PHENIX Collaboration

# Measurement of charm and bottom production from semileptonic hadron decays
in $p$$+$$p$ collisions at $\sqrt{s}=200$ GeV

C. Aidala  Department of Physics, University of Michigan, Ann Arbor, Michigan
48109-1040, USA  Y. Akiba<EMAIL_ADDRESS>RIKEN Nishina Center for
Accelerator-Based Science, Wako, Saitama 351-0198, Japan  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA  M.
Alfred  Department of Physics and Astronomy, Howard University, Washington, DC
20059, USA  V. Andrieux  Department of Physics, University of Michigan, Ann
Arbor, Michigan 48109-1040, USA  N. Apadula  Iowa State University, Ames, Iowa
50011, USA  H. Asano  Kyoto University, Kyoto 606-8502, Japan  RIKEN Nishina
Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan  B. Azmoun
Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  V. Babintsev  IHEP Protvino, State Research Center of Russian
Federation, Institute for High Energy Physics, Protvino, 142281, Russia  N.S.
Bandara  Department of Physics, University of Massachusetts, Amherst,
Massachusetts 01003-9337, USA  K.N. Barish  University of California-
Riverside, Riverside, California 92521, USA  S. Bathe  Baruch College, City
University of New York, New York, New York, 10010 USA  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA  A.
Bazilevsky  Physics Department, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  M. Beaumier  University of California-Riverside,
Riverside, California 92521, USA  R. Belmont  University of Colorado, Boulder,
Colorado 80309, USA  Physics and Astronomy Department, University of North
Carolina at Greensboro, Greensboro, North Carolina 27412, USA  A. Berdnikov
Saint Petersburg State Polytechnic University, St. Petersburg, 195251 Russia
Y. Berdnikov  Saint Petersburg State Polytechnic University, St. Petersburg,
195251 Russia  D.S. Blau  National Research Center “Kurchatov Institute”,
Moscow, 123098 Russia  National Research Nuclear University, MEPhI, Moscow
Engineering Physics Institute, Moscow, 115409, Russia  J.S. Bok  New Mexico
State University, Las Cruces, New Mexico 88003, USA  M.L. Brooks  Los Alamos
National Laboratory, Los Alamos, New Mexico 87545, USA  J. Bryslawskyj  Baruch
College, City University of New York, New York, New York, 10010 USA
University of California-Riverside, Riverside, California 92521, USA  V.
Bumazhnov  IHEP Protvino, State Research Center of Russian Federation,
Institute for High Energy Physics, Protvino, 142281, Russia  S. Campbell
Columbia University, New York, New York 10027 and Nevis Laboratories,
Irvington, New York 10533, USA  V. Canoa Roman  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
R. Cervantes  Department of Physics and Astronomy, Stony Brook University,
SUNY, Stony Brook, New York 11794-3800, USA  C.Y. Chi  Columbia University,
New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533,
USA  M. Chiu  Physics Department, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  I.J. Choi  University of Illinois at Urbana-Champaign,
Urbana, Illinois 61801, USA  J.B. Choi  Deceased  Chonbuk National University,
Jeonju, 561-756, Korea  Z. Citron  Weizmann Institute, Rehovot 76100, Israel
M. Connors  Georgia State University, Atlanta, Georgia 30303, USA  RIKEN BNL
Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000,
USA  N. Cronin  Department of Physics and Astronomy, Stony Brook University,
SUNY, Stony Brook, New York 11794-3800, USA  M. Csanád  ELTE, Eötvös Loránd
University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary  T. Csörgő  Eszterházy
Károly University, Károly Róbert Campus, H-3200 Gyöngyös, Mátrai út 36,
Hungary  Institute for Particle and Nuclear Physics, Wigner Research Centre
for Physics, Hungarian Academy of Sciences (Wigner RCP, RMKI) H-1525 Budapest
114, POBox 49, Budapest, Hungary  T.W. Danley  Department of Physics and
Astronomy, Ohio University, Athens, Ohio 45701, USA  M.S. Daugherity  Abilene
Christian University, Abilene, Texas 79699, USA  G. David  Physics Department,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA  Debrecen
University, H-4010 Debrecen, Egyetem tér 1, Hungary  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
K. DeBlasio  University of New Mexico, Albuquerque, New Mexico 87131, USA  K.
Dehmelt  Department of Physics and Astronomy, Stony Brook University, SUNY,
Stony Brook, New York 11794-3800, USA  A. Denisov  IHEP Protvino, State
Research Center of Russian Federation, Institute for High Energy Physics,
Protvino, 142281, Russia  A. Deshpande  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  E.J. Desmond  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  A. Dion  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  D. Dixit  Department of Physics and Astronomy, Stony Brook
University, SUNY, Stony Brook, New York 11794-3800, USA  J.H. Do  Yonsei
University, IPAP, Seoul 120-749, Korea  A. Drees  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
K.A. Drees  Collider-Accelerator Department, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  J.M. Durham  Los Alamos National Laboratory,
Los Alamos, New Mexico 87545, USA  A. Durum  IHEP Protvino, State Research
Center of Russian Federation, Institute for High Energy Physics, Protvino,
142281, Russia  A. Enokizono  RIKEN Nishina Center for Accelerator-Based
Science, Wako, Saitama 351-0198, Japan  Physics Department, Rikkyo University,
3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan  H. En’yo  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
S. Esumi  Tomonaga Center for the History of the Universe, University of
Tsukuba, Tsukuba, Ibaraki 305, Japan  B. Fadem  Muhlenberg College, Allentown,
Pennsylvania 18104-5586, USA  W. Fan  Department of Physics and Astronomy,
Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA  N. Feege
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  D.E. Fields  University of New Mexico,
Albuquerque, New Mexico 87131, USA  M. Finger  Charles University, Ovocný trh
5, Praha 1, 116 36, Prague, Czech Republic  M. Finger, Jr  Charles University,
Ovocný trh 5, Praha 1, 116 36, Prague, Czech Republic  S.L. Fokin  National
Research Center “Kurchatov Institute”, Moscow, 123098 Russia  J.E. Frantz
Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA
A. Franz  Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  A.D. Frawley  Florida State University, Tallahassee, Florida
32306, USA  Y. Fukuda  Tomonaga Center for the History of the Universe,
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  C. Gal  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  P. Gallus  Czech Technical University, Zikova 4, 166 36
Prague 6, Czech Republic  E.A. Gamez  Department of Physics, University of
Michigan, Ann Arbor, Michigan 48109-1040, USA  P. Garg  Department of Physics,
Banaras Hindu University, Varanasi 221005, India  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
H. Ge  Department of Physics and Astronomy, Stony Brook University, SUNY,
Stony Brook, New York 11794-3800, USA  F. Giordano  University of Illinois at
Urbana-Champaign, Urbana, Illinois 61801, USA  Y. Goto  RIKEN Nishina Center
for Accelerator-Based Science, Wako, Saitama 351-0198, Japan  RIKEN BNL
Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000,
USA  N. Grau  Department of Physics, Augustana University, Sioux Falls, South
Dakota 57197, USA  S.V. Greene  Vanderbilt University, Nashville, Tennessee
37235, USA  M. Grosse Perdekamp  University of Illinois at Urbana-Champaign,
Urbana, Illinois 61801, USA  T. Gunji  Center for Nuclear Study, Graduate
School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033,
Japan  H. Guragain  Georgia State University, Atlanta, Georgia 30303, USA  T.
Hachiya  Nara Women’s University, Kita-uoya Nishi-machi Nara 630-8506, Japan
RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198,
Japan  RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  J.S. Haggerty  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  K.I. Hahn  Ewha Womans
University, Seoul 120-750, Korea  H. Hamagaki  Center for Nuclear Study,
Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo
113-0033, Japan  H.F. Hamilton  Abilene Christian University, Abilene, Texas
79699, USA  S.Y. Han  Ewha Womans University, Seoul 120-750, Korea  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
J. Hanks  Department of Physics and Astronomy, Stony Brook University, SUNY,
Stony Brook, New York 11794-3800, USA  S. Hasegawa  Advanced Science Research
Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-
gun, Ibaraki-ken 319-1195, Japan  T.O.S. Haseler  Georgia State University,
Atlanta, Georgia 30303, USA  X. He  Georgia State University, Atlanta, Georgia
30303, USA  T.K. Hemmick  Department of Physics and Astronomy, Stony Brook
University, SUNY, Stony Brook, New York 11794-3800, USA  J.C. Hill  Iowa State
University, Ames, Iowa 50011, USA  K. Hill  University of Colorado, Boulder,
Colorado 80309, USA  A. Hodges  Georgia State University, Atlanta, Georgia
30303, USA  R.S. Hollis  University of California-Riverside, Riverside,
California 92521, USA  K. Homma  Hiroshima University, Kagamiyama, Higashi-
Hiroshima 739-8526, Japan  B. Hong  Korea University, Seoul, 02841  T. Hoshino
Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan  N.
Hotvedt  Iowa State University, Ames, Iowa 50011, USA  J. Huang  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
S. Huang  Vanderbilt University, Nashville, Tennessee 37235, USA  K. Imai
Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata
Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan  M. Inaba  Tomonaga
Center for the History of the Universe, University of Tsukuba, Tsukuba,
Ibaraki 305, Japan  A. Iordanova  University of California-Riverside,
Riverside, California 92521, USA  D. Isenhower  Abilene Christian University,
Abilene, Texas 79699, USA  S. Ishimaru  Nara Women’s University, Kita-uoya
Nishi-machi Nara 630-8506, Japan  D. Ivanishchev  PNPI, Petersburg Nuclear
Physics Institute, Gatchina, Leningrad region, 188300, Russia  B.V. Jacak
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  M. Jezghani  Georgia State University,
Atlanta, Georgia 30303, USA  Z. Ji  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, USA  X. Jiang  Los
Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  B.M. Johnson
Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  Georgia State University, Atlanta, Georgia 30303, USA  D.
Jouan  IPN-Orsay, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, BP1,
F-91406, Orsay, France  D.S. Jumper  University of Illinois at Urbana-
Champaign, Urbana, Illinois 61801, USA  J.H. Kang  Yonsei University, IPAP,
Seoul 120-749, Korea  D. Kapukchyan  University of California-Riverside,
Riverside, California 92521, USA  S. Karthas  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
D. Kawall  Department of Physics, University of Massachusetts, Amherst,
Massachusetts 01003-9337, USA  A.V. Kazantsev  National Research Center
“Kurchatov Institute”, Moscow, 123098 Russia  V. Khachatryan  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  A. Khanzadeev  PNPI, Petersburg Nuclear Physics Institute,
Gatchina, Leningrad region, 188300, Russia  C. Kim  University of California-
Riverside, Riverside, California 92521, USA  Korea University, Seoul, 02841
E.-J. Kim  Chonbuk National University, Jeonju, 561-756, Korea  M. Kim  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
Department of Physics and Astronomy, Seoul National University, Seoul 151-742,
Korea  D. Kincses  ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P.
s. 1/A, Hungary  E. Kistenev  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  J. Klatsky  Florida State
University, Tallahassee, Florida 32306, USA  P. Kline  Department of Physics
and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800,
USA  T. Koblesky  University of Colorado, Boulder, Colorado 80309, USA  D.
Kotov  PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region,
188300, Russia  Saint Petersburg State Polytechnic University, St. Petersburg,
195251 Russia  S. Kudo  Tomonaga Center for the History of the Universe,
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  B. Kurgyis  ELTE, Eötvös
Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary  K. Kurita
Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo
171-8501, Japan  Y. Kwon  Yonsei University, IPAP, Seoul 120-749, Korea  J.G.
Lajoie  Iowa State University, Ames, Iowa 50011, USA  A. Lebedev  Iowa State
University, Ames, Iowa 50011, USA  S. Lee  Yonsei University, IPAP, Seoul
120-749, Korea  S.H. Lee  Iowa State University, Ames, Iowa 50011, USA
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  M.J. Leitch  Los Alamos National Laboratory,
Los Alamos, New Mexico 87545, USA  Y.H. Leung  Department of Physics and
Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
N.A. Lewis  Department of Physics, University of Michigan, Ann Arbor, Michigan
48109-1040, USA  X. Li  Los Alamos National Laboratory, Los Alamos, New Mexico
87545, USA  S.H. Lim  Los Alamos National Laboratory, Los Alamos, New Mexico
87545, USA  Yonsei University, IPAP, Seoul 120-749, Korea  M.X. Liu  Los
Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  V.-R. Loggins
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA  S.
Lökös  ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A,
Hungary  Eszterházy Károly University, Károly Róbert Campus, H-3200 Gyöngyös,
Mátrai út 36, Hungary  K. Lovasz  Debrecen University, H-4010 Debrecen,
Egyetem tér 1, Hungary  D. Lynch  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  T. Majoros  Debrecen University,
H-4010 Debrecen, Egyetem tér 1, Hungary  Y.I. Makdisi  Collider-Accelerator
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
M. Makek  Department of Physics, Faculty of Science, University of Zagreb,
Bijenička c. 32 HR-10002 Zagreb, Croatia  V.I. Manko  National Research Center
“Kurchatov Institute”, Moscow, 123098 Russia  E. Mannel  Physics Department,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA  M. McCumber
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  P.L.
McGaughey  Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
D. McGlinchey  University of Colorado, Boulder, Colorado 80309, USA  Los
Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  C. McKinney
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA  M.
Mendoza  University of California-Riverside, Riverside, California 92521, USA
W.J. Metzger  Eszterházy Károly University, Károly Róbert Campus, H-3200
Gyöngyös, Mátrai út 36, Hungary  A.C. Mignerey  University of Maryland,
College Park, Maryland 20742, USA  A. Milov  Weizmann Institute, Rehovot
76100, Israel  D.K. Mishra  Bhabha Atomic Research Centre, Bombay 400 085,
India  J.T. Mitchell  Physics Department, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  Iu. Mitrankov  Saint Petersburg State
Polytechnic University, St. Petersburg, 195251 Russia  G. Mitsuka  KEK, High
Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan
RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198,
Japan  RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  S. Miyasaka  RIKEN Nishina Center for Accelerator-Based
Science, Wako, Saitama 351-0198, Japan  Department of Physics, Tokyo Institute
of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan  S. Mizuno  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
Tomonaga Center for the History of the Universe, University of Tsukuba,
Tsukuba, Ibaraki 305, Japan  P. Montuenga  University of Illinois at Urbana-
Champaign, Urbana, Illinois 61801, USA  T. Moon  Yonsei University, IPAP,
Seoul 120-749, Korea  D.P. Morrison  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  S.I. Morrow  Vanderbilt
University, Nashville, Tennessee 37235, USA  T. Murakami  Kyoto University,
Kyoto 606-8502, Japan  RIKEN Nishina Center for Accelerator-Based Science,
Wako, Saitama 351-0198, Japan  J. Murata  RIKEN Nishina Center for
Accelerator-Based Science, Wako, Saitama 351-0198, Japan  Physics Department,
Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan  K.
Nagai  Department of Physics, Tokyo Institute of Technology, Oh-okayama,
Meguro, Tokyo 152-8551, Japan  K. Nagashima  Hiroshima University, Kagamiyama,
Higashi-Hiroshima 739-8526, Japan  RIKEN Nishina Center for Accelerator-Based
Science, Wako, Saitama 351-0198, Japan  T. Nagashima  Physics Department,
Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan
J.L. Nagle  University of Colorado, Boulder, Colorado 80309, USA  M.I. Nagy
ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary
I. Nakagawa  RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama
351-0198, Japan  RIKEN BNL Research Center, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  K. Nakano  RIKEN Nishina Center for
Accelerator-Based Science, Wako, Saitama 351-0198, Japan  Department of
Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551,
Japan  C. Nattrass  University of Tennessee, Knoxville, Tennessee 37996, USA
S. Nelson  Florida A&M University, Tallahassee, FL 32307, USA  T. Niida
Tomonaga Center for the History of the Universe, University of Tsukuba,
Tsukuba, Ibaraki 305, Japan  R. Nishitani  Nara Women’s University, Kita-uoya
Nishi-machi Nara 630-8506, Japan  R. Nouicer  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA  T.
Novák  Eszterházy Károly University, Károly Róbert Campus, H-3200 Gyöngyös,
Mátrai út 36, Hungary  Institute for Particle and Nuclear Physics, Wigner
Research Centre for Physics, Hungarian Academy of Sciences (Wigner RCP, RMKI)
H-1525 Budapest 114, POBox 49, Budapest, Hungary  N. Novitzky  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  A.S. Nyanin  National Research Center “Kurchatov Institute”,
Moscow, 123098 Russia  E. O’Brien  Physics Department, Brookhaven National
Laboratory, Upton, New York 11973-5000, USA  C.A. Ogilvie  Iowa State
University, Ames, Iowa 50011, USA  J.D. Orjuela Koop  University of Colorado,
Boulder, Colorado 80309, USA  J.D. Osborn  Department of Physics, University
of Michigan, Ann Arbor, Michigan 48109-1040, USA  A. Oskarsson  Department of
Physics, Lund University, Box 118, SE-221 00 Lund, Sweden  G.J. Ottino
University of New Mexico, Albuquerque, New Mexico 87131, USA  K. Ozawa  KEK,
High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801,
Japan  Tomonaga Center for the History of the Universe, University of Tsukuba,
Tsukuba, Ibaraki 305, Japan  V. Pantuev  Institute for Nuclear Research of the
Russian Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312,
Russia  V. Papavassiliou  New Mexico State University, Las Cruces, New Mexico
88003, USA  J.S. Park  Department of Physics and Astronomy, Seoul National
University, Seoul 151-742, Korea  S. Park  RIKEN Nishina Center for
Accelerator-Based Science, Wako, Saitama 351-0198, Japan  Department of
Physics and Astronomy, Seoul National University, Seoul 151-742, Korea
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  S.F. Pate  New Mexico State University, Las
Cruces, New Mexico 88003, USA  M. Patel  Iowa State University, Ames, Iowa
50011, USA  W. Peng  Vanderbilt University, Nashville, Tennessee 37235, USA
D.V. Perepelitsa  Physics Department, Brookhaven National Laboratory, Upton,
New York 11973-5000, USA  University of Colorado, Boulder, Colorado 80309, USA
G.D.N. Perera  New Mexico State University, Las Cruces, New Mexico 88003, USA
D.Yu. Peressounko  National Research Center “Kurchatov Institute”, Moscow,
123098 Russia  C.E. PerezLara  Department of Physics and Astronomy, Stony
Brook University, SUNY, Stony Brook, New York 11794-3800, USA  J. Perry  Iowa
State University, Ames, Iowa 50011, USA  R. Petti  Physics Department,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA  M. Phipps
Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  University of Illinois at Urbana-Champaign, Urbana, Illinois
61801, USA  C. Pinkenburg  Physics Department, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  R.P. Pisani  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  A. Pun  Department of
Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA  M.L. Purschke
Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  P.V. Radzevich  Saint Petersburg State Polytechnic
University, St. Petersburg, 195251 Russia  K.F. Read  Oak Ridge National
Laboratory, Oak Ridge, Tennessee 37831, USA  University of Tennessee,
Knoxville, Tennessee 37996, USA  D. Reynolds  Chemistry Department, Stony
Brook University, SUNY, Stony Brook, New York 11794-3400, USA  V. Riabov
National Research Nuclear University, MEPhI, Moscow Engineering Physics
Institute, Moscow, 115409, Russia  PNPI, Petersburg Nuclear Physics Institute,
Gatchina, Leningrad region, 188300, Russia  Y. Riabov  PNPI, Petersburg
Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia  Saint
Petersburg State Polytechnic University, St. Petersburg, 195251 Russia  D.
Richford  Baruch College, City University of New York, New York, New York,
10010 USA  T. Rinn  Iowa State University, Ames, Iowa 50011, USA  S.D. Rolnick
University of California-Riverside, Riverside, California 92521, USA  M.
Rosati  Iowa State University, Ames, Iowa 50011, USA  Z. Rowan  Baruch
College, City University of New York, New York, New York, 10010 USA  J.
Runchey  Iowa State University, Ames, Iowa 50011, USA  A.S. Safonov  Saint
Petersburg State Polytechnic University, St. Petersburg, 195251 Russia  T.
Sakaguchi  Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  H. Sako  Advanced Science Research Center, Japan Atomic
Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken
319-1195, Japan  V. Samsonov  National Research Nuclear University, MEPhI,
Moscow Engineering Physics Institute, Moscow, 115409, Russia  PNPI, Petersburg
Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia  M.
Sarsour  Georgia State University, Atlanta, Georgia 30303, USA  S. Sato
Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata
Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan  C.Y. Scarlett
Florida A&M University, Tallahassee, FL 32307, USA  B. Schaefer  Vanderbilt
University, Nashville, Tennessee 37235, USA  B.K. Schmoll  University of
Tennessee, Knoxville, Tennessee 37996, USA  K. Sedgwick  University of
California-Riverside, Riverside, California 92521, USA  R. Seidl  RIKEN
Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  A. Sen  Iowa State University, Ames, Iowa 50011, USA
University of Tennessee, Knoxville, Tennessee 37996, USA  R. Seto  University
of California-Riverside, Riverside, California 92521, USA  A. Sexton
University of Maryland, College Park, Maryland 20742, USA  D. Sharma
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  I. Shein  IHEP Protvino, State Research
Center of Russian Federation, Institute for High Energy Physics, Protvino,
142281, Russia  T.-A. Shibata  RIKEN Nishina Center for Accelerator-Based
Science, Wako, Saitama 351-0198, Japan  Department of Physics, Tokyo Institute
of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan  K. Shigaki
Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan  M.
Shimomura  Iowa State University, Ames, Iowa 50011, USA  Nara Women’s
University, Kita-uoya Nishi-machi Nara 630-8506, Japan  T. Shioya  Tomonaga
Center for the History of the Universe, University of Tsukuba, Tsukuba,
Ibaraki 305, Japan  P. Shukla  Bhabha Atomic Research Centre, Bombay 400 085,
India  A. Sickles  University of Illinois at Urbana-Champaign, Urbana,
Illinois 61801, USA  C.L. Silva  Los Alamos National Laboratory, Los Alamos,
New Mexico 87545, USA  D. Silvermyr  Department of Physics, Lund University,
Box 118, SE-221 00 Lund, Sweden  B.K. Singh  Department of Physics, Banaras
Hindu University, Varanasi 221005, India  C.P. Singh  Department of Physics,
Banaras Hindu University, Varanasi 221005, India  V. Singh  Department of
Physics, Banaras Hindu University, Varanasi 221005, India  M.J. Skoby
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040,
USA  M. Slunečka  Charles University, Ovocný trh 5, Praha 1, 116 36, Prague,
Czech Republic  K.L. Smith  Florida State University, Tallahassee, Florida
32306, USA  M. Snowball  Los Alamos National Laboratory, Los Alamos, New
Mexico 87545, USA  R.A. Soltz  Lawrence Livermore National Laboratory,
Livermore, California 94550, USA  W.E. Sondheim  Los Alamos National
Laboratory, Los Alamos, New Mexico 87545, USA  S.P. Sorensen  University of
Tennessee, Knoxville, Tennessee 37996, USA  I.V. Sourikova  Physics
Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
P.W. Stankus  Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
S.P. Stoll  Physics Department, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  T. Sugitate  Hiroshima University, Kagamiyama, Higashi-
Hiroshima 739-8526, Japan  A. Sukhanov  Physics Department, Brookhaven
National Laboratory, Upton, New York 11973-5000, USA  T. Sumita  RIKEN Nishina
Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan  J. Sun
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  Z. Sun  Debrecen University, H-4010 Debrecen,
Egyetem tér 1, Hungary  S. Suzuki  Nara Women’s University, Kita-uoya Nishi-
machi Nara 630-8506, Japan  J. Sziklai  Institute for Particle and Nuclear
Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences
(Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49, Budapest, Hungary  K. Tanida
Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata
Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan  RIKEN BNL Research
Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
Department of Physics and Astronomy, Seoul National University, Seoul 151-742,
Korea  M.J. Tannenbaum  Physics Department, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  S. Tarafdar  Vanderbilt University,
Nashville, Tennessee 37235, USA  Weizmann Institute, Rehovot 76100, Israel  A.
Taranenko  National Research Nuclear University, MEPhI, Moscow Engineering
Physics Institute, Moscow, 115409, Russia  G. Tarnai  Debrecen University,
H-4010 Debrecen, Egyetem tér 1, Hungary  R. Tieulent  Georgia State
University, Atlanta, Georgia 30303, USA  IPNL, CNRS/IN2P3, Univ Lyon,
Université Lyon 1, F-69622, Villeurbanne, France  A. Timilsina  Iowa State
University, Ames, Iowa 50011, USA  T. Todoroki  RIKEN BNL Research Center,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA  Tomonaga
Center for the History of the Universe, University of Tsukuba, Tsukuba,
Ibaraki 305, Japan  M. Tomášek  Czech Technical University, Zikova 4, 166 36
Prague 6, Czech Republic  C.L. Towell  Abilene Christian University, Abilene,
Texas 79699, USA  R.S. Towell  Abilene Christian University, Abilene, Texas
79699, USA  I. Tserruya  Weizmann Institute, Rehovot 76100, Israel  Y. Ueda
Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan  B. Ujvari
Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary  H.W. van Hecke
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  J.
Velkovska  Vanderbilt University, Nashville, Tennessee 37235, USA  M. Virius
Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic  V. Vrba
Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic
Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance
2, 182 21 Prague 8, Czech Republic  N. Vukman  Department of Physics, Faculty
of Science, University of Zagreb, Bijenička c. 32 HR-10002 Zagreb, Croatia
X.R. Wang  New Mexico State University, Las Cruces, New Mexico 88003, USA
RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  Z. Wang  Baruch College, City University of New York, New
York, New York, 10010 USA  Y.S. Watanabe  Center for Nuclear Study, Graduate
School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033,
Japan  C.P. Wong  Georgia State University, Atlanta, Georgia 30303, USA  C.L.
Woody  Physics Department, Brookhaven National Laboratory, Upton, New York
11973-5000, USA  C. Xu  New Mexico State University, Las Cruces, New Mexico
88003, USA  Q. Xu  Vanderbilt University, Nashville, Tennessee 37235, USA  L.
Xue  Georgia State University, Atlanta, Georgia 30303, USA  S. Yalcin
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony
Brook, New York 11794-3800, USA  Y.L. Yamaguchi  RIKEN BNL Research Center,
Brookhaven National Laboratory, Upton, New York 11973-5000, USA  Department of
Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York
11794-3800, USA  H. Yamamoto  Tomonaga Center for the History of the Universe,
University of Tsukuba, Tsukuba, Ibaraki 305, Japan  A. Yanovich  IHEP
Protvino, State Research Center of Russian Federation, Institute for High
Energy Physics, Protvino, 142281, Russia  J.H. Yoo  Korea University, Seoul,
02841  RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New
York 11973-5000, USA  I. Yoon  Department of Physics and Astronomy, Seoul
National University, Seoul 151-742, Korea  H. Yu  New Mexico State University,
Las Cruces, New Mexico 88003, USA  Peking University, Beijing 100871, People’s
Republic of China  I.E. Yushmanov  National Research Center “Kurchatov
Institute”, Moscow, 123098 Russia  W.A. Zajc  Columbia University, New York,
New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA  A.
Zelenski  Collider-Accelerator Department, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA  Y. Zhai  Iowa State University, Ames, Iowa
50011, USA  S. Zharko  Saint Petersburg State Polytechnic University, St.
Petersburg, 195251 Russia  L. Zou  University of California-Riverside,
Riverside, California 92521, USA

###### Abstract

Measurements of the differential production of electrons from open-heavy-
flavor hadrons with charm- and bottom-quark content in $p$$+$$p$ collisions at
$\sqrt{s}=200$ GeV are presented. The measurements proceed through displaced-
vertex analyses of electron tracks from the semileptonic decay of charm and
bottom hadrons using the PHENIX silicon-vertex detector. The relative
contribution of electrons from bottom decays to inclusive heavy-flavor-
electron production is found to be consistent with fixed-order-plus-next-to-
leading-log perturbative-QCD calculations within experimental and theoretical
uncertainties. These new measurements in $p$$+$$p$ collisions provide a
precision baseline for comparable forthcoming measurements in A$+$A
collisions.

##  I Introduction

Charm and bottom quarks are collectively referred to as heavy-flavor quarks.
Their production in elementary $p$$+$$p$ collisions is of interest from a
variety of vantage points, both in high-energy particle and nuclear physics.

From a fundamental standpoint, unlike light quarks the large masses of heavy-
flavor quarks (compare $m_{c}\approx 1280$ MeV/$c^{2}$ and $m_{b}\approx 4180$
MeV/$c^{2}$ with $m_{u}\approx 2.2$ MeV/$c^{2}$ and $m_{d}\approx 4.7$
MeV/$c^{2}$) Tanabashi  _et al._ (2018) are such that their production can be
calculated using perturbative quantum chromodynamics (pQCD) even at low
$p_{T}$. At leading order (LO), heavy quark production proceeds via gluon
fusion and quark-antiquark annihilation. At next-to-leading order (NLO),
processes such as flavor excitation and gluon splitting are involved. In this
regime, divergences are regulated by the mass of the heavy quarks, which acts
as an infrared cutoff except when the quark $p_{T}$ is greater than its mass
Andronic  _et al._ (2016). In that case, logarithmic divergences appear. The
most advanced analytic pQCD techniques currently available allow for such
divergences to be resummed, giving rise to the fixed-order-plus-next-to-
leading-log (FONLL) approach Cacciari  _et al._ (2005). Unfortunately, FONLL
calculations exhibit very large error bands associated predominantly with
uncertainties in the heavy quark masses and the renormalization scales,
motivating the need for comparisons with experimental data.

A wealth of heavy-flavor-production data exists both at the Relativistic Heavy
Ion Collider (RHIC) Averbeck (2013) and the Large Hadron Collider (LHC)
Andronic  _et al._ (2016). At the LHC, such measurements comprise cross
section measurements of inclusive heavy-flavor leptons, as well as of
individual $D$ (containing charm) and $B$ (containing bottom) meson states. At
RHIC, such measurements are consistent with FONLL calculations within
uncertainties, yet systematically higher than the central value predicted by
the theory. It is thus of interest to arrive at a simultaneous measurement of
charm and bottom production at RHIC energies to leverage the distinct masses
of these quarks to provide constraints for pQCD calculations.

Now, from the standpoint of high energy nuclear physics, heavy-ion collisions
at RHIC and the LHC produce deconfined nuclear matter—known as the quark-gluon
plasma (QGP). The QGP produced in these colliders can be characterized as a
strongly coupled fluid Shuryak (2017) exhibiting, among other properties,
substantial color opacity. This refers to the ability of the medium to hinder
the passage of color charges, resulting in the energy loss of such particles
Gyulassy and Plumer (1990). Charm and bottom quarks are excellent probes of
color opacity because they originate primarily from early-stage hard-parton-
scattering processes, and thus transit through the entire evolution of the QGP
medium Averbeck (2013).

The yield of heavy-flavor electrons at RHIC scales with the number of binary
nucleon-nucleon collisions Adler  _et al._ (2005); Adare  _et al._ (2007a) as
a consequence of charm and bottom conservation by the strong interaction.
Nevertheless, their spectrum is modified in central Au$+$Au collisions
relative to the $p$$+$$p$ baseline, as quantified by the nuclear modification
factor $R_{AA}$ Adare  _et al._ (2007a). Heavy quarks are redistributed in
momentum space, such that a strong suppression of heavy-flavor electrons is
observed for $p_{T}>5$ GeV/$c$, comparable in magnitude to that observed for
light quarks Adcox  _et al._ (2002); Adler  _et al._ (2003).

This constitutes a puzzling observation, as it challenges traditional
interpretations of energy loss as proceeding exclusively through gluon
radiation, requiring the inclusion of additional collisional mechanisms. To
shed light on the interplay of radiative and collisional energy loss by
leveraging the mass difference between charm and bottom, the PHENIX
collaboration has measured separated heavy-flavor-quark yields from
semileptonic decay electrons in Au$+$Au collisions using the silicon-vertex-
detector upgrade Adare  _et al._ (2016). Nuclear modification factors $R_{AA}$
were calculated using a $p$$+$$p$ baseline measurement by the STAR
collaboration Aggarwal  _et al._ (2010) obtained via electron-hadron
correlations with limited kinematic reach and large uncertainties.

In this paper, we present a new baseline measurement of heavy-flavor
separation in $p$$+$$p$ at $\sqrt{s}=200$ GeV using the same displaced-vertex
analysis technique used in a previous PHENIX measurement made in Au$+$Au
collisions at $\sqrt{s}=200$ GeV Adare  _et al._ (2016). Our new results with
smaller uncertainties and extended kinematic range provide a valuable update
for future measurements of heavy-flavor modification

##  II Experimental Setup

Figure 1: Schematic view of the PHENIX detector configuration along the beam
axis in the 2015 run period. The indicated subsystems are identified in the
text.

Figure 1 shows a transverse (beam) view of the PHENIX detector and its
subsystems. Two midrapidity spectrometers, called the central arms, are shown
on either side of the central magnet. With an acceptance of $|\eta|<0.35$ and
$\Delta\phi=\pi/2$, each arm provides tracking and particle identification
capabilities. The magnetic field is generated by two pairs of coils in the
pole faces of the central magnet such that when electric current runs in the
same direction in both coils, a maximum field strength of 0.9 T is achieved at
the beam location. A detailed description of the PHENIX detector is given in
Ref. Adcox  _et al._ (2003a); Mannel (2007); Akiba  _et al._ (2004).

The drift chambers and three layers of multiwire-proportional pad chambers are
the subsystems used for charged particle tracking Adcox  _et al._ (2003b). The
Ring Imaging Čerenkov (RICH) detector and the electromagnetic calorimeter
(EMCal) are the subsystems used for electron identification. The RICH Aizawa
_et al._ (2003) comprises two independent volumes, one in each detector arm,
filled with CO2. The gas acts as a dielectric medium, in which electrons emit
Čerenkov radiation for $p_{T}>20$ MeV/$c$; pions can also emit light in the
RICH above $p_{T}\approx 5$ GeV/$c$. The EMCal Aphecetche  _et al._ (2003),
which comprises lead-glass (PbGl) and lead-scintillator (PbSc) modules, is
used to identify electrons based on the transverse shape of an electromagnetic
shower and the ratio of the particle’s energy deposit in the EMCal to the
momentum of the reconstructed track.

Figure 2: Cross sectional view of the VTX detector showing the relative
positions of individual layers B0, B1, B2, and B3 from smallest to largest
radius.

Figure 2 shows the finely segmented silicon-vertex detector (VTX) Mannel
(2007); Nouicer  _et al._ (2009), which was installed as an upgrade in 2011 to
provide tracking close to the interaction region, capable of reconstructing
the primary vertex with a resolution on the order of 150 $\mu$m in $p$$+$$p$
collisions. The VTX comprises two arms with four independent layers arranged
around the beam pipe at nominal radii of $r=2.6$, 5.1, 11.8, and 16.7 cm. The
material budget, expressed as a percentage of a radiation length is, for each
layer, $X_{0}(\%)=1.28$, 1.28, 5.43, and 5.43. Simultaneously with the VTX a
new, thinner, beryllium beam pipe was installed in 2011 with a material budget
of $X_{0}(\%)=0.22$. Each layer comprises a series of ladders extending
longitudinally. The VTX has an acceptance of $|\eta|<1$ and $\Delta\phi\approx
0.8\pi$ per arm. Going from smallest to largest radius, individual layers are
named B0, B1, B2, and B3. The innermost layers, B0 and B1, were constructed
using silicon-pixel technology developed at CERN Ichimiya  _et al._ (2009).
Pixels in these layers have dimensions $50\mu{\rm m}\times 425\mu{\rm m}$, and
are arranged into lattices of $256\times 32$ pixels which are read out by a
single ALICE1LHCb sensor-readout chip Snoyes  _et al._ (2000). Four readout
chips constitute one sensor module, with four sensor modules in a single
ladder. Layers B0 and B1 have 5 and 10 ladders per arm, respectively. Layers
B2 and B3, were constructed using a novel silicon-stripixel technology
developed at Brookhaven National Laboratory. Each $4.34\times 6.46$ cm sensor
in these layers is segmented into $80\mu{\rm m}\times 1000\mu{\rm m}$
stripixels. These are implanted with two serpentine metal strips defining two
readout directions, $X$ and $U$, such that the two-dimensional location of hit
positions can be determined. Layers B2 and B3 have 8 and 12 ladders per arm,
respectively, with 5(6) sensors per ladder in B2(B3). Stripixel sensors are
read out using the SVX4 readout chip, developed by a collaboration between
Fermilab and Lawrence Berkeley National Laboratory Krieger  _et al._ (2004).

##  III Methods

The goal of this analysis is to measure the invariant yield of heavy-flavor
electrons, independently for charm and bottom decays. This is accomplished by
exploiting the fact that hadrons with bottom content have a longer lifetime
than those with charm, as shown in Table 1 for $B$ and $D$ mesons Tanabashi
_et al._ (2018). As will be described in the following subsection, the
provenance of heavy flavor electron tracks is determined statistically based
on the distance of closest approach in the transverse plane (DCAT) between the
tracks and the beam center, which is the point relative to which they are
reconstructed,

Table 1: Lifetime $c\tau_{0}$ of selected $D$ and $B$ states Tanabashi  _et al._ (2018). |  | Particle | Lifetime $c\tau_{0}$ |  |
---|---|---|---|---|---
|  | $D^{0}$ | 129.9 $\mu$m |  |
|  | $D^{+}$ | 311.8 $\mu$m |  |
|  | $B^{0}$ | 457.2 $\mu$m |  |
|  | $B^{+}$ | 491.1 $\mu$m |  |

Thus, the longer lifetime of the $B$, and its decay kinematics, will result in
a broader DCAT distribution than for electrons from the shorter-lived $D$
mesons. However, the measured electron candidate sample contains not only
heavy flavor electrons, but also abundant background from a variety of sources
(i.e., decays of $\pi^{0}$, $\eta$, $\rho$, $\omega$ $J/\psi$, $K^{\pm}$,
$K_{s}^{0}$, $\Upsilon$ mesons and the Drell-Yan process, as well as
conversions of direct and decay photons), each with its own characteristic
DCAT shape. Once this background has been determined, the DCAT distribution of
inclusive heavy flavor electrons can be isolated. The individual contributions
from charm and bottom can then be obtained through an inversion procedure
often referred to as unfolding Choudalakis . We outline the steps involved in
the analysis as follows:

  1. 1.

Measure the DCAT distribution of hadrons and electrons candidate tracks in
data, as a function of track $p_{T}$.

  2. 2.

Model the DCAT distributions of nonheavy-flavor background in the candidate
electron sample by simulating the following electron sources: $\pi^{0}$,
$\eta$, direct photons, $J/\psi$, $K_{s}^{0}$, $K^{\pm}$, and hadron
contamination.

  3. 3.

Determine the fraction of electrons attributable to each of the background
sources considered, thus normalizing the background DCAT distributions
relative to those of electron candidates in data.

  4. 4.

Separate the contribution of charm and bottom decays to the electron sample
using Bayesian inference techniques. This step is constrained by the measured
electron DCAT distributions, as well as by the invariant yield of inclusive
heavy-flavor electrons, previously published by the PHENIX collaboration Adare
_et al._ (2011a).

This analysis used 110 pb-1 of integrated luminosity collected during the 2015
$p$$+$$p$ RHIC running period. A family of EMCal-RICH triggers were used to
maximize the number of electron tracks available for analysis. These triggers
segment the calorimeter and RICH detector into a series of tiles, triggering
on events in which a certain energy threshold is exceeded in a calorimeter
tile, and for some triggers requiring that a spatial match can be found in the
RICH.

###  III.1 Measuring Track DCAT

Track reconstruction is carried out using the central arm spectrometers, as
detailed in Ref. Adare  _et al._ (2007a). Electron candidates within
$1.5<p_{T}{\rm[GeV/\textit{c}]}<6.0$ are identified by matching reconstructed
tracks with hits in the RICH, and energy deposits in the EMCal.

Electrons traversing the RICH emit Čerenkov light, which is amplified by
photomultiplier tubes (PMT). A maximum displacement of 5 cm is allowed between
a track projection and the centroid of the hit PMTs. For tracks with $p_{T}<5$
GeV/$c$, at least one PMT hit is required in the RICH, whereas at higher
$p_{T}$ at least three hits are required, given that pions in this kinematic
region begin to radiate in the RICH.

Additionally, the energy $E$ deposited by a track in the EMCal is required to
match its momentum $p$, since—unlike hadrons—electrons deposit the majority of
their energy in the calorimeter. This is quantified through the variable
$dep=(E/p-\mu_{E/p})/\sigma_{E/p}$, where $\mu_{E/p}$ and $\sigma_{E/p}$
correspond to the mean and width of a Gaussian fit to the distribution of the
energy-momentum ratio $E/p$ around $E/p=1$, respectively. A cut on $|dep|<2$
is then used to select electrons.

Additional cuts involving the EMCal include restricting the displacement in
$\Delta z$ and $\Delta\phi$ between the track projection and the calorimeter
shower to within three standard deviations. Finally, a cut on the probability
that a given EMCal cluster originates from an electromagnetic shower—as
determined from the shower shape—is used to reject hadrons.

Once identified in the central arms, reconstructed tracks are projected back
to the VTX detector, where an iterative algorithm described in Ref. Adare  _et
al._ (2016) is used to associate the track with VTX hits to create a VTX-
associated track. Such tracks are required to have a hit in each of the two
innermost layers of the VTX, and at least one hit in either of the outer
layers, and to satisfy $\chi^{2}_{{\rm vtx}}/{\rm ndf}<2$ to ensure the
quality of the fit.

Figure 3: Schematic diagram illustrating the definition of track DCAT in the
transverse plane, as DCA${}_{T}=L-R$.

Figure 3 shows a schematic diagram defining the DCAT of a VTX-associated
track. The circular track projection is shown in the transverse plane, where a
constant magnetic field exists over the region covered by the VTX detector.
The DCAT is then defined as ${\rm DCA}_{T}=L-R$, where $L$ is the distance
between the beam center and the center of the projection, and $R$ is the
projection radius. The beam center is defined as the geometric center of the
transverse region over which beam collisions occur, is constant over a given
run period, and exhibits a Gaussian spread of width
$\sigma_{x}^{{\rm(beam)}}\approx 130$ $\mu{\rm m}$ and
$\sigma_{y}^{{\rm(beam)}}\approx 100$ $\mu{\rm m}$. Notice that DCAT is a
signed quantity which is not generally symmetric around zero, because
electrons from some background sources exhibit asymmetric DCAT distributions
depending on the decay kinematics of their parent particles.

In a previous PHENIX analysis Adare  _et al._ (2016), the DCAT was defined
relative to the primary vertex of the collision, rather than the beam center.
The primary vertex is determined using tracks reconstructed from VTX hits
alone, with no reliance on the central arm tracking subsystems. However, given
the low multiplicity of $p$$+$$p$ collisions, such a procedure does not
converge to a vertex for approximately 50% all $p$$+$$p$ events. Furthermore,
when it does converge—and particularly in events with electron tracks—the low
number of reconstructed tracks makes it likely that the primary vertex is
biased towards a displaced vertex and thus unsuitable for analysis. The choice
of using the beam center for DCAT determination is further justified because
the primary-vertex resolution is quite similar to the beam spot spread. Table
2 shows the resolution of the precise vertex in the transverse plane, as a
function of the number of reconstructed VTX tracks used in its determination.
The resolution improves significantly with increasing number of tracks.
However, due to the limited coverage of the VTX, the average number of tracks
used to calculate the primary vertex in $p$$+$$p$ collisions is 3.2, such that
the corresponding resolution is broader than the beam spread.

Table 2: Resolution of the primary vertex in the transverse plane, as a function of the number of reconstructed VTX tracks available for its determination. | Number | $\sigma_{x}^{{\rm vertex}}$ | $\sigma_{y}^{{\rm vertex}}$ |
---|---|---|---|---
| of Tracks | $[\mu{\rm m}]$ | $[\mu{\rm m}]$ |
| 2 | 296.5 | 207.0 |
| 3 | 195.0 | 141.2 |
| 4 | 157.3 | 113.7 |
| 5 | 132.7 | 97.0 |
| 6 | 118.8 | 77.8 |
| 7 | 98.8 | 72.8 |
| 8 | 89.6 | 60.3 |
Figure 4: DCAT distribution of hadron tracks in data within $1.8{\rm
GeV}/c<p_{T}<2.1{\rm GeV}/c$, calculated relative to the beam center position.

Figure 4 shows the DCAT distribution of hadron tracks within
$1.8<p_{T}{\rm[GeV}/c]<2.1$, where the histogram corresponds to counts of
tracks passing the analysis cuts, with no correction for acceptance or
efficiency effects. Hadron tracks are subject to the same quality requirements
as electron tracks, but are identified as hadrons by requiring no RICH PMT
hits. The very prominent Gaussian peak centered at ${\rm DCA}_{T}=0$ is
attributed to particles originating from the primary collision point, with its
width reflecting the beam spread, convolved with the track-pointing
resolution. On the other hand, the broad tails can be attributed to long-lived
light hadrons which decay, as well as background. It is observed that the DCAT
resolution improves with increasing track $p_{T}$. For this analysis, DCAT
distributions of electron candidate tracks were measured in 10 $p_{T}$ bins
between $1.5<p_{T}{\rm[GeV}/c]<6.0$.

###  III.2 Modeling Electron Background Sources

In addition to heavy-flavor-decay electrons, the electron sample determined by
applying the track cuts described in the previous section contains
contributions from a variety of background sources. Namely, we consider $(i)$
photonic electrons from the Dalitz decay of $\pi^{0}$ and $\eta$ mesons, as
well as photon conversions; $(ii)$ nonphotonic electrons from the decay of
$J/\psi$ and the three-body decay of $K^{\pm}$ and $K_{s}^{0}$ (collectively
called $Ke3$ electrons); and $(iii)$ hadrons which are misidentified as
electrons.

To isolate the heavy-flavor signal of interest, it is necessary to properly
account for the background. Conversion electrons constitute the single largest
source of background in this analysis owing to the material budget of the the
VTX with $X_{0}(\%)=13.42$ of a radiation length. In the following subsection
we describe a strategy that uses the fine segmentation of the VTX itself to
reject the vast majority of conversions based on the narrow opening angle
topology of conversion electron pairs. The remaining background, both photonic
and nonphotonic, is accounted for by constructing an electron cocktail
normalized relative to the measured electron sample.

Of the background electron sources, all but misidentified hadrons can be
modeled using previous measurements of primary (i.e., $\pi^{0}$, $\eta$,
$J/\psi$, $K^{\pm}$,$K^{0}_{s}$) particle production combined with a knowledge
of their decay modes and geant3 simulations of the PHENIX detector.
Contributions from other sources of electrons, like the decay of vector mesons
such as the $\Upsilon$, $\phi$, $\omega$ and $\rho$, as well as the Drell-Yan
process, were found to contribute negligibly to the total electron background
in the kinematic region of interest.

####  III.2.1 Photonic Electron Background

Photonic electrons originate from the Dalitz decay ($X\rightarrow
e^{+}e^{-}\gamma$) of $\pi^{0}$ and $\eta$ mesons, and from the conversion of
photons ($\gamma\rightarrow e^{+}e^{-}$) interacting with the beam pipe or the
VTX detector itself, where the photons are either direct photons or a hadronic
decay product. To model this background, we start with the published cross
section of $\pi^{0}$, $\eta$ and direct photons in $p$$+$$p$ at $\sqrt{s}=200$
GeV Adare  _et al._ (2010, 2009a); Adler  _et al._ (2007); Adare  _et al._
(2007b). Single particles are then generated between $0<p_{T}{\rm[GeV/}c]<20$
according to the published spectrum. For $\pi^{0}$ and $\eta$, accounting for
branching ratios, the decay is forced to proceed exclusively through channels
involving photons or electrons in the final state. The decay photons and
electrons are fed through a geant3 simulation of the PHENIX detector, where
the same reconstruction code and track cuts used in data are applied. The
resulting reconstructed electron yield is normalized by the number of
simulated primary particles, thus correctly describing the relative
contribution of each primary source to the total photonic electron yield.

As previously mentioned, conversion electrons constitute the most significant
source of background in this analysis, originating from the beam pipe as well
as all four layers of the VTX. We can eliminate 80% of conversion electrons by
imposing the requirement that tracks used in analysis have a hit in each of
the innermost two layers of the VTX, thereby discarding electron tracks
originating in the outer layers.

Given the narrow opening angle between the $e^{+}e^{-}$ pair from photon
conversions, a veto cut is defined to minimize the remaining conversions from
the beam pipe and innermost two layers. In this approach, tracks with a VTX
hit in close proximity, within a certain window in $\Delta\phi$ and $\Delta
z$, are rejected. As illustration, if a conversion occurs in the beam pipe, or
in B0, then nearby pairs of hits will be found in subsequent detector layers.
If at least one of these electrons is reconstructed as a track, the conversion
veto cut will reject it based on the presence of at least one nearby hit
within the window in any layer.

Figure 5: Track $p_{T}$-dependent window in ${\rm chrg}\times\Delta\phi$ used
in the conversion veto cut in the pixel detector layers, where chrg is the
charge of a given track and $\Delta\phi$ is the azimuthal separation between
clusters, one of which is associated with the track.

The size of the conversion veto window in ${\rm chrg}\times\Delta\phi$, where
chrg is the charge of the track and $\Delta\phi$ is the azimuthal distance
between track and cluster on the surface of a VTX chip, is shown in Fig. 5. It
depends on the track $p_{T}$, as well as the layer where the nearby cluster is
found. In general, because the bend of conversion electron pairs in the
magnetic field decreases with photon momentum, the windows become narrower
with increasing electron $p_{T}$. Furthermore, due to multiple scattering as
well as the separation of electron pairs in the magnetic field, windows in the
outer layers are larger than in the inner layers. The windows are asymmetric
because the quantity ${\rm chrg}\times\Delta\phi$ is positive by construction;
the negative side of the window is populated by mismeasured tracks which do
not yield a positive ${\rm chrg}\times\Delta\phi$. In the longitudinal
direction, the conversion veto window is $|\Delta z|<0.05$ cm in the innermost
two VTX layers, and $|\Delta z|<0.1$ cm in the outermost two.

Figure 6: Conversion veto cut survival rates for nonphotonic, and photonic
electrons from various sources. The total photonic survival rate is the
weighted average of the individual sources.

The survival rate $\varepsilon$ of electrons from a given source is defined as
the probability that they will not be rejected by the conversion veto cut.
Figure 6 shows the survival rate of electrons from photonic and nonphotonic
sources as a function of electron track $p_{T}$, where the nonphotonic
survival rate has been estimated using hadrons in data as a proxy. The
survival rate of photonic electrons has been further broken down by background
source, namely $\pi^{0}$ and $\eta$ decays, as well as photon conversions.

Conversion electrons, such as those shown from direct photons, have the lowest
survival rate of all. Electrons from $\pi^{0}$ and $\eta$ mesons have a higher
survival probability because they include—in addition to photon
conversions—Dalitz electron pairs which have a wider opening angle than
conversions pairs. The survival rate of all photonic electrons combined is
shown in blue in Fig. 6 to be approximately 20%. This demonstrates the ability
of the conversion veto cut to reject a substantial fraction of the photonic
background. In contrast, the survival rate of nonphotonic electrons is very
high, at approximately 90%. The conversion veto cut rejects a small fraction
of nonphotonic electrons due to the presence of uncorrelated random hits in
the window, which affect all tracks regardless of their provenance. The
particular size of the conversion veto windows used in this analysis
represents a compromise between maintaining a large window for background
rejection, and limiting its size to minimize the inclusion of uncorrelated
hits.

After applying the conversion veto cut on electrons in the photonic cocktail,
the contribution of each primary particle source to the total photonic
background can be calculated, as shown in Fig. 7(a). Electrons from $\pi^{0}$
(both Dalitz and from the conversion of decay photons) dominate the background
for all $p_{T}$, with direct photon external conversions becoming more
significant at higher $p_{T}$.

####  III.2.2 Non-photonic Electron Background

Non-photonic electrons in this analysis correspond to those from the decay of
$J/\psi$ mesons, as well as the three-body decays of $K^{\pm}$ and
$K_{s}^{0}$, collectively known as $Ke3$ electrons ($K{\rightarrow}e\nu\pi$).
Other background electron sources, namely the decays of vector mesons such as
the $\Upsilon$, $\rho$, $\omega$, and $\phi$ were considered in the background
cocktail, but were found to contribute negligibly.

Figure 7: (a) Fraction of electrons from individual photonic sources relative
to the total photonic electron background as determined by constructing a
background electron cocktail. (b) Fraction of electrons from individual
nonphotonic sources relative to the total photonic background.

The approach to modeling nonphotonic background is similar to that used for
photonic sources. Namely, single particles are generated according to their
respective published cross section, as measured by the PHENIX collaboration
Adare  _et al._ (2012, 2011b, 2011c), forced to decay, and the resulting
particles fed through a geant3 simulation of the detector. Applying the full
set of analysis track cuts, including the conversion veto cut, we complete the
background electron cocktail. The fraction of nonphotonic electrons from each
source, relative to the total photonic background is shown in Fig. 7(b).
Notice that the $J/\psi$ contribute more to the background cocktail than any
other background source above $p_{T}\approx 3.5$ GeV/$c$.

####  III.2.3 Hadron Contamination

Despite the electron identification cuts described in the previous section,
some hadron tracks will incorrectly be tagged as electrons. This contribution
to the electron sample is modest and is estimated in two independent ways,
making use of EMCal and RICH signals.

Unlike hadrons, electron tracks deposit the majority of their energy in the
EMCal, as quantified by the ratio $E/p$, where $E$ is the calorimeter energy
and $p$ is the track momentum. The variable $dep$, as previously defined,
takes the shape of a Gaussian of zero mean and unit width for true electron
tracks. In contrast, the $dep$ distribution of hadron tracks exhibits a very
different shape. Thus, a template is constructed, as a function of $p_{T}$, by
fitting the $dep$ distribution of hadrons tracks in data. The $dep$
distribution of electron candidates is then fit with a combination of the
hadron template plus a Gaussian, with a single free parameter corresponding to
their relative contribution. The value of this parameter provides an estimate
of the fraction of hadron contamination in the sample.

An independent way of estimating the hadron contamination is to exploit the
fact that imposing a cut requiring a minimum number of PMTs fired in the RICH
provides greater rejection power for hadron tracks than for electrons. The
fraction of hadrons rejected by such a cut can be estimated from hadron tracks
in data, while the fraction of rejected electrons can be determined through
geant3 simulation of single electrons. With these two pieces of information it
is possible to isolate the number of hadrons and electrons in the candidate
electron sample, thus determining the contamination fraction.

Figure 8: Fraction of electron candidates in data attributed to hadron
contamination as a function of $p_{T}$.

The weighted average of the two independent estimates of hadron contamination
is taken as the nominal value, with their difference as a systematic
uncertainty, as shown in Fig. 8. The systematic uncertainties are assigned to
encompass both estimates and are asymmetric.

Another source of contamination comprises electron tracks identified in the
central arms which are associated with uncorrelated random hits in the VTX
detector, leading to the creation of a spurious VTX-associated track. The
degree of contamination arising in this manner was quantified by rotating all
hits in the VTX in azimuth and polar angles by a small amount and attempting
to re-associate central arm tracks with the rotated hits. Given the low
multiplicity of $p$$+$$p$ collisions, the contribution of misassociated
central-arm tracks was found to be negligible, unlike in Au$+$Au collisions
where it is significant.

###  III.3 Normalizing Electron Background DCAT

In 2015—the year in which the $p$$+$$p$ data was collected—the VTX detector
exhibited a time-varying acceptance from a changing number of dead, cold, and
hot channels across the surface of each detector layer over time. This
precluded the measurement of an electron candidate sample fully corrected for
acceptance and efficiency effects. As a result, the simulated electrons in the
background cocktail are not corrected for acceptance and efficiency, but
simply constructed in such a way that the same reconstruction code and
analysis cuts used in data are applied.

The cocktail can then be used to calculate the fraction of electrons from each
background source relative to the total photonic background. However, to use
this information to determine their normalization relative to the total sample
of electron candidates, it is necessary to determine the fraction of electron
candidates attributable to photonic background. This is accomplished via a
data-driven method relying on the conversion veto cut.

Figure 9: Fraction of photonic electrons to inclusive electrons in data, as a
function of electron $p_{T}$.

Let $N_{P}$ and $N_{\rm NP}$ be the number of photonic and nonphotonic
electrons in the electron candidate sample obtained without applying the
conversion veto cut. Also, let $\varepsilon_{P}$ and $\varepsilon_{UC}$ be the
veto cut survival rate of photonic electrons due to correlated effects and due
to noncorrelated effects, respectively. In this nomenclature, heavy-flavor
electrons are part of the nonphotonic sample. The number of electrons measured
without the conversion veto cut is then simply

$N_{e}=N_{P}+N_{\rm NP},$ (1)

while the number of measured electrons that pass the veto cut is given by

$\tilde{N}_{e}=\varepsilon_{P}\times\varepsilon_{UC}\times
N_{P}+\varepsilon_{UC}\times N_{\rm NP},$ (2)

where $N_{P}$ is modified by both $\varepsilon_{P}$ and $\varepsilon_{UC}$
because photonic electrons are also susceptible to rejection from uncorrelated
hits in the window. Taken together, Eqs. 1 and 2 form a system of equations
with $N_{P}$ and $N_{\rm NP}$ as the only unknowns, yielding

$N_{P}=\frac{\tilde{N}_{e}-N_{e}\varepsilon_{UC}}{\varepsilon_{UC}(\varepsilon_{P}-1)},$
(3)

and

$N_{\rm
NP}=\frac{N_{e}\varepsilon_{P}\varepsilon_{UC}-\tilde{N}_{e}}{\varepsilon_{UC}(\varepsilon_{P}-1)}.$
(4)

The fraction of photonic electrons in the sample with the conversion veto cut
applied is then

$F_{P}=\frac{\varepsilon_{P}\varepsilon_{UC}N_{P}}{\varepsilon_{P}\varepsilon_{UC}N_{P}+\varepsilon_{UC}N_{\rm
NP}},$ (5)

and is shown in Fig. 9 as a function of electron $p_{T}$. Using $F_{P}$, the
fraction of candidate electrons attributable to each photonic source in data
is

$f_{i}^{{\rm phot}}=F_{P}(1-F_{{\rm
contam}})\frac{\tilde{N}_{i}}{\tilde{N}_{\pi^{0}}+\tilde{N}_{\eta}+\tilde{N}_{\gamma}},$
(6)

where $i$ is an index referring to a primary particle species (i.e.,
$\pi^{0},\eta,\gamma$); $\tilde{N}_{i}$ is the number of electrons from the
$i^{{\rm th}}$ source that pass the conversion veto cut in the electron
cocktail, and $1-F_{{\rm contam}}$ is the purity of the electron sample from
hadron contamination.

In the case of nonphotonic background, it is impossible to construct a similar
expression because the electron cocktail does not include contributions from
heavy-flavor mesons. Therefore, the nonphotonic background is normalized
relative to the simulated $\pi^{0}$ electron yield, whose absolute
normalization has been previously determined, as follows

$f_{j}^{{\rm nonphot}}=f_{\pi^{0}}^{{\rm
phot}}\frac{\tilde{N}_{j}}{\tilde{N}_{\pi^{0}}},$ (7)

with $j$ indexing the primary particles giving rise to nonphotonic electrons
(i.e., $J/\psi$ and $Ke3$).

Figure 10: Fraction of the measured candidate electron sample attributable to
various sources of background electrons as a function of $p_{T}$. Figure 11:
DCAT distribution of candidate electron tracks within
$1.8<p_{T}{\rm[GeV/}c]<2.1$, which pass the conversion veto cut. Also shown
are the absolutely normalized DCAT distributions from each simulated
background electron source, as well as hadron contamination.

These factors, shown in Fig. 10, are used to normalize the DCAT distribution
of each background electron source relative to the electron candidate sample.
Fig. 11 shows the DCAT distribution of electrons from each background species
within $1.8<p_{T}{\rm[GeV/}c]<2.1$, normalized relative to the total number of
electron candidates in that $p_{T}$ bin. Unlike prompt electrons, which
exhibit a Gaussian DCAT shape, K$e$3 electrons originate from long-lived kaon
decays, which results in their characteristic DCAT shape.

Table 3: Resolution of the DCAT distribution of charged pion tracks as reconstructed in data and in Monte Carlo geant3 simulations of the PHENIX detector. | Electron $p_{T}$ | Data Resolution | MC Resolution |
---|---|---|---|---
| [GeV/$c$] | [$\mu$m] | [$\mu$m] |
| $1.5<p_{T}<1.8$ | 134.1 | 122.1 |
| $1.8<p_{T}<2.1$ | 131.7 | 121.0 |
| $2.1<p_{T}<2.4$ | 130.1 | 119.9 |
| $2.4<p_{T}<2.7$ | 128.9 | 118.9 |
| $2.7<p_{T}<3.0$ | 127.9 | 118.5 |
| $3.0<p_{T}<3.5$ | 126.8 | 118.2 |
| $3.5<p_{T}<4.0$ | 126.2 | 117.9 |
| $4.0<p_{T}<4.5$ | 125.5 | 117.6 |
| $4.5<p_{T}<5.0$ | 125.1 | 117.2 |
| $5.0<p_{T}<6.0$ | 124.8 | 116.9 |

In general, the resolution of the DCAT is a consequence of the width of the
beam spot convolved with the track-pointing resolution. However, the
simulations used to create the background electron cocktail were run using a
single reference value for the beam spot size, which in reality fluctuates
over time during data-taking. Therefore, it is necessary to correct for the
difference in resolution between simulations and data. This was accomplished
by comparing, as a function of $p_{T}$, the DCAT resolution of charged pions
in data and simulation, as quoted in Table 3 deriving a $p_{T}$-dependent
factor such that the simulated DCAT distributions could be broadened to match
the resolution in data. This broadening factor was applied to electrons from
every species in the background electron cocktail.

###  III.4 Heavy-Flavor Separation via Unfolding

Having normalized the electron background DCAT distributions, it is possible
to isolate the corresponding distributions of electrons from heavy-flavor
decays in data. If the shapes of the parent hadron spectra were known a
priori, it would be a straightforward matter to use the knowledge of heavy-
flavor-decay kinematics to determine the shape of the DCAT distributions of
charm and bottom electrons separately, whose relative normalization could then
be constrained by the measured inclusive DCAT.

Figure 12: Invariant cross section of inclusive heavy-flavor-electron
production in $p$$+$$p$ collisions, as measured by the PHENIX experiment Adare
_et al._ (2011a), and used as input for the flavor-electron-separation-
unfolding procedure.

However, because such spectral shapes are not known for $D$ and $B$ mesons, it
becomes necessary to solve an inverse problem where the model parameters
(i.e., the spectrum of hadrons containing open charm and bottom, as a function
of $p_{T}$) are inferred from data observations, namely the DCAT and spectrum
of inclusive heavy-flavor electrons. For the spectrum, an earlier PHENIX
measurement Adare  _et al._ (2011a) was used, shown in Fig. 12.

To solve the inverse problem, it is necessary to construct a mapping from the
model parameters to the data. Given that the heavy-flavor-decay kinematics are
known, it is possible to assign a probability for a heavy flavor hadron at a
given $p_{T}^{(h)}$ to decay into an electron with a certain $p_{T}^{(e)}$ and
DCAT. Such mapping makes it possible to quantify the likelihood that a given
set of trial hadron spectra is consistent with the measured electron spectrum
and DCAT distributions.

We use a probabilistic approach Choudalakis  to the unfolding problem based on
Bayesian inference, identical to that used by PHENIX to separate charm and
bottom electron yields in Au$+$Au collisions Adare  _et al._ (2016). Let
$\mathbf{Y}^{{\rm data}}$ be a vector whose individual elements correspond to
the yield of inclusive heavy-flavor electrons, as shown in Fig. 12. Similarly,
$\mathbf{D}_{j}^{{\rm data}}$ is a vector of the binned DCAT distribution of
electrons in data, for tracks in the $j^{{\rm th}}$ $p_{T}$ bin, out of nine
bins between $1.5<p_{T}{\rm[GeV}/c]<6.0$. The two observables are combined in
a ‘data’ vector

$\bm{x}=(\mathbf{Y}^{{\rm data}},\mathbf{D}_{0}^{{\rm
data}},\ldots,\mathbf{D}_{8}^{{\rm data}}).$ (8)

The model parameters are also represented as a vector

$\bm{\theta}=(\bm{\theta}_{c},\bm{\theta}_{b}),$ (9)

where $\bm{\theta}_{c}$ and $\bm{\theta}_{b}$ correspond to the charm and
bottom hadron yields, respectively, in 17 $p_{T}$ bins each, between
$0<p_{T}{\rm[GeV}/c]<20$.

Bayes’ theorem, as written below

$P(\bm{\theta}\mid\bm{x})=\frac{P(\bm{x}\mid\bm{\theta})\pi(\bm{\theta})}{P(\bm{x})},$
(10)

relates the probability that a given set of model parameters $\bm{\theta}$ are
true given the data $\bm{x}$, to the probability that the data follow from an
assumed set of model parameters. While the former probability—known as the
posterior—is a difficult quantity to estimate, the latter—known as the
likelihood—is straightforward to compute given the knowledge of heavy-flavor
decays. The quantity $\pi(\bm{\theta})$, known as the prior, corresponds to
the knowledge of the model parameters prior to the data being analyzed. The
denominator $P(\bm{x})$, sometimes known as the evidence, provides the
normalization for the posterior. Thus, Bayes’ theorem allows us to take a
first guess regarding the model parameters, as encoded in the prior, and
refine it through the inclusion of data in the likelihood.

The 17 bins for both the charm and bottom hadron spectra within
$0<p_{T}^{(h)}{\rm[GeV}/c]<20$, as represented by $\bm{\theta}$, define a
34-dimensional space of model parameters. Starting with an initial set of
values given by the prior $\pi(\bm{\theta})$, corresponding to the charm and
bottom yields as calculated with pythia111We used pythia6.2, with parton
distribution functions (PDFs) given by CTEQ5L. The following parameters were
modified: MSEL = 5, MSTP(91) = 1, PARP(91) = 1.5, MSTP(33) = 1, PARP(31) =
2.5. For bottom (charm) hadron studies, PARJ(13) = 0.75 (0.63), PARJ(2) = 0.29
(0.2), PARJ(1) = 0.35 (0.15)., the unfolding proceeds by drawing trial sets of
hadron yields, corresponding to individual points in the multi-dimensional
parameter space. Because sampling such a large-dimensional space uniformly is
computationally prohibitive, we use a Markov chain Monte Carlo (MCMC)
algorithm Foreman-Mackey  _et al._ (2013), which proceeds iteratively until
convergence of the final solution is achieved. In this analysis, three
iterations suffice for convergence with 500 parallel “walkers” and 1000 burn-
in steps, as described in Foreman-Mackey  _et al._ (2013).

For each trial $\bm{\theta}$, we predict an electron $p_{T}$ spectrum and DCAT
distribution as follows

$\bm{Y}(\bm{\theta})=\bm{M}^{(\bm{Y})}\bm{\theta}_{c}+\bm{M}^{(\bm{Y})}\bm{\theta}_{b},$
(11)
$\bm{D}_{j}(\bm{\theta})=\bm{M}_{j}^{(\bm{D})}\bm{\theta}_{c}+\bm{M}_{j}^{(\bm{D})}\bm{\theta}_{b},$
(12)

where $\bm{M}^{\bm{Y}}:p_{T}^{(h)}\rightarrow p_{T}^{(e)}$ is a matrix
encoding the probability of a hadron of $p_{T}^{(h)}$ of any rapidity to yield
an electron of $p_{T}^{(e)}$ at midrapidity, while
$\bm{M}_{j}^{(\bm{D})}:p_{T}^{(h)}\rightarrow{\rm DCA}_{T}^{(e)}$ encodes the
probability of yielding an electron at a given DCAT value. The construction of
these matrices using the pythia generator is described in detail in Ref. Adare
_et al._ (2016), and includes the decays of charm hadrons
($D^{\pm}$,$D^{0}$,$D_{s}$, and $\Lambda_{c}$), and bottom hadrons ($B^{\pm}$,
$B^{0}$, $B_{s}$m and $\Lambda_{b}$). Additional Monte Carlo generators could
be used to construct the matrix, but this would be computationally
prohibitive. For the purposes of this analysis, an additional matrix was
introduced to model the detector response, mapping the truth $p_{T}$ and DCAT
values in $\bm{M}^{(\bm{Y})}$ and $\bm{M}_{j}^{(\bm{D})}$ to their
reconstructed counterparts, allowing for a direct comparison between the data
and the predicted distributions from a given set of trial parameters
$\bm{\theta}$.

The predicted spectrum and DCAT distributions are then used to compute the
(log)likelihood as follows

$\begin{split}\ln P(\bm{x}\mid\bm{\theta})&=\ln P(\bm{Y}^{{\rm
data}}\mid\bm{Y}(\bm{\theta}))\\\ &+\sum_{j=0}^{8}\ln P(\bm{D}_{j}^{{\rm
data}}\mid\bm{D}_{j}(\bm{\theta})),\end{split}$ (13)

where the log-likelihood for the $\bm{Y}^{{\rm data}}$ term is modeled as a
multi-variate Gaussian with diagonal covariance, while the log-likelihood for
the $\bm{D}_{j}$ term is modeled by a multivariate Poisson distribution, with
full details provided in Ref. Adare  _et al._ (2016).

To constrain the shape of the unfolded charm and bottom spectra, ensuring its
smoothness, a regularization term is added to the log-likelihood function, as
follows

$\ln\pi(\bm{\theta})=-\alpha^{2}(|\bm{LR}_{c}|^{2}+|\bm{LR}_{b}|^{2}),$ (14)

where $\bm{R}_{c}$ and $\bm{R}_{b}$ correspond to the ratios of the trial
vector of charm and bottom spectra to the prior. The matrix $\bm{L}$ is a
$17\times 17$ discretized second-order finite-difference matrix, effectively
corresponding to the second derivative operator. Thus, the addition of this
term enhances the log-likelihood for solutions with large curvature,
effectively penalizing deviations from smoothness. The optimal regularization
strength $\alpha$ is determined by carrying out a scan of various possible
parameter values and calculating the total log-likelihood of the unfolding
solution in each case, comparing it to the case with no regularization. The
desired optimal value is that which maximizes the log-likelihood, and is found
to be $\alpha=1$.

Figure 13: (a) Joint probability distributions of bottom and charm hadron
yields. The marginalized distribution for each $p_{T}$ bin is shown along the
diagonal. Correlations among bins are shown in the upper triangular [green]
area for $p_{T}^{c}$ and $p_{T}^{c}$, the far-right triangular [blue] area for
$p_{T}^{b}$ and $p_{T}^{b}$, and the lower-left [orange] area for $p_{T}^{b}$
and $p_{T}^{c}$. (b)-(d) Correlation between charm and bottom yields in two
particular $p_{T}$ bins, along with the marginalized distributions in those
bins. See text for details.

The end result of the Monte Carlo exploration of the parameter space is a set
of probability distributions for each of the 34 model parameters,
corresponding to the value of each bin of the charm and bottom hadron spectra
integrated over all rapidities, including the correlations among them, as
depicted in Fig. 13(a). The diagonal of the triangle shows the marginal
probability distribution for each of the 17 bins of the charm and bottom
hadron spectra. Correlations among bins are shown in the upper triangular
[green] area for $p_{T}^{c}$ and $p_{T}^{c}$, the far-right triangular [blue]
area for $p_{T}^{b}$ and $p_{T}^{b}$, and the lower-left square [orange] area
for $p_{T}^{b}$ and $p_{T}^{c}$. Panels Fig. 13(b) and (d) show the marginal
distributions in detail for charm and bottom hadrons in two selected $p_{T}$
bins. We select the parameter that maximizes the marginal distributions as the
desired value of the spectrum at each bin; the 16th and 84th quantiles of the
distribution are taken as the 1$\sigma$ uncertainty associated with the point
estimate, as indicated by the dotted lines.

Panel Fig. 13(c) shows the joint probability distribution of the charm and
bottom hadron yields for the $p_{T}$ bins in Fig. 13(b) and (d). The shape of
the distribution indicates the existence of a strong negative correlation
between the yields in the bins at hand. It is possible to see that the bins
are largely uncorrelated, except for intermediate $p_{T}^{b}$ and $p_{T}^{c}$,
where a strong negative correlation exists due to the yields being similar in
this kinematic region. For the correlations among bins in the same hadron
spectrum, a very strong positive correlation is seen among neighboring $p_{T}$
bins owing to the smoothness requirement on the unfolded spectra, which is
imposed via regularization.

Figure 14: Inclusive heavy-flavor-electron invariant yield from the refolded
charm and bottom yields (closed squares [red]) compared to published data
(closed circles [gray]). Individual refolded spectra from charm and bottom are
shown in green and blue, respectively. Figure 15: DCAT distribution of
electron candidates in various $p_{T}$ bins, along with the contribution from
total background electrons (brown) and the refolded electrons from charm
(green) and bottom (blue) hadron decays. The sum of these three components is
shown in red, and the ratio with the data is shown in the bottom panels. The
shaded gray areas indicate the region over which the DCAT provides constraints
for the unfolding procedure.

The unfolded yield of charm and bottom hadrons can be tested for consistency
with the inputs provided, namely the spectrum and DCAT distributions of
inclusive heavy-flavor electrons, by applying the decay matrices to the
unfolded result. Figure 14 shows the so-called ‘refolded’ spectra of charm
(bottom) electrons in green (blue), along with their sum, in red. The refolded
inclusive spectrum compares very well with the published spectrum, as shown by
the ratio plot in the bottom panel. Similarly, Fig. 15 shows, for every
electron $p_{T}$ bin, the refolded inclusive electron DCAT distributions, its
charm and bottom components, and the total background DCAT, obtained as
discussed in section III.3. The ratio plots in the bottom panel demonstrate an
excellent agreement with the DCAT of measured electrons. The shaded gray
region indicates the range over which the DCAT is used in the unfolding
procedure. Notice that bottom electrons have a broader DCAT than those from
charm, as expected.

##  IV Systematic Uncertainties

The unfolding procedure, as described in section III.4, takes the measured
electron DCAT distributions and published electron spectrum as inputs, along
with their corresponding statistical uncertainties, which are propagated to
the final result. However, additional sources of systematic uncertainty must
be taken into account. Namely, we identify the following as the most
significant:

  1. 1.

the normalization of individual sources in the background electron cocktail;

  2. 2.

the systematic uncertainty on the inclusive heavy-flavor electron spectrum;

  3. 3.

the choice of the regularization parameter strength $\alpha$ in the unfolding
procedure; and

  4. 4.

the choice of prior used in the unfolding.

The uncertainty associated with the normalization of individual electron
background components originates from the parameterization of the associated
primary particle spectrum. Each spectrum is repeatedly deformed randomly
within the extent of its own statistical and systematic uncertainties, with a
new parameterization being obtained at every iteration. The RMS value of all
parameterizations is then taken as the associated systematic uncertainty. In
this manner, a systematic uncertainty will exist for every background electron
source in the cocktail. Their combined effect on the unfolded result is
estimated by running the unfolding procedure for every combination of
individual background normalizations, raised and lowered by their associated
parameterization uncertainty.

To estimate the $p_{T}$-correlated systematic uncertainties associated with
the inclusive heavy-flavor-electron spectrum, we deform the shape of the
spectrum by tilting and kinking the curve about two pivot points, at
$p_{T}=2.5$ GeV/$c$ and $p_{T}=5.0$ GeV/$c$. The choice of these points is
motivated by specific features of the previous analysis which produced the
inclusive heavy-flavor-electron spectrum Adare  _et al._ (2011a), related to
the method of background subtraction. Tilting refers to a rotation of the
spectrum about one of the two pivots, such that the first and last points go
up and down, respectively, by a fraction of their systematic uncertainty. The
kinking of the spectrum introduces a deformation whereby the spectrum takes on
a “v” shape at the pivots. This procedure resulted in 8 variations of the
spectrum. The ones that resulted in the largest deviation from the nominal
unfolded result were taken as the associated systematic uncertainty.

Section III.4 described how the optimal value of the regularization strength
$\alpha$ maximizes the total log-likelihood of the unfolded solution. An
uncertainty on this value is determined by finding the values of $\alpha$
around the maximum which lead to a decrease of the log-likelihood by half a
unit, effectively corresponding to a 1$\sigma$ uncertainty. The deviations of
the unfold result obtained with these values ($\alpha=0.71$ and
$\alpha=1.55$), relative to the nominal result when using the optimal
parameter, define the extent of the associated systematic uncertainty.

Finally, a systematic uncertainty is associated with the choice of
$\bm{\theta}_{{\rm prior}}$. The magnitude of this uncertainty is estimated by
selecting a different prior and evaluating the change in the unfold result. In
particular, the heavy-flavor-hadron yields obtained with pythia were scaled by
a modified blast wave calculation, as described in Ref. Adare  _et al._
(2014). Because a feature of Markov chains, such as the one used in this
analysis, is that the probability of reaching a given state is independent of
the starting point, the sensitivity to the initial choice of prior is expected
to be minimal after a sufficient number of iterations.

Figure 16: Fractional uncertainty on the bottom electron fraction, defined as
$1\pm$ the relative uncertainty of each source.

Figure 16 shows the relative contribution of each source of uncertainty as a
function of $p_{T}$, to the unfolded fraction of electrons from bottom decays.
The most significant contribution comes from the unfold uncertainty, which
originates from the statistical uncertainty on the inclusive heavy-flavor
spectrum and DCAT as it is propagated through the unfold procedure. The next
most significant contribution comes from the background electron cocktail and
its normalization, supplying an approximate 10% uncertainty at low $p_{T}$.
The total systematic uncertainty is obtained by adding the contributions of
every source in quadrature.

##  V Results and Discussion

Figure 17 shows the invariant cross section of charm and bottom hadrons
integrated over all rapidity, corresponding to the values that maximize the
probability distribution associated with each hadron $p_{T}$ bin, shown along
the diagonal of Fig. 13. The uncertainties incorporate both the unfolding
uncertainty (which includes the propagation of the total uncertainty in the
inclusive heavy-flavor-electron measurements provided as input) as well as the
systematic uncertainties discussed in section IV. The uncertainty band is
narrowest in the region where electron DCAT measurements provide constraint to
the unfold procedure, namely $1.5<p_{T}{\rm[GeV/}c]<6.0$. As presented, the
hadron cross section is integrated over rapidity by construction, following
directly from the procedure used to populate the decay matrices used in the
unfolding procedure. Namely, hadrons simulated in pythia at all rapidities are
allowed to decay, recording only the probability of producing an electron
within $|\eta|<0.35$. It thus follows that the cross sections in Fig. 17
depend on the hadron rapidity distribution implemented in the pythia
generator. This model dependence implies an associated uncertainty which has
not been evaluated since, as previously mentioned, this would be
computationally prohibitive. Furthermore, the model dependence is reduced when
applying the decay matrix to arrive at results in electron space.

Figure 17: Unfolded charm and bottom hadron yields in bins of of transverse
momentum. The yields are integrated over all rapidities, and the error bars
depict the combined statistical and systematic uncertainties.

To compare the unfolded differential hadron cross sections to existing
measurements, we use the pythia generator to calculate the ratio of open
heavy-flavor hadrons of a given species at midrapidity relative to inclusive-
hadron production as a function of $p_{T}$. In this manner, the unfolded yield
of $D^{0}$ mesons within $|y|<1$ can be compared to a measurement by the STAR
collaboration Adamczyk  _et al._ (2012) obtained by fully reconstructing the
hadron decays, as shown in Fig. 18. The unfolded $D^{0}$ yield is fit with a
modified Hagedorn function, with the ratio of data relative to the fit being
shown in the bottom panel. Good agreement with results published by STAR is
observed within uncertainties.

Figure 18: Unfolded differential cross section of $D^{0}$ mesons at
midrapidity $|y|<1$, compared to a corresponding measurement by the STAR
experiment Adamczyk  _et al._ (2014) obtained by direct reconstruction of the
hadron decays.

The model dependence of the unfolded charm and bottom cross sections can be
reduced by applying the decay model—that is, multiplying the hadron cross
sections by the decay matrices—to obtain the refolded cross section of heavy-
flavor-decay electrons in the PHENIX central arm acceptance. The result can be
normalized to obtain the fully invariant differential cross sections shown in
Fig. 19, where the $b\rightarrow e$ curve has been scaled down by a factor of
100 for ease of visualization. Also shown are FONLL222We used the current
default parameters with CTEQ6.6 PDFs. Central values: $m_{b}=4.75$ GeV,
$m_{c}=1.5$ GeV,
$\mu_{\mathrm{R}}=\mu_{\mathrm{F}}=\mu_{0}=\sqrt{\mathrm{m}^{2}+p_{T}^{2}}$.
Scales uncertainties: $\mu_{0}/2<\mu_{\mathrm{R}}$,
$\mu_{\mathrm{F}}<2\mu_{0}$ with $1/2<\mu_{\mathrm{R}}/\mu_{\mathrm{F}}<2$.
Mass uncertainties: $m_{b}=4.5$, 5.0 GeV, $m_{c}=1.3$, 1.7 GeV, summed in
quadrature to scales uncertainties. PDFs uncertainties are calculated
according to the individual PDF set recipe, and summed in quadrature to scales
and mass uncertainties. Branching ratios: BR(D$\rightarrow$l)=0.103,
BR(B$\rightarrow$l)=0.1086, BR(B$\rightarrow$D$\rightarrow$l)=0.096,
BR(B$\rightarrow$D)=0.823, BR(B$\rightarrow$D*)=0.173,
BR(B${\rightarrow}J/\psi$)=0.0116, and BR(B${\rightarrow}\psi(2S)$)=0.00307.
pQCD calculations Cacciari  _et al._ (2005), which are in reasonable agreement
with both charm and bottom cross sections within uncertainties. The large
uncertainties in FONLL are driven by variations in the factorization and
renormalization scales, as well as uncertainties in the heavy quark masses and
the PDFs used. The central FONLL curves in Fig. 19 correspond to the total
cross sections for charm and bottom of $\sigma_{c}(\rm FONLL)=242~{}\mu$b and
$\sigma_{b}(\rm FONLL)=1.80~{}\mu$b. Notice that, unlike the rapidity-
integrated hadron observables in Figs. 17 and 18, the electron spectra in Fig.
19 are reported at midrapidity by construction, following from the definition
of the decay matrix. Like other heavy-flavor measurements at RHIC, the results
presented are higher than the FONLL calculation. However, it is notable that
the agreement with the central FONLL prediction improves at high $p_{T}$,
where the effects of the quark mass in the calculation become less
significant.

Figure 19: Refolded spectra of electrons at midrapidity from charm and bottom
decays, compared to FONLL calculations Cacciari  _et al._ (2005). The bottom
electron spectrum has been scaled down by a factor of 100 for easier
comparison. Figure 20: Fraction of bottom electrons obtained with the
unfolding procedure (red), compared to a pQCD FONLL calculation (gray)
Cacciari  _et al._ (2005), with uncertainties arising from the quark masses
and regularization scales. Figure 21: Fraction of bottom electrons obtained
with the unfolding procedure (red), compared to previous measurements by
PHENIX Adare  _et al._ (2009b) and STAR Aggarwal  _et al._ (2010) using
electron-hadron correlations. Also shown are theory comparisons to a pQCD
FONLL calculation Cacciari  _et al._ (2005).

The ratio of electrons from bottom to inclusive heavy-flavor decays,
$b\rightarrow e/(c\rightarrow e{\rm}+{\rm}b\rightarrow e)$, can be constructed
from the electron cross sections, and is shown in Fig. 20. In this
measurement, the electrons from the feed-down decay $b\rightarrow c\rightarrow
e$ are considered part of the bottom electron sample. The contribution of
bottom decays to the inclusive electron sample is seen to increase sharply
with $p_{T}$, coming to dominate over that of charm quarks above $p_{T}\approx
4$ GeV/$c$. The solid gray line corresponds to the FONLL calculation, with its
uncertainty depicted by dashed gray lines. The measured bottom electron
fraction is observed to be consistent with the FONLL calculation within
uncertainties. In particular, good agreement with the central FONLL value is
seen below $p_{T}\approx 3$ GeV/$c$, with the measured fraction rising
slightly above that at higher $p_{T}$.

Figure 21 shows a comparison of the unfolded bottom electron fraction with
earlier measurements made by the STAR Aggarwal  _et al._ (2010) and PHENIX
Adare  _et al._ (2009b) collaborations using electron-hadron and electron-$D$
correlations. It is apparent that the size of the dataset, combined with the
unfolding method used in the present analysis provides a result with smaller
total uncertainty and significantly extended kinematic reach at low $p_{T}$.
Furthermore, the unfolded result provides a more direct determination of the
bottom electron fraction since—unlike the earlier measurements—it does not
depend on model-dependent pythia templates of event kinematics to describe the
shape of electron-hadron correlations.

The previous PHENIX electron-hadron results, plotted with blue markers, are in
good agreement with the new unfolded measurement. Similarly, the STAR
measurement—while systematically lower—is also consistent with the unfolded
bottom fraction on account of its large combined statistical and systematic
uncertainties. The degree of agreement between these two measurements was
quantified by calculating—under the null hypothesis that the two results are
equal—the probability of obtaining a difference more extreme than that
currently observed between the measurements. The resulting $p$-value using a
two-sample chi-square statistic is found to be 0.15, indicating that the null
hypothesis cannot be rejected. In short, both the unfold and the STAR bottom
fraction measurements are consistent given the uncertainties.

##  VI Summary

We have reported on a new measurement of the differential-invariant production
cross section of separated-heavy-flavor electrons in $p$$+$$p$ collisions at
$\sqrt{s}=200$ GeV, at midrapidity $|\eta|<0.35$ and within
$1.0<p_{T}^{(e)}<9.0$ GeV/$c$. The measurement proceeds via an unfolding
analysis where the yield of open-heavy-flavor hadrons is inferred from the
inclusive-heavy-flavor electron spectrum, and the electron DCAT distribution
measured with the PHENIX silicon-vertex detector. The individual yields of
charm and bottom electrons, as well as the bottom electron fraction, are found
to be consistent with FONLL calculations. This measurement will provide a
precision baseline for future-heavy-flavor-separation analyses. In particular,
forthcoming PHENIX results using a high-statistics Au$+$Au dataset promise to
reduce current uncertainties and shed light on the centrality dependence of
charm and bottom suppression.

###### Acknowledgements.

We thank the staff of the Collider-Accelerator and Physics Departments at
Brookhaven National Laboratory and the staff of the other PHENIX participating
institutions for their vital contributions. We acknowledge support from the
Office of Nuclear Physics in the Office of Science of the Department of
Energy, the National Science Foundation, Abilene Christian University Research
Council, Research Foundation of SUNY, and Dean of the College of Arts and
Sciences, Vanderbilt University (U.S.A), Ministry of Education, Culture,
Sports, Science, and Technology and the Japan Society for the Promotion of
Science (Japan), Conselho Nacional de Desenvolvimento Científico e Tecnológico
and Fundação de Amparo à Pesquisa do Estado de São Paulo (Brazil), Natural
Science Foundation of China (People’s Republic of China), Croatian Science
Foundation and Ministry of Science and Education (Croatia), Ministry of
Education, Youth and Sports (Czech Republic), Centre National de la Recherche
Scientifique, Commissariat à l’Énergie Atomique, and Institut National de
Physique Nucléaire et de Physique des Particules (France), Bundesministerium
für Bildung und Forschung, Deutscher Akademischer Austausch Dienst, and
Alexander von Humboldt Stiftung (Germany), J. Bolyai Research Scholarship,
EFOP, the New National Excellence Program (ÚNKP), NKFIH, and OTKA (Hungary),
Department of Atomic Energy and Department of Science and Technology (India),
Israel Science Foundation (Israel), Basic Science Research and SRC(CENuM)
Programs through NRF funded by the Ministry of Education and the Ministry of
Science and ICT (Korea). Physics Department, Lahore University of Management
Sciences (Pakistan), Ministry of Education and Science, Russian Academy of
Sciences, Federal Agency of Atomic Energy (Russia), VR and Wallenberg
Foundation (Sweden), the U.S. Civilian Research and Development Foundation for
the Independent States of the Former Soviet Union, the Hungarian American
Enterprise Scholarship Fund, the US-Hungarian Fulbright Foundation, and the
US-Israel Binational Science Foundation.

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