b

Physics Letters B 603 (2004) 130–137

www.elsevier.com/locate/physlet

Measurement of cross sections forD0D̄0 andD+D− productionin e+e− annihilation at

√s = 3.773 GeV

BES Collaboration

M. Ablikim a, J.Z. Baia, Y. Banj, J.G. Biana, X. Caia, J.F. Changa, H.F. Cheno,H.S. Chena, H.X. Chena, J.C. Chena, Jin Chena, Jun Chenf, M.L. Chena, Y.B. Chena,

S.P. Chib, Y.P. Chua, X.Z. Cuia, H.L. Daia, Y.S. Daiq, Z.Y. Denga, L.Y. Donga,S.X. Dua, Z.Z. Dua, J. Fanga, S.S. Fangb, C.D. Fua, H.Y. Fua, C.S. Gaoa, Y.N. Gaon,

M.Y. Gonga, W.X. Gonga, S.D. Gua, Y.N. Guoa, Y.Q. Guoa, K.L. Hea, M. Hek,X. Hea, Y.K. Henga, H.M. Hua, T. Hua, L. Huangf, X.P. Huanga, X.B. Jia, Q.Y. Jiaj,C.H. Jianga, X.S. Jianga, D.P. Jina, S. Jina, Y. Jina, Y.F. Laia, F. Li a, G. Li a, H.H. Li a,J. Li a, J.C. Lia, Q.J. Lia, R.B. Li a, R.Y. Li a, S.M. Li a, W.G. Li a, X.L. Li g, X.Q. Li i,

X.S. Li n, Y.F. Liangm, H.B. Liaoe, C.X. Liu a, F. Liue, Fang Liuo, H.M. Liu a,J.B. Liua, J.P. Liup, R.G. Liua, Z.A. Liu a, Z.X. Liu a, F. Lua, G.R. Lud, J.G. Lua,

C.L. Luoh, X.L. Luo a, F.C. Mag, J.M. Maa, L.L. Ma k, Q.M. Maa, X.Y. Ma a,Z.P. Maoa, X.H. Mo a, J. Niea, Z.D. Niea, H.P. Pengo, N.D. Qia, C.D. Qianl, H. Qinh,

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. Shij, H.S. Suna, S.S. Suno, Y.Z. Suna, Z.J. Suna, X. Tanga,

N. Taoo, Y.R. Tiann, G.L. Tonga, D.Y. Wanga, J.Z. Wanga, K. Wango, L. Wanga,L.S. Wanga, M. Wanga, P. Wanga, P.L. Wanga, S.Z. Wanga, W.F. Wanga, Y.F. Wanga,

Zhe Wanga, Z. Wanga, Zheng Wanga, Z.Y. Wanga, C.L. Weia, D.H. Weic, N. Wua,Y.M. Wu a, X.M. Xia a, X.X. Xie a, B. Xin g, G.F. Xua, H. Xua, Y. Xu a, S.T. Xuea,

M.L. Yano, F. Yangi, H.X. Yanga, J. Yango, S.D. Yanga, Y.X. Yangc, M. Yea,M.H. Yeb, Y.X. Ye o, L.H. Yi f, Z.Y. Yi a, C.S. Yua, G.W. Yua, C.Z. Yuana, J.M. Yuana,

Y. Yuana, Q. Yuea, S.L. Zanga, Yu. Zenga, Y. Zengf, B.X. Zhanga, B.Y. Zhanga,C.C. Zhanga, D.H. Zhanga, H.Y. Zhanga, J. Zhanga, J.Y. Zhanga, J.W. Zhanga,

L.S. Zhanga, Q.J. Zhanga, S.Q. Zhanga, X.M. Zhanga, X.Y. Zhangk, Y.J. Zhangj,Y.Y. Zhanga, Yiyun Zhangm, Z.P. Zhango, Z.Q. Zhangd, D.X. Zhaoa, J.B. Zhaoa,

J.W. Zhaoa, M.G. Zhaoi, P.P. Zhaoa, W.R. Zhaoa, X.J. Zhaoa, Y.B. Zhaoa,H.Q. Zhengj, J.P. Zhenga, L.S. Zhenga, Z.P. Zhenga, X.C. Zhonga, B.Q. Zhoua,

0370-2693/$ – see front matter 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2004.10.029

BES Collaboration / Physics Letters B 603 (2004) 130–137 131

TheseeV.n for

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

a Institute of High Energy Physics, Beijing 100039, People’s Republic of Chinab China Center for Advanced Science and Technology, Beijing 100080, People’s Republic of China

c Guangxi Normal University, Guilin 541004, People’s Republic of Chinad Henan Normal University, Xinxiang 453002, People’s Republic of China

e Huazhong Normal University, Wuhan 430079, People’s Republic of Chinaf Hunan University, Changsha 410082, People’s Republic of China

g Liaoning University, Shenyang 110036, People’s Republic of Chinah Nanjing Normal University, Nanjing 210097, People’s Republic of China

i Nankai University, Tianjin 300071, People’s Republic of Chinaj Peking University, Beijing 100871, People’s Republic of China

k Shandong University, Jinan 250100, People’s Republic of Chinal Shanghai Jiaotong University, Shanghai 200030, 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 Science and Technology of China, Hefei 230026, People’s Republic of Chinap Wuhan University, Wuhan 430072, People’s Republic of China

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

Received 15 July 2004; received in revised form 13 October 2004; accepted 15 October 2004

Available online 2 November 2004

Editor: L. Rolandi

Abstract

The cross sections forD0D̄0 andD+D− production at 3.773 GeV have been measured with BES-II detector at BEPC.measurements are made by analyzing a data sample of about 17.3 pb−1 collected at the center-of-mass energy of 3.773 GObserved cross sections for the charm pair production are radiatively corrected to obtain the tree level cross sectioDD̄

production. A measurement of the total tree level hadronic cross section is obtained from the tree levelDD̄ cross section andan extrapolation of theRuds below the open charm threshold. 2004 Elsevier B.V. All rights reserved.

eV,

-

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edredmine

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rmvelionotal

nic

1. Introduction

Around the center-of-mass energy of 3.770 Gthe ψ(3770) resonance is produced ine+e− anni-hilation, and open charm pairs,D0D̄0 and D+D−,are mainly produced inψ(3770) decays. So the measurement of the cross sections forD0D̄0 andD+D−production at an energy point around 3.770 GeVvery important in the understanding ofψ(3770) de-cays. A coupled-channel model[1] predicts that thecross section forψ(3770) production is about 3 nb anthat theψ(3770) decay exclusively intoD0D̄0 andD+D−. Experimental results on the measuremen

E-mail address:rongg@mail.ihep.ac.cn(G. Rong).

theD0D̄0, D+D− andDD̄ cross sections can be usto test the theoretical prediction. Also the measuvalues of the cross sections can be used to deterthe branching fraction forψ(3770) → nonDD̄ usingthe measured cross section forψ(3770) → hadrons atthe same energy point. The determination of the pawidth ofψ(3770) → nonDD̄ has great interest sincewould be helpful for investigating the mixing betweS and D waves in its wave function[2], and in turn tohelp in developing the potential model[1].

In addition, by adding the tree level open chacross section to an extrapolation of the tree lehadronic cross section for the light hadron productin the region below the open charm threshold, the ttree level hadronic cross section can be obtained[3,4].The tree level cross section for inclusive hadro

132 BES Collaboration / Physics Letters B 603 (2004) 130–137

umdel.om

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event production in thee+e− annihilation at all en-ergies is needed to calculate the effects of vacupolarization on the parameters of the Standard MoThe largest uncertainty in this calculation arises frthe uncertainties in the measured inclusive hadroniccross sections in the open charm threshold region.ditionally, the tree level hadronic cross sectionsmeasured by counting inclusive hadronic events.ing the measured cross sections for theDD̄ productionin the charm threshold region, we can also measuretree level inclusive hadronic cross sections.

2. The BES-II detector

BES-II is a conventional cylindrical magnetic dtector that is described in detail in Ref.[5]. A 12-layervertex chamber (VC) surrounding the beryllium bepipe provides input to the event trigger, as well asordinate information. A forty-layer main drift chamb(MDC) located just outside the VC yields precise msurements of charged particle trajectories with a sangle coverage of 85% of 4π ; it also provides ion-ization energy loss (dE/dx) measurements which aused for particle identification. Momentum resolutiof 1.7%

√1+ p2 (p in GeV/c) anddE/dx resolution

of 8.5% for Bhabha scattering electrons are obtaifor the data taken at

√s = 3.773 GeV. An array of

48 scintillation counters surrounding the MDC mesures the time of flight (TOF) of charged particles wa resolution of about 180 ps for electrons. Outsthe TOF, a 12 radiation length, lead-gas barrel shocounter (BSC), operating in limited streamer momeasures the energies of electrons and photons80% of the total solid angle with an energy resolutof σE/E = 0.22/

√E (E in GeV) and spatial resolu

tions ofσφ = 7.9 mrad andσZ = 2.3 cm for electronsA solenoidal magnet outside the BSC provides a 0.magnetic field in the central tracking region of the dtector. Three double-layer muon counters instrumthe magnet flux return and serve to identify muowith momentum greater than 500 MeV/c. They cover68% of the total solid angle.

3. Data sample and method to determine σDD̄

The data used for this analysis were collectedthe center-of-mass energy of 3.773 GeV with the B

r

jing Spectrometer[5] at Beijing Electron Positron Collider. The total integrated luminosity of the data sis 17.3 pb−1, which is obtained based on analysislarge angle Bhabha scattering from the same data

The measurements of the cross sections forD0D̄0 and D+D− production are made basedthe analysis of singly taggedD0 andD+ events. Atthe center-of-mass energy

√s = 3.773 GeV, theD0

(through this Letter, charge conjugation is implieandD+ are produced in pair via the process of

(1)e+e− → D0D̄0,D+D−.

The total observed numberND0tag

(ND+tag

) of D0 (D+)

meson and the observed cross sectionσ obsD0D̄0 (σ obs

D+D− )are related as

(2)σ obsD0D̄0 =

ND0tag

2× L × B × ε,

and

(3)σ obsD+D− =

ND+tag

2× L × B × ε,

whereL is the integrated luminosity of the data sused in the analysis,B is the branching fraction fodecay mode in question, andε is the efficiency de-termined from Monte Carlo for reconstruction of thdecay mode.

In the measurements of the cross sections,singly tagged neutral and chargedD mesons are observed in the invariant mass spectra of the daugparticles from theD decay.

4. Data analysis

4.1. Event selection

The neutral and chargedD mesons are reconstructed in the final states ofK−π+, K−π+π+π−andK−π+π+. Events which contain at least two rconstructed charged-tracks with good helix fits arelected. In order to ensure well-measured 3-momenvectors and reliable charged-particle identification,charged tracks used in the single tag analysis arequired to be within|cosθ | < 0.85, whereθ is the anglewith respect to beam direction. All tracks must orinate from the interaction region, which require ththe closest approach of the charged track inxy plane

BES Collaboration / Physics Letters B 603 (2004) 130–137 133

nti-eion. Inateaon

es-gy-f thevesreeith

ofl-

the

ededl the

yand

na-f

ack-

,

k-e the

ere

ay

r

m

ated

hehee

-

is less than 2.0 cm and thez position of the chargedtrack is less than 20.0 cm. Pions and kaons are idefied by means of TOF anddE/dx measurements. Thpion identification requires a consistency with the phypothesis at a confidence level greater than 0.1%order to reduce misidentification, the kaon candidis required to have a larger confidence level for a khypothesis than that for a pion hypothesis.

4.2. Analysis of inclusiveD meson events

Taking advantage of theDD̄ pair production, weuse a kinematic fit to candidateD0 or D+ decaysto improve the ratio of signal to noise and mass rolution in the invariant mass spectrum. The enerconstraint is imposed on the measured momenta oD daughter particles via the kinematic fit to improthe measured charged trackthree-momenta. Eventwith a kinematic fit probability greater than 1% aaccepted. If more than one combination satisfies thfit probability greater than 1%, the combination wthe largest fit probability is retained.

The resulting distributions of the fitted massesKmπ (m = 1, or 2, or 3) combinations, which are caculated using the fitted momentum vectors fromkinematic fit, are shown inFig. 1. The signals forD0

andD+ production are clearly observed in the fittmass spectra. A maximum likelihood fit is performto the mass spectrum, a Gaussian is used to modesignal shape and a special function[6]1 is used to de-scribe the background shape. TheD0 andD+ yieldsobtained from this fit is given inTable 1.

The sameKmπ combinations from other decamodes can also pass the above selection criteriathe distributions of the fitted masses of the combitions are with a small peak around the masses oD

1 A Gaussian function was assumed for the signal. The bground shape was

(1.0+ p1y + p2y2)

N

√1−

(x

Eb

)2xe

−f(1− x

Eb

)2

,

whereN

√1− (

xEb

)2xe

−f(1− x

Eb

)2

is ARGUS background shape

x is the fitted mass,Eb is the beam energy,y = (Eb − x)/(Eb −1.82), N , f , p1 andp2 are the fit parameters; the ARGUS bacground shape was used by ARGUS experiment to parametrizbackground for fittingB mass peaks. For detail, see[7].

Fig. 1. Distribution of the fitted masses of theKmπ (m = 1,or 2, or 3) combinations for three singly tagged modes, wh(a) and (b) are for the decay modes ofD0 → K−π+ andD0 → K−π+π+π−, respectively, and the (c) is for the decmode ofD+ → K−π+π+.

Table 1Singly taggedD0 and D+ samples. Where theMfit is the fittedmass of singly taggedD meson, theNobs

Dtagis the observed numbe

of singly taggedD meson and theNDtag is the “true” number ofthe singly taggedD meson after correcting the contamination froother decay modes

Tag mode Mfit [MeV/c2] NobsDtag

NDtag

K−π+ 1865.5± 0.1 1642.8± 49.9 1627.4± 49.9K−π+π+π− 1865.4± 0.1 1327.2± 48.6 1299.1± 48.6K−π+π+ 1870.2± 0.1 2029.3± 57.4 2010.8± 57.4

mesons. The rates of the contaminations are evaluto be 0.0094, 0.0212 and 0.0091 for theD0 → K−π+,D0 → K−π+π+π− and D+ → K−π+π+, respec-tively. After correcting the observed numbers of tsingly taggedD events for these combinations, t“true” numbers of theD signal events for the thresingly taggedD modes are obtained to be 1627± 50,1299± 49 and 2011± 57.Table 1summarizes the results of the inclusiveD analysis.

134 BES Collaboration / Physics Letters B 603 (2004) 130–137

-

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5. Observed cross sections for D0D̄0 and D+D−production

5.1. Monte Carlo efficiency

To estimate the reconstructed efficiencies ofD0 →K−π+, D0 → K−π+π+π− andD+ → K−π+π+,the Monte Carlo samples ofDD̄ production and decays are generated according to Eq.(1), where the ratioof the neutral over the totalDD̄ production cross section is set to be 0.58. BothD and D̄ mesons decato all possible modes according to the branching fractions quoted from PDG[8]. The generated events asimulated with a GEANT based Monte Carlo pacage. All decay processes which contribute to thecay modes in question are considered in estimathe efficiencies. Detailed Monte Carlo studies giveefficiencies to be(35.26± 0.19)%, (13.73± 0.09)%and(25.00± 0.13)% for the reconstruction ofD0 →K−π+, D0 → K−π+π+π− and D+ → K−π+π+decay modes, respectively.

5.2. Observed cross sections

Inserting the number of the singly taggedD eventsand the efficiencies for each of the three decay mothe σDD̄ × B of D0D̄0 andD+D− are obtained andthe results are shown inTable 2. The first error isstatistical and second systematic which arise frthe uncertainty in the measured luminosity (∼ 3%),tracking (∼ 2% per track), particle identificatio(∼ 0.5%/track), kinematic fit (∼ 1%), fitting para-

Table 2Summary of the observed cross section times branching fractio

Mode σDD̄ × B [nb]

D0 → K−π+ 0.133±0.004±0.008D0 → K−π+π+π− 0.273±0.010±0.025D+ → K−π+π+ 0.233±0.007±0.018

meters (∼ 3%) and Monte Carlo statistics (∼ 0.6%).The total systematic uncertainty is obtained by addall systematic uncertainties in quadrature. A compison of our measuredσD × B with that measured bMARK-II [9] and MARK-I [10] is given inTable 3.The observed cross section forD+D− production isobtained by dividing theσDD̄ × B by branching frac-tion quoted from PDG[8], which gives

(4)σ obsD+D− = (2.56± 0.08± 0.26) nb.

The observed cross sections forD0D̄0 productionareσ obs

D0D̄0= (3.50± 0.11) nb andσ obs

D0D̄0= (3.66±

0.13) nb, which are determined from the analysisthe singly tagged modes ofD0 → K−π+ andD0 →K−π+π+π−, respectively; where the errors are stistical. Averaging the two observed cross sectionsD0D̄0 production gives the average of the obsercross section forD0D̄0 production to be

(5)σ obsD0D̄0

= (3.58± 0.09± 0.31) nb,

where the first error is statistical and second systatic which is estimated based on the averaged tcharged tracks in the two modes of the single taAdding the observed cross sections of the neutralcharged modes together gives the observed crosstion for DD̄ production to be

(6)σ obsDD̄

= (6.14± 0.12± 0.50) nb,

where the first error is statistical and the second stematic. In the estimation of the systematic errorthe σ obs

DD̄, sources of systematic uncertainty are s

regated into components that are common or inpendent forD0 andD+ measurements. The commcomponents are the uncertainty in the measuredtegrated luminosity, the uncertainty in tracking athe uncertainty in particle identification. Since the asolute branching fraction scale forD+ → K−π+π+and D0 → K−π+π+π− depend on the branchinfraction scale forD0 → K−π+, the total percentag

Table 3A comparison ofσD × B measured by this experiment, MARK-I and MARK-II experiments

Mode σD × B [nb] (this experiment)Ecm = 3.773 GeV

σD × B [nb] (MARK-II)Ecm = 3.771 GeV

σD × B [nb] (MARK-I)Ecm = 3.774 GeV

K−π+ 0.27± 0.02 0.24± 0.02 0.25± 0.05K−π+π+π− 0.55± 0.05 0.68± 0.11 0.36± 0.10K−π+π+ 0.47± 0.04 0.38± 0.05 0.36± 0.06

BES Collaboration / Physics Letters B 603 (2004) 130–137 135

d by

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n-m-ddeded

s.ere

c-intn).rgy

to

re-ncend

atethetialossVsec-on.-rn

rm

c-

total

d

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s,

Table 4Comparison of the observed cross section with that measureMARK-III [11] experiment

σobsDD̄

[nb]

(this experiment)Ecm = 3.773 GeV

σobsDD̄

[nb]

(MARK-III)Ecm = 3.768 GeV

σD0D̄0 3.58± 0.09± 0.31 2.90± 0.25± 0.30

σD+D− 2.56± 0.08± 0.26 2.10± 0.30± 0.15

uncertainty for the two channel branching fractio(6.6% and 4.1%) are split into a common compnent that matches the percentage uncertainty forD0 → K−π+ branching fraction (2.3%) and indepedent components (6.2% and 3.4%). All other systeatic uncertainties are treated as independent and ain quadrature. The common uncertainties are adlinearly.

As a comparison,Table 4lists the observed crossections forD0D̄0 andD+D− production at the c.menergies of 3.773 GeV and 3.768 GeV, which wmeasured by this experiment and MARK-III[11].

6. Radiative corrections

In any e+e− colliding beam experiment, the eletron (positron) always radiates at the interaction pobecause of the potential of the positron (electroSince this radiation (bremsstrahlung) carries eneaway, the actual center-of-mass energy for thee+e−annihilation is reduced by bremsstrahlung√

s(1− x), wherexEbeam is the total energy of theemitted photons. The bremsstrahlung is principallysponsible for the distortions to the tree level resonaline shape, while the self energy of the electron apositron and the vertex corrections to the initial staffect the overall factors to change the scale ofcross section. All of these corrections are called inistate radiation (ISR) corrections. The tree level crsection forDD̄ production at the energy of 3.773 Gecan be obtained by correcting the observed crosstion for the effects of the ISR and vacuum polarizati

The observed cross section,σ obs, at the nominal energy

√s can be written as a convolution of the Bo

cross sectionσB(s(1 − x)) and a sampling function

d

f (x, s),

σ obs(s) =1∫

0

dx f (x, s)σB(s(1− x)

)(7)× (

1+ δVP(s(1− x)

)).

The vacuum polarization correction(1+δVP) includesboth leptonic and hadronic terms. It varies from chathreshold to 4.14 GeV by less than±2% [3]. In thisdata analysis, we treat it as a constant of

(8)(1+ δVP) = 1.047± 0.024.

Since we are interested in theψ(3770) resonance inthis analysis, we take theσB to be the bare Breit–Wigner cross section

(9)σB(E) = 12πΓ 0eeΓtot(E)

(E2 − M2)2 + M2Γ 2tot(E)

,

whereΓ 0ee = Γee/(1 + δVP), M andΓee are the mass

and leptonic width of theψ(3770) resonance, respetively; E is the center-of-mass energy;Γtot(E) is cho-sen to be energy dependent and normalized to thewidth Γtot at the peak of the resonance[8,12]. TheΓtot(E) is defined as

(10)Γtot(E) = Γ0

p3D0

1+(rpD0)2 + p3

D±1+(rpD± )2

p03

D0

1+(rp0D0)2 + p03

D±1+(rp0

D± )2

,

wherep0D is the momentum of theD mesons produce

at the peak ofψ(3770), p is the momentum of theD mesons produced at the c.m. energy

√s, Γ0 is the

width of theψ(3770) at the peak, andr is the inter-action radius which was set to be 0.5 fm. In the cculation of the Born order cross section, theψ(3770)resonance parametersM = 3769.9 ± 2.5 MeV; Γ0 =23.6± 2.7 MeV andΓee = 0.26± 0.04 keV[8] wereused.

In the structure function approach introducedKuraev and Fadin[13,14], the sampling function cabe written as

(11)f (x, s) = βxβ−1δV +S + δH ,

whereβ is the electron equivalent radiator thicknes

(12)β = 2α

π

(ln

s

m2 − 1

),

e

136 BES Collaboration / Physics Letters B 603 (2004) 130–137

d

adn-Theelyved

ec-

s athe

er-n-

the

ion

mi-

edic-

]

vel

ys-of

ared

V.

δV +S = 1+ 3

4β + α

π

(π2

3− 1

2

)

(13)+ β2

24

(1

3ln

s

m2e

+ 2π2 − 37

4

),

(14)δH = δH1 + δH

2 ,

(15)δH1 = −β

(1− x

2

),

δH2 = 1

8β2

[4(2− x) ln

1

x

(16)

− 1+ 3(1− x)2

xln(1− x) − 6+ x

].

In the above formula,me is the electron mass anα is the fine structure constant. Theψ(3770) width(∼ 24 MeV) is much large than the energy spre(∼ 1.37 MeV) of BEPC. So the effect of the beam eergy spread on the cross section could be ignored.ψ(3770) is generally assumed to decay exclusivinto DD̄. Taking these considerations, the obsercross section of Eq.(7) should be replaced by

(17)

σ obs(s) = (1+ δVP)

1−4M2D/s∫

0

dx f (x, s)σB(s(1− x)

)

in calculation of the radiative corrections. The corrtion factor for the radiative effects is gived by

(18)g = σ obs

σB.

Fig. 2shows the factor of the radiative corrections afunction of the nominal center-of-mass energy. Atcenter-of-mass energy

√s = 3.773 GeV, the factor is

(19)g = 0.779± 0.031,

where the error is the uncertainty arising from therors on theψ(3770) resonance parameters. The ucertainty is mainly due to the error of the mass ofresonance.

7. Cross section for DD̄ production

The tree level cross section forDD̄ productionis obtained by dividing the observed cross sectby the factor of the radiative corrections. At

√s =

Fig. 2. The factor of radiative corrections as a function of the nonal center-of-mass energy.

Table 5Comparison of tree level cross section measurements with prtion of the coupled-channel model at

√s = 3.773 GeV

Experiment [nb] Coupled-channel model [nb

σD0D̄0 4.60±0.12±0.45 1.80σD+D− 3.29±0.10±0.37 1.28σDD̄

7.88±0.15±0.74 3.08

3.773 GeV, the charged, neutral and total tree leD pair production cross sections are

(20)σD0D̄0 = (4.60± 0.12± 0.45) nb,

(21)σD+D− = (3.29± 0.10± 0.37) nb,

and

(22)σDD̄ = (7.88± 0.15± 0.74) nb,

where the first error is statistical and the second stematic which include the uncertainty in the factorthe radiative corrections. These results are compto the coupled-channel model prediction inTable 5.

8. Measurement of RD and R

The tree level cross section forµ+µ− productionin QED is given by

(23)σe+e−→µ+µ− = 86.8 nb

E2cm

,

where theEcm is the center-of-mass energy in GeA measurement ofRD [4] is obtained by dividing

BES Collaboration / Physics Letters B 603 (2004) 130–137 137

ich

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n

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Cbyun-25,

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ds

7

I-

66

.)

02)

2σDD̄ by the tree level muon pair cross section, whgives

(24)RD = 2.58± 0.05± 0.24.

BES-II experiment measuredRuds [15], which is theratio of the tree level light hadron (containing tu,d and s light quarks) cross section over that fµ+µ− production in the energy region from 2.03.0 GeV. Theoretical expectation is thatRuds is ap-proximately independent of center-of-mass energthis region[3]. Fitting to theRuds values at 9 energy points in the energy region, we obtainRuds =2.26 ± 0.14. Assuming thatψ(3770) decays exclu-sively into DD̄, the value ofR is evaluated usingR = RD/2+ Ruds , which gives

(25)R = 3.55± 0.03± 0.18.

9. Summary

In summary, using the 17.3 pb−1 of data collectedwith the BES-II detector at BEPC at center-of-maenergy

√s = 3.773 GeV, the observed cross sectio

for D0D̄0, D+D− and DD̄ production have beemeasured. Those areσ obs

D0D̄0= (3.58±0.09±0.31)nb,

σ obsD+D− = (2.56±0.08±0.26) nb andσ obs

DD̄= (6.14±

0.12± 0.50) nb. The tree level cross sections for tD0D̄0, D+D− and DD̄ production are determineto be σD0D̄0 = (4.60 ± 0.12 ± 0.45) nb, σD+D− =(3.29± 0.10± 0.37) nb andσDD̄ = (7.88± 0.15±0.74) nb, which are about a factor 2.5 times largthan that predicted by the coupled-channel model.ing the measuredRuds in the energy region from 2.to 3.0 GeV from BES-II experiment and assumithat ψ(3770) only decays toDD̄, the total tree levecross section for inclusive hadronic event productat 3.773 GeV is obtained to beR = 3.55±0.03±0.18.

Acknowledgements

The BES Collaboration thanks the staff of BEPfor their hard efforts. This work is supported in partthe National Natural Science Foundation of Chinader contracts Nos. 19991480, 10225524, 102255the Chinese Academy of Sciences under contNo. KJ 95T-03, the 100 Talents Program of CAS uder Contract Nos. U-11, U-24, U-25, and the Knowedge Innovation Project of CAS under Contract NU-602, U-34 (IHEP); by the National Natural ScienFoundation of China under Contract No. 101750(USTC), and No. 10225522 (Tsinghua University).

References

[1] E. Eichten, et al., Phys. Rev. D 21 (1980) 203.[2] J.L. Rosner, hep-ph/0405196.[3] BES Collaboration, J.Z. Bai, et al., Phys. Rev. D 62 (200

012002.[4] M.W. Coles, et al., Phys. Rev. D 26 (1982) 2190.[5] BES Collaboration, J.Z. Bai, et al., Nucl. Instrum. Metho

A 458 (2001) 627.[6] BES Collaboration, M. Ablikim, et al., Phys. Lett. B 59

(2004) 39.[7] I.C. Brock, Mn-Fit, a fitting and plotting package using M

NUIT, Version 4.07, December 22, 2000.[8] Particle Data Group, K. Hagiwara, et al., Phys. Rev. D

(2002).[9] R.H. Schindler, et al., Phys. Rev. D 24 (1981) 78.

[10] I. Peruzzi, et al., Phys. Rev. Lett. 39 (1977) 1301;D.L. Scharre, et al., Phys. Rev. Lett. 40 (1978) 74.

[11] J. Adler, et al., Phys. Rev. Lett. 60 (1988) 89.[12] R.H. Schindler, et al., Phys. Rev. D 21 (1980) 2716.[13] E.A. Kuraev, V.S. Fadin, Sov. J. Nucl. Phys. 41 (1985) 466[14] G. Altarelli, G. Martinelli, CERN Yellow Report 86-02 (1986

47;O. Nicrosini, L. Trentadue, Phys. Lett. B 196 (1987) 551.

[15] BES Collaboration, J.Z. Bai, et al., Phys. Rev. Lett. 88 (20101802.