CDF Collaboration222With visitors from aIstituto Nazionale di Fisica Nucleare,
Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy, bUniversity of CA
Irvine, Irvine, CA 92697, USA, cUniversity of CA Santa Barbara, Santa Barbara,
CA 93106, USA, dUniversity of CA Santa Cruz, Santa Cruz, CA 95064, USA,
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, jUniversity of Fukui, Fukui City, Fukui Prefecture, Japan
910-0017, kUniversidad Iberoamericana, Mexico D.F., Mexico, lIowa State
University, Ames, IA 50011, USA, mUniversity of Iowa, Iowa City, IA 52242,
USA, nKinki University, Higashi-Osaka City, Japan 577-8502, oKansas State
University, Manhattan, KS 66506, USA, pUniversity of Manchester, Manchester
M13 9PL, United Kingdom, qQueen Mary, University of London, London, E1 4NS,
United Kingdom, rUniversity of Melbourne, Victoria 3010, Australia, sMuons,
Inc., Batavia, IL 60510, USA, tNagasaki Institute of Applied Science,
Nagasaki, Japan, uNational Research Nuclear University, Moscow, Russia,
vUniversity of Notre Dame, Notre Dame, IN 46556, USA, wUniversidad de Oviedo,
E-33007 Oviedo, Spain, xTexas Tech University, Lubbock, TX 79609, USA,
yUniversidad Tecnica Federico Santa Maria, 110v Valparaiso, Chile, zYarmouk
University, Irbid 211-63, Jordan, hhOn leave from J. Stefan Institute,
Ljubljana, Slovenia,

# Measurement of the top-quark mass in the lepton+jets channel using a matrix
element technique with the CDF II detector

T. Aaltonen  Division of High Energy Physics, Department of Physics,
University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki,
Finland  B. Álvarez Gonzálezw Instituto de Fisica de Cantabria, CSIC-
University of Cantabria, 39005 Santander, Spain  S. Amerio  Istituto Nazionale
di Fisica Nucleare, Sezione di Padova-Trento, bbUniversity of Padova, I-35131
Padova, Italy  D. Amidei  University of Michigan, Ann Arbor, Michigan 48109,
USA  A. Anastassov  Northwestern University, Evanston, Illinois 60208, 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  A. Apresyan  Purdue University, West Lafayette,
Indiana 47907, USA  T. Arisawa  Waseda University, Tokyo 169, Japan  A.
Artikov  Joint Institute for Nuclear Research, RU-141980 Dubna, Russia  J.
Asaadi  Texas A&M University, College Station, Texas 77843, USA  W. Ashmanskas
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  B.
Auerbach  Yale University, New Haven, Connecticut 06520, USA  A. Aurisano
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  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.
Barriadd Istituto Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa,
ddUniversity of Siena and eeScuola Normale Superiore, I-56127 Pisa, Italy  P.
Bartos  Comenius University, 842 48 Bratislava, Slovakia; Institute of
Experimental Physics, 040 01 Kosice, Slovakia  M. Baucebb Istituto Nazionale
di Fisica Nucleare, Sezione di Padova-Trento, bbUniversity of Padova, I-35131
Padova, Italy  G. Bauer  Massachusetts Institute of Technology, Cambridge,
Massachusetts 02139, USA  F. Bedeschi  Istituto Nazionale di Fisica Nucleare
Pisa, ccUniversity of Pisa, ddUniversity of Siena and eeScuola Normale
Superiore, I-56127 Pisa, Italy  D. Beecher  University College London, London
WC1E 6BT, United Kingdom  S. Behari  The Johns Hopkins University, Baltimore,
Maryland 21218, USA  G. Bellettinicc Istituto Nazionale di Fisica Nucleare
Pisa, ccUniversity of Pisa, ddUniversity of Siena and eeScuola Normale
Superiore, I-56127 Pisa, Italy  J. Bellinger  University of Wisconsin,
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  M. Binkley111Deceased Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  D. Bisellobb Istituto Nazionale di
Fisica Nucleare, Sezione di Padova-Trento, bbUniversity of Padova, I-35131
Padova, Italy  I. Bizjakhh University College London, London WC1E 6BT, United
Kingdom  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. Brigliadoriaa Istituto
Nazionale di Fisica Nucleare Bologna, aaUniversity of Bologna, I-40127
Bologna, Italy  A. Brisuda  Comenius University, 842 48 Bratislava, Slovakia;
Institute of Experimental Physics, 040 01 Kosice, Slovakia  C. Bromberg
Michigan State University, East Lansing, Michigan 48824, USA  E. Brucken
Division of High Energy Physics, Department of Physics, University of Helsinki
and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland  M.
Bucciantoniocc Istituto Nazionale di Fisica Nucleare Pisa, ccUniversity of
Pisa, ddUniversity of Siena and eeScuola Normale Superiore, I-56127 Pisa,
Italy  J. Budagov  Joint Institute for Nuclear Research, RU-141980 Dubna,
Russia  H.S. Budd  University of Rochester, Rochester, New York 14627, USA  S.
Budd  University of Illinois, Urbana, Illinois 61801, USA  K. Burkett  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  G. Busettobb
Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, bbUniversity
of Padova, I-35131 Padova, Italy  P. Bussey  Glasgow University, Glasgow G12
8QQ, United Kingdom  A. Buzatu  Institute of Particle Physics: McGill
University, Montréal, Québec, Canada H3A 2T8; Simon Fraser University,
Burnaby, British Columbia, Canada V5A 1S6; University of Toronto, Toronto,
Ontario, Canada M5S 1A7; and TRIUMF, Vancouver, British Columbia, Canada V6T
2A3  C. Calancha  Centro de Investigaciones Energeticas Medioambientales y
Tecnologicas, E-28040 Madrid, Spain  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  M. Campbell  University of Michigan, Ann Arbor, Michigan
48109, USA  F. Canelli11 Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  B. Carls  University of Illinois, Urbana, Illinois 61801,
USA  D. Carlsmith  University of Wisconsin, Madison, Wisconsin 53706, USA  R.
Carosi  Istituto Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa,
ddUniversity of Siena and eeScuola Normale Superiore, I-56127 Pisa, Italy  S.
Carrillok University of Florida, Gainesville, Florida 32611, USA  S. Carron
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  B. Casal
Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005
Santander, Spain  M. Casarsa  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  A. Castroaa Istituto Nazionale di Fisica Nucleare
Bologna, aaUniversity of Bologna, I-40127 Bologna, Italy  P. Catastini
Harvard University, Cambridge, Massachusetts 02138, USA  D. Cauz  Istituto
Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, ggUniversity of
Udine, I-33100 Udine, Italy  V. Cavaliere  University of Illinois, Urbana,
Illinois 61801, USA  M. Cavalli-Sforza  Institut de Fisica d’Altes Energies,
ICREA, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona),
Spain  A. Cerrie Ernest Orlando Lawrence Berkeley National Laboratory,
Berkeley, California 94720, USA  L. Cerritoq 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, ccUniversity of Pisa, ddUniversity of Siena and eeScuola
Normale Superiore, I-56127 Pisa, Italy  G. Chlachidze  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  F. Chlebana  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  D. Chokheli  Joint
Institute for Nuclear Research, RU-141980 Dubna, Russia  J.P. Chou  Harvard
University, Cambridge, Massachusetts 02138, USA  W.H. Chung  University of
Wisconsin, Madison, Wisconsin 53706, USA  Y.S. Chung  University of Rochester,
Rochester, New York 14627, USA  C.I. Ciobanu  LPNHE, Universite Pierre et
Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France  M.A. Cioccidd Istituto
Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena
and eeScuola Normale Superiore, I-56127 Pisa, Italy  A. Clark  University of
Geneva, CH-1211 Geneva 4, Switzerland  C. Clarke  Wayne State University,
Detroit, Michigan 48201, USA  G. Compostellabb Istituto Nazionale di Fisica
Nucleare, Sezione di Padova-Trento, bbUniversity of Padova, I-35131 Padova,
Italy  M.E. Convery  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  J. Conway  University of California, Davis, Davis, California
95616, USA  M.Corbo  LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS,
UMR7585, Paris, F-75252 France  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  F. Cresciolicc
Istituto Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity
of Siena and eeScuola Normale Superiore, I-56127 Pisa, Italy  C. Cuenca
Almenar  Yale University, New Haven, Connecticut 06520, USA  J. Cuevasw
Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005
Santander, Spain  R. Culbertson  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  D. Dagenhart  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  N. d’Ascenzou LPNHE, Universite
Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France  M. Datta
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  P. de
Barbaro  University of Rochester, Rochester, New York 14627, USA  S. De Cecco
Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, ffSapienza
Università di Roma, I-00185 Roma, Italy  G. De Lorenzo  Institut de Fisica
d’Altes Energies, ICREA, Universitat Autonoma de Barcelona, E-08193,
Bellaterra (Barcelona), Spain  M. Dell’Orsocc Istituto Nazionale di Fisica
Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena and eeScuola
Normale Superiore, I-56127 Pisa, Italy  C. Deluca  Institut de Fisica d’Altes
Energies, ICREA, Universitat Autonoma de Barcelona, E-08193, Bellaterra
(Barcelona), Spain  L. Demortier  The Rockefeller University, New York, New
York 10065, USA  J. Dengb Duke University, Durham, North Carolina 27708, USA
M. Deninno  Istituto Nazionale di Fisica Nucleare Bologna, aaUniversity of
Bologna, I-40127 Bologna, Italy  F. Devoto  Division of High Energy Physics,
Department of Physics, University of Helsinki and Helsinki Institute of
Physics, FIN-00014, Helsinki, Finland  M. d’Erricobb Istituto Nazionale di
Fisica Nucleare, Sezione di Padova-Trento, bbUniversity of Padova, I-35131
Padova, Italy  A. Di Cantocc Istituto Nazionale di Fisica Nucleare Pisa,
ccUniversity of Pisa, ddUniversity of Siena and eeScuola Normale Superiore,
I-56127 Pisa, Italy  B. Di Ruzza  Istituto Nazionale di Fisica Nucleare Pisa,
ccUniversity of Pisa, ddUniversity of Siena and eeScuola Normale Superiore,
I-56127 Pisa, Italy  J.R. Dittmann  Baylor University, Waco, Texas 76798, USA
M. D’Onofrio  University of Liverpool, Liverpool L69 7ZE, United Kingdom  S.
Donaticc Istituto Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa,
ddUniversity of Siena and eeScuola Normale Superiore, I-56127 Pisa, Italy  P.
Dong  Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  M.
Dorigo  Istituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste,
ggUniversity of Udine, I-33100 Udine, Italy  T. Dorigo  Istituto Nazionale di
Fisica Nucleare, Sezione di Padova-Trento, bbUniversity of Padova, I-35131
Padova, Italy  K. Ebina  Waseda University, Tokyo 169, Japan  A. Elagin  Texas
A&M University, College Station, Texas 77843, USA  A. Eppig  University of
Michigan, Ann Arbor, Michigan 48109, USA  R. Erbacher  University of
California, Davis, Davis, California 95616, USA  D. Errede  University of
Illinois, Urbana, Illinois 61801, USA  S. Errede  University of Illinois,
Urbana, Illinois 61801, USA  N. Ershaidatz LPNHE, Universite Pierre et Marie
Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France  R. Eusebi  Texas A&M
University, College Station, Texas 77843, USA  H.C. Fang  Ernest Orlando
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA  S.
Farrington  University of Oxford, Oxford OX1 3RH, United Kingdom  M. Feindt
Institut für Experimentelle Kernphysik, Karlsruhe Institute of Technology,
D-76131 Karlsruhe, Germany  J.P. Fernandez  Centro de Investigaciones
Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain  C.
Ferrazzaee Istituto Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa,
ddUniversity of Siena and eeScuola Normale Superiore, I-56127 Pisa, Italy  R.
Field  University of Florida, Gainesville, Florida 32611, USA  G. Flanagans
Purdue University, West Lafayette, Indiana 47907, USA  R. Forrest  University
of California, Davis, Davis, California 95616, USA  M.J. Frank  Baylor
University, Waco, Texas 76798, USA  M. Franklin  Harvard University,
Cambridge, Massachusetts 02138, USA  J.C. Freeman  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  Y. Funakoshi  Waseda University,
Tokyo 169, Japan  I. Furic  University of Florida, Gainesville, Florida 32611,
USA  M. Gallinaro  The Rockefeller University, New York, New York 10065, USA
J. Galyardt  Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
J.E. Garcia  University of Geneva, CH-1211 Geneva 4, Switzerland  A.F.
Garfinkel  Purdue University, West Lafayette, Indiana 47907, USA  P. Garosidd
Istituto Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity
of Siena and eeScuola Normale Superiore, I-56127 Pisa, Italy  H. Gerberich
University of Illinois, Urbana, Illinois 61801, USA  E. Gerchtein  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  S. Giaguff
Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, ffSapienza
Università di Roma, I-00185 Roma, Italy  V. Giakoumopoulou  University of
Athens, 157 71 Athens, Greece  P. Giannetti  Istituto Nazionale di Fisica
Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena and eeScuola
Normale Superiore, I-56127 Pisa, Italy  K. Gibson  University of Pittsburgh,
Pittsburgh, Pennsylvania 15260, USA  C.M. Ginsburg  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  N. Giokaris  University of Athens,
157 71 Athens, Greece  P. Giromini  Laboratori Nazionali di Frascati, Istituto
Nazionale di Fisica Nucleare, I-00044 Frascati, Italy  M. Giunta  Istituto
Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena
and eeScuola Normale Superiore, I-56127 Pisa, Italy  G. Giurgiu  The Johns
Hopkins University, Baltimore, Maryland 21218, USA  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  Texas
A&M University, College Station, Texas 77843, USA  N. Goldschmidt  University
of Florida, Gainesville, Florida 32611, 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  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  S. Grinstein  Institut
de Fisica d’Altes Energies, ICREA, Universitat Autonoma de Barcelona, E-08193,
Bellaterra (Barcelona), Spain  C. Grosso-Pilcher  Enrico Fermi Institute,
University of Chicago, Chicago, Illinois 60637, USA  R.C. Group55 Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  J. Guimaraes da
Costa  Harvard University, Cambridge, Massachusetts 02138, USA  Z. Gunay-
Unalan  Michigan State University, East Lansing, Michigan 48824, USA  C. Haber
Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California
94720, USA  S.R. Hahn  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  E. Halkiadakis  Rutgers University, Piscataway, New
Jersey 08855, USA  A. Hamaguchi  Osaka City University, Osaka 588, Japan  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  D. Hare  Rutgers University, Piscataway, New Jersey 08855, USA  M. Hare
Tufts University, Medford, Massachusetts 02155, USA  R.F. Harr  Wayne State
University, Detroit, Michigan 48201, USA  K. Hatakeyama  Baylor University,
Waco, Texas 76798, USA  C. Hays  University of Oxford, Oxford OX1 3RH, United
Kingdom  M. Heck  Institut für Experimentelle Kernphysik, Karlsruhe Institute
of Technology, D-76131 Karlsruhe, Germany  J. Heinrich  University of
Pennsylvania, Philadelphia, Pennsylvania 19104, USA  M. Herndon  University of
Wisconsin, Madison, Wisconsin 53706, USA  S. Hewamanage  Baylor University,
Waco, Texas 76798, USA  D. Hidas  Rutgers University, Piscataway, New Jersey
08855, USA  A. Hocker  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  W. Hopkinsf Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  D. Horn  Institut für Experimentelle Kernphysik,
Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany  S. Hou
Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
R.E. Hughes  The Ohio State University, Columbus, Ohio 43210, USA  M. Hurwitz
Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
U. Husemann  Yale University, New Haven, Connecticut 06520, USA  N. Hussain
Institute of Particle Physics: McGill University, Montréal, Québec, Canada H3A
2T8; Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6;
University of Toronto, Toronto, Ontario, Canada M5S 1A7; and TRIUMF,
Vancouver, British Columbia, Canada V6T 2A3  M. Hussein  Michigan State
University, East Lansing, Michigan 48824, USA  J. Huston  Michigan State
University, East Lansing, Michigan 48824, USA  G. Introzzi  Istituto Nazionale
di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena and
eeScuola Normale Superiore, I-56127 Pisa, Italy  M. Ioriff Istituto Nazionale
di Fisica Nucleare, Sezione di Roma 1, ffSapienza Università di Roma, I-00185
Roma, 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  Duke University, Durham, North Carolina 27708, 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
M.K. Jha  Istituto Nazionale di Fisica Nucleare Bologna, aaUniversity of
Bologna, I-40127 Bologna, Italy  S. Jindariani  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  W. Johnson  University of
California, Davis, Davis, California 95616, 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  S.Y. Jun  Carnegie Mellon University,
Pittsburgh, Pennsylvania 15213, USA  T.R. Junk  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  T. Kamon  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 588, Japan  W. Ketchum  Enrico
Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA  J. Keung
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA  V.
Khotilovich  Texas A&M University, College Station, Texas 77843, USA  B.
Kilminster  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
H.S. 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  H.W. 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  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  M.J. Kim
Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare,
I-00044 Frascati, Italy  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  S.H. Kim  University of Tsukuba, Tsukuba, Ibaraki 305,
Japan  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  S.
Klimenko  University of Florida, Gainesville, Florida 32611, USA  K.
Kondo††footnotemark:  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  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  D.
Krop  Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637,
USA  N. Krumnackl Baylor University, Waco, Texas 76798, USA  M. Kruse  Duke
University, Durham, North Carolina 27708, USA  V. Krutelyovc Texas A&M
University, College Station, Texas 77843, USA  T. Kuhr  Institut für
Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131
Karlsruhe, Germany  M. Kurata  University of Tsukuba, Tsukuba, Ibaraki 305,
Japan  S. Kwang  Enrico Fermi Institute, University of Chicago, Chicago,
Illinois 60637, USA  A.T. Laasanen  Purdue University, West Lafayette, Indiana
47907, USA  S. Lami  Istituto Nazionale di Fisica Nucleare Pisa, ccUniversity
of Pisa, ddUniversity of Siena and eeScuola Normale Superiore, I-56127 Pisa,
Italy  S. Lammel  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  M. Lancaster  University College London, London WC1E 6BT, United
Kingdom  R.L. Lander  University of California, Davis, Davis, California
95616, USA  K. Lannonv The Ohio State University, Columbus, Ohio 43210, USA
A. Lath  Rutgers University, Piscataway, New Jersey 08855, USA  G. Latinocc
Istituto Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity
of Siena and eeScuola Normale Superiore, I-56127 Pisa, Italy  T. LeCompte
Argonne National Laboratory, Argonne, Illinois 60439, USA  E. Lee  Texas A&M
University, College Station, Texas 77843, USA  H.S. Lee  Enrico Fermi
Institute, University of Chicago, Chicago, Illinois 60637, USA  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  S.W. Leex
Texas A&M University, College Station, Texas 77843, USA  S. Leocc Istituto
Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena
and eeScuola Normale Superiore, I-56127 Pisa, Italy  S. Leone  Istituto
Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena
and eeScuola Normale Superiore, I-56127 Pisa, Italy  J.D. Lewis  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  A. Limosanir
Duke University, Durham, North Carolina 27708, USA  C.-J. Lin  Ernest Orlando
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA  J.
Linacre  University of Oxford, Oxford OX1 3RH, United Kingdom  M. Lindgren
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  E.
Lipeles  University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA  A.
Lister  University of Geneva, CH-1211 Geneva 4, Switzerland  D.O. Litvintsev
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  C. Liu
University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA  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. Lucchesibb Istituto Nazionale di Fisica
Nucleare, Sezione di Padova-Trento, bbUniversity of Padova, I-35131 Padova,
Italy  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. Lysak  Comenius University, 842 48 Bratislava, Slovakia; Institute of
Experimental Physics, 040 01 Kosice, Slovakia  R. Madrak  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  K. Maeshima  Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  K. Makhoul
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA  S.
Malik  The Rockefeller University, New York, New York 10065, USA  G. Mancaa
University of Liverpool, Liverpool L69 7ZE, United Kingdom  A. Manousakis-
Katsikakis  University of Athens, 157 71 Athens, Greece  F. Margaroli  Purdue
University, West Lafayette, Indiana 47907, USA  C. Marino  Institut für
Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131
Karlsruhe, Germany  M. Martínez  Institut de Fisica d’Altes Energies, ICREA,
Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain  R.
Martínez-Ballarín  Centro de Investigaciones Energeticas Medioambientales y
Tecnologicas, E-28040 Madrid, Spain  P. Mastrandrea  Istituto Nazionale di
Fisica Nucleare, Sezione di Roma 1, ffSapienza Università di Roma, I-00185
Roma, Italy  M.E. Mattson  Wayne State University, Detroit, Michigan 48201,
USA  P. Mazzanti  Istituto Nazionale di Fisica Nucleare Bologna, aaUniversity
of Bologna, I-40127 Bologna, Italy  K.S. McFarland  University of Rochester,
Rochester, New York 14627, USA  P. McIntyre  Texas A&M University, College
Station, Texas 77843, USA  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 and Helsinki Institute of Physics, FIN-00014,
Helsinki, Finland  A. Menzione  Istituto Nazionale di Fisica Nucleare Pisa,
ccUniversity of Pisa, ddUniversity of Siena and eeScuola Normale Superiore,
I-56127 Pisa, Italy  C. Mesropian  The Rockefeller University, New York, New
York 10065, USA  T. Miao  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  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  Harvard University, Cambridge, Massachusetts 02138, USA
N. Moggi  Istituto Nazionale di Fisica Nucleare Bologna, aaUniversity of
Bologna, I-40127 Bologna, Italy  M.N. Mondragonk Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  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  R. Moore  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  M.J. Morello  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  J. Morlock  Institut für
Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131
Karlsruhe, Germany  P. Movilla Fernandez  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  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. Mussiniaa Istituto Nazionale di Fisica Nucleare
Bologna, aaUniversity 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
Texas A&M University, College Station, Texas 77843, USA  C. Neu  University of
Virginia, Charlottesville, Virginia 22906, USA  M.S. Neubauer  University of
Illinois, Urbana, Illinois 61801, USA  J. Nielsend Ernest Orlando Lawrence
Berkeley National Laboratory, Berkeley, California 94720, USA  L. Nodulman
Argonne National Laboratory, Argonne, Illinois 60439, USA  O. Norniella
University of Illinois, Urbana, Illinois 61801, USA  E. Nurse  University
College London, London WC1E 6BT, United Kingdom  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  I. Oksuzian  University of Virginia, Charlottesville,
Virginia 22906, USA  T. Okusawa  Osaka City University, Osaka 588, Japan  R.
Orava  Division of High Energy Physics, Department of Physics, University of
Helsinki and 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  S. Pagan Grisobb Istituto
Nazionale di Fisica Nucleare, Sezione di Padova-Trento, bbUniversity of
Padova, I-35131 Padova, Italy  C. Pagliarone  Istituto Nazionale di Fisica
Nucleare Trieste/Udine, I-34100 Trieste, ggUniversity of Udine, I-33100 Udine,
Italy  E. Palenciae Instituto de Fisica de Cantabria, CSIC-University of
Cantabria, 39005 Santander, Spain  V. Papadimitriou  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  A.A. Paramonov  Argonne
National Laboratory, Argonne, Illinois 60439, USA  J. Patrick  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  G. Paulettagg Istituto
Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, ggUniversity of
Udine, I-33100 Udine, Italy  M. Paulini  Carnegie Mellon University,
Pittsburgh, Pennsylvania 15213, USA  C. Paus  Massachusetts Institute of
Technology, Cambridge, Massachusetts 02139, USA  D.E. Pellett  University of
California, Davis, Davis, California 95616, USA  A. Penzo  Istituto Nazionale
di Fisica Nucleare Trieste/Udine, I-34100 Trieste, ggUniversity of Udine,
I-33100 Udine, Italy  T.J. Phillips  Duke University, Durham, North Carolina
27708, USA  G. Piacentino  Istituto Nazionale di Fisica Nucleare Pisa,
ccUniversity of Pisa, ddUniversity of Siena and eeScuola Normale Superiore,
I-56127 Pisa, Italy  E. Pianori  University of Pennsylvania, Philadelphia,
Pennsylvania 19104, USA  J. Pilot  The Ohio State University, Columbus, Ohio
43210, 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, Wisconsin 53706, USA  K.
Potamianos  Purdue University, West Lafayette, Indiana 47907, USA  O.
Poukhov††footnotemark:  Joint Institute for Nuclear Research, RU-141980 Dubna,
Russia  F. Prokoshiny Joint Institute for Nuclear Research, RU-141980 Dubna,
Russia  A. Pronko  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  F. Ptohosg Laboratori Nazionali di Frascati, Istituto Nazionale di
Fisica Nucleare, I-00044 Frascati, Italy  E. Pueschel  Carnegie Mellon
University, Pittsburgh, Pennsylvania 15213, USA  G. Punzicc Istituto Nazionale
di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena and
eeScuola Normale Superiore, I-56127 Pisa, Italy  J. Pursley  University of
Wisconsin, Madison, Wisconsin 53706, USA  A. Rahaman  University of
Pittsburgh, Pittsburgh, Pennsylvania 15260, USA  V. Ramakrishnan  University
of Wisconsin, Madison, Wisconsin 53706, USA  N. Ranjan  Purdue University,
West Lafayette, Indiana 47907, USA  I. Redondo  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, ffSapienza Università di
Roma, I-00185 Roma, Italy  T. Riddick  University College London, London WC1E
6BT, United Kingdom  F. Rimondiaa Istituto Nazionale di Fisica Nucleare
Bologna, aaUniversity of Bologna, I-40127 Bologna, Italy  L. Ristori44 Fermi
National Accelerator Laboratory, Batavia, Illinois 60510, USA  A. Robson
Glasgow University, Glasgow G12 8QQ, United Kingdom  T. Rodrigo  Instituto de
Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain  T.
Rodriguez  University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
E. Rogers  University of Illinois, Urbana, Illinois 61801, USA  S. Rollih
Tufts University, Medford, Massachusetts 02155, USA  R. Roser  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  M. Rossi  Istituto
Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, ggUniversity of
Udine, I-33100 Udine, Italy  F. Rubbo  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  F. Ruffinidd Istituto Nazionale di Fisica
Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena and eeScuola
Normale Superiore, I-56127 Pisa, 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  A.
Safonov  Texas A&M University, College Station, Texas 77843, USA  W.K.
Sakumoto  University of Rochester, Rochester, New York 14627, USA  Y. Sakurai
Waseda University, Tokyo 169, Japan  L. Santigg Istituto Nazionale di Fisica
Nucleare Trieste/Udine, I-34100 Trieste, ggUniversity of Udine, I-33100 Udine,
Italy  L. Sartori  Istituto Nazionale di Fisica Nucleare Pisa, ccUniversity of
Pisa, ddUniversity of Siena and eeScuola Normale Superiore, I-56127 Pisa,
Italy  K. Sato  University of Tsukuba, Tsukuba, Ibaraki 305, Japan  V.
Savelievu LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris,
F-75252 France  A. Savoy-Navarro  LPNHE, Universite Pierre et Marie
Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France  P. Schlabach  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  A. Schmidt  Institut für
Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131
Karlsruhe, Germany  E.E. Schmidt  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  M.P. Schmidt††footnotemark:  Yale University,
New Haven, Connecticut 06520, USA  M. Schmitt  Northwestern University,
Evanston, Illinois 60208, USA  T. Schwarz  University of California, Davis,
Davis, California 95616, USA  L. Scodellaro  Instituto de Fisica de Cantabria,
CSIC-University of Cantabria, 39005 Santander, Spain  A. Scribanodd Istituto
Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena
and eeScuola Normale Superiore, I-56127 Pisa, Italy  F. Scuri  Istituto
Nazionale di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena
and eeScuola Normale Superiore, I-56127 Pisa, Italy  A. Sedov  Purdue
University, West Lafayette, Indiana 47907, USA  S. Seidel  University of New
Mexico, Albuquerque, New Mexico 87131, USA  Y. Seiya  Osaka City University,
Osaka 588, Japan  A. Semenov  Joint Institute for Nuclear Research, RU-141980
Dubna, Russia  F. Sforzacc Istituto Nazionale di Fisica Nucleare Pisa,
ccUniversity of Pisa, ddUniversity of Siena and eeScuola Normale Superiore,
I-56127 Pisa, Italy  A. Sfyrla  University of Illinois, Urbana, Illinois
61801, USA  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. Shimojimat University of Tsukuba, Tsukuba, Ibaraki 305, Japan
S. Shiraishi  Enrico Fermi Institute, University of Chicago, Chicago, Illinois
60637, USA  M. Shochet  Enrico Fermi Institute, University of Chicago,
Chicago, Illinois 60637, USA  I. Shreyber  Institution for Theoretical and
Experimental Physics, ITEP, Moscow 117259, Russia  A. Simonenko  Joint
Institute for Nuclear Research, RU-141980 Dubna, Russia  P. Sinervo  Institute
of Particle Physics: McGill University, Montréal, Québec, Canada H3A 2T8;
Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6; University
of Toronto, Toronto, Ontario, Canada M5S 1A7; and TRIUMF, Vancouver, British
Columbia, Canada V6T 2A3  A. Sissakian††footnotemark:  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  A. Soha  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  S. Somalwar  Rutgers University,
Piscataway, New Jersey 08855, USA  V. Sorin  Institut de Fisica d’Altes
Energies, ICREA, Universitat Autonoma de Barcelona, E-08193, Bellaterra
(Barcelona), Spain  P. Squillacioti  Istituto Nazionale di Fisica Nucleare
Pisa, ccUniversity of Pisa, ddUniversity of Siena and eeScuola Normale
Superiore, I-56127 Pisa, Italy  M. Stancari  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  M. Stanitzki  Yale University, New
Haven, Connecticut 06520, USA  R. St. Denis  Glasgow University, Glasgow G12
8QQ, United Kingdom  B. Stelzer  Institute of Particle Physics: McGill
University, Montréal, Québec, Canada H3A 2T8; Simon Fraser University,
Burnaby, British Columbia, Canada V5A 1S6; University of Toronto, Toronto,
Ontario, Canada M5S 1A7; and TRIUMF, Vancouver, British Columbia, Canada V6T
2A3  O. Stelzer-Chilton  Institute of Particle Physics: McGill University,
Montréal, Québec, Canada H3A 2T8; Simon Fraser University, Burnaby, British
Columbia, Canada V5A 1S6; University of Toronto, Toronto, Ontario, Canada M5S
1A7; and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3  D. Stentz
Northwestern University, Evanston, Illinois 60208, USA  J. Strologas
University of New Mexico, Albuquerque, New Mexico 87131, USA  G.L. Strycker
University of Michigan, Ann Arbor, Michigan 48109, USA  Y. Sudo  University of
Tsukuba, Tsukuba, Ibaraki 305, Japan  A. Sukhanov  University of Florida,
Gainesville, Florida 32611, 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  J. Thome  Carnegie Mellon
University, Pittsburgh, Pennsylvania 15213, USA  G.A. Thompson  University of
Illinois, Urbana, Illinois 61801, USA  E. Thomson  University of Pennsylvania,
Philadelphia, Pennsylvania 19104, USA  P. Ttito-Guzmán  Centro de
Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid,
Spain  S. Tkaczyk  Fermi National Accelerator Laboratory, Batavia, Illinois
60510, USA  D. Toback  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. Tonelli  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-Trento,
bbUniversity of Padova, I-35131 Padova, Italy  M. Trovatoee Istituto Nazionale
di Fisica Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena and
eeScuola Normale Superiore, I-56127 Pisa, Italy  Y. Tu  University of
Pennsylvania, Philadelphia, Pennsylvania 19104, USA  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  A. Varganov  University of Michigan, Ann
Arbor, Michigan 48109, USA  F. Vázquezk University of Florida, Gainesville,
Florida 32611, USA  G. Velev  Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  C. Vellidis  University of Athens, 157 71 Athens, Greece
M. Vidal  Centro de Investigaciones Energeticas Medioambientales y
Tecnologicas, E-28040 Madrid, Spain  I. Vila  Instituto de Fisica de
Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain  R. Vilar
Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005
Santander, Spain  J. Vizán  Instituto de Fisica de Cantabria, CSIC-University
of Cantabria, 39005 Santander, Spain  M. Vogel  University of New Mexico,
Albuquerque, New Mexico 87131, USA  G. Volpicc Istituto Nazionale di Fisica
Nucleare Pisa, ccUniversity of Pisa, ddUniversity of Siena and eeScuola
Normale Superiore, I-56127 Pisa, Italy  P. Wagner  University of Pennsylvania,
Philadelphia, Pennsylvania 19104, USA  R.L. Wagner  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  T. Wakisaka  Osaka City University,
Osaka 588, Japan  R. Wallny  University of California, Los Angeles, Los
Angeles, California 90024, USA  S.M. Wang  Institute of Physics, Academia
Sinica, Taipei, Taiwan 11529, Republic of China  A. Warburton  Institute of
Particle Physics: McGill University, Montréal, Québec, Canada H3A 2T8; Simon
Fraser University, Burnaby, British Columbia, Canada V5A 1S6; University of
Toronto, Toronto, Ontario, Canada M5S 1A7; and TRIUMF, Vancouver, British
Columbia, Canada V6T 2A3  D. Waters  University College London, London WC1E
6BT, United Kingdom  M. Weinberger  Texas A&M University, College Station,
Texas 77843, USA  W.C. Wester III  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  B. Whitehouse  Tufts University, Medford,
Massachusetts 02155, USA  D. Whitesonb University of Pennsylvania,
Philadelphia, Pennsylvania 19104, USA  A.B. Wicklund  Argonne National
Laboratory, Argonne, Illinois 60439, USA  E. Wicklund  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  S. Wilbur  Enrico Fermi
Institute, University of Chicago, Chicago, Illinois 60637, USA  F. Wick
Institut für Experimentelle Kernphysik, Karlsruhe Institute of Technology,
D-76131 Karlsruhe, Germany  H.H. Williams  University of Pennsylvania,
Philadelphia, Pennsylvania 19104, USA  J.S. Wilson  The Ohio State University,
Columbus, Ohio 43210, USA  P. Wilson  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  B.L. Winer  The Ohio State University, Columbus,
Ohio 43210, USA  P. Wittichg Fermi National Accelerator Laboratory, Batavia,
Illinois 60510, USA  S. Wolbers  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  H. Wolfe  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
588, Japan  J. Yamaoka  Duke University, Durham, North Carolina 27708, USA  T.
Yang  Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
U.K. Yangp Enrico Fermi Institute, University of Chicago, Chicago, Illinois
60637, USA  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  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. Yoshidaj Osaka City University, Osaka 588,
Japan  G.B. Yu  Duke University, Durham, North Carolina 27708, USA  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  S.S. Yu
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  J.C. Yun
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA  A.
Zanetti  Istituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste,
ggUniversity of Udine, I-33100 Udine, Italy  Y. Zeng  Duke University, Durham,
North Carolina 27708, USA  S. Zucchelliaa Istituto Nazionale di Fisica
Nucleare Bologna, aaUniversity of Bologna, I-40127 Bologna, Italy

###### Abstract

A measurement of the top-quark mass is presented using Tevatron data from
proton-antiproton collisions at center-of-mass energy $\sqrt{s}=1.96$ TeV
collected with the CDF II detector. Events are selected from a sample of
candidates for production of $t\bar{t}$ pairs that decay into the lepton+jets
channel. The top-quark mass is measured with an unbinned maximum likelihood
method where the event probability density functions are calculated using
signal and background matrix elements, as well as a set of parameterized jet-
to-parton transfer functions. The likelihood function is maximized with
respect to the top-quark mass, the signal fraction in the sample, and a
correction to the jet energy scale (JES) calibration of the calorimeter jets.
The simultaneous measurement of the JES correction ($\Delta_{\mathrm{JES}}$)
amounts to an additional in situ jet energy calibration based on the known
mass of the hadronically decaying $W$ boson. Using the data sample of 578
lepton+jets candidate events, corresponding to 3.2 fb-1 of integrated
luminosity, the top-quark mass is measured to be $m_{t}=\rm 172.4\pm
1.4\>(stat+\Delta_{\mathrm{JES}})\pm 1.3\>(syst)~{}GeV/{\it c}^{2}$.

###### pacs:

14.65.Ha,13.85.-t,12.15.Ff

The top-quark mass, $m_{t}$, is an intrinsic parameter of the standard model
(SM) of particle physics and is of particular importance due to its strikingly
large value. As a result, the top quark has a large effect on radiative
corrections to electroweak processes and has a Yukawa coupling to the Higgs
field of $\mathcal{O}(1)$, which may provide insight into the mechanism of
electroweak symmetry breaking Bhattacharyya (2011).

The Higgs boson mass, $m_{H}$, is not predicted by the SM, but constraints on
its value can be derived from the calculation of radiative corrections to the
$W$ boson mass, $m_{W}$, and from the values of other precision electroweak
variables LEP and Tevatron Electroweak Working Groups, and SLD electroweak
heavy flavour groups (2010). These corrections depend primarily on $\ln m_{H}$
and $m_{t}^{2}$, and thus precision measurements of $m_{W}$ and $m_{t}$
provide important constraints on $m_{H}$.

The dominant top-quark production process is pair production via the strong
interaction. At Fermilab’s Tevatron this process is initiated by $p\bar{p}$
collisions at center-of-mass energy $\sqrt{s}=\rm 1.96~{}TeV$. Because of its
large mass, the top quark decays rapidly with lifetime $\tau_{t}\sim 10^{-25}$
s Abazov et al. (2011) — fast enough that it has essentially no time to
interact and may be considered as a free quark. This allows a direct
measurement of its mass from the daughter particles from its decay, and as a
result $m_{t}$ has the lowest relative uncertainty of all of the quark masses
Nakamura et al. (2010).

In the SM top quarks decay via the weak interaction, predominantly to $W$
bosons and $b$ quarks as $t\bar{t}\to W^{+}b\>W^{-}\bar{b}$. $W$ bosons decay
into lower-mass fermion-antifermion pairs: a charged lepton and a neutrino
($W^{+}\to\bar{\ell}\nu_{\ell}$ or $W^{-}\to\ell\bar{\nu}_{\ell}$), “leptonic
decay”; or an up-type quark and a down-type quark ($W^{+}\to
q\bar{q}^{\prime}$ or $W^{-}\to\bar{q}q^{\prime}$), “hadronic decay”. The
result presented here uses the lepton+jets decay channel (with
$q\bar{q}^{\prime}b\ell\bar{\nu_{\ell}}\bar{b}$ or
$\bar{\ell}\nu_{\ell}b\bar{q}q^{\prime}\bar{b}$ in the final state), where one
of the two $W$ bosons decays leptonically into an electron or a muon, and the
other decays hadronically. All the quarks in the final state evolve into jets
of hadrons. Events with tau leptons are not selected directly, but may
contribute a few percent of the total sample via leptonic cascade decays or
fake jets. The most recent $m_{t}$ measurements obtained at the Tevatron using
the lepton+jets topology are reported in Ref. Tevatron Electroweak Working
Group (2011), while the results of an earlier version of the present analysis
using 955 pb-1 of integrated luminosity are reported in Ref. Abulencia et al.
(2007). The distinctive feature of this analysis is the use of matrix element
calculations to describe the dominant background contribution. The result
presented here uses a more than three times larger data sample than the
earlier version, and employs a more detailed likelihood function.

The leptons and jets resulting from the top-antitop quark pair ($t\bar{t}$)
decay are detected in the CDF II general-purpose particle detector that is
described in detail elsewhere Blair et al. (1996). Azimuthally and forward-
backward symmetric about the beam-line, the detector contains a high precision
particle tracking system immersed in a 1.4 T magnetic field and surrounded by
calorimetry, with muon detectors on the outside. A right-handed spherical co-
ordinate system is employed, with the polar angle $\theta$ measured from the
proton beam direction, the azimuthal angle $\phi$ in the plane perpendicular
to the beam-line, and the distance $r$ from the center of the detector.
Transverse energy and momentum are defined as $E_{T}\equiv E\sin\theta$ and
$p_{T}\equiv p\sin\theta$, where $E$ and $p$ denote energy and momentum.
Pseudorapidity is defined as $\eta\equiv-\ln\tan\left(\theta/2\right)$.

Electron | $E_{T}$ | $>\rm 20~{}GeV$ | $|\eta|<1.1$
---|---|---|---
or Muon | $p_{T}$ | $>\rm 20~{}GeV/{\it c}$ | $|\eta|<1.0$
$\not\\!\\!E_{T}$ | $\not\\!\\!E_{T}$ | $>\rm 20~{}GeV$ | $|\eta|<3.6$
Jets | $E_{T}$ | $>\rm 20~{}GeV$ | $|\eta|<2.0$
Four jets; at least one from a $b$ quark
Table 1: Event selection criteria.

This measurement makes use of CDF II data collected between February 2002 and
August 2008, representing approximately 3.2 fb-1 of integrated luminosity. The
event selection criteria (Table 1) are tuned to select the lepton+jets final-
state particles, requiring that each event must have exactly one high-$E_{T}$
electron or high-$p_{T}$ muon, exactly four high-$E_{T}$ jets, and a
significant amount of missing $E_{T}$, $\not\\!\\!E_{T}$ Abulencia et al.
(2006), characteristic of the undetected neutrino. Jets are reconstructed
using a cone algorithm Abe et al. (1992), with the cone radius $\Delta
R\equiv\sqrt{\left(\Delta\eta\right)^{2}+\left(\Delta\phi\right)^{2}}=0.4$. At
least one of the four jets must be identified as originating from a $b$ quark
via the SECVTX algorithm Acosta et al. (2005a), which detects displaced
secondary vertices characteristic of the decay of long-lived $b$ hadrons. A
total of 578 events are selected, of which 76% are expected to be $t\bar{t}$
events (Table 2). Of the 24% of events expected to be background, it is
predicted that 69% arise from the production of a $W$ boson in conjunction
with 4 jets ($W$+jets), 19% come from multi-jet QCD production (non-$W$),
while the remaining 12% are from sources such as diboson and single-top-quark
production. These fractions are estimated using theoretical cross-sections,
Monte Carlo (MC) simulated events, and data. The $t\bar{t}$ events are
generated using the Lund Monte Carlo program PYTHIA Sjostrand et al. (2006),
with a top-quark mass of $\rm 175~{}GeV/{\it c}^{2}$ and a $t\bar{t}$
production cross section of $6.7\pm 0.8$ pb Kidonakis and Vogt (2003). The
$W+$jets and $Z+$jets events are generated using the ALPGEN generator Mangano
et al. (2003) while the single-top-quark events are generated using the
MADEVENT package Alwall et al. (2007), in both cases also using PYTHIA to
perform the parton showering and hadronization. Diboson events are also
generated using PYTHIA. In addition, data are used for non-$W$ events Acosta
et al. (2005b).

sample | # of events | % of total | % of bkg
---|---|---|---
$t\bar{t}$ signal | 425.0 $\pm$ 58.9 | 76.0% | -
$W+$jets | 92.6 $\pm$ 15.9 | 16.6% | 69.0%
non-$W$ | 25.0 $\pm$ 12.5 | 4.5% | 18.7%
single top quark | 6.6 $\pm$ 0.4 | 1.2% | 4.9%
diboson | 6.0 $\pm$ 0.6 | 1.1% | 4.5%
$Z+$jets | 3.9 $\pm$ 0.5 | 0.7% | 2.9%
total | 559.2 $\pm$ 67.0 | 100% | -
Observed | 578 |  |
Table 2: Number of expected signal and background events, corresponding to the
total integrated luminosity of 3.2 fb-1. The percentages are used when
generating Monte Carlo simulated experiments.

This analysis employs an unbinned maximum likelihood method Abulencia et al.
(2007); Abazov et al. (2004, 2005). The $m_{t}$-dependent probability density
function (p.d.f.) is calculated for each event in the data sample:

$\mathcal{P}(k)=\nu_{\mathrm{sig}}P_{s}(k)+(1-\nu_{\mathrm{sig}})P_{b}(k)\mathrm{,}$
(1)

where $k\equiv(E_{i},\vec{p}_{i})$ represents the measured kinematic
quantities of the event, $P_{s}$ and $P_{b}$ are respectively the normalized
p.d.f.s for signal and background events, and $\nu_{\mathrm{sig}}$ is the
signal fraction parameter (constrained $0\leq\nu_{\mathrm{sig}}\leq 1$).
Signal events are defined as events consistent with $q\bar{q}\rightarrow
t\bar{t}$ production and $t\bar{t}$ decay into the lepton+jets channel, as
described by the leading-order (LO) matrix element evaluated by Mahlon and
Parke Mahlon and Parke (1996). Background events are assumed to be described
by a matrix element for $W+$jets production, which is calculated using a sum
of 1286 $W+$4-partons amplitudes for 592 subprocesses encoded in the VECBOS MC
event generator Berends et al. (1991). This approximation does mean that there
are some events that, in principle, are not described by either $P_{s}$ or
$P_{b}$, including non-$W$, single top, diboson, $Z+$jets, and
$W+bb+$2-partons events, as well as $W+$jets events from $W+$0-, 1-, 2- and
3-partons processes. However, studies with MC simulated events show that the
ratio $P_{b}/P_{s}$ calculated for all of these event types is similar to that
for $W+$4-partons events, and that, in practice, such events mostly contribute
to the likelihood function via the $P_{b}$ term and do not add any more bias
than the $W+$4-partons events or than the poorly reconstructed $t\bar{t}$
events themselves Linacre (2010). Any residual bias in the measured top-quark
mass is removed at the end, as described later in the paper.

The signal and background p.d.f.s, $P_{s}$ and $P_{b}$, are constructed in
analogous fashions, starting with the appropriately normalized parton-level
differential cross-section Nakamura et al. (2010), $d\hat{\sigma}_{s}$ or
$d\hat{\sigma}_{b}$, which is then convolved with parton distribution
functions (PDFs) and a jet-to-parton transfer function $W(k,\varkappa)$.
$P_{s}$ is thus given by

$\displaystyle
P_{s}(k;m_{t},\Delta_{\mathrm{JES}})=\frac{1}{n_{jp}}\sum_{\mathrm{jet\>perm.}}^{n_{jp}}\frac{1}{\hat{\sigma}_{s}(m_{t})}\frac{1}{A_{s}(m_{t},\Delta_{\mathrm{JES}})}\times$
(2) $\displaystyle\int
d\hat{\sigma}_{s}(\varkappa;m_{t})\;dx_{\mathrm{Bj}}^{1}dx_{\mathrm{Bj}}^{2}\;W(k,\varkappa;\Delta_{\mathrm{JES}})\;f(x_{\mathrm{Bj}}^{1})(x_{\mathrm{Bj}}^{2})\mathrm{,}$

where $\varkappa\equiv(\varepsilon_{i},\vec{\pi}_{i})$ represents the actual
event parton-level kinematic quantities corresponding to the measured
quantities $k$, and parameter $\Delta_{\mathrm{JES}}$ is defined in the next
paragraph. The PDFs $f(x_{\mathrm{Bj}})$ define the probability density for a
colliding parton to carry a longitudinal momentum fraction $x_{\mathrm{Bj}}$
and are given by CTEQ5L Lai et al. (2000). $A_{s}$ is the mean acceptance
function for signal events, a normalization term that is the consequence of
the constriction of the phase-space of the integral by the event selection
cuts and by the detector acceptance. The average over the jet permutations,
$n_{jp}$, is due to ambiguity in assigning final state jets to partons. The
fact that the two light quarks in the final state are indistinguishable allows
the reduction from the original 24 permutations to 12 in the expression for
$P_{s}$, and the $b$-tagging information allows a further reduction to 6
assignments for events with one identified $b$-jet and 2 for events with both
$b$-jets identified. In the similar expression for $P_{b}$, all 24
permutations are averaged.

The jet-to-parton transfer function $W(k,\varkappa)$ is a p.d.f. describing
the probability density for an event with out-going partons and charged lepton
with $\varkappa$ to be measured as reconstructed $k$. The charged lepton is
assumed to be well-measured, allowing the use of a Dirac $\delta$-function to
represent the mapping between its parton-level momentum, $\vec{\pi}_{\ell}$,
and its reconstructed momentum, $\vec{p}_{\ell}$. For the four jets, the
function is obtained by parameterizing the jet-to-parton mapping observed in
fully simulated PYTHIA $t\bar{t}$ events. These events contain all of the
information about the original partons as well as the measured jets. The
simulation includes physical effects, such as radiation and hadronization, as
well as the effects of measurement resolution and of the jet reconstruction
algorithm. The parameterization is made in two parts that are assumed to be
independent: the energy transfer function $W_{E}$, describing the jet energies
$E$, and the angular transfer function $W_{A}$, describing the mapping for the
jet angles. The jet-to-parton transfer function is thus given by

$\displaystyle W(k,\varkappa;\Delta_{\mathrm{JES}})$
$\displaystyle=\delta^{3}(\vec{p}_{\ell}-\vec{\pi}_{\ell})\>W_{A}$ (3)
$\displaystyle\times\prod_{i=1}^{4}{\left(\frac{1}{E_{i}p_{i}}W_{E}^{i}(E_{i},\varepsilon_{i};\Delta_{\mathrm{JES}})\right)}\mathrm{.}$

The reconstructed jet energies, $E_{i}$, used in the function $W_{E}$ are not
just the raw calorimeter energy deposits, but are first calibrated so that
they represent the combined energies released in the calorimeter by the many
particles constituting each jet. This is achieved using the CDF jet energy
scale (JES) calibration Bhatti et al. (2006), which is subject to a
significant systematic uncertainty. The uncertainties of individual jet energy
measurements, $\sigma(E_{i})$, are therefore correlated, and their fractional
JES uncertainty, $\sigma(E_{i})/E_{i}$, is typically $\sim 3\%$. If this were
included as a systematic uncertainty on the measured $m_{t}$ it would reduce
the measurement precision drastically; in fact, each 1% of fractional JES
uncertainty would add about $\rm 1~{}GeV/{\it c}^{2}$ uncertainty to the
measured $m_{t}$ Affolder et al. (2001). However, such a treatment
overestimates the uncertainty because the energies of the two daughter jets of
the hadronically decaying $W$ boson can be constrained based on the known $W$
boson mass. Applying this constraint to all events in the data sample while
allowing the jet energies to be shifted results in the in situ measurement of
the JES correction, $\Delta_{\mathrm{JES}}$, defined as the number of
$\sigma(E_{i})$ values by which the energy of each jet is shifted in the
likelihood fit. This effectively re-calibrates the measured jet energies based
on the known $W$ boson mass and replaces a large component of the JES
systematic uncertainty with a much smaller statistical uncertainty on the
$\Delta_{\mathrm{JES}}$. The $\Delta_{\mathrm{JES}}$ dependence of the jet
energies is included in the parameterization of the function $W_{E}$. This
parameterization is made in eight bins in pseudorapidity $|\eta|$, separately
for light and $b$-jets, using a sum of two Gaussians as a function of the
difference between the parton energies and the corrected jet energies as
measured in a sample of PYTHIA $t\bar{t}$ events that pass the same selection
criteria as the data.

In an earlier version of this analysis Abulencia et al. (2007), the jet-to-
parton transfer functions for all jet angles were approximated by Dirac
$\delta$-functions. The introduction of the function $W_{A}$ was motivated by
a discrepancy noticed in simulated $t\bar{t}$ events in the 2-jet effective
invariant mass of the hadronically decaying $W$ boson, $m_{W}$. Even when the
true simulated parton-level jet energies are used, instead of the
corresponding reconstructed detector-level values, the use of the measured jet
angles rather than their parton-level values causes a significant shift of the
reconstructed $m_{W}$ from its nominal value, as illustrated in Fig. 1.

Figure 1:  The reconstructed 2-jet invariant mass of the hadronically decaying
$W$ boson, $m_{W}$, for measured jet angles (solid line) and for parton-level
angles (dotted line), obtained after assuming the primary parton energy as jet
energy. For ease of comparison, the parton-level distribution is normalized so
that the maxima of the two distributions are the same.

There is also a negative skewness in the distribution for measured angles, and
since parton-level jet energies are used, the observed effects are due to the
differences between the measured angles and the parton-level angles alone. The
peak of the $m_{W}$ distribution, when fit by a Breit-Wigner distribution,
corresponds to a $W$ boson pole mass of $\rm 79.5~{}GeV/{\it c}^{2}$, a
$\rm-0.9~{}GeV/{\it c}^{2}$ shift from its parton-level value of $\rm
80.4~{}GeV/{\it c}^{2}$. This is found to be a result of a correlation between
the measured jet directions: the measured angle, $\alpha_{12}$, between the
two jets is, on average, reduced so that the two jets appear closer together
than their parent partons, which can be seen in Fig. 2. Since the apparent $W$
boson mass is utilized to measure $\Delta_{\mathrm{JES}}$ and thus calibrate
the measured jet energies, a jet-to-parton transfer function describing the
change in the angle $\alpha_{12}$ is important in making an accurate
measurement of $\Delta_{\mathrm{JES}}$ and thus the top-quark mass. The
function $W_{A}$ also describes a much smaller correlation effect seen in the
angle $\alpha_{Wb}$ between the hadronic-side $b$-jet and the hadronically
decaying $W$ boson. The function $W_{A}$ is thus parameterized using two
different functions, $W^{12}_{A}$ and $W^{Wb}_{A}$, describing the mappings
for the angles $\alpha_{12}$ and $\alpha_{Wb}$. The remaining angles describe
resolution effects rather than the correlations and, due to computational
constraints, are assumed to be well measured with their contributions to
$W_{A}$ approximated by Dirac delta functions.

The functions $W^{12}_{A}$ and $W^{Wb}_{A}$ are both fit using a sum of a
skew-Cauchy distribution and two Gaussians, describing the change in the
cosine of the relevant angle, $\Delta\cos{(\alpha_{12})}$ and
$\Delta\cos{(\alpha_{Wb})}$, from partons to measured jets. Since the
correlation effects are stronger in jets that are closer together, the
functions are parameterized in bins of $\cos(\alpha_{12})$ and
$\cos(\alpha_{Wb})$, respectively; one example for each function is shown in
Fig. 2.

Figure 2: Examples of parameterization of the functions $W^{12}_{A}$ and
$W^{Wb}_{A}$ in the bins where $0.2<\cos{(\alpha_{12})}<0.4$ and
$0.2<\cos{(\alpha_{Wb})}<0.4$. The histograms show MC simulation events and
the curves represent the parameterization.

The $m_{W}$ distribution after convolution with the function $W_{A}$ is shown
in Fig. 3. The skewness is removed and the mean value agrees well with the
parton-level distribution.

Figure 3:  The $m_{W}$ distribution for measured angles from Fig. 1 is plotted
(solid line) after convolution with the function $W_{A}$. For ease of
comparison, the parton-level distribution (dotted line) is normalized so that
the maxima of the two distributions are the same.

The 20 integration variables (3 for each final-state particle and the
$x_{\mathrm{Bj}}$ for each initial state parton, assuming zero transverse
momentum for the $t\bar{t}$ pair) in the expression for the signal and
background p.d.f.s (Eq. 2) are reduced to 16 by integrating over the
4-momentum conservation Dirac $\delta$-function inherent in the expression for
$d\hat{\sigma}_{s}$. The charged lepton 3-momentum integration and all but two
of the jet angular integrations are made trivial by the Dirac
$\delta$-functions in the function $W(k,\varkappa)$, leaving 7 integration
variables. In $P_{s}$, this is further reduced to 5 variables via a change of
variables to the squared masses of the top quarks and by using the narrow-
width approximation for the Breit-Wigner distributions of both top-quark
decays in the $t\bar{t}$ matrix element. The integral is then evaluated using
the VEGAS Lepage (1978) adaptive Monte Carlo integration algorithm Abulencia
et al. (2007), which uses importance sampling, which means that the sample
points are concentrated in the regions that make the largest contribution to
the integral.

The treatment of $P_{b}$ is unchanged since the previous version of this
analysis Abulencia et al. (2007), except for the updated energy transfer
function $W_{E}$. The integrand in the expression for $P_{b}$ is much more
computationally intensive than for $P_{s}$ and a simplified Monte Carlo method
of integration is employed, giving reasonable convergence with an execution
time comparable to that of $P_{s}$. The simplifications used in this
computation of $P_{b}$ include setting the function $W_{A}$ to a Dirac
$\delta$-function for all angles, using a narrow width approximation for the
$W$ boson decay, and neglecting the $\Delta_{\mathrm{JES}}$ dependence of the
function $W_{E}$. Therefore, the value of $P_{b}$ for each event does not
depend on the likelihood parameters $m_{t}$ and $\Delta_{\mathrm{JES}}$, while
$P_{s}$ is a two-dimensional function of those parameters Abulencia et al.
(2007). In this approximation, the product of the background p.d.f.
normalization terms (corresponding to the variables $\hat{\sigma}_{b}\cdot
A_{b}$ in Eq. 2) is set to a constant, whose value is chosen to optimize the
statistical sensitivity of the method, effectively providing an appropriate
relative normalization with respect to $P_{s}$.

The log-likelihood function is given as a sum over the 578 events in the
sample:

$\displaystyle\ln\,$
$\displaystyle\mathcal{L}(k;m_{t},\Delta_{\mathrm{JES}},\nu_{\mathrm{sig}})=$
(4)
$\displaystyle\sum^{578}_{i=1}\ln\left[\nu_{\mathrm{sig}}{P_{s}(k_{i};m_{t},\Delta_{\mathrm{JES}})}+(1-\nu_{\mathrm{sig}})P_{b}(k_{i})\right]\mathrm{.}$

It is calculated on a two-dimensional $31\times 17$ grid in $m_{t}$ and
$\Delta_{\mathrm{JES}}$, spanning $145\leq m_{t}\leq\rm 205~{}GeV/{\it c}^{2}$
and $-4.8\leq\Delta_{\mathrm{JES}}\leq 4.8$, with a spacing between grid
points of $\rm 2~{}GeV/{\it c}^{2}$ in $m_{t}$ and 0.6 in
$\Delta_{\mathrm{JES}}$. To optimize computational time, the bin size is
chosen to be as large as possible without appreciably affecting the fit
result. The third likelihood parameter, the signal fraction parameter
$\nu_{\mathrm{sig}}$, is allowed to vary continuously (within the constraint
$0\leq\nu_{\mathrm{sig}}\leq 1$), and the likelihood function is maximized
with respect to $\nu_{\mathrm{sig}}$ at each point on the grid using the
MINUIT program James (2000). The resulting surface described on the grid is
the profile log-likelihood, maximized for $\nu_{\mathrm{sig}}$. The top-quark
mass, $m_{t}$, and the jet energy scale correction, $\Delta_{\mathrm{JES}}$,
are measured by making a two-dimensional parabolic fit to the surface,
consistent with the expectation for the likelihood function to be Gaussian
near its maximum. The maximum of the parabola gives the measured $m_{t}$ and
$\Delta_{\mathrm{JES}}$, while the measured $\nu_{\mathrm{sig}}$ is taken from
its value at the grid point of maximum likelihood. The estimated one-$\sigma$
statistical uncertainty of the measurement is represented by the ellipse
corresponding to a change in log-likelihood $\Delta\ln\mathcal{L}=0.5$ from
the maximum of the fitted parabola. The values of $m_{t}$ and
$\Delta_{\mathrm{JES}}$ are anti-correlated (Fig. 4). No correlation is
observed between $\nu_{\mathrm{sig}}$ and $m_{t}$ or $\Delta_{\mathrm{JES}}$.

The accuracy of the measured $m_{t}$ and $\Delta_{\mathrm{JES}}$, and their
uncertainties, are checked using ensembles of MC simulated experiments, using
the MC samples previously mentioned with the addition of 22 $t\bar{t}$ samples
generated with values of $m_{t}$ between $161$ and $\rm 185~{}GeV/{\it
c}^{2}$. The numbers of $t\bar{t}$ events and those of the various backgrounds
are Poisson fluctuated around the values shown in Table 2. Studies of the
relationships between the known input simulation parameters and their
corresponding measurements show no evidence of bias when a clean sample of MC
simulated $t\bar{t}$ events is used, containing only lepton+jets events with
correct jet-parton matching. However, the presence of signal events with jets
which are poorly or incorrectly matched to partons and events which do not
match the decay hypothesis biases the likelihood fit result and increases the
pull width. The presence of background events also biases the fit, due to the
backgrounds that are not well described by $P_{b}$ and the approximations in
$P_{b}$. The bias is removed using a set of functions obtained from a fit to
the MC simulation and parameterized in terms of the measured
$\Delta_{\mathrm{JES}}$ and $\nu_{\mathrm{sig}}$ Linacre (2010). This amounts
to adding $\rm 1.1~{}GeV/{\it c}^{2}$ to the $m_{t}$ value produced by the
likelihood fit and multiplying the uncertainty by 1.26 so that the pull width
is consistent with unity. The systematic uncertainty due to this measurement
calibration is small, as shown in Table 3.

Despite the reduction from the in situ $\Delta_{\rm JES}$ calibration, the
remaining uncertainty from JES obtained by varying the parameters in JES
Bhatti et al. (2006) is among the largest systematic uncertainties of the
measurement (Table 3). Other significant systematic uncertainties are mainly a
result of assumptions made in the simulation of the events that are used in
the tuning and calibration of the measurement method. In most cases, they are
evaluated by varying different aspects of the MC simulation, such as signal MC
generator (PYTHIA versus HERWIG Corcella et al. (2002)), color reconnection
model tune (Apro versus ACRpro Skands and Wicke (2007); Wicke and Skands
(2008); Skands (2009)), and parameters of initial and final state radiation
(ISR and FSR). A detailed description of the systematic effects has been
published elsewhere Aaltonen et al. (2009). The systematic uncertainties for
each effect are added in quadrature, resulting in a total estimated systematic
uncertainty of $\rm 1.3~{}GeV/{\it c}^{2}$ (Table 3).

Systematic | (GeV/c2)
---|---
MC Generator | 0.70
Residual JES | 0.65
Color Reconnection | 0.56
$b$-jet energy | 0.39
Background | 0.45
ISR and FSR | 0.23
Multiple Hadron Interactions | 0.22
PDFs | 0.13
Lepton Energy | 0.12
Measurement Calibration | 0.12
Total | 1.31
Table 3: Contributions to the total expected systematic uncertainty.

The measurement is made using the data sample of 578 events, yielding

$\displaystyle m_{t}$ $\displaystyle=172.4\rm\pm
1.4\>(stat\mathrm{+}\Delta_{\mathrm{JES}})\pm 1.3\>(sys)~{}GeV/{\it c}^{2}$
$\displaystyle m_{t}$ $\displaystyle=172.4\rm\pm 1.9\>(total)~{}GeV/{\it
c}^{2}\mathrm{,}$ (5)

with $\rm\Delta_{\mathrm{JES}}=0.3\pm 0.3\>(stat)$. The central value and the
contour ellipses corresponding to the one-, two- and three-$\sigma$
statistical confidence intervals of the measurement are illustrated in Fig. 4.
The overall statistical uncertainty on the measured top-quark mass is labeled
“stat+$\Delta_{\mathrm{JES}}$” because it includes the uncertainty on $m_{t}$
due to the statistical uncertainty on the measured $\Delta_{\mathrm{JES}}$,
i.e. the uncertainty is given by half of the full width of the one-$\sigma$
contour of Fig. 4.

In conclusion, a precise measurement of the top-quark mass has been presented
using CDF lepton+jets candidate events corresponding to an integrated
luminosity of 3.2 fb-1. Using an improved matrix element method with an in
situ jet energy calibration, the top quark mass is measured to be $m_{t}=\rm
172.4\pm 1.9~{}GeV/{\it c}^{2}$.

Figure 4: The measurement result and the contour ellipses of the parabolic fit
corresponding to the one-, two- and three-$\sigma$ confidence intervals for
the statistical uncertainty on $m_{t}$ and $\Delta_{\mathrm{JES}}$.

###### Acknowledgements.

We thank the Fermilab staff and the technical staffs of the participating
institutions for their vital contributions. This work was supported by the
U.S. Department of Energy and National Science Foundation; the Italian
Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture,
Sports, Science and Technology of Japan; the Natural Sciences and Engineering
Research Council of Canada; the National Science Council of the Republic of
China; the Swiss National Science Foundation; the A.P. Sloan Foundation; the
Bundesministerium für Bildung und Forschung, Germany; the Korean World Class
University Program, the National Research Foundation of Korea; the Science and
Technology Facilities Council and the Royal Society, UK; the Institut National
de Physique Nucleaire et Physique des Particules/CNRS; the Russian Foundation
for Basic Research; the Ministerio de Ciencia e Innovación, and Programa
Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; the Academy of Finland;
and the Australian Research Council (ARC).

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