An improved limit for Gamma(ee) of X(3872) and Gamma(ee) measurement of psi(3686)

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

An

improved

limit

for



_ee

of

X

(3872)

and



_ee

measurement

of

ψ (3686)

BESIII

Collaboration

M. Ablikim

a

,

M.N. Achasov

i

,

1

,

X.C. Ai

a

,

O. Albayrak

e

,

M. Albrecht

d

,

D.J. Ambrose

av

,

A. Amoroso

az

,

bb

,

F.F. An

a

,

Q. An

aw

,

J.Z. Bai

a

,

R. Baldini Ferroli

t

,

Y. Ban

ag

,

D.W. Bennett

s

,

J.V. Bennett

e

,

M. Bertani

t

,

D. Bettoni

v

,

J.M. Bian

au

,

F. Bianchi

az

,

bb

,

E. Boger

y

,

8

,

O. Bondarenko

aa

,

I. Boyko

y

,

R.A. Briere

e

,

H. Cai

bd

,

X. Cai

a

,

O. Cakir

ap

,

2

_,

_{A. Calcaterra}

t

_,

G.F. Cao

a

,

S.A. Cetin

aq

,

J.F. Chang

a

,

G. Chelkov

y

,

3

,

G. Chen

a

,

H.S. Chen

a

,

H.Y. Chen

b

,

J.C. Chen

a

,

M.L. Chen

a

,

S.J. Chen

ae

,

X. Chen

a

,

X.R. Chen

ab

,

Y.B. Chen

a

,

H.P. Cheng

q

,

X.K. Chu

ag

,

G. Cibinetto

v

,

D. Cronin-Hennessy

au

,

H.L. Dai

a

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J.P. Dai

aj

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A. Dbeyssi

n

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D. Dedovich

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Z.Y. Deng

a

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A. Denig

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I. Denysenko

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M. Destefanis

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F. De Mori

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Y. Ding

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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

a

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S.X. Du

bf

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P.F. Duan

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J.Z. Fan

ao

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J. Fang

a

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S.S. Fang

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X. Fang

aw

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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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Y. 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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T. Hu

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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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O.B. Kolcu

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B. Kopf

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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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C. Leng

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C.H. Li

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Cheng Li

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J.C. Li

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D.X. Lin

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B.J. Liu

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F.H. Liu

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Fang Liu

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Feng Liu

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H.H. Liu

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H.M. 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

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Zhiqing Liu

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H. Loehner

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H.J. Lu

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J.G. Lu

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Y.P. Lu

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C.L. Luo

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X.L. Luo

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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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L.L. Ma

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Q.M. Ma

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S. Ma

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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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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

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Y.J. Mo

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C. Morales Morales

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K. Moriya

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N.Yu. Muchnoi

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1

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H. Muramatsu

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Y. Nefedov

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F. Nerling

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I.B. Nikolaev

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Z. Ning

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S. Nisar

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S.L. Niu

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X.Y. Niu

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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. Pettersson

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J.L. 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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Z.H. Qin

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J.F. Qiu

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K.H. Rashid

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C.F. Redmer

x

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H.L. Ren

r

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M. Ripka

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G. Rong

a

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X.D. Ruan

l

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V. Santoro

v

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A. Sarantsev

y

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6

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M. Savrié

w

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K. Schoenning

bc

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S. Schumann

x

,

W. Shan

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,

http://dx.doi.org/10.1016/j.physletb.2015.08.013

0370-2693/©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

M. Shao

aw

,

C.P. Shen

b

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P.X. Shen

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X.Y. Shen

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H.Y. Sheng

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W.M. Song

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C.J. Tang

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X. Tang

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I. Tapan

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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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S.P. Wen

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U. Wiedner

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M. Wolke

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L.H. Wu

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L.G. Xia

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

c_{BeijingInstituteofPetrochemicalTechnology,Beijing102617,People’sRepublicofChina} d_{BochumRuhr-University,D-44780Bochum,Germany}

e_{CarnegieMellonUniversity,Pittsburgh,PA 15213,USA}

f_{CentralChinaNormalUniversity,Wuhan430079,People’sRepublicofChina}

g_{ChinaCenterofAdvancedScienceandTechnology,Beijing100190,People’sRepublicofChina}

h_{COMSATSInstituteofInformationTechnology,Lahore,DefenceRoad,OffRaiwindRoad,54000Lahore,Pakistan} i_{G.I.BudkerInstituteofNuclearPhysicsSBRAS(BINP),Novosibirsk630090,Russia}

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

l_{GuangXiUniversity,Nanning530004,People’sRepublicofChina}

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

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

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

t_{INFNLaboratoriNazionalidiFrascati,I-00044,Frascati,Italy} u_{INFNandUniversityofPerugia,I-06100,Perugia,Italy} v_{INFNSezionediFerrara,I-44122,Ferrara,Italy} w_{UniversityofFerrara,I-44122,Ferrara,Italy}

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

z_{JustusLiebigUniversityGiessen,II.PhysikalischesInstitut,Heinrich-Buff-Ring16,D-35392Giessen,Germany} aa_{KVI-CART,UniversityofGroningen,NL-9747AAGroningen,TheNetherlands}

ab_{LanzhouUniversity,Lanzhou730000,People’sRepublicofChina} ac_{LiaoningUniversity,Shenyang110036,People’sRepublicofChina} ad_{NanjingNormalUniversity,Nanjing210023,People’sRepublicofChina} ae_{NanjingUniversity,Nanjing210093,People’sRepublicofChina} af_{NankaiUniversity,Tianjin300071,People’sRepublicofChina} ag_{PekingUniversity,Beijing100871,People’sRepublicofChina} ah_{SeoulNationalUniversity,Seoul,151-747,RepublicofKorea} ai_{ShandongUniversity,Jinan250100,People’sRepublicofChina}

aj_{ShanghaiJiaoTongUniversity,Shanghai200240,People’sRepublicofChina} ak_{ShanxiUniversity,Taiyuan030006,People’sRepublicofChina}

al_{SichuanUniversity,Chengdu610064,People’sRepublicofChina} am_{SoochowUniversity,Suzhou215006,People’sRepublicofChina} an_{SunYat-SenUniversity,Guangzhou510275,People’sRepublicofChina} ao_{TsinghuaUniversity,Beijing100084,People’sRepublicofChina} ap_{IstanbulAydinUniversity,34295Sefakoy,Istanbul,Turkey} aq_{DogusUniversity,34722Istanbul,Turkey}

ar_{UludagUniversity,16059Bursa,Turkey}

as_{UniversityofChineseAcademyofSciences,Beijing100049,People’sRepublicofChina} at_{UniversityofHawaii,Honolulu,HI 96822,USA}

au_{UniversityofMinnesota,Minneapolis,MN 55455,USA} av_{UniversityofRochester,Rochester,NY 14627,USA}

aw_{UniversityofScienceandTechnologyofChina,Hefei230026,People’sRepublicofChina} ax_{UniversityofSouthChina,Hengyang421001,People’sRepublicofChina}

ay_{UniversityofthePunjab,Lahore-54590,Pakistan} az_{UniversityofTurin,I-10125,Turin,Italy}

ba_{UniversityofEasternPiedmont,I-15121,Alessandria,Italy} bb_{INFN,I-10125,Turin,Italy}

bc_{UppsalaUniversity,Box516,SE-75120Uppsala,Sweden} bd_{WuhanUniversity,Wuhan430072,People’sRepublicofChina} be_{ZhejiangUniversity,Hangzhou310027,People’sRepublicofChina} bf_{ZhengzhouUniversity,Zhengzhou450001,People’sRepublicofChina}

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Articlehistory:

Received11May2015

Receivedinrevisedform20July2015 Accepted4August2015

Availableonline7August2015 Editor:V.Metag Keywords: X(3872) ψ(3686) ee Charmoniumspectroscopy BESIII

Using thedatasetstakenatcenter-of-massenergiesabove4 GeVbytheBESIII detectorattheBEPCII

storage ring, we search for the reaction e+e−→

γ

ISRX(3872)→

γ

ISR

π

+

π

−J/ψ via the Initial State

Radiation technique. The production of aresonance with quantum numbers JPC₌₁++ _{such as the}

X(3872) viasingle photon e+e− annihilation isforbidden, but isallowed by anext-to-leading order

boxdiagram.WedonotobserveasignificantsignalofX(3872),andthereforegiveanupperlimitforthe

electronic widthtimesthe branchingfractioneeX(3872)B(X(3872)→

π

+

π

−J/ψ)<0.13 eV atthe 90%

confidencelevel.Thismeasurementimprovesuponexistinglimitsbyafactorof46.Usingthesamefinal

state,wealsomeasuretheelectronicwidthoftheψ(3686)tobeeeψ (3686)=2213±18stat±99syseV.

©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense

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

1. Introduction

The X

(

3872

)

resonance was observed in 2003by Belle [1] in thedecaychannel

π

+

π

−J

/ψ

.Theexistenceofthisstatewaslater confirmedbyseveralother experiments[2–6].The observationof the decay channel X

(

3872

)

→

γ

J

/ψ

implies that the state has even C-parity [5,7,8]. The quantum numbers were finally deter-minedtobe JPC

=

1++ [5,9].However,theintrinsicnatureofthe resonance is still unknown and has led to many conjectures. It is a good candidate for a tetraquark state but also for a meson moleculeasitsmassisclosetothe D0_D

¯

∗0_{threshold[10].The}

re-centobservationofthedecay Y

(

4260

)

→

γ

X

(

3872

)

byBESIII [6] impliesthatthe X

(

3872

)

couldbeamesonmolecule,assuggested by a model dependent calculation [11]. On the other hand, the largedecay rateof X

(

3872

)

→

γ

ψ(

3686

)

observedby BaBarand LHCb, comparedto X

(

3872

)

→

γ

J

/ψ

hintsat a tetraquark state explanation[8,12,13].Oneoftheinterestingquantities,whichmay helptorevealthestructureofthe X

(

3872

)

isitselectronic width



ee.A recentorder-of-magnitudecalculationusingaVectorMeson Dominance model predicts



eeX(3872)

≈

0

.

03 eV [14], without any prior assumption regarding the nature ofthe X

(

3872

)

.For com-parison,calculationsforthe



ee oftheordinary1++ charmonium state

χ

c1 have beencarried out [15] andthe electronic widthis foundtobeintherangebetween0

.

044 eV and0

.

46 eV.Thiswas alsoconfirmedinamorerecentcalculation[14].

*

Correspondingauthor.

E-mailaddress:ripka@uni-mainz.de(M. Ripka).

1 _{AlsoattheNovosibirskStateUniversity,Novosibirsk,630090,Russia.} 2 _{AlsoatAnkaraUniversity,06100Tandogan,Ankara,Turkey.}

3 _{AlsoattheMoscowInstituteofPhysicsandTechnology,Moscow141700,Russia}

andattheFunctionalElectronicsLaboratory,TomskStateUniversity,Tomsk,634050, Russia.

4 _{CurrentlyatIstanbulArelUniversity,34295Istanbul,Turkey.} 5 _{AlsoattheUniversity ofTexasatDallas,Richardson,TX 75083,USA.} 6 _{AlsoattheNRC“KurchatovInstitute”,PNPI,188300,Gatchina,Russia.} 7 _{AlsoatBogaziciUniversity,34342Istanbul,Turkey.}

8 _{AlsoattheMoscowInstituteofPhysicsandTechnology,Moscow141700,Russia.}

Fig. 1. ISR production of X(3872)via a box diagram.

The currentupperlimit for



eeX(3872) isatthe

O(

102

)

eV level [16],whichis threeorders ofmagnitudelargerthan the theoret-ical prediction.The aim of this work is to obtain a significantly improvedexperimental value fortheelectronic widthof X

(

3872

)

thatmaybecontrastedwithpredictionsof



ee withinvarious the-oreticalmodelsmakingdifferentassumptionsregardingthenature oftheX

(

3872

)

.

The productionof a 1++ resonance has never been observed in e+e− annihilation sofar.Such a processmayoccur viaa two-photon box diagram as depicted in Fig. 1. In order to search for a possible signal we analyze data taken by the BESIII de-tector at center-of-mass (c.m.) energies above 3.872 GeV, using the Initial State Radiation (ISR) technique. The ISR photon re-duces the available c.m. energy, such that the X

(

3872

)

can be produced resonantly via the two-photon process. In the process

e+e−

→

γISR

X

(

3872

)

we search for the X

(

3872

)

in its decay to

π

+

π

−J

/ψ

with J

/ψ

→ 

+



−(



=

μ

ande).The

π

+

π

−J

/ψ

mass spectrumisexpectedtobedominatedbythewell knownprocess

Table 1

Valuesfortheintegrals(Iψ (3686)andIX(3872)),theefficiencies(ψ (3686)andX(3872)),theeventyieldNψ (obs3686)andtheelectronicwidths( ψ (3686)

ee and X(3872)

ee B(X(3872)→

π+π−J/ψ)).Theerrorsshownarestatisticalonly.

c.m. energy [GeV] 4.009 4.230 4.260 4.360 L[pb−1_{] 482 1092 826 540} Iψ (3686)[pb/keV] 310 172 161 133 IX(3872)[pb/keV] 671 247 225 174 εψ (3686) 0.303 0.286 0.286 0.282 εX(3872) 0.314 0.324 0.325 0.327 Nψ (2S) _{4168±65 5026±71 3547±60 1846±43} eeψ (3686)[eV] 2198±34 2232±32 2223±38 2176±51 eeX(3872)B(X(3872)→π+π−J/ψ)at 90% C.L. [eV] 0.630 0.314 0.319 0.646

2. BESIIIdetector,dataandMonteCarlo

BESIIIis a generalpurposedetector,covering 93% ofthe solid angle.Itisoperatingatthee+e−double-ringcolliderBEPCII.A de-taileddescriptionofthefacilities isgiveninRef.[18].BESIII con-sists of four main components: (a) The helium-based 43 layer maindrift chamber (MDC) provides an average single-hit resolu-tionof135 μm,andamomentumresolutionof0.5%for charged-particleat1 GeV/cina1 Tmagneticfield.(b)Theelectromagnetic calorimeter (EMC) consists of 6240 CsI(Tl) crystals, arrayed in a cylindrical structure (barrel) and two endcaps. The energy reso-lution for 1.0 GeV photons is 2.5% (5%) in the barrel (endcaps), whilethepositionresolutionis6 mm(9 mm)inthebarrel (end-caps).(c) The time-of-fight system (TOF) is constructed of 5 cm thickplasticscintillatorsandincludes88detectorsof2.4 mlength in two layers in the barrel and 96 fan-shaped detectors in the endcaps.Thebarrel(endcap)timeresolutionof80 ps(110 ps) pro-vides2sigmaK

/

π

separationformomentauptoabout1.0 GeV/c. (d)The muoncounter (MUC)consistsof resistiveplatechambers inninebarrelandeightendcaplayers.Itisincorporatedinthe re-turnironofthesuperconductingmagnet.Itspositionresolutionis about2 cm.

AGEANT4[19,20]baseddetectorsimulationpackageisusedto modelthe detectorresponse. This analysisis based onfour data samplestakenatc.m.energiesof4.009 GeV,4.230 GeV,4.260 GeV and4.360 GeVbytheBESIIIdetector.Theintegratedluminosityof each data sample islisted in Table 1. The total integrated lumi-nosityis

L

tot

=

2

.

94 fb−1.We simulatethe e+e−

→

X

(

3872

)

γISR

signalprocess using evtgen[21,22],which invokesthe vectorisr generatormodel[23] fortheISR processandthe common

ρ

J

/ψ

modelforthedecayX

(

3872

)

→

π

+

π

−J

/ψ

.TheMonteCarlo(MC) simulationofthee+e−

→

γISR

ψ(

3686

)

processwasperformed us-ing the phokhara generator [25]. For the background study we simulatethee+e−

→

η

J

/ψ

processwith evtgen andthee+e−

→

γISRπ

+

π

−

π

+

π

−processwith phokhara.

3. Eventselection

Fortheeventselection,werequirefourchargedtrackswithnet chargezero.Thepointofclosestapproachtothee+e−interaction pointisrequiredtobewithin

±

10 cminthebeamdirectionand 1 cmintheplaneperpendiculartothebeamdirection.Asthe J

/ψ

resonancecarriesmostofthetotalmomentum,thefinalstate lep-tonscanbedistinguishedfrompionsbytheir momentainthelab frame.Trackswithmomentum p

>

1 GeV

/

c in thelabframe are identifiedasleptons,whereastrackswithp

<

600 MeV

/

c are iden-tifiedaspions.Theparticleidentificationforleptonsisachievedby measuringtheratiooftheenergydepositedintheEMCdividedby thetrack’smomentum measuredintheMDC(E

/

p).IfE

/

p

>

0

.

4, weassumetheleptontobeanelectron,otherwiseitisconsidered a muon candidate. The E

/

p distributions of data and MC agree well,andMCstudies showthat thebackgroundfor J

/ψ

→

e+e−

is negligible. The resolution of the invariant mass of the lepton pairs is16 MeV

/

c2. We requiretheir invariant mass M

(

+



−

)

to bewithin3

.

05

≤

M

(

+



−

)

≤

3

.

14 GeV

/

c2_{forthe J}

_/ψ

_signal

selec-tion.Furthermoretheopeninganglebetweenthetwopiontracks is required to satisfy cos

α

π π

≤

0

.

6 to remove background from e+e−

→

η

J

/ψ

as well as background from mis-identified elec-tronswhichoriginatefrom

γ

-conversion.Dueto theboostofthe

η

meson in the laboratory frame, the opening angles of its de-cay products are small.The reaction e+e−

→

γ

X

(

3872

)

recently observed byBESIII [6],where thephoton comes fromaradiative transitionoftheY

(

4260

)

,representsanirreduciblebackgroundto oursignalprocess.Toavoidthisbackground,theISRphotonis re-quiredtobeemittedatsmallpolarangles

|

cos

θ

ISR

|

>

0

.

95,almost

colinear to the beamdirection. The photon polar angle distribu-tion of the E1 transition Y

(

4260

)

→

γ

X

(

3872

)

measured in [6] proves thatthisbackgroundcontributioncanbeneglected inthis polaranglerange.SincetheISRphotoncannotbedetectedinthis region of the detector, its energy andpolar angle are calculated fromthemissingmomentumoftheevent(untaggedISRphoton). As thephotonfromtheradiative decaychannelis predominantly emittedatlargepolarangles,anoptimalsignaltobackground ra-tioisobtainedinthisway.AnMCsimulationstudyshowsthatthe

Y

(

4260

)

→

γ

X

(

3872

)

backgroundcan beneglected intheregion ofsmallpolaranglesoftheISRphoton.Toimprovetheresolution of the

π

+

π

−J

/ψ

mass spectrum and to further remove back-ground, a two-constraint (2C) kinematicfit underthe hypothesis ofthe

γ

ISRπ+

π

−



+



−finalstateisperformed.Thetwoconstraints arethe J

/ψ

massfortheleptonpairandthemassofthemissing ISRphoton,whichiszero.Weaccepteventswith

χ

2

2C

<

15. 4.

π

+

π

−J

/ψ

massspectrum

The invariant mass distributions of M

(

π

+

π

−J

/ψ)

for data, signal simulation, and simulation of the dominant background

e+e−

→

η

J

/ψ

are shownin Fig. 2. All the selection criteria

de-scribed above have been applied here. As expected, the mass

spectrum isdominated by the

ψ(

3686

)

resonance.No significant

X

(

3872

)

peakisobservedatanyofthefourc.m.energies.Hence, wesetanupperlimitfortheelectronicwidthofX

(

3872

)

.InFig. 2, thebluedotted histogramrepresents thesignalsimulation ofthe

X

(

3872

)

witharbitrarynormalization.Thebackgroundchannelsof

e+e−

→

π

+

π

−

π

+

π

−

γISR

ande+e−

→

η

J

/ψ

with

η



→

γ π

+

π

−

are found to be negligible in an MC simulation study. The back-groundchannele+e−

→

η

J

/ψ

with

η

→

π

+

π

−

π

0 _{isdisplayedas}

theorangedash-dottedlineinFig. 2.

Unbinnedmaximumlikelihoodfitsareperformedtoextractthe yieldsof

ψ(

3686

)

and X

(

3872

)

eventsateachc.m.energy,where thelineshapesofbackgroundarerepresentedbypolynomial func-tions andthelineshapesof

ψ(

3686

)

and X

(

3872

)

are described bytheMCshapeconvolutedwithaGaussianfunctionwhichtakes intoaccount resolutiondifferencesbetweendataandMC simula-tion.WeusethesameparametersoftheGaussianfunctionforthe

Fig. 2. Theπ+π−J/ψmassdistributionsat(a)√s=4.009 GeV,(b)4.230 GeV,(c)4.260 GeV and(d)4.360 GeV.Dotswitherrorbarsaredata,thesolidredlinesarethe fitcurves,thebluedashedhistogramsareMCsimulatedX(3872)signalevents,whicharenormalizedarbitrarily,andtheorangedot-dashedhistogramsareMCsimulated

ηJ/ψ backgroundevents.

tworesonances.Thefitresultsaredisplayedasthesolidredcurves inFig. 2.The eventyields of

ψ(

3686

)

fromthefitsare shownin Table 1.

5. Calculationof



ee

Themeasuredradiativeeventyield NA oftheprocesse+e−

→

γISR

A canbeexpressedasafunctionofx

≡

1

−

M(π+π_s−J/ψ )2 [26]: dNA

dx

=

W

(

s

,

x

)

ε

A

L

σ

(

e

+_e−

_→

_A

₎

_B

₍

_A

_→

_f

_{) ,}

₍₁₎

where s is the squared c.m. energy, W

(

s

,

x

)

denotes the radi-ator function,

ε

A is the corresponding reconstruction efficiency,

L

is the integrated luminosity,

σ

(

e+e−

→

A

)

is the Born cross section to produce A in e+e− annihilation,

B(

A

→

f

)

=

B(

A

→

π

+

π

−J

/ψ)

B(

J

/ψ

→ 

+



−

)

istheproductofthebranching frac-tionsofA decayingintothefinalstate f .

Therelationshipbetweentheelectronicwidth



ee andtheBorn crosssectionreads:

σ

(

e+e−

→

A

)

=

12

π



ee



tot

(

s

−

M2_A

)

2

+ 

tot2 M2A

,

(2)

wheres

= (

1

−

x

)

s,



ee(



tot)istheelectronic(total)widthofthe

resonanceA,andMAisitsmass.Eq.(1)mustbeintegratedovers inanappropriateregionaroundtheresonance A.Theintegralonly involvesthe Breit–Wigner functionin theBorn cross section and theradiatorfunction.Hence itcan beseparatedfromthe quanti-tiesdeterminedinthemeasurement,suchthattheintegralenters thecalculation oftheelectronic widthasafactordenoted by IA. ThisfactorisgivenbyIA

=

12

π



tot



x2 x1dx W(s,x) (s−M2 A)2+2totM2A .The lim-itsoftheintegralarechosentocoincidewiththesignalregion.

UsingEq.(1),theelectronicwidthtimesthebranchingfraction

B(

A

→

π

+

π

−J

/ψ)

canthenbeobtainedviatherelation



_eeA

B

(

A

→

π

+

π

−J

/ψ )

=

NA

ε

A

L

IA

B

(

J

/ψ

→ 

+



−

)

,

(3)

whichisusedtodeterminethe electronicwidthsof X

(

3872

)

and

ψ(

3686

)

.Asnosignificantsignal isfoundinthecaseof X

(

3872

)

, we calculatean upper limit for



eeX(3872). For thebranching frac-tionswetakethelatestBESIIIvalues

B(ψ(

3686

)

→

π

+

π

−J

/ψ)

=

(

34

.

98

±

0

.

45

)

% and

B(

J

/ψ

→ 

+



−

)

= (

11

.

96

±

0

.

05

)

%[27].The reconstruction efficiencies

ε

A are extracted from the signal MC sample e+e−

→

γISR

X

(

3872

)

and e+e−

→

γISR

ψ(

3686

)

, respec-tively. We apply an additional relative correction factor of 2%, whichstemsfromadata-MCdifference foundinthe

χ

2

distribu-tions.Toobtainthiscorrectionfactor,thenumberofeventsinthe background-free

ψ(

3686

)

mass region

(

3

.

62

<

M

(

π

+

π

−J

/ψ)

<

3

.

75 GeV

/

c2

)

passingthe

χ

2

2C

<

15 requirementrelative toall

re-constructed events in MC is compared to the respective number obtainedfromdata.Allthevaluesfortheefficiencies andthe in-tegrals IA at each c.m. energy point are listed in Table 1. The statisticalerrorsoftheefficienciesarenegligible.Firstwecompute the electronic width of

ψ(

3686

)

, which is denoted by



eeψ (3686). This serves asa benchmark andvalidation of our method,since the electronic width of

ψ(

3686

)

isalready knownwith high ac-curacy [16].Applying thenumbers for

ψ(

3686

)

listed inTable 1 to Eq. (3), we obtain the value for



ψ (ee3686) at each of the four energy points separately, as shown in Table 1. We calculate the error weighted average of the electronic widthof

ψ(

3686

)

from the foursingle measurements in Table 1, whichgives



eeψ (3686)

=

(

2213

±

18stat

)

eV.

Since no X

(

3872

)

signal isobserved,we setan upperlimitat the 90% confidence level (C.L.) for its electronic width. Applying the Bayesianmethod,we performlikelihood scansateach ofthe four data sets of the electronic width times the branching frac-tion, whichisproportional tothe X

(

3872

)

eventyield parameter

Ni accordingtoEq.(3).Thisprovides fourlikelihood curves,that aredenotedbyLi

(

γ

)

,i

=

1

. . .

4,where

γ

= 

eeX(3872)

B(

X

(

3872

)

→

π

+

π

−J

/ψ)

. We look for the values

γ

_iup that yield 90% of the likelihood integral over

γ

from zero to infinity:



γ

up

i

0 d

γ

Li

(

γ

)

=

0

.

9



₀∞d

γ

Li

(

γ

)

. Inorder tocombine thefour measurements, we constructthe likelihood ofthe combinedmeasurement. The four single likelihood curvesare scaled such that they havethe same valueattheirrespectivemaxima.Wetaketheproductofthe like-lihood scan curves of the single measurements. The upper limit

γ

_totup atthe90%C.L.of

γ

isdeterminedfrom

γtotup



0 d

γ

4



i=1 Li

(

γ

)

=

0

.

9 ∞



0 d

γ

4



i=1 Li

(

γ

) .

Weobtain

γ

totup

= 

X(3872) ee

B(

X

(

3872

)

→

π

+

π

−J

/ψ)

=

0

.

125 eV at the90%C.L.

6. Estimationofsystematicuncertainties

The luminosity is measured using large angle Bhabha events, andtheuncertaintyisestimatedtobe1%[28].Theuncertainty re-latedto thetracking efficiencyis1% per charged track[6].Since the final state has four charged tracks, we estimate an uncer-tainty of 4% for the whole event. Applying our J

/ψ

selection both to data and the

ψ(

3686

)

γISR

MC simulation, the obtained event yield differs by 0.2%, which we take as systematic uncer-tainty for the J

/ψ

selection. To correct for differences between dataandMCsimulationinthe

χ

2

2C distribution,anefficiency

cor-rectionof2% was determined.Varyingthe

χ

2

2C selectionand

cal-culating theefficiency correction factoragain ateach energy, we obtaina corresponding uncertainty of0.4% of thecorrection fac-torin theluminosity weighted average. Theintegrals IA have an uncertainty of 0.7%, due to the precision of the numerical inte-gration (0.5%)andthe calculation ofthe radiatorfunction (0.5%). Therelativeuncertainties ofthebranchingfraction

B(ψ(

3686

)

→

π

+

π

−J

/ψ)

and

B(

J

/ψ

→ 

+



−

)

are1.3% and0.5%,respectively. There is no correlation between these branching fractions [27]. We take 1.4% as the systematic uncertainty from the branching fractions for the electronic width of

ψ(

3686

)

. In the calculation of



eeX(3872)

B(

X

(

3872

)

→

π

+

π

−J

/ψ)

onlythe branching fraction

B(

J

/ψ

→ 

+



−

)

appears.Hence, thecorresponding uncertaintyis 0.5%.Toestimate thesystematicuncertaintyduetothewidth as-sumed for X

(

3872

)

, we change the width by

±

0

.

2 MeV

/

c2 _and

repeat the entire fitting procedure. The maximal relative differ-enceofthese resultsfromthe resultobtained withthe standard widthisfoundtobe2.7%intheluminosity-weightedaverage.The detectionefficiency of ISR X

(

3872

)

events was determined from an MC simulation using the vectorisr model [23], since this fi-nalstate isnotavailable inthe phokhara eventgenerator.Onthe otherhand,the ISR

ψ(

3686

)

detectionefficiencywas determined usingthe phokhara event generator, whichsimulates ISR events with0.5%precision[24].ToobtaintheuncertaintyoftheISR sim-ulationwiththe vectorisr model,wecompare theefficienciesof ISR

ψ(

3686

)

eventsgeneratedwiththe phokhara eventgenerator [25]andthe vectorisr module[23].Theluminosity-weighted av-eragedifferenceisfoundtobe3.4%betweenthem,whichistaken assystematicuncertaintyforthe vectorisr model.

For



eeψ (3686)afurthersystematicuncertaintyoccursduetothe choice ofthe fit function. In orderto deal with thisuncertainty, wedeterminethenumberofNMC_{ψ (3686)}usingasecondfitfunction, whichisadoubleGaussianforthe

ψ(

3686

)

peakplusaGaussian

Table 2

Sourcesofsystematicuncertaintiesandtheircontribution(%).

Source σsysX(3872) σψ ( 3686) sys Luminosity 1.0 1.0 Tracking 4.0 4.0 J/ψselection 0.2 0.2 Kinematic fit 0.4 0.4 Integrals IA 0.7 0.7 Branching ratio 0.5 1.4 X(3872)width 2.7 – ISR simulation 3.4 – ψ(3686)fit model – 1.0 Total 6.1 4.5

forthe X

(

3872

)

plusaconstantforbackground.Inthe luminosity-weightedaverage,thisfitmodeldiffersby1.0%,whichistakenas systematicuncertainty.Signal eventswitha hardfinal state radi-ation (FSR)photon arerejectedsince the J

/ψ

mass isconstraint inthekinematicfit.ThusFSReffectsarenegligible.Systematic un-certaintiesfromthebackgroundshapeandthefitrangehavebeen found to be negligible.The full list ofsystematicuncertainties is showninTable 2.Assumingthesourcestobeindependent,the to-tal systematicuncertainty forthe electronic width of X

(

3872

)

is 6

.

1%, while in the case of

ψ(

3686

)

we find a systematic uncer-taintyof4

.

5%.

7. Summary

We have performed a search of the process e+e−

→

γISR

X

(

3872

)

→

γISRπ

+

π

−J

/ψ

using the ISR untagged method,

where the production of X

(

3872

)

in e+e− annihilations is pos-sibleviaatwo-photonboxdiagram.Nosignificant X

(

3872

)

signal is observed in the

π

+

π

−J

/ψ

mass spectrum. We set an upper limit for the electronic width of X

(

3872

)

. By combiningall four datasets,wefinallyobtain



eeX(3872)

B

(

X

(

3872

)

→

π

+

π

−J

/ψ ) <

0

.

13 eV

at the 90% C.L. Here we have multiplied the upper limit by a factor 1

/(

1

−

σsys

)

in order to take the systematic uncertain-ties into account. Our measurement improves upon the current limit



eeX(3872)

B(

X

(

3872

)

→

π

+

π

−J

/ψ)

<

6

.

2 eV at the 90% C.L.

[17] by a factor of 46. If we assume the branching fraction

B(

X

(

3872

)

→

π

+

π

−J

/ψ) >

3% [16,29],weobtain anupperlimit forthe electronic width of X

(

3872

)

to be



eeX(3872)

<

4

.

3 eV. For the firsttime we obtaina value for



eeX(3872) onthe

O(

eV

)

level, whichisthelevelpredictedforordinarycharmoniumstates[15]. However, ourupperlimitisstill largerthan atheoretical calcula-tion[14]whichpredicts



ee



0

.

03 eV.Theresultsshould encour-age theorists to compute the electronic width of X

(

3872

)

under differentassumptionsregardingitsintrinsicnatureandtoconfront thesecalculationswithourmeasurement.Thismightleadtonew insightsregardingthenatureof X

(

3872

)

.

Wehavealsomeasuredtheelectronicwidthofthewell-known

ψ(

3686

)

resonancewiththeresult:



eeψ (3686)

=



2213

±

18stat

±

99sys



eV

.

ThisisinagreementwiththePDG[16]fit,whichis

(

2360

±

40

)

eV. Withasimilaraccuracyastheonereportedin[30],thisisthebest individualmeasurementof



eeψ (3686)todate.

Acknowledgements

The BESIII collaboration thanks the staff of BEPCII and the IHEPcomputingcenterfortheirstrongsupport.Thisworkis

sup-ported in part by the National Key Basic Research Program of China under Contract No. 2015CB856700; National Natural Sci-enceFoundation of China (NSFC) under Contract Nos. 11125525,

11235011,11322544, 11335008,11425524; theChinese Academy

of Sciences (CAS) Large-Scale Scientific Facility Program; Joint Large-Scale Scientific Facility Funds of the NSFC and CAS

un-der Contract Nos. 11179007, U1232201, U1332201; CAS under

Contract Nos. KJCX2-YW-N29, KJCX2-YW-N45; 100 Talents

Pro-gram of CAS; INPAC and Shanghai Key Laboratory for Particle

Physics and Cosmology; German Research Foundation DFG

un-der Contract No. CRC-1044; Seventh Framework Programme of

the European Union under Marie Curie International Incoming

Fellowship Grant Agreement No. 627240; Istituto Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey under ContractNo. DPT2006K-120470;Russian FoundationforBasic Re-searchunderContractNo. 14-07-91152;U.S.DepartmentofEnergy

under Contract Nos. DE-FG02-04ER41291, DE-FG02-05ER41374,

DE-FG02-94ER40823, DESC0010118; U.S. National Science

Foun-dation;UniversityofGroningen(RuG)andtheHelmholtzzentrum

für Schwerionenforschung GmbH (GSI), Darmstadt; WCU

Pro-gram of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0.

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