Measurement of singly Cabibbo-suppressed decays D-0 -> pi(0)pi(0)pi(0), pi(0)pi(0)eta, pi(0)eta eta and eta eta eta

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

singly

Cabibbo-suppressed

decays

D

0 →

π

0

π

0

π

0 ,

π

0

π

0

η

,

π

0

ηη

and

ηηη

BESIII

Collaboration

M. Ablikim

a

,

M.N. Achasov

i

,

4

,

S. Ahmed

n

,

M. Albrecht

d

,

A. Amoroso

bf

,

bh

,

F.F. An

a

,

Q. An

bc

,

ap

,

J.Z. Bai

a

,

Y. Bai

ao

,

O. Bakina

z

,

R. Baldini Ferroli

t

,

Y. Ban

ah

,

D.W. Bennett

s

,

J.V. Bennett

e

,

N. Berger

y

,

M. Bertani

t

,

D. Bettoni

v

,

J.M. Bian

az

,

F. Bianchi

bf

,

bh

,

E. Boger

z

,

2

,

I. Boyko

z

,

R.A. Briere

e

,

H. Cai

bj

,

X. Cai

a

,

ap

,

O. Cakir

as

,

A. Calcaterra

t

,

G.F. Cao

a

,

aw

,

S.A. Cetin

at

,

J. Chai

bh

,

J.F. Chang

a

,

ap

,

G. Chelkov

z

,

2

,

3

,

G. Chen

a

,

H.S. Chen

a

,

aw

,

J.C. Chen

a

,

M.L. Chen

a

,

ap

,

P.L. Chen

bd

,

S.J. Chen

af

,

X.R. Chen

ac

,

Y.B. Chen

a

,

ap

,

X.K. Chu

ah

,

G. Cibinetto

v

,

H.L. Dai

a

,

ap

,

J.P. Dai

ak

,

8

,

A. Dbeyssi

n

,

D. Dedovich

z

,

Z.Y. Deng

a

,

A. Denig

y

,

I. Denysenko

z

,

M. Destefanis

bf

,

bh

,

F. De Mori

bf

,

bh

,

Y. Ding

ad

,

C. Dong

ag

,

J. Dong

a

,

ap

,

L.Y. Dong

a

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aw

,

M.Y. Dong

a

,

ap

,

aw

,

Z.L. Dou

af

,

S.X. Du

bl

,

P.F. Duan

a

,

J. Fang

a

,

ap

,

S.S. Fang

a

,

aw

,

Y. Fang

a

,

R. Farinelli

v

,

w

,

L. Fava

bg

,

bh

,

S. Fegan

y

,

F. Feldbauer

y

,

G. Felici

t

,

C.Q. Feng

bc

,

ap

,

E. Fioravanti

v

,

M. Fritsch

y

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n

,

C.D. Fu

a

,

Q. Gao

a

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X.L. Gao

bc

,

ap

,

Y. Gao

ar

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Y.G. Gao

f

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Z. Gao

bc

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ap

,

B. Garillon

y

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I. Garzia

v

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K. Goetzen

j

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L. Gong

ag

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W.X. Gong

a

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,

W. Gradl

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M. Greco

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M.H. Gu

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Y.T. Gu

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A.Q. Guo

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R.P. Guo

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Y.P. Guo

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Z. Haddadi

ab

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S. Han

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X.Q. Hao

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F.A. Harris

ax

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K.L. He

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X.Q. He

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F.H. Heinsius

d

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T. Held

d

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Y.K. Heng

a

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ap

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T. Holtmann

d

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Z.L. Hou

a

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H.M. Hu

a

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T. Hu

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Y. Hu

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G.S. Huang

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J.S. Huang

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X.T. Huang

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X.Z. Huang

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Z.L. Huang

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T. Hussain

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W. Ikegami Andersson

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Q. Ji

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Q.P. Ji

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X.B. Ji

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X.L. Ji

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X.S. Jiang

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D.P. Jin

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S. Jin

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Y. Jin

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T. Johansson

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A. Julin

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N. Kalantar-Nayestanaki

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X.L. Kang

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X.S. Kang

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M. Kavatsyuk

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B.C. Ke

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T. Khan

bc

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ap

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A. Khoukaz

ba

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P. Kiese

y

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R. Kliemt

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L. Koch

aa

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O.B. Kolcu

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6

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B. Kopf

d

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M. Kornicer

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M. Kuemmel

d

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M. Kuessner

d

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M. Kuhlmann

d

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A. Kupsc

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W. Kühn

aa

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J.S. Lange

aa

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M. Lara

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P. Larin

n

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L. Lavezzi

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H. Leithoff

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C. Leng

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C. Li

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Cheng Li

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F. Li

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Kang Li

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H. Liang

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Y.F. Liang

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Y.T. Liang

aa

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G.R. Liao

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D.X. Lin

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B. Liu

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B.J. Liu

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C.X. Liu

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D. Liu

bc

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F.H. Liu

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Fang Liu

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Feng Liu

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H.B. Liu

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H.M. Liu

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Huanhuan Liu

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Huihui Liu

p

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J.B. Liu

bc

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J.Y. Liu

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K. Liu

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K.Y. Liu

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Ke Liu

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L.D. Liu

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P.L. Liu

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Q. Liu

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S.B. Liu

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X. Liu

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Y.B. Liu

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Z.A. Liu

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Zhiqing Liu

y

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Y.F. Long

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X.C. Lou

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H.J. Lu

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J.G. Lu

a

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ap

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Y. Lu

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Y.P. Lu

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C.L. Luo

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M.X. Luo

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X.L. Luo

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F.E. Maas

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Q.A. Malik

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C. Morales Morales

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N.Yu. Muchnoi

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H. Muramatsu

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A. Mustafa

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Y. Nefedov

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F. Nerling

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I.B. Nikolaev

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4

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Z. Ning

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S. Nisar

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S.L. Niu

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S.L. Olsen

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Q. Ouyang

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S. Pacetti

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Y. Pan

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M. Papenbrock

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P. Patteri

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https://doi.org/10.1016/j.physletb.2018.04.017

(2)

M. Pelizaeus

d

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J. Pellegrino

bf

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H.P. Peng

bc

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K. Peters

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J. Pettersson

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J.L. Ping

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R.G. Ping

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A. Pitka

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R. Poling

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V. Prasad

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a

a_Institute_of_High_Energy_Physics,_Beijing_100049,_People’s_Republic_of_China b_Beihang_University,_Beijing_100191,_People’s_Republic_of_China

c_Beijing_Institute_of_{Petrochemical}_Technology,_Beijing_102617,_People’s_Republic_of_China d_Bochum_{Ruhr-University,}_D-44780_Bochum,_Germany

e_Carnegie_Mellon_University,_Pittsburgh,_{PA 15213,}_USA

f_Central_China_Normal_University,_Wuhan_430079,_People’s_Republic_of_China

g_China_Center_of_Advanced_Science_and_Technology,_Beijing_100190,_People’s_Republic_of_China

h_COMSATS_Institute_of_Information_Technology,_Lahore,_Defence_Road,_Off_Raiwind_Road,₅₄₀₀₀_Lahore,_Pakistan i_G.I._Budker_Institute_of_Nuclear_Physics_SB_RAS_(BINP),_Novosibirsk_630090,_Russia

j_GSI_{Helmholtzcentre}_for_Heavy_Ion_Research_GmbH,_D-64291_Darmstadt,_Germany k_Guangxi_Normal_University,_Guilin_541004,_People’s_Republic_of_China

l_Guangxi_University,_Nanning_530004,_People’s_Republic_of_China

m_Hangzhou_Normal_University,_Hangzhou_310036,_People’s_Republic_of_China n_Helmholtz_Institute_Mainz,_{Johann-Joachim-Becher-Weg}_45,_D-55099_Mainz,_Germany o_Henan_Normal_University,_Xinxiang_453007,_People’s_Republic_of_China

p_Henan_University_of_Science_and_Technology,_Luoyang_471003,_People’s_Republic_of_China q_Huangshan_College,_Huangshan_245000,_People’s_Republic_of_China

r_Hunan_University,_Changsha_410082,_People’s_Republic_of_China s_Indiana_University,_Bloomington,_{IN 47405,}_USA

t_INFN_Laboratori_Nazionali_di_Frascati,_I-00044,_Frascati,_Italy u_INFN_and_University_of_Perugia,_I-06100,_Perugia,_Italy v_INFN_Sezione_di_Ferrara,_I-44122,_Ferrara,_Italy w_University_of_Ferrara,_I-44122,_Ferrara,_Italy

x_Institute_of_Physics_and_Technology,_Peace_Ave._54B,_Ulaanbaatar_13330,_Mongolia

y_Johannes_Gutenberg_University_of_Mainz,_{Johann-Joachim-Becher-Weg}_45,_D-55099_Mainz,_Germany z_Joint_Institute_for_Nuclear_Research,₁₄₁₉₈₀_Dubna,_Moscow_region,_Russia

aa_{Justus-Liebig-Universitaet}_Giessen,_II._{Physikalisches}_Institut,_{Heinrich-Buff-Ring}_16,_D-35392_Giessen,_Germany ab_KVI-CART,_University_of_Groningen,_NL-9747_AA_Groningen,_the_Netherlands

ac

LanzhouUniversity,Lanzhou730000,People’sRepublicofChina ad_Liaoning_University,_Shenyang_110036,_People’s_Republic_of_China ae_Nanjing_Normal_University,_Nanjing_210023,_People’s_Republic_of_China af_Nanjing_University,_Nanjing_210093,_People’s_Republic_of_China ag_Nankai_University,_Tianjin_300071,_People’s_Republic_of_China ah_Peking_University,_Beijing_100871,_People’s_Republic_of_China ai_Seoul_National_University,_Seoul,_{151-747, Republic}_of_Korea aj_Shandong_University,_Jinan_250100,_People’s_Republic_of_China

(3)

ak_Shanghai_Jiao_Tong_University,_Shanghai_200240,_People’s_Republic_of_China al_Shanxi_University,_Taiyuan_030006,_People’s_Republic_of_China

am_Sichuan_University,_Chengdu_610064,_People’s_Republic_of_China an_Soochow_University,_Suzhou_215006,_People’s_Republic_of_China ao_Southeast_University,_Nanjing_211100,_People’s_Republic_of_China

ap_State_Key_Laboratory_of_Particle_Detection_and_Electronics,_Beijing_100049,_Hefei_230026,_People’s_Republic_of_China aq_Sun_Yat-Sen_University,_Guangzhou_510275,_People’s_Republic_of_China

ar_Tsinghua_University,_Beijing_100084,_People’s_Republic_of_China as_Ankara_University,₀₆₁₀₀_Tandogan,_Ankara,_Turkey at_Istanbul_Bilgi_University,₃₄₀₆₀_Eyup,_Istanbul,_Turkey au_Uludag_University,₁₆₀₅₉_Bursa,_Turkey

av_Near_East_University,_Nicosia,_North_Cyprus,_Mersin_10,_Turkey

aw_University_of_Chinese_Academy_of_Sciences,_Beijing_100049,_People’s_Republic_of_China ax_University_of_Hawaii,_Honolulu,_{HI 96822,}_USA

ay_University_of_Jinan,_Jinan_250022,_People’s_Republic_of_China az_University_of_Minnesota,_Minneapolis,_{MN 55455,}_USA

ba_University_of_Muenster,_{Wilhelm-Klemm-Str.}_9,₄₈₁₄₉_Muenster,_Germany

bb_University_of_Science_and_Technology_Liaoning,_Anshan_114051,_People’s_Republic_of_China bc_University_of_Science_and_Technology_of_China,_Hefei_230026,_People’s_Republic_of_China bd

UniversityofSouthChina,Hengyang421001,People’sRepublicofChina be_University_of_the_Punjab,_Lahore_54590,_Pakistan

bf_University_of_Turin,_I-10125,_Turin,_Italy

bg_University_of_Eastern_Piedmont,_I-15121,_Alessandria,_Italy bh_INFN,_I-10125,_Turin,_Italy

bi_Uppsala_University,_Box_516,_SE-75120_Uppsala,_Sweden bj_Wuhan_University,_Wuhan_430072,_People’s_Republic_of_China bk_Zhejiang_University,_Hangzhou_310027,_People’s_Republic_of_China bl_Zhengzhou_University,_Zhengzhou_450001,_People’s_Republic_of_China

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Articlehistory:

Received16March2018

Receivedinrevisedform5April2018 Accepted8April2018

Availableonline10April2018 Editor:W.-D.Schlatter Keywords: BESIII D0_meson Hadronicdecays Branchingfractions

Using adata sample of e+e− collision data corresponding to an integrated luminosity of 2.93 fb−1

collected with the BESIII detector ata center-of-mass energy of √s=3.773 GeV, we search for the singlyCabibbo-suppresseddecaysD0→

π

0

_π

0

_π

0_,

_π

0

_π

0

_η

_,

_π

0

_ηη

_and

_ηηη

_using_the_double_tag_method.

The absolute branching fractions are measured to be B(D0_→

_π

0

_π

0

_π

0₎_{= (}₂_.₀_±₀_.₄_±₀_.₃₎_×₁₀−4_,

B(D0_→

_π

0

_π

0

_η

₎_{= (}₃_.₈_±₁_.₁_±₀_.₇₎_×₁₀−4 _and _B(_D0_→

_π

0

_ηη

₎_{= (}₇_.₃_±₁_.₆_±₁_.₅₎_×₁₀−4_with _the

statisticalsigniﬁcancesof4.8

σ

,3.8

σ

and5.5

σ

,respectively,wheretheﬁrstuncertaintiesarestatistical andthesecondonessystematic.NosigniﬁcantsignalofD0_→

_ηηη

_is_found,_and_the_upper_limit_on_its

decaybranchingfractionissettobe_B(D0_→

_ηηη

_{) <}₁_.₃_×₁₀−4_at_the_90%_conﬁdence_level.

1. Introduction

Thestudyofcharmedmesondecays,whichinvolvebothstrong and weak interactions, is an interesting and challenging ﬁeld in particle physics. Experimental measurements of charmed meson decays yield essential information for understanding the intrin-sic decay mechanism and provide inputs to theoretical

calcula-*

Correspondingauthor.

E-mailaddress:sa004043@mail.ustc.edu.cn(Y. Pan). 1 _Also_at_Bogazici_University,₃₄₃₄₂_Istanbul,_Turkey.

2 _Also_at_the_Moscow_Institute_of_Physics_and_Technology,_Moscow_141700,_Russia. 3 _Also_at_the _Functional_Electronics_Laboratory,_Tomsk _State_University,_Tomsk, 634050,Russia.

4 _Also_at_the_Novosibirsk_State_University,_Novosibirsk,_630090,_Russia. 5 _Also_at_the_NRC_“Kurchatov_{Institute”,}_PNPI,_188300,_Gatchina,_Russia. 6 _Also_at_Istanbul_Arel_University,₃₄₂₉₅_Istanbul,_Turkey.

7 _Also_at_Goethe_University_Frankfurt,₆₀₃₂₃_Frankfurt_am_Main,_Germany. 8 _Also_at_Key_Laboratory_for_Particle_Physics,_Astrophysics_and_Cosmology, Min-istryofEducation;Shanghai KeyLaboratoryfor ParticlePhysicsand Cosmology; Institute ofNuclearand Particle Physics,Shanghai 200240, People’sRepublic of China.

9 _Government_College_Women_University,_Sialkot_{51310, Punjab,}_Pakistan. 10 _Currently_at:_Center_for_Underground_Physics,_Institute_for_Basic_Science, Dae-jeon34126,RepublicofKorea.

tionsandpredictions.Forexample,Ref. [1] suggeststhatthe mea-surement of the branching fraction (BF) of the hadronic decay

D0

→

π

0

_π

0

_π

0 _may_shed _light _on _the _{understanding} _of_the _role of isospin symmetryin D0 _decays _to_three-pion _ﬁnal _states,_and the isospinnature of thenon-resonant contribution.Additionally, thestudyofthehadronicdecaysofcharmedmesonsprovides im-portantinputsforthestudiesof

B physics [2

].

The singly Cabibbo-suppressed (SCS) decaysof the D0 _meson to three neutral pseudoscalar particles, D0

→

π

0

_π

0

_π

0_,

_π

0

_π

0

_η

_,

π

0

_ηη

_and

_ηηη

_,_proceed_dominantly_through_internal _{W -emission} and W -exchange diagrams. Experimental studies ofthese decays are challenging due to the dominant presence of neutral parti-cles (photons) in theﬁnal states,low BFsandhigh backgrounds. Until now, only asearch for D0

_→

_π

0

_π

0

_π

0 _decay _has_been per-formedbytheCLEO Collaborationwitha

ψ(3770)

datasampleof 281pb−1 in2006 [3].Usingthe“singletag”(ST)method,inwhich one D0 _or _D

¯

0 _meson_is _found _in_each _event, _they _obtained_a _BF upperlimitof3.5

×

10−4 atthe90% conﬁdencelevel(C.L.).

InthisLetter, wepresentmeasurements oftheBFsoftheSCS decays D0

_→

_π

0

_π

0

_π

0_,

_π

0

_π

0

_η

_,

_π

0

_ηη

_and

_ηηη

_with_the _“double tag” (DT) technique andadata sample corresponding toan inte-grated luminosity of 2.93 fb−1 [4], collected at a center-of-mass energy of

√

s

=

3.773 GeV withthe BESIII detectoratthe BEPCII

(4)

e+e− collider.Throughoutthe Letter,charge conjugatemodesare alwaysimplied,unlessexplicitlymentioned.

2. BESIIIdetectorandMonteCarlosimulation

BESIII [5] isacylindricalspectrometer composedof a helium-gas-based main drift chamber (MDC), a plastic scintillator time-of-flight(TOF)system,aCsI(Tl)electromagneticcalorimeter(EMC), a superconductingsolenoidprovidinga1.0 Tmagneticfield,anda muoncounter.The chargedparticle momentumresolution inthe MDCis0.5%atatransversemomentum of1GeV/c andthe pho-ton energyresolutionin the EMCat 1GeV, is 2.5% inthe barrel regionand5.0%intheend-capregion.Particleidentification(PID) combinestheionizationenergyloss(dE

/

dx) intheMDC with in-formation from the TOF to identify particle types. More details about the design and performance of the detector are given in Ref. [5].

GEANT4-based [6] Monte Carlo (MC) simulation software is

used to understand the backgrounds and to determine the

de-tectioneﬃciencies. Thegenerator KKMC_[₇_,₈_{] is}_used_to _simulate the

e

+e−collisionincorporatingtheeffectsofbeam-energyspread and initial-state radiation (ISR). An inclusive MC sample includ-ing D0D

¯

0_, _D+_D− _and_non-D_{D events,}

¯

_ISR _production_of

_ψ(3686)

and J

/ψ,

andcontinuumprocesses

e

+e−

→

qq (q

¯

=

u

,

d

,

s) isused to study the potential backgrounds. The known decay modesas speciﬁed in the Particle Data Group (PDG) [9] are generated by EVTGEN [10,11],whiletheremainingunknowndecaysof charmo-niumaremodeledbyLundCharm [12].

3. Analysisstrategy

Atthe

ψ(3770)

resonance, D0_D

¯

0 _pairs _are _produced _in _a co-herent1−−statewithoutadditionalparticles.ADTmethod,which wasﬁrstdevelopedbytheMARK-IIICollaboration [13,14],isused tomeasuretheabsoluteBFs.WeﬁrstselectSTeventsinwhicha

¯

D0mesonisreconstructedinaspeciﬁchadronicdecaymode.Then wesearchfor

D

0_decays_in_the_remaining_tracks,_and_DT_events_are thosewhere D0D

¯

0 _pairs_are _fully_{reconstructed.}_The _absolute_BFs forD0decaysarecalculatedby

B

sig

₌

N sig DT

B

int

α Nα_ST

_DTsig,α

/

α ST

,

(1)

wherethe superscript ‘sig’ representsa speciﬁc D0 signal decay,

Nα_ST,

α

ST and

sig,α

DT are the yield of ST events, the ST detection efficiency and DT detection efficiency for a specific ST mode

α

, respectively,while

N

sig_DT isthetotalyieldforDTsignalevents,and

B

int_is_the_product_of_the_decay_BFs_for_the_intermediate _states_in the

D

0 _signal_decay.

4. Dataanalysis

ChargedtracksarereconstructedfromhitsintheMDCandare requiredtohaveapolarangle

θ

satisfying

|

cos

θ

|

<

0.93.Thepoint of the closest approach of any charged track to the interaction point(IP) is required tobe within 1 cm inthe plane perpendic-ulartothe beamand

±

10 cm alongthebeam. Informationfrom theTOF systemandthe dE

/

dx information inthe MDCare com-binedtoformPIDC.L.sforthe

π

and K hypotheses. Eachtrackis assignedtotheparticletypewiththehighestPIDC.L.

Photon candidates are reconstructed using clusters of energy depositedintheEMCcrystals.Theenergyisrequiredtobelarger than 25 MeV in the barrel region (

|

cos

θ

|

<

0.8) or 50 MeV in

Table 1

Requirementson E (in GeV),ST yieldsindata (NSTα),ST (STα (in%)) and DT (DTπ0π0π0,α,

π0_π0_η,α DT ,

π0_ηη,α DT and

ηηη,α

DT (in%))eﬃciencies.Theuncertaintiesare statisticalonly.BFsof

π

0 _and

_η

_decays_to_two_photons_are_not_included_in_the eﬃciencies. ST mode K+π− K+π−π0 _K+_π−_π−_π+ E (−0.027,0.025) (−0.071,0.041) (−0.025,0.022) NαST 530634±739 1030144±1129 707080±925 STα 64.83±0.04 33.75±0.02 38.01±0.02 DTπ0π0π0,α 10.56±0.02 4.46±0.01 4.78±0.02 DTπ0π0η,α 9.74±0.02 4.09±0.01 4.38±0.01 DTπ0ηη,α 8.23±0.02 3.47±0.01 3.58±0.01 DTηηη,α 10.02±0.02 4.14±0.01 4.57±0.01

the end-capregion (0.86

<

|

cos

θ

|

<

0.92). The energy deposited innearbyTOF countersisincludedtoimprovethereconstruction eﬃciency andenergyresolution. The difference ofthe EMC time fromthe eventstart time isrequired to be within

[

0,700

]

ns to suppresselectronicnoiseandshowersunrelatedtotheevent.

The

π

0 _and

_η

_candidates_are _{reconstructed}_from_photon_pairs by requiring the invariant masses Mγ γ to satisfy 115

<

Mγ γ

<

150 MeV/c2_or₅₁₅

_<

_{Mγ γ}

_<

_{570 MeV/c}2_,_{respectively.}_To_improve theresolution,thephotonpairsareﬁttedkinematically constrain-ing their masses to the nominal

π

0 _or

_η

_{masses [}₉_], _and _the resultingenergies andmomenta ofthetwo photonsareused for subsequentanalysis.

TheSTcandidates areselectedby reconstructing D

¯

0 _decays_to

K+

π

−

,

K+

π

−

π

0 _and

_K

+

_π

−

_π

−

_π

+_._Two_variables,_the_energy

dif-ference

E

≡

ED

−

Ebeam andthebeam-energy-constrainedmass

MBC

≡

E2

beam

/

c4

−

p2D

/

c2,areusedtoidentifytheD

¯

0 candidates.

Here, Ebeam isthebeamenergy,andED

(

pD

)

isthe reconstructed

energy (momentum) ofthe D

¯

0 candidate in the

e

+e− center-of-masssystem.ThoseD

¯

0_candidates_are_accepted_for_further_analysis thatsatisfy MBC

>

1.83 GeV/c2 andmode-dependent

E require-ments,whichareapproximatelythreetimesthevalueofthe reso-lutionaroundtheD

¯

0 nominalmass [9],assummarizedinTable1. ForeachSTmode,ifthereismorethanonecandidateintheevent, theonewiththeminimum

|

E

|

isselected.

The

M

BCdistributionsoftheacceptedD

¯

0candidatesareshown inFig.1,where D

¯

0 signalsareobservedwithrelativelylow back-grounds.Binnedmaximumlikelihoodﬁtstothe

M

BCdistributions areperformedtoobtaintheSTyields.Intheﬁts,thesignalshape ismodeledbytheMCsimulatedshapeconvolvedwithaGaussian functionrepresentingthedifferencebetweendataandMC simula-tion comingfromthebeam-energy spread,ISR, the

ψ(3770)

line shape, and resolution. The combinatorial background is modeled by an ARGUS function [15]. The STyields are calculated by sub-tracting the integrated ARGUS background yields from the total eventscountedin thesignal region1.859

<

MBC

<

1.871 GeV/c2. The STeﬃciencyis studiedusingthe sameprocedure onthe in-clusiveMCsample. TheresultingSTyields andthecorresponding STeﬃcienciesaresummarizedinTable1.

Candidatesfor theSCS decays, D0

_→

_π

0

_π

0

_π

0_,

_π

0

_π

0

_η

_,

_π

0

_ηη

and

ηηη

, are selected inthe systemrecoiling against the tagged

¯

D0.Onlyeventswithoutanyadditionalchargedtrackarechosen. The D0 _signal _decays _are _{reconstructed} _with_any_combination _of theselected

π

0 _and

_η

_candidates_that_have_not _been_used_in_the ST side and do not sharethe same photon candidate. To distin-guishthesignaldecayfromcombinatorialbackgrounds,theenergy difference

E and thebeam-constrainedmass

M

BC arealso calcu-latedforeachacceptedcombination.AD0 candidateisacceptedif itsatisﬁesamode-dependent

E requirement, whichcorresponds to three times the value of the resolution around the

E peak

(5)

Fig. 1. (Coloronline.) Fitstothe MBC distributionsofthe candidatesfor theST modes:(a)D¯0_→_K+_π−_,_(b)_D_¯0_→_K+_π−_π0_and_(c)_D¯0_→_K+_π−_π−_π+_._Points

withanerrorbar aredata,the bluesolidlinesarethetotalﬁt curves,thered dashedlinesarethesignalshapes,andthegreenlong-dashedlinesarethe back-groundshapes.

basedonMCsimulation,assummarizedinTable2.Theshiftand asymmetry ofthe

E distributions are mainlyduetothe energy lossintheEMCformulti-photonﬁnalstates.Iftherearemultiple combinations fora given signal decay inan event, the one with theminimum

|

E

|

isselected.

Except for the decay D0

_→

_ηηη

_, _MC _studies _indicate _that

the selected candidates have large backgrounds from D0

_→

π

0

_π

0

_π

0

_π

0 _decay, _which _has _a _relatively _large _decay _BF, _and contain some background events from cross feeds between

sig-nal channels. Both backgrounds peak around the nominal D0

mass [9] intheMBC distributions.Toreduce thebackgroundfrom

D0

→

π

0

_π

0

_π

0

_π

0 _in _D0

_→

_π

0

_π

0

_π

0 _and

_π

0

_π

0

_η

_decays,_the_joint chi-square

χ

2

4π

=

4

i=1

χ

π2i isrequiredtobelarger than20ifthe candidateeventhasatleastfourindependent

π

0 _candidates_(not including

π

0 _candidates _from_the _ST_side)._Here,

_χπ

i

=

Mi

γ γ−mπ0

σi

γ γ

for the ith

π

0 _candidate _is _calculated _with _the

_{γ γ}

_invariant mass M_{γ γ (before}i the kinematic ﬁt) and its resolution

σ

i

γ γ , as

well as the

π

0 _nominal _mass

mπ0 [9]. To reduce the cross feed between the signal decays, we deﬁne the analogical joint chi-square variables,

χ

2 A BC

= (

M1 γ γ−mA σ1 γ γ

)

2

_{+ (}

M2γ γ−mB σ2 γ γ

)

2

_{+ (}

M3γ γ−mC σ3 γ γ

)

2_, where mA(B,C) is the nominal mass of

π

0 or

η

[9], and

re-quire

χ

2

π0_π0_η

>

20 for D0

→

π

0

π

0

π

0 decay,

χ

_π20_π0_π0

>

20 for

D0

_→

_π

0

_π

0

_η

_decay_as_well_as

_χ

2

π0_π0_π0

>

20 and

χ

_π20_π0_η

>

20 for

D0

_→

_π

0

_ηη

_decay.

However, MC studies indicate that backgrounds remain from

photon mis-combinationsin

π

0 _and

_η

_candidates._These _are_due to the matches ofa good photon with noise in the EMC, which usuallycorrespondstoafakelowenergyphoton.Furthermore,the MCindicatesthatthisbackgroundcanbereducedbyrequiringno othercombinationwiththesameﬁnalstateandwith

χ

2

_<

_20._For instanceforD0

→

π

0

_π

0

_π

0_,_this_requirement_loses_only_5%_of sig-naleventswhileitrejects30%ofmis-combinationbackground.

For D0

_→

_π

0

_π

0

_π

0 _and

_π

0

_π

0

_η

_decays, _the _events _with _any

π

0

_π

0 _invariant _mass _satisfying ₄₄₅

_<

Mπ0_π0

<

535 MeV/c2 are vetoed to reject the backgrounds from the Cabibbo-favored (CF) decays D0

_→

_K0

S

π

0 and K0S

η

with K0S

→

π

0

π

0, which have

ex-actlythesameﬁnalstatesasthesignalchannels.

Withthe aboveselection criteria, the MBC distributions ofthe accepted D0 _candidate _events _in _data _are _shown _in _Fig. ₂_. _The

D0

→

π

0

_π

0

_π

0_,

_π

0

_π

0

_η

_and

_π

0

_ηη

_signals_are _clear,_but_no obvi-ous D0

_→

_ηηη

_signal _is _observed. _The _peaking _backgrounds _are dominated by the decay D0

_→

_π

0

_π

0

_π

0

_π

0_, _and _the _CF _decays

D0

→

K0_S

π

0

_/

_η

_for _D0

_→

_π

0

_π

0

_π

0

_/

_η

_. _The _{contributions}_from _the cross feeds are smalland will be considered in determining the signalyields.Themis-combinationbackgroundisnegligible.

To determine the signal yields of the decays D0

→

π

0

_π

0

_π

0_,

π

0

_π

0

_η

_, _and

_π

0

_ηη

_, _unbinned _maximum _likelihood _ﬁts _are per-formed tothe MBC distributions.The probability densityfunction (PDF) for signal is modeled with the MC simulated shape con-volved with a Gaussian function representing the resolution dif-ference anda potential massshift betweendataandMC simula-tion. The peakingbackgroundsfrom theCF decay D0

→

K0_S

π

0

_/

_η

(BKG I) and the decay D0

_→

_π

0

_π

0

_π

0

_π

0 _(BKG _II) _as_well _as _the cross feeds (BKG III)are alsoincluded inthe ﬁt.The combinato-rial background (BKG IV)is modeled by an ARGUS function [15]. The shapesofthevariouspeakingbackgroundsaremodeledwith those of MC simulations, andthe corresponding magnitudes are ﬁxed to thevaluesestimatedwitha datadrivenmethod.We se-lecta controlsample of D0

→

π

0

_π

0

_π

0

_π

0 _from_data_with_an ap-proach similar to the signal selection, andobtain the yield N4π0 froma ﬁtto theresulting MBC distribution. AmixedMC sample, which includes the possible resonant decays D0

→ ¯

K∗

(892)

0

π

0_,

ηπ

0_, _K0

Sf0, f0(980)

π

0

π

0, KL0

π

0, K0SKS0 and

η

π

0, is generated

withknownBFs [9] andissubjecttotheselectioncriteriaof

D

0

_→

π

0

_π

0

_π

0 _and _D0

_→

_π

0

_π

0

_π

0

_π

0 _to _evaluate_the_{mis-identiﬁcation} rate

3π0 andthedetectioneﬃciency

₄_π0,respectively.The mag-nitude of the background D0

_→

_π

0

_π

0

_π

0

_π

0 _in _the _selection _of

D0

→

π

0

_π

0

_π

0 _is _given_by _N

4π0

·

₃_π0

/

₄_π0. Similar data driven approaches areapplied to determine themagnitudeof the peak-ingbackground D0

_→

_π

0

_π

0

_π

0

_π

0_,_the_cross_feed_and_the_number ofCFdecays

D

0

_→

_K0

S

π

0

/

η

ineachsignaldecay.Theresultingﬁts

for

D

0

_→

_π

0

_π

0

_π

0_,

_π

0

_π

0

_η

_and

_π

0

_ηη

_are_shown_in_Figs.₂_(a),_(b) and(c),respectively.Thesignalyields andstatisticalsigniﬁcances, which are estimated from the likelihood difference between the ﬁts with and without the signal included after considering the

Table 2

Summaryof E requirements,signalyields(NsigDT),statisticalsigniﬁcances,BFsbythismeasurement andinthePDG [9].Theﬁrstandseconduncertaintiesarestatisticalandsystematic,respectively.The upperlimitissetatthe90%C.L.

Mode E(GeV) NsigDT Signiﬁcance B(×10−4) BPDG(×10−4)

π0_π0_π0 (−0.115,0.059) 60±13 4.8σ 2.0±0.4±0.3 <3.5 π0_π0_η (−0.088,0.053) 42±12 3.8σ 3.8±1.1±0.7 – π0_ηη ₍₋₀_.₀₆₁_,₀_.₀₄₅₎ ₂₇_±₆ ₅_.₅_σ ₇_.₃_±₁_.₆_±₁_.₅ _– ηηη (−0.030,0.028) – – <1.3 –

(6)

Fig. 2. (Coloronline.) FitstotheMBCdistributionsoftheacceptedcandidateevents for(a)D0_→_π0_π0_π0_,_(b)_D0_→_π0_π0_η_,_(c)_D0_→_π0_ηη_and_(d)_D0_→_ηηη_._Dots witherrorbarsaredata,thebluesolidlinesarethetotalﬁtcurves,andthered dot-tedlinesarethesignalshapes.Thegreendashed,magentadash-dotted,orangedash two-dottedandbluelong-dashedlinesdenoteBKGI,BKGII,BKGIIIandBKG IV(see text),respectively.Thevioletlongdash-dottedlinesaretheremainingD0_D_¯0 back-ground.Theinsetinplot(d)showsthenormalizedlikelihooddistributionincluding thesystematicuncertainty,asafunctionoftheexpectedBF.Thebluearrow indi-catestheupperlimitontheBFatthe90%C.L.

changeinthe numberofdegreesof freedom,are summarizedin Table2.

Sincenoobvious D0

→

ηηη

signal isobserved,anupperlimit onitsdecayBF isdetermined.Weﬁt the

M

BC distributionofthe

D0

→

ηηη

candidateevents,wherethesignalisdescribed bythe MCsimulatedshapeconvolutedwithaGaussianfunction andthe backgroundby an ARGUS function. The parameters of the Gaus-sianfunctionareﬁxedtothoseobtainedintheﬁtofD0

_→

_π

0

_ηη

decay. The resultant best ﬁt is shown in Fig. 2 (d). The PDF for theexpectedsignal yieldistakentobethenormalizedlikelihood

L

versus the BF in the ﬁt, incorporating the systematic uncer-tainties as described below, and is shown as the inset plot in Fig.2(d).TheupperlimitontheBFatthe90%C.L.,corresponding to

₀up

L(

x

)

dx

/

₀∞

L(

x

)

dx

=

0.9,iscalculatedtobe

<

1.3

×

10−4.

The detection eﬃciencies for various decays of interest must take intoaccount the effectofany intermediatestates. The exis-tenceofintermediatestatesinthe

D

0_three-body_decays_is inves-tigatedbyexaminingthecorrespondingDalitzplots.Exceptforthe decay D0

_→

_π

0

_ηη

_, _no _obvious _intermediate _states _are _observed. Therefore,thedetectioneﬃcienciesforthedecays

D

0

_→

_π

0

_π

0

_π

0_,

Fig. 3. (Coloronline.) FitstotheMπ0_ηdistribution.Dotswitherrorbarsaredata, thebluesolidlineisthetotalﬁtcurve,andthereddottedlineisthesignalshape. Thebluelong-dashedlineisthebackgroundestimatedfromtheinclusiveMC.

π

0

_π

0

_η

_and

_ηηη

_are _obtained _with _MC _samples _of _three-body phasespacedecaywithuniformangulardistributions.

Forthedecay D0

_→

_π

0

_ηη

_,_the

_a

₀₍₉₈₀₎0 _is_evident _in_the

_π

0

_η

invariant mass _Mπ0_{η distribution.} Fig. 3 shows the Mπ0_η spec-trumof23eventswithtwoentriesper eventfromthedata sam-ple withadditional requirements

−

0.023

<

E

<

0.020 GeV and 1.859

<

MBC

<

1.871 GeV/c2.Anunbinnedmaximumlikelihoodﬁt isperformedonthe_Mπ0_{η distribution}todetermine the

a

0(980)0 signalyield.

Intheﬁt,theshapeofthe

a

0(980)0isdescribedwiththeshape fromtheMCsample ofD0

→

a0(980)0

η

→

π

0

_ηη

_,_which_has_two components:one withthe

π

0 _combined_with_the_correct

_η

com-ingfromthe

a

0(980)0 decay,andtheotherwiththe

π

0 _combined with the wrong

η

coming directly from the D0 decay. The ﬁrst peaks aroundthe a0(980)0 _mass,_while _the _second _contributes_a broadshapeinthe _Mπ0_{η distribution.}TheMCshapeisconvolved witha Gaussian function to account for themass resolution dif-ference betweendata and MC simulation. In the MC simulation, the intermediate a0(980)0 state is parameterized withthe Flatté formula [16] with the central mass and the a0(980)0 coupling constants comingfromtheCrystalBarrelexperiment [17,18].The componentfromthedirect

D

0 _three-body_decay_is_included_in_the ﬁt, andits shape isthe MC simulated shape,which is similar to that ofthewrong

η

contributionin the

a

0(980)0 _shape._We _also includethe backgroundin theﬁt, whereits shape isdetermined fromtheinclusiveMCsample.Bothmagnitudesforthe

D

0 three-bodydecaycomponentandbackgroundareleftfreeinthefit.The fitcurvesareshowninFig.3.Thefityields are21

±

5 eventsfor the

a

0(980)0 signaland0

±

4 eventsforthe D0 directthree-body decay, which impliesthe predominant process in thethree-body decayof

D

0

_→

_π

0

_ηη

_is _D0

_→

_a₀₍₉₈₀₎0

_η

_.

Wealsoperformaﬁtwithoutthe

a

0(980)0signalincluded,and thestatisticalsigniﬁcanceofthe

a

0(980)0_signal_is_calculated_with the change of likelihood value withrespect to that of the nom-inal fittaking into account the change ofnumber offreedom in the fit. The significance for the a0(980)0 signal is only 2.6

σ

, al-thoughitisthepredominantcomponentinthethree-body decay. Therefore,inthedecayof D0

→

π

0

_ηη

_,_the_detection_eﬃciency_is estimatedwiththeMCsampleofD0

→

a0(980)0

η

→

π

0

_ηη

_as de-scribedabove.

TheresultantDTeﬃcienciesforvariousdecaysarelistedin Ta-ble 1. The BFs of these decays are calculated with Eq. (1), and summarizedinTable2.

5. Systematicuncertainties

WiththeDTtechnique,theBFmeasurementsareinsensitiveto systematicscomingfromtheSTsidesincetheymostly cancel.For