Zoua aInstitute of High Energy Physics, Beijing 100039, People’s Republic of China bChina Center for Advanced Science and Technology CCAST, Beijing 100080, People’s Republic of China cGu
Trang 1First observations of ψ(2S) and χ cJ (1P) decays
to four-body final states h + h − K 0
S K S 0✩
BES Collaboration
M Ablikima, J.Z Baia, Y Banj, J.G Biana, X Caia, J.F Changa, H.F Chenp, H.S Chena, H.X Chena, J.C Chena, Jin Chena, Jun Chenf, M.L Chena, Y.B Chena, S.P Chib, Y.P Chua, X.Z Cuia, H.L Daia, Y.S Dair, Z.Y Denga, L.Y Donga, S.X Dua, Z.Z Dua, J Fanga, S.S Fangb, C.D Fua, H.Y Fua, C.S Gaoa, Y.N Gaon, M.Y Gonga, W.X Gonga, S.D Gua, Y.N Guoa, Y.Q Guoa, Z.J Guoo, F.A Harriso, K.L Hea, M Hek, X Hea, Y.K Henga, H.M Hua, T Hua, G.S Huanga,2, L Huangf, X.P Huanga, X.B Jia, Q.Y Jiaj, C.H Jianga, X.S Jianga, D.P Jina, S Jina, Y Jina, Y.F Laia, F Lia, G Lia, H.H Lia, J Lia, J.C Lia, Q.J Lia, R.B Lia, R.Y Lia, S.M Lia, W.G Lia, X.L Lig, X.Q Lii, X.S Lin, Y.F Liangm, H.B Liaoe, C.X Liua,
F Liue, Fang Liup, H.M Liua, J.B Liua, J.P Liuq, R.G Liua, Z.A Liua, Z.X Liua,
F Lua, G.R Lud, J.G Lua, C.L Luoh, X.L Luoa, F.C Mag, J.M Maa, L.L Mak, Q.M Maa, X.Y Maa, Z.P Maoa, X.H Moa, J Niea, Z.D Niea, S.L Olseno, H.P Pengp, N.D Qia, C.D Qianl, H Qinh, 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 Shij, H.S Suna, S.S Sunp, Y.Z Suna, Z.J Suna, X Tanga, N Taop, Y.R Tiann, G.L Tonga, G.S Varnero, D.Y Wanga, J.Z Wanga, K Wangp, L Wanga, L.S Wanga,
M Wanga, P Wanga, P.L Wanga, S.Z Wanga, W.F Wanga, Y.F Wanga, Zhe Wanga,
Z Wanga, Zheng Wanga, Z.Y Wanga, C.L Weia, D.H Weic, N Wua, Y.M Wua, X.M Xiaa, X.X Xiea, B Xing, G.F Xua, H Xua, Y Xua, S.T Xuea, M.L Yanp,
F Yangi, H.X Yanga, J Yangp, S.D Yanga, Y.X Yangc, M Yea, M.H Yeb, Y.X Yep, L.H Yif, Z.Y Yia, C.S Yua, G.W Yua, C.Z Yuana, J.M Yuana, Y Yuana, Q Yuea, S.L Zanga, Yu Zenga, Y Zengf, B.X Zhanga, B.Y Zhanga, C.C Zhanga, D.H Zhanga, H.Y Zhanga, J Zhanga, J.Y Zhanga, J.W Zhanga, L.S Zhanga, Q.J Zhanga, S.Q Zhanga, X.M Zhanga, X.Y Zhangk, Y.J Zhangj, Y.Y Zhanga, Yiyun Zhangm, Z.P Zhangp, Z.Q Zhangd, D.X Zhaoa, J.B Zhaoa, J.W Zhaoa, M.G Zhaoi, P.P Zhaoa, W.R Zhaoa, X.J Zhaoa, Y.B Zhaoa, Z.G Zhaoa,1
0370-2693/$ – see front matter 2005 Elsevier B.V All rights reserved.
doi:10.1016/j.physletb.2005.09.050
Trang 2H.Q Zhengj, J.P Zhenga, L.S Zhenga, Z.P Zhenga, X.C Zhonga, 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, Z.A Zhua, B.A Zhuanga, B.S Zoua
aInstitute of High Energy Physics, Beijing 100039, People’s Republic of China
bChina Center for Advanced Science and Technology (CCAST), Beijing 100080, People’s Republic of China
cGuangxi Normal University, Guilin 541004, People’s Republic of China
dHenan Normal University, Xinxiang 453002, People’s Republic of China
eHuazhong Normal University, Wuhan 430079, People’s Republic of China
fHunan University, Changsha 410082, People’s Republic of China
gLiaoning University, Shenyang 110036, People’s Republic of China
hNanjing Normal University, Nanjing 210097, People’s Republic of China
iNankai University, Tianjin 300071, People’s Republic of China
jPeking University, Beijing 100871, People’s Republic of China
kShandong University, Jinan 250100, People’s Republic of China
lShanghai Jiaotong University, Shanghai 200030, People’s Republic of China
mSichuan University, Chengdu 610064, People’s Republic of China
nTsinghua University, Beijing 100084, People’s Republic of China
oUniversity of Hawaii, Honolulu, HI 96822, USA
pUniversity of Science and Technology of China, Hefei 230026, People’s Republic of China
qWuhan University, Wuhan 430072, People’s Republic of China
rZhejiang 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 χ c0 , χ c1 , and χ c2 decays to π+π−K0
SKS0and K+K−K0
SKS0, as well as ψ (2S) decay to π+π−K0
SKS0, are presented The branching fractions of these decay channels are determined using 14× 106ψ (2S) events collected at
BE-SII/BEPC The branching fractions of χ c0 , χ c2 → K0
SKS0are 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:wangzhe@ihep.ac.cn (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 χ cJ (J = 0, 1,
2) two- and four-body hadronic decays with inclusion
of a pair of K0mesons are presented This analysis is
Trang 3based on 14× 106 ψ (2S) decays collected with
BE-SII at the BEPC e+e−collider A sample of 6.42 pb−1
data taken at 3.65 GeV is used for continuum
back-ground studies
2 BES detector
The BESII detector is described elsewhere [9]
Charged particle momenta are determined with a
res-olution of σ p /p = 1.78%1+ p2 (p in GeV/c) in
a 40-layer main drift chamber (MDC) Particle
iden-tification is accomplished using specific ionization
(dE/dx) information in the drift chamber and
time-of-flight (TOF) information in a barrel-like array of
48 scintillation counters The dE/dx resolution is
σ dE/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 σ E /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
resolu-tions, as well as to optimize selection criteria and
esti-mate backgrounds Under the assumption of a pure E1
transition, the distribution of polar angle θ of the
pho-ton in ψ (2S) → γ χ cJ decays is given by 1+ k cos2θ
[11]with k = 1, −1
3, and 131 for J = 0, 1, and 2,
re-spectively The angular distributions for KS0 mesons
from χ c0,2 → K0
SKS0 decays are produced according
to the model of χ cJ → M ¯ M[12], where M stands for
a 0−meson Angular distributions for daughters from
other decays are generated isotropically in the
center-of-mass system of the ψ (2S) or χ cJ
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
z coordinates at the first layer of the BSC, dz,
be-tween good photons and each charged track must
sat-isfy 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
identifica-tion χ2is 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
be-ing a kaon prob(K) > 0.01; otherwise it is regarded as
a pion For final states containing only pions, no parti-cle 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
re-lated checks are described in detail elsewhere [13]
A KS0 candidate must satisfy |M π+π− − M K0
S| <
20 MeV and have a decay length transverse to the
beam axis R xy > 0.3 cm The KS0 sideband sam-ple, used for background estimation, is selected with
one π+π−pair within the K0
S mass window and the
other pair in the KS0 mass sideband region defined
by 40 MeV < |M π+π−− M K0
S| < 60 MeV.
Four constraint (4C) kinematic fits are performed
on the selected events for the following decay modes:
(1) ψ (2S) → γ K0
SKS0, (2) ψ (2S) → γ π+π−K0
SKS0,
and (3) ψ (2S) → γ K+K−K0
SKS0 The fits are made
to each combination of a good photon and two KS0
candidates in an event, the combination with the
min-imum χ4C2 is selected, and the χ4C2 is required to be
less than 35 The associated probability prob4Cis cal-culated
Background from ψ (2S) → π+π−J /ψ decay is
removed by calculating the mass recoiling, Mrecoil, against all pairs of oppositely charged tracks, assum-ing them to be pions, and requirassum-ing|Mrecoil−M J /ψ | >
25 MeV Background contamination from continuum production is found to be negligible for all decay chan-nels
An unbinned maximum likelihood method is used
in fitting the signal for all decay channels except
ψ (2S) → h+h−K0K0 The branching fractions of
Trang 4Fig 1 Distribution of K0SKS0invariant mass of ψ (2S) → γ K0
SKS0candidates (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 χ cJ (J = 0, 1, 2) needed in the
measure-ment are taken from Particle Data Group (PDG)
ta-bles[8]
4.1 ψ (2S) → γ K0
SKS0
The decay ψ (2S) → γ K0
SKS0has one photon plus
a pair of KS0 candidates The event should have four
charged tracks with total charge zero The loose
pho-ton selection, selection-A, is applied because of the
low background in the channel The KS0KS0 invariant
mass distribution of the selected events is shown in
Fig 1 A few KS0 sideband events survive the
selec-tion, which is consistent with the low background
ob-served in Fig 1(a) No background is expected from
ψ (2S) → γ χ cJ with χ cJ → 2(π+π−) for J = 0, 1, 2
and ψ (2S) → γ χ c1 with χ c1 → K0
SK±π∓according
to the analysis of simulated MC events
The KS0KS0invariant mass distribution is fitted with
two Breit–Wigner resonances for χ c0 and χ c2, each convoluted with Gaussian resolution functions, plus
a second-order polynomial background The χ c0,2
widths in the fitting are fixed to their PDG values[8] The resulting fit is shown inFig 1(b) Including the
χ c1resonance in the fit yields zero events for the CP
violating decay χ c1 → K0
SKS0
4.2 ψ (2S) → γ π+π−K0
SKS0
The ψ (2S) → γ π+π−K0
SKS0 decay channel con-tains one photon and six charged tracks with total charge zero The requirements here are similar to the previous case, but there are two additional
pi-ons Background from π/K misidentification is sup-pressed by the requirement prob4C(γ π+π−K0
SKS0) >
prob4C(γ K+K−K0K0) The π+π−K0K0 invariant
Trang 5Fig 2 Distribution of π+π−K0
SKS0invariant mass for ψ (2S) → γ π+π−K0
SKS0candidates 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 χcJbackground level, and
the dark shaded area is KS0sideband The solid line in (b) is the fit.
mass distribution for selected events is shown in
Fig 2
InFig 2there are two kinds of background in the
mass region between 3.0 and 3.64 GeV/c2: (1)
back-ground corresponding to KS0sidebands, and (2) ψ (2S)
decays and χ cJ decays different from the signal
chan-nel, 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
en-hanced in the χ cJ signal region MC studies show
that the smooth background spread over the whole
mass region from (2) results mainly from the
follow-ing decay channels: (a) ψ (2S) → γ χ cJ with χ cJ →
3(π+π−) and χ
cJ → K+K−K0
SKS0, (b) ψ (2S)→
π0π+π−K0
SKS0, and (c) ψ (2S) → ωK0
SKS0with ω→
π+π−π0 Background events in the high mass
re-gion above 3.64 GeV/c2inFig 2are from ψ (2S)→
π+π−K0
SKS0 decays combined with an unassociated low energy photon
The π+π−K0
SKS0 invariant mass distribution
be-tween 3.0 to 3.64 GeV/c2 is fitted with three Breit–
Wigner resonances χ cJ (J = 0, 1, 2), convoluted with
Gaussian resolution functions, plus a second-order
polynomial background The widths of the χ c0,1,2 res-onances in the fit are fixed to their PDG values The fit
is shown inFig 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 sam-ple for data is fitted with a fake signal shape, found
by fitting the MC KS0sideband sample, plus a second order polynomial background The numbers of
side-band background events, 5.3, 0.6 and 5.5 for χ c0 , χ c1 and χ c2, respectively, are then subtracted from the to-tal numbers of events in three peaks
Trang 6Fig 3 Distribution of K+K−K0
SKS0invariant mass of ψ (2S) → γ K+K−K0
SKS0candidates 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−K0
SKS0
The ψ (2S) → γ K+K−K0
SKS0decay has the same
topology as ψ (2S) → γ π+π−K0
SKS0, and thus it is subject to similar event selection criteria except for
the kaon identification requirement for two of the
charged tracks First, the KS0KS0 pair is searched for
under the assumption that all charged tracks are
pi-ons Kaon identification is only done for the two
charged tracks remaining after reconstruction of the
KS0KS0pair We also require prob4C(γ K+K−K0
SKS0)
> prob4C(γ π+π−K0
SKS0) for the 4C kinematic fit
probabilities to suppress contamination from ψ (2S)→
γ π+π−K0
SKS0 decays The K+K−K0
SKS0 invariant mass distribution for selected events is shown in
Fig 3
As seen fromFig 3, only one event survives from
the KS0 sideband sample for data MC events for
the following possible background channels are
gen-erated: (1) ψ (2S) → γ χ cJ with χ cJ → 3(π+π−)
and π+π−K0
SKS0, (2) ψ (2S) → π+π−K0
SKS0, and
(3) ψ (2S) → ωK0
SKS0with ω → π+π−π0 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
neg-ligible background comes from decays of ψ (2S)→
φK∗ 0K0→ π0K+K−K0K0
The K+K−K0
SKS0invariant mass distribution is
fit-ted with three Breit–Wigner resonances, χ cJ (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 χ cJ (J = 0, 1, 2), but also the masses of the χ c1
and χ c2in the fitting are fixed to their PDG values The fitting results are shown in theFig 3
4.4 ψ (2S) → h+h−K0
SKS0
The selection of ψ (2S) → h+h−K0
SKS0decays re-quires six charged tracks with total charge zero and no good photon in the event, as defined above Good pho-tons are rejected with the tight selection, selection-B,
in order to gain higher detection efficiency for
sig-nal events The KS0 reconstruction uses all combina-tions of oppositely charged tracks assuming all tracks
are pions To further suppress background of ψ (2S)
radiative decays, a requirement on the missing
mo-mentum of six charged tracks is employed: Pmiss<
80 MeV The two charged tracks h+ and h−
recoil-ing against the KS0pair are assumed to have the same
mass m Using energy–momentum conservation, the mass squared m2is calculated from
(1)
m2=E
4+ (P2
h+− P2
h−)2− 2E2(P2
h++ P2
h−)
Trang 7Fig 4 Distribution of invariant mass squared of the two remaining charged particles after KS0KS0selection for ψ (2S) → h+h−K0
SK0S (a) Points
with error bars are data The histogram is the KS0sideband background (b) Points with error bars are the data with the KS0sideband background subtracted The solid line is the fit.
where E = M ψ(2S) − E K0
SK0
S, and P h±is the
momen-tum of h+ or h− The distribution of m2for selected
events is shown inFig 4 The peak at low mass is
con-sistent with π+π−; there is no evidence for K+K−.
Two events from the continuum data sample
sur-vive the above selection and their effect will be
in-cluded in the systematic error No background is
found in MC studies of the following decay
chan-nels: (1) ψ (2S) → γ χ cJ with χ cJ → 3(π+π−),
π+π−K0
SKS0, and K+K−K0
SKS0 and (2) ψ (2S)→
ωKS0KS0 with ω → π+π−π0 Background estimated
using the KS0sideband data is subtracted from the
ob-served 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 theFig 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 iden-tification, 5% for the 4C kinematic fit, and 2.1% for
the KS0 reconstruction efficiency A correction
fac-tor 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 back-ground shape function contributes a difference of fi-nal 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
Trang 8branch-Table 1
Summary of the fitting results Errors for the signal yield ns , background n b , mass M , and mass squared m2are statistical The detection
σ
(MeV/c2)
χ c0 → K0
χ c1 → K0
χ c2 → K0
χ c0 → π+π−K0
χ c1 → π+π−K0
χ c2 → π+π−K0
χ c0 → K+K−K0
χ c1 → K+K−K0
χ c2 → K+K−K0
(GeV2/c4) (%)
σ (10−3)
(GeV2/c4)
ψ (2S) → π+π−K0
ing fractions for KS0→ π+π− and ψ (2S) → γ χ cJ
(J = 0, 1, 2) In ψ(2S) → π+π−K0
SKS0 decay, with two events found in continuum data, an additional
er-ror of 7.7% is added
4.6 Result and discussion
Possible resonance structures have been searched
for the χ c0 → π+π−K0
SKS0 final state which is the channel with the highest number of observed events
Some excess for inclusive decays of K∗(892)+ →
KS0π+, f0(1710) → K0
SKS0, ρ(770) → π+π− and
f0(980) → π+π− can be seen from the selected
events Insufficient statistics and complicated
struc-tures in these decay modes make it difficult to identify
clear signals for two-body decays with intermediate
resonances Efficiencies for final states with
reso-nances, such as
K∗(892)+K∗(892)−, K∗
0(1430)+K∗
0(1430)−,
K∗
0(1430)+K∗
2(1430)−,
f0(1370)f0(1710), f0(980)f0(980),
f0(980)f0(2200) and K1(1270)0K0
[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−K0
SKS0in our measurements include those
of both non-resonance and intermediate resonance Final results of signal yield and branching
frac-tions for the χ cJ (1P) and ψ(2S) two- and
four-body hadronic decays involving KS0 pair production are summarized in Table 1 The masses of the χ cJ (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
frac-tions of χ cJ (J = 0, 1, 2) decays to π+π−K0
SKS0and
K+K−K0
SKS0, as well ψ (2S) decay to π+π−K0
SKS0
are observed for the first time The branching fractions
of χ c0 and χ c2 decays to KS0KS0 are measured with improved precision
Decay rates, determined using updated χ cJ to-tal widths [8] and branching fractions for χ cJ →
π0π0, π+π− (J = 0, 2) and χ cJ → p ¯p (J = 1, 2)
decays [8], provide support for the COM (see Ta-ble 3) According to isospin symmetry, the χ cJ →
K0K¯0and K+K−decays should have the same
par-tial width Assuming equal decay widths for χ cJ →
KS0KS0 and K L0K L0, we find that the partial width of
the χ c0 → K0K¯0 decay estimated using the result
obtained in this Letter is not consistent (2.7σ ) with the COM prediction for χ → K+K−, while the
Trang 9Table 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
Channel BR(ψ (2S) → γ χ c )BR(χ c → X)
(10 −4) BRPDG(χ c → X)[8]
(10 −4)
χ c0 → K0
SKS0 30.2 ± 1.9 ± 3.3 35.1 ± 2.2 ± 4.7 21 ± 6
χ c1 → K0
χ c2 → K0
SKS0 5.72 ±0.76±0.63 8.9 ± 1.2 ± 1.3 7.2 ±2.7
χ c0 → π+π−K0
χ c1 → π+π−K0
SKS0 6.7 ± 2.6 ± 1.1 8.0 ± 3.1 ± 1.5 –
χ c2 → π+π−K0
SKS0 20.7 ± 3.9 ± 3.3 32.4 ± 6.1 ± 6.2 –
χ c0 → K+K−K0
SKS0 13.8 ± 3.9 ± 2.5 16.0 ± 4.6 ± 3.2 –
χ c1 → K+K−K0
SKS0 2.1 ± 1.6 ± 0.4 2.5 ± 1.9 ± 0.5 –
< 4.2 (CL = 90%) < 5.1 (CL = 90%)
χ c2 → K+K−K0
SKS0 1.6 ± 1.6 ± 0.3 2.6 ± 2.4 ± 0.5 –
< 3.5 (CL = 90%) < 5.5 (CL = 90%)
(10 −4)
BRPDG(ψ (2S) → X)[8]
(10 −4)
ψ (2S) → π+π−K0
Table 3
Comparison of partial widths for χ cJ → ππ, K ¯ K and p ¯p decays
between PDG [8] and the COM predictions Also shown is the result
based on this analysis
in KeV/c2
Γ i (COM)
in KeV/c2
χ c0 → π+π− 49.5 ± 6.7 45.4[5]
χ c2 → π+π− 3.73 ± 0.64 3.64[5]
χ c0 → π0π0 25.3 ± 3.3 23.5[5]
χ c2 → π0π0 2.3 ± 1.5 1.93[5]
χ c1 → p ¯p 0.066 ± 0.015 0.05627[6]
χ c2 → p ¯p 0.143 ± 0.018 0.15419[6]
χ c2 → K+K− 1.98 ± 0.47 2.89[5]
χ c0 → K0K¯0 71± 12 (this Letter)
χ c2 → K0K¯0 3.76 ±0.80 (this Letter)
agreement between them for the corresponding χ c2
decay is within 1.1σ A comparison for the χ cJ →
K+K− (J = 0, 2) decays shows that the
discrep-ancy between PDG values and the COM predictions
is 2.2σ and 1.9σ for χ c0 and χ c2 decays,
respec-tively
Furthermore, the sum of all known χ c0 two-body
branching fractions is less than 2% It therefore is
important to measure more χ cJ decay modes,
includ-ing 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 χ cJ decays to many-body 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 com-puting 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 Na-tional Natural Science Foundation of China under con-tracts Nos 19991480, 10225524, 10225525, the Chi-nese 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 Innova-tion 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 De-partment of Energy under Contract No DE-FG02-04ER41291 (University of Hawaii)
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