b

Physics Letters B 630 (2005) 14–20

www.elsevier.com/locate/physlet

Measurement of the cross section fore+e− → pp̄ atcenter-of-mass energies from 2.0 to 3.07 GeV

BES Collaboration

M. Ablikim a, J.Z. Baia, Y. Bank, J.G. Biana, X. Caia, H.F. Chenp, H.S. Chena,H.X. Chena, J.C. Chena, Jin Chena, Y.B. Chena, S.P. Chib, Y.P. Chua, X.Z. Cuia,Y.S. Dair, Z.Y. Denga, L.Y. Donga,1, Q.F. Dongn, S.X. Dua, Z.Z. Dua, J. Fanga,S.S. Fangb, C.D. Fua, C.S. Gaoa, Y.N. Gaon, S.D. Gua, Y.T. Gud, Y.N. Guoa,

Y.Q. Guoa, Z.J. Guoo, F.A. Harriso, K.L. Hea, M. Hel, Y.K. Henga, H.M. Hua, T. Hua,G.S. Huanga,2, X.P. Huanga, X.T. Huangl, X.B. Jia, X.S. Jianga, J.B. Jiaol, D.P. Jina,

S. Jina, Yi Jin a, Y.F. Laia, G. Li b, H.B. Li a, H.H. Li a, J. Li a, R.Y. Li a, S.M. Li a,W.D. Li a, W.G. Li a, X.L. Li h, X.Q. Li j, Y.L. Li d, Y.F. Liangm, H.B. Liaof, C.X. Liu a,

F. Liu f, Fang Liup, H.H. Liu a, H.M. Liu a, J. Liuk, J.B. Liua, J.P. Liuq, R.G. Liua,Z.A. Liu a, F. Lua, G.R. Lue, H.J. Lup, J.G. Lua, C.L. Luoi, F.C. Mah, H.L. Maa,

L.L. Ma a, Q.M. Maa, X.B. Mae, Z.P. Maoa, X.H. Mo a, J. Niea, S.L. Olseno,H.P. Pengp, N.D. Qia, H. Qini, J.F. Qiua, Z.Y. Rena, G. Ronga, L.Y. Shana, L. Shanga,

D.L. Shena, X.Y. Shena, H.Y. Shenga, F. Shia, X. Shik,3, H.S. Suna, J.F. Suna,S.S. Suna, Y.Z. Suna, Z.J. Suna, Z.Q. Tand, X. Tanga, Y.R. Tiann, G.L. Tonga,

G.S. Varnero, D.Y. Wanga, L. Wanga, L.S. Wanga, M. Wanga, P. Wanga, P.L. Wanga,W.F. Wanga,4, Y.F. Wanga, Z. Wanga, Z.Y. Wanga, Zhe Wanga, Zheng Wangb,

C.L. Weia, D.H. Weia, N. Wua, X.M. Xia a, X.X. Xie a, B. Xin h,2, G.F. Xua, Y. Xu j,M.L. Yanp, F. Yangj, H.X. Yanga, J. Yangp, Y.X. Yangc, M.H. Yeb, Y.X. Ye p,Z.Y. Yi a, G.W. Yua, C.Z. Yuana, J.M. Yuana, Y. Yuana, S.L. Zanga, Y. Zengg,

Yu Zenga, B.X. Zhanga, B.Y. Zhanga, C.C. Zhanga, D.H. Zhanga, H.Y. Zhanga,J.W. Zhanga, J.Y. Zhanga, Q.J. Zhanga, X.M. Zhanga, X.Y. Zhangl, Yiyun Zhangm,

Z.P. Zhangp, Z.Q. Zhange, D.X. Zhaoa, J.W. Zhaoa, M.G. Zhaoj, P.P. Zhaoa,W.R. Zhaoa, Z.G. Zhaoa,5, H.Q. Zhengk, J.P. Zhenga, Z.P. Zhenga, L. Zhoua,

N.F. Zhoua, K.J. Zhua, Q.M. Zhua, Y.C. Zhua, Y.S. Zhua, Yingchun Zhua,6, Z.A. Zhua,B.A. Zhuanga, X.A. Zhuanga, B.S. Zoua

0370-2693/$ – see front matter 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2005.09.044

BES Collaboration / Physics Letters B 630 (2005) 14–20 15

BESII

a Institute of High Energy Physics, Beijing 100049, People’s Republic of Chinab China Center for Advanced Science and Technology (CCAST), Beijing 100080, People’s Republic of China

c Guangxi Normal University, Guilin 541004, People’s Republic of Chinad Guangxi University, Nanning 530004, People’s Republic of China

e Henan Normal University, Xinxiang 453002, People’s Republic of Chinaf Huazhong Normal University, Wuhan 430079, People’s Republic of China

g Hunan University, Changsha 410082, People’s Republic of Chinah Liaoning University, Shenyang 110036, People’s Republic of China

i Nanjing Normal University, Nanjing 210097, People’s Republic of Chinaj Nankai University, Tianjin 300071, People’s Republic of Chinak Peking University, Beijing 100871, People’s Republic of Chinal Shandong University, Jinan 250100, People’s Republic of China

m Sichuan University, Chengdu 610064, People’s Republic of Chinan Tsinghua University, Beijing 100084, People’s Republic of China

o University of Hawaii, Honolulu, HI 96822, USAp University of Science and Technology of China, Hefei 230026, People’s Republic of China

q Wuhan University, Wuhan 430072, People’s Republic of Chinar Zhejiang University, Hangzhou 310028, People’s Republic of China

Received 28 June 2005; accepted 7 September 2005

Available online 30 September 2005

Editor: M. Doser

Abstract

Cross sections fore+e− → pp̄ have been measured at 10 center-of-mass energies from 2.0 to 3.07 GeV by theexperiment at the BEPC, and proton electromagnetic form factors in the time-like region have been determined. 2005 Elsevier B.V. All rights reserved.

nic

60,

07,

.ire,

9,

hetrix

thetric

en-re-

ssare-

edn–ss

1. Introduction

Positron–electron annihilation produces hadrofinal states with an amplitude proportional to

(1)A ∼ e2

sjµJµ,

E-mail address: lihh@mail.ihep.ac.cn(H.H. Li).1 Current address: Iowa State University, Ames, IA 50011-31

USA.2 Current address: Purdue University, West Lafayette, IN 479

USA.3 Current address: Cornell University, Ithaca, NY 14853, USA4 Current address: Laboratoire de l’Accélératear Linéa

F-91898 Orsay, France.5 Current address: University of Michigan, Ann Arbor, MI 4810

USA.6 Current address: DESY, D-22607 Hamburg, Germany.

wheree is the charge of the electron,s is the squareof the center-of-mass energy,jµ is thee+e− current,andJµ is the hadronic current for the final state. Tobject of many experiments is to measure the maelements ofJµ. In e+e− → pp̄, a pair of spin-1/2baryons with internal structure are produced, andcurrent contains two independent form factors, elecand magnetic,GE(s) andGM(s) [1].

Understanding nucleon structure is one of the ctral problems of hadronic physics. In the time-likegion, two processes,e+e− → pp̄ and pp̄ → e+e−,are used to measure the proton form factorsGE(s) andGM(s) as functions of the square of center-of-maenergys. Data samples in previous experimentslimited [2–8]. For 6< s < 8 GeV2, there are no experimental results at present.

In this Letter, we use the data from the upgradBeijing Spectrometer (BESII) at the Beijing ElectroPositron Collider (BEPC) covering the center-of-ma

16 BES Collaboration / Physics Letters B 630 (2005) 14–20

,tionm

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energy of 2.0–3.0 GeV in 1999[9] and the data at 2.22.6, and 3.07 GeV in 2004 to measure the cross secof e+e− → pp̄, and also determine the proton forfactor in this energy range.

2. BES detector

BES is a conventional solenoidal magnet dettor that is described in detail in Ref.[10]; BESII isthe upgraded version of the detector[11]. A 12-layervertex chamber (VC) surrounding the beam pipe pvides trigger and coordinate information. A forty-laymain drift chamber (MDC), located radially outsidthe VC, provides trajectory and energy loss (dE/dx)information for charged tracks over 85% of thetal solid angle. The momentum resolution isσp/p =0.017

√1+ p2 (p in GeV/c), and thedE/dx resolu-

tion for hadron tracks is∼ 8%. An array of 48 scin-tillation counters surrounding the MDC measurestime-of-flight (TOF) of charged tracks with a resoltion of ∼ 200 ps for hadrons. Radially outside the TOsystem is a 12 radiation length, lead-gas barrel shocounter (BSC). This measures the energies of etrons and photons over∼ 80% of the total solid anglewith an energy resolution ofσE/E = 22%/

√E (E in

GeV). Outside of the solenoidal coil, which provide

0.4 tesla magnetic field over the tracking volume, isiron flux return that is instrumented with three doublayers of counters that identify muons of momentgreater than 0.5 GeV/c.

A GEANT3 based Monte Carlo (MC) prograwith detailed consideration of the detector perfmance (such as dead electronic channels) is usesimulate the BESII detector. The consistency betwdata and Monte Carlo has been carefully checkemany high purity physics channels, and the agreemis quite reasonable[12].

3. Event selection

To selecte+e− → pp̄, the following criteria areused:

(1) There must be two oppositely charged trackthe MDC. Each track should have a good helix fitthe polar angle range|cosθ | < 0.8 in the MDC, andthe point of closest approach of the tracks to the beaxis should be within 2 cm in the radial direction awithin 15 cm of the interaction point longitudinally.

(2) Tracks should be back-to-back.Fig. 1 showsthe acollinearity (Acol) distributions for Monte Car(MC) simulated events at

√s = 2.0, 2.2, 2.6, and

case.

Fig. 1. Acol distributions for MCe+e− → pp̄ at√

s = 2.0, 2.2, 2.6, and 3.0 GeV. The arrows show the selection requirement for each

BES Collaboration / Physics Letters B 630 (2005) 14–20 17

Fig. 2. Distributions of the ratio of the deposited energy in the BSC and the momentum for final state particles of MCe+e− → pp̄ events andBhabha events at

√s = 2.2, 2.6, and 3.0 GeV. Left plots are protons, right are positrons.

ionentuire,

Cn.

da-

or

-

orher

eria

e-

us-

a

3.0 GeV. Because of energy loss, the Acol distributfor low energy charged particles is somewhat differfrom higher energy ones. For 2.0 GeV data, we reqthat Acol is less than 10◦, and for other energy pointsless than 3◦.

(3) To remove Bhabha events,Ep/pp < 0.6 is re-quired, whereEp is the deposited energy in the BSand pp is the momentum of the candidate protoFig. 2 shows Ep/pp distributions for protons anpositrons for MC e+e− → pp̄ events and Bhabhevents at

√s = 2.2, 2.6, and 3.0 GeV. This require

ment removes most Bhabha background.(4) The momentum is required to be within 3σp

of the nominal proton (antiproton) momentum fe+e− → pp̄ at each energy point, whereσp is the mo-mentum resolution.

(5) Lastly, dE/dx information is used to identify pp̄ pairs at

√s = 2.0 and 2.2 GeV, and TOF

information is used at all other energy points[13].

Each charged track must satisfy Probp > 0.01, whereProbp is the particle identification confidence level fthe proton or antiproton hypothesis determined eitfrom dE/dx or TOF information.

The numbers of events passing the selection critare listed inTable 1.

4. Luminosity

The integrated luminosity is determined from largangle Bhabha events using

(2)L= Nee

εeetrg · A · Cε · σee

,

whereNee is the number of Bhabha events selecteding BSC information only,εee

trg is the trigger efficiencyfor Bhabha events,A is the acceptance of Bhabh

18 BES Collaboration / Physics Letters B 630 (2005) 14–20

,nd the

ical

;

Table 1Summary of results at center-of-mass energies from 2.0 to 3.07 GeV.N is the number ofe+e− → pp̄ events,L is the integrated luminosityε is the detection efficiency,Fε is the detection efficiency correction factor from the PID efficiency difference between the MC sample areal data, 1+ δ is the initial state radiation correction factor,Fc is the correction factor for the Coulomb effect,Ff is the final state radiationcorrection factor,σ0 is the measured lowest order cross section, and|G| is the form factor. In the last two columns, the first error is statistand the second is systematic√

s (GeV) N L (nb−1) ε Fε 1+ δ Fc Ff σ0 (pb) |G| (×10−3)

2.0 3+2.3−1.9 45.8± 1.4 0.53± 0.03 0.41 0.89 1.03 0.99 330+253

−209± 24 175+67−55 ± 6

2.2 29± 5.4 123.5± 3.7 0.56± 0.02 1.04 0.98 1.02 0.99 408± 76± 22 179± 17± 5

2.4 2+2.2−1.3 61.0± 1.6 0.48± 0.02 1.03 1.04 1.02 0.98 64+73

−41 ± 4 72+41−23 ± 2

2.5 5+2.8−2.2 47.0± 1.0 0.50± 0.02 0.99 1.07 1.02 0.98 201+113

−91 ± 13 131+37−29 ± 4

2.6 24± 4.9 1351± 24 0.51± 0.02 0.96 1.10 1.02 0.98 33± 7± 2 54± 6± 2

2.7 2+2.2−1.3 71.6± 2.1 0.48± 0.02 1.00 1.13 1.02 0.98 51+58

−32 ± 5 70+39−22 ± 3

2.8 2+2.2−1.3 89.0± 1.8 0.50± 0.02 0.96 1.17 1.02 0.98 40+45

−25 ± 4 63+36−20 ± 3

2.9 0 94.0± 2.6 0.49± 0.02 0.96 1.20 1.02 0.98 < 51 < 73

3.0 4+2.8−1.7 947± 22 0.50± 0.02 0.96 1.24 1.01 0.98 7+5

−3 ± 1 28+10−6 ± 1

3.07 9+3.8−2.7 2347± 59 0.49± 0.02 0.96 1.27 1.01 0.98 7+3

−2 ± 1 27+6−4 ± 1

Table 2The relative systematic error (%):�ε/ε is the contribution from detection efficiency, including the MC statistical error (errN ), the PID difference(errPID) and tracking efficiency difference (errtrack) between MC and real data;�εtrig/εtrig is the contribution from the trigger efficiency�L/L is the contribution from luminosity; and BG is the contribution from the background contamination√

s (GeV) �ε/ε �εtrig/εtrig �L/L BG Total

errN errPID errtrack Total

2.0 0.4 5.0 4.0 6.4 0.5 3.0 1.5 7.32.2 0.4 0.6 4.0 4.1 0.5 3.0 1.5 5.32.4 0.5 0.9 4.0 4.1 0.5 2.7 4.4 6.62.5 0.4 1.0 4.0 4.1 0.5 2.2 4.4 6.42.6 0.4 1.0 4.0 4.1 0.5 1.8 4.4 6.32.7 0.5 1.0 4.0 4.2 0.5 2.9 7.8 9.32.8 0.4 1.9 4.0 4.4 0.5 2.0 7.8 9.22.9 0.5 1.9 4.0 4.4 0.5 2.8 7.8 9.43.0 0.4 1.9 4.0 4.4 0.5 2.3 7.8 9.33.07 0.5 1.9 4.0 4.4 0.5 2.5 7.8 9.3

me

r-ionss

of

ford

ner-rite-ies,

be

events estimated by MC simulation using the saselection criteria as for the data,Cε is the efficiencycorrection factor, which is used to correct for diffeences between the MC and data angular distributdue to the ribs in the BSC, andσee is the Bhabha crossection.

5. Efficiency

A MC simulation is used for the determinationthe detection efficiency. In thee+e− → pp(γ ) gen-

erator, corrections for initial state radiation[14], theCoulomb effect, and final state radiation[15] havebeen taken into account. The correction factorsthese items, 1+ δ, Fc, andFf , respectively, are listein Table 1.

For each energy point, 50 000 MC events are geated. MC events must satisfy the same selection cria as used for the real data. The detection efficiencε, are given inTable 1.

The trigger efficiencyεtrig for hadronic eventsis about 100%, and the error is estimated to0.5%.

BES Collaboration / Physics Letters B 630 (2005) 14–20 19

re-nts o

they,ffi-

rorD)the

-

areor

tionhe

Atcyrgy

r-

m

nelsuntas

n

The integrated luminosity and the trigger measument were the same as those used in measuremeRefs.[9,16].

6. Systematic errors

Systematic errors come from uncertainties indetection efficiency, trigger efficiency, luminositand background contamination. The detection eciency uncertainty includes the MC statistical erand the differences in the particle identification (PIand tracking efficiencies for the MC sample andreal data.

There are fewe+e− → pp̄ events, sop andp̄ sam-ples fromJ/ψ → π+π−pp̄ are used for the PID efficiency study. The momenta of the candidatep andp̄

tracks are required to be within 30 MeV/c of the ex-pected values for each energy point. The samplesobtained without using PID. The PID efficiency f

feach energy point is then determined by the fracof p andp̄ tracks that pass PID selection criteria. Tsame method is used for MCJ/ψ → π+π−pp̄ eventsto determine the PID efficiency for the MC data.2.0 GeV, there is a large difference in PID efficienbetween the MC sample and the data, so for all enepoints detection efficiencies (Fε) are corrected for thisdifference, and the errors in the PID efficiency diffeence are taken as a source of systematic error.

For e+e− → pp̄, possible backgrounds are froe+e− → e+e−(γ ), µ+µ−(γ ), π+π−, K+K−, andpp̄π0. MC events are generated for these five chanat

√s = 2.2, 2.6 and 3.0 GeV to estimate the amo

of background contamination, which is includeda systematic error: 1.5% for 2.0 and 2.2 GeV, 4.4%for 2.4, 2.5, and 2.6 GeV, and 7.8% for other energypoints.

Systematic errors are listed inTable 2. An uncer-tainty of 1.0% is taken for the initial state radiatiocorrection.

Fig. 3. Form factors measured by BES and other experiments. The line shows the energy dependence of|G(s)| by fitting all measurements.

20 BES Collaboration / Physics Letters B 630 (2005) 14–20

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.;

7. Results and summary

The total cross section is determined from

(3)σT = N

L · ε′ · εtrig(ε′ = ε · Fε),

whereN is the number ofe+e− → pp̄ events,L isthe integrated luminosity,ε′ is the corrected detectioefficiency, andεtrig is the trigger efficiency. The lowesorder cross section is determined from

(4)σ0 = σT

(1+ δ) · Fc · Ff

,

where 1+ δ, Fc, andFf are correction factors for initial state radiation, the Coulomb effect, and final stradiation, respectively.

The form factor can be calculated from the theorical lowest order cross section[8]

(5)σ0 = 4πα2ν

3s

(1+ 2m2

p

s

)∣∣G(s)∣∣2,

in whichα is the fine structure constant,ν is the protonvelocity, mp is the proton mass, and|G| is the formfactor assuming|GE | = |GM |.

The cross section ofe+e− → pp̄ and proton formfactor have been measured for 10 center-of-massergies between 2.0 and 3.07 GeV. The measuredues are listed inTable 1. There is no signal found a√

s = 2.9 GeV, but upper limits on the cross sectiand the form factor at the 90% C.L. are given, usthe method from Ref.[17].

For large momentum transfers pQCD predicts[18]thats2G should be nearly proportional to the squarethe running coupling constant for strong interactioα2

s (s), yielding the relation

(6)|G| = C

s2 ln2(s/Λ2),

whereΛ = 0.3 GeV is the QCD scale parameter andC

is a free parameter. InFig. 3, BES results are comparewith other experimental proton form factor resulThe line is the|G(s)| energy dependence obtainedfitting all measurements with Eq.(6), and the result isconsistent with the pQCD prediction.

Acknowledgements

The BES Collaboration thanks the staff of BEPfor their hard efforts. This work is supported in partthe National Natural Science Foundation of Chinader Contract Nos. 10491300, 10225524, 10225510425523, the Chinese Academy of Sciencesder Contract No. KJ 95T-03, the 100 Talents Pgram of CAS under Contract Nos. U-11, U-24,25, and the Knowledge Innovation Project of CAunder Contract Nos. U-602, U-34 (IHEP), the Ntional Natural Science Foundation of China undContract No. 10225522 (Tsinghua University), andDepartment of Energy under Contract No. DE-FG04ER41291 (U Hawaii).

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