Measurement of the leptonic decay width of J/psi using initial state radiation

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

leptonic

decay

width

of

J

/ψ

using

initial

state

radiation

BESIII

Collaboration

M. Ablikim

a

,

M.N. Achasov

i

,

6

,

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

,

1

,

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

,

4

,

I. Boyko

y

,

R.A. Briere

e

,

H. Cai

bd

,

X. Cai

a

,

1

_,

_{O. Cakir}

ap

,

2

_,

_{A. Calcaterra}

t

_,

_{G.F. Cao}

a

_,

_{S.A. Cetin}

aq

_,

J.F. Chang

a

,

1

,

G. Chelkov

y

,

4

,

5

,

G. Chen

a

,

H.S. Chen

a

,

H.Y. Chen

b

,

J.C. Chen

a

,

M.L. Chen

a

,

1

,

S.J. Chen

ae

,

X. Chen

a

,

1

,

X.R. Chen

ab

,

Y.B. Chen

a

,

1

,

H.P. Cheng

q

,

X.K. Chu

ag

,

G. Cibinetto

v

,

H.L. Dai

a

,

1

,

J.P. Dai

aj

,

A. Dbeyssi

n

,

D. Dedovich

y

,

Z.Y. Deng

a

,

A. Denig

x

,

I. Denysenko

y

,

M. Destefanis

az

,

bb

,

F. De Mori

az

,

bb

,

Y. Ding

ac

,

C. Dong

af

,

J. Dong

a

,

1

,

L.Y. Dong

a

,

M.Y. Dong

a

,

1

,

S.X. Du

bf

,

P.F. Duan

a

,

E.E. Eren

aq

,

J.Z. Fan

ao

,

J. Fang

a

,

1

,

S.S. Fang

a

,

X. Fang

aw

,

1

,

Y. Fang

a

,

L. Fava

ba

,

bb

,

F. Feldbauer

x

,

G. Felici

t

,

C.Q. Feng

aw

,

1

,

E. Fioravanti

v

,

M. Fritsch

n

,

x

_,

_{C.D. Fu}

a

_,

_{Q. Gao}

a

_,

_{X.Y. Gao}

b

_,

_{Y. Gao}

ao

_,

_{Z. Gao}

aw

,

1

_,

_{I. Garzia}

v

_,

_{C. Geng}

aw

,

1

_,

K. Goetzen

j

,

W.X. Gong

a

,

1

,

W. Gradl

x

,

M. Greco

az

,

bb

,

M.H. Gu

a

,

1

,

Y.T. Gu

l

,

Y.H. Guan

a

,

A.Q. Guo

a

,

L.B. Guo

ad

,

Y. Guo

a

,

Y.P. Guo

x

,

Z. Haddadi

aa

,

A. Hafner

x

,

S. Han

bd

,

Y.L. Han

a

,

X.Q. Hao

o

,

F.A. Harris

at

,

K.L. He

a

,

Z.Y. He

af

,

T. Held

d

,

Y.K. Heng

a

,

1

,

Z.L. Hou

a

,

C. Hu

ad

,

H.M. Hu

a

,

J.F. Hu

az

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bb

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T. Hu

a

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1

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Y. Hu

a

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G.M. Huang

f

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G.S. Huang

aw

,

1

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H.P. Huang

bd

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J.S. Huang

o

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X.T. Huang

ai

,

Y. Huang

ae

,

T. Hussain

ay

,

Q. Ji

a

,

Q.P. Ji

af

,

X.B. Ji

a

,

X.L. Ji

a

,

1

,

L.L. Jiang

a

,

L.W. Jiang

bd

,

X.S. Jiang

a

,

1

,

X.Y. Jiang

af

,

J.B. Jiao

ai

,

Z. Jiao

q

,

D.P. Jin

a

,

1

,

S. Jin

a

,

T. Johansson

bc

,

A. Julin

au

,

N. Kalantar-Nayestanaki

aa

,

X.L. Kang

a

,

X.S. Kang

af

,

M. Kavatsyuk

aa

,

B.C. Ke

e

,

P. Kiese

x

,

R. Kliemt

n

,

B. Kloss

x

,

O.B. Kolcu

aq

,

9

,

B. Kopf

d

,

M. Kornicer

at

,

W. Kuehn

z

,

A. Kupsc

bc

,

J.S. Lange

z

,

M. Lara

s

,

P. Larin

n

,

C. Leng

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,

C. Li

bc

,

C.H. Li

a

,

Cheng Li

aw

,

1

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D.M. Li

bf

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F. Li

a

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1

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G. Li

a

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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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T. Li

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W.D. Li

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W.G. Li

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X.N. Li

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X.Q. Li

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Z.B. Li

an

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H. Liang

aw

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1

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Y.F. Liang

al

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Y.T. Liang

z

,

G.R. Liao

k

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D.X. Lin

n

,

B.J. Liu

a

,

C.X. Liu

a

,

F.H. Liu

ak

,

Fang Liu

a

,

Feng Liu

f

,

H.B. Liu

l

,

H.H. Liu

p

,

H.H. Liu

a

,

H.M. Liu

a

,

J. Liu

a

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J.B. Liu

aw

,

1

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J.P. Liu

bd

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J.Y. Liu

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K. Liu

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K.Y. Liu

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L.D. Liu

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P.L. Liu

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Q. Liu

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S.B. Liu

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X. Liu

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X.X. Liu

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Y.B. Liu

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Z.A. Liu

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1

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Zhiqiang Liu

a

,

Zhiqing Liu

x

,

∗

,

H. Loehner

aa

,

X.C. Lou

a

,

1

,

8

,

H.J. Lu

q

,

J.G. Lu

a

,

1

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R.Q. Lu

r

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Y. Lu

a

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Y.P. Lu

a

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1

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C.L. Luo

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M.X. Luo

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T. Luo

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X.L. Luo

a

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1

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M. Lv

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X.R. Lyu

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F.C. Ma

ac

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H.L. Ma

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L.L. Ma

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Q.M. Ma

a

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T. Ma

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X.N. Ma

af

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X.Y. Ma

a

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F.E. Maas

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M. Maggiora

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Y.J. Mao

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J.G. Messchendorp

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J. Min

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T.J. Min

a

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R.E. Mitchell

s

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X.H. Mo

a

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1

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Y.J. Mo

f

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C. Morales Morales

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K. Moriya

s

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N.Yu. Muchnoi

i

,

6

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H. Muramatsu

au

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Y. Nefedov

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F. Nerling

n

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I.B. Nikolaev

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6

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Z. Ning

a

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S. Nisar

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S.L. Niu

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S.L. Olsen

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Q. Ouyang

a

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1

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S. Pacetti

u

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P. Patteri

t

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M. Pelizaeus

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H.P. Peng

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j

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J. Pettersson

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J.L. Ping

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R.G. Ping

a

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R. Poling

au

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V. Prasad

a

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Y.N. Pu

r

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M. Qi

ae

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S. Qian

a

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1

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C.F. Qiao

as

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L.Q. Qin

ai

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N. Qin

bd

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X.S. Qin

a

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Y. Qin

ag

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Z.H. Qin

a

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1

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J.F. Qiu

a

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K.H. Rashid

ay

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C.F. Redmer

x

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H.L. Ren

r

,

M. Ripka

x

,

G. Rong

a

,

Ch. Rosner

n

,

X.D. Ruan

l

,

http://dx.doi.org/10.1016/j.physletb.2016.08.011

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V. Santoro

v

,

A. Sarantsev

y

,

7

,

M. Savrié

w

,

K. Schoenning

bc

,

S. Schumann

x

,

W. Shan

ag

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M. Shao

aw

,

1

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C.P. Shen

b

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P.X. Shen

af

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X.Y. Shen

a

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H.Y. Sheng

a

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W.M. Song

a

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X.Y. Song

a

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S. Sosio

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S. Spataro

az

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G.X. Sun

a

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J.F. Sun

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1

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Y.Z. Sun

a

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Z.J. Sun

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1

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Z.T. Sun

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C.J. Tang

al

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X. Tang

a

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I. Tapan

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E.H. Thorndike

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M. Tiemens

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L.H. Wu

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a

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

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

e_Carnegie_Mellon_University,_Pittsburgh,_{PA 15213,}_USA

f_Central_China_Normal_University,_Wuhan_430079,_People’s_Republic_of_China

g_China_Center_of_Advanced_Science_and_Technology,_Beijing_100190,_People’s_Republic_of_China

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

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

l_GuangXi_University,_Nanning_530004,_People’s_Republic_of_China

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

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

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

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

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

z_Justus_Liebig_University_Giessen,_II._{Physikalisches}_Institut,_{Heinrich-Buff-Ring}_16,_D-35392_Giessen,_Germany aa_KVI-CART,_University_of_Groningen,_NL-9747_AA_Groningen,_The_Netherlands

ab_Lanzhou_University,_Lanzhou_730000,_People’s_Republic_of_China ac_Liaoning_University,_Shenyang_110036,_People’s_Republic_of_China ad_Nanjing_Normal_University,_Nanjing_210023,_People’s_Republic_of_China ae_Nanjing_University,_Nanjing_210093,_People’s_Republic_of_China af_Nankai_University,_Tianjin_300071,_People’s_Republic_of_China ag_Peking_University,_Beijing_100871,_People’s_Republic_of_China ah_Seoul_National_University,_Seoul,_{151-747, Republic}_of_Korea ai_Shandong_University,_Jinan_250100,_People’s_Republic_of_China

aj_Shanghai_Jiao_Tong_University,_Shanghai_200240,_People’s_Republic_of_China ak_Shanxi_University,_Taiyuan_030006,_People’s_Republic_of_China

al_Sichuan_University,_Chengdu_610064,_People’s_Republic_of_China am_Soochow_University,_Suzhou_215006,_People’s_Republic_of_China an_Sun_Yat-Sen_University,_Guangzhou_510275,_People’s_Republic_of_China ao_Tsinghua_University,_Beijing_100084,_People’s_Republic_of_China ap_Istanbul_Aydin_University,₃₄₂₉₅_Sefakoy,_Istanbul,_Turkey aq_Dogus_University,₃₄₇₂₂_Istanbul,_Turkey

(3)

ar_Uludag_University,₁₆₀₅₉_Bursa,_Turkey

as_University_of_Chinese_Academy_of_Sciences,_Beijing_100049,_People’s_Republic_of_China at_University_of_Hawaii,_Honolulu,_{HI 96822,}_USA

au_University_of_Minnesota,_Minneapolis,_{MN 55455,}_USA av_University_of_Rochester,_Rochester,_{NY 14627,}_USA

aw_University_of_Science_and_Technology_of_China,_Hefei_230026,_People’s_Republic_of_China ax_University_of_South_China,_Hengyang_421001,_People’s_Republic_of_China

ay_University_of_the_Punjab,_{Lahore-54590,}_Pakistan az_University_of_Turin,_I-10125,_Turin,_Italy

ba_University_of_Eastern_Piedmont,_I-15121,_Alessandria,_Italy bb_INFN,_I-10125,_Turin,_Italy

bc_Uppsala_University,_Box_516,_SE-75120_Uppsala,_Sweden bd_Wuhan_University,_Wuhan_430072,_People’s_Republic_of_China be_Zhejiang_University,_Hangzhou_310027,_People’s_Republic_of_China bf_Zhengzhou_University,_Zhengzhou_450001,_People’s_Republic_of_China

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Articlehistory: Received8April2016

Receivedinrevisedform14July2016 Accepted5August2016

Availableonline9August2016 Editor:V.Metag

Keywords: J/ψresonance Electronicwidth Initialstateradiation BESIII

Usingadatasetof2.93 fb−1takenatacenter-of-massenergyof√s=3.773 GeV withtheBESIIIdetector atthe BEPCIIcollider,wemeasure theprocess e+e−→ J/ψ

γ

→

μ

+

μ

−

γ

and determine theproduct ofthe branchingfractionand theelectronicwidth _Bμμ· ee= (333.4±2.5stat±4.4sys) eV. Usingthe

earlier-published BESIIIresult for

B

μμ= (5.973±0.007stat±0.037sys)%,wederivethe J/ψ electronic

width

ee= (5.58±0.05stat±0.08sys)keV.

Theelectronicwidthofthe J

/ψ

resonance

ee

≡

ee

(

J

/ψ)

has

beenmeasuredby BaBar[1]andCLEO-c [2],employing the tech-niqueofInitialStateRadiation(ISR),inwhichoneofthebeam par-ticlesradiatesaphoton.Consequently,theinvariantmassrange be-lowthecenter-of-massenergyofthe

e

+e−colliderbecomes avail-able.Usingadifferentmethod,the kedr experimentalsomeasured itselectronicwidthwithimprovedprecision[3].Inthispaper,we study the process e+e−

→

μ

+

μ

−

γ

using the ISR method with

μ

+

μ

− invariant mass m2μ between 2.8 and 3.4 GeV/c2, which

coversthecharmoniumresonance J

/ψ

.Thecrosssection

σ

J/ψγ

≡

σ

(

e+e−

→

J

/ψ

γ

→

μ

+

μ

−

γ

)

isproportional to

ee

· B

μμ, where

B

μμ

≡

B(

J

/ψ

→

μ

+

μ

−

)

isthe branching fractionofthe muonic

decay of the J

/ψ

resonance. With the precise measurement of

B

μμ from BESIII [4], wehavetheopportunity toobtain

ee with

highprecision. Thedifferential crosssection of

σ

J/ψγ can be ex-pressedintermsofthecenter-of-massenergysquared

s as

d

σ

J/ψ

(s,

m2μ

)

dm2μ

=

2m2μ

s W

(s,m

2μ

)B W

(m

2μ

),

(1)

where

W

(

s

,

m2μ

)

istheradiatorfunction,describingthe

probabil-ity that one of the beam particles emits an ISR photon [5], and

*

Correspondingauthor.

E-mailaddress:liuz@uni-mainz.de(Z. Liu).

1 _Also _at _State _Key _Laboratory _of _Particle _Detection _and _Electronics, _Beijing

100049,Hefei230026,People’sRepublicofChina.

2 _Also_at_Ankara_University,₀₆₁₀₀_Tandogan,_Ankara,_Turkey. 3 _Also_at_Bogazici_University,₃₄₃₄₂_Istanbul,_Turkey.

4 _Also_at_the_Moscow_Institute_of_Physics_and_Technology,_Moscow_141700,_Russia. 5 _Also_at_the _Functional_Electronics_Laboratory,_Tomsk _State_University,_Tomsk,

634050,Russia.

6 _Also_at_the_Novosibirsk_State_University,_Novosibirsk,_630090,_Russia. 7 _Also_at_the_NRC_“Kurchatov_{Institute”,}_PNPI,_188300,_Gatchina,_Russia. 8 _Also_at_the_{University of}_Texas_at_Dallas,_Richardson,_{TX 75083,}_USA. 9 _Currently_at_Istanbul_Arel_University,₃₄₂₉₅_Istanbul,_Turkey.

B W

(

m2μ

)

is the Breit–Wigner function. W

(

s

,

m2μ

)

is calculated

by the phokhara event generator, withan estimatedaccuracy of 0.5%[6].TheBreit–Wignerfunctionis

B W

(m

2μ

)

=

12

π

B

μμ

·

ee

tot

(m

2₂_μ

−

M2_J_/ψ

)

2

₊

_M2 J/ψ

tot2

,

(2)

[7]inwhich

totand

M

J/ψarethe J

/ψ

fullwidthandmass.Both values are taken from the world averages [7]. The cross section

σ

J/ψγ over aspeciﬁed

m

2μ range canbeexpressedusing:

σ

J/ψγ

(s)

=

NJ/ψ

· L

=

ee

· B

μμ

·

I(s), (3)

where

N

J/ψ isthenumberofsignaleventswithinthemassrange afterbackgroundsubtraction,

istheselectioneﬃciencyobtained fromaMonteCarlo(MC)simulation,

L

istheintegrated luminos-ityofthedataset,andI

(

s

)

istheintegral

I(s)

≡

m

max

mmin

2m2μ

s W

(s,m

2μ

)b(m

2μ

)dm

2μ

,

(4)

in which b

(

m2μ

)

≡

B W

(

m2μ

)/

ee

· B

μμ. A mass range between mmin

=

2

.

8 GeV

/

c2 and mmax

=

3

.

4 GeV

/

c2 is chosen in which NJ/ψ isdetermined.

The above equationsdonot take into accountinterference ef-fects of the resonant

μ

+

μ

− production via J

/ψ

and the non-resonant e+e−

→

μ

+

μ

−

γ

QED production. At lowest order in the ﬁnestructure constant

α

, thesecanbe includedby replacing

B W

(

m2μ

)

by[8] B W

(m

2μ

)

=

4

π α

2 3m2₂_μ

1

− ζ(

m2μ

)

2

−

1

,

(5) with

(4)

ζ (m

2μ

)

=

3

α

· B

μμ

·

ee

totMJ/ψ M2 J/ψ

−

m22μ

−

iMJ/ψ

tot (6)

and

b

(

m2μ

)

byitsequivalent

b

(

m2μ

)

≡

B W

(

m2μ

)/

ee

· B

μμ. The

interferenceisnon-symmetrical aroundthe peak; destructive be-low and constructive above. The radiator function gives a larger weighttolowerphotonenergies,correspondingtohigherdi-muon invariant masses. This changes the m2μ shape around the peak

asymmetrically. Replacing b

(

m2μ

)

by b

(

m2μ

)

informula (4) and

usingtheworldaverage [7]for

ee

· B

μμ enhances I

(

s

)

by about

2.2%.Thefunction

b

(

m2μ

)

dependson

ee

· B

μμ. Hence,an

itera-tiveprocedureisusedforitsextraction.

Weuse

e

+e− collision datacollected atthe Beijing Spectrom-eter III (BESIII) experiment. The BESIII detector [9] is located at the double-ring e+e− Beijing Electron Positron Collider (BEPCII). ThecylindricalBESIIIdetectorcovers93%ofthefullsolidangle.It consistsof thefollowing detectorsystems: (1) A MultilayerDrift Chamber(MDC) ﬁlled witha Helium-based gas, composed of43 layers,providingaspatial resolutionof135 μmandamomentum resolutionof0.5%forchargedtracksat1 GeV/c inamagneticﬁeld of1T.(2) A Time-of-Flightsystem(TOF),composedof176plastic scintillatorcountersinthebarrelpart,and96countersinthe end-caps.Thetimeresolutioninthebarrelis80ps and110psinthe endcaps.Formomenta upto1 GeV/c a 2

σ

K/

π

separationis ob-tained.(3)A CsI(Tl) Electro-Magnetic Calorimeter(EMC), withan energyresolutionof 2.5%in thebarrel and5% inthe endcapsat anenergyof1 GeV.(4)AMuonChamber(MUC)consistingofnine barrelandeightendcapresistiveplatechamberlayerswitha2 cm positionresolution.

We analyze 2.93 fb−1 [10] of data taken at

√

s

=

3

.

773 GeV intwo separate runs in2010 and 2011. A Geant4-based [11,12]

MonteCarlo(MC)simulationisusedtodetermineeﬃcienciesand studybackgrounds.TosimulatetheISRprocess

e

+e−

→

μ

+

μ

−

γ

, we usethe phokhara event generator[6,13].It includesISR and ﬁnal state radiation(FSR)correctionsup to next-to-leadingorder (NLO).Hadronic ISRproduction isalsosimulatedwith phokhara. Bhabhascatteringissimulatedusingthe babayaga 3.5event gen-erator [14]. Continuum MC is produced with the kkmc genera-tor[15].

Werequirethe presenceofatleast twochargedtracks inthe MDCwithnetchargezero.Thepointsofclosestapproachfromthe interactionpoint(IP)forthesetwotracksarerequiredtobewithin acylinderof1 cmradiusinthetransversedirectionand

±

10 cm oflength along the beamaxis. Incase of three-track events, we choose the track pair with net charge zero which is closest to the IP.The polarangle

θ

ofthe tracksisrequired tobe foundin theﬁducialvolumeoftheMDC,0

.

4rad

< θ <

π

−

0

.

4rad,where

θ

isthepolarangleofthetrackwithrespecttothebeamaxis.We requirethetransversemomentum

p

t tobegreaterthan300 MeV/c

foreachtrack.Toenhancestatisticsandtosuppressnon-ISR back-ground, we investigate untagged ISR events, where the ISR pho-ton isemitted undera smallangle

θ

γ , almostcollinear withthe beam,andthereforedoesnotendupintheﬁducialvolumeofthe EMC. This is a new approach with respect to BaBar and CLEO-c (bothusedtaggedISRphotons),whichhasbeenprovedtobevalid andeffectivebyusingthe phokhara eventgenerator[16].A one-constraint (1C) kinematic ﬁt is performed under the hypothesis

e+e−

→

μ

+

μ

−

γ

, using as input the two selected charged track candidatesaswellasthefour-momentumoftheinitial

e

+e− sys-tem.Theconstraintisamissingmasslessparticle.Theﬁtimposes overall energy and momentum balance. The

χ

2

1C value returned

bythe ﬁtisrequiredto besmaller than10.In addition,the pre-dictedmissingphotonanglewithrespecttothebeamaxis,

θ

γ , has tobesmallerthan 0

.

3 radiansorgreaterthan

π

−

0

.

3 radiansin thelabframe.Radiative Bhabhascattering

e

+e−

γ

(

γ

)

hasacross

Table 1

Totalnumberofnon-muonbackgroundeventsbetween 2.8≤m2μ≤3.4 GeV/c2 obtained with MC samples, whicharenormalizedtotheluminosityofthedataset.

Final state Background events

e+e−(γ) negl. π+π−γ 8.4±2.9 π+π−π0_γ ₃_.₃_±₁_.₈ π+π−π0_π0_γ ₀_.₃_±₀_.₆ π+π−π+π−γ negl. K+K−γ 1.7±1.3 K0_K0_γ _negl. p pγ negl. Continuum 1.7±1.3 ψ(3770)→D+D− negl. ψ(3770)→D0_D0 _negl. ψ(3770)→non D D 11.2±3.4 J/ψ→nonμμ 11.8±3.5

sectionthatisuptothreeordersofmagnitudelargerthanthe sig-nalcrosssection.Therefore,electrontracksneedtobesuppressed. Anelectron particleidentiﬁcation(PID)algorithm isusedforthis purpose,employinginformationfromtheMDC,TOFandEMC[17]. The probabilitiesforthetrackbeingamuon P

(

μ

)

oran electron

P

(

e

)

arecalculated,and P

(

μ

)

>

P

(

e

)

isrequiredforbothcharged tracks,which leadsto an electronsuppression ofmorethan96%. Tofurthersuppresshadronicbackground,an ArtiﬁcialNeural Net-work (ANN)builtonthe TMVApackage[18] isused.The ANN is describedindetailinRef.[10].Bothchargedtracksarerequiredto haveaclassiﬁeroutputvalue

y

ANN ofthismethodsmallerthan0.3

to be treatedasmuons, leading toa signal lossof lessthan30% andabackgroundrejectionofmorethan99%.

Backgroundbeyondtheradiative processes

μ

+

μ

−

γ

is studied withMC simulations. Table 1 liststhe numberofevents remain-ing afterallpreviously described requirementsinthe massrange between2.8and3.4 GeV/c2_._About ₄

_.

₈

_×

₁₀5 _events_are _found_in

thedatawithinthisrange.Thebackgroundfractionisfoundtobe smallerthan0.04%foreachofthe150

m

2μ massbins.Wesubtract

itfromthedatabinbybin.

The selection eﬃciency

is determined based on signal MC events. It is obtained as the ratio of the measured number of events afterall selection requirements N_measuredtrue to all generated ones

N

true

generated only.ThetrueMC sampleof J

/ψ

decayswiththe

full

θ

γ range, whichdoesnotcontainthedetectorreconstruction, is used here by applying efficiency correctionsto each track for muon tracking reconstruction, electron-PID, and ANN efficiency. Thesecorrectionshavebeenderived inRef.[10].We find

tobe (32.04

±

0.09)%,where the erroris dueto thesize of thesignal MCsample.

Thenumberof J

/ψ

events NJ/ψ isdeterminedfromabinned maximumlikelihoodﬁttodata.Theﬁtfunction f

(

x

)

usedis

f

(x)

=

NJ/ψ

M(x)

⊗

G(x)

+

Ntotal

−

NJ/ψ

p(x), (7)

where M

(

x

)

describes theshape ofthe MC-simulated J

/ψ

peak. We extract the shapefrom a MC simulationof the J

/ψ

produc-tion using a certain

ee

· B

μμ value as an input, together with

QED

μ

+

μ

−

γ

production (including interference effects) as sim-ulated with the phokhara event generator. Then, the histogram

M

(

x

)

isobtainedby subtractinga pureQED

μ

+

μ

−

γ

MCsample. It is shown in Fig. 1, using the world average [7] for

ee

· B

μμ

asinput.Totake intoaccount differencesinmass resolutions be-tweendataandMCsimulation,M

(

x

)

isconvolved(denotedbythe operator

⊗

) with a Gaussian distribution G

(

x

)

withmean x and

¯

width

σ

,whoseparameters aredetermined bytheﬁt todata.To describethenon-resonantQEDproductionintheﬁt,apolynomial offourthorderisused,

(5)

Fig. 1. MChistogramfromthe phokhara generatorafterfulldetector simulation usedfortheﬁt.Thevalueofee· BμμusedforgenerationistheonefromRef.[7].

Fig. 2. Fittothedatausingtheﬁnalvalueofee· Bμμ fromTable 3intheMC histogramfortheﬁt.

p(x)

=

4

i=0

aixi

.

(8)

Ntotal is the constant number of data events between 2.8 and

3.4 GeV/c2_._Free_parameters _in_the_ﬁt_are _N

J/ψ,x, σ

¯

,andthe co-eﬃcients ai (i

=

1

, . . . ,

4). Hence, NJ/ψ can be obtained directly by the fit. The fit resultis shown in Fig. 2; we find x

¯

= (

2

.

6

±

0

.

1

)

MeV

/

c2,

σ

= (

10

.

5

±

0

.

2

)

MeV

/

c2,and

χ

2

_/

_ndf

₌

₁₄₉

_.

₈

_/

_143.

Equation

(3)

isusedtodetermine

ee

· B

μμ in aniterative

pro-cess. In each iteration, we simulatethe histogram M

(

x

)

and cal-culate I

(

s

)

(including interferencecorrections), usinga

ee

· B

μμ

inputvalue,andextractthe

ee

· B

μμ output withEq.(3).This

re-sult is used as input for the next iteration. We choose the PDG value [7] asthe starting value. The results of each iteration are summarizedin Table 3. Afterthree iterations the resultbecomes stablewithinfourdecimalplaces,whichcorrespondstothe exper-imentaluncertainty.Astheﬁnalvalueweﬁnd

ee

· B

μμ

= (

333

.

4

±

2

.

5stat

±

4

.

4sys

)

eV

,

wheretheﬁrsterroristhestatisticaluncertaintyfromtheﬁt pro-cedure,andtheseconderroristhesystematicuncertainty.

All systematic uncertainties are summarized in Table 2. They aresummedupinquadraturetobe1.3%.Theyarederived as fol-lows:

Table 2

Summaryofthesystematicuncertainties.

Source Uncertainty

(%) Background subtraction negl. Muon tracking eﬃciency 0.5

Muon ANN eﬃciency 0.5

Muon e-PID eﬃciency 0.5

1C kinematic ﬁt 0.5

Angular acceptance 0.1

Luminosity 0.5

Radiator function 0.5

Parametrizing the interference 0.2 Variation of ﬁt range 0.3

Sum 1.3

Table 3

Resultsoftheiterationsteps.Asthestartingvalue,thePDG2014oneisused.The errorsarethestatisticalones.

Step ee· Bμμ

inputvalue

ee· Bμμ output value[eV]

1 PDG value[7] 333.9±2.5

2 result of step 1 333.3±2.5

(1)IntegralI

(

s

)

:ThedifferenceinI

(

s

)

,whenenhancingor de-creasingthevalue of

ee

· B

μμ within ﬁvestandard deviationsof

the error,claimedby Ref.[7],issmallerthan0.2%.Thisdeviation isconsideredasthesystematicuncertaintyofaccommodatingthe interferenceeffectsin

I

(

s

)

.

(2)Backgroundsubtraction:Aconservativeuncertaintyof100% isassumedfortheMCsamples.Hence,thesystematicuncertainty dueto backgroundsubtractionis smallerthan 0.04%per binand canthereforebeneglected.

(3) Eﬃciency

:The data-MC eﬃciencycorrectionshavebeen studiedinRef.[10].Thecorrespondingsystematicuncertaintiesare listed in

Table 2

. Theyarefound tobe smallerthan 0.5%in each case.

(4)Toestimatetheuncertaintyintroducedbytherequirements on

θ

γ and χ2

1C, the resolutiondifferences betweendata andMC

simulation inthesevariablesare obtained. Incaseof

θ

γ , we ﬁnd the resolution difference tobe

(

66

±

3

)

×

10−5 radians,by com-paringanISRphotontaggedclean

μ

+

μ

−

γ

samplebothfromdata and MC simulation. In case of

χ

2

1C, we determine the eﬃciency

of theapplied requirement

χ

2

1C

<

10 in dataandMC simulation.

Wevarythisrequirementindatasuchthattheeﬃcienciesindata and MC simulation are the same. The difference to the actually usedrequirementistakenasresolutiondifference,whichweﬁnd tobe

(

1

.

1

±

0

.

1

)

unitsin

χ

2

1C.Toachieveabetterdescriptionof

,

both variablesaresmearedinthesignalMC samplewitha Gaus-sian withameanvalue ofzeroandawidthcorresponding tothe resolution difference.Toestimate thecontribution tothe system-aticuncertainty,thesevariablesarealsovariedwitha

±

1 standard deviation,andthedifferencein

istakenasthesystematic uncer-tainty,whichisfoundto belessthan0.5%for

χ

2

1C andnegligible

for

θ

γ .

(5)Thechosenmassrangebetween2.8and3.4 GeV/c2isvaried within0.1 GeV/c2,usingtheﬁnalvalueof

ee

· B

μμ after the

iter-ation procedure.The differencein

ee

· B

μμ is smaller than0.3%,

andisusedasasystematicuncertainty.

(6)TheluminosityhasbeenmeasuredinRefs. [19,10]withan uncertaintyof0.5%.

(7)Theradiatorfunctionisextractedfromthe phokhara event generator[13]andhasanuncertaintyof0.5%.

(6)

Table 4

ResultsoftheBaBar[1],CLEO-c[2]andKEDR[3]measurementscomparedtothiswork.

Measurement ee· Bμμ[eV] UsedBμμvalue [%] ee[keV]

BaBar 330.1±7.7stat±7.3sys 5.88±0.10[20] 5.61±0.20

CLEO-c 338.4±5.8stat±7.1sys 5.953±0.056stat±0.042sys[21] 5.68±0.11stat±0.13sys

KEDR 331.8±5.2stat±6.3sys 5.94±0.06[22] 5.59±0.12

This work 333.4±2.5stat±4.4sys 5.973±0.007stat±0.037sys[4] 5.58±0.05stat±0.08sys

(8)The angularacceptanceofthechargedtracksisstudied by varyingthis requirementby morethan threestandard deviations ofthe angular resolution, andstudying the corresponding differ-enceintheﬁnalresult.Anuncertaintyoflessthan0.1%isfound.

With

B

μμ

= (

5

.

973

±

0

.

007stat

±

0

.

038sys

)

% from an

indepen-dentBESIIImeasurement[4],ourmeasurementyields

ee

= (

5

.

58

±

0

.

05stat

±

0

.

08sys

)

keV

.

Ourmeasurementof

ee

· B

μμ is consistentwiththeresultsfrom

BaBar[1],CLEO-c[2]andKEDR[3].Themeasuredvaluefor

ee is

moreprecise,assummarizedin

Table 4

.

Insummary,we have usedthe ISR process e+e−

→

J

/ψ

γ

→

μ

+

μ

−

γ

tomeasure

ee

· B

μμ

= (

333

.

4

±

2

.

5stat

±

4

.

4sys

)

eV with

atotalrelativeuncertaintyof1.5%.CombinedwiththeBESIII mea-surementof Bμμ, we obtain

ee

= (

5

.

58

±

0

.

05stat

±

0

.

08sys

)

keV

witharelativeprecisionof1.7%.

The BESIII Collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; National Natural Sci-enceFoundation ofChina (NSFC) underContractsNos.11125525, 11235011,11322544,11335008, 11425524; theChinese Academy ofSciences (CAS) Large-Scale Scientiﬁc Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); the Collabora-tive InnovationCenter for ParticlesandInteractions(CICPI);Joint Large-Scale Scientiﬁc Facility Funds of the NSFC and CAS under Contracts Nos. 11179007, U1232201, U1332201; CAS under Con-tracts Nos. KJCX2-YW-N29, KJCX2-YW-N45; 100 Talents Program of CAS; INPAC and Shanghai Key Laboratory for Particle Physics andCosmology;GermanResearchFoundationDFGunderContract No.CollaborativeResearchCenterCRC-1044;InstitutoNazionaledi Fisica Nucleare, Italy; Ministry of Development of Turkey under ContractNo.DPT2006K-120470; RussianFoundation forBasic Re-searchunderContractNo.14-07-91152;U.S.DepartmentofEnergy

under Contracts Nos. DE-FG02-04ER41291, DE-FG02-05ER41374, DE-FG02-94ER40823,DESC0010118;U.S.NationalScience Founda-tion; University of Groningen (RuG) and the Helmholtzzentrum fuer 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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