DSpace at VNU: First observations ofψ(2S)andχcJ(1P)decays to four-body final statesh + h −K0 SK0 S

Physics Letters B 630 (2005) 21–30
www.elsevier.com/locate/physletb

First observations of ψ(2S) and χcJ (1P) decays
to four-body final states h+ h−KS0KS0 ✩
BES Collaboration
M. Ablikim a , J.Z. Bai a , Y. Ban j , J.G. Bian a , X. Cai a , J.F. Chang a , H.F. Chen p ,
H.S. Chen a , H.X. Chen a , J.C. Chen a , Jin Chen a , Jun Chen f , M.L. Chen a , Y.B. Chen a ,
S.P. Chi b , Y.P. Chu a , X.Z. Cui a , H.L. Dai a , Y.S. Dai r , Z.Y. Deng a , L.Y. Dong a ,
S.X. Du a , Z.Z. Du a , J. Fang a , S.S. Fang b , C.D. Fu a , H.Y. Fu a , C.S. Gao a , Y.N. Gao n ,
M.Y. Gong a , W.X. Gong a , S.D. Gu a , Y.N. Guo a , Y.Q. Guo a , Z.J. Guo o , F.A. Harris o ,
K.L. He a , M. He k , X. He a , Y.K. Heng a , H.M. Hu a , T. Hu a , G.S. Huang a,2 , L. Huang f ,
X.P. Huang a , X.B. Ji a , Q.Y. Jia j , C.H. Jiang a , X.S. Jiang a , D.P. Jin a , S. Jin a , Y. Jin a ,
Y.F. Lai a , F. Li a , G. Li a , H.H. Li a , J. Li a , J.C. Li a , Q.J. Li a , R.B. Li a , R.Y. Li a ,
S.M. Li a , W.G. Li a , X.L. Li g , X.Q. Li i , X.S. Li n , Y.F. Liang m , H.B. Liao e , C.X. Liu a ,
F. Liu e , Fang Liu p , H.M. Liu a , J.B. Liu a , J.P. Liu q , R.G. Liu a , Z.A. Liu a , Z.X. Liu a ,
F. Lu a , G.R. Lu d , J.G. Lu a , C.L. Luo h , X.L. Luo a , F.C. Ma g , J.M. Ma a , L.L. Ma k ,
Q.M. Ma a , X.Y. Ma a , Z.P. Mao a , X.H. Mo a , J. Nie a , Z.D. Nie a , S.L. Olsen o ,
H.P. Peng p , N.D. Qi a , C.D. Qian l , H. Qin h , J.F. Qiu a , Z.Y. Ren a , G. Rong a ,
L.Y. Shan a , L. Shang a , D.L. Shen a , X.Y. Shen a , H.Y. Sheng a , F. Shi a , X. Shi j ,
H.S. Sun a , S.S. Sun p , Y.Z. Sun a , Z.J. Sun a , X. Tang a , N. Tao p , Y.R. Tian n ,
G.L. Tong a , G.S. Varner o , D.Y. Wang a , J.Z. Wang a , K. Wang p , L. Wang a , L.S. Wang a ,
M. Wang a , P. Wang a , P.L. Wang a , S.Z. Wang a , W.F. Wang a , Y.F. Wang a , Zhe Wang a ,
Z. Wang a , Zheng Wang a , Z.Y. Wang a , C.L. Wei a , D.H. Wei c , N. Wu a , Y.M. Wu a ,
X.M. Xia a , X.X. Xie a , B. Xin g , G.F. Xu a , H. Xu a , Y. Xu a , S.T. Xue a , M.L. Yan p ,
F. Yang i , H.X. Yang a , J. Yang p , S.D. Yang a , Y.X. Yang c , M. Ye a , M.H. Ye b , Y.X. Ye p ,
L.H. Yi f , Z.Y. Yi a , C.S. Yu a , G.W. Yu a , C.Z. Yuan a , J.M. Yuan a , Y. Yuan a , Q. Yue a ,
S.L. Zang a , Yu. Zeng a , Y. Zeng f , B.X. Zhang a , B.Y. Zhang a , C.C. Zhang a ,
D.H. Zhang a , H.Y. Zhang a , J. Zhang a , J.Y. Zhang a , J.W. Zhang a , L.S. Zhang a ,
Q.J. Zhang a , S.Q. Zhang a , X.M. Zhang a , X.Y. Zhang k , Y.J. Zhang j , Y.Y. Zhang a ,
Yiyun Zhang m , Z.P. Zhang p , Z.Q. Zhang d , D.X. Zhao a , J.B. Zhao a , J.W. Zhao a ,

M.G. Zhao i , P.P. Zhao a , W.R. Zhao a , X.J. Zhao a , Y.B. Zhao a , Z.G. Zhao a,1
0370-2693/$ – see front matter  2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.physletb.2005.09.050


22

BES Collaboration / Physics Letters B 630 (2005) 21–30

H.Q. Zheng j , J.P. Zheng a , L.S. Zheng a , Z.P. Zheng a , X.C. Zhong a , B.Q. Zhou a ,
G.M. Zhou a , L. Zhou a , N.F. Zhou a , K.J. Zhu a , Q.M. Zhu a , Y.C. Zhu a , Y.S. Zhu a ,
Yingchun Zhu a , Z.A. Zhu a , B.A. Zhuang a , B.S. Zou a
a Institute of High Energy Physics, Beijing 100039, People’s Republic of China
b 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 China
d Henan Normal University, Xinxiang 453002, People’s Republic of China
e Huazhong Normal University, Wuhan 430079, People’s Republic of China
f Hunan University, Changsha 410082, People’s Republic of China
g Liaoning University, Shenyang 110036, People’s Republic of China
h Nanjing Normal University, Nanjing 210097, People’s Republic of China
i Nankai University, Tianjin 300071, People’s Republic of China
j Peking University, Beijing 100871, People’s Republic of China
k Shandong University, Jinan 250100, People’s Republic of China
l Shanghai Jiaotong University, Shanghai 200030, People’s Republic of China
m Sichuan University, Chengdu 610064, People’s Republic of China
n Tsinghua University, Beijing 100084, People’s Republic of China
o University of Hawaii, Honolulu, HI 96822, USA
p University of Science and Technology of China, Hefei 230026, People’s Republic of China
q Wuhan University, Wuhan 430072, People’s Republic of China
r Zhejiang University, Hangzhou 310028, People’s Republic of China

Received 11 May 2005; accepted 7 September 2005
Available online 30 September 2005
Editor: M. Doser

Abstract
First observations of χc0 , χc1 , and χc2 decays to π + π − KS0 KS0 and K + K − KS0 KS0 , as well as ψ(2S) decay to π + π − KS0 KS0 ,
are presented. The branching fractions of these decay channels are determined using 14 × 106 ψ(2S) events collected at BESII/BEPC. The branching fractions of χc0 , χc2 → KS0 KS0 are measured with improved statistical precision.
 2005 Elsevier B.V. All rights reserved.
PACS: 13.25.Gv; 12.38.Qk; 14.40.Gx

1. Introduction
Experimental data on charmonia and their decay
properties are essential input to test QCD models and
QCD based calculations. The importance of the Color
Octet Mechanism (COM) [1] in radiative decays of
The h± denote charged pions or kaons.
E-mail address: (Zhe Wang).
1 Visiting professor to University of Michigan, Ann Arbor, MI
48109, USA.
2 Current address: Purdue University, West Lafayette, IN 47907,
USA.
✩

the Υ [2], J /ψ production in inclusive B decays [3],
as well as inclusive decays of P-wave charmonia [4]
has been emphasized for many years. Recently, QCD
predictions of two-body exclusive decays of P-wave
charmonium with the inclusion of the COM have been
made [5,6] and compared to previous measurements

[7,8]. More experimental data of two- and four-body
exclusive decays of P-wave charmonia with improved
precision are important for further testing this new
QCD approach including the effect of the COM.
In this Letter, results on ψ(2S) and χcJ (J = 0, 1,
2) two- and four-body hadronic decays with inclusion
of a pair of KS0 mesons are presented. This analysis is


BES Collaboration / Physics Letters B 630 (2005) 21–30

based on 14 × 106 ψ(2S) decays collected with BESII at the BEPC e+ e− collider. A sample of 6.42 pb−1
data taken at 3.65 GeV is used for continuum background studies.

2. BES detector
The BESII detector is described elsewhere [9].
Charged particle momenta are determined with a resolution of σp /p = 1.78% 1 + p 2 (p in GeV/c) in
a 40-layer main drift chamber (MDC). Particle identification is accomplished using specific ionization
(dE/dx) information in the drift chamber and timeof-flight (TOF) information in a barrel-like array of
48 scintillation counters. The dE/dx resolution is
σdE/dx = 8%; the TOF resolution is σTOF = 200 ps for
hadrons. A 12-radiation-length barrel shower counter
(BSC) measures energies
of photons with a resolution
√
of σE /E = 21%/ E (E in GeV).

3. Monte Carlo simulation
A Geant3 based Monte Carlo, SIMBES [10], which
simulates the detector response, including interactions

of secondary particles in the detector material, is used
to determine detection efficiencies and mass resolutions, as well as to optimize selection criteria and estimate backgrounds. Under the assumption of a pure E1
transition, the distribution of polar angle θ of the photon in ψ(2S) → γ χcJ decays is given by 1 + k cos2 θ
1
for J = 0, 1, and 2, re[11] with k = 1, − 13 , and 13
spectively. The angular distributions for KS0 mesons
from χc0,2 → KS0 KS0 decays are produced according
to the model of χcJ → M M¯ [12], where M stands for
a 0− meson. Angular distributions for daughters from
other decays are generated isotropically in the centerof-mass system of the ψ(2S) or χcJ .

4. Data analysis
To be regarded as a good photon, a shower cluster
in the BSC must have an energy deposit of more than
50 MeV and at least one hit in the first six layers of
the BSC. To remove soft photons emitted by charged
particles, the differences of azimuthal angles, dφ, and

23

z coordinates at the first layer of the BSC, dz, between good photons and each charged track must satisfy either a loose requirement (selection-A: dφ > 10◦
or dz > 0.3 m) or a tight requirement (selection-B:
dφ > 20◦ or dz > 1.0 m). Here the z coordinate is
defined to point in the positron direction.
Each charged track is required to have a good helix
fit. For final states containing charged kaons, particle
identification is required; usable particle identification
information in one or both of the MDC (dE/dx) and
TOF subsystems is necessary. A particle identification χ 2 is calculated for each track for the pion, kaon
or proton hypotheses using this information, and the

associated probability prob is determined. A track is
identified as a kaon, if the probability of the track being a kaon prob(K) > 0.01; otherwise it is regarded as
a pion. For final states containing only pions, no particle identification is done and all tracks are assumed to
be pions.
Each event is required to contain two KS0 mesons.
The reconstruction of the decay KS0 → π + π − and related checks are described in detail elsewhere [13].
A KS0 candidate must satisfy |Mπ + π − − MK 0 | <
S
20 MeV and have a decay length transverse to the
beam axis Rxy > 0.3 cm. The KS0 sideband sample, used for background estimation, is selected with
one π + π − pair within the KS0 mass window and the
other pair in the KS0 mass sideband region defined
by 40 MeV < |Mπ + π − − MK 0 | < 60 MeV.
S
Four constraint (4C) kinematic fits are performed
on the selected events for the following decay modes:
(1) ψ(2S) → γ KS0 KS0 , (2) ψ(2S) → γ π + π − KS0 KS0 ,
and (3) ψ(2S) → γ K + K − KS0 KS0 . The fits are made
to each combination of a good photon and two KS0
candidates in an event, the combination with the min2 is selected, and the χ 2 is required to be
imum χ4C
4C
less than 35. The associated probability prob4C is calculated.
Background from ψ(2S) → π + π − J /ψ decay is
removed by calculating the mass recoiling, Mrecoil ,
against all pairs of oppositely charged tracks, assuming them to be pions, and requiring |Mrecoil − MJ /ψ | >
25 MeV. Background contamination from continuum
production is found to be negligible for all decay channels.
An unbinned maximum likelihood method is used
in fitting the signal for all decay channels except

ψ(2S) → h+ h− KS0 KS0 . The branching fractions of


24

BES Collaboration / Physics Letters B 630 (2005) 21–30

Fig. 1. Distribution of KS0 KS0 invariant mass of ψ(2S) → γ KS0 KS0 candidates. (a) Points with error bars are data, and the histogram is sideband
background. (b) Points with error bars are data, and the solid line is the fit described in the text.

ψ(2S) → γ χcJ (J = 0, 1, 2) needed in the measurement are taken from Particle Data Group (PDG) tables [8].
4.1. ψ(2S) → γ KS0 KS0
The decay ψ(2S) → γ KS0 KS0 has one photon plus
a pair of KS0 candidates. The event should have four
charged tracks with total charge zero. The loose photon selection, selection-A, is applied because of the
low background in the channel. The KS0 KS0 invariant
mass distribution of the selected events is shown in
Fig. 1. A few KS0 sideband events survive the selection, which is consistent with the low background observed in Fig. 1(a). No background is expected from
ψ(2S) → γ χcJ with χcJ → 2(π + π − ) for J = 0, 1, 2
and ψ(2S) → γ χc1 with χc1 → KS0 K ± π ∓ according
to the analysis of simulated MC events.

The KS0 KS0 invariant mass distribution is fitted with
two Breit–Wigner resonances for χc0 and χc2 , each
convoluted with Gaussian resolution functions, plus
a second-order polynomial background. The χc0,2
widths in the fitting are fixed to their PDG values [8].
The resulting fit is shown in Fig. 1(b). Including the
χc1 resonance in the fit yields zero events for the CP
violating decay χc1 → KS0 KS0 .

4.2. ψ(2S) → γ π + π − KS0 KS0
The ψ(2S) → γ π + π − KS0 KS0 decay channel contains one photon and six charged tracks with total
charge zero. The requirements here are similar to
the previous case, but there are two additional pions. Background from π/K misidentification is suppressed by the requirement prob4C (γ π + π − KS0 KS0 ) >
prob4C (γ K + K − KS0 KS0 ). The π + π − KS0 KS0 invariant


BES Collaboration / Physics Letters B 630 (2005) 21–30

25

Fig. 2. Distribution of π + π − KS0 KS0 invariant mass for ψ(2S) → γ π + π − KS0 KS0 candidates. Points with error bars are data. The light shaded
area in (a) is background simulation, where some unknown branching ratios are normalized to agree with the overall χcJ background level, and
the dark shaded area is KS0 sideband. The solid line in (b) is the fit.

mass distribution for selected events is shown in
Fig. 2.
In Fig. 2 there are two kinds of background in the
mass region between 3.0 and 3.64 GeV/c2 : (1) background corresponding to KS0 sidebands, and (2) ψ(2S)
decays and χcJ decays different from the signal channel, where the decays also include a pair of KS0
mesons. Studies with KS0 sideband events for both
data and MC show that KS0 sideband background
from wrong combinations of π + π − is slightly enhanced in the χcJ signal region. MC studies show
that the smooth background spread over the whole
mass region from (2) results mainly from the following decay channels: (a) ψ(2S) → γ χcJ with χcJ →
3(π + π − ) and χcJ → K + K − KS0 KS0 , (b) ψ(2S) →
π 0 π + π − KS0 KS0 , and (c) ψ(2S) → ωKS0 KS0 with ω →
π + π − π 0 . Background events in the high mass region above 3.64 GeV/c2 in Fig. 2 are from ψ(2S) →

π + π − KS0 KS0 decays combined with an unassociated

low energy photon.
The π + π − KS0 KS0 invariant mass distribution between 3.0 to 3.64 GeV/c2 is fitted with three Breit–
Wigner resonances χcJ (J = 0, 1, 2), convoluted with
Gaussian resolution functions, plus a second-order
polynomial background. The widths of the χc0,1,2 resonances in the fit are fixed to their PDG values. The fit
is shown in Fig. 2. The numbers of events in the three
peaks determined from the fit include signal and KS0
sideband background, which is somewhat enhanced
in the regions of the peaks. The KS0 sideband sample for data is fitted with a fake signal shape, found
by fitting the MC KS0 sideband sample, plus a second
order polynomial background. The numbers of sideband background events, 5.3, 0.6 and 5.5 for χc0 , χc1
and χc2 , respectively, are then subtracted from the total numbers of events in three peaks.


26

BES Collaboration / Physics Letters B 630 (2005) 21–30

Fig. 3. Distribution of K + K − KS0 KS0 invariant mass of ψ(2S) → γ K + K − KS0 KS0 candidates. Points with error bars are data, and the histogram
is sideband background. The solid line is the fit.

4.3. ψ(2S) → γ K + K − KS0 KS0
The ψ(2S) → γ K + K − KS0 KS0 decay has the same
topology as ψ(2S) → γ π + π − KS0 KS0 , and thus it is
subject to similar event selection criteria except for
the kaon identification requirement for two of the
charged tracks. First, the KS0 KS0 pair is searched for
under the assumption that all charged tracks are pions. Kaon identification is only done for the two
charged tracks remaining after reconstruction of the
KS0 KS0 pair. We also require prob4C (γ K + K − KS0 KS0 )

> prob4C (γ π + π − KS0 KS0 ) for the 4C kinematic fit
probabilities to suppress contamination from ψ(2S) →
γ π + π − KS0 KS0 decays. The K + K − KS0 KS0 invariant
mass distribution for selected events is shown in
Fig. 3.
As seen from Fig. 3, only one event survives from
the KS0 sideband sample for data. MC events for
the following possible background channels are generated: (1) ψ(2S) → γ χcJ with χcJ → 3(π + π − )
and π + π − KS0 KS0 , (2) ψ(2S) → π + π − KS0 KS0 , and
(3) ψ(2S) → ωKS0 KS0 with ω → π + π − π 0 . However,
no event from these background channels survives the
selection criteria. Another study with a large sample
of simulated ψ(2S) → anything [14] shows that negligible background comes from decays of ψ(2S) →
φK ∗ 0 K 0 → π 0 K + K − KS0 KS0 .

The K + K − KS0 KS0 invariant mass distribution is fitted with three Breit–Wigner resonances, χcJ (J = 0,
1, 2), convoluted with Gaussian resolution functions,
plus a flat background. Because of low statistics in the
signal region, not only the widths and mass resolutions
for the χcJ (J = 0, 1, 2), but also the masses of the χc1
and χc2 in the fitting are fixed to their PDG values. The
fitting results are shown in the Fig. 3.
4.4. ψ(2S) → h+ h− KS0 KS0
The selection of ψ(2S) → h+ h− KS0 KS0 decays requires six charged tracks with total charge zero and no
good photon in the event, as defined above. Good photons are rejected with the tight selection, selection-B,
in order to gain higher detection efficiency for signal events. The KS0 reconstruction uses all combinations of oppositely charged tracks assuming all tracks
are pions. To further suppress background of ψ(2S)
radiative decays, a requirement on the missing momentum of six charged tracks is employed: Pmiss <
80 MeV. The two charged tracks h+ and h− recoiling against the KS0 pair are assumed to have the same
mass m. Using energy–momentum conservation, the

mass squared m2 is calculated from
m2 =

E 4 + (Ph2+ − Ph2− )2 − 2E 2 (Ph2+ + Ph2− )
4E 2

,

(1)


BES Collaboration / Physics Letters B 630 (2005) 21–30

27

Fig. 4. Distribution of invariant mass squared of the two remaining charged particles after KS0 KS0 selection for ψ(2S) → h+ h− KS0 KS0 . (a) Points
with error bars are data. The histogram is the KS0 sideband background. (b) Points with error bars are the data with the KS0 sideband background
subtracted. The solid line is the fit.

where E = Mψ(2S) − EKS0 KS0 , and Ph± is the momentum of h+ or h− . The distribution of m2 for selected
events is shown in Fig. 4. The peak at low mass is consistent with π + π − ; there is no evidence for K + K − .
Two events from the continuum data sample survive the above selection and their effect will be included in the systematic error. No background is
found in MC studies of the following decay channels: (1) ψ(2S) → γ χcJ with χcJ → 3(π + π − ),
π + π − KS0 KS0 , and K + K − KS0 KS0 and (2) ψ(2S) →
ωKS0 KS0 with ω → π + π − π 0 . Background estimated
using the KS0 sideband data is subtracted from the observed number of signal events. A MC study shows
that the shape of the charged pion signal in the m2
spectrum is well described by a Gaussian function, and
its mean and resolution are consistent with data. The
spectrum is fitted with a Gaussian signal function and

a flat background using a binned maximum likelihood

fit where the resolution is fixed to the MC determined
value. The fitting result is shown in the Fig. 4.
4.5. Systematic errors
Systematic errors for the efficiency are caused by
differences between data and MC simulation. Our
studies have determined these errors to be 2% per
track for the tracking efficiency, 2% for photon identification, 5% for the 4C kinematic fit, and 2.1% for
the KS0 reconstruction efficiency. A correction factor due to the overestimate of the KS0 reconstruction
efficiency of the MC relative to data is determined
to be 95.8%. The change of fitting range and background shape function contributes a difference of final results less than 3%. Other systematic errors arise
from the uncertainties in the total number of ψ(2S)
events, (14.00 ± 0.56) × 106 [15], and in the branch-


28

BES Collaboration / Physics Letters B 630 (2005) 21–30

Table 1
Summary of the fitting results. Errors for the signal yield ns , background nb , mass M, and mass squared m2 are statistical. The detection
efficiency and resolution σ for each decay channel from MC are shown
ns

Channel
χc0 → KS0 KS0

nb

322 ± 20

χc1 → KS0 KS0

0

χc2 → KS0 KS0

6.4 ± 2.6

65.1 ± 8.7

χc0 → π + π − KS0 KS0

152 ± 14

χc1 → π + π − KS0 KS0
χc2 → π + π − KS0 KS0

χc0 → K + K − KS0 KS0

13.3
12.8

3555.7 ± 1.8

8.48

11.8

3412.9 ± 2.0

2.03

16.8

2.20

16.4

2.04

17.2

16.8 ± 4.8

3415.4 ± 6.1

0.91

16.1

3.2 ± 2.4

1.8 ± 0.8

fixed

1.12

15.3

2.3 ± 2.2

1.8 ± 0.8

fixed

1.05

15.9

nb

m2 (10−3 )
(GeV2 /c4 )

(%)

σ (10−3 )
(GeV2 /c4 )

18.0 ± 3.1

2.82

26.5

83.2 ± 9.4

4.6. Result and discussion
Possible resonance structures have been searched
for the χc0 → π + π − KS0 KS0 final state which is the
channel with the highest number of observed events.
Some excess for inclusive decays of K ∗ (892)+ →
KS0 π + , f0 (1710) → KS0 KS0 , ρ(770) → π + π − and
f0 (980) → π + π − can be seen from the selected
events. Insufficient statistics and complicated structures in these decay modes make it difficult to identify
clear signals for two-body decays with intermediate
resonances. Efficiencies for final states with resonances, such as
K0∗ (1430)+ K0∗ (1430)− ,

K0∗ (1430)+ K2∗ (1430)− ,
f0 (980)f0 (980),

f0 (980)f0 (2200) and

7.96
8.50

3501.1 ± 6.2

ing fractions for KS0 → π + π − and ψ(2S) → γ χcJ
(J = 0, 1, 2). In ψ(2S) → π + π − KS0 KS0 decay, with
two events found in continuum data, an additional error of 7.7% is added.

f0 (1370)f0 (1710),

3413.1 ± 1.2
fixed

3548.2 ± 3.1

ns

K ∗ (892)+ K ∗ (892)− ,

σ
(MeV/c2 )

57 ± 11

χc2 → K + K − KS0 KS0

ψ(2S) → π + π − KS0 KS0

(%)

19.8 ± 7.7

χc1 → K + K − KS0 KS0

Channel

MχcJ
(MeV/c2 )

K1 (1270)0 K 0

[16] are studied using phase-space MC events. The

averaged difference in efficiency between final states
with and without intermediate resonance is estimated
to be 7.7%, which is regarded as systematic error in

the measurements of the branching fractions for the
four-body final states. The results of four-body final
states h+ h− KS0 KS0 in our measurements include those
of both non-resonance and intermediate resonance.
Final results of signal yield and branching fractions for the χcJ (1P) and ψ(2S) two- and fourbody hadronic decays involving KS0 pair production
are summarized in Table 1. The masses of the χcJ
(J = 0, 1, 2) extracted from the fits are also listed.
The 90% confidence level (CL) upper limits on the
branching fractions in the table are obtained using the
Feldman–Cousins method [17]. The branching fractions of χcJ (J = 0, 1, 2) decays to π + π − KS0 KS0 and
K + K − KS0 KS0 , as well ψ(2S) decay to π + π − KS0 KS0
are observed for the first time. The branching fractions
of χc0 and χc2 decays to KS0 KS0 are measured with
improved precision.
Decay rates, determined using updated χcJ total widths [8] and branching fractions for χcJ →
π 0 π 0 , π + π − (J = 0, 2) and χcJ → p p¯ (J = 1, 2)
decays [8], provide support for the COM (see Table 3). According to isospin symmetry, the χcJ →
K 0 K¯ 0 and K + K − decays should have the same partial width. Assuming equal decay widths for χcJ →
KS0 KS0 and KL0 KL0 , we find that the partial width of
the χc0 → K 0 K¯ 0 decay estimated using the result
obtained in this Letter is not consistent (2.7σ ) with
the COM prediction for χc0 → K + K − , while the


BES Collaboration / Physics Letters B 630 (2005) 21–30

29

Table 2
The branching fractions from this measurement, as well as previous results, are listed. The first and second errors for the branching fractions
BR are statistical and systematic, respectively
BR(ψ(2S) → γ χc )BR(χc → X)
(10−5 )

Channel

BR(χc → X)
(10−4 )

χc0 → KS0 KS0

30.2 ± 1.9 ± 3.3

35.1 ± 2.2 ± 4.7

χc1 → KS0 KS0

< 0.6 (CL = 90%)

< 0.8 (CL = 90%)

χc2
χc0

→ KS0 KS0
→ π + π − KS0 KS0

→ π + π − KS0 KS0
→ π + π − KS0 KS0
→ K + K − KS0 KS0
→ K + K − KS0 KS0

5.72±0.76±0.63
55.8 ± 5.1 ± 8.9

BRPDG (χc → X) [8]
(10−4 )
21 ± 6
–

8.9 ± 1.2 ± 1.3
65 ± 6 ± 12

7.2±2.7
–

6.7 ± 2.6 ± 1.1

8.0 ± 3.1 ± 1.5

–

20.7 ± 3.9 ± 3.3

32.4 ± 6.1 ± 6.2

–

13.8 ± 3.9 ± 2.5

16.0 ± 4.6 ± 3.2

–

2.1 ± 1.6 ± 0.4
< 4.2 (CL = 90%)
1.6 ± 1.6 ± 0.3
< 3.5 (CL = 90%)

2.5 ± 1.9 ± 0.5
< 5.1 (CL = 90%)
2.6 ± 2.4 ± 0.5
< 5.5 (CL = 90%)

–

Channel

–

BR(ψ(2S) → X)
(10−4 )

BRPDG (ψ(2S) → X) [8]
(10−4 )

ψ(2S) → π + π − KS0 KS0

–

χc1
χc2
χc0
χc1

χc2 → K + K − KS0 KS0

2.20 ± 0.25 ± 0.37

Table 3
Comparison of partial widths for χcJ → π π, K K¯ and pp¯ decays
between PDG [8] and the COM predictions. Also shown is the result
based on this analysis
Decay
χc0 → π + π −
χc2 → π + π −
χc0 → π 0 π 0
χc2 → π 0 π 0
χc1 → p p¯
χc2 → p p¯
χc0 → K + K −
χc2 → K + K −
χc0 → K 0 K¯ 0
χc2 → K 0 K¯ 0

Γi (PDG)
in KeV/c2

49.5 ± 6.7
3.73 ± 0.64
25.3 ± 3.3
2.3 ± 1.5
0.066 ± 0.015
0.143 ± 0.018
61 ± 10
1.98 ± 0.47
71 ± 12 (this Letter)
3.76±0.80 (this Letter)

Γi (COM)
in KeV/c2
45.4 [5]
3.64 [5]
23.5 [5]
1.93 [5]
0.05627 [6]
0.15419 [6]
38.6 [5]
2.89 [5]

agreement between them for the corresponding χc2
decay is within 1.1σ . A comparison for the χcJ →
K + K − (J = 0, 2) decays shows that the discrepancy between PDG values and the COM predictions
is 2.2σ and 1.9σ for χc0 and χc2 decays, respectively.
Furthermore, the sum of all known χc0 two-body
branching fractions is less than 2%. It therefore is
important to measure more χcJ decay modes, including two-body modes with intermediate resonance and
many-body modes, because of their large contribution

–

–

to the hadronic decay width. Theoretical predictions
with inclusion of the COM for χcJ decays to manybody final states are required for comparison with data.
Acknowledgements
The BES Collaboration thanks the staff of BEPC
for their hard efforts and the members of IHEP computing center for their helpful assistance, and also
K.T. Chao and J.X. Wang for helpful discussions on
the COM. This work is supported in part by the National Natural Science Foundation of China under contracts Nos. 19991480, 10225524, 10225525, the Chinese Academy of Sciences under contract No. KJ 95T03, the 100 Talents Program of CAS under Contract
Nos. U-11, U-24, U-25, and the Knowledge Innovation Project of CAS under Contract Nos. U-602, U-34
(IHEP); by the National Natural Science Foundation
of China under Contract No. 10175060 (USTC), and
No. 10225522 (Tsinghua University); and by the Department of Energy under Contract No. DE-FG0204ER41291 (University of Hawaii).
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