Physics Letters B 652 (2007) 238–244

www.elsevier.com/locate/physletb

Precision measurements of the mass, the widths of ψ(3770) resonanceand the cross section σ [e+e− → ψ(3770)] at Ecm = 3.7724 GeV

BES Collaboration

M. Ablikim a, J.Z. Bai a, Y. Ban k, J.G. Bian a, X. Cai a, H.F. Chen o, H.S. Chen a, H.X. Chen a,J.C. Chen a, Jin Chen a, Y.B. Chen a, S.P. Chi b, Y.P. Chu a, X.Z. Cui a, Y.S. Dai q, Z.Y. Deng a,L.Y. Dong a,1, Q.F. Dong n, S.X. Du a, Z.Z. Du a, J. Fang a, S.S. Fang b, C.D. Fu a, C.S. Gao a,

Y.N. Gao n, S.D. Gu a, Y.T. Gu d, Y.N. Guo a, Y.Q. Guo a, K.L. He a, M. He l, Y.K. Heng a, H.M. Hu a,T. Hu a, X.P. Huang a, X.T. Huang l, X.B. Ji a, X.S. Jiang a, J.B. Jiao l, D.P. Jin a, S. Jin a, Yi Jin a,Y.F. Lai a, 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. Liang m, H.B. Liao f, C.X. Liu a, F. Liu f, Fang Liu o, H.H. Liu a, H.M. Liu a,J. Liu k, J.B. Liu a, J.P. Liu p, R.G. Liu a, Z.A. Liu a, F. Lu a, G.R. Lu e, H.J. Lu o, J.G. Lu a, C.L. Luo i,F.C. Ma h, H.L. Ma a, L.L. Ma a, Q.M. Ma a, X.B. Ma e, Z.P. Mao a, X.H. Mo a, J. Nie a, H.P. Peng o,

N.D. Qi a, H. Qin i, J.F. Qiu a, Z.Y. Ren a, G. Rong a,∗, L.Y. Shan a, L. Shang a, D.L. Shen a,X.Y. Shen a, H.Y. Sheng a, F. Shi a, X. Shi k,2, H.S. Sun a, J.F. Sun a, S.S. Sun a, Y.Z. Sun a, Z.J. Sun a,

Z.Q. Tan d, X. Tang a, Y.R. Tian n, G.L. Tong a, D.Y. Wang a, L. Wang a, L.S. Wang a, M. Wang a,P. Wang a, P.L. Wang a, W.F. Wang a,3, Y.F. Wang a, Z. Wang a, Z.Y. Wang a, Zhe Wang a,

Zheng Wang b, C.L. Wei a, D.H. Wei a, N. Wu a, X.M. Xia a, X.X. Xie a, B. Xin h,4, G.F. Xu a, Y. Xu j,M.L. Yan o, F. Yang j, H.X. Yang a, J. Yang o, Y.X. Yang c, M.H. Ye b, Y.X. Ye o, Z.Y. Yi a, G.W. Yu a,C.Z. Yuan a, J.M. Yuan a, Y. Yuan a, S.L. Zang a, Y. Zeng g, Yu Zeng a, B.X. Zhang a, B.Y. Zhang a,C.C. Zhang a, D.H. Zhang a, H.Y. Zhang a, J.W. Zhang a, J.Y. Zhang a, Q.J. Zhang a, X.M. Zhang a,X.Y. Zhang l, Yiyun Zhang m, Z.P. Zhang o, Z.Q. Zhang e, D.X. Zhao a, J.W. Zhao a, M.G. Zhao a,

P.P. Zhao a, W.R. Zhao a, H.Q. Zheng k, J.P. Zheng a, Z.P. Zheng a, L. Zhou a, N.F. Zhou a, K.J. Zhu a,Q.M. Zhu a, Y.C. Zhu a, Y.S. Zhu a, Yingchun Zhu a,5, Z.A. Zhu a, B.A. Zhuang a,

X.A. Zhuang a, B.S. Zou a

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 China

l Shandong University, Jinan 250100, People’s Republic of Chinam 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

0370-2693/$ – see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2007.06.074

BES Collaboration / Physics Letters B 652 (2007) 238–244 239

Received 17 March 2007; received in revised form 28 May 2007; accepted 29 June 2007

Available online 18 July 2007

Editor: M. Doser

Abstract

By analyzing the R values measured at 68 energy points in the energy region between 3.650 and 3.872 GeV reported in our previous paper,we have precisely measured the mass, the total width and the leptonic width of the ψ(3770) resonance to be Mψ(3770) = 3772.4 ± 0.4 ±0.3 MeV, Γ tot

ψ(3770)= 28.5 ± 1.2 ± 0.2 MeV and Γ ee

ψ(3770)= 277 ± 11 ± 13 eV, respectively. We have measured the leptonic branching fraction

of the ψ(3770) decays and the ψ(3770) production cross section at its peak to be B[ψ(3770) → e+e−] = (0.97 ± 0.03 ± 0.05) × 10−5 andσ prd[e+e− → ψ(3770)] = 10.0 ± 0.3 ± 0.5 nb, respectively. The latter one results in the corresponding observed cross section of σ obs[e+e− →ψ(3770)] = 7.2 ± 0.2 ± 0.4 nb. We have also measured Ruds = 2.121 ± 0.023 ± 0.084 for the continuum light hadron production in the regionfrom 3.650 to 3.872 GeV.© 2007 Elsevier B.V. All rights reserved.

1. Introduction

Precise measurements of the mass Mψ(3770), the total widthΓ tot

ψ(3770) and the leptonic width Γ eeψ(3770) of the ψ(3770) reso-

nance, and improved measurements of the leptonic branchingfraction for ψ(3770) → e+e− and the cross section σ [e+e− →ψ(3770)] for the ψ(3770) production at c.m. (center of mass)energy Ecm = Mψ(3770) in e+e− annihilation are very impor-tant for better understanding the nature of the ψ(3770) reso-nance. The ψ(3770) resonance is thought to be a mixture of theD-wave and S-wave of the angular momentum eigenstates ofthe cc̄ system. The detailed mixing scheme affects the ψ(3770)

production and decays. So precise measurements of these quan-tities would give us some useful information about the nature ofthe ψ(3770) resonance and offer some insights into the inter-nal wave functions of the charmonium, which are beneficial tounderstand the dynamics of the 1−− resonance production ine+e− annihilation. Potential or quarkonium models based onQCD can calculate the masses [1–3] of the cc̄ bound states, thetotal widths of the ψ(3770) and other resonances [2,3], and thewidth for ψ(3770) → DD̄ [3,4]. The Lattice QCD (LQCD) cancalculate the mass spectra of the QQ̄ system (heavy quark andanti-quark system, such as the cc̄ and bb̄ system) [5]. If one canmore precisely measure the masses and the widths of the QQ̄

system, the results of these measurements can be used to test thecalculations of the quantities by the models and by the LQCDtheory. Moreover, these measurements can in turn be used toextract two fundamental parameters in QCD, the c-quark massand the strong coupling constant αs(s) at this mass scale [5],here s = E2

cm is the c.m. energy squared. In recent days, new

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

1 Current address: Iowa State University, Ames, IA 50011-3160, USA.2 Current address: Cornell University, Ithaca, NY 14853, USA.3 Current address: Laboratoire de l’Accélératear Linéaire, Orsay, F-91898,

France.4 Current address: Purdue University, West Lafayette, IN 47907, USA.5 Current address: DESY, D-22607, Hamburg, Germany.

results of the measured quantities related to the ψ(3770) pro-duction and decays were reported [6,7]. These improve ourknowledge on charmonium production and decays, especiallyimprove our understanding of the nature of the ψ(3770) reso-nance.

In addition to these measurements, precise measurement ofthe cross section for continuum light hadron (containing u, d

and s quarks) production in or nearby the ψ(3770) resonanceis important for testing the validity of the perturbative QCD(pQCD) calculation on the cross section. This measurementwould be beneficial for us to understand the mechanism of thecontinuum light hadron production in or nearby the resonanceregion(s).

In this Letter, we report the precise measurements ofMψ(3770), Γ tot

ψ(3770) and Γ eeψ(3770), and the improved measure-

ments of the leptonic branching fraction B[ψ(3770) → e+e−]and the cross section σ [e+e− → ψ(3770)] at the c.m. energyEcm = Mψ(3770) with the data taken with the BES-II detec-tor [8] at the BEPC collider in December, 2003. We also reportmeasurement of the Ruds value for the continuum light hadronproduction in the region from 3.650 to 3.872 GeV, which wasmeasured from the same data sample.

2. The BES-II detector

The BES-II detector is a conventional cylindrical magneticspectrometer. A 12-layer vertex chamber (VC) surrounding theberyllium beam pipe provides input to the event trigger, as wellas coordinate information. A forty-layer main drift chamber(MDC) located just outside the VC yields precise measure-ments of charged particle trajectories with a solid angle cov-erage of 85% of 4π ; it also provides ionization energy loss(dE/dx) measurements which are used for particle identifi-cation. Momentum resolution of 1.7%

√1 + p2 (p in GeV/c)

and dE/dx resolution of 8.5% for Bhabha scattering electronsare obtained for the data taken at

√s = 3.773 GeV. An ar-

ray of 48 scintillation counters surrounding the MDC measuresthe time of flight (TOF) of charged particles with a resolutionof about 180 ps for electrons. Outside the TOF, a 12 radia-

240 BES Collaboration / Physics Letters B 652 (2007) 238–244

Table 1Summary of the Ruds(c)+ψ(3770)(Ecm) values measured at 68 energy points quoted from Ref. [9]

Ecm (GeV) Ruds(c)+ψ(3770) Ecm (GeV) Ruds(c)+ψ(3770) Ecm (GeV) Ruds(c)+ψ(3770) Ecm (GeV) Ruds(c)+ψ(3770)

3.6500 2.157 ± 0.035 ± 0.086 3.7584 3.025 ± 0.108 ± 0.148 3.7726 3.777 ± 0.145 ± 0.185 3.7826 3.326 ± 0.115 ± 0.1633.6600 2.131 ± 0.105 ± 0.085 3.7596 3.076 ± 0.102 ± 0.151 3.7730 3.563 ± 0.120 ± 0.175 3.7838 3.154 ± 0.114 ± 0.1553.6920 2.034 ± 0.092 ± 0.081 3.7608 3.138 ± 0.089 ± 0.154 3.7742 3.373 ± 0.113 ± 0.165 3.7850 2.879 ± 0.107 ± 0.1413.7000 2.079 ± 0.079 ± 0.083 3.7620 2.992 ± 0.110 ± 0.147 3.7754 3.641 ± 0.125 ± 0.178 3.7862 2.902 ± 0.105 ± 0.1423.7080 2.197 ± 0.083 ± 0.088 3.7622 3.207 ± 0.114 ± 0.157 3.7766 3.498 ± 0.119 ± 0.171 3.7874 2.957 ± 0.111 ± 0.1453.7160 2.177 ± 0.086 ± 0.087 3.7634 3.345 ± 0.122 ± 0.164 3.7778 3.570 ± 0.121 ± 0.175 3.7886 2.571 ± 0.097 ± 0.1263.7240 2.125 ± 0.086 ± 0.085 3.7646 3.585 ± 0.126 ± 0.176 3.7790 3.360 ± 0.117 ± 0.165 3.7898 2.576 ± 0.099 ± 0.1263.7320 2.156 ± 0.086 ± 0.086 3.7658 3.381 ± 0.119 ± 0.166 3.7798 3.477 ± 0.136 ± 0.170 3.7900 2.849 ± 0.106 ± 0.1403.7400 2.190 ± 0.099 ± 0.088 3.7670 3.760 ± 0.130 ± 0.184 3.7802 3.427 ± 0.125 ± 0.168 3.7950 2.751 ± 0.101 ± 0.1353.7480 2.371 ± 0.106 ± 0.116 3.7682 3.451 ± 0.124 ± 0.169 3.7804 3.382 ± 0.137 ± 0.166 3.8000 2.212 ± 0.091 ± 0.1083.7500 2.517 ± 0.085 ± 0.123 3.7694 3.611 ± 0.125 ± 0.177 3.7808 3.336 ± 0.129 ± 0.163 3.8100 2.171 ± 0.092 ± 0.0873.7512 2.637 ± 0.090 ± 0.129 3.7706 3.580 ± 0.123 ± 0.175 3.7810 3.464 ± 0.138 ± 0.170 3.8200 2.367 ± 0.109 ± 0.0953.7524 2.615 ± 0.095 ± 0.128 3.7714 3.538 ± 0.139 ± 0.173 3.7812 3.396 ± 0.130 ± 0.166 3.8300 2.354 ± 0.101 ± 0.0943.7536 2.652 ± 0.093 ± 0.130 3.7716 3.634 ± 0.146 ± 0.178 3.7814 3.514 ± 0.124 ± 0.172 3.8400 2.296 ± 0.104 ± 0.0923.7548 2.733 ± 0.093 ± 0.134 3.7718 3.939 ± 0.133 ± 0.193 3.7816 2.944 ± 0.137 ± 0.144 3.8500 2.372 ± 0.115 ± 0.0953.7560 2.585 ± 0.090 ± 0.127 3.7720 3.636 ± 0.134 ± 0.178 3.7818 3.140 ± 0.125 ± 0.154 3.8600 2.371 ± 0.105 ± 0.0953.7572 2.942 ± 0.107 ± 0.144 3.7722 3.652 ± 0.143 ± 0.179 3.7822 3.253 ± 0.124 ± 0.159 3.8720 2.308 ± 0.117 ± 0.092

tion length, lead-gas barrel shower counter (BSC), operating inself-quenching streamer mode, measures the energies of elec-trons and photons over 80% of the total solid angle with anenergy resolution of σE/E = 0.22/

√E (E in GeV) and spatial

resolutions of σφ = 7.9 mrad and σZ = 2.3 cm for electrons.A solenoidal magnet outside the BSC provides a 0.4 T magneticfield in the central tracking region of the detector. Three double-layer muon counters instrument the magnet flux return, andserve to identify muons of momentum greater than 500 MeV/c.They cover 68% of the total solid angle.

3. Data analysis

3.1. The previously measured R values

The measurements of Mψ(3770), Γ totψ(3770), and Γ ee

ψ(3770)

are based on analyzing the R(Ecm) values measured at 68energy points in the region between 3.650 and 3.872 GeV.The quantity R(Ecm) is defined as the ratio σ(e+e− →hadrons)/(σ (e+e− → μ+μ−), with σ(e+e− → μ+μ−) =3πα2(0)/4s, here α(0) is the fine structure constant at the low-est energy limit. In Ref. [9] we reported measurements of thequantities Ruds, Rhad(Ecm) and Ruds(c)+ψ(3770)(Ecm) which arethe R(Ecm) values for the continuum light hadron productionaround the DD̄ threshold, the R(Ecm) values including the con-tributions from the continuum hadrons and all 1−− resonancesat all energies, and the R(Ecm) values accounting for the con-tributions from both the continuum hadron production and thedecays for ψ(3770) → hadrons, respectively. All of these arecorrected for the initial state radiative (ISR) and vacuum po-larization corrections. Table 1 summarizes the Ruds(c)+ψ(3770)

values reported in Ref. [9], where the first error is statistical andthe second systematic. The statistical error includes both thestatistical uncertainty in the measured hadronic events and thepoint-to-point systematic uncertainties arising from the statisti-cal uncertainty in the measured luminosity and the uncertaintyin the Monte Carlo efficiency [9]. Ref. [10] discussed the mea-

Table 2The sources of the relative systematic uncertainties in the measured R valuesquoted from Ref. [9]

Sources of error Uncnt. in R[%] (3.650 GeV)

Uncnt. in R[%] (3.773 GeV)

Luminosity ∼ 1.9 ∼ 1.9Hadron selection ∼ 2.5 ∼ 2.5Monte Carlo Modeling ∼ 2.0 ∼ 2.0ISR & |1 + Π(Ecm)|2 ∼ 1.5 ∼ 1.5ψ(3770) parameters ∼ 2.7Total ∼ 4.0 ∼ 4.9

surements of the R values with the BES-II detector in moredetails.

The systematic uncertainties in the measured R values arisefrom the uncertainties in hadronic event selections, MonteCarlo simulation, measurement of the luminosity, and the radia-tive corrections. Table 2 summarizes the sources of the system-atic uncertainties of the measured R values [9]. Adding theseuncertainties in quadrature yields the total relative systematicuncertainties in the measured R values to be ∼4.0% for thedata taken in the regions outside the ψ(3770) resonance and tobe ∼4.9% for the data taken at 3.773 GeV.

In this Letter we do further analysis of the measured R val-ues as shown in Table 1 to measure Mψ(3770), Γ tot

ψ(3770) andΓ ee

ψ(3770). With these measured quantities we determine the lep-tonic branching fraction for ψ(3770) → e+e− and the crosssection σ [e+e− → ψ(3770) → hadrons] at Ecm = Mψ(3770).

3.2. Fit to the R values

The points with error bars in Fig. 1 show the Ruds(c)+ψ(3770)

(Ecm) values measured at different c.m. energies. The errorbars are the statistical errors. To extract the values of Mψ(3770),Γ tot

ψ(3770) and Γ eeψ(3770) we fit these Ruds(c)+ψ(3770)(Ecm) values

to a theoretical formula describing the expected values for theseR at each of the energy points. The theoretical formula is afunction of Mψ(3770), Γ tot , Γ ee , and the momentum of

ψ(3770) ψ(3770)

BES Collaboration / Physics Letters B 652 (2007) 238–244 241

Fig. 1. Ruds(c)+ψ(3770)(Ecm) versus the c.m. energy (see text). (For interpre-tation of the references to color in this figure legend, the reader is referred tothe weld version of this Letter.)

the D meson from ψ(3770) decays or continuum production.We make a χ2 fit to the measured Ruds(c)+ψ(3770)(Ecm) val-ues. The objective function to be minimized in the fit is definedas

(1)

χ2 =68∑i=1

(Ruds(c)+ψ(3770)(Ecm)i − R

expectuds(c)+ψ(3770)(Ecm)i

σRuds(c)+ψ(3770)(Ecm)i

)2

,

where Ruds(c)+ψ(3770)(Ecm)i is the measured value with thestatistical error σRuds(c)+ψ(3770)(Ecm)i (i.e., the first error of theRuds(c)+ψ(3770)(Ecm) value as listed in Table 1) at the ith c.m.energy, and R

expectuds(c)+ψ(3770)(Ecm)i is the expected value for

Ruds(c)+ψ(3770)(Ecm) at the ith c.m. energy.R

expectuds(c)+ψ(3770)(Ecm) describes the combined ψ(3770) reso-

nance shape and the non-resonant hadronic background, whichis written as

Rexpectuds(c)+ψ(3770)(Ecm)

(2)=∞∫

0

dWG(W,Ecm)Rexpectψ(3770)

(Ecm) + Ruds(c)(Ecm),

in which

(3)G(W,Ecm) = 1√2πΔBEPC

e− (W−Ecm)2

2Δ2BEPC

describes the distribution of the BEPC machine energy, whereΔBEPC is the energy spread of the BEPC. Assuming that thereare no other new structures and effects, we use a pure p-wavezero order Breit–Wigner function with energy-dependent totalwidths to describe the ψ(3770) production and its decay intoinclusive hadrons. The expected ψ(3770) resonance shape is

taken as

(4)

Rexpectψ(3770)(Ecm)

= 3s

4πα2(0)

× 12πΓ 0eeψ(3770)Γψ(3770)(Ecm)

(E2cm − M2

ψ(3770))2 + [Mψ(3770)Γψ(3770)(Ecm)]2

,

with Γ 0eeψ(3770) = |1 − Π(Ecm)|2Γ ee

ψ(3770), where Γ 0eeψ(3770) and

Γ eeψ(3770) are the bare leptonic width excluding the vacuum po-

larization effects and experimental leptonic width includingthe vacuum polarization effects, respectively; 1/|1 − Π(Ecm)|2is the vacuum polarization correction function [12] includingthe contributions from all 1−− resonances, the QED contin-uum hadron spectrum as well as the contributions from thelepton pairs (e+e−, μ+μ− and τ+τ−) [13], the total widthΓψ(3770)(Ecm) is chosen to be energy dependent defined as

Γψ(3770)(Ecm) = ΓD0D̄0(Ecm) + ΓD+D−(Ecm)

(5)+ Γnon-DD̄(Ecm),

in which [14]

(6)ΓD0D̄0(Ecm) = Γ totψ(3770)θ00

(pD0)3

(p0D0)

3

1 + (rp0D0)

2

1 + (rpD0)2B00,

(7)ΓD+D−(Ecm) = Γ totψ(3770)θ+−

(pD+)3

(p0D+)3

1 + (rp0D+)2

1 + (rpD+)2B+−,

and

(8)Γnon-DD̄(Ecm) = Γ totψ(3770)[1 − B00 − B+−],

where p0D and pD are the momenta of the D mesons produced

at the peak of the ψ(3770) resonance and at the c.m. energyEcm, respectively; Γ tot

ψ(3770)is the total width of the ψ(3770)

resonance at its peak, B00 and B+− are the branching fractionsfor ψ(3770) → D0D̄0 and ψ(3770) → D+D− [14], respec-tively, r is the interaction radius of the cc̄ system, θ00 and θ+−are the step functions to account for the thresholds of the D0D̄0

and D+D− production, respectively.The non-resonant background shape is taken as

(9)Ruds(c)(Ecm) = Ruds(Ecm) + R(c)(Ecm),

with

(10)R(c)(Ecm) = fDD̄

[(pD0

ED0

)3

θ00 +(

pD+

ED+

)3

θ+−],

where Ruds(Ecm) is the R value for the continuum light hadronproduction; R(c)(Ecm) is the R value due to the continuum DD̄

(D0D̄0 and D+D−) production; ED0 and ED+ are the energiesof the D0 and the D+ mesons produced at Ecm, respectively.

In the fit we left Mψ(3770), Γ totψ(3770), Γ ee

ψ(3770), Ruds, r ,and fDD̄ free; we fixed the BEPC machine energy spread atΔBEPC = 1.343 ± 0.029 MeV [14]. Since we do not select theDD̄ events from these data samples, we cannot leave B00 andB+− free in the fit. Instead we set the ratio B00/B+− = 1.3 ±0.1 [14,15] and the branching fraction for ψ(3770) → DD̄ tobe B[ψ(3770) → DD̄] = B00 + B+− = (84 ± 7)% [10,14] inthe fit.

242 BES Collaboration / Physics Letters B 652 (2007) 238–244

Table 3The measured mass Mψ(3770) , total width Γ tot

ψ(3770)and leptonic width

Γ eeψ(3770)

of the ψ(3770) resonance along with those measured previously bythe BES Collaboration [14]

Mψ(3770) (MeV) Γ totψ(3770)

(MeV) Γ eeψ(3770)

(eV) Note

3772.4 ± 0.4 ± 0.3 28.5 ± 1.2 ± 0.2 277 ± 11 ± 13 This work3772.2 ± 0.7 ± 0.3 26.9 ± 2.4 ± 0.3 251 ± 26 ± 11 [14]

3.3. The results

3.3.1. Measurements of Mψ(3770), Γ totψ(3770), Γ ee

ψ(3770) and RudsThe curve (blue line) in Fig. 1 gives the fit to the data,

the straight (yellow) line shows the quantity Ruds obtainedfrom the fit and the dashed (red) line shows the variation ofthe quantity Ruds(c)(Ecm) with the c.m. energy as given inEqs. (9)–(10). χ2/ndf for this fit is 94/61 = 1.5. The largerχ2s are mainly from the four energy points, which are atEcm = 3.7886,3.7898,3.80 and 3.81 GeV. The sum over χ2sfrom these four energy points is 31. If we exclude these fourpoints in the fit, we would obtain χ2/ndf = 65/57 = 1.1. The“dip” of the Ruds(c)+ψ(3770)(Ecm) values around 3.80 GeV maybe due to some unknown effects.6 Table 3 summarizes the re-sults from the fit, where the first error is the statistical and thesecond systematic. The fit gives

Ruds = 2.121 ± 0.023 ± 0.084

in the energy region from 3.650 to 3.872 GeV, where the errorsare statistical and systematic, respectively. The fit also gives

r = 41 ± 458 fm,

where the error is from the fit.7 From the fit we obtain

fDD̄ = 2.4 ± 1.7 ± 0.6,

where the first error is statistical and the second systematic.The systematic errors of the measured quantities arise

mainly from the common systematic uncertainties (∼ 4.0%in the regions outside the ψ(3770) resonance and ∼ 4.9%at Ecm = 3.773 GeV as shown in Table 2) of the measuredRuds(c)+ψ(3770), the uncertainty (±0.029 MeV) of the BEPCmachine energy spread, and the uncertainty (±7%) of thebranching fraction for the decay ψ(3770) → DD̄. In estimateof the systematic errors of the measured quantities due to theseuncertainties, we shift the measured value of Ruds(c)+ψ(3770)

and the fixed parameters by ±1σ to measure the changes ofthe quantities. To study the effect of using the different Breit–Wigner function on the measured quantities, we replace the rel-ativistic Breit–Wigner function in Eq. (4) by the non-relativistic

6 The analysis author would like to suggest the BES-III (BES-III at BEPC-II)and/or CLEO (CLEO-c at CERS) Collaborations to check whether this “dip”is due to physical reason with larger statistical cross section scan data to becollected at more sampling points around Ecm = 3.80 GeV in the future.

7 Since the parameter r is not sensitive to varying the fixed parameters andthe measured Ruds(c)+ψ(3770) values, and it changes from several fm to severalhundred fm in different fits, we do not set the systematic error on the fitted valuehere. If we fixed r at a value from several fm to several thousand fm in the fit,the quantities Mψ(3770) , Γ tot , Γ ee and Ruds are almost unchanged.

ψ(3770) ψ(3770)

Table 4The sources of the systematic uncertainties in the measured quantities

Sources of error ΔMψ(3770)

[MeV]ΔΓ tot

ψ(3770)[MeV]ΔΓ ee

ψ(3770)[eV]ΔRuds

Ruds(c)+ψ(3770) 0.0 0.1 13 0.084ΔBEPC 0.0 0.0 0.1 0.000B[ψ(3770) → DD̄] 0.1 0.1 0.1 0.006Energy Calibration 0.3 0.0 0.0 0.000Breit–Wigner function 0.0 0.0 0.1 0.001Total 0.3 0.2 13 0.084

Breit–Wigner function to fit the data and measure the shifts ofthe measured quantities due to this change. Table 4 summa-rizes the changes of the measured Mψ(3770), Γ tot

ψ(3770), Γ eeψ(3770)

and Ruds due to the shifts of Ruds(c)+ψ(3770) and the fixed pa-rameters, and due to the change of the Breit–Wigner function.Adding these changes of the measured quantities in quadratureyields the total systematic errors of the quantities to be 0.3 MeV,0.2 MeV, 13 eV and 0.084 as shown in the table, respectively.The systematic error of fDD̄ arises mainly from the uncertain-ties (±0.5) and (±0.3) due to varying B[ψ(3770) → DD̄] andRuds(c)+ψ(3770) by ±1σ , respectively, and (±0.1) due to thechange of the Breit–Wigner function. fDD̄ is not sensitive to theother fixed parameters. Adding these uncertainties in quadra-ture yields the total systematic error of ±0.6.

As a comparison, the same quantities measured by the BESCollaboration obtained by analyzing different cross sectionscan data sets [14] are also listed in Table 3. The measured Rudsvalue from this fit is consistent with Ruds = 2.141 ± 0.025 ±0.085 obtained by weighting the first 8 Ruds(c)+ψ(3770)(Ecm)

values below the DD̄ threshold [9]. Fig. 2 illustrates the com-parisons of the measured quantities (circles with error bars)with those measured by the MARK-I, DELCO and MARK-IICollaborations [17–19] from analyzing the cross section scandata and those measured by the BELLE and CLEO Collabora-tions [20,21] from analyzing other kind of data. For a compari-son we also plot the mass (dots) of the 13D1 state of the cc̄ sys-tem and the partial width (squares [3,4]) for ψ(3770) → DD̄

predicted by the models [2,3,16] in recent years and calculatedby the LQCD theory [5] in the figure.

3.3.2. Measurements of B[ψ(3770) → e+e−] and σψ(3770)

The leptonic branching fraction is defined as [11]

(11)B[ψ(3770) → e+e−] = Γ ee

ψ(3770)

Γ totψ(3770)

.

Inserting this relation in Eq. (4) and fitting to the data againyields the measured leptonic branching fraction. In the fit weleft Mψ(3770), Γ tot

ψ(3770), B[ψ(3770) → e+e−], Ruds, r , andfDD̄ free; we fixed the other parameters at the values as dis-cussed in Section 3.2. Table 5 lists the measured leptonicbranching fraction, where the first error is statistical and thesecond systematic. For a comparison the branching fractionmeasured by the BES Collaboration from analysis of differentdata sets and the world average [11] are also summarized in thetable.

BES Collaboration / Physics Letters B 652 (2007) 238–244 243

Fig. 2. Comparison of the measured quantities obtained by analyzing the crosssection scan data and other kind of data from different experiments along withthose predicted by the models and by the LQCD theory; the dots are the pre-dicted mass of the 13D1 state of the cc̄ system and the squares the expectedpartial width for ψ(3770) → DD̄ (see text).

Table 5The leptonic branching fraction of ψ(3770)

Experiment B[ψ(3770) → e+e−] [×10−5]

This work 0.97 ± 0.03 ± 0.05BES [14] 0.93 ± 0.06 ± 0.03PDG [11] 1.05 ± 0.14

Table 6The cross sections for the ψ(3770) production measured at Ecm = Mψ(3770) ,obtained by analyzing the cross section scan data over the ψ(3770) resonanceor over both the ψ(3770) and ψ(3686) resonances

Experiment σ prd[e+e− → ψ(3770)] [nb] σ obs[e+e− → ψ(3770)] [nb]

This work 10.0 ± 0.3 ± 0.5 7.2 ± 0.2 ± 0.4BES [14] 9.6 ± 0.7 ± 0.4 6.9 ± 0.5 ± 0.3MARK-II [19] 9.3 ± 1.4

At the peak of the ψ(3770) resonance, the production crosssection is given by

(12)σprdψ(3770) = 12π

M2ψ(3770)

Γ eeψ(3770)

Γ totψ(3770)

,

which gives the bare leptonic width

(13)Γ 0eeψ(3770) = |1 − Π(Ecm)|2

12πσ

prdψ(3770)M

2ψ(3770)Γ

totψ(3770).

To measure the production cross section, we fit to the data againwith inserting the bare leptonic width in Eq. (4). In the fit weleft Mψ(3770), Γ tot

ψ(3770), σprdψ(3770), Ruds, r , and fDD̄ free; we also

fixed the other parameters at the values as discussed in Sec-tion 3.2. Table 6 summarizes the result from the fit, where thefirst error is statistical and the second systematic. The produc-tion cross section σ

prdψ(3770) excludes the initial state radiative

corrections. To obtain its corresponding observed cross sectionσ obs

ψ(3770), we multiply σprdψ(3770) by a radiative correction fac-

tor of 0.721 ± 0.013, which includes the initial state radiativeeffects. Table 6 also summarizes the observed cross sections ob-tained from this analysis, where the first error is statistical andthe second systematic including the systematic uncertainty dueto the uncertainty in the radiative correction factor. In the ta-ble the cross sections measured by the MARK-II Collaborationand by the BES Collaboration from analysis of different crosssection scan data [14] are also summarized for comparison.

Analysis of systematic uncertainties on the measured branch-ing fraction and the cross sections shows that they are domi-nated by those due to R measurements whereas other contribu-tions produce negligible effect. We estimate the total systematicerrors of B[ψ(3770) → e+e−] and σ

prdψ(3770)

to be 0.05 × 10−5

and 0.49 nb, respectively.

4. Summary

In summary, we measured the mass of the ψ(3770) reso-nance with a precision of more than a factor of 4 better thanthe one of the PDG [11] average. The precise measurementof the mass combined with the measured masses of other cc̄

states could be used to calibrate the calculations of the cc̄ spec-trum and to extract αs(s) at this mass scale [5]. Our measuredΓ tot

ψ(3770) = 28.5 ± 1.2 ± 0.2 MeV is larger than the PDG aver-

age Γ totψ(3770) = 23.0±2.7 MeV [11], and with a precision more

than a factor of 2 better than that of the PDG average. It is alsoobviously larger than the predictions by the coupled channelmodels [3,4] by more than 7σ , where σ is the error of the mea-sured value of the total width of ψ(3770). Our measured lep-tonic width of ψ(3770) is consistent within error with the PDGaverage [11], but with a better accuracy than the PDG aver-age. The measured leptonic branching fraction B[ψ(3770) →e+e−] = (0.97 ± 0.03 ± 0.05) × 10−5 from this work is con-sistent within error with the PDG average and with the onemeasured by the BES Collaboration previously [14], but witha precision of more than a factor of 2 better than the PDG aver-age. We measured the ψ(3770) production cross section to beσ

prdψ(3770) = 10.0 ± 0.3 ± 0.5 nb at Ecm = Mψ(3770), correspond-

ing the observed cross section of σ obsψ(3770) = 7.2 ± 0.2 ± 0.4 nb.

These improved measurements of the quantities would be help-ful to understand the nature of the ψ(3770) resonance. Fromthe analysis we also measured Ruds = 2.121 ± 0.023 ± 0.084in the energy range from 3.650 to 3.872 GeV. This informationwould be beneficial for us in the understanding of the contin-uum hadron production in or nearby the resonance region(s).

244 BES Collaboration / Physics Letters B 652 (2007) 238–244

The measured Ruds can directly be used to extract αs(s) at thisenergy scale.

Acknowledgements

The BES Collaboration thanks the staff of BEPC for theirhard efforts. This work is supported in part by the NationalNatural Science Foundation of China under contracts Nos.19991480, 10225524, 10225525, the Chinese Academy of Sci-ences under contract No. KJ 95T-03, the 100 Talents Pro-gram of CAS under Contract Nos. U-11, U-24, U-25, and theKnowledge Innovation Project of CAS under Contract Nos.U-602, U-34(IHEP); by the National Natural Science Founda-tion of China under Contract No. 10175060 (USTC), and No.10225522 (Tsinghua University).

References

[1] E. Eichten, K. Gottfried, et al., Phys. Rev. Lett. 34 (1975) 369.[2] E. Eichten, K. Gottfried, et al., Phys. Rev. D 21 (1980) 203.[3] K. Heikkilä, N.A. Törnqvist, Phys. Rev. D 29 (1983) 110.[4] E. Eichten, K. Lane, C. Quigg, Phys. Rev. Lett. 69 (2004) 094019.[5] C.T.H. Davies, K. Hornbostel, et al., Phys. Rev. D 52 (1995) 6519.[6] M. Ablikim, et al., BES Collaboration, Phys. Lett. B 603 (2004) 130;

M. Ablikim, et al., BES Collaboration, Nucl. Phys. B 727 (2005) 395;M. Ablikim, et al., BES Collaboration, Phys. Lett. B 641 (2006) 145;M. Ablikim, et al., BES Collaboration, Phys. Rev. Lett. 97 (2006) 121801;M. Ablikim, et al., BES Collaboration, HEP & NP 28 (4) (2004) 325;M. Ablikim, et al., BES Collaboration, Phys. Lett. B 605 (2005) 63;M. Ablikim, et al., BES Collaboration, Phys. Rev. D 70 (2004) 077101;M. Ablikim, et al., BES Collaboration, Phys. Rev. D 72 (2005) 072007;G. Rong for BES Collaboration Int. J. Mod. Phys. 21 (2006) 5416.

[7] N.E. Adam, et al., CLEO Collaboration, Phys. Rev. Lett. 96 (2006)082004;T.E. Coan, et al., CLEO Collaboration, Phys. Rev. Lett. 96 (2006) 182002;G.S. Huang, et al., CLEO Collaboration, Phys. Rev. Lett. 96 (2006)032003;G.S. Adams, et al., CLEO Collaboration, Phys. Rev. D 73 (2006) 012002;D. Cronin-Hennessy, et al., CLEO Collaboration, Phys. Rev. D 74 (2006)012005;R.A. Briere, et al., CLEO Collaboration, Phys. Rev. D 74 (2006) 031106;D. Besson, et al., CLEO Collaboration, Phys. Rev. Lett. 96 (2006) 092002.

[8] J.Z. Bai, et al., BES Collaboration, Nucl. Instrum. Methods A 458 (2001)627.

[9] M. Ablikim, et al., BES Collaboration, hep-ex/0612054;M. Ablikim, et al., BES Collaboration, Phys. Rev. Lett. 97 (2006) 262001.

[10] M. Ablikim, et al., BES Collaboration, Phys. Lett. B 641 (2006) 145.[11] W.-M. Yao, et al., Particle Data Group, J. Phys. G 33 (2006) 1.[12] F.A. Berends, G.J. Komen, Phys. Lett. B 63 (1976) 432;

A.B. Arbuzov, E.A. Kuraev, et al., JHEP 9710 (1997) 006.[13] D.H. Zhang, G. Rong, C.J. Chen, Phys. Rev. D 74 (2006) 054012.[14] M. Ablikim, et al., BES Collaboration, Phys. Rev. Lett. 97 (2006) 121801.[15] M. Ablikim, et al., BES Collaboration, Nucl. Phys. B 727 (2005) 395.[16] S. Ono, Phys. Rev. D 20 (1979) 2975;

S. Ono, Z. Phys. C 8 (1981) 7;A. Martin, Phys. Lett. B 100 (1981) 511;L. Richardson, Phys. Lett. B 82 (1979) 272;W. Buchmüller, S.-H.H. Tye, Phys. Rev. D 24 (1981) 132;G. Bhanot, S. Rudaz, Phys. Lett. B 78 (1978) 119;H. Krasemann, S. Ono, Nucl. Phys. B 154 (1979) 283.

[17] P.A. Rapidis, et al., MARK-I Collaboration, Phys. Rev. Lett. 39 (1977)526.

[18] W. Bacino, et al., DELCO Collaboration, Phys. Rev. Lett. 40 (1978) 671.[19] R.H. Schindler, et al., MARK-II Collaboration, Phys. Rev. D 21 (1980)

2716.[20] R. Chistov, et al., BELLE Collaboration, Phys. Rev. Lett. 93 (2004)

051803.[21] D. Besson, et al., CLEO Collaboration, Phys. Rev. Lett. 96 (2006) 092002.