Dark photon search in the mass range between 1.5 and 3.4 GeV/c

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Dark

photon

search

in

the

mass

range

between

1.5 and

3.4 GeV/c

2 BESIII

Collaboration

M. Ablikim

a

,

M.N. Achasov

i

,

6

,

X.C. Ai

a

,

O. Albayrak

e

,

M. Albrecht

d

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D.J. Ambrose

av

,

A. Amoroso

az

,

bb

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_{F.F. An}

a

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_{Q. An}

aw

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1

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_{J.Z. Bai}

a

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_{R. Baldini Ferroli}

t

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_{Y. Ban}

ag

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_{D.W. Bennett}

s

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J.V. Bennett

e

,

M. Bertani

t

,

D. Bettoni

v

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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

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1

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H.P. Cheng

q

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X.K. Chu

ag

,

G. Cibinetto

v

,

H.L. Dai

a

,

1

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J.P. Dai

aj

,

A. Dbeyssi

n

,

D. Dedovich

y

,

Z.Y. Deng

a

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A. Denig

x

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I. Denysenko

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M. Destefanis

az

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bb

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F. De Mori

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Y. Ding

ac

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C. Dong

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J. Dong

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1

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L.Y. Dong

a

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M.Y. Dong

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1

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S.X. Du

bf

,

P.F. Duan

a

,

E.E. Eren

aq

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J.Z. Fan

ao

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J. Fang

a

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1

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S.S. Fang

a

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X. Fang

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Y. Fang

a

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L. Fava

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F. Feldbauer

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G. Felici

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C.Q. Feng

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E. Fioravanti

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M. Fritsch

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C.D. Fu

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Q. Gao

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X.Y. Gao

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Y. Gao

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I. Garzia

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C. Geng

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K. Goetzen

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W.X. Gong

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M.H. Gu

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Y.P. Guo

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A. Hafner

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Y.L. Han

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X.Q. Hao

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F.A. Harris

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K.L. He

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T. Held

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Y.K. Heng

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J.S. Huang

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X.T. Huang

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T. Hussain

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Q. Ji

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Q.P. Ji

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X.B. Ji

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X.L. Ji

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L.L. Jiang

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L.W. Jiang

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X.S. Jiang

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X.Y. Jiang

af

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J.B. Jiao

ai

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Z. Jiao

q

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D.P. Jin

a

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1

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S. Jin

a

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T. Johansson

bc

,

A. Julin

au

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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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P. Kiese

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R. Kliemt

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B. Kloss

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O.B. Kolcu

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9

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B. Kopf

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M. Kornicer

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W. Kuehn

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A. Kupsc

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J.S. Lange

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M. Lara

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P. Larin

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C. Li

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Cheng Li

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B.J. Liu

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C.X. Liu

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Fang Liu

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Feng Liu

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H.B. Liu

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H.J. Lu

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K. Moriya

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N.Yu. Muchnoi

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I.B. Nikolaev

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S. Nisar

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S.L. Niu

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S.L. Olsen

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S. Pacetti

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E-mailaddress:guo@uni-mainz.de(Y.P. Guo).

https://doi.org/10.1016/j.physletb.2017.09.067

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K.H. Rashid

ay

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C.F. Redmer

x

,

H.L. Ren

r

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M. Ripka

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G. Rong

a

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Ch. Rosner

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X.D. Ruan

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V. Santoro

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A. Sarantsev

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M. Savrié

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K. Schoenning

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S. Schumann

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W. Shan

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M. Shao

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C.P. Shen

b

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P.X. Shen

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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_Helmholtz_{Centre 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

NanjingUniversity,Nanjing210093,People’sRepublicofChina 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

(3)

aq_Dogus_University,₃₄₇₂₂_Istanbul,_Turkey 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: Received11May2017

Receivedinrevisedform19July2017 Accepted22September2017 Availableonline28September2017 Editor:V.Metag

Keywords: Darkphotonsearch Initialstateradiation BESIII

Usingadatasetof2.93fb−1takenatacenter-of-massenergy√s=3.773 GeVwiththeBESIIIdetector at the BEPCII collider, we perform asearch for an extra U(1) gauge boson, also denoted as a dark photon.We examinetheinitialstateradiationreactionse+e−_→e+e−

γ

ISR ande+e−→

μ

+

μ

−

γ

ISR for thissearch,wherethedarkphotonwouldappearasanenhancementintheinvariantmassdistribution oftheleptonicpairs.Weobservenoobviousenhancementinthemassrangebetween1.5and3.4 GeV/c2 andseta90%conﬁdencelevelupperlimitonthemixingstrengthofthedarkphotonandtheStandard Modelphoton.Weobtainacompetitivelimitinthetestedmassrange.

Severalastrophysicalanomalies,whichcannot beeasily under-stoodinthecontextoftheStandardModel(SM)ofparticlephysics orastrophysics, havebeen discussedin relationto a dark,so far unobserved sector [1], which couples very weakly withSM par-ticles. The most straightforward model consists of an extra U(1) forcecarrier,alsodenotedasadarkphoton,

γ

,whichcouplesto theSM via kinetic mixing[2]. Ithas beenshowninRef. [1]that thedarkphotonhastoberelativelylight,ontheMeV/c2_to_GeV/c2 massscale,toexplaintheastrophysicalobservations.Furthermore, itwas realized,that adarkphotonofsimilarmasscould also ex-plain the presently observed deviation on the level of 3 to 4

σ

betweenthemeasurementandtheSM predictionof

(

g

−

2

)

μ[3].

These facts and the work by Bjorken and collaborators [4] trig-gered searches for the dark photon at particle accelerators in a worldwideeffort[5,6].Differentexperimentalsetupscanbeused, like ﬁxed-target (e.g. Refs. [7,8]), beam dump (e.g. Refs. [9,10]), orlow-energycolliderexperiments(e.g.Refs.[11,12]).Themixing strength

ε

=

α

/

α

, where

α

is the coupling ofthe dark photon to the electromagneticcharge and

α

the ﬁne structure constant, is constrained by previous measurements to be below approxi-mately 10−2 [4].

Inthisletterwe presentadarkphotonsearch,using2.93 fb−1

[13] of data taken at

√

s

=

3

.

773 GeV obtainedwith the Beijing SpectrometerIII(BESIII).Themeasurementexploitstheprocess of

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_University_of_Texas_at_Dallas,_Richardson,_{TX 75083,}_USA. 9 _Currently_at_Istanbul_Arel_University,₃₄₂₉₅_Istanbul,_Turkey.

initial state radiation (ISR), in which one of the beam particles radiates a photon. In this way, the available energy to produce ﬁnal statesis reduced, andthe di-lepton invariant massesbelow the center-of-massenergyofthe e+e− colliderbecome available. The same method has been used by the BaBar experiment [11, 12],whereadarkphotonmass

mγ

between0.02and10.2GeV/c2 and

ε

valuesintheorder of10−3_–10−4 _have_been_excluded. _We searchfortheprocesses

e

+e−

→

γ

ISR

→

l+l−

γ

ISR (l

=

μ

,

e) with leptonic invariant masses

m

l+l− between1.5and 3.4GeV/c2. The

ISR QED processes

e

+e−

→

μ

+

μ

−

γ

ISR and e+e−

→

e+e−

γ

ISR are irreduciblebackgroundchannels.However, thedarkphotonwidth isexpectedtobesmallerthantheresolutionoftheexperiment[4]

and,thus,a

γ

signalwouldleadtoanarrowstructureatthemass ofthedarkphotoninthe

m

l+l− massspectrumontopofthe

con-tinuumQEDbackground.

The BESIII detector islocated atthe double-ring e+e− Beijing Electron PositronCollider (BEPCII)[14].The cylindrical BESIII de-tectorcovers93%ofthefullsolidangle.Itconsistsofthefollowing detectorsystems.(1)AMultilayerDriftChamber(MDC)ﬁlledwith a helium-gas mixture, composed of 43 layers, which provides a spatial resolutionof135 μmandamomentum resolutionof0.5% forchargedtracksat1GeV/c inamagneticﬁeldof1 T.(2) A Time-of-Flight system(TOF),builtwith176plasticscintillator counters inthebarrelpart,and96countersintheendcaps.Thetime res-olution in thebarrel (end caps) is 80ps (110 ps).For momenta up to 1 GeV/c, thisprovides a 2

σ

K/

π

separation. (3) A CsI(Tl) Electro-Magnetic Calorimeter (EMC) withan energy resolutionof 2.5% inthebarreland5% intheendcapsatan energyof1 GeV. (4) A MuonCounter(MUC)consistingofninebarrelandeight end-capresistiveplatechamberlayerswitha2 cmpositionresolution. For the simulation of ISR processes e+e−

→

μ

+

μ

−

γ

ISR and

π

+

π

−

γ

ISR, the phokhara event generator [15,16], which in-cludes ISR and ﬁnal state radiation (FSR)corrections up to next-to-leading order, is used. Bhabha scattering is simulated with babayaga _3.5 _[17]_. _Continuum _Monte _Carlo _(MC) _events, _as _well as the resonant

ψ(

3770

)

decays to DD,

¯

non-DD,

¯

and the ISR

(4)

Fig. 1. Leptonicinvariantmassdistributionsmμ+μ−andme+e− afterapplyingtheselectionrequirements.Shownisdata(points)andMCsimulation(shadedarea),whichis scaledtotheluminosityofthedataset.Themarkedareaaroundthe J/ψresonanceisexcludedintheanalysis.ThelowerpanelshowstheratioofdataandMCsimulation (points)andtheratioofﬁtcurveandMCsimulation(histogram).

production of

ψ

and J

/ψ

, are simulated with the kkmc gen-erator [18]. All MC generators, which are the most appropriate choicesfor the processes studied,have been interfacedwith the geant4-based[19,20]detectorsimulation.

Theselectionof

μ

+

μ

−

γ

ISR and

e

+e−

γ

ISR eventsis straightfor-ward.WerequirethepresenceoftwochargedtracksintheMDC withnetcharge zero.The pointsofclosestapproach fromthe in-teractionpoint(IP)forthesetwotracksare requiredtobe within acylinderof1cmradiusinthetransversedirectionand

±

10cm oflengthalongthebeamaxis.Thepolaranglewithrespecttothe beamaxis

θ

ofthetracksisrequiredtobeintheﬁducialvolume oftheMDC: 0

.

4

< θ <

π

−

0

.

4 radians.Inorder tosuppress spi-ralingtracks,werequirethetransversemomentum pt tobeabove

300 MeV/c forbothtracks.

Muon particleidentiﬁcation isused [21]. The probabilities for beingamuon P

(

μ

)

andbeinganelectron P

(

e

)

arecalculated us-inginformationfromMDC,TOF,EMC,andMUC.Forbothcharged tracks, P

(

μ

)

>

P

(

e

)

is required. To select electrons, the ratio of themeasuredenergyintheEMC,

E,

tothemomentum

p obtained

fromthe MDC is used. Both chargedtracks must satisfy E

/

p

>

0.8 c.

Theradiatorfunction[22],whichdescribestheradiationofan ISRphoton,ispeakedatsmall

θ

valueswithrespecttothebeam axis.DifferentfromBaBar,weuseuntaggedISRevents,wherethe ISR photon is emitted at a small angle

θ

γ and is not detected within the angular acceptance of the EMC, to increase statistics. A one constraint (1C) kinematic ﬁt, applying energy and mo-mentumconservation,is performedwiththehypothesis e+e−

→

μ

+

μ

−

γ

ISR or e+e−

→

e+e−

γ

ISR, using asinput the two selected chargedtrack candidates, as well asthe four momentum of the initial

e

+e− system.The constraintisthemassofamissing pho-ton.Theﬁtquality condition

χ

2

1C

/

(dof

=

1)

<

20 isappliedinthe

μ

+

μ

−

γ

ISR case,where dofisthedegree offreedom. Tosuppress non-ISRbackground,theangleofthemissingphoton,

θ

γ , predicted bythe1Ckinematicﬁt,isrequiredtobesmallerthan0.1 radians orgreater than

π

−

0

.

1 radians.We apply strongerrequirements forthe

e

+e−

γ

ISR ﬁnalstate,toprovideabettersuppressionofthe non-ISR background which is higher in the e+e− channel com-paredto the

μ

+

μ

− channel.In thiscase,

χ

2

1C

/

(dof

=

1)

<

5, and

θ

γ

<

0

.

05 radians,or

θ

γ

>

π

−

0

.

05 radians.

Background in addition to the radiative QED processes

μ

+

μ

−

γ

ISR and

e

+e−

γ

ISR,whichisirreducible,isstudiedwithMC simulationsand isnegligible forthe e+e−

γ

ISR ﬁnal state, andon theorderof3%for

μ

+

μ

−invariantmassesbelow2 GeV/c2dueto muonmisidentiﬁcation,andnegligibleabove.Thisremaining

back-ground comes mostly from

π

+

π

−

γ

ISR events.We subtract their contribution using a MC sample, produced with the phokhara generator. The subtraction ofthis background leads to a system-aticuncertaintyduetothegeneratorprecisionsmallerthan0.5%.

The

μ

+

μ

− and

e

+e− invariantmassdistributions,_mμ+_μ− and

me+e−,whichareshownseparatelyin

Fig. 1

,aremainlydominated

bytheQEDbackgroundbutcouldcontainthesignalsittingontop oftheseirreducibleevents.Forcomparisonwithdata,MC simula-tion,scaledtotheluminosityofdata,isshown,althoughitisnot used inthesearch forthedark photon.Inthisanalysis, the dark photon mass range mγ between 1.5 and 3.4 GeV/c2 _is _studied. Below1.5GeV/c2the

π

+

π

−

γ

ISRcrosssectionwithmuon misiden-tiﬁcation dominatesthe _mμ+_μ− spectrum. Above 3.4 GeV/c2 the hadronic

q

q process

¯

cannotbesuppressedsuﬃcientlyby the

χ

2

1C requirement.Inordertosearchfornarrowstructuresontopofthe QED background,4th order polynomial functionsto describe the continuumQEDareﬁttedtothedatadistributionsshownin

Fig. 1

. The massrangearound thenarrow J

/ψ

resonancebetween2.95 and3.2GeV/c2 _is_excluded.

The differences between the

μ

+

μ

−

γ

ISR and e+e−

γ

ISR event yields andtheir respective 4thorder polynomialsare added.The combineddifferencesare represented bythe blackdots in Fig. 2. A darkphotoncandidatewouldappearasapeakinthisplot.The observed statistical signiﬁcances are less than 3

σ

everywhere in the explored region. The significance in each invariant mass bin isdefinedasthecombineddifferencesbetweendataandthe 4th order polynomials, divided by the combined statistical errors of both final states. In conclusion, we observe no dark photon sig-nalfor1.5 GeV/c2

_<

_mγ

_<

_{3.4 GeV/c}2_,_where

_mγ

_is_equal_to_the leptonicinvariant mass

m

l+l−.Theexclusionlimitatthe90%

con-ﬁdencelevelisdeterminedwithaproﬁlelikelihoodapproach[23]. Alsoshownin

Fig. 2

asa functionof

m

l+l− isthebin-by-bin

cal-culated exclusion limit, including the systematicuncertainties as explainedbelow.

Tocalculatetheexclusionlimitonthemixingparameter

ε

2_,_the formulafromRef.[4]isused

σ

i

(

e+e−

→

γ

ISR

→

l+l−

γ

ISR

)

σ

i

(

e+e−

→

γ

∗

γ

ISR

→

l+l−

γ

ISR

)

=

Nup_i

(

e+e−

→

γ

ISR

→

l+l−

γ

ISR

)

NB i

(

e+e−

→

γ

∗

γ

ISR

→

l+l−

γ

ISR

)

·

1

=

3

π

· ε

2

_·

_m γ 2Nl_f+l−

α

· δ

l+l− m

,

(1)

(5)

Fig. 2. Thesumofthedifferencesbetweenthe

μ

+μ−γISRande+e−γISReventyields andtheirrespective4thorderpolynomials(dotswith errorbars).Thesolid his-togramrepresentstheexclusionlimitwiththe90%conﬁdence,calculatedwitha proﬁlelikelihoodapproachand includingthe systematicuncertainty.The region aroundthe J/ψresonancebetween2.95and3.2 GeV/c2_is_excluded.

where i represents the i-th mass bin,

α

is the electromagnetic ﬁne structure constant, mγ the dark photon mass,

γ

∗ the SM photon,and

δ

l_m+l− (l

=

μ

,

e) thebinwidthoftheleptonpair invari-antmassspectrum,10MeV/c2.Themassresolutionofthelepton pairsdeterminedwithMC for

e

+e− and

μ

+

μ

− isbetween5and 12 MeV/c2_. _The _cross _section _ratio _upper _limit _in _Eq. ₍₁₎ _is de-termined from the exclusion upper limit (Nup₎ _corrected _by _the eﬃciencyloss(

) duetothebinwidthdividedbythenumberof

μ

+

μ

−

γ

ISR and

e

+e−

γ

ISRevents(NB)correctedasdescribedbelow. Theeﬃciencylosscausedbytheincompletenessofsignaleventsin one bin is calculated with

₋5 MeV_{5 MeV}/c_/2_c2G

(

0

,

σ

)

dm

/

_∞

−∞G

(

0

,

σ

)

dm, whereG

(

0

,

σ

)

istheGaussian function usedtodescribe themass resolution.

The QED cross section

σ

i

(

e+e−

→

γ

∗

γ

ISR

→

l+l−

γ

ISR

)

must only take into account annihilation processes of theinitial e+e−

beamparticles,whereadarkphotoncouldbeproduced.Thus,the eventyieldofthe

e

+e−

γ

ﬁnalstatehastobecorrectedduetothe existence ofSM Bhabhascattering. This correction isobtained in binsof

m

e+e− bydividingthe

e

+e−annihilationeventsonlybythe

sumofeventsoftheannihilationandBhabhascatteringprocesses. Theﬁrstisgeneratedwiththe phokhara eventgeneratorby gen-eratingthe

μ

+

μ

−

γ

ﬁnalstateandreplacingthemuonmasswith theelectronmass.Thelatterisgeneratedwiththe babayaga@nlo

generator[24].Thecorrectionfactorvariesbetween2%and8% de-pendingon

m

e+e−.

The numberofﬁnal statesforthe darkphoton Nl+l−

f includes

thephasespaceabovethe

l

+l−productionthresholdoftheleptons

l

=

μ

,

e, andisgivenby Nl+l−

f

=

tot

/

ll [25],where

ll

≡ (

γ

→

l+l−

)

istheleptonic

γ

widthand

tot isthetotal

γ

width.These

widthsaretakenfromRef.[25]

ll

=

αε

2 3m2 γ

(

m2_γ

+

2m2l

)

m2 γ

−

4m2l (2)

tot

=

ee

+ μμ

· (

1

+

R

(

√

s

)) ,

(3) where

ee

≡ (

γ

→

e+e−

)

,

μμ

≡ (

γ

→

μ

+

μ

−

)

,and R

(

√

s

)

is

thetotalhadroniccrosssection R value[26]asafunctionof

√

s.

The systematicuncertaintiesare includedinthecalculation of the exclusion limit. The main source is the uncertaintyof the R

value taken from Ref. [26], which enters the calculation of the

Nl_f+l− andleads to a massdependent systematic uncertainty be-tween 3.0and6.0%. Othersources are backgroundsubtractionas described above (

<

0.5%), the ﬁtting error of the polynomial ﬁt to data (

<

1%), the Bhabha scattering correction factor using the phokharaand babayaga@nlo eventgenerator(

<

1%),anddata-MC differencesof theleptonic mass resolution.Toquantifythe latter one,westudythedata-MCresolutiondifferenceofthe J

/ψ

reso-nanceforthe

μ

+

μ

−and

e

+e−decays,separately.Theresonanceis ﬁttedwithadoubleGaussianfunctionindataandMCsimulation, andthewidthdifferenceis(3

.

7

±

1

.

8)%for

μ

+

μ

−and(0

.

7

±

5

.

3)% for

e

+e−.The differencesaretakeninto considerationinthe cal-culations, andthe uncertainty inthe differences(1%) is takenas the systematic uncertainty of the data-MC differences. The mass dependent total systematic uncertainty, whichvaries from3.5 to 6.5%dependingonmass,isusedbin-by-binintheupperlimit.

Theﬁnalresult,themixingstrength

ε

asafunctionofthedark photon mass, is shownin Fig. 3, includingthe systematic uncer-tainties. Itprovides a comparableupperlimit toBaBar[11,12] in the studied

mγ

massrange.Alsoshown arethe exclusionlimits fromKLOE[27–30],WASA-at-COSY[31],HADES[32],PHENIX[33], A1 at MAMI [7,8], NA48/2 [34], APEX [35], and the beam-dump experiments E774 [9], andE141 [10].The

ε

values,whichwould explainthediscrepancybetweenthemeasurementandtheSM cal-culationoftheanomalousmagneticmomentofthemuon [3]are displayedin

Fig. 3

astheboldsolidlinewitha2

σ

band.

In conclusion, we perform a search for a darkphoton in the massrangebetween1.5and3.4 GeV/c2,wherewedonotobserve

Fig. 3. Exclusionlimitatthe90%conﬁdencelevelonthemixingparameter

ε

asafunctionofthedarkphotonmass.Theboldsolidlinerepresentsthe

ε

values,whichwould explainthediscrepancybetweenthemeasurementandtheSMcalculationoftheanomalousmagneticmomentofthemuon[3],togetherwithits2σ band.

(6)

asigniﬁcantsignal. Wesetupperlimitsonthemixingparameter

ε

between10−3 and10−4 asafunctionofthedarkphotonmass witha conﬁdencelevelof90%.This isacompetitive limitinthis dark photon mass range. The BESIII results, which are based on twoyearsofdatataking,arealreadycompetitivetothelargeBaBar datasamples,basedon9yearsofrunning.Thisispossibledueto theuseofuntaggedISReventsforthedarkphotonsearchaswell asthefactthatthecenter-of-massenergyoftheBEPCIIcollideris closertothemass regiontested. Wealsouse adifferentanalysis approach,whichhasnodependenceontheradiatorfunction.

The BESIII collaboration thanks the staff of BEPCII and the IHEPcomputingcenterfortheir strongsupport.Thisworkis sup-portedin part by National Key Basic Research Program of China underContractNo.2015CB856700;NationalNaturalScience Foun-dationofChina(NSFC)underContractsNos.11235011,11335008, 11425524,11625523,11635010;theChineseAcademyofSciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellencein Particle Physics(CCEPP); JointLarge-Scale Scientific FacilityFundsoftheNSFCandCASunderContractsNos.U1332201, U1532257, U1532258; CAS under Contracts Nos. KJCX2-YW-N29, KJCX2-YW-N45,QYZDJ-SSW-SLH003; 100TalentsProgramofCAS; National 1000 Talents Program of China; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Re-search Foundation DFG under Contracts Nos. Collaborative Re-searchCenterCRC1044,FOR2359;IstitutoNazionalediFisica Nu-cleare,Italy;JointLarge-ScaleScientificFacilityFundsoftheNSFC andCAS; Koninklijke Nederlandse Akademie van Wetenschappen (KNAW)underContractNo.530-4CDP03;MinistryofDevelopment ofTurkeyunderContractNo.DPT2006K-120470;NationalNatural ScienceFoundationofChina(NSFC);NationalScienceand Technol-ogyfund;TheSwedishResarchCouncil;U.S.DepartmentofEnergy underContractsNos.DE-FG02-05ER41374,DE-SC-0010118, DE-SC-0010504,DE-SC-0012069; University ofGroningen (RuG)andthe HelmholtzzentrumfuerSchwerionenforschungGmbH(GSI), Darm-stadt;WCUProgramofNationalResearchFoundationofKorea un-derContractNo.R32-2008-000-10155-0.

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