Resonances in and

b

Physics Letters B 607 (2005) 243–253

www.elsevier.com/locate/physlet

Resonances inJ/ψ → φπ+π− andφK+K−

BES Collaboration

M. Ablikim a, J.Z. Baia, Y. Bank, J.G. Biana, D.V. Buggt, X. Caia, J.F. Changa,H.F. Chenq, H.S. Chena, H.X. Chena, J.C. Chena, Jin Chena, Jun Cheng, M.L. Chena,

Y.B. Chena, S.P. Chib, Y.P. Chua, X.Z. Cuia, H.L. Daia, Y.S. Dais, Z.Y. Denga,L.Y. Donga,1, Q.F. Dongo, S.X. Dua, Z.Z. Dua, J. Fanga, S.S. Fangb, C.D. Fua,

H.Y. Fua, C.S. Gaoa, Y.N. Gaoo, M.Y. Gonga, W.X. Gonga, S.D. Gua, Y.N. Guoa,Y.Q. Guoa, Z.J. Guop, F.A. Harrisp, K.L. Hea, M. Hel, X. Hea, Y.K. Henga, H.M. Hua,T. Hua, G.S. Huanga,3, X.P. Huanga, X.T. Huangl, X.B. Jia, C.H. Jianga, X.S. Jianga,D.P. Jina, S. Jina, Y. Jina, Yi Jin a, Y.F. Laia, F. Li a, G. Li b, H.H. Li a, J. Li a, J.C. Lia,

Q.J. Lia, 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. Liangn, H.B. Liaof, C.X. Liu a, F. Liu f, Fang Liuq, H.H. Liu a, H.M. Liu a, J. Liuk,

J.B. Liua, J.P. Liur, R.G. Liua, Z.A. Liu a, Z.X. Liu a, F. Lua, G.R. Lue, H.J. Luq,J.G. Lua, C.L. Luoi, L.X. Luo d, X.L. Luo a, F.C. Mah, H.L. Maa, J.M. Maa, L.L. Ma a,

Q.M. Maa, X.B. Mae, X.Y. Ma a, Z.P. Maoa, X.H. Mo a, J. Niea, Z.D. Niea,S.L. Olsenp, H.P. Pengq, N.D. Qia, C.D. Qianm, 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, X. Tanga, N. Taoq,

Y.R. Tiano, G.L. Tonga, G.S. Varnerp, D.Y. Wanga, J.Z. Wanga, K. Wangq, L. Wanga,L.S. Wanga, M. Wanga, P. Wanga, P.L. Wanga, S.Z. Wanga, W.F. Wanga,4, Y.F. Wanga,Z. Wanga, Z.Y. Wanga, Zhe Wanga, Zheng Wangb, C.L. Weia, D.H. Weia, Y.M. Wu a,X.M. Xia a, X.X. Xie a, B. Xin h,2, G.F. Xua, H. Xua, S.T. Xuea, M.L. Yanq, F. Yangj,H.X. Yanga, J. Yangq, Y.X. Yangc, M. Yea, M.H. Yeb, Y.X. Ye q, L.H. Yi g, Z.Y. Yi a,

C.S. Yua, 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. Zhanga, J.W. Zhanga, J.Y. Zhanga, Q.J. Zhanga, S.Q. Zhanga, X.M. Zhanga,

X.Y. Zhangl, Y.Y. Zhanga, Yiyun Zhangn, Z.P. Zhangq, Z.Q. Zhange, D.X. Zhaoa,J.B. Zhaoa, J.W. Zhaoa, M.G. Zhaoj, P.P. Zhaoa, W.R. Zhaoa, X.J. Zhaoa, Y.B. Zhaoa,

Z.G. Zhaoa,5, H.Q. Zhengk, J.P. Zhenga, L.S. Zhenga, Z.P. Zhenga, X.C. Zhonga,

0370-2693/$ – see front matter 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2004.12.041

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244 BES Collaboration / Physics Letters B 607 (2005) 243–253

curately:

th.

r

B.Q. Zhoua, G.M. Zhoua, 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 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 Chinal Shandong University, Jinan 250100, People’s Republic of China

m Shanghai Jiaotong University, Shanghai 200030, People’s Republic of Chinan Sichuan University, Chengdu 610064, People’s Republic of Chinao Tsinghua University, Beijing 100084, People’s Republic of China

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

r Wuhan University, Wuhan 430072, People’s Republic of Chinas Zhejiang University, Hangzhou 310028, People’s Republic of China

t Queen Mary, University of London, London E1 4NS, UK

Received 29 October 2004; accepted 10 December 2004

Available online 22 December 2004

Editor: W.-D. Schlatter

Abstract

A partial wave analysis is presented ofJ/ψ → φπ+π− andφK+K− from a sample of 58MJ/ψ events in the BES IIdetector. Thef0(980) is observed clearly in both sets of data, and parameters of the Flatté formula are determined acM = 965± 8(stat) ± 6(syst) MeV/c2, g1 = 165± 10± 15 MeV/c2, g2/g1 = 4.21± 0.25± 0.21. Theφππ data also exhibit astrongππ peak centred atM = 1335 MeV/c2. It may be fitted withf2(1270) and a dominant 0+ signal made fromf0(1370)interfering with a smallerf0(1500) component. There is evidence that thef0(1370) signal is resonant, from interference wif2(1270). There is also a state inππ with M = 1790+40

−30 MeV/c2 andΓ = 270+60−30 MeV/c2; spin 0 is preferred over spin 2

This state,f0(1790), is distinct fromf0(1710). TheφKK̄ data contain a strong peak due tof ′2(1525). A shoulder on its uppe

side may be fitted by interference betweenf0(1500) andf0(1710). 2004 Elsevier B.V. All rights reserved.

PACS: 13.25.Gv; 14.40.Gx; 13.40.Hq

E-mail address: [email protected](L.Y. Dong).1 Current address: Iowa State University, Ames, IA 50011-3160, USA.2 Current address: Purdue University, West Lafayette, IN 47907, USA.3 Current address: Cornell University, Ithaca, NY 14853, USA.4 Current address: Laboratoire de l’Accélératear Linéaire, F-91898 Orsay, France.5 Current address: University of Michigan, Ann Arbor, MI 48109, USA.6 Current address: DESY, D-22607 Hamburg, Germany.

mailto:[email protected]

BES Collaboration / Physics Letters B 607 (2005) 243–253 245

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The processesJ/ψ → φπ+π− andφK+K− havebeen studied previously in the Mark III[1] andDM2 [2] experiments, provide useful information othe nature of the scalar mesons involved[3,4]. Here wereport BES II data on these channels with much larstatistics from a sample of 58 millione+e− → J/ψ

interactions. Thef0(980), f0(1370) and a state withmass at 1790 MeV/c2 and with spin 0 preferred ovespin 2, called thef0(1790) throughout this Letter, arstudied here. A particular feature is thatf0(1790) →ππ is strong, but there is littleor no corresponding signal for decays toKK̄. This behavior is incompatiblwith f0(1710), which is known to decay dominantly tKK̄ ; this indicates the presence of two distinct staf0(1710) andf0(1790).

A detailed description of the BES II detectorgiven in Ref.[5]. It has a cylindrical geometry arounthe beam axis. Trajectories of charged particlesmeasured in the vertex chamber (VC) and main dchamber (MDC); these are surrounded by a solenomagnet providing a field of 0.4 T. Photons are dtected in a Barrel Shower Counter (BSC) comprizof a sandwich array of lead and gas chambers. Pcle identification is accomplished using time-of-flight(TOF) information from the TOF scintillator array located immediately outside the MDC and thedE/dx

information from the MDC.Events must have four charged tracks with to

charge zero. These tracks are required to lie wwithin the MDC acceptance with a polar angleθ satis-fying |cosθ | < 0.80 and to have their point of closeapproach to the beam within 2 cm of the beam aand within 20 cm of the centre of the interactiongion along the beam axis. Further, events must saa four-constraint (4C) kinematic fit withχ2 < 40.

Kaons, pions, and protons are identified by timof-flight, dE/dx, and also by kinematic fitting. Thσ of the TOF measurement is 180 ps. Kaons mayidentified by TOF anddE/dx up to a momentum o800 MeV/c. The 4C kinematic fit provides additiongood separation betweenφππ and φKK; residualcrosstalk between these channels is negligible.

TheK+K− invariant mass distributions forJ/ψ →K+K−π+π− andJ/ψ → K+K−K+K− are shownin Fig. 1(a) and (c); in the latter case, theK+K−pair with invariant mass closest to theφ is plot-ted. The peaks of theφ lie at 1019.7 ± 0.2 and1020.0 ± 0.2 MeV/c2 in (a) and (c), in reasonab

agreement with the value of the Particle Data Gro(PDG)[6]. In both cases, there is a clearφ signal overa modest background of events due toK+K−π+π−or K+K−K+K− without aφ. The curves in (a) and(c) show the background, assuming it follows a phspace dependence onM(K+K−). The resulting background is (19.0 ± 1.5)% in (a) and (6.2 ± 1.6)%in (c). Events containing aφ are selected by requiing at least one kaon identified by TOF ordE/dx and|MK+K− − Mφ | < 15 MeV/c2.

Before discussing the main physics results, itnecessary to deal with an important background aing in J/ψ → K+K−π+π−. Events for the study othis background channel are selected in a sidebining M(K+K−) = 1.045–1.09 GeV/c2. Fig. 2 showsDalitz plots and mass projections for these sideevents; Dalitz plots forφπ+π− and φK+K− dataare shown inFig. 3. For theK+K−π+π− sidebin,there is a strong peak in theφπ mass distribution oFig. 2(b) centred at 1500 MeV/c2 with a full-widthof 200 MeV/c2. This φπ peak is of interest becausof an earlier report of a possible exotic state closethis mass with quantum numbersJp = 1− [7]. The re-flection of this peak produces a horizontal band atbottom ofFig. 2(a); it projects to a broad peak centrat 2450 MeV/c2 in Fig. 2(b). ForK+K−K+K− side-bin events ofFig. 2(c), there is no corresponding peat low mass inφK, Fig. 2(d).

In order to investigate the nature of this peak, welect events in the mass range 1400–1600MeV/c2 fromFig. 2(b). Mass distributions ofK+π− and K−π+pairs are shown inFig. 2(e) and corresponding distrbutions forK+π+ andK−π− in Fig. 2(f). There isa strongK∗(890) peak visible inFig. 2(e) but onlya broad peak inFig. 2(f). It can be shown that thpresence ofK∗(890) in the background, combinewith kinematic selection in a narrow range ofK+K−masses, can generate the peak position and widthe spurious peak inφπ .

A similar effect arises in selectedφππ events.Fig. 3(b) showsM(φπ) for events selected asφπ+π−by requiringM(K+K−) within ±15 MeV/c2 of theφ mass. There is again aφπ peak, centred now a1460 MeV/c2. Again it can be shown that the peakconsistent entirely with background. There is no snificant evidence for an exoticφπ state. If it weremisinterpreted as aφπ state, fits show that it requirea φ combined with anL = 1 pion coming from the


dse

Fig. 1. TheK+K− invariant mass distributions for (a)J/φ → K+K−π+π−, (c) J/ψ → K+K−K+K− ; curves show the fitted backgrounand a Gaussian fit to theφ; (b) and (d) show mass projections for events selected within±15 MeV/c2 of theφ; (e) and (f) show mass projectionafter cutting events within±100 MeV/c2 of the central mass ofK∗(890); curves in (e) show the fitted background and a Gaussian fit to thφ.

sisto

hefor

re-

in-

nst

ueler

or

K∗1(890), hence quantum numbersJP = 1−, 0−, or

2−.We have carried through a full partial wave analy

in three alternative ways: (a) making a cut in orderexclude events lying within±80 MeV/c2 of the cen-tral mass ofK∗(890), which is slightly narrower thanthe selection ofFig. 1; (b) including into the fit an in-coherent background fromK∗(890)Kπ ; and (c) mak-ing a background subtraction which allows for tshift in mass and width between sidebin and datathe background peak inφπ at 1500 MeV/c2. Resultsof these three approaches agree within errors. We

gard the first method as the most reliable, since it isdependent of any modeling of the background.Figs. 4and 5show the fit from this approach. The cut agaiK∗(890) eliminates theφπ peak at 1460 MeV/c2, asshown inFig. 4(d). It also eliminates backgrounds dto channelsK∗(1430)K∗(890), observed in the finastateK+K−π+π−. It reduces the background undthe φ in Fig. 1(e) to (13.5 ± 1.4)%; after the back-ground subtraction, the number ofφπ+π− events fallsto 4180.

The branching fractions for production ofφππ andφKK̄ are determined allowing for the efficiencies f


Fig. 2. Dalitz plots for a sidebin to theφ with M(K+K−) = 1.045 to 1.09 GeV/c2 for (a)K+K−π+π− data, (c)K+K−K+K− data; (b) and(d) show projections againstφπ± andφK± mass; the mass distributions for (e)M(K+π−) andM(K−π+), (f) M(K+π+) andM(K−π−)

for events from (a) in theφπ mass range 1400–1600 MeV/c2.

ob-

een

r-m-

nals

edi-e oftelydens in

detecting the two channels and correcting for unserved neutral states. Results are:B(J/ψ → φππ) =(1.63± 0.03± 0.20)× 10−3 andB(J/ψ → φKK̄) =(2.14±0.04±0.22)×10−3. The main contributions tothe systematic errors come from differences betwdata and Monte Carlo simulation for theφ selection,K∗(890) cut, and particle identification; from uncetainties in the MDC wire resolution; and the total nuber ofJ/ψ events.

We turn now to the physics revealed by diagobands in the Dalitz plots ofFig. 3and mass projectionof Figs. 4 and 5. There is a strongf0(980) → π+π−

signal inFig. 4(c) and a low mass peak inFig. 5(c)due tof0(980) → K+K−. Secondly, theφπ+π− dataexhibit in Fig. 4(c) the clearest signal yet observfor f0(1370) → π+π−. Several authors have prevously expressed doubts concerning the existencf0(1370), but present data cannot be fitted adequawithout it. Both Mark III and DM2 groups observea similar peak with lower statistics. There have beearlier reports of similar but less conspicuous peakππ → KK̄ from experiments at ANL[8,9] and BNL[10]. A third feature in theφπ+π− data inFig. 4(c) isa clear peak at around 1775 MeV/c2.


Fig. 3. Dalitz plots for (a)J/ψ → φπ+π−, (c) J/ψ → φK+K− ; (b) and (d) show the projections againstφπ andφK mass.

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The φK+K− data of Fig. 5(c) contain a strongf ′

2(1525) peak. However, it is asymmetric and monly be fitted by including on its upper sidef0(1710)interfering with other components.

We now describe the maximum likelihood fitthe data. Amplitudes are fitted to relativistic tensexpressions which are documented in Ref.[11]. Thefull angular dependence of decays of theφ andπ+π−or K+K− resonances is fitted, including correlatiobetween them. The line-shape of theφ is not fitted,because theφ is much narrower than the experimenresolution. We include production ofJP = 0+ reso-nances with orbital angular momentum� = 0 and 2 inthe production processJ/ψ → φf0. For production off2, there is one amplitude with� = 0 and three with� = 2, where� and the spin off2 may combine tomake overall spinS = 0, 1 or 2. The one possible� = 4amplitude makes a negligible contribution. The acctance, determined from a Monte Carlo simulationincluded in the maximum likelihood fit. All figureshown here are uncorrected for acceptance, whicapproximately uniform across Dalitz plots exceptthe effect of theK∗(890) cut.

The background subtraction is made by giving dpositive weight in log likelihood and sidebin even

negative weight; the sidebin events (suitably weighby K+K− phase space) then cancel background indata sample.

The φπ+π− and φK+K− data are fitted simultaneously, constraining resonance masses and wto be the same in both sets of data.Table 1 showsbranching fractions of each component, as well aschanges in log likelihood when each componendropped from the fit and remaining componentsre-optimized.

We begin the discussion withφK+K− data. Thereis a conspicuous peak due tof ′

2(1525). The shoulderon its upper side is fitted mostly byf0(1710) inter-fering withf0(1500), but there is also a possible smcontribution fromf0(1790) interfering withf0(1500).The overall contributions toφK+K− are shown by theupper histograms inFig. 5(c) and (d).

The f2(1270) signal reported below inφππ dataallows a calculation of thef2(1270) → K+K− signalexpected inφK+K−, using the branching fraction ratio betweenKK̄ andππ of the PDG. Its contributionis negligibly small.

We discuss next the fit tof0(980). In φπ+π− data,it interferes with a broad component well fitted by tσ pole[12]. This component interferes constructive


s;
Fig. 4. (a) and (b) show measured and fitted Dalitz plots forJ/ψ → φπ+π− after cuttingK∗(890) events, (c) and (d) show mass projectionthe upper histogram shows the maximum likelihoodfit and the lower one shows background; (e) shows thef0 contribution from the fit (fullhistogram) and the lower curve theσ contribution, (f) thef2(1270) contribution.
tté

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om

with the lower side of thef0(980) in Fig. 4(c). Its mag-nitude is shown by the lower curve inFig. 4(e).

Thef0(980) amplitude has been fitted to the Flaform [13]

(1)f = 1

M2 − s − i(g1ρππ + g2ρKK̄).

Hereρ is Lorentz invariant phase space, 2k/√

s, wherek refers to theπ or K momentum in the rest framof the resonance. The present data offer the optunity to determine the ratiog2/g1 accurately. Thisis done by determining the number of events duef0(980) → ππ and → K+K− and comparing with

the prediction from the Flatté formula, as follows. Ater making the best fit to the data, the fittedf0(980) →π+π− signal is integrated over the mass range fr0.9 to 1.0 GeV/c2. The fittedf0(980) → K+K− sig-nal is integrated over the mass range 1.0–1.2 GeV/c2,so as to avoid sensitivity to the tail of thef0(980) athigh mass. The latter integral is given by

(2)0.5∫

ds∣∣f (980)

∣∣2ρ(K+K−)

ε(K+K−)

and the former by

(3)2

∫ds

∣∣f (980)∣∣2ρ(ππ)ε

(π+π−)

.
3


Fig. 5. (a) and (b) show measured and fitted Dalitz plots forJ/ψ → φK+K−, (c) and (d) mass projections forJ/ψ → φK+K− data,compared with histograms from the fit; (e) shows thef0 contribution from the fit (full histogram) and the lower curve thef0(980) contribution,(f) the f ′

2(1525) contribution from the fit (full histogram).

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ly,ofor

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d

-

Hereε(K+K−) andε(π+π−) are detection efficiencies. The numerical factors at the beginning of eacexpression take into account (a) there are equal nbers of decays toK+K− and K0K̄0 and (b) two-thirds of ππ decays are toπ+π− and one third toπ0π0.

By an iterative process which converges rapidthe ratiog2/g1 is adjusted until the ratio of these twintegrals reproduces the fitted numbers of eventsφK+K− andφπ+π−. The result isg2/g1 = 4.21±0.25(stat) ± 0.21(syst). The systematic error arisefrom (i) varying the choice of side bins and the magtude of the background under theφ peak, (ii) changes

in the fit when small amplitudes such asf0(1500)andf2(1270) → K+K− andσ → K+K− are omit-ted from the fit, (iii) changing the mass and widthother components within errors and different choiof σ parameterization from Ref.[12]. The result is aconsiderable improvement on earlier determinatioThe mass andg1 are adjusted to achieve the best ovall fit to the peak inφπ+π− data. Values areM =965± 8± 6 MeV/c2, g1 = 165± 10± 15 MeV/c2.

The ratio g2/g1 is only weakly correlated withM andg1. However,g2 is rather strongly correlatewith M. This arises because the termig2ρKK(s) in theBreit–Wigner denominator, Eq.(1), continues analyti


er

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the

-

f

e

isev-eson.ichng

y

m-

cally below theKK threshold to−g2

√(4M2

K/s) − 1.It then contributes to the real part of the Breit–Wignamplitude and interacts with the term (M2 − s). Wefind that the correlation is given bydg2/dM = −5.9;the mass goes down asg2 goes up. Other correlationare weak:dg1/dM = −0.75 anddr/dg1 = −0.068,wherer = g2/g1.

We consider next the peak inφππ centred at amass of 1335 MeV/c2. An initial fit was made tof2(1270) and onef0. Thef0 optimizes atM = 1410±50 MeV/c2, Γ = 270± 45 MeV/c2, where errorscover systematic variations when small ingrediein the fit are changed. However, bothf0(1500) andf0(1370) can contribute. Addingf0(1500), log like-lihood improves by 51: an 8.5 standard deviation iprovement for four degrees of freedom. Also the fittheππ mass distribution improves visibly. Therefothree components are required in the 1335 MeV/c2

peak:f2(1270), f0(1370) and f0(1500). Removingf0(1370) makes log likelihood worse by 83, a 10standard deviation effect.

Angular correlations between decays ofφ andf2

are very sensitive to the presence off2(1270), whichis accurately determined. It optimizes atM = 1275±15 MeV/c2, Γ = 190±20 MeV/c2, values consistenwith f2(1270). The fact that its mass and width agrwell with PDG values rules out the possibility that tremainder of the signal in this mass range is duespin 2; otherwise the fit tof2(1270) would be severelyaffected. Angular distributions for the remaining coponents are indeed consistent with isotropic decaygular distributions from spin 0.

The f0(1370) interferes with f0(1500) andf2(1270). This helps to makef0(1370) more con-spicuous than in other data. However, because ofinterferences, its mass and width are not accuratelytermined. The mass off0(1370) is 1350± 5 MeV/c,where the error is the quadratic sum of the systemand statistical errors.

The width of f0(1370) is somewhat more stable. It is determined essentially by the full widof the peak inφπ+π− of 270 MeV/c2; interfer-ences withf2(1270) and f0(1500) affect this num-ber only by small amounts and the fitted width265± 40 MeV/c2. If both f0(1370) and f0(1500)are removed, log likelihood is worse by 595. Remoing f0(1500) from the fit perturbs the mass fitted

f0(1370) upwards to 1410± 50 MeV/c2; this is obvi-ously due to the fact thatf0(1370) is trying to simulatethe missingf0(1500) component.

The presence of a peak due tof0(1370) is stronglysuggestive of a resonance. In order to check for renant phase variation, we have tried replacing theplitude by its modulus, without any phase variatioIn this case, log likelihood is worse by 39, nearly astandard deviation effect for a change of one degof freedom. The conclusion is that thef0(1370) peakis resonant. It is not possible to display the phaserectly, since it is determined by interferences betwtwo f0(1370) and fourf2(1270) amplitudes.

The magnitude of the signal due tof0(1370) →K+K− in the fit gives a branching fraction ratio

(4)B[f0(1370) → KK̄]B[f0(1370) → ππ] = 0.08± 0.08.

This value is somewhat lower than reported by the Pticle Data Group[6]. The reason is the conspicuosignal inππ but absence of any corresponding pein K+K−.

Next we consider the peak inπ+π− at1775 MeV/c2 in Fig. 4(c). It fits well with JP = 0+with M = 1790+40

−30 MeV/c2, Γ = 270+60−30 MeV/c2.

The fitted mass is in reasonable accord withf0(1770) reported in Crystal Barrel data on̄pp →(ηη)π0 [14]: M = 1770± 12 MeV/c2, Γ = 220±40 MeV/c2. Allowing for the number of fitted parameters,f0(1790) is more than a 15σ signal. Itcannot arise fromf0(1710), since the magnitude of0(1710) → K+K− is small (seeTable 1), and it isknown that the branching fraction ratio off0(1710)betweenππ andKK̄ is < 0.11 at the 95% confidenclevel [15]; accordingly, thef0(1710) → ππ signal inpresent data should be negligibly small.

We now consider possible fits with anf2 instead.The decay angular distribution in this mass rangeconsistent with isotropy. So there is no positiveidence for spin 2. However, four spin 2 amplitudare capable of simulating a flat angular distributiIn consequence, spin 2 gives a log likelihood whis worse than spin 0 by only 4.5 after reoptimiziits mass and width. Iff0(1710) is then added withPDG mass and width, it improves log likelihood ba further 2.0; this confirms the result fromωK+K−data thatf0(1710) has a negligible decay toππ . Ourexperience elsewhere is that using four helicity a


Gstical

Table 1Parameters of fitted resonances and branching fractions for each channel; improvements inS = log likelihood when the channel is added. PDmeans that the mass and width are fixed to the PDG value. For thef0(980), see the parameterization in the text. The errors are the statiand systematic errors added in quadrature

Channel Mass (MeV/c2) Width (MeV/c2) B(J/ψ → φX,X → ππ) (×10−4) B(J/ψ → φX,X → KK̄) (×10−4) S

f0(980) 965± 10 see text 5.4± 0.9 4.5± 0.8 1181f0(1370) 1350± 50 265± 40 4.3± 1.1 0.3± 0.3 83f0(1500) PDG PDG 1.7± 0.8 0.8± 0.5 51f0(1790) 1790+40

−30 270+60−30 6.2± 1.4 1.6± 0.8 488

f2(1270) 1275± 15 190± 20 2.3± 0.5 0.1± 0.1 241σ 1.6± 0.6 0.2± 0.1 120f ′

2(1525) 1521± 5 77± 15 – 7.3± 1.1 440f0(1710) PDG PDG – 2.0± 0.7 64

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plitudes instead of 2 adds considerable flexibilitythe fit. The spin 2 amplitude with� = 0 has a distinc-tive term 3 cos2 απ − 1, whereαπ is the decay angleof the π+ in the resonance rest frame, with respto the direction of the recoilφ. Simulation of spin 0requires largeJ = 2, � = 2 and 4 amplitudes to produce compensating terms in sin2 απ and hence a flaangular distribution. Large contributions from� = 2are unlikely in view of the low momentum availabto the resonance and the consequent� = 2 centrifu-gal barrier. If theJ = 2 hypothesis is fitted only with� = 0, log likelihood is worse by 95 than for spinWe conclude that the state is most likely spin zero.

It is not possible to fit the shoulder inφK+K−at 1650 MeV/c2 accurately by interference betwef0(1500) and f0(1790), using thef0(1790) massand width found inφππ data. Even if one accepthe poor fit this gives, the branching fraction raKK̄/ππ assuming only onef0 resonance here i0.55 ± 0.10. This is a factor 14 lower than that rported in Ref.[15] for f0(1710). For a resonancebranching fractions must be independent of prodtion mechanism. The large discrepancy in branchfractions implies the existence of two distinct staat 1710 and 1790 MeV/c2, the former decaying dominantly to KK̄ and the latter dominantly toππ . Thef0(1790) is a natural candidate for the radial excitatiof f0(1370). There is earlier evidence for it decayinto 4π in J/ψ → γ (4π) data[16,17], with mass andwidth close to those observed here. There, spin 0preferred strongly over spin 2.

The shoulder inφK+K− at 1650 MeV/c2 is fit-ted with interference betweenf0(1500) andf0(1710),which is known to decay strongly toKK̄ . If both

Fig. 6. Angular distributions inφπ+π− data (crosses) forαπ , theangle of theπ+ from fJ decay with respect to the direction offJ

in its rest frame. The upper histograms shows the ft, and the loone the background. The dashed histogram shows the accepta

f0(1710) andf0(1790) are included in the fit, theris only a small improvement fromf0(1790).

Masses, widths and branching fractions are giin Table 1. The errors arise mainly from (i) varyinthe choice of side bins and the magnitude of the baground under theφ peak, (ii) adding or removing smacomponents such asf0(1500), f2(1270) → K+K−,andσ → K+K− and (iii) varying the mass and widtof every component within errors and using differeσ parameterizations reported in Ref.[12]. It also in-cludes the uncertainty in the number ofJ/ψ eventsand the difference between two alternative choiceMDC wire resolution simulation.

Finally, angular distributions for both productioand decay have been examined for each resonpeak. There are no significant discrepancies betweedata and fit. A fit is shown for thef0(1790) peak inFig. 6 to the decay angleαπ of theππ pair, with re-


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spect to the recoilφ; the deep dip at cosαπ = ±0.75is due to theK∗(890) cut. The remaining angular distribution fits well to spin 0.

It is remarkable thatφππ data contain large signadue to several states which are predominantly nstrange:f2(1270), f0(1370), f0(1500) andf0(1790);direct production with theφ should favourss̄ states.There is no agreed explanation.

In summary, the data reported here have threeportant features. Firstly, the parameters off0(980) areall well determined. Secondly, there is the clearestnal to date off0(1370) → π+π−; a resonant phasvariation is required, from interference withf2(1270).Thirdly, there is a clear peak inππ at 1775 MeV/c2,consistent withf0(1790); spin 2 is less likely thanspin 0. If thef0(1790) resonance is used to fit thshoulder at 1650 MeV/c2 in φK+K−, the branchingfraction to pions divided by that to kaons is incosistent with the upper limit for the ratio observedRef. [15] for f0(1710), this requires two distinct resonancesf0(1790) andf0(1710).

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. 19991480, 10225524, 10225the Chinese Academy of Sciences under contractKJ 95T-03, the 100 Talents Program of CAS undContract Nos. U-11, U-24, U-25, and the KnowledInnovation Project of CAS under Contract Nos.602, U-34 (IHEP); by the National Natural ScienFoundation of China under Contract No. 101750

(USTC), No. 10225522 (Tsinghua University); and tDepartment of Energy under Contract No. DE-FG94ER40833 (U Hawaii). We wish to acknowledgenancial support from the Royal Society for collabotion between the BES group and Queen Mary, Lonunder contract Q771.

References

[1] L. Kopke, Recent Mark III results on radiative and hadronJ/ψ decays, in: Proc. XXIII Int. Conf. on High EnergPhysics, Berkeley 1986, World Scientific, Singapore, 19p. 692.

[2] DM2 Collaboration, A. Falvard, et al., Phys. Rev. D 38 (1982706.

[3] L. Kopke, N. Wermes, Phys. Rep. 174 (1989) 68, and reences therein.

[4] L. Roca, J.E. Palomar, E. Oset, H.C. Chiang, Nucl. Phys. A(2004) 127, and references therein.

[5] BES Collaboration, J.Z. Bai, et al., Nucl. Instrum. MethoA 458 (2001) 627.

[6] Particle Data Group, S. Eidelman, et al., Phys. Lett. B 5(2004) 1.

[7] S. Bitjokov, et al., Sov. J. Nucl. Phys. 38 (1983) 727, YaFiz. 38 (1983) 1205.

[8] V.A. Polychronakos, et al., Phys. Rev. D 19 (1979) 1317;A.D. Martin, E.N. Ozmutlu, Nucl. Phys. B 158 (1979) 520.

[9] D. Cohen, et al., Phys. Rev. D 22 (1980) 2595.[10] A. Etkin, et al., Phys. Rev. D 25 (1982) 1786.[11] B.S. Zou, D.V. Bugg, Eur. Phys. J. A 16 (2003) 537.[12] BES Collaboration, M. Ablikim, et al., Phys. Lett. B 59

(2004) 149.[13] S.M. Flatté, Phys. Lett. B 63 (1976) 224.[14] A. Anisovich, et al., Phys. Lett. B 449 (1999) 154.[15] BES Collaboration, M. Ablikim, et al., Phys. Lett. B 60

(2004) 138.[16] D.V. Bugg, et al., Phys. Lett. B 353 (1995) 378.[17] BES Collaboration, J.Z. Bai, et al., Phys. Lett. 472 (2000) 2

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