Measurement of the absolute branching fraction of D+ › K¯ 0e +?e via K¯ 0 › ? 0? 0 *

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Measurement of the absolute branching fraction of D+ → K̅0 e+νe via K0 0 0

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Measurement of the absolute branching fraction of D

_{→ ¯}

K

e

ν

via

¯

K

_{→ π}

π

M. Ablikim(ð&A)1 _{M. N. Achasov}9,e _{X. C. Ai(Mh)}1 _{O. Albayrak}5 _{M. Albrecht}4 _{D. J. Ambrose}44 A. Amoroso49A,49C _{F. F. An(S¥¥)}1 _{Q. An(Sj)}46,a _{J. Z. Bai(xµz)}1 _{R. Baldini Ferroli}20A

Y. Ban(])31 _{D. W. Bennett}19 _{J. V. Bennett}5 _{M. Bertani}20A _{D. Bettoni}21A _{J. M. Bian(>ì´)}43 F. Bianchi49A,49C _{E. Boger}23,c _{I. Boyko}23 _{R. A. Briere}5 _{H. Cai(éÓ)}51 _{X. Cai(é)}1,a _{O. Cakir}40A A. Calcaterra20A _{G. F. Cao(ùIL)}1 _{S. A. Cetin}40B _{J. F. Chang(~§~)}1,a _{G. Chelkov}23,c,d

G. Chen(f)1 _{H. S. Chen(Ú))}1 _{H. Y. Chen(°)}2 _{J. C. Chen(ôA)}1 _{M. L. Chen(çw)}1,a S. Chen(¢)41 _{S. J. Chen(„)}29 _{X. Chen(•î)}1,a _{X. R. Chen(RJ)}26 _{Y. B. Chen(y)}1,a H. P. Cheng(§Ú²)17 _{X. K. Chu(±#%)}31 _{G. Cibinetto}21A _{H. L. Dai(“ö )}1,a _{J. P. Dai(“ï²)}34 A. Dbeyssi14 _{D. Dedovich}23 _{Z. Y. Deng("fý)}1 _{A. Denig}22 _{I. Denysenko}23 _{M. Destefanis}49A,49C F. De Mori49A,49C _{Y. Ding(¶])}27 _{C. Dong(‡)}30 _{J. Dong(·)}1,a _{L. Y. Dong(Â)}1

M. Y. Dong(²Â)1,a _{Z. L. Dou(Î[)}29 _{S. X. Du(ÚÖk)}53 _{P. F. Duan(ã+œ)}1 _{J. Z. Fan(‰¨²)}39 J. Fang(ï)1,a _{S. S. Fang(’V­)}1 _{X. Fang(ù)}46,a _{Y. Fang(´)}1 _{R. Farinelli}21A,21B _{L. Fava}49B,49C O. Fedorov23 _{F. Feldbauer}22 _{G. Felici}20A _{C. Q. Feng(µ~“)}46,a _{E. Fioravanti}21A _{M. Fritsch}14,22 C. D. Fu(F¤Å)1 _{Q. Gao(p˜)}1 _{X. L. Gao(pc[)}46,a _{X. Y. Gao(pR)}2 _{Y. Gao(pw)}39 Z. Gao(pª)46,a _{I. Garzia}21A _{K. Goetzen}10 _{L. Gong(÷w)}30 _{W. X. Gong(÷©ü)}1 a _{W. Gradl}22 M. Greco49A,49C _{M. H. Gu(ÞÊ)}1,a _{Y. T. Gu($e)}12 _{Y. H. Guan(+L¦)}1 _{A. Q. Guo(HOr)}1 L. B. Guo(HáÅ)28 _{R. P. Guo(HX)}1 _{Y. Guo(HT)}1 _{Y. P. Guo(HŒ±)}22 _{Z. Haddadi}25 _{A. Hafner}22 S. Han(¸W)51 _{X. Q. Hao(ÏUŸ)}15 _{F. A. Harris}42 _{K. L. He(Ûx)}1 _{T. Held}4 _{Y. K. Heng(ï&)}1,a Z. L. Hou(û£9)1 _{C. Hu(Ò)}28 _{H. M. Hu(°²)}1 _{J. F. Hu(U¸)}49A,49C _{T. Hu(7)}1,a

Y. Hu(™)1 _{G. S. Huang(‘1^)}46,a _{J. S. Huang(‘7Ö)}15 _{X. T. Huang(‘57)}33 X. Z. Huang(‘¡§)29 _{Y. Huang(‘])}29 _{Z. L. Huang(‘œ )}27 _{T. Hussain}48 _{Q. Ji(V)}1

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P. R. Li(oJ)41 _{Q. Y. Li(oé)}33 _{T. Li(oC)}33 _{W. D. Li(o¥À)}1 _{W. G. Li(o¥I)}1 X. L. Li(o¡ )33 _{X. N. Li(oI)}1,a _{X. Q. Li(oÆd)}30 _{Y. B. Li(oÆ)}2 _{Z. B. Li(o“W)}38

H. Liang(ùh)46,a _{Y. F. Liang(ù]œ)}36 _{Y. T. Liang(ù‹c)}24 _{G. R. Liao( 2H)}11 _{D. X. Lin(R)}14 B. Liu(4X)34 _{B. J. Liu(4ô)}1 _{C. X. Liu(4SD)}1 _{D. Liu(4Å)}46,a _{F. H. Liu(44m)}35

Fang Liu(4)1 _{Feng Liu(4¸)}6 _{H. B. Liu(4÷)}12 _{H. H. Liu(4®¦)}16 _{H. H. Liu(4)}1

Received 3 May 2016, Revised 29 June 2016

∗_{Supported by National Key Basic Research Program of China (2009CB825204, 2015CB856700), National Natural Science Foundation} of China (NSFC) (10935007, 11125525, 11235011, 11305180, 11322544, 11335008, 11425524, 11475123), Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program, CAS Center for Excellence in Particle Physics (CCEPP), Collaborative Innovation Center for Particles and Interactions (CICPI), Joint Large-Scale Scientific Facility Funds of NSFC and CAS (11179007, U1232201, U1332201, U1532101), CAS (KJCX2-YW-N29, KJCX2-YW-N45), 100 Talents Program of CAS, National 1000 Talents Program of China, IN-PAC and Shanghai Key Laboratory for Particle Physics and Cosmology, German Research Foundation DFG (Collaborative Research Center CRC-1044), Istituto Nazionale di Fisica Nucleare, Italy, Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) (530-4CDP03), Ministry of Development of Turkey (DPT2006K-120470), National Natural Science Foundation of China (NSFC) (11405046, U1332103), Russian Foundation for Basic Research (14-07-91152), Swedish Resarch Council, U. S. Department of Energy (DE-FG02-04ER41291, DE-FG02-05ER41374, DE-SC0012069, DESC0010118), U.S. National Science Foundation, University of Groningen (RuG) and Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt, WCU Program of National Research Foundation of Korea (R32-2008-000-10155-0).

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3_{and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy}

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F. Nerling14 _{I. B. Nikolaev}9,e _{Z. Ning(wó)}1,a _{S. Nisar}8 _{S. L. Niu(Ú^|)}1,a _{X. Y. Niu(Ú՞)}1 S. L. Olsen(29)32 _{Q. Ouyang(î+)}1,a _{S. Pacetti}20B _{Y. Pan()}46,a _{P. Patteri}20A _{M. Pelizaeus}4 H. P. Peng($°²)46,a _{K. Peters}10,i _{J. Pettersson}50 _{J. L. Ping(²\Ô)}28 _{R. G. Ping(²Jf)}1

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E. H. Thorndike44 _{M. Tiemens}25 _{M. Ullrich}24 _{I. Uman}40D _{G. S. Varner}42 _{B. Wang(R)}30

B. L. Wang(T9)41 _{D. Wang(À)}31 _{D. Y. Wang(Œ])}31 _{K. Wang(‰)}1,a _{L. L. Wang( )}1 L. S. Wang((Ô)1 _{M. Wang(ƒ)}33 _{P. Wang(²)}1 _{P. L. Wang(û)}1 _{W. Wang(è)}1,a W. P. Wang(‘²)46,a _{X. F. Wang(<œ)}39 _{Y. Wang()}37 _{Y. D. Wang(ä&)}14

Y. F. Wang(Š)1,a _{Y. Q. Wang(æ_)}22 _{Z. Wang()}1,a _{Z. G. Wang(“f)}1,a

Z. H. Wang(“÷)46 a _{Z. Y. Wang(–])}1 _{Z. Y. Wang(m )}1 _{T. Weber}22 _{D. H. Wei(Ÿ“¬)}11 P. Weidenkaff22 _{S. P. Wen(©aª)}1 _{U. Wiedner}4 _{M. Wolke}50 _{L. H. Wu(Î(¦)}1 _{L. J. Wu(ÇëC)}1 Z. Wu(ǜ)1,a _{L. Xia(g[)}46,a _{L. G. Xia(gåg)}39 _{Y. Xia(g‰)}18 _{D. Xiao(Å)}1 _{H. Xiao(Ó)}47 Z. J. Xiao(
)28 _{Y. G. Xie(‰2)}1,a _{Q. L. Xiu(?“[)}1,a _{G. F. Xu(NIu)}1 _{J. J. Xu(M··)}1 L. Xu(MX)1 _{Q. J. Xu(MŸ)}13 _{Q. N. Xu(MŸc)}41 _{X. P. Xu(M#²)}37 _{L. Yan(î )}49A,49C W. B. Yan(>©I)46,a _{W. C. Yan(A©¤)}46,a _{Y. H. Yan(ô[ù)}18 _{H. J. Yang( °
)}34 H. X. Yang( öÊ)1 _{L. Yang( 7)}51 _{Y. X. Yang( [#)}11 _{M. Ye(“r)}1,a _{M. H. Ye(“µÇ)}7 J. H. Yin(Ðdh)1 _{B. X. Yu(|ˌ)}1,a _{C. X. Yu(’XR)}30 _{J. S. Yu(|'v)}26 _{C. Z. Yuan()}1 W. L. Yuan(©9)29 _{Y. Yuan()}1 _{A. Yuncu}40B,b _{A. A. Zafar}48 _{A. Zallo}20A _{Y. Zeng(Q)}18 Z. Zeng(Qó)46,a _{B. X. Zhang(ÜZ#)}1 _{B. Y. Zhang(Ü])}1,a _{C. Zhang(ܶ)}29 _{C. C. Zhang(ÜS)}1 D. H. Zhang(܈u)1 _{H. H. Zhang(Ü÷Ó)}38 _{H. Y. Zhang(Ùù‰)}1,a _{J. Zhang(ÜA)}1

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J. Y. Zhang(Üï])1 _{J. Z. Zhang(ܵz)}1 _{K. Zhang(Ü%)}1 _{L. Zhang(Ü[)}1 _{S. Q. Zhang(ܬ)}30 X. Y. Zhang(ÜÆ)33 _{Y. Zhang(Ü)}1 _{Y. H. Zhang(ÜÕõ)}1,a _{Y. N. Zhang(܉w)}41

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A. Zhemchugov23,c _{B. Zheng(xÅ)}47 _{J. P. Zheng(xï²)}1,a _{W. J. Zheng(x©·)}33 _{Y. H. Zheng(xð)}41 B. Zhong(¨Q)28 _{L. Zhou(±s)}1,a _{X. Zhou(±)}51 _{X. K. Zhou(±¡x)}46,a _{X. R. Zhou(±I)}46,a X. Y. Zhou(±,Œ)1 _{K. Zhu(Áp)}1 _{K. J. Zhu(Á‰
)}1,a _{S. Zhu(ÁR)}1 _{S. H. Zhu(Á­°)}45

X. L. Zhu(ÁƒX)39 _{Y. C. Zhu(ÁCS)}46,a _{Y. S. Zhu(Á[))}1 _{Z. A. Zhu(ÁgS)}1 _{J. Zhuang(Bï)}1,a L. Zotti49A,49C _{B. S. Zou(qXt)}1 _{J. H. Zou(qZð)}1

(BESIII Collaboration)

1_{Institute of High Energy Physics, Beijing 100049, China} 2 _{Beihang University, Beijing 100191, China}

3_{Beijing Institute of Petrochemical Technology, Beijing 102617, China} 4_{Bochum Ruhr-University, D-44780 Bochum, Germany} 5_{Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA}

6 _{Central China Normal University, Wuhan 430079, China} 7_{China Center of Advanced Science and Technology, Beijing 100190, China}

8 _{COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan} 9 _{G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia}

10_{GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany} 11_{Guangxi Normal University, Guilin 541004, China}

12_{Guangxi University, Nanning 530004, China} 13_{Hangzhou Normal University, Hangzhou 310036, China}

14_{Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany} 15_{Henan Normal University, Xinxiang 453007, China}

16_{Henan University of Science and Technology, Luoyang 471003, China} 17_{Huangshan College, Huangshan 245000, China}

18_{Hunan University, Changsha 410082, China} 19 _{Indiana University, Bloomington, Indiana 47405, USA}

20_{(A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN and University of Perugia, I-06100, Perugia, Italy} 21_{(A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy}

22_{Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany} 23_{Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia}

24_{Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany} 25_{KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands}

26_{Lanzhou University, Lanzhou 730000, China} 27_{Liaoning University, Shenyang 110036, China} 28_{Nanjing Normal University, Nanjing 210023, China}

29_{Nanjing University, Nanjing 210093, China} 30_{Nankai University, Tianjin 300071, China} 31_{Peking University, Beijing 100871, China} 32_{Seoul National University, Seoul, 151-747 Korea}

33_{Shandong University, Jinan 250100, China} 34_{Shanghai Jiao Tong University, Shanghai 200240, China}

35_{Shanxi University, Taiyuan 030006, China} 36_{Sichuan University, Chengdu 610064, China}

37_{Soochow University, Suzhou 215006, China} 38_{Sun Yat-Sen University, Guangzhou 510275, China}

39_{Tsinghua University, Beijing 100084, China}

40_{(A)Ankara University, 06100 Tandogan, Ankara, Turkey; (B)Istanbul Bilgi University, 34060 Eyup, Istanbul, Turkey; (C)Uludag}

University, 16059 Bursa, Turkey; (D)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey

41_{University of Chinese Academy of Sciences, Beijing 100049, China} 42 _{University of Hawaii, Honolulu, Hawaii 96822, USA} 43_{University of Minnesota, Minneapolis, Minnesota 55455, USA}

44_{University of Rochester, Rochester, New York 14627, USA} 45_{University of Science and Technology Liaoning, Anshan 114051, China}

46_{University of Science and Technology of China, Hefei 230026, China} 47_{University of South China, Hengyang 421001, China}

48_{University of the Punjab, Lahore-54590, Pakistan}

49_{(A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125,}

Turin, Italy

50_{Uppsala University, Box 516, SE-75120 Uppsala, Sweden} 51_{Wuhan University, Wuhan 430072, China} 52_{Zhejiang University, Hangzhou 310027, China} 53_{Zhengzhou University, Zhengzhou 450001, China}

a_{Also at State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, China} b_{Also at Bogazici University, 34342 Istanbul, Turkey}

c_{Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia} d_{Also at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia}

e _{Also at the Novosibirsk State University, Novosibirsk, 630090, Russia} f _{Also at the NRC ”Kurchatov Institute, PNPI, 188300, Gatchina, Russia}

g _{Also at University of Texas at Dallas, Richardson, Texas 75083, USA} h_{Also at Istanbul Arel University, 34295 Istanbul, Turkey} i_{Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany}

Abstract: By analyzing 2.93 fb−1 _{data collected at the center-of-mass energy}√_{s= 3.773 GeV with the BESIII}

detector, we measure the absolute branching fraction of the semileptonic decay D+

→ ¯K0_e+_ν

e to be B(D+ →

¯ K0_e+_ν

e) = (8.59 ± 0.14 ± 0.21)% using ¯K0→ K0S→ π0π0, where the first uncertainty is statistical and the second

systematic. Our result is consistent with previous measurements within uncertainties..

Keywords: charmed mesons, semileptonic decays, absolute branching fraction, BESIII/BEPCII PACS: 13.20.Fc, 14.40.Lb DOI:10.1088/1674-1137/40/11/113001

1

Introduction

The study of semileptonic decays of D mesons can shed light on the strong and weak effects in charmed meson decays. The absolute branching fraction B of the semileptonic decay D+

→ ¯K0_e+_ν

e can be used to ex-tract the form factor fK

+(0) of the hadronic weak current or the quark mixing matrix element |Vcs| [1], which are important to calibrate the lattice quantum chromody-namics calculation on fK

+(0) and to test the unitarity of the quark mixing matrix. In addition, the measured B(D+_{→ ¯K}0_e+_ν

e) can also be used to test isospin sym-metry in the D+_{→ ¯K}0_e+_ν

e and D0→ K−e+νedecays [2– 5]. Therefore, improving the measurement precision of B(D+ _{→ ¯K}0_e+_ν

e) will be helpful to better understand the D decay mechanisms.

Measurements of B(D+_{→ ¯K}0_e+_ν

e) via ¯K0 → K0S→ π+_π− _{have been performed by the MARKIII, BES,} CLEO and BESIII Collaborations [2–6]. Recently, a measurement of B(D+

→ ¯K0 Le

+_ν

e) has been carried out by the BESIII Collaboration [7]. However, no measure-ment of B(D+

→ ¯K0_e+_ν

e) using ¯K0 → K0S→ π

0_π0 _has been reported so far. As a first step, we present in this paper a measurement of B(D+ → ¯K0_e+_ν e) using ¯K0→ K0 S → π 0_π0_{, based on an analysis of 2.93 fb}−1 _{of e}+_e− collision data [8, 9] accumulated at the center-of-mass energy√s = 3.773 GeV with the BESIII detector [10]. Since the fK

+(0)|Vcs| measurement with the D0→ K−e+νe decay has achieved an accuracy of about 0.6% in our pre-vious work [11], this analysis only aims to measure the absolute branching fraction for D+_{→ ¯K}0_e+_ν

e.

2

BESIII detector and Monte Carlo

The BESIII detector is a cylindrical detector with solid-angle 93% of 4π that operates at the BEPCII col-lider. It consists of several main components. A 43-layer main drift chamber (MDC) surrounding the beam pipe performs precise determinations of charged particle trajectories and provides ionization energy loss (dE/dx) measurements that are used for charged particle identifi-cation (PID). An array of time-of-flight counters (TOF) is located radially outside the MDC and provides ad-ditional charged particle identification information. A CsI(Tl) electromagnetic calorimeter (EMC) surrounds the TOF and is used to measure the energies of photons and electrons. A solenoidal superconducting magnet lo-cated outside the EMC provides a 1 T magnetic field in the central tracking region of the detector. The iron flux return of the magnet is instrumented with about 1272 m2 of resistive plate muon counters (MUC) arranged in nine layers in the barrel and eight layers in the endcaps that are used to identify muons with momentum greater than 0.5 GeV/c. More details about the BESIII detector are described in Ref. [10].

A GEANT4-based [12] Monte Carlo (MC) simula-tion software, which includes the geometric descripsimula-tion and a simulation of the response of the detector, is used to determine the detection efficiency and to esti-mate the potential backgrounds. An inclusive MC sam-ple, which includes generic ψ(3770) decays, initial state radiation (ISR) production of ψ(3686) and J/ψ, QED (e+_e−_{→ e}+_e−_{, µ}+_µ−_{, τ}+_τ−_{) and q¯q (q = u, d, s)} contin-uum processes, is produced at√s = 3.773 GeV. The MC events of ψ(3770) decays are produced by a combination of the MC generators KKMC [13, 14] and PHOTOS [15], in which the effects of ISR [16] and Final State Radiation (FSR) are considered. The known decay modes of char-monium states are generated using EvtGen [17, 18] with the branching fractions taken from the Particle Data Group (PDG) [19], and the unknown decay modes are generated using LundCharm [20]. The D+

→ ¯K0_e+_ν e signal is modeled by the modified pole model [21].

3

Measurement

3.1 Single tag D− _mesons

With a mass of 3.773 GeV just above the open charm threshold, the ψ(3770) resonance decays predominately into D0_D¯0 _{or D}+_D− _{meson pairs. In each event, if a} D− _{meson can be fully reconstructed via its decay into} hadrons (in the following called the single tag (ST) D−_), there must be a recoiling D+ _{meson. Using a double} tag technique which was first employed by the MARKIII Collaboration [22], we can measure the absolute branch-ing fraction of the D+_{→ ¯K}0_e+_ν

e decay. Throughout the paper, charge conjugation is implied.

The ST D− _{mesons are reconstructed using six} hadronic decay modes: K+_π−_π−_{, K}0

Sπ−, K +_π−_π−_π0_, K0 Sπ−π 0_{, K}0 Sπ

+_π−_π− _{and K}+_K−_π−_{. The daughter} par-ticles K0

S and π

0 _{are reconstructed via K}0 S→ π

+_π− _and π0

→ γγ, respectively.

All charged tracks are required to be reconstructed within the good MDC acceptance |cosθ| < 0.93, where θ is the polar angle of the track with respect to the positron beam direction. All tracks except those from K0

S decays are required to originate from the interaction region de-fined as Vxy < 1.0 cm and |Vz| < 10.0 cm. Here, Vxy and |Vz| are the distances of closest approach to the In-teraction Point (IP) of the reconstructed track in the plane transverse to and along the beam direction, re-spectively. For PID of charged particles [23], we com-bine the dE/dx and TOF information to calculate Con-fidence Levels for the pion and kaon hypotheses (CLπ and CLK). A charged track is taken as kaon (pion) if it has CLK> CLπ (CLπ> CLK).

The charged tracks from K0

S decays are required to satisfy |Vz| < 20.0 cm. The two oppositely charged tracks, which are assumed as π+_π− _{without PID, are}

constrained to originate from a common vertex. A π+_π− combination is considered as a K0

S candidate if its in-variant mass lies in the mass window |Mπ+π−− MK0

S| < 12 MeV/c2_{, where M} K0 S is the nominal K 0 S mass [24]. The π+_π− _{combinations with L/σ}

L > 2 are retained, where σL is the uncertainty of the K0S reconstructed de-cay length L.

Photon candidates are selected by using the EMC information. The shower time is required to be within 700 ns of the event start time, which is the interval of the trigger start time to the real collision time [25]. The shower energy is required to be greater than 25 (50) MeV in the barrel (endcap) region. The opening angle be-tween the candidate shower and the closest charged track is required to be greater than 10◦_{. A γγ combination is} considered as a π0 _{candidate if its invariant mass falls} in (0.115, 0.150) GeV/c2_{. To obtain better mass} reso-lution for the D− _{candidates, the γγ invariant mass is} constrained to the π0 _{nominal mass [24] via a kinematic} fit.

To suppress combinatorial backgrounds, we define the variable ∆E = EmKnπ−Ebeam, which is the difference between the measured energy of the mKnπ (m = 1, 2; n = 1, 2, 3) combination (EmKnπ) and the beam en-ergy (Ebeam). For each ST mode, if there is more than

one mKnπ combination satisfying the above selection criteria, only the one with the minimum |∆E| is kept. The ∆E is required to be within (−25,+25) MeV for the K+_π−_π−_{, K}0

Sπ−, K 0 Sπ

+_π−_π−_{and K}+_K−_π− combina-tions, and be within (−55,+40) MeV for the K+_π−_π−_π0 and K0

Sπ−π

0 _{combinations.}

To measure the yield of ST D− _{mesons, we perform} maximum likelihood fits to the spectra of the beam en-ergy constrained masses MBC=pEbeam2 /c4−|~pmKnπ|2/c2 of the accepted mKnπ combinations, as shown in Fig. 1. Here, ~pmKnπ is the measured momentum of the mKnπ combination. In the fits, the D−_{signal is modeled by the} MC simulated MBC distribution convolved with a double Gaussian function, and the combinatorial background is described by an ARGUS function [26]. The parameters of the double Gaussian function and the ARGUS func-tion are float. The candidates in the ST D− _signal re-gion defined as (1.863, 1.877) GeV/c2_{are kept for further} analysis. Single-tag reconstruction efficiencies STare es-timated by analyzing the inclusive MC sample. The ST yields NSTand the ST efficiencies are summarized in Ta-ble 1. The total ST yield is Ntot

ST= 1522474±2215, where the uncertainty is the quadratic sum of the uncertainties from all the MBC fits.

(a) (b) (c) (d) (e) (f) 1.82 1.86 1.88 1.82 1.86 1.88 0 5 0 5 10 15 0 5 10 0 5 10 0 10 20 0 20 40 60 80 (×10 3) MBC/(GeV/c2) MBC/(GeV/c2) ev ents /(0.25 M eV/ c 2)

Fig. 1. (color online) Fits to the MBC spectra of the (a) K+π−π−, (b) K0Sπ−, (c) K+π−π−π0, (d) K0Sπ−π0, (e)

K0

Sπ+π−π−and (f) K+K−π− combinations. The dots with error bars are data, the blue solid curves are the fit

results, the red dashed curves are the fitted backgrounds and the pair of red arrows in each sub-figure denote the ST D−_{signal region.}

Table 1. Summary of the ST yields (Ni

ST), the ST and DT efficiencies (iST and iDT), and the reconstruction

efficiencies of D+

→ ¯K0_e+

νe(iD+_→K¯0e+νe). The efficiencies do not include the branching fractions for K

0 S→ π

+

π−

(used in the reconstruction of ST D−_{mesons), ¯K}0

→ π0

π0 and π0

→ γγ. The uncertainties are statistical only. The index i represents the ith ST mode.

ST mode i Ni ST iST(%) iDT(%) Di+_→K¯0_e+_νe (%) D−_→K+_π−_π− _{782669±990 50.61±0.06 13.39±0.07 26.45±0.14} D−→K0 Sπ− 91345±320 50.41±0.17 13.81±0.22 27.40±0.44 D−→K+_π−_π−_π0 _{251008±1135 26.74±0.09 6.23±0.06 23.29±0.25} D−→_K0 Sπ−π0 215364±1238 27.29±0.07 6.88±0.07 25.21±0.28 D−→_K0 Sπ+π−π− 113054±889 28.31±0.12 6.74±0.10 23.79±0.37 D−→_K+_K−_π− _{69034±460 40.83±0.24 10.54±0.20 25.81±0.50}

3.2 Double tag events

In the system recoiling against the ST D− _mesons, the D+

→ ¯K0_e+_ν

ecandidates, called the double tag (DT) events, are selected via ¯K0

→ K0 S→ π

0_π0_{. It is required} that there be at least four good photons and only one good charged track that have not been used in the ST se-lection. The good charged track, photons and π0_mesons are selected using the same criteria as those used in the ST selection. If there are multiple π0_π0 _combinations satisfying these selection criteria, only the combination with the minimum value of χ2

1(π

0_{→ γγ) + χ}2 2(π

0_{→ γγ)} is retained, where the χ2

1 and χ 2

2 are the chi-squares of the mass constrained fits on π0 _{→ γγ. A π}0_π0 com-bination is considered as a ¯K0 _{candidate if its} invari-ant mass falls in (0.45, 0.51) GeV/c2_{. For electron PID,} we combine the dE/dx, TOF and EMC information to calculate Confidence Levels for the electron, pion and kaon hypotheses (CLe, CLπand CLK), respectively. The electron candidate is required to have CLe> 0.001 and CLe/(CLe+CLπ+CLK) > 0.8, and to have a charge oppo-site to the ST D−_{meson. To partially recover the effects} of FSR and bremsstrahlung, the four-momenta of pho-ton(s) within 5◦_{of the initial electron direction are added} to the electron four-momentum measured by the MDC. To suppress the backgrounds associated with fake pho-ton(s), we require that the maximum energy (Eextra γ

max ) of any of the extra photons, which have not been used in the DT selection, be less than 300 MeV.

In order to obtain the information of the missing neu-trino, we define the kinematic quantity

Umiss≡ Emiss−|~pmiss|, (1) where Emissand |~pmiss| are the total energy and momen-tum of the missing particle in the event, respectively. Emiss is calculated by

Emiss= Ebeam−EK¯0−E_e+, (2) where EK¯0 and E_e+ are the energies carried by ¯K0 and e+

, respectively. |~pmiss| is calculated by

|~pmiss| = |~pD+− ~pK¯0− ~pe+|, (3)

where ~pD+, ~p_K¯0 and ~p_e+ are the momenta of D+, ¯K0 and e+_{, respectively. To obtain better U}

miss resolution, ~pD+ is constrained by ~ pD+= −ˆp_D− ST q E2 beam−m 2 D+, (4) where ˆpD−

ST is the momentum direction of the ST D

− meson and mD+ is the D+ nominal mass [24].

To determine the number of DT events, we perform a maximum likelihood fit to the Umissdistribution of the accepted DT candidates, as shown in Fig. 2. In the fit, the DT signal and the combinatorial background are modeled by the MC simulated Umissshapes, respectively. From the fit, we obtain the DT yield in data as

NDT= 5013 ±78, (5) where the uncertainty is from Umissfit.

Fig. 2. (color online) Fit to the Umiss distribution

of the D+

→ ¯K0_e+

νe candidates. The dots with

error bars are data, the blue solid curve is the fit result, the black dotted and the red dashed curves are the fitted signal and background.

3.3 Branching fraction

The efficiency of reconstructing the DT events, called the DT efficiency DT, is determined by analyzing the sig-nal MC events. The DT efficiencies obtained from MC simulations are corrected by the differences of π0 recon-struction efficiencies between data and MC simulations

for the signal side. Dividing DT by ST, we obtain the reconstruction efficiency for D+

→ ¯K0_e+_ν

e in each ST mode, D+_→K¯0_e+_νe, as summarized in Table 1. Weight-ing them by the ST yields observed in data, we obtain the averaged reconstruction efficiency of D+_{→ ¯K}0_e+_ν

e ¯

D+_→K¯0e+νe= (25.58 ±0.11)%, (6) which does not include the branching fractions of ¯K0_→ π0_π0 _{and π}0_{→ γγ.}

The branching fraction of D+ _{→ ¯K}0_e+_ν

e is deter-mined by B(D+ → ¯K0_e+_ν e) = NDT Ntot ST¯D+_→K¯0_e+νeB( ¯K 0_{→ π}0_π0_)B2_(π0_{→ γγ)}, (7) where NDT is the DT yield, NSTtot is the total ST yield, ¯

D+_→K¯0e+νe is the averaged reconstruction efficiency of D+

→ ¯K0_e+_ν

e, B( ¯K0 → π0π0) and B(π0 → γγ) are the branching fractions of ¯K0

→ π0_π0 _{and π}0

→ γγ [24], re-spectively. Here, we assume that K0

Sconstitutes half the decays of the neutral kaons.

Inserting the numbers of NDT, NSTtot, ¯D+_→K¯0_e+_νe, B( ¯K0 → π0_π0 ) and B(π0 → γγ) in Eq. (7), we obtain B(D+ → ¯K0_e+_ν e) = (8.59 ±0.14)%, where the uncertainty is statistical only. 3.4 Systematic uncertainty

In the measurement of the branching fraction, the systematic uncertainty arises from the uncertainties in the fits to the MBC spectra of the ST candidates, the ∆E, MBC and ¯K0(π0π0) mass requirements, the π0 re-construction, the e+ _{tracking, the e}+ _{PID, the E}extra γ

max requirement, the Umiss fit, the χ21+ χ

2

2 selection method, the MC statistics, the quoted branching fractions and the MC generator.

The uncertainty in the fits to the MBCspectra of the ST candidates is estimated to be 0.5% by observing the relative change of the ST yields of data and MC when varying the fit range, the combinatorial background shape or the endpoint of the ARGUS function. To es-timate the uncertainties in the ∆E, MBC and ¯K0(π0π0) mass requirements, we examine the change in branch-ing fractions when enlargbranch-ing the ∆E selection window by 5 or 10 MeV; varying the MBC selection window by ±1 MeV/c2 _{and using alternative ¯K}0_(π0_π0_{) mass} win-dows (0.460, 0.505), (0.470, 0.500), (0.480, 0.500) GeV/c2_, respectively. The maximum changes in the branching fractions, 0.3%, 0.2%, and 0.9%, are assigned as the systematic uncertainties. The π0 _{reconstruction} effi-ciency is examined by analyzing the DT hadronic decays D0

→ K−_π+ _{and K}−_π+_π+_π− _{versus ¯D}0 _{→ K}+_π−_π0 and K0

S(π

+_π−_)π0_{. The difference of the π}0 reconstruc-tion efficiencies between data and MC is found to be

(−1.0 ± 1.0)% per π0_{. The systematic uncertainty in π}0 reconstruction is taken to be 1.0% for each π0 _after cor-recting the MC efficiency of D+

→ ¯K0_e+_ν

e to data. The data-MC differences of the e+_{tracking and PID} efficien-cies are estimated by analyzing e+_e−_{→ γe}+_e− _events. To consider different kinematic distributions of e+_{, the} data-MC differences are re-weighted by the momentum and cos θ distributions of e+_{in the D}+_{→ ¯K}0_e+_ν

edecays. The re-weighted data-MC difference 0.5% is quoted as the systematic uncertainties of the e+ _{tracking and PID} efficiencies. The uncertainty in the Eextra γ

max requirement is estimated to be 0.1% by analyzing the DT hadronic D ¯D decays. The uncertainty in the Umiss fit is assigned to be 0.5%, which is obtained by comparing with the nominal value of the branching fraction measured with an alternative signal shape obtained with different re-quirements on the MC-truth matched signal shape, an alternative background shape after changing the relative ratios of the dominant backgrounds (doubling each of the simulated backgrounds for D0_D¯0_{, D}+_D−_{and q¯q} con-tinuum processes), and alternative fit range (±50 MeV). The difference of 0.3% in the π0_π0 _acceptance efficien-cies of the minimum χ2

1+ χ 2

2 requirement between data and MC, which is estimated by the DT hadronic decays D0_{→ K}−_π+_π0_{versus ¯D}0_{→ K}+_π−_π0_{, is assigned as a} sys-tematic uncertainty due to the χ2

1+χ 2

2selection method. In this analysis, the ¯K0_{→ K}0

S(π

0_π0_{) mesons from the} sig-nal side are formed with photon candidates reconstructed under the assumption that they originate at the IP. We examine the DT efficiencies of the signal MC events in which the lifetimes of K0

Smeson from the signal side are set to the nominal value and 0, respectively. The differ-ence of these two DT efficiencies, which is less than 0.2%, is taken as the systematic uncertainty of the K0

S(π 0_π0₎ reconstruction. The uncertainties in the MC statistics

Table 2. Relative systematic uncertainties (in %) in the measurement of B(D+ → ¯K0_e+ νe). source uncertainty MBC fit 0.5 ∆E requirement 0.3 MBC∈(1.863, 1.877) GeV/c2 0.2 Mπ0π0∈(0.45, 0.51) GeV/c 2 _0.9 π0 reconstruction 2.0 tracking for e+ _0.5 PID for e+ _0.5

Eextra γmax <0.3 GeV 0.1

Umissfit 0.5 χ2 1+ χ22selection method 0.3 K0 S(π0π0) reconstruction 0.2 MC statistics 0.5 B( ¯K0_{→ π}0_π0_{) 0.2} MC generator 0.1 total 2.5

and the B( ¯K0

→ π0_π0_{) are 0.5% and 0.2% [24],} respec-tively. In our previous work, the uncertainty in the signal MC generator is estimated to be 0.1%, which is obtained by comparing the DT efficiencies before and after re-weighting the q2_{(= (p}

D− pK)2) distribution of the signal MC events of D0 _{→ K}−_e+_ν

e to the distribution found in data [11], where the pD and pK are the four-momenta of the D and K mesons. The systematic uncertainties are summarized in Table 2. Adding all uncertainties in quadrature, we obtain the total systematic uncertainty to be 2.5%.

3.5 Validation

The analysis procedure is examined by an input and output check using an inclusive MC sample equivalent

to a luminosity of 3.26 fb−1_{. Using the same selection} criteria as those used in data analysis, we obtain the ST yield, the DT yield and the weighted reconstruction effi-ciency of D+_{→ ¯K}0_e+_ν

e to be 1683631 ± 1768, 5802 ± 85 and (26.07 ± 0.11)%, where no efficiency correction has been performed. Based on these numbers, we determine the branching fraction B(D+_{→ ¯K}0_e+_ν

e) = (8.82±0.13)%, where the uncertainty is statistical only. The measured branching fraction is in excellent agreement with the in-put value of 8.83%.

To validate the reliability of the MC simulation, we examine the cos θ and momentum distributions of ¯K0_and e+ _{of the D}+

→ ¯K0_e+_ν

e candidates, as shown in Fig. 3. We can see that the consistency between simulation and data is very good.

−0.5 −1.0 0 0.5 1.0 0.2 0.6 1.0 cos θ p/(GeV/c) 0 0 100 100 100 200 200 200 300 300 400 0 0 200 400 ev ent s/( 0.0 4 GeV/ c) ev ent s/( 0.0 8 ) D E F G

Fig. 3. (color online) Comparisons of the cos θ and momentum distributions of ¯K0_{((a), (b)) and e}+ _{((c), (d)) of the}

D+

→ ¯K0_e+

νecandidates. The dots with error bars are data, the red histograms are the inclusive MC events, and

the light black hatched histograms are the MC simulated backgrounds. These events satisfy a tight requirement of −0.06GeV < Umiss<+0.06 GeV.

4

Summary and discussion

Based on the analysis of 2.93 fb−1 _{data collected at} √

s = 3.773 GeV with the BESIII detector, we mea-sure the absolute branching fraction B(D+_{→ ¯K}0_e+_ν

e) = (8.59 ± 0.14 ± 0.21)%, using ¯K0 → K0 S→ π 0_π0_{. Figure 4} presents a comparison of B(D+ → ¯K0_e+_ν e) measured in this work with the results obtained by other experiments. Our result is well consistent with the other measurements within uncertainties and has a precision comparable to the PDG value [24]. Our measurement will be helpful

to improve the precision of the world average value of B(D+

→ ¯K0_e+_ν e).

Combining the PDG values for B(D0

→ K−_e+_ν e), B(D+

→ ¯K0_e+_ν

e) [24], and the lifetimes of D0 and D+ mesons (τD0 and τ_D+) [24] with the value of B(D+ →

¯ K0_e+_ν

e) measured in this work, we determine Γ (D0_{→ K}−_e+_ν e) ¯ Γ (D+_{→ ¯K}0_e+_ν e) =B(D 0_{→ K}−_e+_ν e) ×τD+ ¯ B(D+_{→ ¯K}0_e+_ν e) ×τD0 = 0.969 ±0.025, (8) where ¯B(D+ → ¯K0_e+_ν

branching fraction based on the PDG value and the one measured in this work. Combining with the branching

fraction measured in this work, the precision of the test of the isospin symmetry is improved.

8 9 10 11 12 13 14 B(D+_→K0_e+_ν e)(%) BESII [3] CLEO [4, 5] K0_→+_− K0_→+_− K0_→0_0 K0_→K0 L PDG [24] BESIII [7] This work – – – – – –

Fig. 4. (color online) Comparison of the B(D+

→ ¯K0_e+

νe) measured in this work with those measured by other

experiments, where the slash band is the world averaged branching fraction with uncertainty. For the BESIII measurement using ¯K0

→ K0

L, we take B(D+→ ¯K0e+νe) = 2B(D+→ K0Le+νe).

The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support.

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