of 13
Measurements of
B
ò
D
s
1
X
decays
D. Gibaut, K. Kinoshita, and P. Pomianowski
Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
B. Barish, M. Chadha, S. Chan, D. F. Cowen, G. Eigen, J. S. Miller, C. O’ Grady, J. Urheim, A. J. Weinstein, and
F. Wu
̈
rthwein
California Institute of Technology, Pasadena, California 91125
D. M. Asner, M. Athanas, D. W. Bliss, W. S. Brower, G. Masek, and H. P. Paar
University of California, San Diego, La Jolla, California 92093
J. Gronberg, C. M. Korte, R. Kutschke, S. Menary, R. J. Morrison, S. Nakanishi, H. N. Nelson, T. K. Nelson, C. Qiao,
J. D. Richman, D. Roberts, A. Ryd, H. Tajima, and M. S. Witherell
University of California, Santa Barbara, California 93106
R. Balest, K. Cho, W. T. Ford, M. Lohner, H. Park, P. Rankin, and J. G. Smith
University of Colorado, Boulder, Colorado 80309-0390
J. P. Alexander, C. Bebek, B. E. Berger, K. Berkelman, K. Bloom, T. E. Browder,
*
D. G. Cassel, H. A. Cho,
D. M. Coffman, D. S. Crowcroft, M. Dickson, P. S. Drell, D. J. Dumas, R. Ehrlich, R. Elia, P. Gaidarev, M. Garcia-Sciveres,
B. Gittelman, S. W. Gray, D. L. Hartill, B. K. Heltsley, S. Henderson, C. D. Jones, S. L. Jones, J. Kandaswamy,
N. Katayama, P. C. Kim, D. L. Kreinick, T. Lee, Y. Liu, G. S. Ludwig, J. Masui, J. Mevissen, N. B. Mistry, C. R. Ng,
E. Nordberg, J. R. Patterson, D. Peterson, D. Riley, and A. Soffer
Cornell University, Ithaca, New York 14853
P. Avery, A. Freyberger, K. Lingel, J. Rodriguez, S. Yang, and J. Yelton
University of Florida, Gainesville, Florida 32611
G. Brandenburg, D. Cinabro, T. Liu, M. Saulnier, R. Wilson, and H. Yamamoto
Harvard University, Cambridge, Massachusetts 02138
T. Bergfeld, B. I. Eisenstein, J. Ernst, G. E. Gladding, G. D. Gollin, M. Palmer, M. Selen, and J. J. Thaler
University of Illinois, Champaign-Urbana, Illinois 61801
K. W. Edwards, K. W. McLean, and M. Ogg
Carleton University, Ottawa, Ontario, Canada K1S 5B6 and the Institute of Particle Physics, Canada
A. Bellerive, D. I. Britton, E. R. F. Hyatt, R. Janicek, D. B. MacFarlane, P. M. Patel, and B. Spaan
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8 and the Institute of Particle Physics, Canada
A. J. Sadoff
Ithaca College, Ithaca, New York 14850
R. Ammar, P. Baringer, A. Bean, D. Besson, D. Coppage, N. Copty, R. Davis, N. Hancock, M. Kelly, S. Kotov,
I. Kravchenko, N. Kwak, and H. Lam
University of Kansas, Lawrence, Kansas 66045
Y. Kubota, M. Lattery, M. Momayezi, J. K. Nelson, S. Patton, R. Poling, V. Savinov, S. Schrenk, and R. Wang
University of Minnesota, Minneapolis, Minnesota 55455
M. S. Alam, I. J. Kim, Z. Ling, A. H. Mahmood, J. J. O’Neill, H. Severini, C. R. Sun, and F. Wappler
State University of New York at Albany, Albany, New York 12222
G. Crawford, R. Fulton, D. Fujino, K. K. Gan, K. Honscheid, H. Kagan, R. Kass, J. Lee, M. Sung, C. White, A. Wolf, and
M. M. Zoeller
Ohio State University, Columbus, Ohio 43210
PHYSICAL REVIEW D
1 MAY 1996
VOLUME 53, NUMBER 9
53
0556-2821/96/53
~
9
!
/4734
~
13
!
/$10.00
4734
© 1996 The American Physical Society
X. Fu, B. Nemati, W. R. Ross, P. Skubic, and M. Wood
University of Oklahoma, Norman, Oklahoma 73019
M. Bishai, J. Fast, E. Gerndt, J. W. Hinson, R. L. McIlwain, T. Miao, D. H. Miller, M. Modesitt, D. Payne, E. I. Shibata,
I. P. J. Shipsey, and P. N. Wang
Purdue University, West Lafayette, Indiana 47907
L. Gibbons, Y. Kwon, S. Roberts, and E. H. Thorndike
University of Rochester, Rochester, New York 14627
T. E. Coan, J. Dominick, V. Fadeyev, I. Korolkov, M. Lambrecht, S. Sanghera, V. Shelkov, T. Skwarnicki, R. Stroynowski,
I. Volobouev, and G. Wei
Southern Methodist University, Dallas, Texas 75275
M. Artuso, M. Gao, M. Goldberg, D. He, N. Horwitz, G. C. Moneti, R. Mountain, F. Muheim, Y. Mukhin, S. Playfer,
Y. Rozen, S. Stone, X. Xing, and G. Zhu
Syracuse University, Syracuse, New York 13244
J. Bartelt, S. E. Csorna, Z. Egyed, and V. Jain
Vanderbilt University, Nashville, Tennessee 37235
~
CLEO Collaboration
!
~
Received 19 October 1995
!
This paper describes new measurements from CLEO of the inclusive
B
!
D
s
1
X
branching fraction as well as
the
B
1
!
D
s
(
*
)
1
D
̄
(
*
)
0
and
B
0
!
D
s
(
*
)
1
D
(
*
)
2
branching fractions. The inclusive branching fraction is
B
(
B
!
D
s
1
X
)
5
(12.11
6
0.39
6
0.88
6
1.38)% where the first error is statistical, the second is the systematic
error, and the third is the error due to the uncertainty in the
D
s
1
!
f
p
1
branching fraction. The branching
fractions for the
B
!
D
s
(
*
)
1
D
̄
(
*
)
modes are found to be between 0.9% and 2.4% and are significantly more
precise than previous measurements. The sum of the
B
!
D
s
(
*
)
1
D
̄
(
*
)
branching fractions is consistent with the
results of fits to the inclusive
D
s
1
momentum spectrum. Factorization is used to arrive at a value for
f
D
s
, the
D
s
1
decay constant.
PACS number
~
s
!
: 13.25.Hw
I. INTRODUCTION
The large samples of
B
mesons being collected by experi-
mental groups at
e
1
e
2
and hadron colliders have allowed
for ever more precise measurements of
B
meson decay prop-
erties. Theoretical calculations are unable to simultaneously
describe the total inclusive
B
to charm rate and the semilep-
tonic branching fraction of the
B
meson
@
1
#
. It has been
conjectured that
b
quark to charm quark transitions where
the
W
1
materializes as
c
̄
s
are large
@
2
#
. The external spec-
tator
B
meson decay diagram, shown in Fig. 1, leads to a
D
s
(
*
)
1
in the final state whereas the internal
W
1
decay dia-
gram results in the production of charmonium
@
3
#
. This paper
reports new measurements of
B
!
D
s
1
X
decays from CLEO.
1
After a short description of the detector and the criteria
used to select neutral and charged particle candidates, there
are two sections dealing with the measurements of the inclu-
sive
B
!
D
s
1
X
branching fraction and the exclusive
B
!
D
s
(
*
)
1
D
̄
(
*
)
branching fractions. Under the assumption
that the charged and neutral
B
decay rates and lifetimes are
equal, the charged and neutral
B
branching fractions are av-
eraged and compared with theoretical predictions. This is
followed by a discussion of a fit to the inclusive
D
s
1
momen-
tum spectrum. The final section describes two methods using
factorization to extract
f
D
s
, the
D
s
1
decay constant.
II. EVENT AND TRACK SELECTION
The data used in this analysis were selected from hadronic
events produced in
e
1
e
2
annihilations at the Cornell Elec-
tron Storage Ring
~
CESR
!
. The data sample consists of an
integrated luminosity of 2.03
6
0.04 fb
2
1
collected at the
Y
(4S) resonance
~
referred to as on-resonance data
!
and
0.97
6
0.02 fb
2
1
at a center-of-mass energy just below the
*
Permanent address: University of Hawaii at Manoa.
1
Reference to a specific state or decay means that the charge-
conjugate state or decay has been included. The notation
D
s
1
(
*
)
in
this context means either
D
s
1
or
D
s
*
1
.In
B
!
D
s
(
*
)
1
D
̄
(
*
)
,
D
̄
is a
generic representation of the
c
̄
q
mesons, the
D
2
and
D
̄
0
, while the
symbol (
!
) implies that the branching fraction for both the nonex-
cited and excited states of the meson were separately measured.
FIG. 1. The spectator diagram for
B
!
D
s
(
*
)
1
D
̄
(
*
)
decay.
53
4735
MEASUREMENTS OF
B
!
D
s
1
X
DECAYS
threshold for producing
BB
̄
mesons
~
referred to as off-
resonance or continuum data
!
. The on-resonance data corre-
sponds to (2.19
6
0.04)
3
10
6
BB
̄
pairs.
The CLEO II detector measures both neutral and charged
particles with excellent resolution and efficiency
@
4
#
. Had-
ronic events are selected by requiring a minimum of three
charged tracks, a total visible energy greater than 15% of the
center-of-mass energy
~
this reduces contamination from two-
photon interactions and beam-gas events
!
, and a primary ver-
tex within
6
5cminthe
z
direction and
6
2cminthe
r
-
f
plane of the nominal collision point. Since the
B
mesons are
produced almost at rest, their decay products are uniformly
distributed throughout the volume of the detector leading to
events that tend to be ‘‘spherical’’ in shape. Continuum
e
1
e
2
!
qq
̄
(
q
5
u
,
d
,
s
,
c
) events are more jetlike in struc-
ture. The shape variable
R
2
, which is the ratio of the second
Fox-Wolfram moment to the zeroth moment
@
5
#
, is found to
be useful in discriminating between
BB
̄
events and those in
which lighter mass quarks are produced. Only events with
R
2
,
0.35 are used in this analysis.
All charged tracks are required to be consistent with hav-
ing originated from within
6
5cminthe
z
direction and
6
5mminthe
r
-
f
plane of the primary vertex. Tracks are
also required to have
dE
/
dx
information which is consistent
with the proposed particle hypothesis.
III. THE INCLUSIVE
B
ò
D
s
1
X
BRANCHING FRACTION
The
D
s
1
mesons in the on-resonance data set originate
from
B
meson decays and from continuum production via
e
1
e
2
!
cc
̄
. Therefore, in order to measure
B
(
B
!
D
s
1
X
), it
is necessary to subtract the continuum contribution from the
total yield of
D
s
1
mesons in the on-resonance data set.
The
D
s
1
!
f
p
1
,
f
!
K
1
K
2
decay channel was chosen
for the inclusive
B
!
D
s
1
X
measurement because it offers the
best combination of detection efficiency, branching fraction,
and signal to background ratio. The
K
1
K
2
invariant mass is
required to be within 10 MeV of the
f
mass. Two angles are
useful for suppressing background:
~
1
!
the
f
helicity angle
u
H
, which is the angle in the
f
rest frame between the
direction of the
K
1
and the
D
s
1
direction, and
~
2
!
the
D
s
1
decay angle
u
D
, which is the angle in the
D
s
1
rest frame
between the
f
direction and
D
s
1
direction in the lab frame.
The signal follows a cos
2
u
H
distribution while the back-
ground is flat in cos
u
H
so requiring
u
cos
u
H
u
.
0.35 eliminates
35% of the background events while retaining 96% of the
signal. The cos
u
D
distribution for the signal is flat. The
cos
u
D
,
0.75 requirement suppresses combinatorial back-
ground from abundant low momentum pions that peaks near
cos
u
D
5
1.
The efficiency of these selection criteria is calculated
from a Monte Carlo simulation. Figure 2 shows the
D
s
1
de-
tection efficiency as a function of
x
, the scaled
D
s
1
momen-
tum, where
x
[
p
D
s
1
/
p
max
and
p
max
5
A
E
beam
2
2
m
D
s
1
2
. The
end point for
D
s
1
mesons produced in
B
decay is
x
5
0.46.
The on-resonance yield of
D
s
1
mesons as a function of
scaled momentum is extracted by fitting the
f
p
1
-invariant
mass plot in bins of
x
. The bin size of 0.03 is an order of
magnitude larger than the resolution in
x
. The fitting func-
tion consists of a straight line parametrization of the combi-
natorial background and a Gaussian describing the signal.
The width of the Gaussian is fixed to the value found from
fitting the Monte Carlo sample. The rms resolution increases
linearly with momentum from 6 MeV at low momentum to 8
MeV as
x
approaches 1. The
D
s
1
mass was allowed to vary
as a function of momentum in a first pass of fitting to the
data and then was fixed to the average value of 1.9686 GeV
in the final pass. For illustration purposes, the
f
p
1
mass
spectra and resultant fits for an
x
bin width of 0.07 are shown
in Fig. 3. The
D
s
1
momentum spectrum before efficiency
correction is shown in Fig. 4.
The fact that there are no
D
s
1
mesons from
B
decay with
x
.
0.5 is used to create a continuum momentum spectrum
with maximum statistics. The momentum spectrum for
continuum-produced
D
s
1
mesons is constructed from the
sum of the on- and off-resonance data for
x
.
0.5 and only
the off-resonance data, scaled by the ratio of on/off luminosi-
ties, for
x
,
0.5. The number of
D
s
1
mesons per momentum
bin for this ‘‘constructed’’ continuum data sample is ex-
FIG. 2. The efficiency for reconstructing
D
s
1
!
f
p
1
,
f
!
K
1
K
2
as a function of scaled
D
s
1
momentum for the selection
criteria described in the text. The curve is the result of fitting a 2nd
order polynomial to the data points.
FIG. 3. The
f
p
1
mass spectra for the on-resonance
~
points with
error bars
!
and unscaled off-resonance
~
hatched histogram
!
data sets
in
x
bins of 0.07 from
~
a
!
0.0
<
x
,
0.07 to
~
h
!
0.49
<
x
,
0.56.
4736
53
D. GIBAUT
et al.
tracted in the same manner as described above. The resulting
continuum
D
s
1
momentum spectrum, properly rescaled, is
shown in Fig. 4. It is fit with a function that was found to
describe the Monte Carlo continuum
D
s
1
momentum spec-
trum. The values of this function, also shown in Fig. 4, are
subtracted, bin by bin, from the on-resonance
D
s
1
momen-
tum spectrum to give the raw
~
i.e., not efficiency corrected
!
yield of 2537
6
83
D
s
1
mesons produced in
B
decays.
Figure 5 shows the
D
s
1
momentum spectrum after con-
tinuum subtraction and correction for detection efficiency.
From the total yield of 9111
6
299
D
s
1
mesons from
B
decay,
the inclusive branching fraction is calculated to be
B
~
B
!
D
s
1
X
!
5
F
~
12.11
6
0.39
6
0.88
!
3
S
3.5
6
0.4%
B
~
D
s
1
!
f
p
1
!
D
G
%,
where the first error is statistical, the second is the systematic
error, and the third error is due to the uncertainty in the
D
s
1
!
f
p
1
branching fraction
@
6
#
. This value for
B
(
B
!
D
s
1
X
) is larger than the previous CLEO and
ARGUS measurements shown in Table I.
The largest error in the measurement is the 11% uncer-
tainty in the
D
s
1
!
f
p
1
branching fraction. This error is
displayed separately to distinguish it from the 7.2% system-
atic error associated with detector effects and the analysis
method. The contributions to the systematic error are listed
in Table II. The uncertainties in the number of
BB
̄
pairs and
in the
f
!
K
1
K
2
branching fraction are included but the
dominant source is the uncertainty in the tracking efficiency.
A 2% per track uncertainty in the track finding efficiency
FIG. 4. The on-resonance
~
solid dots
!
and scaled ‘‘constructed’’
continuum
~
open circles
!
D
s
1
momentum spectra before efficiency
correction. The function is the result of the fit described in the text.
FIG. 5. The continuum-subtracted, efficiency-corrected yield of
D
s
1
mesons as a function of
x
.
TABLE I. Measurements of
B
(
B
!
D
s
1
X
). The first error is sta-
tistical and the second is the systematic error. A value of
B
(
D
s
1
!
f
p
1
)
5
(3.5
6
0.4)% is common to all measurements so
the error on this quantity is not included in the systematic errors.
Experiment
B
(
B
!
D
s
1
X
)
CLEO II
(12.11
6
0.39
6
0.88) %
ARGUS
~
92
!@
7
#
(8.34
6
1.11
6
0.89) %
CLEO-1.5
@
8
#
(8.74
6
1.31
6
0.86) %
ARGUS
~
87
!@
9
#
(12.1
6
3.4) %
CLEO-I
@
10
#
(10.9
6
2.9) %
TABLE II. Systematic errors for
B
(
B
!
D
s
1
X
).
Source
Error
~
%
!
Signal shape
1.46
Background shape
0.36
Continuum subtraction
0.30
x
dependence of the efficiency
1.97
Bin width
0.99
f
mass interval
0.52
Particle identification criteria
0.67
R
2
0.72
Track quality criteria
0.27
Angular selection criteria
1.12
Monte Carlo statistics
0.29
Total for
D
s
1
yield
3.14
B
(
f
!
K
1
K
2
)
1.83
Number of
BB
̄
1.80
Tracking efficiency
6.00
Total systematic error
7.24
53
4737
MEASUREMENTS OF
B
!
D
s
1
X
DECAYS
results in a 6% systematic error for the
D
s
1
!
f
p
1
,
f
!
K
1
K
2
decay chain. The other sources of systematic er-
ror on the
D
s
1
yield listed in Table II contribute 3.1% to the
total systematic error.
IV. EXCLUSIVE
B
ò
D
S
Ñ
*
Ö
1
D
̄
Ñ
*
Ö
DECAYS
The near hermeticity of the CLEO II detector coupled
with its excellent photon detection and charged particle re-
construction capabilities allow for the reconstruction of all
eight
B
0
!
D
s
(
*
)
1
D
(
*
)
2
and
B
1
!
D
s
(
*
)
1
D
̄
(
*
)0
modes. The
D
s
(
*
)
1
and
D
(
*
)
decay channels used, the mass selection
criteria, and the assumed branching fractions, are given in
Tables III and IV. The allowed mass intervals correspond to
2.5 standard deviations for channels where the mass resolu-
tion dominates the observed width, and to one natural width
otherwise. The
D
s
1
and
D
0
branching fractions are given
relative to those for the two normalizing modes:
D
s
1
!
f
p
1
and
D
0
!
K
2
p
1
. The values for all absolute
branching fractions and relative branching ratios are taken
from
@
6
#
except for
B
(
D
0
!
K
2
p
1
)
@
11
#
,
B
(
D
1
!
K
2
p
1
p
1
)/
B
(
D
0
!
K
2
p
1
)
@
12
#
, and the
D
*
branching fractions
@
13
#
, where CLEO measurements are
used since they dominate the world average and their use
allows for the cancellation of some common systematic er-
rors.
The data sample and the event selection criteria are the
same as were used in the inclusive analysis. The track quality
criteria are also the same except for the ‘‘slow’’
p
1
from
D
*
1
!
D
0
p
1
decays which has just the
r
-
f
distance of
closest approach requirement applied. Photon candidates are
required to have deposited more than 30 MeV of energy in
the calorimeter, to be isolated from charged tracks, and to
have a lateral energy deposition consistent with that expected
for a photon. Photons used for reconstructing the
D
s
*
1
!
D
s
1
g
decay chain have a minimum energy require-
ment of 90 MeV and must have been detected within the
‘‘barrel’’ region of the detector, defined by
u
cos
u
u
,
0.707
where
u
is the angle between the photon momentum vector
and the
z
axis. For
p
0
or
h
mesons, one of the daughter
photons can be from outside of the barrel where the mini-
mum photon energy requirement is raised to 50 MeV.
The allowed mass intervals and branching fractions for
the various noncharmed resonances used in this analysis are
given in Table V. In
p
0
/
h
decays to two photons, the decay
angle
u
D
, which is the angle in the
p
0
/
h
rest frame between
the direction of one the photons and the
p
0
/
h
direction in
the lab frame, can be used to reduce combinatorial back-
ground from low energy photons. A
u
cos
u
D
u
,
0.9 criterion is
used.
Since the
Y
(4S) decays only to
BB
̄
, the
B
meson energy
is equal to the beam energy. This can be used to select
B
meson candidates by requiring that
D
E
, the difference be-
tween the measured sum of the charged and neutral energies
of the daughters of the
B
candidate and the beam energy, be
close to zero. The
D
s
(
*
)
1
and
D
(
*
)
candidates, as well as the
p
0
and
h
candidates, are kinematically fitted to their known
masses so as to improve the resolution in
D
E
. The
D
E
reso-
lution is about 10 MeV and is independent of decay mode
TABLE IV. The
D
(
*
)
mass intervals and branching fractions.
Decay mode
Mass or
D
M
interval
~
GeV
!
Branching fraction
D
*
1
!
D
0
p
1
0.1430
,
m
D
*
1
2
m
D
0
,
0.1480
0.681
6
0.010
D
*
0
!
D
0
p
0
0.1406
,
m
D
*
0
2
m
D
0
,
0.1446
0.636
6
0.023
D
0
!
K
2
p
1
1.8457
,
m
K
2
p
1
,
1.8833
0.0391
6
0.0008
Decay mode
Mass interval
~
GeV
!
B
/
B
(
D
0
!
K
2
p
1
)
D
0
!
K
2
p
1
p
0
1.8355
,
m
K
2
p
1
p
0
,
1.8935
3.43
6
0.24
D
0
!
K
2
p
1
p
2
p
1
1.849
,
m
K
2
p
1
p
2
p
1
,
1.8800
2.02
6
0.11
D
1
!
K
2
p
1
p
1
1.8530
,
m
K
2
p
1
p
1
,
1.8856
2.35
6
0.16
TABLE III. The
D
s
(
*
)
1
mass intervals and branching fractions.
Decay mode
Mass or
D
M
interval
~
GeV
!
Branching fraction
D
s
*
1
!
D
s
1
g
0.132
,
m
D
s
*
1
2
m
D
s
1
,
0.152
1.0
D
s
1
!
f
p
1
1.9542
,
m
f
p
1
,
1.9822
0.035
6
0.004
Decay mode
Mass interval
~
GeV
!
B
/
B
(
D
s
1
!
f
p
1
)
D
s
1
!
K
0
K
1
1.9532
,
m
K
S
0
K
1
,
1.9832
1.01
6
0.25
D
s
1
!
K
*
0
K
1
1.9530
,
m
K
*
0
K
1
,
1.9835
0.95
6
0.10
D
s
1
!
f
r
1
1.9442
,
m
f
r
1
,
1.9922
1.86
6
0.48
D
s
1
!
h
p
1
1.9374
,
m
h
p
1
,
1.9990
0.54
6
0.11
D
s
1
!
h
r
1
1.9338
,
m
h
r
1
,
2.0036
2.86
6
0.54
4738
53
D. GIBAUT
et al.
according to a Monte Carlo simulation of
B
!
D
s
(
*
)
1
D
̄
(
*
)
events.
2
All
B
candidates must have
u
D
E
u
<
25 MeV. In the
case of multiple candidates in a specific
B
meson decay
chain, only the candidate with the smallest absolute value of
D
E
is selected. The
B
mass resolution can be improved by
using the beam-constrained mass (
M
B
), defined by
M
B
2
5
E
beam
2
2
S
(
i
p
i
W
D
2
,
~
1
!
where
p
i
W
is the momentum of the
i
th daughter of the
B
candidate. The
M
B
resolution of about 2.6 MeV is deter-
mined by the beam energy spread and is a factor of 10 better
than the resolution in invariant mass obtained from simply
summing the four-momenta of the
B
daughters.
Two other useful variables are the
B
production angle
u
B
, which is the angle between the
B
meson direction in the
lab frame and the beam axis, and the sphericity angle
u
S
,
which is the angle between the sphericity axis of the particles
which form the
B
candidate and the sphericity axis of the
other particles in the event. For
B
mesons, the production
angle follows a sin
2
u
B
distribution whereas the continuum
background is flat in this variable. Conversely, continuum
events have large values of cos
u
S
whereas the signal is flat in
cos
u
S
. The production and sphericity angle criteria are
B
decay channel dependent because of differing background
levels. A helicity angle requirement is also used for the
D
s
1
D
̄
*
final states where the signal follows a cos
2
u
H
distri-
bution, and for the
D
s
*
1
D
̄
final states where the signal fol-
lows a sin
2
u
H
distribution. The values of the angular selec-
tion criteria used in the analysis are given in Table VI.
The beam-constrained mass plot for the sum of the eight
B
0
and
B
1
decay channels is shown in Fig. 6. The function
which is fitted to the data to extract the yield of
B
mesons
contains two parts:
~
1
!
a background function which is linear
for
M
B
,
5.282 GeV and parabolic, with a kinematic cutoff,
for larger values of
M
B
@
14
#
, and
~
2
!
a Gaussian to describe
the signal. The background function is forced to simulta-
neously fit the beam-constrained mass distribution for the
D
E
sideband, defined by 30
,
u
D
E
u
,
55 MeV, so as to better
constrain the shape of the background. This is essential for
some of the decay channels where the number of background
events is insufficient to constrain the background. The mass
and width from the fit to the sum of all modes are consistent
with those obtained from the Monte Carlo simulation. The
total in the peak is 171
6
18 events.
The beam-constrained mass plots for the individual
B
0
and
B
1
decay channels are shown in Figs. 7 and 8. The mass
and width for these fits are fixed to the value obtained from
the fit to the sum of all the modes.
The branching fractions are calculated as
3
B
~
B
!
D
s
~
*
!
1
D
̄
~
*
!
!
5
1
N
BB
̄
N
D
s
~
*
!
1
D
̄
~
*
!
(
i
(
j
B
i
B
j
́
ij
,
~
2
!
where
N
BB
̄
is the number of
BB
̄
pairs,
N
D
s
(
*
)
1
D
̄
(
*
)
is the
number of signal events extracted from the fit to the beam-
constrained mass distribution,
B
i
is the branching fraction of
the
i
th charm decay mode, and
́
ij
is the reconstruction ef-
ficiency for the combination of the
i
th
D
s
1
decay channel and
the
j
th
D
̄
decay channel
@
15
#
. The resulting exclusive
branching fractions are listed in Table VII where the first
error is the statistical error, the second error is the systematic
error from all sources other than the uncertainty in the nor-
malizing branching fractions,
B
(
D
s
1
!
f
p
1
) and
B
(
D
0
!
K
2
p
1
), and the third error is that due to the uncer-
tainty in the normalizing branching fractions, which is com-
pletely dominated by the uncertainty in
B
(
D
s
1
!
f
p
1
).
The systematic errors associated with the uncertainty in
the detection efficiencies of charged tracks and neutral clus-
ters are calculated in the following manner. A tracking effi-
ciency error of 2% per track is assumed except for the
‘‘slow’’
p
1
from
D
*
1
!
D
0
p
1
decays where an additional
4.6% is added in quadrature
~
making the total systematic
error for the slow pion to be 5%
!
. This additional error arises
because the tracking efficiency is rising sharply at low mo-
mentum. The tracking errors add linearly except for the ad-
ditional 4.6% on the slow pion. For example, for the
D
*
1
!
D
0
p
1
,
D
0
!
K
2
p
1
p
1
p
2
decay chain, the system-
atic
error
associated
with
tracking
is
A
(5
3
2)
2
1
4.6
2
5
11%. The systematic errors associated
with neutrals, 3% per photon and 5% per
p
0
or
h
, are also
added linearly. The charged and neutral systematic errors are
then added in quadrature. The total systematic error due to
uncertainties in efficiencies is then the weighted average of
the systematic errors of the particular decay channels where
2
This occurs because the low momentum
p
1
,
p
0
,or
g
that dif-
ferentiates the eight different modes contributes negligibly to the
D
E
resolution.
3
Equal production of charged and neutral
B
mesons is assumed.
TABLE V. Allowed mass intervals and branching fractions for
the noncharmed mesons.
Decay mode
Mass interval
~
GeV
!
Branching fraction
p
0
!
gg
0.1200
,
m
gg
,
0.1500 0.9880
6
0.0003
h
!
gg
0.5174
,
m
gg
,
0.5774
0.388
6
0.005
K
0
!
K
S
0
!
p
1
p
2
0.4877
,
m
p
1
p
2
,
0.5077 0.3431
6
0.0014
f
!
K
1
K
2
1.0095
,
m
K
1
K
2
,
1.0295 0.491
6
0.009
K
*
0
!
K
1
p
2
0.8461
,
m
K
1
p
2
,
0.9461
0.667
r
1
!
p
1
p
0
0.6161
,
m
p
1
p
0
,
0.9201
1.0
TABLE VI. The
B
meson candidate angular selection criteria.
Decay mode
u
cos
u
B
uu
cos
u
S
uu
cos
u
H
u
B
1
!
D
s
1
D
̄
0
<
0.75
<
0.95
-
B
1
!
D
s
*
1
D
̄
0
<
0.75
<
0.95
<
0.80
B
1
!
D
s
1
D
̄
*
0
<
0.75
<
0.95
>
0.35
B
1
!
D
s
*
1
D
̄
*
0
<
0.85
<
0.95
-
B
0
!
D
s
1
D
2
<
0.75
<
0.95
-
B
0
!
D
s
*
1
D
2
<
0.85
<
0.95
<
0.80
B
0
!
D
s
1
D
*
2
<
0.85
-
>
0.35
B
0
!
D
s
*
1
D
*
2
---
53
4739
MEASUREMENTS OF
B
!
D
s
1
X
DECAYS
the weight is
́
ï
B
for that particular decay channel. The sys-
tematic error due to the uncertainties in the relative branch-
ing fractions is calculated in the same manner. These are the
two dominant sources of systematic error.
The other possible sources of systematic error which were
investigated include: cross-feed between the eight channels,
uncertainty in the efficiency due to the method of choosing
the candidate with the smallest
u
D
E
u
, parametrization of the
background in the beam-constrained mass plots, and particle
identification requirements. There is a non-negligible contri-
bution to the systematic error due to the background param-
etrization for the
B
!
D
s
1
D
̄
modes where the background in
the beam-constrained mass plot is significant.
V. THE
B
ò
D
S
Ñ
*
Ö
1
D
̄
Ñ
*
Ö
DECAY RATES
In the dominant process leading to a two-body decay of
the type
B
!
D
s
(
*
)
1
D
(
*
)
, shown in Fig. 1, the
D
s
(
*
)
1
is pro-
duced from the fragmentation of the
W
1
. The analogous
b
!
u
transitions lead to final states like
D
s
1
p
2
but these
decay rates are down by roughly
u
V
ub
/
V
cb
u
2
'
0.006 com-
pared to
b
!
c
transitions
@
16,17
#
.A
D
s
1
is not produced in
internal
W
1
decay. The decay
B
!
D
s
(
*
)
1
D
̄
(
*
)
can also pro-
ceed through the ‘‘penguin’’ decay mode
b
̄
!
s
̄
g
,
g
!
cc
̄
but
this is expected to be small. Other processes, such as anni-
hilation and
W
-exchange, lead to final states like
D
s
1
K
(
*
)
but
there is no evidence that these processes are significant in
B
meson decay
@
16,17
#
. None of these scenarios leads to a
significant difference in the charged and neutral
B
!
D
s
(
*
)
1
D
̄
(
*
)
decay rates.
The equivalence of the charged and neutral decay rates
can be tested using the exclusive branching fractions and
t
(
B
1
)/
t
(
B
0
)
[
t
1
/0
5
0.98
6
0.09
@
6
#
. The results are given
in Table VIII where, for a given decay mode
~
e.g.,
B
!
D
s
1
D
̄
*
),
B
1
(0)
denotes the branching fraction for the
charged
~
neutral
!
B
to decay via this mode. Most of the
FIG. 6. The beam-constrained mass for the sum of the eight
B
!
D
s
(
*
)
1
D
̄
(
*
)
modes. The solid histogram is the data within the
D
E
signal window while the filled histogram is the data in the
D
E
sidebands
~
as described in the text
!
. The curve is the result of
the fit described in the text.
FIG. 7. The beam-constrained mass plots for the
B
1
decay
modes:
~
a
!
D
s
1
D
̄
0
,
~
b
!
D
s
*
1
D
̄
0
,
~
c
!
D
s
1
D
̄
*
0
, and
~
d
!
D
s
*
1
D
̄
*
0
. The
solid histogram is the data within the
D
E
signal window while the
filled histogram is the data in the
D
E
sidebands
~
as described in the
text
!
. The curve is the result of the fit described in the text.
FIG. 8. The beam-constrained mass plots for the
B
0
decay
modes:
~
a
!
D
s
1
D
2
,
~
b
!
D
s
*
1
D
2
,
~
c
!
D
s
1
D
*
2
, and
~
d
!
D
s
*
1
D
*
2
.
The solid histogram is the data within the
D
E
signal window while
the filled histogram is the data in the
D
E
sidebands
~
as described in
the text
!
. The curve is the result of the fit described in the text.
4740
53
D. GIBAUT
et al.