.25 +.53 +.43 +.41 +.35 +.2 +.28 +.17 +.11 +.85 1 +.33 +.35 +.79 +.49 +.33 +.72 +.74 +.74 +.72 +.68 +.67 +.47 +.21 +.08 +.15 +.13 +.06 +.06 +.01 +.11 +.1 -.02 -.09 -.01 +.01 -.01 -.01 +.01 -.14 +.01 -.06 -.05
0013 -.51 +.17 +.35 +.29 +.27 +.24 +.13 +.19 +.11 +.08 +.58 +.33 1 -.21 +.52 +.35 +.15 +.5 +.49 +.46 +.48 +.46 +.45 +.36 +.15 +.06 +.1 +.09 +.04 +.04 -.01 +.07 +.05 +.07 -.07 0 0 -.01 -.01 +.01 -.1 -.07 -.06 -.05
0014 -.28 +.09 +.2 +.16 +.15 +.13 +.08 +.1 +.06 +.06 +.32 +.35 -.21 1 +.29 +.26 -.04 +.28 +.27 +.28 +.26 +.21 +.26 +.09 +.08 +.03 +.05 +.05 +.02 +.02 0 +.03 +.01 0 -.07 0 0 -.01 -.01 +.01 -.05 -.01 -.03 -.02
0015 -.82 +.27 +.57 +.46 +.44 +.38 +.22 +.3 +.2 +.13 +.89 +.79 +.52 +.29 1 +.58 +.35 +.77 +.78 +.77 +.76 +.71 +.71 +.5 +.09 +.04 +.06 +.05 +.05 +.02 0 +.03 -.02 -.03 -.06 0 0 -.01 -.02 +.03 +.04 +.03 +.04 +.03
0016 -.55 +.18 +.38 +.32 +.3 +.26 +.15 +.22 +.06 +.11 +.61 +.49 +.35 +.26 +.58 1 -.09 +.52 +.53 +.52 +.52 +.49 +.48 +.35 +.1 +.03 +.08 +.07 +.03 +.02 0 +.04 -.03 -.01 -.1 0 +.01 -.01 -.02 +.02 0 +.01 -.02 -.01
0017 -.31 +.1 +.21 +.18 +.17 +.14 +.08 +.12 +.11 -.03 +.33 +.33 +.15 -.04 +.35 -.09 1 +.3 +.3 +.29 +.29 +.25 +.28 +.16 +.03 -.02 +.04 +.04 +.02 +.04 0 +.04 -.03 -.06 -.06 0 +.01 -.01 -.01 -.02 +.03 +.05 +.01 +.01
0018 -.95 +.3 +.66 +.5 +.5 +.43 +.24 +.34 +.2 +.13 +.83 +.72 +.5 +.28 +.77 +.52 +.3 1 +.91 +.92 +.89 +.85 +.83 +.6 +.51 +.16 +.43 +.35 +.09 +.1 -.07 +.23 -.16 -.23 -.16 +.02 0 -.01 -.03 +.01 +.21 +.18 +.12 +.1
0019 -.96 +.31 +.66 +.53 +.51 +.44 +.25 +.34 +.2 +.14 +.84 +.74 +.49 +.27 +.78 +.53 +.3 +.91 1 +.91 +.91 +.84 +.85 +.59 +.52 +.16 +.44 +.36 +.09 +.1 +.03 +.23 -.07 -.17 -.08 -.06 +.04 -.01 -.02 +.02 +.21 +.2 +.12 +.11
0020 -.94 +.31 +.66 +.53 +.48 +.42 +.25 +.34 +.19 +.13 +.82 +.74 +.46 +.28 +.77 +.52 +.29 +.92 +.91 1 +.87 +.84 +.83 +.6 +.51 +.16 +.43 +.35 +.08 +.1 -.05 +.23 -.13 -.24 -.13 +.01 +.01 -.02 -.03 +.01 +.21 +.2 +.12 +.11
0021 -.94 +.3 +.65 +.52 +.5 +.42 +.24 +.33 +.19 +.13 +.82 +.72 +.48 +.26 +.76 +.52 +.29 +.89 +.91 +.87 1 +.82 +.83 +.57 +.51 +.16 +.43 +.35 +.08 +.1 +.04 +.23 -.07 -.16 -.07 -.08 +.04 -.01 -.02 +.02 +.2 +.19 +.12 +.1
0022 -.88 +.28 +.61 +.49 +.47 +.35 +.21 +.31 +.18 +.12 +.76 +.68 +.46 +.21 +.71 +.49 +.25 +.85 +.84 +.84 +.82 1 +.73 +.55 +.47 +.15 +.4 +.33 +.08 +.09 -.04 +.21 -.1 -.21 -.1 +.01 +.02 -.01 -.03 +.02 +.19 +.18 +.11 +.1
0023 -.88 +.28 +.61 +.49 +.46 +.4 +.22 +.31 +.18 +.12 +.77 +.67 +.45 +.26 +.71 +.48 +.28 +.83 +.85 +.83 +.83 +.73 1 +.53 +.48 +.15 +.4 +.33 +.08 +.09 +.01 +.21 -.06 -.15 -.07 -.04 +.03 -.01 -.02 +.02 +.19 +.18 +.11 +.1
0024 -.62 +.2 +.43 +.35 +.33 +.28 +.02 +.22 +.13 +.09 +.54 +.47 +.36 +.09 +.5 +.35 +.16 +.6 +.59 +.6 +.57 +.55 +.53 1 +.33 +.11 +.28 +.23 +.05 +.06 -.01 +.15 -.09 -.16 -.07 +.01 +.02 -.01 -.02 +.01 +.13 +.13 +.08 +.07
0025 -.54 +.18 +.38 +.3 +.29 +.25 +.14 +.18 +.08 +.05 +.25 +.21 +.15 +.08 +.09 +.1 +.03 +.51 +.52 +.51 +.51 +.47 +.48 +.33 1 +.23 +.6 +.49 +.05 +.04 -.01 +.25 -.03 -.23 -.05 +.01 +.04 -.01 -.02 +.09 +.12 +.28 +.19 +.17
0026 -.17 +.06 +.12 +.1 +.1 +.09 +.05 +.06 +.03 -.01 +.09 +.08 +.06 +.03 +.04 +.03 -.02 +.16 +.16 +.16 +.16 +.15 +.15 +.11 +.23 1 +.18 +.15 +.01 +.01 0 -.66 -.03 +.37 -.01 0 -.02 0 -.01 +.19 +.07 -.44 +.05 +.04
0027 -.46 +.15 +.32 +.25 +.24 +.2 +.12 +.16 +.07 +.05 +.16 +.15 +.1 +.05 +.06 +.08 +.04 +.43 +.44 +.43 +.43 +.4 +.4 +.28 +.6 +.18 1 +.29 +.05 +.1 0 +.27 -.15 -.25 0 0 +.05 -.01 -.01 0 +.35 +.3 -.33 +.33
0028 -.37 +.12 +.26 +.2 +.19 +.16 +.09 +.12 +.06 +.04 +.15 +.13 +.09 +.05 +.05 +.07 +.04 +.35 +.36 +.35 +.35 +.33 +.33 +.23 +.49 +.15 +.29 1 +.05 +.08 0 +.23 -.1 -.19 +.03 0 +.04 -.01 -.01 0 +.26 +.23 +.32 -.54
0029 -.09 -.31 +.06 -.46 -.49 -.45 -.29 -.61 -.31 -.19 +.07 +.06 +.04 +.02 +.05 +.03 +.02 +.09 +.09 +.08 +.08 +.08 +.08 +.05 +.05 +.01 +.05 +.05 1 +.06 0 +.03 +.31 -.02 0 +.01 +.01 +.01 +.01 +.21 +.03 +.03 +.01 +.01
0030 -.1 +.02 +.07 +.03 +.03 +.02 +.01 -.03 +.05 +.06 +.07 +.06 +.04 +.02 +.02 +.02 +.04 +.1 +.1 +.1 +.1 +.09 +.09 +.06 +.04 +.01 +.1 +.08 +.06 1 0 -.13 -.02 -.03 0 0 +.03 0 0 -.76 +.08 +.05 +.01 +.01
0031 0 0 -.01 0 -.02 -.01 -.02 0 0 0 0 +.01 -.01 0 0 0 0 -.07 +.03 -.05 +.04 -.04 +.01 -.01 -.01 0 0 0 0 0 1 0 +.07 +.04 +.07 -.83 +.03 +.01 +.03 +.01 -.01 0 -.01 -.01
0032 -.24 +.08 +.17 +.13 +.12 +.1 +.06 +.11 +.06 +.07 +.12 +.11 +.07 +.03 +.03 +.04 +.04 +.23 +.23 +.23 +.23 +.21 +.21 +.15 +.25 -.66 +.27 +.23 +.03 -.13 0 1 -.06 -.48 -.02 0 +.05 0 0 -.08 +.17 +.57 +.06 +.05
0033 +.08 -.14 -.05 -.44 -.43 -.36 -.23 -.29 -.15 -.1 +.1 +.1 +.05 +.01 -.02 -.03 -.03 -.16 -.07 -.13 -.07 -.1 -.06 -.09 -.03 -.03 -.15 -.1 +.31 -.02 +.07 -.06 1 +.23 +.17 -.02 -.01 +.2 +.39 +.14 -.55 -.18 -.21 -.18
0034 +.17 -.06 -.12 -.09 -.09 -.07 -.04 -.06 -.03 -.03 +.04 -.02 +.07 0 -.03 -.01 -.06 -.23 -.17 -.24 -.16 -.21 -.15 -.16 -.23 +.37 -.25 -.19 -.02 -.03 +.04 -.48 +.23 1 +.16 -.01 -.04 +.01 +.02 +.09 -.31 -.89 -.22 -.19
0035 +.08 -.03 -.06 -.03 -.04 -.04 -.02 -.03 -.01 -.01 +.02 -.09 -.07 -.07 -.06 -.1 -.06 -.16 -.08 -.13 -.07 -.1 -.07 -.07 -.05 -.01 0 +.03 0 0 +.07 -.02 +.17 +.16 1 -.02 +.02 +.01 +.01 0 -.12 -.1 -.26 -.23
0036 -.01 0 +.01 -.01 0 0 +.01 0 0 0 0 -.01 0 0 0 0 0 +.02 -.06 +.01 -.08 +.01 -.04 +.01 +.01 0 0 0 +.01 0 -.83 0 -.02 -.01 -.02 1 0 0 +.01 0 +.01 +.01 +.02 +.01
0037 -.04 +.01 +.03 +.02 +.02 +.01 +.01 +.01 +.01 +.01 +.01 +.01 0 0 0 +.01 +.01 0 +.04 +.01 +.04 +.02 +.03 +.02 +.04 -.02 +.05 +.04 +.01 +.03 +.03 +.05 -.01 -.04 +.02 0 1 +.01 +.01 -.03 +.06 +.07 +.03 +.02
0038 +.01 -.03 -.01 -.32 -.29 -.24 -.15 -.09 -.04 -.04 -.01 -.01 -.01 -.01 -.01 -.01 -.01 -.01 -.01 -.02 -.01 -.01 -.01 -.01 -.01 0 -.01 -.01 +.01 0 +.01 0 +.2 +.01 +.01 0 +.01 1 +.51 +.06 0 0 0 0
0039 +.02 -.07 -.01 -.62 -.57 -.46 -.3 -.17 -.08 -.07 -.02 -.01 -.01 -.01 -.02 -.02 -.01 -.03 -.02 -.03 -.02 -.03 -.02 -.02 -.02 -.01 -.01 -.01 +.01 0 +.03 0 +.39 +.02 +.01 +.01 +.01 +.51 1 +.12 0 -.01 0 0
0040 -.02 -.07 +.01 -.17 -.16 -.14 -.09 -.28 -.29 -.26 +.01 +.01 +.01 +.01 +.03 +.02 -.02 +.01 +.02 +.01 +.02 +.02 +.02 +.01 +.09 +.19 0 0 +.21 -.76 +.01 -.08 +.14 +.09 0 0 -.03 +.06 +.12 1 -.04 -.11 +.01 +.01
0041 -.22 +.07 +.15 +.11 +.11 +.09 +.05 +.07 +.04 +.03 -.13 -.14 -.1 -.05 +.04 0 +.03 +.21 +.21 +.21 +.2 +.19 +.19 +.13 +.12 +.07 +.35 +.26 +.03 +.08 -.01 +.17 -.55 -.31 -.12 +.01 +.06 0 0 -.04 1 +.37 +.39 +.33
0042 -.21 +.07 +.14 +.11 +.1 +.09 +.05 +.07 +.04 +.04 -.04 +.01 -.07 -.01 +.03 +.01 +.05 +.18 +.2 +.2 +.19 +.18 +.18 +.13 +.28 -.44 +.3 +.23 +.03 +.05 0 +.57 -.18 -.89 -.1 +.01 +.07 0 -.01 -.11 +.37 1 +.25 +.22
0043 -.13 +.04 +.09 +.07 +.07 +.06 +.03 +.04 +.03 +.01 -.11 -.06 -.06 -.03 +.04 -.02 +.01 +.12 +.12 +.12 +.12 +.11 +.11 +.08 +.19 +.05 -.33 +.32 +.01 +.01 -.01 +.06 -.21 -.22 -.26 +.02 +.03 0 0 +.01 +.39 +.25 1 +.07
0044 -.11 +.04 +.08 +.06 +.06 +.05 +.03 +.04 +.02 +.01 -.09 -.05 -.05 -.02 +.03 -.01 +.01 +.1 +.11 +.11 +.1 +.1 +.1 +.07 +.17 +.04 +.33 -.54 +.01 +.01 -.01 +.05 -.18 -.19 -.23 +.01 +.02 0 0 +.01 +.33 +.22 +.07 1

TABLE V: Correction factor correlation matrix. The top row and left column show correction factor codes. Each element of the matrix shows the correlation between
the correction factors corresponding to the column and row. Each matrix element is dimensionless; the elements along the diagonal are unity; the matrix is symmetric;
positive elements indicate positive correlation, and negative elements anti-correlation.
 35

jet
3
pT distribution
10

dσγγjet /dp jet [fb/GeV]

102 γ γ +jet (NLOJET++ 3.0.0)
γ
10
pT > 10 GeV/c, Rγ j > 0.4, ∈=0.5

10-1

10-2 FULL
10
-3
LO
10-4
0 20 40 60 80 100 120 140 160 180 200
Pjet (GeV/c)

K-factor as PT of jet
6

dσ/dp jet /dσ/dp jet (LO)

5 FULL/LO

FIG. 16: Variation of the k-factors for inclusive W and Z 2

production under different choices of parton distribution func- 1

tions, from the Alekhin parton distribution error set [47]. The
correlation of the uncertainty on these two k-factors due to 0
0 20 40 60 80 100 120 140 160 180 200
uncertainty in the parton distribution functions is 0.955. Pjet (GeV/c)

FIG. 17: Calculation of the γγj k-factor, as a function of jet

explicitly acknowledges this high degree of correlation. transverse momentum. The effect of changing the factoriza-
Theoretical constraints on all other k-factors are as- tion scale by a factor of two in either direction is also shown
sumed to be uncorrelated with each other, not because (small black points with error bars).
the uncertainties of these calculations are indeed uncor-
related, but rather because the correlations among these
computations are poorly known. 0011, 0012, 0013, 0014. These correction factors
0002, 0003. The cosmic γ and cosmic j back- correspond to k-factors for W production in association
grounds are estimated using events recorded in the CDF with zero, one, two, and three or more jets, respectively.
data with one or more reconstructed photons and with A linear combination of these correction factors is con-
two or fewer reconstructed tracks. The use of events with strained by the requirement that the inclusive W pro-
two or fewer reconstructed tracks is a new technique for duction cross section is consistent with the NNLO calcu-
estimating these backgrounds. These correction factors lation of Ref. [47]. The values of these correction factors,
are primarily constrained by the number of events in the and their trend of decreasing as the number of jets in-
Vista γ /p and j /p final states. The values are related creases, depends heavily on the choice of renormalization
to (and consistent with) the fraction of bunch crossings and factorization scales. The individual correction fac-
with one or more inelastic pp̄ interactions, complicated tors are not explicitly constrained by a NLO calculation.
slightly by the requirement that any jet falling in the fi- 0015, 0016, 0017. These correction factors corre-
nal state j /p has at least 5 GeV of track pT within a cone spond to k-factors for Z production in association with
of 0.4 relative to the jet axis. zero, one, and two or more jets, respectively. A linear
0004, 0005, 0006, 0007. The NLOJET++ calcula- combination of these correction factors is constrained by
tion of the γj inclusive k-factor constrains the cross sec- the requirement that the inclusive Z production cross sec-
tion weighted sum of the γj, γ2j, γ3j, and γ4j correction tion is consistent with the NNLO calculation of Ref. [47].
factors to 1.25 ± 0.15 [43, 44]. 0018, 0019. The two k-factors for dijet production
0008, 0009, 0010. The DIPHOX calculation of the correspond to two bins in p̂T , the pT of the hard two
inclusive γγ cross section at NLO constrains the weighted to two scattering in the parton center of mass frame.
sum of these correction factors to 2.0±0.15 [45]. From Ta- These correction factors are constrained by a NLO cal-
ble I, the γγj k-factor (0009) appears anomalously large. culation [48], and show expected behavior as a function
Figure 17 shows a calculation of this γγj k-factor using of p̂T .
NLOJET++ [43, 44] as a function of summed transverse 0020, 0021. The two k-factors for 3-jet production,
momentum. The NLO correction to the LO prediction is corresponding to two bins in p̂T , are unconstrained by
found to be large, and not manifestly inconsistent with any NLO calculation, but show reasonable behavior as a
the value for this k-factor determined from the Vista function of p̂T .
fit. The cross section for γγ2j production has not been 0022, 0023. The k-factors for 4-jet production, cor-
calculated at NLO. responding to two bins in p̂T , are unconstrained by any
36

NLO calculation, but show reasonable behavior as a func- c. Fake rates

tion of p̂T .
0024. The k-factor for the production of five or more 0032. The fake rate p(e → γ) for electrons to be mis-
jets, constrained primarily by the Vista low-pT 5j final reconstructed as photons in the plug region of the detec-
state, is found to be close to unity. tor is added on top of the significant number of electrons
misreconstructed as photons by CdfSim.
0033. In Vista, the contribution of jets faking elec-
trons is modeled by applying a fake rate p(j → e) to
b. Identification efficiencies Monte Carlo jets. Vista represents the first large
scale Tevatron analysis in which a completely Monte
Carlo based modeling of jets faking electrons is em-
The correction factors in this section, although billed ployed. Significant understanding of the physical mecha-
as “identification efficiencies,” are truly ratios of the iden- nisms contributing to this fake rate has been achieved,
tification efficiency in the data relative to the identifica- as summarized in Appendix A 1. Consistency with
tion efficiency in CdfSim. A correction factor value of this understanding is required; for example, p(j → e) ≈
unity indicates a proper modeling of the overall identi- p(j → γ)p(γ → e). The value of this correction factor is de-
fication efficiency by CdfSim; a correction factor value termined primarily by the number of events in the Vista
of 0.5 indicates that CdfSim overestimates the overall final state ej, where the electron is identified in the cen-
identification efficiency by a factor of two. tral region of the CDF detector. It is notable that this
0025. The central electron identification efficiency fake rate is independent of global event properties, and
scale factor is close to unity, indicating the central elec- that a consistent simultaneous understanding of the ej,
tron efficiency measured in data is similar (to within 1%) e2j, e3j, and e4j final states is obtained.
to the central electron efficiency in the CDF detector sim- 0034. The value of the fake rate p(j → e) in the plug
ulation. This reflects an emphasis within CDF on tuning region of the CDF detector is roughly one order of mag-
the detector simulation for central electrons. The deter- nitude larger than the corresponding fake rate p(j → e)
mination of this correction factor is dominated by the in the central region of the detector, consistent with an
Vista final states e / p and e+ e− , where one of the elec- understanding of the relative performance of the detec-
trons has |η| < 1. tor in the central and plug regions for the identification
0026. The plug electron identification efficiency scale of electrons. This correction factor is determined primar-
factor is several percent less than unity, indicating that ily by the number of events in the Vista final state ej,
the CDF detector simulation slightly overestimates the where the electron is identified in the plug region of the
electron identification efficiency in the plug region of the CDF detector.
CDF detector. The determination of this correction fac- 0035. In Vista, the contribution of jets faking
tor is dominated by the Vista final states e / p and e+ e− , muons is modeled by applying a fake rate p(j → µ)
where one of the electrons has |η| > 1. to Monte Carlo jets. Vista represents the first large
0027, 0028. To reduce backgrounds hypothesized to scale Tevatron analysis in which a completely Monte
arise from pion and kaon decays in flight with a substan- Carlo based modeling of jets faking muons is employed.
tially mismeasured track, a very good track fit in the The value obtained from the Vista fit is seen to be
CDF tracker is required. Partially due to this tight track roughly one order of magnitude smaller than the fake
fit requirement, CDF muon identification efficiencies in rate p(j → e) in the central region of the detector, consis-
the regions |η| < 0.6 and 0.6 < |η| < 1.5 are overesti- tent with our understanding of the physical mechanisms
mated in the CDF detector simulation by over 10%. The underlying these fake rates, as described in Appendix A 1.
determination of the identification efficiencies p(µ → µ) is The value of this correction factor is determined primar-
dominated by the Vista final states µ / p and µ+ µ− . ily by the number of events in the Vista final state jµ.
0036. The fake rate p(j → b) has pT dependence ex-
0029. The central photon identification efficiency
plicitly imposed. The number of tracks inside a typical
scale factor is determined primarily by the number of
jet, and hence the probability that a secondary vertex
events in the Vista final states jγ and γγ. The uncer-
is (mis)reconstructed, increases with jet pT . The values
tainty on this correction factor is highly correlated with
of these correction factors are consistent with the mistag
the uncertainties on the γj k-factor, the p(j → γ) fake
rate determined using secondary vertices reconstructed
rate, and the γγ k-factor.
on the other side of the beam axis with respect to the di-
0030. The plug photon identification efficiency scale rection of the tagged jet [49]. The value of this correction
factor is determined primarily by the number of events factor is determined primarily by the number of events
in the Vista final state γγ. The uncertainty on this in the Vista final states bj and bb.
correction factor is highly correlated with the uncertainty 0037, 0038. The fake rate p(j → τ ) decreases with jet
on the plug p(j → γ) fake rate. pT , since the number of tracks inside a typical jet in-
0031. The b-jet identification efficiency is determined creases with jet pT . The values of these correction factors
to be consistent with the prediction from CdfSim. are determined primarily by the number of events in the
 37

Vista final state jτ . APPENDIX B: SLEUTH DETAILS

0039, 0040. The fake rate p(j → γ) is determined sep-
arately in the central and plug regions of the CDF de- This appendix elaborates on the Sleuth partitioning
tector. The values of these correction factors are deter- rule, and on the minimum number of events required for
mined primarily by the number of events in the Vista a final state to be considered by Sleuth.
final states jγ and γγ. The value obtained for 0039 is
consistent with the value obtained from a study using de-
tailed information from the central preshower detector. 1. Partitioning
The fake rate determined in the plug region is notice-
ably higher than the fake rate determined in the central
Table VI lists the Vista final states associated with
region, as expected.
each Sleuth final state.

d. Trigger efficiencies 2. Minimum number of events

0041. The central electron trigger inefficiency is dom- This section expands on a subtle point in the definition
inated by not correctly reconstructing the electron’s track of the Sleuth algorithm: for purely practical considera-
at the first online trigger level. tions, only final states in which three or more events are
observed in the data are considered.
0042. The plug electron trigger inefficiency is due to
Suppose Pe+ e− bb̄ = 10−6 ; then in computing P̃ all final
inefficiencies in clustering at the second online trigger
states with b > 10−6 must be considered and accounted
level.
for. (A final state with b = 10−7 , on the other hand,
0043, 0044. The muon trigger inefficiencies in the counts as only ≈ 0.1 final states, since the fraction of
regions |η| < 0.6 and 0.6 < |η| < 1.0 derive partly from hypothetical similar experiments in which P < 10−6 in
tracking inefficiency, and partly from an inefficiency in this final state is equal to the fraction of hypothetical
reconstructing muon stubs in the CDF muon chambers. similar experiments in which one or more events is seen
in this final state, which is 10−7 .) This is a large practical
The value of these corrections factors are consis- problem, since it requires that all final states with b >
tent with other trigger efficiency measurements made 10−6 be enumerated and estimated, and it is difficult to
using additional information [50]. do this believably.
To solve this problem, let Sleuth consider only final
states with at least dmin events observed in the data. The
goal is to be able to find P̃ < 10−3 . There will be some
e. Energy scales number Nfs (bmin ) of final states with expected number
of events b > bmin , writing Nfs explicitly as a function
The Vista infrastructure also allows the jet energy of bmin ; thus bmin must be chosen to be sufficiently large
scale to be treated as a correction factor. At present this that all of these Nfs (bmin ) final states can be enumerated
correction factor is not used, since there is no discrepancy and estimated. The time cost of simulating events is such
requiring it. that the integrated luminosity of Monte Carlo events is at
To understand the effect of introducing such a correc- most 100 times the integrated luminosity of the data; this
tion factor, a jet energy scale correction factor is added practical constraint restricts bmin > 0.01. The number of
and constrained to 1±0.03, reflecting the jet energy scale Sleuth Tevatron Run II final states with b > 0.01 is
determination at CDF [13]. The fit returns a value with Nfs (bmin = 0.01) ≈ 103 .
a very small error, since this correction factor is highly For small Pmin , keeping the first term in a binomial
constrained by the low-pT 2j, 3j, e j, and e 2j final states. expansion yields P̃ = PminNfs (bmin ), where Pmin is the
Assuming perfectly correct modeling of jets faking elec- smallest P found in any final state. From the discussion
trons, as described in Appendix A 1, this is a correct above, the computation of P̃ from Pmin can only be jus-
energy scale error. The inclusion of additional correction tified if Pmin > (bmin dmin ); if otherwise, final states with
factor degrees of freedom to reflect possible imperfections b < bmin will need to be accounted for. Thus P̃ can be
in this modeling of jets faking electrons increases the en- confidently computed only if P̃ > (bmin dmin )Nfs (bmin ).
ergy scale error. The interesting conclusion is that the Solving this inequality for dmin and inserting values
jet energy scale (considered as a lone free parameter) is from above,
very well constrained by the large number of dijet events;
adjustment to the jet energy scale must be accompanied log10 P̃ − log10 Nfs (bmin ) −3 − 3
dmin ≥ ≈ = 3. (B1)
by simultaneous adjustment of other correction factors log10 bmin −2
(such as the dijet k-factor) in order to retain agreement
with data. A believable trials factor can be computed if dmin ≥ 3.
38

Sleuth Vista Final States Sleuth Vista Final States

bb̄ bj, b2j, 2bj, 2b, 3b ℓ+ τ + jj e+ τ + 2j, µ+ τ + 2j, e+ τ + 3j

bb̄ℓ+ ℓ− e+ e− bj, e+ e− b2j, µ+ µ− bj, µ+ µ− b2j, ℓ+ τ − jj e+ τ − 2j, e+ τ − 3j, µ+ τ − 2j, µ+ τ − 3j
e+ e− 2b ℓ+ ℓ′+ e+ µ+ , e+ µ+ j
bb̄ℓ+ ℓ− 2j e+ e− b3j, µ+ µ− b3j ℓ+ ℓ′+ p
/ e+ µ+ j p
/, e+ µ+ p
/
bb̄ℓ+ ℓ− 2j p
/ µ+ µ− 2b2j /
p ℓ+ ℓ′− e+ µ− , e+ µ− j
bb̄ℓ+ ℓ− /
p e+ e− b2j /
p, e+ e− bj p
/, µ+ µ− bj p
/, ℓ+ ℓ′− γ p
/ e+ µ− γj p/
µ+ µ− b2j /p, e+ e− 2bj p
/, e+ e− 2b p
/, µ+ µ− 2b p
/
ℓ+ ℓ′− p
/ e+ µ− p/, e+ µ− j p
/, e+ µ− b p
/
bb̄ℓ+ 2jγ /
p e+ γb3j /
p, µ+ γb3j p/
Wγ µ+ γ p
/, e+ γ p
/, µ+ γj p
/, e+ γj p
/
W bb̄jj e+ b3j /
p, µ+ b3j /
p, e+ 2b2j p
/, µ+ 2b2j p
/
ℓ+ τ − γ e+ τ − γ
bb̄ℓ+ ℓ′+ e+ µ+ 2b
W e+ p
/, µ+ p /, e+ j p/, µ+ j p
/, e+ b p
/, µ+ b p/
bb̄ℓ+ ℓ′− e+ µ− bj
ℓ+ τ + p
/ e+ τ + p/, µ+ τ + p/, e+ τ + j p
/, µ+ τ + j p
/
bb̄ℓ+ ℓ′− p
/ e+ µ− bj p
/, e+ µ− b2j p
/
ℓ+ τ − p
/ e+ τ − p/, e+ τ − j p
/, µ+ τ − p/, µ+ τ − j p
/
bb̄ℓ+ γ /
p µ+ γb2j /
p
ℓ+ τ + e+ τ + , e+ τ + j, µ+ τ + , µ+ τ + j
W bb̄ e+ bj /
p, µ+ bj /
p, e+ b2j p/, µ+ b2j p
/, e+ 2b p
/,
ℓ+ τ − e+ τ − , µ+ τ − , e+ τ − j, µ+ τ − j, e+ τ − b
e+ 2bj /
p, µ+ 2bj /
p, µ+ 2b p
/
W γ4j µ+ γ4j p/, e+ γ4j p/
pτ −
bb̄ℓ+ / + −
µ τ bj / p
W 4j e+ 4j p
/, µ+ 4j p
/
bb̄ℓ+ τ + e+ τ + bj
ℓ+ 4jτ − e+ τ − 4j
bb̄ℓ+ τ − e+ τ − bj, e+ τ − 2b
W γγ e+ 2γ p
/, µ+ 2γ p
/
bb̄2j b3j, 2b2j
jj 2j, 3j
bb̄2jγ γb3j, γ2b2j
γjj γ2j, γ3j
bb̄2jγ /
p γb3j /
p
γp
/jj γ2j p
/, γ3j p
/
bb̄2j /
p b3j /
p, 2b2j /
p
jj p
/ 3j p
/, 2j p
/
bb̄γγ2j 2γb3j
τp
/jj τ + 2j p
/, τ + 3j p
/
γbb̄ γbj, γb2j, γ2b, γ2bj, γ3b
γγjj 2γ2j, 2γ3j
bb̄γ /
p γbj /
p, γb2j /
p, γ2b p
/
jjγγ p
/ 2γ2j p
/
bb̄ /
p b2j /
p, bj /
p, 2bj /
p, 2b p
/
γγγjj 3γ2j
γγbb̄ 2γbj, 2γb2j, 2γ2b
γj γj, γb
ℓ+ ℓ− e+ e− , e+ e− j, µ+ µ− , µ+ µ− j, e+ e− b,
µ+ µ− b γp
/ γp
/, γj p
/, γb p
/

ℓ+ ℓ− 2j e+ e− 2j, e+ e− 3j, µ+ µ− 2j, µ+ µ− 3j τp

/γ τ+γ p
/, τ + γj p
/

ℓ+ ℓ− 2jγ e+ e− γ2j, e+ e− γ3j, µ+ µ− γ2j, µ+ µ− γ3j jp

/ jp
/, b p
/

ℓ+ ℓ− 2j /p e+ e− 2j /
p, e+ e− 3j p
/, µ+ µ− 2j p
/, µ+ µ− 3j p
/ τp
/ τ+j p
/, τ + b p
/

ℓ+ ℓ− τ + 2j p
/ e+ e− τ + 2j bb̄bb̄ 3bj

ℓ+ ℓ− ℓ′ γ /
p e+ µ+ µ− γj W bb̄bb̄ e+ 3bj p
/

ℓ+ ℓ− ℓ′ /
p e+ µ+ µ− , e+ e− µ+ , e+ e− µ+ p
/ ℓ+ ℓ+ 2e+ , 2e+ j, 2µ+

ℓ+ ℓ− γ e+ e− γ, µ+ µ− γ, e+ e− γj, µ+ µ− γj ℓ+ ℓ− ℓ+ jj p
/ 2e+ e− 2j, 2e+ e− 3j

ℓ+ ℓ− γ p
/ e+ e− γj /
p, e+ e− γ p
/ ℓ+ ℓ− ℓ+ p
/ 2e+ e− , 2e+ e− j, 2e+ e− p
/

ℓ+ ℓ− γτ + p
/ e+ e− τ + γ ℓ+ ℓ+ jj 2e+ 2j

ℓ+ ℓ− /
p e+ e− /
p, e+ e− j p
/, µ+ µ− p
/, µ+ µ− j p
/, ℓ+ ℓ+ ℓ′− p
/ e+ 2µ− p/
e+ e− b /
p ℓ+ ℓ+ γ 2e+ γ
ℓ+ ℓ− /
pτ + e+ e− τ + , e+ e− τ + j, µ+ µ− τ + ℓ+ ℓ+ γ p
/ 2e+ γ p
/
ℓ+ ℓ− 4j e+ e− 4j, µ+ µ− 4j ℓ+ ℓ+ p
/ 2e+ p
/, 2e+ j p
/
ℓ+ ℓ− 4j /
p e+ e− 4j /
p ℓ+ ℓ+ 4j 2e+ 4j
ℓ+ ℓ− τ + 4j /
p e+ e− τ + 4j 4j 4j
ℓ+ ℓ′+ jj e+ µ+ 3j γ4j γ4j
ℓ+ ℓ′+ /
pjj e+ µ+ 2j /
p γ4j p
/ γ4j p
/
ℓ+ ℓ′− jj e+ µ− 2j 4j p
/ 4j p
/
ℓ+ ℓ′− /
pjj e+ µ− 3j /p, e+ µ− 2j p
/ τ+ p/4j τ + 4j p
/
W γjj µ+ γ2j /p, e+ γ2j p
/, µ+ γ3j p
/, e+ γ3j p
/ γγ4j 2γ4j
W jj e+ 2j /
p, µ+ 2j /
p, e+ 3j p
/, µ+ 3j p
/ γγ 2γ, 2γj, 2γb
ℓ+ τ + p
/jj µ+ τ + 3j /
p γγ p
/ 2γ p
/, 2γj p
/
ℓ+ τ − p
/jj e+ τ − 2j /
p, e+ τ − 3j p
/, µ+ τ − 3j p
/, µ+ τ − 2j p
/ 3γ 3γ, 3γj

TABLE VI: Correspondence between Sleuth and Vista final states. The first column shows the Sleuth final state formed
by merging the populated Vista final states in the second column. Charge conjugates of each Vista final state are implied.

At the other end of the scale, computational strength a time limit is exceeded. If the time limit is exceeded
limits the maximum number of events Sleuth is able before P is determined to within the desired fractional
to consider to . 104 . Excesses in which the number of precision of 5%, Sleuth returns an upper bound on P,
events exceed 104 are expected to be identified by Vista’s and indicates explicitly that only an upper bound has
normalization statistic. been determined. For the data described in this article,
For each final state, pseudo experiments are run until the desired precision is obtained.
P is determined to within a fractional precision of 5% or

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40

p < 0.5 after accounting for the trials factor, σ is quoted [56] The electron and muon efficiencies shown in this table
as positive if the number of observed data events ex- are different from the correction factors 0025 and 0027
ceeds the standard model prediction, and negative if the in Table I, which show the ratio of the object efficien-
number of observed data events is less than the standard cies in the data to the object identification efficiencies in
model prediction. CdfSim.