of 11
B
A
B
AR
-PUB-13/008
SLAC-PUB-15835
Evidence for the baryonic decay
B
0
D
0
Λ
Λ
J. P. Lees, V. Poireau, and V. Tisserand
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),
Universit ́e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
E. Grauges
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
A. Palano
ab
INFN Sezione di Bari
a
; Dipartimento di Fisica, Universit`a di Bari
b
, I-70126 Bari, Italy
G. Eigen and B. Stugu
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
D. N. Brown, L. T. Kerth, Yu. G. Kolomensky, M. J. Lee, and G. Lynch
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
H. Koch and T. Schroeder
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphysik 1, D-44780 Bochum, Germany
C. Hearty, T. S. Mattison, J. A. McKenna, and R. Y. So
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
A. Khan
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
V. E. Blinov
ac
, A. R. Buzykaev
a
, V. P. Druzhinin
ab
, V. B. Golubev
ab
, E. A. Kravchenko
ab
, A. P. Onuchin
ac
,
S. I. Serednyakov
ab
, Yu. I. Skovpen
ab
, E. P. Solodov
ab
, K. Yu. Todyshev
ab
, and A. N. Yushkov
a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 630092
c
, Russia
D. Kirkby, A. J. Lankford, and M. Mandelkern
University of California at Irvine, Irvine, California 92697, USA
B. Dey, J. W. Gary, O. Long, and G. M. Vitug
University of California at Riverside, Riverside, California 92521, USA
C. Campagnari, M. Franco Sevilla, T. M. Hong, D. Kovalskyi, J. D. Richman, and C. A. West
University of California at Santa Barbara, Santa Barbara, California 93106, USA
A. M. Eisner, W. S. Lockman, B. A. Schumm, and A. Seiden
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
D. S. Chao, C. H. Cheng, B. Echenard, K. T. Flood, D. G. Hitlin, P. Ongmongkolkul, and F. C. Porter
California Institute of Technology, Pasadena, California 91125, USA
R. Andreassen, Z. Huard, B. T. Meadows, B. G. Pushpawela, M. D. Sokoloff, and L. Sun
University of Cincinnati, Cincinnati, Ohio 45221, USA
P. C. Bloom, W. T. Ford, A. Gaz, U. Nauenberg, J. G. Smith, and S. R. Wagner
University of Colorado, Boulder, Colorado 80309, USA
R. Ayad
and W. H. Toki
arXiv:1401.5990v1 [hep-ex] 23 Jan 2014
2
Colorado State University, Fort Collins, Colorado 80523, USA
B. Spaan
Technische Universit ̈at Dortmund, Fakult ̈at Physik, D-44221 Dortmund, Germany
R. Schwierz
Technische Universit ̈at Dresden, Institut f ̈ur Kern- und Teilchenphysik, D-01062 Dresden, Germany
D. Bernard and M. Verderi
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
S. Playfer
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
D. Bettoni
a
, C. Bozzi
a
, R. Calabrese
ab
, G. Cibinetto
ab
, E. Fioravanti
ab
,
I. Garzia
ab
, E. Luppi
ab
, L. Piemontese
a
, and V. Santoro
a
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara
b
, I-44122 Ferrara, Italy
R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro,
S. Martellotti, P. Patteri, I. M. Peruzzi,
M. Piccolo, M. Rama, and A. Zallo
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
R. Contri
ab
, E. Guido
ab
, M. Lo Vetere
ab
, M. R. Monge
ab
, S. Passaggio
a
, C. Patrignani
ab
, and E. Robutti
a
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
B. Bhuyan and V. Prasad
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
M. Morii
Harvard University, Cambridge, Massachusetts 02138, USA
A. Adametz and U. Uwer
Universit ̈at Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
H. M. Lacker
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, D-12489 Berlin, Germany
P. D. Dauncey
Imperial College London, London, SW7 2AZ, United Kingdom
U. Mallik
University of Iowa, Iowa City, Iowa 52242, USA
C. Chen, J. Cochran, W. T. Meyer, and S. Prell
Iowa State University, Ames, Iowa 50011-3160, USA
A. V. Gritsan
Johns Hopkins University, Baltimore, Maryland 21218, USA
N. Arnaud, M. Davier, D. Derkach, G. Grosdidier, F. Le Diberder,
A. M. Lutz, B. Malaescu,
P. Roudeau, A. Stocchi, and G. Wormser
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et Universit ́e Paris-Sud 11,
Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
J. P. Coleman, J. R. Fry, E. Gabathuler, D. E. Hutchcroft, D. J. Payne, and C. Touramanis
3
University of Liverpool, Liverpool L69 7ZE, United Kingdom
A. J. Bevan, F. Di Lodovico, and R. Sacco
Queen Mary, University of London, London, E1 4NS, United Kingdom
G. Cowan
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
J. Bougher, D. N. Brown, and C. L. Davis
University of Louisville, Louisville, Kentucky 40292, USA
A. G. Denig, M. Fritsch, W. Gradl, K. Griessinger, A. Hafner, E. Prencipe, and K. R. Schubert
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Kernphysik, D-55099 Mainz, Germany
R. J. Barlow
§
and G. D. Lafferty
University of Manchester, Manchester M13 9PL, United Kingdom
E. Behn, R. Cenci, B. Hamilton, A. Jawahery, and D. A. Roberts
University of Maryland, College Park, Maryland 20742, USA
R. Cowan, D. Dujmic, and G. Sciolla
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
R. Cheaib, P. M. Patel,
and S. H. Robertson
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
P. Biassoni
ab
, N. Neri
a
, and F. Palombo
ab
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
L. Cremaldi, R. Godang,
∗∗
P. Sonnek, and D. J. Summers
University of Mississippi, University, Mississippi 38677, USA
M. Simard and P. Taras
Universit ́e de Montr ́eal, Physique des Particules, Montr ́eal, Qu ́ebec, Canada H3C 3J7
G. De Nardo
ab
, D. Monorchio
ab
, G. Onorato
ab
, and C. Sciacca
ab
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
M. Martinelli and G. Raven
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
C. P. Jessop and J. M. LoSecco
University of Notre Dame, Notre Dame, Indiana 46556, USA
K. Honscheid and R. Kass
Ohio State University, Columbus, Ohio 43210, USA
J. Brau, R. Frey, N. B. Sinev, D. Strom, and E. Torrence
University of Oregon, Eugene, Oregon 97403, USA
E. Feltresi
ab
, M. Margoni
ab
, M. Morandin
a
, M. Posocco
a
, M. Rotondo
a
, G. Simi
a
, F. Simonetto
ab
, and R. Stroili
ab
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
S. Akar, E. Ben-Haim, M. Bomben, G. R. Bonneaud, H. Briand,
G. Calderini, J. Chauveau, Ph. Leruste, G. Marchiori, J. Ocariz, and S. Sitt
Laboratoire de Physique Nucl ́eaire et de Hautes Energies,
IN2P3/CNRS, Universit ́e Pierre et Marie Curie-Paris6,
4
Universit ́e Denis Diderot-Paris7, F-75252 Paris, France
M. Biasini
ab
, E. Manoni
a
, S. Pacetti
ab
, and A. Rossi
a
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
C. Angelini
ab
, G. Batignani
ab
, S. Bettarini
ab
, M. Carpinelli
ab
,
††
G. Casarosa
ab
, A. Cervelli
ab
, F. Forti
ab
,
M. A. Giorgi
ab
, A. Lusiani
ac
, B. Oberhof
ab
, E. Paoloni
ab
, A. Perez
a
, G. Rizzo
ab
, and J. J. Walsh
a
INFN Sezione di Pisa
a
; Dipartimento di Fisica, Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
D. Lopes Pegna, J. Olsen, and A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
R. Faccini
ab
, F. Ferrarotto
a
, F. Ferroni
ab
, M. Gaspero
ab
, L. Li Gioi
a
, and G. Piredda
a
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
C. B ̈unger, O. Gr ̈unberg, T. Hartmann, T. Leddig, C. Voß, and R. Waldi
Universit ̈at Rostock, D-18051 Rostock, Germany
T. Adye, E. O. Olaiya, and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
S. Emery, G. Hamel de Monchenault, G. Vasseur, and Ch. Y`eche
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
F. Anulli,
‡‡
D. Aston, D. J. Bard, J. F. Benitez, C. Cartaro, M. R. Convery, J. Dorfan, G. P. Dubois-Felsmann,
W. Dunwoodie, M. Ebert, R. C. Field, B. G. Fulsom, A. M. Gabareen, M. T. Graham, C. Hast,
W. R. Innes, P. Kim, M. L. Kocian, D. W. G. S. Leith, P. Lewis, D. Lindemann, B. Lindquist, S. Luitz,
V. Luth, H. L. Lynch, D. B. MacFarlane, D. R. Muller, H. Neal, S. Nelson, M. Perl, T. Pulliam,
B. N. Ratcliff, A. Roodman, A. A. Salnikov, R. H. Schindler, A. Snyder, D. Su, M. K. Sullivan, J. Va’vra,
A. P. Wagner, W. F. Wang, W. J. Wisniewski, M. Wittgen, D. H. Wright, H. W. Wulsin, and V. Ziegler
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
W. Park, M. V. Purohit, R. M. White,
§§
and J. R. Wilson
University of South Carolina, Columbia, South Carolina 29208, USA
A. Randle-Conde and S. J. Sekula
Southern Methodist University, Dallas, Texas 75275, USA
M. Bellis, P. R. Burchat, T. S. Miyashita, and E. M. T. Puccio
Stanford University, Stanford, California 94305-4060, USA
M. S. Alam and J. A. Ernst
State University of New York, Albany, New York 12222, USA
R. Gorodeisky, N. Guttman, D. R. Peimer, and A. Soffer
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
S. M. Spanier
University of Tennessee, Knoxville, Tennessee 37996, USA
J. L. Ritchie, A. M. Ruland, R. F. Schwitters, and B. C. Wray
University of Texas at Austin, Austin, Texas 78712, USA
J. M. Izen and X. C. Lou
University of Texas at Dallas, Richardson, Texas 75083, USA
F. Bianchi
ab
, F. De Mori
ab
, A. Filippi
a
, D. Gamba
ab
, and S. Zambito
ab
5
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
L. Lanceri
ab
and L. Vitale
ab
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, I-34127 Trieste, Italy
F. Martinez-Vidal, A. Oyanguren, and P. Villanueva-Perez
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
H. Ahmed, J. Albert, Sw. Banerjee, F. U. Bernlochner, H. H. F. Choi, G. J. King, R. Kowalewski,
M. J. Lewczuk, T. Lueck, I. M. Nugent, J. M. Roney, R. J. Sobie, and N. Tasneem
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
T. J. Gershon, P. F. Harrison, and T. E. Latham
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
H. R. Band, S. Dasu, Y. Pan, R. Prepost, and S. L. Wu
University of Wisconsin, Madison, Wisconsin 53706, USA
Evidence is presented for the baryonic
B
meson decay
B
0
D
0
Λ
Λ
based on a data sample of
471
×
10
6
B
B
pairs collected with the
B
A
B
AR
detector at the PEP-II asymmetric
e
+
e
collider
located at the SLAC National Accelerator Laboratory. The branching fraction is determined to be
B
(
B
0
D
0
Λ
Λ
) = (9
.
8
+2
.
9
2
.
6
±
1
.
9)
×
10
6
, corresponding to a significance of 3
.
4 standard deviations
including systematic uncertainties. A search for the related baryonic
B
meson decay
B
0
D
0
Σ
0
Λ
with
Σ
0
Λγ
is performed and an upper limit
B
(
B
0
D
0
Σ
0
Λ
+
B
0
D
0
Λ
Σ
0
)
<
3
.
1
×
10
5
is
determined at 90% confidence level.
PACS numbers: 13.25.Hw, 13.60.Rj, 14.20.Lq
I. INTRODUCTION
Little is known about the mechanism of baryon pro-
duction in weak decays or in the hadronization process.
Baryons are produced in (6
.
8
±
0
.
6)% of all
B
meson
decays [1]. Due to this large rate,
B
meson decays can
provide important information about baryon production.
Due to the low energy scale, perturbative quantum chro-
modynamics (QCD) cannot be applied to this process.
Furthermore, latice QCD calculations are not available.
The description of baryonic
B
decays thus relies on phe-
nomenological models.
Now at the University of Tabuk, Tabuk 71491, Saudi Arabia
Also with Universit`a di Perugia, Dipartimento di Fisica, Perugia,
Italy
Now at Laboratoire de Physique Nucl ́aire et de Hautes Energies,
IN2P3/CNRS, Paris, France
§
Now at the University of Huddersfield, Huddersfield HD1 3DH,
UK
Deceased
∗∗
Now at University of South Alabama, Mobile, Alabama 36688,
USA
††
Also with Universit`a di Sassari, Sassari, Italy
‡‡
Also with INFN Sezione di Roma, Roma, Italy
§§
Now at Universidad T ́ecnica Federico Santa Maria, Valparaiso,
Chile 2390123
Pole models [2] are a common tool used in theoretical
studies of hadronic decays. Meson pole models predict
an enhancement at low baryon-antibaryon masses. In
many three-body decays into a baryon, an antibaryon
and a meson, the baryon-antibaryon pair can be de-
scribed by a meson pole, i.e., the decay of a virtual
meson with a mass below threshold. This leads to a
steeply falling amplitude at the threshold of the baryon-
antibaryon mass, and explains the enhancement observed
in decays such as
B
Λ
c
[3, 4],
B
p
pK
[5–7],
and
B
0
D
0
p
p
[8, 9].
In addition to the meson pole models described above,
there are baryon pole models in which the initial state de-
cays through the strong interaction into a pair of baryons.
Then, one of these baryons decays via the weak interac-
tion into a baryon and a meson. For such baryon pole
models no enhancement at threshold in the dibaryon in-
variant mass is expected.
The decay of a
B
meson into a
D
0
meson and a pair
of baryons has been the object of several theoretical in-
vestigations [10, 11]. Ref. [11] predicts the branching
fractions for
B
0
D
0
Λ
Λ
decays and for the sum of the
B
0
D
0
Λ
Σ
0
and
B
0
D
0
Σ
0
Λ
decays to be
B
(
B
0
D
0
Λ
Λ
) = (2
±
1)
×
10
6
,
B
(
B
0
D
0
Λ
Σ
0
+
B
0
D
0
Σ
0
Λ
) = (1
.
8
±
0
.
5)
×
10
5
.
(1)
It is impractical to separate the
B
0
D
0
Λ
Σ
0
and
B
0
D
0
Σ
0
Λ
decays since each leads to the final state
Λ
Λγ
.
6
̄
d
c
̄
u
d
u
q
̄
q
̄
u
̄
d
b
̄
B
0
D
0
N
̄
N
b
̄
d
c
̄
u
u
d
q
̄
q
̄
u
̄
d
̄
B
0
D
0
N
̄
N
b
̄
d
c
̄
u
d
u
q
̄
q
̄
u
̄
d
̄
B
0
D
0
N
̄
N
FIG. 1: Leading-order Feynman diagrams for the decays
B
0
D
0
N
N
. Setting
q
=
u
leads to the
D
0
p
p
final state and setting
q
=
s
to the
D
0
Λ
Λ
,
D
0
Σ
0
Λ
,
D
0
Λ
Σ
0
, and
D
0
Σ
0
Σ
0
final states.
As can be seen from the Feynman diagrams shown in
Fig. 1, the only difference between the
B
0
D
0
p
p
decay
on the one hand and the
B
0
D
0
Λ
Λ
and
B
0
D
0
Σ
0
Λ
decays on the other hand is the replacement of a
u
u
pair
with an
s
s
pair. In the hadronization process,
s
s
-pair
production is suppressed by about a factor of three com-
pared to
u
u
- or
d
d
-pair production [12]. Furthermore,
since both
Λ
and
Σ
0
baryons can be produced, there
are four possible final states with an
s
s
pair (
Λ
Λ
,
Λ
Σ
0
,
Σ
0
Λ
, and
Σ
0
Σ
0
) compared to only one for a
u
u
pair
(
p
p
), neglecting the production of excited baryons. As-
suming equal production rates for these four modes and
that the spin-1
/
2 states dominate, a suppression of a fac-
tor of
12 is expected for
B
0
D
0
Λ
Λ
decays compared
to
B
0
D
0
p
p
decays, where the branching fraction of the
latter process is
B
(
B
0
D
0
p
p
) = (1
.
04
±
0
.
04)
×
10
4
[1].
The branching fraction for
B
0
D
0
Λ
Λ
has been mea-
sured by the Belle Collaboration to be
B
(
B
0
D
0
Λ
Λ
) =
(10
.
5
+5
.
7
4
.
4
±
1
.
4)
×
10
6
[13]. There are no previous results
for the
B
0
D
0
Σ
0
Λ
decay mode.
II. THE
B
A
B
AR
EXPERIMENT
This analysis is based on a data sample of 429 fb
1
[14], corresponding to 471
×
10
6
B
B
pairs, collected with
the
B
A
B
AR
detector at the PEP-II asymmetric-energy
e
+
e
collider at the SLAC National Accelerator Labo-
ratory at center-of-mass energies near and equal to the
Υ
(4
S
) mass. The reconstruction efficiency is determined
through use of Monte Carlo (MC) simulation, based on
the EvtGen [15] program for the event generation and
the GEANT4 [16] package for modeling of the detector
response. The MC events are generated uniformly in the
B
0
D
0
Λ
Λ
and
B
0
D
0
Σ
0
Λ
phase space.
The
B
A
B
AR
detector is described in detail elsewhere
[17, 18]. Charged particle trajectories are measured with
a five-layer double-sided silicon vertex tracker and a 40-
layer drift chamber immersed in a 1
.
5 T axial mag-
netic field. Charged particle identification is provided by
ionization energy measurements in the tracking cham-
bers and by Cherenkov-radiation photons recorded with
an internally reflecting ring-imaging detector. Electrons
and photons are reconstructed with an electromagnetic
calorimeter.
III. RECONSTRUCTION OF
Λ
BARYON,
D
0
MESON, AND
B
0
MESON CANDIDATES
We reconstruct
Λ
baryons through the decay mode
Λ
and
D
0
mesons through the modes
D
0
K
π
+
,
D
0
K
π
+
π
+
π
, and
D
0
K
π
+
π
0
[19].
Charged kaon and proton candidates are required to sat-
isfy particle identification criteria. Charged pions are se-
lected as charged tracks that are not identified as a kaon
or proton.
Candidate
π
0
mesons are reconstructed from two sep-
arated energy deposits in the electromagnetic calorime-
ter not associated with charged tracks. To discriminate
against neutral hadrons, the shower shape of each de-
posit is required to be consistent with that of a photon
[20]. Furthermore, we require
E
(
γ
1
)
>
0
.
125 GeV and
E
(
γ
2
)
>
0
.
04 GeV, where
E
(
γ
1
) and
E
(
γ
2
) are the ener-
gies of the photon candidates, with
E
(
γ
1
)
> E
(
γ
2
). The
photon-photon invariant mass is required to lie in the
range
m
(
γγ
)
[0
.
116
,
0
.
145] GeV
/c
2
.
The
Λ
daughters are fit to a common vertex and the re-
constructed mass is required to lie within three standard
deviations of the nominal value [1], where the standard
deviation is the mass resolution. We select
Λ
candidates
by requiring the flight significance
L
t
L
t
to exceed 4,
where
L
t
is the
Λ
flight length in the transverse plane
and
σ
L
t
its uncertainty. The
Σ
0
baryons are produced in
the decay
Σ
0
Λγ
, and the photon is not reconstructed.
The
D
0
daughter candidates are fit to a common vertex
and the reconstructed mass is required to lie within three
times the mass resolution from their nominal values [1].
The signal-to-background ratio for
D
0
K
π
+
π
0
is im-
proved by making use of the resonant substructure of this
decay, which is well known. Using results from the E691
Collaboration [21], we calculate the probability
w
Dalitz
for a
D
0
candidate to be located at a certain position in
the Dalitz plane. We require
w
Dalitz
>
0
.
02. Figure 2
shows the Dalitz plot distributions, based on simulation,
for candidates selected with and without the
w
Dalitz
re-
7
)
4
/c
2
(GeV
2
0
π
π
m
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
)
4
/c
2
(GeV
2
π
K
m
0.5
1
1.5
2
2.5
3
+
ρ
-
K*(892)
0
K*(892)
+
ρ
FIG. 2: Dalitz plot for simulated
D
0
K
π
+
π
0
events be-
fore (gray stars) and after (black crosses) the
w
Dalitz
>
0
.
02
requirement. Resonant decays are indicated.
quirement.
The
D
0
and
Λ
candidates are constrained to their nom-
inal masses in the reconstruction of the
B
0
candidates.
We apply a fit to the entire decay chain and require the
probability for the vertex fit to be larger than 0
.
001.
To reduce background from
e
+
e
q
q
events with
q
=
u,d,s,c
, we apply a selection on a Fisher discriminant
F
that combines the values of
|
cos
θ
Thr
|
, where
θ
Thr
is the
angle between the thrust axis of the
B
candidate and the
thrust axis formed from the remaining tracks and clusters
in the event;
|
cos
θ
z
|
, where
θ
z
is the angle between the
B
thrust axis and the beam axis;
|
cos
φ
|
, where
φ
is the
angle between the
B
momentum and the beam axis; and
the normalized second Fox Wolfram moment [22]. All
these quantities are defined in the center-of-mass frame.
All selection criteria are summarized in Table I.
TABLE I: Summary of selection criteria.
Selection criterion
Selected candidates
Λ/
Λ
mass
m
[1
.
112
,
1
.
120] GeV
/c
2
Flight significance
L
t
L
t
>
4
D
0
K
π
mass
m
[1
.
846
,
1
.
882] GeV
/c
2
D
0
K
π
+
π
+
π
mass
m
Kπππ
[1
.
852
,
1
.
876] GeV
/c
2
Lateral parameter
γ
1
0
.
05
<
LAT(
γ
1
)
<
0
.
55
Lateral parameter
γ
2
LAT(
γ
2
)
>
0
.
075
Calorimeter energy
γ
1
E
(
γ
1
)
>
0
.
125 GeV
Calorimeter energy
γ
2
E
(
γ
2
)
>
0
.
04 GeV
π
0
mass
m
γγ
[0
.
116
,
0
.
145] GeV
/c
2
D
0
K
π
+
π
0
mass
m
Kππ
0
[1
.
81
,
1
.
89] GeV
/c
2
Dalitz weight
w
Dalitz
>
0
.
02
B
vertex probability
p
(
B
)
>
0
.
001
Fisher discriminant
F
>
0
.
1
IV. FIT STRATEGY
We determine the number of signal candidates with a
two-dimensional unbinned extended maximum likelihood
fit to the invariant mass
m
(
D
0
Λ
Λ
) and the energy sub-
stituted mass
m
ES
. The latter is defined as
m
ES
=
(
s/
2 +
p
0
·
p
B
)
2
/E
2
0
−|
p
|
2
B
,
(2)
where
s
is the center-of-mass energy,
p
B
the
B
can-
didate’s momentum, and (
E
0
,
p
0
) the four-momentum
vector of the
e
+
e
system, each given in the laboratory
frame. Both
m
(
D
0
Λ
Λ
) and
m
ES
are centered at the
B
mass for well reconstructed
B
decays.
Due to the small mass difference of 76
.
9 MeV
/c
2
[1]
between the
Λ
and
Σ
0
baryons,
B
0
D
0
Σ
0
Λ
decays,
where the
Σ
0
decays radiatively as
Σ
0
Λγ
, are a source
of background. Such events peak at the
B
mass in
m
ES
and are slightly shifted in
m
(
D
0
Λ
Λ
) with respect to
B
0
D
0
Λ
Λ
(Fig. 3). We account for this decay by including
an explicit term in the likelihood function (see below),
whose yield is determined in the fit.
We divide the data sample into three subsamples cor-
responding to the
D
0
decay modes. Given their different
signal-to-background ratios, we determine the number of
signal candidates in a simultaneous fit to the three in-
dependent subsamples. We describe each
B
0
D
0
Λ
Λ
signal sample with the product of a Novosibirsk func-
tion in
m
ES
and a sum of two Gaussian functions
f
GG
in
m
(
D
0
Λ
Λ
) assuming that
m
ES
and
m
(
D
0
Λ
Λ
) are not
correlated. We study simulated samples of signal and
background events and find no significant correlation be-
tween
m
ES
and
m
(
D
0
Λ
Λ
). The Novosibirsk function is
defined as
f
Novo
(
m
ES
) = exp
[
1
2
(
ln
2
[1 +
λα
(
m
ES
μ
)]
α
2
+
α
2
)]
,
λ
= sinh(
α
ln 4)
/
(
σα
ln 4)
,
(3)
with
μ
the mean value,
σ
the width, and
α
the tail pa-
rameter. The decay
B
0
D
0
Σ
0
Λ
is described by the
product of a Novosibirsk
f
Novo1
0
function in
m
ES
and
a sum of another Novosibirsk function
f
Novo2
0
and a
Gaussian
G
Σ
0
in
m
(
D
0
Λ
Λ
). All parameters are deter-
mined using Monte Carlo simulated events and are fixed
in the final fit. Background from
e
+
e
q
q
events and
other
B
meson decays is modeled by the product of an
ARGUS function [23] in
m
ES
and a first order polynomial
in
m
(
D
0
Λ
Λ
).
The full fit function is defined as
8
)
2
(GeV/c
ES
m
5.25
5.26
5.27
5.28
5.29
)
2
) (GeV/c
Λ
Λ
0
m(D
5.2
5.25
5.3
5.35
0
50
100
150
200
250
)
2
(GeV/c
ES
m
5.25
5.26
5.27
5.28
5.29
)
2
) (GeV/c
Λ
Λ
0
m(D
5.2
5.25
5.3
5.35
0
2
4
6
8
10
12
14
16
18
20
FIG. 3: Distributions for
B
0
D
0
Λ
Λ
(left) and
B
0
D
0
Σ
0
Λ
reconstructed as
B
0
D
0
Λ
Λ
(right) for the
D
0
K
π
+
mode
in simulated events.
f
Fit
j
=
f
Λ
j
+
f
Σ
0
j
+
f
Bkg
j
=
f
Novo
j
(
m
ES
)
×
f
GG
j
(
m
(
D
0
Λ
Λ
)
)
+
f
Novo1
0
j
(
m
ES
)
×
[
f
Novo2
0
j
(
m
(
D
0
Λ
Λ
)
)
+
G
Σ
0
j
(
m
(
D
0
Λ
Λ
)
)
]
+
f
ARGUS
j
(
m
ES
)
×
f
Poly
j
(
m
(
D
0
Λ
Λ
)
)
,
(4)
where the index
j
corresponds to the three
D
0
decay
modes.
The branching fraction is determined from
B
(
B
0
D
0
Λ
Λ
) =
N
(
B
0
D
0
Λ
Λ
)
2
N
B
0
B
0
×
ε
Λ
×
1
B
(
Λ
)
2
B
(
D
0
X
)
,
(5)
where
N
(
B
0
D
0
Λ
Λ
) is the fitted signal yield,
N
B
0
B
0
the
number of the
B
0
B
0
pairs assuming
B
(
Υ
(4
S
)
B
0
B
0
) =
0
.
5,
ε
Λ
the total reconstruction efficiency, and
B
(
Λ
)
and
B
(
D
0
X
) the branching fractions for the daughter
decays of
Λ
and
D
0
, respectively. An analogous expres-
sion holds for
B
(
B
0
D
0
Σ
0
Λ
). We perform a simulta-
neous fit of the three
D
0
decay channels to obtain:
N
Λ
=
N
(
B
0
D
0
Λ
Λ
)
ε
Λ
B
(
D
0
X
)
,
N
Σ
0
=
N
(
B
0
D
0
Σ
0
Λ
)
ε
Σ
0
B
(
D
0
X
)
.
(6)
The likelihood function is given by
L
=
j
e
(
ε
Λ
j
B
j
N
Λ
+
N
Bkg
j
+
ε
Σ
0
j
B
j
N
Σ
0
)
N
(
j
)!
N
(
j
)
k
[
ε
Λ
j
B
j
N
Λ
f
Λ
j
(
m
ES
k
,m
(
D
0
Λ
Λ
)
k
)
+
N
Bkg
j
f
Bkg
j
(
m
ES
k
,m
(
D
0
Λ
Λ
)
k
)
+
ε
Σ
0
j
B
j
N
Σ
0
f
Σ
0
j
(
m
ES
k
,m
(
D
0
Λ
Λ
)
k
)
]
,
(7)
where
B
j
is the branching fraction for the
j
th
D
0
decay,
N
Bkg
j
the number of combinatorial background events in
the
j
th subsample,
N
Λ
and
N
Σ
0
the yields of
B
0
D
0
Λ
Λ
and
B
0
D
0
Σ
0
Λ
, and
ε
Λ
j
and
ε
Σ
0
j
the efficiencies for the
j
th
D
0
decay.
9
V. SYSTEMATIC UNCERTAINTIES
We consider the following systematic uncertainties: the
uncertainties associated with the number of
B
B
events,
the particle identification (PID) algorithm, the tracking
algorithm, the
π
0
reconstruction, the
D
0
and
Λ
branching
fractions, the efficiency correction, and the fitting algo-
rithm.
The uncertainty associated with the number of
B
B
pairs is 0
.
6%. We determine the systematic uncertainty
associated with the PID by applying different PID se-
lections and comparing the result with the nominal se-
lection. The difference is 0
.
8%, which is assigned as the
PID uncertainty. The systematic uncertainty associated
with the tracking algorithm depends on the number of
charged tracks in the decay. We assign a systematic un-
certainty of 0
.
9% for the
D
0
K
π
+
and
D
0
K
π
+
π
0
decays and 1
.
2% for the
D
0
K
π
+
π
+
π
decay. A 3%
uncertainty is assigned to account for the
π
0
reconstruc-
tion in
D
0
K
π
+
π
0
decays. A detailed description of
these detector-related systematic uncertainties is given in
Ref. [18].
We rely on the known
D
0
branching fractions in our
fit. To estimate the associated systematic uncertainty we
vary each branching fraction by one standard deviation of
its uncertainty [1] and define the systematic uncertainty
to be the maximum deviation observed with respect to
the nominal analysis. We divide
m
(
Λ
Λ
) into six bins and
determine the total reconstruction efficiency
ε
i
in each
bin. We determine the uncertainty due to the use of the
average efficiency ̄
ε
by studying
|
ε
i
̄
ε
|
/
̄
ε
as a function
of
m
(
Λ
Λ
). We average these values and take the result
of 16
.
3% (
D
0
K
π
+
), 19
.
6% (
D
0
K
π
+
π
0
), and
16
.
8% (
D
0
K
π
+
π
+
π
) as our estimate of the sys-
tematic uncertainty for the efficiency. We estimate the
systematic uncertainty due to the fit procedure by inde-
pendently varying the fit ranges of
m
ES
and
m
(
D
0
Λ
Λ
).
The largest differences in the signal yield are 3
.
9% for the
change of the
m
ES
fit range and 2
.
1% for the change of the
m
(
D
0
Λ
Λ
) fit range. To check our background model, we
use a second-order polynomial in
m
(
D
0
Λ
Λ
) instead of a
first-order polynomial. The signal yield changes by 1
.
1%.
We use an ensemble of simulated data samples reflecting
our fit results to verify the stability of the fit. We gen-
erate 1000 such samples with shapes and yields fixed to
our results and repeat the final fit. We find no bias in
the signal-yield results. All systematic uncertainties are
summarized in Table II.
The total systematic uncertainty, obtained by adding
all sources in quadrature, is 20
.
1%.
TABLE II: Summary of the systematic uncertainties for
B
0
D
0
Λ
Λ
.
Source
Relative uncertainty
B
B
counting
0
.
6%
Particle identification
0
.
8%
Tracking
D
0
K
π
+
0
.
9%
D
0
K
π
+
π
0
0
.
9%
D
0
K
π
+
π
+
π
1
.
2%
π
0
systematics
D
0
K
π
+
π
0
3
.
0%
D
0
and
Λ
branching fractions
2
.
9%
Efficiency correction
D
0
K
π
+
16
.
3%
D
0
K
π
+
π
0
19
.
6%
D
0
K
π
+
π
+
π
16
.
8%
Fit procedure
4
.
6%
Total uncertainty
20
.
1%
VI. RESULTS
The one-dimensional projections of the fit are shown
in Fig. 4. We find
N
Λ
= 1880
+560
500
,
N
Σ
0
= 2870
+1680
1560
.
(8)
The
statistical
significance
is
calculated
as
2 log
L
0
/L
S
, where
L
0
is the likelihood value
for a fit without a signal component and
L
S
is the
likelihood value for the nominal fit. The statistical sig-
nificance of the combined
B
0
D
0
Λ
Λ
and
B
0
D
0
Σ
0
Λ
yields is 3
.
9 standard deviations (
σ
), while those of the
individual
B
0
D
0
Λ
Λ
and
B
0
D
0
Σ
0
Λ
results are
3
.
4
σ
and 1
.
2
σ
, respectively. Compared to the statistical
uncertainty the additive systematic uncertainties are
negligible. We therefore quote the statistical significance
as the global significance.
The branching fractions are
B
(
B
0
D
0
Λ
Λ
) =
(
9
.
8
+2
.
9
2
.
6
±
1
.
9
)
×
10
6
,
B
(
B
0
D
0
Σ
0
Λ
+
B
0
D
0
Λ
Σ
0
) =
(
15
+9
8
±
3
)
×
10
6
,
(9)
where the first uncertainties represent the statistical un-
certainties and the second the systematic uncertainties.
As a cross-check of the method, independent fits to the
three sub-samples are performed. The results of each of
these fits are consistent with each other and with the
nominal combined fit.
Since the statistical significance for
B
(
B
0
D
0
Σ
0
Λ
+
B
0
D
0
Λ
Σ
0
) is low, a Bayesian upper limit at the 90%
confidence level is calculated by integrating the likelihood
function:
B
(
B
0
D
0
Σ
0
Λ
+
B
0
D
0
Λ
Σ
0
)
<
3
.
1
×
10
5
.
(10)
10
)
2
(GeV/c
ES
m
5.2
5.21
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
)
2
Events / ( 3.6 MeV/c
0
2
4
6
8
10
12
14
)
2
) (GeV/c
Λ
Λ
0
m(D
5.15
5.2
5.25
5.3
5.35
5.4
)
2
Events / ( 10 MeV/c
0
1
2
3
4
5
6
7
)
2
(GeV/c
ES
m
5.2
5.21
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
)
2
Events / ( 3.6 MeV/c
0
10
20
30
40
50
60
70
)
2
) (GeV/c
Λ
Λ
0
m(D
5.15
5.2
5.25
5.3
5.35
5.4
)
2
Events / ( 10 MeV/c
0
2
4
6
8
10
12
14
16
18
)
2
(GeV/c
ES
m
5.2
5.21
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
)
2
Events / ( 3.6 MeV/c
0
10
20
30
40
50
)
2
) (GeV/c
Λ
Λ
0
m(D
5.15
5.2
5.25
5.3
5.35
5.4
)
2
Events / ( 10 MeV/c
0
2
4
6
8
10
12
14
16
FIG. 4: Results of the combined fit. The
m
ES
projection is shown for
m
(
D
0
Λ
Λ
)
[5
.
15
,
5
.
31] GeV
/c
2
and the
m
(
D
0
Λ
Λ
)
projection for
m
ES
[5
.
272
,
5
.
286] GeV
/c
2
. The solid line shows the result of the fit, the dashed curve indicates the
B
0
D
0
Σ
0
Λ
contribution, and the shaded histogram the combinatorial background. From top to bottom:
D
0
K
π
+
,
D
0
K
π
+
π
0
, and
D
0
K
π
+
π
+
π
subsamples.
To investigate the threshold dependence, we perform
the fit in bins of
m
(
Λ
Λ
) and examine the resulting distri-
bution after accounting for the reconstruction efficiency
and
D
0
branching fractions. The results are shown in
Fig. 5. No enhancement in the
B
0
D
0
Λ
Λ
event rate is
observed at the baryon-antibaryon mass threshold within
the uncertainties, in contrast to
B
0
D
0
p
p
decays, which
do exhibit such an enhancement [8].
We compare our results for the
B
0
D
0
Λ
Λ
and
B
0
D
0
Σ
0
Λ
branching fractions to theoretical pre-
dictions. The result we obtain for the
B
0
D
0
Σ
0
Λ
branching fraction is consistent with the prediction of
B
(
B
0
D
0
Σ
0
Λ
+
B
0
D
0
Λ
Σ
0
) = (18
±
5)
×
10
6
from Ref. [11]. However, the obtained result for the
B
0
D
0
Λ
Λ
branching fraction is larger than the predic-
tion of
B
(
B
0
D
0
Λ
Λ
) = (2
±
1)
×
10
6
[11] by a factor
of
B
(
B
0
D
0
Λ
Λ
)
exp
B
(
B
0
D
0
Λ
Λ
)
theo
= 4
.
9
±
3
.
0
.
(11)
We further determine
B
(
B
0
D
0
Σ
0
Λ
+
B
0
D
0
Λ
Σ
0
)
B
(
B
0
D
0
Λ
Λ
)
= 1
.
5
±
0
.
9
,
(12)
which is in agreement with our assumption that all four
modes
B
0
D
0
Λ
Λ
,
B
0
D
0
Σ
0
Λ
,
B
0
D
0
Λ
Σ
0
, and
B
0
D
0
Σ
0
Σ
0
are produced at equal rates. For the ratio
of branching fractions we find
B
(
B
0
D
0
Λ
Λ
)
B
(
B
0
D
0
p
p
)
=
1
10
.
6
±
3
.
7
,
(13)
using
B
(
B
0
D
0
p
p
) = (1
.
04
±
0
.
04)
×
10
4
[1]. This
is in agreement with the expected suppression of 1
/
12
discussed in the introduction.
11
)
2
) (GeV/c
Λ
Λ
m(
2.4
2.6
2.8
3
3.2
3.4
)
2
Events / (0.2 GeV/c
0
200
400
600
800
FIG. 5: Distribution of the invariant baryon-antibaryon
mass for
D
0
-branching-fraction and efficiency-corrected
B
0
D
0
Λ
Λ
signal candidates.
The data points represent the
B
A
B
AR
data and the shaded histogram indicates phase-space-
distributed simulated events, scaled to match the area under
the data.
VII. SUMMARY
We find evidence for the baryonic
B
decay
B
0
D
0
Λ
Λ
.
We determine the branching fraction to be
B
(
B
0
D
0
Λ
Λ
) = (9
.
8
+2
.
9
2
.
6
±
1
.
9)
×
10
6
with a significance of
3
.
4
σ
including systematic uncertainties. This is in agree-
ment with the Belle measurement [13].
We find no
evidence for an enhancement in the invariant baryon-
antibaryon mass distribution near threshold. Our re-
sult for the branching fraction deviates from theoreti-
cal predictions based on measurements of
B
0
D
0
p
p
but agrees with simple models of hadronization. We
find no evidence for the decay
B
0
D
0
Σ
0
Λ
and cal-
culate a Bayesian upper limit at 90% confidence level of
B
(
B
0
D
0
Σ
0
Λ
+
B
0
D
0
Λ
Σ
0
)
<
3
.
1
×
10
5
. This
result is in agreement with the theoretical expectation.
We are grateful for the extraordinary contributions of
our PEP-II colleagues in achieving the excellent luminos-
ity and machine conditions that have made this work pos-
sible. The success of this project also relies critically on
the expertise and dedication of the computing organiza-
tions that support
B
A
B
AR
. The collaborating institutions
wish to thank SLAC for its support and the kind hospital-
ity extended to them. This work is supported by the US
Department of Energy and National Science Foundation,
the Natural Sciences and Engineering Research Council
(Canada), the Commissariat `a l’Energie Atomique and
Institut National de Physique Nucl ́eaire et de Physique
des Particules (France), the Bundesministerium f ̈ur Bil-
dung und Forschung and Deutsche Forschungsgemein-
schaft (Germany), the Istituto Nazionale di Fisica Nu-
cleare (Italy), the Foundation for Fundamental Research
on Matter (The Netherlands), the Research Council of
Norway, the Ministry of Education and Science of the
Russian Federation, Ministerio de Ciencia e Innovaci ́on
(Spain), and the Science and Technology Facilities Coun-
cil (United Kingdom). Individuals have received support
from the Marie-Curie IEF program (European Union),
the A. P. Sloan Foundation (USA) and the Binational
Science Foundation (USA-Israel).
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