of 5
V
OLUME
80, N
UMBER
13
PHYSICAL REVIEW LETTERS
30 M
ARCH
1998
New Measurement of
B
!
D
p
p
Branching Fractions
G. Brandenburg,
1
R. A. Briere,
1
Y. S. Gao,
1
D. Y.-J. Kim,
1
R. Wilson,
1
H. Yamamoto,
1
T. E. Browder,
2
F. Li,
2
Y. Li,
2
J. L. Rodriguez,
2
T. Bergfeld,
3
B. I. Eisenstein,
3
J. Ernst,
3
G. E. Gladding,
3
G. D. Gollin,
3
R. M. Hans,
3
E. Johnson,
3
I. Karliner,
3
M. A. Marsh,
3
M. Palmer,
3
M. Selen,
3
J. J. Thaler,
3
K. W. Edwards,
4
A. Bellerive,
5
R. Janicek,
5
D. B. MacFarlane,
5
K. W. McLean,
5
P. M. Patel,
5
A. J. Sadoff,
6
R. Ammar,
7
P. Baringer,
7
A. Bean,
7
D. Besson,
7
D. Coppage,
7
C. Darling,
7
R. Davis,
7
N. Hancock,
7
S. Kotov,
7
I. Kravchenko,
7
N. Kwak,
7
S. Anderson,
8
Y. Kubota,
8
M. Lattery,
8
S. J. Lee,
8
J. J. O’Neill,
8
S. Patton,
8
R. Poling,
8
T. Riehle,
8
V. Savinov,
8
A. Smith,
8
M. S. Alam,
9
S. B. Athar,
9
Z. Ling,
9
A. H. Mahmood,
9
H. Severini,
9
S. Timm,
9
F. Wappler,
9
A. Anastassov,
10
S. Blinov,
10,
* J. E. Duboscq,
10
K. D. Fisher,
10
D. Fujino,
10,
R. Fulton,
10
K. K. Gan,
10
T. Hart,
10
K. Honscheid,
10
H. Kagan,
10
R. Kass,
10
J. Lee,
10
M. B. Spencer,
10
M. Sung,
10
A. Undrus,
10,
* R. Wanke,
10
A. Wolf,
10
M. M. Zoeller,
10
B. Nemati,
11
S. J. Richichi,
11
W. R. Ross,
11
P. Skubic,
11
M. Wood,
11
M. Bishai,
12
J. Fast,
12
E. Gerndt,
12
J. W. Hinson,
12
N. Menon,
12
D. H. Miller,
12
E. I. Shibata,
12
I. P. J. Shipsey,
12
M. Yurko,
12
L. Gibbons,
13
S. D. Johnson,
13
Y. Kwon,
13
S. Roberts,
13
E. H. Thorndike,
13
C. P. Jessop,
14
K. Lingel,
14
H. Marsiske,
14
M. L. Perl,
14
S. F. Schaffner,
14
D. Ugolini,
14
R. Wang,
14
X. Zhou,
14
T. E. Coan,
14
V. Fadeyev,
15
I. Korolkov,
15
Y. Maravin,
15
I. Narsky,
15
V. Shelkov,
15
J. Staeck,
15
R. Stroynowski,
15
I. Volobouev,
15
J. Ye,
15
M. Artuso,
16
A. Efimov,
16
F. Frasconi,
16
M. Gao,
16
M. Goldberg,
16
D. He,
16
S. Kopp,
16
G. C. Moneti,
16
R. Mountain,
16
S. Schuh,
16
T. Skwarnicki,
16
S. Stone,
16
G. Viehhauser,
16
X. Xing,
16
J. Bartelt,
17
S. E. Csorna,
17
V. Jain,
17
S. Marka,
17
A. Freyberger,
18
R. Godang,
18
K. Kinoshita,
18
I. C. Lai,
18
P. Pomianowski,
18
S. Schrenk,
18
G. Bonvicini,
19
D. Cinabro,
19
R. Greene,
19
L. P. Perera,
19
G. J. Zhou,
19
B. Barish,
20
M. Chadha,
20
S. Chan,
20
G. Eigen,
20
J. S. Miller,
20
C. O’Grady,
20
M. Schmidtler,
20
J. Urheim,
20
A. J. Weinstein,
20
F. Würthwein,
20
D. M. Asner,
21
D. W. Bliss,
21
W. S. Brower,
21
G. Masek,
21
H. P. Paar,
21
V. Sharma,
21
J. Gronberg,
22
T. S. Hill,
22
R. Kutschke,
22
D. J. Lange,
22
S. Menary,
22
R. J. Morrison,
22
H. N. Nelson,
22
T. K. Nelson,
22
C. Qiao,
22
J. D. Richman,
22
D. Roberts,
22
A. Ryd,
22
M. S. Witherell,
22
R. Balest,
23
B. H. Behrens,
23
K. Cho,
23
W. T. Ford,
23
H. Park,
23
P. Rankin,
23
J. Roy,
23
J. G. Smith,
23
J. P. Alexander,
24
C. Bebek,
24
B. E. Berger,
24
K. Berkelman,
24
K. Bloom,
24
D. G. Cassel,
24
H. A. Cho,
24
D. M. Coffman,
24
D. S. Crowcroft,
24
M. Dickson,
24
P. S. Drell,
24
K. M. Ecklund,
24
R. Ehrlich,
24
R. Elia,
24
A. D. Foland,
24
P. Gaidarev,
24
B. Gittelman,
24
S. W. Gray,
24
D. L. Hartill,
24
B. K. Heltsley,
24
P. I. Hopman,
24
J. Kandaswamy,
24
N. Katayama,
24
P. C. Kim,
24
D. L. Kreinick,
24
T. Lee,
24
Y. Liu,
24
G. S. Ludwig,
24
J. Masui,
24
J. Mevissen,
24
N. B. Mistry,
24
C. R. Ng,
24
E. Nordberg,
24
M. Ogg,
24,
J. R. Patterson,
24
D. Peterson,
24
D. Riley,
24
A. Soffer,
24
C. Ward,
24
M. Athanas,
25
P. Avery,
25
C. D. Jones,
25
M. Lohner,
25
C. Prescott,
25
J. Yelton,
25
and J. Zheng
25
(CLEO Collaboration)
1
Harvard University, Cambridge, Massachusetts 02138
2
University of Hawaii at Manoa, Honolulu, Hawaii 96822
3
University of Illinois, Champaign-Urbana, Illinois 61801
4
Carleton University, Ottawa, Ontario, Canada K1S 5B6
and the Institute of Particle Physics, Canada
5
McGill University, Montréal, Québec, Canada H3A 2T8
and the Institute of Particle Physics, Canada
6
Ithaca College, Ithaca, New York 14850
7
University of Kansas, Lawrence, Kansas 66045
8
University of Minnesota, Minneapolis, Minnesota 55455
9
State University of New York at Albany, Albany, New York 12222
10
Ohio State University, Columbus, Ohio 43210
11
University of Oklahoma, Norman, Oklahoma 73019
12
Purdue University, West Lafayette, Indiana 47907
13
University of Rochester, Rochester, New York 14627
14
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309
15
Southern Methodist University, Dallas, Texas 75275
16
Syracuse University, Syracuse, New York 13244
17
Vanderbilt University, Nashville, Tennessee 37235
18
Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
19
Wayne State University, Detroit, Michigan 48202
20
California Institute of Technology, Pasadena, California 91125
21
University of California, San Diego, La Jolla, California 92093
2762
0031-9007
y
98
y
80(13)
y
2762(5)$15.00
© 1998 The American Physical Society
V
OLUME
80, N
UMBER
13
PHYSICAL REVIEW LETTERS
30 M
ARCH
1998
22
University of California, Santa Barbara, California 93106
23
University of Colorado, Boulder, Colorado 80309-0390
24
Cornell University, Ithaca, New York 14853
25
University of Florida, Gainesville, Florida 32611
(
Received 25 June 1997
)
The decays
Y
s
4
S
d
!
B
B
, followed by
B
!
D
p
p
and
D
p
!
D
p
, permit reconstruction of all
kinematic quantities that describe the sequence without reconstruction of the
D
, with reasonably low
backgrounds. Using an integrated
e
1
e
2
luminosity of
3.1
fb
2
1
accumulated at the
Y
s
4
S
d
by the CLEO-
II detector, we report measurements of
B
s
B
0
!
D
p
1
p
2
d
s
2.81
6
0.11
6
0.21
6
0.05
d
3
10
2
3
and
B
s
B
2
!
D
p
0
p
2
d
s
4.34
6
0.33
6
0.34
6
0.18
d
3
10
2
3
.
[S0031-9007(98)05684-1]
PACS numbers: 13.25.Hw
The study of
B
decays to exclusively hadronic final
states has been limited because samples in available data
are small. In this paper, we employ a technique, a
“partial reconstruction,” that can increase the acceptance
of the sequence
Y
s
4
S
d
!
B
B
,
B
!
D
p
p
,
D
p
!
D
p
by
1 order of magnitude with respect to the more usual
technique, “full reconstruction,” where all particles in the
final state are reconstructed. For example, in a recent
analysis [1] using the latter technique, 248 out of
,
8700
possible
B
0
!
D
p
1
p
2
decays were reconstructed; in
this Letter, we report the reconstruction of
,
2600
B
0
!
D
p
1
p
2
from the same set of data. We report on the
measurement of two of the
B
!
D
p
p
branching fractions
with partial reconstruction, and we probe the factorization
hypothesis. The partial reconstruction might enable an
interesting sensitivity to a small
CP
asymmetry in
B
0
!
D
p
1
p
2
decays [2].
Both the CLEO [1,3] and ARGUS [4] collaborations
reported measurements of
B
!
D
p
p
based on the full
reconstruction technique. In the analysis of data presented
in this Letter, all kinematic quantities that describe the
decay chain
B
!
D
p
p
f
,
D
p
!
D
p
s
are reconstructed
from measurements of the three-momenta of the two
pions, one fast
s
p
f
d
and one slow
s
p
s
d
,
$
p
f
and
$
p
s
; the
D
from
D
p
decay is undetected, which yields an order of
magnitude increase in acceptance over full reconstruction,
and removes systematic uncertainty introduced by
D
branching fractions.
The basic idea was described in [5]: A
B
from
Y
s
4
S
d
decay is nearly at rest and the energy release in the
D
p
!
D
p
decay is small, so the decay products
p
s
and
p
f
are
nearly back to back. The smearing introduced in [5] by
neglect of the detailed kinematics of the decay sequence is
much larger than the smearing caused by errors in either
the measurement of the pion momenta, or by the error in
knowledge of the magnitude of the initial
B
momentum.
Complete evaluation of the detailed kinematics leads to a
significant improvement in the description of the shape of
the signal, the shape of the background, and rejection of
the background.
To fully describe the kinematics of the decay, 20
parameters are required: four for each four-vector of the
five particles
B
,
D
p
,
p
f
,
D
, and
p
s
. Energy-momentum
conservation can be applied twice, in the
B
!
D
p
p
f
and
D
p
!
D
p
s
decays, yielding eight equations; the
masses of the five particles can be assumed; and the
center-of-mass energy of the
e
1
e
2
collisions can be used
to obtain the magnitude of the three-momentum of the
initial
B
. The six free parameters that remain describe
the kinematics of the decay sequence. These can be
thought of as six angles: two that describe the
B
direction,
two angles
s
u
p
f
,
f
p
f
d
that describe the direction of the
p
f
in the
B
rest frame, and two angles
s
u
p
s
,
f
p
s
d
that
describe the direction of the
p
s
in the
D
p
rest frame.
We evaluate those six angles from the measurement of
the three components of the
p
f
momentum and the three
components of the
p
s
momentum.
The angles that provide effective discrimination be-
tween signal and background are
u
p
f
and
u
p
s
, for which
the explicit expressions are
cos
u
p
f
2b
B
s
E
p
f
2
E
p
D
p
d
2
P
p
f
1
j
$
p
f
j
2
2
j
P
D
p
j
2
2
g
2
B
b
B
M
B
P
p
f
and
(1)
cos
u
p
s
2b
D
p
s
E
p
s
2
E
p
D
d
2
P
p
s
1
j
$
p
s
j
2
2
j
P
D
j
2
2
g
2
D
p
b
D
p
M
D
p
P
p
s
,
(2)
where
E
p
f
,
E
p
D
p
, and
P
p
f
are the energy and momentum
of the
p
f
and
D
p
in the
B
center of mass;
E
p
s
,
E
p
D
,
and
P
p
s
are the energy and momentum of the
p
s
and
D
in the
D
p
center of mass;
g
B
s
D
p
d
,
b
B
s
D
p
d
, and
M
B
s
D
p
d
are the Lorentz factor, the velocity, and the mass of the
B
s
D
p
d
in the lab frame. The magnitude of the
D
p
and
D
momenta in the lab frame,
j
P
D
p
j
and
j
P
D
j
, are determined
by applying energy-momentum conservation in the decay
chain. For signal, the magnitudes of these cosines will
tend to fall into the “physical” region, less than one.
The signal distribution will be uniform in cos
u
p
f
(because
the
B
has spin 0), and as cos
2
u
p
s
(because the
D
p
has
helicity 0), before consideration of detector acceptance,
efficiency, and resolution. Detector resolution sometimes
pushes signal events into the “nonphysical” region, where
the magnitude of one or both of the cosines exceeds unity.
Backgrounds usually fall into the nonphysical region. The
variables cos
u
p
f
and cos
u
p
s
tend to depend linearly on
j
$
p
f
j
and
j
$
p
s
j
once the dependence of
j
P
D
p
j
and
j
P
D
j
on
these variables is included.
The angle between the plane of the
B
!
D
p
p
f
decay
and the plane of the
D
p
!
D
p
s
decay,
f
f
p
f
2f
p
s
,is
reconstructed in the following manner. In the lab frame,
2763
V
OLUME
80, N
UMBER
13
PHYSICAL REVIEW LETTERS
30 M
ARCH
1998
the
D
p
direction must lie on a small cone of angle
a
f
around the direction
opposite
to the
p
f
. Simultaneously,
the
D
p
must
also
lie on a second small cone of angle
a
s
around the direction of the
p
s
. The expressions for these
angles are
cos
a
f
M
2
B
2
M
2
D
p
2
M
2
p
2
j
P
D
p
jj
$
p
f
j
2
1
b
D
p
b
f
and
cos
a
s
2
M
2
D
p
1
M
2
p
2
M
2
D
2
j
P
D
p
jj
$
p
s
j
1
1
b
D
p
b
s
,
(3)
where the momenta and velocities are measured in the
lab frame. The decay kinematics limit
a
f
#
0.14
and
a
s
#
0.28
. Intersection of these two cones determines
the
D
p
directions, of which, in practice, there are two: a
so-called quadratic ambiguity. For both
D
p
directions,
cos
f
cos
d2
cos
a
f
cos
a
s
sin
a
f
sin
a
s
,
(4)
where
d
is the angle between
$
p
s
and the direction
opposite to
$
p
f
. For most signal events
j
cos
f
j
,
1
,or
“physical.” Signal events with imperfect measurement of
the pion momenta, as well as nonsignal events, can result
in
j
cos
f
j
.
1
, in most cases because
d.a
f
1a
s
.
The data used in this analysis were selected from
hadronic events produced in
e
1
e
2
annihilations at the
Cornell Electron Storage Ring (CESR). The data sample
consists of
3.1
fb
2
1
collected with the CLEO-II detector
[6] at the
Y
s
4
S
d
resonance (referred to as “on resonance”)
and
1.6
fb
2
1
at a center-of-mass energy just below the
threshold for production of
B
B
pairs (referred to as
“off resonance”). The on-resonance data correspond to
s
3.27
6
0.06
d
3
10
6
B
B
pairs. The off-resonance data
are used to model the background from non
-
B
B
decays.
Charged pions that are consistent with production at
the
e
1
e
2
annihilation position and that penetrate all
layers of the CLEO-II tracking system are identified by
means of time-of-flight, specific ionization, and shower
development in the CsI calorimeter and surrounding muon
identifier. Neutral pions are reconstructed primarily from
information in the CsI calorimeter [6].
Events with two pions are classified according to
the net charge, which is 0 or
6
1
for signal.
The
fast pion is charged, but the slow pion can be either
charged
s
p
2
f
p
1
s
d
or neutral
s
p
2
f
p
0
s
d
.
Only
D
p
6
de-
cays yield slow charged pions, but slow neutral pions
are produced from both
D
p
0
and
D
p
6
decays, and so
the
p
2
f
p
0
s
sample will contain contributions from both
B
0
!
D
p
1
p
2
and
B
2
!
D
p
0
p
2
. We further require
that events satisfy the “
D
p
cone overlap requirement”:
j
cos
d2
cos
a
f
cos
a
s
j
,
sin
a
f
sin
a
s
1
0.02
,
which
allows for detector resolution.
Some events satisfy all requirements two or more
times, usually through combinations of one fast pion
with several distinct slow pions. In signal Monte Carlo
studies, 5% (24%) of
p
2
f
p
1
s
s
p
2
f
p
0
s
d
events have more
than one possible slow charged (neutral) pion. In
p
2
f
p
0
s
events, we select the neutral pion whose mass is closest
to the nominal
p
0
mass and, in
p
2
f
p
1
s
events, the
two pion candidate with the smallest value of
j
cos
d2
cos
a
f
cos
a
s
j
is selected.
The dominant sources of background are non
-
B
B
events. The distribution of decay products in these events
tends to be jetlike, while, in
B
B
events, the decay products
tend to be distributed uniformly in angle. To suppress
non
-
B
B
events, each candidate event must satisfy
R
2
,
0.275
, where
R
2
is the ratio of the second Fox-Wolfram
moment to the zeroth moment [7]. We also reject events
where the momentum of any charged track exceeds the
maximum possible from a
B
decay,
2.45
GeV
y
c
.
To extract the branching fractions, we perform a two-
dimensional fit in cos
u
p
f
and cos
u
p
s
, where the fit region is
j
cos
u
p
f
j
,
1.65
and
2
1.6
,
cos
u
p
s
,
5.0
. The
p
2
f
p
1
s
and
p
2
f
p
0
s
data samples are fit simultaneously using
the
MINUIT
[8] program. The fitting function combines
contributions from the
B
!
D
p
p
signal, other
B
decays,
and a fixed amount of non
-
B
B
background as described
below.
The non
-
B
B
background shape and rate is determined
from a sample of off-resonance data that has been scaled
for the relative luminosities and cross sections between
the on-resonance and off-resonance data samples. The
cos
u
p
f
and cos
u
p
s
distributions in non
-
B
B
events are
primarily determined by the
p
f
and
p
s
momentum
spectra in those events. Additionally, the shape is affected
by the
D
p
cone overlap requirement, which admits the
most events when
a
s
is largest, which occurs roughly
when cos
u
p
s
̄
0
. The shape of the background is, thus,
roughly
~
sin
2
u
p
s
, which is the complement of the signal,
~
cos
2
u
p
s
.
A large sample of simulated
B
B
events shows that
this background is dominated by modes that are able
to produce a fast pion candidate, such as
B
!
D
s
6
,0
d
X
,
where the
X
system is predominantly
p
,
r
,or
mn
m
, and
the
D
s
6
,0
d
can be in an excited state. The background
distribution in cos
u
p
f
is determined by the kinematics of
the fast pion from the
B
decay. Slow pions are plentiful
in these
B
B
background samples. When fast and slow
pion candidates come from different
B
’s, the resulting
distribution in cos
u
p
s
resembles the non
-
B
B
distribution.
When both candidates come from the same
B
decay, the
distribution in
u
p
s
and
u
p
f
is distinctive, but unlike that of
the signal: The branching ratios of modes that enter the
final sample in this manner are allowed to float in the final
fit, either constrained by a Gaussian to the central value
and error in [9] or left unconstrained, if no measurement
is available. The branching fractions used in the
p
2
f
p
1
s
and the
p
2
f
p
0
s
samples are constrained to be equal.
One
B
decay background mode is handled differently.
The Cabibbo-suppressed mode
B
!
D
p
K
is essentially
indistinguishable from
B
!
D
p
p
in the partial recon-
struction. We assume that the ratio of branching fractions,
B
s
B
!
D
p
K
dy
B
s
B
!
D
p
p
d
, is given by the ratio of the
decay constants for kaons and pions,
f
K
y
f
p
, the ratio of
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FIG. 1. The projections of the data histogram in cos
u
p
f
and
cos
u
p
s
with the fitting function for the
p
2
f
p
1
s
fit.
the CKM matrix elements,
V
us
y
V
ud
, and the ratio of form
factors. The product of these ratios is determined to be
s
7.69
6
0.08
d
%
[10,11]. The assumed
B
!
D
p
K
rate is
subtracted, with adjustment for acceptance.
The projections of the data and the fitting function in
cos
u
p
f
and cos
u
p
s
are shown in Fig. 1 for the
p
2
f
p
1
s
fit
and in Fig. 2 for the
p
2
f
p
0
s
fit. The sidebands outside of
the signal region tend to determine the background nor-
malization, and are fitted well by the background func-
tions. The sharp turn-on of signal at
6
1
can be seen while
the background distribution in cos
u
p
s
shows the expected
peaking in the signal region due to the
D
p
cone overlap
requirement. The confidence level for the
p
2
f
p
1
s
s
p
2
f
p
0
s
d
fit alone is 29% (2%). No structure is observed in the
residuals of the fit and confidence level for the combined
fit is 3%. The fitted number of signal events is given
in Table I along with the product of acceptance and effi-
ciency and the relevant
D
p
branching fraction. The back-
ground subtracted plots for the
p
2
f
p
1
s
and
p
2
f
p
0
s
fits for
the cos
u
p
s
projection are shown in Fig. 3. The peaks are
asymmetric because the acceptance functions for charged
and neutral slow pions have momentum dependences.
The systematic uncertainty was determined to be 7.5%
for
B
0
!
D
p
1
p
2
and 8.3% for
B
2
!
D
p
0
p
2
. The
error is dominated by uncertainties in the slow pion
reconstruction efficiency,
B
decay background shape, and
simulation of the
R
2
requirement. Additional errors come
from the uncertainty in the number of
B
B
pairs produced,
signal shape smearing. Monte Carlo statistics, and the
simulation of cos
d
.
To convert from fitted yields to branching fractions,
we use the value of
s
3.27
6
0.06
d
3
10
6
B
B
pairs pro-
duced and assume that the ratio of
B
1
B
2
to
B
0
B
0
pro-
duction
s
f
12
y
f
00
d
is one. This is in agreement with the
FIG. 2. The projections of the data histogram in cos
u
p
f
and
cos
u
p
s
with the fitting function for the
p
2
f
p
0
s
fit.
current CLEO measurement of
f
12
t
B
6
y
f
00
t
B
0
1.15
6
0.17
6
0.06
[12] and the value [9] for the ratio of life-
times
t
B
6
y
t
B
0
1.03
6
0.06
. We find
B
s
B
0
!
D
p
1
p
2
d
s
2.81
6
0.11
6
0.21
6
0.05
d
3
10
2
3
,
(5)
B
s
B
2
!
D
p
0
p
2
d
s
4.34
6
0.33
6
0.34
6
0.18
d
3
10
2
3
,
(6)
where the first error is statistical, the second is systematic,
and the third comes from the uncertainty in the
D
p
!
D
p
branching fractions.
To compare with the factorization hypothesis [13], we
take the ratio of charged to neutral branching fractions,
in which the systematic uncertainties due to the number
of
B
B
events, the
R
2
requirement, and the fast pion
reconstruction cancel. The ratio is measured to be
r
1.55
6
0.14
6
0.15
.
An implementation of the factorization hypothesis [14]
predicts that
r
is equal to
s
1
1
1.29
a
2
y
a
1
d
2
. The coeffi-
cient
a
1
̄
1
describes the “external spectator amplitude,”
where the
W
hadronizes to a single pion, and
a
2
describes
TABLE I. The yield of signal events from the fits. The
D
p
branching fractions are not included in the calculation of accep-
tance (acc.) times efficiency (eff.).
Mode
Yield
acc.
3
eff.
B
s
D
p
!
D
p
d
B
0
!
D
p
1
p
2
;
D
p
1
!
D
0
p
1
2612
6
102
0.42
68.3%
B
0
!
D
p
1
p
2
;
D
p
1
!
D
1
p
0
513
6
21
0.18
30.6%
B
2
!
D
p
0
p
2
;
D
p
0
!
D
0
p
0
1560
6
115
0.18
61.9%
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FIG. 3. The background-subtracted projections of the data
histogram in cos
u
p
s
for the
p
2
f
p
1
s
and
p
2
f
p
0
s
fits. The dashed
line is the signal shape.
the internal, color-suppressed amplitudes, and is expected
to be rather smaller than 1. The measurement of
r
yields
a
2
y
a
1
of
0.19
6
0.04
6
0.05
. Another ratio,
B
s
B
0
!
D
p
0
p
0
dy
B
s
B
0
!
D
p
1
p
2
d
, is given by
0.84
3
s
a
2
y
a
1
d
2
using the same model. From the results quoted above, the
factorization hypothesis predicts, in the absence of final
state interactions,
B
s
B
0
!
D
p
0
p
0
d
8.5
6
10
2
5
, about
5 times smaller than the current [15] experimental limit.
We searched for the suppressed modes which produce
a fast neutral pion. In
p
0
f
p
1
s
events, no signal was
observed. The confidence level of the fit was 73%,
indicating good agreement between the background shape
and the data. We limit the doubly CKM-suppressed mode
to
B
s
B
2
!
D
p
2
p
0
d
,
1.7
3
10
2
4
at 90% confidence
level. For internal color-suppressed modes, the superior
background rejection of the full reconstruction technique
[15] leads to better sensitivity, except in the case of
B
0
!
D
p
0
h
0
. We set a limit of
B
s
B
0
!
D
p
0
h
0
d
,
14
3
10
2
4
at 90% confidence level. The confidence level of the fit
was 10%.
We gratefully acknowledge the effort of the CESR
staff in providing us with excellent luminosity and
running conditions. This work was supported by the
National Science Foundation, the U.S. Department of
Energy, the Heisenberg Foundation, the Alexander von
Humboldt Stiftung, Research Corporation, the Natural
Sciences and Engineering Research Council of Canada,
and the A. P. Sloan Foundation.
*Permanent address: BINP, RU-630090 Novosibirsk,
Russia.
Permanent
address:
Lawrence
Livermore
National
Laboratory, Livermore, CA 94551.
Permanent address: University of Texas, Austin, TX
78712.
[1] B. Barish
et al.,
contribution to the 1997 European
Physical Society Meeting, Jerusalem, Report No. CLEO
CONF 97-01, 1997 (unpublished).
[2] R. G. Sachs, Report No. EFI-85-22, 1985 (unpublished);
R. G. Sachs,
The Physics of Time Reversal
(University of
Chicago, Chicago, IL, 1987), pp. 257 – 261; I. I. Bigi and
A. I. Sanda, Nucl. Phys.
B281
, 41 (1987); I. Dunietz and
R. G. Sachs, Phys. Rev. D
37
, 3186 (1988).
[3] CLEO Collaboration, M. S. Alam
et al.,
Phys. Rev. D
50
,
43 (1994).
[4] ARGUS Collaboration, H. Albrecht
et al.,
Z. Phys. C
48
,
543 (1990).
[5] CLEO Collaboration, R. Giles
et al.,
Phys. Rev. D
30
,
2279 (1984).
[6] CLEO Collaboration, Y. Kubota
et al.,
Nucl. Instrum.
Methods Phys. Res., Sect. A
320
, 66 (1992).
[7] G. C. Fox and S. Wolfram, Phys. Rev. Lett.
41
, 1581
(1978).
[8] I. Brock, A Fitting and Plotting Package Using MINUIT,
CLEO/CSN Note 245-B, Revised (1992) (unpublished);
F. James, MINUIT, Function Minimization and Error
Analysis, CERN Program Library Long Writeup D506,
1994 (unpublished).
[9] R. M. Barnett
et al.,
Phys. Rev. D
54
, 488 – 506 (1996).
[10] R. M. Barnett
et al.,
Phys. Rev. D
54
, 94 (1996);
54
, 319
(1996).
[11] M. Neubert and B. Stech, Report No. hep-ph/9705292
[
Heavy Flavours,
edited by A. J. Buras and M. Linder
(World Scientific, Singapore, to be published), 2nd ed.].
[12] CLEO Collaboration, C. S. Jessop
et al.,
Phys. Rev. Lett.
79
, 4533 (1997).
[13] M. Bauer, B. Stech, and M. Wirbel, Z. Phys. C
29
, 637
(1985).
[14] M. Neubert, V. Rieckert, B. Stech, and Q. P. Xu, in
Heavy
Flavours,
edited by A. J. Buras and H. Lindner (World
Scientific, Singapore, 1992).
[15] CLEO Collaboration, B. Nemati
et al.,
Report No. CLNS
97/1503 (to be published).
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