V
OLUME
80, N
UMBER
6
PHYSICAL REVIEW LETTERS
9 F
EBRUARY
1998
Flavor-Specific Inclusive
B
Decays to Charm
T. E. Coan,
1
V. Fadeyev,
1
I. Korolkov,
1
Y. Maravin,
1
I. Narsky,
1
V. Shelkov,
1
J. Staeck,
1
R. Stroynowski,
1
I. Volobouev,
1
J. Ye,
1
M. Artuso,
2
F. Azfar,
2
A. Efimov,
2
M. Goldberg,
2
D. He,
2
S. Kopp,
2
G. C. Moneti,
2
R. Mountain,
2
S. Schuh,
2
T. Skwarnicki,
2
S. Stone,
2
G. Viehhauser,
2
X. Xing,
2
J. Bartelt,
3
S. E. Csorna,
3
V. Jain,
3,
*
K. W. McLean,
3
S. Marka,
3
R. Godang,
4
K. Kinoshita,
4
I. C. Lai,
4
P. Pomianowski,
4
S. Schrenk,
4
G. Bonvicini,
5
D. Cinabro,
5
R. Greene,
5
L. P. Perera,
5
G. J. Zhou,
5
B. Barish,
6
M. Chadha,
6
S. Chan,
6
G. Eigen,
6
J. S. Miller,
6
C. O’Grady,
6
M. Schmidtler,
6
J. Urheim,
6
A. J. Weinstein,
6
F. Würthwein,
6
D. W. Bliss,
7
G. Masek,
7
H. P. Paar,
7
S. Prell,
7
V. Sharma,
7
D. M. Asner,
8
J. Gronberg,
8
T. S. Hill,
8
D. J. Lange,
8
R. J. Morrison,
8
H. N. Nelson,
8
T. K. Nelson,
8
J. D. Richman,
8
D. Roberts,
8
A. Ryd,
8
M. S. Witherell,
8
R. Balest,
9
B. H. Behrens,
9
W. T. Ford,
9
A. Gritsan,
9
H. Park,
9
J. Roy,
9
J. G. Smith,
9
J. P. Alexander,
10
C. Bebek,
10
B. E. Berger,
10
K. Berkelman,
10
K. Bloom,
10
V. Boisvert,
10
D. G. Cassel,
10
H. A. Cho,
10
D. S. Crowcroft,
10
M. Dickson,
10
S. von Dombrowski,
10
P. S. Drell,
10
K. M. Ecklund,
10
R. Ehrlich,
10
A. D. Foland,
10
P. Gaidarev,
10
L. Gibbons,
10
B. Gittelman,
10
S. W. Gray,
10
D. L. Hartill,
10
B. K. Heltsley,
10
P. I. Hopman,
10
J. Kandaswamy,
10
P. C. Kim,
10
D. L. Kreinick,
10
T. Lee,
10
Y. Liu,
10
N. B. Mistry,
10
C. R. Ng,
10
E. Nordberg,
10
M. Ogg,
10,
†
J. R. Patterson,
10
D. Peterson,
10
D. Riley,
10
A. Soffer,
10
B. Valant-Spaight,
10
C. Ward,
10
M. Athanas,
11
P. Avery,
11
C. D. Jones,
11
M. Lohner,
11
C. Prescott,
11
J. Yelton,
11
J. Zheng,
11
G. Brandenburg,
12
R. A. Briere,
12
A. Ershov,
12
Y. S. Gao,
12
D. Y.-J. Kim,
12
R. Wilson,
12
H. Yamamoto,
12
T. E. Browder,
13
Y. Li,
13
J. L. Rodriguez,
13
T. Bergfeld,
14
B. I. Eisenstein,
14
J. Ernst,
14
G. E. Gladding,
14
G. D. Gollin,
14
R. M. Hans,
14
E. Johnson,
14
I. Karliner,
14
M. A. Marsh,
14
M. Palmer,
14
M. Selen,
14
J. J. Thaler,
14
K. W. Edwards,
15
A. Bellerive,
16
R. Janicek,
16
D. B. MacFarlane,
16
P. M. Patel,
16
A. J. Sadoff,
17
R. Ammar,
18
P. Baringer,
18
A. Bean,
18
D. Besson,
18
D. Coppage,
18
C. Darling,
18
R. Davis,
18
S. Kotov,
18
I. Kravchenko,
18
N. Kwak,
18
L. Zhou,
18
S. Anderson,
19
Y. Kubota,
19
S. J. Lee,
19
J. J. O’Neill,
19
S. Patton,
19
R. Poling,
19
T. Riehle,
19
A. Smith,
19
M. S. Alam,
20
S. B. Athar,
20
Z. Ling,
20
A. H. Mahmood,
20
H. Severini,
20
S. Timm,
20
F. Wappler,
20
A. Anastassov,
21
J. E. Duboscq,
21
D. Fujino,
21,
‡
K. K. Gan,
21
T. Hart,
21
K. Honscheid,
21
H. Kagan,
21
R. Kass,
21
J. Lee,
21
M. B. Spencer,
21
M. Sung,
21
A. Undrus,
21,
§
R. Wanke,
21
A. Wolf,
21
M. M. Zoeller,
21
B. Nemati,
22
S. J. Richichi,
22
W. R. Ross,
22
P. Skubic,
22
M. Bishai,
23
J. Fast,
23
J. W. Hinson,
23
N. Menon,
23
D. H. Miller,
23
E. I. Shibata,
23
I. P. J. Shipsey,
23
M. Yurko,
23
S. Glenn,
24
S. D. Johnson,
24
Y. Kwon,
24,
k
S. Roberts,
24
E. H. Thorndike,
24
C. P. Jessop,
25
K. Lingel,
25
H. Marsiske,
25
M. L. Perl,
25
V. Savinov,
25
D. Ugolini,
25
R. Wang,
25
and X. Zhou
25
(CLEO Collaboration)
1
Southern Methodist University, Dallas, Texas 75275
2
Syracuse University, Syracuse, New York 13244
3
Vanderbilt University, Nashville, Tennessee 37235
4
Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
5
Wayne State University, Detroit, Michigan 48202
6
California Institute of Technology, Pasadena, California 91125
7
University of California, San Diego, La Jolla, California 92093
8
University of California, Santa Barbara, California 93106
9
University of Colorado, Boulder, Colorado 80309-0390
10
Cornell University, Ithaca, New York 14853
11
University of Florida, Gainesville, Florida 32611
12
Harvard University, Cambridge, Massachusetts 02138
13
University of Hawaii at Manoa, Honolulu, Hawaii 96822
14
University of Illinois, Urbana-Champaign, Illinois 61801
15
Carleton University Ottawa, Ontario, Canada K1S 5B6
and the Institute of Particle Physics, Canada
16
McGill University, Montréal Québec, Canada H3A 2T8
and the Institute of Particle Physics, Canada
17
Ithaca College, Ithaca, New York 14850
18
University of Kansas, Lawrence, Kansas 66045
19
University of Minnesota, Minneapolis, Minnesota 55455
20
State University of New York at Albany, Albany, New York 12222
21
Ohio State University, Columbus, Ohio 43210
22
University of Oklahoma, Norman, Oklahoma 73019
23
Purdue University, West Lafayette, Indiana 47907
1150
0031-9007
y
98
y
80(6)
y
1150(6)$15.00
© 1998 The American Physical Society
V
OLUME
80, N
UMBER
6
PHYSICAL REVIEW LETTERS
9 F
EBRUARY
1998
24
University of Rochester, Rochester, New York 14627
25
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309
(
Received 23 October 1997
)
We have measured the branching fractions for
B
!
̄
DX
,
B
!
DX
, and
B
!
̄
DX
,
1
n
. From these
results and some previously measured branching fractions, we obtain
B
s
b
!
c
̄
cs
d
≠
s
21.9
6
3.7
d
%
,
B
s
b
!
sg
d
,
6.8%
at 90% C.L., and
B
s
D
0
!
K
2
p
1
d
≠
s
3.69
6
0.20
d
%
. Implications for the “
B
semileptonic decay problem” (measured branching fraction being below theoretical expectations) are
discussed. With the increase in the value of
B
s
b
!
c
̄
cs
d
due to
B
!
DX
, the discrepancy is no
longer statistically compelling.
[S0031-9007(97)05231-9]
PACS numbers: 13.25.Hw, 13.20.He, 14.40.Nd
There has been a longstanding problem in heavy flavor
physics of the measured
B
semileptonic decay branching
fraction [1] being smaller than theoretical expectations
[2,3]. One possible explanation [2] is a larger-than-
expected flavor-changing neutral current ( FCNC) contri-
bution, due to new physics. Another [3] is an enhanced
rate for
b
!
c
̄
cs
0
(
s
0
denotes the weak isospin partner of
c
). An argument against an enhanced
b
!
c
̄
cs
0
rate is
that it would conflict with the measured branching frac-
tion for
B
!
̄
DX
plus
B
!
DX
. That measurement re-
lies on a knowledge of
B
s
D
0
!
K
2
p
1
d
, however, and if
that is in error, the measurement of the branching fraction
of
B
to charm or anticharm will also be in error. We ad-
dress all three issues by measuring the yields of the flavor-
specific inclusive
B
decay processes
B
!
DX
,
B
!
̄
DX
,
and
B
!
̄
DX
,
1
n
in a sample of
B
̄
B
events in which at
least one
B
decays semileptonically. ( Herein, “
B
” repre-
sents an average over
B
0
and
B
1
,“
D
” a sum over
D
0
and
D
1
, and “
̄
D
” a sum over
̄
D
0
and
D
2
[4]. We use the
term “lower vertex
D
” for a
D
produced from the charm
quark from
b
!
cW
2
, and “upper vertex
D
” for a
̄
D
pro-
duced from the charm quark from
W
2
!
̄
cs
.)
These yields, and ratios among them, provide informa-
tion on the above-mentioned issues as follows:
(i) The fraction of semileptonic
B
decays that proceed
through
B
!
̄
DX
,
1
n
,
f
SL
, differs from 100% only
because of small contributions from
b
!
u
,
n
and
B
!
D
2
s
KX
,
1
n
(“lower vertex
D
s
”). The measured fraction
is inversely proportional to the assumed
D
absolute
branching fraction (in our case
B
s
D
0
!
K
2
p
1
d
and
scaling the yield to agree with expectations gives a new
method for measuring that branching fraction.
(ii) The fraction of all
B
decays that proceed through
B
!
̄
DX
,
f
all
, differs from 100% because of
b
!
u
decays, lower vertex
D
s
, formation of
c
̄
c
bound states,
formation of charmed baryons, and FCNC processes such
as
b
!
sg
,
b
!
dg
,
b
!
sq
̄
q
,
b
!
dq
̄
q
(which we
will refer to collectively as “
b
!
sg
”). As all processes
except
b
!
sg
have been measured, the ratio
f
all
y
f
SL
provides a measurement of the branching fraction for
b
!
sg
. By taking the ratio of
f
all
to
f
SL
, rather than
just using
f
all
, we eliminate the dependence on the
D
0
!
K
2
p
1
branching ratio, and reduce the dependence on the
D
detection efficiency.
(iii) The process
B
!
DX
proceeds via the quark-level
process
̄
b
!
̄
cc
̄
s
0
, and thus the ratio of the yields for
B
!
DX
and
B
!
̄
DX
, i.e., ratio of upper to lower vertex
charm, provides information on the rate of that process
relative to
̄
b
!
̄
cu
̄
d
0
.
The typical inclusive
B
decay branching fraction mea-
surement averages over
B
and
̄
B
initial states for a given
final state, and, consequently, averages over particle and
antiparticle final states for a given initial state (
B
or
̄
B
), losing the flavor-specific information sought here. In
1987, CLEO developed a technique for measuring inclu-
sive
B
decay branching fractions separately to particle and
antiparticle final states, and applied it to inclusive kaon
decays [5,6]. Here we apply similar techniques to inclu-
sive charm decays.
The principle underlying the 1987 technique is that if
one
B
from a
B
̄
B
pair from the
Y
(4S) decays semilep-
tonically, with a high momentum lepton, then the other
decay products from that
B
will have substantial angular
correlations with the lepton, tending to come off back-
to-back to it, while the decay products from the other
B
have negligible angular correlations with the lepton. The
lepton tags the flavor of its parent
B
, and thus also the
other
B
(with a correction needed for mixing). By plot-
ting the distribution in the angle between
D
,
1
(and
̄
D
,
2
)
pairs, and separately the distribution in the angle between
D
,
2
(and
̄
D
,
1
) pairs, and extracting an isotropic com-
ponent and a peaking component from each, yields are
obtained for four processes:
B
!
̄
DX
,
1
n
,
B
!
DX
,
1
n
,
B
!
̄
DX
, and
B
!
DX
. Of these,
B
!
DX
,
1
n
should
be zero.
For low
D
momenta, the technique just described loses
statistical power and becomes sensitive to the shape as-
sumed in fitting for the peaking component. ( In the
limit that the
D
momentum vanishes, the
D
-lepton an-
gular correlation clearly contains no information.) Con-
sequently, we have developed a second technique, based
on charge correlations alone. We measure three yields:
the number of
D
,
2
(and
̄
D
,
1
) pairs, equal to the sum of
B
!
̄
DX
,
1
n
and
B
!
DX
yields in a lepton-tagged data
sample; the number of
D
,
1
(and
̄
D
,
2
) pairs, equal to the
sum of
B
!
DX
,
1
n
and
B
!
̄
DX
yields in the lepton-
tagged sample; and the number of
D
(and
̄
D
) mesons in
an untagged sample, equal to the sum of
B
!
̄
DX
and
1151
V
OLUME
80, N
UMBER
6
PHYSICAL REVIEW LETTERS
9 F
EBRUARY
1998
B
!
DX
yields in the untagged sample. Using the fact
that the rate for
B
!
DX
,
1
n
vanishes, and scaling the
last-mentioned yield by the ratio of the sizes of the tagged
and untagged data samples, these yields give the yields for
the other three processes:
B
!
̄
DX
,
1
n
,
B
!
̄
DX
, and
B
!
DX
. Using a combination of the angular correlation
and charge correlation techniques, we have obtained these
three yields for the sum of
D
0
and
D
1
mesons.
The data were taken with the CLEO detector [7] at
the Cornell Electron Storage Ring (CESR), and consist
of
3.2
fb
2
1
on the
Y
(4S) resonance and
1.6
fb
2
1
at
a center-of-mass energy 60 MeV below the resonance.
The on-resonance sample contains
3.3
3
10
6
B
̄
B
events
and
10
3
10
6
continuum events. The CLEO detector
measures charged particles over
95%
of
4
p
steradians
with a system of cylindrical drift chambers. Its barrel
and end cap CsI electromagnetic calorimeters cover
98%
of
4
p
. Hadron identification is provided by specific
ionization
s
dE
y
dx
d
measurements in the outermost drift
chamber and by time-of-flight counters ( TOF). Muons are
identified by their ability to penetrate iron; electrons by
dE
y
dx
, comparison of track momentum with calorimeter
cluster energy, and track /cluster position matching.
We select hadronic events containing at least four
charged tracks. We require a value of the ratio of Fox-
Wolfram parameters [8],
R
2
;
H
2
y
H
0
,
0.5
, to suppress
continuum events. Events containing at least one lepton
with momentum between 1.5 and
2.8
GeV
y
c
and surviv-
ing a
c
!
,
1
,
2
veto are scanned for
D
0
,
D
1
, and charge
conjugates. ( For the untagged sample, we drop the lep-
ton requirement.) We detect
D
0
and
D
1
via the
K
2
p
1
and
K
2
p
1
p
1
decay mode, respectively. Tracks used
as candidate
D
decay products must have
dE
y
dx
and / or
TOF values within
2
s
of expectations for the particle
assignment made (
K
or
p
). For
D
0
!
K
2
p
1
, particle
identification must rule out the
̄
D
0
!
p
2
K
1
option.
We histogram candidate
D
masses for four intervals in
cos
u
D
2
,
and four intervals in
D
momentum, separately for
the two charge correlations with the lepton. These 64 mass
distributions are fit to double-Gaussian signal peaks and
polynomial backgrounds, to extract
D
yields. These are
corrected for detection efficiency, determined by a Monte
Carlo simulation augmented by studies of particle ID effi-
ciency that use data (a sample of
D
p
1
!
D
0
p
1
,
D
0
!
K
2
p
1
events). Overall efficiencies are typically
35%
.
We perform small subtractions for continuum background
(using below —
Y
(4S) — resonance data) and for hadrons
misidentified as leptons (using hadrons in place of lep-
tons and weighting by the probability that a hadron is
misidentified as a lepton). Small corrections are made to
the
D
0
yields for the singly Cabibbo-suppressed decays
D
0
y
̄
D
0
!
K
2
K
1
and
D
0
y
̄
D
0
!
p
2
p
1
which combine
with a single failure of particle ID to make satellite peaks,
for the doubly Cabibbo-suppressed decay
D
0
!
K
1
p
2
[9], and for double failures of particle ID, with
p
2
K
1
treated as
K
2
p
1
. A small correction is made to
D
1
yields
for the decay
D
1
s
!
K
2
K
1
p
1
with the
K
1
misidentified
as a
p
1
.
The
D
yields for each momentum interval, charge
correlation, and
D
type are histogrammed vs cos
u
D
2
,
,16
distributions in all. For the high
D
momentum intervals
1.3 – 1.95 and
1.95
2.6
GeV
y
c
, we fit the
,
2
D
angular
distributions to an isotropic component and a backward-
peaking component, with fitting functions obtained from
Monte Carlo simulation. We fit the
,
1
D
angular dis-
tributions to an isotropic component alone. For the low
D
momentum intervals 0.0 – 0.65 and
0.65
1.3
GeV
y
c
,
we use the charge correlation technique, summing
over cos
u
D
2
,
.
We sum the yields so obtained over
D
momentum intervals, and over charged and neutral
D
’s, correcting for
D
0
and
D
6
branching fractions,
using
B
s
D
0
!
K
2
p
1
d
≠
3.91%
[10], and
B
s
D
1
!
K
2
p
1
p
1
dy
B
s
D
0
!
K
2
p
1
d
≠
2.35
[11]. We obtain
yields for
D
and the lepton from the same
B
, and from
different
B
’s, as follows.
N
s
D
,
2
1
̄
D
,
1
, same
B
d
≠
s
3.75
6
0.11
d
3
10
5
,
N
s
D
,
2
1
̄
D
,
1
, different
B
’s)
≠
s
6.66
6
0.77
d
3
10
4
, and
N
s
D
,
1
1
̄
D
,
2
, different
B
’s)
≠
s
3.18
6
0.08
d
3
10
5
in a sample containing
4.24
3
10
5
leptons. For illustrative purposes, we show
cos
u
D
2
,
distributions summed over momentum inter-
vals and over
D
0
and
D
1
, ( Fig. 1). The
,
2
D
1
,
1
̄
D
distribution shows strong back-to-back peaking from
B
!
̄
DX
,
1
n
, while the
,
2
̄
D
1
,
1
D
shows no such
peaking, due to the nonexistence of
B
!
DX
,
1
n
.
One also notes a much larger isotropic component in
,
2
̄
D
1
,
1
D
because of the large rate for
B
!
̄
DX
and
FIG. 1. Yield of
D
,
events vs cos
u
D
2
,
.
D
0
,
2
1
D
1
,
2
plus charge conjugate, summed over
D
momentum, are shown
as solid circles, while
̄
D
0
,
2
1
D
2
,
2
plus charge conjugate,
summed over
D
momentum, are shown as open squares.
1152
V
OLUME
80, N
UMBER
6
PHYSICAL REVIEW LETTERS
9 F
EBRUARY
1998
a small rate for
B
!
DX
(and a small rate for mixing
B
0
!
̄
B
0
!
DX
).
If the lepton and
D
come from the same
B
, then the
lepton tags
that
B
correctly. The lepton can’t be from a
decay of
D
because that
D
was
detected
via a hadronic
decay mode. It can’t be from
c
because the rate for
B
!
c
̄
DX
is negligible. If there are two
D
’s from the same
B
, leptons from either one will be below our
1.5
GeV
y
c
momentum cut. If the
B
has mixed, nonetheless the lepton
correctly tags the
b
flavor at the instant of decay, which
is what is relevant for understanding the
D
from the
same
B
. But, if the lepton and
D
come from different
B
’s, then the tagging of
both
B
’s is now imperfect: the
ancestor of the lepton because leptons from charm decay
and leptons from
c
now contribute; and the ancestor of the
D
for those reasons and, in addition, because of
B
0
2
̄
B
0
mixing. Corrections are thus required when using the
yields involving lepton and
D
from different
B
’s. These
corrections depend on
f
m
(the probability that a lepton
mistags its ancestor
B
) and
x
(the mixing parameter).
We extract three distinct pieces of physics from the
three yields given above. For each, we have considered
systematic errors due to uncertainties in each of the pre-
viously mentioned corrections, uncertainties from fitting
mass peaks and cos
u
D
2
,
distributions, and uncertainties
in efficiency and
D
branching fractions.
(i) First, consider
G
s
B
!
DX
dy
G
s
B
!
̄
DX
d
, the ratio
of “upper vertex” charm to “lower vertex” charm. This
ratio
U
y
L
is obtained from
x
≠
N
s
D
,
2
1
̄
D
,
1
,
dif-
ferent
B
’s
dy
N
s
D
,
1
1
̄
D
,
2
,
different
B
’s
d
by correcting
for mixing and mistags.
U
y
L
≠
s
x
2
F
m
dys
1
2
xF
m
d
,
where
F
m
≠
s
f
m
1
f
0
dys
2
2
f
m
2
f
0
d
, and
f
0
≠
f
m
1
x2
2
f
m
x
. We use
x
≠
0.157
as measured by CLEO
with dileptons [12] and
f
m
≠
0.027
as found there,
thereby achieving cancellation of some systematic errors
in
F
m
, giving
F
m
≠
0.112
6
0.011
. From the yields
given above,
x
≠
0.210
6
0.025
, leading to
G
s
B
!
DX
d
G
s
B
!
̄
DX
d
≠
0.100
6
0.026
6
0.016 ,
(1)
where the first error is statistical and the second is sys-
tematic, dominated by the uncertainties in mixing correc-
tion
s
6
0.012
d
and the cos
u
D
2
,
fitting function
s
6
0.008
d
.
This result is surprisingly large, as conventional wisdom
held that
b
!
c
̄
cs
would hadronize dominantly into
D
s
.
However, Buchalla
et al.
[3] have argued that the
D
0
,
D
1
component should be substantial.
In Fig. 2 we plot the momentum distribution of these
upper vertex
D
0
,
D
1
, obtained by applying the analysis
just described to each of the four
D
momentum bins. The
spectrum is softer than that for lower vertex
D
’s, also
shown. It is well described by three-body
D
s
p
d
D
s
p
d
K
s
p
d
phase space, if one allows one or two of the particles
to be the vector states. CLEO has observed such decay
modes [13].
FIG. 2.
D
momentum distributions. Upper vertex
D
0
1
D
1
,
i.e., from
B
!
DX
, are shown as solid squares, while lower
vertex
D
0
1
D
1
, from
̄
B
!
DX
, are shown as open squares,
and lower vertex
D
0
1
D
1
, from
̄
B
!
DX
,
n
, are shown
as solid circles. Vertical scale gives branching fraction per
unit momentum for upper and lower vertex
D
’s, and same
divided by total semileptonic decay branching fraction for semi-
leptonic
D
’s.
(ii) Next, consider the fraction of all
B
decays to
̄
D
,
f
all
, divided by the fraction of semileptonic
B
decays to
̄
D
,
f
SL
, i.e., the double ratio of widths
G
s
B
!
̄
DX
d
G
s
B
!
all
d
y
G
s
B
!
̄
DX
,
1
n
d
G
s
B
!
X
,
1
n
d
.
We obtain this from the ratio
of yields
N
s
D
,
1
1
̄
D
,
2
, different
B
’s
dy
N
s
D
,
2
1
̄
D
,
1
,
same
B
d;
z
. Corrections are required in the “dif-
ferent
B
’s” yield for mixing and mistags. Also, leptons
from unvetoed
c
and from secondary decays (
3.3
6
0.7%
of all leptons) do not contribute to the peaking yield, and
so a correction is required for that, leading to
f
all
y
f
SL
≠
0.967
z
yfs
1
2
0.5
f
m
2
0.5
f
0
ds
1
1
F
m
U
y
L
dg
, where
U
y
L
≠
0.100
, as found above. Applying all corrections, we
have
f
all
y
f
SL
≠
0.901
6
0.034
6
0.015 .
(2)
One expects both
f
all
and
f
SL
to be close to 1.0.
The first ratio will be less than 1.0 because of
b
!
u
transitions (
2
j
V
ub
y
V
cb
j
2
, where the 2 is a phase space
factor), lower vertex
D
s
s
2%
d
, bound
c
̄
c
states (
3.0
6
0.5%
[14]), baryons (
6.5
6
1.5%
[15]), and
b
!
sg
(to
be extracted). The second ratio will be less than 1.0
because of
b
!
u
transitions (
3
j
V
ub
y
V
cb
j
2
, enhanced
by the
1.5
GeV
y
c
lepton momentum requirement) and
lower vertex
D
s
(
1.0
6
0.5%
, suppressed by the lepton
momentum requirement). These lead to
f
all
y
f
SL
≠
1.0
1
j
V
ub
y
V
cb
j
2
2
s
0.010
6
0.005
d
2
s
0.030
6
0.005
d
2
s
0.065
6
0.015
d
2
B
s
b
!
sg
d
.
(3)
1153
V
OLUME
80, N
UMBER
6
PHYSICAL REVIEW LETTERS
9 F
EBRUARY
1998
Here
b
!
sg
is symbolic for all FCNC processes.
Using
j
V
ub
y
V
cb
j
2
≠
0.008
6
0.003
, we obtain
B
s
b
!
sg
d
≠
s
0.2
6
3.4
6
1.5
6
1.7
d
%
, where the first error is
statistical, the second systematic on
z
, and the third the
uncertainties in expression (3). From this we obtain an
upper limit
B
s
b
!
sg
d
,
6.8%
,at
90%
C.L. The dom-
inant components of the systematic error on
z
are from
mixing
s
6
1.2%
d
and unvetoed and secondary leptons
s
6
0.6%
d
.
(iii) Finally, consider the fraction of semileptonic
B
decays to
̄
D
0
or
D
2
, i.e.,
f
SL
;
G
s
B
!
̄
DX
,
1
n
dy
G
s
B
!
X
,
1
n
d
.
We obtain this fraction by dividing
the yield
N
s
D
,
2
1
̄
D
,
1
,
same
B
d
by the number of
leptons from
B
semileptonic decay,
96.7%
of the total
of
4.24
3
10
5
leptons in our sample. We find
0.914
6
0.027
6
0.042
. This number is inversely proportional
to the value used for
B
s
D
0
!
K
2
p
1
d
.
The ex-
pected value of the ratio of widths is
G
s
B
!
̄
DX
,
1
n
dy
G
s
B
!
X
,
1
n
d
≠
1.0
2
3
j
V
ub
y
V
cb
j
2
2
0.010
6
0.005
s
for
̄
B
!
D
1
s
KX
,
2
n
d
.
Taking
3
j
V
ub
y
V
cb
j
2
≠
0.023
6
0.008
, we find the expected ratio of widths to be
0.968
6
0.010
, differing from the measured value by
one standard deviation.
We set measured and ex-
pected values of the ratio equal to each other and
solve for the
D
0
branching fraction, finding
B
s
D
0
!
K
2
p
1
d
≠
s
3.69
6
0.11
6
0.16
6
0.04
d
%
, where the
first error is statistical, the second systematic in the
measured ratio, and the third systematic in the predicted
ratio. The dominant systematic errors are from uncer-
tainties in
D
detection efficiency
s
6
0.10%
d
, mass peak
fitting
s
6
0.09%
d
, and the ratio of
D
1
to
D
0
branching
ratios
s
6
0.08%
d
.
This value for the branching frac-
tion,
s
3.69
6
0.20
d
%
, is to be compared with recent
measurements by CLEO of
s
3.91
6
0.19
d
%
[10] and
s
3.81
6
0.22
d
%
[16], by ALEPH of
s
3.90
6
0.15
d
%
[17],
and the PDG value of
s
3.83
6
0.12
d
%
[18]. Correlations
among the three CLEO measurements are discussed in
Ref [16].
In Table I we list all the components of
B
decay, give
their branching fractions ( based on measurement or the-
ory), and see if they sum to
100%
. We express some in
terms of
b
SL
, the
B
semileptonic decay branching fraction,
for which we use [1]
s
10.49
6
0.46
d
%
. The factor of 0.25
for
b
!
s
c
or
u
d
tn
is a phase space factor. The factor
r
ud
for
b
!
s
c
or
u
d
ud
0
would be 3 from color count-
ing, but with quantum chromodynamics corrections [19] is
4.0
6
0.4
. This analysis has two pieces of information to
add to Table I. First, the upper vertex
̄
D
0
,
D
2
contribu-
tion of
s
7.9
6
2.2
d
%
is obtained from our measured value
of
G
s
B
!
D
0
or
D
1
X
dy
G
s
B
!
̄
D
0
or
D
2
X
d
, combined
with the rate for inclusive
D
0
1
D
1
63.6%
1
23.5%
d
[20], and leads to a branching fraction for
b
!
s
c
or
u
d
̄
cs
0
of
s
21.9
6
3.7
d
%
. Second, we have a value (with large
errors) for the FCNC term. One sees that the upper ver-
tex
̄
D
0
,
D
2
contribution accounts for close to half of the
shortfall of the sum of all modes from unity. The re-
TABLE I. All components of
B
decay, with their branching
fractions. Upper vertex
̄
D
0
and
D
2
, and
b
!
s
y
dg
,
s
y
dq
̄
q
,
are from this analysis.
The branching fractions for the
separate components making up
b
!
s
c
or
u
d
̄
cs
0
are shown
parenthetically. Errors shown for measured quantities include
both statistical and systematic errors. The two errors shown
for
b
!
s
c
or
u
d
̄
ud
0
are on
b
SL
and
r
ud
, respectively. Note
that the errors from
b
SL
for the first four entries add linearly in
the total.
b
decay modes
Branching fraction
s
%
d
b
!
s
c
or
u
d
e
n
b
SL
10.5
6
0.5
b
!
s
c
or
u
d
mn
b
SL
10.5
6
0.5
b
!
s
c
or
u
d
tn
0.25
b
SL
2.6
6
0.1
b
!
s
c
or
u
d
̄
ud
0
r
ud
b
SL
42.0
6
2.0
6
4.2
b
!
s
c
or
u
d
̄
cs
0
21.9
6
3.7
D
s
s
10.0
6
2.7
d
s
c
̄
c
ds
3.0
6
0.5
d
Baryons
s
1.0
6
0.6
d
Upper vertex
̄
D
0
,
D
2
s
7.9
6
2.2
d
b
!
s
y
dg
,
s
y
dq
̄
q
0.2
6
4.1
Total
87.7
6
7.4
maining shortfall is less than two standard deviations.
If we adjust
r
ud
to bring the sum to
100%
, we find
r
ud
≠
5.2
6
0.6
.
We thank Isard Dunietz for informative conversations.
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, the A. P. Sloan
Foundation, the Swiss National Science Foundation, and
the Yonsei University Faculty Research Fund.
*Permanent address: Brookhaven National Laboratory,
Upton, NY 11973.
†
Permanent address: University of Texas, Austin, TX
78712.
‡
Permanent address: Lawrence Livermore National Labo-
ratory, Livermore, CA 94551.
§
Permanent address: BINP, RU-630090
Novosibirsk,
Russia.
k
Permanent address: Yonsei University, Seoul 120-749,
Korea.
[1] CLEO Collaboration, B. Barish
et al.,
Phys. Rev. Lett.
76
,
1570 (1996).
[2] I. Bigi, B. Blok, M. A. Shifman, and A. Vainshtein, Phys.
Lett. B
323
, 408 (1994).
[3] G. Buchalla, I. Dunietz, and H. Yamamoto, Phys. Lett. B
364
, 188 (1995).
[4] Throughout, charge conjugation of all equations is im-
plied, i.e.,
B
!
̄
DX
includes
̄
B
!
D
̄
X
.
1154
V
OLUME
80, N
UMBER
6
PHYSICAL REVIEW LETTERS
9 F
EBRUARY
1998
[5] Paul L. Tipton, Ph.D. thesis, University of Rochester,
1987.
[6] CLEO Collaboration, M. Alam
et al.,
Phys. Rev. Lett.
58
,
1814 (1987).
[7] CLEO Collaboration, Y. Kubota
et al.,
Nucl. Instrum.
Methods Phys. Res., Sect A
320
, 66 (1992).
[8] G. Fox and S. Wolfram, Phys Rev. Lett.
41
, 1581 (1978).
[9] CLEO Collaboration, D. Cinabro
et al.,
Phys. Rev. Lett.
72
, 1406 (1994).
[10] CLEO Collaboration, D. Akerib
et al.,
Phys. Rev. Lett.
71
,
3070 (1993).
[11] CLEO Collaboration, R. Balest
et al.,
Phys. Rev. Lett.
72
,
2328 (1994).
[12] CLEO Collaboration, J. Bartelt
et al.,
Phys. Rev. Lett.
71
,
1680 (1993).
[13] CLEO Collaboration Report No. CONF 97-26.
[14] CLEO Collaboration, R. Balest
et al.,
Phys. Rev. D
52
,
2661 (1995).
[15] CLEO Collaboration, G. Crawford
et al.,
Phys. Rev. D
45
,
725 (1992).
[16] M. Artuso
et al.,
CLEO Collaboration Report No. CLEO
97-24 (to be published).
[17] ALEPH Collaboration, R. Barate
et al.,
Phys. Lett. B
403
,
367 (1997).
[18] Particle Data Group, R. M. Barnett
et al.,
Phys. Rev. D
54
,
1 (1996).
[19] E. Bagan, P. Ball, V. M. Braun, and P. Gosdzinsky, Nucl.
Phys.
B432
, 3 (1994).
[20] CLEO Collaboration, L. Gibbons
et al.,
Phys. Rev. D
56
,
3783 (1997).
1155