Measurement of y(CP) in D-0-(D)over-bar(0) oscillation using quantum correlations in e(+)e(-) -> D-0(D)over-bar(0) at root s=3.773 GeV

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

y

_CP

in

D

0 –D

0 oscillation

using

quantum

correlations

in

e

+

e

−

→

D

0 D

0 at

√

s

=

3

.

773 GeV

BESIII

Collaboration

M. Ablikim

a

,

M.N. Achasov

h

,

1

,

X.C. Ai

a

,

O. Albayrak

d

,

M. Albrecht

c

,

D.J. Ambrose

au

,

A. Amoroso

ay

,

ba

,

F.F. An

a

,

Q. An

av

,

J.Z. Bai

a

,

R. Baldini Ferroli

s

,

Y. Ban

af

,

D.W. Bennett

r

,

J.V. Bennett

d

,

M. Bertani

s

,

D. Bettoni

u

,

J.M. Bian

at

,

F. Bianchi

ay

,

ba

,

E. Boger

x

,

8

,

O. Bondarenko

z

,

I. Boyko

x

,

R.A. Briere

d

,

H. Cai

bc

,

X. Cai

a

,

O. Cakir

ao

,

2

,

A. Calcaterra

s

,

G.F. Cao

a

,

S.A. Cetin

ap

,

J.F. Chang

a

,

G. Chelkov

x

,

3

,

G. Chen

a

,

H.S. Chen

a

,

H.Y. Chen

b

,

J.C. Chen

a

,

M.L. Chen

a

,

S.J. Chen

ad

,

X. Chen

a

,

X.R. Chen

aa

,

Y.B. Chen

a

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H.P. Cheng

p

,

X.K. Chu

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G. Cibinetto

u

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D. Cronin-Hennessy

at

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H.L. Dai

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D. Dedovich

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Z.Y. Deng

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I. Denysenko

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C. Dong

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J. Dong

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L.Y. Dong

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M.Y. Dong

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S.X. Du

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P.F. Duan

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J.Z. Fan

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J. Fang

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S.S. Fang

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X. Fang

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Y. Fang

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L. Fava

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F. Feldbauer

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G. Felici

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C.Q. Feng

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E. Fioravanti

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M. Fritsch

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C.D. Fu

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Q. Gao

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K. Goetzen

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W.X. Gong

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M. Greco

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M.H. Gu

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Y.T. Gu

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Y.H. Guan

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A.Q. Guo

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Y.P. Guo

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Z. Haddadi

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A. Hafner

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S. Han

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Y.L. Han

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F.A. Harris

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K.L. He

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Z.Y. He

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T. Held

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Y.K. Heng

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Z.L. Hou

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C. Hu

ac

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H.M. Hu

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J.F. Hu

ay

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T. Hu

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Y. Hu

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G.M. Huang

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G.S. Huang

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H.P. Huang

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J.S. Huang

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X.T. Huang

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Y. Huang

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T. Hussain

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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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L.L. Jiang

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L.W. Jiang

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X.S. Jiang

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J.B. Jiao

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Z. Jiao

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D.P. Jin

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S. 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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R. Kliemt

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B. Kloss

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O.B. Kolcu

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B. Kopf

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M. Kornicer

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W. Kuehn

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A. Kupsc

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W. Lai

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J.S. Lange

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M. Lara

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P. Larin

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C.H. Li

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Cheng Li

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Zhiqiang Liu

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Zhiqing Liu

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H. Loehner

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X.C. Lou

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Y. Lu

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T. Luo

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X.L. Luo

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M. Lv

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X.R. Lyu

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F.C. Ma

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H.L. Ma

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Q.M. Ma

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S. Ma

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T. Ma

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F.E. Maas

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M. Maggiora

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Q.A. Malik

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Y.J. Mao

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Z.P. Mao

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S. Marcello

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J.G. Messchendorp

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J. Min

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T.J. Min

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R.E. Mitchell

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X.H. Mo

a

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Y.J. Mo

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C. Morales Morales

m

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K. Moriya

r

,

N.Yu. Muchnoi

h

,

1

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H. Muramatsu

at

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Y. Nefedov

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F. Nerling

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I.B. Nikolaev

h

,

1

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Z. Ning

a

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S. Nisar

g

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S.L. Niu

a

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X.Y. Niu

a

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S.L. Olsen

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Q. Ouyang

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S. Pacetti

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P. Patteri

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M. Pelizaeus

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H.P. Peng

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K. Peters

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J.L. Ping

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R.G. Ping

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R. Poling

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Y.N. Pu

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M. Qi

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S. Qian

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C.F. Qiao

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L.Q. Qin

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N. Qin

bc

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X.S. Qin

a

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Y. Qin

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Z.H. Qin

a

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J.F. Qiu

a

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K.H. Rashid

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C.F. Redmer

w

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H.L. Ren

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M. Ripka

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G. Rong

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X.D. Ruan

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V. Santoro

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A. Sarantsev

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M. Savrié

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K. Schoenning

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S. Schumann

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W. Shan

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M. Shao

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C.P. Shen

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P.X. Shen

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http://dx.doi.org/10.1016/j.physletb.2015.04.008

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X.Y. Shen

a

,

H.Y. Sheng

a

,

M.R. Shepherd

r

,

W.M. Song

a

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X.Y. Song

a

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S. Sosio

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ba

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S. Spataro

ay

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B. Spruck

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G.X. Sun

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J.F. Sun

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Y.Z. Sun

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Z.J. Sun

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C.J. Tang

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X. Tang

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I. Tapan

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E.H. Thorndike

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M. Tiemens

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D. Toth

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M. Ullrich

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I. Uman

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B. Wang

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

c_Bochum_{Ruhr-University,}_D-44780_Bochum,_Germany d_Carnegie_Mellon_University,_Pittsburgh,_{PA 15213,}_USA

e_Central_China_Normal_University,_Wuhan_430079,_People’s_Republic_of_China

f_China_Center_of_Advanced_Science_and_Technology,_Beijing_100190,_People’s_Republic_of_China

g_COMSATS_Institute_of_Information_Technology,_Lahore,_Defence_Road,_Off_Raiwind_Road,₅₄₀₀₀_Lahore,_Pakistan h_G.I._Budker_Institute_of_Nuclear_Physics_SB_RAS_(BINP),_Novosibirsk_630090,_Russia

i_GSI_{Helmholtzcentre}_for_Heavy_Ion_Research_GmbH,_D-64291_Darmstadt,_Germany j_Guangxi_Normal_University,_Guilin_541004,_People’s_Republic_of_China

k_GuangXi_University,_Nanning_530004,_People’s_Republic_of_China l_Hangzhou_Normal_University,_Hangzhou_310036,_People’s_Republic_of_China m_Helmholtz_Institute_Mainz,_{Johann-Joachim-Becher-Weg}_45,_D-55099_Mainz,_Germany n_Henan_Normal_University,_Xinxiang_453007,_People’s_Republic_of_China

o_Henan_University_of_Science_and_Technology,_Luoyang_471003,_People’s_Republic_of_China p_Huangshan_College,_Huangshan_245000,_People’s_Republic_of_China

q_Hunan_University,_Changsha_410082,_People’s_Republic_of_China r_Indiana_University,_Bloomington,_{IN 47405,}_USA

s_INFN_Laboratori_Nazionali_di_Frascati,_I-00044,_Frascati,_Italy t_INFN_and_University_of_Perugia,_I-06100,_Perugia,_Italy u_INFN_Sezione_di_Ferrara,_I-44122,_Ferrara,_Italy v_University_of_Ferrara,_I-44122,_Ferrara,_Italy

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

y_Justus_Liebig_University_Giessen,_II._{Physikalisches}_Institut,_{Heinrich-Buff-Ring}_16,_D-35392_Giessen,_Germany z

KVI-CART,UniversityofGroningen,NL-9747AAGroningen,TheNetherlands

aa_Lanzhou_University,_Lanzhou_730000,_People’s_Republic_of_China ab_Liaoning_University,_Shenyang_110036,_People’s_Republic_of_China ac_Nanjing_Normal_University,_Nanjing_210023,_People’s_Republic_of_China ad_Nanjing_University,_Nanjing_210093,_People’s_Republic_of_China ae_Nankai_University,_Tianjin_300071,_People’s_Republic_of_China af_Peking_University,_Beijing_100871,_People’s_Republic_of_China ag_Seoul_National_University,_Seoul,_151-747_Republic_of_Korea ah_Shandong_University,_Jinan_250100,_People’s_Republic_of_China

ai_Shanghai_Jiao_Tong_University,_Shanghai_200240,_People’s_Republic_of_China aj_Shanxi_University,_Taiyuan_030006,_People’s_Republic_of_China

ak_Sichuan_University,_Chengdu_610064,_People’s_Republic_of_China al_Soochow_University,_Suzhou_215006,_People’s_Republic_of_China am_Sun_Yat-Sen_University,_Guangzhou_510275,_People’s_Republic_of_China an_Tsinghua_University,_Beijing_100084,_People’s_Republic_of_China ao_Istanbul_Aydin_University,₃₄₂₉₅_Sefakoy,_Istanbul,_Turkey ap_Dogus_University,₃₄₇₂₂_Istanbul,_Turkey

aq_Uludag_University,₁₆₀₅₉_Bursa,_Turkey

ar_University_of_Chinese_Academy_of_Sciences,_Beijing_100049,_People’s_Republic_of_China as_University_of_Hawaii,_Honolulu,_{HI 96822,}_USA

at_University_of_Minnesota,_Minneapolis,_{MN 55455,}_USA au_University_of_Rochester,_Rochester,_{NY 14627,}_USA

(3)

aw_University_of_South_China,_Hengyang_421001,_People’s_Republic_of_China ax_University_of_the_Punjab,_{Lahore-54590,}_Pakistan

ay_University_of_Turin,_I-10125,_Turin,_Italy

az_University_of_Eastern_Piedmont,_I-15121,_Alessandria,_Italy ba_INFN,_I-10125,_Turin,_Italy

bb_Uppsala_University,_Box_516,_SE-75120_Uppsala,_Sweden bc_Wuhan_University,_Wuhan_430072,_People’s_Republic_of_China bd_Zhejiang_University,_Hangzhou_310027,_People’s_Republic_of_China be_Zhengzhou_University,_Zhengzhou_450001,_People’s_Republic_of_China

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Articlehistory:

Received7January2015

Receivedinrevisedform19March2015 Accepted6April2015

Availableonline9April2015 Editor:L.Rolandi Keywords: BESIII D0_–D0_oscillation yCP Quantumcorrelation

Wereportameasurementoftheparameter

y

CP in

D

0–D0oscillationsperformedbytakingadvantageof

quantumcoherencebetweenpairs ofD0_D0_mesons_produced_in

_e

+_e− _{annihilations}_near_threshold._In

thiswork,doubly-tagged

D

0_D0_events,_where_one _{D decays}_to_a

_{CP eigenstate}

_and_the_other_{D decays} in asemileptonicmode,are reconstructedusing adata sampleof2.92 fb−1 collectedwith theBESIII detectoratthecenter-of-massenergyof√s=3.773 GeV.We obtainyCP= (−2.0±1.3±0.7)%,where

theﬁrstuncertaintyisstatisticalandthesecondissystematic.Thisresultiscompatiblewiththecurrent worldaverage.

(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

1.1.Charmoscillation

Itiswell knownthatoscillations betweenmesonand antime-son, also called mixing, can occur when the ﬂavor eigenstates differ from the physical mass eigenstates. These effects provide a mechanism whereby interference in the transition amplitudes

of mesons and antimesons may occur. They may also allow for

manifestation of CP violation (CPV) in the underlying dynamics

[1,2]. Oscillations in the K0_–K0 _[3]_, _B0_–B0 _[4] _and _B0

s–B0s [5]

systemsare established; their oscillationratesare well-measured andconsistentwithpredictionsfromtheStandardModel (SM)[6]. Afteranaccumulationofstrongevidencefromavarietyof exper-iments[7–9], D0_–D0 _oscillations_were _recently_ﬁrmly _established by LHCb[10].The results were soon conﬁrmed by CDF[11] and Belle[12].

Theoscillationsareconventionallycharacterizedbytwo dimen-sionless parameters x

=

m

/

and y

= /

2

, where

m and

are the mass and width differences between the two mass

eigenstatesand

istheaveragedecaywidthofthoseeigenstates. The mass eigenstates can be written as

|

D1,2

=

p

|

D0

±

q

|

D0

, where p and q are complex parameters and

φ

=

arg

(

q

/

p

)

is a CP-violating phase. Using the phase convention CP

|

D0

_{= +|}

_D0

_, theCP eigenstatesoftheD mesoncanbewrittenas

|

DCP+

≡

|

D 0

_{+ |}

_D0

√

2

,

|

DCP−

≡

|

D0

− |

D0

√

2

.

(1)

*

Correspondingauthor.

E-mailaddress:guanyh@ihep.ac.cn(Y.H. Guan).

1 _Also_at_the_Novosibirsk_State_University,_Novosibirsk,_630090,_Russia. 2 _Also_at_Ankara_University,₀₆₁₀₀_Tandogan,_Ankara,_Turkey.

3 _Also_at_the_Moscow_Institute_of_Physics_and_Technology,_Moscow_141700,_Russia andattheFunctionalElectronicsLaboratory,TomskStateUniversity,Tomsk,634050, Russia.

4 _Currently_at_Istanbul_Arel_University,₃₄₂₉₅_Istanbul,_Turkey. 5 _Also_at_University_of_Texas_at_Dallas,_Richardson,_Texas_75083,_USA. 6 _Also_at_the_PNPI,_Gatchina_188300,_Russia.

7 _Also_at_Bogazici_University,₃₄₃₄₂_Istanbul,_Turkey.

8 _Also_at_the_Moscow_Institute_of_Physics_and_Technology,_Moscow_141700,_Russia.

The difference in the effective lifetime between D decaysto CP eigenstatesandﬂavoreigenstatescanbeparameterizedby yCP.In

theabsenceofdirectCPV,butallowing forsmallindirectCPV,we have[13] yCP

=

1 2

y cos

φ

q p

+

p_q

−

x sin

φ

q p

−

p_q

.

(2)

In the absence of CPV,one has

|

p

/

q

|

=

1 and

φ

=

0, leading to yCP

=

y.

Although D0–D0 mixing from short-distance physics is sup-pressedby theCKMmatrix[14,15]andtheGIM mechanism[16], sizeablecharmmixingcanarisefromlong-distanceprocessesand newphysics[1,17].Currentexperimentalprecision[18]isnot suf-ﬁcienttoconcludewhetherphysicsbeyondtheSMisinvolved,and furtherconstraintsareneeded.Sofar,themostprecise determina-tionofthesizeofthemixinghasbeenobtainedbymeasuringthe time-dependent decay rate in the D

→

K±

π

∓ channel [10–12]. However, the resulting information on the mixing parameters x and y is highly correlated. It is important to access the mixing parametersx andy directlytoprovidecomplementaryconstraints. Inthisanalysis,weuseatime-integratedmethodtoextract yCP,

asproposedinthereferences[19–22],whichusesthresholdD0D0 pairproductionine+e−

→

γ

∗

→

D0_D0_._In_this_process,_the_D0_D0 pairisinastateofdeﬁnite C

= −

1,such thatthetwo D mesons necessarilyhaveoppositeCP eigenvalues.The methodutilizesthe semileptonicdecaysof D meson andhence,avoids the complica-tionsfromhadroniceffectsinD decays,thusprovidesacleanand uniquewaytoprobetheD0–D0 oscillation.

1.2. Formalism

In the semileptonic decays of neutral D mesons (denoted as D

→

l),9_the_partial_decay_width_is_only_sensitive_to_ﬂavor_content

anddoesnotdependontheCP eigenvalueoftheparentD meson. However,thetotaldecaywidthofthe DCP±doesdependonitsCP eigenvalue:

CP

±

= (

1

±

yCP

)

.Thus, the semileptonicbranching

fraction ofthe CP eigenstates DCP± is

BD

_CP_±_→l

≈

BD

→l

(

1

∓

yCP),

andyCP canbeobtainedas

(4)

Table 1

D ﬁnalstatesreconstructedinthisanalysis.

Type Mode CP+ K+K−,π+π−, K0 Sπ 0_π0 CP− K0Sπ0, K 0 Sω, K 0 Sη Semileptonic K∓e±ν, K∓μ±ν yCP

≈

1 4

_BD

CP−→l

BD

CP+→l

−

BD

CP+→l

BD

CP−→l

.

(3)

AtBESIII, quantum-correlated D0_D0 _pairs_produced _at thresh-oldallowustomeasure

BD

_CP_±_→l.Speciﬁcally,webeginwithafully

reconstructed D candidatedecaying intoa CP eigenstate, the so-calledSingle Tag(ST). We havethus taggedthe CP eigenvalueof thepartner D meson.ForasubsetoftheSTevents,theso-called Double Tag(DT)events, thistaggedpartner D mesonisalso ob-servedviaoneofthesemileptonicdecaychannels. CP violationin D decays isknown to be very small [18], andcan be safely ne-glected.Therefore,

BD

_CP_∓_→l canbeobtainedas

BD

CP∓→l

=

NCP±;l NCP±

· ε

CP±

ε

CP±;l

,

(4)

whereNCP±(NCP±;l)and

ε

CP±(

ε

CP±;l)denotethesignalyieldsand

detection eﬃciencies of ST decays D

→

CP

±

(DT decays D D

→

CP

±;

l), respectively. For CP eigenstates, as listed in Table 1, we choose modeswith unambiguous CP contentand copiousyields. The CP violation in K0_S decays is known to be very small, it is therefore neglected. The semileptonic modes used for the DT in thisanalysisare K∓e±

ν

andK∓

μ

±

ν

.

1.3. TheBESIIIdetectoranddatasample

The analysispresented in thispaper isbased on a data sam-plewithanintegratedluminosityof2.92 fb−1_[23] _collected_with the BESIII detector [24] at the center-of-mass energy of

√

s

=

3

.

773 GeV.TheBESIIIdetectorisageneral-purposesolenoidal de-tector attheBEPCII [25]double storagerings. Thedetectorhasa geometrical acceptanceof 93% of the full solid angle. We briefly describe thecomponentsof BESIIIfromthe interactionpoint (IP) outwards.Asmall-cellmaindriftchamber(MDC),usinga helium-basedgastomeasuremomentaandspecificionizationsofcharged particles, is surrounded by a time-of-flight (TOF) system based onplasticscintillatorsthat determinestheflighttimesofcharged particles.ACsI(Tl)electromagneticcalorimeter(EMC)detects elec-tromagnetic showers. These componentsare all situatedinside a superconducting solenoidmagnet, that providesa 1.0 Tmagnetic field parallel to the beam direction. Finally, a multi-layer resis-tive plate counter system installed in the iron flux return yoke ofthemagnetisusedto trackmuons. Themomentumresolution for charged tracks in the MDC is 0.5% for a transverse momen-tumof1 GeV

/

c.TheenergyresolutionforshowersintheEMCis 2.5%(5.0%)for1 GeVphotonsinthebarrel(endcap)region.More detailsonthefeaturesandcapabilitiesofBESIIIcanbefound else-where[24].

High-statisticsMonteCarlo(MC) simulationsare usedto eval-uatethedetectioneﬃciencyandto understandbackgrounds.The geant4-based[26]MCsimulationprogramisdesignedtosimulate interactions ofparticles in thespectrometer and thedetector re-sponse.Fortheproduction of

ψ(

3770

)

,the kkmc [27] package is used;thebeamenergyspreadandtheeffectsofinitial-state radi-ation(ISR) areincluded.TheMCsamplesconsist ofthe D D pairs withconsiderationofquantumcoherenceforallmodesrelevantto thisanalysis, non-D D decays of

ψ(

3770

)

, ISR productionof low-mass

ψ

states,andQEDandqq continuum

¯

processes.Theeffective

luminosity ofthe MC samples is about10 times that ofthe an-alyzed data. Known decays recorded by the Particle Data Group (PDG) [6] are generated with evtgen [28,29] using PDG branch-ing fractions, and the remaining unknown decays are generated with lundcharm[30].Final-stateradiation(FSR)ofchargedtracks istakenintoaccountwiththe photos package[31].

2. Eventselectionanddataanalysis

Each chargedtrackisrequiredto satisfy

|

cos

θ

|

<

0

.

93,where

θ

isthepolaranglewithrespecttothebeamaxis.Chargedtracks other than K0

S daughtersare requiredtobewithin 1 cmoftheIP

transversetothebeamlineandwithin10 cmoftheIP alongthe beamaxis.Particleidentiﬁcationforchargedhadronsh (h

=

π

,

K ) is accomplishedby combiningthe measured energyloss (dE

/

dx) inthe MDCandtheﬂight timeobtainedfromtheTOF toforma likelihood

L(

h

)

for eachhadron hypothesis. The K± (

π

±) candi-datesarerequiredtosatisfy

L(

K

)

>

L(

π

)

(

L(

π

)

>

L(

K

)

).

The K0_S candidates are selected with a vertex-constrained ﬁt frompairs ofoppositelychargedtracks,which arerequiredto be within 20 cm of the IP along the beam direction; no constraint in the transverse plane is required. The two charged tracks are not subjected to the particle identiﬁcation discussed above, and are assumedto be pions. We impose 0

.

487 GeV

/

c2

<

_Mπ+_π−

<

0

.

511 GeV

/

c2_, _that _is _within _about₃ _standard _deviations _of _the observed K0

S mass,andthetwotracksareconstrainedtooriginate

fromacommondecayvertexbyrequiringthe

χ

2 _of_the_vertex_ﬁt to belessthan100. Thedecayvertexisrequiredto beseparated from theIP with asigniﬁcance greater than two standard devia-tions.

ReconstructedEMCshowersthatareseparatedfromthe extrap-olated positions ofanycharged tracksby morethan 10standard deviationsaretakenasphotoncandidates.Theenergydepositedin nearbyTOFcountersisincludedtoimprovethereconstruction eﬃ-ciencyandenergyresolution.Photoncandidatesmusthavea min-imum energy of 25 MeV for barrelshowers (

|

cos

θ

|

<

0

.

80) and 50 MeV for end cap showers (0

.

84

<

|

cos

θ

|

<

0

.

92). The show-ers in the gap between the barrel and the end cap regions are poorly reconstructedandthusexcluded.The showertiming is re-quired to be no later than 700 ns after the reconstructed event start time to suppress electronic noise and energy deposits un-related to theevent. The

η

and

π

0 _candidates _are _{reconstructed} frompairsofphotons.DuetothepoorerresolutionintheEMCend capregions,thosecandidateswithbothphotonscomingfromEMC end caps arerejected. The invariant mass Mγ γ is requiredto be 0

.

115 GeV

/

c2

_<

_{Mγ γ}

_<

₀

_.

_{150 GeV}

_/

_c2 _for

_π

0 _and₀

_.

_{505 GeV}

_/

_c2

_<

Mγ γ

<

0

.

570 GeV

/

c2 _for

_η

_candidates. _The _photon _pair _is kine-matically constrainedtothe nominalmass ofthe

π

0 _or

_η

_[6]_to improvethemesonfour-vectorcalculation.

The

ω

candidates are reconstructed through the decay

ω

→

π

+

π

−

π

0_. _For _all _modes _with

_ω

_candidates, _sideband _events _in the _Mπ+_π−_π0 spectrumareusedtoestimatepeakingbackgrounds from non-

ω

D

→

K0_S

π

+

π

−

π

0 _decays._We _take _the _signal _region as (0.7600,0.8050) GeV

/

c2 andthe sideband regions as(0.6000, 0.7300) GeV

/

c2 or(0.8300,0.8525) GeV

/

c2.Theupperedgeofthe right sideband is restrictedbecause of the K∗

ρ

background that alterstheshapeof_Mπ+_π−_π0.Thesidebandsarescaledtothe esti-matedpeakingbackgroundsinthesignalregion.Thescalingfactor is determinedfrom aﬁt tothe _Mπ+_π−_π0 distribution indata,as shown in

Fig. 1

, wherethe

ω

signal is determined with theMC shape convolutedwithaGaussian whoseparametersare leftfree in theﬁt to better matchdataresolution, andthebackground is modeledbyapolynomialfunction.

(5)

Fig. 1. FittotheinvariantmassMπ+π−π0 foreventsreconstructedfromdata.The solidlineisthetotalﬁtandthedashedlineshowsthepolynomialbackground.The shadedareashowsthesignalregionandcross-hatchedareasshowthesidebands.

Table 2

Requirementson

E forSTD candidates.

Mode Requirement (GeV)

K+K− −0.020< E<0.020 π+π− −0.030< E<0.030 K0 Sπ0π0 −0.080< E<0.045 K0Sπ0 −0.070< E<0.040 K0 Sω −0.050< E<0.030 K0 Sη −0.040< E<0.040

2.1.SingletagsusingCP modes

Toidentify the reconstructed D candidates, we use two vari-ables,the beam-constrainedmass MBC andthe energydifference

E,whicharedeﬁnedas

MBC

≡

E2_beam

/

c4

_{− |}

_p

D

|

2

/

c2

,

(5)

E

≡

ED

−

Ebeam

,

(6)

where

pD and ED are the momentumandenergy ofthe D

can-didateinthee+e−center-of-masssystem,andEbeam isthebeam energy.The D signalpeaksatthenominalD mass inMBC andat zeroin

E. We accept only one candidate per mode per event; when multiple candidates are present, the one with the small-est

|

E

|

is chosen. Since the correlation between

E and MBC isfoundtobesmall,thiswillnotbiasthebackgrounddistribution inMBC.Weapplythemode-dependent

E requirementslistedin

Table 2.

For K+K− and

π

+

π

− ST modes, ifcandidate events contain onlytwochargedtracks,thefollowingrequirementsareappliedto suppressbackgroundsfromcosmic rays andBhabhaevents.First, werequireatleastone EMCshower separatedfromthetracksof theSTwithenergylargerthan50 MeV.Second,thetwoSTtracks must not be both identiﬁed as muons or electrons, and, if they havevalidTOF times,thetime differencemustbe lessthan 5 ns. BasedonMCstudies,nopeakingbackgroundispresentinMBCin ourSTmodesexceptforthe K0_S

π

0 _mode. _In_the _K0

S

π

0 STmode,

therearefewbackgroundeventsfromD0

_→

_ρπ

_._From_MC_studies, theestimatedfractionislessthan0

.

5%;thiswillbeconsideredin thesystematicuncertainties.

TheMBCdistributionsforthesixSTmodesareshownin

Fig. 2

.

Unbinned maximum likelihood ﬁts are performed to obtain the

numbersofSTyieldsexceptinthe K0_S

ω

mode,forwhichabinned least-square ﬁt is applied to the MBC distribution after subtrac-tion of the

ω

sidebands. In each ﬁt, the signal shape is derived fromsimulatedsignal eventsconvoluted witha bifurcated Gaus-sianwithfreeparameterstoaccountforimperfectmodelingofthe detectorresolution andbeamenergycalibration.Backgrounds are describedby theARGUS[32] function.Themeasured STyieldsin

Table 3

Yieldsand eﬃciencies ofallST and DTmodes, where NCP± (NCP±;l)and εCP±

(εCP±;l)denotesignalyieldsanddetectioneﬃcienciesofD→CP±(D D→CP±;l),

respectively.Theuncertaintiesarestatisticalonly.

ST Mode NCP± εCP±(%) K+K− 54 494±251 61.32±0.18 π+π− 19 921±174 64.09±0.18 K0 Sπ0π0 24 015±236 16.13±0.08 K0 Sπ0 71 421±285 40.67±0.14 K0 Sω 20 989±243 13.44±0.07 K0 Sη 9878±117 34.39±0.13 DT Mode NCP±;l εCP±;l(%) K+K−, K eν 1216±40 39.80±0.14 π+π−, K eν 427±23 41.75±0.14 K0 Sπ 0_π0_{, K e}_ν ₅₆₀_±₂₈ ₁₁ .05±0.07 K0 Sπ0, K eν 1699±47 26.70±0.12 K0 Sω, K eν 481±30 9.27±0.07 K0 Sη, K eν 243±17 22.96±0.11 K+K−, Kμν 1093±37 36.89±0.14 π+π−, Kμν 400±23 38.43±0.15 K0 Sπ0π0, Kμν 558±28 10.76±0.08 K0 Sπ 0_{, K}_μν ₁₄₇₅_±₄₃ ₂₅ .21±0.12 K0 Sω, Kμν 521±27 8.75±0.07 K0 Sη, Kμν 241±18 21.85±0.11

thesignal regionof1

.

855 GeV

/

c2

_<

_M

BC

<

1

.

875 GeV

/

c2 andthe correspondingeﬃcienciesaregivenin

Table 3

.

2.2. Doubletagsofsemileptonicmodes

In each ST event, we search among the unused tracks and

showersforsemileptonicD

→

K e

(

μ

)

ν

candidates.Werequirethat there be exactly two oppositely-charged tracks that satisfy the ﬁducialrequirementsdescribedabove.

In searchingfor K

μν

decays,kaoncandidates are requiredto satisfy

L(

K

)

>

L(

π

)

.Ifthetwo trackscan passthecriterion, the track with larger

L(

K

)

is taken as the K± candidate, and the other track is assumed to be the

μ

candidate. The energy de-posit in the EMC of the

μ

candidateis required to be lessthan 0.3 GeV. We further require the K

μ

invariant mass MKμ to be lessthan 1

.

65 GeV

/

c2 to reject D

→

K

π

backgrounds.The total energyof remaining unmatched EMC showers, denoted as Eextra, isrequiredtobelessthan0.2 GeVtosuppress D

→

K

π π

0 back-grounds. Toreduce backgrounds from the D

→

K e

ν

process, the ratio

R

_L

(

e

)

≡

L

(

e

)/

[

L

(

e

)

+

L

(

μ

)

+

L

(

π

)

+

L

(

K

)

]

is required to belessthan 0.8,where thelikelihood

L

(

i

)

forthehypothesis i

=

e,

μ

,

π

or K isformed by combining EMC informationwith thedE

/

dx andTOFinformation.

ToselectK e

ν

events,electroncandidatesarerequiredtosatisfy

L

₍

_e

₎

_>

₀

_.

_{001 and}

_R

L

(

e

)

>

0

.

8, where

R

_L

(

e

)

≡

L

(

e

)/

[

L

(

e

)

+

L

₍

_π

₎

₊

_L

₍

_K

₎

_]

_._If_both _tracks_satisfy _these_{requirements,}_the_one

withlarger

R

_L

(

e

)

istakenastheelectron.Theremainingtrackis requiredtosatisfy

L(

K

)

>

L(

π

)

.

The variable Umiss is used to distinguish semileptonic signal eventsfrombackground:

Umiss

≡

Emiss

−

c

|

pmiss

|,

(7)

where, Emiss

≡

Ebeam

−

EK

−

El

,

(8)

pmiss

≡ −

pK

+

pl

+ ˆ

pST

E2 beam

/

c2

−

c2m2D

,

(9)

(6)

Fig. 2. TheMBCdistributionsforSTD candidatesfromdata.ThesolidlineisthetotalﬁtandthedashedlineshowsthebackgroundcontributiondescribedbyanARGUS function.

EK(l) (

pK(l)) is the energy (three-momentum) of K∓ (l±), p

ˆ

ST is theunit vectorinthe directionofthereconstructedCP-tagged D andmD isthenominalD mass. Theuseofthebeamenergyand

the nominal D mass for the magnitude ofthe CP-tagged D

im-provesthe Umiss resolution.Since E equalsto

|

p

|

c foraneutrino, thesignalpeaksatzeroinUmiss.

TheUmissdistributionsareshownin

Fig. 3

,wherethetagged-D is required to be in the region of 1

.

855 GeV

/

c2

_<

_M

BC

<

1

.

875 GeV

/

c2.DTyields,obtainedbyﬁttingtheUmiss spectra,are listedin

Table 3

.Unbinnedmaximumlikelihoodﬁtsareperformed forallmodesexceptformodesincluding

ω

.Formodesincluding an

ω

, binned least-square ﬁts are performedto the

ω

sideband-subtracted Umiss distributions.Ineach ﬁt,the K e

ν

or K

μν

signal ismodeledbytheMC-determined shapeconvolutedwitha bifur-catedGaussianwhereallparametersareallowedtovaryintheﬁt. BackgroundsforK e

ν

arewelldescribedwithaﬁrst-order polyno-mial.However,inthe K

μν

mode,backgroundsaremorecomplex and consist of three parts. The primary background comes from D

→

K

π π

0 _decay. _To _better _control _this _background, _we _select asample of D

→

K

π π

0 _in _data_by_requiring _E

extra

>

0

.

5 GeV, in whichtheUmissshapeofK

π π

0isprovedtobebasicallythesame asthatintheregionofEextra

<

0

.

2 GeV inMCsimulation.The se-lected K

π π

0 _sample_is _used_to _extract_the _resolution_differences in the Umiss shape of K

π π

0 inMC anddata, andto obtain the D

→

K

π π

0_yields_in_E

extra

>

0

.

5 GeV region.Then,inﬁtstoUmiss, theK

π π

0 _is_described_by_the_{resolution-corrected}_shape_from_MC simulationsanditssizeisﬁxedaccordingtotherelativesimulated eﬃciencies ofthe Eextra

>

0

.

5 GeV and Eextra

<

0

.

2 GeV selection criteria.ThesecondbackgroundfromK e

ν

eventsismodeledbya MC-determined shape. Its ratioto thesignal yields is about3.5% based on MC studies andis fixed in the fits. Background in the thirdcategory includesallother backgroundprocesses,whichare welldescribedwithafirst-orderpolynomial.

3. Systematicuncertainties

MostsourcesofuncertaintiesfortheSTorDTeﬃciencies,such astracking, PID,and

π

0_,

_η

_, _K0

S reconstruction, cancelout in

de-termining yCP.The main systematicuncertainties come fromthe

background veto, modeling of the signals and backgrounds, fake tagged signals, and the CP-purity of ST events, as shown in Ta-ble 4.

The cosmic and Bhabha veto is applied only for the K K and

π π

STeventswhichhaveonlytwotracks.Theeffectofthisveto isestimatedbasedonMCsimulation.Wecomparethecaseswith andwithoutthisrequirementandtheresultantrelativechangesin

STeﬃcienciesareabout0.3%forboththeK K and

π π

modes.The resultingsystematicuncertaintyon yCP is0.001.

Peaking backgroundsarestudied fordifferentSTmodes, espe-ciallyfor

ρπ

backgroundsintheK0

S

π

0tagmodeandK0S

π

+

π

−

π

0

backgroundsintheK0_S

ω

tagmode.Basedonastudyofthe inclu-sive MCsamples,thefractionofpeakingbackgroundsin K0_S

π

0 _is 0.3%. Theuncertainties on yCP causedby thisisabout0.001.

Un-certainties fromthesidebandsubtractionofpeakingbackgrounds fortheK0_S

ω

modearestudiedbychangingthesidebandandsignal regions;changesintheeﬃciency-correctedyieldsarenegligible.

Fits to the MBC and Umiss spectracould inducesystematic er-rorsbythemodelingofthesignalandbackgroundshape.The MC-determined signal shapesconvoluted with a Gaussian are found to describe the data well, and systematic uncertainties from the modeling ofthe signal are assumedto be negligible.Toestimate uncertaintiesfrommodelingofbackgrounds,differentmethodsare considered. For the CP ST yields, we include an additional back-groundcomponenttoaccountforthe

ψ(

3770

)

→

D D processwith a shapedetermined byMC simulationwhoseyieldis determined in the ﬁt. The uncertainties in the ﬁts to MBC are uncorrelated among different tag modes, and the obtained change on yCP is

0.001. For the DT semileptonic yields, the polynomial functions that areused todescribe backgroundsinournominalﬁtsare

re-placed by a shape derived from MC simulations. For the K

μν

mode,thesizeofthemainbackgroundK

π π

0 _is_ﬁxed_in_our nom-inal ﬁt,so the statisticaluncertainties of the numberof selected K

π π

0 _events_introduces _a_systematic_error._To_estimate_the asso-ciateduncertainty,wevaryitssizeby

±

1standarddeviationbased on the selected K

π π

0 _samples. _Systematic _{uncertainties} _due _to the Umiss ﬁts aretreatedaspositively correlatedamongdifferent tag modes. We take the maximum change on the resultant yCP,

thatis0.006,assystematicuncertainty.

The DT yields are obtainedfrom the ﬁt to the Umiss spectra. However,onealsohastoconsidereventsthatpeakatUmissbutare backgroundsintheMBCspectra,theso-calledfaketaggedsignals. This issue is examined by ﬁtting to the MBC versus Umiss two-dimensionalplots.Fromthisstudy,thefaketaggedsignal compo-nentisprovedtobeverysmall.Theresultingdifferenceon yCP is

0.002andassignedasasystematicuncertainty.

WestudytheCP-puritiesofSTmodesbysearchingforsame-CP DTsignalsindata.AssumingCP conservationinthecharmsector, the same-CP process is prohibited, unless the studied CP modes are notpure ortheinitial C -odd D0D0 systemisdiluted. TheCP modes involving K0_S are not pure due to the existence of small CPV in K0_–K0 _mixing_[6]_._However, _this_small_effect_is_negligible

(7)

Fig. 3. FittotheUmissdistributionsforselectedDTeventsfromdata.Ineachplot,thesolidlineisthetotalﬁt,thedashedlineinK eνshowsthecontributionofpolynomial backgrounds,andthedash-dottedlineinKμνshowsthecontributionofthemainKπ π0_backgrounds.

Table 4

Summaryofsystematicuncertainties.Relativesystematicuncertaintiesarelistedforeachtagmodeinpercent,whiletheresultingabsoluteuncertaintiesonycpareshown

inthelastcolumn.Negligibleuncertaintiesaredenotedby“–”.

K+K− π+π− K0 Sπ0π0 K0Sπ0 K0Sω K0Sη ycp Background 0.3 0.3 – 0.3 – – 0.001 MBCfit 0.4 0.1 2.4 0.4 0.1 1.4 0.001 Umissfit (K eν) 1.8 1.3 2.4 1.6 8.1 1.2 0.006 Umissfit (Kμν) 3.2 7.0 4.6 2.5 1.7 1.7 Fake tag (K eν) 0.2 1.4 0.9 1.2 3.1 0.4 0.002 Fake tag (Kμν) 1.0 0.7 0.5 0.9 4.8 0.4 CP-purity – – 0.4 – 0.2 0.2 0.001

withourcurrentsensitivity.Hence, K0_S

π

0_is_assumed_to_be_a_clean CP mode, as its background level is very low. As a conservative treatment,westudyDTyieldsof(K0

S

π

0, K0S

π

0) toverifyits pure

CP-oddeigenstatenatureandtheCP-oddenvironmentoftheD0_D0 pair.TheobservednumbersofthisDTsignalsarequitesmall,and weestimatethedilutionofthe C -oddinitialstatetobelessthan 2%at90%conﬁdencelevel.ThisaffectsourmeasurementofyCP by

lessthan0.001.Thepurityofthe K_S0

π

0_mode_is_found_to_be_larger than99%.Duetothecomplexityoftheinvolvednon-resonantand resonantprocessesin K0

S

π

0

π

0 and K0S

ω

,theCP-purities ofthese

tagmodescouldbe contaminated.Wetakethemode K+K− asa cleanCP-eventagtotestK0_S

π

0

_π

0_,_and_take _K0

S

π

0totest KS0

ω

and

K0

S

η

. TheCP-purities of K0S

π

0

π

0, K0S

ω

andK0S

η

areestimatedto

belarger than89.4%, 93.3%and93.9%,respectively. Based onthe

obtained CP purities, the corresponding maximum effect on the determined yCP isassignedassystematicuncertainty.

Systematicuncertainties fromdifferentsourcesareassumedto

be independent and are combined in quadrature to obtain the

overall yCP systematic uncertainties. The resultant total yCP

sys-tematicuncertaintiesis0.007.

4. Results

ThebranchingratiosofK∓e±

ν

andK∓

μ

±

ν

aresummedto ob-tain

BD

_CP_∓_→l

=

BD

CP∓→K eν

+

BD

CP∓→Kμν .Tocombineresultsfrom differentCP modes,thestandardweightedleast-squaremethodis utilized[6].Theweightedsemileptonicbranchingfraction

BD

˜

_CP_±_→l

(8)

Table 5

ValuesofbranchingratioofDCP±→l obtainedfromdifferenttagmodesandthe

combinedbranchingratio.Theerrorsshownarestatisticalonly.

Tag mode BDCP−→K eν(%) BDCP−→Kμν(%) BDCP−→l(%) K+K− 3.44±0.12 3.33±0.12 6.77±0.17 π+π− 3.29±0.18 3.35±0.20 6.64±0.27 K0 Sπ0π0 3.40±0.18 3.48±0.18 6.89±0.26 ˜ BDCP−→l 3.40±0.09 3.37±0.09 6.77±0.12 Tag mode BDCP+→K eν(%) BDCP+→Kμν(%) BDCP+→l(%) K0 Sπ0 3.62±0.10 3.33±0.10 6.96±0.15 K0 Sω 3.32±0.21 3.81±0.21 7.14±0.30 K0Sη 3.68±0.26 3.84±0.29 7.52±0.40 ˜ BDCP+→l 3.58±0.09 3.46±0.09 7.04±0.13

χ

2

=

α

˜

BD

CP±→l

−

B

α_D_CP_±_→_l

2

σ

α CP±

2

,

(10)

where

α

denotesdifferentCP-tagmodesand

σ

α

CP±isthestatistical

errorof

B

α_D

CP±→l forthegiventag mode.The branchingfractions

of

BD

CP±→l andtheobtained

BD

˜

CP±→l arelistedin

Table 5

.Finally,

yCP iscalculatedusingEq.(3),with

BD

CP±→l replacedby

BD

˜

CP±→l.

Weobtain yCP

= (−

2

.

0

±

1

.

3

±

0

.

7

)

%, wheretheﬁrst uncertainty

isstatisticalandthesecondissystematic.

5. Summary

Using quantum-correlated D0D0 pairs produced at

√

s

=

3

.

773 GeV, we employ a CP-tagging technique to obtain the yCP

parameterof D0–D0 oscillations.Underthe assumptionofno di-rect CPV in the D sector, we obtain yCP

= (−

2

.

0

±

1

.

3

(

stat

.)

±

0

.

7

(

syst

.))

%. Thisresultiscompatiblewiththeprevious measure-ments[18,33–35]withinabouttwostandarddeviations.However, theprecision isstill statisticallylimitedandlessprecise thanthe currentworldaverage[6].Futureeffortsusingaglobalﬁt[36]may betterexploittheBESIIIdata,leadingtoamorepreciseresult.

Acknowledgements

TheBESIIICollaboration thanksthestaffofBEPCIIandtheIHEP computingcenterfortheirstrongsupport.Thisworkissupported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; Joint Funds of the National Natu-ral Science Foundation of China under Contracts Nos. 11079008, 11179007,U1232201,U1332201;NationalNaturalScience Founda-tion of China (NSFC) under Contracts Nos. 11125525, 11235011,

11275266,11322544,11335008, 11425524;the ChineseAcademy

ofSciences (CAS) Large-ScaleScientiﬁc Facility Program; CAS

un-der Contracts Nos. KJCX2-YW-N29, KJCX2-YW-N45; 100 Talents

Program of CAS;INPAC andShanghai Key Laboratory forParticle

Physics andCosmology; GermanResearch Foundation DFG under

ContractNo.CollaborativeResearchCenterContractNo. CRC-1044; IstitutoNazionalediFisicaNucleare,Italy;MinistryofDevelopment

of Turkey under Contract No. DPT2006K-120470; Russian

Foun-dation for Basic Research under Contract No. 14-07-91152; U.S. Department ofEnergy under Contracts Nos.DE-FG02-04ER41291,

DE-FG02-05ER41374,DE-FG02-94ER40823,DESC0010118;U.S.

Na-tionalScience Foundation;UniversityofGroningen(RuG)andthe HelmholtzzentrumfuerSchwerionenforschungGmbH(GSI), Darm-stadt;WCUProgramofNationalResearchFoundationofKorea un-derContractNo.R32-2008-000-10155-0.

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