Measurement of Hadronic Mass Moments ⟨ M n X ⟩ in B→ X c ℓν Decays at Belle II
Belle II Collaboration, F. Abudinén, I. Adachi, R. Adak, K. Adamczyk, P. Ahlburg, J. K. Ahn, H. Aihara, N. Akopov, A. Aloisio, F. Ameli, L. Andricek, N. Anh Ky, D. M. Asner, H. Atmacan, V. Aulchenko, T. Aushev, V. Aushev, T. Aziz, V. Babu, S. Bacher, S. Baehr, S. Bahinipati, A. M. Bakich, P. Bambade, Sw. Banerjee, S. Bansal, M. Barrett, G. Batignani, J. Baudot, A. Beaulieu, J. Becker, P. K. Behera, M. Bender, J. V. Bennett, E. Bernieri, F. U. Bernlochner, M. Bertemes, M. Bessner, S. Bettarini, V. Bhardwaj, B. Bhuyan, F. Bianchi, T. Bilka, S. Bilokin, D. Biswas, A. Bobrov, A. Bondar, G. Bonvicini, A. Bozek, M. Bračko, P. Branchini, N. Braun, R. A. Briere, T. E. Browder, D. N. Brown, A. Budano, L. Burmistrov, S. Bussino, M. Campajola, L. Cao, G. Caria, G. Casarosa, C. Cecchi, D. Červenkov, M. -C. Chang, P. Chang, R. Cheaib, V. Chekelian, C. Chen, Y. Q. Chen, Y. -T. Chen, B. G. Cheon, K. Chilikin, K. Chirapatpimol, H. -E. Cho, K. Cho, S. -J. Cho, S. -K. Choi, S. Choudhury, D. Cinabro, L. Corona, L. M. Cremaldi, D. Cuesta, S. Cunliffe, T. Czank, N. Dash, F. Dattola, E. De La Cruz-Burelo, G. De Nardo, M. De Nuccio, G. De Pietro, R. de Sangro, B. Deschamps, M. Destefanis, S. Dey, A. De Yta-Hernandez, A. Di Canto, F. Di Capua, S. Di Carlo, et al. (443 additional authors not shown)
BBelle
BELLE2-CONF-PH-2020-011September 9, 2020
Measurement of Hadronic Mass Moments (cid:104) M n X (cid:105) in B → X c (cid:96)ν (cid:96) Decays atBelle II
F. Abudin´en, I. Adachi,
24, 21
R. Adak, K. Adamczyk, P. Ahlburg,
J. K. Ahn, H. Aihara,
N. Akopov,
A. Aloisio,
97, 40
F. Ameli, L. Andricek, N. Anh Ky,
37, 14
D. M. Asner, H. Atmacan,
V. Aulchenko,
4, 74
T. Aushev, V. Aushev, T. Aziz, V. Babu, S. Bacher, S. Baehr, S. Bahinipati, A. M. Bakich,
P. Bambade,
Sw. Banerjee,
S. Bansal, M. Barrett, G. Batignani,
J. Baudot,
A. Beaulieu,
J. Becker, P. K. Behera, M. Bender, J. V. Bennett,
E. Bernieri, F. U. Bernlochner,
M. Bertemes, M. Bessner,
S. Bettarini,
V. Bhardwaj, B. Bhuyan, F. Bianchi,
T. Bilka, S. Bilokin, D. Biswas,
A. Bobrov,
4, 74
A. Bondar,
4, 74
G. Bonvicini,
A. Bozek, M. Braˇcko,
P. Branchini, N. Braun, R. A. Briere, T. E. Browder,
D. N. Brown,
A. Budano, L. Burmistrov,
S. Bussino,
M. Campajola,
97, 40
L. Cao,
G. Caria,
G. Casarosa,
C. Cecchi,
99, 42
D. ˇCervenkov, M.-C. Chang, P. Chang, R. Cheaib,
V. Chekelian, Y. Q. Chen,
Y.-T. Chen, B. G. Cheon, K. Chilikin, K. Chirapatpimol, H.-E. Cho, K. Cho, S.-J. Cho,
S.-K. Choi, S. Choudhury, D. Cinabro,
L. Corona,
L. M. Cremaldi,
D. Cuesta,
S. Cunliffe, T. Czank,
N. Dash, F. Dattola, E. De La Cruz-Burelo, G. De Nardo,
97, 40
M. De Nuccio, G. De Pietro, R. de Sangro, B. Deschamps,
M. Destefanis,
S. Dey, A. De Yta-Hernandez, A. Di Canto, F. Di Capua,
97, 40
S. Di Carlo,
J. Dingfelder,
Z. Doleˇzal, I. Dom´ınguez Jim´enez, T. V. Dong, K. Dort, D. Dossett,
S. Dubey,
S. Duell,
G. Dujany,
S. Eidelman,
4, 57, 74
M. Eliachevitch,
D. Epifanov,
4, 74
J. E. Fast, T. Ferber, D. Ferlewicz,
G. Finocchiaro, S. Fiore, P. Fischer,
A. Fodor, F. Forti,
A. Frey, M. Friedl, B. G. Fulsom, M. Gabriel, N. Gabyshev,
4, 74
E. Ganiev,
M. Garcia-Hernandez, R. Garg, A. Garmash,
4, 74
V. Gaur,
A. Gaz,
66, 67
U. Gebauer, M. Gelb, A. Gellrich, J. Gemmler, T. Geßler, D. Getzkow, R. Giordano,
97, 40
A. Giri, A. Glazov, B. Gobbo, R. Godang,
P. Goldenzweig, B. Golob,
P. Gomis, P. Grace,
W. Gradl, E. Graziani, D. Greenwald, Y. Guan,
C. Hadjivasiliou, S. Halder, K. Hara,
24, 21
T. Hara,
24, 21
O. Hartbrich,
T. Hauth, K. Hayasaka, H. Hayashii, C. Hearty,
M. Heck, M. T. Hedges,
I. Heredia de la Cruz,
6, 11
M. Hern´andez Villanueva,
A. Hershenhorn,
T. Higuchi,
E. C. Hill,
H. Hirata, M. Hoek, M. Hohmann,
S. Hollitt,
T. Hotta, C.-L. Hsu,
Y. Hu, K. Huang, T. Iijima,
66, 67
K. Inami, G. Inguglia, J. Irakkathil Jabbar, A. Ishikawa,
24, 21
R. Itoh,
24, 21
M. Iwasaki, Y. Iwasaki, S. Iwata, P. Jackson,
W. W. Jacobs, I. Jaegle,
D. E. Jaffe, E.-J. Jang, M. Jeandron,
H. B. Jeon, S. Jia, Y. Jin, C. Joo,
K. K. Joo, I. Kadenko, J. Kahn, H. Kakuno, A. B. Kaliyar, J. Kandra, K. H. Kang, P. Kapusta, R. Karl, G. Karyan,
Y. Kato,
66, 67
H. Kawai, T. Kawasaki, T. Keck, C. Ketter,
H. Kichimi, C. Kiesling, B. H. Kim, C.-H. Kim, D. Y. Kim, H. J. Kim, J. B. Kim, K.-H. Kim,
K. Kim, S.-H. Kim, a r X i v : . [ h e p - e x ] S e p .-K. Kim, Y. Kim, T. D. Kimmel,
H. Kindo,
24, 21
K. Kinoshita,
B. Kirby, C. Kleinwort, B. Knysh,
P. Kodyˇs, T. Koga, S. Kohani,
I. Komarov, T. Konno, S. Korpar,
N. Kovalchuk, T. M. G. Kraetzschmar, P. Kriˇzan,
R. Kroeger,
J. F. Krohn,
P. Krokovny,
4, 74
H. Kr¨uger,
W. Kuehn, T. Kuhr, J. Kumar, M. Kumar, R. Kumar, K. Kumara,
T. Kumita, T. Kunigo, M. K¨unzel,
12, 59
S. Kurz, A. Kuzmin,
4, 74
P. Kvasniˇcka, Y.-J. Kwon,
S. Lacaprara, Y.-T. Lai,
C. La Licata,
K. Lalwani, L. Lanceri, J. S. Lange, K. Lautenbach, P. J. Laycock, F. R. Le Diberder,
I.-S. Lee, S. C. Lee, P. Leitl, D. Levit, P. M. Lewis,
C. Li, L. K. Li,
S. X. Li, Y. M. Li, Y. B. Li, J. Libby, K. Lieret, L. Li Gioi, J. Lin, Z. Liptak,
Q. Y. Liu, Z. A. Liu, D. Liventsev,
S. Longo, A. Loos,
P. Lu, M. Lubej, T. Lueck, F. Luetticke,
T. Luo, C. MacQueen,
Y. Maeda,
66, 67
M. Maggiora,
S. Maity, R. Manfredi,
E. Manoni, S. Marcello,
C. Marinas, A. Martini,
M. Masuda,
15, 77
T. Matsuda,
K. Matsuoka,
66, 67
D. Matvienko,
4, 57, 74
J. McNeil,
F. Meggendorfer, J. C. Mei, F. Meier, M. Merola,
97, 40
F. Metzner, M. Milesi,
C. Miller,
K. Miyabayashi, H. Miyake,
24, 21
H. Miyata, R. Mizuk,
57, 26
K. Azmi,
G. B. Mohanty, H. Moon, T. Moon, J. A. Mora Grimaldo,
A. Morda, T. Morii,
H.-G. Moser, M. Mrvar, F. Mueller, F. J. M¨uller, Th. Muller, G. Muroyama, C. Murphy,
R. Mussa, K. Nakagiri, I. Nakamura,
24, 21
K. R. Nakamura,
24, 21
E. Nakano, M. Nakao,
24, 21
H. Nakayama,
24, 21
H. Nakazawa, T. Nanut, Z. Natkaniec, A. Natochii,
M. Nayak, G. Nazaryan,
D. Neverov, C. Niebuhr, M. Niiyama, J. Ninkovic, N. K. Nisar, S. Nishida,
24, 21
K. Nishimura,
M. Nishimura, M. H. A. Nouxman,
B. Oberhof, K. Ogawa, S. Ogawa, S. L. Olsen, Y. Onishchuk, H. Ono, Y. Onuki,
P. Oskin, E. R. Oxford, H. Ozaki,
24, 21
P. Pakhlov,
57, 65
G. Pakhlova,
26, 57
A. Paladino,
T. Pang,
A. Panta,
E. Paoloni,
S. Pardi, C. Park,
H. Park, S.-H. Park,
B. Paschen,
A. Passeri, A. Pathak,
S. Patra, S. Paul, T. K. Pedlar, I. Peruzzi, R. Peschke,
R. Pestotnik, M. Piccolo, L. E. Piilonen,
P. L. M. Podesta-Lerma, G. Polat, V. Popov, C. Praz, E. Prencipe, M. T. Prim,
M. V. Purohit, N. Rad, P. Rados, R. Rasheed,
M. Reif, S. Reiter, M. Remnev,
4, 74
P. K. Resmi, I. Ripp-Baudot,
M. Ritter, M. Ritzert,
G. Rizzo,
L. B. Rizzuto, S. H. Robertson,
64, 36
D. Rodr´ıguez P´erez, J. M. Roney,
C. Rosenfeld,
A. Rostomyan, N. Rout, M. Rozanska, G. Russo,
97, 40
D. Sahoo, Y. Sakai,
24, 21
D. A. Sanders,
S. Sandilya,
A. Sangal,
L. Santelj,
P. Sartori,
98, 41
J. Sasaki,
Y. Sato, V. Savinov,
B. Scavino, M. Schram, H. Schreeck, J. Schueler,
C. Schwanda, A. J. Schwartz,
B. Schwenker, R. M. Seddon, Y. Seino, A. Selce,
K. Senyo,
I. S. Seong,
J. Serrano, M. E. Sevior,
C. Sfienti, V. Shebalin,
C. P. Shen, H. Shibuya, J.-G. Shiu, B. Shwartz,
4, 74
A. Sibidanov,
F. Simon, J. B. Singh, S. Skambraks, K. Smith,
R. J. Sobie,
A. Soffer, A. Sokolov, Y. Soloviev, E. Solovieva, S. Spataro,
B. Spruck, M. Stariˇc, S. Stefkova, Z. S. Stottler,
R. Stroili,
98, 41
J. Strube, J. Stypula, M. Sumihama,
20, 77
K. Sumisawa,
24, 21
T. Sumiyoshi, D. J. Summers,
W. Sutcliffe,
K. Suzuki, S. Y. Suzuki,
24, 21
H. Svidras, M. Tabata, M. Takahashi, M. Takizawa,
82, 25, 84
U. Tamponi, S. Tanaka,
24, 21
K. Tanida, H. Tanigawa,
N. Taniguchi, Y. Tao,
P. Taras,
F. Tenchini, D. Tonelli, E. Torassa, K. Trabelsi,
T. Tsuboyama,
24, 21
N. Tsuzuki, M. Uchida, I. Ueda,
24, 21
S. Uehara,
24, 21
T. Ueno, T. Uglov,
57, 26
K. Unger, Y. Unno, S. Uno,
24, 21
P. Urquijo,
Y. Ushiroda,
24, 21, 127
Y. Usov,
4, 74
S. E. Vahsen,
R. van Tonder,
G. S. Varner,
K. E. Varvell,
A. Vinokurova,
4, 74
L. Vitale,
V. Vorobyev,
4, 57, 74
A. Vossen, E. Waheed,
2. M. Wakeling, K. Wan,
W. Wan Abdullah,
B. Wang, C. H. Wang, M.-Z. Wang, X. L. Wang, A. Warburton, M. Watanabe, S. Watanuki,
I. Watson,
J. Webb,
S. Wehle, M. Welsch,
C. Wessel,
J. Wiechczynski, P. Wieduwilt, H. Windel, E. Won, L. J. Wu, X. P. Xu, B. Yabsley,
S. Yamada, W. Yan,
S. B. Yang, H. Ye, J. Yelton,
I. Yeo, J. H. Yin, M. Yonenaga, Y. M. Yook, T. Yoshinobu, C. Z. Yuan, G. Yuan,
W. Yuan, Y. Yusa, L. Zani, J. Z. Zhang, Y. Zhang,
Z. Zhang,
V. Zhilich,
4, 74
Q. D. Zhou,
66, 68
X. Y. Zhou, V. I. Zhukova, V. Zhulanov,
4, 74 and A. Zupanc (Belle II Collaboration) Aix Marseille Universit´e, CNRS/IN2P3, CPPM, 13288 Marseille, France Beihang University, Beijing 100191, China Brookhaven National Laboratory, Upton, New York 11973, U.S.A. Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russian Federation Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A. Centro de Investigacion y de Estudios Avanzados delInstituto Politecnico Nacional, Mexico City 07360, Mexico Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic Chiang Mai University, Chiang Mai 50202, Thailand Chiba University, Chiba 263-8522, Japan Chonnam National University, Gwangju 61186, South Korea Consejo Nacional de Ciencia y Tecnolog´ıa, Mexico City 03940, Mexico Deutsches Elektronen–Synchrotron, 22607 Hamburg, Germany Duke University, Durham, North Carolina 27708, U.S.A. Institute of Theoretical and Applied Research(ITAR), Duy Tan University, Hanoi 100000, Vietnam Earthquake Research Institute, University of Tokyo, Tokyo 113-0032, Japan Forschungszentrum J¨ulich, 52425 J¨ulich, Germany Department of Physics, Fu Jen Catholic University, Taipei 24205, Taiwan Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) andInstitute of Modern Physics, Fudan University, Shanghai 200443, China II. Physikalisches Institut, Georg-August-Universit¨at G¨ottingen, 37073 G¨ottingen, Germany Gifu University, Gifu 501-1193, Japan The Graduate University for Advanced Studies (SOKENDAI), Hayama 240-0193, Japan Gyeongsang National University, Jinju 52828, South Korea Department of Physics and Institute of NaturalSciences, Hanyang University, Seoul 04763, South Korea High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan J-PARC Branch, KEK Theory Center, High Energy AcceleratorResearch Organization (KEK), Tsukuba 305-0801, Japan Higher School of Economics (HSE), Moscow 101000, Russian Federation Indian Institute of Science Education and Research Mohali, SAS Nagar, 140306, India Indian Institute of Technology Bhubaneswar, Satya Nagar 751007, India Indian Institute of Technology Guwahati, Assam 781039, India Indian Institute of Technology Hyderabad, Telangana 502285, India Indian Institute of Technology Madras, Chennai 600036, India Indiana University, Bloomington, Indiana 47408, U.S.A. Institute for High Energy Physics, Protvino 142281, Russian Federation Institute of High Energy Physics, Vienna 1050, Austria Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China Institute of Particle Physics (Canada), Victoria, British Columbia V8W 2Y2, Canada Institute of Physics, Vietnam Academy of Science and Technology (VAST), Hanoi, Vietnam Instituto de Fisica Corpuscular, Paterna 46980, Spain INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy INFN Sezione di Napoli, I-80126 Napoli, Italy INFN Sezione di Padova, I-35131 Padova, Italy INFN Sezione di Perugia, I-06123 Perugia, Italy INFN Sezione di Pisa, I-56127 Pisa, Italy INFN Sezione di Roma, I-00185 Roma, Italy INFN Sezione di Roma Tre, I-00146 Roma, Italy INFN Sezione di Torino, I-10125 Torino, Italy INFN Sezione di Trieste, I-34127 Trieste, Italy Advanced Science Research Center, Japan Atomic Energy Agency, Naka 319-1195, Japan Johannes Gutenberg-Universit¨at Mainz, Institut f¨ur Kernphysik, D-55099 Mainz, Germany Justus-Liebig-Universit¨at Gießen, 35392 Gießen, Germany Institut f¨ur Experimentelle Teilchenphysik, KarlsruherInstitut f¨ur Technologie, 76131 Karlsruhe, Germany Kitasato University, Sagamihara 252-0373, Japan Korea Institute of Science and Technology Information, Daejeon 34141, South Korea Korea University, Seoul 02841, South Korea Kyoto Sangyo University, Kyoto 603-8555, Japan Kyungpook National University, Daegu 41566, South Korea P.N. Lebedev Physical Institute of the Russian Academyof Sciences, Moscow 119991, Russian Federation Liaoning Normal University, Dalian 116029, China Ludwig Maximilians University, 80539 Munich, Germany Luther College, Decorah, Iowa 52101, U.S.A. Malaviya National Institute of Technology Jaipur, Jaipur 302017, India Max-Planck-Institut f¨ur Physik, 80805 M¨unchen, Germany Semiconductor Laboratory of the Max Planck Society, 81739 M¨unchen, Germany McGill University, Montr´eal, Qu´ebec, H3A 2T8, Canada Moscow Physical Engineering Institute, Moscow 115409, Russian Federation Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602, Japan Institute for Advanced Research, Nagoya University, Nagoya 464-8602, Japan Nara Women’s University, Nara 630-8506, Japan Department of Physics, National Taiwan University, Taipei 10617, Taiwan National United University, Miao Li 36003, Taiwan H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342, Poland Niigata University, Niigata 950-2181, Japan Novosibirsk State University, Novosibirsk 630090, Russian Federation Okinawa Institute of Science and Technology, Okinawa 904-0495, Japan Osaka City University, Osaka 558-8585, Japan Research Center for Nuclear Physics, Osaka University, Osaka 567-0047, Japan Pacific Northwest National Laboratory, Richland, Washington 99352, U.S.A. Panjab University, Chandigarh 160014, India Peking University, Beijing 100871, China Punjab Agricultural University, Ludhiana 141004, India Meson Science Laboratory, Cluster for Pioneering Research, RIKEN, Saitama 351-0198, Japan Seoul National University, Seoul 08826, South Korea Showa Pharmaceutical University, Tokyo 194-8543, Japan Soochow University, Suzhou 215006, China Soongsil University, Seoul 06978, South Korea J. Stefan Institute, 1000 Ljubljana, Slovenia Taras Shevchenko National Univ. of Kiev, Kiev, Ukraine Tata Institute of Fundamental Research, Mumbai 400005, India Department of Physics, Technische Universit¨at M¨unchen, 85748 Garching, Germany Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel Toho University, Funabashi 274-8510, Japan Department of Physics, Tohoku University, Sendai 980-8578, Japan Tokyo Institute of Technology, Tokyo 152-8550, Japan Tokyo Metropolitan University, Tokyo 192-0397, Japan Universidad Autonoma de Sinaloa, Sinaloa 80000, Mexico Dipartimento di Scienze Fisiche, Universit`a di Napoli Federico II, I-80126 Napoli, Italy Dipartimento di Fisica e Astronomia, Universit`a di Padova, I-35131 Padova, Italy Dipartimento di Fisica, Universit`a di Perugia, I-06123 Perugia, Italy
Dipartimento di Fisica, Universit`a di Pisa, I-56127 Pisa, Italy
Universit`a di Roma “La Sapienza,” I-00185 Roma, Italy
Dipartimento di Matematica e Fisica, Universit`a di Roma Tre, I-00146 Roma, Italy
Dipartimento di Fisica, Universit`a di Torino, I-10125 Torino, Italy
Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy
Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, H3C 3J7, Canada
Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
Universit´e de Strasbourg, CNRS, IPHC, UMR 7178, 67037 Strasbourg, France
Department of Physics, University of Adelaide, Adelaide, South Australia 5005, Australia
University of Bonn, 53115 Bonn, Germany
University of British Columbia, Vancouver, British Columbia, V6T 1Z1, Canada
University of Cincinnati, Cincinnati, Ohio 45221, U.S.A.
University of Florida, Gainesville, Florida 32611, U.S.A.
University of Hawaii, Honolulu, Hawaii 96822, U.S.A.
University of Heidelberg, 68131 Mannheim, Germany
Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia
University of Louisville, Louisville, Kentucky 40292, U.S.A.
National Centre for Particle Physics, University Malaya, 50603 Kuala Lumpur, Malaysia
University of Maribor, 2000 Maribor, Slovenia
School of Physics, University of Melbourne, Victoria 3010, Australia
University of Mississippi, University, Mississippi 38677, U.S.A.
University of Miyazaki, Miyazaki 889-2192, Japan
University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.
University of Science and Technology of China, Hefei 230026, China
University of South Alabama, Mobile, Alabama 36688, U.S.A.
University of South Carolina, Columbia, South Carolina 29208, U.S.A.
School of Physics, University of Sydney, New South Wales 2006, Australia
Department of Physics, University of Tokyo, Tokyo 113-0033, Japan
Kavli Institute for the Physics and Mathematics of theUniverse (WPI), University of Tokyo, Kashiwa 277-8583, Japan
University of Victoria, Victoria, British Columbia, V8W 3P6, Canada Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, U.S.A.
Wayne State University, Detroit, Michigan 48202, U.S.A.
Yamagata University, Yamagata 990-8560, Japan
Alikhanyan National Science Laboratory, Yerevan 0036, Armenia
Yonsei University, Seoul 03722, South Korea
Abstract
We present measurements of the first six hadronic mass moments in semileptonic B → X c (cid:96)ν (cid:96) decays. Thehadronic mass moments, together with other observables of inclusive B decays, can be used to determine theCKM matrix element (cid:12)(cid:12) V cb (cid:12)(cid:12) and mass of the b -quark m b in the context of Heavy Quark Expansions of QCD.The Belle II data recorded at the Υ ( ) resonance in 2019 and 2020 (March-July), corresponding to anintegrated luminosity of 34 . − , is used for this measurement. The decay Υ ( ) → B B is reconstructedby applying the hadronic tagging algorithm provided by the Full Event Interpretation to fully reconstruct one B meson. The second B meson is reconstructed inclusively by selecting a high-momentum lepton. The X c system is identified by the remaining reconstructed tracks and clusters in the electromagnetic calorimeter. Wereport preliminary results for the hadronic mass moments (cid:104) M n X (cid:105) with n = 1 , . . . ,
6, measured as a function ofa lower cut on the lepton momentum in the signal B rest frame. . INTRODUCTION The mass moments (cid:104) M n X (cid:105) of the hadronic system in inclusive semileptonic B → X c (cid:96)ν (cid:96) decayscan be used to measure non-perturbative QCD parameters and the CKM matrix element | V cb | . Thestate-of-the-art procedure relies on combining the information from mass moments, with measuredmoments from the lepton energy spectrum and B → X s γ information, to perform a combined fitusing theory predictions building on the Heavy Quark Expansions of QCD to determine | V cb | andthe b quark mass m b . See e.g. Ref. [1] for a recent review.This work presents the first results of hadronic mass moments (cid:104) M n X (cid:105) with n = 1 , . . . ,
6, measuredat the Belle II experiment. In this analysis, semileptonic B → X c (cid:96)ν (cid:96) decays are reconstructedinclusively by selecting a high-momentum lepton. The other B meson is fully reconstructed inhadronic modes via the Full Event Interpretation (FEI) [2]. This B meson is referred to as thetag-side B meson ( B tag ) throughout this note. We subtract the remaining background componentsby assigning a continuous signal probability as a function of the reconstructed mass of the hadronic X c system ( M X ) to each event. A calibration procedure is applied to correct for a bias in thereconstructed M X spectrum due to experimental effects. The hadronic mass moments are calculatedas a weighted mean of the calibrated M X distribution, where the events are weighted with theaforementioned signal probability.The rest of this note is organized as follows. Section 2 briefly describes the Belle II detectorand how the inclusive B → X c (cid:96)ν (cid:96) decays are simulated. The reconstruction of the Υ ( ) eventsis discussed in Section 3. The procedure for subtracting remaining background components fromthe measured M X spectrum is introduced in Section 4. Section 5 discusses the extraction andcalibration of the reconstructed M X distributions. In addition, the handling of statistical andsystematic uncertainties is explained and the measured M X values are given. Finally, Section 6presents our conclusions.
2. BELLE II DETECTOR AND DATA SET
The Belle II detector [3] is operated at the SuperKEKB electron-positron collider [4] and islocated at the KEK laboratory in Tsukuba, Japan. The detector consists of several nested detectorsubsystems arranged around the beam pipe in a cylindrical geometry. Sub-detectors relevant forthis analysis are briefly described here; a description of the full detector is given in [3, 5]. Theinnermost subsystem is the vertex detector, which includes two layers of silicon pixel detectors andfour outer layers of silicon strip detectors. Currently, the second pixel layer is installed to cover onlya small part of the solid angle, while the remaining vertex detector layers are fully installed. Mostof the tracking volume consists of a helium and ethane-based small-cell drift chamber. Surroundingthe drift chamber (CDC), the Cherenkov-light imaging and time-of-propagation detector providescharged-particle identification in the barrel region. In the forward end-cap, this function is providedby a proximity-focusing, ring-imaging Cherenkov detector with an aerogel radiator. The nextsub-detector layer consists of the electromagnetic calorimeter (ECL), composed of barrel and twoend-cap sections made of CsI(Tl) crystals. The inner detector is immersed in a uniform magneticfield with a field strength of 1 . K and muon identification system.The data sample used in this analysis was collected in 2019 and from March to July 2020 at acenter-of-mass (CM) energy of √ s = 10 .
58 GeV, corresponding to the mass of the Υ ( ) resonance.The energies of the electron and positron beams are 7 GeV and 4 GeV, respectively, resulting in aboost of βγ = 0 .
28 of the CM frame relative to the laboratory frame. The integrated luminosity of7
ABLE I: Branching fractions used in the simulation of B → X c (cid:96)ν (cid:96) decays in this analysis B Value B + Value B B → D (cid:96) + ν (cid:96) (2 . ± . × − (2 . ± . × − B → D ∗ (cid:96) + ν (cid:96) (5 . ± . × − (5 . ± . × − B → D (cid:96) + ν (cid:96) (4 . ± . × − (4 . ± . × − ( (cid:44) → D ∗ π ) B → D (cid:96) + ν (cid:96) (3 . ± . × − (2 . ± . × − ( (cid:44) → Dππ ) B → D ∗ (cid:96) + ν (cid:96) (1 . ± . × − (1 . ± . × − ( (cid:44) → D ∗ π ) B → D ∗ (cid:96) + ν (cid:96) (2 . ± . × − (2 . ± . × − ( (cid:44) → Dπ ) B → D ∗ (cid:96) + ν (cid:96) (3 . ± . × − (3 . ± . × − ( (cid:44) → Dπ ) B → D (cid:48) (cid:96) + ν (cid:96) (4 . ± . × − (4 . ± . × − ( (cid:44) → D ∗ π ) B → Dπ (cid:96) + ν (cid:96) (1 . ± . × − (1 . ± . × − B → D ∗ π (cid:96) + ν (cid:96) (1 . ± . × − (1 . ± . × − B → Dππ (cid:96) + ν (cid:96) (0 . ± . × − (0 . ± . × − B → D ∗ ππ (cid:96) + ν (cid:96) (2 . ± . × − (2 . ± . × − B → Dη (cid:96) + ν (cid:96) (2 . ± . × − (2 . ± . × − B → D ∗ η (cid:96) + ν (cid:96) (2 . ± . × − (2 . ± . × − B → X c (cid:96)ν (cid:96) (10 . ± . × − (10 . ± . × − the data sample amounts to 34 . − .Monte Carlo (MC) samples of B meson decays are simulated using the EvtGen generator [6].The sample size corresponds to an integrated luminosity of 200 fb − . The interactions of particlesinside the detector are simulated using Geant4 [7]. Electromagnetic final-state radiation (FSR)is simulated using the
PHOTOS [8] package. The simulation of the continuum background process e + e − → qq ( q = u , d , s , c ) is carried out with KKMC [9], interfaced with
Pythia [10]. All recordedcollisions and simulated events were analyzed in the basf2 framework [11] and a summary of thetrack and ECL reconstruction algorithms can be found in Ref. [12] and Ref. [5], respectively.The B → X c (cid:96)ν (cid:96) spectrum is modeled as a mixture of resonant and non-resonant decays. B → D (cid:96)ν (cid:96) decays are modeled using the BGL form factors [13] with central values taken from the fitin Ref. [14]. To simulate B → D ∗ (cid:96)ν (cid:96) decays, the CLN form factors [15] are used with central valuestaken from Ref. [16]. The decays of the four orbitally excited D meson states ( D , D ∗ , D (cid:48) and D ∗ ),denoted as D ∗∗ , are simulated with a LLSW form factor inspired parametrization [17], using thecentral values and parametrization from Ref. [18]. The non-resonant part of the X c spectrum issimulated as a composition of B → D ( ∗ ) π(cid:96)ν (cid:96) , B → D ( ∗ ) ππ(cid:96)ν (cid:96) and B → D ( ∗ ) η(cid:96)ν (cid:96) decays. The firstdecay is simulated using the decay model proposed by Goity and Roberts [19], while the remainingtwo decays are modeled with a pure phase-space prescription. The branching fractions used for thesimulation of B → X c (cid:96)ν (cid:96) decays are given in Table I.
3. EVENT RECONSTRUCTION Υ ( ) → B B events are tagged by fully reconstructing one B meson decaying hadronically, also8eferred to as the tag-side B tag meson. The other B meson is reconstructed inclusively by selectinga high-momentum lepton. The X -system is defined by the rest of the event (ROE), consistingof additional unassigned charged particles and neutral clusters in the ECL. Event-level pre-cutsare applied to reduce the number of continuum and low-multiplicity background components. Weselect events with at least four reconstructed charged tracks. Additionally, we require at least twotracks with | d | < . | z | < p T > . /c , as well as at least two ECL clusterswith E > . θ inside the CDC acceptance. Here, z denotes the signeddistance in the z direction (parallel to the beams and the magnetic field) of closest approach to theinteraction point (POCA). Further, d is the signed distance transverse to the z direction to thePOCA. To reject continuum events, the event is required to pass R < .
4, where R is the ratio ofthe second to the zeroth Fox-Wolfram moment [20]. These event shape variables are calculatedusing all charged tracks and ECL clusters passing the selection criteria mentioned above. Finally,the event is required to have a greater visible energy in the CM frame than 4 GeV, while the totalenergy in the ECL is required to lie between 2 < E ECL < The tag-side B tag candidate is reconstructed using the hadronic tagging algorithm provided bythe Full Event Interpretation (FEI) [2]. The FEI uses a fully automated approach to hierarchicallyreconstruct a tag-side B meson and infers a signal probability P FEI for each reconstructed B tag candidate based on multivariate analysis (MVA) techniques. The algorithm uses an exclusivereconstruction approach resulting in O (10 (cid:48) B decay chains. We use a skimmed versionof the data with reconstructed B tag candidates passing P FEI > . M bc > .
24 GeV /c and | ∆ E | < . M bc and energy difference ∆ E are defined as M bc = (cid:114) s − ( p ∗ B tag ) , (1)∆ E = E ∗ B tag − √ s , (2)where p ∗ B tag and E ∗ B tag denote the reconstructed B tag three-momentum and energy, respectively, inthe CM frame. To further reduce the combinatorial complexity, only the three candidates with thehighest FEI signal probability per event for the B tag candidates are considered in the subsequentstages of the analysis. B → X (cid:96)ν (cid:96) Decays
We select e ± , µ ± and K ± candidates by using the normalized charged particle identification(PID) from sub-detector information. The e ± , µ ± and K ± candidates are required to have a PIDvalue greater than 0.9, 0.9 and 0.6, respectively. Additionally, the respective tracks are requiredto pass dr < | dz | < θ value inside the CDCacceptance. Here, dr and dz denote the track’s d and z values, respectively, of its POCA relativeto the interaction point. To construct the ROE object, we reconstruct all remaining tracks andECL clusters assuming that they are π ± and photons, respectively.Electron candidates are corrected for bremsstrahlung by identifying suitable photon candidates.At this stage, the selected light-lepton candidates ( (cid:96) = e , µ ) are combined with the B tag candidatesto form an Υ ( ) candidate. Due to the fully reconstructed tag-side candidate and the knowninitial state of the e + e − collision, the lepton momentum in the signal B rest frame, denoted as p ∗ (cid:96) ,9s accessible. We require lepton candidates with p ∗ (cid:96) > . /c . The charge correlations betweenthe b quark of the B tag and the signal lepton candidates are not considered when recombining the Υ ( ) candidate, resulting in the eight reconstruction channels B +tag (cid:96) ± and B (cid:96) ± . In the finalanalysis, only the B +tag (cid:96) − and B (cid:96) ± are considered as signal channels. The two B +tag (cid:96) + channelsare background enriched and used to verify the description of the background modeling.The hadronic X -system is identified from the ROE of the Υ ( ) candidate. The ROE isconstructed using the remaining charged particle and photon candidates that were not used inthe reconstruction of the Υ ( ) candidate. The mass hypothesis of the individual track objectis based on the PID selection. Remaining tracks associated with a kaon likelihood greater than0 . Υ ( ) decay, we consider only tracks in the ROEwith dr < | dz | < θ value within the CDC acceptance.Low-momentum tracks curling inside the CDC are removed prior to construction of the ROE. Photoncandidates are required to pass a region-dependent cut. We select only photons with p T >
20 MeVand P Zernike > . p T >
30 MeV and P Zernike > .
15 and p T >
20 MeV and P Zernike > . P Zernike denotes theMVA classifier output using Zernike moments [21] of the different clusters. A second ROE object isconstructed with the same selection criteria for the B tag candidate. It is used to calculate a set ofcontinuum suppression variables consisting of CLEO cones [22], modified Fox-Wolfram moments[23] and thrust information. These variables are used as input for a boosted decision tree (BDT)to separate B B from continuum events. We use the BDT algorithm implemented in the
FastBDT library [24].To further reject backgrounds from leptons of secondary decays, misidentified hadrons orcontinuum events, a cut-based approach is chosen.Secondary leptons and hadronic fakes are reduced by selecting signal lepton candidates passing p ∗ (cid:96) > . /c . To improve the purity of the tag-side reconstruction, we require B tag candidateswith P FEI > .
01 and M bc > .
27 GeV /c . Continuum events are rejected by cutting on theclassifier output of the continuum suppression BDT P CS . We select candidates with P CS > . X -system, we require the absolute value of the totalcharge of the reconstructed event Q tot = Q B tag + Q (cid:96) + Q X to be less than or equal to one, explicitlyallowing a charge imbalance. Further, the X -system is required to contain at least one chargedparticle. The missing momentum p miss and missing energy E miss are required to be greater than0 . /c and 0 . E miss − c · p miss should be smaller than0 . p µ miss = p µe + e − − p µ B tag − p µ(cid:96) − p µ X . (3)The event selection criteria are summarized in Table II. If multiple B tag (cid:96) combinations arepresent in an event after applying all selection criteria, a best candidate selection (BCS) basedon the highest p ∗ (cid:96) is performed. In the case where the same lepton is combined with two differenttag-side candidates, the B tag candidate with the smallest ∆ E is chosen.Figure 1 shows the reconstructed M X distribution for the full recorded data set with a totalintegrated luminosity of 34 . − . The displayed MC sample corresponds to an integrated luminosityof 100 fb − and has been scaled to match the luminosity of the recorded data set. The MCcomponents are corrected for differences in PID and FEI efficiencies between data and simulation.We correct fake lepton candidates matched to a π particle on MC level. The FEI correction factorsfor the B B components are determined in Ref. [25], while the correction factors for the continuumcomponent are determined in the side-band of the continuum suppression BDT.10
ABLE II: Event selection criteria applied to the reconstructed Υ ( ) candidates.Variable Applied Cut Value p ∗ (cid:96) > . /cM bc > .
27 GeV /c P FEI > . P CS > . | Q tot | ≤ N tracks , X ≥ E miss > . p miss > . /c | E miss − c · p miss | < . E v e n t s / ( . G e V / c ) ×10 Belle II (preliminary) L dt = 34.6 fb B X u B DB DB D other
B X c B X
CascadeHadronFakeother
BBe + e qq UncertaintyData M X [GeV/c ]0.751.001.25 D a t a / M C FIG. 1: Reconstructed M X distribution with event selection criteria and BCS applied. The uncertainty bandcovers the MC statistics, signal lepton PID efficiency and pion fake rate correction, and the FEI efficiencycorrection for B B and continuum events. At the bottom the per bin ratio of data and MC is shown. Thegrey boxes display the ratio between the MC expectation taking into account its uncertainty and the nominalvalue.
4. BACKGROUND SUBTRACTION
The calculation of the hadronic mass moments of B → X c (cid:96)ν (cid:96) decays requires the subtractionof the remaining background components from the measured events. To verify the description ofthe background components in MC, the background enriched reconstruction channels B +tag (cid:96) + areused. A two component template fit of the M X distribution is used to determine the number of11 E v e n t s / ( . G e V / c ) B + + p > 1.0 GeV Belle II (preliminary) L dt = 34.6 fb M X [GeV/c ]0.751.001.25 D a t a / M C M X [GeV/c ]0100200300400500600 E v e n t s / ( . G e V / c ) Belle II (preliminary) L dt = 34.6 fb B + + p > 1.0 GeV N bkg,fit N bkg,MC = 1.03 ± 0.05SignalBackgroundMC UncertaintyData FIG. 2: M X distribution in the B + (cid:96) + channels for a lower limit of p ∗ (cid:96) > . /c . The pre-fit M X spectrumsplit into sub-components and the post-fit distribution of the two component template fit are shown in theleft and right plot, respectively. background events in data. The background component yield is fitted, while the normalization ofthe signal template is fixed. This check is performed for different lower limits on p ∗ (cid:96) . The ratio ofthe fitted number of background events to the MC expectation is compatible to unity for all lower p ∗ (cid:96) cuts. Figure 2 shows the pre-fit M X spectrum split into sub-components in the B +tag (cid:96) + channelfor a lower limit on the lepton momentum of p ∗ (cid:96) > . /c as well as the post-fit distribution ofthe signal and background fit.We subtract the background by assigning a signal probability to each event. The signal probability w i ( M X ) is determined from a fit of the bin-wise difference between the measured M X spectrumand the remaining background MC components normalized to the measured distribution w i ( M X ) = N data i − N bkg , MC i N data i , (4)where the index i denotes the corresponding M X bin. To get a continuous description of thesignal probability, we fit a series of Legendre polynomials to the bin-wise probabilities. Priorto fitting, the fit-range is transformed to the interval [ − ,
1] to exploit the orthogonal nature ofthe polynomials. The order of the Legendre polynomial is determined by cutting off the serieswhen the next higher order fitted coefficient is compatible with zero. If the fit reaches a minimumin the background dominated low or high hadronic mass values, the polynomial is replaced bya constant value equal to the found minimum. The procedure is performed for different lowerlimits on the lepton momentum p ∗ (cid:96) . Figure 3 shows the fitted signal probability as a functionof the reconstructed M X with p ∗ (cid:96) > . /c and the measured M X spectrum compared to thebackground MC components. 12 E v e n t s / ( . G e V / c ) ×10 p > 0.8 GeV Belle II (preliminary) L dt = 34.6 fb B X u B DB DB D other
B X c B X
CascadeHadronFakeother
BBe + e qq UncertaintyData M X [GeV/c ]0.751.001.25 D a t a / M C FIG. 3: The left column shows the M X distribution in data and background MC (normalized to the eventsin data) for p ∗ (cid:96) > . /c . The corresponding background subtraction factors w i are shown in the rightcolumn together with a fitted Legendre polynomial of degree 7. If the fit has a minimum at the left or righttail, the polynomial is replaced with a constant value. The uncertainties are from statistical uncertaintiesonly.
5. MEASUREMENT OF HADRONIC MASS MOMENTS5.1. Extraction of Moments
To extract unbiased moments, the measured M n X spectrum has to be corrected for effects thatdistort the measured distribution. We derive calibration functions based on MC simulation todescribe the relationship between the reconstructed moments (cid:104) M n X , reco (cid:105) and the moments calculatedat the generator level (cid:104) M n X , true (cid:105) . Both moments are calculated in bins of the generator level M n X distribution. We find a linear relationship between (cid:104) M n X , reco (cid:105) and (cid:104) M n X , true (cid:105) , which allows us tocalculate a calibrated M X value M n X , calib = M n X − c ( E miss − p miss , X mult , p ∗ (cid:96) ) m ( E miss − p miss , X mult , p ∗ (cid:96) ) . (5)Here c and m denote the fitted intercept and slope of the linear calibration functions, respectively.Since the bias of the measured M X spectrum is not constant over the available phase-space, thecalibration is performed in bins of p ∗ (cid:96) , E miss − p miss , and the particle multiplicity of the X -systemdenoted as X mult . We use bins in p ∗ (cid:96) with a width of 0 . /c between 0 . . /c and onebin for p ∗ (cid:96) ≥ . /c . A binning of [ − . , . , . , .
5] GeV and [1 , ,
30] is used for E miss − c · p miss and X mult , respectively. Due to limited statistics in the phase space above p ∗ (cid:96) ≥ . /c , theadditional binning in E miss − c · p miss and X mult is not used in this region. Figure 4 shows anexample of three calibration curves for (cid:104) M X (cid:105) in three bins of p ∗ (cid:96) and one bin in E miss − c · p miss and X mult . Figure 5 shows the second hadronic mass moment (cid:104) M X (cid:105) from signal MC before andafter the application of the calibration procedure. The second moments of the B → X c (cid:96)ν (cid:96) MC atgenerator level with and without the application of event selection criteria are also shown.Together with the signal probability w i and the calibrated M X , calib distribution, the (cid:104) M n X (cid:105) canbe calculated without unfolding the measured M X spectrum. The hadronic mass moments are13 .0 2.5 3.0 3.5 4.0< M X, true > [GeV/c ]1.52.02.53.03.54.0 < M X , r e c o > [ G e V / c ] Belle II (simulation)
Belle II (simulation)
Belle II (simulation) E miss p miss (0.05, 0.2] GeVX mult (0, 8] p (0.8, 0.9] GeV p (1.4, 1.5] GeV p (1.9, 3.0] GeV FIG. 4: Example of the calibration curves for the first moment (cid:104) M X (cid:105) in bins of E miss − p miss , X mult and p ∗ (cid:96) .The moments (cid:104) M X , reco (cid:105) versus (cid:104) M X , true (cid:105) calculated in bins of M X , true are shown. The uncertainty of thecalibration curves takes into account the statistical uncertainty on the fitted slope and intercept. The reddashed reference line shows (cid:104) M X , true (cid:105) = (cid:104) M X , reco (cid:105) calculated as a weighted average using (cid:104) M n X (cid:105) = (cid:80) i w i ( M X ) M X , calib ni (cid:80) i w i ( M X ) × C calib × C true . (6)The two additional factors C calib and C true correct a remaining bias due to the calibration andselection efficiencies for different B → X c (cid:96)ν (cid:96) components. The factor C calib = (cid:104) M n X , true (cid:105) / (cid:104) M n X , calib (cid:105) corrects the remaining bias of the calibrated moments and the true moments for each lower limit on p ∗ (cid:96) . We observe remaining bias corrections ranging between 1 .
001 for the first moment up to 0 .
988 forthe fourth moment. To correct a possible bias due to the event selection criteria applied, we applya second correction factor C true = (cid:104) M n X , true , signal (cid:105) / (cid:104) M n X , true (cid:105) . Here, (cid:104) M n X , true , signal (cid:105) are the momentsof the generator M X spectrum of our simulated B → X c (cid:96)ν (cid:96) decays without the application of theaforementioned event selection criteria. Only a cut on the generator level lepton momentum in thesignal B meson rest frame is applied. To be able to correct for the effect of final state radiationon the lepton momentum, the MC sample used to calculate (cid:104) M n X , true , signal (cid:105) does not include thesimulation of radiative photons with PHOTOS . We obtain values for C true ranging from 1 .
02 to 1 . p ∗ (cid:96) cut. For higher p ∗ (cid:96) cuts the C true ranges from 1 .
00 to 1 .
01 for the highest cut value.
We identify several sources of statistical and systematic uncertainties. The total uncertainty iscalculated by adding statistical and systematic uncertainties in quadrature.For the statistical uncertainty, we consider two different components. The (cid:104) M n X (cid:105) are calculatedas a weighted mean over all events. We calculate the variance of the weighted mean as [26] V ( (cid:104) M n X (cid:105) ) = n ( n − (cid:80) ni w i n (cid:88) i w i ( M n X , calib ,i − (cid:104) M n X (cid:105) ) . (7)We verifie the validity of this formula applying a bootstrapping approach. The second part of thestatistical uncertainty is given by the statistical uncertainty of the polynomial coefficients of thesignal probability function. The uncertainty is propagated by using error propagation to calculate14 .8 1.0 1.2 1.4 1.6 1.8 p Cut [GeV/c]3.03.54.04.55.05.5 < M X > [( G e V / c ) ] Belle II (simulation)
True w/o SelectionRecoTrueCalibrated
FIG. 5: Second hadronic mass moment (cid:104) M X (cid:105) calculated on signal MC for different lower limits on p ∗ (cid:96) . Theplotted moments are the measured uncalibrated, calibrated and true moments after the application of allanalysis selection criteria. In addition, the true (cid:104) M X (cid:105) calculated from the MC sample without any selectioncriteria applied are shown as red crosses. the uncertainty on the signal probability. To estimate the impact of the propagated uncertaintyon the measured (cid:104) M n X (cid:105) , the calculation of the moments is repeated with varied signal probabilityvalues. The total statistical uncertainty is calculated by summing both uncertainties in quadrature.To estimate the impact of systematic uncertainties, the following effects are taken into account:1. Statistical uncertainty on the linear calibration functions:The used linear calibration functions are determined using a dedicated MC sample of B → X c (cid:96)ν (cid:96) decays. Both the slope and the intercept have statistical uncertainties and arecorrelated. To propagate the uncertainties correctly with their correlations, the eigenvaluesand eigenvectors of the covariance matrix are used to calculate two orthogonal variations ofboth parameters via c ± i = c nomi ± (cid:112) λ i ˆ e i , (8)where c nomi and c ± i denote the nominal and varied parameters, respectively, of the linearcalibration function. λ i and ˆ e i are the i -th eigenvalue and eigenvector of the parametercovariance matrix. In total, we get two ( i = 1 ,
2) independent variations of the determinedparameters.The impact of these uncertainties is estimated by repeating the calculation of the M X moments and taking the total value of the difference of each variation divided by two as asource of uncertainty. A larger set of MC events would reduce this systematic.2. FEI and PID efficiency correction uncertainty:The FEI efficiency correction uncertainty is propagated by varying the efficiency correctionby its uncertainty and repeating the determination of the background subtraction weights.Again, the uncertainty is taken as half of the total value of the resulting difference of (cid:104) M n X (cid:105) calculated with varied probabilities.The PID uncertainty is estimated using the set of varied nominal weights in bins of M X . ThePID correction for each event is varied by the estimated bin-wise uncertainty. To gauge theimpact of this source of uncertainty, the same method as for the FEI efficiency uncertaintydetermination is used. 15. B → X u (cid:96)ν (cid:96) branching fraction uncertainty:The B → X u (cid:96)ν (cid:96) branching fraction uncertainty is estimated to be 14% using the latestexperimental average of (2 . ± .
30) % [27]. The corresponding MC component is variedaccordingly and the signal probability function is redetermined using the varied MC sample.4. Statistical uncertainty on the bias correction factor C calib × C true :The remaining bias correction also contains a statistical uncertainty due to the limited numberof MC events used to determine it. The M X moments are calculated by varying the biascorrection factor according to this statistical uncertainty.5. Composition of higher mass X c states:The bias correction factor C true yields a significant correction to the final result. The originof this correction is the underlying modeling of the higher mass states of the B → X c (cid:96)ν (cid:96) spectrum, which has changed in comparison to previous analyses. The uncertainty of thiscorrection factor is determined by assigning a 100% uncertainty to the branching fraction ofthe non-resonant part of the X c spectrum and repeating the calculation for C true . The 100%uncertainty on the non-resonant B → X c (cid:96)ν (cid:96) branching fractions is a conservative choice, sincethe decays contributing to this region of the spectrum are not determined experimentally.The resulting uncertainty is propagated to the (cid:104) M n X (cid:105) values by repeating the calculation withthe varied C true and taking the absolute value of the difference to the nominal moments asthe systematic uncertainty.To estimate the total systematic uncertainty, all considered sources of systematics are added inquadrature. The measured hadronic mass moments are shown in Figure 6 as a function of a lower limit onthe lepton momentum in the signal B rest frame. The results of previous analyses performed byBaBar [28] and Belle [29] are shown for comparison. The results agree within the uncertainties, butthe current precision is not yet competitive. The numerical values, together with the itemization ofthe full statistical and systematic uncertainties, are given in Appendix A. The measured momentsshow a clear dependence on the p ∗ (cid:96) cut, resulting in smaller (cid:104) M n X (cid:105) values for higher p ∗ (cid:96) cuts. Theuncertainties of the moments for lower p ∗ (cid:96) cuts are dominated by the systematic components, whilethose for higher p ∗ (cid:96) cuts have a higher statistical uncertainty.16 .8 1.0 1.2 1.4 1.6 1.8 p Cut [GeV/c]2.0002.0252.0502.0752.1002.1252.150 < M X > [ G e V / c ] Belle II (preliminary) L dt = 34.6 fb Belle IIBaBar (2007) p Cut [GeV/c]4.04.24.44.64.8 < M X > [( G e V / c ) ] Belle II (preliminary) L dt = 34.6 fb Belle IIBaBar (2007)Belle (2006) p Cut [GeV/c]8.08.59.09.510.010.511.0 < M X > [( G e V / c ) ] Belle II (preliminary) L dt = 34.6 fb Belle IIBaBar (2007) p Cut [GeV/c]161820222426 < M X > [( G e V / c ) ] Belle II (preliminary) L dt = 34.6 fb Belle IIBaBar (2007)Belle (2006) p Cut [GeV/c]40506070 < M X > [( G e V / c ) ] Belle II (preliminary) L dt = 34.6 fb Belle IIBaBar (2007) p Cut [GeV/c]80100120140160180 < M X > [( G e V / c ) ] Belle II (preliminary) L dt = 34.6 fb Belle IIBaBar (2007)
FIG. 6: Measured (cid:104) M n X (cid:105) moments as a function of different p ∗ (cid:96) cuts. The error-bars correspond to thestatistical (inner) and total (outer) uncertainty calculated by adding the statistical and systematic error inquadrature. A comparison to previous (cid:104) M n X (cid:105) measurements from BaBar (2007) and Belle (2006) is shown asreference points. The current precision is not yet competitive with the previous results.
6. SUMMARY
We have presented a preliminary measurement the first six moments of the hadronic massspectrum in B → X c (cid:96)ν (cid:96) decays. The (cid:104) M n X (cid:105) are measured as a function of a lower cut on the leptonmomentum in the signal B rest frame p ∗ (cid:96) . The results agree with previous measurements within theiruncertainties, but tend to higher nominal values for lower cuts on p ∗ (cid:96) . The moments are calculatedas a weighted mean using signal probabilities as event-wise weights. The achieved precision is not17et competitive with previous analyses. The systematic uncertainties, in particular, can decrease infutures measurements by reducing the bias in the reconstructed M X distribution as well as moreextensive studies on the composition of unmeasured parts of the B → X c (cid:96)ν (cid:96) spectrum. Acknowledgements
We thank the SuperKEKB group for the excellent operation of the accelerator; the KEKcryogenics group for the efficient operation of the solenoid; and the KEK computer group for on-sitecomputing support. This work was supported by the following funding sources: Science Committeeof the Republic of Armenia Grant No. 18T-1C180; Australian Research Council and research grantNos. DP180102629, DP170102389, DP170102204, DP150103061, FT130100303, and FT130100018;Austrian Federal Ministry of Education, Science and Research, and Austrian Science Fund No. P31361-N36; Natural Sciences and Engineering Research Council of Canada, Compute Canada andCANARIE; Chinese Academy of Sciences and research grant No. QYZDJ-SSW-SLH011, NationalNatural Science Foundation of China and research grant Nos. 11521505, 11575017, 11675166,11761141009, 11705209, and 11975076, LiaoNing Revitalization Talents Program under contractNo. XLYC1807135, Shanghai Municipal Science and Technology Committee under contract No.19ZR1403000, Shanghai Pujiang Program under Grant No. 18PJ1401000, and the CAS Center forExcellence in Particle Physics (CCEPP); the Ministry of Education, Youth and Sports of the CzechRepublic under Contract No. LTT17020 and Charles University grants SVV 260448 and GAUK404316; European Research Council, 7th Framework PIEF-GA-2013-622527, Horizon 2020 MarieSklodowska-Curie grant agreement No. 700525 ‘NIOBE,’ and Horizon 2020 Marie Sklodowska-CurieRISE project JENNIFER2 grant agreement No. 822070 (European grants); L’Institut Nationalde Physique Nucl´eaire et de Physique des Particules (IN2P3) du CNRS (France); BMBF, DFG,HGF, MPG, AvH Foundation, and Deutsche Forschungsgemeinschaft (DFG) under Germany’sExcellence Strategy – EXC2121 “Quantum Universe”’ – 390833306 (Germany); Department ofAtomic Energy and Department of Science and Technology (India); Israel Science Foundationgrant No. 2476/17 and United States-Israel Binational Science Foundation grant No. 2016113;Istituto Nazionale di Fisica Nucleare and the research grants BELLE2; Japan Society for thePromotion 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; NationalResearch Foundation (NRF) of Korea Grant Nos. 2016R1D1A1B01010135, 2016R1D1A1B02012900,2018R1A2B3003643, 2018R1A6A1A06024970, 2018R1D1A1B07047294, 2019K1A3A7A09033840,and 2019R1I1A3A01058933, Radiation Science Research Institute, Foreign Large-size ResearchFacility Application Supporting project, the Global Science Experimental Data Hub Center of theKorea Institute of Science and Technology Information and KREONET/GLORIAD; UniversitiMalaya RU grant, Akademi Sains Malaysia and Ministry of Education Malaysia; Frontiers of ScienceProgram 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 andthe 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-1440-0321, S-0256-1438, andS-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 andresearch grant Nos. MOST106-2112-M-002-005-MY3 and MOST107-2119-M-002-035-MY3, and theMinistry of Education (Taiwan); Thailand Center of Excellence in Physics; TUBITAK ULAKBIM18Turkey); Ministry of Education and Science of Ukraine; the US National Science Foundationand research grant Nos. PHY-1807007 and PHY-1913789, and the US Department of Energyand research grant Nos. DE-AC06-76RLO1830, DE-SC0007983, DE-SC0009824, DE-SC0009973,DE-SC0010073, DE-SC0010118, DE-SC0010504, DE-SC0011784, DE-SC0012704; and the NationalFoundation for Science and Technology Development (NAFOSTED) of Vietnam under contract No103.99-2018.45. [1] P. Gambino et al. , “Challenges in Semileptonic B Decays”, (6, 2020) , arXiv:2006.07287 .[2] T. Keck et al. , “The Full Event Interpretation”,
Computing and Software for Big Science no. 1, (Feb,2019) . http://dx.doi.org/10.1007/s41781-019-0021-8 .[3] Belle II , T. Abe, “Belle II Technical Design Report”, (2010) , arXiv:1011.0352 .[4] K. Akai et al. , “SuperKEKB Collider”,
Nucl. Instrum. Meth. A (2018) 188–199, arXiv:1809.01958 .[5]
Belle II , W. Altmannshofer et al. , “The Belle II Physics Book”,
PTEP no. 12, (2019) 123C01, arXiv:1808.10567 . [Erratum: PTEP 2020, 029201 (2020)].[6] D. Lange, “The EvtGen particle decay simulation package”,
Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment no. 1,(2001) 152 – 155. .[7]
GEANT4 , S. Agostinelli et al. , “GEANT4: A Simulation toolkit”,
Nucl.Instrum.Meth.
A506 (2003)250–303.[8] E. Barberio et al. , “Photos a universal Monte Carlo for QED radiative corrections in decays”,
Computer Physics Communications no. 1, (1991) 115 – 128. .[9] B. Ward, S. Jadach, and Z. Was, “Precision calculation for e + e − → f : The KKMC project”, Nucl.Phys. B Proc. Suppl. (2003) 73–77, arXiv:hep-ph/0211132 .[10] T. Sjstrand et al. , “A brief introduction to PYTHIA 8.1”,
Computer Physics Communications no. 11, (Jun, 2008) 852867. http://dx.doi.org/10.1016/j.cpc.2008.01.036 .[11]
Belle II Framework Software Group , T. Kuhr et al. , “The Belle II Core Software”,
Comput.Softw. Big Sci. no. 1, (2019) 1, arXiv:1809.04299 .[12] Belle II Tracking , V. Bertacchi et al. , “Track Finding at Belle II”, (3, 2020) , arXiv:2003.12466 .[13] C. Boyd et al. , “Precision corrections to dispersive bounds on form factors”,
Physical Review D no. 11, (Dec, 1997) 68956911. http://dx.doi.org/10.1103/PhysRevD.56.6895 .[14] Belle , R. Glattauer et al. , “Measurement of the decay B → D (cid:96)ν (cid:96) in fully reconstructed events anddetermination of the Cabibbo-Kobayashi-Maskawa matrix element | V cb | ”, Physical Review D no. 3,(Feb, 2016) . http://dx.doi.org/10.1103/PhysRevD.93.032006 .[15] I. Caprini et al. , “Dispersive bounds on the shape of B → D ∗ (cid:96)ν (cid:96) form factors”, Nuclear Physics B no. 1, (1998) 153 – 181.[16] Y. Amhis et al. , “Averages of b -hadron, c -hadron, and τ -lepton properties as of summer 2016”, TheEuropean Physical Journal C no. 12, (Dec, 2017) .[17] A. Leibovich et al. , “Semileptonic B decays to excited charmed mesons”, Physical Review D no. 1,(Jan, 1998) 308330. http://dx.doi.org/10.1103/PhysRevD.57.308 .[18] F. Bernlochner and Z. Ligeti, “Semileptonic B ( s ) decays to excited charmed mesons with e, µ , τ andsearching for new physics with R ( D ∗∗ )”, Physical Review D no. 1, (Jan, 2017) . http://dx.doi.org/10.1103/PhysRevD.95.014022 .[19] J. Goity and W. Roberts, “Soft pion emission in semileptonic B -meson decays”, Physical Review D no. 7, (Apr, 1995) 34593477. http://dx.doi.org/10.1103/PhysRevD.51.3459 .[20] G. Fox and S. Wolfram, “Observables for the Analysis of Event Shapes in e + e − Annihilation andOther Processes”,
Phys. Rev. Lett. (1978) 1581.[21] A. Hershenhorn et al. , “ECL shower shape variables based on Zernike moments”, Internal Note (Jan,2017) .[22] D. Asner et al. , “Search for exclusive charmless hadronic B decays”, Phys. Rev. D (Feb, 1996)1039–1050.
23] A. J. Bevan et al. , “The Physics of the B Factories”,
The European Physical Journal C no. 11, (Nov,2014) . http://dx.doi.org/10.1140/epjc/s10052-014-3026-9 .[24] T. Keck, “FastBDT: A Speed-Optimized Multivariate Classification Algorithm for the Belle IIExperiment”, Comput. Softw. Big Sci. no. 1, (2017) 2. https://doi.org/10.1007/s41781-017-0002-8 .[25] W. Sutcliffe, “Performance of Full Event Interpretation and a calibration with B → X(cid:96)ν decays in earlyphase III data”,
Internal Note (Jul, 2019) .[26] D. Gatz and L. Smith, “The standard error of a weighted mean concentration. Bootstrapping vs othermethods”,
Atmospheric Environment no. 11, (1995) 1185 – 1193. .[27] Particle Data Group , M. Tanabashi et al. , “Review of Particle Physics”,