of 7
Search for the decay
B
ò
D
s
1
1
Ñ
2536
Ö
X
M. Bishai, J. Fast, J. W. Hinson, N. Menon, D. H. Miller, E. I. Shibata, I. P. J. Shipsey, and M. Yurko
Purdue University, West Lafayette, Indiana 47907
S. Glenn, S. D. Johnson, Y. Kwon,
*
S. Roberts, and E. H. Thorndike
University of Rochester, Rochester, New York 14627
C. P. Jessop, K. Lingel, H. Marsiske, M. L. Perl, V. Savinov, D. Ugolini, R. Wang, and X. Zhou
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309
T. E. Coan, V. Fadeyev, I. Korolkov, Y. Maravin, I. Narsky, V. Shelkov, J. Staeck, R. Stroynowski, I. Volobouev,
and J. Ye
Southern Methodist University, Dallas, Texas 75275
M. Artuso, F. Azfar, A. Efimov, M. Goldberg, D. He, S. Kopp, G. C. Moneti, R. Mountain, S. Schuh, T. Skwarnicki,
S. Stone, G. Viehhauser, and X. Xing
Syracuse University, Syracuse, New York 13244
J. Bartelt, S. E. Csorna, V. Jain,
K. W. McLean, and S. Marka
Vanderbilt University, Nashville, Tennessee 37235
R. Godang, K. Kinoshita, I. C. Lai, P. Pomianowski, and S. Schrenk
Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
G. Bonvicini, D. Cinabro, R. Greene, L. P. Perera, and G. J. Zhou
Wayne State University, Detroit, Michigan 48202
B. Barish, M. Chadha, S. Chan, G. Eigen, J. S. Miller, C. O’Grady, M. Schmidtler, J. Urheim, A. J. Weinstein,
and F. Wu
̈
rthwein
California Institute of Technology, Pasadena, California 91125
D. W. Bliss, G. Masek, H. P. Paar, S. Prell, and V. Sharma
University of California, San Diego, La Jolla, California 92093
D. M. Asner, J. Gronberg, T. S. Hill, D. J. Lange, R. J. Morrison, H. N. Nelson, T. K. Nelson, J. D. Richman, D. Roberts,
A. Ryd, and M. S. Witherell
University of California, Santa Barbara, California 93106
R. Balest, B. H. Behrens, W. T. Ford, A. Gritsan, H. Park, J. Roy, and J. G. Smith
University of Colorado, Boulder, Colorado 80309-0390
J. P. Alexander, C. Bebek, B. E. Berger, K. Berkelman, K. Bloom, V. Boisvert,
D. G. Cassel, H. A. Cho, D. S. Crowcroft, M. Dickson, S. von Dombrowski, P. S. Drell, K. M. Ecklund, R. Ehrlich,
A. D. Foland, P. Gaidarev, L. Gibbons, B. Gittelman, S. W. Gray, D. L. Hartill, B. K. Heltsley, P. I. Hopman,
J. Kandaswamy, P. C. Kim, D. L. Kreinick, T. Lee, Y. Liu, N. B. Mistry, C. R. Ng, E. Nordberg, M. Ogg,
J. R. Patterson, D. Peterson, D. Riley, A. Soffer, B. Valant-Spaight, and C. Ward
Cornell University, Ithaca, New York 14853
M. Athanas, P. Avery, C. D. Jones, M. Lohner, C. Prescott, J. Yelton, and J. Zheng
University of Florida, Gainesville, Florida 32611
G. Brandenburg, R. A. Briere, A. Ershov, Y. S. Gao, D. Y.-J.Kim, R. Wilson, and H. Yamamoto
Harvard University, Cambridge, Massachusetts 02138
T. E. Browder, Y. Li, and J. L. Rodriguez
University of Hawaii at Manoa, Honolulu, Hawaii 96822
PHYSICAL REVIEW D
1 APRIL 1998
VOLUME 57, NUMBER 7
57
0556-2821/98/57
~
7
!
/3847
~
7
!
/$15.00
3847
© 1998 The American Physical Society
T. Bergfeld, B. I. Eisenstein, J. Ernst, G. E. Gladding, G. D. Gollin, R. M. Hans, E. Johnson, I. Karliner, M. A. Marsh,
M. Palmer, M. Selen, and J. J. Thaler
University of Illinois, Urbana-Champaign, Illinois 61801
K. W. Edwards
Carleton University, Ottawa, Ontario, Canada K1S 5B6
and the Institute of Particle Physics, Canada
A. Bellerive, R. Janicek, D. B. MacFarlane, and P. M. Patel
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, C. Darling, R. Davis, S. Kotov, I. Kravchenko, N. Kwak,
and L. Zhou
University of Kansas, Lawrence, Kansas 66045
S. Anderson, Y. Kubota, S. J. Lee, J. J. O’Neill, S. Patton, R. Poling, T. Riehle, and A. Smith
University of Minnesota, Minneapolis, Minnesota 55455
M. S. Alam, S. B. Athar, Z. Ling, A. H. Mahmood, H. Severini, S. Timm, and F. Wappler
State University of New York at Albany, Albany, New York 12222
A. Anastassov, J. E. Duboscq, D. Fujino,
§
K. K. Gan, T. Hart, K. Honscheid, H. Kagan, R. Kass, J. Lee, M. B. Spencer,
M. Sung, A. Undrus,
i
R. Wanke, A. Wolf, and M. M. Zoeller
Ohio State University, Columbus, Ohio 43210
B. Nemati, S. J. Richichi, W. R. Ross, and P. Skubic
University of Oklahoma, Norman, Oklahoma 73019
~
CLEO Collaboration
!
~
Received 23 October 1997; published 10 March 1998
!
We have searched for the decay
B
!
D
s
1
1
( 2536)
X
and measured an upper limit for the inclusive branching
fraction of
B
(
B
!
D
s
1
1
X
)
,
0.96% at the 90% confidence level. This limit is small compared with the total
expected
B
!
D
̄
(
*
)
D
(
*
)
KX
rate. Assuming factorization, the
D
s
1
1
decay constant is constrained to be
f
D
s
1
1
,
114
MeV at the 90% confidence level, at least 2.5 times smaller than that of
D
s
1
.
@
S0556-2821
~
98
!
01809-8
#
PACS number
~
s
!
: 13.25.Hw, 14.40.Nd
I. INTRODUCTION
One of the outstanding issues in
B
meson physics is the
semileptonic branching fraction puzzle. Experimentally
B
(
B
!
Xl
n
) is measured to be ( 10.43
6
0.24% )
@
1
#
, whereas
theoretical calculations have difficulties accommodating a
branching fraction below
;
12.5%
@
2
#
. One way to reduce
the theoretical expectations is through a twofold enhance-
ment in the assumed
b
̄
!
c
̄
cs
̄
rate
@
3
#
, which is estimated to
be
;
15% from the measured inclusive rates for
B
!
D
s
1
X
and
B
!
c
X
.
Recently, Buchalla
et al.
@
4
#
and Blok
et al.
@
5
#
have sug-
gested that a significant fraction of the
b
̄
!
c
̄
cs
̄
transition
hadronizes into
B
!
D
̄
DKX
. This is supported by CLEO’s
@
6
#
observation of ‘‘wrong-sign’’
D
mesons from
B
decays,
B
(
B
!
DX
)
5
( 7.9
6
2.2) % , where the
D
comes from the vir-
tual
W
1
!
cs
̄
. The ALEPH
@
7
#
and DELPHI
@
8
#
Collabora-
tions have also observed sizeable
B
!
D
(
*
)
D
̄
(
*
)
X
decay
rates. Exclusive
B
decays involving wrong-sign
D
mesons
can result from
~
1
!
resonant
B
!
D
̄
(
*
)
D
s
**
decays, where the
W
1
!
cs
̄
hadronizes to an excited
D
s
1
meson that decays
into
DKX
, and
~
2
!
non-resonant
B
!
D
̄
(
*
)
D
(
*
)
K
decays.
This paper explores one possibility in the first case, namely,
the decays
B
!
D
s
1
1
( 2536)
X
where
D
s
1
1
is the narrow P-wave
D
s
1
meson with
J
P
5
1
1
. The ‘‘upper-vertex’’ production of
D
s
1
1
from
W
1
!
cs
̄
hadronization is shown in Fig. 1
~
a
!
.In
*
Permanent address: Yonsei University, Seoul 120-749, Korea.
Permanent address: Brookhaven National Laboratory, Upton, NY
11973.
Permanent address: University of Texas, Austin, TX 78712
§
Permanent address: Lawrence Livermore National Laboratory,
Livermore, CA 94551.
i
Permanent address: BINP, RU-630090 Novosibirsk, Russia.
3848
57
M. BISHAI
et al.
addition,
D
s
1
1
mesons can be produced from ‘‘lower-vertex’’
decays
b
!
cu
̄
d
with the creation of an
ss
̄
quark pair, as
shown in Fig. 1
~
b
!
. This produces right-sign
D
mesons; how-
ever, the decay rate is expected to be small. Throughout this
paper charge conjugate states are implied.
Continuum
D
s
1
1
production has been thoroughly studied
@
1
#
. The
D
s
1
1
is just above the
D
*
K
mass threshold and de-
cays dominantly into
D
*
0
K
1
and
D
*
1
K
0
. Other possible
decay channels are negligible:
D
s
(
*
)
1
p
0
due to isospin con-
servation,
D
s
(
*
)
1
(
n
p
) due to Okubo-Zweig-Iizuka
~
OZI
!
rule suppression
@
9
#
,
DK
or
D
s
1
p
0
due to angular momen-
tum and parity conservation, and
D
s
(
*
)
1
g
due to the small
radiative decay rate.
II. DATA SAMPLE AND EVENT SELECTION
The data used in this analysis were selected from hadronic
events collected by the CLEO II detector at the Cornell Elec-
tron Storage Ring
~
CESR
!
. The CLEO II detector
@
10
#
is a
large solenoidal detector with 67 tracking layers and a CsI
electromagnetic calorimeter that provides efficient
p
0
recon-
struction. The data consist of an integrated luminosity of
3.11 fb
2
1
at the
Y
(4
S
) resonance, corresponding to 3.3
3
10
6
BB
̄
events. To evaluate non-
BB
̄
backgrounds we also
collected 1.61 fb
2
1
of ‘‘continuum’’ data 60 MeV below
the
Y
(4
S
) resonance.
The inclusive
B
!
D
s
1
1
X
decay is studied by reconstruct-
ing the decay channels
D
s
1
1
!
D
*
0
K
1
and
D
*
1
K
S
0
using the
decay modes
D
*
0
!
D
0
p
0
and
D
*
1
!
D
0
p
1
. The
D
0
is re-
constructed using the decay modes
D
0
!
K
2
p
1
and
K
2
p
1
p
0
. Hadronic events are required to satisfy the ratio of
Fox-Wolfram moments
@
11
#
R
2
5
H
2
/
H
0
,
0.3 to reduce the
background from continuum events.
Charged tracks, except pions from
K
S
0
decays, are re-
quired to be consistent with coming from the primary inter-
action point. Charged kaon and pion candidates are identified
using specific ionization (
dE
/
dx
) and, when available, time-
of-flight
~
TOF
!
information. For kaon identification, we con-
sider the relative probability for a charged track to be a kaon,
R
K
5
P
K
/(
P
p
1
P
K
1
P
p
) , where
P
is the
x
2
probability for a
given particle hypothesis. The requirement on
R
K
depends
on the decay mode of interest. Pion candidates are identified
by requiring the
dE
/
dx
and, when available, TOF informa-
tion to be within 3 standard deviations (
s
) of that expected
for pions. We select
K
S
0
candidates through the decay to
p
1
p
2
by requiring a decay vertex displaced from the pri-
mary interaction point and a
K
S
0
invariant mass within
10 MeV/
c
2
of its nominal value. We reconstruct
p
0
candi-
dates through the decay to
gg
by requiring candidates to
have an invariant mass within 2.5 standard deviations (
s
'
5 MeV/
c
2
) of the nominal
p
0
mass.
The
K
2
p
1
and
K
2
p
1
p
0
combinations are required to
have a kaon identification of
R
K
.
0.5 and 0.7, respectively,
and an invariant mass within 15 and 25 MeV/
c
2
(
;
2
s
)of
the nominal
D
0
mass, respectively. In addition, we select
regions of the
D
0
!
K
2
p
1
p
0
Dalitz plot to take advantage
of the known resonant substructure
@
12
#
. For the
D
s
1
1
!
D
*
0
K
1
mode, the Dalitz cut reduces the signal efficiency
by 40% and the background by 80%. We relax the Dalitz cut
for the
D
*
1
K
S
0
mode since the combinatoric background is
substantially lower.
The
D
*
1
!
D
0
p
1
candidates are required to have a mass
difference
M
(
D
0
p
1
)
2
M
(
D
0
) within 1.5 MeV/
c
2
(
;
2
s
)
of the nominal value of 145.4 MeV/
c
2
, where
M
(
X
) is the
reconstructed invariant mass of
X
. Similarly, the
D
*
0
!
D
0
p
0
candidates are required to have a mass difference
M
(
D
0
p
0
)
2
M
(
D
0
) within 1.5 MeV/
c
2
(
;
2
s
) of the nomi-
nal value of 142.1 MeV/
c
2
. To form
D
s
1
1
candidates charged
kaons are combined with
D
*
0
candidates and
K
S
0
’s are com-
bined with
D
*
1
candidates. Since the primary kaons from
D
s
1
1
!
D
*
0
K
1
decays have low momentum, we can impose a
stringent
R
K
.
0.9 requirement on the
K
1
with negligible
loss of efficiency. The
D
s
1
1
candidates are required to have a
scaled momentum
x
p
5
p
D
s
1
1
/
A
E
beam
2
2
M
D
s
1
1
2
,
0.45, which
is the kinematic limit for
B
!
D
s
1
1
X
decays.
~
We ignore the
negligible contributions from
b
!
u
decays.
!
Upper-vertex
D
s
1
1
production results in a maximum
x
p
of 0.35, and this
requirement is imposed when determining the
D
s
1
1
decay
constant. The
D
s
1
1
decay channels with
p
0
’s in the final state
often have multiple
D
s
1
1
candidates per event. We select the
candidate with the highest
x
2
probability of being a
D
s
1
1
,
which is derived from the invariant masses of the recon-
structed
p
0
,
D
0
, and
D
*
mesons.
III. RAW YIELDS
The
D
s
1
1
signal is identified using the
D
*
K
mass differ-
ence,
D
M
1
5
M
(
D
*
0
K
1
)
2
M
(
D
*
0
)
2
M
K
1
and
D
M
2
5
M
(
D
*
1
K
S
0
)
2
M
(
D
*
1
)
2
M
K
S
0
, where
M
K
1
and
M
K
S
0
are
the known masses
@
1
#
. The
D
*
K
mass difference signal has
a resolution that is two to four times smaller than the corre-
sponding signal in the reconstructed
D
*
K
invariant mass
distribution. The
D
M
1
and
D
M
2
distributions are shown in
Fig. 2, where the
D
0
!
K
2
p
1
and
K
2
p
1
p
0
modes have
been added together. The data are fit with a Gaussian signal
and a threshold background function. The Gaussian width is
fixed to that expected from a GEANT-based Monte Carlo
simulation
@
13
#
(
s
5
2.4
2
3.6 MeV/
c
2
, depending on the
mode
!
and the mean is fixed to the measured
D
s
1
1
mass dif-
ference from continuum data (
D
M
1
'
35 MeV/
c
2
and
D
M
2
'
27 MeV/
c
2
. ) We observe 42
6
14 signal events in
the
D
*
0
K
1
mode and 9
6
6 events in the
D
*
1
K
S
0
mode.
However, when the
D
*
0
K
1
candidates are further subdi-
vided into the
D
0
!
K
2
p
1
and
K
2
p
1
p
0
decay channels
there is a discrepancy in the
D
s
1
1
yields. As shown in Fig. 3,
we observe 10
6
8 signal events in the
D
M
1
distribution for
FIG. 1. Feynman diagrams for
~
a
!
B
!
D
s
1
1
X
decays producing
D
s
1
1
at the upper vertex and
~
b
!
B
!
D
s
1
2
X
decays producing
D
s
1
2
at
the lower vertex.
57
3849
SEARCH FOR THE DECAY
B
!
D
s
1
1
( 2536)
X
the
D
0
!
K
2
p
1
channel and 33
6
12
D
s
1
1
signal events for
the
D
0
!
K
2
p
1
p
0
channel. After accounting for branching
fractions and efficiencies, discussed below, this results in a
2.2
s
discrepancy in the
D
*
0
K
1
rates between the two
D
0
modes. We cannot rule out the fact that background sources
may be contributing a false
D
s
1
1
signal in the
D
0
!
K
2
p
1
p
0
channel, but not in the
D
0
!
K
2
p
1
channel.
However, no such mechanism has been uncovered. To be
conservative, we choose to quote only an upper limit for the
decay
B
!
D
s
1
1
X
.
Since the
D
s
1
1
reconstruction efficiency increases rapidly
with
x
p
and the
D
s
1
1
momentum distribution from
B
decays
is not known, we compute the inclusive
B
!
D
s
1
1
X
branching
fraction by dividing the data into four equal regions of
x
p
from 0.05 to 0.45 and summing the efficiency corrected
yields. The
D
s
1
1
!
D
*
0
K
1
and
D
*
1
K
0
branching fractions
are equal according to isospin, and their ratio has been mea-
sured to be within 30% of unity
@
14
#
. We measure the
branching fraction
B
!
D
s
1
1
X
to be ( 0.77
6
0.22) % from the
D
*
0
K
1
mode and ( 0.28
6
0.37) % from the
D
*
1
K
S
0
mode,
where the error is statistical only. The two measurements are
statistically consistent. The
x
p
distribution for our
D
s
1
1
can-
didates is shown in Fig. 4.
IV. CROSS CHECKS
Several cross checks, shown in Fig. 5, were performed to
corroborate the validity of the
D
s
1
1
signal. The scaled con-
tinuum background from data after satisfying all selection
cuts is negligible, and there is no excess in the
D
M
1
signal
region ( 3
6
5 events
!
. The uncertainty in the continuum
D
s
1
1
contribution is included in the systematic error. There is also
no evidence of peaking in the
D
M
1
signal region for wrong-
sign
D
*
0
K
2
combinations ( 0
6
9 events
!
,
D
0
mass side-
bands ( 5
6
5 events
!
, and
D
*
0
mass sidebands (
2
4
6
6
events
!
.
We have also searched for the
D
0
signal from
D
s
1
1
!
D
*
0
K
1
candidates in the
D
M
1
signal region,
u
D
M
1
2
35 MeV/
c
2
u
,
10 MeV/
c
2
, by relaxing the
D
0
mass cut
and histogramming the invariant mass of all
K
2
p
1
and
K
2
p
1
p
0
combinations that satisfy the remaining selection
criteria. In events with multiple candidates per
D
0
decay
mode we select the candidate with the highest
x
2
probability,
which is derived from the reconstructed
p
0
and
D
s
1
1
masses.
We observe 100
6
15
D
0
events. However, there are also
real
D
0
’s in the random
D
*
0
K
1
combinations under the
D
s
1
1
FIG. 2. The mass difference distribution for
~
a
!
D
*
0
K
1
and
~
b
!
D
*
1
K
S
0
candidates from
B
meson decays.
FIG. 3. The
D
M
1
mass difference distribution for
D
*
0
K
1
can-
didates from the
~
a
!
D
0
!
K
2
p
1
and
~
b
!
D
0
!
K
2
p
1
p
0
decay
channels.
FIG. 4. The efficiency corrected yield for our
B
!
D
s
1
1
X
candi-
dates as a function of the
D
s
1
1
scaled momentum
x
p
. The kinematic
limit from upper-vertex and lower-vertex
B
!
D
s
1
1
X
decays is
x
p
,
0.35 and
x
p
,
0.45, respectively.
3850
57
M. BISHAI
et al.
peak; after a
D
M
1
sideband subtraction the
D
0
invariant
mass spectrum yields 44
6
18 events
@
see Fig. 6
~
a
!#
. This is
consistent with our
D
s
1
1
!
D
*
0
K
1
yield in Fig. 2.
Similarly, we have studied the
D
*
0
signal from
D
s
1
1
!
D
*
0
K
1
candidates in the
D
M
1
signal region. We observe
59
6
15
D
0
events. As in the
D
0
case there are also real
D
*
0
’s in the random
D
*
0
K
1
combinations under the
D
s
1
1
peak. After a
D
M
1
sideband subtraction the
D
*
0
mass dif-
ference spectrum yields 25
6
18 events
@
see Fig. 6
~
b
!#
, con-
sistent with our
D
s
1
1
!
D
*
0
K
1
yield.
Finally, we have studied the
D
s
1
1
production from con-
tinuum
e
1
e
2
!
cc
̄
events. The selection criteria is similar to
that used to find
D
s
1
1
from
B
decays, but since continuum
charm production has a hard fragmentation, we require
x
p
.
0.5. In addition, we remove the
R
2
,
0.3 cut, relax the
charged kaon identification to
R
K
.
0.1, and remove the Dal-
itz cut for
D
0
!
K
2
p
1
p
0
. The mass difference distribution
for
D
*
0
K
1
and
D
*
1
K
S
0
combinations are shown in Fig. 7,
where the
D
0
!
K
2
p
1
and
K
2
p
1
p
0
modes have been
added together. We extract the
D
s
1
1
signal by fitting the data
with a Gaussian signal and a threshold background function.
The Gaussian width is fixed to the value predicted by Monte
Carlo ( 2.1 MeV/
c
2
) , and the mean is allowed to float. We
observe 222
6
19 events in the
D
s
1
1
!
D
*
0
K
1
mode with a
mass difference of 35.0
6
0.2 MeV/
c
2
~
statistical error only
!
,
and 101
6
11 events in the
D
s
1
1
!
D
*
1
K
S
0
mode with a mass
difference of 27.5
6
0.3 MeV/
c
2
. The results are consistent
with the previous CLEO analysis
@
14
#
.
V. SYSTEMATIC ERRORS AND FINAL RESULTS
There are several sources of systematic error. We assign a
systematic error of 16% to account for the 2.2
s
discrepancy
between the
D
*
0
K
1
rates for the
D
0
!
K
2
p
1
and
K
2
p
1
p
0
modes. This accommodates different methods of computing
the weighted average of the
B
!
D
s
1
1
X
branching fraction
from the four separate decay chains. Uncertainties in the
D
M
value of
6
0.3 MeV/
c
2
from fits to the continuum
D
s
1
1
pro-
duction were used to set a systematic error of 1% and 16% in
the
D
*
0
K
1
and
D
*
1
K
S
0
yields from
B
decays, respectively.
Uncertainties due to reconstruction efficiencies include 1.5%
per charged track, 5% per
p
0
, 5% for slow pions from
D
*
,
and 5% for
K
S
0
. We also include systematic errors of 7% for
Monte Carlo statistics, 5% for kaon identification and the
Dalitz decay cut efficiency, 4% for uncertainties in the yield
for
x
p
,
0.05, and 8% for uncertainties in the continuum
D
s
1
1
contribution that passes our selection criteria. The total sys-
tematic error is 25%.
Averaging the
D
*
0
K
1
and
D
*
1
K
S
0
modes together, we
obtain
B
(
B
!
D
s
1
1
X
)
5
( 0.64
6
0.19
6
0.16) % . Since the
D
s
1
1
signal is observed largely in only one decay mode
D
s
1
1
!
D
*
0
K
1
with
D
0
!
K
2
p
1
p
0
, and since there is a discrep-
ancy between this mode and the corresponding mode involv-
ing
D
0
!
K
2
p
1
, we instead prefer to quote an upper limit on
FIG. 5. The normalized
D
*
0
K
1
mass difference distributions
from
~
a
!
continuum events,
~
b
!
D
*
0
K
2
‘‘wrong-sign’’ combina-
tions,
~
c
!
D
0
mass sidebands, and
~
d
!
D
*
0
mass sidebands.
FIG. 6.
~
a
!
The invariant mass distribution for
K
2
p
1
and
K
2
p
1
p
0
combinations from
D
*
0
K
1
candidates in the
D
M
1
signal
region, after sideband subtraction.
~
b
!
The
D
*
0
mass difference
distribution from
D
*
0
K
1
candidates in the
D
M
1
signal region, after
sideband subtraction.
FIG. 7. The mass difference distribution for
~
a
!
D
*
0
K
1
and
~
b
!
D
*
1
K
S
0
candidates from continuum
e
1
e
2
!
cc
̄
events.
57
3851
SEARCH FOR THE DECAY
B
!
D
s
1
1
( 2536)
X
the branching fraction to be
B
,
0.96% at the 90% C.L.
@
15
#
This decay rate limit is small relative to the total rate ex-
pected for
B
!
D
̄
(
*
)
D
(
*
)
KX
of about ( 7.9
6
2.2) % from the
wrong-sign
D
meson yield in
B
decays
@
6
#
. This is not sur-
prising considering the
cs
̄
system has appreciable phase
space beyond the
D
s
1
1
mass
@
4
#
. Also, CLEO’s
@
16
#
recent
observation of exclusive
B
!
D
̄
(
*
)
D
(
*
)
K
decays shows that
the
D
(
*
)
K
invariant mass distribution lies mostly above the
D
s
1
1
mass.
VI.
D
s
1
1
DECAY CONSTANT
Measurement of the
B
!
D
s
1
1
X
decay rate also provides an
estimate of the
D
s
1
1
decay constant,
f
D
s
1
1
, assuming that the
D
s
1
1
comes dominantly from upper-vertex decays. The inclu-
sive decay rate for
B
mesons into ground state or excited
D
s
1
mesons can be calculated assuming factorization
@
17
#
:
G
~
B
!
D
s
X
!
5
G
F
2
u
V
cb
V
cs
u
2
16
p
M
b
3
a
1
2
f
D
s
2
I
~
x
,
y
!
where
a
1
is the Bauer-Stech-Wirbel
~
BSW
!@
18
#
parameter
for the effective charged current, and
I
(
x
,
y
) is a kinematic
factor with
x
5
M
D
s
2
/
M
b
2
and
y
5
M
c
2
/
M
b
2
. For scalar or pseu-
doscalar
D
s
mesons,
I
(
x
,
y
)
5
A
(1
2
x
2
y
)
2
2
4
xy
(1
2
x
2
2
y
2
xy
1
y
2
) , and for vector or axial-vector
D
s
mesons,
I
(
x
,
y
)
5
A
(1
2
x
2
y
)
2
2
4
xy
(1
1
x
2
2
x
2
2
2
y
1
xy
1
y
2
).
We have tightened the
x
p
requirement to
x
p
,
0.35 since
this is the kinematic limit for upper-vertex
B
!
D
s
1
1
D
̄
X
de-
cays. The production of ground state and excited
D
s
1
mesons
from lower-vertex decays such as
B
̄
!
D
s
1
1
K
̄
X
is expected to
be suppressed. This is certainly true for
B
!
D
s
1
X
decays
where the fraction of
D
s
1
produced at the lower-vertex is
measured to be 0.172
6
0.079
6
0.026
@
19
#
. Moreover, there
is no evidence of
D
s
1
1
production in the region
x
p
5
0.35
2
0.45 where lower-vertex production is likely to occur
~
see
Fig. 4
!
. However, there is an excess of
B
!
D
s
1
1
X
candidates
observed at low
x
p
,
0.15
~
as seen in Fig. 4
!
which cannot
arise from factorizable upper-vertex contributions, and hence
should not be included in computing
f
D
s
1
1
from the above
equation. We use ( 75
6
25) % of the measured
B
!
D
s
1
1
X
branching fraction to account for these uncertainties in the
lower-vertex and non-factorizable contributions to
D
s
1
1
.
With the assumption
f
D
s
1
5
f
D
s
*
1
we can extract
f
D
s
1
1
from
the ratio of inclusive rates:
B
~
B
!
D
s
1
1
X
!
B
~
B
!
D
s
1
X
!
5
G
~
B
!
D
s
1
1
X
!
G
~
B
!
D
s
1
X
!
1
G
~
B
!
D
s
*
1
X
!
'
0.49
S
f
D
s
1
1
f
D
s
1
D
2
.
Many systematic errors cancel in the ratio. From our upper
limit on
B
!
D
s
1
1
X
and CLEO’s
@
20
#
measurement of
B
(
B
!
D
s
1
X
)
5
( 12.11
6
0.39
6
0.88
6
1.38) % ,
we
derive
f
D
s
1
1
/
f
D
s
1
,
0.40 at the 90% C.L. The central value is
f
D
s
1
1
/
f
D
s
1
5
0.29
6
0.06
6
0.06, where the first error is due to
the total error in the inclusive
B
!
D
s
1
X
and
B
!
D
s
1
1
X
branching fractions, and the second is the uncertainty in the
non-factorizable and lower-vertex contributions to the
B
!
D
s
1
1
X
decay rate. Using the measured value of
f
D
s
1
5
280
6
40 MeV
@
20
#
gives
f
D
s
1
1
5
81
6
26 MeV which corre-
sponds to an upper limit of
f
D
s
1
1
,
114 MeV. This limit ac-
commodates the prediction of
f
D
s
1
1
5
87
6
19 MeV by Veseli
and Dunietz
@
21
#
.
VII. CONCLUSIONS
In summary, we have searched for
B
mesons decaying
into the P-wave
D
s
1
1
( 2536) meson. The upper limit of
B
(
B
!
D
s
1
1
X
)
,
0.96% at the 90% C.L. accounts for at most only
a fraction of the total wrong-sign
B
!
DX
rate. Assuming
factorization, the decay constant
f
D
s
1
1
is at least a factor of
2.5 times smaller than the decay constant for the pseudo-
scalar
D
s
1
.
ACKNOWLEDGMENTS
We gratefully acknowledge the effort of the CESR staff in
providing us with excellent luminosity and running condi-
tions. J.P.A., J.R.P., and I.P.J.S. thank the NYI program of
the NSF, M.S. thanks the PFF program of the NSF, G.E.
thanks the Heisenberg Foundation, K.K.G., M.S., H.N.N.,
T.S., and H.Y. thank the OJI program of DOE, J.R.P., K.H.,
M.S. and V.S. thank the A.P. Sloan Foundation, R.W. thanks
the Alexander von Humboldt Stiftung, M.S. thanks Research
Corporation, and S.D. thanks the Swiss National Science
Foundation for support. This work was supported by the Na-
tional Science Foundation, the U.S. Department of Energy,
and the Natural Sciences and Engineering Research Council
of Canada.
@
1
#
Particle Data Group, R. M. Barnett
et al.
, Phys. Rev. D
54
,1
~
1996
!
.
@
2
#
I. Bigi, B. Blok, M. Shifman, and A. Vainshtein, Phys. Lett. B
323
, 408
~
1994
!
.
@
3
#
A. F. Falk, M. B. Wise, and I. Dunietz, Phys. Rev. D
51
, 1183
~
1995
!
; E. Bagan, P. Ball, V. M. Braun, and P. Gosdzinsky,
Phys. Lett. B
324
, 362
~
1995
!
; M. B. Voloshin, Phys. Rev. D
51
, 3948
~
1995
!
.
@
4
#
G. Buchalla, I. Dunietz, and H. Yamamoto, Phys. Lett. B
364
,
188
~
1995
!
.
@
5
#
B. Blok, M. Shifman, and N. Uraltsev, Nucl. Phys.
B494
, 237
~
1997
!
.
3852
57
M. BISHAI
et al.
@
6
#
CLEO Collaboration, T. E. Coan
et al.
, Phys. Rev. Lett.
80
,
1150
~
1998
!
.
@
7
#
ALEPH Collaboration, A. M. Stacey, in
ICHEP’96
, Proceed-
ings of the 1996 International Conference on High Energy
Physics, Warsaw, Poland, edited by Z. Ajduk and A. Wrob-
lewski
~
World Scientific, Singapore, 1997
!
.
@
8
#
DELPHI Collaboration, M. L. Andrieux, in
ICHEP’96
@
7
#
.
@
9
#
S. Okubo, Phys. Lett.
5B
, 165
~
1963
!
; G. Zweig, CERN Re-
port 8419/TH412
~
1964
!
; I. Iizuka, Prog. Theor. Phys. Suppl.
37
,21
~
1966
!
.
@
10
#
CLEO Collaboration, Y. Kubota
et al.
, Nucl. Instrum. Meth-
ods Phys. Res. A
320
,66
~
1992
!
.
@
11
#
G. Fox and S. Wolfram, Phys. Rev. Lett.
41
, 1581
~
1978
!
.
@
12
#
E691 Collaboration, J. C. Anjos
et al.
, Phys. Rev. D
48
,56
~
1993
!
.
@
13
#
R. Brun
et al.
,
GEANT
3.15, CERN DD/EE/84-1.
@
14
#
CLEO Collaboration, J. Alexander
et al.
, Phys. Lett. B
303
,
377
~
1993
!
.
@
15
#
The 90% upper limit is derived, assuming Gaussian statistics,
by adding 1.28 times the total error to the central value.
@
16
#
CLEO Collaboration, M. Bishai
et al.
, contributed to the 1997
International Europhysics Conference on High Energy Phys-
ics, Jerusalem, Israel.
@
17
#
J. H. Kuhn, S. Nussinov, and R. Ruckl, Z. Phys. C
5
, 117
~
1980
!
.
@
18
#
M. Bauer, B. Stech, and M. Wirbel, Z. Phys. C
29
, 637
~
1985
!
.
@
19
#
CLEO Collaboration, X. Fu
et al.
, contributed to the 1995 In-
ternational Europhysics Conference on High Energy Physics,
Brussels, Belgium.
@
20
#
CLEO Collaboration, D. Gibaut
et al.
, Phys. Rev. D
53
, 4734
~
1996
!
.
@
21
#
S. Veseli and I. Dunietz, Phys. Rev. D
54
, 6803
~
1996
!
.
57
3853
SEARCH FOR THE DECAY
B
!
D
s
1
1
( 2536)
X