Study of e(+)e(-) -> p(p)over-bar in the vicinity of psi(3770)

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Study

of

e

+

e

−

→

p

p in

¯

the

vicinity

of

ψ (

3770

)

BESIII

Collaboration

M. Ablikim

a

,

M.N. Achasov

h

,

1

_,

_{X.C. Ai}

a

_,

_{O. Albayrak}

d

_,

_{M. Albrecht}

c

_,

_{D.J. Ambrose}

ar

_,

F.F. An

a

,

Q. An

as

,

J.Z. Bai

a

,

R. Baldini Ferroli

s

,

Y. Ban

ac

,

J.V. Bennett

r

,

M. Bertani

s

,

J.M. Bian

aq

,

E. Boger

v

,

2

,

O. Bondarenko

w

,

I. Boyko

v

,

S. Braun

an

,

R.A. Briere

d

,

H. Cai

az

,

X. Cai

a

,

O. Cakir

ak

,

A. Calcaterra

s

,

G.F. Cao

a

,

S.A. Cetin

al

,

J.F. Chang

a

,

G. Chelkov

v

,

3

,

G. Chen

a

,

H.S. Chen

a

,

J.C. Chen

a

,

M.L. Chen

a

,

S.J. Chen

aa

,

X. Chen

a

,

X.R. Chen

x

,

Y.B. Chen

a

,

H.P. Cheng

p

,

X.K. Chu

ac

,

Y.P. Chu

a

,

D. Cronin-Hennessy

aq

,

H.L. Dai

a

,

J.P. Dai

a

,

D. Dedovich

v

,

Z.Y. Deng

a

,

A. Denig

u

,

I. Denysenko

v

,

M. Destefanis

av

,

ax

,

W.M. Ding

ae

,

Y. Ding

y

,

C. Dong

ab

,

J. Dong

a

,

L.Y. Dong

a

,

M.Y. Dong

a

,

S.X. Du

bb

,

J.Z. Fan

aj

,

J. Fang

a

,

S.S. Fang

a

,

Y. Fang

a

,

L. Fava

aw

,

ax

,

C.Q. Feng

as

,

C.D. Fu

a

,

O. Fuks

v

,

2

,

Q. Gao

a

,

Y. Gao

aj

,

C. Geng

as

,

K. Goetzen

i

,

W.X. Gong

a

,

W. Gradl

u

,

M. Greco

av

,

ax

,

M.H. Gu

a

,

Y.T. Gu

k

,

Y.H. Guan

a

,

L.B. Guo

z

,

T. Guo

z

,

Y.P. Guo

u

,

Y.L. Han

a

,

F.A. Harris

ap

,

K.L. He

a

,

M. He

a

,

Z.Y. He

ab

,

T. Held

c

,

Y.K. Heng

a

,

Z.L. Hou

a

,

C. Hu

z

,

H.M. Hu

a

,

J.F. Hu

an

,

T. Hu

a

,

G.M. Huang

e

,

G.S. Huang

as

,

H.P. Huang

az

,

J.S. Huang

n

,

L. Huang

a

,

X.T. Huang

ae

,

Y. Huang

aa

,

T. Hussain

au

,

C.S. Ji

as

,

Q. Ji

a

,

Q.P. Ji

ab

,

X.B. Ji

a

,

X.L. Ji

a

,

L.L. Jiang

a

,

L.W. Jiang

az

,

X.S. Jiang

a

,

J.B. Jiao

ae

,

Z. Jiao

p

,

D.P. Jin

a

,

S. Jin

a

,

T. Johansson

ay

,

N. Kalantar-Nayestanaki

w

,

X.L. Kang

a

,

X.S. Kang

ab

,

M. Kavatsyuk

w

,

B. Kloss

u

,

B. Kopf

c

,

M. Kornicer

ap

,

W. Kühn

an

,

A. Kupsc

ay

,

W. Lai

a

,

J.S. Lange

an

,

M. Lara

r

,

P. Larin

m

,

M. Leyhe

c

,

C.H. Li

a

,

Cheng Li

as

,

Cui Li

as

,

D. Li

q

,

D.M. Li

bb

,

F. Li

a

,

G. Li

a

,

H.B. Li

a

,

J.C. Li

a

,

K. Li

l

,

K. Li

ae

,

Lei Li

a

,

P.R. Li

ao

,

Q.J. Li

a

,

T. Li

ae

,

W.D. Li

a

,

W.G. Li

a

,

X.L. Li

ae

,

X.N. Li

a

,

X.Q. Li

ab

,

Z.B. Li

ai

,

H. Liang

as

,

Y.F. Liang

ag

,

Y.T. Liang

an

,

∗

,

D.X. Lin

m

,

B.J. Liu

a

,

C.L. Liu

d

,

C.X. Liu

a

,

F.H. Liu

af

,

Fang Liu

a

,

Feng Liu

e

,

H.B. Liu

k

,

H.H. Liu

o

,

H.M. Liu

a

,

J. Liu

a

,

J.P. Liu

az

,

K. Liu

aj

,

K.Y. Liu

y

,

P.L. Liu

ae

,

Q. Liu

ao

,

S.B. Liu

as

,

X. Liu

x

,

Y.B. Liu

ab

,

Z.A. Liu

a

,

Zhiqiang Liu

a

,

Zhiqing Liu

u

,

H. Loehner

w

,

X.C. Lou

a

,

4

,

G.R. Lu

n

,

H.J. Lu

p

,

H.L. Lu

a

,

J.G. Lu

a

,

X.R. Lu

ao

,

Y. Lu

a

,

Y.P. Lu

a

,

C.L. Luo

z

,

M.X. Luo

ba

,

T. Luo

ap

,

X.L. Luo

a

,

M. Lv

a

,

F.C. Ma

y

,

H.L. Ma

a

,

Q.M. Ma

a

,

S. Ma

a

,

T. Ma

a

,

X.Y. Ma

a

,

F.E. Maas

m

,

M. Maggiora

av

,

ax

,

Q.A. Malik

au

,

Y.J. Mao

ac

,

Z.P. Mao

a

,

J.G. Messchendorp

w

,

J. Min

a

,

T.J. Min

a

,

R.E. Mitchell

r

,

X.H. Mo

a

,

Y.J. Mo

e

,

H. Moeini

w

,

C. Morales Morales

m

,

K. Moriya

r

,

N.Yu. Muchnoi

h

,

1

,

H. Muramatsu

aq

,

Y. Nefedov

v

,

F. Nerling

m

,

I.B. Nikolaev

h

,

1

,

Z. Ning

a

,

S. Nisar

g

,

X.Y. Niu

a

,

S.L. Olsen

ad

,

Q. Ouyang

a

,

S. Pacetti

t

,

M. Pelizaeus

c

,

H.P. Peng

as

,

K. Peters

i

,

J.L. Ping

z

,

R.G. Ping

a

,

R. Poling

aq

,

M. Qi

aa

,

S. Qian

a

,

C.F. Qiao

ao

,

L.Q. Qin

ae

,

N. Qin

az

,

X.S. Qin

a

,

Y. Qin

ac

,

Z.H. Qin

a

,

J.F. Qiu

a

,

K.H. Rashid

au

,

C.F. Redmer

u

,

M. Ripka

u

,

G. Rong

a

,

X.D. Ruan

k

,

A. Sarantsev

v

,

5

,

*

Correspondingauthor.

1 _Also_at_the_Novosibirsk_State_University,_Novosibirsk,_630090,_Russia.

2 _Also_at_the_Moscow_Institute_of_Physics_and_Technology,_Moscow_141700,_Russia.

3 _Also_at_the_Moscow_Institute_of_Physics_and_Technology,_Moscow_141700,_Russia_and_at_the_Functional_Electronics_Laboratory,_Tomsk_State_University,_Tomsk,_634050, Russia.

4 _Also_at_University_of_Texas_at_Dallas,_Richardson,_{TX 75083,}_USA. 5 _Also_at_the_PNPI,_Gatchina_188300,_Russia.

http://dx.doi.org/10.1016/j.physletb.2014.06.013

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K. Schoenning

ay

,

S. Schumann

u

,

W. Shan

ac

,

M. Shao

as

,

C.P. Shen

b

,

X.Y. Shen

a

,

H.Y. Sheng

a

,

M.R. Shepherd

r

,

W.M. Song

a

,

X.Y. Song

a

,

S. Spataro

av

,

ax

,

B. Spruck

an

,

G.X. Sun

a

,

J.F. Sun

n

,

S.S. Sun

a

,

Y.J. Sun

as

,

Y.Z. Sun

a

,

Z.J. Sun

a

,

Z.T. Sun

as

,

C.J. Tang

ag

,

X. Tang

a

,

I. Tapan

am

,

E.H. Thorndike

ar

,

D. Toth

aq

,

M. Ullrich

an

,

I. Uman

al

,

G.S. Varner

ap

,

B. Wang

ab

,

D. Wang

ac

,

D.Y. Wang

ac

,

K. Wang

a

,

L.L. Wang

a

,

L.S. Wang

a

,

M. Wang

ae

,

P. Wang

a

,

P.L. Wang

a

,

Q.J. Wang

a

,

S.G. Wang

ac

,

W. Wang

a

,

X.F. Wang

aj

,

Y.D. Wang

s

,

Y.F. Wang

a

,

Y.Q. Wang

u

,

Z. Wang

a

,

Z.G. Wang

a

,

Z.H. Wang

as

,

Z.Y. Wang

a

,

D.H. Wei

j

,

J.B. Wei

ac

,

P. Weidenkaff

u

,

S.P. Wen

a

,

M. Werner

an

,

U. Wiedner

c

,

M. Wolke

ay

,

L.H. Wu

a

,

N. Wu

a

,

Z. Wu

a

,

L.G. Xia

aj

,

Y. Xia

q

,

D. Xiao

a

,

Z.J. Xiao

z

,

Y.G. Xie

a

,

Q.L. Xiu

a

,

G.F. Xu

a

,

L. Xu

a

,

Q.J. Xu

l

,

Q.N. Xu

ao

,

X.P. Xu

ah

,

Z. Xue

a

,

L. Yan

as

,

W.B. Yan

as

,

W.C. Yan

as

,

Y.H. Yan

q

,

H.X. Yang

a

,

L. Yang

az

,

Y. Yang

e

,

Y.X. Yang

j

,

H. Ye

a

,

M. Ye

a

,

M.H. Ye

f

,

B.X. Yu

a

,

C.X. Yu

ab

,

H.W. Yu

ac

,

J.S. Yu

x

,

S.P. Yu

ae

,

C.Z. Yuan

a

,

W.L. Yuan

aa

,

Y. Yuan

a

,

A. Yuncu

al

,

A.A. Zafar

au

,

A. Zallo

s

,

S.L. Zang

aa

,

Y. Zeng

q

,

B.X. Zhang

a

,

B.Y. Zhang

a

,

C. Zhang

aa

,

C.B. Zhang

q

,

C.C. Zhang

a

,

D.H. Zhang

a

,

H.H. Zhang

ai

,

H.Y. Zhang

a

,

J.J. Zhang

a

,

J.Q. Zhang

a

,

J.W. Zhang

a

,

J.Y. Zhang

a

,

J.Z. Zhang

a

,

S.H. Zhang

a

,

X.J. Zhang

a

,

X.Y. Zhang

ae

,

Y. Zhang

a

,

Y.H. Zhang

a

,

Z.H. Zhang

e

,

Z.P. Zhang

as

,

Z.Y. Zhang

az

,

G. Zhao

a

,

J.W. Zhao

a

,

Lei Zhao

as

,

Ling Zhao

a

,

M.G. Zhao

ab

,

Q. Zhao

a

,

Q.W. Zhao

a

,

S.J. Zhao

bb

,

T.C. Zhao

a

,

X.H. Zhao

aa

,

Y.B. Zhao

a

,

Z.G. Zhao

as

,

A. Zhemchugov

v

,

2

_,

_{B. Zheng}

at

_,

_{J.P. Zheng}

a

_,

_{Y.H. Zheng}

ao

_,

_{B. Zhong}

z

_,

_{L. Zhou}

a

_,

Li Zhou

ab

,

X. Zhou

az

,

X.K. Zhou

ao

,

X.R. Zhou

as

,

X.Y. Zhou

a

,

K. Zhu

a

,

K.J. Zhu

a

,

X.L. Zhu

aj

,

Y.C. Zhu

as

,

Y.S. Zhu

a

,

Z.A. Zhu

a

,

J. Zhuang

a

,

B.S. Zou

a

,

J.H. Zou

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

e_Central_China_Normal_University,_Wuhan_430079,_People’s_Republic_of_China

f_China_Center_of_Advanced_Science_and_Technology,_Beijing_100190,_People’s_Republic_of_China

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

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

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

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

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

s_INFN_Laboratori_Nazionali_di_Frascati,_I-00044,_Frascati,_Italy t_INFN_and_University_of_Perugia,_I-06100,_Perugia,_Italy

u_Johannes_Gutenberg_University_of_Mainz,_{Johann-Joachim-Becher-Weg}_45,_D-55099_Mainz,_Germany v_Joint_Institute_for_Nuclear_Research,₁₄₁₉₈₀_Dubna,_Moscow_Region,_Russia

w_KVI,_University_of_Groningen,_NL-9747_AA_Groningen,_The_Netherlands x_Lanzhou_University,_Lanzhou_730000,_People’s_Republic_of_China y_Liaoning_University,_Shenyang_110036,_People’s_Republic_of_China z

NanjingNormalUniversity,Nanjing210023,People’sRepublicofChina aa_Nanjing_University,_Nanjing_210093,_People’s_Republic_of_China ab_Nankai_University,_Tianjin_300071,_People’s_Republic_of_China ac_Peking_University,_Beijing_100871,_People’s_Republic_of_China ad_Seoul_National_University,_Seoul,_151-747,_Republic_of_Korea ae_Shandong_University,_Jinan_250100,_People’s_Republic_of_China af_Shanxi_University,_Taiyuan_030006,_People’s_Republic_of_China ag_Sichuan_University,_Chengdu_610064,_People’s_Republic_of_China ah_Soochow_University,_Suzhou_215006,_People’s_Republic_of_China ai_Sun_Yat-Sen_University,_Guangzhou_510275,_People’s_Republic_of_China aj_Tsinghua_University,_Beijing_100084,_People’s_Republic_of_China ak_Ankara_University,_Dogol_Caddesi,₀₆₁₀₀_Tandogan,_Ankara,_Turkey al_Dogus_University,₃₄₇₂₂_Istanbul,_Turkey

am_Uludag_University,₁₆₀₅₉_Bursa,_Turkey an_Universität_Giessen,_D-35392_Giessen,_Germany

ao_University_of_Chinese_Academy_of_Sciences,_Beijing_100049,_People’s_Republic_of_China ap_University_of_Hawaii,_Honolulu,_{HI 96822,}_USA

aq_University_of_Minnesota,_Minneapolis,_{MN 55455,}_USA ar_University_of_Rochester,_Rochester,_{NY 14627,}_USA

as_University_of_Science_and_Technology_of_China,_Hefei_230026,_People’s_Republic_of_China at_University_of_South_China,_Hengyang_421001,_People’s_Republic_of_China

au_University_of_the_Punjab,_Lahore_54590,_Pakistan av_University_of_Turin,_I-10125,_Turin,_Italy

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aw_University_of_Eastern_Piedmont,_I-15121,_Alessandria,_Italy ax_INFN,_I-10125,_Turin,_Italy

ay_Uppsala_University,_Box_516,_SE-75120_Uppsala,_Sweden az_Wuhan_University,_Wuhan_430072,_People’s_Republic_of_China ba_Zhejiang_University,_Hangzhou_310027,_People’s_Republic_of_China bb_Zhengzhou_University,_Zhengzhou_450001,_People’s_Republic_of_China

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Articlehistory: Received24March2014

Receivedinrevisedform26May2014 Accepted6June2014

Availableonline10June2014 Editor: V.Metag

Keywords: BESIII

Charmoniumdecay Protonformfactor

Using2917 pb−1 ofdataaccumulatedat3.773 GeV,44.5 pb−1 ofdata accumulatedat3.65 GeV and

data accumulated during a ψ(3770) line-shape scan with the BESIII detector, the reactione+e−_→

pp is¯ studied considering a possible interference between resonant and continuum amplitudes. The

cross sectionofe+e−→ ψ(3770) →p¯p,

σ

(e+e−→ ψ(3770) →pp¯),isfound tohave two solutions,

determinedtobe

(

0.059+0.070

−0.020±0.012)pb withthephaseangle

φ

= (255.8+

39.0

−26.6±4.8)◦(<0.166 pb at

the90%conﬁdencelevel),or

σ

(e+e−→ ψ(3770) →pp¯) = (2.57+₋0₀_..12₁₃±0.12)pb with

φ

= (266.9+₋6₆._.1₃±

0.9)◦bothofwhichagreewithadestructiveinterference.Usingtheobtainedcrosssectionof

ψ(

3770) →

pp,¯ thecrosssectionofpp¯→ ψ(3770),whichisusefulinformationforthefuturePANDAexperiment,is

estimatedtobeeither

(

9.8₋+₃11_.₉.8)nb (<27.5 nb at90% C.L.)or

(

425.6₋+₄₃42._.9₇)nb.

(http://creativecommons.org/licenses/by/3.0/).FundedbySCOAP3.

1. Introduction

At

e

+e− colliders,charmoniumstateswith JP C

₌

₁−−_,_such_as

the J

/ψ

,

ψ(

3686

)

,and

ψ(

3770

)

,areproduced throughelectron– positron annihilation into a virtual photon. These charmonium statescanthendecayintolighthadronsthrougheitherthe three-gluon process (e+e−

→ ψ →

ggg

→

hadrons) or the one-photon process (e+e−

→ ψ →

γ

∗

→

hadrons). In addition to the above twoprocesses,thenon-resonant process (e+e−

→

γ

∗

→

hadrons)

plays an importantrole, especially inthe

ψ(

3770

)

energyregion wherethenon-resonantproductioncrosssectioniscomparableto theresonantone.

The

ψ(

3770

)

, the lowest lying 1−− charmonium state above the DD threshold,

¯

isexpectedtodecay dominantlyintothe OZI-allowed DD ﬁnal

¯

states [1,2].However, assuming nointerference effects between resonant and non-resonant amplitudes, the BES Collaboration found a large total non-DD branching

¯

fraction of

(

14

.

5

±

1

.

7

±

5

.

8

)

% [3–6].AlaterworkbytheCLEOCollaboration,

which included interference between one-photon resonant and

one-photon non-resonant amplitudes (assuming no interference with the three-gluon amplitude), found a contradictory non-DD

¯

branching fraction of

(

−

3

.

3

±

1

.

4₋+₄6._.6₈

)

% [7]. These different re-sultscouldbecausedbyinterferenceeffects.Moreover,ithasbeen notedthatthe interferenceofthenon-resonant (continuum) am-plitude with the three-gluon resonant amplitude should not be neglected[8].Toclarifythesituation,manyexclusivenon-DD de-

¯

caysofthe

ψ(

3770

)

havebeen investigated[9,10].Lowstatistics, however,especially inthe scan data sets havenot permitted the inclusionofinterferenceeffectsintheseexclusivestudies.

BESIIIhascollectedtheworld’slargestdatasampleof

e

+e− col-lisions at3

.

773 GeV. Analyzedtogether withdata samplestaken during a

ψ(

3770

)

line-shape scan, investigations ofexclusive de-cays, taking into account the interference of resonant and non-resonant amplitudesare nowpossible. Recently, the decay chan-nel of

ψ(

3770

)

→

pp

¯

π

0 _[11] _has _been _studied _considering _the abovementionedinterference.InthisLetter,wereportonastudy of the two-body ﬁnal state e+e−

→

pp in

¯

the vicinity of the

ψ(

3770

)

based on data sets collected with the upgraded Beijing Spectrometer (BESIII)locatedattheBeijingElectron–Positron Col-lider (BEPCII) [12]. The data sets include 2917 pb−1 of data at 3

.

773 GeV, 44

.

5 pb−1 of data at 3

.

65 GeV [13], anddata taken during a

ψ(

3770

)

line-shapescan in theenergyrangefrom 3

.

74 to3

.

90 GeV.

2. BESIIIdetector

The BEPCII is a modern accelerator featuring a multi-bunch

double ring and high luminosity, operating with beam

ener-gies between 1.0 and 2

.

3 GeV and a design luminosity of 1

×

1033 _cm−2_s−1_. _The _BESIII _detector _is _a _{high-performance} gen-eralpurpose detector.It iscomposed ofa helium-gasbaseddrift chamber (MDC) for charged-particle tracking andparticle identi-ﬁcation byspeciﬁcionization

dE

/

dx, aplasticscintillator time-of-flight (TOF)systemforadditionalparticleidentification, aCsI (Tl) electromagnetic calorimeter (EMC) for electronidentification and photon detection, a super-conducting solenoid magnet providing

a 1.0 Tesla magnetic ﬁeld, and a muon detector composed of

resistive-plate chambers. The momentum resolution for charged particlesat1 GeV

/

c is 0

.

5%.The energyresolutionof1 GeV pho-tonsis 2

.

5%. Moredetails onthe acceleratoranddetectorcanbe foundinRef.[12].

A geant4-based [14] Monte Carlo (MC) simulation software

package, which includes a description of the geometry, material, and response of the BESIII detector, is used for detector simu-lations. The signal andbackground processes are generated with

dedicated models that have been packaged and customized for

BESIII [15]. Initial-state radiation (ISR) effects are not included at the generator level for the eﬃciency determination, but are corrected later using a standard ISR correction procedure [16, 17]. In the ISR correction, phokhara [18] is used to produce a MC-simulated sample of e+e−

→

γ

ISRpp (without γ

¯

ISRJ

/ψ

and

γ

ISR

ψ(

3686

)

).Fortheestimationofbackgroundsfrom

γ

ISR

ψ(

3686

)

and e+e−

→ ψ(

3770

)

→

DD,

¯

MC-simulated samples witha size equivalentto10timesthesizeofdatasamplesareanalyzed.

3. Eventselection

Theﬁnalstateinthisdecayischaracterizedbyoneprotonand one antiproton. Twocharged tracks withopposite charge are re-quired.Eachtrackisrequiredtohaveitspointofclosestapproach tothebeamaxiswithin10 cm oftheinteractionpointinthebeam directionandwithin 1 cm ofthebeamaxisintheplane perpen-diculartothebeam.Thepolarangleofthetrackisrequiredtobe withintheregion

|

cos

θ

|

<

0

.

8.

The TOF information is used to calculate particle identiﬁca-tion (PID)probabilitiesforpion,kaonandprotonhypotheses[19]. Foreachtrack, theparticletypeyieldingthelargestprobability is

(4)

Fig. 1. ComparisonsbetweenexperimentalandMCsimulationdataofselectede+e−→pp events¯ at3.773 GeV.(a) Theinvariantmassofp¯p calculatedwithraw4-momenta; (b) theanglebetweentheprotonandantiproton (θpp¯)intherestframeoftheoveralle+e−CMSsystem;(c) themagnitudeoftheprotonmomentum;(d) thecosθofthe

protonmomentum.TheblackhistogramsareMCsimulationsandtheredcrossesareexperimentaldata.(Forinterpretationofthereferencestocolorinthisﬁgurelegend, thereaderisreferredtothewebversionofthisarticle.)

assigned.Here,themomentumofprotonishigh(

>

1

.

6 GeV

/

c). For

thishigh momentum protons andantiprotons, the PID eﬃciency

is about95%. The ratio ofkaons to be mis-identiﬁed as protons is about5%. Inthis analysis, one charged trackis requiredto be identiﬁedasaprotonandtheotheroneasanantiproton.

Theanglebetweentheprotonandantiproton(

θ

pp¯)intherest

frame of the overall e+e− CMSsystem is required to be greater than 179 degrees. Finally, for both tracks, the absolute

differ-ence between the measured and the expected momentum (e.g.

1

.

637 GeV

/

c for the

ψ(

3770

)

data sample) should be less than 40 MeV

/

c (about 3

σ

).

Afterimposingtheaboveeventselectioncriteria,684

±

26 can-didateeventsremainfromthe

ψ(

3770

)

dataset.Comparisons be-tween experimental and MC data are plotted in Fig. 1. The MC simulationagreeswiththeexperimentaldata.Forotherdatasets, signal events are selected with similar selection criteria. Signal yieldsarelistedinTable 1.

4. Backgroundestimation

Background from ISR to the lower lying

ψ(

3686

)

resonance, whichisnottakenintoaccountintheISRcorrectionprocedure,is estimatedwithasampleofMC-simulateddata.Thenumberof ex-pectedbackgroundeventsfromthisprocessis0.1andisneglected inthisanalysis.

Backgroundfrom

ψ(

3770

)

→

DD is

¯

estimatedwithaninclusive MC sample and can also be neglected. Exclusive channels, such as e+e−

→

K+K−,

μ

+

μ

−,

τ

+

τ

−, pp

¯

π

0_, _p_p

_¯

_γ

_are _also _studied. The total background contribution is estimated to be 0.4 events, which is equivalent to a contamination ratio of 0.06%. Contribu-tions from decay channels with unmeasured branching fractions forthe

ψ(

3770

)

are estimatedby the branching fractions ofthe correspondingdecaychannelsof

ψ(

3686

)

.Thesebackground con-tributions fromunmeasured decaymodesare takeninto account inthe systematicuncertainty (0.06%) instead of beingsubtracted directly.

The data set at 3

.

65 GeV contains a contribution from the

ψ(

3686

)

tail, whose cross section is estimated to be 0

.

136

±

0

.

012 nb [6]. The normalized contribution from this tail, 0.89 events,isalsostatisticallysubtractedfromtherawsignalyield.

5. Determinationofcrosssections

The observed cross sections at the center-of-mass energies

√

s

=

3

.

65,3

.

773 GeV andthefourteendifferentenergypoints in the vicinity of the

ψ(

3770

)

resonance are determined according to

σ

=

Nsig

L ,where

is thedetectioneﬃciency determinedfrom

MC simulationandL is theintegratedluminosityforeachenergy point.TheobservedcrosssectionsarelistedinTable 1.Forenergy points with no signiﬁcant signal, upper limits on the cross sec-tionat90%C.L.aregivenusingtheFeldman–Cousinsmethodfrom Ref.[20].

The observedcrosssection of

e

+e−

→

pp contains

¯

the lowest orderBorncrosssectionandsomehigherordercontributions.The BaBarCollaboration[21,22]hastakenintoaccountbremsstrahlung,

e+e− self-energy andvertexcorrectionsintheir radiative correc-tion. Vacuumpolarization isincludedintheir reportedcross sec-tion. This corrected cross section, which is the sum of the Born crosssectionandthecontributionofvacuumpolarization,iscalled thedressedcrosssection.InordertousetheBaBarmeasurements of

σ

(

e+e−

→

pp

¯

)

[21,22] inourinvestigation, aradiative correc-tion isperformedto calculatethedressedcrosssection usingthe method described in Refs. [16,17]. With the observed cross sec-tions asourinitialinput,a ﬁtto theline-shapeequation (Eq.(1)) isperformediteratively.Ateachiteration,theISRcorrectionfactors arecalculatedandthedressedcrosssectionsareupdated.The cal-culation convergesaftera few iterations (

∼

5). Thedressed cross section ateachdatapoint islistedinTable 1.Asareference, the Born cross sectionsare also calculatedandgiven inTable 1. The Born cross section around 3.773 GeV is in excellent agreement withapreviousmeasurementobtainedwithCLEOdata[23].

(5)

Table 1

Summaryofresultsatcenter-of-massenergiesfrom3.65to3.90 GeV.Nsigisthenumberofe+e−→pp events;¯

isthedetectioneﬃciency;L istheintegratedluminosity;

(1+ δ)dressedistheinitialstateradiationcorrectionfactorwithoutthevacuumpolarizationcorrection;and

σ

obs,

σ

dressedand

σ

Bornaretheobservedcrosssection,thedressed crosssectionandtheBorncrosssection,respectively.

√

s (GeV) Nsig (%) L (pb−1) (1+ δ)dressed σobs(pb) σdressed(pb) σBorn(pb) 3.650 26.0±5.1 62.6±0.4 44.5 0.76 0.90±0.18±0.06 1.19±0.24±0.08 1.12±0.22±0.08 3.748 1.0+1.8 −0.6 61.2±0.4 3.57 0.76 0.46+ 0.83 −0.28±0.03 0.60+ 1.08 −0.36±0.04 0.54+ 0.97 −0.32±0.04 3.752 3.0+2.3 −1.9 60.8±0.4 6.05 0.76 0.82+ 0.63 −0.52±0.06 1.07+ 0.82 −0.68±0.08 0.96+ 0.74 −0.61±0.07 3.755 4.0+2.8 −1.7 61.7±0.4 7.01 0.77 0.93+ 0.65 −0.39±0.06 1.21+ 0.85 −0.51±0.09 1.09+ 0.76 −0.46±0.08 3.760 4.0+₋21..87 62.4±0.4 8.65 0.77 0.74+ 0.52 −0.32±0.05 0.96+ 0.67 −0.41±0.07 0.87+ 0.61 −0.37±0.06 3.766 0.0+₋10..30 62.4±0.4 5.57 0.79 0.00+ 0.37 −0.00(<0.70) 0.00+ 0.47 −0.00(<0.89) 0.00+ 0.43 −0.00(<0.81) 3.772 0.0+₋10..30 62.5±0.4 3.68 0.80 0.00+ 0.56 −0.00(<1.06) 0.00+ 0.70 −0.00(<1.33) 0.00+ 0.64 −0.00(<1.20) 3.773 684.0±26 62.3±0.4 2917 0.80 0.38±0.01±0.03 0.47±0.02±0.04 0.43±0.02±0.03 3.778 0.0+1.3 −0.0 62.6±0.4 3.61 0.78 0.00+ 0.57 −0.00(<1.08) 0.00+ 0.74 −0.00(<1.39) 0.00+ 0.66 −0.00(<1.25) 3.784 0.0+1.3 −0.0 62.4±0.4 4.57 0.75 0.00+ 0.45 −0.00(<0.85) 0.00+ 0.60 −0.00(<1.14) 0.00+ 0.54 −0.00(<1.02) 3.791 1.0+1.8 −0.6 62.1±0.4 6.10 0.74 0.26+ 0.48 −0.16±0.02 0.35+ 0.64 −0.21±0.02 0.32+ 0.57 −0.19±0.02 3.798 3.0+₋21..39 61.9±0.4 7.64 0.75 0.63+ 0.49 −0.40±0.04 0.85+ 0.65 −0.54±0.06 0.77+ 0.59 −0.48±0.05 3.805 1.0+₋10..86 61.5±0.4 4.34 0.75 0.37+ 0.67 −0.22±0.03 0.50+ 0.90 −0.30±0.04 0.45+ 0.81 −0.27±0.03 3.810 20.0±4.5 62.4±0.4 52.60 0.75 0.61±0.14±0.04 0.81±0.18±0.06 0.73±0.16±0.05 3.819 1.0+1.8 −0.6 61.4±0.4 1.05 0.75 1.55+ 2.79 −0.93±0.11 2.06+ 3.70 −1.23±0.14 1.85+ 3.34 −1.11±0.13 3.900 12.0+4.3 −3.2 61.7±0.4 52.61 0.76 0.37+ 0.13 −0.10±0.03 0.49+ 0.17 −0.13±0.03 0.44+ 0.16 −0.12±0.03

6. Fittothecrosssection

To extract the

ψ(

3770

)

→

pp cross

¯

section, the total cross section asa function of

√

s is constructed anda ﬁt to the mea-sured values is performed. As discussed in the introduction, the measured cross section is composed of three contributions: the three-gluonresonantprocess ( A3g),theone-photonresonant pro-cess ( Aγ )andthe non-resonant process ( Acon). Forthe exclusive

lighthadrondecayofthe

ψ(

3770

)

,thecontributionofthe electro-magneticprocess Aγ isnegligible comparedtothat ofthe three-gluonstronginteraction

A

3g[24].Theresonantamplitudecanthen bewrittenasAψ

≡

A3g

+

Aγ

∼

A3g.Finally,thetotalcrosssection canbeconstructedwithonlytwoamplitudes,Aψ andAcon,

σ

(

s

)

=

Acon

+

Aψeiφ

2

=

σ

con

(

s

)

+ √

σ

ψ mψ

Γ

ψ s

−

m2_ψ

+

imψ

Γ

ψ eiφ

2

,

(1)

wheremψ and

Γψ

are the massandwidthofthe

ψ(

3770

)

[25],

respectively;

φ

describesthephaseanglebetweenthe continuum andresonant amplitudes,which is a free parameter to be deter-mined in the ﬁt;and

σ

ψ isthe resonant cross section, which is

alsoafreeparameter.

Thecontinuumcrosssection,

σ

con,hasbeenmeasuredbymany

experiments [21,22,26,27]. In Ref. [26] from the BESII Collabora-tion,

σ

conwasmeasuredfrom2 to3

.

07 GeV,andiswell-described

withan

s dependence

accordingto

σ

con

(

s

)

=

4

π α

2_v 3s

1

+

2m 2 p s

G

(

s

)

2

,

(2)

G

(

s

)

=

C s2_ln2

₍

_s

_/Λ

2

₎

.

(3) Here

α

istheﬁne-structureconstant;

m

p isthenominalproton

mass;

v is

theprotonvelocityinthe

e

+e−restframe;

G

(

s

)

isthe effectiveproton form factor [27];

Λ

=

0

.

3 GeV is the QCD scale parameter;and

C is

afreeparameter.

Thedressedcross sectionsinTable 1,togetherwiththeBaBar measurementsofthecrosssectionsbetween3 and4 GeV,are ﬁt-tedwithEq.(1).Inthisﬁt,26 datapointsareconsidered:16points from this investigation by BESIII, 5 points from Ref. [21] and 5

Table 2

Summaryoftheextractedresultsfordifferentsolutionsoftheﬁt.Upperlimitsare determinedat90% C.L. Solution σdressed (ψ (3770)→pp¯)(pb) φ(◦) (1) 0.059₋+00..070020±0.012 255.8+ 39.0 −26.6±4.8 (<0.166 at 90% C.L.) (2) 2.57₋+00..1213±0.12 266.9+ 6.1 −6.3±0.9 points fromRef.[22]. Thefree parametersare thephaseangle

φ

, theresonantcrosssection

σ

ψ,and

C from

theformfactor

describ-ingthecontributionofthecontinuum.Fig. 2showsthedatapoints andtheﬁtresult.

The ﬁt yields a

χ

2

_/

_{ndf of}₁₃

_.

₄

_/

_23. _Two _solutions _are _found withthesame

χ

2 _and_the_same_parameter

_{C of}

₍

₆₂

_.

₀

_±

₂

_.

₃

₎

_GeV4_.

Two solutions are found because the cross section in Eq. (1)

is constructed with the square of two amplitudes. This multi-solution problem has been explained in Ref. [28]. A dip indi-cating destructive interference is seen clearly in the ﬁt (the red solid line in Fig. 2). The ﬁrst solution for the cross section is

σ

dressed

(

e+e−

→ ψ(

3770

)

→

pp

¯

)

= (

0

.

059+₋00..070020

)

pb witha phase angle

φ

= (

255

.

8₋+39₂₆_..0₆

)

◦ (

<

0

.

166 pb at the90% C.L.). Thesecond solutionis

σ

dressed

(

e+e−

→ ψ(

3770

)

→

pp

¯

)

= (

2

.

57+₋00..1213

)

pb with aphaseangle

φ

= (

266

.

9₋+₆6._.1₃

)

◦.

For comparison, an alternative ﬁt with only the BESIII data

points is performed. Two solutions are found with the same

χ

2

_/

_{ndf of}₆

_.

₈

_/

_{13 and}_the_same_parameter

_{C of}

₍

₆₂

_.

₆

_±

₄

_.

₁

₎

_GeV4_. The ﬁrst solution for the cross section is

σ

dressed

(

e+e−

→

ψ(

3770

)

→

pp

¯

)

= (

0

.

067₋+₀0._.088₀₃₄

)

pb with a phase angle

φ

=

(

253

.

8+₋40₂₅._.7₄

)

◦. Thesecond solutionis

σ

dressed

(

e+e−

→ ψ(

3770

)

→

pp

¯

)

= (

2

.

59

±

0

.

20

)

pb with a phase angle

φ

= (

266

.

4

±

6

.

3

)

◦. These two solutions agree with those from the previous ﬁt, but havelargeruncertainties.

Table 2showsasummaryofthefitresults,wherethefirsterror isfromthefitandtheseconderrorisfromthecorrelated system-aticuncertainties.

7. Systematicuncertaintystudy

Thesourcesofsystematicuncertaintyinthecrosssection mea-surementsare divided intotwo categories: uncorrelatedand

(6)

cor-Fig. 2. Fittothedressedcrosssectionofe+e−→pp as¯ afunctionofcenter-of-mass energy.Theredsolidlineshowstheﬁtcurve.Thesolidsquarepointswitherror barsarefromBESIII.TheopencirclesarefromtheBaBarmeasurementsofRef.[21], andtheopentrianglesfromRef.[22].Theinsetshowsazoomoftheregioninthe vicinityoftheψ(3770).(Forinterpretationofthereferencestocolorinthisﬁgure legend,thereaderisreferredtothewebversionofthisarticle.)

related uncertainties between different energy points. The for-merincludes onlythestatisticaluncertaintyin theMC simulated samples (0.4%), which can be directly considered in the ﬁt. The latter refers to the uncertainties that are correlated among dif-ferent energy points, such as the tracking (4% for two charged tracks), particle identiﬁcation (4% for both proton and antipro-ton),andintegratedluminosity.The integratedluminosityforthe

data was measured by analyzing large angle Bhabha scattering

events [13] and has a total uncertainty of 1.1% at each energy point.

To estimate the uncertainty from the radiative corrections, a differentcorrectionprocedureusingthestructure-function meth-od [29] is applied, and the difference in results from these two correctionprocedures (2%)istakenastheuncertainty.To investi-gatetheimpactofthepossibleinconsistencyoftheMCsimulation andexperimentaldata,analternativeMCsimulatedsampleis gen-erated witha differentprotonmomentum resolution (15%better than the previous MC sample), and the change in the ﬁnal re-sults (1.4%)istakenastheuncertainty.

In addition, the uncertainty on the reconstruction eﬃciency from the unmeasured angular distribution of the proton in the rest frame of the overall e+e− CMS system is also studied. Ac-cording to hadron helicity conservation, the angular distribution of

ψ

→

p

¯

p can be expressed as _dcosdN_θ

∝

1

+

α

cos2

θ

, where

θ

is theanglebetweenthe protonandthepositronbeamdirectionin thecenter-of-masssystem.Thetheoreticalvalueof

α

=

0

.

813[30] is used to produce the MC simulated sample in this analysis. In the case of

ψ(

3686

)

→

p

¯

p, the mean value of

α

measured by E835 (0.67

±

0.16) [31] differs by 0

.

13 from the theoretical value of 0

.

80. To obtain a conservative uncertainty, an alternative MC simulated sample with

α

=

0

.

683 is used and the difference in theresults (1.0%)istakenastheuncertainty.Theuncertaintyfrom theanglecutbetweentheprotonandantiprotonisinvestigatedby varyingtheanglecut(from178.9to179.5degrees)andthe differ-ence (2.2%)istakenastheuncertainty.

Allof theabove sources ofuncertaintyare applied tothe ob-served cross section at each energy point. The total systematic uncertaintyoftheindividualenergypointsis6.7%.

Thesystematicuncertainties ontheparametersextractedfrom theﬁt,suchas

σ

dressed

(ψ (3770)→p¯p)andthephaseangle

φ

,areestimated

bythe“offsetmethod”[32],inwhichtheerrorpropagationis de-terminedfromshiftingthedatabytheaforementionedcorrelated

uncertaintiesandaddingthedeviationsinquadrature.Inaddition, a1 MeV uncertaintyforthebeamenergymeasurementsofallthe datapointsisconsideredintheﬁt.

8. Summaryanddiscussion

Using 2917 pb−1 ofdatacollectedat3

.

773 GeV,44

.

5 pb−1 of data collected at 3

.

65 GeV and data collected during a

ψ(

3770

)

line-shape scan with the BESIII detector, the reaction e+e−

→

pp has

¯

been studied. To extract the cross section of e+e−

→

ψ(

3770

)

→

pp,

¯

a ﬁt, takingintoaccount the interferenceof res-onant andcontinuumamplitudes,is performed.In this investiga-tion, the measured cross sectionsof e+e−

→

pp from

¯

the BaBar experiment are included ina simultaneous ﬁt to put more con-straintsonthecontinuumamplitude.Thedressedcrosssectionof

e+e−

→ ψ(

3770

)

→

pp is

¯

extractedfromtheﬁtandshownin Ta-ble 2.

Withtheobtaineddressedcrosssectionof

e

+e−

→ ψ(

3770

)

→

pp,

¯

the branching fraction Bψ (3770)→p¯p is determined to be

(

7

.

1₋+₂8._.6₉

)

×

10−6 or

(

3

.

1

±

0

.

3

)

×

10−4, by dividing the dressed crosssectionof

e

+e−

→ ψ(

3770

)

[7].Eventhelargersolutionhas a relatively small branching fraction comparing to the large to-talnon-DD branching

¯

fraction.Thus,the pp channel

¯

alonecannot explainthelargenon-DD branching

¯

fractionfromBESII.

Using thebranching fractionof

ψ(

3770

)

→

pp,

¯

thecross sec-tionofitstimereversedreaction

p

¯

→ ψ(

3770

)

canbeestimated usingtheBreit–Wignerformula[25]:

σ

pp¯→ψ(3770)

(

s

)

=

4

π

(

2 J

+

1

)

(

s

−

4m2p

)

Bψ (3770)→pp¯ 1

+ [

2

(

√

s

−

Mψ

)/Γ

ψ

]

2 (4)

where Mψ and

Γ

ψ are themassandwidthofthe

ψ(

3770

)

reso-nance, J is the spinof the

ψ(

3770

)

,and

m

p is theprotonmass.

For thecondition

√

s

=

Mψ, the crosssection

σ

(

pp

¯

→ ψ(

3770

))

is estimatedto beeither

(

9

.

8+₋11₃_.₉.8

)

nb (

<

27

.

5 nb at90% C.L.)or

(

425

.

6+₋42₄₃._.9₇

)

nb.

ThefuturePANDA (anti-Proton

¯

ANnihilationsatDArmstadt) ex-periment isone ofthe key projectsat theFacility forAntiproton and Ion Research (FAIR), which is currently under construction at GSI, Darmstadt. It will perform precise studies of antiproton– protonannihilationswithvariousinternalprotonornucleartargets andanantiproton beaminthemomentumrangefrom1

.

5 GeV

/

c

to 15 GeV

/

c. In PANDA,

¯

a detailedinvestigation of the charmo-niumspectrumandtheopencharmchannelsisforeseen.Forthis physics program, it isimportant toobtain experimental informa-tion on the so far unknown open charm cross sections,both to evaluateluminosity requirementsandtodesigndetector. Theoret-icalestimationsvarywithseveralordersofmagnitude[33–41].In the physics performance report for PANDA

¯

[42], the DD produc-

¯

tion crosssection is estimatedto be 6

.

35 nb, withtheunknown branching ratioof

ψ(

3770

)

→

pp scaled

¯

fromtheknownratioof

J

/ψ

→

pp.

¯

In thispaper,the crosssection of

σ

(

pp

¯

→ ψ(

3770

))

hasbeendetermined.Astheﬁrstcharmoniumstateabovethe DD

¯

threshold,

ψ(

3770

)

couldbeusedasasourceofopencharm pro-duction.

In this paper, two solutions on the cross section of

σ

(

pp

¯

→

ψ(

3770

))

are obtained. It is impossibleto distinguish these two solutions withour data.The ﬁrstsolution,

(

9

.

8₋+11₃_.₉.8

)

nb, is com-patiblewithasimplescalingfrom J

/ψ

usedinthePANDA physics

¯

performancereport.Thesecondsolution,withthecrosssectionof

(7)

Acknowledgements

The BESIII Collaboration thanks the staff of BEPCII and the

computing center for their strong support. This work is

sup-ported in part by the Ministry of Science and Technology of

China underContract No. 2009CB825200; JointFunds of the Na-tional Natural Science Foundation of China under Contracts Nos. 11079008,11179007,U1332201;NationalNaturalScience Founda-tion of China (NSFC) under Contracts Nos. 10625524, 10821063,

10825524, 10835001, 10935007, 11125525, 11235011; the

Chi-neseAcademyofSciences(CAS)Large-ScaleScientiﬁcFacility

Pro-gram; CAS under Contracts Nos.KJCX2-YW-N29, KJCX2-YW-N45;

100 Talents Program of CAS; German Research Foundation DFG

under Contract No. Collaborative Research Center CRC-1044; Is-tituto Nazionale di Fisica Nucleare, Italy; Ministry of

Develop-ment of Turkey under Contract No. DPT2006K-120470; U.S.

De-partment of Energy under Contracts Nos. DE-FG02-04ER41291,

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

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

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