Measurement of the
B
0
!
‘
þ
and
B
þ
!
ð0Þ
‘
þ
branching fractions, the
B
0
!
‘
þ
and
B
þ
!
‘
þ
form-factor shapes, and determination of
j
V
ub
j
P. del Amo Sanchez,
1
J. P. Lees,
1
V. Poireau,
1
E. Prencipe,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
M. Martinelli,
3a,3b
D. A. Milanes,
3a,3b
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
L. Sun,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
I. L. Osipenkov,
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
A. Randle-Conde,
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
S. Curry,
10
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
E. C. Martin,
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. West,
12
A. M. Eisner,
13
C. A. Heusch,
13
J. Kroseberg,
13
W. S. Lockman,
13
A. J. Martinez,
13
T. Schalk,
13
B. A. Schumm,
13
A. Seiden,
13
L. O. Winstrom,
13
C. H. Cheng,
14
D. A. Doll,
14
B. Echenard,
14
D. G. Hitlin,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
A. Y. Rakitin,
14
R. Andreassen,
15
M. S. Dubrovin,
15
G. Mancinelli,
15
B. T. Meadows,
15
M. D. Sokoloff,
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
H. Jasper,
18
T. M. Karbach,
18
A. Petzold,
18
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
J. E. Watson,
21
M. Andreotti,
22a,22b
D. Bettoni,
22a
C. Bozzi,
22a
R. Calabrese,
22a,22b
A. Cecchi,
22a,22b
G. Cibinetto,
22a,22b
E. Fioravanti,
22a,22b
P. Franchini,
22a,22b
E. Luppi,
22a,22b
M. Munerato,
22a,22b
M. Negrini,
22a,22b
A. Petrella,
22a,22b
L. Piemontese,
22a
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
23
M. Nicolaci,
23
S. Pacetti,
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
S. Tosi,
24a,24b
B. Bhuyan,
25
V. Prasad,
25
C. L. Lee,
26
M. Morii,
26
A. Adametz,
27
J. Marks,
27
U. Uwer,
27
F. U. Bernlochner,
28
M. Ebert,
28
H. M. Lacker,
28
T. Lueck,
28
A. Volk,
28
P. D. Dauncey,
29
M. Tibbetts,
29
P. K. Behera,
30
U. Mallik,
30
C. Chen,
31
J. Cochran,
31
H. B. Crawley,
31
L. Dong,
31
W. T. Meyer,
31
S. Prell,
31
E. I. Rosenberg,
31
A. E. Rubin,
31
A. V. Gritsan,
32
Z. J. Guo,
32
N. Arnaud,
33
M. Davier,
33
D. Derkach,
33
J. Firmino da Costa,
33
G. Grosdidier,
33
F. Le Diberder,
33
A. M. Lutz,
33
B. Malaescu,
33
A. Perez,
33
P. Roudeau,
33
M. H. Schune,
33
J. Serrano,
33
V. Sordini,
33,
‡
A. Stocchi,
33
L. Wang,
33
G. Wormser,
33
D. J. Lange,
34
D. M. Wright,
34
I. Bingham,
35
C. A. Chavez,
35
J. P. Coleman,
35
J. R. Fry,
35
E. Gabathuler,
35
R. Gamet,
35
D. E. Hutchcroft,
35
D. J. Payne,
35
C. Touramanis,
35
A. J. Bevan,
36
F. Di Lodovico,
36
R. Sacco,
36
M. Sigamani,
36
G. Cowan,
37
S. Paramesvaran,
37
A. C. Wren,
37
D. N. Brown,
38
C. L. Davis,
38
A. G. Denig,
39
M. Fritsch,
39
W. Gradl,
39
A. Hafner,
39
K. E. Alwyn,
40
D. Bailey,
40
R. J. Barlow,
40
G. Jackson,
40
G. D. Lafferty,
40
J. Anderson,
41
R. Cenci,
41
A. Jawahery,
41
D. A. Roberts,
41
G. Simi,
41
J. M. Tuggle,
41
C. Dallapiccola,
42
E. Salvati,
42
R. Cowan,
43
D. Dujmic,
43
G. Sciolla,
43
M. Zhao,
43
D. Lindemann,
44
P. M. Patel,
44
S. H. Robertson,
44
M. Schram,
44
P. Biassoni,
45a,45b
A. Lazzaro,
45a,45b
V. Lombardo,
45a
F. Palombo,
45a,45b
S. Stracka,
45a,45b
L. Cremaldi,
46
R. Godang,
46,
x
R. Kroeger,
46
P. Sonnek,
46
D. J. Summers,
46
X. Nguyen,
47
M. Simard,
47
P. Taras,
47
G. De Nardo,
48a,48b
D. Monorchio,
48a,48b
G. Onorato,
48a,48b
C. Sciacca,
48a,48b
G. Raven,
49
H. L. Snoek,
49
C. P. Jessop,
50
K. J. Knoepfel,
50
J. M. LoSecco,
50
W. F. Wang,
50
L. A. Corwin,
51
K. Honscheid,
51
R. Kass,
51
J. P. Morris,
51
N. L. Blount,
52
J. Brau,
52
R. Frey,
52
O. Igonkina,
52
J. A. Kolb,
52
R. Rahmat,
52
N. B. Sinev,
52
D. Strom,
52
J. Strube,
52
E. Torrence,
52
G. Castelli,
53a,53b
E. Feltresi,
53a,53b
N. Gagliardi,
53a,53b
M. Margoni,
53a,53b
M. Morandin,
53a
M. Posocco,
53a
M. Rotondo,
53a
F. Simonetto,
53a,53b
R. Stroili,
53a,53b
E. Ben-Haim,
54
G. R. Bonneaud,
54
H. Briand,
54
G. Calderini,
54
J. Chauveau,
54
O. Hamon,
54
Ph. Leruste,
54
G. Marchiori,
54
J. Ocariz,
54
J. Prendki,
54
S. Sitt,
54
M. Biasini,
55a,55b
E. Manoni,
55a,55b
A. Rossi,
55a,55b
C. Angelini,
56a,56b
G. Batignani,
56a,56b
S. Bettarini,
56a,56b
M. Carpinelli,
56a,56b,
k
G. Casarosa,
56a,56b
A. Cervelli,
56a,56b
F. Forti,
56a,56b
M. A. Giorgi,
56a,56b
A. Lusiani,
56a,56c
N. Neri,
56a,56b
E. Paoloni,
56a,56b
G. Rizzo,
56a,56b
J. J. Walsh,
56a
D. Lopes Pegna,
57
C. Lu,
57
J. Olsen,
57
A. J. S. Smith,
57
A. V. Telnov,
57
F. Anulli,
58a
E. Baracchini,
58a,58b
G. Cavoto,
58a
R. Faccini,
58a,58b
F. Ferrarotto,
58a
F. Ferroni,
58a,58b
M. Gaspero,
58a,58b
L. Li Gioi,
58a
M. A. Mazzoni,
58a
G. Piredda,
58a
F. Renga,
58a,58b
T. Hartmann,
59
T. Leddig,
59
H. Schro
̈
der,
59
R. Waldi,
59
T. Adye,
60
B. Franek,
60
E. O. Olaiya,
60
F. F. Wilson,
60
S. Emery,
61
G. Hamel de Monchenault,
61
G. Vasseur,
61
Ch. Ye
`
che,
61
M. Zito,
61
M. T. Allen,
62
D. Aston,
62
D. J. Bard,
62
R. Bartoldus,
62
J. F. Benitez,
62
C. Cartaro,
62
M. R. Convery,
62
J. Dorfan,
62
G. P. Dubois-Felsmann,
62
W. Dunwoodie,
62
R. C. Field,
62
M. Franco Sevilla,
62
B. G. Fulsom,
62
A. M. Gabareen,
62
M. T. Graham,
62
P. Grenier,
62
C. Hast,
62
W. R. Innes,
62
M. H. Kelsey,
62
H. Kim,
62
P. Kim,
62
M. L. Kocian,
62
D. W. G. S. Leith,
62
S. Li,
62
B. Lindquist,
62
S. Luitz,
62
H. L. Lynch,
62
D. B. MacFarlane,
62
H. Marsiske,
62
D. R. Muller,
62
H. Neal,
62
S. Nelson,
62
C. P. O’Grady,
62
I. Ofte,
62
M. Perl,
62
T. Pulliam,
62
B. N. Ratcliff,
62
A. Roodman,
62
A. A. Salnikov,
62
V. Santoro,
62
R. H. Schindler,
62
J. Schwiening,
62
PHYSICAL REVIEW D
83,
052011 (2011)
1550-7998
=
2011
=
83(5)
=
052011(16)
052011-1
Ó
2011 American Physical Society
A. Snyder,
62
D. Su,
62
M. K. Sullivan,
62
S. Sun,
62
K. Suzuki,
62
J. M. Thompson,
62
J. Va’vra,
62
A. P. Wagner,
62
M. Weaver,
62
W. J. Wisniewski,
62
M. Wittgen,
62
D. H. Wright,
62
H. W. Wulsin,
62
A. K. Yarritu,
62
C. C. Young,
62
V. Ziegler,
62
X. R. Chen,
63
W. Park,
63
M. V. Purohit,
63
R. M. White,
63
J. R. Wilson,
63
S. J. Sekula,
64
M. Bellis,
65
P. R. Burchat,
65
A. J. Edwards,
65
T. S. Miyashita,
65
S. Ahmed,
66
M. S. Alam,
66
J. A. Ernst,
66
B. Pan,
66
M. A. Saeed,
66
S. B. Zain,
66
N. Guttman,
67
A. Soffer,
67
P. Lund,
68
S. M. Spanier,
68
R. Eckmann,
69
J. L. Ritchie,
69
A. M. Ruland,
69
C. J. Schilling,
69
R. F. Schwitters,
69
B. C. Wray,
69
J. M. Izen,
70
X. C. Lou,
70
F. Bianchi,
71a,71b
D. Gamba,
71a,71b
M. Pelliccioni,
71a,71b
M. Bomben,
72a,72b
L. Lanceri,
72a,72b
L. Vitale,
72a,72b
N. Lopez-March,
73
F. Martinez-Vidal,
73
A. Oyanguren,
73
J. Albert,
74
Sw. Banerjee,
74
H. H. F. Choi,
74
K. Hamano,
74
G. J. King,
74
R. Kowalewski,
74
M. J. Lewczuk,
74
C. Lindsay,
74
I. M. Nugent,
74
J. M. Roney,
74
R. J. Sobie,
74
T. J. Gershon,
75
P. F. Harrison,
75
T. E. Latham,
75
E. M. T. Puccio,
75
H. R. Band,
76
S. Dasu,
76
K. T. Flood,
76
Y. Pan,
76
R. Prepost,
76
C. O. Vuosalo,
76
and S. L. Wu
76
(
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, CNRS/IN2P3, Ecole Polytechnique, 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
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
28
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstra
e 15, D-12489 Berlin, Germany
29
Imperial College London, London, SW7 2AZ, United Kingdom
30
University of Iowa, Iowa City, Iowa 52242, USA
31
Iowa State University, Ames, Iowa 50011-3160, USA
32
Johns Hopkins University, Baltimore, Maryland 21218, USA
33
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
34
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
35
University of Liverpool, Liverpool L69 7ZE, United Kingdom
36
Queen Mary, University of London, London, E1 4NS, United Kingdom
37
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
38
University of Louisville, Louisville, Kentucky 40292, USA
39
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
40
University of Manchester, Manchester M13 9PL, United Kingdom
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
052011 (2011)
052011-2
41
University of Maryland, College Park, Maryland 20742, USA
42
University of Massachusetts, Amherst, Massachusetts 01003, USA
43
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
44
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
45a
INFN Sezione di Milano, I-20133 Milano, Italy
45b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
46
University of Mississippi, University, Mississippi 38677, USA
47
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
48a
INFN Sezione di Napoli, I-80126 Napoli, Italy
48b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
49
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
50
University of Notre Dame, Notre Dame, Indiana 46556, USA
51
Ohio State University, Columbus, Ohio 43210, USA
52
University of Oregon, Eugene, Oregon 97403, USA
53a
INFN Sezione di Padova, I-35131 Padova, Italy
53b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
54
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
55a
INFN Sezione di Perugia, I-06100 Perugia, Italy
55b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
56a
INFN Sezione di Pisa, I-56127 Pisa, Italy
56b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
56c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
57
Princeton University, Princeton, New Jersey 08544, USA
58a
INFN Sezione di Roma, I-00185 Roma, Italy
58b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
59
Universita
̈
t Rostock, D-18051 Rostock, Germany
60
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
61
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
62
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
63
University of South Carolina, Columbia, South Carolina 29208, USA
64
Southern Methodist University, Dallas, Texas 75275, USA
65
Stanford University, Stanford, California 94305-4060, USA
66
State University of New York, Albany, New York 12222, USA
67
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
68
University of Tennessee, Knoxville, Tennessee 37996, USA
69
University of Texas at Austin, Austin, Texas 78712, USA
70
University of Texas at Dallas, Richardson, Texas 75083, USA
71a
INFN Sezione di Torino, I-10125 Torino, Italy
71b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
72a
INFN Sezione di Trieste, I-34127 Trieste, Italy
72b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
73
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
74
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
75
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
76
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 7 October 2010; published 24 March 2011)
We report the results of a study of the exclusive charmless semileptonic decays,
B
þ
!
ð0Þ
‘
þ
and
B
0
!
‘
þ
, undertaken with approximately
464
10
6
B
B
pairs collected at the
ð
4
S
Þ
resonance with
the
BABAR
detector. The analysis uses events in which the signal
B
decays are reconstructed with a loose
neutrino reconstruction technique. We obtain partial branching fractions for
B
þ
!
‘
þ
and
B
0
!
‘
þ
decays in three and 12 bins of
q
2
, respectively, from which we extract the
f
þ
ð
q
2
Þ
form-
factor shapes and the total branching fractions
B
ð
B
þ
!
‘
þ
Þ¼ð
0
:
36
0
:
05
stat
0
:
04
syst
Þ
10
4
*
Now at Temple University, Philadelphia, PA 19122, USA.
†
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
‡
Also with Universita
`
di Roma La Sapienza, I-00185 Roma, Italy.
x
Now at University of South Alabama, Mobile, AL 36688, USA.
k
Also with Universita
`
di Sassari, Sassari, Italy.
MEASUREMENT OF THE
B
0
!
‘
þ
...
PHYSICAL REVIEW D
83,
052011 (2011)
052011-3
and
B
ð
B
0
!
‘
þ
Þ¼ð
1
:
42
0
:
05
stat
0
:
07
syst
Þ
10
4
. We also measure
B
ð
B
þ
!
0
‘
þ
Þ¼
ð
0
:
24
0
:
08
stat
0
:
03
syst
Þ
10
4
. We obtain values for the magnitude of the CKM matrix element
j
V
ub
j
using three different QCD calculations.
DOI:
10.1103/PhysRevD.83.052011
PACS numbers: 13.20.He, 12.15.Hh, 12.38.Qk, 14.40.Nd
I. INTRODUCTION
A precise measurement of the CKM matrix [
1
] element
j
V
ub
j
will constrain the description of weak interactions
and
CP
violation in the standard model. The rate for
exclusive charmless semileptonic decays involving a scalar
meson is proportional to
j
V
ub
f
þ
ð
q
2
Þj
2
, where the form
factor
f
þ
ð
q
2
Þ
depends on
q
2
, the square of the momentum
transferred to the lepton-neutrino pair. Values of
f
þ
ð
q
2
Þ
are
given by unquenched lattice QCD (LQCD) calculations
[
2
,
3
], reliable only at large
q
2
(
*
16 GeV
2
), and by light
cone sum rules (LCSR) calculations [
4
,
5
], based on ap-
proximations only valid at small
q
2
(
&
16 GeV
2
). The
value of
j
V
ub
j
can thus be determined by the measurement
of partial branching fractions of charmless semileptonic
B
decays. Extraction of the
f
þ
ð
q
2
Þ
form-factor shapes
from exclusive decays [
6
] such as
B
0
!
‘
þ
[
7
] and
B
þ
!
ð0Þ
‘
þ
may be used to test theoretical calculations
[
8
]. The values of the branching fractions (BF) of the
B
þ
!
ð0Þ
‘
þ
decays will also improve our knowledge
of the composition of charmless semileptonic decays and
help constrain the size of the gluonic singlet contribution to
the form factors for these decays [
5
].
In this paper, we present measurements of the partial
BFs
B
ð
B
þ
!
‘
þ
;q
2
Þ
and
B
ð
B
0
!
‘
þ
;q
2
Þ
in
three and 12 bins of
q
2
, respectively, as well as the total
BFs for all three decay modes. Values of the total BFs were
previously reported in Refs. [
7
,
9
–
12
]. We use the values of
B
ð
q
2
Þ
for the
B
0
!
‘
þ
mode with form-factor cal-
culations [
2
–
4
] to obtain values of
j
V
ub
j
. Values of
j
V
ub
j
have previously been extracted from
B
0
!
‘
þ
mea-
surements by CLEO [
9
],
BABAR
[
7
,
10
,
13
], and Belle [
11
].
A very recent measurement by
BABAR
[
14
] will be dis-
cussed in Sec.
VII
.
II. DATA SAMPLE AND SIMULATION
We use a sample of
464
10
6
B
B
pairs corresponding
to an integrated luminosity of
422
:
6fb
1
collected at the
ð
4
S
Þ
resonance with the
BABAR
detector [
15
] at the PEP-
II asymmetric-energy
e
þ
e
storage rings and a sample of
44 fb
1
collected approximately 40 MeV below the
ð
4
S
Þ
resonance (denoted ‘‘off-resonance data’’). Detailed
Monte Carlo (MC) simulations are used to optimize the
signal selections, to estimate the signal efficiencies, and
to obtain the shapes of the signal and background distri-
butions. MC samples are generated for
ð
4
S
Þ!
B
B
events,
e
þ
e
!
u
u=d
d=s
s=c
c=
þ
(continuum) events,
and dedicated
B
B
samples containing
B
0
!
‘
þ
and
B
þ
!
ð0Þ
‘
þ
signal decays. The signal MC events are
produced with the
FLATQ2
generator [
16
] and are re-
weighted to reproduce the
f
þ
ð
q
2
;;c
B
Þ
Becirevic-
Kaidalov (BK) parametrization [
17
], where the values of
the shape and normalization parameters,
and
c
B
, are
taken from Ref. [
7
]. The
BABAR
detector’s acceptance
and response are simulated using the
GEANT4
package [
15
].
III. EVENT RECONSTRUCTION AND
CANDIDATE SELECTION
We reconstruct the
B
0
!
‘
þ
and
B
þ
!
ð0Þ
‘
þ
decays. The
meson is reconstructed in the
!
and
!
þ
0
decay channels (combined BF of
62%) while the
0
is reconstructed in the
0
!
þ
channel, followed by the
!
decay (product BF of
17.5%) [
18
]. The
0
!
0
decay channel suffers from
large backgrounds, and we do not consider it. We carry out
an untagged analysis with a loose neutrino reconstruction
technique [
7
], thereby obtaining a large candidate sample.
Event reconstruction with the
BABAR
detector is de-
scribed in detail elsewhere [
15
]. Electrons (muons) are
identified by their characteristic shower signatures in
the electromagnetic calorimeter (muon detector), while
charged hadrons are identified using the Cherenkov
detector and
dE=dx
measurements in the drift chamber.
The average electron (muon) reconstruction efficiency is
93% (70%), while its misidentification probability is
<
0
:
2%
(
<
1
:
5%
). The neutrino four-momentum,
P
¼
ðj
~
p
miss
j
;
~
p
miss
Þ
, is inferred from the difference between
the momentum of the colliding-beam particles
~
p
beams
and
the vector sum of the momenta of all the particles detected
in a single event
~
p
tot
, such that
~
p
miss
¼
~
p
beams
~
p
tot
.To
evaluate
E
tot
, the energy sum of all the particles, we assume
zero mass for all neutrals since photons are difficult to
disentangle from neutral hadrons, and we take the mass
given by the particle identification selectors for the charged
particles. In this analysis, we calculate the momentum
transfer as
q
2
¼ð
P
B
P
meson
Þ
2
instead of
q
2
¼
ð
P
‘
þ
P
Þ
2
, where
P
B
,
P
meson
, and
P
‘
are the four-
momenta of the
B
meson, of the
,
,or
0
meson, and
of the lepton, respectively. With this choice, the value of
q
2
is unaffected by any misreconstruction of the rest of the
event. Here
P
B
has an effective value. To estimate this
value, we first combine the lepton with a
,
,or
0
meson
to form the so-called
Y
pseudoparticle. The angle
BY
between the
Y
and
B
momenta in the
ð
4
S
Þ
frame can be
determined by assuming
B
!
Y
. In this frame, the
Y
momentum, the
B
momentum, and the angle
BY
define a
cone with the
Y
momentum as its axis and where the true
B
momentum lies somewhere on the surface of the cone. The
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
052011 (2011)
052011-4
B
rest frame is thus known up to an azimuthal angle
defined with respect to the
Y
momentum. The value of
q
2
is
then computed as the average of four
q
2
values correspond-
ing to four possible angles,
,
þ
=
2
,
þ
,
þ
3
=
2 rad
, where the angle
is chosen randomly
and where the four values of
q
2
are weighted by the factor
sin
2
B
,
B
being the angle between the
B
direction and the
beam direction in the
ð
4
S
Þ
frame [
19
]. We note that,
BY
being a real angle,
j
cos
BY
j
1
. We correct for the re-
construction effects on the
q
2
resolution (
0
:
51 GeV
2
)by
applying an unregularized unfolding algorithm to the mea-
sured
q
2
spectra [
20
].
The candidate selections are optimized to maximize the
ratio
S=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
S
þ
B
Þ
p
in the MC simulation, where
S
is the
number of signal events and
B
is the total number of
background events. The continuum background is
suppressed by requiring the ratio of second to zeroth
Fox-Wolfram moments [
21
] to be smaller than 0.5. This
background is further suppressed for
B
0
!
‘
þ
by
selections on the number of charged particle tracks and
neutral calorimeter clusters [
22
] that reject radiative
Bhabha and converted photon processes. We ensure that
the momenta of the lepton and meson candidates are kine-
matically compatible with a real signal decay by requiring
that a geometrical vertex fit of the two particles gives a
2
probability greater than 0.01 and that their angles in the
laboratory frame be between 0.41 and 2.46 rad with respect
to the
e
-beam direction, the acceptance of the detector. To
avoid
J=
c
!
þ
decays, we reject
B
0
!
þ
candidates if the
Y
mass corresponds to the
J=
c
mass.
The electron (muon) tracks are required to have momenta
greater than 0.5 (1.0) GeVin the laboratory frame to reduce
misidentified leptons and secondary decays such as
D
!
X‘
,
J=
c
,
, and kaon decays. Furthermore, the
momenta of the lepton and the meson are restricted to
enhance signal over background. We require the following:
for
B
0
!
‘
þ
decays,
j
~
p
‘
j
>
2
:
2 GeV
or
j
~
p
j
>
1
:
3 GeV
or
j
~
p
‘
jþj
~
p
j
>
2
:
8 GeV
; for
B
þ
!
‘
þ
de-
cays,
j
~
p
‘
j
>
2
:
1 GeV
or
j
~
p
j
>
1
:
3 GeV
or
j
~
p
‘
jþj
~
p
j
>
2
:
8 GeV
; and for
B
þ
!
0
‘
þ
decays,
j
~
p
‘
j
>
2
:
0 GeV
or
j
~
p
0
j
>
1
:
65 GeV
or
0
:
69
j
~
p
‘
jþj
~
p
0
j
>
2
:
4 GeV
(all
asterisked variables are in the center-of-mass frame). For
the
B
þ
!
ð0Þ
‘
þ
decays, we restrict the reconstructed
masses of the
0
and
to lie in the intervals
0
:
92
<m
0
<
0
:
98 GeV
and
0
:
51
<m
<
0
:
57 GeV
. For these decays,
we also reject events with
q
2
higher than
16 GeV
2
, since
the signal is dominated by background in that range. Most
backgrounds are reduced by
q
2
-dependent selections on
the angle (
cos
thrust
) between the thrust axes of the
Y
and
of the rest of the event, on the polar angle (
miss
) associated
with
~
p
miss
, on the invariant missing mass squared (
m
2
miss
¼
E
2
miss
j
~
p
miss
j
2
) divided by twice the missing energy
(
E
miss
¼
E
beams
E
tot
), and on the angle (
cos
‘
) between
the direction of the
W
boson (
‘
and
combined) in the rest
frame of the
B
meson and the direction of the lepton in the
rest frame of the
W
boson. The
q
2
selections are shown
in Fig.
1
and their effects illustrated in Fig.
2
for
B
0
!
‘
þ
decays. In Fig.
2
, a single vertical line
indicates a fixed cut; a set of two vertical lines represent
a
q
2
-dependent cut. The position of the two lines corre-
sponds to the minimum and maximum values of the cut,
as shown in Fig.
1
. The functions describing the
q
2
dependence are given in Tables
V
,
VI
, and
VII
of the
Appendix for the three decays under study. For
B
þ
!
‘
þ
decays, more background is rejected by requiring
that
j
cos
V
j
<
0
:
95
, where
V
is the helicity angle of the
meson [
16
].
The kinematic variables
E
¼ð
P
B
P
beams
s=
2
Þ
=
ffiffiffi
s
p
and
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
s=
2
þ
~
p
B
~
p
beams
Þ
2
=E
2
beams
~
p
2
B
q
are used in
a two-dimensional extended maximum-likelihood fit [
23
]
to separate signal from background. Here,
ffiffiffi
s
p
is the center-
of-mass energy of the colliding particles and
P
B
¼
P
meson
þ
P
‘
þ
P
, in the laboratory frame. We only retain
candidates with
j
E
j
<
1
:
0 GeV
and
m
ES
>
5
:
19 GeV
,
thereby removing the region with large backgrounds
from the fit. On average, fewer than 1.14 candidates are
observed per event. For events with multiple candidates,
only the candidate with the largest value of
cos
‘
is kept.
The signal event reconstruction efficiency varies between
8.3% and 14.6% for
B
0
!
‘
þ
, and 1.4% and 2.6% for
B
þ
!
‘
þ
decays (
channel), depending on
q
2
.Itis
0.6% for both
B
þ
!
‘
þ
(
þ
0
channel) and
B
þ
!
0
‘
þ
decays.
)
2
(GeV
2
q
01020
cut value
l
θ
cos
-1.0
-0.8
-0.6
-0.4
-0.2
-0.0
)
2
(GeV
2
q
01020
cut value
l
θ
cos
-1.0
-0.8
-0.6
-0.4
-0.2
-0.0
)
2
(GeV
2
q
01020
cut value
thrust
θ
cos
0.5
0.6
0.7
0.8
0.9
1.0
)
2
(GeV
2
q
01020
cut value
thrust
θ
cos
0.5
0.6
0.7
0.8
0.9
1.0
)
2
(GeV
2
q
01020
cut value (rad)
miss
θ
0.0
0.2
0.4
0.6
0.8
1.0
)
2
(GeV
2
q
01020
cut value (rad)
miss
θ
0.0
0.2
0.4
0.6
0.8
1.0
)
2
(GeV
2
q
01020
cut value (GeV)
miss
/2E
miss
2
m
0.0
0.5
1.0
1.5
2.0
)
2
(GeV
2
q
01020
cut value (GeV)
miss
/2E
miss
2
m
0.0
0.5
1.0
1.5
2.0
FIG. 1. Distributions of the selection values in the signal
region for the
q
2
-dependent variables used in the analysis of
B
0
!
‘
þ
decays. The vertical axis represents the selection
value for a given
q
2
value. We reject an event when its value is in
the shaded region.
MEASUREMENT OF THE
B
0
!
‘
þ
...
PHYSICAL REVIEW D
83,
052011 (2011)
052011-5
IV. BACKGROUNDS AND SIGNAL EXTRACTION
Backgrounds can be broadly grouped into three main
categories: decays arising from
b
!
u‘
transitions (other
than the signal), decays in other
B
B
events (excluding
b
!
u‘
), and decays in continuum events. For the
B
0
!
‘
þ
mode only, in which there are many events,
each of the first two categories is further split into a
background category where the pion and the lepton come
from the decay of the same
B
, and a background category
where the pion and the lepton come from the decay of
different
B
mesons.
Given the sufficient number of events for the
‘
decay mode, the data samples can be subdivided into 12
bins of
q
2
for the signal and two bins for each of the five
background categories. Two bins are used for each back-
ground category since the background
q
2
spectra are not
that well known and need to be adjusted in the fit when the
number of events is sufficiently large to permit it. The
q
2
ranges of the background binning for the
B
0
!
‘
þ
decay are
½
0
;
18
;
26
:
4
GeV
2
for the
b
!
u‘
same
B
category,
½
0
;
22
;
26
:
4
GeV
2
for the
b
!
u‘
both
B
cate-
gory,
½
0
;
10
;
26
:
4
GeV
2
for the other
B
B
same
B
category,
½
0
;
14
;
26
:
4
GeV
2
for the other
B
B
both
B
category
and
½
0
;
22
;
26
:
4
GeV
2
for the continuum category. In
each case, the
q
2
ranges of the two bins are chosen to
contain a similar number of events. All the signal and
background events, in each
q
2
bin, are fitted simulta-
neously. For the
ð0Þ
‘
modes, a smaller number of events
leads us to restrict the signal and each of the three back-
ground categories to a single
q
2
bin, except for the signal in
the
‘
mode when
!
, which is investigated in
three bins of
q
2
.
We use the
E
-
m
ES
histograms, obtained from the MC
simulation as two-dimensional probability density func-
tions (PDFs), in our fit to the data to extract the yields of
the signal and backgrounds as a function of
q
2
. As an initial
estimate, the MC continuum background yield and
q
2
-dependent shape are first normalized to match the yield
and
q
2
-dependent shape of the off-resonance data control
sample. This results in a large statistical uncertainty due to
the small number of events in the off-peak data. To im-
prove the statistical precision, the continuum background,
initially normalized to the off-peak data, is allowed to vary
in the fit to the data for the
‘
and
‘
ð
Þ
modes,
where we have a large number of events. The fit result is
compatible with the off-peak prediction within, at most,
1 standard deviation. Because of an insufficient number of
events, the
b
!
u‘
background is fixed in the fit for the
ð0Þ
‘
modes, and the continuum contribution is also fixed
for the
‘
ð
3
Þ
and
0
‘
modes. Whenever a background
is not varied in the fit, it is fixed to the MC prediction,
except for the continuum background which is fixed to its
normalized yield and
q
2
-dependent shape using the off-
resonance data. The background parameters which are free
in the fit require an adjustment of less than 10% with
respect to the MC predictions. For illustration purposes
only, we show in Fig.
3
E
and
m
ES
fit projections in the
l
θ
cos
-1
-0.5
0
0.5
1
Events per 0.0
5
0
100
200
300
l
θ
cos
-1
-0.5
0
0.5
1
Events per 0.0
5
0
100
200
300
thrust
θ
cos
0
0.2
0.4
0.6
0.8
1
Events per 0.02
0
200
400
600
800
thrust
θ
cos
0
0.2
0.4
0.6
0.8
1
Events per 0.02
0
200
400
600
800
(rad)
miss
θ
0123
Events per 0.05 rad
0
200
400
600
800
(rad)
miss
θ
0123
Events per 0.05 rad
0
200
400
600
800
signal
ν
l
π
→
0
B
both B
ν
ul
→
b
same B
ν
ul
→
b
both B
B
other B
same B
B
other B
continuum
(GeV)
mi
ss
/2E
miss
2
m
-2
-1
0
1
2
3
Events per 0.1 GeV
0
500
1000
1500
(GeV)
mi
ss
/2E
miss
2
m
-2
-1
0
1
2
3
Events per 0.1 GeV
0
500
1000
1500
FIG. 2 (color online). Distributions in the signal region for the
q
2
-dependent selections used in the analysis of
B
0
!
‘
þ
decays. The arrows indicate the rejected regions. All the selec-
tions have been applied except for the one of interest. In each
panel, the signal area is scaled to the area of the total back-
ground.
(GeV)
ES
m
5.20 5.22 5.24 5.26 5.28
Events per 0.005 GeV
0
500
1000
1500
2000
(GeV)
ES
m
5.20 5.22 5.24 5.26 5.28
Events per 0.005 GeV
0
500
1000
1500
2000
signal
ν
l
π
→
0
B
both B
ν
ul
→
b
same B
ν
ul
→
b
both B
B
other B
same B
B
other B
continuum
data
a)
2
< 16 GeV
2
0 < q
E (GeV)
∆
-1
-0.5
0
0.5
1
Events per 0.08 GeV
0
500
1000
1500
E (GeV)
∆
-1
-0.5
0
0.5
1
Events per 0.08 GeV
0
500
1000
1500
c)
E (GeV)
∆
-1
-0.5
0
0.5
1
0
500
1000
E (GeV)
∆
-1
-0.5
0
0.5
1
0
500
1000
d)
(GeV)
ES
m
5.20 5.22 5.24 5.26 5.28
0
500
1000
(GeV)
ES
m
5.20 5.22 5.24 5.26 5.28
0
500
1000
b)
2
< 26.4 GeV
2
16 < q
FIG. 3 (color online). Projections of the data and fit results for
the
B
0
!
‘
þ
decays, in the signal-enhanced region:
(a,b)
m
ES
with
0
:
16
<
E<
0
:
20 GeV
and (c,d)
E
with
m
ES
>
5
:
268 GeV
. The distributions (a,c) and (b,d) are projec-
tions for
q
2
<
16 GeV
2
and for
q
2
>
16 GeV
2
, respectively.
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
052011 (2011)
052011-6
signal-enhanced region for
B
0
!
‘
þ
decays in two
ranges of
q
2
corresponding to the sum of eight bins below
and four bins above
q
2
¼
16 GeV
2
, respectively.
More detailed
E
and
m
ES
fit projections in each
q
2
bin
are also shown in Figs.
8
and
9
of the Appendix for the
B
0
!
‘
þ
decays. The data and the fit results are in
good agreement. Fit projections for
B
þ
!
ð0Þ
‘
þ
, only
available below
q
2
¼
16 GeV
2
, are shown in Fig.
4
. Table
I
gives the total fitted yields in the full
q
2
range for the signal
and each background category as well as the
2
values and
degrees of freedom for the overall fit region. The yield
values in the
B
þ
!
‘
þ
column are the result of the fit to
the combined
and
3
modes.
V. SYSTEMATIC UNCERTAINTIES
Systematic uncertainties on the values of the partial
branching fractions,
B
ð
q
2
Þ
, and their correlations among
the
q
2
bins have been investigated. These uncertainties are
estimated from the variations of the resulting partial BF
values (or total BF values for
B
þ
!
0
‘
þ
decays) when
the data are reanalyzed with different simulation parameters
and reweightings. For each parameter, we use the full MC
data set to generate new
E
-
m
ES
distributions (‘‘MC event
samples’’) by varying randomly only the parameter of
interest over a complete (
>
3
) Gaussian distribution
whose standard deviation is given by the uncertainty on
the specific parameter under investigation. One hundred
such samples are generated for each parameter.
Uncertainties due to
B
counting and final state radiation
are estimated by generating only one sample. Each MC
sample is analyzed the same way as real data to determine
values of
B
ð
q
2
Þ
(or total BF values for
B
þ
!
0
‘
þ
decays). The contribution of the parameter to the systematic
uncertainty is given by the rms value of the distribution of
these values over the 100 samples.
The systematic uncertainties due to the imperfect
description of the detector in the simulation are computed
by using the uncertainties, determined from control
samples, on the tracking efficiency of all charged particle
tracks, on the particle identification efficiencies of signal
candidate tracks, on the calorimeter efficiencies (varied
separately for photons and
K
0
L
), on the energy deposited
in the calorimeter by
K
0
L
mesons, as well as on their
production spectrum. The reconstruction of these neutral
particles affects the analysis through the neutrino recon-
struction. The uncertainties due to the generator-level in-
puts to the simulation are given by the uncertainties in the
BFs of the background processes
b
!
u‘
and
b
!
c‘
,in
the BFs of the secondary decays producing leptons [
18
], and
in the BFs of the
ð
4
S
Þ!
B
B
decays [
8
]. The
B
!
X‘
form-factor uncertainties, where
X
¼ð
;;!;
ð0Þ
;
D;D
Þ
, are given by recent calculations or measurements
[
18
]. The uncertainties in the heavy quark parameters used
in the simulation of nonresonant
b
!
u‘
events are given
in Ref. [
24
]. We assign an uncertainty of 20% [
25
] to the
final state radiation (FSR) corrections calculated by
PHOTOS
[
26
]. Finally, the uncertainties due to the modeling of the
continuum are established by using the uncertainty in its
q
2
distribution shape and, when the continuum background is
fixed, the uncertainty in the total yield, both given by
comparisons with the off-resonance data control sample.
The list of all the systematic uncertainties, as well as
their values for the partial and total BFs, are given in
Tables
VIII
and
IX
of the Appendix. The item ‘‘Signal
MC stat error’’ in these tables includes the systematic
uncertainty due to the unfolding procedure. The correlation
matrices obtained in the measurement of the partial BFs
are presented in Tables
X
,
XI
, and
XII
. A condensed
version of all the uncertainties is given in Table
II
together
(GeV)
ES
m
5.20 5.22 5.24 5.26 5.28
Events per 0.005 GeV
0
100
200
300
400
signal
ν
l
η
→
B
ν
ul
→
b
B
other B
continuum
data
a)
2
< 16 GeV
2
0 < q
(GeV)
ES
m
5.20 5.22 5.24 5.26 5.28
Events per 0.005 GeV
0
100
200
300
400
(GeV
)
ES
m
5.20 5.22 5.24 5.26 5.28
0
20
40
60
80
signal
ν
’l
η
→
B
ν
ul
→
b
B
other B
continuum
data
b)
2
< 16 GeV
2
0 < q
(GeV
)
ES
m
5.20 5.22 5.24 5.26 5.28
0
20
40
60
80
E (GeV)
∆
-1
-0.5
0
0.5
1
Events per 0.08 GeV
0
100
200
300
400
c)
E (GeV)
∆
-1
-0.5
0
0.5
1
Events per 0.08 GeV
0
100
200
300
400
E (GeV)
∆
-1
-0.5
0
0.5
1
0
20
40
60
d)
E (GeV)
∆
-1
-0.5
0
0.5
1
0
20
40
60
FIG. 4 (color online). Projections of the data and fit results
for the
B
þ
!
ð0Þ
‘
þ
decays, in the signal-enhanced region:
(a,b)
m
ES
with
0
:
16
<
E<
0
:
20 GeV
and (c,d)
E
with
m
ES
>
5
:
268 GeV
. The distributions (a,c) and (b,d) are projec-
tions for the
B
þ
!
‘
þ
and
B
þ
!
0
‘
þ
decays, respec-
tively, both for
q
2
<
16 GeV
2
.
TABLE I. Fitted yields in the full
q
2
range for the signal and
each background category, total number of MC and data events,
and values of
2
for the fit region.
Decay mode
‘
þ
‘
þ
0
‘
þ
Signal
11 778
435
888
98
141
46
b
!
u‘
27 793
929
2201 (fixed) 204 (fixed)
Other
B
B
80 185
963 17 429
247 2660
82
Continuum
27 790
814
3435
195
517 (fixed)
MC events
147 546
467 23 953
183 3522
68
Data events
147 529
384 23 952
155 3517
59
2
=
ndf
411
=
386
56
=
52
19
=
17
MEASUREMENT OF THE
B
0
!
‘
þ
...
PHYSICAL REVIEW D
83,
052011 (2011)
052011-7
with signal yields and partial BFs in selected
q
2
ranges.
The values given for the
B
þ
!
‘
þ
decays are those
obtained from the fits to the distributions of the
!
and
!
þ
0
channels combined. The larger relative
uncertainties occurring in bin 12 of Table
VIII
are due to
poorly reconstructed events, and to the small raw yield in
that bin. The former arises from the presence of a large
number of low momentum pions and a large background.
This makes it difficult to select the right pion and results in
a larger absolute uncertainty on the fitted yield. The small
yield leads to a fairly large unfolding correction in this bin
and thus to a considerably reduced unfolded yield. On the
other hand, the unfolding process increases the absolute
uncertainty only slightly. The reduced yield, together with
the larger absolute uncertainty, leads to the larger relative
uncertainties reported in the table.
VI. RESULTS
The partial BFs are calculated for
B
0
!
‘
þ
and
B
þ
!
‘
þ
decays using the unfolded signal yields, the
signal efficiencies given by the simulation, and the BFs
B
ð
ð
4
S
Þ!
B
0
B
0
Þ¼
0
:
484
0
:
006
and
B
ð
ð
4
S
Þ!
B
þ
B
Þ¼
0
:
516
0
:
006
[
8
]. We obtain the total BFs
B
ð
B
0
!
‘
þ
Þ¼ð
1
:
42
0
:
05
stat
0
:
07
syst
Þ
10
4
,
B
ð
B
þ
!
‘
þ
Þ¼ð
0
:
36
0
:
05
stat
0
:
04
syst
Þ
10
4
,
and
B
ð
B
þ
!
0
‘
þ
Þ¼ð
0
:
24
0
:
08
stat
0
:
03
syst
Þ
10
4
.
The BF value for
B
þ
!
0
‘
þ
has a significance of
3
:
2
when we take into account only the statistical uncer-
tainty [
27
]. Taking into account the effect of the systematic
uncertainty, which increases the total uncertainty by about
8%, leads to a reduced significance of
3
:
0
. The BF value,
obtained from a fit to the combined
and
3
channels of
the
B
þ
!
‘
þ
decays, is in good agreement with the
weighted average of the total BFs obtained separately for
the
and
3
channels. Consistent results are obtained
when dividing the final data set into chronologically or-
dered subsets, and electron only and muon only subsets,
modifying the
q
2
or the
E
and
m
ES
binnings, and varying
the event selection requirements.
The experimental
B
ð
q
2
Þ
distributions are displayed in
Fig.
5
for
B
0
!
‘
þ
decays and in Fig.
6
for
B
þ
!
‘
þ
decays, together with theoretical predictions. To
allow a direct comparison with the theoretical predictions,
which do not include FSR effects, the experimental distri-
butions in these figures have been obtained with the effi-
ciency given by the ratio of
q
2
unfolded events generated
after all the cuts, with a simulation which includes FSR, to
the total number of events generated before any cut and
with no FSR effects i.e. with
PHOTOS
switched off. We
obtain the
f
þ
ð
q
2
Þ
shape from a fit to these distributions.
The
2
function minimized in the fit to the
f
þ
ð
q
2
Þ
shape
TABLE II. Values of signal yields,
B
ð
q
2
Þ
, and their relative uncertainties (%) for
B
0
!
‘
þ
,
B
þ
!
‘
þ
, and
B
þ
!
0
‘
þ
decays.
Decay mode
‘
þ
‘
þ
0
‘
þ
q
2
range (
GeV
2
)
q
2
<
12
q
2
<
16
q
2
>
16
Full
q
2
range
q
2
<
16
q
2
<
16
Yield
6541.6
8422.1
3355.4
11 777.6
887.9
141.0
BF (
10
4
)
0.83
1.09
0.33
1.42
0.36
0.24
Statistical error
3.9
3.7
7.6
3.5
12.5
32.8
Detector effects
3.1
3.5
6.1
4.0
8.0
8.8
Continuum bkg
0.9
0.8
1.0
0.7
0.3
7.1
B
!
X
u
‘
bkg
2.0
1.7
4.2
2.0
7.6
6.7
B
!
X
c
‘
bkg
0.6
0.7
1.8
1.0
1.2
2.6
Other effects
2.3
2.2
3.2
2.3
3.4
4.6
Total uncertainty
5.9
5.9
11.3
6.3
17.0
35.8
)
2
(GeV
2
Unfolded q
0
5
10
15
20
25
)
2
(2 GeV
×
2
q
∆
)/
2
B(q
∆
0
2
4
6
8
10
12
14
16
-6
10
×
LCSR
FNAL/MILC
HPQCD
BGL fit to data
BK fit to data
data
FIG. 5 (color online). Partial
B
ð
q
2
Þ
spectrum in 12 bins of
q
2
for
B
0
!
‘
þ
decays. The data points are placed in the
middle of each bin whose width is defined in Table
VIII
. The
smaller error bars are statistical only while the larger ones also
include systematic uncertainties. The solid green and black
curves show the result of the fit to the data of the BK [
17
] and
BGL [
28
] parametrizations, respectively. The data are also
compared to unquenched LQCD calculations (HPQCD [
2
],
FNAL [
3
]) and a LCSR calculation [
4
].
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
052011 (2011)
052011-8