Measurement of Singly Cabibbo-Suppressed Decays D → ωππ

M. Ablikim1, M. N. Achasov10,c, P. Adlarson64, S. Ahmed15, M. Albrecht4, A. Amoroso63A,63C , Q. An60,48,

Anita21, Y. Bai47, O. Bakina29, R. Baldini Ferroli23A, I. Balossino24A, Y. Ban38,k, K. Begzsuren26, J. V. Bennett5,

N. Berger28, M. Bertani23A, D. Bettoni24A, F. Bianchi63A,63C , J Biernat64, J. Bloms57, A. Bortone63A,63C ,

I. Boyko29, R. A. Briere5, H. Cai65, X. Cai1,48, A. Calcaterra23A, G. F. Cao1,52, N. Cao1,52, S. A. Cetin51B ,

J. F. Chang1,48, W. L. Chang1,52, G. Chelkov29,b, D. Y. Chen6, G. Chen1, H. S. Chen1,52, M. L. Chen1,48,

S. J. Chen36, X. R. Chen25, Y. B. Chen1,48, W. S. Cheng63C , G. Cibinetto24A, F. Cossio63C , X. F. Cui37,

H. L. Dai1,48, J. P. Dai42,g, X. C. Dai1,52, A. Dbeyssi15, R. B. de Boer4, D. Dedovich29, Z. Y. Deng1, A. Denig28,

I. Denysenko29, M. Destefanis63A,63C , F. De Mori63A,63C , Y. Ding34, C. Dong37, J. Dong1,48, L. Y. Dong1,52,

M. Y. Dong1,48,52, S. X. Du68, J. Fang1,48, S. S. Fang1,52, Y. Fang1, R. Farinelli24A, L. Fava63B,63C , F. Feldbauer4,

G. Felici23A, C. Q. Feng60,48, M. Fritsch4, C. D. Fu1, Y. Fu1, X. L. Gao60,48, Y. Gao38,k, Y. Gao61, Y. G. Gao6,

I. Garzia24A,24B , E. M. Gersabeck55, A. Gilman56, K. Goetzen11, L. Gong37, W. X. Gong1,48, W. Gradl28,

M. Greco63A,63C , L. M. Gu36, M. H. Gu1,48, S. Gu2, Y. T. Gu13, C. Y Guan1,52, A. Q. Guo22, L. B. Guo35,

R. P. Guo40, Y. P. Guo28, Y. P. Guo9,h, A. Guskov29, S. Han65, T. T. Han41, T. Z. Han9,h, X. Q. Hao16,

F. A. Harris53, K. L. He1,52, F. H. Heinsius4, T. Held4, Y. K. Heng1,48,52, M. Himmelreich11,f , T. Holtmann4,

Y. R. Hou52, Z. L. Hou1, H. M. Hu1,52, J. F. Hu42,g, T. Hu1,48,52, Y. Hu1, G. S. Huang60,48, L. Q. Huang61,

X. T. Huang41, Z. Huang38,k, N. Huesken57, T. Hussain62, W. Ikegami Andersson64, W. Imoehl22, M. Irshad60,48,

S. Jaeger4, S. Janchiv26,j , Q. Ji1, Q. P. Ji16, X. B. Ji1,52, X. L. Ji1,48, H. B. Jiang41, X. S. Jiang1,48,52,

X. Y. Jiang37, J. B. Jiao41, Z. Jiao18, S. Jin36, Y. Jin54, T. Johansson64, N. Kalantar-Nayestanaki31, X. S. Kang34,

R. Kappert31, M. Kavatsyuk31, B. C. Ke43,1, I. K. Keshk4, A. Khoukaz57, P. Kiese28, R. Kiuchi1, R. Kliemt11,

L. Koch30, O. B. Kolcu51B,e, B. Kopf4, M. Kuemmel4, M. Kuessner4, A. Kupsc64, M. G. Kurth1,52, W. Kuhn30,

J. J. Lane55, J. S. Lange30, P. Larin15, L. Lavezzi63C , H. Leithoff28, M. Lellmann28, T. Lenz28, C. Li39, C. H. Li33,

Cheng Li60,48, D. M. Li68, F. Li1,48, G. Li1, H. B. Li1,52, H. J. Li9,h, J. L. Li41, J. Q. Li4, Ke Li1, L. K. Li1, Lei Li3,

P. L. Li60,48, P. R. Li32, S. Y. Li50, W. D. Li1,52, W. G. Li1, X. H. Li60,48, X. L. Li41, Z. B. Li49, Z. Y. Li49,

H. Liang60,48, H. Liang1,52, Y. F. Liang45, Y. T. Liang25, L. Z. Liao1,52, J. Libby21, C. X. Lin49, B. Liu42,g,

B. J. Liu1, C. X. Liu1, D. Liu60,48, D. Y. Liu42,g, F. H. Liu44, Fang Liu1, Feng Liu6, H. B. Liu13, H. M. Liu1,52,

Huanhuan Liu1, Huihui Liu17, J. B. Liu60,48, J. Y. Liu1,52, K. Liu1, K. Y. Liu34, Ke Liu6, L. Liu60,48, Q. Liu52,

S. B. Liu60,48, Shuai Liu46, T. Liu1,52, X. Liu32, Y. B. Liu37, Z. A. Liu1,48,52, Z. Q. Liu41, Y. F. Long38,k,

X. C. Lou1,48,52, F. X. Lu16, H. J. Lu18, J. D. Lu1,52, J. G. Lu1,48, X. L. Lu1, Y. Lu1, Y. P. Lu1,48, C. L. Luo35,

M. X. Luo67, P. W. Luo49, T. Luo9,h, X. L. Luo1,48, S. Lusso63C , X. R. Lyu52, F. C. Ma34, H. L. Ma1, L. L. Ma41,

M. M. Ma1,52, Q. M. Ma1, R. Q. Ma1,52, R. T. Ma52, X. N. Ma37, X. X. Ma1,52, X. Y. Ma1,48, Y. M. Ma41,

F. E. Maas15, M. Maggiora63A,63C , S. Maldaner28, S. Malde58, Q. A. Malik62, A. Mangoni23B , Y. J. Mao38,k,

Z. P. Mao1, S. Marcello63A,63C , Z. X. Meng54, J. G. Messchendorp31, G. Mezzadri24A, T. J. Min36, R. E. Mitchell22,

X. H. Mo1,48,52, Y. J. Mo6, N. Yu. Muchnoi10,c, H. Muramatsu56, S. Nakhoul11,f , Y. Nefedov29, F. Nerling11,f ,

I. B. Nikolaev10,c, Z. Ning1,48, S. Nisar8,i, S. L. Olsen52, Q. Ouyang1,48,52, S. Pacetti23B , X. Pan46, Y. Pan55,

A. Pathak1, P. Patteri23A, M. Pelizaeus4, H. P. Peng60,48, K. Peters11,f , J. Pettersson64, J. L. Ping35, R. G. Ping1,52,

A. Pitka4, R. Poling56, V. Prasad60,48, H. Qi60,48, H. R. Qi50, M. Qi36, T. Y. Qi2, S. Qian1,48, W.-B. Qian52,

Z. Qian49, C. F. Qiao52, L. Q. Qin12, X. P. Qin13, X. S. Qin4, Z. H. Qin1,48, J. F. Qiu1, S. Q. Qu37, K. H. Rashid62,

K. Ravindran21, C. F. Redmer28, A. Rivetti63C , V. Rodin31, M. Rolo63C , G. Rong1,52, Ch. Rosner15, M. Rump57,

A. Sarantsev29,d, Y. Schelhaas28, C. Schnier4, K. Schoenning64, D. C. Shan46, W. Shan19, X. Y. Shan60,48,

M. Shao60,48, C. P. Shen2, P. X. Shen37, X. Y. Shen1,52, H. C. Shi60,48, R. S. Shi1,52, X. Shi1,48, X. D Shi60,48,

J. J. Song41, Q. Q. Song60,48, W. M. Song27, Y. X. Song38,k, S. Sosio63A,63C , S. Spataro63A,63C , F. F. Sui41,

G. X. Sun1, J. F. Sun16, L. Sun65, S. S. Sun1,52, T. Sun1,52, W. Y. Sun35, X Sun20,l, Y. J. Sun60,48, Y. K Sun60,48,

Y. Z. Sun1, Z. T. Sun1, Y. H. Tan65, Y. X. Tan60,48, C. J. Tang45, G. Y. Tang1, J. Tang49, V. Thoren64,

B. Tsednee26, I. Uman51D, B. Wang1, B. L. Wang52, C. W. Wang36, D. Y. Wang38,k, H. P. Wang1,52, K. Wang1,48,

L. L. Wang1, M. Wang41, M. Z. Wang38,k, Meng Wang1,52, W. H. Wang65, W. P. Wang60,48, X. Wang38,k,

X. F. Wang32, X. L. Wang9,h, Y. Wang49, Y. Wang60,48, Y. D. Wang15, Y. F. Wang1,48,52, Y. Q. Wang1,

Z. Wang1,48, Z. Y. Wang1, Ziyi Wang52, Zongyuan Wang1,52, D. H. Wei12, P. Weidenkaff28, F. Weidner57,

S. P. Wen1, D. J. White55, U. Wiedner4, G. Wilkinson58, M. Wolke64, L. Wollenberg4, J. F. Wu1,52, L. H. Wu1,

L. J. Wu1,52, X. Wu9,h, Z. Wu1,48, L. Xia60,48, H. Xiao9,h, S. Y. Xiao1, Y. J. Xiao1,52, Z. J. Xiao35, X. H. Xie38,k,

Y. G. Xie1,48, Y. H. Xie6, T. Y. Xing1,52, X. A. Xiong1,52, G. F. Xu1, J. J. Xu36, Q. J. Xu14, W. Xu1,52, X. P. Xu46,

L. Yan63A,63C , L. Yan9,h, W. B. Yan60,48, W. C. Yan68, Xu Yan46, H. J. Yang42,g, H. X. Yang1, L. Yang65,

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J. H. Yin1, Z. Y. You49, B. X. Yu1,48,52, C. X. Yu37, G. Yu1,52, J. S. Yu20,l, T. Yu61, C. Z. Yuan1,52,

W. Yuan63A,63C , X. Q. Yuan38,k, Y. Yuan1, Z. Y. Yuan49, C. X. Yue33, A. Yuncu51B,a, A. A. Zafar62, Y. Zeng20,l,

B. X. Zhang1, Guangyi Zhang16, H. H. Zhang49, H. Y. Zhang1,48, J. L. Zhang66, J. Q. Zhang4, J. W. Zhang1,48,52,

J. Y. Zhang1, J. Z. Zhang1,52, Jianyu Zhang1,52, Jiawei Zhang1,52, L. Zhang1, Lei Zhang36, S. Zhang49,

S. F. Zhang36, T. J. Zhang42,g, X. Y. Zhang41, Y. Zhang58, Y. H. Zhang1,48, Y. T. Zhang60,48, Yan Zhang60,48,

Yao Zhang1, Yi Zhang9,h, Z. H. Zhang6, Z. Y. Zhang65, G. Zhao1, J. Zhao33, J. Y. Zhao1,52, J. Z. Zhao1,48,

Lei Zhao60,48, Ling Zhao1, M. G. Zhao37, Q. Zhao1, S. J. Zhao68, Y. B. Zhao1,48, Y. X. Zhao Zhao25,

Z. G. Zhao60,48, A. Zhemchugov29,b, B. Zheng61, J. P. Zheng1,48, Y. Zheng38,k, Y. H. Zheng52, B. Zhong35,

C. Zhong61, L. P. Zhou1,52, Q. Zhou1,52, X. Zhou65, X. K. Zhou52, X. R. Zhou60,48, A. N. Zhu1,52, J. Zhu37, K. Zhu1,

K. J. Zhu1,48,52, S. H. Zhu59, W. J. Zhu37, X. L. Zhu50, Y. C. Zhu60,48, Z. A. Zhu1,52, B. S. Zou1, J. H. Zou1

(BESIII Collaboration)

1 Institute of High Energy Physics, Beijing 100049, People’s Republic of China2 Beihang University, Beijing 100191, People’s Republic of China

3 Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China4 Bochum Ruhr-University, D-44780 Bochum, Germany

5 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA6 Central China Normal University, Wuhan 430079, People’s Republic of China

7 China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China8 COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan

9 Fudan University, Shanghai 200443, People’s Republic of China10 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia

11 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany12 Guangxi Normal University, Guilin 541004, People’s Republic of China

13 Guangxi University, Nanning 530004, People’s Republic of China14 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China

15 Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany16 Henan Normal University, Xinxiang 453007, People’s Republic of China

17 Henan University of Science and Technology, Luoyang 471003, People’s Republic of China18 Huangshan College, Huangshan 245000, People’s Republic of China

19 Hunan Normal University, Changsha 410081, People’s Republic of China20 Hunan University, Changsha 410082, People’s Republic of China21 Indian Institute of Technology Madras, Chennai 600036, India

22 Indiana University, Bloomington, Indiana 47405, USA23 (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN and University of Perugia, I-06100,

Perugia, Italy24 (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy

25 Institute of Modern Physics, Lanzhou 730000, People’s Republic of China26 Institute of Physics and Technology, Peace Ave. 54B, Ulaanbaatar 13330, Mongolia

27 Jilin University, Changchun 130012, People’s Republic of China28 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany

29 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia30 Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen,

Germany31 KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands

32 Lanzhou University, Lanzhou 730000, People’s Republic of China33 Liaoning Normal University, Dalian 116029, People’s Republic of China

34 Liaoning University, Shenyang 110036, People’s Republic of China35 Nanjing Normal University, Nanjing 210023, People’s Republic of China

36 Nanjing University, Nanjing 210093, People’s Republic of China37 Nankai University, Tianjin 300071, People’s Republic of China38 Peking University, Beijing 100871, People’s Republic of China

39 Qufu Normal University, Qufu 273165, People’s Republic of China

3

40 Shandong Normal University, Jinan 250014, People’s Republic of China41 Shandong University, Jinan 250100, People’s Republic of China

42 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China43 Shanxi Normal University, Linfen 041004, People’s Republic of China

44 Shanxi University, Taiyuan 030006, People’s Republic of China45 Sichuan University, Chengdu 610064, People’s Republic of China46 Soochow University, Suzhou 215006, People’s Republic of China

47 Southeast University, Nanjing 211100, People’s Republic of China48 State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, People’s Republic of

China49 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China

50 Tsinghua University, Beijing 100084, People’s Republic of China51 (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,

Turkey52 University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

53 University of Hawaii, Honolulu, Hawaii 96822, USA54 University of Jinan, Jinan 250022, People’s Republic of China

55 University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom56 University of Minnesota, Minneapolis, Minnesota 55455, USA

57 University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster, Germany58 University of Oxford, Keble Rd, Oxford, UK OX13RH

59 University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China60 University of Science and Technology of China, Hefei 230026, People’s Republic of China

61 University of South China, Hengyang 421001, People’s Republic of China62 University of the Punjab, Lahore-54590, Pakistan

63 (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy;

(C)INFN, I-10125, Turin, Italy64 Uppsala University, Box 516, SE-75120 Uppsala, Sweden

65 Wuhan University, Wuhan 430072, People’s Republic of China66 Xinyang Normal University, Xinyang 464000, People’s Republic of China

67 Zhejiang University, Hangzhou 310027, People’s Republic of China68 Zhengzhou University, Zhengzhou 450001, People’s Republic of China

a Also at Bogazici University, 34342 Istanbul, Turkeyb Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia

c Also at the Novosibirsk State University, Novosibirsk, 630090, Russiad Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia

e Also at Istanbul Arel University, 34295 Istanbul, Turkeyf Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany

g Also at Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key

Laboratory for Particle Physics and Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240,

People’s Republic of Chinah Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics,

Fudan University, Shanghai 200443, People’s Republic of Chinai Also at Harvard University, Department of Physics, Cambridge, MA, 02138, USA

j Currently at: Institute of Physics and Technology, Peace Ave.54B, Ulaanbaatar 13330, Mongoliak Also at State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, People’s

Republic of Chinal School of Physics and Electronics, Hunan University, Changsha 410082, China

Using 2.93 fb−1 of e+e− collision data taken at a center-of-mass energy of 3.773 GeV by theBESIII detector at the BEPCII, we measure the branching fractions of the singly Cabibbo-suppresseddecays D → ωππ to be B(D0 → ωπ+π−) = (1.33 ± 0.16 ± 0.12) × 10−3 and B(D+ → ωπ+π0) =(3.87±0.83±0.25)×10−3, where the first uncertainties are statistical and the second ones systematic.

4

The statistical significances are 12.9σ and 7.7σ, respectively. The precision of B(D0 → ωπ+π−) isimproved by a factor of 2.1 over prior measurements, and B(D+ → ωπ+π0) is measured for thefirst time. No significant signal for D0 → ωπ0π0 is observed, and the upper limit on the branchingfraction is B(D0 → ωπ0π0) < 1.10 × 10−3 at the 90% confidence level. The branching fractions ofD → ηππ are also measured and consistent with existing results.

PACS numbers: 14.40.Lb, 13.25.Gv, 13.60.Le, 11.30.Hv

I. INTRODUCTION

The study of multi-body hadronic decays of charmedmesons is important to understand the decay dynam-ics of both strong and weak interactions. It also pro-vides important input to the beauty sector for the testof Standard Model (SM) predictions. For instance,the self-conjugate decay D0 → ωπ+π− can be used toimprove the measurement of the Cabibbo-Kobayashi-Maskawa (CKM) angle γ via B± → D0K± [1–3], andthe unmeasured decay D+ → ωπ+π0 is a potential back-ground in the semi-tauonic decay B → Dτντ . Theratio of branching fractions (BFs ) R(D), defined asB(B → Dτντ )/B(B → Dlνl) (l = e, µ), probes lep-ton flavor universality (LFU). The current world aver-age measurement of R(D) is around 3.1σ away from theSM prediction [4, 5], which is evidence of LFU violation.However, the BFs of many multi-body hadronic decays,especially for singly Cabibbo-suppressed (SCS) or dou-bly Cabibbo-suppressed (DCS) decays of D mesons, arestill either unknown or imprecise due to low decay ratesor huge backgrounds. Precise measurements of these de-cays are desirable in several areas.

Until now, for the SCS decays D → ωππ, only thebranching fraction of D0 → ωπ+π− has been measured;CLEO found B(D0 → ωπ+π−) = (1.6± 0.5)× 10−3 [6],where the precision is limited by low statistics. The dataused in this analysis is a ψ(3770) sample with an inte-grated luminosity of 2.93 fb−1 [7] collected at a center-of-mass energy of 3.773 GeV with the BESIII detectorat the BEPCII collider. It provides an excellent oppor-tunity to improve these measurements. Furthermore, inthe decay ψ(3770)→ D0D0, the D0 and D0 mesons arecoherent and of opposite CP eigenvalues. Thus, a suf-ficiently large sample can also be used to measure thefractional CP -content of the decay D0 → ωπ+π−, whichis necessary to relate the CP -violating observables to theCKM angle γ via the so-called quasi-GLW method [1].

In this paper, we present measurements of the abso-lute BFs of the SCS decays D → ωππ with the “dou-ble tag” (DT) technique, pioneered by the MARK-IIIcollaboration [8]. The advantage of this technique is toreduce the combinatorial backgrounds from non-DD de-cays with a cost of loss of the statistics. The ω mesonsare reconstructed in the π+π−π0 final states. We alsomeasure the BFs for D → ηππ with the subsequent de-cay η → π+π−π0, which are used to verify the resultsmeasured with the η → γγ decay mode and theoreticalmodels [9, 10]. Throughout the paper, the charge conju-gate modes are always implied, unless explicitly stated.

II. BESIII DETECTOR AND MONTE CARLOSIMULATION

BESIII is a cylindrical spectrometer covering 93% ofthe total solid angle. It consists of a helium-gas-basedmain drift chamber (MDC), a plastic scintillator time-of-flight (TOF) system, a CsI(Tl) electromagnetic calorime-ter (EMC), a superconducting solenoid providing a 1.0 Tmagnetic field, and a muon counter. The momentumresolution of a charged particle in the MDC is 0.5% at atransverse momentum of 1 GeV/c, and the energy reso-lution of a photon in the EMC is 2.5(5.0)% at 1 GeVin the barrel (end-cap) region. Particle identification(PID) is performed by combining the ionization energyloss (dE/dx) measured by the MDC and the informationfrom TOF. The details about the design and detectorperformance are provided in Ref. [11].

Monte Carlo (MC) simulation based on Geant4 [12]is used to optimize the event selection criteria, study thepotential backgrounds and evaluate the detection efficien-cies. The generator KKMC [13] simulates the e+e− col-lision incorporating the effects of beam energy spreadand initial-state-radiation (ISR). An inclusive MC sam-ple, containing DD and non-DD events, ISR productionof ψ(3686) and J/ψ, and continuum processes e+e− → qq(q = u, d, s), is used to study the potential backgrounds.The known decays as specified in the Particle Data Group(PDG) [14] are simulated by EvtGen [15], while the re-maining unknown decays by LundCharm [16].

III. ANALYSIS STRATEGY

We first select “Single Tag” (ST) events in which the Dmeson candidate is reconstructed in a specific hadronicdecay mode. Then the D meson candidate of interest isreconstructed with the remaining tracks. The absoluteBFs for DT D decays are calculated by,

Bsig =N sig

DT

Bint∑i

N iST εsig,iDT / εiST

, (1)

where N sigDT and N i

ST are the yields of DT signal events

and ST events, εiST and εsig,iDT are the ST and DT detectionefficiencies for a specific ST mode i, respectively, and Bintis the product of the BFs of the intermediate states ω/ηand π0 in the subsequent decays of the D meson.

5

IV. DATA ANALYSIS

For each tag mode, the D meson candidates are re-constructed from all possible combinations of final stateparticles with the following selection criteria. Chargedtracks, not utilized for K0

S reconstruction, are requiredto have their distance of closest approach to the inter-action point (IP) be within 1 cm in the plane perpen-dicular to the beam and ±10 cm along the beam. Thepolar angle θ with respect to the z-axis is required tosatisfy | cos θ| < 0.93. PID is performed to determinelikelihood L values for the π± and K± hypotheses, andLπ > LK and LK > Lπ are required for the π± and K±

candidates, respectively.The K0

S candidates are reconstructed from a pair ofoppositely charged tracks. These two tracks are assumedto be pions without performing PID and are required tobe within ±20 cm from the IP along the beam direction,but with no constraint in the transverse plane. A fitof the two pions to a common vertex is performed, anda K0

S candidate is required to have a χ2 of the vertex-constrained fit less than 100. The π+π− invariant massMπ+π− is required to be within three standard devia-tions from the K0

S nominal mass [14], 0.487 < Mπ+π− <0.511 GeV/c2. The decay length of each selected K0

S can-didate should be further than two standard deviationsfrom the IP.

Photon candidates are reconstructed from clusters ofenergy deposits in the EMC. The energy deposited innearby TOF counter is included to improve the recon-struction efficiency and energy resolution. The energy ofeach photon is required to be larger than 25 MeV in thebarrel region (| cos θ| < 0.8) or 50 MeV in the end-capregion (0.86 < | cos θ| < 0.92). The EMC timing of thephoton is required to be within 700 ns relative to theevent start time to suppress electronic noise and energydeposits unrelated to the event. A π0 candidate is re-constructed from a photon pair with an invariant masswithin [0.115, 0.150] GeV/c2, and at least one photonshould be detected in the EMC barrel region. To im-prove the momentum resolution, a kinematic fit is carriedout constraining the invariant mass of the selected pho-ton pair to the π0 nominal mass [14], and the resultantkinematic variables are used in the subsequent analysis.

In this analysis, the ST events are selected by re-constructing D0 candidates with K+π−,K+π−π0 andK+π−π−π+ final states and D− candidates withK+π−π−, K+π−π−π0, K0

Sπ−, K0

Sπ−π0, K0

Sπ−π−π+

and K+K−π− final states, which comprise approxi-mately 26% and 28% of total D0 and D− (referred to asD later) decays, respectively. Two variables, the energydifference ∆E ≡ ED − Ebeam and the beam-constrainedmass M tag

BC ≡√E2

beam/c4 − p2D/c2, are used to identify

the D candidates. Here Ebeam is the beam energy, andED(pD) is the reconstructed energy (momentum) of theD candidate in the e+e− center-of-mass system. Thesuccessful D candidate must satisfy M tag

BC > 1.84 GeV/c2

and a mode-dependent ∆E requirement, which is approx-

imately three times its resolution. For an individual STmode, if there are multiple candidates in an event, theone with the minimum |∆E| is selected. In the decayprocess D0 → K+π−π+π−, to remove backgrounds fromD0 → K0

SK+π−, the invariant mass of any π+π− is re-

quired to satisfy |Mπ+π− −MK0S| > 30 MeV/c2, where

MK0S

is the nominal mass of K0S [14].

To determine the ST yield, a binned maximum like-lihood fit is performed to the M tag

BC distribution of se-lected candidate events for each ST mode. The signal isdescribed by the MC simulated shape convolved with aGaussian function which accounts for the resolution dif-ference between data and MC simulation, and the com-binatorial background is described by an ARGUS func-tion [17] with a fixed endpoint parameter Ebeam. The fitcurves are presented in Fig. 1.

1.84 1.86 1.88

20

40

310×

(a)

1.84 1.86 1.88

20

40

60

310×

(d)

1.84 1.86 1.88

5

10

15

310×

(g)

1.84 1.86 1.88

20

40

60

310×

(b)

1.84 1.86 1.88

5

10

15

310×

(e)

1.84 1.86 1.88

5

10

310×

(h)

1.84 1.86 1.88

20

40

310×

(c)

1.86 1.88)2 (GeV/ctag

BCM

0

2.3

4.6

6.9

9.2310×

(f)

1.86 1.88

2

4

6

310×

(i)

)2E

ntrie

s/(0

.25

MeV

/c

FIG. 1. (color online) Fits to the M tagBC distributions for the

ST modes: (a) D0 → K+π−, (b) D0 → K+π−π0, (c) D0 →K+π−π−π+, (d) D− → K+π−π−, (e) D− → K+π−π−π0,(f) D− → K0

Sπ−, (g) D− → K0

Sπ−π0, (h) D− → K0

Sπ−π−π+

and (i) D− → K+K−π−. Black dots with error bars rep-resent data, green dashed-dot curves are the combinatorialbackground, red dashed curves are the signal shape and theblue solid curves are the total fit curves.

The same procedure is used on the inclusive MC sam-ple to determine the ST efficiency. The correspondingST yields and efficiencies for each individual tag modeare summarized in Tables I and II for D0 and D− de-cays, respectively. Here the yields for D0 → K+π−,K+π−π0 and K+π−π+π− decays include the contribu-tions from the DCS decays D0 → K−π+, K−π+π0 andK−π+π−π+, respectively.

For the DT candidates, we further reconstruct the de-cays D0 → π+π−π0π+π− and π+π−π0π0π0 as well asD+ → π+π−π0π+π0 using the remaining π± and π0 can-didates. The corresponding ∆E and M sig

BC requirementsdistinguish signal candidates from combinatorial back-grounds. The ∆E distribution is required to be within3.0 (3.5) times of its resolution for D0 → π+π−π0π+π−

6

TABLE I. The ST yields in data (NST), the efficiencies for ST (εST in %) and DT (εmodesDT in %) for D0 decays. The uncertainties

are statistical only.

Mode N iST εiST εωπ

+π−DT εηπ

+π−

DT εωπ0π0

DT εηπ0π0

DTK+π− 542900± 780 66.7± 0.02 11.18± 0.08 12.94± 0.07 0.58± 0.02 0.56± 0.02K+π−π0 1065800± 1280 35.1± 0.01 5.92± 0.06 6.73± 0.02 0.31± 0.01 0.25± 0.01K+π−π−π+ 606310± 890 33.5± 0.01 4.48± 0.06 5.08± 0.04 0.22± 0.01 0.23± 0.01

TABLE II. The ST yields in data (NST), the efficiencies forST (εST in %) and DT (εmodes

DT in %) for D− decays. Theuncertainties are statistical only.

Mode N iST εiST εωπ

+π0

DT εηπ+π0

DTK+π−π− 794890± 959 49.7± 0.03 2.47± 0.06 2.57± 0.02K+π−π−π0 216720± 609 22.4± 0.03 0.56± 0.04 0.99± 0.03K0Sπ

− 97769± 333 52.8± 0.10 2.30± 0.06 2.67± 0.03K0Sπ

−π0 224880± 661 27.6± 0.04 1.28± 0.04 1.29± 0.04K0Sπ

−π−π+ 130300± 513 36.0± 0.07 1.50± 0.04 1.56± 0.04K−K+π− 70299± 326 40.7± 0.11 2.39± 0.06 2.35± 0.04

(D0 → π+π−π0π0π0 and D+ → π+π−π0π+π0) decays.For a given signal mode, if there are multiple combi-nations in an event, the one with the minimum |∆E|is selected. Since the signal final states contain multi-ple pions, an irreducible background with the same fi-nal state is that from the Cabibbo-favored (CF) pro-cesses including K0

S → ππ, and a candidate is vetoedif the invariant mass of any ππ combination lies withinthe K0

S mass window, i.e., 0.475 < Mπ+π− < 0.520 or0.448 < Mπ0π0 < 0.548 GeV/c2. Four possible π+π−π0

combinations exist in the decays D0 → π+π−π0π+π−

and D+ → π+π−π0π+π0, while there are three π+π−π0

combinations in D0 → π+π−π0π0π0. Combinations withthe invariant mass Mπ+π−π0 less than 0.9 GeV/c2 areretained for further analysis. The inclusion of multiplecombinations for an event avoids peaking background inthe Mπ+π−π0 distribution with a cost of additional com-binatorial backgrounds.

After applying the above selection criteria in bothST and DT sides including M sig

BC > 1.84 GeV/c2, theMπ+π−π0 distributions are shown in Fig. 2, where the ωand η signals are clear that might originate from eitherD → ω/ηππ decays or various background processes.

The two-dimensional (2D) distribution of M tagBC versus

M sigBC is shown in Fig. 3. The signal of ψ(3770) → DD

(including the background with the same final states, butwithout ω/η signals) is expected to concentrate around

the intersection of M tagBC = M sig

BC = MD, where MD

is the D nominal mass. The background events fromψ(3770) → DD with a correctly reconstructed D me-son and an incorrectly reconstructed D meson (namelyBKGI) distribute along the horizontal and vertical bands

with M tagBC (M sig

BC) = MD. The background events fromthe e+e− → qq process (BKGII) spread along the diago-

nal, and do not peak in either the M tagBC or M sig

BC distribu-

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

100

200 MCD(3686), non-Dψ/ψJ/γ, qq→-e+e

MC0

D0D→(3770)ψ MC

-D+D→(3770)ψ

data

(a)

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

)2E

ntrie

s/(0

.005

GeV

/c

100

200(b)

)2 (GeV/c0π-π+πM0.6 0.80

5

10

15(c)

FIG. 2. Fits to the Mπ+π−π0 distributions for the processes:(a) D0 → π+π−π0π+π−, (b) D+ → π+π−π0π+π0 and (c)D0 → π+π−π0π0π0, together with the background predic-tions from various MC samples shown by the histograms withdiagonal pattern lines. The MC samples of ψ(3770) → DDdecays include various background processes only. Black dotswith error bars are data, dashed red curves are combinatorialbackground, dotted cyan and green curves are η and ω sig-nals, and the solid blue curves are the total fit curves. Thetwo green and cyan arrow lines represent the ω and η signalregions, respectively, and the two red arrows represent theirlow- and high-sideband regions.

tion. A small background including both e+e− → qq andψ(3770) → DD, with neither D nor D correctly recon-structed (BKGIII), is assumed to distribute uniformly in

the M tagBC versus M sig

BC phase space (PHSP).

To determine the signal yields (including the back-ground with same final states but without ω/η signals),a 2D unbinned maximum likelihood fit is performed tothe M tag

BC versus M sigBC distribution of candidate events

within the ω(η) signal region, defined as 0.74(0.52) <Mπ+π−π0 < 0.82(0.57) GeV/c2. The probability density

7

1.84 1.86 1.88)2 (GeV/c

tag

BCM

1.86

1.88

BKGItag0D

BK

GI

sig0D

ISR

BKGII

1.84 1.86 1.88

)2 (GeV/ctagBCM

1.84

1.86

1.88

BKGItag±D

BK

GI

sig±D IS

R

BKGII

)2 (

GeV

/csi

gB

CM

FIG. 3. The 2D distributions of M tagBC versus M sig

BC for theDT candidate events of ψ(3770) → D0D0 (top) and D+D−

(bottom).

function (PDF) includes those of signal and three kindsof backgrounds, described as:

• Signal: A (M sigBC,M

tagBC ),

• BKGI: B(M tagBC )× C (M sig

BC;Ebeam, ξMsigBC, ρ) + B(M sig

BC)× C (M tagBC ;Ebeam, ξMtag

BC, ρ),

• BKGII: C ((M sigBC +M tag

BC ); 2 · Ebeam, ξ, ρ)(F ·G((M sigBC −M

tagBC ); 0, σ0)) + (1−F ) ·G((M sig

BC −MtagBC ); 0, σ1)),

• BKGIII: C (M sigBC;Ebeam, ξMsig

BC, ρ)× C (M tag

BC ;Ebeam, ξMtagBC, ρ),

where A and B are 2D and one-dimensional (1D) sig-

nal PDFs for Msig/tagBC distributions, which are described

with the simulated signal shapes convolved with 2D and1D Gaussian functions, respectively, to account for theresolution difference between data and MC simulation.C (x,Eend, ξ, ρ) is an ARGUS function [17] with a fixedendpoint of Ebeam and two free parameters of ξ and ρ.F is the fraction of a Gaussian function G(x; 0, σi), the

mean of which is zero and the width σi is (M sigBC +M tag

BC )

dependent: σi = ai(MsigBC + M tag

BC ) + ci (i = 0, 1). F ,ai and ci are floated in the fit. The projection plots ofM tag

BC and M sigBC are shown in Fig. 4, and the signal yields

(Nω/ηSG ) are summarized in Table III.

To estimate the background with the same final states,but without ω/η signal included (BKGIV), the samefit is performed on the candidate events within the ωand η sideband regions, defined as (0.65 < Mπ+π−π0 <0.71) ∪ (0.85 < Mπ+π−π0 < 0.90) GeV/c2 and (0.44 <Mπ+π−π0 < 0.49)∪(0.60 < Mπ+π−π0 < 0.65) GeV/c2, re-spectively. The corresponding fit curves and signal yields

(Nω/ηSB ) are shown in Fig. 5 and Table III. Additionally,

there is also a small peaking background from the CFprocesses D0 → K0

Sω/η (BKGV) from events survivingthe K0

S mass window veto due to its large decay BF. Thecorresponding contributions (NBKGV

peak ) are estimated by:

8

1.84 1.85 1.86 1.87 1.88)2 (GeV/csig

MCm

50

100

-π+πω→0D

1.84 1.85 1.86 1.87 1.88)2 (GeV/csig

MCm

20

40

60

80

0π+πω→+D

1.84 1.85 1.86 1.87 1.88)2 (GeV/csig

MCm

5

10

0π0πω→0D

1.84 1.85 1.86 1.87 1.88

0

50

100

150

Tag side

1.84 1.85 1.86 1.87 1.88)2 (GeV/cBCM

0

50

100

Tag side

1.84 1.85 1.86 1.87 1.88

0

5

10

15

20

Tag side

)2E

ntrie

s/(0

.50

MeV

/c

1.84 1.86 1.88)2 (GeV/csig

MCm

10

20

-π+πη→0D

1.84 1.86 1.88)2 (GeV/csig

MCm

5

10

15

0π+πη→+D

1.84 1.86 1.88)2 (GeV/csig

MCm

1

2

3

0π0πη→0D

1.84 1.86 1.88

0

10

20

30

Tag side

1.84 1.86 1.88)2 (GeV/cBCM

0

10

20

Tag side

1.84 1.86 1.88

0

2

4

6

Tag side

)2E

ntrie

s/(0

.50

MeV

/c

FIG. 4. Projection plots of the 2D fit to the distribution of M tagBC versus M sig

BC for the DT candidate events in (top) ω and(bottom) η signal regions. Black dots with error bars are data, the solid blue, dashed green, dotted cyan and dashed-dottedred, long dashed-dotted pink and long dashed brown curves represent the overall fit results, signal, BKGI, BKGII, and BKGIII,respectively. In each panel, the top plot is for M sig

BC and bottom for M tagBC .

NBKGVpeak = B ·

∑i

N iSTε

iDT

εiST, (2)

where N iST and εiST are the ST yield and efficiency for

tag mode i, respectively, as described in Eq. 1, B is theproduct of the BFs of the decay D0 → K0

Sω/η as wellas its subsequent decays, taken from the PDG [14], εiDTis the DT detection efficiency for the D0 → K0

Sω/η de-cay, evaluated from exclusive MC samples. The resultantNBKGV

peak for each individual process is summarized in Ta-

ble III, where the uncertainties include those from theBFs and statistics of the MC samples.

The signal yield N sigDT is given by

N sigDT = N

ω/ηSG − f ·N

ω/ηSB −N

BKGVpeak , (3)

where the correction factor f is the ratio of backgroundBKGIV yield in the ω/η signal region to that in the side-band regions. In practice, f is determined by performinga fit to the Mπ+π−π0 distribution, as shown in Fig. 2.In the fit, the ω/η signal is described by the sum of twoCrystal Ball functions [18], which have the same mean

9

1.84 1.85 1.86 1.87 1.88)2 (GeV/csig

MCm

50

100

-π+πω→0D

1.84 1.85 1.86 1.87 1.88)2 (GeV/csig

MCm

20

40

60

0π+πω→+D

1.84 1.85 1.86 1.87 1.88)2 (GeV/csig

MCm

5

10

0π0πω→0D

1.84 1.85 1.86 1.87 1.88

0

50

100

Tag side

1.84 1.85 1.86 1.87 1.88)2 (GeV/cBCM

0

50

100

Tag side

1.84 1.85 1.86 1.87 1.88

0

5

10

15

20

Tag side

)2E

ntrie

s/(0

.50

MeV

/c

1.84 1.86 1.88)2 (GeV/csig

MCm

10

20

-π+πη→0D

1.84 1.86 1.88)2 (GeV/csig

MCm

10

20

0π+πη→+D

1.84 1.86 1.88)2 (GeV/csig

MCm

2

4

6

0π0πη→0D

1.84 1.86 1.88

0

10

20

30

Tag side

1.84 1.86 1.88)2 (GeV/cBCM

0

10

20

30

Tag side

1.84 1.86 1.88

0

2

4

6

Tag side

)2E

ntrie

s/(0

.50

MeV

/c

FIG. 5. Projection plots of the 2D fit to the distribution of M tagBC versus M sig

BC for the DT candidate events in (top) ω and(bottom) η sideband regions. Black dots with error bars are data, the solid blue, dashed green, dotted cyan and dashed-dottedred, long dashed-dotted pink and long dashed brown curves are the overall fit results, signal, BKGI, BKGII, and BKGIII,respectively. In each panel, the top plot is for M sig

BC and bottom for M tagBC .

TABLE III. The yields of signal and individual backgrounds (see text) as well as the correction factor f , statistical significance(Sig.), Bint and BFs from this measurement and the PDG [14]. Here and below, the first and second uncertainties are statisticaland systematic, respectively. The upper limits are set at the 90% C.L..

Decay mode Nω/ηSG f (%) N

ω/ηSB NBKGV

peak NsigDT Sig. Bint Bsig (×10−3) BPDG (×10−3)

D0 → ωπ+π− 908.0± 39.4 74.6± 1.5 610.5± 35.1 41.4± 2.5 411.2± 48.3 12.9σ 0.882 1.33± 0.16± 0.12 1.6± 0.5D+ → ωπ+π0 474.0± 42.8 73.3± 1.2 329.0± 34.3 — 232.9± 49.8 7.7σ 0.872 3.87± 0.83± 0.25 —D0 → ωπ0π0 20.2± 10.5 75.2± 5.6 22.1± 10.0 19.0± 1.2 −15.4± 13.0 0.6σ 0.862 < 1.10 —D0 → ηπ+π− 151.3± 14.6 42.6± 0.9 115.0± 15.3 6.1± 0.2 96.2± 16.0 8.3σ 0.227 1.06± 0.18± 0.07 1.09± 0.16D+ → ηπ+π0 61.5± 14.3 41.4± 0.7 47.3± 16.4 — 41.9± 15.8 3.5σ 0.224 2.47± 0.93± 0.16 1.38± 0.35D0 → ηπ0π0 5.7± 3.8 40.6± 3.3 13.1± 4.8 2.0± 0.1 −1.6± 4.3 0.1σ 0.221 < 2.38 0.38± 0.13

10

and resolution values, but opposite side tails, and thebackground by a reversed ARGUS function defined asEq. 4 in Ref. [19] with a fixed endpoint parameter cor-responding to the Mπ+π−π0 threshold. The signal DTefficiencies, as summarized in Tables I and II for D0 andD+ decays, respectively, are determined by the same ap-proach on the inclusive MC sample, which is the mixtureof signal MC samples generated with a unified PHSP dis-tribution and various backgrounds. Based on the aboveresults, the decay BFs are calculated according to Eq. 1,and are summarized in Table III. To determine the sta-tistical significance of signals for each individual process,analogous fits are performed by fixing the signal yieldsto those of the sum of backgrounds BKGIV and BKGV,and the resultant likelihood values L0 are used to cal-culate the statistical significance S =

√−2 ln(L0/Lmax),

as summarized in Table III, where Lmax is the likelihoodvalue of the nominal fit.

V. SYSTEMATIC UNCERTAINTIES

According to Eq. 1, the uncertainties in the BF mea-surements include those associated with the detection ef-ficiencies, ST and DT event yields as well as the BFs ofthe intermediate state decays.

With the DT method, the uncertainties associatedwith the detection efficiency from the ST side cancel. Theuncertainty from the detection efficiency of the signal sideincludes tracking, PID, π0 reconstruction, ∆E require-ment, K0

S veto and ω/η mass window requirement aswell as the signal MC modeling. The uncertainties fromthe tracking, PID and π0 reconstruction are 0.5%, 0.5%,and 2.0%, respectively, which are obtained by studyinga DT control sample ψ(3770) → DD with hadronic de-cays of D via a partial reconstruction method [20, 21].The uncertainties associated with the ∆E requirement,K0S veto and ω/η mass window requirement are studied

with control samples of D0 → 2(π+π−)π0, π+π−3π0 andD+ → 2(π+π0)π−, which have the same final state asthe signal channels, include all possible intermediate res-onances and have higher yields than the signal processes.These control samples are selected with the DT method,and their yields are obtained by fitting M sig

BC distribu-tions. To study the uncertainty from ∆E, the controlsamples are alternatively selected with a relatively loose∆E requirement, i.e. |∆E| < 0.1 GeV, and then withthe nominal ∆E requirement. The ratio of the two sig-nal yields is taken as the corresponding efficiency. Thesame approach is implemented with both data and theinclusive MC sample, and the difference in efficiencies istaken as the uncertainty. For the K0

S veto uncertaintystudies, we enlarge the K0

S veto mass window of the con-trol samples by 10 MeV/c2, and the relative differencein the efficiencies between data and inclusive MC sam-ple is taken as the uncertainty. The uncertainties fromthe ω/η mass window requirement are studied by enlarg-ing the corresponding mass windows by 2 MeV/c2 and

the resulting difference in efficiency between data andMC simulation is taken as the uncertainty. In the anal-ysis, the three-body signal processes are simulated withthe uniform PHSP distribution, the corresponding un-certainties are estimated with alternative MC samples,which assume ππ from the ρ resonance decay, and theresultant changes in efficiencies are considered as the un-certainties.

The uncertainty related to the ST yield comes fromthe fit procedure, and includes the signal and backgroundshapes and the fit range. The uncertainty from the signalshape are estimated by alternatively describing the signalwith a kernel estimation [22] of the signal MC derivedshape convolved with a bifurcated Gaussian function.The uncertainty from the background shape is estimatedby alternatively describing the shape with a modified AR-

GUS function [17] (x2/Ebeam)(1− x2

E2beam

)ρ · eξ(1− x2

E2beam

).

The uncertainty from the fit range of M tagBC is obtained

with a wider fit range, (1.835, 1.8865) GeV/c2. The al-ternative fits with the above different scenarios are per-formed, and the resulting changes of signal yields aretaken as the systematic uncertainties. The total uncer-tainties associated with the ST yields are the quadraturesum of individual values.

The uncertainty associated with the DT yield is fromthe fit procedure and background subtraction. The un-certainty from the fit procedure includes the signal andbackground shapes as well as the fit bias. We perform analternative 2D fit to the M tag

BC versus M sigBC distribution.

The signal A (B) is described with the kernel estima-tion [22] of the unbinned 2D (1D) signal MC derivedshape convolved with a Gaussian function. The shapeof the background is described with a modified ARGUSfunction [17] as described above. The relative changes inthe signal yields are taken as the uncertainties. In thisanalysis, the 2D fit procedure is validated by repeatingthe fit on a large number of pseudo-experiments, whichare a mixture of signals generated with various embed-ded events and a fixed amount of background events ex-pected from the real data. The resultant average shiftof the signal yield is taken as the systematic uncertainty.As discussed above, the background BKGIV is estimatedwith the events in ω/η sideband regions and incorpo-rating a correction factor f . This induces uncertaintiesfrom the definition of sideband regions and the correc-tion factor. The uncertainty from sideband regions isestimated by changing their ranges. The correction fac-tor f is determined by fitting the Mπ+π−π0 distributionof surviving candidates, which is composed of the eventsD → 5π including all possible intermediate states (e.g.ω/η → π+π−π0 or ρ→ ππ) and other backgrounds thatmay affect f . The procedure to determine f is validatedwith the inclusive MC sample and its constituentD → 5πevents in the inclusive MC sample. The resultant f val-ues obtained with these two MC samples are found tobe consistent with each other and data, and the differ-ence between the two MC results is taken as the uncer-

11

TABLE IV. Systematic uncertainties and their sources. Here ‘Negl.’ means ‘Negligible’.

Source D0 → ω/ηπ+π− D0 → ω/ηπ0π0 D+ → ω/ηπ+π0

ωπ+π− ηπ+π− ωπ0π0 ηπ0π0 ωπ+π0 ηπ+π0

Additive systematic uncertainties (events)Signal PDFs 8.0 1.0 4.3 0.2 3.7 0.2Fit bias 2.7 1.2 0.3 0.2 2.4 0.7Non-peaking background PDF 0.2 0.2 0.1 0.1 0.2 0.3BKGIV contribution 3.9 4.0 3.2 0.7 4.9 0.5BKGV contribution Negl. Negl. Negl. Negl. – –Total 9.3 4.3 5.4 0.8 6.6 0.9

Multiplicative systematic uncertainties (%)Tracking 2.0 2.0 1.0 1.0 1.5 1.5PID 2.0 2.0 1.0 1.0 1.5 1.5π0 reconstruction 2.0 2.0 6.0 6.0 4.0 4.0∆E requirement 1.7 1.7 1.7 1.7 0.3 0.3K0S veto 0.8 0.8 1.4 1.4 0.8 0.8ω/η signal region 0.2 0.2 0.2 0.2 0.2 0.2

MC generator 2.0 3.0 – – 3.5 3.5ST yield 1.2 1.2 1.2 1.2 0.4 0.4Strong-phase in D0 decays 7.3 0.8 7.3 7.3 – –B(ω/η → π+π−π0) 0.8 1.2 0.8 1.2 0.8 1.2B(π0 → γγ) Negl. Negl. Negl. Negl. Negl. Negl.Total 8.7 5.3 9.9 10.0 5.9 6.0

tainty. The background BKGV is estimated accordingto Eq. 2, and the corresponding uncertainties are fromthe BFs, ST yields and detection efficiencies, where thefirst one has been considered as described above. Exceptfor the uncertainty related to the K0

S veto requirement,which is strongly dependent on the K0

S mass resolution,the uncertainties associated with the other requirementsand BFs are fully correlated with those of the signal,and cancel. To evaluate the uncertainty associated withthe K0

S veto requirement, we obtain the difference ofK0S mass resolution between data and MC simulation

using the control sample of D0 → K0Sπ

+π−π0. Thenwe smear the Mππ distribution of the background MCsamples D0 → K0

Sω/η by a Gaussian function with thedifferences as parameters. The resultant change of theefficiency is taken as the uncertainty and is found to benegligible.

In this analysis, the D0D0 pair is from the ψ(3770)decays, and is quantum correlated, thus additional un-certainty associated with the strong-phase is consid-ered. In practice, the absolute BF is calculated as,BsigCP± = 1

1−cif (2fCP+−1)Bsig [23], where Bsig is calcu-

lated from Eq. 1, cif are the strong-phase correction

factors of the flavor tags D0 → K+π−, K+π−π0 andK+π−π−π+ [4, 24], and fCP+

is the fraction of theCP+ component of D0 → ω/ηππ. The fCP+

value forD0 → ηπ+π− is taken from Ref. [26], and the correspond-ing systematic uncertainty is determined to be 0.8%. Theuncertainties for D0 → ωππ and ηπ0π0 are 7.3%, whichare obtained by assuming fCP+

= 0 or 1 due to the lim-ited statistics. Future BESIII ψ(3770) data will enable ameasurement of the fCP+

of D0 → ω/ηπ+π− decays [25].

The uncertainties associated with Bint are obtainedfrom Ref. [14]. All the uncertainties discussed above are

summarized in Table IV. The uncertainties associatedwith the DT yields, which may affect the significance ofobservation, are classified into the additive terms, whilethe others are multiplicative terms. Assuming all the un-certainties to be uncorrelated, the total uncertainties inthe BF measurements are obtained by adding the indi-vidual ones in quadrature. The N sig

DT systematic uncer-

tainty is given by√σadd2 + (σmult ×N sig

DT)2, where σaddand σmult are the total additive and multiplicative uncer-tainties, respectively.

VI. RESULTS

The absolute BFs of D0 → ω/ηπ+π− and D+ →ω/ηπ+π0 are calculated with Eq. 1. Since the signifi-cance of D0 → ω/ηπ0π0 is less than 1σ, we computeupper limits on the BFs for these two decays at the 90%confidence level (C.L.) by integrating their likelihood ver-sus BF curves from zero to 90% of the total curve. Theeffect of the systematic uncertainty is incorporated byconvolving the likelihood curve with a Gaussian functionwith a width equal to the systematic uncertainty. Allresults are summarized in Table III.

VII. SUMMARY

In summary, we perform the BF measurements ofSCS decays D → ωππ using 2.93 fb−1 of ψ(3770) datasample collected by the BESIII detector. The BFs ofD0 → ωπ+π− and D+ → ωπ+π0 are determined to be(1.33±0.16±0.12)×10−3 and (3.87±0.83±0.25)×10−3,respectively. The precision of the BF for D0 → ωπ+π− is

12

improved by a factor 2.1 over the CLEO measurement [6]and the decay process D+ → ωπ+π0 is measured for thefirst time. These measurements are important inputs tobeauty physics to improve the precision of the CKM an-gle γ via B± → D0(→ ωπ+π−)K± [1, 3] and the semi-tauonic decay B0 → D∗±τ∓(→ π+π−π∓)ντ [4]. No evi-dence ofD0 → ωπ0π0 is found, and the upper limit on theBF at the 90% C.L. is 1.10× 10−3. Meanwhile, the BFsof D0 → ηπ+π− and D+ → ηπ+π0 as well as the upperlimit on the BF of D0 → ηπ0π0 at 90% C.L. are measuredto be (1.06±0.18±0.07)×10−3, (2.47±0.93±0.16)×10−3,and less than 2.38 × 10−3, respectively, with the decaymode η → π+π−π0. The results are consistent with pre-vious measurements [26, 27].

VIII. ACKNOWLEDGEMENTS

The BESIII collaboration thanks the staff of BEPCII,the IHEP computing center and the supercomputing cen-ter of USTC for their strong support. This work is sup-ported in part by National Key Basic Research Programof China under Contract No. 2015CB856700; NationalNatural Science Foundation of China (NSFC) under Con-tracts Nos. 11335008, 11375170, 11425524, 11475164,

11475169, 11605196, 11605198, 11625523, 11635010,11705192, 11735014, 11822506, 11835012, 11935015,11935016, 11935018, 11961141012, 11950410506; 64th

batch of Postdoctoral Science Fund Foundation undercontract No. 2018M642516; the Chinese Academy ofSciences (CAS) Large-Scale Scientific Facility Program;Joint Large-Scale Scientific Facility Funds of the NSFCand CAS under Contracts Nos. U1732263, U1832207;CAS Key Research Program of Frontier Sciences underContracts Nos. QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040; 100 Talents Program of CAS; INPAC andShanghai Key Laboratory for Particle Physics and Cos-mology; ERC under Contract No. 758462; German Re-search Foundation DFG under Contracts Nos. Collab-orative Research Center CRC 1044, FOR 2359; IstitutoNazionale di Fisica Nucleare, Italy; Ministry of Develop-ment of Turkey under Contract No. DPT2006K-120470;National Science and Technology fund; STFC (UnitedKingdom); Olle Engkvist Foundation under Contract No.200-0605; The Knut and Alice Wallenberg Foundation(Sweden) under Contract No. 2016.0157; The Royal So-ciety, UK under Contracts Nos. DH140054, DH160214;The Swedish Research Council; U.S. Department of En-ergy under Contracts Nos. DE-FG02-05ER41374, DE-SC-0012069

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