Physics Letters B 642 (2006) 197–202

www.elsevier.com/locate/physletb

Measurements of χcJ → K+K−K+K− decays

BES Collaboration

M. Ablikim a, J.Z. Bai a, Y. Ban l, J.G. Bian a, X. Cai a, H.F. Chen q, 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 t, L.Y. Diao i,Z.Y. Deng a, Q.F. Dong o, S.X. Du a, J. Fang a, S.S. Fang b, C.D. Fu a, C.S. Gao a, Y.N. Gao o,S.D. Gu a, Y.T. Gu d, Y.N. Guo a, Y.Q. Guo a, Z.J. Guo q, F.A. Harris q, K.L. He a, M. He m,

Y.K. Heng a, H.M. Hu a, T. Hu a, G.S. Huang a,1, X.T. Huang m, X.B. Ji a, X.S. Jiang a, X.Y. Jiang e,J.B. Jiao m, D.P. Jin a, S. Jin a, Yi Jin h, 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 a, X.N. Li a, X.Q. Li k, Y.L. Li d, Y.F. Liang n, H.B. Liao a,B.J. Liu a, C.X. Liu a, F. Liu f, Fang Liu a, H.H. Liu a, H.M. Liu a, J. Liu l, J.B. Liu a, J.P. Liu s,Q. Liu a, R.G. Liu a, Z.A. Liu a, Y.C. Lou e, F. Lu a, G.R. Lu e, J.G. Lu a, C.L. Luo j, F.C. Ma i,

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, S.L. Olsen q,H.P. Peng q,4, R.G. Ping a, N.D. Qi a, H. Qin a, J.F. Qiu a, Z.Y. Ren a, G. Rong a, L.Y. Shan a,

L. Shang a, C.P. Shen a, D.L. Shen a, X.Y. Shen a, H.Y. Sheng a, 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, G.L. Tong a, G.S. Varner q, D.Y. Wang a, L. Wang a,

L.L. Wang a, L.S. Wang a, M. Wang a, P. Wang a, P.L. Wang a, W.F. Wang a,2, 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, U. Wiedner p, N. Wu a, X.M. Xia a,X.X. Xie a, G.F. Xu a, X.P. Xu f, Y. Xu k, M.L. Yan r, H.X. Yang a, Y.X. Yang c, M.H. Ye b, Y.X. Ye r,

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.Q. Zhang a, H.Y. Zhang a, J.W. Zhang a,J.Y. Zhang a, S.H. Zhang a, X.M. Zhang a, X.Y. Zhang m, Yiyun Zhang n, Z.P. Zhang r, D.X. Zhao a,

J.W. Zhao a, M.G. Zhao a, P.P. Zhao a, W.R. Zhao a, Z.G. Zhao a,3, H.Q. Zheng l, J.P. Zheng a,Z.P. Zheng a, L. Zhou a, N.F. Zhou a,3, K.J. Zhu a, Q.M. Zhu a, Y.C. Zhu a, Y.S. Zhu a,

Yingchun Zhu a,4, 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 Jinan University, Jinan 250022, People’s Republic of China

i Liaoning University, Shenyang 110036, People’s Republic of Chinaj Nanjing Normal University, Nanjing 210097, People’s Republic of China

k Nankai University, Tianjin 300071, People’s Republic of Chinal Peking University, Beijing 100871, People’s Republic of China

m Shandong University, Jinan 250100, People’s Republic of Chinan Sichuan University, Chengdu 610064, People’s Republic of Chinao Tsinghua University, Beijing 100084, People’s Republic of China

p Uppsala University, Department of Nuclear and Particle Physics, Box 535, SE-75121 Uppsala, Swedenq University of Hawaii, Honolulu, HI 96822, USA

0370-2693/$ – see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2006.09.040

198 BES Collaboration / Physics Letters B 642 (2006) 197–202

r University of Science and Technology of China, Hefei 230026, People’s Republic of Chinas Wuhan University, Wuhan 430072, People’s Republic of China

t Zhejiang University, Hangzhou 310028, People’s Republic of China

Received 17 July 2006; accepted 13 September 2006

Available online 4 October 2006

Editor: M. Doser

Abstract

Using 14M ψ(2S) events taken with the BESII detector, χcJ → 2(K+K−) decays are studied. For the four-kaon final state, the branchingfractions are B(χc0,1,2 → 2(K+K−)) = (3.48 ± 0.23 ± 0.47) × 10−3, (0.70 ± 0.13 ± 0.10) × 10−3, and (2.17 ± 0.20 ± 0.31) × 10−3. For theφK+K− final state, the branching fractions, which are measured for the first time, are B(χc0,1,2 → φK+K−) = (1.03 ± 0.22 ± 0.15) × 10−3,(0.46 ± 0.16 ± 0.06) × 10−3, and (1.67 ± 0.26 ± 0.24) × 10−4. For the φφ final state, B(χc0,2 → φφ) = (0.94 ± 0.21 ± 0.13) × 10−3 and(1.70 ± 0.30 ± 0.25) × 10−3.© 2006 Elsevier B.V. All rights reserved.

1. Introduction

Exclusive quarkonium decays provide an important labora-tory for investigating perturbative quantum chromodynamics.Compared with J/ψ and ψ(2S) decays, there is much lessknowledge on χcJ decays which have parity and charge con-jugation PC = ++. Relatively few exclusive decays of the χcJ

have been measured. For the χcJ → vector–vector (VV) mode,measurements of χcJ → φφ [1], K∗(892)0K̄∗(892)0 [2], andωω [3] have been reported. The search for new decay modesand measurements with higher precision will help in better un-derstanding various χcJ decay mechanisms [4,5] and the natureof 3PJ cc̄ bound states.

Furthermore, the decays of χcJ , especially χc0 and χc2,provide a direct window on glueball dynamics in the 0++and 2++ channels since the hadronic decays may proceed viacc̄ → gg → qq̄qq̄ . Recently, a paper by Zhao [6] points outthat the decay branching fractions for scalar glueball candi-dates (f0(1370), f0(1500), and f0(1710)) in χc0 decays maybe predicted by a factorization scheme, in which some parame-ters can be fitted with B(χcJ → ωω,K∗(892)0K̄∗(892)0, φφ).The measurement precision of B(χcJ → V V ) will affect theuncertainties of the fitted parameters. Also, these fitted parame-ters will help clarify the role played by OZI-rule violation andSU(3) flavor breaking in the decays.

In this analysis, χcJ → K+K−K+K− is studied usingψ(2S) radiative decays. The branching fractions of χcJ →K+K−K+K− and χc0,2 → φφ are measured with higher sta-tistics, and those of χcJ decaying to φK+K− are measured forthe first time.

* Corresponding author.E-mail address: wangzy@mail.ihep.ac.cn (Z.Y. Wang).

1 Current address: Purdue University, West Lafayette, IN 47907, USA.2 Current address: Laboratoire de l’Accélérateur Linéaire, F-91898 Orsay,

France.3 Current address: University of Michigan, Ann Arbor, MI 48109, USA.4 Current address: DESY, D-22607 Hamburg, Germany.

2. The BES detector

The Beijing Spectrometer (BES) is a conventional solenoidalmagnet detector that is described in detail in Ref. [7]; BESIIis the upgraded version of the BES detector [8]. A 12-layervertex chamber (VC) surrounding the beam pipe provides trig-ger and position information. A forty-layer main drift chamber(MDC), located radially outside the VC, provides trajectory andenergy loss (dE/dx) information for charged tracks over 85%of the total solid angle. The momenta resolution is σp/p =0.017

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

hadron tracks is ∼ 8%. An array of 48 scintillation counterssurrounding the MDC measures the time-of-flight (TOF) ofcharged tracks with a resolution of ∼ 200 ps for hadrons. Out-side of the TOF counters is a 12-radiation-length barrel showercounter (BSC) composed of gas tubes interleaved with leadsheets. This measures the energies of electrons and photonsover ∼ 80% of the total solid angle with an energy resolution ofσE/E = 22%/

√E (E in GeV). Outside of the solenoidal coil,

which provides a 0.4 tesla magnetic field over the tracking vol-ume, is an iron flux return that is instrumented with three doublelayers of counters that identify muons of momenta greater than0.5 GeV/c.

A GEANT3 based Monte Carlo (MC) program with detailedconsideration of the detector performance (such as dead elec-tronic channels) is used to simulate the BESII detector. Theconsistency between data and Monte Carlo has been carefullychecked in many high purity physics channels, and the agree-ment is quite reasonable [9].

3. Event selection

The data sample used for this analysis consists of (14.00 ±0.56) × 106ψ(2S) events [10] collected with the BESII de-tector at the center-of-mass energy

√s = Mψ(2S). The χcJ →

K+K−K+K− channels are investigated using ψ(2S) radiativedecays to χcJ . Events with four charged tracks and one to three

BES Collaboration / Physics Letters B 642 (2006) 197–202 199

Fig. 1. χ2 distribution of 4C fit for χc0 → K+K−K+K− . Histogram denotesMC and error bars denote data.

photons are selected. Each charged track is required to be wellfitted by a helix and to have a polar angle, θ , within the fidu-cial region | cos θ | < 0.8. To ensure tracks originate from the

interaction region, we require Vxy =√

V 2x + V 2

y < 2 cm and

|Vz| < 20 cm, where Vx , Vy , and Vz are the x, y, and z coordi-nates of the point of closest approach of each charged track tothe beam axis. All charged tracks must be identified as kaonsusing the combined dE/dx and TOF information.

A neutral cluster is considered to be a photon candidate if itis located within the BSC fiducial region (| cos θ | < 0.75), theenergy deposited in the BSC is greater than 50 MeV, the firsthit appears in the first 6 radiation lengths, the angle betweenthe cluster and the nearest charged track is more than 15◦, andthe angle between the direction of cluster development and thedirection of the photon emission is less than 40◦.

A four constraint (4C) kinematic fit under the ψ(2S) →γK+K−K+K− hypothesis is performed, and the χ2 of thefit is required to be less than 25. For events with two orthree photon candidates, the combination having the mini-mum χ2 is chosen. In addition, χ2

γK+K−K+K− < χ2γπ+π−π+π−

and χ2γK+K−K+K− < χ2

γπ+π−K+K− are required to suppress

background contamination from ψ(2S) → γπ+π−π+π− andψ(2S) → γπ+π−K+K−. Fig. 1 shows the χ2 distribution ofdata and MC for the process of χc0 → K+K−K+K−.

With four selected kaons, there are four ways to com-bine oppositely charged kaons, and two combinations ofM

(1)

K+K−M(2)

K+K− pairs can be formed. The combination that hasone of its MK+K− closest to the φ mass is selected for furtheranalysis.

Fig. 2 shows the distribution of M(1)

K+K− versus M(2)

K+K− forselected events. There are two clear bands near 1.02 GeV/c2

which correspond to the φK+K− final state. The insert in theupper right corner, is the enlarged view of the lower left corner,and a clear φφ signal can be seen. Fig. 3 shows the correspond-ing M

(1)

K+K− versus M(2)

K+K− distribution for MC ψ(2S) →γχc1, χc1 → φK+K− and φφ, using B(χc1 → φK+K−) :B(χc1 → φφ) = 2 : 1.

Fig. 2. M(1)

K+K− versus M(2)

K+K− for candidate events.

Fig. 3. M(1)

K+K− versus M(2)

K+K− for MC ψ(2S) → γχc1, χc1 → φK+K−and φφ events after event selection.

Fig. 4. MK+K− distribution of all four possible K+K− combinations.(b) MK+K− distribution for MC ψ(2S) → γχc1, χc1 → K+K−K+K− .

To investigate intermediate resonances in (K+K−) finalstates, the invariant mass distribution of all four possibleK+K− combinations are plotted in Fig. 4(a). Except for the φ,no other obvious resonance is seen.

To test if the above selection criteria will cause “fake”φ signals, ψ(2S) → γχc1, χc1 → K+K−K+K− MC eventsare generated according to phase space. Fig. 4(b) shows theMK+K− distribution of these events using the same selectionas for data. No peak is seen around the φ signal region.

200 BES Collaboration / Physics Letters B 642 (2006) 197–202

Fig. 5. Background shape obtained from MC simulation. (a) ψ(2S) →π0K+K−K+K−. (b) ψ(2S) → γK+K−K+K− .

4. MC simulation

For each of the channels studied 100 000 MC events are gen-erated. The proper angular distributions for the photons emittedin ψ(2S) → γχcJ are used [11]. Phase space is used for theχcJ → 2(K+K−) decays (including intermediate states, e.g.χcJ → φφ).

5. Background study

Possible backgrounds come from ψ(2S) → γχcJ , χcJ →π+π−π+π−, π+π−K+K−, KsKπ , and π+π−pp̄; ψ(2S) →π0K+K−K+K−; and phase space ψ(2S) → γK+K−K+K−.100 000 MC events are generated for each of the first four back-ground channels where the angular distribution for the radiativephoton is generated the same as for the signal channels whilethe χcJ decays are generated according to phase space. Thecontamination from these backgrounds to each signal chan-nel is less than 1.0%, which is negligible. 100 000 MC eventsare also generated for each of the last two background chan-nels according to phase space. For ψ(2S) → π0K+K−K+K−,Fig. 5(a) shows the MK+K−K+K− distribution in the region 3.2–3.7 GeV/c2. Using the branching fraction measured by CLEOc[12], the number of events from this channel is expected tobe 23 ± 7. For ψ(2S) → γK+K−K+K−, the MK+K−K+K−distribution is shown in Fig. 5(b). This branching fraction iscurrently unavailable. However, comparing the MK+K−K+K−distribution from this channel and that from data, shown inFig. 6, the contribution from ψ(2S) → γK+K−K+K− back-ground should be small. No χcJ peaks are seen in Fig. 5(a)and (b). Thus, the fitted number of χcJ signal events is insen-sitive to the shape of the function used to describe the totalbackground.

We have also considered possible background fromψ(2S) → γχc0, χc0 → f0(980)f0(980) → K+K−K+K−.Using the branching ratio for χc0 → f0(980)f0(980) →π+π−K+K− [13], the ratio B(f0(980) → K+K−)/

(B(f0(980) → K+K−) + B(f0(980) → π+π−)) [13], andMC efficiencies for these processes, the estimated number off0(980)f0(980) → K+K−K+K− events is about 6, which arespread over a relatively wide region compared with the width ofthe φ [14]. Thus, this background in the φ region is negligiblysmall.

Fig. 6. Breit–Wigner fit to χcJ signals (a) with all candidate events and (b) withthe φK+K− region events.

6. Mass spectrum fit

6.1. χcJ → 2(K+K−)

Fig. 6(a) shows the high mass (> 3.2 GeV/c2) 2(K+K−) in-variant mass distribution using all candidate events in ψ(2S) →γχcJ ,χcJ → 2(K+K−). Clear χcJ signals can be seen inthis figure. A fit with Breit–Wigner functions convoluted withGaussian resolution functions (about 15 MeV/c2 for χcJ sig-nals in all channels studied) yields the number of χcJ events:Nχc0 = 278 ± 18, Nχc1 = 54 ± 10, and Nχc2 = 160 ± 14. MCsimulation gives detection efficiencies of 5.9%, 6.3%, and 5.8%for J = 0, 1, and 2, respectively.

6.2. χcJ → φK+K−

The χcJ → φK+K− events are clustered as two bandsaround the φ mass in Fig. 2. The φK+K− region is de-fined by M

(i)

K+K− ∈ (1.08,2.4) GeV/c2 and M(j �=i)

K+K− ∈ (1.00,

1.04) GeV/c2 (i, j = 1,2). Fig. 6(b) shows the MφK+K− dis-tribution for these events, and clear χcJ signals can be seen. MCsimulation gives detection efficiencies of 5.9%, 6.2%, and 5.6%for J = 0,1, and 2, respectively. A fit with Breit–Wigner func-tions convoluted with Gaussian resolution functions yields thenumber of χcJ events: Nχc0 = 53.5 ± 8.3, Nχc1 = 19.2 ± 5.6,and Nχc2 = 56.3 ± 8.2.

In order to determine the contribution from non-resonantψ(2S) → γχcJ ,χcJ → 2(K+K−) events in the φK+K− re-gion, we analyze the non-resonant 2(K+K−) region, definedby M

(i)

K+K− ∈ (1.1,2.4) GeV/c2 (i = 1,2) in Fig. 2. The num-ber of events in this region is Nnr

t = 238. Fig. 7(a) shows theMK+K−K+K− distribution for the non-resonant 2(K+K−) re-gion events, where three clean χcJ peaks are seen with verylittle background. A fit with Breit–Wigner functions convolutedwith Gaussian resolution functions yields: Nχnr

c0= 144.1 ±

12.7, Nχnrc1

= 21.5 ± 5.5, and Nχnrc2

= 39.4 ± 6.9.Fig. 7(b) shows the φ signal for the φK+K− region events.

The fit yields 143 ± 14 signal events and Nbg = 25 back-ground events from non-resonant 2(K+K−) events within a3σ window (1.00–1.04 GeV/c2) in the φ signal region. Wecalculate the non-resonant 2(K+K−) contribution to Nχc0 ,Nχc1 , and Nχc2 assuming that the proportion of χc0, χc1, andχc2 events is the same for non-resonant 2(K+K−) events in

BES Collaboration / Physics Letters B 642 (2006) 197–202 201

Fig. 7. (a) Breit–Wigner fit to χcJ using non-resonant 2(K+K−) region events.(b) Fit to φ signal with φK+K− region events.

Fig. 8. Fit to χcJ signals in φφ final state.

the non-resonant and the φK+K− regions. For χc0, the non-resonant contribution is Nn

χc0= Nnr

χc0· Nbg/N

nrt = 15.1 ± 1.3.

Similarly, we obtain Nnχc1

= 2.3 ± 0.6, and Nnχc2

= 4.1 ± 0.7.Therefore, the number of φK+K− events, after subtracting thenon-resonant 2(K+K−) events, is Nχc0 = 38.4 ± 8.4, Nχc1 =16.9 ± 5.6, and Nχc2 = 52.2 ± 8.2.

6.3. χcJ → φφ

The signal region for χcJ → φφ events is a 40 MeV/c2 ×40 MeV/c2 square around the φ mass in Fig. 2. Fig. 8 showsthe Mφφ distribution for these φφ events, and clear χc0,2 signalscan be seen. MC simulation gives detection efficiencies of 9.0%and 8.6% for J = 0 and 2, respectively. A fit yields the numberof events for χcJ : Nχc0 = 27.8 ± 5.8 and Nχc2 = 42.7 ± 7.1.

The two bands near the φ mass in Fig. 2, used to extract theχcJ → φK+K− signal in Section 6.2, are taken as the sidebandregion for the φφ events. They include both the φK+K− eventsand non-resonant K+K−K+K− events. From MC simulationthe event distributions in the two bands are nearly uniform. Thenumber of normalized sideband events in the φφ signal regionare

Nsdχc0

= 53.5 ± 8.3

f≈ 1.6 ± 0.3,

Nsdχc2

= 56.3 ± 8.2

f≈ 1.7 ± 0.3,

Table 1Systematic error (%). In the wire resolution row, the numbers from left to rightcorrespond to ψ(2S) → 2(K+K−), φK+K−, and φφ

Source χc0 χc1 χc2

Wire resolution 8.9, 9.8, 10.0 9.3, 9.9, – 9.7, 9.6, 10.1Particle ID 8 8 8Photon efficiency 2 2 2Background shape negligible negligible negligibleNumber of ψ(2S) 4 4 4B(ψ(2S) → γχcJ ) 4.3 4.6 4.9B(φ → K+K−) 1.2 1.2 1.2

Total χcJ → 2(K+K−) 13.5 13.9 14.3χcJ → φK+K− 14.1 14.3 14.2χcJ → φφ 14.3 – 14.5

respectively, where the factor f = 33 is the ratio of the sidebandarea to the φφ signal region area. Thus we obtain the number ofevents in χcJ → φφ: Nχc0 = 26.2 ± 5.8 and Nχc2 = 41.0 ± 7.1.

7. Systematic error

The systematic error in these branching fraction measure-ments includes the uncertainties caused by wire resolution, par-ticle ID, photon efficiency, and the number of ψ(2S) events.

The systematic error caused by MDC tracking and the kine-matic fit are estimated by using simulations with different MDCwire resolutions [9]. For particle ID, the combined informationof dE/dx and TOF is used. An error of 2% is assigned for eachcharged track [15] and each photon [9]. The errors introducedby branching fractions of intermediate states are taken from theParticle Data Group (PDG) [16].

The total systematic errors, determined by the sum of allsources added in quadrature, are listed in Table 1. The uncer-tainty from B(φ → K+K−) contributes once in the systematicerror estimation for χcJ → φK+K− and twice in φφ, while itdoes not contribute in χcJ → 2(K+K−). For the uncertaintiescaused by wire resolution, there are some slight differences forthe different decay channels.

8. Results

For χcJ → 2(K+K−) (including intermediate states), thebranching fractions are calculated using

B(χcJ → 2

(K+K−)) = NχcJ

Nψ(2S) ·B(ψ(2S) → γχcJ ) · ε̄ ,

where the average detection efficiency ε̄ is given by

ε̄ = NχcJ− NφK+K− − Nφφ

NχcJ

· ε2(K+K−)

+ NφK+K−

NχcJ

· εφK+K− + Nφφ

NχcJ

· εφφ.

Similarly, we can calculate the branching fractions for χcJ →φK+K−, φφ with corresponding efficiency expressions. Ta-ble 2 lists our measurement results, together with the PDGvalues.

202 BES Collaboration / Physics Letters B 642 (2006) 197–202

Table 2χcJ → 2(K+K−) branching fractions

Channel 2(K+K−)(×10−3) φK+K−(×10−3) φφ(×10−3)

BESII PDG BESII BESII PDG

χc0 3.48 ± 0.23 ± 0.47 2.1 ± 0.4 1.03 ± 0.22 ± 0.15 0.94 ± 0.21 ± 0.13 0.9 ± 0.5χc1 0.70 ± 0.13 ± 0.10 0.39 ± 0.17 0.46 ± 0.16 ± 0.06 − −χc2 2.17 ± 0.20 ± 0.31 1.41 ± 0.35 1.67 ± 0.26 ± 0.24 1.70 ± 0.30 ± 0.25 1.9 ± 0.7

In summary, the decays of χcJ → 2(K+K−) are studied,and the corresponding branching fractions including intermedi-ate states are given. The decay χcJ → φK+K− is observed forthe first time. The branching fractions for χcJ → 2(K+K−)

and χcJ → φφ are measured with higher precision; Table 2lists the comparison of the measured branching fractions be-tween BESII and the PDG. Our measurement for χcJ →φφ, together with the two measurements of χcJ → ωω andK̄∗(892)0K∗(892)0, will be helpful in understanding the na-ture of χcJ states.

Acknowledgements

The BES Collaboration thanks the staff of BEPC and com-puting center for their hard efforts. This work is supported inpart by the National Natural Science Foundation of China un-der contracts Nos. 10491300, 10225524, 10225525, 10425523,the Chinese Academy of Sciences under contract No. KJ 95T-03, the 100 Talents Program of CAS under Contract Nos. U-11,U-24, U-25, and the Knowledge Innovation Project of CAS un-der Contract Nos. U-602, U-34 (IHEP), the National NaturalScience Foundation of China under Contract No. 10225522(Tsinghua University), the Swedish research Council (VR),and the Department of Energy under Contract No. DE-FG02-04ER41291 (U Hawaii).

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