b

Physics Letters B 630 (2005) 7–13

www.elsevier.com/locate/physlet

First observation ofχcJ → ωω decays

BES Collaboration

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

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

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

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

R.G. Liua, Z.A. Liu a, F. Lua, G.R. Lue, H.J. Lup, J.G. Lua, C.L. Luoi, F.C. Mah,H.L. Maa, L.L. Ma a, Q.M. Maa, X.B. Mae, Z.P. Maoa, X.H. Mo a, J. Niea,

S.L. Olseno, H.P. Pengp, N.D. Qia, H. Qini, J.F. Qiua, Z.Y. Rena, G. Ronga,L.Y. Shana, L. Shanga, D.L. Shena, X.Y. Shena, H.Y. Shenga, F. Shia, X. Shik,3,

H.S. Suna, J.F. Suna, S.S. Suna, Y.Z. Suna, Z.J. Suna, Z.Q. Tand, X. Tanga, Y.R. Tiann,G.L. Tonga, G.S. Varnero, D.Y. Wanga, L. Wanga, L.S. Wanga, M. Wanga, P. Wanga,

P.L. Wanga, W.F. Wanga,4, Y.F. Wanga, Z. Wanga, Z.Y. Wanga, Zhe Wanga,Zheng Wangb, C.L. Weia, D.H. Weia, N. Wua, X.M. Xia a, X.X. Xie a, B. Xin h,2,

G.F. Xua, Y. Xu j, M.L. Yanp, F. Yangj, H.X. Yanga, J. Yangp, Y.X. Yangc, M.H. Yeb,Y.X. Ye p, Z.Y. Yi a, G.W. Yua, C.Z. Yuana, J.M. Yuana, Y. Yuana, S.L. Zanga,Y. Zengg, Yu Zenga, B.X. Zhanga B.Y. Zhanga, C.C. Zhanga, D.H. Zhanga,

H.Y. Zhanga, J.W. Zhanga, J.Y. Zhanga, Q.J. Zhanga, X.M. Zhanga, X.Y. Zhangl,Yiyun Zhangm, Z.P. Zhangp, Z.Q. Zhange, D.X. Zhaoa, J.W. Zhaoa, M.G. Zhaoj,

P.P. Zhaoa, W.R. Zhaoa, H.Q. Zhengk, Z.G. Zhaoa,5, J.P. Zhenga, Z.P. Zhenga,L. Zhoua, N.F. Zhoua, K.J. Zhua, Q.M. Zhua, Y.C. Zhua, Y.S. Zhua, Yingchun Zhua,6,

Z.A. Zhua, B.A. Zhuanga, X.A. Zhuanga, B.S. Zoua

a Institute of High Energy Physics, Beijing 100049, People’s Republic of China

0370-2693/$ – see front matter 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2005.08.133

8 BES Collaboration / Physics Letters B 630 (2005) 7–13

II

nals are

b China Center for Advanced Science and Technology (CCAST), Beijing 100080, People’s Republic of Chinac Guangxi Normal University, Guilin 541004, People’s Republic of China

d Guangxi University, Nanning 530004, People’s Republic of Chinae Henan Normal University, Xinxiang 453002, People’s Republic of China

f Huazhong Normal University, Wuhan 430079, People’s Republic of Chinag Hunan University, Changsha 410082, People’s Republic of China

h Liaoning University, Shenyang 110036, People’s Republic of Chinai Nanjing Normal University, Nanjing 210097, People’s Republic of China

j Nankai University, Tianjin 300071, People’s Republic of Chinak Peking University, Beijing 100871, People’s Republic of Chinal Shandong University, Jinan 250100, People’s Republic of China

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

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

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

Received 22 June 2005; accepted 31 August 2005

Available online 29 September 2005

Editor: M. Doser

Abstract

Decays ofχc0,2 → ωω are observed for the first time using a sample of 14.0 × 106 ψ(2S) events collected with the BESdetector. The branching ratios are determined to beB(χc0 → ωω) = (2.29±0.58±0.41)×10−3 andB(χc2 → ωω) = (1.77±0.47± 0.36) × 10−3, where the first errors are statistical and the second systematic. The significances of the two sig4.4σ and 4.7σ , respectively. 2005 Elsevier B.V. All rights reserved.

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1. Introduction

Exclusive quarkoninum decays provide an imptant laboratory for investigating perturbative quantchromodynamics. Compared withJ/ψ andψ(2S) de-cays, one has much less knowledge onPC = ++χcJ

decays. While a few exclusive decays ofχcJ have been

E-mail address:wangzy@mail.ihep.ac.cn(Z. Wang).1 Current address: Iowa State University, Ames, IA 50011-31

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

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

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

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

measured, many decay modes remain unknown.theχcJ → vector vector mode, only measurementsχcJ → φφ [1] andχcJ → K∗(892)0K̄∗(892)0 [2] areavailable with low statistics. Precise measurementsmore channels will help in better understandingvariousχcJ decay mechanisms[3,4] and the nature o3PJ cc̄ bound states.

Further, the decays ofχcJ , especiallyχc0 andχc2,provide a direct window on glueball dynamics in t0++ and 2++ channels since the hadronic decays mproceed viacc̄ → gg → qq̄qq̄.

Recently, the branching ratio forχc0 → f0(980)×f0(980) [5] has been measured by the BES Collabotion. In the present analysis, a search forχc0,2 decay-ing into π+π−π0π+π−π0 final states is carried ouusing 14 millionψ(2S) events[6] accumulated at thupgraded BES detector (BESII). Signals ofχc0 andχc2 decaying toω pairs inψ(2S) radiative decays arobserved for the first time.

BES Collaboration / Physics Letters B 630 (2005) 7–13 9

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2. The BES detector

The Beijing Spectrometer (BES) is a conventiosolenoidal magnet detector that is described in detaRef.[7]; BESII is the upgraded version of the BES dtector[8]. A 12-layer vertex chamber (VC) surrouning the beam pipe provides trigger and position infmation. A forty-layer main drift chamber (MDC), located radially outside the VC, provides trajectory aenergy loss (dE/dx) information for charged trackover 85% of the total solid angle. The momentum relution isσp/p = 0.017

√1+ p2 (p in GeV/c), and the

dE/dx resolution for hadron tracks is∼ 8%. An ar-ray of 48 scintillation counters surrounding the MDmeasures the time-of-flight (TOF) of charged tracwith a resolution of∼ 200 ps for hadrons. Outsidof the TOF counters is a 12-radiation-length barshower counter (BSC) comprised of gas proportiotubes interleaved with lead sheets. This measuresenergies of electrons and photons over∼ 80% of thetotal solid angle with an energy resolution ofσE/E =22%/

√E (E in GeV). Outside of the solenoidal co

which provides a 0.4 Tesla magnetic field overtracking volume, is an iron flux return that is instrmented with three double layers of counters that idtify muons of momentum greater than 0.5 GeV/c.

A GEANT3 based Monte Carlo (MC) prograwith detailed consideration of the detector perfmance (such as dead electronic channels) is usesimulate the BESII detector. The consistency betwdata and Monte Carlo has been carefully checkemany high purity physics channels, and the agreemis quite reasonable[9].

3. Event selection

3.1. ωω signal

In this analysis,χcJ → ωω → π+π−π0π+π−π0

channels are investigated usingψ(2S) radiative de-cays toχcJ . Events with four charged tracks and fior six photons are selected. Each charged track isquired to be well fit by a helix and to have a poangle,θ , within the fiducial region|cosθ | < 0.8. Toensure tracks originate from the interaction region,

requireVxy =√

V 2x + V 2

y < 2 cm and|Vz| < 20 cm,

whereVx , Vy , andVz are thex, y andz coordinates ofthe point of closest approach of each track to the beaxis. Events with a recoil massMrec within (3.08–3.12) GeV/c2 are removed to suppress backgrounfrom ψ ′ → π+π−J/ψ . Here Mrec is the mass recoiling against two oppositely charged tracks anddetermined using all track combinations.

A neutral cluster is considered to be a photon cdidate if it is located within the BSC fiducial regio(|cosθ | < 0.8), the energy deposited in the BSCgreater than 40 MeV, the first hit appears in the fi10 radiation lengths, and the angle between the cluand the nearest charged track is greater than 6◦.

A six constraint (6-C) kinematic fit to the hypothesisψ(2S) → γπ+π−π0π+π−π0 with the invariantmass of the two photon pairs constrained to theπ0

mass is performed, and theχ2 of the 6-C fit is re-quired to be less than 15. For events with six pton candidates, the combination having the minimχ2 is chosen, and the probability of the 6-C fitrequired to be larger than that of the 7-C fit to thypothesisψ(2S) → 2π+2π−3π0 to suppress potential background fromψ(2S) → ωπ+π−π0π0 →2π+2π−3π0.

Since there are fourω pair combinations fromπ+π−π0π+π−π0, theω pair with the minimumR,which is defined as

R =√(

M(1)

π+π−π0 − 783)2 + (

M(2)

π+π−π0 − 783)2

,

is chosen for further analysis. Here,Mπ+π−π0 is theinvariant mass of three pions, and superscripts (1)denote different pion combinations. Therefore, theronly one entry for each event.

Figs. 1 and 2show mass distributions for candidaevents in the high mass (M6π > 3.2 GeV/c2) and lowmass regions (M6π < 3.2 GeV/c2), respectively. Here(a) is the scatter plot ofM(1)

π+π−π0 versusM(2)

π+π−π0,(b) is theMπ+π−π0 distribution recoiling against thoppositeω, selected by requiring|Mπ+π−π0 − 783| <50 MeV/c2, and (c) is theMωω invariant mass distribution for events in theω pair signal region, defined bR < 50 MeV/c2. In Fig. 1, a clearω signal can be seein (b), and clearχc0 andχc2 signals in (c), indicatingthe existence ofχc0,2 → ωω decays. By contrast, ithe lowM6π mass region, shown inFig. 2, theω pairsignal is less significant than in the high mass reg

10 BES Collaboration / Physics Letters B 630 (2005) 7–13

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Fig. 1. Distributions of events surviving the selection criteriascribed in the text withM6π > 3.2 GeV/c2. (a) M

π+π−π0 versusM

π+π−π0, (b) Mπ+π−π0 recoiling against the oppositeω, se-

lected by requiring|Mπ+π−π0 − 783| < 50 MeV/c2, and (c)Mωω

invariant mass distribution for events where theω pair satisfiesR < 50 MeV/c2.

In the following, onlyω pair events in the high masare studied.

In order to test if the selection criteria in this anasis will give ‘fake’ ω pair events from non-ω pairevents, 300 000 MC simulatedψ → γχc0 → γ 6π

events are generated in whichχc0 decays to 6π ac-cording to phase space.Fig. 3 shows theMπ+π−π0

distributions of the surviving MC phase space eveafter requiring the same selection criteria as for thedata. No peak around theω mass is seen, which showthat theω pair selection criteria in this analysis do ngenerate fakeω pair signals.

The annular region around theω pair signal circle,shown inFig. 1(a), is taken as the sideband regioFig. 4 shows theM6π sideband distributions define

Fig. 2. Distributions defined as inFig. 1 but with M6π <

3.2 GeV/c2.

Fig. 3. Mπ+π−π0 distributions from MC phase space simulat

ψ(2S) → γχc0, χc0 → π+π−π0π+π−π0.

using the radiusR to be (a) 150< R < 300 MeV/c2

and (b) 100< R < 200 MeV/c2. No obviousχcJ sig-nals are seen in these sideband distributions.

BES Collaboration / Physics Letters B 630 (2005) 7–13 11

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Fig. 4.M6π distribution of events in sideband regions (a) 150< R <

300 MeV/c2 and (b) 100< R < 200 MeV/c2.

3.2. MC simulation

A MC simulation of ψ(2S) → γχcJ ,χcJ → ωω

is used to determine the detection efficiency. Tproper angular distributions of the photon emittedψ(2S) → γχcJ are used[10]. Fig. 5shows the distri-butions, identical to those inFig. 1 for MC simulatedψ(2S) → γχc0, χc0 → ωω events passing the samselection criteria as for the real data. MC simulaψ(2S) → γχc2, χc2 → ωω events have similar distributions.

3.3. Mass spectrum fit

The Maximum Likelihood (ML) method is used tfit theMωω mass spectrum of events in theω pair sig-nal region (Fig. 1(c)). The χ0,2 signal functions aredetermined from MC simulation, as shown inFig. 5(c)for χc0, while the background function is taken frothe sideband distribution, shown inFig. 4(a). The fitresult is represented by the solid curve inFig. 6, andthe fit yields

Nχc0 = 38.1± 9.6,Nχc2 = 27.7± 7.4.

The statistical significances ofχc0 andχc2 are 4.4σ

and 4.7σ , respectively, which are estimated fro√2 lnL, where lnL is the difference between th

logarithmic ML values of the fit with and without thcorresponding signal function.

4. Systematic error

The systematic error in this branching ratio mesurement includes the uncertainties in the MDC traing efficiency, photon efficiency, kinematic fit, bacground shape, number ofψ(2S) events, etc.

Fig. 5. Distributions defined as inFig. 1 from MC simulatedψ(2S) → γχc0, χc0 → ωω events.

Fig. 6. Fit of theMωω distribution. Dots with error bars are data, thesolid histogram represents the maximum likelihood fit result, andthe dashed histogram is the sideband background.

12 BES Collaboration / Physics Letters B 630 (2005) 7–13

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4.1. MDC tracking efficiency and photon efficienc

For charged tracks, the uncertainty of the trackefficiency is determined by comparing data and Mfor some very cleanJ/ψ decay channels[9], and anerror of 2% is found for each track. A similar compaison has also been performed for photons[11], and thedifference is also about 2% for a single photon.

4.2. Kinematic fit

The systematic error associated with the kinemfit is due to differences between data and MC simlation in the determination of the track momentuthe track fitting error matrix, and the photon enerand direction. The effect is estimated by using twosumptions for the MDC wire resolution in the evesimulation; the difference is determined to be 8.4which is taken as the systematic error.

4.3. Background shape

Two different sidebandM6π spectrum shapesshown inFig. 4, are used as the background functioThe difference in the number ofχc0,2 events obtainedwith the two different shapes is taken as a systemerror.

4.4. Binning, fit range, and signal region

The differences caused by different binning andranges in theωω mass spectrum fit are 1.4% and 3.2for χc0 andχc2, respectively. Different sized signal rgions yield differences of 3.4% and 4.3% forχc0 andχc2, respectively, which are taken as a systematicror.

4.5. Angular distribution ofχcJ → ωω

Forχc0 → ωω decay, phase space gives a goodproximation to the angular distribution of theω mesonin theχc0 rest frame since its spin is zero. Forχc2 de-cays, we use a MC generator based on effective th[12] with different parameters to generate correspoing angular distributions for the final state particleThe efficiency difference between these tests andphase space generator is estimated to be 9.4%, wis included as the systematic error.

Table 1Individual sources and total systematic error (%)

Source χc0 → ωω χc2 → ωω

Track efficiency 8 8Photon efficiency 10 106-C fit 8.4 8.4Background shape 6.0 1.0Signal region 3.4 4.3Binning and fit range 1.4 3.2Angular distribution – 9.4No. of ψ(2S) events 4 4B(ψ(2S) → γχcJ ) 5.1 6.7B(ω → 3π) 0.9 0.9B(π0 → γ γ ) 0.0 0.0

Total 18.1 20.4

4.6. Branching ratios of intermediate states

Errors on intermediate state branching ratiosobtained from the PDG[13] except forB(ψ(2S) →γχcJ ), where recent CLEO results[14] are used.Ta-ble 1 summarizes all contributions to the systemaerrors, and the total systematic error is determinedadding all systematic errors in quadrature.

5. Results

The branching ratio ofB(χcJ → ωω) is determinedfrom

B(χcJ → ωω) = NobsχcJ

Nψ(2S) · f1 · f 22 · f 2

3 · ε ,

whereNobsχcJ

is the number of events selected,Nψ(2S)

the total number ofψ(2S) events,ε is the detection efficiency for the investigated channel, andf1, f2 andf3are the branching ratios ofψ(2S) → γχcJ ,ω → 3π ,andπ0 → γ γ , respectively.Table 2lists theχc0,2 →ωω branching ratio results, together with the quantitused in the branching ratio calculation.

In summary,ωω signals in the decay ofχc0,2 areobserved, and their branching ratios measured forfirst time.χc0 andχc2 decays toωω have similar de-cay branching ratios, which is different from othχcJ → V V decays(χcJ → φφ, K̄∗(892)0K∗(892)0).This measurement, together with previous measments ofχcJ → V V , will be helpful in understandingthe nature ofχcJ states.

BES Collaboration / Physics Letters B 630 (2005) 7–13 13

Table 2Branching ratio results and relevant quantities

Quantity χc0 → ωω χc2 → ωω

Number of events 38.1± 9.6 27.7± 7.4Efficiency (%) 1.66 1.55Nψ(2S)(×106) 14.00± 0.56 14.00± 0.56

B(ω → π+π−π0) (%) 89.1± 0.7 89.1± 0.7B(π0 → γ γ ) (%) 98.798± 0.032 98.798± 0.032B(ψ(2S) → γχcJ ) (%) 9.22± 0.47 9.33± 0.63

B(χcJ → ωω) ·B(ψ(2S) → χcJ )(×10−4) 2.12±0.53±0.37 1.65±0.44±0.32B(χcJ → ωω)(×10−3) 2.29±0.58±0.41 1.77±0.47±0.36

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Acknowledgements

The BES Collaboration thanks the staff of BEPfor their hard efforts. This work is supported in paby the National Natural Science Foundation of Chunder contracts Nos. 10491300, 10225524, 1022510425523, the Chinese Academy of Sciences uncontract No. KJ 95T-03, the 100 Talents ProgramCAS under Contract Nos. U-11, U-24, U-25, andKnowledge Innovation Project of CAS under Cotract Nos. U-602, U-34 (IHEP), the National Naural Science Foundation of China under Contract10225522 (Tsinghua University), and the Departmof Energy under Contract No. DE-FG02-04ER412(U Hawaii).

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