of 5
Direct measurement of
B
Ñ
D
s
1
ò
f
X
1
Ö
J. Z. Bai,
1
O. Bardon,
5,
*
I. Blum,
10
A. Breakstone,
8
T. Burnett,
11
G. P. Chen,
1
H. F. Chen,
3
J. Chen,
4
S. J. Chen,
1
S. M. Chen,
1
Y. Chen,
1
Y. B. Chen,
1
Y. Q. Chen,
1
B. S. Cheng,
1
R. F. Cowan,
5
X. Z. Cui,
1
H. L. Ding,
1
Z. Z. Du,
1
W. Dunwoodie,
7
X. L. Fan,
1
J. Fang,
1
C. S. Gao,
1
M. L. Gao,
1
S. Q. Gao,
1
P. Gratton,
10
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
M. He,
6
D. G. Hitlin,
2
G. Y. Hu,
1
T. Hu,
1
X. Q. Hu,
1
D. Q. Huang,
1
Y. Z. Huang,
1
J. M. Izen,
10
C. H. Jiang,
1
S. Jin,
1
Y. Jin,
1
L. Jones,
2
S. H. Kang,
1
Z. J. Ke,
1
M. H. Kelsey,
2
B. K. Kim,
10
D. Kong,
8
Y. F. Lai,
1
H. B. Lan,
1
P. F. Lang,
1
A. Lankford,
9
F. Li,
1
J. Li,
1
P. Q. Li,
1
Q. Li,
6
R. B. Li,
1
W. Li,
1
W. D. Li,
1
W. G. Li,
1
X. H. Li,
1
X. N. Li,
1
S. Z. Lin,
1
H. M. Liu,
1
J. Liu,
1
J. H. Liu,
1
Q. Liu,
1
R. G. Liu,
1
Y. Liu,
1
Z. A. Liu,
1
X. C. Lou,
10
B. Lowery,
10
J. G. Lu,
1
J. Y. Lu,
1
S. Luo,
1
Y. Luo,
1
A. M. Ma,
1
E. C. Ma,
1
J. M. Ma,
1
R. Malchow,
4
M. Mandelkern,
9
H. S. Mao,
1
Z. P. Mao,
1
X. C. Meng,
1
H. L. Ni,
1
J. Nie,
1
S. L. Olsen,
8
J. Oyang,
2
D. Paluselli,
8
L. J. Pan,
8
J. Panetta,
2
F. Porter,
2
E. Prabhakar,
2
N. D. Qi,
1
Y. K. Que,
1
G. Rong,
1
M. Schernau,
9
B. Schmid,
9
J. Schultz,
9
Y. Y. Shao,
1
D. L. Shen,
1
H. Shen,
1
X. Y. Shen,
1
H. Y. Sheng,
1
H. Z. Shi,
1
E. Soderstrom,
7
X. F. Song,
1
J. Standifird,
10
D. Stoker,
9
F. Sun,
1
H. S. Sun,
1
S. J. Sun,
1
J. Synodinos,
7
Y. P. Tan,
1
S. Q. Tang,
1
W. Toki,
4
G. L. Tong,
1
F. Wang,
1
L. S. Wang,
1
L. Z. Wang,
1
M. 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
W. J. Wisniewski,
7
D. M. Xi,
1
X. M. Xia,
1
P. P. Xie,
1
D. Z. Xu,
1
R. S. Xu,
1
Z. Q. Xu,
1
S. T. Xue,
1
J. Yan,
1
W. G. Yan,
1
C. M. Yang,
1
C. Y. Yang,
1
H. Yang,
10
W. Yang,
4
M. H. Ye,
1
S. Z. Ye,
1
K. Young,
11
C. S. Yu,
1
C. X. Yu,
1
Z. Q. Yu,
1
C. Z. Yuan,
1
B. Y. Zhang,
1
C. C. Zhang,
1
D. H. Zhang,
1
H. L. Zhang,
1
J. Zhang,
1
J. W. Zhang,
1
L. S. Zhang,
1
S. Q. Zhang,
1
Y. Zhang,
1
Y. Y. Zhang,
1
D. X. 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
X. F. Zhou,
1
Y. H. 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
China’s University of Science and Technology, Hefei 230026, People’s Republic of China
4
Colorado State University, Fort Collins, Colorado 80523
5
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
6
Shandong University, Jinan 250100, 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 Texas at Dallas, Richardson, Texas 75083-0688
11
University of Washington, Seattle, Washington 98195
~
Received 21 July 1997; published 4 December 1997
!
The absolute inclusive branching fraction of
D
s
1
!
f
X
1
has been measured from data collected by the BES
detector at a center-of-mass energy of 4.03 GeV, corresponding to an integrated luminosity of 22.3 pb
2
1
.At
this energy, direct pair production
e
1
e
2
!
D
s
1
D
s
2
has been observed. We have selected
D
s
candidate events
by reconstructing five hadronic decay modes
D
s
1
!
f
p
1
,
K
̄
0
*
K
1
,
K
̄
0
K
1
,
f
0
p
1
and
K
0
K
2
p
1
p
1
and have
searched for inclusive
f
’s in the recoiling
D
s
2
. We observed three recoiling
f
’s in the 166.4
6
31.8
D
s
candidate events, which leads to the absolute branching fraction
B
(
D
s
1
!
f
X
1
)
5
( 17.8
2
7.2
1
15.1
2
6.3
1
0.6
) % and
B
(
D
s
1
!
f
p
1
)
5
( 3.6
2
1.6
1
3.1
2
1.3
1
0.4
)%.
@
S0556-2821
~
97
!
02423-5
#
PACS number
~
s
!
: 13.25.Ft, 14.40.Lb
The main experimental difficulties in charmed particle de-
cays are the problems of overall normalization and the pre-
cise determination of charm branching fractions. Previously,
we have reported the absolute model-independent branching
ratio of
D
s
1
!
f
p
1
@
1
#
. Here we consider the absolute
branching fraction of
D
s
1
!
inclusive
f
, which contributes
toward our understanding of the overall
D
s
branching frac-
tion scale. Moreover the absolute inclusive branching frac-
tion of
D
s
1
!
f
X
1
@
2
#
is used in
B
s
0
B
̄
s
0
oscillation
@
3
#
and
B
s
mixing
@
4
#
measurements at the CERN
e
1
e
2
LEP and Col-
lider Detector at Fermilab
~
CDF
!
.
In this paper, we report a direct and model independent
measurement of the
D
s
inclusive
f
branching fraction using
the BES detector at the Beijing Electron Positron Collider
~
BEPC
!
. The data were obtained using the BES detector, and
correspond to a total integrated luminosity of 22.3 pb
2
1
as
determined by large angle Bhabha scattering events at a
center-of-mass energy of 4.03 GeV. This is just above
e
1
e
2
!
D
s
1
D
s
2
threshold.
The BES detector is a conventional cylindrical detector,
which is described in detail in Ref.
@
5
#
. A four-layer central
drift chamber
~
CDC
!
surrounding the beampipe provides
*
Present address: Northeastern University, Boston, MA.
PHYSICAL REVIEW D
1 JANUARY 1998
VOLUME 57, NUMBER 1
57
0556-2821/97/57
~
1
!
/28
~
5
!
/$10.00
28
© 1997 The American Physical Society
trigger information. Outside the CDC, a forty-layer main
drift chamber
~
MDC
!
provides tracking and energy loss
(
dE
/
dx
) information on charged tracks over
;
85% of the
total
solid
angle.
The
momentum
resolution
is
s
p
/
p
5
0.017
A
1
1
p
2
(
p
in GeV/
c
) , and the energy loss
(
dE
/
dx
) resolution is
;
11% for hadron tracks and
;
8.5%
for Bhabha electrons. Scintillation counters that surround the
MDC provide time-of-flight
~
TOF
!
measurements with reso-
lutions of
;
450 ps for hadrons and
;
330 ps for Bhabha
events. Outside the TOF system, a 12-radiation-length, lead-
gas barrel shower counter
~
BSC
!
, operating in limited
streamer mode, measures the energies of electrons and pho-
tons over
;
80% of the total solid angle. Surrounding the
BSC, a solenoidal magnet provides a 0.4 T magnetic field in
the central tracking region of the detector. Three double-
layer muon counters
~
MUC
!
instrument the magnet flux re-
turn and serve to identify muons of momentum greater than
0.5 GeV/
c
. They cover
;
68% of the total solid angle with
longitudinal
~
transverse
!
spatial resolution of 5 cm
~
3cm
!
.
In this experiment, the
D
s
signal has been detected via
five hadronic decay modes:
D
s
1
!
f
p
1
,
K
̄
0
*
K
1
,
K
̄
0
K
1
,
f
0
p
1
or
K
0
K
2
p
1
p
1
. The subresonances are detected by
the decays
f
!
K
1
K
2
,
K
̄
0
*
!
K
2
p
1
,
K
̄
0
!
K
S
0
!
p
1
p
2
,
and
f
0
!
p
1
p
2
. Each candidate was formed using well-
reconstructed tracks. Each track’s closest approach to the
origin was required to be smaller than 1.2 cm in the
xy
plane
and 15 cm in the
z
direction. For the
f
0
p
mode, the vertex-
ing requirements were tightened to 0.65 cm in the
xy
plane
and9cminthe
z
direction due to larger backgrounds. Ver-
texing requirements were not applied to candidate pions
from
K
S
0
decay. The proper decay time of
K
S
0
candidates was
required to be between 0.01 and 0.33 ns. Additionally in the
K
0
K
2
p
1
p
1
mode, the
K
S
0
vertex was required to have the
difference between the
z
coordinates of the two tracks to be
within 4 cm, and the
xy
alignment of the parent momentum
with the line from the interaction point to the
K
S
0
vertex was
required to have a confidence level
.
5 %. A fiducial require-
ment,
u
cos
u
u
,
0.85 was used for charged tracks. Both TOF
and
dE
/
dx
systems were used to reduce background from
random combinations of different particles. Time-of-flight
and
dE
/
dx
information associated with each track was re-
quired to be consistent with the assigned mass interpretation
with a confidence level
.
1 % . Kaon candidates were re-
quired to have
x
2
(
K
)
,
x
2
(
p
) . Pion candidates were re-
quired
to
have
x
2
(
p
)
,
x
2
(
K
)
and
additionally
x
2
(
p
)
,
x
2
(
e
) for
f
0
p
1
candidates. Candidates for
f
,
K
̄
0
*
,
K
̄
0
, and
f
0
were required to be within 18, 60, 20, and 30
MeV/
c
2
, respectively, of the nominal mass.
Additional background rejection was obtained with helic-
ity angle cuts for the
f
and
K
̄
0
*
. We required
u
cos
u
K
u
.
0.25
in the
f
rest frame for the
f
p
mode and
u
cos
u
K
u
.
0.4 in the
K
̄
0
*
rest frame for the
K
̄
0
*
K
mode.
The production of
D
s
has a sin
2
u
distribution with respect
to the beam direction. In single tag modes with large back-
grounds, the signal-to-noise ratio can be improved by only
using tags with small values of cos
u
. We required
u
cos
u
D
s
u
,
0.7 for the
K
̄
0
*
K
1
mode, and
u
cos
u
D
s
u
,
0.85 for
both the
f
0
p
1
and the
K
̄
0
K
1
modes.
Candidates satisfying these criteria were subjected to a
one-constraint
~
1C
!
kinematic fit to the beam energy. Those
having a fit confidence level
.
1 % for
f
p
1
,
K
̄
0
*
K
1
and
K
̄
0
K
1
,
.
5 % for
K
0
K
2
p
1
p
1
, and
.
10% for
f
0
p
1
were
retained. The unbinned maximum likelihood fit to each
single tag plot
@
Figs. 1
~
a
!
–1
~
e
!#
gave the number of single
tag events (
N
sngl
i
) , and fitting to Fig. 1
~
f
!
gave a total of
166.4
6
31.8
D
s
single tags above background.
Double tagged
D
s
events were obtained by reconstructing
a
f
!
K
1
K
2
recoiling against one of the five
D
s
single tag
modes. Recoiling
f
’s were selected with the same track and
particle identification requirements described earlier for the
f
p
single tag mode.
f
candidates were required to be within
18 MeV/
c
2
of the
f
mass
~
3 times the resolution for the
reconstructed
f
mass
!
. A total of 3 double tag events
~
Fig. 2
!
were found, and the characteristics of these events are sum-
marized in Table I.
A direct measurement of
B
f
X
is obtained from the num-
ber of single tag events (
N
sngl
) , the number of double tag
events (
N
dbl
) , and the inclusive
f
efficiency (
e
dbl
) as fol-
lows:
B
f
X
5
N
dbl
N
sngl
3
e
dbl
3
B
~
f
!
K
1
K
2
!
.
~
1
!
The inclusive
f
double tag efficiency,
e
dbl
, was determined
using Monte Carlo simulation for each of the five modes
~
Table II
!
.
A
D
s
tag side band method was used to estimate the back-
ground in the double tag sample. As consistency checks
three different methods were used in the background estima-
tion: recoil
f
side band method, tag subresonance side band
method, and Monte Carlo background studies.
The
D
s
tag side band regions
~
Fig. 2
!
were defined from
1.79–1.957 GeV/
c
2
and from 1.981–2.105 GeV/
c
2
. One
f
was found recoiling from a sideband of the
K
̄
0
*
K
1
tag. No
background event was detected in the
f
p
1
side band region.
For both
f
p
1
and
K
̄
0
*
K
1
channels, we have normalized
the tag side bands by the ratio of single tag events in the
signal and side band regions. Poisson errors for a single
event in the
K
̄
0
*
K
1
side band region implies an estimated
background of 0.13
2
0.04
1
0.30
. In order to express the uncertainty
of the
f
p
mode background, we have used the 84.1 % con-
fidence level upper limit for zero events giving 0.0
2
0.0
1
0.26
.
There is no background event from the the recoil
f
mass
side band
~
Fig. 2
!
method.
All analyses were repeated using the side bands of the tag
subresonances, 0.965–1.001 and 1.037–1.073 GeV/
c
2
for
f
,
0.712–0.832 and 0.952–1.072 GeV/
c
2
for
K
̄
*
0
, 0.4376–
0.4776 and 0.5176–0.5576 GeV/
c
2
for
K
̄
0
, 0.89–0.95 and
1.01–1.07 GeV/
c
2
for
f
0
. No event passed the selection cri-
teria, leading to an estimate of zero background events in our
double tag sample.
Finally, large Monte Carlo samples of
D
*
1
D
2
,
D
*
0
D
0
,
D
*
1
D
*
2
, and
D
*
0
D
*
0
were used to estimate backgrounds
from these sources. These samples correspond to 6.4, 5.9, 5.3
and 5.0 times the real data sample respectively. All Monte
Carlo background events in the double tag signal region were
rejected.
57
29
DIRECT MEASUREMENT OF
B
(
D
s
1
!
f
X
1
)
FIG. 1. Kinematically fit mass of
D
s
candidates. The curves are the result of unbinned fits to the data.
FIG. 2. Double tag candidates.
30
57
J. Z. BAI
et al.
Since there are no signal events in the
K
̄
0
K
1
,
f
0
p
1
, and
K
0
K
2
p
1
p
1
modes, the background estimates do not affect
the shape of the likelihood function.
Combining all four different methods gives estimated
backgrounds of 0.0
2
0.0
1
0.26
events for the
f
p
1
mode and
0.13
2
0.04
1
0.30
events for the
K
̄
0
*
K
mode. The background uncer-
tainties contribute
2
35.0
1
1.0
%
3
B
f
X
to the systematic error for
the branching fraction
B
f
X
.
The value of
B
f
X
is obtained using a maximum likelihood
method. The likelihood function,
L
i
~
B
f
X
,
N
sngl
i
;
e
dbl
i
,
N
dbl
i
,
N
bg
i
!
,
is constructed from Eq.
~
1
!
using a Poisson distribution to
describe the number of double tag events and a Gaussian
distribution to describe the single tag sample:
L
~
B
f
X
!
5
)
i
L
mar
i
~
B
f
X
!
,
~
2
!
where
i
refers to the single tag mode. The marginalized like-
lihood function for each of the five different
D
s
modes is
obtained by integrating out the single tag uncertainty:
L
mar
i
~
B
f
X
!
5
E
dN
̃
sngl
i
L
i
~
B
f
X
,
N
̃
sngl
i
!
3
exp
F
2
1
2
S
N
sngl
i
2
N
̃
sngl
i
d
N
sngl
i
D
2
G
A
2
p
d
N
sngl
i
.
The likelihood function
L
i
is given by
L
i
5
A
i
N
dbl
i
N
dbl
i
!
e
2
A
i
,
where
A
i
[
B
f
X
N
sngl
i
e
dbl
i
B
~
f
!
K
1
K
2
!
1
N
bg
i
.
The value of the likelihood function,
L
(
B
f
X
) , is shown in
Fig.
3.
The
maximum
likelihood
solution
is
B
f
X
5
( 17.8
2
7.2
1
15.1
) % , where the statistical errors are obtained
by integrating the function; the area under the curve between
the peak value and
2
1
s
(
1
1
s
) corresponds to 68% of the
total area below
~
above
!
the peak position.
Several systematic uncertainties affect this measurement.
The inclusive
f
efficiency,
e
dbl
, introduces a systematic er-
ror for
B
f
X
of 2.4 %
3
B
f
X
. The choice of a background
functional form and fit interval for the single tag sample
introduces a 2.0 %
3
B
f
X
uncertainty. Finally, the double
tag background estimate is responsible for a
2
35.0
1
1.0
%
3
B
f
X
un-
certainty. After combining the systematic errors in quadra-
ture, the final result for
B
f
X
is
TABLE III. Inclusive
f
decay modes of
D
s
~
PDG 1996
!
.
Decay mode
Branching fraction ( % )
G
i
/
G
f
p
D
s
1
!
f
e
1
n
1.9
6
0.5
0.54
6
0.05
D
s
1
!
fm
1
n
1.9
6
0.5
0.54
6
0.05
D
s
1
!
f
p
1
3.6
6
0.9
1.00
D
s
1
!
f
p
1
p
0
9
6
5
2.4
6
1.0
6
0.5
D
s
1
!
f
p
1
p
1
p
2
1.8
6
0.6
0.51
6
0.12
D
s
1
!
f
K
1
,
0.05
,
0.071
Total
18.2
6
5.2
5.0
6
1.0
6
0.5
TABLE I. Properties of the double tag candidates.
Event
1
2
3
Tagging
D
s
Decay
f
p
1
f
p
1
K
̄
0
*
K
1
Subsystem mass
~
GeV/
c
2
)
1.0090
1.0229
0.8345
D
s
invariant mass
~
GeV/
c
2
)
1.9723
1.9694
1.9678
1C
D
s
fitmass
~
GeV/
c
2
)
1.9662
1.9686
1.9684
Recoiled
f
mass
~
GeV/
c
2
)
1.0068
1.0306
1.0125
Number of visible charged tracks
6
5
6
Number of isolated showers
5
3
1
TABLE II. Result of the measurement.
Decay mode
N
sngl
i
N
dbl
i
e
dbl
i
N
bg
i
f
p
1
37.5
6
6.7
2
0.202
6
0.004
0.0
2
0.0
1
0.26
K
̄
0
*
K
1
66.3
6
14.3
1
0.200
6
0.005
0.13
2
0.04
1
0.30
K
̄
0
K
1
27.0
6
8.8
0
0.190
6
0.004
N/A
f
0
p
1
18.3
6
7.0
0
0.180
6
0.005
N/A
K
0
K
2
p
1
p
1
21.4
6
6.9
0
0.181
6
0.007
N/A
FIG. 3. The variation of the normalized likelihood function with
respect to
B
f
X
; the unshaded area under the curve denotes the 68%
confidence interval.
57
31
DIRECT MEASUREMENT OF
B
(
D
s
1
!
f
X
1
)
B
f
X
5
~
17.8
2
7.2
1
15.1
2
6.3
1
0.6
!
%.
This is a direct measurement of the
D
s
inclusive
f
branching
fraction that is model-independent. The present world aver-
age value from indirect or model-dependent procedures is
B
f
X
5
( 18.2
6
5.2) %
~
Table III
!
.
LEP experiments
@
3
#
and CDF
@
4
#
have used a theoreti-
cally inspired method to estimate
B
f
X
from
B
f
p
. The theo-
retical
D
s
1
branching fractions are evaluated from the BSW
model
@
6
#
, giving
B
(
D
s
1
!
f
X
1
)
5
~
4.84
6
0.51
!
b
s
@
7
#
,
where
b
s
is the measured branching fraction of
D
s
1
!
f
p
1
.
Using the Particle Data Group
~
PDG
!~
1996
!@
8
#
value yields
B
f
X
5
( 17.4
6
4.7) % .
A measurement of
B
f
p
can be obtained from
B
f
X
using
the sum of exclusive measurements shown in the Table III
under the assumption that no significant decays of the
D
s
to
f
remain unmeasured. Scaling
B
f
X
by the sum of the world
average values of
G
i
/
G
f
p
gives
B
f
p
5
( 3.6
2
1.6
1
3.1
2
1.3
1
0.4
) % . This
value
is
consistent
with
the
previous
BES
result
B
f
p
5
( 3.9
2
1.9
1
5.1
2
1.1
1
1.8
)%
@
1
#
.
We would like to thank the staffs of the BEPC accelerator
and the Computing Center at the Institute of High Energy
Physics
~
Beijing
!
. This work 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 Nos. 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
~
University of Hawaii
!
, DE-FG03-95ER40925
~
UT Dallas
!
;
by the U.S. National Science Foundation, Grant No.
PHY9203212
~
University of Washington
!
.
@
1
#
J. Z. Bai
et al.
, Phys. Rev. D
52
, 3781
~
1995
!
.
@
2
#
Throughout the paper, reference to a particular charge configu-
ration implies reference to the charge conjugate configuration
as well.
@
3
#
X. C. Lou, in
Proceeding of the Workshop on B Physics at
Hadron Accelerators
, Snowmass, Colorado, 1993, edited by C.
Shekhar Mishra and P. McBride
~
Fermilab, Batavia, 1994
!
.
@
4
#
John E. Skarha and A. Barry Wicklund, in
Proceeding of the
Workshop on B Physics at Hadron Accelerators
@
3
#
.
@
5
#
J. Z. Bai
et al.
, Nucl. Instrum. Methods Phys. Res. A
344
, 319
~
1994
!
;J.Z.Bai
et al.
, Phys. Rev. Lett.
69
, 3021
~
1992
!
.
@
6
#
M. Bauer, B. Stech, and M. Wirbel, Z. Phys. C
34
, 103
~
1987
!
.
@
7
#
P. Roudeau and A. Stocchi
~
unpublished
!
.
@
8
#
Particle Data Group, R. Barnett
et al.
, Review of Particle
Physics, Phys. Rev. D
54
,1
~
1996
!
.
32
57
J. Z. BAI
et al.