of 6
Search for
c
Ñ
2
S
Ö
production in
e
1
e
2
annihilations at 4.03 GeV
J. Z. Bai,
1
J. G. Bian,
1
I. Blum,
11
Z. W. Chai,
1
G. P. Chen,
1
H. F. Chen,
10
J. Chen,
3
J. C. Chen,
1
Y. Chen,
1
Y. B. Chen,
1
Y. Q. Chen,
1
B. S. Cheng,
1
X. Z. Cui,
1
H. L. Ding,
1
L. Y. Ding,
1
L. Y. Dong,
1
Z. Z. Du,
1
W. Dunwoodie,
7
S. Feng,
1
C. S. Gao,
1
M. L. Gao,
1
S. Q. Gao,
1
P. Gratton,
11
J. H. Gu,
1
S. D. Gu,
1
W. X. Gu,
1
Y. F. Gu,
1
Y. N. Guo,
1
S. W. Han,
1
Y. Han,
1
F. A. Harris,
8
J. He,
1
J. T. He,
1
M. He,
5
D. G. Hitlin,
2
G. Y. Hu,
1
H. M. Hu,
1
J. L. Hu,
1
Q. H. Hu,
1
T. Hu,
1
X. Q. Hu,
1
J. D. Huang,
1
Y. Z. Huang,
1
J. M. Izen,
11
C. H. Jiang,
1
Y. Jin,
1
Z. J. Ke,
1
M. H. Kelsey,
2
B. K. Kim,
11
D. Kong,
8
Y. F. Lai,
1
P. F. Lang,
1
A. Lankford,
9
C. G. Li,
1
D. Li,
1
H. B. Li,
1
J. Li,
1
P. Q. Li,
1
R. B. Li,
1
W. Li,
1
W. D. Li,
1
W. G. Li,
1
X. H. Li,
1
X. N. Li,
1
H. M. Liu,
1
J. Liu,
1
J. H. Liu,
1
R. G. Liu,
1
Y. Liu,
1
X. C. Lou,
11
B. Lowery,
11
F. Lu,
1
J. G. Lu,
1
J. Y. Lu,
1
L. C. Lu,
1
C. H. Luo,
1
A. M. Ma,
1
E. C. Ma,
1
J. M. Ma,
1
R. Malchow,
3
M. Mandelkern,
9
H. S. Mao,
1
Z. P. Mao,
1
X. C. Meng,
1
J. Nie,
1
S. L. Olsen,
8
J. Oyang,
2
D. Paluselli,
8
L. J. Pan,
8
J. Panetta,
2
F. Porter,
2
N. D. Qi,
1
X. R. Qi,
1
C. D. Qian,
6
J. F. Qiu,
1
Y. H. Qu,
1
Y. K. Que,
1
G. Rong,
1
M. Schernau,
9
B. Schmid,
9
J. Schultz,
9
Y. Y. Shao,
1
B. W. Shen,
1
D. L. Shen,
1
H. Shen,
1
X. Y. Shen,
1
H. Y. Sheng,
1
H. Z. Shi,
1
X. F. Song,
1
J. Standifird,
11
D. Stoker,
9
F. Sun,
1
H. S. Sun,
1
S. Q. Tang,
1
W. Toki,
3
G. L. Tong,
1
F. Wang,
1
L. S. Wang,
1
L. Z. Wang,
1
M. Wang,
1
Meng Wang,
1
P. Wang,
1
P. L. Wang,
1
S. M. Wang,
1
T. J. Wang,
1,
*
Y. Y. Wang,
1
M. Weaver,
2
C. L. Wei,
1
Y. G. Wu,
1
D. M. Xi,
1
X. M. Xia,
1
P. P. Xie,
1
Y. Xie,
1
Y. H. Xie,
1
W. J. Xiong,
1
C. C. Xu,
1
G. F. Xu,
1
S. T. Xue,
1
J. Yan,
1
W. G. Yan,
1
C. M. Yang,
1
C. Y. Yang,
1
J. Yang,
1
W. Yang,
3
X. F. Yang,
1
M. H. Ye,
1
S. W. Ye,
10
Y. X. Ye,
10
K. Yi,
1
C. S. Yu,
1
C. X. Yu,
1
Y. H. Yu,
4
Z. Q. Yu,
1
Z. T. Yu,
1
C. Z. Yuan,
1
Y. Yuan,
1
B. Y. Zhang,
1
C. C. Zhang,
1
D. H. Zhang,
1
Dehong Zhang,
1
H. L. Zhang,
1
J. Zhang,
1
J. L. Zhang,
1
J. W. Zhang,
1
L. S. Zhang,
1
Q. J. Zhang,
1
S. Q. Zhang,
1
X. Y. Zhang,
5
Y. Zhang,
1
Y. Y. Zhang,
1
D. X. Zhao,
1
H. W. Zhao,
1,†
J. W. Zhao,
1
M. Zhao,
1
W. R. Zhao,
1
J. P. Zheng,
1
L. S. Zheng,
1
Z. P. Zheng,
1
G. P. Zhou,
1
H. S. Zhou,
1
L. Zhou,
1
Q. M. Zhu,
1
Y. C. Zhu,
1
Y. S. Zhu,
1
and B. A. Zhuang
1
~
BES Collaboration
!
1
Institute of High Energy Physics, Beijing 100039, People’s Republic of China
2
California Institute of Technology, Pasadena, California 91125
3
Colorado State University, Fort Collins, Colorado 80523
4
Hangzhou University, Hangzhou 310028, People’s Republic of China
5
Shandong University, Jinan 250100, People’s Republic of China
6
Shanghai Jiaotong University, Shanghai 200030, People’s Republic of China
7
Stanford Linear Accelerator Center, Stanford, California 94309
8
University of Hawaii, Honolulu, Hawaii 96822
9
University of California at Irvine, Irvine, California 92717
10
University of Science and Technology of China, Hefei 230026, People’s Republic of China
11
University of Texas at Dallas, Richardson, Texas 75083-0688
~
Received 8 October 1997; published 6 March 1998
!
A search is performed for the production of the
c
(2
S
)in
e
1
e
2
annihilation at a center-of-mass energy of
4.03 GeV using the BES detector operated at the Beijing Electron Positron Collider
~
BEPC
!
. The kinematic
features of the reconstructed
c
(2
S
) signal are consistent with its being produced only in association with an
energetic photon resulting from initial state radiation
~
ISR
!
. Limits are placed on
c
(2
S
) production from the
decay of unknown charmonia or metastable hybrids that might be produced in
e
1
e
2
annihilations at 4.03 GeV.
Under the assumption that the observed cross section for
c
(2
S
) production is due entirely to ISR, the partial
width
G
ee
of the
c
(2
S
) is measured to be 2.07
6
0.32 keV.
@
S0556-2821
~
98
!
01309-5
#
PACS number
~
s
!
: 13.65.
1
i, 14.40.Gx
I. INTRODUCTION
In
e
1
e
2
annihilations at a center of mass energy of 4.03
GeV the
c
(2
S
) can be produced via
~
1
!
initial state radiation
~
ISR
!
of a photon by the
e
1
or
e
2
, followed by
e
1
e
2
!
c
(2
S
),
~
2
!
e
1
e
2
!
p
0
c
(2
S
) , where the
p
0
can be produced in
the hadronization of
cc
̄
into
c
(2
S
)
p
0
, orinatwo
photon process where
gg
couples to a
p
0
,
~
3
!
decays of charmonium states more massive than the
c
(2
S
) , and
~
4
!
decays
of
possible
metastable
hybrids
(
qq
̄
g
)
produced in
e
1
e
2
annihilations at 4.03 GeV.
Reaction
~
1
!
is well described by QED, and is expected to
be dominant. Process
~
2
!
proceeds through two virtual pho-
tons, or an isospin-violating hadronic interaction, and is ex-
pected to be suppressed relative to
~
1
!@
1,2
#
. Unless there is a
new charmonium state produced in
e
1
e
2
annihilation at this
*
Deceased.
Present address: Beijing University, Beijing, China.
PHYSICAL REVIEW D
1 APRIL 1998
VOLUME 57, NUMBER 7
57
0556-2821/98/57
~
7
!
/3854
~
6
!
/$15.00
3854
© 1998 The American Physical Society
energy, process
~
3
!
should be absent in the data. The possi-
bility of the existence of metastable hybrids with mass
;
4 GeV has been proposed
@
3
#
to explain the
c
(2
S
)
anomaly observed in
pp
̄
collisions at the Fermilab Tevatron
@
4
#
. It is of interest to search for these metastable hybrids via
reaction
~
4
!
; their existence might be revealed through an
excess
c
(2
S
) production in
e
1
e
2
collisions.
In this paper,
c
(2
S
) production in
e
1
e
2
collisions at a
center-of-mass energy of 4.03 GeV is reported using BES
data taken at the Beijing Electron Positron Collider
~
BEPC
!
.
Evidence for processes
~
2
!
,
~
3
!
and
~
4
!
is sought by measur-
ing an excess of
c
(2
S
) events above QED ISR production.
Since the center of mass energy is not far above the
c
(2
S
)
threshold, reactions
~
1
!
~
4
!
should yield events of low
charge multiplicity, when the
c
(2
S
) is excluded. Therefore
events containing
c
(2
S
) at this energy are expected to have
very distinctive kinematic features, and can be readily sepa-
rated from other events.
The following sections describe the BES detector, the
identification of electrons and muons, the reconstruction of
the
c
(2
S
) , a study of the kinematic features and production
rate of the
c
(2
S
) , limits on the production of
c
(2
S
) due to
reactions
~
3
!
and
~
4
!
, and a determination of the partial
width,
G
ee
, of the
c
(2
S
).
II. THE BES DETECTOR AND EVENT SELECTION
The BES detector has been discussed in detail previously
@
5
#
. The detector elements crucial to the present measure-
ment are now described briefly.
Charged particle tracking is provided by a 10 superlayer
main drift chamber
~
MDC
!
operated inside a 0.4 T axial
magnetic field. Each superlayer contains four layers of sense
wires measuring both the position and the specific ionization
( dE/d
x
) of charged particles. The magnet coil surrounds a
time-of-flight
~
TOF
!
counter array and an electromagnetic
calorimeter
~
ECAL
!
composed of proportional tubes and
lead sheets. A muon detector system is outside the magnet
coil; it consists of three double layers of streamer tubes, and
measures the coordinates of muons in z and in
r
f
with reso-
lutions of 5 cm and 3 cm, respectively.
This analysis is based on hadronic events recorded with
the BES detector. A data sample of 22.3 pb
2
1
was collected
in
e
1
e
2
annihilations at a center-of-mass energy of 4.03
GeV.
III. RECONSTRUCTION OF THE
c
Ñ
2
S
Ö
Additional selection criteria are imposed on the BES had-
ronic events in this analysis. Each charged track must satisfy
the following criteria:
~
1
!
at least 10 drift chamber hits must be used on the
fitted track, and the track fit must be of good quality;
~
2
!
u
cos
u
u
,
0.88, where
u
is the polar angle of the track;
~
3
!
the momentum of the track must be less than
2.0 GeV/
c
, and its transverse momentum must be
greater than 50 MeV/
c
;
~
4
!
the distance of closest approach to the beam in the
transverse plane must be less than 3 cm, and must
occur along the beam direction within
6
20 cm
~
4.5
s
!
of the center of the detector;
~
5
!
u
cos
u
l
u
,
0.90, where
u
l
is the lepton helicity angle in
the dilepton rest frame.
In addition, a particle species dependent correction for
energy loss in the beam pipe is made for all charged tracks.
A correction of
2
0.42% is also applied to the momentum of
each charged track to compensate for a shift in the BES
magnetic field.
Events containing four or more charged tracks are
searched for
c
(2
S
) production, where the
c
(2
S
) is detected
by means of the decay
c
(2
S
)
!
pp
J
/
c
,
J
/
c
!
e
1
e
2
or
m
1
m
2
.
A. Selection of electrons and muons
Three detector components, the main drift chamber, the
TOF counter array, and the shower counter, are used for
electron identification. The dE/d
x
and TOF measurements
for charged tracks must be consistent with those of an elec-
tron. A shower shape quantity using the weighted number of
hits in each ECAL layer is formed. A momentum dependent
cut on this quantity is chosen to identify electrons based on
the fact that electrons have more hits in the ECAL than had-
rons and the longitudinal shower development has a pattern
which is different from that of hadrons. This selection is
identical to the procedure used in
@
6
#
. The efficiency for
electron identification is measured to be ( 86
6
1 ) % above a
momentum of 1.2 GeV/
c
using
J
/
c
!
e
1
e
2
events selected
in the BES data collected at the
c
(2
S
) energy.
Muons are identified based on their associated muon
counter hits only. For a track with transverse momentum
greater than 0.75 GeV/
c
, at least two good muon layer hits
have to be matched to the track. Above a transverse momen-
tum of 0.95 GeV/
c
, all three muon layers must have good
associated hits. Here good hits are those that are within the
projected
f
angle range of the charged track, where this
range is determined from studying a cosmic ray muon
sample. The efficiency for muon identification, determined
from reconstructed
c
(2
S
)
!
J
/
c
pp
,
J
/
c
!
m
1
m
2
decays,
is measured to be ( 77
6
1 ) % for p
.
1.2 GeV/
c
.
B. Reconstruction of the
c
Ñ
2
S
Ö
The
c
(2
S
) is reconstructed in the decay
c
(2
S
)
!
J
/
c
p
1
p
2
, where
J
/
c
!
m
1
m
2
or
e
1
e
2
.A
J
/
c
candi-
date, defined as an event with dilepton invariant mass be-
tween 2.5 and 3.25 GeV, is combined with a pair of oppo-
sitely charged tracks, where at least one track has been
identified as a pion according to dE/d
x
and TOF measure-
ments. An asymmetric cut on the
l
1
l
2
mass is applied to
include those
J
/
c
!
e
1
e
2
events where the
e
1
or
e
2
has
radiated a hard photon, thus yielding a
l
1
l
2
invariant mass
which is significantly lower than the nominal
J
/
c
mass. The
difference in invariant mass between
l
1
l
2
p
1
p
2
and
l
1
l
2
is
shown in Fig. 1 for the two decay modes. In this mass dif-
ference, the measurement uncertainties in the lepton mo-
menta tend to cancel. This permits the inclusion of
J
/
c
tail
events, thereby increasing the detection efficiency. From
high statistics
c
(2
S
) runs we determine the mass resolution
to be
;
9.4 MeV/
c
2
for
c
(2
S
) events in this mass distribu-
tion. Clear
c
(2
S
) signals are reconstructed in both the
e
and
57
3855
SEARCH FOR
c
(2
S
) PRODUCTION IN
e
1
e
2
...
m
modes. The distribution in Fig. 1 is fit with a signal Gauss-
ian on a smooth polynomial background; the fit value of the
center is found to be 588
6
1 MeV/
c
2
, in good agreement
with the Particle Data Group
~
PDG
!
value of 589.1
6
0.1 MeV/
c
2
@
7
#
.
In order to estimate the number of
c
(2
S
) events, the
range 560– 616 MeV/
c
2
is defined as the
c
(2
S
) signal re-
gion, as shown by the arrows in Fig. 1. For the muon mode,
Monte Carlo simulation and studies of data collected on the
c
(2
S
) resonance show that there is no combinatorial back-
ground, and that events away from the
c
(2
S
) signal region
are genuine
c
(2
S
) decays that are mis-reconstructed. All
events in the signal region are interpreted as signal, and this
yields 41.0
6
6.4
c
(2
S
) events. A
6
4 % systematic error
is assigned to the
c
(2
S
) signal. For the electron mode,
two background regions, 409– 541 MeV/
c
2
and 635– 767
MeV/
c
2
, are chosen to estimate the background contribution
in the
c
(2
S
) region. There are 80 events in the signal region,
and 64 events in the background side-bands which imply
13.7
6
1.7 background events in the signal region. After per-
forming the background subtraction, it is estimated that there
are 66.3
6
9.0
c
(2
S
) events in the electron mode. Combining
the
m
and
e
modes, the distribution of Fig. 1 yields 107.3
6
11.0
6
4.3
c
(2
S
) events, where the first error is statistical
and the second is the systematic error resulting from the
method used in estimating the background.
IV. KINEMATIC DISTRIBUTIONS
FOR THE
c
Ñ
2
S
Ö
SIGNAL
A. Monte Carlo simulation
The reconstruction efficiencies for the
c
(2
S
) are esti-
mated using a Monte Carlo simulation of the BES detector,
with the generated events being subjected to the same recon-
struction procedure used in the BES data reconstruction. The
ISR
e
1
e
2
!
gc
(2
S
) events are generated at a center-of-
mass energy of 4.03 GeV, with the
c
(2
S
) polar angle dis-
tributions as described in
@
1
#
. Other types of events are gen-
erated assuming a uniform angular distribution around the
electron direction. The detection efficiencies for the
c
(2
S
)
are calculated based on different charmonium production
mechanisms as outlined in
~
1
!
~
4
!
, where the measured e/
m
identification efficiencies have been used. The
c
(2
S
) effi-
ciencies are found not to vary significantly among these
models. These efficiencies are used for the calculation of
production rates in Sec. V. The small spread among these
efficiencies is treated as a systematic error, and is included in
the rate measurements.
B. Kinematic features of the
c
Ñ
2
S
Ö
The
c
(2
S
) distributions from reactions in
~
1
!
~
4
!
have
some unique kinematical features. Figure 2a shows the
cos
u
c
(2
S
)
distribution as predicted by QED for the ISR
c
(2
S
) , where
u
c
(2
S
)
is the angle between directions of the
c
(2
S
) and the positron. The ISR
c
(2
S
) peak sharply in the
forward and backward directions. For interactions
~
2
!
~
4
!
this angular distribution is expected to be rather uniform.
Reaction
~
1
!
results in a simple two body
gc
(2
S
) final
state, where the
c
(2
S
) momentum, as shown in Fig. 3a,
peaks at 329 MeV/
c
with a width entirely due to the experi-
mental resolution. The momenta of
c
(2
S
) particles from
processes such as
e
1
e
2
!
c
(2
S
)
p
0
would peak at a value of
303 MeV/
c
. This important difference in momentum pro-
vides a crucial separation between
~
1
!
, the dominant source
of
c
(2
S
) , and
~
3
!
and
~
4
!
, which involve the interesting
physics that is being sought.
For the electron channel, the
c
(2
S
) momentum resolution
is degraded as a result of final state radiation, and is signifi-
cantly worse than that of the
c
(2
S
) reconstructed in the
muon channel. To compensate for this energy loss, a 2-C
kinematic fit is performed on the
c
(2
S
) candidates for which
FIG. 1. The invariant mass difference between
l
1
l
2
p
1
p
2
and
l
1
l
2
, where
l
5
e
~
histogram
!
or
m
~
hatched histogram
!
. The arrows
denote the
c
(2
S
) signal region.
FIG. 2. Distribution in cos
u
c
(
2
S
)
~
a
!
for the ISR
c
(2
S
) predicted
by QED, and
~
b
!
for the
c
(2
S
) candidates selected from the data.
3856
57
J. Z. BAI
et al.
the
e
1
e
2
pairs and the
e
1
e
2
p
1
p
2
are constrained to M
J
/
c
( 3.0969 GeV/
c
2
) and M
c
(2
S
)
( 3.686 GeV/
c
2
) , respectively.
This 2-C fit significantly improves the momentum resolution
of the
c
(2
S
) , to the extent that the improved momentum
resolution for the electron channel is compatible with that of
the muon channel. The rms width of the combined
c
(2
S
)
momentum distribution is 26 MeV/
c
. Hereafter, the
c
(2
S
)
reconstructed using
e
and
m
pairs are treated together.
The cos
u
c
(2
S
)
and
p
c
(2
S
)
distributions for the events in the
c
(2
S
) signal region are shown in Fig. 2b and Fig. 3b, re-
spectively. The cos
u
c
(2
S
)
distribution in Fig. 2b follows
closely that of the ISR distribution in Fig. 2a. A
Kolmogorov-Smirnov comparison between the ISR predic-
tion of Fig. 2a, and the observed cos
u
c
(2
S
)
distribution of
Fig. 2b, yields a probability of 75.2% that these distributions
have the same shape. The fit performed to the
p
c
(2
S
)
spec-
trum in Fig. 3b yields a central value 336
6
4 MeV/
c
for the
Gaussian momentum distribution, in good agreement with
the expectation of 329 MeV/
c
for the two body final state
e
1
e
2
!
gc
(2
S
) . These kinematic features show that the
c
(2
S
) signal is consistent with being produced entirely via
reaction
~
1
!
, the initial state radiation interaction.
V. THE PRODUCTION RATE OF THE
c
Ñ
2
S
Ö
A. Inclusive
c
Ñ
2
S
Ö
production rate
To determine the inclusive production rate, the
c
(2
S
)
signals in Fig. 1 are corrected for reconstruction efficiency,
and the decay branching fractions of the mode studied. The
branching
fractions
@
7
#
B
(
c
(2
S
)
!
J
/
c
p
1
p
2
)
5
( 32.4
6
2.6) % ,
B
(
J
/
c
!
e
1
e
2
)
5
( 6.02
6
0.19) % ,
and
B
(
J
/
c
!
m
1
m
2
)
5
( 6.01
6
0.19) % have been used. Monte Carlo
simulations yield estimated detection efficiencies of ( 18.9
6
0.1) % and ( 22.9
6
0.1) % for
c
(2
S
)
!
J
/
c
p
1
p
2
, where
J
/
c
!
m
1
m
2
and
e
1
e
2
, respectively, and where the errors
are statistical only. The corresponding cross section is
s
Ñ
e
1
e
2
!
c
~
2
S
!
X
Ö
5
592
6
61
6
68 pb
in
e
1
e
2
annihilations at 4.03 GeV, averaged over the
e
and
m
channels. The second errors are systematic, and arise from
uncertainties in particle identification (
6
3.1% ) , determina-
tion of number of signal events (
6
4%), the
absolute scale
of the momentum measurement for the
c
(2
S
)(
6
2.7% ) ,
possible mode dependence of the
c
(2
S
) detection efficiency
(
6
2.7% ) , luminosity uncertainty (
6
0.9 pb
2
1
) , and errors
on relevant
J
/
c
and
c
(2
S
) branching fractions (
6
8.6% ) .
This result compares well with the value expected for pro-
cess
~
1
!
which is 612
6
60 pb, using the value 2.14
6
0.21 keV for
G
ee
@
7
#
of the
c
(2
S
) , the error being due to
the uncertainty in
G
ee
.
B. Limit on a new charmonium decaying into
J
/
c
p
1
p
2
A search has been made for a new
3
D
2
charmonium state
with a mass of 3.836 GeV/
c
2
which has been reported in the
decay mode
J
/
c
p
1
p
2
@
8
#
. The selection criteria are identi-
cal to those used in the
c
(2
S
) reconstruction. This charmo-
nium state should be observed in Fig. 1 at around
736.4 MeV/
c
2
if the production cross section and branching
fraction are sufficiently large. No enhancement is observed at
this mass in Fig. 1. The mass region 718– 755 MeV/
c
2
is
considered as the signal region, and corresponds to a
6
2
s
window at the mass of the reported charmonium state. The
mass regions 635–699 MeV and 774–950 MeV are defined
as background control regions, and events inside them are
used to estimate the background in the signal region. A total
of 9 and 47 events are found in the signal and background
regions, respectively, leading to an estimate of 1.7
2
1.7
1
3.2
excess
events for a resonance at the reported
3
D
2
mass. The detec-
tion efficiency is identical to that of the
c
(2
S
) . A 95% C.L.
upper
limit
for
s
Ñ
e
1
e
2
!
3
D
2
( 3836)
1
anything
Ö
3
B
Ñ
3
D
2
( 3836)
!
J
/
c
p
1
p
2
Ö
is set at 12 pb in
e
1
e
2
anni-
hilations at 4.03 GeV.
C. Limit on
X
ò
gc
Ñ
2
S
Ö
In this analysis it is assumed that the
c
(2
S
) from un-
known charmonium decays of the type
X
!
gc
(2
S
) has a
flat angular distribution in the lab frame. Candidate
c
(2
S
)
events are selected by requiring
u
cos
u
c
(2
S
)
u
,
0.80. Averaging
over the
e
and
m
modes, about 83% of the ISR
c
(2
S
) events
are rejected, and an efficiency of 80% for
X
!
gc
(2
S
)is
obtained. No momentum selection is made on the
c
(2
S
)in
order to maintain uniform detection efficiency for
X
!
gc
(2
S
) for all possible
X
masses.
Background from ISR is estimated by assuming that all
c
(2
S
) events in the
u
cos
u
c
(2
S
)
u
.
0.80 region are due to ISR;
Fig. 2 is then used to estimate the ISR contribution to the
region
u
cos
u
c
(2
S
)
u
,
0.80. The detection efficiency obtained
from a simulation of the detector is found to be ( 16.9
6
0.1) % , averaged over the
e
and
m
modes.
The result is shown in Table I. A total of 23.2
6
5.8
c
(2
S
)
events satisfy the selection criteria, with an expected ISR
background of 16.9
6
2.0 events. A 95% C.L. upper limit for
s
(
e
1
e
2
!
X
1
anything)
3
B
Ñ
X
!
gc
(2
S
)
Ö
,
107 pb is set.
In deriving this limit, the same systematic uncertainties de-
scribed in Sec. V A have been taken into account.
D. Limit on
c
Ñ
2
S
Ö
from decays of metastable hybrids
A metastable hybrid,
qq
̄
g
, would decay into a
c
(2
S
) plus
at least a pion
@
3
#
. The
c
(2
S
) momentum is lower than that
of the
c
(2
S
) from ISR. In this search, it is required that
u
cos
u
c
(2
S
)
u
,
0.80 and
p
c
(2
S
)
,
303 MeV/
c
. The momentum
cut is placed one standard deviation below the mean momen-
tum of the ISR
c
(2
S
) . These cuts jointly reject about 95%
of the ISR
c
(2
S
) . The overall detection efficiency for
qq
̄
g
!
c
(2
S
)
p
0
is found to be ( 7.6
6
0.1) % . This efficiency
would be higher if an additional particle were present in the
decay.
TABLE I. Summary of
c
(2
S
) cross section data.
Reaction
Number of
c
(2
S
)
Estimated
ISR contrib.
Cross section
or limit
~
pb
!
~
95% C.L.
!
ISR
107
6
12
all
592
6
61
6
68
3
D
2
( 3863)
1.7
2
1.7
1
3.2
none
,
12
X
!
gc
(2
S
)
23.2
6
5.8
16.9
6
2.0
,
107
qq
̄
g
!
c
(2
S
)X
7.6
6
3.0
5.0
6
0.6
,
117
57
3857
SEARCH FOR
c
(2
S
) PRODUCTION IN
e
1
e
2
...
The results are listed in Table I. A total of 7.6
6
3.0
c
(2
S
)
events pass these cuts, with an expected background of 5.0
6
0.6 from ISR, leading to an excess of 2.6
2
2.6
1
3.1
c
(2
S
)
events.
Correcting for detection efficiency and relevant branching
fractions,
the
cross
section
s
(
e
1
e
2
!
qq
̄
g
)
3
B
Ñ
qq
̄
g
!
c
(2
S
)X
Ö
is found to be less than 117 pb at 95% C.L.
Estimates of the systematic errors have been included in this
limit.
E.
G
ee
of the
c
Ñ
2
S
Ö
After various possibilities have been considered, no evi-
dence has been found for the production of
c
(2
S
) , other
than by ISR. Assuming that the observed
c
(2
S
) events are
entirely due to the ISR production mechanism,
G
ee
of the
c
(2
S
) can be extracted from the measured cross section. In
the QED calculation, the ISR cross section is directly pro-
portional to
G
ee
of the
c
(2
S
) . The value
G
ee
5
2.07
6
0.32 keV is determined, which is comparable in precision
to the values 2.1
6
0.3 keV and 2.0
6
0.3 keV obtained by
Mark I
@
9
#
and by DASP
@
10
#
, respectively. The latter value
has been corrected for radiative effects to 2.2
6
0.3 keV by
Alexander
et al.
@
11
#
, who then give the Mark I and DASP
average,
G
ee
5
2.14
6
0.21 keV, which is the value reported
in the PDG summary
@
7
#
. Combining this with the present
measurement, a new world average of 2.12
6
0.18 keV is ob-
tained for
G
ee
. It should be noted that the value of
G
ee
ob-
tained in this analysis corresponds to the left hand side of Eq.
~
9
!
of Ref.
@
11
#
, i.e., it contains the factor ( 1
1
d
v
p
) repre-
senting the vacuum polarization corrections. All other QED
corrections to second order have been explicitly included in
the sampling function used to evaluate the luminosity contri-
bution at mass value of the
c
(2
S
).
VI. SUMMARY
Using BES data taken at the BEPC collider, a search has
been performed for production of the
c
(2
S
)in
e
1
e
2
anni-
hilations at a center-of-mass energy of 4.03 GeV. The kine-
matic features of the observed
c
(2
S
) signal are consistent
with its being exclusively produced from the initial state
radiation process, for which the value
s
Ñ
e
1
e
2
!
gc
(2
S
)
Ö
5
592
6
61
6
68 pb has been obtained. The following 95%
C.L.
upper
limits
have
been
obtained:
s
Ñ
e
1
e
2
!
3
D
2
( 3836)
1
anything
Ö
3
B
Ñ
3
D
2
( 3836)
!
J
/
c
p
1
p
2
Ö
.
12pb,
s
(
e
1
e
2
!
X
1
anything)
3
B
Ñ
X
!
gc
(2
S
)
Ö
,
107 pb, where
X
is an unknown state, and
s
(
e
1
e
2
!
qq
̄
g
)
3
B
Ñ
qq
̄
g
!
c
(2
S
)
1
anything)
,
117 pb for the production of meta-
stable hybrids at 4.03 GeV. Using the measured ISR cross
section,
G
ee
of the
c
(2
S
) is determined to be 2.07
6
0.32 keV.
ACKNOWLEDGMENTS
We would like to thank the staffs of the BEPC accelerator
and the Computing Center at the Institute of High Energy
Physics, Beijing, for their outstanding scientific efforts. The
work of the BES Collaboration was supported in part by the
National Natural Science Foundation of China under Con-
tract No. 19290400 and the Chinese Academy of Sciences
under Contract No. KJ85
~
IHEP
!
; by the Department of En-
ergy under Contract No. DE-FG03-92ER40701
~
Caltech
!
,
DE-FG03-93ER40788
~
Colorado State University
!
, DE-
AC02-76ER03069
~
MIT
!
, DE-AC03-76SF00515
~
SLAC
!
,
DE-FG03-91ER40679
~
UC Irvine
!
, DE-FG03-94ER40833
~
U Hawaii
!
, DE-FG03-95ER40925
~
UT Dallas
!
; by the U.S.
National Science Foundation, Grant No. PHY9203212
~
Uni-
versity of Washington
!
; and by the Texas National Research
Laboratory Commission under Contract Nos. RGFY91B5,
RGFY92B5
~
Colorado State
!
, and RCFY93-316H
~
UT Dal-
las
!
.
FIG. 3.
~
a
!
Simulated momentum distribution for
c
(2
S
) pro-
duced via ISR;
~
b
!
the momentum distribution for reconstructed
c
(2
S
) candidates
~
histogram
!
, and the expected background distri-
bution
~
dashed histogram
!
estimated using
J
/
c
side bands; the fit is
to a Gaussian of rms deviation 26 MeV/
c
, above a linear back-
ground distribution.
3858
57
J. Z. BAI
et al.
@
1
#
G. Bonneau and F. Martin, Nucl. Phys.
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, 381
~
1971
!
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2
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Particle Data Group, R. M. Barnett
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,
180
~
1996
!
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@
3
#
F. E. Close, Phys. Lett. B
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!
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4
#
CDF Collaboration, F. Abe
et al.
, Phys. Rev. Lett.
79
, 572
~
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5
#
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1994
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!
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57
3859
SEARCH FOR
c
(2
S
) PRODUCTION IN
e
1
e
2
...