of 11
Branching fraction measurement of
B
þ
!
!‘
þ

decays
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
A. Palano,
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
R. Y. So,
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
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
B. A. Schumm,
13
A. Seiden,
13
D. S. Chao,
14
C. H. Cheng,
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
U. Nauenberg,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
*
W. H. Toki,
17
B. Spaan,
18
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
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
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
K. Griessinger,
40
A. Hafner,
40
E. Prencipe,
40
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
C. Dallapiccola,
43
R. Cowan,
44
D. Dujmic,
44
G. Sciolla,
44
R. Cheaib,
45
D. Lindemann,
45
P. M. Patel,
45
S. H. Robertson,
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
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
G. Simi,
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
J. Olsen,
58
A. J. S. Smith,
58
A. V. Telnov,
58
F. Anulli,
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
J. F. Benitez,
63
C. Cartaro,
63
M. R. Convery,
63
J. Dingfelder,
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
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
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
J. L. Ritchie,
70
A. M. Ruland,
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
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
PHYSICAL REVIEW D
87,
032004 (2013)
1550-7998
=
2013
=
87(3)
=
032004(11)
032004-1
Ó
2013 American Physical Society
(
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
Facultat de Fisica, Departament ECM, Universitat de Barcelona, 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
Institute of Physics, University of Bergen, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory, 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
Institute for Particle Physics, University of California at Santa Cruz, 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, USA
28
Universita
̈
t Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
29
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, 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,
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
Royal Holloway and Bedford New College, University of London, 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
Laboratory for Nuclear Science, Massachusetts Institute of Technology, 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
48
Physique des Particules, Universite
́
de Montre
́
al, 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, The Netherlands
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
032004 (2013)
032004-2
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 30 May 2012; published 12 February 2013)
We present a measurement of the
B
þ
!
!‘
þ

branching fraction based on a sample of 467 million
B

B
pairs recorded by the
BABAR
detector at the SLAC PEP-II
e
þ
e

collider. We observe
1125

131
signal
decays, corresponding to a branching fraction of
B
ð
B
þ
!
!‘
þ

Þ¼ð
1
:
21

0
:
14

0
:
08
Þ
10

4
, where
the first error is statistical and the second is systematic. The dependence of the decay rate on
q
2
, the
invariant mass squared of the leptons, is compared to QCD predictions of the form factors based on a
quark model and light-cone sum rules.
DOI:
10.1103/PhysRevD.87.032004
PACS numbers: 14.40.Nd, 12.15.Hh, 13.20.He
I. INTRODUCTION
Most theoretical and experimental studies of exclusive
B
!
X
u
‘
decays have focused on
B
!
‘
decays,
while
B
!
‘
and
B
þ
!
!‘
þ

[
1
] decays involving
the vector mesons

and
!
have received less attention.
Here
is an electron or muon, and
X
refers to a hadronic
state, with the subscript
c
or
u
signifying whether the state
carries charm or is charmless. Measurements of the
branching fraction of
B
!
‘
are impacted by an irre-
ducible
B
!
X
u
‘
background, typically the dominant
source of systematic uncertainty. In studies of
B
þ
!
!‘
þ

, that background can be suppressed to a larger
degree, since the
!
width is about 15 times smaller than
that of the

. Extractions of the Cabibbo-Kobayashi-
Maskawa matrix element
j
V
ub
j
from
B
þ
!
!‘
þ

and
B
!
‘
decay rates have greater uncertainties than those
*
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.
{
Deceased.
BRANCHING FRACTION MEASUREMENT OF
...
PHYSICAL REVIEW D
87,
032004 (2013)
032004-3
from
B
!
‘
, due to higher backgrounds and more
complex form-factor dependencies. The persistent discrep-
ancy between
j
V
ub
j
measurements based on inclusive and
exclusive charmless decays is a motivation for the study of
different exclusive
B
!
X
u
‘
decays [
2
,
3
].
Measurements of
B
ð
B
þ
!
!‘
þ

Þ
have been reported
by Belle [
4
,
5
]; a measurement by
BABAR
has been per-
formed on a partial data set [
6
]. In this analysis we use
the full
BABAR
data set to measure the total branching
fraction
B
ð
B
þ
!
!‘
þ

Þ
and partial branching fractions

B
ð
B
þ
!
!‘
þ

Þ
=

q
2
in five
q
2
intervals, where
q
2
refers
to the momentum transfer squared to the lepton system.
The differential decay rate for
B
þ
!
!‘
þ

is given
by [
7
]
d
ð
B
þ
!
!‘
þ

Þ
d
q
2
¼j
V
ub
j
2
G
2
F
q
2
p
!
96

3
m
2
B
c
2
V
½j
H
0
j
2
þj
H
þ
j
2
þj
H

j
2

;
(1)
where
p
!
is the magnitude of the
!
momentum in the
B
rest frame,
m
B
is the
B
mass, and
G
F
is the Fermi coupling
constant. The isospin factor
c
V
is equal to
ffiffiffi
2
p
for
B
þ
!
!‘
þ

[
8
]. As described in a related
BABAR
paper [
9
], the
three helicity functions
H
0
,
H
þ
, and
H

can be expressed
in terms of two axial vector form factors
A
1
and
A
2
and one
vector form factor
V
, which describe strong interaction
effects,
H

ð
q
2
Þ¼ð
m
B
þ
m
!
Þ

A
1
ð
q
2
Þ
2
m
B
p
!
ð
m
B
þ
m
!
Þ
2
V
ð
q
2
Þ

;
H
0
ð
q
2
Þ¼
m
B
þ
m
!
2
m
!
ffiffiffiffiffi
q
2
p


ð
m
2
B

m
2
!

q
2
Þ
A
1
ð
q
2
Þ

4
m
2
B
p
2
!
ð
m
B
þ
m
!
Þ
2
A
2
ð
q
2
Þ

:
We compare the measured
q
2
dependence of the decay rate
with form factor predictions based on light-cone sum rules
(LCSR) [
8
] and the ISGW2 quark model [
10
]. We also use
these form factor calculations and the measured branching
fraction to extract
j
V
ub
j
.
II. DETECTOR, DATA SET, AND SIMULATION
The data used in this analysis were recorded with the
BABAR
detector at the PEP-II
e
þ
e

collider operating at
the

ð
4
S
Þ
resonance. We use a data sample of
426 fb

1
,
corresponding to (
467

5
) million produced
B

B
pairs. In
addition, we use
44 fb

1
of data collected 40 MeV below
the
B

B
production threshold. This off-resonance sample is
used to validate the simulation of the non-
B

B
contributions
whose principal source is
e
þ
e

annihilation to
q

q
pairs,
where
q
¼
u
,
d
,
s
,
c
.
The PEP-II collider and
BABAR
detector have been
described in detail elsewhere [
11
]. Charged particles are
reconstructed in a five-layer silicon tracker positioned close
to the beam pipe and a forty-layer drift chamber. Particles of
different masses are distinguished by their ionization en-
ergy loss in the tracking devices and by a ring-imaging
Cerenkov detector. Electromagnetic showers from elec-
trons and photons are measured in a finely segmented CsI
(Tl) calorimeter. These detector components are embedded
in a 1.5 T magnetic field of a superconducting solenoid; its
steel flux return is segmented and instrumented with planar
resistive plate chambers and limited streamer tubes to detect
muons that penetrate the magnet coil and steel.
We use Monte Carlo (MC) techniques [
12
,
13
] to simu-
late the production and decay of
B

B
and
q

q
pairs and the
detector response [
14
], to estimate signal and background
efficiencies and resolutions, and to extract the expected
signal and background distributions. The size of the simu-
lated sample of generic
B

B
events exceeds the
B

B
data
sample by about a factor of 3, while the MC samples for
inclusive and exclusive
B
!
X
u
‘
decays exceed the data
samples by factors of 15 or more. The MC sample for
q

q
events is about twice the size of the
q

q
contribution in the

ð
4
S
Þ
data.
The MC simulation of semileptonic decays uses the
same models as in a recent
BABAR
analysis [
9
]. The
simulation of inclusive charmless semileptonic decays
B
!
X
u
‘
is based on predictions of a heavy quark ex-
pansion [
15
] for the differential decay rates. For the simu-
lation of
B
!
‘
decays we use the ansatz of Ref. [
16
]
for the
q
2
dependence, with the single parameter

BK
set to
the value determined in a previous
BABAR
analysis [
17
].
All other exclusive charmless semileptonic decays
B
!
X
u
‘
, including the signal, are generated with form factors
determined by LCSR [
8
,
18
]. For
B
!
D‘
and
B
!
D

‘
decays we use parametrizations of the form factors [
19
,
20
]
based on heavy quark effective theory; for the generation
of the decays
B
!
D

‘
, we use the ISGW2 model [
10
].
III. CANDIDATE SELECTION
In the following, we describe the selection and kine-
matic reconstruction of signal candidates, the definition of
the various background classes, and the application of
neural networks to further suppress these backgrounds.
The primary challenge in studying charmless semilep-
tonic
B
decays is to separate signal decays from Cabibbo-
favored
B
!
X
c
‘
decays, which have a branching fraction
approximately 50 times larger than that of
B
!
X
u
‘
.A
significant background also arises due to multi-hadron
continuum events.
Based on the origin of the candidate lepton we distin-
guish the following three categories of events: (1)
Signal
candidates with a charged lepton from a true
B
þ
!
!‘
þ

decay; (2)
B

B
background with a charged lepton from all
nonsignal
B

B
events; (3)
Continuum background
from
e
þ
e

!
q

q
events. The
!
meson is reconstructed in its
dominant decay,
!
!

þ



0
. For each of the three
categories of events we distinguish correctly reconstructed
!
!

þ



0
decays (true-
!
) from combinatorial-
!
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
032004 (2013)
032004-4
candidates, for which at least one of the reconstructed
pions originates from a particle other than the
!
.
A. Preselection
Signal candidates are selected from events with at least
four charged tracks, since a
B
þ
!
!‘
þ

decay leaves
three tracks and the second
B
in the event is expected to
produce at least one track. The magnitude of the sum of the
charges of all reconstructed tracks is required to be less
than two, helping to reject events with at least two unde-
tected particles.
The preselection places requirements on the recon-
structed lepton,
!
meson, and neutrino from the
B
þ
!
!‘
þ

decay. At this stage in the analysis, we allow for
more than one candidate per event.
The lepton is identified as either an electron or muon.
The electron identification efficiency is greater than 90%
and constant as a function of momentum above 1 GeV,
while the muon identification efficiency is 65%–75% for
momenta of 1.5–3 GeV. The pion misidentification rates
are about 0.1% for the electron selector and 1% for the
muon selector. The lepton is required to have a momentum
in the center-of-mass (c.m.) frame greater than 1.6 GeV.
This requirement significantly reduces the background
from hadrons that are misidentified as leptons and also
removes a large fraction of true leptons from secondary
decays or photon conversions and from
B
!
X
c
‘
decays.
The acceptance of the detector for leptons covers polar
angles in the range
0
:
41



2
:
54 rad
.
For the reconstruction of the decay
!
!

þ



0
,we
require that the candidate charged pions are not identified
as leptons or kaons. The reconstructed
!
mass must be in
the range
680
<m
3

<
860 MeV
, and the

0
candidate
is required to have an invariant mass of
115
<m

<
150 MeV
. To reduce combinatorial
!
background, we
require minimum momenta for the three pion candidates,
p


>
200 MeV
and
p

0
>
400 MeV
, and also energies
of at least 80 MeV for photons from the

0
candidate.
The charged lepton candidate is combined with a
!
candidate to form a so-called
Y
candidate. The charged
tracks associated with the
Y
candidate are fitted to a
common vertex
Y
vtx
. This vertex fit must yield a

2
proba-
bility
Prob
ð

2
;Y
vtx
Þ
>
0
:
1
. To further reduce backgrounds
without significant signal losses, we impose two-
dimensional restrictions on the momenta of the lepton
and
!
. Each
Y
candidate must satisfy at least one of the
following conditions on the c.m. momentum of the lepton
and
!
:
p

!
>
1
:
3
,or
p

>
2
:
0
,or
p

þ
p

!
>
2
:
65 GeV
,
where quantities with an asterisk refer to the c.m. frame.
These requirements reject background candidates that are
inconsistent with the phase space of the signal decay. The
condition
j
cos

BY
j
1
:
0
, where
cos

BY
¼ð
2
E

B
E

Y

M
2
B

M
2
Y
Þ
=
ð
2
p

B
p

Y
Þ
is the cosine of the angle between
the momentum vectors of the
B
meson and the
Y
candidate,
should be fulfilled for a well-reconstructed
Y
candidate
originating from a signal decay [
21
]. The energy
E

B
and
momentum
p

B
of the
B
meson are not measured event by
event. Specifically,
E

B
¼
ffiffiffi
s
p
=
2
, where
ffiffiffi
s
p
is the c.m. en-
ergy of the colliding beams, and the
B
momentum is
derived as
p

B
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E

2
B

m
2
B
q
. To allow for the finite reso-
lution of the detector, we impose the requirement

1
:
2
<
cos

BY
<
1
:
1
.
The neutrino four-momentum is inferred from the
missing energy and momentum of the whole event:
ð
E
miss
;
~
p
miss
Þ¼ð
E
e
þ
e

;
~
p
e
þ
e

Þð
P
i
E
i
;
P
i
~
p
i
Þ
,
where
E
e
þ
e

and
~
p
e
þ
e

are the energy and momentum of the
colliding beam particles, and the sums are performed
over all tracks and all calorimeter clusters without an
associated track. If all tracks and clusters in an event are
well measured, and there are no undetected particles
besides a single neutrino, then the measured distribution
of the missing mass squared,
m
2
miss
¼
E
2
miss

p
2
miss
, peaks
at zero. We require the reconstructed neutrino mass to be
consistent with zero,
j
m
2
miss
=
ð
2
E
miss
Þj
<
2
:
5 GeV
, and the
missing momentum to exceed 0.5 GeV. The polar angle
of the missing momentum vector is also required to pass
through the fiducial region of the detector,
0
:
3
<
miss
<
2
:
2 rad
.
Other restrictions are applied to suppress
q

q
back-
ground, which has a two-jet topology in contrast to
B

B
events with a more uniform angular distribution of the
tracks and clusters. Events must have
R
2

0
:
5
, where
R
2
is the second normalized Fox-Wolfram moment [
22
],
determined from all charged and neutral particles in the
event. We also require
cos

thrust

0
:
9
, where


thrust
is
the angle between the thrust axis of the
Y
candidate’s decay
particles and the thrust axis of all other detected particles
in the event. We require
L
2
<
3
:
0 GeV
, with
L
2
¼
P
i
p

i
cos
2


i
, where the sum runs over all tracks in the
event excluding the
Y
candidate, and
p

i
and


i
refer to
the c.m. momenta and the angles measured with respect to
the thrust axis of the
Y
candidate.
We reject candidates that have a charged lepton and
a low-momentum charged pion consistent with a
B
0
!
D

þ

,
D

!

D
0


slow
decay as described in Ref. [
23
].
The kinematic consistency of the candidate decay
with a signal
B
decay is ascertained by restrictions
on two variables, the beam-energy substituted
B
mass
m
ES
, and the difference between the reconstructed
and expected energy of the
B
candidate

E
.In
the laboratory frame these variables are defined as
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
s=
2
þ
~
p
B

~
p
e
þ
e

Þ
2
=E
2
e
þ
e


p
2
B
q
and

E
¼
ð
P
e
þ
e


P
B

s=
2
Þ
=
ffiffiffi
s
p
, where
P
B
¼ð
E
B
;
~
p
B
Þ
and
P
e
þ
e

¼ð
E
e
þ
e

;
~
p
e
þ
e

Þ
are the four-momenta of the
B
meson and the colliding beams, respectively. For correctly
reconstructed signal
B
decays, the

E
distribution is cen-
tered at zero, and the
m
ES
distribution peaks at the
B
mass.
We restrict candidates to

0
:
95
<

E<
0
:
95 GeV
and
5
:
095
<m
ES
<
5
:
295 GeV
.
BRANCHING FRACTION MEASUREMENT OF
...
PHYSICAL REVIEW D
87,
032004 (2013)
032004-5
B. Neural network selection
To separate signal candidates from the remaining back-
ground, we employ two separate neural networks (NN) to
suppress
q

q
background and
B
!
X
c
‘
background. The
q

q
NN is trained on a sample passing the preselection
criteria, while the
B
!
X
c
‘
NN is trained on a sample
passing both the preselection and the
q

q
neural network
criteria. The training is performed with signal and back-
ground MC samples. These NN are multilayer perceptrons
that have two hidden layers with seven and three nodes.
The variables used as inputs to the
q

q
NN are
R
2
,
L
2
,
cos

thrust
,
cos

BY
,
m
2
miss
=
ð
2
E
miss
Þ
,
Prob
ð

2
;Y
vtx
Þ
, the
polar angle of the missing momentum vector in the labo-
ratory frame, and the Dalitz plot amplitude
A
Dalitz
¼

j
~
p

þ

~
p


j
, with the

þ
and


momenta measured
in the
!
rest frame and scaled by a normalization factor

.
True
!
mesons typically have larger values of
A
Dalitz
than
combinatorial
!
candidates reconstructed from unrelated
pions. The
B
!
X
c
‘
NN uses the same variables, except
for
cos

thrust
, which is replaced by
cos

W‘
, the helicity
angle of the lepton, defined as the angle between the
momentum of the lepton in the rest frame of the virtual
W
and the momentum of the
W
in the rest frame of the
B
.
The data and MC simulation agree well for the NN input
variables at each stage of the selection. The NN discrim-
inators are chosen by maximizing
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2
sig
þð
1

bkg
Þ
2
q
,
where

sig
is the efficiency of the signal and
bkg
is the
fraction of the background misidentified as signal.
The selection efficiencies for the various stages of the
candidate selection for the signal and background compo-
nents are given in Table
I
. After the preselection and NN
selection, 21% of events in data contribute multiple
B
þ
!
!‘
þ

candidates. The candidate with the largest value of
Prob
ð

2
;Y
vtx
Þ
is retained. For the remaining candidates,
the reconstructed 3-pion mass is required to be consistent
with the
!
nominal mass [
24
],
j
m
3


m!
j
<
23 MeV
.
The overall signal efficiency is 0.73% if the reconstructed
candidate includes a true
!
and 0.21% if it includes a
combinatorial
!
. The efficiencies of the
B

B
and
q

q
back-
grounds are suppressed by several orders of magnitude
relative to the signal.
C. Data-MC comparisons
The determination of the number of signal events relies
heavily on the MC simulation to correctly describe the
efficiencies and resolutions, as well as the distributions
for signal and background sources. Therefore a significant
effort has been devoted to detailed comparisons of data and
MC distributions, for samples that have been selected to
enhance a given source of background.
Specifically, we have studied the MC simulation of
the neutrino reconstruction for a control sample of
B
0
!
D

þ

decays, with
D

!

D
0


slow
and

D
0
!
K
þ



0
. This final state is similar to that of the
B
þ
!
!‘
þ

decay, except for the addition of the slow pion


s
and the substitution of a
K
þ
for a

þ
. This control sample
constitutes a high-statistics and high-purity sample on
which to test the neutrino reconstruction. We compare
data and MC distributions for the control sample and find
good agreement for the variables used in the preselection
and as inputs to the NN. We have also used this sample to
study the resolution of the neutrino reconstruction and its
impact on
q
2
,
m
ES
, and

E
.
IV. SIGNAL EXTRACTION
A. Fit method
We determine the signal yields by performing an
extended binned maximum-likelihood fit to the observed
three-dimensional

E
-
m
ES
-
q
2
distributions. The fit tech-
nique [
25
] accounts for the statistical fluctuations of the
data and MC samples.
For this fit the

E
-
m
ES
plane is divided into 20 bins, as
shown in Fig.
1
, and the data are further subdivided into
five bins in
q
2
, chosen to contain roughly equal numbers of
signal events. The
q
2
resolution is dominated by the neu-
trino reconstruction. It can be improved by substituting the
missing energy with the magnitude of the missing momen-
tum and by rescaling
~
p
miss
to force

E
¼
0
,
q
2
corr
¼
½ð
E
;
~
p
Þþ
p
miss
;
~
p
miss
Þ
2
, where
¼
1


E=E
miss
.
This correction to
q
2
is used in the fit.
TABLE I. Successive efficiencies (in %) predicted by MC
simulation for each stage of the selection, for true- and
combinatorial-
!
signal, and backgrounds from
B

B
and
q

q
events.
Source
true-
!
signal
combinatorial-
!
signal
B

Bq

q
Preselection
1.9
4.8
0.0094 0.00073
Neural nets
43
17
7.9
11
3-pion mass
88
26
24
30
Total (product) 0.73
0.21
0.00018 0.000024
0
5
10
15
20
25
30
35
40
45
(GeV)
ES
m
5.1
5.15
5.2
5.25
E (GeV)
-0.5
0
0.5
FIG. 1 (color). Distribution of

E
versus
m
ES
for true-
!
signal
MC. The 20 bins into which the plane is divided for the fit
histogram are overlaid.
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
032004 (2013)
032004-6
We describe the measured

E
-
m
ES
-
q
2
distribution as a
sum of four contributions:
B
þ
!
!‘
þ

signal (both
true-
!
and combinatoric-
!
), true-
!B

B
, true-
!q

q
, and
the sum of the combinatorial-
!
background from
B

B
and
q

q
events.
While the

E
-
m
ES
shapes for the signal and true-
!B

B
and
q

q
sources are taken from MC samples, we choose to
represent the dominant combinatorial-
!
background by
the distributions of data events in the
m
3

sidebands,
thereby reducing the dependence on MC simulation of
these backgrounds. The normalization of these background
data is taken from a fit to the 3-

mass distribution in the
range
0
:
680
<m
3

<
0
:
880 GeV
. To obtain a sample cor-
responding to the combinatorial-
!
background from
B

B
and
q

q
events only, we subtract the MC simulated
m
3

contribution of the small combinatorial-
!B
þ
!
!‘
þ

signal sample. To the resulting
m
3

distribution, we fit
the sum of a relativistic Breit-Wigner convolved with a
normalized Gaussian function, and the combinatorial
background described by a second degree polynomial.
The resulting fit to the
m
3

distribution for the all-
q
2
sample is shown in Fig.
2
. The

2
per number of degrees
of freedom (dof) for the fits are within the range expected
for good fits. The fitted background function is used
to determine the weights to apply to the upper and lower
sidebands to scale them to the expected yield of
combinatorial-
!B

B
and
q

q
background in the
m
3

peak region.
The peak and two sideband regions are chosen to have a
width of 46 MeVand are separated by 23 MeV, as indicated
in Fig.
2
. Since the normalization of the combinatorial-
!
signal contribution depends on the fitted signal yield,
which is
a priori
unknown, this component is determined
iteratively.
The fit has seven free parameters, five for the signal
yields in each
q
2
bin, and one each for the yields of the
true-
!B

B
and
q

q
backgrounds; the shapes of the distri-
butions are taken from MC simulations. The fitted yields
are expressed as scale factors relative to the default yields
of the MC simulation. The total signal yield is taken as the
sum of the fitted yields in the individual
q
2
bins, taking into
account correlations.
B. Fit results
The fitting procedure has been validated on pseudoex-
periments generated from the MC distributions. We find
no biases, and the uncertainties follow the expected
statistical distribution.
The yields of the signal, true-
!B

B
, and true-
!q

q
components obtained from the binned maximum-
likelihood fit to

E
-
m
ES
-
q
2
are presented in Table
II
.
Projections of the fitted distributions of
m
ES
for the all-
q
2
fit and for the five-
q
2
bins fit are shown in Fig.
3
. The
agreement between the data and fitted MC samples is
reasonable for distributions of

E
,
m
ES
, and
q
2
, as indi-
cated by the

2
=
dof
of the fit,
106
=
93
, which has a proba-
bility of 16%. The fixed combinatorial-
!
background yield
accounts for 83% of all backgrounds. The correlations
among the parameters are listed in Table
III
. The strongest
correlation is

72%
, between the signal and
q

q
yields in
the first
q
2
bin, which contains most of the
q

q
background.
The correlation between signal and
B

B
background is
strongest in the last
q
2
bin,

40%
, because of a large
contribution from other
B
!
X
u
‘
decays. Correlations
among signal yields are significantly smaller.
The branching fraction,
B
ð
B
þ
!
!‘
þ

Þ
, averaged
over electron and muon channels, is defined as
B
ð
B
þ
!
!‘
þ

Þ¼
P
i
ð
N
sig
i
=
sig
i
Þ
=
ð
4
f

N
B

B
Þ
, where
N
sig
i
refers to
the number of reconstructed electron and muon signal
events in
q
2
bin
i
,

sig
i
is the reconstruction efficiency,
f

is the fraction of
B
þ
B

decays in all
B

B
events, and
N
B

B
is
the number of produced
B

B
events. The factor of 4 comes
from the fact that
B
is quoted as the average of
¼
e
and
samples, not the sum, and the fact that either of the two
B
mesons in the
B
þ
B

event may decay into the signal mode.
The
q
2
resolution in the signal region is
0
:
36 GeV
2
,
smaller than the width of the
q
2
bins. To account for the
finite
q
2
resolution, the background-subtracted, efficiency-
corrected spectrum is adjusted by deriving from the signal
MC the ratio of the true and reconstructed
q
2
spectra,
ð
d
B
=
d
q
2
true
Þ
=
ð
d
B
=
d
q
2
reco
Þ
. The ratio is low by

9%
at
low
q
2
, and closer to 1.0 at higher values of
q
2
. The partial
and total branching fractions listed in Table
IV
are cor-
rected for the effects of finite
q
2
resolution and efficiency.
V. SYSTEMATIC UNCERTAINTIES
Table
V
summarizes the contributions to the systematic
uncertainty. The event reconstruction systematic uncertain-
ties are most sensitive to the neutrino reconstruction, which
depends on the detection of all of the particles in the event.
(GeV)
π
3
m
0.7
0.75
0.8
0.85
Candidates / (0.002 GeV)
0
200
400
600
FIG. 2 (color online). Fit to the distribution of
m
3

for data
from the all-
q
2
sample, with MC combinatorial-
!
signal sub-
tracted. The dashed (red) and dotted (blue) curves describe the
fitted peaking and combinatorial background functions, respec-
tively, and the solid (black) curve is their sum. The peak and
sideband regions are also indicated.
BRANCHING FRACTION MEASUREMENT OF
...
PHYSICAL REVIEW D
87,
032004 (2013)
032004-7
To assess the impact of the uncertainty of the measured
efficiencies for charged tracks, the MC signal and back-
ground samples are reprocessed and the analysis is
repeated, after tracks have been eliminated at random
with a probability determined by the uncertainty in the
tracking efficiency. Similarly, we evaluate the impact from
uncertainties in the photon reconstruction efficiency by
eliminating photons at random as a function of the photon
energy. Since a
K
0
L
leaves no track and deposits only a
small fraction of its energy in the calorimeter, the recon-
struction of the neutrino is impacted. The uncertainty on
the
K
0
L
MC simulation involves the shower energy depos-
ited by the
K
0
L
in the calorimeter, the
K
0
L
detection effi-
ciency, and the inclusive
K
0
L
production rate as a function
of momentum from
B

B
events.
The impact of the changes to the simulated background
distributions that enter the fit are smaller than for the
signal, since the large combinatorial backgrounds are taken
TABLE II. Number of events and their statistical uncertainties, as determined from the fit, compared with the number of observed
events in data. The combinatorial-
!
background (bkgd.) yields are fixed in the fit; the quoted uncertainties are derived from the
sideband subtraction.
q
2
range (
GeV
2
)
0–4
4–8
8–10
10–12
12–21
0–21
All signal
257

72
238

44
161

32
177

32
293

57
1125

131
True-
!
signal
238
209
136
137
168
869
Combinatorial-
!
signal
19
28
25
40
125
256
B

B
(true-
!
)
105

19
192

34
154

27
195

34
411

73
1057

187
q

q
(true-
!
)
409

96
145

34
65

15
34

864

15
716

167
Combinatorial-
!
bkgd.
1741

23
1818

24
1240

20
1520

22
3913

35
10232

57
Data
2504

50
2433

49
1605

40
1858

43
4738

69
13138

115
Candidates / (0.01 GeV)
0
50
100
(GeV)
ES
m
5.1
5.15
5.2
5.25
0.5
1
1.5
Candidates / (0.01 GeV)
0
20
40
60
(GeV)
ES
m
5.1
5.15
5.2
5.25
0.5
1
1.5
Candidates / (0.01 GeV)
0
50
100
(GeV)
ES
m
5.1
5.15
5.2
5.25
0.5
1
1.5
Candidates / (0.01 GeV)
0
50
100
150
(GeV)
ES
m
5.1
5.15
5.2
5.25
0.5
1
1.5
Candidates / (0.01 GeV)
0
20
40
60
(GeV)
ES
m
5.1
5.15
5.2
5.25
0.5
1
1.5
Candidates / (0.01 GeV)
0
200
400
(GeV)
ES
m
5.1
5.15
5.2
5.25
0.5
1
1.5
FIG. 3 (color online). Distributions of
m
ES
after the fit and the ratio of the data to the fitted predictions, for five separate
q
2
bins and
the full
q
2
range, in the

E
signal band,

0
:
25
<

E

0
:
25 GeV
. The points represent data with statistical uncertainties, while the
stacked histograms represent the sum of fitted source components, signal (white), true-
!B

B
(light gray), true-
!q

q
(dark gray), and
combinatorial-
!
background (diagonally thatched).
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
032004 (2013)
032004-8
from data, rather than MC simulations. As an estimate of
the impact of these variations of the MC-simulated distri-
butions on the
q
2
-dependent signal yield, we combine the
observed reduction in the signal distribution with the
impact of the changes to
q

q
and
B

B
backgrounds on the
signal yield, taking into account the correlations obtained
from the fit (see Table
III
). Since the correlations between
signal and backgrounds are small at high
q
2
, the impact of
the uncertainties in the background are also modest. This
procedure avoids large statistical fluctuations of the fit
procedure that have been observed to be larger than the
changes in the detection efficiencies. However, this proce-
dure does not account for the small changes in the shape of
the distributions, and we therefore sum the magnitude of
the changes for signal and background, rather than adding
them in quadrature or taking into account the signs of
the correlations of the signal and backgrounds in a given
q
2
bin.
We assign an uncertainty on the identification efficiency
of electrons and muons, as well as on the lepton and kaon
vetoes of the
!
daughter pions, based on the change in
signal yield after varying the selector efficiencies within
their uncertainties.
The uncertainty in the calculation of the LCSR form
factors impacts the uncertainty on the branching fraction
because it affects the predicted
q
2
distribution of the signal
and thereby the fitted signal yield. We assess the impact by
varying the form factors within their uncertainties. We
include the uncertainty on the branching fraction of the
!
decay,
B
ð
!
!

þ



0
Þ¼ð
89
:
2

0
:
7
Þ
10

2
[
24
].
To evaluate the uncertainty from radiative corrections,
candidates are reweighted by 20% of the difference
between the spectra with and without PHOTOS [
26
],
which models the final state radiation of the decay.
The uncertainty on the true-
!
backgrounds has a small
impact on the signal yield since these components repre-
sent a small fraction of the total sample. To assess the
uncertainty of the

E
-
m
ES
-
q
2
shapes of the true-
!q

q
and
true-
!B

B
samples, the fit is repeated after the events are
reweighted to reproduce the inclusive
!
momentum dis-
tribution measured in
B

B
and
q

q
events. We also assess the
uncertainty on the modeling of the semileptonic back-
grounds by varying the branching fractions and form fac-
tors of the exclusive and inclusive
B
!
X
u
‘
[
24
] and
B
!
X
c
‘
backgrounds [
3
] within their uncertainties.
To assess the uncertainties that result from the MC
prediction of the
m
3

distribution of the combinatorial-
!
signal, we use the uncorrected distribution, in which the
combinatorial-
!
signal is not subtracted from the
m
3

sidebands, and the signal fit parameter is set to scale only
the true-
!
signal contribution. Twenty percent of the dif-
ference between the nominal and uncorrected results is
taken as the systematic uncertainty; it is largest for
12
<
q
2
<
21 GeV
2
because the fraction of combinatorial-
!
TABLE III. Correlations among the fit scale factors
p
s
k
for the
simulated source
s
and
q
2
bin
k
. The scale factors for
q

q
and
B

B
apply to the full
q
2
range.
p
q

q
p
B

B
p
!‘
1
p
!‘
2
p
!‘
3
p
!‘
4
p
!‘
5
p
q

q
1.000

0
:
466

0
:
724

0
:
106

0
:
031
0.051 0.088
p
B

B
1.000 0.223

0
:
249

0
:
253

0
:
284

0
:
401
p
!‘
1
1.000 0.121 0.061 0.001

0
:
011
p
!‘
2
1.000 0.105 0.094 0.128
p
!‘
3
1.000 0.088 0.121
p
!‘
4
1.000 0.125
p
!‘
5
1.000
TABLE IV. Measured
B
þ
!
!‘
þ

branching fraction and
partial branching fractions in bins of
q
2
with statistical and
systematic uncertainties.
q
2
(
GeV
2
)

B
(

10

4
)
0–4
0
:
214

0
:
060

0
:
024
4–8
0
:
200

0
:
037

0
:
010
8–10
0
:
147

0
:
029

0
:
010
10–12
0
:
169

0
:
031

0
:
098
12–21
0
:
482

0
:
093

0
:
038
0–12
0
:
730

0
:
083

0
:
054
0–21
1
:
212

0
:
140

0
:
084
TABLE V. Systematic uncertainties in % on the branching
fraction.
q
2
range (
GeV
2
)
0–4 4–8 8–10 10–12 12–21 0–21
Event reconstruction
Tracking efficiency
3.9 1.5 2.8 2.3 1.1 2.0
Photon efficiency
2.0 1.7 3.3 1.1 0.6 1.5
K
L
detection
4.8 1.8 2.5 1.1 1.4 1.9
Lepton identification
1.6 1.5 1.5 1.2 1.2 1.3
K=‘
veto of
!
daughters
1.7 1.7 1.7 1.7 1.8 1.7
Signal simulation
Signal form factors
6.3 1.5 1.1 2.9 4.6 4.8
B
ð
!
!

þ



0
Þ
0.8 0.8 0.8 0.8 0.8 0.8
Radiative corrections
0.4 0.3 0.2 0.1 0.2 0.2
True
-
!
background
q

q

E
-
m
ES
-
q
2
shapes
2.6 0.1 0.4 0.2 0.3 0.5
B

B

E
-
m
ES
-
q
2
shapes
2.0 0.9 1.8 0.2 0.1 0.8
B
!
X
c
‘
B
and FF
0.2 0.6 0.3 0.2 0.2 0.2
B
!
X
u
‘
B
and FF
0.3 0.4 0.4 0.3 0.5 0.4
Combinatorial
-
!
sources
Signal
m
3

distribution
0.6 0.5 0.4 1.1 3.7 1.5
Bkgd. yield, stat. error
4.2 1.0 0.9 0.9 2.0 1.7
Bkgd. yield, ansatz error
1.7 2.2 2.7 2.7 3.5 0.9
B
production
B

B
counting
1.1 1.1 1.1 1.1 1.1 1.1
f

1.2 1.2 1.2 1.2 1.2 1.2
Systematic uncertainty
11.1 5.2 6.8 5.8 7.9 6.9
Statistical uncertainty
28.1 18.7 20.0 18.1 19.4 11.6
Total uncertainty
30.2 19.4 21.1 19.0 20.9 13.5
BRANCHING FRACTION MEASUREMENT OF
...
PHYSICAL REVIEW D
87,
032004 (2013)
032004-9