BELLE2-CONF-PH-2021-010

July 20, 2021

# Measurement of the branching fraction for $B^{0}\rightarrow\pi^{0}\pi^{0}$
decays reconstructed in 2019–2020 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  Institute of Theoretical and
Applied Research (ITAR), 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  National Research University Higher School of
Economics, 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  Faculty of Chemistry and Chemical
Engineering, 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  Institute of Theoretical and Applied Research (ITAR), Duy Tan
University, Hanoi 100000, Vietnam  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  Faculty of Chemistry and Chemical Engineering,
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
National Research University Higher School of Economics, 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  National Research University Higher School of
Economics, 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  F. Pham  School of Physics, University of
Melbourne, Victoria 3010, Australia  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  National Research University Higher School of Economics, 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  National
Research University Higher School of Economics, 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 the first reconstruction of the $B^{0}\rightarrow\pi^{0}\pi^{0}$
decay mode at Belle II using samples of 2019 and 2020 data that correspond to
62.8 $\mbox{\,fb}^{-1}$ of integrated luminosity. We find $14.0^{+6.8}_{-5.6}$
signal decays, corresponding to a significance of 3.4 standard deviations and
determine a branching ratio of
$\mathcal{B}(B^{0}\rightarrow\pi^{0}\pi^{0})=[0.98^{+0.48}_{-0.39}\pm
0.27]\times 10^{-6}$. The results agree with previous determinations and
contribute important information to an early assessment of detector
performance and Belle II’s potential for future determinations of
$\alpha/\phi_{2}$ using
$\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}\rightarrow\pi\pi$
modes.

Belle II, $B^{0}\rightarrow\pi^{0}\pi^{0}$, charmless

##  1 Introduction

Effective constraints on physics beyond the Standard Model are provided by
high-precision measurements. The study of charmless decays at Belle II can
provide improved measurements of the Cabibbo–Kobayashi–Maskawa (CKM) angle
$\alpha/\phi_{2}\equiv\textrm{arg}(-\frac{V_{td}V^{*}_{cb}}{V_{ud}V^{*}_{ub}})$,
where $V_{ij}$ are elements of the quark-mixing matrix. If
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow\pi^{+}\pi^{-}$
decays proceeded through only the tree level ($b\rightarrow u$) process, the
mixing-induced ${\it CP}$ violation parameter, $\mathcal{S}_{CP}$, would be
proportional to sin$(2\phi_{2})$. However the value of $\phi_{2}$ is shifted
by an amount $\Delta\phi_{2}$ due to the presence of penguin contributions
($b\rightarrow d$). The tree and penguin contributions can be disentangled
using $B\rightarrow\pi\pi$ isospin relations Gronau1990 .

$A^{+0}=\frac{1}{\sqrt{2}}A^{+-}+A^{00},\quad\bar{A}^{-0}=\frac{1}{\sqrt{2}}\bar{A}^{+-}+\bar{A}^{00}$
(1)

where $A^{ij}$ is the amplitude of the decay
$\bar{B}\rightarrow\pi^{i}\pi^{j}$ and is represented geometrically in the
complex plane in Figure 1.

Figure 1: Geometrical representation of the isospin triangular relations in
the complex plane of
$\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{i+j}\rightarrow\mathit{{h}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{i}\mathit{{h}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{j}$
amplitudes. The blue and the red shaded areas correspond to the isospin
triangles. The angle between the ${\it CP}$ conjugate charged amplitudes
$A^{+-}$ and $\bar{A}^{+-}$ corresponds to twice the weak phase $\alpha_{\rm
eff}/\phi_{2,{\rm eff}}$ (orange solid arcs). The angle between the ${\it CP}$
conjugate charged amplitudes $A^{+0}$ and $\bar{A}^{+0}$ corresponds to twice
the CKM angle $\alpha/\phi_{2}$ (green solid arc). The other triangles with
lighter shading represent the mirror solutions allowed by the discrete
ambiguities in the isospin relationships, with the corresponding values for
$\alpha/\phi_{2}$ represented by the green dashed curves.

Taking advantage of these relations requires precise measurements of the
branching fraction $\mathcal{B}$ and ${\it CP}$ violation parameters of each
$B\rightarrow\pi\pi$ decay. The relatively large uncertainties on the current
value of
$\mathcal{B}(\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow\pi^{0}\pi^{0})$
and
$\mathcal{A}_{CP}(\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow\pi^{0}\pi^{0})$,
measured by BaBar BaBar:2007uoe  and Belle Belle:2017lyb , poses the greatest
limitation to fully exploiting the isospin relation. The
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow\pi^{0}\pi^{0}$
mode has a low branching ratio, ($1.59\pm 0.26)\times 10^{-6}$ Zyla:2020zbs ,
since it is both color-suppressed and, at tree level, is proportional to the
CKM matrix element $V_{ub}$, whose magnitude is small. In addition, the
$\pi^{0}$ decays via $\pi^{0}\rightarrow\gamma\gamma$ with a branching ratio
of $\approx$ 99% and hence the final state particles consist entirely of
photons. Belle II with its clean $e^{+}e^{-}$ environment and large acceptance
for photons ranging from 20 MeV to 4 GeV is the only running experiment that
can competitively study this decay mode.

The Belle II experiment features significantly upgraded detectors and new
analysis software providing better particle identification, background
suppression and $\it B$-meson flavour determination compared to its
predecessor Belle. The Belle II experiment, complete with its silicon vertex
detector, commenced taking data in March 2019. The sample used in this
analysis corresponds to an integrated luminosity of 62.8 $\mbox{\,fb}^{-1}$ at
the $\Upsilon(4S)$ resonance. We report the first Belle II measurement of the
branching fraction of the $B^{0}\rightarrow\pi^{0}\pi^{0}$ decay. Charge-
conjugate decays are implied in what follows.

##  2 Belle II detector

A full description of the Belle II detector is given in Ref. Belle-II:2010dht
. The detector consists of several subdetectors arranged in a cylindrical
structure around the beam pipe. Compared to its predecessor Belle
Belle:2000cnh , a pixel detector (PXD) has been added at a minimum radius of
1.4 cm. This improves the resolution of the impact parameter to about 12
$\mu$m in the transverse direction for high momentum tracks Belle-II:2018jsg ,
which helps to reject background events for this analysis. The PXD is
surrounded by a four-layer double-sided silicon strip detector, referred to as
the silicon vertex detector, and a central drift chamber (CDC). A time-of-
propagation counter and an aerogel ring-imaging Cherenkov counter cover the
barrel and forward endcap regions of the detector, respectively, and are
essential for charged-particle identification (PID). The electromagnetic
calorimeter (ECL) makes up the remaining volume inside a superconducting
solenoid, which operates at 1.5 T. A dedicated detector to identify
$K^{0}_{L}$ mesons and muons is installed in the outermost part of the
detector. The z-axis of the laboratory frame is defined as the symmetry axis
of the solenoid, and the positive direction is approximately given by the
incoming electron beam. The polar angle $\theta$, as well as the longitudinal
and the transverse direction are defined with respect to the z-axis. The ECL
is most relevant for this work as it is the only subdetector that can detect
photons.

###  2.1 Data and simulation

We use all 2019-2020 data corresponding to an integrated luminosity of 62.8
$\mbox{\,fb}^{-1}$ collected with the Belle II detector at the asymmetric-
energy $e^{+}e^{-}$ collider SuperKEKB Akai:2018mbz , which is located at the
KEK laboratory in Tsukuba, Japan. Data were collected at the center-of-mass
(c.m.) energy of the $\Upsilon{(4S)}$ resonance
($\sqrt{s}=10.58\mathrm{\,Ge\kern-1.00006ptV}$). The energies of the electron
and positron beams are 7 GeV and 4 GeV, respectively, resulting in a boost of
$\beta\gamma=0.28$ of the c.m. frame relative to the laboratory frame. We also
use all off-resonance data collected at an energy about 60 MeV lower and
corresponds to an integrated luminosity of 9.2 $\mbox{\,fb}^{-1}$. All events
are required to satisfy loose hadronic event selection criteria, based on
total energy and neutral-particle multiplicity in the events, targeted at
reducing sample sizes to a manageable level with minimal impact on signal
efficiency. All data are processed using the Belle II analysis software
Kuhr:2018lps .

We use GEANT4 GEANT4:2002zbu  based Monte Carlo (MC) simulation data to
optimize the event selection, compare the distribution observed in
experimental data with expectations, and model the distribution in fits. We
use $2\times 10^{6}$ signal simulated data. Generic background MC samples
consists of charged and neutral B meson pairs
($\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{B}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$
and $B^{+}B^{-}$), and continuum processes ($e^{+}e^{-}\rightarrow$
$q\overline{q}$ with $q=u,d,s,c$ quarks) in realistic proportions, which
correspond to a 4 $\mbox{\,ab}^{-1}$ sample. To validate our experimental
procedure, the $B^{0}\rightarrow\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}(\rightarrow
K^{-}\pi^{+}\pi^{0})\pi^{0}$ decay is used as a control mode as it contains
two $\pi^{0}$ particles in the final state. The total yield is expected to be
10 – 20 times larger than the expected signal yield from the
$B^{0}\rightarrow\pi^{0}\pi^{0}$ decay. We use $1\times 10^{6}$ simulated
control-mode events.

##  3 Event Selection and Candidate Reconstruction

We form photon candidates by requiring the energy in the ECL barrel and
endcaps to be greater than 20 MeV and 22.5 MeV respectively. Further photon
selections using a binary boosted decision-tree classifier, described in
subsection 3.1, is applied to suppress hadronic interactions and photons from
non-signal sources. The photon candidates are paired to form $\pi^{0}$
candidates and we require the invariant mass and helicitiy angle to be
$0.105<M_{\gamma\gamma}<0.150{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and
$|\text{cos}\theta_{helicity}|<0.98$, respectively, to suppress combinatorial
background from collinear soft photons. The mass of the $\pi^{0}$ candidates
is constrained to its known value in a kinematic fit to improve the momentum
resolution. The $B$ meson candidates are reconstructed by pairing the
$\pi^{0}$ candidates. To select signal $B$, two kinematic variables are
defined,

${M_{\rm bc}}=\sqrt{E_{\rm beam}^{2}-|\vec{p}_{B}|^{2}},\quad{\Delta
E}=E_{B}-\sqrt{s}/2$ (2)

where $M_{\rm bc}$, is the mass-energy relation where the energy of the $B$
meson has been replaced by half of the c.m. energy, which is extremely well-
defined by the accelerator, and $\vec{p_{B}}$ is the $B$ meson momentum, both
measured in the $\Upsilon(4S)$ frame. ${\Delta E}=E_{B}-\sqrt{s}/2$ is the
difference between the total energy of the $B$ candidate and half the
collision energy, both measured in the $\Upsilon(4S)$ frame. $B$ meson
candidates are required to have $5.26<{M_{\rm
bc}}<5.29~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and $-0.3<{\Delta
E}<0.2~{}\mathrm{\,Ge\kern-1.00006ptV}$. For correctly reconstructed $B$ meson
candidates, ${\Delta E}$ should peak at zero except for resolution. However,
observed ${\Delta E}$ distributions peak below zero since energy is lost via
either electromagnetic interactions in the material before the calorimeter or
via energy leakage from the ECL cluster. In addition, the photon energy and
momentum can only be determined from the ECL cluster energy and hence there is
a small correlation between ${\Delta E}$ and ${M_{\rm bc}}$ in our
reconstructed
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow\pi^{0}\pi^{0}$
events.

###  3.1 Optimized photon selection

Due to the long decay time of signal in CsI(Tl), Bhabha events
($e^{+}e^{-}\rightarrow e^{+}e^{-}$) can deposit large amounts of energy in
the CsI(Tl) crystals of the ECL that are still present when another hadronic
event occurs. A random photon from the hadronic event can be combined with the
residual energy (misreconstructed photon) in the CsI(Tl) crystals to form a
$\pi^{0}$. This misreconstructed $\pi^{0}$ and a genuine $\pi^{0}$ can then be
misreconstructed into a
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$
candidate. In the Belle analysis of
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow\pi^{0}\pi^{0}$
Julius:2017jso , these were suppressed by requiring ECL signals to be in time
with the rest of the $e^{+}e^{-}$ event. Rather than using one-dimensional
requirements on the photon’s time of interaction, we train a fast boosted
decision-tree (FBDT) Keck:2017gsv  to distinguish between genuine and
misreconstructed photons using ECL variables that have high discriminating
power. To create samples of genuine and misreconstructed photons, we
reconstruct $B^{0}\rightarrow\pi^{0}\pi^{0}$ candidates in simulated signal-
only data with no requirements on the photons. Photons that do not originate
from the signal are regarded as misreconstructed. We train and validate data
using two independent data sets consisting of 50 000 genuine and 50 000
misreconstructed photons. We find that this classifier, which we call the
photonMVA, can efficiently suppress most misreconstructed photons. Based on MC
studies requiring the photonMVA output to exceed 0.2 retains 97.05% of genuine
photons while rejecting 73.3% of misreconstructed photons.

To validate the photonMVA we use the
$D^{*+}\rightarrow\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}(\rightarrow
K^{0}_{S}(\rightarrow\pi^{+}\pi^{-})\pi^{0})\pi^{+}$ decay mode. The
reconstruction uses similar final state selections as the signal decay. We
first reconstruct $\pi^{\pm}$ candidates from charged-particle candidates
reconstructed in the full polar-angle acceptance
($17^{\circ}<\theta<150^{\circ}$), and originating close to the interaction
point in the longitudinal ($|dz|<3.0$ cm) and radial ($|dr|<0.5$ cm)
directions to reduce beam-background-induced tracks. For ${K^{0}_{s}}$
reconstruction, we pair oppositely charged $\pi^{\pm}$ candidates and require
that they originate from a common space-point and have dipion mass in the
range 0.47 – 0.53 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. For $D^{0}$
reconstruction, we combine the ${K^{0}_{s}}$ with a $\pi^{0}$ and require that
candidates have masses in the range 1.80 – 2.50
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ with momenta in the c.m. frame
greater than 2.5 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Finally, we
reconstruct $D^{*+}$ candidates by combining the $D^{0}$ and $\pi^{+}$ in a
kinematic vertex fit. We choose one candidate per event by selecting the
$\pi^{0}$ candidate with the lowest $\chi^{2}$ value of the mass-constraint
diphoton fit. The difference between the mass of the $D^{*+}$ and
$\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$,
$\Delta M=M_{D^{*+}}-M_{\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}}$,
is a powerful discriminator between signal and background. We require
$0.144<\Delta M<0.147{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ to ensure the
$D^{*+}$ is reconstructed with high purity.

The final-state reconstruction is performed with and without the photonMVA
requirement. The signal yields and backgrounds are determined using fits to
the $\Delta M$ distribution. The signal and background retention are
consistent between MC and experimental data. Requiring the photonMVA to exceed
0.2 reduces the $D^{*+}$ background by 47% (absolute) and reduces signal
reconstruction efficiency by 3.7% (absolute) compared to the standard photon
selection manfredi2021measurements . In addition we compare the photonMVA
distribution in the MC and 62.8 $\mbox{\,fb}^{-1}$ data as shown in Figure 2
and find that they are in agreement.

Figure 2: The output of the FBDT classifier for photons in
$D^{*+}\rightarrow\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\pi^{+}$,
$\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow
K^{0}_{\scriptscriptstyle S}\pi^{0}$, $K^{0}_{\scriptscriptstyle
S}\rightarrow\pi^{+}\pi^{-}$ decays.

##  4 Multivariate background suppression

The $B^{0}\rightarrow\pi^{0}\pi^{0}$ decay has large continuum background even
relative to other charmless $B$ decay modes because of its small branching
ratio. To discriminate against such background, we use the FBDT classifier to
combines 28 variables associated with event topology, which are known to
provide statistical discrimination between $B$-meson signal and continuum
background. We additionally require that these variables have correlations
with ${\Delta E}$ and ${M_{\rm bc}}$ below 5%. We train the classifier to
identify statistically significant signal and background features using
unbiased simulated samples. We validate the input and output distributions of
the classifier by comparing data with simulation using the control mode
$B^{0}\rightarrow\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}(\rightarrow
K^{-}\pi^{+}\pi^{0})\pi^{0}$. No inconsistency is observed.

The optimal FBDT threshold is determined by maximizing the figure of merit
$S/\sqrt{S+B}$, where $S$ and $B$ are the simulated signal and background
yield, respectively, both determined in the signal-enhanced region
$5.27~{}<{M_{\rm bc}}~{}<5.29{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and
$-0.1~{}<{\Delta E}~{}<0.15\mathrm{\,Ge\kern-1.00006ptV}$. The resulting
threshold criterion rejects 97.8% of the background while retaining 57.9% of
the signal. The signal efficiency after $B^{0}\rightarrow\pi^{0}\pi^{0}$
candidate reconstruction and continuum suppression is 21%. About 1.6% of
selected events have more than one candidate. We choose the candidate with the
minimum absolute deviation, $|dM(\pi^{0}_{1})|+|dM(\pi^{0}_{2})|$, of the
reconstructed invariant masses from the known value. This is 98% efficient in
selecting the correct
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$.
In addition, we reconstruct the vertex of the accompanying tag-side $B$ meson
and identify the flavor using a category-based flavor tagger Abudinen:2019hcr
.

To validate the FBDT, 9.2 $\mbox{\,fb}^{-1}$ of off-resonance data is used as
it contains only continuum events. We apply the same
$B^{0}\rightarrow\pi^{0}\pi^{0}$ selection as discussed previously except for
the requirements $M_{bc}>5.2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and
$|{\Delta E}|<0.5\mathrm{\,Ge\kern-1.00006ptV}$ imposed to retain as many
continuum events as possible. We impose the FBDT requirement and determine the
continuum rejection to be 97.4%, which agrees with MC expectation.

Backgrounds due to non-signal $B$ decays are denoted as $B\kern
1.79993pt\overline{\kern-1.79993ptB}{}$. All the $B\kern
1.79993pt\overline{\kern-1.79993ptB}{}$ background effectively consists of
$B^{+}\rightarrow\rho^{+}\pi^{0}$ decays where the charged pion from the
subsequent $\rho^{+}\rightarrow\pi^{+}\pi^{0}$ is unreconstructed, and
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow
K^{0}_{S}(\rightarrow\pi^{0}\pi^{0})\pi^{0}$ decays where one of the $\pi^{0}$
is unreconstructed. This background peaks at similar values of ${M_{\rm bc}}$
and $T_{c}$ but has ${\Delta E}$ shifted to negative values due to missing
energy from the unreconstructed particle. Since the topology of $B\kern
1.79993pt\overline{\kern-1.79993ptB}{}$ events is similar to the signal mode,
the FBDT removes approximately the same fraction of $B\kern
1.79993pt\overline{\kern-1.79993ptB}{}$ and signal events.

##  5 Determination of signal yields

Signal yields are determined with a three-dimensional (${M_{\rm bc}},{\Delta
E}$, $T_{c}$) simultaneous unbinned maximum likelihood fit for each $b$
flavor, $q$, in 8 bins of the dilution factor, $r$. $T_{c}$ is the log
transform of the continuum suppression FBDT variable and is used to transform
the FBDT output into a Gaussian-like shape. By convention $q=+1$ tags a
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$
while $q=-1$ tags a $\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{B}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$.
The dilution factor is determined by a category-based flavor tagger
Abudinen:2019hcr  with $r=0$ meaning no flavor discrimination between
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$
and $\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{B}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$
and $r=1$ meaning unambiguous flavor assignment. Bins are spaced so that each
bin has an approximately equal number of candidates. Fit models are determined
empirically from simulation, with shifts of peak positions in ${\Delta E}$
determined in the $B^{0}\rightarrow\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}(\rightarrow
K^{-}\pi^{+}\pi^{0})\pi^{0}$ control mode. A negative shift in ${\Delta E}$
relative to simulated data is observed. The value of the shift favored by
control data is determined using a likelihood-ratio test to be $-10$ MeV. This
is included in the ${\Delta E}$ fit model for the signal and $B\kern
1.79993pt\overline{\kern-1.79993ptB}{}$ component.

To validate the MC $q\cdot r$ distributions, we compare the $q\cdot r$
fractions in experimental and simulated data restricted to a continuum-
enriched sideband defined as $5.20<{M_{\rm
bc}}<5.26{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ where continuum events are
dominant. The continuum suppression requirement is removed to have a
sufficient sample size. The results show excellent agreement.

For all components, $T_{c}$ is modelled using the sum of a Gaussian and a
bifurcated Gaussian with a common mean to avoid peak splitting. For the signal
and $B\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ components, the
correlation between ${M_{\rm bc}}$ and ${\Delta E}$ is taken into account with
a two-dimensional kernel density estimation. We employ a data-driven method to
determine the parameters of the continuum background probability density
function (PDF) by fitting to the sideband region defined as $5.24<{M_{\rm
bc}}<5.27{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and $0.1<{\Delta
E}<0.3\mathrm{\,Ge\kern-1.00006ptV}$. The range is limited since selections
too far from the signal region may accept candidates too far kinematically
from the signal region. The $B\kern 1.79993pt\overline{\kern-1.79993ptB}{}$
background has a negligible contribution as within both ranges, only 0.07%
survive and we expect $B\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ to be
only a tenth of the total background. All signal and $B\kern
1.79993pt\overline{\kern-1.79993ptB}{}$ PDF parameters are fixed from
simulated data while all continuum PDF parameters are fixed from experimental
sideband data. The PDF parameters are identical for all $q.r$ bins. The
signal, continuum and $B\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ bin
fractions are fixed while the yields are allowed to float. The full PDF for
the signal component is given by

$P^{s}_{i}({M_{\rm bc}},{\Delta E},T_{c},q)=[1-q\times\Delta
w_{i}+q(1-2w_{i})\times(1-2\chi_{d})\mathcal{A}_{CP}]P^{s}({M_{\rm
bc}},{\Delta E},T_{c}),$ (3)

where $q$ is determined for the $i^{th}$ bin of the data set, $P^{s}({M_{\rm
bc}},{\Delta E},T_{c})$ is the signal PDF in ${M_{\rm bc}}$, ${\Delta E}$, and
$T_{c}$, $\mathcal{A}_{CP}$ is the direct ${\it CP}$ violation parameter,
$\chi_{d}=0.1875\pm 0.0017$ is the time-integrated
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{B}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$-mixing
asymmetry, $w_{i}$ is the wrong-tag fraction, and $\Delta w_{i}$ is the
difference in wrong tag fraction between positive and negative b-flavor tags
for bin $i$. The values of $w_{i}$, and $\Delta w_{i}$ are all fixed from MC.
The $\mathcal{A}_{CP}$ parameter is allowed to float but is not reported due
to limited statistics.

##  6 Systematic uncertainties

With the current 62.8 $\mbox{\,fb}^{-1}$ data set the dominant uncertainty is
statistical. As more experimental data are collected, the systematic
uncertainties will become more important. At this stage, we only examine the
largest sources of systematic uncertainty. We assume the sources to be
independent and add in quadrature the corresponding uncertainties. Table 1
summarizes the systematic uncertainty.

###  6.1 $\pi^{0}$ reconstruction efficiency

The systematic uncertainty associated with possible data-simulation
discrepancies is studied using the decays
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow
D^{*-}(\rightarrow\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}(\rightarrow
K^{+}\pi^{-}\pi^{0})\pi^{-})\pi^{+}$ and
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow
D^{*-}(\rightarrow\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}(\rightarrow
K^{+}\pi^{-})\pi^{-})\pi^{+}$ where the selection of charged particles is
identical and the $\pi^{0}$ selection is the same as the signal mode. The
signal yields of the two control channels are used to determine the $\pi^{0}$
reconstruction efficiency

$\epsilon^{\pi^{0}}=\frac{N(K^{-}\pi^{+}\pi^{0})}{N(K^{-}\pi^{+})}\cdot\frac{\mathcal{B}(\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow
K^{+}\pi^{-})}{\mathcal{B}(\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\rightarrow
K^{+}\pi^{-}\pi^{0})\cdot\mathcal{B}(\pi^{0}\rightarrow\gamma\gamma)}$ (4)

We compare the yields obtained from fits to the ${\Delta E}$ distribution of
reconstructed $B$ candidates and obtain an efficiency $\epsilon^{\pi^{0}}_{\rm
data}$ in data that agrees with the value observed in simulation within a 10%
uncertainty, which is used as a systematic uncertainty. The uncertainties on
the efficiencies for two $\pi^{0}$s are completely correlated and hence our
total systematic uncertainty is 20%.

###  6.2 Number of $B\kern 1.79993pt\overline{\kern-1.79993ptB}{}$

The calculation of the branching fraction uses the number of
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{B}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$
pairs, which is computed using the integrated luminosity, the
$e^{+}e^{-}\rightarrow\Upsilon{(4S)}$ cross-section BaBar:2014omp , and the
known value of the branching fraction of
$\Upsilon{(4S)}\rightarrow\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{B}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$.
We assign a systematic uncertainty of 1.34%, which includes the uncertainties
on the above quantities and uncertainties associated with the beam-energy
spread and potential offset of the c.m. energy.

###  6.3 Continuum PDF modeling

The continuum is modelled with an ARGUS function for ${M_{\rm bc}}$, a first
order Chebyshev function for ${\Delta E}$, and the sum of a Gaussian and
bifurcated Gaussian for $T_{c}$. The continuum background uses a total of 8
parameters, which are fixed from a fit to the sideband. The sideband for
${M_{\rm bc}}$ is defined as $0.1<{\Delta E}<0.2$ GeV while the sideband for
${\Delta E}$ and $T_{c}$ is defined as $5.26<{M_{\rm bc}}<5.27$ GeV/c2. We
vary the eight parameters of the sideband-based modeling of continuum
accounting for correlation and obtain a 10% systematic uncertainty.

Source | Systematic Uncertainty (%) |
---|---|---
$\pi^{0}$ efficiency | 20.0 |
$N(B\kern 1.79993pt\overline{\kern-1.79993ptB}{})$ | 1.34 |
Continuum PDF | 10.0 |
Total | 22.4 |
Table 1: Major systematic uncertainties where the total is calculated by
adding all the systematic uncertainties in quadrature.

##  7 Determination of branching ratio

We determine the branching fraction as

$\mathcal{B}=\frac{N}{\epsilon\times 2\times N_{B\kern
1.25995pt\overline{\kern-1.25995ptB}{}}}$ (5)

where $N$ is the signal yield obtained from the fits, $\epsilon$ is the
reconstruction and selection efficiency, and $N_{B\kern
1.25995pt\overline{\kern-1.25995ptB}{}}$ is the number of
$\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}\bar{\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}}$
pairs. The number of
$\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}\bar{\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}}$
pairs is obtained from the product of the measured integrated luminosity, the
$e^{+}e^{-}\rightarrow\Upsilon(4S)$ cross section ($1.110\pm 0.008$ nb)
BaBar:2014omp , and the $\Upsilon(4S)\rightarrow
B\mathit{{\mathit{{B}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}$
branching fraction ($f^{00}=0.487\pm 0.010\pm 0.008$) BaBar:2005uwr .

Based on simulations, we expect a signal yield of $21.0\pm 3.4$ events and 373
background events in our selection region. In data, we obtain a signal yield
of $14.0^{+6.8}_{-5.6}$ as shown in Figure 4 with a statistical significance
of 3.4 and 403 background events in our selection region. The statistical
significance is assessed by comparing the likelihood ratio observed in data
with the distribution on a sample of background-only simulated experiments.
The branching fraction is calculated to be
$\mathcal{B}(B^{0}\rightarrow\pi^{0}\pi^{0})=(0.98^{+0.48}_{-0.39}\pm
0.24)\times 10^{-6}$. The first uncertainties are statistical while the second
is systematic. This agrees with the previously measured value, ($1.59\pm
0.26)\times 10^{-6}$. The result is summarized in Table 2. The yield for the
control mode is $295\pm 31$, as shown in Figure 3, consistent with 288
expected from simulation.

Decay |  $\epsilon$ [%] |  Yield |  $\mathcal{B}[10^{-6}]$
---|---|---|---
$B^{0}\rightarrow\pi^{0}\pi^{0}$ |  21.0 |  $14.0^{+6.8}_{-5.6}$ | $0.98^{+0.48}_{-0.39}$
Table 2: Summary of signal efficiency $\epsilon$, signal yield in 2019-2020
Belle II data and resulting branching fraction. Only the statistical
contributions to the uncertainties are given here.

Figure 3: Distributions of ${\Delta E}$ (top), ${M_{\rm bc}}$ (middle), and
$T_{c}$ (bottom) for $B^{0}\rightarrow\mathit{{\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{D}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}^{0}(\rightarrow
K^{-}\pi^{+}\pi^{0})\pi^{0}$ reconstructed in 2019–2020 Belle II data. The
distributions are shown in signal-enriched regions of $5.275<{M_{\rm
bc}}<5.285{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and $-1<T_{c}<2$ for
${\Delta E}$, $-0.1<{\Delta E}<0.05\mathrm{\,Ge\kern-1.00006ptV}$ and
$-1<T_{c}<2$ for ${M_{\rm bc}}$ and $5.275<{M_{\rm
bc}}<5.285{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and $-0.1<{\Delta
E}<0.05\mathrm{\,Ge\kern-1.00006ptV}$ for $T_{c}$. Fit projections are
overlaid.

Figure 4: Distributions of ${\Delta E}$ (top), ${M_{\rm bc}}$ (middle), and
$T_{c}$ (bottom) for $B^{0}\rightarrow\pi^{0}\pi^{0}$ reconstructed in
2019–2020 Belle II data. The distributions are shown in signal-enriched
regions of $5.275<{M_{\rm bc}}<5.285{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$
and $-1<T_{c}<2$ for ${\Delta E}$, $-0.1<{\Delta
E}<0.05\mathrm{\,Ge\kern-1.00006ptV}$ and $-1<T_{c}<2$ for ${M_{\rm bc}}$ and
$5.275<{M_{\rm bc}}<5.285{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and
$-0.1<{\Delta E}<0.05\mathrm{\,Ge\kern-1.00006ptV}$ for $T_{c}$. Fit
projections are overlaid.

##  8 Summary

We report the first reconstruction of the $B^{0}\rightarrow\pi^{0}\pi^{0}$
decay in Belle II using 62.8 $\mbox{\,fb}^{-1}$ of data. An improved method of
selecting photons for signal reconstruction, photonMVA, that utilizes a
boosted decision tree rather than rectangular cuts is validated on
experimental data. We find a signal yield of $14.0^{+6.8}_{-5.6}$ events,
corresponding to a significance of 3.4 standard deviations and determine
$\mathcal{B}(B^{0}\rightarrow\pi^{0}\pi^{0})=(0.98^{+0.48}_{-0.39}\pm
0.27)\times 10^{-6}$, where the first uncertainty is statistical and the
second, systematic. With much larger data samples that are expected in the
near future, Belle II will be able to measure the direct CP violation
parameter, $\mathcal{A_{CP}}(B^{0}\rightarrow\pi^{0}\pi^{0})$ and provide
improved constraints on $\alpha/\phi_{2}$.

##  9 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.

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