Measurement of B\rightarrow D^{(*)}\tau\nu using full reconstruction tags

Measurement of using full reconstruction tags

I. Adachi High Energy Accelerator Research Organization (KEK), Tsukuba    H. Aihara Department of Physics, University of Tokyo, Tokyo    K. Arinstein Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    T. Aso Toyama National College of Maritime Technology, Toyama    V. Aulchenko Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    T. Aushev École Polytechnique Fédérale de Lausanne (EPFL), Lausanne Institute for Theoretical and Experimental Physics, Moscow    T. Aziz Tata Institute of Fundamental Research, Mumbai    S. Bahinipati University of Cincinnati, Cincinnati, Ohio 45221    A. M. Bakich School of Physics, University of Sydney, NSW 2006    V. Balagura Institute for Theoretical and Experimental Physics, Moscow    Y. Ban Peking University, Beijing    E. Barberio University of Melbourne, School of Physics, Victoria 3010    A. Bay École Polytechnique Fédérale de Lausanne (EPFL), Lausanne    I. Bedny Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    K. Belous Institute of High Energy Physics, Protvino    V. Bhardwaj Panjab University, Chandigarh    B. Bhuyan India Institute of Technology Guwahati, Guwahati    M. Bischofberger Nara Women’s University, Nara    S. Blyth National United University, Miao Li    A. Bondar Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    A. Bozek H. Niewodniczanski Institute of Nuclear Physics, Krakow    M. Bračko University of Maribor, Maribor J. Stefan Institute, Ljubljana    J. Brodzicka H. Niewodniczanski Institute of Nuclear Physics, Krakow    T. E. Browder University of Hawaii, Honolulu, Hawaii 96822    M.-C. Chang Department of Physics, Fu Jen Catholic University, Taipei    P. Chang Department of Physics, National Taiwan University, Taipei    Y.-W. Chang Department of Physics, National Taiwan University, Taipei    Y. Chao Department of Physics, National Taiwan University, Taipei    A. Chen National Central University, Chung-li    K.-F. Chen Department of Physics, National Taiwan University, Taipei    P.-Y. Chen Department of Physics, National Taiwan University, Taipei    B. G. Cheon Hanyang University, Seoul    C.-C. Chiang Department of Physics, National Taiwan University, Taipei    R. Chistov Institute for Theoretical and Experimental Physics, Moscow    I.-S. Cho Yonsei University, Seoul    S.-K. Choi Gyeongsang National University, Chinju    Y. Choi Sungkyunkwan University, Suwon    J. Crnkovic University of Illinois at Urbana-Champaign, Urbana, Illinois 61801    J. Dalseno Max-Planck-Institut für Physik, München Excellence Cluster Universe, Technische Universität München, Garching    M. Danilov Institute for Theoretical and Experimental Physics, Moscow    A. Das Tata Institute of Fundamental Research, Mumbai    M. Dash IPNAS, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061    A. Drutskoy University of Cincinnati, Cincinnati, Ohio 45221    W. Dungel Institute of High Energy Physics, Vienna    S. Eidelman Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    D. Epifanov Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    M. Feindt Institut für Experimentelle Kernphysik, Universität Karlsruhe, Karlsruhe    H. Fujii High Energy Accelerator Research Organization (KEK), Tsukuba    M. Fujikawa Nara Women’s University, Nara    N. Gabyshev Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    A. Garmash Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    G. Gokhroo Tata Institute of Fundamental Research, Mumbai    P. Goldenzweig University of Cincinnati, Cincinnati, Ohio 45221    B. Golob Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana J. Stefan Institute, Ljubljana    M. Grosse Perdekamp University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 RIKEN BNL Research Center, Upton, New York 11973    H. Guo University of Science and Technology of China, Hefei    H. Ha Korea University, Seoul    J. Haba High Energy Accelerator Research Organization (KEK), Tsukuba    B.-Y. Han Korea University, Seoul    K. Hara Nagoya University, Nagoya    T. Hara High Energy Accelerator Research Organization (KEK), Tsukuba    Y. Hasegawa Shinshu University, Nagano    N. C. Hastings Department of Physics, University of Tokyo, Tokyo    K. Hayasaka Nagoya University, Nagoya    H. Hayashii Nara Women’s University, Nara    M. Hazumi High Energy Accelerator Research Organization (KEK), Tsukuba    D. Heffernan Osaka University, Osaka    T. Higuchi High Energy Accelerator Research Organization (KEK), Tsukuba    Y. Horii Tohoku University, Sendai    Y. Hoshi Tohoku Gakuin University, Tagajo    K. Hoshina Tokyo University of Agriculture and Technology, Tokyo    W.-S. Hou Department of Physics, National Taiwan University, Taipei    Y. B. Hsiung Department of Physics, National Taiwan University, Taipei    H. J. Hyun Kyungpook National University, Taegu    Y. Igarashi High Energy Accelerator Research Organization (KEK), Tsukuba    T. Iijima Nagoya University, Nagoya    K. Inami Nagoya University, Nagoya    A. Ishikawa Saga University, Saga    H. Ishino [ Tokyo Institute of Technology, Tokyo    K. Itoh Department of Physics, University of Tokyo, Tokyo    R. Itoh High Energy Accelerator Research Organization (KEK), Tsukuba    M. Iwabuchi The Graduate University for Advanced Studies, Hayama    M. Iwasaki Department of Physics, University of Tokyo, Tokyo    Y. Iwasaki High Energy Accelerator Research Organization (KEK), Tsukuba    T. Jinno Nagoya University, Nagoya    M. Jones University of Hawaii, Honolulu, Hawaii 96822    N. J. Joshi Tata Institute of Fundamental Research, Mumbai    T. Julius University of Melbourne, School of Physics, Victoria 3010    D. H. Kah Kyungpook National University, Taegu    H. Kakuno Department of Physics, University of Tokyo, Tokyo    J. H. Kang Yonsei University, Seoul    P. Kapusta H. Niewodniczanski Institute of Nuclear Physics, Krakow    S. U. Kataoka Nara University of Education, Nara    N. Katayama High Energy Accelerator Research Organization (KEK), Tsukuba    H. Kawai Chiba University, Chiba    T. Kawasaki Niigata University, Niigata    A. Kibayashi High Energy Accelerator Research Organization (KEK), Tsukuba    H. Kichimi High Energy Accelerator Research Organization (KEK), Tsukuba    C. Kiesling Max-Planck-Institut für Physik, München    H. J. Kim Kyungpook National University, Taegu    H. O. Kim Kyungpook National University, Taegu    J. H. Kim Sungkyunkwan University, Suwon    S. K. Kim Seoul National University, Seoul    Y. I. Kim Kyungpook National University, Taegu    Y. J. Kim The Graduate University for Advanced Studies, Hayama    K. Kinoshita University of Cincinnati, Cincinnati, Ohio 45221    B. R. Ko Korea University, Seoul    S. Korpar University of Maribor, Maribor J. Stefan Institute, Ljubljana    M. Kreps Institut für Experimentelle Kernphysik, Universität Karlsruhe, Karlsruhe    P. Križan Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana J. Stefan Institute, Ljubljana    P. Krokovny High Energy Accelerator Research Organization (KEK), Tsukuba    T. Kuhr Institut für Experimentelle Kernphysik, Universität Karlsruhe, Karlsruhe    R. Kumar Panjab University, Chandigarh    T. Kumita Tokyo Metropolitan University, Tokyo    E. Kurihara Chiba University, Chiba    E. Kuroda Tokyo Metropolitan University, Tokyo    Y. Kuroki Osaka University, Osaka    A. Kusaka Department of Physics, University of Tokyo, Tokyo    A. Kuzmin Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    Y.-J. Kwon Yonsei University, Seoul    S.-H. Kyeong Yonsei University, Seoul    J. S. Lange Justus-Liebig-Universität Gießen, Gießen    G. Leder Institute of High Energy Physics, Vienna    M. J. Lee Seoul National University, Seoul    S. E. Lee Seoul National University, Seoul    S.-H. Lee Korea University, Seoul    J. Li University of Hawaii, Honolulu, Hawaii 96822    A. Limosani University of Melbourne, School of Physics, Victoria 3010    S.-W. Lin Department of Physics, National Taiwan University, Taipei    C. Liu University of Science and Technology of China, Hefei    D. Liventsev Institute for Theoretical and Experimental Physics, Moscow    R. Louvot École Polytechnique Fédérale de Lausanne (EPFL), Lausanne    J. MacNaughton High Energy Accelerator Research Organization (KEK), Tsukuba    F. Mandl Institute of High Energy Physics, Vienna    D. Marlow Princeton University, Princeton, New Jersey 08544    A. Matyja H. Niewodniczanski Institute of Nuclear Physics, Krakow    S. McOnie School of Physics, University of Sydney, NSW 2006    T. Medvedeva Institute for Theoretical and Experimental Physics, Moscow    Y. Mikami Tohoku University, Sendai    K. Miyabayashi Nara Women’s University, Nara    H. Miyake Osaka University, Osaka    H. Miyata Niigata University, Niigata    Y. Miyazaki Nagoya University, Nagoya    R. Mizuk Institute for Theoretical and Experimental Physics, Moscow    A. Moll Max-Planck-Institut für Physik, München Excellence Cluster Universe, Technische Universität München, Garching    T. Mori Nagoya University, Nagoya    T. Müller Institut für Experimentelle Kernphysik, Universität Karlsruhe, Karlsruhe    R. Mussa INFN - Sezione di Torino, Torino    T. Nagamine Tohoku University, Sendai    Y. Nagasaka Hiroshima Institute of Technology, Hiroshima    Y. Nakahama Department of Physics, University of Tokyo, Tokyo    I. Nakamura High Energy Accelerator Research Organization (KEK), Tsukuba    E. Nakano Osaka City University, Osaka    M. Nakao High Energy Accelerator Research Organization (KEK), Tsukuba    H. Nakayama Department of Physics, University of Tokyo, Tokyo    H. Nakazawa National Central University, Chung-li    Z. Natkaniec H. Niewodniczanski Institute of Nuclear Physics, Krakow    K. Neichi Tohoku Gakuin University, Tagajo    S. Neubauer Institut für Experimentelle Kernphysik, Universität Karlsruhe, Karlsruhe    S. Nishida High Energy Accelerator Research Organization (KEK), Tsukuba    K. Nishimura University of Hawaii, Honolulu, Hawaii 96822    O. Nitoh Tokyo University of Agriculture and Technology, Tokyo    S. Noguchi Nara Women’s University, Nara    T. Nozaki High Energy Accelerator Research Organization (KEK), Tsukuba    A. Ogawa RIKEN BNL Research Center, Upton, New York 11973    S. Ogawa Toho University, Funabashi    T. Ohshima Nagoya University, Nagoya    S. Okuno Kanagawa University, Yokohama    S. L. Olsen Seoul National University, Seoul    W. Ostrowicz H. Niewodniczanski Institute of Nuclear Physics, Krakow    H. Ozaki High Energy Accelerator Research Organization (KEK), Tsukuba    P. Pakhlov Institute for Theoretical and Experimental Physics, Moscow    G. Pakhlova Institute for Theoretical and Experimental Physics, Moscow    H. Palka H. Niewodniczanski Institute of Nuclear Physics, Krakow    C. W. Park Sungkyunkwan University, Suwon    H. Park Kyungpook National University, Taegu    H. K. Park Kyungpook National University, Taegu    K. S. Park Sungkyunkwan University, Suwon    L. S. Peak School of Physics, University of Sydney, NSW 2006    M. Pernicka Institute of High Energy Physics, Vienna    R. Pestotnik J. Stefan Institute, Ljubljana    M. Peters University of Hawaii, Honolulu, Hawaii 96822    L. E. Piilonen IPNAS, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061    A. Poluektov Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    K. Prothmann Max-Planck-Institut für Physik, München Excellence Cluster Universe, Technische Universität München, Garching    B. Riesert Max-Planck-Institut für Physik, München    M. Rozanska H. Niewodniczanski Institute of Nuclear Physics, Krakow    H. Sahoo University of Hawaii, Honolulu, Hawaii 96822    K. Sakai Niigata University, Niigata    Y. Sakai High Energy Accelerator Research Organization (KEK), Tsukuba    N. Sasao Kyoto University, Kyoto    O. Schneider École Polytechnique Fédérale de Lausanne (EPFL), Lausanne    P. Schönmeier Tohoku University, Sendai    J. Schümann High Energy Accelerator Research Organization (KEK), Tsukuba    C. Schwanda Institute of High Energy Physics, Vienna    A. J. Schwartz University of Cincinnati, Cincinnati, Ohio 45221    R. Seidl RIKEN BNL Research Center, Upton, New York 11973    A. Sekiya Nara Women’s University, Nara    K. Senyo Nagoya University, Nagoya    M. E. Sevior University of Melbourne, School of Physics, Victoria 3010    L. Shang Institute of High Energy Physics, Chinese Academy of Sciences, Beijing    M. Shapkin Institute of High Energy Physics, Protvino    V. Shebalin Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    C. P. Shen University of Hawaii, Honolulu, Hawaii 96822    H. Shibuya Toho University, Funabashi    S. Shiizuka Nagoya University, Nagoya    S. Shinomiya Osaka University, Osaka    J.-G. Shiu Department of Physics, National Taiwan University, Taipei    B. Shwartz Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    F. Simon Max-Planck-Institut für Physik, München Excellence Cluster Universe, Technische Universität München, Garching    J. B. Singh Panjab University, Chandigarh    R. Sinha Institute of Mathematical Sciences, Chennai    A. Sokolov Institute of High Energy Physics, Protvino    E. Solovieva Institute for Theoretical and Experimental Physics, Moscow    S. Stanič University of Nova Gorica, Nova Gorica    M. Starič J. Stefan Institute, Ljubljana    J. Stypula H. Niewodniczanski Institute of Nuclear Physics, Krakow    A. Sugiyama Saga University, Saga    K. Sumisawa High Energy Accelerator Research Organization (KEK), Tsukuba    T. Sumiyoshi Tokyo Metropolitan University, Tokyo    S. Suzuki Saga University, Saga    S. Y. Suzuki High Energy Accelerator Research Organization (KEK), Tsukuba    Y. Suzuki Nagoya University, Nagoya    F. Takasaki High Energy Accelerator Research Organization (KEK), Tsukuba    N. Tamura Niigata University, Niigata    K. Tanabe Department of Physics, University of Tokyo, Tokyo    M. Tanaka High Energy Accelerator Research Organization (KEK), Tsukuba    N. Taniguchi High Energy Accelerator Research Organization (KEK), Tsukuba    G. N. Taylor University of Melbourne, School of Physics, Victoria 3010    Y. Teramoto Osaka City University, Osaka    I. Tikhomirov Institute for Theoretical and Experimental Physics, Moscow    K. Trabelsi High Energy Accelerator Research Organization (KEK), Tsukuba    Y. F. Tse University of Melbourne, School of Physics, Victoria 3010    T. Tsuboyama High Energy Accelerator Research Organization (KEK), Tsukuba    K. Tsunada Nagoya University, Nagoya    Y. Uchida The Graduate University for Advanced Studies, Hayama    S. Uehara High Energy Accelerator Research Organization (KEK), Tsukuba    Y. Ueki Tokyo Metropolitan University, Tokyo    K. Ueno Department of Physics, National Taiwan University, Taipei    T. Uglov Institute for Theoretical and Experimental Physics, Moscow    Y. Unno Hanyang University, Seoul    S. Uno High Energy Accelerator Research Organization (KEK), Tsukuba    P. Urquijo University of Melbourne, School of Physics, Victoria 3010    Y. Ushiroda High Energy Accelerator Research Organization (KEK), Tsukuba    Y. Usov Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    G. Varner University of Hawaii, Honolulu, Hawaii 96822    K. E. Varvell School of Physics, University of Sydney, NSW 2006    K. Vervink École Polytechnique Fédérale de Lausanne (EPFL), Lausanne    A. Vinokurova Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    C. C. Wang Department of Physics, National Taiwan University, Taipei    C. H. Wang National United University, Miao Li    J. Wang Peking University, Beijing    M.-Z. Wang Department of Physics, National Taiwan University, Taipei    P. Wang Institute of High Energy Physics, Chinese Academy of Sciences, Beijing    X. L. Wang Institute of High Energy Physics, Chinese Academy of Sciences, Beijing    M. Watanabe Niigata University, Niigata    Y. Watanabe Kanagawa University, Yokohama    R. Wedd University of Melbourne, School of Physics, Victoria 3010    J.-T. Wei Department of Physics, National Taiwan University, Taipei    J. Wicht High Energy Accelerator Research Organization (KEK), Tsukuba    L. Widhalm Institute of High Energy Physics, Vienna    J. Wiechczynski H. Niewodniczanski Institute of Nuclear Physics, Krakow    E. Won Korea University, Seoul    B. D. Yabsley School of Physics, University of Sydney, NSW 2006    H. Yamamoto Tohoku University, Sendai    Y. Yamashita Nippon Dental University, Niigata    M. Yamauchi High Energy Accelerator Research Organization (KEK), Tsukuba    C. Z. Yuan Institute of High Energy Physics, Chinese Academy of Sciences, Beijing    Y. Yusa IPNAS, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061    C. C. Zhang Institute of High Energy Physics, Chinese Academy of Sciences, Beijing    L. M. Zhang University of Science and Technology of China, Hefei    Z. P. Zhang University of Science and Technology of China, Hefei    V. Zhilich Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    V. Zhulanov Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk    T. Zivko J. Stefan Institute, Ljubljana    A. Zupanc J. Stefan Institute, Ljubljana    N. Zwahlen École Polytechnique Fédérale de Lausanne (EPFL), Lausanne    O. Zyukova Budker Institute of Nuclear Physics, Novosibirsk Novosibirsk State University, Novosibirsk
Abstract

We present measurements of and decays using 604.5 fb of data collected at the resonance with the Belle detector at the KEKB asymmetric-energy collider. Events are tagged by fully reconstructing one of the mesons in hadronic modes. We obtain , , , where the first error is statistical, the second is systematic, and the third is due to the uncertainty in the branching fraction for the normalization mode.

preprint: BELLE-CONF-0901 NTLP Preprint 2009-03

now at ]Okayama University, Okayama The Belle Collaboration

I Introduction

The semileptonic decay to channel, , is a sensitive probe of extensions to the Standard Model (SM). In the SM, it occurs via an external emission diagram with predicted branching fractions of % and % for the and modes, respectively Chen06 (). On the other hand, in extensions of the SM, such as the Two Higgs Doublet Models (2HDM) and the Minimal Supersymmetric Standard Model (MSSM), a charged Higgs boson () may contribute to the decay amplitude at tree level, and the branching fraction may be modified significantly Grzad92 (); Tanaka95 (); Kiers97 (); Itoh05 (); Nierste07 (). Both and the purely leptonic decay have similar sensitivity to bosons with different theoretical systematics; the former suffers from uncertainty in the form factor, while the latter requires knowledge of the decay constant . Therefore, the two decays provide complementary approaches to searching for signatures in decays.

Experimentally, measurements of the decays are challenging because at least two neutrinos are present in the final state. The Belle collaboration has previously reported the first observation of the decay , by inclusively reconstructing the accompanying via a 4-vector sum of all the charged and neutral tracks other than the and daughter track candidates. The reported branching fraction is Belle_Dsttaunu (). In this paper, we present new measurements of and decays. Here we fully reconstruct one of the mesons in the event, referred to hereafter as the tag side (), and compare properties of the remaining particles, referred to as the signal side (), to those expected for signal and background. The method allows us to strongly suppress the combinatorial backgrounds, and correctly calculate the missing mass which discriminates the signal from background. Using a similar technique, the BaBar collaboration has reported the branching fractions, % and %, where the third uncertainty is from the normalization mode. They also measured distributions of the lepton momentum and the squared momentum transfer BaBar_Dtaunu ().

In order to avoid experimental bias, the signal region in data is blinded until the event selection criteria are finalized. Inclusion of the charge conjugate decays is implied throughout this paper.

Ii Experiment and Data Set

The analysis is based on the data recorded with the Belle detector at the KEKB asymmetric-energy collider operating at the center-of-mass (c.m.) energy of the resonance. KEKB consists of a low energy ring (LER) of 3.5 GeV positrons and a high energy ring (HER) of 8 GeV electrons KEKB (). The data set used in this analysis corresponds to an integrated luminosity of fb and contains events.

The Belle detector is a large-solid-angle magnetic spectrometer that consists of a silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter (ECL) comprised of CsI(Tl) crystals located inside a super-conducting solenoid coil that provides a 1.5 T magnetic field. Muons and mesons are identified by arrays of resistive plate counters interspersed in the iron yoke (KLM). The detector is described in detail elsewhere BELLE ().

A detailed Monte Carlo (MC) simulation, based on the GEANT package GEANT (), is used to estimate the signal detection efficiency and to study the background. Large samples of the signal decays are generated with the EVTGEN package Evtgen () using the ISGW II form factor model ISGW2 (). To model the and backgrounds, large generic and MC samples, corresponding to about twice the integrated luminosity of data are used. To further increase the MC statistics, we also use special MC samples, corresponding to and pairs, where events are filtered based on event generator information before running the time consuming GEANT detector simulation.

Iii Event Reconstruction and Selection

iii.1 Tag-side Reconstruction

Charged particle tracks are reconstructed from hits in the SVD and CDC. They are required to satisfy track quality cuts based on their impact parameters relative to the measured profile of the interaction point (IP) of the two beams. Charged kaons are identified by combining information on ionization loss () in the CDC, Cherenkov light yields in the ACC and time-of-flight measured by the TOF system. For the nominal requirement, the kaon identification efficiency is approximately and the probability of misidentifying a pion as a kaon is about . Hadron tracks that are not identified as kaons are treated as pions. Tracks satisfying the lepton identification criteria, as described below, are removed from consideration. Electron identification is based on a combination of in CDC, the response of the ACC, shower shape in the ECL, position matching between ECL clusters and the track, and the ratio of the energy deposited in the ECL to the momentum measured by the tracking system. Muon candidates are selected using range of tracks measured in KLM and the deviation of hits from the extrapolated track trajectories. The lepton identification efficiencies are estimated to be about 90% for both electrons and muons in the momentum region above 1.2 GeV/. The hadron misidentification rate is measured using reconstructed decays and found to be less than 0.2% for electrons and 1.5% for muons in the same momentum region. mesons are reconstructed using pairs of charged tracks that have an invariant mass within  MeV/ of the known mass and a well reconstructed vertex that is displaced from the IP. Candidate ’s are required to have a minimum energy deposit  MeV. Candidate mesons are reconstructed using pairs with invariant masses between 117 and 150 MeV/. For slow ’s used in reconstruction, the minimum energy requirement is lowered to 30 MeV.

candidates are reconstructed in the following decay modes: , , , , and , , , . Candidate and mesons are reconstructed in the and decay modes, by requiring their invariant masses to be within  MeV/ of the nominal mass. We then select candidates by combining a candidate and a pion with invariant mass between 0.7 and 1.6 GeV/ and require that the charged tracks form a good vertex. meson candidates are reconstructed in the following decay modes: , , , , , , , and , , , , , , , . The candidates are required to have an invariant mass within ( is the mass resolution) of the nominal mass value depending on the mode. mesons are reconstructed as , , , , and . candidates from modes that include a pion are required to have a mass difference within  MeV/ of its nominal value. For decays with a photon, we require that the mass difference be within  MeV/ of the nominal value.

The selection of candidates is based on the beam-constrained mass and the energy difference . Here, and are the reconstructed energy and momentum of the candidate in the c.m. system, and is the beam energy in the c.m. frame. The background from jet-like continuum events () is suppressed on the basis of event topology: we require the normalized second Fox-Wolfram moment (R2 () to be smaller than 0.5, and , where is the angle between the thrust axis of the candidate and that of the remaining tracks in the event. The latter requirement is not applied to , and decays, where the continuum background is small. For the candidate, we require and . If an event has multiple candidates, we choose the one having the smallest based on deviations from the nominal values of , the candidate mass, and the mass difference if applicable. The number of and candidates in the selected region are and , respectively. By fitting the distribution to the sum of an empirical parameterization of the background shape Albrecht () and a signal shape Bloom:1983pc (), we estimate that in the selected region there are  (with purity=0.58) and  (with purity=0.51) events, respectively.

iii.2 Signal-side Reconstruction

In the events where a is reconstructed, we search for decays of into a , and a neutrino. In the present analysis, the lepton is identified in the leptonic decay modes, and . We require that the charge/flavor of the daughter particles and the meson are consistent with the flavor, opposite to the flavor. The loss of signal due to mixing is estimated by the MC simulation.

The procedures to reconstruct charged particles () and neutral particles () for the signal side are the same as those used for the tag side. For candidates, we require a minimum energy threshold of 50 MeV for the barrel, and 100 (150) MeV for the forward (backward) end-cap ECL. A higher threshold is used for the endcap ECL, where the effect of beam background is more severe. We also require that the lepton momentum in the laboratory frame exceeds 0.6 GeV/ to ensure good lepton identification efficiency.

The decay modes used for reconstruction are slightly different from those used for the tagging side: , , , , , , , and , , . The candidates are required to have an invariant mass within of the nominal mass value. mesons are reconstructed using the same decay modes as on the tagging side: , , and , . candidates are required to have a mass difference within of the nominal value.

For signal selection, we use the following variables that characterize the signal decay: the missing mass squared in the event (), the momentum (in the c.m. system) of the daughter leptons (), and the extra energy in the ECL (). The missing mass squared is calculated as , using the energy and momenta of the , the candidate and the lepton from the decay. The signal decay is characterized by large due to the presence of more than two neutrinos in the final state. The lepton momenta () distribute lower than those from primary decays. The extra energy in the ECL () is the sum of the energies of photons that are not associated with either the or the reconstruction. ECL clusters with energies greater than 50 MeV in the barrel, and 100 (150) MeV in the forward (backward) end-cap ECL are used to calculate . For signal events, must be either zero or a small value arising from beam background hits, therefore, signal events peak at low . On the other hand, background events are distributed toward higher due to the contribution from additional neutral clusters. We also require that the event has no extra charged tracks and no candidate other than those from the signal decay and those used in the reconstruction. Table 1 summarizes the cuts to define the signal region. The cuts are optimized by maximizing the figure of merit (F.O.M.), defined as , where are the number of signal (total background) events in the signal region, assuming the SM branching fractions for the and the modes.

Cut variable
Number of extra tracks
Number of extra
 GeV/  GeV/
 GeV/  GeV/
 GeV  GeV
Table 1: Summary of the signal selection criteria.

iii.3 Signal Detection Efficiency and Expected Background

Table 2 lists the signal detection efficiencies, which are estimated from signal MC simulation, with the selection criteria shown in Table 1. Taking account of the cross talks between and modes, the signal detection efficiency () is defined as,

(1)

where represents the yield of the generated -th mode reconstructed in the -th mode. is the branching fraction of the -th mode including the sub-decay ( and ) branching fractions. is the number of events fully reconstructed on the tagging side. Table 2 also shows, in parentheses, the efficiencies without cuts on and . These are the two variables used to extract the signal yields.

Recon’d mode Generated modes
() ()
() ()
Recon’d mode Generated modes
() ()
() ()
Table 2: Signal detection efficiency (%) matrix for (top) and (bottom) modes. The values in parenthesis are the efficiencies without cuts on and .

According to the MC simulation, the expected number of signal (background) events in the signal region is 19(48) for , 7(13) for , 18(25) for , and 7(6) for . The major background sources are semileptonic decays, , and (60-70% depending on the decay mode). The remaining background comes from hadronic decays including a meson in the final state. Background from processes are found to be small (less than one event). As shown in Table 2, the cross talk between and arises, when a pion or a photon is missed in the reconstruction of , or when a random photon is combined with a to form a fake . The cross-feed to other or tag samples is negligibly small.

Iv Calibration using the Sample

We use () decays as control samples to calibrate the background MC simulation and to verify the simulation. We also use these decays to normalize the extracted signal yields. We select decays using the same selection requirements as , but without the cut on the momentum of the daughter lepton and with and  GeV. The four calibration decay modes: , , , and , peak around zero in the missing mass distributions, as shown in Figure 1.

The yields of the calibration modes are extracted by fitting the distributions with expected shapes based on MC simulation for the signal and the background. The major background in each distribution arises from other semileptonic decays, where a pion or a photon is missed (i.e. is reconstructed as if the soft or from the is missed), or a random photon is used in reconstruction (i.e. misreconstructed as ). Here the two distributions for and candidates are fitted simultaneously. Table 3 lists the yields extracted for each calibration decay mode, which include the yields detected as cross talk; for example, the yield of is the sum of decays measured in the and distributions. When we compare the extracted yields with expected yields from the MC simulation, the ratio of the measured to the expected yields () are found to be , depending on the mode. The ratios are used as scale factors to correct the normalization in the MC simulation for semileptonic decays, which are the major backgrounds in the detection.

Yield 1156 44 2152 76 338 21 769 35
Efficiency (%) 8.97 0.05 6.86 0.08 11.3 0.12 5.43 0.04

Table 3: Yields and efficiencies of the calibration modes.
Figure 1: Distribution of missing mass squared () for (top-left), (top-right), (bottom-left), and (bottom-right). Data are plotted as points with error bars, the results of the fit (solid line) along with the signal (dashed red line), other semileptonic decays (dotted blue line) and misidentified hadronic events (hatched histogram) components are also shown.

Figure 2 compares the distribution for the control samples in data and the MC simulation after the correction. The agreement between the data and the MC simulation is satisfactory, and valid the simulation. We also confirm that the number of events found in the sideband of the signal region is consistent within statistics for the data and the scaled MC simulation. Here the sideband is defined by  GeV, and  GeV/c, for all four signal modes.

Figure 2: Comparison of distributions for the control samples in data and the MC simulation.

V Signal Extraction

The and signal yields are extracted using unbinned extended maximum likelihood fits to the two-dimensional distributions obtained after the selection of the signal decays. The fit components are two signal modes; and , and the backgrounds from , and other processes. The likelihood is constructed as,

(2)

where

(3)

Here and represent the number of events and the two-dimensional probability density function (PDF) as a function of and , respectively, for process . In the fit to the distribution, the cross-feed () and background () are not included, because their contribution are found to be small according to the MC simulation. The fit region is defined by for all four signal modes.

The two-dimensional PDF’s for and processes are obtained by taking the product of a one-dimensional PDF for each variable, as the correlations between and are found to be small in the MC simulation. The one-dimensional PDF’s for are modeled by asymmetric Gaussian or double Gaussian distributions, whereas the PDF’s for are histograms obtained from the MC simulation. The PDF for other background processes () uses the two-dimensional histograms obtained from MC simulation, since correlations between the two variables are significant for these background processes, which mainly come from hadronic decays.

We fit the distributions for and tags separately. The cross talk between the two tags is found to be small according to the MC simulation. For each and tag, we then fit simultaneously the two distributions for the and components. The ratio of the number of events found in the two distributions is constrained according to the efficiency matrix shown in Table  2.

The above procedure to extract the signal yields has been tested by “toy MC experiments”: in each experiment, the number of events in each bin is generated according to Poisson statistics, with the mean () fixed to the number of events found in the MC simulation, including the signals with the SM branching fraction. The distributions are then fit with the procedure described in the previous subsection. We generate 500 experiments, and we confirm that the means of the extracted yields are consistent with the input values.

The signal extraction procedure has also been checked by performing a fit to sample distributions from generic MC events, which are the sum of the generic and processes, where semileptonic to decays, , and , are removed from the samples. For all four signal decays, the signal yields obtained are consistent with zero within the statistical uncertainty.

Vi Results and Systematic Uncertainties

In this paper, we present a relative measurement; we extract the yields of both the signal mode and the normalization mode to deduce the four ratios,

(4)
(5)
(6)
(7)

The yields of the normalization modes are extracted as described in Section IV. For the signal modes, after finalizing the signal selection criteria and completing the studies in previous sections, we have opened the signal region, and performed the fits with the procedure described in Section V. Figures 3 and 4 show the fit results for and , respectively. There are excesses in the signal region for all four decay modes. Figure 5 shows the signal likelihood curves, while Table 4 summarizes the results. The extracted yields (statistical significances) are , , , and , for , , and , respectively. The efficiency , shown in Table 4, corresponds to the sum of the signal yields measured in and selections. The ratio of to are calculated as,

(8)

Note that the efficiency is the average over electron and muon modes, while the yields are extracted for the sum of the two modes.

Figure 3: Fit results for (top) and (bottom). The (left) and (right) distributions are shown with the signal selection cut on the other variable listed in Table 1.
Figure 4: Fit results for (top) and (bottom). The (left) and (right) distributions are shown with the signal selection cut on the other variable listed in Table 1.
Figure 5: Likelihood curves as a function of signal yields for (top-left) and (top-right). (bottom-left) and (bottom-right). Red (black) curves show the likelihood with (without) the systematic uncertainty
Quantity
98.6 99.8
[%] 6.20 0.08 3.86 0.08
[%] 70.2 46.8
3.8 (4.4) 3.9 (5.2)
[%] 1.51 0.15 3.04 0.22

Quantity

17.2 25.0
[%] 6.86 0.09 2.09 0.04
[%] 47.6 48.1
2.6 (2.8) 4.7 (5.9)
[%] 1.01 0.10 2.56 0.10
Table 4: Summary of the results; extracted yields from the fitting, , the efficiency to detect the signal in either of and selections, , the deduced ratio of to , , significance of the signal with (without) systematic errors, , deducued branching fraction, .

Table 5 summarizes the systematic errors related to the ratio measurement, where reconstruction efficiency errors are largely cancel out. The following systematic errors are considered.

  • shape: The systematic error due to uncertainties in the shape is estimated by varying the PDF parameters. The fitting procedure is repeated for each parameter variation, and relative changes in the extracted yields are added in quadrature. This method will give conservative estimates, as there are correlations in resolutions between decay modes.

  • shape: The systematic error due to uncertainties in the shape is estimated by varying the content of each PDF histogram bin by its statistical error. The fitting procedure is repeated for each bin variation, and relative changes in the extracted yields are added in quadrature.

  • branching fraction: The systematic errors due to uncertainties in the component is estimated by varying the branching fraction for each component by based on the Belle results in Livent (). The relative change in the extracted yields is assigned as the systematic error.

  • cross-feed: In our nominal fitting procedure, the rates of the cross-feed between and decays are fixed to the values in the MC simulation, for both the signal and normalization decays. The uncertainty is estimated by taking the relative change in the extracted yield for the normalization decays, when the cross-feed component is floated in the fit.

  • branching fraction: The systematic error due to uncertainties in the branching fraction of decay modes is evaluated by changing the branching fractions by the uncertainties in the PDG values PDG2006 ().

The total systematic error is the quadratic sum of all individual ones.

Source [%] [%] [%] [%]
shape +9.10/-7.89 +9.86/-10.7 +6.39/-5.78 +5.80/-6.12
shape +10.6/-7.58 +7.01/-9.73 +9.03/-7.27 +9.84/-4.97
+0.35/-0.41 +0.75/-0.02 +4.50/-2.56 +0.58/-0.28
cross-feed +7.05/-6.86 +5.12/-5.34 +5.77/-6.01 +3.48/-3.37
0.3 0.3 0.3 0.3

Total
+15.7/-12.9 +13.2/-15.4 +13.3/-11.4 +12.0/-8.58

Table 5: Summary of the systematic errors.

With the systematic errors shown in Table 5, the final results for the four ratios are,

(9)
(10)
(11)
(12)

where the first error is the statistical and the second error is the systematic. Including the systematic uncertainties for the yields convolved in the likelihood (Figure 5), the significances of the excesses (in units of ) are found to be and for , , and , respectively.

Using the branching fractions for the