of 14
Search for the decay modes
B

!
h

‘
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
D. A. Milanes,
3a
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
D. J. Asgeirsson,
7
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
A. Khan,
8
V. E. Blinov,
9
A. R. Buzykaev,
9
V. P. Druzhinin,
9
V. B. Golubev,
9
E. A. Kravchenko,
9
A. P. Onuchin,
9
S. I. Serednyakov,
9
Yu. I. Skovpen,
9
E. P. Solodov,
9
K. Yu. Todyshev,
9
A. N. Yushkov,
9
M. Bondioli,
10
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
D. P. Stoker,
10
H. Atmacan,
11
J. W. Gary,
11
F. Liu,
11
O. Long,
11
G. M. Vitug,
11
C. Campagnari,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
J. Kroseberg,
13
W. S. Lockman,
13
A. J. Martinez,
13
T. Schalk,
13
B. A. Schumm,
13
A. Seiden,
13
C. H. Cheng,
14
D. A. Doll,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
A. Y. Rakitin,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
M. Nagel,
16
U. Nauenberg,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
*
W. H. Toki,
17
B. Spaan,
18
M. J. Kobel,
19
K. R. Schubert,
19
R. Schwierz,
19
D. Bernard,
20
M. Verderi,
20
P. J. Clark,
21
S. Playfer,
21
D. Bettoni,
22a
C. Bozzi,
22a
R. Calabrese,
22a,22b
G. Cibinetto,
22a,22b
E. Fioravanti,
22a,22b
I. Garzia,
22a,22b
E. Luppi,
22a,22b
M. Munerato,
22a,22b
M. Negrini,
22a,22b
L. Piemontese,
22a
V. Santoro,
22a
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
23
P. Patteri,
23
I. M. Peruzzi,
23,
M. Piccolo,
23
M. Rama,
23
A. Zallo,
23
R. Contri,
24a,24b
E. Guido,
24a,24b
M. Lo Vetere,
24a,24b
M. R. Monge,
24a,24b
S. Passaggio,
24a
C. Patrignani,
24a,24b
E. Robutti,
24a
B. Bhuyan,
25
V. Prasad,
25
C. L. Lee,
26
M. Morii,
26
A. J. Edwards,
27
A. Adametz,
28
J. Marks,
28
U. Uwer,
28
H. M. Lacker,
29
T. Lueck,
29
P. D. Dauncey,
30
P. K. Behera,
31
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
W. T. Meyer,
32
S. Prell,
32
A. E. Rubin,
32
A. V. Gritsan,
33
Z. J. Guo,
33
N. Arnaud,
34
M. Davier,
34
D. Derkach,
34
G. Grosdidier,
34
F. Le Diberder,
34
A. M. Lutz,
34
B. Malaescu,
34
P. Roudeau,
34
M. H. Schune,
34
A. Stocchi,
34
G. Wormser,
34
D. J. Lange,
35
D. M. Wright,
35
I. Bingham,
36
C. A. Chavez,
36
J. P. Coleman,
36
J. R. Fry,
36
E. Gabathuler,
36
D. E. Hutchcroft,
36
D. J. Payne,
36
C. Touramanis,
36
A. J. Bevan,
37
F. Di Lodovico,
37
R. Sacco,
37
M. Sigamani,
37
G. Cowan,
38
D. N. Brown,
39
C. L. Davis,
39
A. G. Denig,
40
M. Fritsch,
40
W. Gradl,
40
A. Hafner,
40
E. Prencipe,
40
K. E. Alwyn,
41
D. Bailey,
41
R. J. Barlow,
41,
G. Jackson,
41
G. D. Lafferty,
41
E. Behn,
42
R. Cenci,
42
B. Hamilton,
42
A. Jawahery,
42
D. A. Roberts,
42
G. Simi,
42
C. Dallapiccola,
43
R. Cowan,
44
D. Dujmic,
44
G. Sciolla,
44
D. Lindemann,
45
P. M. Patel,
45
S. H. Robertson,
45
M. Schram,
45
P. Biassoni,
46a,46b
N. Neri,
46a
F. Palombo,
46a,46b
S. Stracka,
46a,46b
L. Cremaldi,
47
R. Godang,
47,
§
R. Kroeger,
47
P. Sonnek,
47
D. J. Summers,
47
X. Nguyen,
48
M. Simard,
48
P. Taras,
48
G. De Nardo,
49a,49b
D. Monorchio,
49a,49b
G. Onorato,
49a,49b
C. Sciacca,
49a,49b
M. Martinelli,
50
G. Raven,
50
C. P. Jessop,
51
K. J. Knoepfel,
51
J. M. LoSecco,
51
W. F. Wang,
51
K. Honscheid,
52
R. Kass,
52
J. Brau,
53
R. Frey,
53
N. B. Sinev,
53
D. Strom,
53
E. Torrence,
53
E. Feltresi,
54a,54b
N. Gagliardi,
54a,54b
M. Margoni,
54a,54b
M. Morandin,
54a
M. Posocco,
54a
M. Rotondo,
54a
F. Simonetto,
54a,54b
R. Stroili,
54a,54b
S. Akar,
55
E. Ben-Haim,
55
M. Bomben,
55
G. R. Bonneaud,
55
H. Briand,
55
G. Calderini,
55
J. Chauveau,
55
O. Hamon,
55
Ph. Leruste,
55
G. Marchiori,
55
J. Ocariz,
55
S. Sitt,
55
M. Biasini,
56a,56b
E. Manoni,
56a,56b
S. Pacetti,
56a,56b
A. Rossi,
56a,56b
C. Angelini,
57a,57b
G. Batignani,
57a,57b
S. Bettarini,
57a,57b
M. Carpinelli,
57a,57b,
k
G. Casarosa,
57a,57b
A. Cervelli,
57a,57b
F. Forti,
57a,57b
M. A. Giorgi,
57a,57b
A. Lusiani,
57a,57c
B. Oberhof,
57a,57b
E. Paoloni,
57a,57b
A. Perez,
57a
G. Rizzo,
57a,57b
J. J. Walsh,
57a
D. Lopes Pegna,
58
C. Lu,
58
J. Olsen,
58
A. J. S. Smith,
58
A. V. Telnov,
58
F. Anulli,
59a
G. Cavoto,
59a
R. Faccini,
59a,59b
F. Ferrarotto,
59a
F. Ferroni,
59a,59b
M. Gaspero,
59a,59b
L. Li Gioi,
59a
M. A. Mazzoni,
59a
G. Piredda,
59a
C. Bu
̈
nger,
60
O. Gru
̈
nberg,
60
T. Hartmann,
60
T. Leddig,
60
H. Schro
̈
der,
60
C. Voss,
60
R. Waldi,
60
T. Adye,
61
E. O. Olaiya,
61
F. F. Wilson,
61
S. Emery,
62
G. Hamel de Monchenault,
62
G. Vasseur,
62
Ch. Ye
`
che,
62
D. Aston,
63
D. J. Bard,
63
R. Bartoldus,
63
C. Cartaro,
63
M. R. Convery,
63
J. Dorfan,
63
G. P. Dubois-Felsmann,
63
W. Dunwoodie,
63
M. Ebert,
63
R. C. Field,
63
M. Franco Sevilla,
63
B. G. Fulsom,
63
A. M. Gabareen,
63
M. T. Graham,
63
P. Grenier,
63
C. Hast,
63
W. R. Innes,
63
M. H. Kelsey,
63
P. Kim,
63
M. L. Kocian,
63
D. W. G. S. Leith,
63
P. Lewis,
63
B. Lindquist,
63
S. Luitz,
63
V. Luth,
63
H. L. Lynch,
63
D. B. MacFarlane,
63
D. R. Muller,
63
H. Neal,
63
S. Nelson,
63
M. Perl,
63
T. Pulliam,
63
B. N. Ratcliff,
63
A. Roodman,
63
A. A. Salnikov,
63
R. H. Schindler,
63
A. Snyder,
63
D. Su,
63
M. K. Sullivan,
63
J. Va’vra,
63
A. P. Wagner,
63
M. Weaver,
63
W. J. Wisniewski,
63
M. Wittgen,
63
D. H. Wright,
63
H. W. Wulsin,
63
C. C. Young,
63
V. Ziegler,
63
W. Park,
64
M. V. Purohit,
64
R. M. White,
64
J. R. Wilson,
64
A. Randle-Conde,
65
S. J. Sekula,
65
M. Bellis,
66
J. F. Benitez,
66
P. R. Burchat,
66
T. S. Miyashita,
66
M. S. Alam,
67
J. A. Ernst,
67
R. Gorodeisky,
68
N. Guttman,
68
D. R. Peimer,
68
A. Soffer,
68
P. Lund,
69
S. M. Spanier,
69
R. Eckmann,
70
J. L. Ritchie,
70
A. M. Ruland,
70
C. J. Schilling,
70
R. F. Schwitters,
70
B. C. Wray,
70
J. M. Izen,
71
X. C. Lou,
71
F. Bianchi,
72a,72b
D. Gamba,
72a,72b
L. Lanceri,
73a,73b
L. Vitale,
73a,73b
F. Martinez-Vidal,
74
A. Oyanguren,
74
PHYSICAL REVIEW D
86,
012004 (2012)
1550-7998
=
2012
=
86(1)
=
012004(14)
012004-1
Ó
2012 American Physical Society
H. Ahmed,
75
J. Albert,
75
Sw. Banerjee,
75
F. U. Bernlochner,
75
H. H. F. Choi,
75
G. J. King,
75
R. Kowalewski,
75
M. J. Lewczuk,
75
I. M. Nugent,
75
J. M. Roney,
75
R. J. Sobie,
75
N. Tasneem,
75
T. J. Gershon,
76
P. F. Harrison,
76
T. E. Latham,
76
E. M. T. Puccio,
76
H. R. Band,
77
S. Dasu,
77
Y. Pan,
77
R. Prepost,
77
and S. L. Wu
77
(
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite
́
de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
10
University of California at Irvine, Irvine, California 92697, USA
11
University of California at Riverside, Riverside, California 92521, USA
12
University of California at Santa Barbara, Santa Barbara, California 93106, USA
13
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California 91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, USA
18
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
19
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
20
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
21
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
22a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
22b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
23
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
24a
INFN Sezione di Genova, I-16146 Genova, Italy
24b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
25
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
26
Harvard University, Cambridge, Massachusetts 02138, USA
27
Harvey Mudd College, Claremont, California 91711
28
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
29
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstr. 15, D-12489 Berlin, Germany
30
Imperial College London, London, SW7 2AZ, United Kingdom
31
University of Iowa, Iowa City, Iowa 52242, USA
32
Iowa State University, Ames, Iowa 50011-3160, USA
33
Johns Hopkins University, Baltimore, Maryland 21218, USA
34
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, IN2P3/CNRS et Universite
́
Paris-Sud 11, Centre Scientifique d’Orsay,
B. P. 34, F-91898 Orsay Cedex, France
35
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
36
University of Liverpool, Liverpool L69 7ZE, United Kingdom
37
Queen Mary, University of London, London, E1 4NS, United Kingdom
38
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
39
University of Louisville, Louisville, Kentucky 40292, USA
40
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
41
University of Manchester, Manchester M13 9PL, United Kingdom
42
University of Maryland, College Park, Maryland 20742, USA
43
University of Massachusetts, Amherst, Massachusetts 01003, USA
44
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
45
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
46a
INFN Sezione di Milano, I-20133 Milano, Italy
46b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
47
University of Mississippi, University, Mississippi 38677, USA
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
012004 (2012)
012004-2
48
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
49a
INFN Sezione di Napoli, I-80126 Napoli, Italy
49b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
50
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, Netherlands
51
University of Notre Dame, Notre Dame, Indiana 46556, USA
52
Ohio State University, Columbus, Ohio 43210, USA
53
University of Oregon, Eugene, Oregon 97403, USA
54a
INFN Sezione di Padova, I-35131 Padova, Italy
54b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
55
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
56a
INFN Sezione di Perugia, I-06100 Perugia, Italy
56b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
57a
INFN Sezione di Pisa, I-56127 Pisa, Italy
57b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
57c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
58
Princeton University, Princeton, New Jersey 08544, USA
59a
INFN Sezione di Roma, I-00185 Roma, Italy
59b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
60
Universita
̈
t Rostock, D-18051 Rostock, Germany
61
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
62
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
63
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
64
University of South Carolina, Columbia, South Carolina 29208, USA
65
Southern Methodist University, Dallas, Texas 75275, USA
66
Stanford University, Stanford, California 94305-4060, USA
67
State University of New York, Albany, New York 12222, USA
68
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
69
University of Tennessee, Knoxville, Tennessee 37996, USA
70
University of Texas at Austin, Austin, Texas 78712, USA
71
University of Texas at Dallas, Richardson, Texas 75083, USA
72a
INFN Sezione di Torino, I-10125 Torino, Italy
72b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
73a
INFN Sezione di Trieste, I-34127 Trieste, Italy
73b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
74
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
75
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
76
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
77
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 16 April 2012; published 16 July 2012)
We present a search for the lepton flavor violating decay modes
B

!
h

‘
(
h
¼
K
,

;
¼
e
,

)
using the
BABAR
data sample, which corresponds to
472

10
6
B

B
pairs. The search uses events where
one
B
meson is fully reconstructed in one of several hadronic final states. Using the momenta of the
reconstructed
B
,
h
, and
candidates, we are able to fully determine the

four-momentum. The resulting

candidate mass is our main discriminant against combinatorial background. We see no evidence for
B

!
h

‘
decays and set a 90% confidence level upper limit on each branching fraction at the level of a
few times
10

5
.
DOI:
10.1103/PhysRevD.86.012004
PACS numbers: 13.25.Hw, 14.40.Nd
I. INTRODUCTION
The standard model (SM) of electroweak interactions
does not allow charged lepton flavor violation or flavor-
changing neutral currents in tree-level interactions [
1
].
Lepton flavor violating decays of
B
mesons can occur at
the one-loop level through processes that involve neutrino
mixing, but these are highly suppressed by powers of
m
2

=m
2
W
[
2
] and have predicted branching fractions many
*
Present address: University of Tabuk, Tabuk 71491, Saudi
Arabia.
Also at Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
Present address: University of Huddersfield, Huddersfield
HD1 3DH, United Kingdom.
§
Present address: University of South Alabama, Mobile,
Alabama 36688, USA.
k
Also at Universita
`
di Sassari, Sassari, Italy.
SEARCH FOR THE DECAY MODES
...
PHYSICAL REVIEW D
86,
012004 (2012)
012004-3
orders of magnitude below the current experimental sensi-
tivity. However, in many extensions of the SM,
B
decays
involving lepton flavor violation and/or flavor-changing
neutral currents interactions are greatly enhanced [
2
5
].
In some cases, decays involving the second and third
generations of quarks and leptons are particularly sensitive
to physics beyond the SM [
3
].
Until recent years, experimental information on
B
decays to final states containing

leptons has been weak
or absent. The presence of at least one neutrino from the

decay prevents direct reconstruction of the

, making it
difficult to distinguish
B
!
X
decays from the abundant
semileptonic
B
!
X‘
;
¼
e
,

decays. The high-
luminosity
B
factory experiments have developed the tech-
nique of using a fully reconstructed hadronic
B
decay (the
‘‘tag’’
B
) to determine the three-momentum of the other
B
(the ‘‘signal’’
B
)in

ð
4
S
Þ!
B

B
events, which enables the

to be indirectly reconstructed. This technique assigns all
detected tracks and neutral objects to either the tag
B
or the
signal
B
. Recent applications of this technique by
BABAR
are the searches for
B
þ
!
K
þ

[
6
],
B
0
!



[
7
]
and
B
þ
!

þ

[
8
]. We present an update of our search
for
B
þ
!
K
þ

[
6
] and the first search for the decays
B
þ
!
K
þ
e
,
B
þ
!

þ

, and
B
þ
!

þ
e
[
9
].
The signal branching fraction is determined by using the
ratio of the number of
B
!
h‘
(
h
¼
K

,


) signal
candidates to the yield of control samples of
B
þ
!

D
ðÞ
0
þ

;

D
0
!
K
þ


events from a fully reconstructed
hadronic
B

decay sample. Continuum background is sup-
pressed for each decay channel using a likelihood ratio
based on event shape information, unassociated calorime-
ter clusters, and the quality of muon identification for
channels that have a muon in the final state. Final signal
candidates are selected requiring the indirectly recon-
structed

mass to fall in a narrow window around the
known

mass. The yield and estimated background in the

mass signal window are used to estimate and set upper
limits on the signal branching fractions. We followed the
principle of a blind analysis, to avoid experimenter’s bias,
by not revealing the number of events in the signal window
until after all analysis procedures were decided.
II. DATA SAMPLE AND DETECTOR
DESCRIPTION
We use a data sample of
472

10
6
B

B
pairs in
429 fb

1
of
integrated luminosity, delivered by the PEP-II asymmetric-
energy
e
þ
e

collider and recorded by the
BABAR
experiment
at the SLAC National Accelerator Laboratory. This corre-
sponds to the entire

ð
4
S
Þ
data sample.
The
BABAR
experiment is described in detail elsewhere
[
10
]. Trajectories of charged particles are reconstructed
by a double-sided, five-layer silicon vertex tracker (SVT)
and a 40-layer drift chamber (DCH). The SVT provides
precision measurements for vertex reconstruction and
stand-alone tracking for very low momentum tracks, with
transverse momentum less than
120 MeV
=c
. The tracking
system is inside a 1.5 T superconducting solenoid. Both the
SVT and the DCH provide specific ionization (
dE=dx
)
measurements that are used in particle identification
(PID). Just beyond the radius of the DCH lies an array of
fused silica bars which are part of the detector of internally
reflected Cherenkov radiation (DIRC). The DIRC provides
excellent charged-hadron PID. A CsI(Tl) crystal electro-
magnetic calorimeter (EMC) is used to reconstruct photons
and identify electrons. The minimum EMC cluster energy
used in this analysis is 30 MeV. The iron of the flux return
for the solenoid is instrumented with resistive plate cham-
bers and limited streamer tubes, which are used in the
identification of muons.
Monte Carlo (MC) simulated samples for our
B
!
h‘
signals and for all relevant SM processes are generated with
EvtGen [
11
]. We model the
BABAR
detector response using
GEANT4
[
12
]. The
B
!
h‘
decays are generated using a
uniform three-body phase space model and the background
MC sample combines SM processes:
e
þ
e

!

ð
4
S
Þ!
B

B
,
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
,
c
), and
e
þ
e

!

þ


.The
number of simulated Monte Carlo events corresponds to
integrated luminosities equivalent to 3 times the data for
B

B
events and 2 times the data for the continuum processes.
Each Monte Carlo sample is reweighted to correspond to an
integrated luminosity equivalent to the data.
The data and MC samples in this analysis are processed
and generated with consistent database conditions deter-
mined from the detector response and analyzed using
BABAR
analysis software release tools.
III. EVENT RECONSTRUCTION
In each event, we require a fully reconstructed hadronic
B

decay, which we refer to as the tag
B
meson candidate
or
B
tag
. We then search for the signal
B
!
h‘
decay in the
rest of the event, which we refer to as the signal
B
meson
candidate or
B
sig
. The notation
B
!
h‘
refers to one
of the following eight final states that we consider, where
the primary hadron
h
is a
K
or

and the primary lepton
is a

or
e
:
B
þ
!
K
þ



þ
,
B
þ
!
K
þ

þ


,
B
þ
!
K
þ


e
þ
,
B
þ
!
K
þ

þ
e

,
B
þ
!

þ



þ
,
B
þ
!

þ

þ


,
B
þ
!

þ


e
þ
, and
B
þ
!

þ

þ
e

. In all
cases, we require that the

decays to a ‘‘one-prong’’ final
state [

!
e


,

!



, and

n
0
Þ

with
n

0
].
The branching fraction for

decays to a one-prong final
state is 85%.
The

ð
4
S
Þ!
B
þ
B

decay requires the
B
sig
three-
momentum to be opposite from that of the
B
tag
(

~
p
tag
)
and the
B
sig
energy to be equal to the beam energy (
E
beam
)
in the
e
þ
e

center-of-mass reference frame [
13
]. These
constraints allow us to reconstruct the

indirectly using
~
p

¼
~
p
tag

~
p
h

~
p
;E

¼
E
beam

E
h

E
;
m

¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E
2

j
~
p

j
2
q
;
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
012004 (2012)
012004-4
where
ð
E

;
~
p

Þ
,
ð
E
h
;
~
p
h
Þ
, and
ð
E
;
~
p
Þ
are the correspond-
ing four-momenta of the reconstructed signal objects. The
indirectly reconstructed

mass (
m

) peaks sharply at the
true

mass in
B
!
h‘
signal events and has a very broad
distribution for combinatorial background events. To avoid
experimental bias, we did not look at events in the data
with
m

within

175 MeV
=c
2
of the nominal

mass until
all analysis procedures were established.
A. Tag
B
reconstruction
The
B
tag
is fully reconstructed in one of many final states
[
14
] of the form
B

!
D
ðÞ
0
X

. The notation
D
ðÞ
0
refers
to either a
D
0
or a
D

0
which decays to either
D
0

or
D
0

0
.
The
D
0
is reconstructed in the
K


þ
,
K


þ



þ
,
K


þ

0
, and
K
0
S

þ


channels, with
K
0
S
!

þ


and

0
!

. The
X

represents a system of charged
and neutral hadrons composed of
n
1


,
n
2
K

,
n
3
K
0
S
,
and
n
4

0
; subject to the constraints
n
1
þ
n
2

5
,
n
3

2
,
n
4

2
, and total charge

1
.
Each distinct
B
tag
decay mode has an associated
a
priori
purity, defined as the number of peaking events
divided by the number of peaking plus combinatorial
events, where peaking and combinatorial yields are ob-
tained from fits to the energy-substituted invariant mass
m
ES

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E
2
beam
j
~
p
tag
j
2
q
distributions for each distinct
B
tag
decay mode. We only consider
B
tag
decay modes with a
purity greater than 10% and choose the
B
tag
candidate with
the highest purity in the event. If there is more than one
B
tag
candidate with the same purity, we choose the one with
reconstructed energy closest to the beam energy. The
B
tag
candidate must have
m
ES
>
5
:
27 GeV
=c
2
and
E
tag
within 3
standard deviations of
E
beam
. A charged
B
tag
candidate is
properly reconstructed in approximately 0.25% of all
B

B
events.
B. Particle identification
PID algorithms are used to identify kaons, pions, pro-
tons, muons, and electrons. We use an error-correcting
output code algorithm [
15
] with 36 input variables to
identify electrons, pions, and protons. The error-correcting
output code combines multiple bootstrap aggregated deci-
sion tree binary classifiers trained to separate
e
,

,
K
, and
p
. The most important inputs for electron identification are
the EMC energy divided by the track momentum, several
EMC shower shape variables, and the deviation from the
expected values divided by the measurement uncertainties
of the Cherenkov angle and of the
dE=dx
for the
e
,

,
K
and
p
hypotheses. Neutral clusters in the EMC that are
consistent with bremsstrahlung radiation are used to cor-
rect the momentum and energy of electron candidates. A

candidate from an
e

track is consistent with bremsstrah-
lung radiation if the corresponding three-momenta are
within
j


j
<
35 mrad
and
j


j
<
50 mrad
, with respect
to the polar and azimuthal angles of the beam axis.
Muons and kaons are identified using a bagging decision
trees [
16
] algorithm with 30 (36) input variables for the
muon (kaon) selection. For muons, the most important
input variables are the number and position of the hits in
the instrumented flux return, the difference between the
expected and measured DCH
dE=dx
for the muon
hypothesis, and the energy deposited in the EMC. For
kaons, the most important variables are the kaon and
pion likelihoods based on the measured Cherenkov angle
in the DIRC and the difference between the expected and
measured
dE=dx
for the kaon hypothesis.
We define several quality levels of particle identification
for use in the analysis. The ‘‘loose’’ levels have higher
efficiency but also higher misidentification probabilities.
The ‘‘tight’’ levels have lower misidentification probabil-
ities and efficiencies. Table
I
summarizes the selection
efficiency and misidentification probabilities of the PID
selection algorithms used. A ‘‘very loose’’ (VL)
K
-PID
algorithm is used for identifying the primary
K
in
B
!
K‘
, while a ‘‘very tight’’ (VT)
K
-PID algorithm, with
lower efficiency but much smaller misidentification proba-
bility, is used to reject
B
sig
candidates where a nonkaon
track passes the VT
K
-PID criteria. Four quality levels of

-PID are used. In order of decreasing efficiency and
TABLE I. PID efficiencies and misidentification probabilities for the algorithms used in the analysis. The values are approximate and
representative only for the laboratory frame momentum (
p
lab
) specified (when given). More than one algorithm is used for kaons and
muons. The abbreviations VL, L, T, and VT stand for selection quality levels very loose, loose, tight, and very tight.
Type
Efficiency
Misidentification probability
K
-VL
>
95%
<
6%
for

and

with
p
lab
<
3
:
5 GeV
=c
K
-VT
>
85%
1%
for

and

with
p
lab
<
3
:
5 GeV
=c
>
98%
<
20%
for
K
p
80%
<
0
:
5%
for
K
,

,

,
e

-VL
90%
<
15%
for

with
p
lab
<
1
:
25 GeV
=c
,
<
4%
for

with
p
lab
>
1
:
25 GeV
=c

-L
80%
<
5%
for

with
p
lab
<
1
:
25 GeV
=c
,
<
2%
for

with
p
lab
>
1
:
25 GeV
=c

-T
75%
<
3%
for

with
p
lab
<
1
:
25 GeV
=c
,
1%
for

with
p
lab
>
1
:
25 GeV
=c

-VT
70%
<
2%
for

with
p
lab
<
1
:
25 GeV
=c
,
<
1%
for

with
p
lab
>
1
:
25 GeV
=c
e
95%
<
0
:
2%
for

,
K
,
p
SEARCH FOR THE DECAY MODES
...
PHYSICAL REVIEW D
86,
012004 (2012)
012004-5
misidentification probability, they are VL, loose (L),
tight (T), and VT.
C. Signal
B
reconstruction
The eight
B
!
h‘
decay modes are independently
analyzed. Tracks for the signal
B
reconstruction must
satisfy the following criteria: the distance of closest ap-
proach to the beam axis in the transverse plane must be less
than 1.5 cm; the
z
position of the distance-of-closest-
approach point must be less than 2.5 cm from the primary
vertex of the event; the transverse momentum must be
>
50 MeV
=c
; and the momentum must be
<
10 GeV
=c
.
After selecting the best
B
tag
candidate, we require exactly
three tracks satisfying the above criteria remain in the
event (excluding the
B
tag
daughters) and that the sum of
the charges of these tracks be the opposite of the
B
tag
candidate charge. We refer to these three tracks as the
B
sig
daughters.
We require the primary hadron, which is the
h
in
B
!
h‘
, to be one of the two
B
sig
daughters with the same
charge as the
B
sig
candidate. The primary hadron must pass
the
K
-VL-PID criteria for the
B
!
K‘
modes and the

-PID criteria for the
B
!
‘
modes. For the
B
!
K‘
modes, if both of the
B
sig
daughters with the same charge
meet the minimal
K
-PID criteria, the one with the highest
K
-PID quality level is selected as the primary
K

. If they
have the same
K
-PID quality level, we choose the one with
the lower momentum as the primary
K

. For the
B
!
‘
modes, if both
B
sig
daughters with the same charge meet
the

-PID criteria, we choose the one that gives
m

closest
to the true

mass. This algorithm does not produce an
artificial peak in the signal window of the background
m

distribution. Once the primary hadron candidate has been
assigned, the

daughter and primary lepton are uniquely
defined for a given
B
!
h‘
mode from the remaining two
B
sig
daughters based on their electric charge.
The primary lepton, which is the
in
B
!
h‘
, must
pass either the
e
-PID or the loosest

-PID criteria (

-VL).
We remove events where any of the three
B
sig
daughters
passes the
p
-PID criteria, or where any of the three
B
sig
daughters passes the
K
-VT-PID criteria, with the exception
of the
K

in
B
!
K‘
.
By requiring exactly three
B
sig
daughters, we are re-
stricting the selection to one-prong

decays. For each of
the eight
B
!
h‘
modes, we divide the selection into
three

decay channels: electron, muon, and pion. From
now on, we use ‘‘modes’’ to refer to types of
B
!
h‘
decays and ‘‘channels’’ to refer to types of

decays. The
three

decay channels are analyzed in parallel, with differ-
ent background rejection criteria applied. If the

daughter
satisfies the
e
-PID criteria, the event is assigned to the
electron channel. If the

daughter does not satisfy the
e
-PID, but does satisfy the

-VL-PID criteria, the event is
assigned to the muon channel. If the

daughter passes
neither the
e
-PID or the

-VL-PID, the event is assigned to
the pion channel. This ensures that an event does not get
double counted and categorized into another

decay chan-
nel for a given
B
!
h‘
mode.
Background events with a
B
!
h
ð
c

c
Þ
;
ð
c

c
Þ!
þ

decay can pass our signal selection criteria. We remove
events in the electron (muon) and pion

decay channels of
the
B
!
he
(
B
!
h
) modes if the invariant mass of the
primary lepton and

daughter,
m
‘‘
, is consistent with a
dilepton charmonium decay:
3
:
03
<m
‘‘
<
3
:
14 GeV
=c
2
for the
J=
c
or
3
:
60
<m
‘‘
<
3
:
75 GeV
=c
2
for the
c
ð
2
S
Þ
.
The core dilepton invariant mass resolution for these char-
monium decays is on the order of
12 MeV
=c
2
. These
charmonium vetoes effectively remove the charmonium
background at a minimal cost in signal efficiency. We
also require
m
‘‘
>
0
:
1 GeV
=c
2
for
B
!
he
candidates
in the electron and pion channels to remove candidates
where the primary electron and the

daughter are consis-
tent with originating from a photon conversion.
D.
B

B
background and the
m
ð
K
Þ
invariant mass requirement
After the selection described above, the dominant back-
ground is due to
B

B
events, where the
B
tag
is properly
reconstructed. However, the largest background source
differs depending on the charge of the primary lepton
relative to the charge of the
B
sig
candidate.
When the primary lepton charge is the same as the
B
sig
charge, such as a
B
þ
!
K
þ


þ
candidate, the dominant
background comes from semileptonic
B
decays, such as
B
þ
!

D
ðÞ
0
þ

;

D
0
!
K
þ
X

, where
X

contains a


,
e

,or


and perhaps other charged and/or neutral daugh-
ters that are not reconstructed. For example, the final state
tracks
K
þ


þ
are identical for this background with

D
0
!
K
þ


and the
B
þ
!
K
þ


þ
signal decay with


!




. On the other hand, when the primary lepton
charge is opposite to the
B
sig
charge, such as for a
B
þ
!
K
þ

þ

candidate, the dominant background comes
from semileptonic
D
decays, such as
B
þ
!

D
ðÞ
0
X
þ
;

D
0
!
K
þ



.
To reduce these backgrounds, we reject
B
sig
candidates
where two of the
B
sig
daughters are kinematically compat-
ible with originating from a charm decay, as described
below. For the four
B
!
K‘
modes, we define the vari-
able
m
ð
K
Þ
as the invariant mass of the primary
K
and
the
B
sig
daughter that has opposite charge to this
K
.In
computing
m
ð
K
Þ
, the non-
K
track is assumed to be a
pion. Distributions of
m
ð
K
Þ
for the background and
signal MC are shown in Fig.
1
for
B
!
K
. For the four
B
!
‘
modes, we define
m
ð
K
Þ
by combining two
B
sig
daughters that have opposite charge. Of the two
B
sig
daughters with the same charge as the
B
sig
candidate, we
choose the one with the highest
K
-PID quality level. We
assume that the kaon is one of the
B
sig
daughters with the
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
012004 (2012)
012004-6
same charge as the
B
sig
candidate and the pion is the
B
sig
daughter with the opposite charge as the
B
sig
candidate.
If the two
B
sig
daughters with the same charge as the
B
sig
candidate have the same
K
-PID quality level, we use the
daughter with higher momentum as the kaon in the
m
ð
K
Þ
calculation.
We require
m
ð
K
Þ
>
1
:
95 GeV
=c
2
. This rejects be-
tween 97% and 99% of the background while retaining
between 32% and 37% of the signal for the
B
þ
!
h
þ


þ
modes. For the
B
þ
!

þ

þ

modes, the
m
ð
K
Þ
require-
ment rejects 85% and 89% of the

þ

þ


and

þ

þ
e

background while retaining 72% and 65% of the signal,
respectively. For the
B
þ
!
K
þ

þ

modes, the
m
ð
K
Þ
requirement rejects 92% and 96% of the
K
þ

þ


and
K
þ

þ
e

background while retaining 63% and 62% of the
signal, respectively.
IV.
B
!
D
ðÞ
0
‘
CONTROL SAMPLE
We select a control sample of semileptonic
B
decays
of the form
B
þ
!

D
ðÞ
0
þ

;

D
0
!
K
þ


by requiring
m
ð
K
Þ
to be near the
D
0
mass,
1
:
845
<m
ð
K
Þ
<
1
:
885 GeV
=c
2
. The
D
ðÞ
0
‘
control sample has a negli-
gible amount of combinatorial background. In our search
for
B
!
h‘
, we normalize the
B
!
h‘
branching
fraction by using the measured
D
ðÞ
0
‘
yield taken from
the control sample. We determine the relative amounts
of
B
mesons that decay to

D
0
,

D

0
, and higher resonances
(

D

0
) using the reconstructed center-of-mass energy
difference
E

¼
p

¼j
~
p
tag

~
p
K

~
p


~
p
j
;

E
D‘
¼
E
K
þ
E

þ
E
þ
E


E
beam
:
For
B
þ
!

D
0
þ

decays,

E
D‘
is centered at zero. The
missing neutral particles from

D

0
and

D

0
decays shift

E
D‘
in the negative direction.
The expected observed yields of
D‘
and
h‘
as func-
tions of their branching fractions are given by
N
D‘
¼
N
0
B
D‘

D‘
tag

D‘
;
(1)
N
h‘
¼
N
0
B
h‘

h‘
tag

h‘
;
(2)
where
N
0
is the number of
B

B
events,
B
D‘
(
B
h‘
) is the
branching fraction for
B
!
D‘
(
B
!
h‘
),

D‘
tag
(

h‘
tag
)is
the
B
tag
reconstruction efficiency in
B

B
events that contain
a
D‘
(
h‘
) decay on the signal side,

D‘
(

h‘
) is the
signal-side reconstruction efficiency for
D‘
(
h‘
), and
the symbol
D‘
represents either
B
þ
!

D

0
þ

or
B
þ
!

D
0
þ

. Solving for the expected
h‘
event yield gives
N
h‘
¼
B
h‘

h‘
S
0
;
(3)
where we have defined a common factor
)
2
) (GeV/c
π
m(K
0
0.5
1
1.5
2
2.5
3
3.5
4
2
Events / 50 MeV/c
0
500
1000
1500
2000
2500
3000
all backgrounds
+
μ
-
τ
+
K
+
B
τ
ν
-
π
)
0
π
(n
-
τ
)
2
) (GeV/c
π
m(K
0
0.5
1
1.5
2
2.5
3
3.5
4
2
Events / 50 MeV/c
0
20
40
60
80
100
120
signal MC
)
2
) (GeV/c
π
m(K
0
0.5
1
1.5
2
2.5
3
3.5
4
2
Events / 50 MeV/c
0
500
1000
1500
2000
2500
3000
all backgrounds
-
μ
+
τ
+
K
+
B
τ
ν
+
π
)
0
π
(n
+
τ
)
2
) (GeV/c
π
m(K
0
0.5
1
1.5
2
2.5
3
3.5
4
2
Events / 50 MeV/c
0
20
40
60
80
100
120
signal MC
FIG. 1 (color online). Distributions of
m
ð
K
Þ
for the (a, b)
B
þ
!
K
þ



þ
;


n
0
Þ




and (c, d)
B
þ
!
K
þ

þ


;

þ
!
ð
n
0
Þ

þ



channels. The top row shows the data (points) compared with the background MC (solid line). The area of the background
MC distribution has been normalized to the area of the data distribution. The bottom row shows the (b)
B
þ
!
K
þ



þ
and
(d)
B
þ
!
K
þ

þ


signal MC. The normalization of the bottom row is arbitrary. The dotted vertical line is at
1
:
95 GeV
=c
2
, which is
the minimum allowed value of
m
ð
K
Þ
for the signal selection. The peak in the top row just below
1
:
95 GeV
=c
2
is from

D
0
!
K
þ


decays.
SEARCH FOR THE DECAY MODES
...
PHYSICAL REVIEW D
86,
012004 (2012)
012004-7
S
0
¼
N
D‘
B
D‘

D‘


h‘
tag

D‘
tag

:
(4)
Table
II
gives the tag-side efficiency ratios determined
from MC samples. We find the ratios to be close to 1,
indicating that the signal-side decay does not strongly
influence the tag-side reconstruction efficiency, and does
not depend on the primary lepton or hadron flavor.
Figure
2
shows the results of unbinned maximum
likelihood fits of the

E
D‘
distributions for the
B
þ
!

D
ðÞ
0

þ

and
B
þ
!

D
ðÞ
0
e
þ

control samples. The fits
have independent

D
0
,

D

0
, and

D

0
components. Any
residual combinatorial background is included in the

D

0
component. The

D
0
and

D

0
component probability
density functions (PDFs) are each modeled with the sum of
a Gaussian and a Crystal Ball function [
17
]. The

D

0
component PDF is the sum of a Gaussian and a bifurcated
Gaussian, which has different width parameters above and
below the mean. The overall normalization of each com-
ponent, the core Gaussian mean and width of the

D
0
component, and the relative fraction of the Crystal Ball
function within the

D

0
component are all parameters of
the likelihood that are varied in its maximization.
The results of the

E
D‘
maximum likelihood
fits and
S
0
calculations are given in Table
III
. We use the
following branching fractions [
18
] in the calculation of
S
0
:
B
ð
B

!
D
0



Þ¼ð
2
:
23

0
:
11
Þ
%
,
B
ð
B

!
D

0



Þ¼
ð
5
:
68

0
:
19
Þ
%
,and
B
ð
D
0
!
K


þ
Þ¼ð
3
:
87

0
:
05
Þ
%
.
The four determinations of
S
0
are all consistent with each
other, as expected.
V. CONTINUUM BACKGROUND REJECTION
After the
m
ð
K
Þ
>
1
:
95 GeV
=c
2
requirement, the
B

B
background is highly suppressed. The remaining back-
ground is dominated by continuum quark-pair production
(
e
þ
e

!
q

q
;
q
¼
u
,
d
,
s
,
c
). We combine the variables
described in this section in a likelihood ratio
L
R
¼
Q
i
P
s
ð
x
i
Þ
Q
i
P
s
ð
x
i
Þþ
Q
i
P
b
ð
x
i
Þ
(5)
where
x
i
is one of a set of variables that discriminate
against background, and
P
s
ð
x
i
Þ
(
P
b
ð
x
i
Þ
) is the PDF for
variable
x
i
in signal (background) events.
The variables used in the
L
R
calculation are
(i)
j
cos

thr
j
the absolute value of the cosine of the angle

thr
between the
B
tag
thrust axis and the thrust axis of
the remainder of the event (

B
sig
); the thrust axis is
defined as the direction
^
a
which maximizes
P
j
^
a
~
p
j
,
where
j
represents all particles assigned to a particu-
lar
B
candidate,
(ii)
P
E
cal
the scalar sum of all EMC neutral cluster
energy that is not associated with the
B
tag
candidate
or bremsstrahlung radiation from any
e
candidates,
where the threshold cluster energy is 100 MeV
(50 MeV) in the forward (barrel) region of the
detector,
TABLE II. Tag-side reconstruction efficiency ratios deter-
mined from MC samples. The uncertainty includes both statis-
tical and systematic sources.
Efficiency ratio

modes
e
modes

K‘
tag
=
D‘
tag
0
:
96

0
:
05
0
:
98

0
:
07

‘
tag
=
D‘
tag
0
:
95

0
:
04
0
:
97

0
:
06
TABLE III. Results of the

E
D‘
maximum likelihood fits and
S
0
calculations. The uncertainties on
N
D‘
and

D‘
are statis-
tical. The efficiency

D‘
is determined from a Monte Carlo
sample. The uncertainty on
S
0
includes the uncertainties on the
B
and
D
branching fractions.
D‘
mode
N
D‘

D‘
S
0
D
0

513

38
ð
47
:
8

0
:
9
Þ
%
ð
12
:
0

1
:
2
Þ
10
5
D

0

1234

49
ð
50
:
8

0
:
5
Þ
%
ð
10
:
7

0
:
8
Þ
10
5
D
0
e
484

46
ð
48
:
2

0
:
9
Þ
%
ð
11
:
4

1
:
5
Þ
10
5
D

0
e
1368

58
ð
52
:
2

0
:
5
Þ
%
ð
11
:
7

1
:
1
Þ
10
5
(GeV)
)
μν
(D
E
-0.6
-0.4
-0.2
-0
0.2
Events / 0.020 GeV
0
20
40
60
80
100
120
140
(GeV)
(D
E
-0.6
-0.4
-0.2
-0
0.2
Events / 0.020 GeV
0
20
40
60
80
100
120
140
(GeV)
)
ν
(De
E
-0.6
-0.4
-0.2
-0
0.2
Events / 0.020 GeV
0
20
40
60
80
100
120
140
160
(GeV)
)
ν
(De
E
-0.6
-0.4
-0.2
-0
0.2
Events / 0.020 GeV
0
20
40
60
80
100
120
140
160
FIG. 2 (color online). Distributions of the three-component

E
D‘
unbinned maximum likelihood fits of the data for the
(a)
B
!
D
ðÞ
0

and (b)
B
!
D
ðÞ
0
e
control samples. In each
plot, the points represent the data, the solid blue curve is the sum
of all PDFs, the long-dashed green curve is the
D
0
component,
the dash-dotted purple curve is the
D

0
component, and the
dotted blue curve is the
D

0
component, which also includes
any residual combinatorial background.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
012004 (2012)
012004-8
(iii)
primary

-
PID quality level
, where, for the
B
!
h
modes, we include the highest quality
level (VL, L, T, VT) of the primary

candidate,
and
(iv)
secondary

-
PID quality level
, where we include
the highest quality level (VL, L, T, VT) of the

-daughter

candidate, if applicable.
We fit histograms of the
j
cos

thr
j
and
P
E
cal
signal and
background MC distributions using polynomials of up to
thr
θ
cos
0
0.2
0.4
0.6
0.8
1
Events / 0.02
0
50
100
150
200
250
all backgrounds
+
μ
-
τ
+
K
+
B
τ
ν
-
π
)
0
π
(n
-
τ
thr
θ
cos
0
0.2
0.4
0.6
0.8
1
Events / 0.02
0
5
10
15
20
25
signal MC
FIG. 3 (color online). Distributions of
j
cos

thr
j
for background
(top) and signal MC (bottom), for the
B
þ
!
K
þ



þ
;


!
ð
n
0
Þ




channel. The points (solid line) in the top figure are
the data (background MC). The background MC has been
normalized to match the area of the data distribution. The
normalization of the signal MC is arbitrary. The solid red curve
is the result of the polynomial fit of the MC distribution.
(GeV)
cal
E
Σ
012345
Events / 200 MeV
0
2
4
6
8
all backgrounds
(GeV)
cal
E
Σ
012345
Events / 200 MeV
0
20
40
60
80
signal MC
+
μ
-
τ
+
K
+
B
τ
ν
e
ν
-
e
-
τ
(GeV)
cal
E
Σ
012345
Events / 200 MeV
0
2
4
6
8
all backgrounds
(GeV)
cal
E
Σ
012345
Events / 200 MeV
0
20
40
60
80
signal MC
+
μ
-
τ
+
K
+
B
τ
ν
μ
ν
-
μ
-
τ
(GeV)
cal
E
Σ
012345
Events / 200 MeV
0
20
40
60
80
100
120
140
all backgrounds
(GeV)
cal
E
Σ
012345
Events / 200 MeV
0
20
40
60
80
100
120
140
signal MC
+
μ
-
τ
+
K
+
B
τ
ν
-
π
)
0
π
(n
-
τ
FIG. 4 (color online). Distributions of
P
E
cal
for background (top) and signal MC (bottom), for the
B
þ
!
K
þ



þ
mode;


!
e



e


(left),


!







(middle), and


n
0
Þ




(right). The events where
P
E
cal
¼
0
have been separated from the
main distribution and plotted in a bin below zero for clarity. The points (solid line) in the top figure are the data (background MC). The
background MC has been normalized to match the area of the data distribution. The normalization of the signal MC is arbitrary.
The solid red curve is the result of the polynomial fit of the MC distribution.
Likelihood Ratio
0
0.2
0.4
0.6
0.8
1
Events / 0.03
0
100
200
300
400
all backgrounds
Likelihood Ratio
0
0.2
0.4
0.6
0.8
1
Events / 0.03
0
50
100
150
200
signal MC
+
μ
-
τ
+
K
+
B
τ
ν
-
π
)
0
π
(n
-
τ
FIG. 5. Likelihood ratio (
L
R
) output distributions of back-
ground (top) and signal MC (bottom), for the
B
þ
!
K
þ



þ
;


n
0
Þ




channel. The points (solid line)
in the top figure are the data (background MC). The background
MC has been normalized to match the area of the data distribu-
tion. The normalization of the signal MC is arbitrary.
SEARCH FOR THE DECAY MODES
...
PHYSICAL REVIEW D
86,
012004 (2012)
012004-9
order eight to define the PDFs for those variables. The
PDFs for the muon-PID quality level are normalized histo-
grams, with one bin for each muon-PID quality level.
For each of the eight signal
B
decay modes, we construct
a distinct
L
R
for each of the three

channels (
e
,

, and

).
This corresponds to 24 different likelihood ratios. In the
final selection, described in Sec.
VIII
, we impose a mini-
mum
L
R
requirement for each

channel in each of the
eight
B
!
h‘
modes.
Figure
3
shows the background and signal
j
cos

thr
j
distributions for the

channel of the
B
þ
!
K
þ



þ
mode. The continuum background peaks sharply near
j
cos

thr
1
because the events have a back-to-back jet-
like topology. The signal
j
cos

thr
j
distribution is roughly
uniform because the detected decay products in
B

B
events
are more isotropically distributed.
Figure
4
shows
P
E
cal
distributions for the three

channels of the
B
þ
!
K
þ



þ
mode. The events where
P
E
cal
¼
0
, due to the absence of unassociated neutral
clusters above the minimum energy threshold, are not
included in the polynomial fit and treated separately. The
P
E
cal
¼
0
events are plotted below zero in Fig.
4
for
clarity. The signal MC
P
E
cal
distributions peak at zero,
as expected, while the background rarely has
P
E
cal
¼
0
but rather has a distribution that peaks between 1 and
2 GeV. The signal MC
P
E
cal
distributions for the

channel extend to higher values, compared to the
e
and

channels, due to hadronic

decays that produce a single


with one or more neutral pions.
Figure
5
shows background and signal MC
L
R
distribu-
tions for the
B
þ
!
K
þ



þ
;


n
0
Þ




channel.
The background peaks sharply near zero and the signal peaks
sharply near one. The value of the
L
R
selection for each

channel in each of the eight signal modes is chosen by
determining the lowest upper limiton the branching fractions
under the null hypothesis with MC pseudoexperiments. We
vary the minimum
L
R
requirement in intervals of 0.05.
VI. SIGNAL AND BACKGROUND ESTIMATION
In our signal selection, we require the indirectly re-
constructed

mass
m

to be within

60 MeV
=c
2
of the
)
2
(GeV/c
τ
m
0
0.5
1
1.5
2
2.5
3
2
Events / 120 MeV/c
0
2
4
6
8
10
12
+
μ
-
τ
+
K
+
B
)
2
(GeV/c
τ
m
1.6
1.8
2
2
/ 20 MeV/c
Arb. Units
)
2
(GeV/c
τ
m
0
0.5
1
1.5
2
2.5
3
2
Events / 120 MeV/c
0
2
4
6
8
10
12
14
16
18
20
22
-
μ
+
τ
+
K
+
B
)
2
(GeV/c
τ
m
1.6
1.8
2
2
/ 20 MeV/c
Arb. Units
)
2
(GeV/c
τ
m
0
0.5
1
1.5
2
2.5
3
2
Events / 120 MeV/c
0
1
2
3
4
5
6
7
8
+
e
-
τ
+
K
+
B
)
2
(GeV/c
τ
m
1.6
1.8
2
2
/ 20 MeV/c
Arb. Units
τ
)
2
(GeV/c
m
0
0.5
1
1.5
2
2.5
3
2
Events / 120 MeV/c
0
2
4
6
8
10
12
14
16
18
20
22
-
e
+
τ
+
K
+
B
)
2
(GeV/c
τ
m
1.6
1.8
2
2
/ 20 MeV/c
Arb. Units
FIG. 6 (color online). Observed distributions of the

invariant mass for the
B
!
K‘
modes. The distributions show the sum of the
three

channels
ð
e; ; 
Þ
. The points with error bars are the data. The solid line is the background MC which has been normalized to
the area of the data distribution. The dashed vertical lines indicate the
m

signal window range. The inset shows the
m

distribution for
signal MC.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
012004 (2012)
012004-10
world average

mass
1
:
777 GeV
=c
2
[
18
]. The relative
signal efficiency after the
m

signal window requirement
is around 84% (78%) for the
B
!
h
(
B
!
he
)
modes. We optimized the
m

signal windows, consi-
dering windows in the range of

50 MeV
=c
2
to

175 MeV
=c
2
. Our optimization metric was the average
expected signal branching fraction 90% confidence level
upper limit from a set of toy experiments simulating
background-only data sets. In each toy experiment, we
generate a value for the observed number of events in
the signal window using a random number that we take
from a Poisson distribution with the mean value set to
the expected number of background events. We find that
a
m

signal window of

60 MeV
=c
2
gives the lowest
expected branching fraction upper limits for all

decay
channels.
The background distribution in
m

is very wide and
slowly varying. We use a broad
m

sideband from 0 to
3
:
5 GeV
=c
2
, excluding the signal window, to estimate the
background in the
m

signal window with
b
¼
R
b
N
sb
;
(6)
where
b
is the number of background events in the signal
window,
N
sb
is the number of background events in the
m

sideband, and
R
b
is the expected signal-to-sideband
ratio (
b=N
sb
). The ratio
R
b
is determined from the ratio
of selected background events in the
m

signal window
(
b
) and the
m

sideband (
N
sb
) in the background
Monte Carlo.
Figs.
6
and
7
show the observed, signal MC, and
background MC
m

distributions for the
B
!
K‘
and
B
!
‘
modes, respectively. Table
IV
gives the re-
sults for the observed numbers of sideband events
N
sb
;i
,
signal-to-sideband ratios
R
b;i
, expected numbers of
background events
b
i
, numbers of observed events
n
i
,
and signal efficiencies

h‘;i
for each

channel
i
. All of
the observed numbers of events
n
i
in the
m

signal
window are statistically consistent with the expected
backgrounds
b
i
, thus there is no evidence for any
B
!
h‘
decay.
)
2
(GeV/c
τ
m
0
0.5
1
1.5
2
2.5
3
2
Events / 120 MeV/c
0
2
4
6
8
10
12
14
16
18
20
+
μ
-
τ
+
π
+
B
)
2
(GeV/c
τ
m
1.6
1.8
2
2
/ 20 MeV/c
Arb. Units
)
2
(GeV/c
τ
m
0
0.5
1
1.5
2
2.5
3
2
Events / 120 MeV/c
0
10
20
30
40
50
60
70
-
μ
+
τ
+
π
+
B
)
2
(GeV/c
τ
m
1.6
1.8
2
2
/ 20 MeV/c
Arb. Units
)
2
(GeV/c
τ
m
0
0.5
1
1.5
2
2.5
3
2
Events / 120 MeV/c
0
2
4
6
8
10
12
14
16
18
20
+
e
-
τ
+
π
+
B
)
2
(GeV/c
τ
m
1.6
1.8
2
2
/ 20 MeV/c
Arb. Units
)
2
(GeV/c
τ
m
0
0.5
1
1.5
2
2.5
3
2
Events / 120 MeV/c
0
5
10
15
20
25
30
35
40
-
e
+
τ
+
π
+
B
)
2
(GeV/c
τ
m
1.6
1.8
2
2
/ 20 MeV/c
Arb. Units
FIG. 7 (color online). Observed distributions of the

invariant mass for the
B
!
‘
modes. The distributions show the sum of the
three

channels
ð
e; ; 
Þ
. The points with error bars are the data. The solid line is the background MC which has been normalized to
the area of the data distribution. The dashed vertical lines indicate the
m

signal window range. The inset shows the
m

distribution for
signal MC.
SEARCH FOR THE DECAY MODES
...
PHYSICAL REVIEW D
86,
012004 (2012)
012004-11