Measurement of the branching fraction and CP asymmetry for B→D¯0π decays

Measurement of the branching fraction and CP asymmetry for B → D ¯

⁰

π decays

T. Bloomfield ,⁵²M. E. Sevior,⁵²I. Adachi,^19,15H. Aihara,⁸⁸S. Al Said,^82,37D. M. Asner,³V. Aulchenko,^4,66T. Aushev,²¹ R. Ayad,⁸²V. Babu,⁸ S. Bahinipati,²⁴P. Behera,²⁶J. Bennett,⁵³M. Bessner,¹⁸T. Bilka,⁵J. Biswal,³⁴A. Bobrov,^4,66 G. Bonvicini,⁹³A. Bozek,⁶³M. Bračko,^50,34T. E. Browder,¹⁸M. Campajola,^31,58L. Cao,²D.Červenkov,⁵M.-C. Chang,¹¹

V. Chekelian,⁵¹A. Chen,⁶⁰B. G. Cheon,¹⁷K. Chilikin,⁴⁴H. E. Cho,¹⁷ K. Cho,³⁹ S.-J. Cho,⁹⁵S.-K. Choi,¹⁶Y. Choi,⁸⁰ S. Choudhury,²⁵D. Cinabro,⁹³S. Cunliffe,⁸ S. Das,⁴⁹N. Dash,²⁶G. De Nardo,^31,58 R. Dhamija,²⁵F. Di Capua,^31,58 Z. Doležal,⁵ T. V. Dong,¹²S. Dubey,¹⁸S. Eidelman,^4,66,44D. Epifanov,^4,66T. Ferber,⁸D. Ferlewicz,⁵²B. G. Fulsom,⁶⁸

R. Garg,⁶⁹V. Gaur,⁹²A. Garmash,^4,66A. Giri,²⁵ P. Goldenzweig,³⁵C. Hadjivasiliou,⁶⁸S. Halder,⁸³O. Hartbrich,¹⁸ K. Hayasaka,⁶⁵H. Hayashii,⁵⁹M. T. Hedges,¹⁸M. Hernandez Villanueva,⁵³W.-S. Hou,⁶²C.-L. Hsu,⁸¹T. Iijima,^57,56 G. Inguglia,²⁹A. Ishikawa,^19,15R. Itoh,^19,15 M. Iwasaki,⁶⁷Y. Iwasaki,¹⁹ W. W. Jacobs,²⁷ E.-J. Jang,¹⁶S. Jia,¹² Y. Jin,⁸⁸ C. W. Joo,³⁶K. K. Joo,⁶A. B. Kaliyar,⁸³K. H. Kang,⁴²G. Karyan,⁸T. Kawasaki,³⁸C. H. Kim,¹⁷D. Y. Kim,⁷⁹H. J. Kim,⁴² S. H. Kim,⁷⁶Y.-K. Kim,⁹⁵ T. D. Kimmel,⁹²P. Kodyš,⁵T. Konno,³⁸ A. Korobov,^4,66S. Korpar,^50,34 E. Kovalenko,^4,66

P. Križan,^46,34R. Kroeger,⁵³P. Krokovny,^4,66M. Kumar,⁴⁹R. Kumar,⁷²K. Kumara,⁹³Y.-J. Kwon,⁹⁵K. Lalwani,⁴⁹ J. S. Lange,¹³I. S. Lee,¹⁷S. C. Lee,⁴²C. H. Li,⁴⁵J. Li,⁴²Y. B. Li,⁷⁰L. Li Gioi,⁵¹J. Libby,²⁶K. Lieret,⁴⁷D. Liventsev,^93,19

T. Luo,¹²C. MacQueen,⁵² M. Masuda,^87,73 T. Matsuda,⁵⁴D. Matvienko,^4,66,44M. Merola,^31,58 F. Metzner,³⁵ K. Miyabayashi,⁵⁹R. Mizuk,^44,21G. B. Mohanty,⁸³S. Mohanty,^83,91H. K. Moon,⁴⁰R. Mussa,³²M. Nakao,^19,15 Z. Natkaniec,⁶³A. Natochii,¹⁸L. Nayak,²⁵M. Nayak,⁸⁵M. Niiyama,⁴¹N. K. Nisar,³S. Nishida,^19,15H. Ono,^64,65Y. Onuki,⁸⁸ P. Oskin,⁴⁴P. Pakhlov,^44,55G. Pakhlova,^21,44S. Pardi,³¹H. Park,⁴²S.-H. Park,¹⁹S. Paul,^84,51T. K. Pedlar,⁴⁸R. Pestotnik,³⁴

L. E. Piilonen,⁹²T. Podobnik,^46,34V. Popov,²¹E. Prencipe,²² M. T. Prim,² M. Ritter,⁴⁷A. Rostomyan,⁸ N. Rout,²⁶ M. Rozanska,⁶³G. Russo,⁵⁸D. Sahoo,⁸³Y. Sakai,^19,15S. Sandilya,²⁵A. Sangal,⁷L. Santelj,^46,34T. Sanuki,⁸⁶V. Savinov,⁷¹

G. Schnell,^1,23J. Schueler,¹⁸ C. Schwanda,²⁹A. J. Schwartz,⁷ Y. Seino,⁶⁵K. Senyo,⁹⁴M. Shapkin,³⁰C. Sharma,⁴⁹ C. P. Shen,¹²J.-G. Shiu,⁶²B. Shwartz,^4,66F. Simon,⁵¹A. Sokolov,³⁰E. Solovieva,⁴⁴ M. Starič,³⁴Z. S. Stottler,⁹² J. F. Strube,⁶⁸M. Sumihama,¹⁴K. Sumisawa,^19,15T. Sumiyoshi,⁹⁰W. Sutcliffe,²M. Takizawa,^77,20,74K. Tanida,³³Y. Tao,¹⁰ F. Tenchini,⁸K. Trabelsi,⁴³M. Uchida,⁸⁹K. Uno,⁶⁵S. Uno,^19,15Y. Usov,^4,66S. E. Vahsen,¹⁸R. Van Tonder,²G. Varner,¹⁸

K. E. Varvell,⁸¹A. Vossen,⁹ E. Waheed,¹⁹C. H. Wang,⁶¹E. Wang,⁷¹M.-Z. Wang,⁶²P. Wang,²⁸M. Watanabe,⁶⁵ S. Watanuki,⁴³O. Werbycka,⁶³J. Wiechczynski,⁶³E. Won,⁴⁰X. Xu,⁷⁸B. D. Yabsley,⁸¹W. Yan,⁷⁵S. B. Yang,⁴⁰H. Ye,⁸

J. H. Yin,⁴⁰C. Z. Yuan,²⁸Z. P. Zhang,⁷⁵V. Zhilich,^4,66V. Zhukova,⁴⁴and V. Zhulanov^4,66

(Belle Collaboration)

1Department of Physics, University of the Basque Country UPV/EHU, 48080 Bilbao

2University of Bonn, 53115 Bonn

3Brookhaven National Laboratory, Upton, New York 11973

4Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

5Faculty of Mathematics and Physics, Charles University, 121 16 Prague

6Chonnam National University, Gwangju 61186

7University of Cincinnati, Cincinnati, Ohio 45221

8Deutsches Elektronen–Synchrotron, 22607 Hamburg

9Duke University, Durham, North Carolina 27708

10University of Florida, Gainesville, Florida 32611

11Department of Physics, Fu Jen Catholic University, Taipei 24205

12Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai 200443

13Justus-Liebig-Universität Gießen, 35392 Gießen

14Gifu University, Gifu 501-1193

15SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

16Gyeongsang National University, Jinju 52828

17Department of Physics and Institute of Natural Sciences, Hanyang University, Seoul 04763

18University of Hawaii, Honolulu, Hawaii 96822

19High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

20J-PARC Branch, KEK Theory Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

21Higher School of Economics (HSE), Moscow 101000

22Forschungszentrum Jülich, 52425 Jülich

23IKERBASQUE, Basque Foundation for Science, 48013 Bilbao

24Indian Institute of Technology Bhubaneswar, Satya Nagar 751007

25Indian Institute of Technology Hyderabad, Telangana 502285

26Indian Institute of Technology Madras, Chennai 600036

27Indiana University, Bloomington, Indiana 47408

28Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049

29Institute of High Energy Physics, Vienna 1050

30Institute for High Energy Physics, Protvino 142281

31INFN—Sezione di Napoli, 80126 Napoli

32INFN—Sezione di Torino, 10125 Torino

33Advanced Science Research Center, Japan Atomic Energy Agency, Naka 319-1195

34J. Stefan Institute, 1000 Ljubljana

35Institut für Experimentelle Teilchenphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe

36Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa 277-8583

37Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah 21589

38Kitasato University, Sagamihara 252-0373

39Korea Institute of Science and Technology Information, Daejeon 34141

40Korea University, Seoul 02841

41Kyoto Sangyo University, Kyoto 603-8555

42Kyungpook National University, Daegu 41566

43Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay

44P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991

45Liaoning Normal University, Dalian 116029

46Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana

47Ludwig Maximilians University, 80539 Munich

48Luther College, Decorah, Iowa 52101

49Malaviya National Institute of Technology Jaipur, Jaipur 302017

50Faculty of Chemistry and Chemical Engineering, University of Maribor, 2000 Maribor

51Max-Planck-Institut für Physik, 80805 München

52School of Physics, University of Melbourne, Victoria 3010

53University of Mississippi, University, Mississippi 38677

54University of Miyazaki, Miyazaki 889-2192

55Moscow Physical Engineering Institute, Moscow 115409

56Graduate School of Science, Nagoya University, Nagoya 464-8602

57Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602

58Universit `a di Napoli Federico II, 80126 Napoli

59Nara Women’s University, Nara 630-8506

60National Central University, Chung-li 32054

61National United University, Miao Li 36003

62Department of Physics, National Taiwan University, Taipei 10617

63H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342

64Nippon Dental University, Niigata 951-8580

65Niigata University, Niigata 950-2181

66Novosibirsk State University, Novosibirsk 630090

67Osaka City University, Osaka 558-8585

68Pacific Northwest National Laboratory, Richland, Washington 99352

69Panjab University, Chandigarh 160014

70Peking University, Beijing 100871

71University of Pittsburgh, Pittsburgh, Pennsylvania 15260

72Punjab Agricultural University, Ludhiana 141004

73Research Center for Nuclear Physics, Osaka University, Osaka 567-0047

74Meson Science Laboratory, Cluster for Pioneering Research, RIKEN, Saitama 351-0198

75Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei 230026

76Seoul National University, Seoul 08826

77Showa Pharmaceutical University, Tokyo 194-8543

78Soochow University, Suzhou 215006

79Soongsil University, Seoul 06978

80Sungkyunkwan University, Suwon 16419

81School of Physics, University of Sydney, New South Wales 2006

82Department of Physics, Faculty of Science, University of Tabuk, Tabuk 71451

83Tata Institute of Fundamental Research, Mumbai 400005

84Department of Physics, Technische Universität München, 85748 Garching

85School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978

86Department of Physics, Tohoku University, Sendai 980-8578

87Earthquake Research Institute, University of Tokyo, Tokyo 113-0032

88Department of Physics, University of Tokyo, Tokyo 113-0033

89Tokyo Institute of Technology, Tokyo 152-8550

90Tokyo Metropolitan University, Tokyo 192-0397

91Utkal University, Bhubaneswar 751004

92Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

93Wayne State University, Detroit, Michigan 48202

94Yamagata University, Yamagata 990-8560

95Yonsei University, Seoul 03722

(Received 25 November 2021; accepted 10 March 2022; published 25 April 2022) We measure the branching fractions andCPasymmetries for the decaysB⁰→D¯⁰π⁰andB^þ→D¯⁰π^þ, using a data sample of 772×10⁶BB¯ pairs collected at the ϒð4SÞ resonance with the Belle detector at the KEKB e^þe⁻ collider. The branching fractions obtained and direct CP asym- metries are BðB⁰→D¯⁰π⁰Þ¼½2.700.06ðstatÞ0.10ðsystÞ×10⁻⁴, BðB^þ→D¯⁰π^þÞ¼½4.530.02ðstatÞ 0.15ðsystÞ×10⁻³, ACPðB⁰→D¯⁰π⁰Þ ¼ ½þ0.422.05ðstatÞ 1.22ðsystÞ%, and ACPðB^þ→D¯⁰π^þÞ ¼

½þ0.190.36ðstatÞ 0.57ðsystÞ%. The measurements of B are the most precise to date and are in good agreement with previous results, as is the measurement of ACPðB^þ→D¯⁰π^þÞ. The measurement ofACP forB⁰→D¯⁰π⁰is the first for this mode, and the value is consistent with Standard Model expectations.

DOI:10.1103/PhysRevD.105.072007

I. INTRODUCTION

The branching fraction (B) of the color-suppressed decay B⁰→D¯⁰π⁰[1]is measured[2–4]to be about a factor of 4 higher than theory predictions made using the “naive” factorization model, where final-state interactions (FSIs) are neglected [5,6]. This has led to a number of new theoretical descriptions of the process[7–14]that include FSIs and also treat isospin-related amplitudes of color- suppressed and color-allowed decays. The B⁰→D¯⁰π⁰ process has been shown to have large nonfactorizable components[14], so precise measurements of its properties are valuable in comparing different theoretical models used to describe it. Many of these models predict a substantial strong phase in the final state. A nonvanishing strong phase difference between two amplitudes is necessary to give rise to direct CP violation [15]. The direct CP-violation parameter, A_CP, for theB→D¯⁰π decay is defined as

A_CP¼ΓðB¯ →D⁰πÞ−ΓðB→D¯⁰πÞ

ΓðB¯ →D⁰πÞ þΓðB→D¯⁰πÞ; ð1Þ where Γ is the partial decay width for the correspond- ing decay.

In the Standard Model (SM), B⁰→D¯⁰π⁰ transitions proceed mainly via the tree-level diagram of Fig.1(a). An exchange diagram [Fig. 1(b)] with the same Cabibbo- Kobayashi-Maskawa matrix (CKM) factors is also present, but, due to Okubo-Zweig-Iizuka (OZI) suppression, is expected to have a much smaller amplitude. As such, directCP violation in this mode is expected to be small, even in the presence of a strong phase difference from FSI.

Measurements of notableCPviolation in this decay would be of significant interest and could hint at contributions from beyond-the-Standard-Model physics diagrams.

Recently theBABARand Belle Collaborations performed time-dependentCP-violation analyses of the related modes B¯⁰→D^ðÞ_CPh⁰, whereh∈π⁰;η;ωandD^ðÞ_CPrefer toDorD in a CP eigenstate [16]. They measure the CP-violation parameters Cð¼−ACPÞ, SCP, and ϕ1 [17], and obtain CðB⁰→D¯⁰h⁰Þ ¼ ð−28Þ×10⁻². This value is consis- tent with the expectation of small A_CP for B⁰→D¯⁰π⁰. However, this result does not exclude larger values up to 0.1, which would be much larger than SM predictions.

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license.

Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

A high precision measurement ofBandACPforB⁰→ D¯⁰π⁰ has further utility in addition to comparison to theoretical predictions, as it is a common control mode for use in rare charmlessB-decays with aπ⁰. The precise measurement of properties of a control mode is important to provide validation and refinement of analysis techniques.

In this paper, we present new measurements of B⁰→ D¯⁰π⁰using the full data sample ofð77210.6Þ×10⁶BB¯ pairs (711fb⁻¹) collected with the Belle detector at the KEKB asymmetric-energy e^þe⁻ (3.5 GeV on 8.0 GeV) collider[18]operating near theϒð4SÞresonance. We also present corresponding measurements of B^þ →D¯⁰π^þ decays, which proceed via a simple spectator diagram with no color suppression.

II. BELLE DETECTOR

The Belle detector [19]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 (ACCs), a barrel- like arrangement of time-of-flight (TOF) scintillation counters, and an electromagnetic calorimeter (ECL) con- sisting of CsI(Tl) crystals. All these detector components are located inside a superconducting solenoid coil that provides a 1.5 T magnetic field. An iron flux return located outside of the coil is instrumented with resistive plate chambers to detectK⁰_Lmesons and to identify muons. Two inner detector configurations were used: a 2.0 cm beam pipe and a three-layer SVD (SVD1) were used for the first sample of152×10⁶ BB¯ pairs, while a 1.5 cm beam pipe, a

four-layer SVD (SVD2), and small cells in the inner layers of the CDC were used to record the remaining 620× 10⁶ BB¯ pairs [20].

We reconstruct B⁰→D¯⁰π⁰ candidates from the sub- sequent decays of theD¯⁰and theπ⁰mesons. We employ two reconstruction modes: B⁰→D¯⁰ð→K^þπ⁻Þπ⁰ (B2b) and B⁰→D¯⁰ð→K^þπ⁻π⁰Þπ⁰ (B_3b). The π⁰ mesons are reconstructed from their decay to two photons.

The flavor of the neutral B-meson (B⁰ or B¯⁰) is determined by the charge of the reconstructed kaon (K^þ orK⁻). This method of flavor tagging is not perfect, as the wrong-sign doubly Cabibbo-suppressed (DCS) decays B¯⁰→D¯⁰π⁰[Fig.1(c)] will result in wrongly tagged flavor.

The same effect occurs with charm DCS decays D⁰→ K^þπ⁻andD⁰→K^þπ⁻π⁰, and charm mixing, although the charm mixing effect is negligibly smaller. These effects can be calculated using the ratio of wrong-sign (Cabibbo- suppressed) to right-sign (Cabibbo-favored) decay rates:

R¼B_WS

B_RS; ð2Þ

whereRðB¯⁰→D¯⁰π⁰Þ has not been measured and thus is approximated withRðB⁰→D^þπ⁻Þ¼ð2.920.380.31Þ×

10⁻⁴ [21], while RðD⁰→K^þπ⁻Þ ¼ ð3.790.18Þ×10⁻³ and RðD⁰→K^þπ⁻π⁰Þ ¼ ð2.120.07Þ×10⁻³ are taken from the Particle Data Group (PDG) [22]. These effects lead to the true value ofBbeingð0.3140.008Þ%lower than the measured value, and the trueACP beingð3.05 0.08Þ×10⁻⁵higher than the measured value. In the case of Bthis is corrected for; however, forA_CP the correction is significantly smaller than our uncertainty and it is neglected.

Photon candidates are mainly taken from clusters in the ECL but additionally are reconstructed from e^þe⁻ pairs resulting from photon conversion in the inner detector.

Photons fromπ⁰decay must have an energy greater than 50ð100ÞMeV in the barrel (end cap) region of the ECL.

The invariant mass of the two-photon combination must lie in the range 104MeV=c²< M_γγ<165MeV=c², corre- sponding to 3σ around the nominal π⁰ mass [22]. We subsequently perform a mass-constrained fit with the requirementχ²<50.

Charged tracks originating from aB-decay are required to have a distance of closest approach with respect to the interaction point of less than 4.0 cm along thez-axis (the direction opposite the positron beam), and of less than 0.3 cm in the plane transverse to thez-axis. Charged kaons and pions are identified using information from the CDC, ACC, and TOF detectors. This information is combined to form a K−π likelihood ratio RK=π¼LK=ðLKþLπÞ, whereL_KðL_πÞis the likelihood of the track being a kaon (pion). Track candidates with RK=π>0.6 (<0.4) are classified as kaons (pions). The typical kaon (pion) (a)

(b)

FIG. 1. Tree-level Feynman diagrams for (a) color-suppressed B⁰→D¯⁰π⁰ decay, (b) W exchange diagram, and (c) color- suppressed and doubly Cabibbo-suppressedB¯⁰→D¯⁰π⁰decay.

identification efficiency is 83% (88%), with a pion (kaon) misidentification probability of 7% (11%).

Two kinematic variables are used to distinguish signal from background: the beam-energy-constrained mass, Mbc≡ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

E²_beam−jp⃗ _Bj²c²

p =c², and the energy difference ΔE≡EB−Ebeam. Here, ⃗pB and EB are the momentum and energy, respectively, of theB-meson candidate evalu- ated in the center-of-mass (c.m.) frame, and Ebeam is the beam energy in the c.m. frame.

Due to energy leakage in the ECL, the reconstructedπ⁰ energy is typically lower than its true value. To compensate for this, we rescale the reconstructedπ⁰momentum to give E_π⁰≡Ebeam−E_D, specifically:

⃗pπ;corr ¼ ⃗pπ×

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðEbeam−E_D⁰Þ²−M²_π0c⁴ q

jpπjc : ð3Þ Using this we calculate a newB-meson momentum,p⃗ _B;corr, then calculate a corrected Mbc (from now on simply referred to asMbc),

Mbc≡

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E²_beam−jp⃗ _B;corrj²c² q

c² : ð4Þ

Rescaling Mbc in this way improves the mass resolution and removes some correlations betweenMbcandΔE. This procedure is only applied to the π⁰ that is the direct daughter of theB⁰.

All candidates satisfying Mbc>5.25GeV=c² and

−0.2GeV<ΔE <0.2GeV are retained for further analy- sis. We find that 16% (47%) of events have more than one B⁰ candidate in the B2b (B3b) reconstruction modes. In these cases, we select one of the reconstructedB⁰-mesons based on the mass differenceΔmðXÞ ¼mPDGðXÞ−MðXÞ, wheremPDGðXÞis the mass reported by the PDG[22]for particle X, andMðXÞ is the reconstructed mass. The best candidate is selected as the B⁰ or B^þ that minimizes ΔmðD⁰Þ. If there are multiple candidates with the same minimal ΔmðD⁰Þ, the one that minimizes Δmðπ⁰Þ is selected. Monte Carlo (MC) simulation studies show that this procedure selects the correctB⁰in 96% (86%) of cases for the B_2b (B_3b) samples.

III. BELLE DETECTOR AND SIGNAL SELECTION Backgrounds to our signal are studied using MC simulation. These simulations use EVTGEN [23] and

PYTHIA [24] to generate the physics interactions at the quark level, and employ GEANT3 [25] to simulate the detector response.

The largest background arises from e^þe⁻→qq¯ðq∈ fu; d; s; cgÞ continuum events. A neural network [26] is used to distinguish the sphericalBB¯ signal from the jetlike continuum background. It combines the following five

observables based on the event topology: a Fisher dis- criminant formed from 17 modified Fox-Wolfram moments [27]; the cosine of the angle between the B-meson candidate direction and the beam axis; the cosine of the angle between the thrust axis[28]of theB-meson candidate and that of the rest of the event (all of these quantities being calculated in the c.m. frame); the separation along thez- axis between the vertex of theB-meson candidate and that of the remaining tracks in the event; the tagging quality variable from a B-meson flavor-tagging algorithm [29].

The training and optimization of the neural network are performed with signal and continuum MC samples. These are divided into five training samples and one verification sample. The output of the neural net (CNN) has a range of ð−1;1Þ, with 1 being the most signal-like and−1being the most backgroundlike.

In order to maximally useCNN information, we impose only a loose requirement onCNNand useCNNas a variable in the fit. We requireCNN>−0.05for both theB2bandB3b

modes. This results in 86% background reduction and 87%

signal efficiency. To facilitate modeling CNN analytically with Gaussian functions, we transform it into an alternative variableC⁰_NN via the formula

C⁰_NN¼log

CNN−C^minNN

C^max_NN −CNN

; ð5Þ

whereC^min_NNis the minimum value of−0.05, andC^max_NN is the maximum value of CNN obtained from the signal MC sample used to verify the training.

There is a significant background arising from b→c transitions, which we refer to as“genericB-”decays. The main components of the genericB background are incor- rectly assigned tracks, combinatorial backgrounds, B⁰→D¯⁰ρ⁰, and B⁰→D¯⁰π⁰ with either D¯⁰→D¯⁰γ or D¯⁰→D¯⁰π⁰. These are investigated with MC simulations of BB¯-decays. To reduce this background, signal candi- dates are selected within 3 standard deviations of the mean values forMbc,ΔE, and the reconstructedπ⁰andD⁰ mass distributions. Low final-state momentum events are excluded with selection criteria on the lab-frame momen- tum of the final-state particles:PðKÞ,PðπÞ,Pðπ⁰_B0Þ, and Pðπ⁰_D¯0Þ. These requirements are listed in Table I.

There is also a very small background component from b→u and b→s transitions that consists mainly of combinatorial background, with some nonresonant B- decays to the same final states (K^þπ⁻π⁰, K^þπ⁻π⁰π⁰, K^þπ⁻π^þ, andK^þπ⁻π^þπ⁰). These are studied using a large MC sample corresponding to 50 times the number ofBB¯ events recorded by Belle. We refer to these background events as“rare.”The yield of these rare events is fixed when fitting for the signal yield based on the most recent branching fractions from the PDG[22].

After all selections have been made forB⁰→D¯⁰π⁰, the reconstruction efficiencies areð27.530.04Þ%for theB_2b mode and ð9.430.02Þ% for the B_3b mode. Including intermediate branching fractions, the overall efficiencies areð1.090.01Þ%andð1.360.01Þ%, respectively.

For B^þ→D¯⁰π^þ, the reconstruction efficiency after all selections is calculated to be ð33.080.04Þ% for the B_2b mode [ð1.310.05Þ% including intermediate branching fractions] and ð9.050.02Þ% for the B_3b mode [ð1.300.05Þ% including intermediate branching fractions].

IV. FITTING STRATEGY

The signal yield andA_CPare extracted via an unbinned extended maximum-likelihood fit to the variablesMbc,ΔE, andC⁰_NN. There are four categories of events fitted:B⁰→ D¯⁰π⁰ orB^þ→D¯⁰π^þ signal events (s), continuum events (c), genericBB¯ events (b), and rareB-decay backgrounds (r). These events are described by probability density functions (PDFs) denoted as P^s, P^c,P^b, andP^r, respec- tively. Separate PDFs are constructed for the B2b andB3b

reconstruction modes, which are fitted as two separate datasets. The data are further divided into events tagged as B⁰ andB¯⁰defined as having flavor q¼ þ1 andq¼−1, respectively, based on the charge of the kaon.

The physics parameters are determined via a simulta- neous fit to the four datasets. The total likelihood is given by

L¼ e⁻ P

jN^j

Q

q;dN_q;d!

×Y

q;d

Y^Nq;d

i¼1

X

j

f^j_dN^jP^j_q;dðMⁱ_bc;ΔEⁱ; C⁰ⁱ_NN; qÞ

; ð6Þ

whereNq;dis the number of events with flavor tagqfor the datasetd(d∈B2b; B3b), andN^jis the number of events in the jth category (j∈s; c; b; r) contributing to the total yield. The fraction of events in the datasetdfor categoryj isf^j_d, withf^j_3b¼1−f^j_2b. The PDFP^j_q;dcorresponds to the jth category in theddataset for flavorqmeasured atMⁱ_bc, ΔEⁱ, and C⁰ⁱ_NN for the ith event.

The PDF for each component is given by

P^j_q;dðM_bc;ΔE; C⁰_NN; qÞ

¼

1−q×A^j_CP 2

×P^j_dðM_bc;ΔE; C⁰_NNÞ: ð7Þ

The model accounts for a possible directCP asymmetry, A^j_CP, and the fractions of signal and backgrounds expected in each reconstruction mode B_2b (B_3b). In Eq. (6), the fractionf^s_dis determined via MC studies of theB_2bandB_3b modes and is fixed in the fit to data, andA^j_CPðj∈c; b; rÞis fixed based on studies of detector bias using sideband data (see Sec.V).

The 20 free parameters in the fit are the number of signal eventsN^s, signal asymmetryA^s_CP, the number of continuum events (N^c) and genericB-decay events (N^b), fractions of backgrounds expected in each reconstruction mode f^j_d (j∈c; b; r), shape parameters of the continuum Mbc

andΔE PDFs, and the mean and width of theB_2b signal MbcandΔEPDFs. The number of rare background events (N^r) is fixed to that expected from MC studies. The effects of these assumptions are included in the systematic uncertainties.

The PDFs used for theMbcandΔEdistributions for the various event types are as follows.

(i) Signal: For theB_2b mode, theMbc PDF is a Crystal Ball function[30], while theΔEPDF is the sum of a Crystal Ball function and a Gaussian with the same mean. The Gaussian component is small and in- cluded to handle the tails of the distribution. For the B_3bmode, there is a strong correlation betweenMbc

andΔE, and no analytic 2D PDF could be found to fit the data satisfactorily. Instead a 2D kernel density estimation (KEST) PDF[31]is used.

(ii) Generic B-decay background: Similar to the B_3b signal, there exist complex correlations betweenMbc

and ΔE, so a 2D KEST PDF obtained from MC simulations is used in both modes.

(iii) Continuum background:Mbcis fitted as an ARGUS function [32], and ΔE as a third-order Chebyshev polynomial, in both modes.

(iv) RareB-decay background: As with a genericBand B_3b signal, the Mbc and ΔE distributions for rare B-decay background are modeled with a 2D KEST PDF in both modes. This PDF is determined using TABLE I. Requirements on kinematic variables employed in

the reconstruction of B⁰→D¯⁰π⁰ decays to minimize generic B-decay background. The subscript identifies the origin of the particle, and theD¯⁰-decay mode is shown in square brackets.

Variable Selected range

Mbc 5.253–5.288GeV=c²

ΔE −0.2–0.2GeV

MðD⁰Þ 1.841–1.882GeV=c²

Mðπ⁰_B0Þ½K^þπ⁻ 104.1–163.1MeV=c² Mðπ⁰_B0Þ½K^þπ⁻π⁰ 105.8–164.4MeV=c² Mðπ⁰_D¯0Þ½K^þπ⁻π⁰ 107.9–162.3MeV=c²

PðKÞ 0.3–3.5GeV=c

PðπÞ 0.3–3.5GeV=c

Pðπ⁰_B0Þ 1.5–3.5GeV=c Pðπ⁰D¯⁰Þ 0.2–3.5GeV=c

MC simulations corresponding to 50 times the luminosity of the Belle dataset.

To fit C⁰NN, three summed Gaussians are used for all components except continuum background, which employed two summed Gaussians. The PDFs for all event types are summarized in Table II.

The fitting procedure and accuracy of the various PDF models are extensively investigated using MC“pseudoex- periments.” In these studies, the signal and rare B back- ground events are selected from large samples of simulated events. Events for e^þe⁻→q¯q and generic B-decay are generated from their respective PDF shapes. For B⁰→D¯⁰π⁰, we observe a small bias of ðþ0.60.3Þ%

in signal yield, andðþ0.040.05Þ%in ACP. We correct for this bias in our final measurements and include a corresponding systematic uncertainty for it. No significant bias is observed for B^þ →D¯⁰π^þ, i.e., only ðþ0.06 0.16Þ%in signal yield andð−0.020.02Þ%in A_CP.

V.B⁺ →D¯⁰π⁺

We first select and fit a sample ofB^þ→D¯⁰π^þ decays.

This sample is not color suppressed and thus has much larger statistics and lower background than the sample of B⁰→D¯⁰π⁰ decays. As well as ensuring the fitted B and ACP are consistent with existing measurements, this mode is used to obtain calibration factors for the fixed shape parameters of the PDFs used to fit B⁰→D¯⁰π⁰ decays to account for any differences between MC and data. In addition, this mode provides a data-driven estimation of the systematic uncertainty associated with the A_CP correction for a detection asymmetry (discussed below).

To account for potential differences in the distribution of fitting variables between MC and data, additional param- eters (calibration factors) are included in the fit to enable small adjustments in the fitted PDF shapes. These calibra- tion factors are applied as mean shifts and width factors to the C⁰NN Gaussians.

To account for small differences between MC and data in the width of theΔEdistribution, the 2D KEST PDF forMbc

and ΔE in B_3b is modified slightly. This is done by modifying each ΔE data point in the MC dataset with a

random shift based on a Gaussian distribution with a mean of 0 GeV and a width of 7 MeV (chosen after testing with a range of widths) and generating a new KEST PDF from this modified data sample.

Fits to the B^þ →D¯⁰π^þ sample are performed to deter- mine the signal yield,A_CP;raw, the continuum background yield, the generic B-decay background yield, and the calibration factors. The rare B-decay background yield is fixed to the value expected from MC simulations.

From the fit we obtainNsig¼84537306andA_CP;raw¼ ð1.970.36Þ%. The uncertainties listed are statistical.

A_CP;raw is the output of the fit without a correction to account for sources of bias. Figure2shows the fits to data inMbc,ΔE, andC⁰_NN.

To account for possible bias in ACP, we perform an analysis over a “sideband” region of data defined as 0.1GeV<ΔE <0.4GeV and 5.255GeV=c²< Mbc<

5.27GeV=c². This region consists almost entirely of continuum events and has an expected ACP of zero.

Counting the number of events in this region we find ACP;sideband¼ ð1.780.38Þ%. We subtract this value from A_CP;raw to correct for the detection asymmetry bias.

The branching fraction is calculated as

B¼Nsig

N_B× mean f^s_2b

ϵ_2b;f^s_3b ϵ_3b

; ð8Þ

where N_B is the number of charged B-mesons in the dataset based on the PDG average value of Bðϒð4SÞ→ B^þB⁻Þ ¼ ð51.40.6%Þ[22]; f^s_d is the fraction of signal events in the dataset d¼2b or 3b (f^s_2b¼0.51, f^s_3b¼0.49); ϵd is the product of the reconstruction effi- ciency, theD¯⁰branching fractionBd, and small corrections for particle identification (PID), and charged-track andπ⁰ reconstruction efficiencies (see Sec.VII) for moded. The π⁰→γγ branching fraction is accounted for in the MC simulation. The resulting values forϵ2bandϵ3bareð1.19 0.03Þ×10⁻² andð1.160.05Þ×10⁻², respectively. The mean is calculated as a generalized weighted mean[33,34]

taking into account correlated and uncorrelated uncertain- ties in a covariance matrix. This approach is used because the difference in systematic uncertainties between the two D¯⁰-decay modes leads to the need to weight them in order to calculate the final branching fraction and uncertainty correctly. Finally, the correction due to DCS decays discussed in Sec.II is made.

The results for B andACP for B^þ →D¯⁰π^þ are

B¼ ð4.530.020.15Þ×10⁻³; ð9Þ A_CP¼ ð0.190.360.57Þ%: ð10Þ The uncertainties quoted are statistical and systematic, respectively. The systematic uncertainties associated TABLE II. Functional forms for PDFs employed by the differ-

ent event categories for fits.

Category Mbc ΔE C⁰NN

SignalB2b Crystal ball Crystal ball + gaussian

Three gaussians SignalB3b 2D KEST PDF Three gaussians

Generic B 2D KEST PDF Three gaussians

Continuum ARGUS Third order Two gaussians Chebyshev polynomial

RareB 2D KEST PDF Three gaussians

with the measurement ofBandACPare explained in detail in Sec. VII, and the contributions of each of these are listed in TablesVandVI, respectively. These results are in agreement with the PDG values [22] of B¼ ð4.68 0.13Þ×10⁻³ and ACP¼ ð−0.70.7Þ%. As a cross- check, we determined B and A_CP for each of the B_2b andB_3d modes separately, and for just the SVD1 dataset.

All are in agreement within statistical uncertainties. The fitted yield for each respective category is listed in Table III.

VI.B⁰→D¯⁰π⁰

After applying the calibration factors determined from studies of the B^þ →D¯⁰π^þ mode to the PDFs, we fit the signalB⁰→D¯⁰π⁰PDFs to data and find444897 signal events and A_CP;raw¼ ð1.482.05Þ%. The uncer- tainties quoted are statistical. As was the case for B^þ→D¯⁰π^þ, A_CP;raw is the value returned from the fit without a correction for sources of bias. Figure 3 shows the signal-enhanced projections of the fits. Figure4shows signal-enhanced projections ofMbcseparated intoB⁰- and B¯⁰-decays.

Using Eq. (8), the PDG value Bðϒð4SÞ→B¯⁰B⁰Þ ¼ ð48.60.6%Þ[22], the fraction of signal events in dataset d, f^s_2b¼0.45, f^s_3b¼0.55, and the efficiencies ϵ_2b¼ ð1.000.03Þ×10⁻² and ϵ_3b¼ ð1.210.07Þ×10⁻², we determine the branching fraction to be

BðB⁰→D¯⁰π⁰Þ ¼ ð2.700.060.10Þ×10⁻⁴; ð11Þ where the quoted uncertainties are statistical and system- atic, respectively. The fitted yield for each respective category is listed in TableIV.

5.255 5.26 5.265 5.27 5.275 5.28 5.2850 1000

2000 3000 4000 5000

5.255 5.26 5.265 5.27 5.275 5.28 5.2850 500

1000 1500 2000 2500 3000 3500 4000 4500 4 2 02 4

42 02 46

0.2 0.15 0.1 0.05 0 0.05 0.1 0.15 0.2 0

2000 4000 6000 8000 10000

0.2 0.15 0.1 0.05 0 0.05 0.1 0.15 0.2 0

1000 2000 3000 4000 5000 6000 7000 4 0 4

4 2 0 2 4

10 8 6 4 2 0 2 4 6 8 10

0 500 1000 1500 2000 2500 3000 3500

10 8 6 4 2 0 2 4 6 8 10

0 500 1000 1500 2000 2500 3000 3500 12 84 04

64 2 02 4

π-

K+

D0

π-

K+

D0

π-

K+

D0

π0

π-

K+

D0 D⁰ K⁺π^-π⁰ D⁰ K⁺π^-π⁰

GeV)-410×Events / (8.3GeV)-410×Events / (8.3 GeV)-2Events /(10GeV)-2Events /(10 Events / (0.5)Events / (0.5)

2] [GeV/c Mbc

2] [GeV/c Mbc

E [GeV]

Δ

E [GeV]

Δ

NN`

CNN

C

`

FIG. 2. Projections of the B^þ→D¯⁰π^þ fit results into the signal region (5.275< Mbc<5.285GeV, −0.05<ΔE <0.05GeV,

−1< C⁰NN<6) forMbc(left),ΔE(middle), andC⁰NN(right) split into theB2bmode (top) andB3b(bottom). The blue short-dashed curve shows the signal PDF, red dotted curve shows theBB¯background PDF, green dash-dotted curve shows the continuum background PDF, pink long-dashed curve shows the (almost negligible) rare background PDF, black line is the fit result, points are data. Also shown underneath each graph are the residual pulls between the data points and fitted PDF.

TABLE III. Fitted number of signal and backgrounds events for the two reconstruction modes (B2b and B3b) of B^þ→D¯⁰π^þ. Uncertainties are statistical only.

Category B_2b mode (×10⁴) B_3b mode (×10⁴)

Signal 4.270.02 4.180.02

Continuum 0.700.01 1.780.3 Generic B 3.580.03 3.870.03

Rare 0.03 (fixed) 0.05 (fixed)

The A_CP correction for the B⁰→D¯⁰π⁰ decay is mea- sured in the same way as for the B^þ→D¯⁰π^þ mode. A sideband region of data is defined as 0.1GeV<ΔE <

0.4GeV and 5.255GeV=c²< Mbc<5.27GeV=c². Events in this region consist almost entirely of continuum with an expectedA_CPof zero. In this region we findACP;sideband¼ ð1.020.64Þ%, and we subtract this value and the fit bias (0.04%) from ACP;raw to correct for detector bias.

The directCP-violation parameter is thus measured to be ACPðB⁰→D¯⁰π⁰Þ ¼ ð0.422.051.22Þ%: ð12Þ

The uncertainties quoted are statistical and systematic, respectively.

VII. SYSTEMATIC UNCERTAINTIES The systematic uncertainties associated with the meas- urement ofB and ACP are as follows.

(i) Number of BB¯ pairs: The uncertainty associated with the measured number of BB¯ pairs in the full dataset collected at Belle is 1.37% [35].

(ii) Bðϒð4SÞ→B⁰B¯⁰Þ: Uncertainty from the branching fractionBðϒð4SÞ→B¯⁰B⁰Þ ¼ ð48.60.6%Þ[22].

(iii) DCS mode correction: The uncertainty due to the correction for doubly Cabibbo-suppressed decays is 0.01% for both B⁰→D¯⁰π⁰ and B^þ→D¯⁰π^þ (see Sec.II).

(iv) Charged-track efficiency: The uncertainty associated with a possible difference in efficiency between MC and data for charged-track reconstruction is found to be 0.35% per track using partially reconstructed D^þ→D⁰ð→π^þπ⁻π⁰Þπ^þ events[35].

(v) π⁰ detection efficiency: The ratio of data to MC efficiency forπ⁰reconstruction is based on a study

5.255 5.26 5.265 5.27 5.275 5.28 5.2850 50

100 150 200 250 300 350

5.255 5.26 5.265 5.27 5.275 5.28 5.2850 50

100 150 200 250 300 350 400 450 2 0 2

2 0 2

0.2 0.15 0.1 0.05 0 0.05 0.1 0.15 0.2 0

50 100 150 200 250 300 350 400 450

0.2 0.15 0.1 0.05 0 0.05 0.1 0.15 0.2 0

100 200 300 400 500 600 2 0 2

2 0 2

10 8 6 4 2 0 2 4 6 8 10

0 50 100 150 200 250 300

10 8 6 4 2 0 2 4 6 8 10

0 50 100 150 200 250 300 350 400 450 500 2 0 2 4

2 0 2

π0

π-

K+

D0 D⁰ K⁺π^-π⁰ D⁰ K⁺π^-π⁰ π-

K+

D0 D⁰ K⁺π^- D⁰ K⁺π^-

GeV)-410×Events / (8.3GeV)-410×Events / (8.3 GeV)-2Events / (10GeV)-2Events / (10 Events / (0.5)Events / (0.5)

2] [GeV/c Mbc

2] [GeV/c Mbc

E [GeV]

Δ

E [GeV]

Δ

NN`

CNN

C

`

FIG. 3. Projections of the B⁰→D¯⁰π⁰ fit results into the signal region (5.275< Mbc<5.285GeV, −0.12<ΔE <0.07GeV,

−1< C⁰NN<6) forMbc(left),ΔE(middle), andC⁰NN(right) split into theB2bmode (top) andB3b(bottom). The blue short-dashed curve shows the signal PDF, red dotted curve shows theBB¯background PDF, green dash-dotted curve shows the continuum background PDF, pink long-dashed curve shows the (almost negligible) rare background PDF, black line is the fit result. Also shown underneath each graph are the residual pulls between the data points and fitted PDF.

TABLE IV. Fitted number of signal and backgrounds events for the two reconstruction modes (B2b and B3b) of B⁰→D¯⁰π⁰. Uncertainties are statistical only.

Category B_2b mode (×10³) B_3b mode (×10³)

Signal 2.010.04 2.440.05

Continuum 4.260.06 16.470.22 Generic B 4.760.10 8.390.18

Rare 0.15 (fixed) 0.47 (fixed)

ofτ⁻ →π⁻π⁰ν_τdecays[36]. This ratio isð962Þ%

per π⁰.

(vi) MC statistics in efficiency calculation: Uncertainty associated with the reconstruction efficiency is based on the binomial statistics of the MC dataset used. This is 0.094% for B⁰→D¯⁰ðK^þπ⁻Þπ⁰, 0.18% for B⁰→D¯⁰ðK^þπ⁻π⁰Þπ⁰, 0.075% for B^þ→ D¯⁰ðK^þπ⁻Þπ^þ, and 0.19% forB^þ→D¯⁰ðK^þπ⁻π⁰Þπ^þ. (vii) D¯⁰-subdecay branching fraction andA_CP: from the

PDG average [22].

(viii) PID efficiency: systematic error associated with a small difference in PID efficiency between MC and data. This is based on an inclusive D^þ→D⁰ðK⁻π^þÞπ^þ study [35]. The uncertainty is calculated as 1.3% forB⁰→D¯⁰ðK^þπ⁻Þπ⁰, 1.3%

for B⁰→D¯⁰ðK^þπ⁻π⁰Þπ⁰, 2.2% for B^þ→ D¯⁰ðK^þπ⁻Þπ^þ, and 2.2% forB^þ→D¯⁰ðK^þπ⁻π⁰Þπ^þ. (ix) Signal decay mode yield ratiof^s_d: The ratio between theD⁰-decay modes in signal,f^s_d, is fixed based on the expected yields from MC. To account for the 5.255 5.26 5.265 5.27 5.275 5.28 5.2850

20 40 60 80 100 120 140

5.255 5.26 5.265 5.27 5.275 5.28 5.2850 20

40 60 80 100 120 140 160

5.255 5.26 5.265 5.27 5.275 5.28 5.2850 50

100 150 200 250

5.255 5.26 5.265 5.27 5.275 5.28 5.2850 20

40 60 80 100 120 140 160 180 200 220 240

21 01 2

21 01 23

21 01 23

2 0 2 4

π

0 +

)

-

π

0

(K

0

D

0

B π

-

)

+

π

0

(K

0

D B

2] [GeV/c M

2] [GeV/c

Mbc M_bc[GeV/c²]

2] [GeV/c Mbc

π

0 0

) π π

+

(K

-

D

0

B

0

GeV)-410×Events / (8.3GeV)-410×Events / (8.3 GeV)-410×Events / (8.3GeV)-410×Events /(8.3

π

0 0

) π π

-

(K

+

D

0

B

0 bc

FIG. 4. Projections of theB⁰→D¯⁰π⁰fit results forMbcinto the signal region (−0.12<ΔE <0.07GeV,−1< C⁰NN<6) forB⁰→ D¯⁰ðK^þπ⁻Þπ⁰(top left),B¯⁰→D⁰ðK⁻π^þÞπ⁰(top right),B⁰→D¯⁰ðK^þπ⁻π⁰Þπ⁰(bottom left),B¯⁰→D⁰ðK⁻π^þπ⁰Þπ⁰(bottom right). The blue short-dashed curve shows the signal PDF, red dotted curve shows theBB¯ background PDF, green dash-dotted curve shows the continuum background PDF, pink long-dashed curve shows the (almost negligible) rare background PDF, black line is the fit result. Also shown underneath each graph are the residual pulls between the data points and fitted PDF.