Measurement of the D -> K- pi(+) strong phase difference in psi(3770) -> D-0(D)over-bar(0)

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

D

→

K

−

π

+

strong

phase

difference

in

ψ (

3770

)

→

D

0

D

0

BESIII

Collaboration

M. Ablikim

a

,

M.N. Achasov

h

,

1

,

X.C. Ai

a

,

O. Albayrak

d

,

M. Albrecht

c

,

D.J. Ambrose

ar

,

F.F. An

a

,

Q. An

as

,

J.Z. Bai

a

,

R. Baldini Ferroli

s

,

Y. Ban

ac

,

D.W. Bennett

r

,

J.V. Bennett

r

,

M. Bertani

s

,

J.M. Bian

aq

,

E. Boger

v

,

5

,

O. Bondarenko

w

,

I. Boyko

v

,

S. Braun

an

,

R.A. Briere

d

,

H. Cai

az

,

X. Cai

a

,

O. Cakir

ak

,

A. Calcaterra

s

,

G.F. Cao

a

,

S.A. Cetin

al

,

J.F. Chang

a

,

G. Chelkov

v

,

2

,

G. Chen

a

,

H.S. Chen

a

,

J.C. Chen

a

,

M.L. Chen

a

,

S.J. Chen

aa

,

X. Chen

a

,

X.R. Chen

x

,

Y.B. Chen

a

,

H.P. Cheng

p

,

X.K. Chu

ac

,

Y.P. Chu

a

,

D. Cronin-Hennessy

aq

,

H.L. Dai

a

,

J.P. Dai

a

,

D. Dedovich

v

,

Z.Y. Deng

a

,

A. Denig

u

,

I. Denysenko

v

,

M. Destefanis

av

,

ax

,

W.M. Ding

ae

,

Y. Ding

y

,

C. Dong

ab

,

J. Dong

a

,

L.Y. Dong

a

,

M.Y. Dong

a

,

S.X. Du

bb

,

J.Z. Fan

aj

,

J. Fang

a

,

S.S. Fang

a

,

Y. Fang

a

,

L. Fava

aw

,

ax

,

C.Q. Feng

as

,

C.D. Fu

a

,

O. Fuks

v

,

5

,

Q. Gao

a

,

Y. Gao

aj

,

C. Geng

as

,

K. Goetzen

i

,

W.X. Gong

a

,

W. Gradl

u

,

M. Greco

av

,

ax

,

M.H. Gu

a

,

Y.T. Gu

k

,

Y.H. Guan

a

,

L.B. Guo

z

,

T. Guo

z

,

Y.P. Guo

u

,

Z. Haddadi

w

,

Y.L. Han

a

,

F.A. Harris

ap

,

K.L. He

a

,

M. He

a

,

Z.Y. He

ab

,

T. Held

c

,

Y.K. Heng

a

,

Z.L. Hou

a

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C. Hu

z

,

H.M. Hu

a

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J.F. Hu

an

,

T. Hu

a

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G.M. Huang

e

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G.S. Huang

as

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H.P. Huang

az

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J.S. Huang

n

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L. Huang

a

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X.T. Huang

ae

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Y. Huang

aa

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T. Hussain

au

,

C.S. Ji

as

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Q. Ji

a

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Q.P. Ji

ab

,

X.B. Ji

a

,

X.L. Ji

a

,

L.L. Jiang

a

,

L.W. Jiang

az

,

X.S. Jiang

a

,

J.B. Jiao

ae

,

Z. Jiao

p

,

D.P. Jin

a

,

S. Jin

a

,

T. Johansson

ay

,

A. Julin

aq

,

N. Kalantar-Nayestanaki

w

,

X.L. Kang

a

,

X.S. Kang

ab

,

M. Kavatsyuk

w

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B. Kloss

u

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B. Kopf

c

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M. Kornicer

ap

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W. Kuehn

an

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A. Kupsc

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W. Lai

a

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J.S. Lange

an

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M. Lara

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P. Larin

m

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M. Leyhe

c

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C.H. Li

a

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Cheng Li

as

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Cui Li

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D. Li

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D.M. Li

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F. Li

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H.B. Li

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J.C. Li

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Jin Li

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K. Li

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K. Li

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Lei Li

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P.R. Li

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Q.J. Li

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T. Li

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W.D. Li

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W.G. Li

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X.L. Li

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X.N. Li

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X.Q. Li

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Z.B. Li

ai

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H. Liang

as

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Y.F. Liang

ag

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Y.T. Liang

an

,

D.X. Lin

m

,

B.J. Liu

a

,

C.L. Liu

d

,

C.X. Liu

a

,

F.H. Liu

af

,

Fang Liu

a

,

Feng Liu

e

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H.B. Liu

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H.H. Liu

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H.M. Liu

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J. Liu

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J.P. Liu

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K. Liu

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K.Y. 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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Zhiqiang Liu

a

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Zhiqing Liu

u

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H. Loehner

w

,

X.C. Lou

a

,

3

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G.R. Lu

n

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H.J. Lu

p

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H.L. Lu

a

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J.G. Lu

a

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Y. Lu

a

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Y.P. Lu

a

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C.L. Luo

z

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M.X. Luo

ba

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T. Luo

ap

,

X.L. Luo

a

,

M. Lv

a

,

X.R. Lyu

ao

,

∗

,

F.C. Ma

y

,

H.L. Ma

a

,

Q.M. Ma

a

,

S. Ma

a

,

T. Ma

a

,

X.Y. Ma

a

,

F.E. Maas

m

,

M. Maggiora

av

,

ax

,

Q.A. Malik

au

,

Y.J. Mao

ac

,

Z.P. Mao

a

,

J.G. Messchendorp

w

,

J. Min

a

,

T.J. Min

a

,

R.E. Mitchell

r

,

X.H. Mo

a

,

Y.J. Mo

e

,

H. Moeini

w

,

C. Morales Morales

m

,

K. Moriya

r

,

N.Yu. Muchnoi

h

,

1

,

H. Muramatsu

aq

,

Y. Nefedov

v

,

F. Nerling

m

,

I.B. Nikolaev

h

,

1

,

Z. Ning

a

,

S. Nisar

g

,

X.Y. Niu

a

,

S.L. Olsen

ad

,

Q. Ouyang

a

,

S. Pacetti

t

,

M. Pelizaeus

c

,

H.P. Peng

as

,

K. Peters

i

,

J.L. Ping

z

,

R.G. Ping

a

,

R. Poling

aq

,

M. Qi

aa

,

S. Qian

a

,

C.F. Qiao

ao

,

L.Q. Qin

ae

,

N. Qin

az

,

X.S. Qin

a

,

Y. Qin

ac

,

Z.H. Qin

a

,

J.F. Qiu

a

,

K.H. Rashid

au

,

C.F. Redmer

u

,

M. Ripka

u

,

G. Rong

a

,

X.D. Ruan

k

,

A. Sarantsev

v

,

4

,

K. Schoenning

ay

,

S. Schumann

u

,

W. Shan

ac

,

M. Shao

as

,

C.P. Shen

b

,

X.Y. Shen

a

,

H.Y. Sheng

a

,

M.R. Shepherd

r

,

W.M. Song

a

,

X.Y. Song

a

,

S. Spataro

av

,

ax

,

B. Spruck

an

,

G.X. Sun

a

,

J.F. Sun

n

,

S.S. Sun

a

,

Y.J. Sun

as

,

Y.Z. Sun

a

,

Z.J. Sun

a

,

Z.T. Sun

as

,

C.J. Tang

ag

,

X. Tang

a

,

I. Tapan

am

,

E.H. Thorndike

ar

,

M. Tiemens

w

,

D. Toth

aq

,

M. Ullrich

an

,

I. Uman

al

,

http://dx.doi.org/10.1016/j.physletb.2014.05.071

0370-2693/©2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/3.0/).Fundedby SCOAP3_.

G.S. Varner

ap

,

B. Wang

ab

,

D. Wang

ac

,

D.Y. Wang

ac

,

K. Wang

a

,

L.L. Wang

a

,

L.S. Wang

a

,

M. Wang

ae

,

P. Wang

a

,

P.L. Wang

a

,

Q.J. Wang

a

,

S.G. Wang

ac

,

W. Wang

a

,

X.F. Wang

aj

,

Y.D. Wang

s

,

Y.F. Wang

a

,

Y.Q. Wang

u

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Z. Wang

a

,

Z.G. Wang

a

,

Z.H. Wang

as

,

Z.Y. Wang

a

,

D.H. Wei

j

,

J.B. Wei

ac

,

P. Weidenkaff

u

,

S.P. Wen

a

,

M. Werner

an

,

U. Wiedner

c

,

M. Wolke

ay

,

L.H. Wu

a

,

N. Wu

a

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Z. Wu

a

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L.G. Xia

aj

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Y. Xia

q

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D. Xiao

a

,

Z.J. Xiao

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Y.G. Xie

a

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Q.L. Xiu

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,

G.F. Xu

a

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L. Xu

a

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Q.J. Xu

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Q.N. Xu

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X.P. Xu

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Z. Xue

a

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L. Yan

as

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W.B. Yan

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W.C. Yan

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Y.H. Yan

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H.X. Yang

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L. Yang

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Y. Yang

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Y.X. Yang

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H. Ye

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M. Ye

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C.Z. Yuan

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Z.P. Zhang

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Ling Zhao

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T.C. Zhao

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B. Zheng

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J.P. Zheng

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Y.H. Zheng

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B. Zhong

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L. Zhou

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Li Zhou

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X. Zhou

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X.K. Zhou

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X.R. Zhou

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X.Y. Zhou

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K. Zhu

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K.J. Zhu

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X.L. Zhu

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Y.C. Zhu

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J. Zhuang

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B.S. Zou

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J.H. Zou

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InstituteofHighEnergyPhysics,Beijing100049,People’sRepublicofChina b_{BeihangUniversity,Beijing100191,People’sRepublicofChina}

c_{BochumRuhr-University,D-44780Bochum,Germany} d_{CarnegieMellonUniversity,Pittsburgh,PA 15213,USA}

e_{CentralChinaNormalUniversity,Wuhan430079,People’sRepublicofChina}

f_{ChinaCenterofAdvancedScienceandTechnology,Beijing100190,People’sRepublicofChina} g_{COMSATSInstituteofInformationTechnology,DefenceRoad,OffRaiwindRoad,54000Lahore,Pakistan} h_{G.I.BudkerInstituteofNuclearPhysicsSBRAS(BINP),Novosibirsk630090,Russia}

i_{GSIHelmholtzcentreforHeavyIonResearchGmbH,D-64291Darmstadt,Germany} j_{GuangxiNormalUniversity,Guilin541004,People’sRepublicofChina}

k_{GuangXiUniversity,Nanning530004,People’sRepublicofChina} l_{HangzhouNormalUniversity,Hangzhou310036,People’sRepublicofChina} m_{HelmholtzInstituteMainz,Johann-Joachim-Becher-Weg45,D-55099Mainz,Germany} n_{HenanNormalUniversity,Xinxiang453007,People’sRepublicofChina}

o_{HenanUniversityofScienceandTechnology,Luoyang471003,People’sRepublicofChina} p_{HuangshanCollege,Huangshan245000,People’sRepublicofChina}

q_{HunanUniversity,Changsha410082,People’sRepublicofChina} r_{IndianaUniversity,Bloomington,IN 47405,USA}

s_{INFNLaboratoriNazionalidiFrascati,I-00044,Frascati,Italy} t_{INFNandUniversityofPerugia,I-06100,Perugia,Italy}

u_{JohannesGutenbergUniversityofMainz,Johann-Joachim-Becher-Weg45,D-55099Mainz,Germany} v_{JointInstituteforNuclearResearch,141980Dubna,Moscowregion,Russia}

w_{KVI,UniversityofGroningen,NL-9747AAGroningen,TheNetherlands} x_{LanzhouUniversity,Lanzhou730000,People’sRepublicofChina} y_{LiaoningUniversity,Shenyang110036,People’sRepublicofChina} z_{NanjingNormalUniversity,Nanjing210023,People’sRepublicofChina} aa_{NanjingUniversity,Nanjing210093,People’sRepublicofChina} ab_{Nankaiuniversity,Tianjin300071,People’sRepublicofChina} ac_{PekingUniversity,Beijing100871,People’sRepublicofChina} ad_{SeoulNationalUniversity,Seoul,151-747Korea}

ae_{ShandongUniversity,Jinan250100,People’sRepublicofChina} af_{ShanxiUniversity,Taiyuan030006,People’sRepublicofChina} ag_{SichuanUniversity,Chengdu610064,People’sRepublicofChina} ah_{SoochowUniversity,Suzhou215006,People’sRepublicofChina} ai_{SunYat-SenUniversity,Guangzhou510275,People’sRepublicofChina} aj_{TsinghuaUniversity,Beijing100084,People’sRepublicofChina} ak_{AnkaraUniversity,DogolCaddesi,06100Tandogan,Ankara,Turkey} al_{DogusUniversity,34722Istanbul,Turkey}

am_{UludagUniversity,16059Bursa,Turkey} an_{UniversitaetGiessen,D-35392Giessen,Germany}

ao_{UniversityofChineseAcademyofSciences,Beijing100049,People’sRepublicofChina} ap_{UniversityofHawaii,Honolulu,HI 96822,USA}

aq_{UniversityofMinnesota,Minneapolis,MN 55455,USA} ar_{UniversityofRochester,Rochester,NY 14627,USA}

as_{UniversityofScienceandTechnologyofChina,Hefei230026,People’sRepublicofChina} at_{UniversityofSouthChina,Hengyang421001,People’sRepublicofChina}

au_{UniversityofthePunjab,Lahore-54590,Pakistan} av_{UniversityofTurin,I-10125,Turin,Italy}

aw_{UniversityofEasternPiedmont,I-15121,Alessandria,Italy} ax_{INFN,I-10125,Turin,Italy}

ay_{UppsalaUniversity,Box516,SE-75120Uppsala,Sweden} az_{WuhanUniversity,Wuhan430072,People’sRepublicofChina} ba_{ZhejiangUniversity,Hangzhou310027,People’sRepublicofChina} bb_{ZhengzhouUniversity,Zhengzhou450001,People’sRepublicofChina}

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Articlehistory:

Received18April2014

Receivedinrevisedform16May2014 Accepted23May2014

Availableonline29May2014 Editor:L.Rolandi

Keywords:

BESIII

D0_–D0_oscillation Strongphasedifference

We study D0_D0_{pairs produced in e}+_e−_{collisions at} √_{s=3.773 GeV using a data sample of 2.92 fb}−1

collected with the BESIII detector. We measured the asymmetry ACP

Kπ of the branching fractions of D→

K−

π

+in CP-odd

and

CP-even

eigenstates to be

(12.7 ±1.3 ±0.7)×10−2_{. A}CP

Kπ can be used to extract

the strong phase difference δKπ between the doubly Cabibbo-suppressed process D0→K−

π

+and the

Cabibbo-favored process D0_→K−

_π

+_{. Using world-average values of external parameters, we obtain} cosδKπ=1.02 ±0.11 ±0.06 ±0.01. Here, the first and second uncertainties are statistical and systematic,

respectively, while the third uncertainty arises from the external parameters. This is the most precise measurement of δKπ to date.

©2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3_.

1. Introduction

Withinthe StandardModel,the short-distance contributionto

D0_–D0_{oscillationsishighlysuppressedbytheGIMmechanism[1]}

andby the magnitudeofthe CKM matrix elements [2]involved. However,longdistanceeffects,whichcannotbereliablycalculated, will also affect the size of mixing. Studies of D0–D0 oscillation provideknowledge ofthe sizeof theselong-distanceeffects and, given improved calculations, can contribute to searches for new physics[3].Inaddition,improvedconstraintsoncharmmixingare importantforstudiesofCP violation(CPV)incharmphysics.

Charmmixingisdescribedbytwodimensionlessparameters x

=

2M1

−

M2

Γ

1

+ Γ

2

y

=

Γ

1

− Γ

2

Γ

1

+ Γ

2

,

whereM1,2 and

Γ1

,2 arethemassesandwidthsofthetwomass

eigenstates in the D0-D0 system. The most precise

determina-tion of the mixing parameters comes from the measurement of

the time-dependent decay rateof the wrong-sign process D0

_→

K+

π

−. These analyses are sensitive to y

≡

ycos

δ

Kπ

−

xsin

δ

Kπ

andx

≡

xcos

δ

Kπ

+

ysin

δ

Kπ [4],where

δ

Kπ is thestrong phase

difference between the doubly Cabibbo-suppressed (DCS) ampli-tudeforD0

→

K−

π

+andthecorrespondingCabibbo-favored(CF) amplitudeforD0

→

K−

π

+.Inparticular,



K−

π

+

|

D0

_



K−

π

+

|

D0

_

= −

re− iδKπ

_,

₍₁₎ where r

=







K−

π

+

|

D 0

_



K−

π

+

|

D0

_



.

Knowledge of

δ

Kπ is important for extracting x and y from x

and y. In addition, a more accurate

δ

Kπ contributes to

preci-siondeterminations ofthe CKM unitarity angle

φ3

6 via the ADS method[5].

Usingquantum-correlated techniques,

δ

Kπ canbe accessed in

themass-thresholdproductionprocess e+e−

→

D0_D0 _{[6].In this}

process,D0 _andD0 _{areinaC -oddquantum-coherentstatewhere}

thetwomesonsnecessarilyhaveoppositeCP eigenvalues[3].Thus,

*

Correspondingauthor.

1 _{AlsoattheNovosibirskStateUniversity,Novosibirsk,630090,Russia.} 2 _{AlsoattheMoscowInstituteofPhysicsandTechnology,Moscow141700,Russia} andattheFunctionalElectronicsLaboratory,TomskStateUniversity,Tomsk,634050, Russia.

3 _{AlsoatUniversityofTexasatDallas,Richardson,TX 75083,USA.} 4 _{AlsoatthePNPI,Gatchina188300,Russia.}

5 _{AlsoattheMoscowInstituteofPhysicsandTechnology,Moscow141700,Russia.} 6 _{γisalsousedintheliterature.}

thresholdproductionprovidesa uniquewaytoidentifythe CP of

oneneutralD byprobingthedecayofthepartnerD.BecauseCPV

in D decays isvery smallcomparedwiththe mixingparameters, we will assume no CPV in our analysis. In this paper, we often referto K−

π

+onlyforsimplicity,butcharge-conjugatemodesare alwaysimpliedwhenappropriate.

WedenotetheasymmetryofCP-taggedD decayratestoK−

π

+

as

A

CP Kπ

≡

B

DS−_→K−π+

−

B

DS+_→K−π+

B

DS−_→K−π+

+

B

DS+_→K−π+

,

(2)

where S

+

(S

−

)denotestheCP-even(CP-odd)eigenstate.To low-estorderinthemixingparameters,wehavetherelation[7,8] 2r cos

δ

Kπ

+

y

= (

1

+

RWS

)

·

A

CPKπ

,

(3)

where RWS is the decay rate ratio of the wrong sign process D0

_→

_K−

_π

+ _{(includingtheDCS decayandD mixingfollowedby}

the CF decay) andthe right sign process D0

→

K−

π

+ (i.e., the CF decay).Here, D0 or D0 referstothestateatproduction.Using external valuesforthe parametersr, y,and RWS,we canextract

δ

Kπ from

A

CP→Kπ .

WeusetheD-taggingmethod[9]toobtainthebranching frac-tions

B

_DS±_→K−π+ as

B

DS±_→K−_π+

=

nK−π+,S± nS±

·

ε

S±

ε

K−π+,S±

.

(4)

Here, nS± and

ε

S± are yields and detection efficiencies of sin-gle tags (ST) of S

±

final states, while nK−π+,S± and

ε

K−π+,S±

are yields and efficiencies of double tags (DT) of (S

±

, K−

π

+) final states, respectively. Based on an 818 pb−1 data sample collected with the CLEO-c detector at

√

s

=

3

.

77 GeV and a morecomplexanalysistechnique,theCLEOCollaborationobtained cos

δ

Kπ

=

0

.

81₋+00..2218−+00..0705 [8]. Using a global fit method including

external inputs for mixing parameters, CLEO obtained cos

δ

Kπ

=

1

.

15+₋0_0..19₁₇+₋0₀._.00₀₈ [8].

In this paper, we present a measurement of

δ

Kπ , using the

quantum correlated productions of D0–D0 mesons at

√

s

=

3

.

773 GeV in e+e− collisions with an integrated luminos-ityof2.92 fb−1 _{[10]collectedwiththeBESIIIdetector[11].} 2. TheBESIIIdetector

The BeijingSpectrometer (BESIII) viewse+e− collisions in the double-ring collider BEPCII. BESIII is a general-purpose detec-tor[11]with93%coverageofthefullsolidangle.Fromthe interac-tionpoint(IP)totheoutside,BESIIIisequippedwithamaindrift chamber (MDC) consisting of 43 layers of drift cells, a time-of-flight(TOF)counterwithdouble-layerscintillatorinthebarrelpart andsingle-layerscintillatorintheend-cappart,anelectromagnetic

Table 1

D decaymodesusedinthisanalysis.

Type Mode Flavored K−π+,K+π− S+ K+K−,π+π−,K0 Sπ0π0,π0π0,ρ0π0 S− K0 Sπ 0 ,K0 Sη,K 0 Sω

calorimeter(EMC)composed of6240CsI(Tl)crystals,a supercon-ductingsolenoidmagnetprovidingamagneticfieldof1.0 Talong the beam direction, and a muon counter containing multi-layer resistiveplatechambersinstalled in thesteel flux-returnyoke of themagnet. TheMDCspatial resolutionisabout135 μm andthe momentumresolutionisabout0.5%forachargedtrackwith trans-versemomentumof1 GeV

/

c.Theenergyresolutionforshowersin theEMCis2.5%at1 GeV.Moredetailsofthespectrometercanbe foundinRef.[11].

3. MCsimulation

MonteCarlo (MC)simulation serves to estimate the detection

efficiency and to understand background components. MC

sam-ples corresponding to about10 times theluminosity ofdata are generatedwitha geant4-based[12]softwarepackage[13],which includessimulationsofthegeometryofthespectrometer and in-teractionsofparticleswiththedetectormaterials. kkmc isusedto modelthebeamenergyspreadandtheinitial-stateradiation(ISR) inthe e+e− annihilations [14]. The inclusiveMC samplesconsist oftheproductionof D D pairswithconsiderationofquantum co-herenceforallmodesrelevanttothisanalysis,thenon-D D decays of

ψ(

3770

)

, the ISR production of low mass

ψ

states, andQED andqq continuum

¯

processes. Knowndecays recordedin the Par-ticleData Group (PDG)[15] are simulated with evtgen [16] and theunknown decayswith lundcharm [17]. Thefinal-state radia-tion(FSR)offchargedtracksistakenintoaccountwiththe photos package[18].MCsamplesofD

→

S

±,

D

→

X ( X denotesinclusive decayproducts)processesareusedtoestimatetheSTefficiencies, andMC samplesof D

→

S

±,

D

→

K

π

processesareusedto esti-matetheDTefficiencies.

4. Dataanalysis

ThedecaymodesusedfortaggingtheCP eigenstatesarelisted in Table 1, where

π

0

_→

_{γ γ}

_,

_η

_→

_{γ γ}

_{, K}0

S

→

π

+

π

− and

ω

→

π

+

π

−

π

0_{.Foreachmode,D candidatesarereconstructedfromall}

possiblecombinationsoffinal-stateparticles,accordingtothe fol-lowingselectioncriteria.

Momenta and impact parameters of charged tracks are

mea-suredbytheMDC.Chargedtracksarerequiredtosatisfy

|

cos

θ

|

<

0

.

93, where

θ

is the polar angle withrespect to the beam axis, andhave a closest approach to the IP within

±

10 cm alongthe beamdirectionand within

±

1 cm in the plane perpendicular to the beamaxis.Particle identification isimplemented by combin-ing the information of normalized energy deposition (dE

/

dx) in

the MDC andthe flight time measurements fromthe TOF. Fora

charged

π

(

K

)

candidate,theprobabilityofthe

π

(

K

)

hypothesisis requiredtobelargerthanthatoftheK

(

π

)

hypothesis.

Photonsare reconstructedasenergydepositionclustersinthe

EMC. The energies of photon candidates must be larger than

25 MeVfor

|

cos

θ

|

<

0

.

8 (barrel)and50 MeVfor0

.

84

<

|

cos

θ

|

<

0

.

92 (end-cap).Tosuppressfakephotonsduetoelectronicnoiseor beambackgrounds,theshowertimemustbelessthan700 nsfrom the event start time [19]. However, in the case that no charged trackisdetected, theeventstarttime is notreliable,andinstead the shower time must be within

±

500 ns from the time ofthe mostenergeticshower.

Table 2

Requirementson E fordifferentD reconstructionmodes.

Mode Requirement (GeV)

K+K− −0.025< E<0.025 π+π− −0.030< E<0.030 K0 Sπ0π0 −0.080< E<0.045 π0_π0 ₋₀ .080< E<0.040 ρ0_π0 _{−0.070< E<0.040} K0 Sπ0 −0.070< E<0.040 K0 Sη −0.040< E<0.040 K0 Sω −0.050< E<0.030 K±π∓ −0.030< E<0.030

Our

π

0 _and

_η

_{candidates are selected from pairs of}

pho-tons with the requirement that at least one photon candidate reconstructed in the barrel is used. The mass windows imposed are 0

.

115 GeV

/

c2

_<

_{mγ γ}

_<

₀

_.

_{150 GeV}

_/

_c2 _for

_π

0 _{candidates and}

0

.

505 GeV

/

c2

<

mγ γ

<

0

.

570 GeV

/

c2 for

η

candidates.Wefurther constrain the invariant mass ofeach photon pairto the nominal

π

0 _or

_η

_{mass,andupdate the fourmomentum ofthe candidate}

accordingtothefitresults.

The K0_S candidates arereconstructed via K0_S

→

π

+

π

− usinga vertex-constrainedfittoallpairsofoppositelychargedtracks,with noparticleidentificationrequirements.Thesetrackshavealooser IP requirement:their closest approachto theIP isrequiredto be lessthan20 cmalongthebeamdirection,withnorequirementin the transverse plane. The

χ

2 _{of the vertexfit is required to be}

lessthan100. Inaddition,a secondfit isperformed,constraining the K0_S momentum to point back to the IP. The flight length, L,

obtainedfromthisfitmustsatisfy L

/

σ

L

>

2,where

σ

L isthe esti-matederroronL. Finally,theinvariantmassofthe

π

+

π

−pairis requiredtobewithin

(

0

.

487

,

0

.

511

)

GeV

/

c2,whichcorrespondsto threetimestheexperimentalmassresolution.

4.1. SingletagsusingCP modes

For the CP-even and CP-oddmodes, the two variables beam-constrainedmassMBCandenergydifference

E areusedto

iden-tifythesignals,definedasfollows: MBC

≡



E2_beam

/

c4

_{− |}

_p

D

|

2

/

c2

,

E

≡

ED

−

Ebeam

.

Here

pD and ED are the total momentum and energy of the D candidate,andEbeam isthebeamenergy.Signalspeakaroundthe

nominal D mass in MBC and around zero in

E. Boundaries of

E requirementsaresetatapproximately

±

3

σ

,exceptthatthose of modes containing a

π

0 _{are set as (}

₋

₄

_σ

_,

₊

₃

_.

₅

_σ

_{) due to the}

asymmetric distributions. In each event, only the combinationof

D candidateswiththeleast

|

E

|

iskeptpermode.

In the K+K− and

π

+

π

− modes, backgrounds ofcosmic rays andBhabhaeventsareremoved withthefollowingrequirements. First, the two charged tracks used as the CP tag must have a TOF time difference lessthan 5 nsand they must not be consis-tentwithbeingamuonpairoranelectron–positronpair.Second, there must be at least one EMC shower (other than those from the CP tagtracks) withan energylargerthan50 MeVoratleast one additional charged trackdetected in the MDC. In the K0

S

π

0 mode, backgroundsdueto D0

→

ρπ

are negligibleafter restrict-ing thedecaylengthof K0

S with L

/

σ

L

>

2.Inthe

ρ

0

π

0 and K0S

ω

modes, massranges of0

.

60 GeV

/

c2

<

_mπ+π−

<

0

.

95 GeV

/

c2 and 0

.

72 GeV

/

c2

<

_mπ+_π−_π0

<

0

.

84 GeV

/

c2 arerequiredfor identify-ing

ρ

and

ω

candidates,respectively.

Fig. 1. TheMBCdistributionsofthesingle-tag(ST) CP modes.Dataareshownaspointswitherrorbars.Thesolidlinesarethetotalfitsandthedashed linesarethe backgroundcontribution.

Table 3

Yieldsandefficienciesofallsingle-tag(ST)anddouble-tag(DT)modes.First,welist theST(CP mode)yields(nS±)andcorrespondingefficiencies(εS±)andthentheDT modeyields(nKπ ,S±)andefficiencies(εKπ ,S±).Uncertaintiesarestatisticalonly.

ST mode nS± εS±(%) K+K− 56 156±261 62.99±0.26 π+π− 20 222±187 65.58±0.26 KS0π0π0 25 156±235 16.46±0.07 π0_π0 _{7610±156 42.77±0.21} ρπ0 _{41 117±354 36.22±0.21} K0 Sπ 0 _{72 710±291 41} .95±0.21 K0 Sη 10 046±121 35.12±0.20 K0 Sω 31 422±215 17.88±0.10 DT mode nKπ ,S± εKπ ,S±(%) Kπ,K+K− 1671±41 42.33±0.21 Kπ,π+π− 610±25 44.02±0.21 Kπ,K0 Sπ0π0 806±29 12.86±0.13 Kπ,π0_π0 _{213±14 30} .42±0.18 Kπ,ρπ0 _{1240±35 25} .48±0.16 Kπ,K0 Sπ0 1689±41 29.06±0.17 Kπ,K0 Sη 230±15 24.84±0.16 Kπ,K0 Sω 747±27 12.60±0.06

Afterapplyingthecriteriaon

E in

Table 2

inalltheCP modes,

weplot their MBC distributionsin Fig. 1,wherethe peaksatthe

nominal D0 _{mass are evident. Maximum likelihood fits to the}

events in Fig. 1 are performed, where in each mode the signals aremodeledwiththereconstructedsignalshapeinMCsimulation convoluted with a smearing Gaussian function, and backgrounds are modeled with the ARGUS function [20]. The Gaussian func-tions are supposed to compensate for the resolution differences betweendataandMC simulation.Basedonthefitresults,the

es-timated yields of the CP modes are givenin Table 3, along with theirMC-determineddetectionefficiencies.

4.2. DoubletagsoftheK−

π

+andCP modes

In the surviving ST CP modes, we reconstruct D

→

K−

π

+

amongtheunusedchargedtracks.TheD

→

K−

π

+candidatemust pass the

E requirement listed in Table 2; in the case of mul-tiple candidates, the one with the smallest

|

E

|

is chosen. The DT signals peak at the nominal D0 _{mass in both MBC(S}

_±)

_and MBC(K

π

)

.Toextractthesignalyields,two-dimensionalmaximum likelihood fits to the distributions of MBC(S

±)

vs. MBC(K

π

)

are performed. The signal shapes are derived from MC simulations,

and the background shapes contain continuum background and

mis-partitioning background where some final-state particles are interchanged between the D0 and D0 candidates in the recon-structionprocess. Fig. 2 showsan exampleofthe resultsforone sampleDTcombination,(K

π

,K0_S

π

0_).

_{Table 3}

_{liststheyieldsofthe}

DTmodesandtheircorresponding detectionefficienciesas deter-minedwithMCsimulations.

5. PuritiesoftheCP modes

It is necessary to determine the CP-purity of our ST modes. For the K0

S

π

0

(

K0S

η

)

mode, the issue is the background un-der the K0_S peak. We use the sideband regions of the K_S0 mass,

[

0

.

470

,

0

.

477

]

GeV

/

c2 and

[

0

.

521

,

0

.

528

]

GeV

/

c2, in the _mπ+_π− distributions, to estimate the backgrounds from

π

+

π

−

π

0

(

π

+

π

−

η

)

.The purityis estimatedtobe 98.5% (almost100%)for the K0_S

π

0

₍

_K0

S

η

)

mode.Forthe K0S

ω

, K0S

π

0

π

0 and

ρ

0

π

0 modes, due to the complexity of the involved non-resonant and reso-nant processes,weevaluate theCP-puritydirectly fromourdata.

Fig. 2. AnillustrationofourDTyieldanalysis,usingtheKπ, K0

Sπ0 mode.Ascatterplot(left)ofthetwoMBC valuesisdisplayed,alongwithprojectionsofthe two-dimensionalfittothesamedata(middleandright).Thesolidlinesarethetotalfitsandthedashedlinesarethebackgroundcontribution.

Table 4

Thesame-CP yieldsandthecorrespondingefficienciesusedinourCP-puritytests. Theuncertaintiesarestatisticalonly.ThelastcolumnpresentstheobtainedfSand

numbersintheparenthesesarethelowerlimitsofthe fSat90%confidencelevel.

Mode (S,S) nS,S εS,S(%) fS(%) K+K−,K0 Sπ0π0 8±3 11.80±0.11 91.6±16.7(>86.8) K+K−,ρ0_π0 _{13±8 24.44±0.16 84.0±12.6(>70.6)} K0 Sπ0,K0Sω 7±3 6.77±0.08 94.6±8.0(>90.6)

We useadditionalDTcombinations,withacleanCP-tagin combi-nationwiththemodewewishtostudy.Welookforsignalswhere bothD mesonsdecaywithequalCP eigenvalue.IfCP isconserved, thesame-CP processisprohibitedinthe quantum-correlated D D

productionatthreshold,unlessourstudiedCP modesarenotpure. Ifwetake fS asthefractionoftherightCP componentsintheCP tagmode,wehavetheyieldsofthesame-CP processwrittenas nS,S

= (

1

−

fS

)

·

nS

·

B

D→S

·

ε

S,S

/

ε

S

,

wheremode Sischosentobe(nearly)pureinitsCP eigenstate.

Wetakethemodes K0_S

π

0 _(S

₋

_)andK+_K−_(S

₊

_)asourclean CP tags to test the S

−

and S

+

purities of our ST modes, re-spectively. We analyze our data to find

(

S

,

S

)

events using se-lectioncriteriasimilartothosedescribedinSection 4.2.However, a simplified procedure is used to obtain the yields. We imple-ment a one-dimensional fit to the MBC(S

)

distributions for the signal mode S of interest,while restrictingthe MBC(S

)

distribu-tionsforthetaggingmodesSinthesignalregion1

.

860 GeV

/

c2

<

MBC(K+K−

)

<

1

.

875 GeV

/

c2 _{and 1}

_.

_{855 GeV}

_/

_c2

_<

_MBC(K0

S

π

0

)

<

1

.

880 GeV

/

c2. The DT signals are described with the signal MC shape convolutedwith aGaussian function, andbackgrounds are modeledwiththeARGUSfunction.

Fig. 3

showstheMBC(S

)

distri-butionsinthe DTeventsandthefits tothedistributions.

Table 4

liststheDTyieldsandthecorrespondingdetectionefficiencies.In thetestedCP modes,theobservednumbersofthesame-CP events are quite small and nearly consistent withzero, which indicates that fS iscloseto1.Thisone-dimensionalfitmayletcertain peak-ingbackgroundssurvive;however,anover-estimatednS,S leadsto amoreconservativeevaluationof fS.

6. Systematicuncertainties

Incalculating

A

CP_{Kπ ,}uncertaintiesofmostofefficiencies cancel out,suchasthosefortracking,particleidentificationand

π

0

_/

_η

_/

_K0

S reconstruction. The efficiency differences

S±

= (

εKεπS±,S±

)

of

K−

π

+betweendataandMCsimulationarestudiedforthemodes

S

±

.Weusecontrolsamplestostudy

S±.TheK−

π

+finalstateis usedforstudying

S±intheK+K−and

π

+

π

−modes;K−

π

+

π

0

isused forthe

π

0

_π

0_,

_ρπ

0_{, K}0

S

π

0 and K0S

η

modes; K−

π

+

π

0

π

0 isused forthe K0_S

π

0

_π

0 _{mode; and K}+

_π

−

_π

−

_π

+ _isusedforthe K0_S

ω

mode.Wedetermine

S±indifferentCP-tagmodesby com-paringtheratiooftheDTyieldstotheSTyieldsbetweendataand

MC. Wefindthat

S± areat1%levelfordifferentCP-tagmodes. Intheformulaof

A

CP_{Kπ ,}thedependenceof

S±ontheCP modeis not canceledout. Theresultingsystematicuncertaintyon

A

CP_{Kπ is} 0

.

2

×

10−2_.

Some systematics arise from effects which act among several

CP modessimultaneously.TheefficiencyofthecosmicandBhabha veto(onlyfortheK K and

π π

modes)isstudiedbasedonthe in-clusiveMCsample.Wecomparetheobtained

A

CP

Kπ withand

with-outthisrequirementandtakethedifferenceof0

.

6

×

10−3_asa

sys-tematic uncertainty.For the CP modesinvolving K0_S, CP-violating K0

L

→

π

+

π

−decaysarealsoconsidered.Usingtheknown branch-ing fraction, we find this causes the change on

A

CP_Kπ to be 0

.

8

×

10−3.

Other systematic uncertainties, relevant to

A

CP

Kπ , are listed in Table 5,whichareuncorrelatedamongdifferentCP modes.

The

E requirementsare mode-dependent.Westudypossible biasesofourrequirements bychanging theirvalues; wetake the maximumvariations oftheresultant

B

DS±_→Kπ as systematic

un-certainties.

Fitting the MBC distributions involves knowledge of detector

smearingandtheeffectsofinitial-stateandfinal-stateradiation.In thecaseofSTfits,wescanthesmearingparameterswithinthe er-rorsdeterminedinournominalfits.ThemaximumchangestonS±

are taken asa systematic uncertainty.For the DT fits, we obtain checksonnKπ,S±withone-dimensionalfitsto MBC(S

)

with inclu-sionoffloatingsmearingfunctions.Theoutcomesof

B

_DS±_→Kπ are

consistent with those determined from the two-dimensional fits, andanysmalldifferencesaretreatedassystematicuncertainties.

SystematiceffectsduetotheCP puritiesarechecked,asstated in Section 5. We introduce the CP purities fS in calculating the

B

DS±_→Kπ under differentCP tagging modes andobtain the

cor-rected

B

_DS±_→Kπ .We setthelowerlimitsof fS andtakethe cor-respondingmaximumchangesaspartofsystematicuncertainties. 7. Results

We combine the branching fractions

B

_DS+_→K−_π+ and

B

DS−_→K−π+ in Eq. (4) from two kinds of the CP modes based

on the standard weighted least-square method [15]. Following Eq.(2),weobtain

A

CP

Kπ

= (

12

.

7

±

1

.

3

±

0

.

7

)

×

10−2,wherethefirst

uncertaintyis statisticalandthesecond issystematic. The mode-dependentsystematicsarepropagatedto

A

CP_{Kπ and}combinedwith the mode-correlatedsystematics.The valuesof

A

CP_{Kπ obtained}for the15differentCP mode combinationsarealsocheckedaslisted in

Table 6

.Withinstatisticaluncertainties,theyareconsistentwith eachother.

With externalinputs ofr2

_{= (}

₃

_.

₅₀

_±

₀

_.

₀₄

₎

_×

₁₀−3_{, y}

_{= (}

₆

_.

₇

_±

0

.

9

)

×

10−3 fromHFAG[21]andRWS

= (

3

.

80

±

0

.

05

)

×

10−3from

PDG [15],cos

δ

Kπ is determinedto be 1

.

02

±

0

.

11

±

0

.

06

±

0

.

01,

where thethird uncertaintyisdueto theerrorsintroduced from theexternalinputs.

Fig. 3. TheMBCdistributionsfromourCP-puritytestsusingsame-CP processes(S,S),withfitstothetotal(solid)andbackground(dashed)contributions.BothS andSare CP eigenstatesofD decays.

Table 5

Asummaryofmode-dependentfractionalsystematicuncertainties,inpercent.A“–”meansthesystematicuncertaintyisnegligible.

Source K+K− π+π− K0 Sπ 0_π0 _π0_π0 _ρ0_π0 _K0 Sπ 0 _K0 Sη K 0 Sω E requirement 0.6 0.5 0.9 0.7 1.8 0.7 0.5 1.5 Fitting 0.9 1.0 1.5 1.7 0.2 0.1 0.8 2.0 CP purity – – 1.8 – 3.5 0.6 – 1.2 Quadratic sum 1.1 1.1 2.5 1.8 3.9 0.9 0.9 2.8 Table 6 ValuesofACP

Kπ inunitsof10−2extractedfromthe15differentcombinationsofCPdecaymodes.Theerrorsshownarestatisticalonly.

CP− CP+ K+K− π+π− K0 Sπ0π0 π0π0 ρπ0 K0 Sπ0 13.8±1.8 14.5±2.4 10.0±2.3 8.0±3.7 12.2±2.0 KS0η 15.5±3.5 16.3±3.9 11.8±3.8 9.7±4.8 14.0±3.6 K0 Sω 13.5±2.2 14.2±2.8 9.7±2.7 7.7±3.9 11.9±2.4 8. Summary

We employ a CP tagging technique to analyze a sample of

2.92 fb−1 quantum-correlated data of e+e−

→

D0D0 at the

ψ(

3770

)

peak. We measuretheasymmetry

A

CP

Kπ

= (

12

.

7

±

1

.

3

±

0

.

7

)

×

10−2.Usingtheinputsofr2andy fromHFAG[21]andRWS

fromPDG[15],weobtaincos

δ

Kπ

=

1

.

02

±

0

.

11

±

0

.

06

±

0

.

01.The

first uncertainty is statistical, the second is systematic, and the third is dueto the external inputs. Our result isconsistent with previous resultsfromCLEO [8].Our resultis themostprecise to date,andhelpstoconstraintheD0–D0mixingparametersandthe angle

φ3

intheunitaritytriangleoftheCKMmatrix.

Acknowledgements

TheBESIIICollaborationthanksthestaffofBEPCIIandthe com-puting center for their strong support. This work is supported in part by the Ministry of Science and Technology of the Peo-ple’s Republic of China under Contract No. 2009CB825200; Na-tional Natural Science Foundation of China (NSFC) under Con-tractsNos.10625524, 10821063, 10825524,10835001, 10935007, 11125525,11235011, 11275266; JointFundsofthe National Nat-uralScienceFoundation ofChina underContractsNos.11079008, 11179007;theChineseAcademyofSciences(CAS)Large-Scale Sci-entificFacility Program;CAS underContractsNos.KJCX2-YW-N29,

KJCX2-YW-N45; 100 Talents Program of CAS; German Research

FoundationDFGunderContractNo. CollaborativeResearchCenter CRC-1044; IstitutoNazionale diFisica Nucleare, Italy; Ministryof DevelopmentofTurkeyunderContractNo.DPT2006K-120470;U.S. Departmentof Energy underContracts Nos.DE-FG02-04ER41291,

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

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

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