BELLE2-CONF-PH-2021-008

Belle II Collaboration

#
Study of $B\rightarrow D^{(*)}h$ decays using $62.8~{}\mathrm{fb}^{-1}$ of
Belle II data

F. Abudinén  INFN Sezione di Trieste, I-34127 Trieste, Italy  I. Adachi  High
Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan  The
Graduate University for Advanced Studies (SOKENDAI), Hayama 240-0193, Japan
R. Adak  Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and
Institute of Modern Physics, Fudan University, Shanghai 200443, China  K.
Adamczyk  H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342,
Poland  P. Ahlburg  University of Bonn, 53115 Bonn, Germany  J. K. Ahn  Korea
University, Seoul 02841, South Korea  H. Aihara  Department of Physics,
University of Tokyo, Tokyo 113-0033, Japan  N. Akopov  Alikhanyan National
Science Laboratory, Yerevan 0036, Armenia  A. Aloisio  Dipartimento di Scienze
Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy  INFN Sezione
di Napoli, I-80126 Napoli, Italy  F. Ameli  INFN Sezione di Roma, I-00185
Roma, Italy  L. Andricek  Semiconductor Laboratory of the Max Planck Society,
81739 München, Germany  N. Anh Ky  Institute of Physics, Vietnam Academy of
Science and Technology (VAST), Hanoi, Vietnam  Duy Tan University, Hanoi
100000, Vietnam  D. M. Asner  Brookhaven National Laboratory, Upton, New York
11973, U.S.A.  H. Atmacan  University of Cincinnati, Cincinnati, Ohio 45221,
U.S.A.  V. Aulchenko  Budker Institute of Nuclear Physics SB RAS, Novosibirsk
630090, Russian Federation  Novosibirsk State University, Novosibirsk 630090,
Russian Federation  T. Aushev  Higher School of Economics (HSE), Moscow
101000, Russian Federation  V. Aushev  Taras Shevchenko National Univ. of
Kiev, Kiev, Ukraine  T. Aziz  Tata Institute of Fundamental Research, Mumbai
400005, India  V. Babu  Deutsches Elektronen–Synchrotron, 22607 Hamburg,
Germany  S. Bacher  H. Niewodniczanski Institute of Nuclear Physics, Krakow
31-342, Poland  S. Baehr  Institut für Experimentelle Teilchenphysik,
Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany  S. Bahinipati
Indian Institute of Technology Bhubaneswar, Satya Nagar 751007, India  A. M.
Bakich  School of Physics, University of Sydney, New South Wales 2006,
Australia  P. Bambade  Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405
Orsay, France  Sw. Banerjee  University of Louisville, Louisville, Kentucky
40292, U.S.A.  S. Bansal  Panjab University, Chandigarh 160014, India  M.
Barrett  High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan  G. Batignani  Dipartimento di Fisica, Università di Pisa,
I-56127 Pisa, Italy  INFN Sezione di Pisa, I-56127 Pisa, Italy  J. Baudot
Université de Strasbourg, CNRS, IPHC, UMR 7178, 67037 Strasbourg, France  A.
Beaulieu  University of Victoria, Victoria, British Columbia, V8W 3P6, Canada
J. Becker  Institut für Experimentelle Teilchenphysik, Karlsruher Institut für
Technologie, 76131 Karlsruhe, Germany  P. K. Behera  Indian Institute of
Technology Madras, Chennai 600036, India  M. Bender  Ludwig Maximilians
University, 80539 Munich, Germany  J. V. Bennett  University of Mississippi,
University, Mississippi 38677, U.S.A.  E. Bernieri  INFN Sezione di Roma Tre,
I-00146 Roma, Italy  F. U. Bernlochner  University of Bonn, 53115 Bonn,
Germany  M. Bertemes  Institute of High Energy Physics, Vienna 1050, Austria
E. Bertholet  Tel Aviv University, School of Physics and Astronomy, Tel Aviv,
69978, Israel  M. Bessner  University of Hawaii, Honolulu, Hawaii 96822,
U.S.A.  S. Bettarini  Dipartimento di Fisica, Università di Pisa, I-56127
Pisa, Italy  INFN Sezione di Pisa, I-56127 Pisa, Italy  V. Bhardwaj  Indian
Institute of Science Education and Research Mohali, SAS Nagar, 140306, India
B. Bhuyan  Indian Institute of Technology Guwahati, Assam 781039, India  F.
Bianchi  Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
INFN Sezione di Torino, I-10125 Torino, Italy  T. Bilka  Faculty of
Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic  S.
Bilokin  Ludwig Maximilians University, 80539 Munich, Germany  D. Biswas
University of Louisville, Louisville, Kentucky 40292, U.S.A.  A. Bobrov
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russian
Federation  Novosibirsk State University, Novosibirsk 630090, Russian
Federation  A. Bondar  Budker Institute of Nuclear Physics SB RAS, Novosibirsk
630090, Russian Federation  Novosibirsk State University, Novosibirsk 630090,
Russian Federation  G. Bonvicini  Wayne State University, Detroit, Michigan
48202, U.S.A.  A. Bozek  H. Niewodniczanski Institute of Nuclear Physics,
Krakow 31-342, Poland  M. Bračko  University of Maribor, 2000 Maribor,
Slovenia  J. Stefan Institute, 1000 Ljubljana, Slovenia  P. Branchini  INFN
Sezione di Roma Tre, I-00146 Roma, Italy  N. Braun  Institut für
Experimentelle Teilchenphysik, Karlsruher Institut für Technologie, 76131
Karlsruhe, Germany  R. A. Briere  Carnegie Mellon University, Pittsburgh,
Pennsylvania 15213, U.S.A.  T. E. Browder  University of Hawaii, Honolulu,
Hawaii 96822, U.S.A.  D. N. Brown  University of Louisville, Louisville,
Kentucky 40292, U.S.A.  A. Budano  INFN Sezione di Roma Tre, I-00146 Roma,
Italy  L. Burmistrov  Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405
Orsay, France  S. Bussino  Dipartimento di Matematica e Fisica, Università di
Roma Tre, I-00146 Roma, Italy  INFN Sezione di Roma Tre, I-00146 Roma, Italy
M. Campajola  Dipartimento di Scienze Fisiche, Università di Napoli Federico
II, I-80126 Napoli, Italy  INFN Sezione di Napoli, I-80126 Napoli, Italy  L.
Cao  University of Bonn, 53115 Bonn, Germany  G. Caria  School of Physics,
University of Melbourne, Victoria 3010, Australia  G. Casarosa  Dipartimento
di Fisica, Università di Pisa, I-56127 Pisa, Italy  INFN Sezione di Pisa,
I-56127 Pisa, Italy  C. Cecchi  Dipartimento di Fisica, Università di Perugia,
I-06123 Perugia, Italy  INFN Sezione di Perugia, I-06123 Perugia, Italy  D.
Červenkov  Faculty of Mathematics and Physics, Charles University, 121 16
Prague, Czech Republic  M.-C. Chang  Department of Physics, Fu Jen Catholic
University, Taipei 24205, Taiwan  P. Chang  Department of Physics, National
Taiwan University, Taipei 10617, Taiwan  R. Cheaib  Deutsches
Elektronen–Synchrotron, 22607 Hamburg, Germany  V. Chekelian  Max-Planck-
Institut für Physik, 80805 München, Germany  C. Chen  Iowa State University,
Ames, Iowa 50011, U.S.A.  Y. Q. Chen  University of Science and Technology of
China, Hefei 230026, China  Y.-T. Chen  Department of Physics, National Taiwan
University, Taipei 10617, Taiwan  B. G. Cheon  Department of Physics and
Institute of Natural Sciences, Hanyang University, Seoul 04763, South Korea
K. Chilikin  P.N. Lebedev Physical Institute of the Russian Academy of
Sciences, Moscow 119991, Russian Federation  K. Chirapatpimol  Chiang Mai
University, Chiang Mai 50202, Thailand  H.-E. Cho  Department of Physics and
Institute of Natural Sciences, Hanyang University, Seoul 04763, South Korea
K. Cho  Korea Institute of Science and Technology Information, Daejeon 34141,
South Korea  S.-J. Cho  Yonsei University, Seoul 03722, South Korea  S.-K.
Choi  Gyeongsang National University, Jinju 52828, South Korea  S. Choudhury
Indian Institute of Technology Hyderabad, Telangana 502285, India  D. Cinabro
Wayne State University, Detroit, Michigan 48202, U.S.A.  L. Corona
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy  INFN Sezione
di Pisa, I-56127 Pisa, Italy  L. M. Cremaldi  University of Mississippi,
University, Mississippi 38677, U.S.A.  D. Cuesta  Université de Strasbourg,
CNRS, IPHC, UMR 7178, 67037 Strasbourg, France  S. Cunliffe  Deutsches
Elektronen–Synchrotron, 22607 Hamburg, Germany  T. Czank  Kavli Institute for
the Physics and Mathematics of the Universe (WPI), University of Tokyo,
Kashiwa 277-8583, Japan  N. Dash  Indian Institute of Technology Madras,
Chennai 600036, India  F. Dattola  Deutsches Elektronen–Synchrotron, 22607
Hamburg, Germany  E. De La Cruz-Burelo  Centro de Investigacion y de Estudios
Avanzados del Instituto Politecnico Nacional, Mexico City 07360, Mexico  G. de
Marino  Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France  G.
De Nardo  Dipartimento di Scienze Fisiche, Università di Napoli Federico II,
I-80126 Napoli, Italy  INFN Sezione di Napoli, I-80126 Napoli, Italy  M. De
Nuccio  Deutsches Elektronen–Synchrotron, 22607 Hamburg, Germany  G. De Pietro
INFN Sezione di Roma Tre, I-00146 Roma, Italy  R. de Sangro  INFN Laboratori
Nazionali di Frascati, I-00044 Frascati, Italy  B. Deschamps  University of
Bonn, 53115 Bonn, Germany  M. Destefanis  Dipartimento di Fisica, Università
di Torino, I-10125 Torino, Italy  INFN Sezione di Torino, I-10125 Torino,
Italy  S. Dey  Tel Aviv University, School of Physics and Astronomy, Tel Aviv,
69978, Israel  A. De Yta-Hernandez  Centro de Investigacion y de Estudios
Avanzados del Instituto Politecnico Nacional, Mexico City 07360, Mexico  A. Di
Canto  Brookhaven National Laboratory, Upton, New York 11973, U.S.A.  F. Di
Capua  Dipartimento di Scienze Fisiche, Università di Napoli Federico II,
I-80126 Napoli, Italy  INFN Sezione di Napoli, I-80126 Napoli, Italy  S. Di
Carlo  Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France  J.
Dingfelder  University of Bonn, 53115 Bonn, Germany  Z. Doležal  Faculty of
Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic  I.
Domínguez Jiménez  Universidad Autonoma de Sinaloa, Sinaloa 80000, Mexico  T.
V. Dong  Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and
Institute of Modern Physics, Fudan University, Shanghai 200443, China  K. Dort
Justus-Liebig-Universität Gießen, 35392 Gießen, Germany  D. Dossett  School of
Physics, University of Melbourne, Victoria 3010, Australia  S. Dubey
University of Hawaii, Honolulu, Hawaii 96822, U.S.A.  S. Duell  University of
Bonn, 53115 Bonn, Germany  G. Dujany  Université de Strasbourg, CNRS, IPHC,
UMR 7178, 67037 Strasbourg, France  S. Eidelman  Budker Institute of Nuclear
Physics SB RAS, Novosibirsk 630090, Russian Federation  P.N. Lebedev Physical
Institute of the Russian Academy of Sciences, Moscow 119991, Russian
Federation  Novosibirsk State University, Novosibirsk 630090, Russian
Federation  M. Eliachevitch  University of Bonn, 53115 Bonn, Germany  D.
Epifanov  Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090,
Russian Federation  Novosibirsk State University, Novosibirsk 630090, Russian
Federation  J. E. Fast  Pacific Northwest National Laboratory, Richland,
Washington 99352, U.S.A.  T. Ferber  Deutsches Elektronen–Synchrotron, 22607
Hamburg, Germany  D. Ferlewicz  School of Physics, University of Melbourne,
Victoria 3010, Australia  T. Fillinger  Université de Strasbourg, CNRS, IPHC,
UMR 7178, 67037 Strasbourg, France  G. Finocchiaro  INFN Laboratori Nazionali
di Frascati, I-00044 Frascati, Italy  S. Fiore  INFN Sezione di Roma, I-00185
Roma, Italy  P. Fischer  University of Heidelberg, 68131 Mannheim, Germany  A.
Fodor  McGill University, Montréal, Québec, H3A 2T8, Canada  F. Forti
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy  INFN Sezione
di Pisa, I-56127 Pisa, Italy  A. Frey  II. Physikalisches Institut, Georg-
August-Universität Göttingen, 37073 Göttingen, Germany  M. Friedl  Institute
of High Energy Physics, Vienna 1050, Austria  B. G. Fulsom  Pacific Northwest
National Laboratory, Richland, Washington 99352, U.S.A.  M. Gabriel  Max-
Planck-Institut für Physik, 80805 München, Germany  N. Gabyshev  Budker
Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russian Federation
Novosibirsk State University, Novosibirsk 630090, Russian Federation  E.
Ganiev  Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
INFN Sezione di Trieste, I-34127 Trieste, Italy  M. Garcia-Hernandez  Centro
de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional,
Mexico City 07360, Mexico  R. Garg  Panjab University, Chandigarh 160014,
India  A. Garmash  Budker Institute of Nuclear Physics SB RAS, Novosibirsk
630090, Russian Federation  Novosibirsk State University, Novosibirsk 630090,
Russian Federation  V. Gaur  Virginia Polytechnic Institute and State
University, Blacksburg, Virginia 24061, U.S.A.  A. Gaz  Dipartimento di Fisica
e Astronomia, Università di Padova, I-35131 Padova, Italy  INFN Sezione di
Padova, I-35131 Padova, Italy  U. Gebauer  II. Physikalisches Institut, Georg-
August-Universität Göttingen, 37073 Göttingen, Germany  M. Gelb  Institut für
Experimentelle Teilchenphysik, Karlsruher Institut für Technologie, 76131
Karlsruhe, Germany  A. Gellrich  Deutsches Elektronen–Synchrotron, 22607
Hamburg, Germany  J. Gemmler  Institut für Experimentelle Teilchenphysik,
Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany  T. Geßler
Justus-Liebig-Universität Gießen, 35392 Gießen, Germany  D. Getzkow  Justus-
Liebig-Universität Gießen, 35392 Gießen, Germany  R. Giordano  Dipartimento di
Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy  INFN
Sezione di Napoli, I-80126 Napoli, Italy  A. Giri  Indian Institute of
Technology Hyderabad, Telangana 502285, India  A. Glazov  Deutsches
Elektronen–Synchrotron, 22607 Hamburg, Germany  B. Gobbo  INFN Sezione di
Trieste, I-34127 Trieste, Italy  R. Godang  University of South Alabama,
Mobile, Alabama 36688, U.S.A.  P. Goldenzweig  Institut für Experimentelle
Teilchenphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
B. Golob  Faculty of Mathematics and Physics, University of Ljubljana, 1000
Ljubljana, Slovenia  J. Stefan Institute, 1000 Ljubljana, Slovenia  P. Gomis
Instituto de Fisica Corpuscular, Paterna 46980, Spain  P. Grace  Department of
Physics, University of Adelaide, Adelaide, South Australia 5005, Australia  W.
Gradl  Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099
Mainz, Germany  E. Graziani  INFN Sezione di Roma Tre, I-00146 Roma, Italy  D.
Greenwald  Department of Physics, Technische Universität München, 85748
Garching, Germany  Y. Guan  University of Cincinnati, Cincinnati, Ohio 45221,
U.S.A.  K. Gudkova  Budker Institute of Nuclear Physics SB RAS, Novosibirsk
630090, Russian Federation  Novosibirsk State University, Novosibirsk 630090,
Russian Federation  C. Hadjivasiliou  Pacific Northwest National Laboratory,
Richland, Washington 99352, U.S.A.  S. Halder  Tata Institute of Fundamental
Research, Mumbai 400005, India  K. Hara  High Energy Accelerator Research
Organization (KEK), Tsukuba 305-0801, Japan  The Graduate University for
Advanced Studies (SOKENDAI), Hayama 240-0193, Japan  T. Hara  High Energy
Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan  The Graduate
University for Advanced Studies (SOKENDAI), Hayama 240-0193, Japan  O.
Hartbrich  University of Hawaii, Honolulu, Hawaii 96822, U.S.A.  K. Hayasaka
Niigata University, Niigata 950-2181, Japan  H. Hayashii  Nara Women’s
University, Nara 630-8506, Japan  S. Hazra  Tata Institute of Fundamental
Research, Mumbai 400005, India  C. Hearty  University of British Columbia,
Vancouver, British Columbia, V6T 1Z1, Canada  Institute of Particle Physics
(Canada), Victoria, British Columbia V8W 2Y2, Canada  M. T. Hedges  University
of Hawaii, Honolulu, Hawaii 96822, U.S.A.  I. Heredia de la Cruz  Centro de
Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional,
Mexico City 07360, Mexico  Consejo Nacional de Ciencia y Tecnología, Mexico
City 03940, Mexico  M. Hernández Villanueva  University of Mississippi,
University, Mississippi 38677, U.S.A.  A. Hershenhorn  University of British
Columbia, Vancouver, British Columbia, V6T 1Z1, Canada  T. Higuchi  Kavli
Institute for the Physics and Mathematics of the Universe (WPI), University of
Tokyo, Kashiwa 277-8583, Japan  E. C. Hill  University of British Columbia,
Vancouver, British Columbia, V6T 1Z1, Canada  H. Hirata  Graduate School of
Science, Nagoya University, Nagoya 464-8602, Japan  M. Hoek  Johannes
Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
M. Hohmann  School of Physics, University of Melbourne, Victoria 3010,
Australia  S. Hollitt  Department of Physics, University of Adelaide,
Adelaide, South Australia 5005, Australia  T. Hotta  Research Center for
Nuclear Physics, Osaka University, Osaka 567-0047, Japan  C.-L. Hsu  School of
Physics, University of Sydney, New South Wales 2006, Australia  Y. Hu
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049,
China  K. Huang  Department of Physics, National Taiwan University, Taipei
10617, Taiwan  T. Humair  Max-Planck-Institut für Physik, 80805 München,
Germany  T. Iijima  Graduate School of Science, Nagoya University, Nagoya
464-8602, Japan  Kobayashi-Maskawa Institute, Nagoya University, Nagoya
464-8602, Japan  K. Inami  Graduate School of Science, Nagoya University,
Nagoya 464-8602, Japan  G. Inguglia  Institute of High Energy Physics, Vienna
1050, Austria  J. Irakkathil Jabbar  Institut für Experimentelle
Teilchenphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
A. Ishikawa  High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan  The Graduate University for Advanced Studies (SOKENDAI),
Hayama 240-0193, Japan  R. Itoh  High Energy Accelerator Research Organization
(KEK), Tsukuba 305-0801, Japan  The Graduate University for Advanced Studies
(SOKENDAI), Hayama 240-0193, Japan  M. Iwasaki  Osaka City University, Osaka
558-8585, Japan  Y. Iwasaki  High Energy Accelerator Research Organization
(KEK), Tsukuba 305-0801, Japan  S. Iwata  Tokyo Metropolitan University, Tokyo
192-0397, Japan  P. Jackson  Department of Physics, University of Adelaide,
Adelaide, South Australia 5005, Australia  W. W. Jacobs  Indiana University,
Bloomington, Indiana 47408, U.S.A.  I. Jaegle  University of Florida,
Gainesville, Florida 32611, U.S.A.  D. E. Jaffe  Brookhaven National
Laboratory, Upton, New York 11973, U.S.A.  E.-J. Jang  Gyeongsang National
University, Jinju 52828, South Korea  M. Jeandron  University of Mississippi,
University, Mississippi 38677, U.S.A.  H. B. Jeon  Kyungpook National
University, Daegu 41566, South Korea  S. Jia  Key Laboratory of Nuclear
Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan
University, Shanghai 200443, China  Y. Jin  INFN Sezione di Trieste, I-34127
Trieste, Italy  C. Joo  Kavli Institute for the Physics and Mathematics of the
Universe (WPI), University of Tokyo, Kashiwa 277-8583, Japan  K. K. Joo
Chonnam National University, Gwangju 61186, South Korea  H. Junkerkalefeld
University of Bonn, 53115 Bonn, Germany  I. Kadenko  Taras Shevchenko National
Univ. of Kiev, Kiev, Ukraine  J. Kahn  Institut für Experimentelle
Teilchenphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
H. Kakuno  Tokyo Metropolitan University, Tokyo 192-0397, Japan  A. B. Kaliyar
Tata Institute of Fundamental Research, Mumbai 400005, India  J. Kandra
Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech
Republic  K. H. Kang  Kyungpook National University, Daegu 41566, South Korea
P. Kapusta  H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342,
Poland  R. Karl  Deutsches Elektronen–Synchrotron, 22607 Hamburg, Germany  G.
Karyan  Alikhanyan National Science Laboratory, Yerevan 0036, Armenia  Y. Kato
Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan
Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602, Japan  H.
Kawai  Chiba University, Chiba 263-8522, Japan  T. Kawasaki  Kitasato
University, Sagamihara 252-0373, Japan  T. Keck  Institut für Experimentelle
Teilchenphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
C. Ketter  University of Hawaii, Honolulu, Hawaii 96822, U.S.A.  H. Kichimi
High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan
C. Kiesling  Max-Planck-Institut für Physik, 80805 München, Germany  B. H. Kim
Seoul National University, Seoul 08826, South Korea  C.-H. Kim  Department of
Physics and Institute of Natural Sciences, Hanyang University, Seoul 04763,
South Korea  D. Y. Kim  Soongsil University, Seoul 06978, South Korea  H. J.
Kim  Kyungpook National University, Daegu 41566, South Korea  K.-H. Kim
Yonsei University, Seoul 03722, South Korea  K. Kim  Korea University, Seoul
02841, South Korea  S.-H. Kim  Seoul National University, Seoul 08826, South
Korea  Y.-K. Kim  Yonsei University, Seoul 03722, South Korea  Y. Kim  Korea
University, Seoul 02841, South Korea  T. D. Kimmel  Virginia Polytechnic
Institute and State University, Blacksburg, Virginia 24061, U.S.A.  H. Kindo
High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan
The Graduate University for Advanced Studies (SOKENDAI), Hayama 240-0193,
Japan  K. Kinoshita  University of Cincinnati, Cincinnati, Ohio 45221, U.S.A.
B. Kirby  Brookhaven National Laboratory, Upton, New York 11973, U.S.A.  C.
Kleinwort  Deutsches Elektronen–Synchrotron, 22607 Hamburg, Germany  B. Knysh
Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France  P. Kodyš
Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech
Republic  T. Koga  High Energy Accelerator Research Organization (KEK),
Tsukuba 305-0801, Japan  S. Kohani  University of Hawaii, Honolulu, Hawaii
96822, U.S.A.  I. Komarov  Deutsches Elektronen–Synchrotron, 22607 Hamburg,
Germany  T. Konno  Kitasato University, Sagamihara 252-0373, Japan  A. Korobov
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russian
Federation  Novosibirsk State University, Novosibirsk 630090, Russian
Federation  S. Korpar  University of Maribor, 2000 Maribor, Slovenia  J.
Stefan Institute, 1000 Ljubljana, Slovenia  N. Kovalchuk  Deutsches
Elektronen–Synchrotron, 22607 Hamburg, Germany  E. Kovalenko  Budker Institute
of Nuclear Physics SB RAS, Novosibirsk 630090, Russian Federation  Novosibirsk
State University, Novosibirsk 630090, Russian Federation  T. M. G.
Kraetzschmar  Max-Planck-Institut für Physik, 80805 München, Germany  F.
Krinner  Max-Planck-Institut für Physik, 80805 München, Germany  P. Križan
Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana,
Slovenia  J. Stefan Institute, 1000 Ljubljana, Slovenia  R. Kroeger
University of Mississippi, University, Mississippi 38677, U.S.A.  J. F. Krohn
School of Physics, University of Melbourne, Victoria 3010, Australia  P.
Krokovny  Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090,
Russian Federation  Novosibirsk State University, Novosibirsk 630090, Russian
Federation  H. Krüger  University of Bonn, 53115 Bonn, Germany  W. Kuehn
Justus-Liebig-Universität Gießen, 35392 Gießen, Germany  T. Kuhr  Ludwig
Maximilians University, 80539 Munich, Germany  J. Kumar  Carnegie Mellon
University, Pittsburgh, Pennsylvania 15213, U.S.A.  M. Kumar  Malaviya
National Institute of Technology Jaipur, Jaipur 302017, India  R. Kumar
Punjab Agricultural University, Ludhiana 141004, India  K. Kumara  Wayne State
University, Detroit, Michigan 48202, U.S.A.  T. Kumita  Tokyo Metropolitan
University, Tokyo 192-0397, Japan  T. Kunigo  High Energy Accelerator Research
Organization (KEK), Tsukuba 305-0801, Japan  M. Künzel  Deutsches
Elektronen–Synchrotron, 22607 Hamburg, Germany  Ludwig Maximilians University,
80539 Munich, Germany  S. Kurz  Deutsches Elektronen–Synchrotron, 22607
Hamburg, Germany  A. Kuzmin  Budker Institute of Nuclear Physics SB RAS,
Novosibirsk 630090, Russian Federation  Novosibirsk State University,
Novosibirsk 630090, Russian Federation  P. Kvasnička  Faculty of Mathematics
and Physics, Charles University, 121 16 Prague, Czech Republic  Y.-J. Kwon
Yonsei University, Seoul 03722, South Korea  S. Lacaprara  INFN Sezione di
Padova, I-35131 Padova, Italy  Y.-T. Lai  Kavli Institute for the Physics and
Mathematics of the Universe (WPI), University of Tokyo, Kashiwa 277-8583,
Japan  C. La Licata  Kavli Institute for the Physics and Mathematics of the
Universe (WPI), University of Tokyo, Kashiwa 277-8583, Japan  K. Lalwani
Malaviya National Institute of Technology Jaipur, Jaipur 302017, India  L.
Lanceri  INFN Sezione di Trieste, I-34127 Trieste, Italy  J. S. Lange  Justus-
Liebig-Universität Gießen, 35392 Gießen, Germany  M. Laurenza  Dipartimento di
Matematica e Fisica, Università di Roma Tre, I-00146 Roma, Italy  INFN Sezione
di Roma Tre, I-00146 Roma, Italy  K. Lautenbach  Justus-Liebig-Universität
Gießen, 35392 Gießen, Germany  P. J. Laycock  Brookhaven National Laboratory,
Upton, New York 11973, U.S.A.  F. R. Le Diberder  Université Paris-Saclay,
CNRS/IN2P3, IJCLab, 91405 Orsay, France  I.-S. Lee  Department of Physics and
Institute of Natural Sciences, Hanyang University, Seoul 04763, South Korea
S. C. Lee  Kyungpook National University, Daegu 41566, South Korea  P. Leitl
Max-Planck-Institut für Physik, 80805 München, Germany  D. Levit  Department
of Physics, Technische Universität München, 85748 Garching, Germany  P. M.
Lewis  University of Bonn, 53115 Bonn, Germany  C. Li  Liaoning Normal
University, Dalian 116029, China  L. K. Li  University of Cincinnati,
Cincinnati, Ohio 45221, U.S.A.  S. X. Li  Key Laboratory of Nuclear Physics
and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan
University, Shanghai 200443, China  Y. B. Li  Key Laboratory of Nuclear
Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan
University, Shanghai 200443, China  J. Libby  Indian Institute of Technology
Madras, Chennai 600036, India  K. Lieret  Ludwig Maximilians University, 80539
Munich, Germany  L. Li Gioi  Max-Planck-Institut für Physik, 80805 München,
Germany  J. Lin  Department of Physics, National Taiwan University, Taipei
10617, Taiwan  Z. Liptak  Hiroshima University, Higashi-Hiroshima, Hiroshima
739-8530, Japan  Q. Y. Liu  Deutsches Elektronen–Synchrotron, 22607 Hamburg,
Germany  Z. A. Liu  Institute of High Energy Physics, Chinese Academy of
Sciences, Beijing 100049, China  D. Liventsev  Wayne State University,
Detroit, Michigan 48202, U.S.A.  High Energy Accelerator Research Organization
(KEK), Tsukuba 305-0801, Japan  S. Longo  Deutsches Elektronen–Synchrotron,
22607 Hamburg, Germany  A. Loos  University of South Carolina, Columbia, South
Carolina 29208, U.S.A.  P. Lu  Department of Physics, National Taiwan
University, Taipei 10617, Taiwan  M. Lubej  J. Stefan Institute, 1000
Ljubljana, Slovenia  T. Lueck  Ludwig Maximilians University, 80539 Munich,
Germany  F. Luetticke  University of Bonn, 53115 Bonn, Germany  T. Luo  Key
Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of
Modern Physics, Fudan University, Shanghai 200443, China  C. Lyu  University
of Bonn, 53115 Bonn, Germany  C. MacQueen  School of Physics, University of
Melbourne, Victoria 3010, Australia  Y. Maeda  Graduate School of Science,
Nagoya University, Nagoya 464-8602, Japan  Kobayashi-Maskawa Institute, Nagoya
University, Nagoya 464-8602, Japan  M. Maggiora  Dipartimento di Fisica,
Università di Torino, I-10125 Torino, Italy  INFN Sezione di Torino, I-10125
Torino, Italy  S. Maity  Indian Institute of Technology Bhubaneswar, Satya
Nagar 751007, India  R. Manfredi  Dipartimento di Fisica, Università di
Trieste, I-34127 Trieste, Italy  INFN Sezione di Trieste, I-34127 Trieste,
Italy  E. Manoni  INFN Sezione di Perugia, I-06123 Perugia, Italy  S. Marcello
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy  INFN
Sezione di Torino, I-10125 Torino, Italy  C. Marinas  Instituto de Fisica
Corpuscular, Paterna 46980, Spain  A. Martini  Dipartimento di Matematica e
Fisica, Università di Roma Tre, I-00146 Roma, Italy  INFN Sezione di Roma Tre,
I-00146 Roma, Italy  M. Masuda  Earthquake Research Institute, University of
Tokyo, Tokyo 113-0032, Japan  Research Center for Nuclear Physics, Osaka
University, Osaka 567-0047, Japan  T. Matsuda  University of Miyazaki,
Miyazaki 889-2192, Japan  K. Matsuoka  High Energy Accelerator Research
Organization (KEK), Tsukuba 305-0801, Japan  D. Matvienko  Budker Institute of
Nuclear Physics SB RAS, Novosibirsk 630090, Russian Federation  P.N. Lebedev
Physical Institute of the Russian Academy of Sciences, Moscow 119991, Russian
Federation  Novosibirsk State University, Novosibirsk 630090, Russian
Federation  J. McNeil  University of Florida, Gainesville, Florida 32611,
U.S.A.  F. Meggendorfer  Max-Planck-Institut für Physik, 80805 München,
Germany  J. C. Mei  Key Laboratory of Nuclear Physics and Ion-beam Application
(MOE) and Institute of Modern Physics, Fudan University, Shanghai 200443,
China  F. Meier  Duke University, Durham, North Carolina 27708, U.S.A.  M.
Merola  Dipartimento di Scienze Fisiche, Università di Napoli Federico II,
I-80126 Napoli, Italy  INFN Sezione di Napoli, I-80126 Napoli, Italy  F.
Metzner  Institut für Experimentelle Teilchenphysik, Karlsruher Institut für
Technologie, 76131 Karlsruhe, Germany  M. Milesi  School of Physics,
University of Melbourne, Victoria 3010, Australia  C. Miller  University of
Victoria, Victoria, British Columbia, V8W 3P6, Canada  K. Miyabayashi  Nara
Women’s University, Nara 630-8506, Japan  H. Miyake  High Energy Accelerator
Research Organization (KEK), Tsukuba 305-0801, Japan  The Graduate University
for Advanced Studies (SOKENDAI), Hayama 240-0193, Japan  H. Miyata  Niigata
University, Niigata 950-2181, Japan  R. Mizuk  P.N. Lebedev Physical Institute
of the Russian Academy of Sciences, Moscow 119991, Russian Federation  Higher
School of Economics (HSE), Moscow 101000, Russian Federation  K. Azmi
National Centre for Particle Physics, University Malaya, 50603 Kuala Lumpur,
Malaysia  G. B. Mohanty  Tata Institute of Fundamental Research, Mumbai
400005, India  H. Moon  Korea University, Seoul 02841, South Korea  T. Moon
Seoul National University, Seoul 08826, South Korea  J. A. Mora Grimaldo
Department of Physics, University of Tokyo, Tokyo 113-0033, Japan  T. Morii
Kavli Institute for the Physics and Mathematics of the Universe (WPI),
University of Tokyo, Kashiwa 277-8583, Japan  H.-G. Moser  Max-Planck-Institut
für Physik, 80805 München, Germany  M. Mrvar  Institute of High Energy
Physics, Vienna 1050, Austria  F. Mueller  Max-Planck-Institut für Physik,
80805 München, Germany  F. J. Müller  Deutsches Elektronen–Synchrotron, 22607
Hamburg, Germany  Th. Muller  Institut für Experimentelle Teilchenphysik,
Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany  G. Muroyama
Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan  C.
Murphy  Kavli Institute for the Physics and Mathematics of the Universe (WPI),
University of Tokyo, Kashiwa 277-8583, Japan  R. Mussa  INFN Sezione di
Torino, I-10125 Torino, Italy  K. Nakagiri  High Energy Accelerator Research
Organization (KEK), Tsukuba 305-0801, Japan  I. Nakamura  High Energy
Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan  The Graduate
University for Advanced Studies (SOKENDAI), Hayama 240-0193, Japan  K. R.
Nakamura  High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan  The Graduate University for Advanced Studies (SOKENDAI),
Hayama 240-0193, Japan  E. Nakano  Osaka City University, Osaka 558-8585,
Japan  M. Nakao  High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan  The Graduate University for Advanced Studies (SOKENDAI),
Hayama 240-0193, Japan  H. Nakayama  High Energy Accelerator Research
Organization (KEK), Tsukuba 305-0801, Japan  The Graduate University for
Advanced Studies (SOKENDAI), Hayama 240-0193, Japan  H. Nakazawa  Department
of Physics, National Taiwan University, Taipei 10617, Taiwan  T. Nanut  J.
Stefan Institute, 1000 Ljubljana, Slovenia  Z. Natkaniec  H. Niewodniczanski
Institute of Nuclear Physics, Krakow 31-342, Poland  A. Natochii  University
of Hawaii, Honolulu, Hawaii 96822, U.S.A.  M. Nayak  Tel Aviv University,
School of Physics and Astronomy, Tel Aviv, 69978, Israel  G. Nazaryan
Alikhanyan National Science Laboratory, Yerevan 0036, Armenia  D. Neverov
Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan  C.
Niebuhr  Deutsches Elektronen–Synchrotron, 22607 Hamburg, Germany  M. Niiyama
Kyoto Sangyo University, Kyoto 603-8555, Japan  J. Ninkovic  Semiconductor
Laboratory of the Max Planck Society, 81739 München, Germany  N. K. Nisar
Brookhaven National Laboratory, Upton, New York 11973, U.S.A.  S. Nishida
High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan
The Graduate University for Advanced Studies (SOKENDAI), Hayama 240-0193,
Japan  K. Nishimura  University of Hawaii, Honolulu, Hawaii 96822, U.S.A.  M.
Nishimura  High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan  M. H. A. Nouxman  National Centre for Particle Physics,
University Malaya, 50603 Kuala Lumpur, Malaysia  B. Oberhof  INFN Laboratori
Nazionali di Frascati, I-00044 Frascati, Italy  K. Ogawa  Niigata University,
Niigata 950-2181, Japan  S. Ogawa  Toho University, Funabashi 274-8510, Japan
S. L. Olsen  Gyeongsang National University, Jinju 52828, South Korea  Y.
Onishchuk  Taras Shevchenko National Univ. of Kiev, Kiev, Ukraine  H. Ono
Niigata University, Niigata 950-2181, Japan  Y. Onuki  Department of Physics,
University of Tokyo, Tokyo 113-0033, Japan  P. Oskin  P.N. Lebedev Physical
Institute of the Russian Academy of Sciences, Moscow 119991, Russian
Federation  E. R. Oxford  Carnegie Mellon University, Pittsburgh, Pennsylvania
15213, U.S.A.  H. Ozaki  High Energy Accelerator Research Organization (KEK),
Tsukuba 305-0801, Japan  The Graduate University for Advanced Studies
(SOKENDAI), Hayama 240-0193, Japan  P. Pakhlov  P.N. Lebedev Physical
Institute of the Russian Academy of Sciences, Moscow 119991, Russian
Federation  Moscow Physical Engineering Institute, Moscow 115409, Russian
Federation  G. Pakhlova  Higher School of Economics (HSE), Moscow 101000,
Russian Federation  P.N. Lebedev Physical Institute of the Russian Academy of
Sciences, Moscow 119991, Russian Federation  A. Paladino  Dipartimento di
Fisica, Università di Pisa, I-56127 Pisa, Italy  INFN Sezione di Pisa, I-56127
Pisa, Italy  T. Pang  University of Pittsburgh, Pittsburgh, Pennsylvania
15260, U.S.A.  A. Panta  University of Mississippi, University, Mississippi
38677, U.S.A.  E. Paoloni  Dipartimento di Fisica, Università di Pisa, I-56127
Pisa, Italy  INFN Sezione di Pisa, I-56127 Pisa, Italy  S. Pardi  INFN Sezione
di Napoli, I-80126 Napoli, Italy  H. Park  Kyungpook National University,
Daegu 41566, South Korea  S.-H. Park  High Energy Accelerator Research
Organization (KEK), Tsukuba 305-0801, Japan  B. Paschen  University of Bonn,
53115 Bonn, Germany  A. Passeri  INFN Sezione di Roma Tre, I-00146 Roma, Italy
A. Pathak  University of Louisville, Louisville, Kentucky 40292, U.S.A.  S.
Patra  Indian Institute of Science Education and Research Mohali, SAS Nagar,
140306, India  S. Paul  Department of Physics, Technische Universität München,
85748 Garching, Germany  T. K. Pedlar  Luther College, Decorah, Iowa 52101,
U.S.A.  I. Peruzzi  INFN Laboratori Nazionali di Frascati, I-00044 Frascati,
Italy  R. Peschke  University of Hawaii, Honolulu, Hawaii 96822, U.S.A.  R.
Pestotnik  J. Stefan Institute, 1000 Ljubljana, Slovenia  M. Piccolo  INFN
Laboratori Nazionali di Frascati, I-00044 Frascati, Italy  L. E. Piilonen
Virginia Polytechnic Institute and State University, Blacksburg, Virginia
24061, U.S.A.  P. L. M. Podesta-Lerma  Universidad Autonoma de Sinaloa,
Sinaloa 80000, Mexico  G. Polat  Aix Marseille Université, CNRS/IN2P3, CPPM,
13288 Marseille, France  V. Popov  Higher School of Economics (HSE), Moscow
101000, Russian Federation  C. Praz  Deutsches Elektronen–Synchrotron, 22607
Hamburg, Germany  S. Prell  Iowa State University, Ames, Iowa 50011, U.S.A.
E. Prencipe  Forschungszentrum Jülich, 52425 Jülich, Germany  M. T. Prim
University of Bonn, 53115 Bonn, Germany  M. V. Purohit  Okinawa Institute of
Science and Technology, Okinawa 904-0495, Japan  N. Rad  Deutsches
Elektronen–Synchrotron, 22607 Hamburg, Germany  P. Rados  Deutsches
Elektronen–Synchrotron, 22607 Hamburg, Germany  S. Raiz  Dipartimento di
Fisica, Università di Trieste, I-34127 Trieste, Italy  INFN Sezione di
Trieste, I-34127 Trieste, Italy  R. Rasheed  Université de Strasbourg, CNRS,
IPHC, UMR 7178, 67037 Strasbourg, France  M. Reif  Max-Planck-Institut für
Physik, 80805 München, Germany  S. Reiter  Justus-Liebig-Universität Gießen,
35392 Gießen, Germany  M. Remnev  Budker Institute of Nuclear Physics SB RAS,
Novosibirsk 630090, Russian Federation  Novosibirsk State University,
Novosibirsk 630090, Russian Federation  P. K. Resmi  Indian Institute of
Technology Madras, Chennai 600036, India  I. Ripp-Baudot  Université de
Strasbourg, CNRS, IPHC, UMR 7178, 67037 Strasbourg, France  M. Ritter  Ludwig
Maximilians University, 80539 Munich, Germany  M. Ritzert  University of
Heidelberg, 68131 Mannheim, Germany  G. Rizzo  Dipartimento di Fisica,
Università di Pisa, I-56127 Pisa, Italy  INFN Sezione di Pisa, I-56127 Pisa,
Italy  L. B. Rizzuto  J. Stefan Institute, 1000 Ljubljana, Slovenia  S. H.
Robertson  McGill University, Montréal, Québec, H3A 2T8, Canada  Institute of
Particle Physics (Canada), Victoria, British Columbia V8W 2Y2, Canada  D.
Rodríguez Pérez  Universidad Autonoma de Sinaloa, Sinaloa 80000, Mexico  J. M.
Roney  University of Victoria, Victoria, British Columbia, V8W 3P6, Canada
Institute of Particle Physics (Canada), Victoria, British Columbia V8W 2Y2,
Canada  C. Rosenfeld  University of South Carolina, Columbia, South Carolina
29208, U.S.A.  A. Rostomyan  Deutsches Elektronen–Synchrotron, 22607 Hamburg,
Germany  N. Rout  Indian Institute of Technology Madras, Chennai 600036, India
M. Rozanska  H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342,
Poland  G. Russo  Dipartimento di Scienze Fisiche, Università di Napoli
Federico II, I-80126 Napoli, Italy  INFN Sezione di Napoli, I-80126 Napoli,
Italy  D. Sahoo  Tata Institute of Fundamental Research, Mumbai 400005, India
Y. Sakai  High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan  The Graduate University for Advanced Studies (SOKENDAI),
Hayama 240-0193, Japan  D. A. Sanders  University of Mississippi, University,
Mississippi 38677, U.S.A.  S. Sandilya  Indian Institute of Technology
Hyderabad, Telangana 502285, India  A. Sangal  University of Cincinnati,
Cincinnati, Ohio 45221, U.S.A.  L. Santelj  Faculty of Mathematics and
Physics, University of Ljubljana, 1000 Ljubljana, Slovenia  J. Stefan
Institute, 1000 Ljubljana, Slovenia  P. Sartori  Dipartimento di Fisica e
Astronomia, Università di Padova, I-35131 Padova, Italy  INFN Sezione di
Padova, I-35131 Padova, Italy  J. Sasaki  Department of Physics, University of
Tokyo, Tokyo 113-0033, Japan  Y. Sato  Department of Physics, Tohoku
University, Sendai 980-8578, Japan  V. Savinov  University of Pittsburgh,
Pittsburgh, Pennsylvania 15260, U.S.A.  B. Scavino  Johannes Gutenberg-
Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany  M. Schram
Pacific Northwest National Laboratory, Richland, Washington 99352, U.S.A.  H.
Schreeck  II. Physikalisches Institut, Georg-August-Universität Göttingen,
37073 Göttingen, Germany  J. Schueler  University of Hawaii, Honolulu, Hawaii
96822, U.S.A.  C. Schwanda  Institute of High Energy Physics, Vienna 1050,
Austria  A. J. Schwartz  University of Cincinnati, Cincinnati, Ohio 45221,
U.S.A.  B. Schwenker  II. Physikalisches Institut, Georg-August-Universität
Göttingen, 37073 Göttingen, Germany  R. M. Seddon  McGill University,
Montréal, Québec, H3A 2T8, Canada  Y. Seino  Niigata University, Niigata
950-2181, Japan  A. Selce  INFN Sezione di Roma Tre, I-00146 Roma, Italy  ENEA
Casaccia, I-00123 Roma, Italy  K. Senyo  Yamagata University, Yamagata
990-8560, Japan  I. S. Seong  University of Hawaii, Honolulu, Hawaii 96822,
U.S.A.  J. Serrano  Aix Marseille Université, CNRS/IN2P3, CPPM, 13288
Marseille, France  M. E. Sevior  School of Physics, University of Melbourne,
Victoria 3010, Australia  C. Sfienti  Johannes Gutenberg-Universität Mainz,
Institut für Kernphysik, D-55099 Mainz, Germany  V. Shebalin  University of
Hawaii, Honolulu, Hawaii 96822, U.S.A.  C. P. Shen  Beihang University,
Beijing 100191, China  H. Shibuya  Toho University, Funabashi 274-8510, Japan
J.-G. Shiu  Department of Physics, National Taiwan University, Taipei 10617,
Taiwan  B. Shwartz  Budker Institute of Nuclear Physics SB RAS, Novosibirsk
630090, Russian Federation  Novosibirsk State University, Novosibirsk 630090,
Russian Federation  A. Sibidanov  University of Hawaii, Honolulu, Hawaii
96822, U.S.A.  F. Simon  Max-Planck-Institut für Physik, 80805 München,
Germany  J. B. Singh  Panjab University, Chandigarh 160014, India  S.
Skambraks  Max-Planck-Institut für Physik, 80805 München, Germany  K. Smith
School of Physics, University of Melbourne, Victoria 3010, Australia  R. J.
Sobie  University of Victoria, Victoria, British Columbia, V8W 3P6, Canada
Institute of Particle Physics (Canada), Victoria, British Columbia V8W 2Y2,
Canada  A. Soffer  Tel Aviv University, School of Physics and Astronomy, Tel
Aviv, 69978, Israel  A. Sokolov  Institute for High Energy Physics, Protvino
142281, Russian Federation  Y. Soloviev  Deutsches Elektronen–Synchrotron,
22607 Hamburg, Germany  E. Solovieva  P.N. Lebedev Physical Institute of the
Russian Academy of Sciences, Moscow 119991, Russian Federation  S. Spataro
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy  INFN
Sezione di Torino, I-10125 Torino, Italy  B. Spruck  Johannes Gutenberg-
Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany  M. Starič
J. Stefan Institute, 1000 Ljubljana, Slovenia  S. Stefkova  Deutsches
Elektronen–Synchrotron, 22607 Hamburg, Germany  Z. S. Stottler  Virginia
Polytechnic Institute and State University, Blacksburg, Virginia 24061, U.S.A.
R. Stroili  Dipartimento di Fisica e Astronomia, Università di Padova, I-35131
Padova, Italy  INFN Sezione di Padova, I-35131 Padova, Italy  J. Strube
Pacific Northwest National Laboratory, Richland, Washington 99352, U.S.A.  J.
Stypula  H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342,
Poland  M. Sumihama  Gifu University, Gifu 501-1193, Japan  Research Center
for Nuclear Physics, Osaka University, Osaka 567-0047, Japan  K. Sumisawa
High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan
The Graduate University for Advanced Studies (SOKENDAI), Hayama 240-0193,
Japan  T. Sumiyoshi  Tokyo Metropolitan University, Tokyo 192-0397, Japan  D.
J. Summers  University of Mississippi, University, Mississippi 38677, U.S.A.
W. Sutcliffe  University of Bonn, 53115 Bonn, Germany  K. Suzuki  Graduate
School of Science, Nagoya University, Nagoya 464-8602, Japan  S. Y. Suzuki
High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan
The Graduate University for Advanced Studies (SOKENDAI), Hayama 240-0193,
Japan  H. Svidras  Deutsches Elektronen–Synchrotron, 22607 Hamburg, Germany
M. Tabata  Chiba University, Chiba 263-8522, Japan  M. Takahashi  Deutsches
Elektronen–Synchrotron, 22607 Hamburg, Germany  M. Takizawa  Meson Science
Laboratory, Cluster for Pioneering Research, RIKEN, Saitama 351-0198, Japan
J-PARC Branch, KEK Theory Center, High Energy Accelerator Research
Organization (KEK), Tsukuba 305-0801, Japan  Showa Pharmaceutical University,
Tokyo 194-8543, Japan  U. Tamponi  INFN Sezione di Torino, I-10125 Torino,
Italy  S. Tanaka  High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan  The Graduate University for Advanced Studies (SOKENDAI),
Hayama 240-0193, Japan  K. Tanida  Advanced Science Research Center, Japan
Atomic Energy Agency, Naka 319-1195, Japan  H. Tanigawa  Department of
Physics, University of Tokyo, Tokyo 113-0033, Japan  N. Taniguchi  High Energy
Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan  Y. Tao
University of Florida, Gainesville, Florida 32611, U.S.A.  P. Taras
Université de Montréal, Physique des Particules, Montréal, Québec, H3C 3J7,
Canada  F. Tenchini  Deutsches Elektronen–Synchrotron, 22607 Hamburg, Germany
D. Tonelli  INFN Sezione di Trieste, I-34127 Trieste, Italy  E. Torassa  INFN
Sezione di Padova, I-35131 Padova, Italy  K. Trabelsi  Université Paris-
Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France  T. Tsuboyama  High Energy
Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan  The Graduate
University for Advanced Studies (SOKENDAI), Hayama 240-0193, Japan  N. Tsuzuki
Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan  M.
Uchida  Tokyo Institute of Technology, Tokyo 152-8550, Japan  I. Ueda  High
Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan  The
Graduate University for Advanced Studies (SOKENDAI), Hayama 240-0193, Japan
S. Uehara  High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan  The Graduate University for Advanced Studies (SOKENDAI),
Hayama 240-0193, Japan  T. Ueno  Department of Physics, Tohoku University,
Sendai 980-8578, Japan  T. Uglov  P.N. Lebedev Physical Institute of the
Russian Academy of Sciences, Moscow 119991, Russian Federation  Higher School
of Economics (HSE), Moscow 101000, Russian Federation  K. Unger  Institut für
Experimentelle Teilchenphysik, Karlsruher Institut für Technologie, 76131
Karlsruhe, Germany  Y. Unno  Department of Physics and Institute of Natural
Sciences, Hanyang University, Seoul 04763, South Korea  S. Uno  High Energy
Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan  The Graduate
University for Advanced Studies (SOKENDAI), Hayama 240-0193, Japan  P. Urquijo
School of Physics, University of Melbourne, Victoria 3010, Australia  Y.
Ushiroda  High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan  The Graduate University for Advanced Studies (SOKENDAI),
Hayama 240-0193, Japan  Department of Physics, University of Tokyo, Tokyo
113-0033, Japan  Y. V. Usov  Budker Institute of Nuclear Physics SB RAS,
Novosibirsk 630090, Russian Federation  Novosibirsk State University,
Novosibirsk 630090, Russian Federation  S. E. Vahsen  University of Hawaii,
Honolulu, Hawaii 96822, U.S.A.  R. van Tonder  University of Bonn, 53115 Bonn,
Germany  G. S. Varner  University of Hawaii, Honolulu, Hawaii 96822, U.S.A.
K. E. Varvell  School of Physics, University of Sydney, New South Wales 2006,
Australia  A. Vinokurova  Budker Institute of Nuclear Physics SB RAS,
Novosibirsk 630090, Russian Federation  Novosibirsk State University,
Novosibirsk 630090, Russian Federation  L. Vitale  Dipartimento di Fisica,
Università di Trieste, I-34127 Trieste, Italy  INFN Sezione di Trieste,
I-34127 Trieste, Italy  V. Vorobyev  Budker Institute of Nuclear Physics SB
RAS, Novosibirsk 630090, Russian Federation  P.N. Lebedev Physical Institute
of the Russian Academy of Sciences, Moscow 119991, Russian Federation
Novosibirsk State University, Novosibirsk 630090, Russian Federation  A.
Vossen  Duke University, Durham, North Carolina 27708, U.S.A.  B. Wach  Max-
Planck-Institut für Physik, 80805 München, Germany  E. Waheed  High Energy
Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan  H. M.
Wakeling  McGill University, Montréal, Québec, H3A 2T8, Canada  K. Wan
Department of Physics, University of Tokyo, Tokyo 113-0033, Japan  W. Wan
Abdullah  National Centre for Particle Physics, University Malaya, 50603 Kuala
Lumpur, Malaysia  B. Wang  Max-Planck-Institut für Physik, 80805 München,
Germany  C. H. Wang  National United University, Miao Li 36003, Taiwan  M.-Z.
Wang  Department of Physics, National Taiwan University, Taipei 10617, Taiwan
X. L. Wang  Key Laboratory of Nuclear Physics and Ion-beam Application (MOE)
and Institute of Modern Physics, Fudan University, Shanghai 200443, China  A.
Warburton  McGill University, Montréal, Québec, H3A 2T8, Canada  M. Watanabe
Niigata University, Niigata 950-2181, Japan  S. Watanuki  Université Paris-
Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France  J. Webb  School of Physics,
University of Melbourne, Victoria 3010, Australia  S. Wehle  Deutsches
Elektronen–Synchrotron, 22607 Hamburg, Germany  M. Welsch  University of Bonn,
53115 Bonn, Germany  C. Wessel  University of Bonn, 53115 Bonn, Germany  J.
Wiechczynski  INFN Sezione di Pisa, I-56127 Pisa, Italy  P. Wieduwilt  II.
Physikalisches Institut, Georg-August-Universität Göttingen, 37073 Göttingen,
Germany  H. Windel  Max-Planck-Institut für Physik, 80805 München, Germany  E.
Won  Korea University, Seoul 02841, South Korea  L. J. Wu  Institute of High
Energy Physics, Chinese Academy of Sciences, Beijing 100049, China  X. P. Xu
Soochow University, Suzhou 215006, China  B. D. Yabsley  School of Physics,
University of Sydney, New South Wales 2006, Australia  S. Yamada  High Energy
Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan  W. Yan
University of Science and Technology of China, Hefei 230026, China  S. B. Yang
Korea University, Seoul 02841, South Korea  H. Ye  Deutsches
Elektronen–Synchrotron, 22607 Hamburg, Germany  J. Yelton  University of
Florida, Gainesville, Florida 32611, U.S.A.  I. Yeo  Korea Institute of
Science and Technology Information, Daejeon 34141, South Korea  J. H. Yin
Korea University, Seoul 02841, South Korea  M. Yonenaga  Tokyo Metropolitan
University, Tokyo 192-0397, Japan  Y. M. Yook  Institute of High Energy
Physics, Chinese Academy of Sciences, Beijing 100049, China  K. Yoshihara
Iowa State University, Ames, Iowa 50011, U.S.A.  T. Yoshinobu  Niigata
University, Niigata 950-2181, Japan  C. Z. Yuan  Institute of High Energy
Physics, Chinese Academy of Sciences, Beijing 100049, China  G. Yuan
University of Science and Technology of China, Hefei 230026, China  Y. Yusa
Niigata University, Niigata 950-2181, Japan  L. Zani  Aix Marseille
Université, CNRS/IN2P3, CPPM, 13288 Marseille, France  J. Z. Zhang  Institute
of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China  Y.
Zhang  University of Science and Technology of China, Hefei 230026, China  Z.
Zhang  University of Science and Technology of China, Hefei 230026, China  V.
Zhilich  Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090,
Russian Federation  Novosibirsk State University, Novosibirsk 630090, Russian
Federation  J. Zhou  Key Laboratory of Nuclear Physics and Ion-beam
Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai
200443, China  Q. D. Zhou  Graduate School of Science, Nagoya University,
Nagoya 464-8602, Japan  Institute for Advanced Research, Nagoya University,
Nagoya 464-8602, Japan  Kobayashi-Maskawa Institute, Nagoya University, Nagoya
464-8602, Japan  X. Y. Zhou  Liaoning Normal University, Dalian 116029, China
V. I. Zhukova  P.N. Lebedev Physical Institute of the Russian Academy of
Sciences, Moscow 119991, Russian Federation  V. Zhulanov  Budker Institute of
Nuclear Physics SB RAS, Novosibirsk 630090, Russian Federation  Novosibirsk
State University, Novosibirsk 630090, Russian Federation  A. Zupanc  J. Stefan
Institute, 1000 Ljubljana, Slovenia

###### Abstract

We report measurements related to hadronic $B$ decays to final states that
contain charm mesons. The analyses are performed on a
$62.8~{}\mathrm{fb}^{-1}$ data set collected by the Belle II experiment at a
center-of-mass energy corresponding to the mass of the $\mathchar
28935\relax(4S)$ resonance. The measurements reported are for the decay modes
$B^{-}\rightarrow D^{0}h^{-}$, $B^{-}\rightarrow D^{*0}h^{-}$,
$\bar{B}^{0}\rightarrow D^{+}h^{-}$ and $\bar{B}^{0}\rightarrow D^{*+}h^{-}$,
where $h=\pi$ or $K$. These modes are either signal or control channels for
measurements related to the unitarity triangle angle $\gamma$ in direct or
time-dependent $CP$-violation measurements. The reported observables are the
ratios between the $B\rightarrow D^{(*)}K$ and $B\rightarrow D^{(*)}\pi$ decay
rates, which are found to be in agreement with previous measurements.

Belle II, $D^{(*)}$, $\gamma$

##  1 Introduction

We report the first measurements at Belle II of observables related to
$B^{-}\rightarrow D^{(*)0}h^{-}$ and $\bar{B}^{0}\rightarrow D^{(*)+}h^{-}$
decays, where $h^{-}$ is either a $\pi^{-}$ or $K^{-}$ meson. (Throughout this
paper charge-conjugate is implied.) These decay modes are of interest for two
reasons. Firstly, the decays $B^{-}\rightarrow D^{(*)0}\pi^{-}$ and
$\bar{B}^{0}\rightarrow D^{(*)+}\pi^{-}$ arise from the favoured $b\rightarrow
c$ transition, which makes them some of the most abundant hadronic $B$ decays
with branching fractions between 0.25% and 0.5% pdg . Therefore, these modes
are important control channels for other fully hadronic $B$-decay
measurements, such as those of time-dependent $CP$ violation and charmless $B$
decays. Secondly, the decays $B^{-}\rightarrow D^{(*)0}K^{-}$ are sensitive to
the $b-d$ Cabibbo-Kobayashi-Maskawa (CKM) ckm  unitarity-triangle angle
$\phi_{3}$ (or $\gamma$) GLW . A more precise determination of $\phi_{3}$ is
one of the primary goals of Belle II b2tip .

An important set of observables related to these modes are the ratios between
the decay rates:

$\displaystyle R^{(*)0}$ $\displaystyle=$
$\displaystyle\frac{\Gamma(B^{-}\rightarrow
D^{(*)0}K^{-})}{\Gamma(B^{-}\rightarrow D^{(*)0}\pi^{-})}$ (1) $\displaystyle
R^{(*)+}$ $\displaystyle=$ $\displaystyle\frac{\Gamma(\bar{B}^{0}\rightarrow
D^{(*)+}K^{-})}{\Gamma(\bar{B}^{0}\rightarrow D^{(*)+}\pi^{-})}\;.$ (2)

These observables can test theoretical predictions, particularly of
factorization and $SU(3)$ symmetry breaking in quantum chromodynamics (QCD)
RQCD . We present measurements of $R^{(*)0/+}$ for four decay modes: (1)
$B^{-}\rightarrow D^{0}h^{-}$, $D^{0}\rightarrow K^{-}\pi^{+}$ or
$D^{0}\rightarrow K^{0}_{\rm S}\pi^{+}\pi^{-}$; (2) $B^{-}\rightarrow
D^{*0}h^{-}$, $D^{*0}\rightarrow D^{0}\pi^{0}$, $D^{0}\rightarrow
K^{-}\pi^{+}$; (3) $\bar{B}^{0}\rightarrow D^{+}h^{-}$, $D^{+}\rightarrow
K^{-}\pi^{+}\pi^{+}$; and (4) $\bar{B}^{0}\rightarrow D^{*+}h^{-}$,
$D^{*+}\rightarrow D^{0}\pi^{+}$, $D^{0}\rightarrow K^{-}\pi^{+}$.

Among these decays $B^{-}\rightarrow D^{0}(K^{0}_{\rm S}\pi^{+}\pi^{-})K^{-}$
is the single most sensitive mode to determine $\phi_{3}$ bondarK0Spipi ; giri
; bellegamma  at Belle II b2tip . Therefore, the demonstration of an efficient
reconstruction of this mode at Belle II is a significant first step toward a
determination of $\phi_{3}$. Hence, a more complex analysis is performed for
$B^{-}\rightarrow D^{0}(K^{0}_{\rm S}\pi^{+}\pi^{-})K^{-}$ compared to the
other modes, which are used as high-statistics control samples or for tests of
QCD.

The remainder of this paper is organised as followed. Section 2 describes the
Belle II detector, as well as the data and simulation samples used in these
analyses. The event selection requirements are outlined in Sec. 3. Section 4
describes how the values of $R^{(*)0/+}$ are determined from the data, the
results are presented and the evaluation of systematic uncertainties
described. Section 5 gives the conclusion and outlook.

##  2 The Belle II detector and data sample

Belle II belleII  is a particle-physics spectrometer with almost $4\pi$ solid-
angle coverage, which is designed to reconstruct the products of electron-
positron collisions produced by the SuperKEKB asymmetric-energy collider
superkekb , located at the KEK laboratory in Tsukuba, Japan. The energies of
the electron and positron beams are 7 GeV and 4 GeV, respectively. Belle II
comprises several subdetectors arranged around the interaction point in a
cylindrical geometry. The innermost subdetector is the vertex detector (VXD),
which uses position-sensitive silicon layers to sample the trajectories of
charged particles (tracks) in the vicinity of the interaction region to
extrapolate the decay positions of their long-lived parent particles. The VXD
includes two inner layers of DEPFET-based pixel sensors and four outer layers
of double-sided silicon microstrip sensors. The second pixel layer is
currently incomplete covering only one sixth of the azimuthal angle. Charged-
particle momenta and charges are measured by a large-radius, helium-ethane,
small-cell central drift chamber (CDC), which also offers charged-particle-
identification information through a measurement of particles’ specific
ionization. A Cherenkov-light angle and time-of-propagation (TOP) detector
surrounding the chamber provides charged-particle identification in the
central detector volume, supplemented by proximity-focusing, aerogel, ring-
imaging Cherenkov (ARICH) detectors in the forward region with respect to the
electron beam. A CsI(Tl)-crystal electromagnetic calorimeter (ECL) provides
electron-energy measurements and photon reconstruction. A solenoid surrounding
the calorimeter generates a uniform axial 1.5 T magnetic field filling its
inner volume. Layers of plastic scintillator and resistive-plate chambers,
interspersed between the magnetic flux-return iron plates, allow for
identification of $K^{0}_{\rm L}$ and muons. The subdetectors most relevant
for this work are the VXD, CDC, TOP, ARICH and ECL.

We use simulated data to optimize the event selection, study background and
compare the distributions observed in experimental data with expectations. We
use signal-only simulated data to model relevant signal features for fits and
determine selection efficiencies. The so-called generic sample consists of
Monte Carlo (MC) simulated events that include $B^{0}{\bar{B}}^{0}$,
$B^{+}B^{-}$, $u\bar{u}$, $d\bar{d}$, $s\bar{s}$, and $c\bar{c}$ processes in
realistic proportions and corresponds in size to more than ten times that of
the $\mathchar 28935\relax(4S)$ data. The generic MC sample is used to study
background and make comparisons with the data. In addition, one million
signal-only events are generated for each decay channel. The $B$-meson decays
are simulated with the EvtGen generator evtgen  and the effect of final-state
electromagnetic radiation is simulated by the Photos package photos . The
simulation of the continuum background process $e^{+}e^{-}\rightarrow
q\bar{q}~{}(q=u,~{}d,~{}s,~{}c)$ is carried out with the KKMC kkmc  generator
interfaced to Pythia pythia . The interactions of particles with the detector
are simulated using Geant4 geant4 .

The data sample consists of all good-quality runs collected at a center-of-
mass energy corresponding to the the $\mathchar 28935\relax(4S)$ resonance
from March 11th, 2019 until July 1st, 2020. The sample size corresponds to an
integrated luminosity of $62.8~{}\mathrm{fb}^{-1}$. Events used in the
analysis are required to satisfy data-skimming selection criteria, which
reduces sample sizes such that the time required to analyse the full data
sample is shortened significantly. These skimming criteria are placed on the
total energy and charged-particle multiplicity in the event; the selection is
almost 100% efficient on signal events rejecting only beam background and low-
multiplicity events, such as those produced in two-photon collisions. All data
are processed using the Belle II analysis software framework basf2 .

##  3 Event selection and reconstruction

The selection has been designed to be largely common among the modes studied.
An overview of the selection is as follows. Initially we select $\pi^{+}$,
$K^{+}$, $\pi^{0}$ and $K^{0}_{\rm S}$ candidates with baseline criteria that
ensure high efficiency and purity. These candidates are combined to form $D$
and $D^{*}$ candidates, which are then combined with an $h^{-}$ candidate to
form $B$ candidates. Constrained vertex and kinematic fits are applied to
ensure consistency with the topology of the decay. We reconstruct
$B^{-}\rightarrow D^{0}h^{-}$, $B^{-}\rightarrow D^{*0}h^{-}$,
$\bar{B}^{0}\rightarrow D^{+}h^{-}$ and $\bar{B}^{0}\rightarrow D^{*+}h^{-}$.
Further, we reconstruct $D^{*+}\rightarrow D^{0}\pi^{+}$ and
$D^{*0}\rightarrow D^{0}\pi^{0}$ cascades, as well as $D^{0}\rightarrow
K^{-}\pi^{+}$, $K^{0}_{\rm S}\pi^{+}\pi^{-}$ and $D^{+}\rightarrow
K^{-}\pi^{+}\pi^{+}$ decays. The remainder of this section describes the
details of the selection criteria.

Charged particle tracks originating from $e^{+}e^{-}$ collisions are selected
by requiring $|dr|<0.5$ cm and $|dz|<3$ cm, where $dr$ and $dz$ represent the
distance of closest approach to the interaction point (IP) in the plane
transverse to and along the $z$ direction, respectively. (In the Belle II
coordinate system, the $z$ axis is aligned with the direction opposite to the
positron beam.) These tracks are then identified as either $K^{+}$ or
$\pi^{+}$ using information from the CDC, TOP and ARICH detectors. We apply
likelihood-ratio requirements of
$\mathcal{L}(K/\pi)=\frac{\mathcal{L}_{K}}{\mathcal{L}_{K}+\mathcal{L}_{\pi}}>0.6$
for a kaon candidate and $\mathcal{L}(K/\pi)<0.6$ for a pion candidate, where
$\mathcal{L}_{K}$ ($\mathcal{L}_{\pi}$) is the likelihood of a track being a
kaon (pion). In order to reduce the pion fake rate, we require
$\cos\theta>-0.6$, where $\theta$ is the polar angle in lab frame of the $\pi$
or $K$ candidate coming directly from the $B$ decay, which is referred to as
the prompt track. This requirement removes the tracks in the backward part of
the detector, which are outside the TOP or ARICH acceptance. The kaon
identification efficiency is approximately 83% and the pion-to-kaon
misidentifiaction rate is about 10%; the latter quantity is obtained from the
simultaneous fit to $B\rightarrow D^{(*)}h^{-}$ data described in Sec. 4.

For $K^{0}_{\rm S}$ reconstruction, we use pairs of oppositely charged tracks
that originate from a common space-point and have an invariant mass consistent
with the nominal $K^{0}_{\rm S}$ mass pdg , when the tracks are reconstructed
assuming the pion mass hypothesis. No particle identification criteria are
applied to these tracks. To improve the purity of the $K_{\rm S}^{0}$
selection, we use a multivariate discriminant implemented as a fast boosted
decision tree (FBDT). Five variables are used as inputs to the FBDT:

  1. 1.

The azimuthal angle between the momentum vector and the vector between the IP
and the decay vertex of the $K^{0}_{\rm S}$ candidate.

  2. 2.

The smaller distance of closest approach between the extrapolated track of one
of the pion candidates and the IP.

  3. 3.

The longer distance of closest approach between the extrapolated track of the
other pion candidate and the IP.

  4. 4.

The flight length of the $K_{\rm S}^{0}$ candidate in the plane transverse to
the beam direction.

  5. 5.

The difference between the measured mass of $K^{0}_{\rm S}$ candidate and the
nominal $K^{0}_{\rm S}$ mass pdg  divided by uncertainty on the measured
$K^{0}_{\rm S}$ candidate mass.

The efficiency and purity of the $K^{0}_{\rm S}$ selection are 91% and 97%,
respectively.

We reconstruct $\pi^{0}$ candidates from photon pairs. The energy of each
photon is required to be greater than 30, 80, and 60 MeV depending upon
whether it is reconstructed in the barrel, forward, and backward endcap region
of the ECL, respectively; the differing thresholds are motivated by the
different levels of beam-induced background within the regions. Requirements
are placed on the helicity angle of the $\pi^{0}$ decay to further reduce
combinatorial candidates constructed from the beam-induced background. We also
restrict the diphoton mass to be between
$120<M_{\gamma\gamma}<145~{}\mathrm{MeV}/c^{2}$. The mass of the $\pi^{0}$
candidates is constrained to its known value in subsequent kinematic fits to
improve its four-momentum resolution.

Invariant-mass restrictions are placed on the the $D$ and $D^{*}$ candidates,
formed from combinations of the selected $\pi^{+}$, $K^{+}$, $K^{0}_{\rm S}$
and $\pi^{0}$ candidates, to reduce combinatorial background:

  * •

$1.84~{}<~{}M(K^{-}\pi^{+})~{}<~{}1.89$ GeV/$c^{2}$;

  * •

$1.85~{}<~{}M(K_{\rm S}^{0}\pi^{-}\pi^{+})~{}<~{}1.88$ GeV/$c^{2}$;

  * •

$1.844~{}<~{}M(K^{-}\pi^{+}\pi^{+})~{}<~{}1.894$ GeV/$c^{2}$;

  * •

$0.140~{}<$ $M(D^{0}\pi^{0})-M(D^{0})~{}<~{}0.144$ GeV/$c^{2}$; and

  * •

$0.143~{}<$ $M(D^{0}\pi^{+})-M(D^{0})~{}<~{}0.147$ GeV/$c^{2}$.

These intervals correspond to between $\pm 3.5\sigma$ and $\pm 4.0\sigma$
about the nominal $D^{(*)}$ masses pdg , where $\sigma$ is the invariant-mass
resolution. To improve the resolution of the selected $D^{(*)}$ candidate’s
four-momentum, it is reconstructed using a kinematic fit that constraints the
reconstructed mass to the known $D^{(*)}$ mass pdg . This fit improves the
resolution of the beam-energy difference [defined in Eq. (4)] by approximately
11%.

$B$-meson candidates are reconstructed by combining a $D$ or $D^{*}$ candidate
with a charged track without any particle identification criteria applied. The
kinematic variables used to discriminate $B$ decays from combinatorial or
partially reconstructed background are the beam-energy-constrained mass

$M_{\rm bc}=\frac{1}{c^{2}}\sqrt{E^{2}_{\rm
beam}-\left(\sum_{i}{\vec{\mathbf{p}}}_{i}c\right)^{2}}\;,$ (3)

and the beam-energy difference

$\Delta E=\sum_{i}E_{i}-E_{\rm beam}\;,$ (4)

where $E_{\rm beam}$ is the beam energy and $(E_{i},\vec{\mathbf{p}}_{i}c)$ is
the four-momentum of the $i^{\rm th}$ decay product of the $B$ candidate; all
quantities are calculated in the center-of-mass frame. For correctly
reconstructed signal, $M_{\rm bc}$ peaks at the nominal mass of the $B$ meson
pdg  and $\Delta E$ peaks at zero. We retain candidates with $M_{\rm bc}>5.27$
GeV/$c^{2}$. The distribution of $\Delta E$ for selected candidates is fit to
determine the values of $R^{(*)+/0}$. Therefore, mode-dependent $\Delta E$
criteria are placed to define the interval over which the distribution is fit.
The reason for the differing $\Delta E$ ranges is two-fold: to remove
partially reconstructed background and to increase sideband control regions
for the two-dimensional fit in the mode $B^{-}\rightarrow D(K_{\rm
S}^{0}\pi^{+}\pi^{-})h^{-}$. The $\Delta E$ criteria are $-0.13<\Delta E<0.15$
GeV for $B^{-}\rightarrow D^{0}(K^{-}\pi^{+})h^{-}$ and $B^{-}\rightarrow
D^{*0}[D^{0}(K^{-}\pi^{+})\pi^{0}]h^{-}$, $-0.13<\Delta E<0.18$ GeV for
$B^{-}\rightarrow D^{0}(K^{0}_{\rm S}\pi^{+}\pi^{-})h^{-}$, and $-0.15<\Delta
E<0.15$ GeV for $\bar{B}^{0}\rightarrow D^{(*)+}h^{-}$.

There are a few background modes that can peak in the same manner as the
signal (‘peaking background’). The decay $B^{-}\rightarrow
J/\psi(\ell^{+}\ell^{-})K^{-}$ may contribute to the background for
$B^{-}\rightarrow D^{0}(K^{-}\pi^{+})\pi^{-}$ or similarly,
$\bar{B}^{0}\rightarrow J/\psi(\ell^{+}\ell^{-})K^{*0}$ for
$\bar{B}^{0}\rightarrow D^{+}(K^{-}\pi^{+}\pi^{+})\pi^{-}$. To reject this
background arising from particle misidentification, we veto candidates
satisfying $M(\pi\pi)$ being within $\pm 3\sigma$ of the nominal $J/\psi$
mass.

Continuum background is suppressed by requiring the ratio of second and zeroth
Fox-Wolfram moments fox , $R_{2}$ $<$ 0.3. This criterion is applied for all
modes except for $B^{-}\rightarrow D(K_{\rm S}^{0}\pi^{+}\pi^{-})h^{-}$, for
which we use instead an FBDT that combines variables known to provide
statistical discrimination between $B$-meson signals and continuum background.
The variables are also required to have negligible correlation with $\Delta E$
and $M_{\rm bc}$. These quantities are associated to event topology, which
relate to both the whole event and signal-only angular configurations. We
train the classifier to identify statistically significant signal and
background features using simulated samples. We use the following event
topology variables for differentiating the signal and continuum: the
likelihood ratio obtained from Fisher discriminants formed from modified
Super-Fox-Wolfram moment skfw , the absolute value of the cosine of the angle
between the $B$ candidate and the $z$ direction in the $e^{+}e^{-}$ center-of-
mass frame, the cosine of the angle between the thrust axis of the signal $B$
and thrust axis of rest-of-the-event (ROE), the difference between the
position of the signal $B$ decay vertex and the vertex of the ROE in the $z$
direction, and $B$ flavor-tagger output ft . The output of the FBDT lies in
the range zero to one, where signal events peak around one and continuum
events peak around zero. The fit to data in this mode includes a variable
related to the FBDT output as well as $\Delta E$. However, to simplify the
background description of this variable, the FBDT output is required to be
greater than 0.2; this criterion rejects 67% of background while retaining 96%
of signal.

After applying all the selection criteria, there can be more than one
candidate per event in the $B^{-}\rightarrow D(K_{\rm
S}^{0}\pi^{+}\pi^{-})h^{-}$ mode with an average multiplicity of approximately
1.06. In such events we retain the candidate that has $M(K_{\rm
S}^{0}\pi^{+}\pi^{-})$ and $M_{\rm bc}$ values closest to the corresponding
nominal values pdg ; the efficiency of this criterion is approximately 65%.
The number of events with multiple candidates is negligible in all other decay
modes studied.

##  4 Results

We select both $B\rightarrow DK$ and $B\rightarrow D\pi$ decays, the
$B\rightarrow D\pi$ branching fraction is typically an order of magnitude
larger than that of $B\rightarrow DK$, hence it can serve as an excellent
calibration sample for the signal determination procedure. Furthermore, there
is a significant background from $B\rightarrow D\pi$ decays in the
$B\rightarrow DK$ sample due to the misidentification of the charged pion as a
kaon; a simultaneous fit to samples enhanced in prompt tracks that are either
pions $[L(K/\pi)<0.6]$ or kaons $[L(K/\pi)>0.6]$, allows this cross-feed to be
directly determined from data. The signal extraction is done by fitting only
the $\Delta E$ distribution simultaneously in pion and kaon enhanced samples
for all the modes other than $B^{-}\rightarrow D^{0}h^{-}$ where
$D^{0}\rightarrow K_{\rm S}^{0}\pi^{+}\pi^{-}$. In this last case, the signal
yield is determined from a two-dimensional extended maximum-likelihood fit to
$\Delta E$ and the transformed FBDT output ($C^{\prime}$). The continuum
suppression FBDT output is transformed using the $\mu$-transformation mutrans1
; mutrans2 . The principal advantage to using this transformation compared to
the commonly used Gaussian transformation (see for example Ch. 9 in Ref.
bfactory ) is that the PDFs can be described by analytic functions that have
fewer parameters.

The yields of the signal $B\rightarrow D^{(*)}\pi$ and $B\rightarrow
D^{(*)}K$, and their cross-feed, in the pion and kaon-enhanced samples can be
expressed by the following relations:

$\displaystyle N^{D^{(*)}\pi}_{\rm pion\;enhanced}$ $\displaystyle=$
$\displaystyle(1-\kappa)\,N^{D^{(*)}\pi}_{\rm tot}$ (5) $\displaystyle
N^{D^{(*)}\pi}_{\rm kaon\;enhanced}$ $\displaystyle=$
$\displaystyle\kappa\,N^{D^{(*)}\pi}_{\rm tot}$ (6) $\displaystyle
N^{D^{(*)}K}_{\rm kaon\;enhanced}$ $\displaystyle=$
$\displaystyle\epsilon\,R^{(*)}\,N^{D^{(*)}\pi}_{\rm tot}$ (7) $\displaystyle
N^{D^{(*)}K}_{\rm pion\;enhanced}$ $\displaystyle=$
$\displaystyle(1-\epsilon)\,R^{(*)}\,N^{D^{(*)}\pi}_{\rm tot}\;.$ (8)

Here the pion fake rate $\kappa$ is a free parameter, as well as $R^{(*)}$ and
$N^{D^{(*)}\pi}_{\rm tot}$, respectively the ratio between the decay rates
defined in Eq. (2) and the signal yield of $B\rightarrow D^{(*)}\pi$ mode. Due
to the low yield of $B\rightarrow D^{(*)}K$ cross feed to the pion-enhanced
sample, the kaon identification efficiency $\epsilon$ is fixed to the value
obtained from the tagged $D$ control samples that are used to calibrate the
particle identification pid_belle2  performance.

|
---|---
|
Figure 1: Signal-enhanced (left) $\Delta E$ and (right) $C^{\prime}$
distributions for $B^{-}\rightarrow D^{0}(K_{\rm S}^{0}\pi^{+}\pi^{-})h^{-}$
for the pion-enhanced (top) and kaon-enhanced (bottom) data sample. The
projection of the total and individual components of a simultaneous unbinned
maximum-likelihood fit are overlaid. The signal-enhancement is achieved by
requiring $|\Delta E|<0.03$ GeV and $0.65<C^{\prime}<1$ on the $C^{\prime}$
and $\Delta E$ distributions, respectively.

Three background components are considered:

  * •

continuum $q\bar{q}$ background;

  * •

combinatorial $B\bar{B}$ background, in which the final state particles could
be coming from both $B$ mesons in an event; and

  * •

cross-feed peaking background from $B^{+}\rightarrow Dh^{+}$, where $h$ =
$\pi$, $K$, in which the charged kaon is misidentified as a pion or vice
versa.

There is no significant correlation between $\Delta E$ and $C^{\prime}$, so
the two-dimensional PDF for each of the components is the product of one-
dimensional $\Delta E$ and $C^{\prime}$ PDFs. The sum of a double Gaussian
function and an asymmetric Gaussian function with a common mean is used as the
PDF to model the $\Delta E$ signal component in both samples. A uniform
distribution is used to model the $C^{\prime}$ signal component in both
samples. The continuum background distribution is modeled with a first-order
polynomial in $\Delta E$ and by the sum of two exponential functions in
$C^{\prime}$. The $\Delta E$ distribution of combinatorial $B\bar{B}$
background in $D\pi$ is described by an exponential function. A first-order
polynomial is added to the above two PDFs in the case of $B\rightarrow DK$
decays. The $C^{\prime}$ distribution in the $B\rightarrow D\pi$
$(B\rightarrow DK)$ sample is modeled by a first-order (third-order)
polynomial. The cross-feed peaking background in $\Delta E$ is modeled by the
sum of a (double) Gaussian and an asymmetric Gaussian in the $B\rightarrow DK$
$(B\rightarrow D\pi)$ sample and a first-order polynomial is used to model the
$C^{\prime}$ distribution for both samples.

All yields are determined from the fit to data. For the $\Delta E$ PDFs the
following parameters are determined in the fit to data: the signal PDF mean
value, polynomial coefficient for continuum background $\Delta E$
distribution, the exponential parameter for $B\bar{B}$ background, and the
difference between the means of the signal and cross-feed peaks in the
$B\rightarrow DK$ sample. For the $C^{\prime}$ PDFs the following parameters
are determined from the fit to data: the polynomial coefficient of the
$B\bar{B}$ background and one of the exponential parameters of the continuum
background. All other shape parameters are fixed to those obtained from fits
to appropriate MC samples. A scaling factor is applied on the $\Delta E$
signal resolution, which is a free parameter in the fit. The signal-enhanced
fit projections for the data are shown in Fig. 1, where the signal regions are
defined as $|\Delta E|<~{}0.03$ GeV and $0.65<C^{\prime}<1$.

For the other modes, in which continuum background is suppressed by simply
requiring $R_{2}<0.3$, the signal yield is extracted using a simultaneous fit
to only the $\Delta E$ distributions in both samples. In few modes, there
remains a peaking background from charmless hadronic $B$ decays which have the
same final state as the signal, e.g. $B\rightarrow K\rho$ for the
$B\rightarrow D(K\pi)\pi$ mode. The peaking background yield is fixed from MC
simulation properly scaled by their measured branching fraction pdg . The fit
projections for the data are shown for $B^{-}\rightarrow
D^{0}(K^{-}\pi^{+})h^{-}$, $B^{-}\rightarrow
D^{*0}[D^{0}(K^{-}\pi^{+})\pi^{0}]h^{-}$, $\bar{B}^{0}\rightarrow
D^{+}(K^{-}\pi^{+}\pi^{+})h^{-}$ and $\bar{B}^{0}\rightarrow D^{(*)+}h^{-}$ in
Figs. 2, 3, 4 and 5, respectively. The measured values of $R^{(*)+}$ and
$R^{(*)0}$ are listed in Tables 1 and 2, respectively. The results reported by
the LHCb Collaboration Aaij:2017ryw ; Aaij:2013qqa ; Aaij:2013xca  are also
given in these tables; these measurements dominate the world-average values
reported by the Particle Data Group (PDG) pdg .

|
---|---
Figure 2: $\Delta E$ distributions for $B^{-}\rightarrow D^{0}(K^{-}\pi^{+})h^{-}$ candidates that are (left) pion-enhanced and (right) kaon-enhanced from an 62.8 fb-1 data sample. The projection of the total and individual components of a simultaneous unbinned maximum-likelihood fit are overlaid. |
---|---
Figure 3: $\Delta E$ distributions for $B^{-}\rightarrow
D^{*0}(D^{0}(K^{-}\pi^{+})\pi^{0})h^{-}$ candidates that are (left) pion-
enhanced and (right) kaon-enhanced from an 62.8 fb-1 data sample. The
projection of the total and individual components of a simultaneous unbinned
maximum-likelihood fit are overlaid.

Figure 4: $\Delta E$ distributions for $\bar{B}^{0}\rightarrow
D^{+}(K^{-}\pi^{+}\pi^{+})h^{-}$ candidates that are (left) pion-enhanced and
(right) kaon-enhanced from an 62.8 fb-1 data sample. The projection of the
total and individual components of a simultaneous unbinned maximum-likelihood
fit are overlaid.
---
Figure 5: $\Delta E$ distributions for $\bar{B}^{0}\rightarrow D^{*+}(D^{0}(K^{-}\pi^{+})\pi^{+})h^{-}$ candidates that are (left) pion-enhanced and (right) kaon-enhanced data sample from an 62.8 fb-1 data sample. The projection of the total and individual components of a simultaneous unbinned maximum-likelihood fit are overlaid. Table 1: $R^{+}$ and $R^{0}$ results compared to those reported by the LHCb Collaboration Aaij:2017ryw ; Aaij:2013qqa . |  $B^{-}\rightarrow D^{0}(K^{-}\pi^{+})h^{-}$ |  $B^{-}\rightarrow D^{0}(K_{\rm S}^{0}\pi^{+}\pi^{-})h^{-}$ |  $\bar{B}^{0}\rightarrow D^{+}h^{-}$
---|---|---|---
Belle II $R^{+/0}~{}(\times 10^{-2})$ |  $7.66\pm 0.55$ ${}^{+0.11}_{-0.08}$ |  $6.32\pm 0.81$ ${}^{+0.09}_{-0.11}$ | $9.22\pm 0.58\pm 0.09$
LHCb $R^{+/0}~{}(\times 10^{-2})$ |  $7.77\pm 0.04\pm 0.07$ Aaij:2017ryw  |  $7.77\pm 0.04\pm 0.07$ Aaij:2017ryw  |  $8.22\pm 0.11\pm 0.25$ Aaij:2013qqa
Table 2: $R^{*+}$ and $R^{*0}$ results compared to those reported by the LHCb Collaboration Aaij:2017ryw ; Aaij:2013xca . |  $B^{-}\rightarrow D^{*0}h^{-}$ |  $\bar{B}^{0}\rightarrow D^{*+}h^{-}$
---|---|---
Belle II $R^{*+/0}~{}(\times 10^{-2})$ | $6.80\pm 1.01\pm 0.07$ |  $5.99\pm 0.82$ ${}^{+0.17}_{-0.08}$
LHCb $R^{*+/0}~{}(\times 10^{-2})$ |  $7.93\pm 0.11\pm 0.56$ Aaij:2017ryw  |  $7.76\pm 0.34\pm 0.26$ Aaij:2013xca

We consider several sources of systematic uncertainties. We assume the sources
are independent, such that the total systematic uncertainty is the sum in
quadrature of the contributions from individual sources. The individual
contributions to the $R^{(*)+/0}$ systematic uncertainties, as well as the
total systematic uncertainties, are reported in Table 3. The major three
sources of systematic uncertainty are the momentum scale factor applied in the
reconstruction to account for the incorrect magnetic field mapping, the fixed
parameters in the PDF shape, and the kaon efficiency. The momentum of charged
particle tracks is corrected from the calibration results obtained with
invariant masses of well-known resonances. Those corrections are varied within
their uncertainty. Those due to the $\Delta E$ PDFs for the $DK$ signal, the
$D\pi$ signal, and the $D\pi$ cross-feed are evaluated by varying the shape
parameters by $\pm 1\sigma$, by replacing common parameter ($\Delta E$ mean of
the $D\pi$ and $DK$ components) by a different parameter. The uncertainties
due to the kaon identification efficiency are obtained by varying the assumed
values by their uncertainties as obtained in data from the tagged $D$ control
samples. The uncertainty due to the peaking background is obtained by varying
its yield by the uncertainty in its estimation.

Table 3: Systematic uncertainties for $R^{*+/0}$ measurements. | $D^{0}(K_{\rm S}^{0}\pi^{+}\pi^{-})h^{-}$ | $D^{0}(K^{-}\pi^{+})h^{-}$ |  $D^{*0}h^{-}$ |  $D^{+}h^{-}$ |  $D^{*+}h^{-}$
---|---|---|---|---|---
Kaon identification $(\times 10^{-2})$ | ${}^{+0.008}_{-0.008}$ | ${}^{+0.010}_{-0.011}$ | ${}^{+0.020}_{-0.019}$ | ${}^{+0.023}_{-0.015}$ | ${}^{+0.014}_{-0.013}$
Momentum correction $(\times 10^{-2})$ | ${}^{+0.065}_{-0.100}$ | ${}^{+0.109}_{-0.064}$ | ${}^{+0.016}_{-0.018}$ | ${}^{+0.054}_{-0.040}$ | ${}^{+0.161}_{-0.030}$
PDF shape $(\times 10^{-2})$ | ${}^{+0.066}_{-0.053}$ | ${}^{+0.030}_{-0.034}$ | ${}^{+0.066}_{-0.064}$ | ${}^{+0.093}_{-0.079}$ | ${}^{+0.039}_{-0.036}$
Cross-feed fraction $(\times 10^{-2})$ | $-$ | ${}^{+0.004}_{-0.005}$ | ${}^{+0.028}_{-0.025}$ | ${}^{+0.009}_{-0.003}$ | ${}^{+0.017}_{-0.014}$
Common mean $(\times 10^{-2})$ | $+0.025$ | $-0.039$ | $+0.004$ | $-0.003$ | $-0.067$
Peaking background $(\times 10^{-2})$ | $-$ | $\pm 0.013$ | $-$ | ${}^{+0.022}_{-0.015}$ | ${}^{+0.002}_{-0.002}$
Total $(\times 10^{-2})$ | ${}^{+0.093}_{-0.114}$ | ${}^{+0.114}_{-0.084}$ | ${}^{+0.071}_{-0.068}$ | ${}^{+0.112}_{-0.091}$ | ${}^{+0.166}_{-0.083}$

##  5 Summary

We have reported measurements of the decay rate ratio between $B\rightarrow
D^{(*)}K^{-}$ and $B\rightarrow D^{(*)}\pi^{-}$. We use data collected by the
Belle II experiment in 2019 and 2020, corresponding to
$62.8~{}\mathrm{fb}^{-1}$ of integrated luminosity, collected at the
$\mathchar 28935\relax(4S)$ resonance. The measurements reported are for the
decay modes $B^{-}\rightarrow D^{0}h^{-}$, $B^{-}\rightarrow D^{*0}h^{-}$,
$\bar{B}^{0}\rightarrow D^{+}h^{-}$ and $\bar{B}^{0}\rightarrow D^{*+}h^{-}$,
where $h=\pi$ or $K$. The results are compatible with the world-average values
reported by the PDG pdg .

## ACKNOWLEDGEMENTS

We thank the SuperKEKB group for the excellent operation of the accelerator;
the KEK cryogenics group for the efficient operation of the solenoid; the KEK
computer group for on-site computing support; and the raw-data centers at BNL,
DESY, GridKa, IN2P3, and INFN for off-site computing support. This work was
supported by the following funding sources: Science Committee of the Republic
of Armenia Grant No. 20TTCG-1C010; Australian Research Council and research
grant Nos. DP180102629, DP170102389, DP170102204, DP150103061, FT130100303,
and FT130100018; Austrian Federal Ministry of Education, Science and Research,
Austrian Science Fund No. P 31361-N36, and Horizon 2020 ERC Starting Grant no.
947006 “InterLeptons”; Natural Sciences and Engineering Research Council of
Canada, Compute Canada and CANARIE; Chinese Academy of Sciences and research
grant No. QYZDJ-SSW-SLH011, National Natural Science Foundation of China and
research grant Nos. 11521505, 11575017, 11675166, 11761141009, 11705209, and
11975076, LiaoNing Revitalization Talents Program under contract No.
XLYC1807135, Shanghai Municipal Science and Technology Committee under
contract No. 19ZR1403000, Shanghai Pujiang Program under Grant No.
18PJ1401000, and the CAS Center for Excellence in Particle Physics (CCEPP);
the Ministry of Education, Youth and Sports of the Czech Republic under
Contract No. LTT17020 and Charles University grants SVV 260448 and GAUK
404316; European Research Council, 7th Framework PIEF-GA-2013-622527, Horizon
2020 ERC-Advanced Grants No. 267104 and 884719, Horizon 2020 ERC-Consolidator
Grant No. 819127, Horizon 2020 Marie Sklodowska-Curie grant agreement No.
700525 ‘NIOBE,’ and Horizon 2020 Marie Sklodowska-Curie RISE project JENNIFER2
grant agreement No. 822070 (European grants); L’Institut National de Physique
Nucléaire et de Physique des Particules (IN2P3) du CNRS (France); BMBF, DFG,
HGF, MPG, and AvH Foundation (Germany); Department of Atomic Energy under
Project Identification No. RTI 4002 and Department of Science and Technology
(India); Israel Science Foundation grant No. 2476/17, United States-Israel
Binational Science Foundation grant No. 2016113, and Israel Ministry of
Science grant No. 3-16543; Istituto Nazionale di Fisica Nucleare and the
research grants BELLE2; Japan Society for the Promotion of Science, Grant-in-
Aid for Scientific Research grant Nos. 16H03968, 16H03993, 16H06492, 16K05323,
17H01133, 17H05405, 18K03621, 18H03710, 18H05226, 19H00682, 26220706, and
26400255, the National Institute of Informatics, and Science Information
NETwork 5 (SINET5), and the Ministry of Education, Culture, Sports, Science,
and Technology (MEXT) of Japan; National Research Foundation (NRF) of Korea
Grant Nos. 2016R1D1A1B01010135, 2016R1D1A1B02012900, 2018R1A2B3003643,
2018R1A6A1A06024970, 2018R1D1A1B07047294, 2019K1A3A7A09033840, and
2019R1I1A3A01058933, Radiation Science Research Institute, Foreign Large-size
Research Facility Application Supporting project, the Global Science
Experimental Data Hub Center of the Korea Institute of Science and Technology
Information and KREONET/GLORIAD; Universiti Malaya RU grant, Akademi Sains
Malaysia and Ministry of Education Malaysia; Frontiers of Science Program
contracts FOINS-296, CB-221329, CB-236394, CB-254409, and CB-180023, and SEP-
CINVESTAV research grant 237 (Mexico); the Polish Ministry of Science and
Higher Education and the National Science Center; the Ministry of Science and
Higher Education of the Russian Federation, Agreement 14.W03.31.0026;
University of Tabuk research grants S-0256-1438 and S-0280-1439 (Saudi
Arabia); Slovenian Research Agency and research grant Nos. J1-9124 and
P1-0135; Agencia Estatal de Investigacion, Spain grant Nos. FPA2014-55613-P
and FPA2017-84445-P, and CIDEGENT/2018/020 of Generalitat Valenciana; Ministry
of Science and Technology and research grant Nos. MOST106-2112-M-002-005-MY3
and MOST107-2119-M-002-035-MY3, and the Ministry of Education (Taiwan);
Thailand Center of Excellence in Physics; TUBITAK ULAKBIM (Turkey); Ministry
of Education and Science of Ukraine; the US National Science Foundation and
research grant Nos. PHY-1807007 and PHY-1913789, and the US Department of
Energy and research grant Nos. DE-AC06-76RLO1830, DE-SC0007983, DE-SC0009824,
DE-SC0009973, DE-SC0010073, DE-SC0010118, DE-SC0010504, DE-SC0011784, DE-
SC0012704, DE-SC0021274; and the Vietnam Academy of Science and Technology
(VAST) under grant DL0000.05/21-23.

## References

  * (1) P.A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
  * (2) N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963); M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973).
  * (3) M. Gronau and D. Wyler, Phys. Lett. B 265, 172 (1991); M. Gronau and D. London, Phys. Lett. B 253, 483 (1991).
  * (4) E. Kou et al. (Belle II Collaboration), Prog. Theor. Exp. Phys. 2019 no 12, 123C01 (2019).
  * (5) R. Fleischer, N. Serra and N. Tuning, Phys. Rev. D 83, 014017 (2011); R. Fleischer, N. Serra and N. Tuning, Phys. Rev. D 82, 034038 (2010).
  * (6) A. Bondar, Proceedings of BINP special analysis meeting on Dalitz analysis, unpublished (2002).
  * (7) A. Giri, Y. Grossman, A. Soffer, and J. Zupan, Phys. Rev. D 68, 054018 (2003).
  * (8) H. Aihara et al. (Belle Collaboration), Phys. Rev. D 85, 112014 (2012).
  * (9) T. Abe et al. (Belle II Collaboration), arXiv:1011.0352 [physics.ins-det] (2010).
  * (10) K. Akai, K. Furukawa, and H. Koiso (SuperKEKB Group), Nucl. Instrum. and Meth. A 907, 188 (2018).
  * (11) D. Lange, Nucl. Instrum. and Meth. A 462, 152 (2001).
  * (12) E. Barberio et al., Comp. Phys. Comm. 66, 115 (1991).
  * (13) B. Ward, S. Jadach and Z. Was, Nucl. Phys. B Proc. Suppl. 116, 73 (2003)
  * (14) T. Sjöstrand et al., Comp. Phys. Comm. 178, 852 (2008).
  * (15) S. Agostinelli et al., Nucl. Instrum. and Meth. A 506, 250 (2003).
  * (16) T. Kuhr et al., Comput. Softw. Big Sci. 3, 1 (2019).
  * (17) G. C. Fox and S. Wolfram, Phys. Rev. Lett. 41, 1581 (1978).
  * (18) H. Lee et al. (Belle Collaboration), Phys. Rev. Lett. 91, 261801 (2003).
  * (19) F. Abudinén et al. (Belle II Collaboration), BELLE2-NOTE-PH-2020-004 at https://docs.belle2.org/record/2054.
  * (20) M. Pivk, Ph.D. thesis (2003), available at https://tel.archives-ouvertes.fr/tel-00002991/document in French.
  * (21) K. Albertsson et al., Toolkit for Multivariate Analysis with Root: User Guide, available at https://root.cern.ch/download/doc/tmva/TMVAUsersGuide.pdf.
  * (22) A. J. Bevan et al., Eur. Phys. J. C 74, 3026 (2014).
  * (23) F. Abudinén et al. (Belle II Collaboration), BELLE2-NOTE-PL-2020-024 at https://docs.belle2.org/record/2052.
  * (24) R. Aaij et al. (LHCb Collaboration), Phys. Lett. B 777, 16 (2018).
  * (25) R. Aaij et al. (LHCb Collaboration), JHEP 1304, 001 (2013).
  * (26) R. Aaij et al. (LHCb Collaboration), Phys. Rev. D 87, 092001 (2013).