††thanks: Deceased††thanks: Deceased††thanks: Deceased††thanks:
Deceased††thanks: Deceased††thanks: Deceased††thanks: Deceased††thanks:
Deceased††thanks: Deceased

CDF Collaboration With visitors from] aUniversity of British Columbia,
Vancouver, BC V6T 1Z1, Canada, bIstituto Nazionale di Fisica Nucleare, Sezione
di Cagliari, 09042 Monserrato (Cagliari), Italy, cUniversity of California
Irvine, Irvine, CA 92697, USA, dInstitute of Physics, Academy of Sciences of
the Czech Republic, 182 21, Czech Republic, eCERN, CH-1211 Geneva,
Switzerland, fCornell University, Ithaca, NY 14853, USA, gUniversity of
Cyprus, Nicosia CY-1678, Cyprus, hOffice of Science, U.S. Department of
Energy, Washington, DC 20585, USA, iUniversity College Dublin, Dublin 4,
Ireland, jETH, 8092 Zürich, Switzerland, kUniversity of Fukui, Fukui City,
Fukui Prefecture, Japan 910-0017, lUniversidad Iberoamericana, Lomas de Santa
Fe, México, C.P. 01219, Distrito Federal, mUniversity of Iowa, Iowa City, IA
52242, USA, nKinki University, Higashi-Osaka City, Japan 577-8502, oKansas
State University, Manhattan, KS 66506, USA, pBrookhaven National Laboratory,
Upton, NY 11973, USA, qIstituto Nazionale di Fisica Nucleare, Sezione di
Lecce, Via Arnesano, I-73100 Lecce, Italy, rQueen Mary, University of London,
London, E1 4NS, United Kingdom, sUniversity of Melbourne, Victoria 3010,
Australia, tMuons, Inc., Batavia, IL 60510, USA, uNagasaki Institute of
Applied Science, Nagasaki 851-0193, Japan, vNational Research Nuclear
University, Moscow 115409, Russia, wNorthwestern University, Evanston, IL
60208, USA, xUniversity of Notre Dame, Notre Dame, IN 46556, USA, yUniversidad
de Oviedo, E-33007 Oviedo, Spain, zCNRS-IN2P3, Paris, F-75205 France,
aaUniversidad Tecnica Federico Santa Maria, 110v Valparaiso, Chile, bbSejong
University, Seoul 143-747, Korea, ccThe University of Jordan, Amman 11942,
Jordan, ddUniversite catholique de Louvain, 1348 Louvain-La-Neuve, Belgium,
eeUniversity of Zürich, 8006 Zürich, Switzerland, ffMassachusetts General
Hospital, Boston, MA 02114 USA, ggHarvard Medical School, Boston, MA 02114
USA, hhHampton University, Hampton, VA 23668, USA, iiLos Alamos National
Laboratory, Los Alamos, NM 87544, USA, jjUniversità degli Studi di Napoli
Federico II, I-80138 Napoli, Italy, kkUniversity of Toronto, Toronto, Ontario
M5S 1A7, Canada

# Measurement of the charge asymmetry of electrons from the decays of $W$
bosons produced in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV

T. Aaltonen  Division of High Energy Physics, Department of Physics,
University of Helsinki, FIN-00014, Helsinki, Finland; Helsinki Institute of
Physics, FIN-00014, Helsinki, Finland  S. Ameriomm Istituto Nazionale di
Fisica Nucleare, Sezione di Padova, mmUniversity of Padova, I-35131 Padova,
Italy  D. Amidei  University of Michigan, Ann Arbor, Michigan 48109, USA  A.
Anastassovw Fermi National Accelerator Laboratory, Batavia, Illinois 60510,
USA  A. Annovi  Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica
Nucleare, I-00044 Frascati, Italy  J. Antos  Comenius University, 842 48
Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice,
Slovakia  G. Apollinari  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  J.A. Appel  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  T. Arisawa  Waseda University, Tokyo 169, Japan
A. Artikov  Joint Institute for Nuclear Research, RU-141980 Dubna, Russia  J.
Asaadi  Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M
University, College Station, Texas 77843, USA  W. Ashmanskas  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  B. Auerbach  Argonne
National Laboratory, Argonne, Illinois 60439, USA  A. Aurisano  Mitchell
Institute for Fundamental Physics and Astronomy, Texas A&M University, College
Station, Texas 77843, USA  F. Azfar  University of Oxford, Oxford OX1 3RH,
United Kingdom  W. Badgett  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  T. Bae  Center for High Energy Physics: Kyungpook
National University, Daegu 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; Chonbuk National University,
Jeonju 561-756, Korea; Ewha Womans University, Seoul, 120-750, Korea  A.
Barbaro-Galtieri  Ernest Orlando Lawrence Berkeley National Laboratory,
Berkeley, California 94720, USA  V.E. Barnes  Purdue University, West
Lafayette, Indiana 47907, USA  B.A. Barnett  The Johns Hopkins University,
Baltimore, Maryland 21218, USA  P. Barriaoo Istituto Nazionale di Fisica
Nucleare Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola Normale
Superiore, I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy,
rrUniversity of Pavia, I-27100 Pavia, Italy  P. Bartos  Comenius University,
842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice,
Slovakia  M. Baucemm Istituto Nazionale di Fisica Nucleare, Sezione di Padova,
mmUniversity of Padova, I-35131 Padova, Italy  F. Bedeschi  Istituto Nazionale
di Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola
Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy,
rrUniversity of Pavia, I-27100 Pavia, Italy  S. Behari  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  G. Bellettininn Istituto
Nazionale di Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity of
Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia, I-27100
Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia, Italy  J. Bellinger
University of Wisconsin-Madison, Madison, Wisconsin 53706, USA  D. Benjamin
Duke University, Durham, North Carolina 27708, USA  A. Beretvas  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  A. Bhatti  The
Rockefeller University, New York, New York 10065, USA  K.R. Bland  Baylor
University, Waco, Texas 76798, USA  B. Blumenfeld  The Johns Hopkins
University, Baltimore, Maryland 21218, USA  A. Bocci  Duke University, Durham,
North Carolina 27708, USA  A. Bodek  University of Rochester, Rochester, New
York 14627, USA  D. Bortoletto  Purdue University, West Lafayette, Indiana
47907, USA  J. Boudreau  University of Pittsburgh, Pittsburgh, Pennsylvania
15260, USA  A. Boveia  Enrico Fermi Institute, University of Chicago, Chicago,
Illinois 60637, USA  L. Brigliadorill Istituto Nazionale di Fisica Nucleare
Bologna, llUniversity of Bologna, I-40127 Bologna, Italy  C. Bromberg
Michigan State University, East Lansing, Michigan 48824, USA  E. Brucken
Division of High Energy Physics, Department of Physics, University of
Helsinki, FIN-00014, Helsinki, Finland; Helsinki Institute of Physics,
FIN-00014, Helsinki, Finland  J. Budagov  Joint Institute for Nuclear
Research, RU-141980 Dubna, Russia  H.S. Budd  University of Rochester,
Rochester, New York 14627, USA  K. Burkett  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  G. Busettomm Istituto Nazionale di
Fisica Nucleare, Sezione di Padova, mmUniversity of Padova, I-35131 Padova,
Italy  P. Bussey  Glasgow University, Glasgow G12 8QQ, United Kingdom  P.
Buttinn Istituto Nazionale di Fisica Nucleare Pisa, nnUniversity of Pisa,
ooUniversity of Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy, qqINFN
Pavia, I-27100 Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia, Italy  A.
Buzatu  Glasgow University, Glasgow G12 8QQ, United Kingdom  A. Calamba
Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA  S. Camarda
Institut de Fisica d’Altes Energies, ICREA, Universitat Autonoma de Barcelona,
E-08193, Bellaterra (Barcelona), Spain  M. Campanelli  University College
London, London WC1E 6BT, United Kingdom  F. Canelliee Enrico Fermi Institute,
University of Chicago, Chicago, Illinois 60637, USA  B. Carls  University of
Illinois, Urbana, Illinois 61801, USA  D. Carlsmith  University of Wisconsin-
Madison, Madison, Wisconsin 53706, USA  R. Carosi  Istituto Nazionale di
Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola
Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy,
rrUniversity of Pavia, I-27100 Pavia, Italy  S. Carrillol University of
Florida, Gainesville, Florida 32611, USA  B. Casalj Instituto de Fisica de
Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain  M. Casarsa
Istituto Nazionale di Fisica Nucleare Trieste, ttGruppo Collegato di Udine,
uuUniversity of Udine, I-33100 Udine, Italy, vvUniversity of Trieste, I-34127
Trieste, Italy  A. Castroll Istituto Nazionale di Fisica Nucleare Bologna,
llUniversity of Bologna, I-40127 Bologna, Italy  P. Catastini  Harvard
University, Cambridge, Massachusetts 02138, USA  D. Cauzttuu Istituto
Nazionale di Fisica Nucleare Trieste, ttGruppo Collegato di Udine,
uuUniversity of Udine, I-33100 Udine, Italy, vvUniversity of Trieste, I-34127
Trieste, Italy  V. Cavaliere  University of Illinois, Urbana, Illinois 61801,
USA  A. Cerrie Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley,
California 94720, USA  L. Cerritor University College London, London WC1E 6BT,
United Kingdom  Y.C. Chen  Institute of Physics, Academia Sinica, Taipei,
Taiwan 11529, Republic of China  M. Chertok  University of California, Davis,
Davis, California 95616, USA  G. Chiarelli  Istituto Nazionale di Fisica
Nucleare Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola Normale
Superiore, I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy,
rrUniversity of Pavia, I-27100 Pavia, Italy  G. Chlachidze  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  K. Cho  Center for High
Energy Physics: Kyungpook National University, Daegu 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; Chonbuk
National University, Jeonju 561-756, Korea; Ewha Womans University, Seoul,
120-750, Korea  D. Chokheli  Joint Institute for Nuclear Research, RU-141980
Dubna, Russia  A. Clark  University of Geneva, CH-1211 Geneva 4, Switzerland
C. Clarke  Wayne State University, Detroit, Michigan 48201, USA  M.E. Convery
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  J. Conway
University of California, Davis, Davis, California 95616, USA  M. Corboz Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  M. Cordelli
Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare,
I-00044 Frascati, Italy  C.A. Cox  University of California, Davis, Davis,
California 95616, USA  D.J. Cox  University of California, Davis, Davis,
California 95616, USA  M. Cremonesi  Istituto Nazionale di Fisica Nucleare
Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola Normale Superiore,
I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy, rrUniversity of
Pavia, I-27100 Pavia, Italy  D. Cruz  Mitchell Institute for Fundamental
Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA
J. Cuevasy Instituto de Fisica de Cantabria, CSIC-University of Cantabria,
39005 Santander, Spain  R. Culbertson  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  N. d’Ascenzov Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  M. Dattahh Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  P. de Barbaro
University of Rochester, Rochester, New York 14627, USA  L. Demortier  The
Rockefeller University, New York, New York 10065, USA  M. Deninno  Istituto
Nazionale di Fisica Nucleare Bologna, llUniversity of Bologna, I-40127
Bologna, Italy  M. D’Erricomm Istituto Nazionale di Fisica Nucleare, Sezione
di Padova, mmUniversity of Padova, I-35131 Padova, Italy  F. Devoto  Division
of High Energy Physics, Department of Physics, University of Helsinki,
FIN-00014, Helsinki, Finland; Helsinki Institute of Physics, FIN-00014,
Helsinki, Finland  A. Di Cantonn Istituto Nazionale di Fisica Nucleare Pisa,
nnUniversity of Pisa, ooUniversity of Siena, ppScuola Normale Superiore,
I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy, rrUniversity of
Pavia, I-27100 Pavia, Italy  B. Di Ruzzap Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  J.R. Dittmann  Baylor University,
Waco, Texas 76798, USA  S. Donatinn Istituto Nazionale di Fisica Nucleare
Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola Normale Superiore,
I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy, rrUniversity of
Pavia, I-27100 Pavia, Italy  M. D’Onofrio  University of Liverpool, Liverpool
L69 7ZE, United Kingdom  M. Dorigovv Istituto Nazionale di Fisica Nucleare
Trieste, ttGruppo Collegato di Udine, uuUniversity of Udine, I-33100 Udine,
Italy, vvUniversity of Trieste, I-34127 Trieste, Italy  A. Driuttittuu
Istituto Nazionale di Fisica Nucleare Trieste, ttGruppo Collegato di Udine,
uuUniversity of Udine, I-33100 Udine, Italy, vvUniversity of Trieste, I-34127
Trieste, Italy  K. Ebina  Waseda University, Tokyo 169, Japan  R. Edgar
University of Michigan, Ann Arbor, Michigan 48109, USA  A. Elagin  Enrico
Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA  R.
Erbacher  University of California, Davis, Davis, California 95616, USA  S.
Errede  University of Illinois, Urbana, Illinois 61801, USA  B. Esham
University of Illinois, Urbana, Illinois 61801, USA  S. Farrington  University
of Oxford, Oxford OX1 3RH, United Kingdom  J.P. Fernández Ramos  Centro de
Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid,
Spain  R. Field  University of Florida, Gainesville, Florida 32611, USA  G.
Flanagant Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
R. Forrest  University of California, Davis, Davis, California 95616, USA  M.
Franklin  Harvard University, Cambridge, Massachusetts 02138, USA  J.C.
Freeman  Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
H. Frisch  Enrico Fermi Institute, University of Chicago, Chicago, Illinois
60637, USA  Y. Funakoshi  Waseda University, Tokyo 169, Japan  C. Galloninn
Istituto Nazionale di Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity
of Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia,
I-27100 Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia, Italy  A.F.
Garfinkel  Purdue University, West Lafayette, Indiana 47907, USA  P. Garosioo
Istituto Nazionale di Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity
of Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia,
I-27100 Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia, Italy  H.
Gerberich  University of Illinois, Urbana, Illinois 61801, USA  E. Gerchtein
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  S. Giagu
Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, ssSapienza
Università di Roma, I-00185 Roma, Italy  V. Giakoumopoulou  National and
Kapodistrian University of Athens, 157 71 Athens, Greece  K. Gibson
University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA  C.M. Ginsburg
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  N.
Giokaris  National and Kapodistrian University of Athens, 157 71 Athens,
Greece  P. Giromini  Laboratori Nazionali di Frascati, Istituto Nazionale di
Fisica Nucleare, I-00044 Frascati, Italy  V. Glagolev  Joint Institute for
Nuclear Research, RU-141980 Dubna, Russia  D. Glenzinski  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  M. Gold  University of
New Mexico, Albuquerque, New Mexico 87131, USA  D. Goldin  Mitchell Institute
for Fundamental Physics and Astronomy, Texas A&M University, College Station,
Texas 77843, USA  A. Golossanov  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  G. Gomez  Instituto de Fisica de Cantabria,
CSIC-University of Cantabria, 39005 Santander, Spain  G. Gomez-Ceballos
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA  M.
Goncharov  Massachusetts Institute of Technology, Cambridge, Massachusetts
02139, USA  O. González López  Centro de Investigaciones Energeticas
Medioambientales y Tecnologicas, E-28040 Madrid, Spain  I. Gorelov  University
of New Mexico, Albuquerque, New Mexico 87131, USA  A.T. Goshaw  Duke
University, Durham, North Carolina 27708, USA  K. Goulianos  The Rockefeller
University, New York, New York 10065, USA  E. Gramellini  Istituto Nazionale
di Fisica Nucleare Bologna, llUniversity of Bologna, I-40127 Bologna, Italy
C. Grosso-Pilcher  Enrico Fermi Institute, University of Chicago, Chicago,
Illinois 60637, USA  J. Guimaraes da Costa  Harvard University, Cambridge,
Massachusetts 02138, USA  S.R. Hahn  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  J.Y. Han  University of Rochester, Rochester,
New York 14627, USA  F. Happacher  Laboratori Nazionali di Frascati, Istituto
Nazionale di Fisica Nucleare, I-00044 Frascati, Italy  K. Hara  University of
Tsukuba, Tsukuba, Ibaraki 305, Japan  M. Hare  Tufts University, Medford,
Massachusetts 02155, USA  R.F. Harr  Wayne State University, Detroit, Michigan
48201, USA  T. Harrington-Taberm Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  K. Hatakeyama  Baylor University, Waco, Texas
76798, USA  C. Hays  University of Oxford, Oxford OX1 3RH, United Kingdom  J.
Heinrich  University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
M. Herndon  University of Wisconsin-Madison, Madison, Wisconsin 53706, USA  A.
Hocker  Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
Z. Hongkk Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M
University, College Station, Texas 77843, USA  W. Hopkinsf Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  S. Hou  Institute of
Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China  R.E. Hughes
The Ohio State University, Columbus, Ohio 43210, USA  U. Husemann  Yale
University, New Haven, Connecticut 06520, USA  M. Husseincc Michigan State
University, East Lansing, Michigan 48824, USA  J. Huston  Michigan State
University, East Lansing, Michigan 48824, USA  G. Introzziqqrr Istituto
Nazionale di Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity of
Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia, I-27100
Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia, Italy  M. Ioriss Istituto
Nazionale di Fisica Nucleare, Sezione di Roma 1, ssSapienza Università di
Roma, I-00185 Roma, Italy  A. Isgrònn Istituto Nazionale di Fisica Nucleare
Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola Normale Superiore,
I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy, rrUniversity of
Pavia, I-27100 Pavia, Italy  A. Ivanovo University of California, Davis,
Davis, California 95616, USA  E. James  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  D. Jang  Carnegie Mellon University, Pittsburgh,
Pennsylvania 15213, USA  B. Jayatilaka  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  E.J. Jeon  Center for High Energy Physics:
Kyungpook National University, Daegu 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; Chonbuk National
University, Jeonju 561-756, Korea; Ewha Womans University, Seoul, 120-750,
Korea  S. Jindariani  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  M. Jones  Purdue University, West Lafayette, Indiana 47907, USA
K.K. Joo  Center for High Energy Physics: Kyungpook National University, Daegu
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; Chonbuk National University, Jeonju 561-756, Korea; Ewha
Womans University, Seoul, 120-750, Korea  S.Y. Jun  Carnegie Mellon
University, Pittsburgh, Pennsylvania 15213, USA  T.R. Junk  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  M. Kambeitz  Institut
für Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131
Karlsruhe, Germany  T. Kamon  Center for High Energy Physics: Kyungpook
National University, Daegu 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; Chonbuk National University,
Jeonju 561-756, Korea; Ewha Womans University, Seoul, 120-750, Korea  Mitchell
Institute for Fundamental Physics and Astronomy, Texas A&M University, College
Station, Texas 77843, USA  P.E. Karchin  Wayne State University, Detroit,
Michigan 48201, USA  A. Kasmi  Baylor University, Waco, Texas 76798, USA  Y.
Katon Osaka City University, Osaka 558-8585, Japan  W. Ketchumii Enrico Fermi
Institute, University of Chicago, Chicago, Illinois 60637, USA  J. Keung
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA  B.
Kilminsteree Fermi National Accelerator Laboratory, Batavia, Illinois 60510,
USA  D.H. Kim  Center for High Energy Physics: Kyungpook National University,
Daegu 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; Chonbuk National University, Jeonju 561-756, Korea;
Ewha Womans University, Seoul, 120-750, Korea  H.S. Kimbb Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  J.E. Kim  Center for
High Energy Physics: Kyungpook National University, Daegu 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;
Chonbuk National University, Jeonju 561-756, Korea; Ewha Womans University,
Seoul, 120-750, Korea  M.J. Kim  Laboratori Nazionali di Frascati, Istituto
Nazionale di Fisica Nucleare, I-00044 Frascati, Italy  S.H. Kim  University of
Tsukuba, Tsukuba, Ibaraki 305, Japan  S.B. Kim  Center for High Energy
Physics: Kyungpook National University, Daegu 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; Chonbuk National
University, Jeonju 561-756, Korea; Ewha Womans University, Seoul, 120-750,
Korea  Y.J. Kim  Center for High Energy Physics: Kyungpook National
University, Daegu 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; Chonbuk National University, Jeonju
561-756, Korea; Ewha Womans University, Seoul, 120-750, Korea  Y.K. Kim
Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
N. Kimura  Waseda University, Tokyo 169, Japan  M. Kirby  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  K. Kondo  Waseda
University, Tokyo 169, Japan  D.J. Kong  Center for High Energy Physics:
Kyungpook National University, Daegu 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; Chonbuk National
University, Jeonju 561-756, Korea; Ewha Womans University, Seoul, 120-750,
Korea  J. Konigsberg  University of Florida, Gainesville, Florida 32611, USA
A.V. Kotwal  Duke University, Durham, North Carolina 27708, USA  M. Kreps
Institut für Experimentelle Kernphysik, Karlsruhe Institute of Technology,
D-76131 Karlsruhe, Germany  J. Kroll  University of Pennsylvania,
Philadelphia, Pennsylvania 19104, USA  M. Kruse  Duke University, Durham,
North Carolina 27708, USA  T. Kuhr  Institut für Experimentelle Kernphysik,
Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany  M. Kurata
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  A.T. Laasanen  Purdue
University, West Lafayette, Indiana 47907, USA  S. Lammel  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  M. Lancaster  University
College London, London WC1E 6BT, United Kingdom  K. Lannonx The Ohio State
University, Columbus, Ohio 43210, USA  G. Latinooo Istituto Nazionale di
Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola
Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy,
rrUniversity of Pavia, I-27100 Pavia, Italy  H.S. Lee  Center for High Energy
Physics: Kyungpook National University, Daegu 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; Chonbuk National
University, Jeonju 561-756, Korea; Ewha Womans University, Seoul, 120-750,
Korea  J.S. Lee  Center for High Energy Physics: Kyungpook National
University, Daegu 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; Chonbuk National University, Jeonju
561-756, Korea; Ewha Womans University, Seoul, 120-750, Korea  S. Leo
University of Illinois, Urbana, Illinois 61801, USA  S. Leone  Istituto
Nazionale di Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity of
Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia, I-27100
Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia, Italy  J.D. Lewis  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  A. Limosanis
Duke University, Durham, North Carolina 27708, USA  E. Lipeles  University of
Pennsylvania, Philadelphia, Pennsylvania 19104, USA  A. Listera University of
Geneva, CH-1211 Geneva 4, Switzerland  Q. Liu  Purdue University, West
Lafayette, Indiana 47907, USA  T. Liu  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  S. Lockwitz  Yale University, New Haven,
Connecticut 06520, USA  A. Loginov  Yale University, New Haven, Connecticut
06520, USA  D. Lucchesimm Istituto Nazionale di Fisica Nucleare, Sezione di
Padova, mmUniversity of Padova, I-35131 Padova, Italy  A. Lucà  Laboratori
Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044
Frascati, Italy  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  J. Lueck  Institut für Experimentelle Kernphysik, Karlsruhe
Institute of Technology, D-76131 Karlsruhe, Germany  P. Lujan  Ernest Orlando
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA  P.
Lukens  Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
G. Lungu  The Rockefeller University, New York, New York 10065, USA  J. Lys
Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California
94720, USA  R. Lysakd Comenius University, 842 48 Bratislava, Slovakia;
Institute of Experimental Physics, 040 01 Kosice, Slovakia  R. Madrak  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  P. Maestrooo
Istituto Nazionale di Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity
of Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia,
I-27100 Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia, Italy  S. Malik
The Rockefeller University, New York, New York 10065, USA  G. Mancab
University of Liverpool, Liverpool L69 7ZE, United Kingdom  A. Manousakis-
Katsikakis  National and Kapodistrian University of Athens, 157 71 Athens,
Greece  L. Marchesejj Istituto Nazionale di Fisica Nucleare Bologna,
llUniversity of Bologna, I-40127 Bologna, Italy  F. Margaroli  Istituto
Nazionale di Fisica Nucleare, Sezione di Roma 1, ssSapienza Università di
Roma, I-00185 Roma, Italy  P. Marinopp Istituto Nazionale di Fisica Nucleare
Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola Normale Superiore,
I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy, rrUniversity of
Pavia, I-27100 Pavia, Italy  K. Matera  University of Illinois, Urbana,
Illinois 61801, USA  M.E. Mattson  Wayne State University, Detroit, Michigan
48201, USA  A. Mazzacane  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  P. Mazzanti  Istituto Nazionale di Fisica Nucleare
Bologna, llUniversity of Bologna, I-40127 Bologna, Italy  R. McNultyi
University of Liverpool, Liverpool L69 7ZE, United Kingdom  A. Mehta
University of Liverpool, Liverpool L69 7ZE, United Kingdom  P. Mehtala
Division of High Energy Physics, Department of Physics, University of
Helsinki, FIN-00014, Helsinki, Finland; Helsinki Institute of Physics,
FIN-00014, Helsinki, Finland  C. Mesropian  The Rockefeller University, New
York, New York 10065, USA  T. Miao  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  E. Michielinmm Istituto Nazionale di Fisica
Nucleare, Sezione di Padova, mmUniversity of Padova, I-35131 Padova, Italy  D.
Mietlicki  University of Michigan, Ann Arbor, Michigan 48109, USA  A. Mitra
Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
H. Miyake  University of Tsukuba, Tsukuba, Ibaraki 305, Japan  S. Moed  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  N. Moggi
Istituto Nazionale di Fisica Nucleare Bologna, llUniversity of Bologna,
I-40127 Bologna, Italy  C.S. Moon  Center for High Energy Physics: Kyungpook
National University, Daegu 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; Chonbuk National University,
Jeonju 561-756, Korea; Ewha Womans University, Seoul, 120-750, Korea  R.
Mooreffgg Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
M.J. Morellopp Istituto Nazionale di Fisica Nucleare Pisa, nnUniversity of
Pisa, ooUniversity of Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy,
qqINFN Pavia, I-27100 Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia,
Italy  A. Mukherjee  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  Th. Muller  Institut für Experimentelle Kernphysik, Karlsruhe
Institute of Technology, D-76131 Karlsruhe, Germany  P. Murat  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  M. Mussinill Istituto
Nazionale di Fisica Nucleare Bologna, llUniversity of Bologna, I-40127
Bologna, Italy  J. Nachtmanm Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  Y. Nagai  University of Tsukuba, Tsukuba, Ibaraki 305,
Japan  J. Naganoma  Waseda University, Tokyo 169, Japan  I. Nakano  Okayama
University, Okayama 700-8530, Japan  A. Napier  Tufts University, Medford,
Massachusetts 02155, USA  J. Nett  Mitchell Institute for Fundamental Physics
and Astronomy, Texas A&M University, College Station, Texas 77843, USA  T.
Nigmanov  University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA  L.
Nodulman  Argonne National Laboratory, Argonne, Illinois 60439, USA  S.Y. Noh
Center for High Energy Physics: Kyungpook National University, Daegu 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; Chonbuk National University, Jeonju 561-756, Korea; Ewha
Womans University, Seoul, 120-750, Korea  O. Norniella  University of
Illinois, Urbana, Illinois 61801, USA  L. Oakes  University of Oxford, Oxford
OX1 3RH, United Kingdom  S.H. Oh  Duke University, Durham, North Carolina
27708, USA  Y.D. Oh  Center for High Energy Physics: Kyungpook National
University, Daegu 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; Chonbuk National University, Jeonju
561-756, Korea; Ewha Womans University, Seoul, 120-750, Korea  T. Okusawa
Osaka City University, Osaka 558-8585, Japan  R. Orava  Division of High
Energy Physics, Department of Physics, University of Helsinki, FIN-00014,
Helsinki, Finland; Helsinki Institute of Physics, FIN-00014, Helsinki, Finland
L. Ortolan  Institut de Fisica d’Altes Energies, ICREA, Universitat Autonoma
de Barcelona, E-08193, Bellaterra (Barcelona), Spain  C. Pagliarone  Istituto
Nazionale di Fisica Nucleare Trieste, ttGruppo Collegato di Udine,
uuUniversity of Udine, I-33100 Udine, Italy, vvUniversity of Trieste, I-34127
Trieste, Italy  E. Palenciae Instituto de Fisica de Cantabria, CSIC-University
of Cantabria, 39005 Santander, Spain  P. Palni  University of New Mexico,
Albuquerque, New Mexico 87131, USA  V. Papadimitriou  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  W. Parker  University of
Wisconsin-Madison, Madison, Wisconsin 53706, USA  G. Paulettattuu Istituto
Nazionale di Fisica Nucleare Trieste, ttGruppo Collegato di Udine,
uuUniversity of Udine, I-33100 Udine, Italy, vvUniversity of Trieste, I-34127
Trieste, Italy  M. Paulini  Carnegie Mellon University, Pittsburgh,
Pennsylvania 15213, USA  C. Paus  Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139, USA  T.J. Phillips  Duke University, Durham,
North Carolina 27708, USA  G. Piacentinoq Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  E. Pianori  University of
Pennsylvania, Philadelphia, Pennsylvania 19104, USA  J. Pilot  University of
California, Davis, Davis, California 95616, USA  K. Pitts  University of
Illinois, Urbana, Illinois 61801, USA  C. Plager  University of California,
Los Angeles, Los Angeles, California 90024, USA  L. Pondrom  University of
Wisconsin-Madison, Madison, Wisconsin 53706, USA  S. Poprockif Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  K. Potamianos  Ernest
Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
A. Pranko  Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley,
California 94720, USA  F. Prokoshinaa Joint Institute for Nuclear Research,
RU-141980 Dubna, Russia  F. Ptohosg Laboratori Nazionali di Frascati, Istituto
Nazionale di Fisica Nucleare, I-00044 Frascati, Italy  G. Punzinn Istituto
Nazionale di Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity of
Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia, I-27100
Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia, Italy  I. Redondo
Fernández  Centro de Investigaciones Energeticas Medioambientales y
Tecnologicas, E-28040 Madrid, Spain  P. Renton  University of Oxford, Oxford
OX1 3RH, United Kingdom  M. Rescigno  Istituto Nazionale di Fisica Nucleare,
Sezione di Roma 1, ssSapienza Università di Roma, I-00185 Roma, Italy  F.
Rimondi  Istituto Nazionale di Fisica Nucleare Bologna, llUniversity of
Bologna, I-40127 Bologna, Italy  L. Ristori  Istituto Nazionale di Fisica
Nucleare Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola Normale
Superiore, I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy,
rrUniversity of Pavia, I-27100 Pavia, Italy  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  A. Robson  Glasgow University,
Glasgow G12 8QQ, United Kingdom  T. Rodriguez  University of Pennsylvania,
Philadelphia, Pennsylvania 19104, USA  S. Rollih Tufts University, Medford,
Massachusetts 02155, USA  M. Ronzaninn Istituto Nazionale di Fisica Nucleare
Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola Normale Superiore,
I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy, rrUniversity of
Pavia, I-27100 Pavia, Italy  R. Roser  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  J.L. Rosner  Enrico Fermi Institute, University
of Chicago, Chicago, Illinois 60637, USA  F. Ruffinioo Istituto Nazionale di
Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity of Siena, ppScuola
Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy,
rrUniversity of Pavia, I-27100 Pavia, Italy  A. Ruiz  Instituto de Fisica de
Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain  J. Russ
Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA  V. Rusu
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  W.K.
Sakumoto  University of Rochester, Rochester, New York 14627, USA  Y. Sakurai
Waseda University, Tokyo 169, Japan  L. Santittuu Istituto Nazionale di Fisica
Nucleare Trieste, ttGruppo Collegato di Udine, uuUniversity of Udine, I-33100
Udine, Italy, vvUniversity of Trieste, I-34127 Trieste, Italy  K. Sato
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  V. Savelievv Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  A. Savoy-
Navarroz Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
P. Schlabach  Fermi National Accelerator Laboratory, Batavia, Illinois 60510,
USA  E.E. Schmidt  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  T. Schwarz  University of Michigan, Ann Arbor, Michigan 48109, USA
L. Scodellaro  Instituto de Fisica de Cantabria, CSIC-University of Cantabria,
39005 Santander, Spain  F. Scuri  Istituto Nazionale di Fisica Nucleare Pisa,
nnUniversity of Pisa, ooUniversity of Siena, ppScuola Normale Superiore,
I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy, rrUniversity of
Pavia, I-27100 Pavia, Italy  S. Seidel  University of New Mexico, Albuquerque,
New Mexico 87131, USA  Y. Seiya  Osaka City University, Osaka 558-8585, Japan
A. Semenov  Joint Institute for Nuclear Research, RU-141980 Dubna, Russia  F.
Sforzann Istituto Nazionale di Fisica Nucleare Pisa, nnUniversity of Pisa,
ooUniversity of Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy, qqINFN
Pavia, I-27100 Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia, Italy  S.Z.
Shalhout  University of California, Davis, Davis, California 95616, USA  T.
Shears  University of Liverpool, Liverpool L69 7ZE, United Kingdom  P.F.
Shepard  University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA  M.
Shimojimau University of Tsukuba, Tsukuba, Ibaraki 305, Japan  M. Shochet
Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
I. Shreyber-Tecker  Institution for Theoretical and Experimental Physics,
ITEP, Moscow 117259, Russia  A. Simonenko  Joint Institute for Nuclear
Research, RU-141980 Dubna, Russia  K. Sliwa  Tufts University, Medford,
Massachusetts 02155, USA  J.R. Smith  University of California, Davis, Davis,
California 95616, USA  F.D. Snider  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  H. Song  University of Pittsburgh, Pittsburgh,
Pennsylvania 15260, USA  V. Sorin  Institut de Fisica d’Altes Energies, ICREA,
Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain  R.
St. Denis  Glasgow University, Glasgow G12 8QQ, United Kingdom  M. Stancari
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  D.
Stentzw Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
J. Strologas  University of New Mexico, Albuquerque, New Mexico 87131, USA  Y.
Sudo  University of Tsukuba, Tsukuba, Ibaraki 305, Japan  A. Sukhanov  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  I. Suslov
Joint Institute for Nuclear Research, RU-141980 Dubna, Russia  K. Takemasa
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  Y. Takeuchi  University of
Tsukuba, Tsukuba, Ibaraki 305, Japan  J. Tang  Enrico Fermi Institute,
University of Chicago, Chicago, Illinois 60637, USA  M. Tecchio  University of
Michigan, Ann Arbor, Michigan 48109, USA  P.K. Teng  Institute of Physics,
Academia Sinica, Taipei, Taiwan 11529, Republic of China  J. Thomf Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  E. Thomson
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA  V. Thukral
Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M
University, College Station, Texas 77843, USA  D. Toback  Mitchell Institute
for Fundamental Physics and Astronomy, Texas A&M University, College Station,
Texas 77843, USA  S. Tokar  Comenius University, 842 48 Bratislava, Slovakia;
Institute of Experimental Physics, 040 01 Kosice, Slovakia  K. Tollefson
Michigan State University, East Lansing, Michigan 48824, USA  T. Tomura
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  D. Tonellie Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  S. Torre  Laboratori
Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044
Frascati, Italy  D. Torretta  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  P. Totaro  Istituto Nazionale di Fisica Nucleare, Sezione
di Padova, mmUniversity of Padova, I-35131 Padova, Italy  M. Trovatopp
Istituto Nazionale di Fisica Nucleare Pisa, nnUniversity of Pisa, ooUniversity
of Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy, qqINFN Pavia,
I-27100 Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia, Italy  F. Ukegawa
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  S. Uozumi  Center for High
Energy Physics: Kyungpook National University, Daegu 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; Chonbuk
National University, Jeonju 561-756, Korea; Ewha Womans University, Seoul,
120-750, Korea  F. Vázquezl University of Florida, Gainesville, Florida 32611,
USA  V. Vecchionn Istituto Nazionale di Fisica Nucleare Pisa, nnUniversity of
Pisa, ooUniversity of Siena, ppScuola Normale Superiore, I-56127 Pisa, Italy,
qqINFN Pavia, I-27100 Pavia, Italy, rrUniversity of Pavia, I-27100 Pavia,
Italy  G. Velev  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  C. Vellidis  National and Kapodistrian University of Athens, 157
71 Athens, Greece  C. Vernieripp Istituto Nazionale di Fisica Nucleare Pisa,
nnUniversity of Pisa, ooUniversity of Siena, ppScuola Normale Superiore,
I-56127 Pisa, Italy, qqINFN Pavia, I-27100 Pavia, Italy, rrUniversity of
Pavia, I-27100 Pavia, Italy  M. Vidal  Purdue University, West Lafayette,
Indiana 47907, USA  R. Vilar  Instituto de Fisica de Cantabria, CSIC-
University of Cantabria, 39005 Santander, Spain  J. Vizándd Instituto de
Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain  M.
Vogel  University of New Mexico, Albuquerque, New Mexico 87131, USA  G. Volpi
Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare,
I-00044 Frascati, Italy  P. Wagner  University of Pennsylvania, Philadelphia,
Pennsylvania 19104, USA  R. Wallnyj Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  S.M. Wang  Institute of Physics, Academia
Sinica, Taipei, Taiwan 11529, Republic of China  D. Waters  University College
London, London WC1E 6BT, United Kingdom  W.C. Wester III  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  D. Whitesonc University
of Pennsylvania, Philadelphia, Pennsylvania 19104, USA  A.B. Wicklund  Argonne
National Laboratory, Argonne, Illinois 60439, USA  S. Wilbur  University of
California, Davis, Davis, California 95616, USA  H.H. Williams  University of
Pennsylvania, Philadelphia, Pennsylvania 19104, USA  J.S. Wilson  University
of Michigan, Ann Arbor, Michigan 48109, USA  P. Wilson  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  B.L. Winer  The Ohio
State University, Columbus, Ohio 43210, USA  P. Wittichf Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  S. Wolbers  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  H. Wolfmeister
The Ohio State University, Columbus, Ohio 43210, USA  T. Wright  University of
Michigan, Ann Arbor, Michigan 48109, USA  X. Wu  University of Geneva, CH-1211
Geneva 4, Switzerland  Z. Wu  Baylor University, Waco, Texas 76798, USA  K.
Yamamoto  Osaka City University, Osaka 558-8585, Japan  D. Yamato  Osaka City
University, Osaka 558-8585, Japan  T. Yang  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  U.K. Yang  Center for High Energy
Physics: Kyungpook National University, Daegu 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; Chonbuk National
University, Jeonju 561-756, Korea; Ewha Womans University, Seoul, 120-750,
Korea  Y.C. Yang  Center for High Energy Physics: Kyungpook National
University, Daegu 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; Chonbuk National University, Jeonju
561-756, Korea; Ewha Womans University, Seoul, 120-750, Korea  W.-M. Yao
Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California
94720, USA  G.P. Yeh  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  K. Yim Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  J. Yoh  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  K. Yorita  Waseda University, Tokyo 169, Japan  T. Yoshidak Osaka
City University, Osaka 558-8585, Japan  G.B. Yu  Center for High Energy
Physics: Kyungpook National University, Daegu 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; Chonbuk National
University, Jeonju 561-756, Korea; Ewha Womans University, Seoul, 120-750,
Korea  I. Yu  Center for High Energy Physics: Kyungpook National University,
Daegu 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; Chonbuk National University, Jeonju 561-756, Korea;
Ewha Womans University, Seoul, 120-750, Korea  A.M. Zanetti  Istituto
Nazionale di Fisica Nucleare Trieste, ttGruppo Collegato di Udine,
uuUniversity of Udine, I-33100 Udine, Italy, vvUniversity of Trieste, I-34127
Trieste, Italy  Y. Zeng  Duke University, Durham, North Carolina 27708, USA
C. Zhou  Duke University, Durham, North Carolina 27708, USA  S. Zucchellill
Istituto Nazionale di Fisica Nucleare Bologna, llUniversity of Bologna,
I-40127 Bologna, Italy  [

###### Abstract

At the Fermilab Tevatron proton-antiproton ($p\bar{p}$) collider, high-mass
electron-neutrino ($e\nu$) pairs are produced predominantly in the process
$p\bar{p}\rightarrow W(\rightarrow e\nu)+X$. The asymmetry of the electron and
positron yield as a function of their pseudorapidity constrain the slope of
the ratio of the $u$\- to $d$-quark parton distributions versus the fraction
of the proton momentum carried by the quarks. This paper reports on the
measurement of the electron-charge asymmetry using the full data set recorded
by the Collider Detector at Fermilab in 2001–2011 and corresponding to 9.1
fb-1 of integrated luminosity. The measurement significantly improves the
precision of the Tevatron constraints on the parton-distribution functions of
the proton. Numerical tables of the measurement are provided.

##  I Introduction

At the Fermilab Tevatron proton-antiproton ($p\bar{p}$) collider, massive
lepton pairs consisting of charged leptons $(\ell)$ and their partner
neutrinos $(\nu)$ are produced in $p\bar{p}$ collisions at the center-of-
momentum energy ($\sqrt{s}$) 1.96 TeV Drell and Yan (1970a); *DrellYanE. In
the standard model, the $\ell\nu$ pair is produced through an intermediate $W$
boson whose production occurs primarily through the quark-antiquark
annihilation process,

$q+\bar{q}^{\prime}\rightarrow W\rightarrow\ell\nu\>,$

where the $q$ and $\bar{q}^{\prime}$ denote the incoming quark and antiquark,
respectively, from the colliding hadrons. In leading-order quantum
chromodynamics (QCD) calculations, 90% of $W^{+}$ bosons are produced via
$u+\bar{d}$ collisions and a similar fraction of $W^{-}$ bosons via
$d+\bar{u}$ collisions.

The production rates of $W^{+}$ and $W^{-}$ bosons exhibit differences as
functions of their kinematic properties over their kinematic range of
production. The momentum distributions of the $u$ ($\bar{u}$) and $d$
($\bar{d}$) quarks from the incoming proton (antiproton) differ, affecting the
$W^{+}$ and $W^{-}$ differential-production rates. Momentum distributions of
quarks and gluons are determined by the parton-distribution functions (PDFs)
of the proton, which must be experimentally derived. Measurements of
production-rate differences can be used to constrain the PDFs. A highly
constraining measurement is the charged-lepton yield asymmetry as a function
of pseudorapidity

$A_{\ell}=\frac{d\sigma^{+}_{\ell}/d\eta-d\sigma^{-}_{\ell}/d\eta}{d\sigma^{+}_{\ell}/d\eta+d\sigma^{-}_{\ell}/d\eta}\;,$
(1)

where $d\sigma^{\pm}_{\ell}/d\eta$ denotes the differential cross section with
respect to the pseudorapidity $\eta$ of charged leptons $\ell^{\pm}$ from the
production of $W^{\pm}$ bosons and their subsequent decay via
$W\rightarrow\ell\nu$. The pseudorapidity is $-\\!\ln\tan(\theta/2)$, where
$\theta$ is the polar angle of the lepton relative to the proton direction.
Effects from the interference between the axial and vector currents of the
electroweak interaction, and from the initial-state interactions of the
colliding partons alter the boson asymmetries. While the leptonic asymmetry
$A_{\ell}$ can be measured well, its interpretation in terms of the underlying
PDFs must include these effects. The Tevatron measurement of $A_{\ell}$
constrains the slope of the ratio of the $d$\- to $u$-quark distribution
functions as a function of the Bjorken scaling parameter, the fraction $x$ of
the proton momentum taken by the colliding quark Bjorken and Paschos (1969).

The leptonic asymmetry $A_{\ell}$ has been measured at the Tevatron collider
with $p\bar{p}$ collisions and at the Large Hadron Collider (LHC) with $pp$
collisions. Tevatron measurements have been reported at $\sqrt{s}=1.8$ TeV by
CDF F. Abe _et al._ (1998), and at $\sqrt{s}=1.96$ TeV by CDF D. Acosta _et
al._ (2005) and D0 V. M. Abazov _et al._ (2008a, b); V. M. Abazov _et al._
(2013); V. M. Abazov _et al._ (2015a); *D0196Ae2E. The boson-level asymmetry
has also been inferred at $\sqrt{s}=1.96$ TeV by CDF T. Aaltonen _et al._
(2009) and D0 V. M. Abazov _et al._ (2014); *D0196Awe1E using a neutrino-
weighting technique Bodek  _et al._ (2008). The LHC measurements at
$\sqrt{s}=7$ (8) TeV have been reported by ATLAS G. Aad _et al._ (2011); M.
Aaboud _et al._ (2017), CMS S. Chatrchyan _et al._ (2011, 2012, 2014) (CMS V.
Khachatryan _et al._ (2016)), and LHCb R. Aaij _et al._ (2014) (LHCb R. Aaij
_et al._ (2016a, b)). Measurements from colliders of different types and
energies provide important constraints for global fits of PDFs because the
compositions of input parton fluxes that produce $W$ bosons differ, and
because the increased precision attainable significantly improves the accuracy
of the fitted PDFs. At the LHC, $W$ bosons are mostly produced through quark-
antiquark collisions as they are at the Tevatron. However, at the Tevatron,
the collisions are primarily between valence quarks while at the LHC,
collisions are primarily between valence and sea quarks.

In this paper, the final CDF measurement of the asymmetry $A_{\ell}$ in the
$W\rightarrow e\nu$ channel111 The $W\rightarrow\mu\nu$ channel is not
considered due to the limited $\eta$ coverage and complexity of the muon
measurement.  is presented, using a data sample corresponding to an integrated
$p\bar{p}$ luminosity of 9.1 fb-1 collected at the Tevatron collider. This
measurement supersedes the previous CDF measurements D. Acosta _et al._
(2005); T. Aaltonen _et al._ (2009), that were based on subsamples at least
nine times smaller.

Section II of the paper provides an overview of the formal definition of the
asymmetries and of the existing theoretical calculations. Section III
introduces the asymmetry measured in this paper. Section IV describes the
experimental apparatus. Section V reports on the selection of data. Section VI
describes the simulation of the reconstructed data. Section VII presents an
overview of the corrections to the data and simulation, and Sec. VIII the
details of those corrections. Section IX presents the measurement of the
asymmetry, Sec. X the systematic uncertainties, and Sec. XI the results.
Finally, Sec. XII presents a summary.

##  II  Asymmetry distributions

In the laboratory frame, the $p\bar{p}$-collision axis is the $z$ axis, with
the positive direction oriented along the direction of the proton. The
transverse component of any vector quantity is defined relative to that axis.
The rapidity, transverse momentum, and mass of a particle are denoted as $y$,
$\vec{P}_{\rm T}$, and $M$, respectively. The energy and momentum of particles
are denoted as $E$ and $\vec{P}$, respectively. The rapidity is
$y=\frac{1}{2}\,\ln[\,(E+P_{\rm z})/(E-P_{\rm z})\,]$, where $P_{\rm z}$ is
the component of the momentum vector along the $z$ axis. For massless
particles, the rapidity reduces to the pseudorapidity $\eta$.

The cross section for the production of $W$ bosons in hadronic collisions,
differential in the rapidity, squared mass, and squared transverse momentum,
is denoted by $d^{3}\sigma_{W}/dydP_{\rm T}^{2}dM^{2}$. The charge asymmetry
at a given $y$ value is defined as

$A_{W}=\frac{d\sigma^{+}_{W}/dy-d\sigma^{-}_{W}/dy}{d\sigma^{+}_{W}/dy+d\sigma^{-}_{W}/dy}\;,$
(2)

where $d\sigma^{\pm}_{W}/dy$ denotes the cross section for $W^{\pm}$
production integrated over $P_{\rm T}^{2}$ and $M^{2}$.

Since the $P_{\rm z}$ component of the neutrino momentum cannot be measured on
an event-by-event basis, the charge asymmetry of the lepton $A_{\ell}(\eta)$
is measured. The cross-section input to $A_{\ell}(\eta)$ is a combination of
the $W$-boson cross section and the angular distribution of the $\ell\nu$ pair
from the $W$-boson decay in the rest frame of the $\ell\nu$ pair,

$\frac{d^{\,5}\sigma_{\ell\nu}}{dydP_{\rm T}^{2}dM^{2}d\cos\vartheta
d\varphi}=\frac{3}{16\pi}\frac{d^{3}\sigma_{W}}{dydP_{\rm T}^{2}dM^{2}}{\cal
N}(\vartheta,\varphi)\>,$

where the angular-distribution function ${\cal N}(\vartheta,\varphi)$ is the
density of $W$ decays as a function of the polar angle $\vartheta$ and
azimuthal angle $\varphi$ of the charged lepton, respectively, and the charge-
specific labels for the $W$-boson cross section and angular-distribution
function are implicit. The decay into the lepton pair exposes a set of
helicity cross sections that characterize the density matrix of the $W$-boson
polarization states that are produced.

In this analysis, the Collins-Soper (CS) rest frame of the $\ell\nu$ pair is
used to quantify ${\cal N}(\vartheta,\varphi)$ Collins and Soper (1977). This
frame is reached from the laboratory frame via two Lorentz boosts, first along
the laboratory $z$-axis into the frame where the $z$ component of the
$\ell\nu$-pair momentum vector is zero, followed by a boost along the
transverse component of the $\ell\nu$-pair momentum vector into its rest
frame. A view of the CS frame is shown in Fig. 1.

Figure 1:  Representation of the CS-coordinate axes $(x,z)$ along with the
laboratory $z$ axis ($z_{lab}$). The three axes are in the plane formed by the
proton ($\vec{P}_{\rm A}$) and antiproton ($\vec{P}_{\rm B}$) momentum vectors
in the $\ell\nu$-pair rest frame. The $z$ axis is the angular bisector of
$\vec{P}_{\rm A}$ and $-\vec{P}_{\rm B}$, the $y$ axis is along the direction
of $\vec{P}_{\rm B}\times\vec{P}_{\rm A}$, and the $x$ axis is in the
direction away from the transverse component of $\vec{P}_{\rm A}+\vec{P}_{\rm
B}$. In the limit of vanishing $P_{\rm T}$, the CS and laboratory axes become
equivalent.

The angular-distribution function is expressed as

$\displaystyle{\cal N}(\vartheta,\varphi)$ $\displaystyle=$
$\displaystyle\>(1+\cos^{2}\vartheta)+$ (3) $\displaystyle
A_{0}\>\frac{1}{2}\>(1-3\cos^{2}\vartheta)+$ $\displaystyle A_{1}\>\sin
2\vartheta\cos\varphi+$ $\displaystyle
A_{2}\>\frac{1}{2}\>\sin^{2}\vartheta\cos 2\varphi+$ $\displaystyle
A_{3}\>\sin\vartheta\cos\varphi+$ $\displaystyle A_{4}\>\cos\vartheta+$
$\displaystyle A_{5}\>\sin^{2}\vartheta\sin 2\varphi+$ $\displaystyle
A_{6}\>\sin 2\vartheta\sin\varphi+$ $\displaystyle
A_{7}\>\sin\vartheta\sin\varphi\>,$

where $A_{0-7}$ are coefficient functions that describe the nonangular parts
of the helicity cross sections relative to the unpolarized cross section
integrated over the polar angles Mirkes (1992); *MirkesA0to7b. In amplitudes
at higher order than the tree level, initial-state interactions of the
colliding partons impart transverse momentum to the boson, affecting the
helicity cross sections. Consequently, $A_{0-7}$ are functions of the $W$
boson $y$, $P_{\rm T}$, and $M$. They vanish when the boson transverse
momentum is zero, except for $A_{4}$ whose value is $\pm 2$ for $W^{\mp}$
decays in QCD calculations at leading order (LO). In electroweak interactions,
the interference between the vector and axial currents produces the
$A_{4}\,\cos\vartheta$ term. The $A_{5-7}$ coefficients appear at second order
in the QCD strong-coupling constant, $\alpha_{s}$, and are small in the CS
frame.

For the $W$-boson cross sections used in comparisons of measurements to
theoretical predictions, next-to-leading-order (NLO) QCD calculations (of
order $\alpha_{s}$) and recent PDFs are used. The powheg-box222 The powheg-box
code is version V2 (svn 3319).  implementation of $W$-boson production
Frixione  _et al._ (2007) and decay to lepton pairs Alioli  _et al._ (2008)
provides the NLO QCD calculation. It is used as an unweighted partonic event
generator. The NLO-production framework implements a Sudakov form factor that
controls the infrared divergence at low-boson $P_{\rm T}$ Sudakov (1956a);
*Sudakov-FFrus, and an interface to parton-showering algorithms that avoids
double counting. The pythia 6.41 parton-showering algorithm is used to produce
the hadron-level event Sjöstrand  _et al._ (2006). The combined implementation
has next-to-leading log resummation accuracy. Parton fluxes of the incoming
proton and antiproton are provided by the recent NNPDF 3.0 set of NLO PDFs
derived with the value of $\alpha_{s}=0.118$ at the $Z$-pole mass R. D. Ball
_et al._ (2015); *nnpdf302; *nnpdf303; *nnpdf304; *nnpdf305; *nnpdf306;
*nnpdf306e; *nnpdf307. The powheg-box calculation with the NNPDF 3.0 NLO PDFs
is the default calculation.

In addition, the resbos NLO calculation Ladinsky and Yuan (1994); *ResBos2;
*ResBos3; *ResBosc221 with CTEQ6.6 NLO PDFs P. M. Nadolsky _et al._ (2008) is
used for the ancillary tuning of $W$-boson production within the powheg-box
calculation. The resbos calculation combines an NLO fixed-order calculation at
high boson $P_{\rm T}$ with the Collins-Soper-Sterman resummation formalism
Collins  _et al._ (1985); *wfactorCSS1; *wfactorCSS2; *wfactorCSS3 at low
boson $P_{\rm T}$, which is an all-orders summation of large terms from gluon
emission calculated to next-to-next-to-leading log accuracy. The intrinsic
$P_{\rm T}$ parameters of pythia 6.41 used for the default calculation are
adjusted333 The adjusted parameters and values are: MSTP(91) = 1, PARP(91) =
1.50 GeV/$c$, PARP(93) = 12 GeV/$c$, and PARP(64) = 0.4.  so that the boson
$P_{\rm T}$ distribution of the region below 30 GeV/$c$ is in good agreement
with that from the resbos calculation. The resbos calculation of the
$\gamma^{*}/Z$ $P_{\rm T}$ distribution in $p\bar{p}$ collisions, which is
kinematically similar to $W$-boson production, agrees with the CDF measurement
based on an integrated luminosity corresponding to 2.1 fb-1 T. Aaltonen _et
al._ (2012).

The current known values for the $W$-boson pole mass $M_{W}$ and resonant
width $\Gamma_{W}$, 80.385 GeV/$c^{2}$ and 2.085 GeV C. Patrignani _et al._
(2016), respectively, are used in the powheg-box and resbos calculations. Both
calculations employ resonant line shapes for the boson-mass distribution with
mass-dependent widths. CDF has modified the powheg-box calculation to use the
recent values of the Cabibbo-Kobayashi-Maskawa matrix Cabibbo (1963);
Kobayashi and Maskawa (1973) elements associated with the weak-interaction
charged current C. Patrignani _et al._ (2016).

Figure 2 illustrates the $d\sigma_{W}^{+}/dy$ and $d\sigma_{\ell}^{+}/d\eta$
cross sections from the powheg-box calculation.

Figure 2:  $d\sigma_{W}^{+}/dy$ and $d\sigma_{\ell}^{+}/d\eta$ cross sections.
The cross section for $W^{+}$-boson ($W$-decay charged-lepton) production in
1.96 TeV proton-antiproton collisions as a function of the rapidity
(pseudorapidity). The cross sections are from the default calculation.

Since the geometry of the colliding $p$ and $\bar{p}$ system is asymmetric
under the reversal of charge and parity (CP), the $d\sigma_{W}^{-}/dy$ and
$d\sigma_{\ell}^{-}/d\eta$ cross sections in a coordinate frame whose
positive-$z$ axis is oriented along the antiproton direction are identical to
those of the positive-charge cross sections shown in Fig. 2, where the
positive-$z$ axis is oriented along the proton direction. In the laboratory
frame of Fig. 2, $d\sigma_{W}^{-}(y)/dy=d\sigma_{W}^{+}(-y)/dy$ and
$d\sigma_{\ell}^{-}(\eta)/d\eta=d\sigma_{\ell}^{+}(-\eta)/d\eta$. Figure 3
illustrates the boson-level charge asymmetry $A_{W}(y)$

Figure 3:  $A_{W}(y)$ and $A_{\ell}(\eta)$ charge asymmetries. The charge-
dependent $W$-boson ($W$-decay charged-lepton) yield asymmetries as functions
of the rapidity (pseudorapidity). The asymmetry distributions are
antisymmetric and from the default calculation.

and the lepton-level charge asymmetry $A_{\ell}(\eta)$ based on the powheg-box
calculation.

##  III  Measured asymmetries

Measurements of the charge asymmetry $A_{\ell}$ within a reconstructed
pseudorapidity interval (bin) can be formally expressed using the observed
cross section $\Delta\sigma=N/({\cal L}\,\epsilon A)$, where $N$ is the number
of observed signal events after background subtraction, ${\cal L}$ the
integrated luminosity, $\epsilon$ the event reconstruction and selection
efficiency, and $A$ the acceptance of events within the kinematic and fiducial
restrictions. When the expressions for the bin-level cross sections of the
electrons and positrons are substituted into Eq. (1), the common integrated
luminosity terms cancel out yielding

$A_{\ell}=\frac{N^{+}/(\epsilon A)^{+}-N^{-}/(\epsilon A)^{-}}{N^{+}/(\epsilon
A)^{+}+N^{-}/(\epsilon A)^{-}}\>,$ (4)

where $N^{+(-)}$ and $(\epsilon A)^{+(-)}$, respectively, represent the $N$
and $\epsilon A$ of positrons (electrons).

In this paper the asymmetry is measured using Eq. (4) over the positron- and
electron-pseudorapidity range of $-3$ to 3 in uniform bins of width 0.2. As
the positrons and electrons in each bin are within the same region of $\eta$,
their reconstruction and selection efficiencies are expected to be similar
except for those that are not charge symmetric. Relative to a cross-section
measurement, the precision of a ratio of cross-section measurements such as
the asymmetry is far less dependent on accurate measurements of all of the
experimental efficiencies.

Details of the experimental apparatus, data set, simulation of the data, and
corrections to the data used in the measurement follow in Secs. IV to VIII.

##  IV  Experimental Apparatus

The CDF II apparatus is a general-purpose detector A. Abulencia _et al._
(2007) at the Fermilab Tevatron, a $p\bar{p}$ collider with $\sqrt{s}=1.96$
TeV. The Cartesian coordinates of the detector are denoted by $x$, $y$, and
$z$. The coordinate system is right-handed with the positive-$z$ axis directed
along the proton direction and the positive-$y$ axis directed vertically
upwards. For particle trajectories, the polar angle $\theta$ is relative to
the positive-$z$ axis and the azimuthal angle $\phi$ is relative to the
positive-$x$ axis. Detector coordinates, denoted by $(\eta_{\rm det},\phi)$,
are defined relative to the center of the detector ($z=0$).

The curvature and momentum $\vec{P}$ of a charged particle are measured in the
magnetic spectrometer, which consists of charged-particle position detectors
(trackers) immersed in a magnetic field. The energy $E$ of photons, electrons,
and hadrons is measured by the calorimeters surrounding the magnetic
spectrometer. The measured energy in the calorimeters (energy flow) transverse
to the beam line is $E_{\rm T}=E\sin\theta$.

The tracking detectors consist of an outer central tracker and an inner
tracker. The central tracker is a 3.1 m long, open-cell drift chamber T.
Affolder _et al._ (2004) that extends radially from 0.4 to 1.4 m. Between the
Tevatron beam pipe and the central tracker is a 2 m long silicon-microstrip
inner tracker T. Aaltonen _et al._ (2013). The central drift-chamber tracker
has 96 tracking layers, and the silicon tracker has seven or eight tracking
layers depending on $\eta_{\rm det}$. Both trackers are immersed in a 1.4 T
axial magnetic field produced by a superconducting solenoid beyond the outer
radius of the drift chamber. Combined, these two trackers provide efficient,
high-resolution tracking and momentum measurement over $|\eta_{\rm det}|<1.3$.

Outside the solenoid is the central-barrel calorimeter that covers the region
$|\eta_{\rm det}|<1.1$ L. Balka _et al._ (1988); S. Bertolucci _et al._
(1988). The forward regions, $1.1<|\eta_{\rm det}|<3.5$, are covered by disk-
shaped end-plug calorimeters M. Albrow _et al._ (2002); G. Apollinari _et al._
(1998); P. de Barbaro (1995). The electromagnetic (EM) and hadronic (HAD)
sections of the calorimeters are scintillator-based sampling calorimeters,
transversely segmented into projective towers that point back to the center of
the detector. The EM-calorimeter energy resolutions measured in test beams
with electrons are $\sigma/E=13.5\%/\sqrt{E_{\rm T}}$ for the central
calorimeter and $\sigma/E=(16\%/\sqrt{E})\oplus 1\%$ for the plug calorimeter,
where the symbol $\oplus$ is a quadrature sum, and $E_{\rm T}$ and $E$ are in
units of GeV. Both the central- and plug-EM calorimeters have preshower and
shower-maximum detectors for electromagnetic-shower identification and
centroid measurements. The shower-maximum detectors within the central- and
plug-EM calorimeters are strip detectors, and are denoted by CES and PES,
respectively.

The combination of the PES detector and silicon tracker provides enhanced
electron-tracking coverage to $|\eta_{\rm det}|=2.8$. A PES detector consists
of eight $45^{\circ}$ wedge-shaped subdetectors assembled into a disk.
Subdetector wedges consist of “strips” made of $5\times 5$ mm2 scintillator
bars organized into two parallel planes, denoted by $u$ and $v$, that span the
length of the fiducial region of the measurement. The $u$ strips are parallel
to one radial edge, and the $v$ are parallel to the other.

The presence of neutrinos in $W\rightarrow\ell\nu$ events is inferred from the
energy-flow measurements on all reconstructed particles in the event. The
transverse momentum of the neutrino balances the vector sum of the transverse-
energy flows. Thus, the negative of this vector sum, called the missing
$\vec{E}_{\rm T}$ and denoted by $\vec{E}\\!\\!\\!/_{\rm T}$, is an estimator
of the neutrino transverse momentum.

##  V  Data Selection

The data set, collected over 2002–2011, is the full CDF Run II sample
corresponding to an integrated $p\bar{p}$ luminosity of 9.1 fb-1. After event
selection, the sample consists of $5.8\times 10^{6}$ events. Section V.1
reports on the online selection of events (triggers) for the charge-asymmetry
measurement. Section V.2 describes the offline selection of electron
candidates, and Sec. V.3 describes the selection of electron-neutrino pairs.

###  V.1  Online event selection

Event samples enriched in signal candidates are selected by means of two
online triggers, central-18 and pem-20_met-15. The central-18 selection
accepts events containing at least one electron candidate in the central
calorimeter with $E_{\rm T}>18$ GeV. Candidates are required to have
electromagnetic-shower clusters in the central calorimeters that are
geometrically matched to tracks from the central tracker. The pem-20_met-15
selection accepts events with an electron candidate in the plug calorimeter
with $E_{\rm T}>20$ GeV and with $E\\!\\!\\!/_{\rm T}>15$ GeV. Electron
candidates in the plug region are not required to geometrically match a track
extrapolation. Values of the $E_{\rm T}$ and $E\\!\\!\\!/_{\rm T}$ quantities
differ from the corresponding values of the offline quantites of Sec. V.2 due
to more refined offline calibrations and calculation techniques.

###  V.2  Offline electron selection

The offline event reconstruction, which includes the application of standard
electron identification and quality requirements, improves the purity of the
sample A. Abulencia _et al._ (2007). Fiducial constraints are applied to
ensure that the electron candidates are reconstructed in instrumented detector
regions. Each electron candidate is required to be associated with a track
whose origin along the beam line $(z_{\rm vtx})$ is restricted to be within
97% of the luminous region, $|z_{\rm vtx}|<60$ cm.

Electron identification in the central region is optimized for electrons of
$P_{\rm T}>10$ GeV/$c$ A. Abulencia _et al._ (2007). It uses information from
the central and silicon trackers, the longitudinal and lateral (tower)
segmentation of the electromagnetic and hadronic calorimeter compartments, and
the CES detector within the electromagnetic calorimeter. The highest quality
of signal selection and background rejection is provided by the trackers in
combination with the CES. An electron candidate must have an associated shower
cluster within the electromagnetic-calorimeter towers and a CES signal
compatible with the lateral profile of an electromagnetic shower. A candidate
must also be associated with a track that extrapolates to the three-
dimensional position of the CES shower centroid. The transverse momentum
associated with the track must be consistent with the corresponding electron-
shower $E_{\rm T}$ via an $E/P$ selection if $P_{\rm T}<50$ GeV/$c$ A.
Abulencia _et al._ (2007). For both the track matching in the CES and the
$E/P$ selection, allowances are included for bremsstrahlung energy loss in the
tracking volume, where material thickness is on average 20% of a radiation
length. The ratio of the measured shower energy in the hadronic calorimeter to
that in the electromagnetic calorimeter, $E_{\rm HAD}/E_{\rm EM}$, must be
consistent with that for electrons.

Electron identification in the plug calorimeter also uses information from the
tracker, from the longitudinal and lateral (tower) segmentation of the
electromagnetic and hadronic calorimeter compartments, and from the PES
detector within the electromagnetic calorimeter. As the plug-calorimeter
geometry differs from the central geometry, the details of the selection
requirements differ.

The plug calorimeters, with sampling planes perpendicular to the beam line,
have much smaller projective towers than the central calorimeter towers and
vary in size as a function of $|\eta_{\rm det}|$ M. Albrow _et al._ (2002).
The preshower detector is the first layer of the electromagnetic calorimeter
and it is instrumented and read out separately. As there are approximately 0.7
radiation lengths of material in front of it, the energy released in this
layer is included in the electromagnetic-cluster shower energy.

Electrons entering the plug calorimeters have reduced geometrical acceptance
in the central tracker for $|\eta_{\rm det}|>1$, which vanishes at $|\eta_{\rm
det}|\approx 1.5$. However, the silicon tracker has good coverage in the
forward region, which is exploited with a calorimetry-seeded tracking
algorithm denoted as “Phoenix.” The electron acceptance of this algorithm is
roughly 90% to $|\eta_{\rm det}|=2.4$ and decreases beyond that value but does
not vanish. With this algorithm, the track helix in the magnetic field is
specified by the position of the $p\bar{p}$ collision vertex, the three-
dimensional position of the electron in the PES, and the helix curvature. The
collision vertex is reconstructed from other tracks in the event. The
curvature is derived from the $E_{\rm T}$ of the shower in the electromagnetic
calorimeter. Two potential helices are formed, one for each charge. The
algorithm projects each helix into the silicon tracker to initialize the track
reconstruction. If both projections yield valid tracks, the higher-quality one
is selected. Depending on its vertex location along the beam line, a track
traverses up to eight layers of silicon, of which the track reconstruction
uses the outer seven layers. The innermost layer has significant electronic
noise and is not used. Phoenix tracks selected for the asymmetry measurement
are required to traverse at least three layers and have at least three silicon
signals. For the high-$E_{\rm T}$ electrons from $\gamma^{*}/Z$-boson decays,
85% of the electrons traverse four or more layers for an average tracking
efficiency of about 80%.

An electron candidate in a plug calorimeter must have a shower cluster of
towers within the electromagnetic calorimeter and an associated signal in the
PES detector. The transverse and lateral profiles of the shower cluster are
required to be consistent with those obtained from test-beam electrons. The
transverse profile is evaluated in a $3\times 3$ detector-tower grid centered
on the highest-energy tower. The goodness-of-fit $\chi^{2}$ between this
profile and the expectation based on the shower-centroid location in the PES
detector is denoted by the quantity $\chi^{2}_{3\times 3}$. The longitudinal
profile is measured using $E_{\rm HAD}/E_{\rm EM}$. Neither a track $P_{\rm
T}$ nor an $E/P$ selection requirement is applied because the reconstruction
method correlates the track momentum to the calorimeter energy. Charge-
misidentification rates of Phoenix tracks increase significantly with
increasing $|\eta_{\rm det}|$ values because the path lengths of the charged
particles within the transverse plane of the magnetic field decrease from 129
to 23 cm. The transverse displacements of particles at the track-exit radii of
the PES detector relative to the trajectories of particles in the absence of a
magnetic field vary quadratically with the path length. The position
resolutions are approximately 1.2 mm.

As electrons from $W\rightarrow e\nu$ decays originate from the $p\bar{p}$
collision vertex, tracks are required to have impact parameters $(d_{0})$,
defined as transverse distances of closest approach to the beam line,
consistent with zero. Tracks in the central and plug regions are required to
have one or more silicon-detector hits and $|d_{0}|<175$ $\mu$m. These mild
requirements are effective for removing unwanted events from the electron
sample.

The high-$E_{\rm T}$ leptons from the production and decay of $W$ bosons are
expected to be produced in isolation from other particles in the event.
Consequently, electron candidates are required to be isolated from other
calorimetric activity. The isolation energy, $E_{\rm iso}$, is defined as the
sum of $E_{\rm T}$ over towers within a cone of radius 0.4 in $(\eta,\phi)$
surrounding the electron cluster. The towers of the electron cluster are not
included in the sum. For central-electron candidates, the isolation
requirement is $E_{\rm iso}/E_{\rm T}<0.1$; and for plug-electron candidates,
it is $E_{\rm iso}<4$ GeV.

As the offline-electron sample contains central electrons from the
$\gamma^{*}/Z$-production, the following criteria are applied to reduce the
fraction of such electrons. These criteria improve the efficiency of event
processing over the large number of events in the sample but do not affect the
asymmetry measurement. Events with two or more electrons with $E_{\rm T}>18$
GeV and $E\\!\\!\\!/_{\rm T}<12.5$ GeV are identified. However, the isolation
and $E_{\rm HAD}/E_{\rm EM}$ requirements are not applied. Electron pairs from
the production of $\gamma^{*}/Z$ bosons are identified following Ref. T.
Aaltonen _et al._ (2016); *cdfAfb9eeprdErr, and pairs with invariant masses
larger than 40 GeV/$c^{2}$ are removed.

For central electrons, the selection criteria have an overall efficiency of
about 85% and result in a high-quality sample of high-$E_{\rm T}$ electrons.
However, the criteria for the plug region result in a sample with significant
background, whose level varies significantly with the topology of the
reconstructed track in the silicon detector. Track- and electron-quality are
combined and made more stringent depending on the background fraction of the
track topology. Details are presented in Appendix A. These more stringent
critera result in a sample whose size is 18% smaller but whose quality is
vastly improved. Overall, the selection efficiency for plug electrons is about
60%. After the application of the event selection criteria of Sec. V.3, the
purities of the central- and plug-electron samples are similar.

###  V.3  Event selection

For the asymmetry measurement, events are required to have high missing
$E_{\rm T}$ and a single high-$E_{\rm T}$ electron. Electrons are accepted if
detected in either the central or plug calorimeters with the following
conditions:

  1. 1.

Central electrons

    1. (a)

$E_{\rm T}>25$ GeV;

    2. (b)

$E\\!\\!\\!/_{\rm T}>25$ GeV;

    3. (c)

$0.05<|\eta_{\rm det}|<1.00$.

  2. 2.

Plug electrons

    1. (a)

$E_{\rm T}>25$ GeV;

    2. (b)

$E\\!\\!\\!/_{\rm T}>25$ GeV;

    3. (c)

$1.2<|\eta_{\rm det}|<2.8$.

The kinematic variables are based on the energy measured in the calorimeter
and on the track direction. Detector pseudorapidity $\eta_{\rm det}$ is
defined with the detector coordinates of its shower-centroid location within
the CES or PES detectors. The missing-$E_{\rm T}$ vector of an event,
$\vec{E}\\!\\!\\!/_{\rm T}$, is derived using energy-flow measurements from
the calorimeters. It is defined as $-\sum_{i}E_{\rm T}^{i}\hat{n}_{i}$, where
the sum is over calorimeter towers, $\hat{n}_{i}$ is the unit vector in the
azimuthal plane that points from the $p\bar{p}$ collision vertex to the center
of the calorimeter tower $i$, and $E_{\rm T}^{i}$ is the corresponding
transverse energy in that tower.

The electron transverse momentum and the missing $E_{\rm T}$ of the event are
combined to form the transverse mass of the boson, $M_{\rm T}$, defined as
$\sqrt{2E_{\rm T}^{e}E_{\rm T}^{\nu}(1-\cos\Delta\phi_{e\nu})}$, where $E_{\rm
T}^{e}$ is the transverse energy of the electron, $E_{\rm T}^{\nu}$ the
missing $E_{\rm T}$ of the event, and $\Delta\phi_{e\nu}$ the azimuthal angle
between them. The small fraction of events with $M_{\rm T}<45$ GeV/$c^{2}$,
which are poorly simulated, is removed.

##  VI  Signal simulation

Data corrections are obtained using a simulation of the data events. The
pythia 6.2 event generator Sjöstrand  _et al._ (2001) with CTEQ5L H. L. Lai
_et al._ (2000) PDFs simulates the LO QCD interaction
$q\bar{q}^{\prime}\rightarrow W$, along with the initial-state QCD radiation
of the colliding quarks via its parton-shower algorithms; decays the boson via
the $W\rightarrow\ell\nu$ channel; and adds quantum-electrodynamics (QED)
final-state radiation (FSR) to the charged lepton. Final-state particles not
produced in the hard scattering, referred to as the underlying event (UE), are
also simulated. The boson-$P_{\rm T}$ and UE parameters are derived from the
pythia configuration pytune 101, a tuning to previous CDF data Sjöstrand  _et
al._ (2001); T. Affolder _et al._ (2000); M. Albrow _et al._ .

The simulation model for the production and decay of $W$ bosons is weighted to
resemble the more precise NLO QCD calculation based on powheg-box and NNPDF
3.0 PDFs, described in Sec. II. Three event-weight tables are used to improve
the agreement. They are a one-dimensional invariant-mass $(M)$ table with high
resolution and a lower-resolution pair of two-dimensional tables in the
variables $(y_{\rm scl},M)$ and $(y_{\rm scl},P_{\rm T})$, where $y_{\rm scl}$
is a scaled rapidity defined as $y_{\rm scl}=y/y_{\rm max}$ with $y_{\rm
max}=\ln\sqrt{s/(M^{2}+P_{\rm T}^{2})}$. As the correction steps are not
independent, they are determined using an iterative procedure. Additionally,
the angular distribution of the $\ell\nu$ pairs is adjusted. For this
correction, the coefficient functions $A_{0-4}$ of Eq. (3) are implemented as
two-dimensional tables in the variables $(y_{\rm scl},P_{\rm
T}/\sqrt{M^{2}+P_{\rm T}^{2}})$ for the pythia and powheg-box distributions444
The extracted values of $A_{0}$ are slightly negative for values of $P_{\rm
T}$ near zero. Offsets are added to these table values so that $A_{0}\geq 0$.
, the values of the ${\cal N}(\vartheta,\varphi)$ functions are calculated for
each event with $A_{5-7}=0$, and the ratio of the values is the adjustment
event weight.

Generated events are first processed by the event simulation, which uses
photos 2.0 to account for QED FSR from promptly decaying final-state hadrons
and their decay products Barberio and Was (1994); *Photos20b; Golonka and Was
(2006), which is not modeled by pythia. In addition, multiple $p\bar{p}$
interactions are added by pythia. This is followed by the CDF II detector
simulation based on geant-3 and gflash Grindhammer  _et al._ (1990). Standard
time-dependent beam and detector conditions are incorporated in the
simulation, including the $p$ and $\bar{p}$ beam line parameters; the
luminous-region profile; the instantaneous and integrated luminosities per
data-taking period; and the calibration of detector elements, which include
electronic gains and malfunctions. The simulated events are reconstructed,
selected, and analyzed in the same way as the experimental data.

The simulation does not describe kinematic distributions such as the $E_{\rm
T}$ of electrons and the missing $E_{\rm T}$ of events with sufficient
accuracy. Modest adjustments are applied to bring the simulation into
agreement with the data.

##  VII  Correction overview

A form of the asymmetry expression [Eq. (4)] which shows the net correction of
the $(\epsilon A)^{+}$ and $(\epsilon A)^{-}$ terms in the measurement is
$(N^{+}\\!-\rho N^{-})/(N^{-}\\!+\rho N^{-})$, where $\rho=(\epsilon
A)^{+}\\!/(\epsilon A)^{-}$. The $(\epsilon A)^{\pm}$ terms are evaluated with
the simulation after adjustments are applied to obtain agreement with the
data. Efficiencies and energies of electrons, energies and distributions of
hadrons, and misidentification rates of the electron charge are suitably
adjusted. All corrections, except those for the rates of charge
misidentification, are independent of the electron charge.

When the correct charge is assigned to the reconstructed electrons of the
simulation, the values of $(\epsilon A)^{+}$ and $(\epsilon A)^{-}$ within an
$\eta$ bin are similar, but vary across $\eta$ bins. Common portions of, and
common uncertainties on, $(\epsilon A)^{+}$ and $(\epsilon A)^{-}$, including
those from the charge-independent corrections, cancel out to first order in
the ratio $\rho$. Figure 4 shows the ratio as a function of $\eta$.

Figure 4:  The ratio $\rho(\eta)$, $(\epsilon A)^{+}\\!/(\epsilon A)^{-}$, as
a function of $\eta$ with the correct charge assigned to the reconstructed
electrons. The uncertainties shown are statistical.

Changes in the acceptance ratio with $\eta$ are due to the $E_{\rm T}$
distributions of the leptons, which are similar in shape when $|\eta|=0$ but
evolve differently as $|\eta|$ increases in value.

An overview of the corrections and the estimation of the backgrounds in the
data is presented in the remainder of this section. Details are presented in
Sec. VIII. As many of the charge-symmetric adjustments are influenced by
others, the determination process is iterative. Among all corrections, only
the charge-misidentification rate of plug electrons has a significant impact
on the asymmetry measurement.

###  VII.1  Electron corrections

Corrections for electrons follow Ref. T. Aaltonen _et al._ (2016);
*cdfAfb9eeprdErr, hereafter referred to as the $ee$-pair analysis. Energy
calibrations and efficiency measurements from the $ee$-pair analysis are used
as initial calibrations in this work because the kinematic properties of the
decay electrons from the production of $\gamma^{*}/Z$ and $W$ bosons are
similar. Corrections to account for differences in the event environment and
selection criteria are applied.

Energy-scale adjustments are applied to the electron energies of both the
simulation and the data so that observed energies match the generator level
values Bodek  _et al._ (2012). The adjustments are applied over the initial
corrections. Energy-resolution adjustments are applied to the simulation so
that its electron-$E_{\rm T}$ distributions are in better agreement with those
of the data. Additional adjustments are also needed in the simulation to
account for relative differences in the amounts of hadronic energy deposited
within electron showers.

###  VII.2  Hadronic corrections

The primary source of hadrons in the simulation is the parton shower
associated with the production of the $W$ boson, which approximates the
production of hadrons from initial-state QCD radiation. A large fraction of
the events contains low-energy parton showers, whose production is
nonperturbative. Additional nonperturbative sources of hadrons that are
difficult to simulate accurately are multiple interactions and the underlying
event. Multiple interactions are independent $p\bar{p}$ interactions within an
event, and vary with the instantaneous luminosity. Their prevalence and impact
vary. The calorimeter response to hadrons from nonperturbative events is
nonlinear and inadequately simulated. Collectively, the hadrons from all
sources are denoted as the recoil system of hadrons.

All sources affect the missing $E_{\rm T}$ and the reconstructed $E_{\rm T}$
of the electron. Due to the kinematic restrictions on the electron and missing
$E_{\rm T}$, event acceptances are affected as well. The calibrations of both
electron and recoil-system quantities are affected by the spatial distribution
of the hadrons relative to the electron.

To orient the spatial distribution of the hadrons, the direction of the recoil
system of hadrons with respect to the electron is specified with the parameter
$\cos(\Delta\phi_{eX})$, where $\Delta\phi_{eX}$ is the azimuthal angle
between the directions of the electron ($e$) and the recoil system of hadrons
($X$) produced with the $W$ boson. It is defined in the transverse-momentum
frame where the net transverse-momentum of the electron and neutrino is zero.
The boost to the frame is defined in terms of the electron $\vec{E}_{\rm T}$
and event missing $\vec{E}_{\rm T}$.

Corrections to quantities of the electron and the recoil system of hadrons are
evaluated in three $\cos(\Delta\phi_{eX})$ ranges, $-1.0$ to $-0.6$, $-0.6$ to
0.6, and 0.6 to 1.0. As these regions are relative to the electron, they are
denoted as the away, transverse, and toward regions, respectively. Figure 5

Figure 5:  Simulated $E_{\rm T}$ distributions of the away, transverse, and
toward regions for the electrons in the plug calorimeter. Distributions for
electrons in the central calorimeter are similar. The bold (black) histogram
is for the away region, the light (blue) histogram is for the transverse
region, and the (green) crosses are for the toward region. Corresponding
$E\\!\\!\\!/_{\rm T}$ distributions follow a similar pattern except that away
and toward are reversed because the direction away from the electron is toward
the neutrino and vice versa.

illustrates the electron-$E_{\rm T}$ distributions in these regions of
$\cos(\Delta\phi_{eX})$. Different kinematic distributions of the leptons are
selected by the acceptances of each region. These selections have a secondary
effect on the $W$-boson distributions, and the $E_{\rm T}$ distributions of
the recoil system in these regions are only slightly different. The kinematic
separations illustrated in Fig. 5 expose direction-dependent differences of
the simulation relative to the data.

Energy-scale corrections are first applied to the energies of the recoil
systems of both the data and simulation so that the observed energies are
calibrated to the generator-level energies Bodek  _et al._ (2012). Additional
corrections are then applied to the simulation that account for data-to-
simulation differences in the energy and spatial distributions of the hadrons.

###  VII.3  Backgrounds

Backgrounds total about 5%. They are simulated for the following processes,
which produce high-$P_{\rm T}$ electrons: $\gamma^{*}/Z\rightarrow
ee,\;\tau\tau$, $W\rightarrow\tau\nu$, dibosons (WW, WZ, ZZ), and $t\bar{t}$
pairs. The model of the QCD background is extracted from an experimental data
sample independent of the signal sample. Background rates are normalized to
the signal rates, and subtracted from distributions of the data.

The fraction of the QCD background in the measurement sample depends on the
location of the electron candidate, but overall is under 2%. Events from QCD
background are due to parton-parton scattering interactions that result in
outgoing partons that fragment into cascades of hadrons called jets. A small
fraction of jet cascades contains electron candidates. QCD events are not
expected to exhibit any $E\\!\\!\\!/_{\rm T}$, but nonzero values are observed
because jets can have reconstructed energies that differ from their underlying
energies, even significantly, due to the resolution of the detector or the
traversal of hadrons into uninstrumented regions of the detector. However, the
number of events with these instrumental effects decreases rapidly with
increasing $E\\!\\!\\!/_{\rm T}$ values.

The amount of QCD background in data is determined via a fit of the QCD model
and signal contributions to the $E\\!\\!\\!/_{\rm T}$ distributions.

###  VII.4  Charge misidentification

Charge-misidentification rates are significant only in the plug regions. They
are accounted for using measurements on $e^{+}e^{-}$ pairs with one electron
in the central region and the other in the plug region. Event selection
follows that of the $ee$-pair analysis. Central-region tracks, whose charges
are well measured, provide the reference charges expected for the plug-region
tracks. Rates are position-dependent and measured over small regions of
$(\eta_{\rm det},\phi)$. As this division limits the statistical precision of
the rates, the rates are not measured as functions of any other parameters.

##  VIII  Data and simulation corrections

###  VIII.1  Event-rate normalizations

The default simulation does not model the trigger and reconstruction
efficiencies observed in the data with the desired precision. Event weights
based on the efficiencies derived from the $ee$-pair analysis are used as the
initial correction to the simulation. The event weights are ratios of the
selection efficiencies observed in data to the simulation versus time,
position in the detector volume (denoted henceforth as detector location), and
instantaneous luminosity.

As the electron-selection criteria of the $e\nu$-pair analysis are more
stringent than those of the $ee$-pair analysis, an additional correction is
determined using the $ee$-pair data. The criteria of the $e\nu$-pair analysis
are applied over those of the $ee$-pair analysis, and efficiencies calculated
for both the data and simulation samples. The efficiency ratio between the
data and simulation provides the additional correction.

Changes of the Tevatron-luminosity profile over time are measured using the
$e\nu$-pair data and incorporated into the simulation. The distributions of
the location of the $p\bar{p}$-collision vertices along the beam line $(z_{\rm
vtx})$ and the number of multiple interactions in an event $(n_{\rm vtx})$
changed significantly with improvements to the beam current and optics of the
Tevatron. Measurements of the $z_{\rm vtx}$ distribution, which has an rms
dispersion of about 30 cm, are organized into seven time intervals
corresponding to the introductions of major improvements in the Tevatron
collider. As $\eta_{\rm det}$ is a function of $z_{\rm vtx}$, inaccuracies
impact the determination of the acceptance. The $n_{\rm vtx}$ quantity is a
measure of the instantaneous luminosity for the event. Measurements of the
$n_{\rm vtx}$ distribution are organized into calibration periods.

Another luminosity parameter, denoted as the average instantaneous luminosity,
is important for corrections to simulated quantities over long periods of
time. This parameter tracks the effects of the beam to the event environment
over multiyear periods associated with major changes in the average $\bar{p}$
current circulating within the Tevatron. Two time intervals need to be taken
into account by the simulation. The first interval covers calibration periods
where the average instantaneous luminosity is relatively low (low-luminosity
period), and the second interval covers calibration periods where the average
instantaneous luminosity is relatively high (high-luminosity period).

The initial coarse correction is refined toward a better resolution in time,
position, and luminosity using the events of the $e\nu$-pair analysis. These
finer extensions are separate for the events with central-region and plug-
region electrons, and use event-count ratios between the data and simulation
as event weights. All corrections are functions of $n_{\rm vtx}$. Some are
functions of the low- or high-luminosity period. Corrections for detector-
location dependencies are functions of $|\eta_{\rm det}|$. For the central
region, the location correction accounts for data-to-simulation differences of
the efficiencies across the CES detector. For the plug region, the correction
accounts for differences of both the efficiencies across the PES detector and
the position-dependent response of EM-calorimeter towers.

###  VIII.2  Selection quantities

The simulated distributions of isolation energy $E_{\rm iso}$ and the plug-
electron $\chi^{2}_{3\times 3}$ are adjusted to improve the agreement with
data. Isolation distributions are used in the analysis of QCD backgrounds. For
electron candidates in the plug region, the adjustments are important because
the criteria for their selection detailed in Appendix A are more stringent.

###  VIII.3  Electron-energy corrections

The initial corrections to the default calibrations use electron pairs where
one is detected in the central calorimeter and the other in the plug
calorimeter. Corrections to the energy scale and resolution are functions of
$(\eta_{\rm det},\phi)$. The scale is also dependent on the low- or high-
luminosity period. The initial corrections also account for the extra energy
in an electron shower from the underlying event and multiple interaction
sources as an average correction over all event topologies. Adjustments to
these energy calibrations are derived for the $e\nu$-pair analysis.

Electron-energy corrections specific to the $e\nu$-pair analysis are
implemented in four steps. The first is the calibration of the electron energy
at the reconstruction level of the simulation to the event-generator level
Bodek  _et al._ (2012). Next, the energy scale of the data is aligned with
that of the simulation. The third step accounts for small but location-
dependent differences between the simulation and the data in the amounts of
shower energy from hadronic sources within electron showers. The
$\cos(\Delta\phi_{eX})$-dependent offsets of the simulated electron-$E_{\rm
T}$ distributions are corrected relative to the data. Finally, the energy
resolution of the simulation is adjusted to improve agreement with the data.

The calibration of the energy scale of the simulation begins by associating
the reconstruction-level electron with its generator-level counterpart. Then
the electron and its companion electrons and photons from QED FSR are
clustered around the seed tower as in the electron reconstruction. The seed
tower is based on the reconstructed electron, and the projection from the
$p\bar{p}$ collision vertex to the tower is achieved by extrapolating the
track helix. The calibration is derived from the distribution of the ratio of
the reconstruction-level energy $E_{\rm rec}$ to the clustered energy at the
generator level $E_{\rm clus}$. In the vicinity of its peak, which occurs at
ratios of about 1.0, the distribution is approximately Gaussian. The energy
scale is adjusted to make it peak at 1.0. There are $|\eta_{\rm
det}|$-dependent adjustments of about 0.5% or less, with the larger shifts
being in the plug region.

The electron-$E_{\rm T}$ distributions are used for the alignment of the
energy scale of the data with that of the simulation. For most EM-calorimeter
towers, the data distributions agree with those of the simulation without any
adjustments. The overall uncertainty of the energy scale based on the
$\chi^{2}$ between the data and the simulation is $\pm 0.04$%.

To measure the energy shifts between the simulation and the data due to the
hadrons, events are separated into classes according to whether the electron
is detected in the central or plug region, instantaneous luminosity, low- or
high-luminosity period, $n_{\rm vtx}$, and the region of
$\cos(\Delta\phi_{eX})$. These groups are denoted as “standard-calibration
groups”. The shapes of the electron-$E_{\rm T}$ distributions for each
$\cos(\Delta\phi_{eX})$ region are similar to those shown in Fig. 5. Along the
rising and falling edges about the peaks of the distributions, small offsets
separating the simulated and experimental data are measured. Observed offsets
are of order 50 (100) MeV for electrons detected in the central (plug)
calorimeter, and vary in magnitude and sign.

The model for the energy-resolution of the simulation is
$\sigma^{2}=c_{0}^{2}E+c_{1}^{2}E^{2}$, where $\sigma$ is the resolution, $E$
the electron energy, $c_{0}$ the sampling term, and $c_{1}$ the miscalibration
or constant term. The sampling term, calibrated with test-beam data, is part
of the default detector simulation. Additional adjustments are applied to the
constant terms of both central- and plug-region electrons so that the
electron-$E_{\rm T}$ distributions agree better with the data.

Simulated electrons of the central region have a slightly broader $E_{\rm T}$
distribution around the peak than in the data. To reduce mismodeling, the
reconstructed energy $E_{\rm rec}$ in the simulation is modified on an event-
by-event basis using $E^{\prime}_{\rm rec}=E_{\rm clus}-f_{\rm rms}\;(E_{\rm
clus}-E_{\rm rec})$, where $E^{\prime}_{\rm rec}$ is the adjusted value and
$f_{\rm rms}$ a parameter. As the $E_{\rm clus}-E_{\rm rec}$ term gives the
fluctuation of the reconstructed energy from its generator-level value, the
$f_{\rm rms}$ parameter rescales the rms of the fluctuations. The optimization
of $f_{\rm rms}$ constrained by the data yields $f_{\rm rms}=0.87\pm 0.03$.

Simulated electrons of the plug region have a narrower $E_{\rm T}$
distribution around the peak than in the data. This is broadened on an event-
by-event basis by incorporating Gaussian fluctuations to the energies that
effectively increase the constant term $c_{1}$ beyond its default value of
0.01. The adjustment is a function of the $|\eta_{\rm det}|$ coordinates of
calorimeter towers and the $p\bar{p}$-interaction count $n_{\rm vtx}$.
Adjusted values for $c_{1}$ range from 0.021 to 0.056 for increasing values of
$|\eta_{\rm det}|$ and $n_{\rm vtx}$. The uncertainty of the $c_{1}$ terms is
estimated by rescaling all terms with a uniform factor, propagating the
effects to the $E_{\rm T}$ distributions, then comparing them to the data.
This results in a relative uncertainty of $\pm$4% on the constant terms.

Figure 6 shows the $E_{\rm T}$ distributions of electrons in the central and
plug regions after all corrections are applied, including the hadronic
corrections of Secs. VIII.5 to VIII.6 and the subtraction of backgrounds
described in Sec. VIII.7.

Figure 6:  Background-subtracted $E_{\rm T}$ distributions of electron
candidates in the central and plug regions. The crosses are the data and the
solid histogram is the simulation. The comparison between the data and the
simulation for electron candidates of the central (plug) region yields a
$\chi^{2}$ of 373 (317) per 200 bins.

All corrections need to be applied because of the correlations among them.
Adjustments based on the $\cos(\Delta\phi_{eX})$ parameter significantly
reduce the biases affecting different regions of the simulated-$E_{\rm T}$
distribution relative to the data.

Figure 7 shows the corresponding $\eta$ distribution

Figure 7:  Background-subtracted $\eta$ distribution of the electron
candidates used in the measurement of the asymmetry. The crosses are the data
and the solid histogram is the simulation. All corrections have been applied.

of the electrons. The valley structures of the distribution reflect the
nonfiducial regions in the central calorimeter ($|\eta|\sim 0$) and between
the central and plug calorimeters ($|\eta|\sim 1.1$). Electron-$E_{\rm T}$
distributions in $\eta$ subregions covered by the central and plug
calorimeters, $|\eta|$ values above and below 0.5 for the central calorimeter
and $|\eta|$ values above and below 1.6 for the plug calorimeter, are
adequately simulated. The shapes of the $E_{\rm T}$ distributions of the
central (plug) subregions are similar to those of the central (plug) region in
Fig. 6. Comparisons between the data and the simulation for the electron
candidates of the four subregions yield statistical-$\chi^{2}$ values ranging
from 360 to 550 for 200 bins.

###  VIII.4  Recoil system of hadrons

The momenta of the $W$ boson ($\vec{P}_{\rm T}^{W}$) and of the recoil system
of final-state particles directly associated with the boson production
($\vec{P}_{\rm T}^{X}$) balance each other in the transverse plane of an event
so that $\vec{P}_{\rm T}^{X}=-\vec{P}_{\rm T}^{W}$. The transverse energy of
the recoil system observed in the detector, denoted by $\vec{E}_{\rm
T}^{X{\rm(obs)}}$, is the quantity $-\vec{E}\\!\\!\\!/_{\rm T}-\vec{E}_{\rm
T}^{e}$, where $\vec{E}_{\rm T}^{e}$ represents the uncorrected contribution
of the electron shower to the missing-$E_{\rm T}$ term.

The observed recoil $\vec{E}_{\rm T}^{X{\rm(obs)}}$ is a combination of the
products of the hard collision producing the $W$ boson and of the other
activity in the event such as the underlying event and multiple interaction
sources. In the QCD parton model, the outgoing parton from the hard collision
recoiling against the $W$ boson fragments into a jet. At large values of the
parton $P_{\rm T}$, the fragmentation results in a collimated jet of particles
in the detector. Energetic final-state partons with sufficiently low values of
$P_{\rm T}$ fragment into jets where a fraction of the particles enter the
beam hole. Hadrons from softer nonperturbative partons are distributed more
broadly.

The calorimeters are calibrated so that particles that undergo electromagnetic
showering have $E/P\approx 1$. However, the response to a hadronic cascade is
intrinsically different from an electromagnetic cascade. In the simulation,
the response of the calorimeters to jet particles is based on the observed
responses from single particles in test beams and collider data A. Bhatti _et
al._ (2006). The measured responses of particles with momenta down to 0.5
GeV/$c$ are incorporated into the gflash model of the calorimeter response.
For a 2 GeV/$c$ hadron, $E/P$ equals about 0.65 and increases with the
particle momentum. As jets typically consist of many low-momentum particles,
the observed energy of the jet in the calorimeters is lower than the momentum
of the underlying particles.

For clustered jets, corrections to transform the jet response of the
calorimeters to the momentum of the underlying jet of particles have been
determined A. Bhatti _et al._ (2006). These jet corrections are validated
using events with $\gamma^{*}/Z$-bosons produced in association with jets,
where the $\gamma^{*}/Z$ bosons are reconstructed from electron and muon
pairs. The transverse momentum of the lepton pair serves as the reference
value for that of the jet to be corrected. The resulting distributions of the
difference between the transverse momenta of the boson and of the jet are
peaked close to zero. The shapes of the distributions are also similar.

The energy scale for the recoil system, which is unclustered, is investigated
using the simulation and the transverse momentum of the system from the event
generator. With the default simulation of the detector, the bias $P_{\rm
T}^{X}-E_{\rm T}^{X{\rm(obs)}}$ increases approximately linearly with $P_{\rm
T}^{X}$ in the region above 30 GeV/$c$. Below 30 GeV/$c$, the detector
response to the particles of the recoil system is nonlinear. Increasing the
energy scale by a factor of 1.175 yields a $\mathcal{O}(1)$ GeV bias, which is
approximately constant to about $\pm 15$% for the region above 30 GeV/$c$.

The energy-scale result of the recoil-system analysis is similar in
characteristics and values to the jet-energy-scale calibration result of Ref.
A. Bhatti _et al._ (2006) for clustered jets. The recoil system in data with
electron pairs from $\gamma^{*}/Z$-boson decays provides a test of the scale
factor. The recoil-system bias of electron-pair events is defined as $P_{\rm
T}^{ee}-E_{\rm T}^{X{\rm(obs)}}$, where $P_{\rm T}^{ee}$ is the transverse
momentum of the pair. As in the simulation, applying a recoil-energy scale of
1.175 also yields a bias that is approximately constant for the region above
30 GeV/$c$.

###  VIII.5  Hadronic calibrations

Calibrations associated with the recoil system of hadrons in the detector are
complex because the hadrons are spread across a large region of the
calorimeter, the calorimeter response is nonlinear, and there are sizeable
regions with cracks in the calorimeter coverage where the response of the
simulation is inadequate A. Bhatti _et al._ (2006). Position-dependent jet
corrections are not applied by default in the missing-$E_{\rm T}$ calculation.

The calibration strategy is to first fix the energy scale of the recoil system
in the data to 1.175, then adjust the corresponding energy scale in the
simulation so that the response matches that of the data for events with
large-$E_{\rm T}^{X{\rm(obs)}}$ values. For the remainder of the calibration,
events are partitioned into the standard-calibration groups. The offsets
between the simulation and data for the $x$ and $y$ components of the
recoil-$E_{\rm T}$ vector and the shapes of the recoil-$E_{\rm T}$
distributions are corrected.

To determine the energy-scale correction factor of the simulation relative to
the data, events with $E_{\rm T}^{X{\rm(obs)}}>30$ GeV are selected for both
the simulation and the data. With this selection, a scale change alters the
profiles of all simulated $E_{\rm T}$ distributions. The simulation scale is
expressed as the product of the data scale and a variable relative scale that
is adjusted using events from the away region of $\cos(\Delta\phi_{eX})$,
where the electron and recoil system are approximately opposite in azimuth. As
the energies of the electron and recoil-system of hadrons are expected to
balance, a scale misalignment appears as an energy offset between the
electron-$E_{\rm T}$ distributions of the data and the simulation. These
distributions are similar to the away-region distribution of Fig. 5, but
peaked near 55 GeV. In order to minimize contamination from multiple
interactions, only the events with $n_{\rm vtx}=1$ are used in the
adjustments. For the low- and high-luminosity periods of the central-region
events, the relative-scale values after the alignments are $0.959\pm 0.006$
and $0.958\pm 0.006$, respectively. For the plug-region events, they are
$0.943\pm 0.007$ and $0.930\pm 0.007$, respectively. These values are used on
all $n_{\rm vtx}$ categories.

The distributions of the $x$ and $y$ components of the recoil-$E_{\rm T}$
vector are centered near the origin, and their offsets from the origin are 1
GeV or less in magnitude, with magnitudes typically increasing with $n_{\rm
vtx}$. Differences between the offsets of the data and the simulation are
measured and applied as event-by-event corrections in the simulation. Next,
the recoil-$E_{\rm T}$ distributions of the simulation are adjusted to match
those of the data using event weights that preserve normalizations. After
these adjustments, data-to-simulation differences in the
$\cos(\Delta\phi_{eX})$ distributions remain. They vary with
$\cos(\Delta\phi_{eX})$, and do not exceed $\pm 10$% for the distribution with
the largest difference. The shapes of the simulated-$\cos(\Delta\phi_{eX})$
distributions are adjusted using event weights. These adjustments modestly
improve the agreements between the data and simulation in the recoil-$E_{\rm
T}$ distributions, but have a large impact on the $E\\!\\!\\!/_{\rm T}$
distributions in conjunction with their effects on the electron-$E_{\rm T}$
distributions.

Figure 8 shows the $E_{\rm T}^{X{\rm(obs)}}$ distribution of the recoil system
for electrons in the central and plug regions

Figure 8:  Background-subtracted $E_{\rm T}^{X{\rm(obs)}}$ distributions for
electron candidates in the central and plug regions. The crosses are the data
and the solid histogram is the simulation. The comparison between the data and
the simulation for electron candidates in the central (plug) region yields a
$\chi^{2}$ of 256 (402) per 240 bins.

after all corrections, including those for the missing-$E_{\rm T}$ of Sec.
VIII.6 and the subtraction of backgrounds described in Sec. VIII.7, are
applied. The simulated distributions are expected to similar to those of the
data.

###  VIII.6 Missing-$E_{\rm T}$ corrections

The corrected-$E\\!\\!\\!/_{\rm T}$ vector of an event is a composite object
obtained from the calibrated-$E_{\rm T}^{X{\rm(obs)}}$ vector by incorporating
the contribution of the calibrated-$E_{\rm T}$ vector of the electron.
Corrections to the electron energy and to the distribution of the electron
relative to the recoil system of hadrons tend to have a significant impact on
the missing-$E_{\rm T}$ of events. The impact is large because the $E_{\rm T}$
of the recoil system of hadrons is typically smaller than that of the electron
and thus the electron shower is a dominant component of all energy deposited
in the calorimeters.

Plug-region events of the high-luminosity period show small missing-$E_{\rm
T}$ differences between data and simulation at values greater than 65 GeV. The
simulated efficiency of the underlying electron in this region is slightly
lower than in the data as the default normalization and efficiency are from
optimizations over all events and are not specific to the high-$E_{\rm T}$
conditions. Adjustments are applied to the simulated-electron efficiency of
the events to mitigate the differences. The integral of the correction amounts
to under 0.1% of all events.

Figure 9 shows the $E\\!\\!\\!/_{\rm T}$ distributions for electrons in the
central and plug regions after all adjustments are applied to the underlying
quantities.

Figure 9:  Background-subtracted $E\\!\\!\\!/_{\rm T}$ distributions for
electron candidates in the central and plug regions. The crosses are the data
and the solid histogram is the simulation. The comparison between the data and
the simulation for electron candidates in the central (plug) region yields a
$\chi^{2}$ of 260 (310) per 200 bins.

The subtraction of backgrounds discussed in Sec. VIII.7 is also applied.

Figure 10 shows the transverse mass ($M_{\rm T}$) distributions for electrons
in the central and plug regions after all adjustments are applied to the
underlying quantities,

Figure 10:  Background-subtracted $M_{\rm T}$ distributions for electron
candidates in the central and plug regions. The crosses are the data and the
solid histogram is the simulation. The comparison between the data and the
simulation for electron candidates in the central (plug) region yields a
$\chi^{2}$ of 384 (402) per 200 bins.

including the subtraction of backgrounds discussed in Sec. VIII.7 . The
$M_{\rm T}$ distribution reflects the azimuthal angular distribution between
the electron and missing-$E_{\rm T}$ quantities of events.

###  VIII.7  Backgrounds

Backgrounds from the central and plug regions are determined separately.
Backgrounds from the processes $\gamma^{*}/Z\rightarrow ee$,
$W\rightarrow\tau\nu$, $\gamma^{*}/Z\rightarrow\tau\tau$, dibosons (WW, WZ,
ZZ), $t\bar{t}$ pairs, and QCD multijets are considered.

Events produced by the $\gamma^{*}/Z\rightarrow ee$ process can occasionally
have significant amounts of missing-$E_{\rm T}$, similar to QCD events.
Electron showers within uninstrumented portions of the detector can result in
significant amounts of missing $E_{\rm T}$ being indicated. However, the
number of such events is relatively small compared to that from the
$W\rightarrow e\nu$ process.

The QCD-background sample is derived from the data. Other backgrounds are
derived from pythia Sjöstrand  _et al._ (2001) samples that are processed with
the detector simulation and in which the integrated luminosity of each sample
matches the data. The diboson and $t\bar{t}$ samples are inclusive and their
normalizations use total cross sections calculated at NLO Campbell and Ellis
(1999) and next-to-next-to-leading order Czakon  _et al._ (2013),
respectively. The $W\rightarrow\tau\nu$ and $Z\rightarrow\tau\tau$ sample
normalizations use the total cross sections from pythia multiplied by the 1.4
ratio of the NLO-to-LO cross sections. The $\gamma^{*}/Z\rightarrow ee$ sample
is the signal sample of the $ee$-pair analysis T. Aaltonen _et al._ (2016);
*cdfAfb9eeprdErr, and data-constrained normalizations derived therein are
utilized. Sample normalizations as mentioned above are referred to as the
default normalizations. All normalizations are implemented as event weights.
This allows background events to be subtracted from (added to) event
distributions via the use of negative (positive) weights.

Candidates of the QCD sample are a subset of the events that fail the event-
selection criteria. Events in this sample fail the $E_{\rm HAD}/E_{\rm EM}$
criterion, but satisfy all other electron-identification criteria except the
isolation criterion. This subset definition enhances the fraction of QCD
events, and, limits the events to those whose kinematic distributions are
closer to those of the QCD events within the signal sample due to the
similarity of the selections. For the background in plug-region events, the
additional requirement on the transverse-shower shape described in Appendix A
is removed because it severely limits the size of the sample.

The QCD sample includes events from non-QCD processes with high-$E_{\rm T}$
electrons. These events are modeled using the same pythia samples of the
$W\rightarrow e\nu$ and background processes. However, events are required to
pass the selection criteria for the QCD sample. Most of the events are from
the $W\rightarrow e\nu$ process.

Figure 11 illustrates the shape of the isolation distributions from the QCD
sample for events of the central and plug regions.

Figure 11:  Shape of the isolation distributions of events in the central and
plug regions of the QCD sample. The bold (black) histogram is the data and the
lighter (blue) histogram is the expected contribution of the non-QCD
processes.

Also shown is the expected contribution of the non-QCD component, normalized
relative to the QCD component. To normalize the non-QCD component of the
sample to the QCD component, events are split into two disjoint sets based on
the isolation energy of the electron candidate. These collections are denoted
as the tight- and loose-isolation sets. Events with central-region candidates
having $E_{\rm iso}/E_{\rm T}<0.05$ and events with plug-region candidates
having $E_{\rm iso}<2$ GeV are assigned to the tight-isolation set. Unassigned
events form the loose-isolation set.

The sole purpose of the tight-isolation set is to provide the normalizations
of the non-QCD processes within the QCD sample. The QCD events of the loose-
isolation set are used as the model for the QCD background within the signal
sample. Normalizations of the various components in the QCD samples are
determined for each standard-calibration group.

Normalizations for the non-QCD processes are derived using the
$E\\!\\!\\!/_{\rm T}$ distribution of events. Events from QCD processes are
concentrated in the region with $E\\!\\!\\!/_{\rm T}$ smaller than
approximately 35 GeV. At higher values, $e\nu$ events from the production of
$W$ bosons dominate while the contribution from QCD production is small. A
single scale applied to the default normalizations of the non-QCD processes is
adjusted so that the simulated distribution in the region above 35 GeV is in
better agreement with that of the data. As the loose-isolation set includes
events from non-QCD processes, their contribution is subtracted to yield the
model of the QCD background within the signal sample.

All events of the model are used for the subtraction of the QCD background
from the signal sample, i.e., the isolation requirement of the signal sample
is not applied. Normalizations for the background are derived using the
$E\\!\\!\\!/_{\rm T}$ distributions of signal events for the data and
simulation. The event yields of the simulation and QCD background are adjusted
in a two-parameter fit so that their sum matches that of the data.

Backgrounds from QCD processes are larger in the plug region and suffer from
insufficiently accurate predictions. To improve the agreement between the
observations and the predictions, events with electron candidates in the plug
region are subdivided further into smaller groups based on the additional
selection criteria for electrons described in the Appendix, and the levels of
the QCD background therein determined.

Examples of the QCD backgrounds in the missing-$E_{\rm T}$ distributions of
plug-region electrons from the high-luminosity period and $n_{\rm vtx}=2$ for
the away, transverse, and toward regions of $\cos(\Delta\phi_{eX})$ is shown
in Fig. 12, where only the

Figure 12:  $E\\!\\!\\!/_{\rm T}$ distributions for electron candidates in the
plug calorimeter from the high-luminosity period with $n_{\rm vtx}=2$ in the
$\cos(\Delta\phi_{eX})$ regions. The (black) crosses are the data, the (red)
histogram overlapping the data is the simulation with all backgrounds, and the
lower histograms are the backgrounds for QCD (brown), $\gamma^{*}/Z\rightarrow
ee$ (blue), and $W\rightarrow\tau\nu$ (green). For the away region, the
backgrounds from top to bottom are QCD, $\gamma^{*}/Z\rightarrow ee$, and
$W\rightarrow\tau\nu$. For the toward region, the order is reversed. For the
transverse region, the backgrounds from top to bottom along the $y$ axis are
QCD, $W\rightarrow\tau\nu$, and $\gamma^{*}/Z\rightarrow ee$.

larger backgrounds are shown to reduce the overlap of histograms.
Distributions for electron candidates in the central calorimeter are similar.

The toward-region distribution is suppressed at low missing-$E_{\rm T}$ values
because most of its events have geometries where the missing-$E_{\rm T}$
vectors are in opposite directions relative to those of the electron and
recoil systems. As the QCD background in this region is small, the data inputs
to the fit do not constrain the QCD normalization. Consequently, the
normalization is fixed to a value determined from an extrapolation that uses
the $\cos(\Delta\phi_{eX})$ distribution of the QCD background, which
decreases exponentially as the value of $\cos(\Delta\phi_{eX})$ increases. All
toward-region distributions are similar and treated the same way.

Plug-region events of the high-luminosity period have small differences
between data and simulation in the electron-$E_{\rm T}$ distribution for
$E_{\rm T}>65$ GeV. In this region, the predicted amount of QCD background is
large, exceeding the signal at $E_{\rm T}>80$ GeV. Adjustments are applied to
the QCD-background shape to mitigate the differences. The integral of the
correction amounts to 0.1% of all events.

The data samples consist of approximately $3\>819\>000$ events for the central
region and $2\>003\>000$ events for the plug region. Table 1 lists the
background composition.

Table 1:  Background composition. Relative uncertainties of the QCD backgrounds are 12% for the central-region electrons and 6% for the plug-region electrons. All simulated backgrounds have a 6% relative uncertainty associated with the integrated luminosity D. Acosta _et al._ (2002) with the exception of the $\gamma^{*}/Z\rightarrow ee$ background, which is well constrained by the electron-pair data T. Aaltonen _et al._ (2016); *cdfAfb9eeprdErr.  Component | Background fraction (%)
---|---
| Central region | Plug region
$W\rightarrow\tau\nu$ | 1.78 | 1.62
QCD | 0.91 | 1.98
$\gamma^{*}/Z\rightarrow ee$ | 1.09 | 0.96
$\gamma^{*}/Z\rightarrow\tau\tau$ | 0.29 | 0.35
Diboson | 0.14 | 0.13
$t\bar{t}$ | 0.08 | 0.04

The fully corrected electron-$E_{\rm T}$ distributions, including the
individual contributions from the various background processes, is shown in
Fig. 13 for events in the central and plug regions.

Figure 13:  $E_{\rm T}$ distributions of electrons in the central and plug
regions. The data are the crosses (black) and the simulation with all
backgrounds is the histogram (red) overlapping the data. The individual
backgrounds are the lower histograms, and from the top to bottom along the
left edge of the plot they are the $W\rightarrow\tau\nu$ (green), QCD (brown),
$\gamma^{*}/Z\rightarrow\tau^{+}\tau^{-}$ (cyan), $\gamma^{*}/Z\rightarrow ee$
(blue), diboson (magenta), and $t\bar{t}$ (purple) contributions. For plug
electrons, $\gamma^{*}/Z\rightarrow ee$ (blue) peaks around 40 GeV.

###  VIII.8  Charge-misidentification rates

The rates of charge misidentification for central-region tracks are small and
are due to interactions of the electrons with the material in the tracking
volume. For tracks associated with plug electrons, the misidentification rates
are significant, and increase with $|\eta_{\rm det}|$. No charge bias is
detected in the track reconstruction. The charge bias and rates of charge
misidentification are studied using $e^{+}e^{-}$ pairs from
$\gamma^{*}/Z$-boson production. The event selection follows the $ee$-pair
analysis except that the track requirements of the $e\nu$-pair analysis are
applied.

For the study of the charge bias of plug-region electrons, the dielectron
masses are limited to the range 66 to 116 GeV/$c^{2}$. Pairs with one electron
in the central region and the other in the plug region are used to determine
the charge bias for plug electrons. The central-region electron provides the
reference charge for the measurement. A positive charge is assigned to the
plug electron if the central-electron charge is negative, and vice versa. The
bias is measured using the asymmetry $A_{\rm b}=(N^{+}-N^{-})/(N^{+}+N^{-})$,
where $N^{\pm}$ is the number of plug electrons with $\pm$ charges. As a
function of $|\eta_{\rm det}|$, the asymmetry of plug electrons is consistent
with zero and integrates to $-0.001\pm 0.002$.

For the measurement of the rates of charge misidentification, the dielectron
masses are limited to exceed 40 GeV/$c^{2}$. For pairs where both electrons
are in the central region, the electron with the largest $E_{\rm T}$ provides
the reference charge for the measurement of the misidentification rate of the
opposing electron. For pairs where one electron is in the central region and
the other is in the plug region, the central-region electron provides the
reference charge for the measurement of the misidentification rate of the
plug-region electron.

Rates of charge misidentification are measured on a $44\times 8$ $(\eta_{\rm
det},\phi)$ grid which reflects the transverse segmentation of the calorimeter
towers. Subdivisions along the $\eta_{\rm det}$ direction correspond to the 44
azimuthal rings of towers, numbered from 0 to 43. The low (high) edge of ring
0 (43), which is adjacent to the beam line, is located at $\eta_{\rm
det}=-3.5$ (3.5); however, these rings are not in the fiducial region.
Subdivisions along the $\phi$ direction correspond to a $45^{\circ}$ section
of adjacent towers in a ring. Each subdivision in $\phi$ is denoted as a
sector.

The sector subdivisions along the $\phi$ direction match the underlying wedge
structure of the PES detector, which provides the exit point for track finding
in the plug region. Each PES wedge is aligned as a single unit with the track
detectors of the central region.

The rate of misidentification, $m^{\pm}$, is the fraction of observed
(simulated) particles with expected (known) charge $\pm$ reconstructed with
the wrong charge. Figure 14 illustrates the average misidentification rates of
electrons and positrons,

Figure 14:  Charge-misidentification rates $m^{\pm}$ averaged over the sectors
of a ring, versus $\eta_{\rm det}$. The bold (black) histogram is for the
data, and the lighter (blue) histogram for the simulation.

where the tower rings are drawn at their locations in $\eta_{\rm det}$ space.
Zones with null rates are not in the fiducial region. In the plug region
$(|\eta_{\rm det}|>1.1)$, rate variations among the $\phi$-sectors of a ring
are significant for both the data and simulation. The data rates include the
effects from discrepancies between the true orientation of each PES wedge and
that specified by the alignments. For the simulation, the alignments are
exact.

For the individual sectors of ring 1 (42) towers near the beam line, the
numbers of events available for the rate measurements range from tens down to
a handful. The quality of the measurements is inadequate. Consequently, a rate
based on the combined events of rings 1 and 2 (42 and 41) within the same PES
wedge is used. The rates of these rings are correlated because they are
adjacent in the same strip detector. However, there are $\eta_{\rm det}$
dependencies as shown in Fig. 14. To account for these dependencies, the
combined rate of rings 1 and 2 (42 and 41) of a PES wedge is scaled by the
ratio of the integrated rate over all sectors of ring 1 (42) to that of the
combined rate integrated over all sectors. The scaled results are consistent
with the original ring 1 (42) rates.

###  VIII.9  Charge-misidentification corrections