Physics Letters B 670 (2008) 179–183

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Physics Letters B

www.elsevier.com/locate/physletb

Measurements of the observed cross sections for e+e− → exclusive light hadronscontaining K 0

S meson at√

s = 3.773 and 3.650 GeV

BES Collaboration

M. Ablikim a, J.Z. Bai a, Y. Bai a, Y. Ban k, X. Cai a, H.F. Chen o, H.S. Chen a, H.X. Chen a, J.C. Chen a, Jin Chen a,X.D. Chen e, Y.B. Chen a, Y.P. Chu a, Y.S. Dai q, Z.Y. Deng a, S.X. Du a, J. Fang a, C.D. Fu n, C.S. Gao a, Y.N. Gao n, S.D. Gu a,Y.T. Gu d, Y.N. Guo a, K.L. He a, M. He l, Y.K. Heng a, J. Hou j, H.M. Hu a, T. Hu a, G.S. Huang a,1, X.T. Huang l,Y.P. Huang a, X.B. Ji a, X.S. Jiang a, J.B. Jiao l, D.P. Jin a, S. Jin a, Y.F. Lai a, H.B. Li a, J. Li a, L. Li a, R.Y. Li a, W.D. Li a,W.G. Li a, X.L. Li a, X.N. Li a, X.Q. Li j, Y.F. Liang m, H.B. Liao a,2, B.J. Liu a, C.X. Liu a, Fang Liu a, Feng Liu f, H.H. Liu a,3,H.M. Liu a, J.B. Liu a,4, J.P. Liu p, H.B. Liu d, J. Liu a, R.G. Liu a, S. Liu h, Z.A. Liu a, F. Lu a, G.R. Lu e, J.G. Lu a, C.L. Luo i,F.C. Ma h, H.L. Ma a, L.L. Ma a,5, Q.M. Ma a, M.Q.A. Malik a, Z.P. Mao a, X.H. Mo a, J. Nie a, R.G. Ping a, N.D. Qi a, H. Qin a,J.F. Qiu a, G. Rong a, X.D. Ruan d, L.Y. Shan a, L. Shang a, D.L. Shen a, X.Y. Shen a, H.Y. Sheng a, H.S. Sun a, S.S. Sun a,Y.Z. Sun a, Z.J. Sun a, X. Tang a, J.P. Tian n, G.L. Tong a, X. Wan a, L. Wang a, L.L. Wang a, L.S. Wang a, P. Wang a,P.L. Wang a, W.F. Wang a,6, Y.F. Wang a, Z. Wang a, Z.Y. Wang a, C.L. Wei a, D.H. Wei c, Y. Weng a, N. Wu a, X.M. Xia a,X.X. Xie a, G.F. Xu a, X.P. Xu f, Y. Xu j, M.L. Yan o, H.X. Yang a, M. Yang a, Y.X. Yang c, M.H. Ye b, Y.X. Ye o, C.X. Yu j,G.W. Yu a, C.Z. Yuan a, Y. Yuan a, S.L. Zang a,7, Y. Zeng g, B.X. Zhang a, B.Y. Zhang a, C.C. Zhang a, D.H. Zhang a,H.Q. Zhang a, H.Y. Zhang a, J.W. Zhang a, J.Y. Zhang a, X.Y. Zhang l, Y.Y. Zhang m, Z.X. Zhang k, Z.P. Zhang o, D.X. Zhao a,J.W. Zhao a, M.G. Zhao a, P.P. Zhao a, B. Zheng a,∗, H.Q. Zheng k, J.P. Zheng a, Z.P. Zheng a, B. Zhong i, L. Zhou a,K.J. Zhu a, Q.M. Zhu a, X.W. Zhu a, Y.C. Zhu a, Y.S. Zhu a, Z.A. Zhu a, Z.L. Zhu c, B.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 Chinac Guangxi Normal University, Guilin 541004, People’s Republic of Chinad Guangxi University, Nanning 530004, People’s Republic of Chinae Henan Normal University, Xinxiang 453002, People’s Republic of Chinaf Huazhong Normal University, Wuhan 430079, People’s Republic of Chinag Hunan University, Changsha 410082, People’s Republic of Chinah Liaoning University, Shenyang 110036, People’s Republic of Chinai 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 Chinam Sichuan University, Chengdu 610064, People’s Republic of Chinan Tsinghua University, Beijing 100084, People’s Republic of Chinao University of Science and Technology of China, Hefei 230026, People’s Republic of Chinap Wuhan University, Wuhan 430072, People’s Republic of Chinaq Zhejiang University, Hangzhou 310028, People’s Republic of China

* Corresponding author.E-mail address: zhengb@mail.ihep.ac.cn (B. Zheng).

1 Current address: University of Oklahoma, Norman, OK 73019, USA.2 Current address: DAPNIA/SPP Batiment 141, CEA Saclay, 91191, Gif sur Yvette Cedex, France.3 Current address: Henan University of Science and Technology, Luoyang 471003, People’s Republic of China.4 Current address: CERN, CH-1211 Geneva 23, Switzerland.5 Current address: University of Toronto, Toronto M5S 1A7, Canada.6 Current address: Laboratoire de l’Accélérateur Linéaire, Orsay, F-91898, France.7 Current address: University of Colorado, Boulder, CO 80309, USA.

0370-2693/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2008.10.050

180 BES Collaboration / Physics Letters B 670 (2008) 179–183

a r t i c l e i n f o a b s t r a c t

Article history:Received 25 August 2008Received in revised form 20 October 2008Accepted 26 October 2008Available online 30 October 2008Editor: W.-D. Schlatter

By analyzing the data sets of 17.3 pb−1 taken at√

s = 3.773 GeV and of 6.5 pb−1 taken at√

s =3.650 GeV with the BES-II detector at the BEPC collider, we measure the observed cross sections forthe exclusive light hadron final states of K 0

S K −π+, K 0S K −π+π0, K 0

S K −π+π+π−, K 0S K −π+π+π−π0,

K 0S K −π+π+π+π−π− and K 0

S K −π+π0π0 produced in e+e− annihilation at the two energy points. Weset the upper limits on the observed cross sections and the branching fractions for ψ(3770) decay tothese final states at 90% C.L.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

The ψ(3770) resonance is expected to decay almost entirelyinto D D̄ meson pairs since its width is almost two orders of mag-nitude larger than that of ψ(3686) [1]. In recent years, the studyof the ψ(3770) non-D D̄ decays becomes an attractive study fieldin the charmonium energy region due to the existing puzzle thatabout 38% of ψ(3770) does not decay into D D̄ meson pairs [2]. Tounderstand the possible excess of the ψ(3770) cross section rela-tive to the D D̄ cross section, BES and CLEO Collaborations mademany efforts to study the ψ(3770) non-D D̄ decays. The CLEO Col-laboration measured the e+e− → ψ(3770) → non-D D̄ cross sec-tion to be (−0.01 ± 0.08+0.41

−0.30) nb [3]. While the BES Collaborationmeasured the branching fraction for ψ(3770) → non-D D̄ decayto be (15 ± 5)% [4–8], which indicates that, contrary to what isgenerally expected, the ψ(3770) might substantially decay intonon-D D̄ final states or there are some new structure or physics ef-fects which may partially be responsible for the largely measurednon-D D̄ branching fraction of the ψ(3770) decays [9,10]. BES Col-laboration observed the first non-D D̄ decay mode for ψ(3770) →J/ψπ+π− , and measured its decay branching fraction to be

B[ψ(3770) → J/ψπ+π−] = (0.34 ± 0.14 ± 0.09)% [11,12]. Thiswas confirmed by CLEO Collaboration [13]. Latter, CLEO Collabora-tion observed more ψ(3770) exclusive non-D D̄ decays, ψ(3770) →J/ψπ0π0, J/ψπ0, J/ψη [13], γχc J ( J = 0,1,2) [14,15] and φη[16], etc. Summing over these measured branching fractions yieldsthe sum of the branching fractions for the ψ(3770) exclusive non-D D̄ decays not more than 2%. In addition, BES and CLEO Collabora-tions also attempted to search for other ψ(3770) exclusive charm-less decays [16–23]. However, the existing results cannot clarify thepossible excess. For better understanding the origin of the possibleexcess, search for more ψ(3770) exclusive charmless decays willbe helpful.

In this Letter, we report measurements of the observed crosssections for the exclusive light hadron final states of K 0

S K −π+(throughout the Letter, charge conjugation is implied),K 0

S K −π+π0, K 0S K −π+π+π− , K 0

S K −π+π+π−π0,K 0

S K −π+π+π+π−π− and K 0S K −π+π0π0 at the center-of-mass

energies of 3.773 and 3.650 GeV with the same method as theone used in our previous works [19–21]. With the measured crosssections at the two energy points, we set the upper limits on theobserved cross sections and the branching fractions for ψ(3770)

decay to these final states. The measurements are made by analyz-ing the data set of 17.3 pb−1 collected at

√s = 3.773 GeV [called

as the ψ(3770) resonance data] and the data set of 6.5 pb−1 col-lected at

√s = 3.650 GeV (called as the continuum data) with the

BES-II detector at the BEPC collider.

2. BES-II detector

The BES-II is a conventional cylindrical magnetic detector that isdescribed in detail in Refs. [24,25]. A 12-layer vertex chamber (VC)surrounding the beryllium beam pipe provides input to the event

trigger, as well as coordinate information. A forty-layer main driftchamber (MDC) located just outside the VC yields precise mea-surements of charged particle trajectories with a solid angle cover-age of 85% of 4π ; it also provides ionization energy loss (dE/dx)measurements which are used for particle identification. Momen-tum resolution of 1.7%

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

of 8.5% for Bhabha scattering electrons are obtained for the datataken at

√s = 3.773 GeV. An array of 48 scintillation counters sur-

rounding the MDC measures the time of flight (TOF) of chargedparticles with a resolution of about 180 ps for electrons. Out-side the TOF, a 12 radiation length, lead-gas barrel shower counter(BSC), operating in limited streamer mode, measures the energiesof electrons and photons over 80% of the total solid angle withan energy resolution of σE/E = 0.22/

√E (E in GeV) and spa-

tial 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 and serveto identify muons with momentum greater than 500 MeV/c. Theycover 68% of the total solid angle.

3. Event selection

In the reconstruction of the K 0S K −π+ , K 0

S K −π+π0,K 0

S K −π+π+π− , K 0S K −π+π+π−π0, K 0

S K −π+π+π+π−π− andK 0

S K −π+π0π0 final states, the K 0S and π0 mesons are recon-

structed through the decays of K 0S → π+π− and π0 → γ γ .

For each candidate event, we require that at least four chargedtracks are well reconstructed in the MDC with good helix fits, andthe polar angle of the tracks satisfying | cos θ | < 0.85. The chargedtracks (except for the K 0

S meson reconstruction) are required tooriginate from the interaction region V xy < 2.0 cm (V xy < 8.0 cm)and |V z| < 20.0 cm, where V xy and |V z| are the closest approachesin the xy-plane and the z direction, respectively.

The charged particles are identified by using the dE/dx andTOF measurements, with which the combined confidence levelsC Lπ and C LK for pion and kaon hypotheses are calculated. Thepion and kaon candidates are required to satisfy C Lπ > 0.001 andC LK > C Lπ , respectively. To reconstruct K 0

S mesons, we requirethat the π+π− meson pairs must originate from a secondary ver-tex which is displaced from the event vertex at least by 4 mm inthe xy-plane.

The photons are selected with the BSC measurements. The goodphoton candidates are required to satisfy the following criteria:the energy deposited in the BSC is greater than 50 MeV, the elec-tromagnetic shower starts in the first 5 readout layers, the anglebetween the photon and the nearest charged track is greater than22◦ [26,27], and the opening angle between the cluster develop-ment direction and the photon emission direction is less than 37◦[26,27].

For each candidate event, there may be several differentcharged and/or neutral track combinations satisfying the aboveselection criteria for exclusive light hadron final states. Each com-

BES Collaboration / Physics Letters B 670 (2008) 179–183 181

bination is subjected to an energy-momentum conservation kine-matic fit. For the processes containing π0 meson in the final states,an additional constraint kinematic fit is imposed on π0 → γ γ .Candidates with a fit probability larger than 1% are accepted. Ifmore than one combination satisfies the selection criteria in anevent, only the combination with the longest decay distance of thereconstructed K 0

S mesons is retained.To suppress the background from the D D̄ decays, we use the

double tag method [28] to remove the D D̄ events. For exam-ple, for the K 0

S K −π+π0 final state, we exclude the all possibleevents from D D̄ decays by rejecting those in which the D and D̄mesons can be reconstructed in the decay modes of D− → K 0

S K −and D+ → π+π0, D− → K −π0 and D+ → K 0

Sπ+ , D̄0 → K 0

Sπ0

and D0 → K −π+ [28]. For the other final states, the events fromD D̄ decays are suppressed similarly. The remaining contaminationsfrom D D̄ decays due to particle misidentification or missing pho-ton(s) are accounted by using Monte Carlo simulation, as discussedin Section 5.

4. Data analysis

In the data analysis, these processes containing K 0S meson in

the final state are studied by examining the invariant mass spectraof the π+π− combinations satisfying the above selection crite-ria for the K 0

S meson reconstruction. The invariant masses of theπ+π− combinations are calculated with the momentum vectorsfrom the K 0

S reconstruction. Fig. 1 shows the resulting distributionof the invariant masses of the π+π− combinations from the se-lected candidates for the K 0

S K −π+ , K 0S K −π+π0, K 0

S K −π+π+π− ,K 0

S K −π+π+π−π0, K 0S K −π+π+π+π−π− and K 0

S K −π+π0π0 fi-nal states. In each figure, the peak around the K 0

S nominal massindicates the production of e+e− → exclusive light hadrons con-taining K 0

S meson. Fitting the π+π− invariant mass spectra with aGaussian function for the K 0

S signal and a flat background yieldsthe number of the events for each process observed from theψ(3770) resonance data and the continuum data. In the fit, theK 0

S mass and its mass resolution are fixed at the values obtainedby analyzing Monte Carlo samples.

5. Background subtraction

Some other events may contribute to the selected candidateevents for e+e− → f ( f represents exclusive light hadron finalstate). These include the events from J/ψ and ψ(3686) decaysdue to ISR returns, the events from the other final states due tomisidentifying a pion as a kaon or reverse, and the events fromD D̄ decays. The number Nb of these contaminations should besubtracted from the number Nobs of the candidates for e+e− → f .The estimation of them can be done based on Monte Carlo sim-ulation. The details about the background subtraction have beendescribed in Ref. [19]. For each background channel except D D̄decays, 50 000 or 100 000 Monte Carlo events are used in thebackground estimation. The Monte Carlo sample of each differentbackground channel is from ten to several thousands times largerthan the data in size.

Monte Carlo study shows that the contaminations fromψ(3770) → J/ψπ+π− , ψ(3770) → J/ψπ0π0, ψ(3770) → J/ψπ0

and ψ(3770) → γχc J ( J = 0,1,2) can be neglected.Even though we have removed the main contaminations from

D D̄ decays in the previous event selection (see Section 3), thereare still some events from D D̄ decays satisfying the selection crite-ria for the light hadron final states due to particle misidentificationor missing photon(s). The number of these contaminations fromD D̄ decays are further removed by analyzing a Monte Carlo sam-ple which is about forty times larger than the ψ(3770) resonance

Fig. 1. The π+π− invariant mass spectra of the candidates for the (a)K 0

S K −π+ , (b) K 0S K −π+π0, (c) K 0

S K −π+π+π− , (d) K 0S K −π+π+π−π0, (e)

K 0S K −π+π+π+π−π− and (f) K 0

S K −π+π0π0 final states selected from theψ(3770) resonance data (left) and the continuum data (right).

data. The Monte Carlo events are generated as e+e− → D D̄ at√s = 3.773 GeV, where the D and D̄ mesons are set to decay into

all possible final states with the branching fractions quoted fromPDG [8].

Subtracting the number Nb of these contaminations from thenumber Nobs of the candidate events, we obtain the net num-ber Nnet of the signal events for each process. For the K 0

S K −π+and K 0

S K −π+π+π+π−π− final states, for which only a few sig-nal events are observed from the continuum data, we set theupper limits Nup on the number of the signal events at 90% C.L.Here, we use the Feldman–Cousins method [29] and assume thatthe background is absent. The numbers of Nobs, Nb and Nnet (orNup) are summarized in the second, third and fourth columns ofTables 1 and 2. For each process, the background events in theψ(3770) resonance data are dominant by D D̄ decays and ψ(3686)

decays. While, there is no D D̄ decay in the continuum data, andthe ψ(3686) production cross section at

√s = 3.650 GeV is much

less than that at√

s = 3.773 GeV. So, the number of the back-ground events in the continuum data can almost be negligible.

6. Results

6.1. Monte Carlo efficiency

To estimate the detection efficiency ε for e+e− → f , we use aphase space generator including initial state radiation and vacuumpolarization corrections [30] with 1/s energy dependence in crosssection. Final state radiation [31] decreases the detection efficiencynot more than 0.5%. Detailed analysis based on Monte Carlo sim-ulation for the BES-II detector [32] gives the detection efficienciesfor each process at

√s = 3.773 and 3.650 GeV, which are summa-

rized in the fifth columns of Tables 1 and 2, where the detectionefficiencies do not include the branching fractions for K 0

S → π+π−and π0 → γ γ , B(K 0

S → π+π−) and B(π0 → γ γ ).

6.2. Observed cross sections

Let Bπ0 = B(π0 → γ γ ) for the modes of K 0S K −π+π0 and

K 0S K −π+π+π−π0, Bπ0 = B2(π0 → γ γ ) for the mode of

K 0S K −π+π0π0 and Bπ0 = 1 for the modes of K 0

S K −π+ ,

182 BES Collaboration / Physics Letters B 670 (2008) 179–183

Table 1The observed cross sections for e+e− → exclusive light hadrons at

√s = 3.773 GeV, where Nobs is the number of events observed from the ψ(3770) resonance data, Nb

is the total number of background events, Nnet is the number of the signal events, ε is the detection efficiency, Δsys is the relative systematic error of the observed crosssection, and σ is the observed cross section.

e+e− → Nobs Nb Nnet ε (%) Δsys (%) σ [pb]K 0

S K −π+ 18.4 ±4.6 0.1 ± 0.0 18.3 ±4.6 10.02±0.14 10.7 15.2±3.8 ± 1.6K 0

S K −π+π0 41.2 ±6.6 1.1 ± 0.2 40.1±6.6 3.52 ±0.08 11.6 96.2±15.9±11.1K 0

S K −π+π+π− 40.0±6.5 1.0 ± 0.2 38.9 ±6.5 3.56 ±0.06 14.2 91.5±15.3±13.0K 0

S K −π+π+π−π0 24.5 ±5.2 1.5 ± 0.3 23.0 ±5.2 0.77±0.03 15.2 253.0 ±57.1±38.4K 0

S K −π+π+π+π−π− 4.8±2.2 0.3 ± 0.1 4.5±2.2 0.84±0.03 18.4 44.4±21.9 ± 8.2K 0

S K −π+π0π0 19.8 ±4.9 2.8 ± 0.5 17.0 ±4.9 0.99±0.04 14.3 147.0 ±42.4±21.0

Table 2The observed cross sections for e+e− → exclusive light hadrons at

√s = 3.650 GeV, where Nobs is the number of events observed from the continuum data, Nup is the

upper limit on the number of the signal events, σ up is the upper limit on the observed cross section set at 90% C.L., and the definitions of the other symbols are the sameas those in Table 1.

e+e− → Nobs Nb Nnet or Nup ε (%) Δsys (%) σ or σ up [pb]K 0

S K −π+ 2 0.0 < 5.91 10.55±0.15 12.9 < 14.3K 0

S K −π+π0 7.7 ± 2.9 0.0 7.7 ± 2.9 3.62 ±0.09 11.6 47.9 ± 18.0 ± 5.6K 0

S K −π+π+π− 13.4 ± 3.8 0.0 13.4 ± 3.8 3.66 ±0.06 14.1 81.4 ± 23.1 ± 11.5K 0

S K −π+π+π−π0 4.6 ± 2.5 0.0 4.6 ± 2.5 0.87±0.03 17.2 119.0 ± 64.7 ± 20.5K 0

S K −π+π+π+π−π− 0 0.0 < 2.44 0.95±0.03 18.1 < 69.7K 0

S K −π+π0π0 3.3 ± 2.0 0.0 3.3 ± 2.0 1.12±0.05 14.1 67.1 ± 40.7 ± 9.5

Table 3The upper limits on the observed cross section σ

upψ(3770)→ f at

√s = 3.773 GeV and the branching fraction Bup

ψ(3770)→ f for ψ(3770) → f are set at 90% C.L. The σψ(3770)→ f iscalculated with Eq. (2), where the first error is the statistical, the second is the independent systematic, and the third is the common systematic error. The upper ∗ denotesthat we neglect the contributions from the continuum production.

Decay Mode σψ(3770)→ f (pb) σupψ(3770)→ f (pb) Bup

ψ(3770)→ f

K 0S K −π+ 15.2±3.8 ± 0.2 ± 1.6∗ < 22.0 < 3.2 × 10−3

K 0S K −π+π0 51.4 ±23.2 ± 2.6 ± 5.8 < 90.7 < 13.3 × 10−3

K 0S K −π+π+π− 15.3±26.5 ± 2.2 ± 2.1 < 59.0 < 8.7 × 10−3

K 0S K −π+π+π−π0 141.6 ±83.2 ± 14.7 ± 20.7 < 284.3 < 41.8 × 10−3

K 0S K −π+π+π+π−π− 44.4 ±21.9 ± 2.1 ± 7.9∗ < 82.7 < 12.2 × 10−3

K 0S K −π+π0π0 84.2 ±57.2 ± 8.3 ± 11.2 < 180.4 < 26.5 × 10−3

K 0S K −π+π+π− and K 0

S K −π+π+π+π−π− , where B(π0 → γ γ )

is the branching fraction for the decay of π0 → γ γ , then the ob-served cross section for e+e− → f can be determined by

σe+e−→ f = Nnet

L × ε × B(K 0S → π+π−) × Bπ0

, (1)

where L is the integrated luminosity of the data set, Nnet is thenumber of the signal events, ε is the detection efficiency andB(K 0

S → π+π−) is the branching fraction for the decay of K 0S →

π+π− . Inserting these numbers in Eq. (1), we obtain the observedcross sections for each process at

√s = 3.773 and 3.650 GeV. They

are summarized in Tables 1 and 2, where the first error is sta-tistical and the second systematic. In the measurements of theobserved cross sections, the systematic errors arise from the un-certainties in integrated luminosity of the data set (2.1% [4,5]),photon selection (2.0% per photon), tracking efficiency (2.0% pertrack), particle identification (0.5% per pion or kaon), kinematic fit(1.5%), K 0

S reconstruction (1.1% [27]), branching fractions quotedfrom PDG [33] (0.03% for B(π0 → γ γ ) and 0.07% for B(K 0

S →π+π−)), Monte Carlo modeling (6.0% [19–21]), Monte Carlo statis-tics (1.4% ∼ 4.4%), background subtraction (0.0% ∼ 3.0%) and fitto mass spectrum (0.4% ∼ 8.5%). Adding these uncertainties inquadrature yields the total systematic error Δsys for each modeat

√s = 3.773 and 3.650 GeV.

The upper limit σupe+e−→ f on the observed cross sections for

the K 0S K −π+ and K 0

S K −π+π+π+π−π− final states at√

s =3.650 GeV are set with Eq. (1) by substituting Nnet with Nup/(1 −Δsys), where Nup is the upper limit on the number of the sig-nal event, and Δsys is the systematic error in the cross sectionmeasurement. Inserting the corresponding numbers in the equa-

tion, we obtain the upper limits on the observed cross sections fore+e− → K 0

S K −π+ and e+e− → K 0S K −π+π+π+π−π− at

√s =

3.650 GeV, which are also listed in Table 2.

6.3. Upper limits on the observed cross sections and the branchingfractions for ψ(3770) → f

If we ignore the possible interference effects between the con-tinuum and resonance amplitudes, and the difference of the vac-uum polarization corrections at

√s = 3.773 and 3.650 GeV, we can

determine the observed cross section σψ(3770)→ f for ψ(3770) → fat

√s = 3.773 GeV by comparing the observed cross sections

σ 3.773 GeVe+e−→ f and σ 3.650 GeV

e+e−→ f for e+e− → f measured at√

s = 3.773and 3.650 GeV, respectively. It can be given by

σψ(3770)→ f = σ 3.773GeVe+e−→ f − fco × σ 3.650GeV

e+e−→ f , (2)

where fco = 3.6502/3.7732 is the normalization factor to considerthe 1/s cross section dependence. The results are summarized inthe second column of Table 3, where the first error is the statis-tical, the second is the independent systematic arising from theuncertainties in the Monte Carlo statistics, in the fit to the massspectrum and in the background subtraction, and the third is thecommon systematic error arising from the other uncertainties asdiscussed in Section 6.2.

The upper limit on the observed cross section σupψ(3770)→ f for

ψ(3770) → f at√

s = 3.773 GeV is set by shifting the cross sectionby 1.64σ , where σ is the total error of the measured cross section.The results on σ

upψ(3770)→ f are summarized in the third column of

Table 3.

BES Collaboration / Physics Letters B 670 (2008) 179–183 183

The upper limit on the branching fraction Bupψ(3770)→ f for

ψ(3770) → f is set by dividing its upper limit on the ob-served cross section σ

upψ(3770)→ f by the observed cross section

σ obsψ(3770) = (7.15 ± 0.27 ± 0.27) nb [19] for the ψ(3770) production

at√

s = 3.773 GeV and a factor (1 − Δσ obsψ(3770)), where Δσ obs

ψ(3770)

is the relative error of the σ obsψ(3770) . The results on Bup

ψ(3770)→ f aresummarized in the last column of Table 3.

7. Summary

In this Letter, we present the measurements of the observedcross sections for K 0

S K −π+ , K 0S K −π+π0, K 0

S K −π+π+π− ,K 0

S K −π+π+π−π0, K 0S K −π+π+π+π−π− and K 0

S K −π+π0π0

produced in e+e− annihilation at√

s = 3.773 and 3.650 GeV. Thesecross sections are obtained by analyzing the data sets of 17.3 pb−1

taken at√

s = 3.773 GeV and of 6.5 pb−1 at√

s = 3.650 GeV withthe BES-II detector at the BEPC collider. By comparing the observedcross sections for each process measured at

√s = 3.773 and 3.650

GeV, we set the upper limits on the observed cross sections andthe branching fractions for ψ(3770) decay to these final states at90% C.L. These measurements provide helpful information to un-derstand the mechanism of the continuum light hadron productionand the discrepancy between the observed cross sections for D D̄and ψ(3770) production.

Acknowledgements

BES Collaboration thanks the staff of BEPC for their hard efforts.This work is supported in part by the National Natural ScienceFoundation of China under contracts Nos. 10491300, 10225524,10225525, 10425523, the Chinese Academy of Sciences under con-tract No. KJ 95T-03, the 100 Talents Program of CAS under ContractNos. U-11, U-24, U-25, the Knowledge Innovation Project of CASunder Contract Nos. U-602, U-34 (IHEP), the National Natural Sci-

ence Foundation of China under Contract No. 10225522 (TsinghuaUniversity).

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