of 11
Measurements of branching fractions for
B
þ
!

þ

,
B
0
!

0

, and
B
0
!
!
B. Aubert,
1
M. Bona,
1
Y. Karyotakis,
1
J. P. Lees,
1
V. Poireau,
1
E. Prencipe,
1
X. Prudent,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
L. Lopez,
3a,3b
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
L. Sun,
4
G. S. Abrams,
5
M. Battaglia,
5
D. N. Brown,
5
R. N. Cahn,
5
R. G. Jacobsen,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
I. L. Osipenkov,
5
M. T. Ronan,
5,
*
K. Tackmann,
5
T. Tanabe,
5
C. M. Hawkes,
6
N. Soni,
6
A. T. Watson,
6
H. Koch,
7
T. Schroeder,
7
D. Walker,
8
D. J. Asgeirsson,
9
B. G. Fulsom,
9
C. Hearty,
9
T. S. Mattison,
9
J. A. McKenna,
9
M. Barrett,
10
A. Khan,
10
V. E. Blinov,
11
A. D. Bukin,
11
A. R. Buzykaev,
11
V. P. Druzhinin,
11
V. B. Golubev,
11
A. P. Onuchin,
11
S. I. Serednyakov,
11
Yu. I. Skovpen,
11
E. P. Solodov,
11
K. Yu. Todyshev,
11
M. Bondioli,
12
S. Curry,
12
I. Eschrich,
12
D. Kirkby,
12
A. J. Lankford,
12
P. Lund,
12
M. Mandelkern,
12
E. C. Martin,
12
D. P. Stoker,
12
S. Abachi,
13
C. Buchanan,
13
J. W. Gary,
14
F. Liu,
14
O. Long,
14
B. C. Shen,
14,
*
G. M. Vitug,
14
Z. Yasin,
14
L. Zhang,
14
V. Sharma,
15
C. Campagnari,
16
T. M. Hong,
16
D. Kovalskyi,
16
M. A. Mazur,
16
J. D. Richman,
16
T. W. Beck,
17
A. M. Eisner,
17
C. J. Flacco,
17
C. A. Heusch,
17
J. Kroseberg,
17
W. S. Lockman,
17
A. J. Martinez,
17
T. Schalk,
17
B. A. Schumm,
17
A. Seiden,
17
L. Wang,
17
M. G. Wilson,
17
L. O. Winstrom,
17
C. H. Cheng,
18
D. A. Doll,
18
B. Echenard,
18
F. Fang,
18
D. G. Hitlin,
18
I. Narsky,
18
T. Piatenko,
18
F. C. Porter,
18
R. Andreassen,
19
G. Mancinelli,
19
B. T. Meadows,
19
K. Mishra,
19
M. D. Sokoloff,
19
P. C. Bloom,
20
W. T. Ford,
20
A. Gaz,
20
J. F. Hirschauer,
20
M. Nagel,
20
U. Nauenberg,
20
J. G. Smith,
20
K. A. Ulmer,
20
S. R. Wagner,
20
R. Ayad,
21,
+
A. Soffer,
21,
W. H. Toki,
21
R. J. Wilson,
21
D. D. Altenburg,
22
E. Feltresi,
22
A. Hauke,
22
H. Jasper,
22
M. Karbach,
22
J. Merkel,
22
A. Petzold,
22
B. Spaan,
22
K. Wacker,
22
M. J. Kobel,
23
W. F. Mader,
23
R. Nogowski,
23
K. R. Schubert,
23
R. Schwierz,
23
J. E. Sundermann,
23
A. Volk,
23
D. Bernard,
24
G. R. Bonneaud,
24
E. Latour,
24
Ch. Thiebaux,
24
M. Verderi,
24
P. J. Clark,
25
W. Gradl,
25
S. Playfer,
25
J. E. Watson,
25
M. Andreotti,
26a,26b
D. Bettoni,
26a
C. Bozzi,
26a
R. Calabrese,
26a,26b
A. Cecchi,
26a,26b
G. Cibinetto,
26a,26b
P. Franchini,
26a,26b
E. Luppi,
26a,26b
M. Negrini,
26a,26b
A. Petrella,
26a,26b
L. Piemontese,
26a
V. Santoro,
26a,26b
R. Baldini-Ferroli,
27
A. Calcaterra,
27
R. de Sangro,
27
G. Finocchiaro,
27
S. Pacetti,
27
P. Patteri,
27
I. M. Peruzzi,
27,
x
M. Piccolo,
27
M. Rama,
27
A. Zallo,
27
A. Buzzo,
28a
R. Contri,
28a,28b
M. Lo Vetere,
28a,28b
M. M. Macri,
28a
M. R. Monge,
28a,28b
S. Passaggio,
28a
C. Patrignani,
28a,28b
E. Robutti,
28a
A. Santroni,
28a,28b
S. Tosi,
28a,28b
K. S. Chaisanguanthum,
29
M. Morii,
29
J. Marks,
30
S. Schenk,
30
U. Uwer,
30
V. Klose,
31
H. M. Lacker,
31
D. J. Bard,
32
P. D. Dauncey,
32
J. A. Nash,
32
W. Panduro Vazquez,
32
M. Tibbetts,
32
P. K. Behera,
33
X. Chai,
33
M. J. Charles,
33
U. Mallik,
33
J. Cochran,
34
H. B. Crawley,
34
L. Dong,
34
W. T. Meyer,
34
S. Prell,
34
E. I. Rosenberg,
34
A. E. Rubin,
34
Y. Y. Gao,
35
A. V. Gritsan,
35
Z. J. Guo,
35
C. K. Lae,
35
A. G. Denig,
36
M. Fritsch,
36
G. Schott,
36
N. Arnaud,
37
J. Be
́
quilleux,
37
A. D’Orazio,
37
M. Davier,
37
J. Firmino da Costa,
37
G. Grosdidier,
37
A. Ho
̈
cker,
37
V. Lepeltier,
37
F. Le Diberder,
37
A. M. Lutz,
37
S. Pruvot,
37
P. Roudeau,
37
M. H. Schune,
37
J. Serrano,
37
V. Sordini,
37,
k
A. Stocchi,
37
G. Wormser,
37
D. J. Lange,
38
D. M. Wright,
38
I. Bingham,
39
J. P. Burke,
39
C. A. Chavez,
39
J. R. Fry,
39
E. Gabathuler,
39
R. Gamet,
39
D. E. Hutchcroft,
39
D. J. Payne,
39
C. Touramanis,
39
A. J. Bevan,
40
C. K. Clarke,
40
K. A. George,
40
F. Di Lodovico,
40
R. Sacco,
40
M. Sigamani,
40
G. Cowan,
41
H. U. Flaecher,
41
D. A. Hopkins,
41
S. Paramesvaran,
41
F. Salvatore,
41
A. C. Wren,
41
D. N. Brown,
42
C. L. Davis,
42
K. E. Alwyn,
43
D. Bailey,
43
R. J. Barlow,
43
Y. M. Chia,
43
C. L. Edgar,
43
G. Jackson,
43
G. D. Lafferty,
43
T. J. West,
43
J. I. Yi,
43
J. Anderson,
44
C. Chen,
44
A. Jawahery,
44
D. A. Roberts,
44
G. Simi,
44
J. M. Tuggle,
44
C. Dallapiccola,
45
X. Li,
45
E. Salvati,
45
S. Saremi,
45
R. Cowan,
46
D. Dujmic,
46
P. H. Fisher,
46
K. Koeneke,
46
G. Sciolla,
46
M. Spitznagel,
46
F. Taylor,
46
R. K. Yamamoto,
46
M. Zhao,
46
P. M. Patel,
47
S. H. Robertson,
47
A. Lazzaro,
48a,48b
V. Lombardo,
48a
F. Palombo,
48a,48b
J. M. Bauer,
49
L. Cremaldi,
49
V. Eschenburg,
49
R. Godang,
49,
{
R. Kroeger,
49
D. A. Sanders,
49
D. J. Summers,
49
H. W. Zhao,
49
M. Simard,
50
P. Taras,
50
F. B. Viaud,
50
H. Nicholson,
51
G. De Nardo,
52a,52b
L. Lista,
52a
D. Monorchio,
52a,52b
G. Onorato,
52a,52b
C. Sciacca,
52a,52b
G. Raven,
53
H. L. Snoek,
53
C. P. Jessop,
54
K. J. Knoepfel,
54
J. M. LoSecco,
54
W. F. Wang,
54
G. Benelli,
55
L. A. Corwin,
55
K. Honscheid,
55
H. Kagan,
55
R. Kass,
55
J. P. Morris,
55
A. M. Rahimi,
55
J. J. Regensburger,
55
S. J. Sekula,
55
Q. K. Wong,
55
N. L. Blount,
56
J. Brau,
56
R. Frey,
56
O. Igonkina,
56
J. A. Kolb,
56
M. Lu,
56
R. Rahmat,
56
N. B. Sinev,
56
D. Strom,
56
J. Strube,
56
E. Torrence,
56
G. Castelli,
57a,57b
N. Gagliardi,
57a,57b
M. Margoni,
57a,57b
M. Morandin,
57a
M. Posocco,
57a
M. Rotondo,
57a
F. Simonetto,
57a,57b
R. Stroili,
57a,57b
C. Voci,
57a,57b
P. del Amo Sanchez,
58
E. Ben-Haim,
58
H. Briand,
58
G. Calderini,
58
J. Chauveau,
58
P. David,
58
L. Del Buono,
58
O. Hamon,
58
Ph. Leruste,
58
J. Ocariz,
58
A. Perez,
58
J. Prendki,
58
S. Sitt,
58
L. Gladney,
59
M. Biasini,
60a,60b
R. Covarelli,
60a,60b
E. Manoni,
60a,60b
C. Angelini,
61a,61b
G. Batignani,
61a,61b
S. Bettarini,
61a,61b
M. Carpinelli,
61a,61b,
**
A. Cervelli,
61a,61b
F. Forti,
61a,61b
M. A. Giorgi,
61a,61b
A. Lusiani,
61a,61c
G. Marchiori,
61a,61b
M. Morganti,
61a,61b
N. Neri,
61a,61b
E. Paoloni,
61a,61b
G. Rizzo,
61a,61b
J. J. Walsh,
61a
D. Lopes Pegna,
62
C. Lu,
62
J. Olsen,
62
A. J. S. Smith,
62
A. V. Telnov,
62
F. Anulli,
63a
E. Baracchini,
63a,63b
G. Cavoto,
63a
D. del Re,
63a,63b
E. Di Marco,
63a,63b
R. Faccini,
63a,63b
F. Ferrarotto,
63a
F. Ferroni,
63a,63b
M. Gaspero,
63a,63b
P. D. Jackson,
63a
L. Li Gioi,
63a
PHYSICAL REVIEW D
78,
112001 (2008)
1550-7998
=
2008
=
78(11)
=
112001(11)
112001-1
Ó
2008 The American Physical Society
M. A. Mazzoni,
63a
S. Morganti,
63a
G. Piredda,
63a
F. Polci,
63a,63b
F. Renga,
63a,63b
C. Voena,
63a
M. Ebert,
64
T. Hartmann,
64
H. Schro
̈
der,
64
R. Waldi,
64
T. Adye,
65
B. Franek,
65
E. O. Olaiya,
65
F. F. Wilson,
65
S. Emery,
66
M. Escalier,
66
L. Esteve,
66
S. F. Ganzhur,
66
G. Hamel de Monchenault,
66
W. Kozanecki,
66
G. Vasseur,
66
Ch. Ye
`
che,
66
M. Zito,
66
X. R. Chen,
67
H. Liu,
67
W. Park,
67
M. V. Purohit,
67
R. M. White,
67
J. R. Wilson,
67
M. T. Allen,
68
D. Aston,
68
R. Bartoldus,
68
P. Bechtle,
68
J. F. Benitez,
68
R. Cenci,
68
J. P. Coleman,
68
M. R. Convery,
68
J. C. Dingfelder,
68
J. Dorfan,
68
G. P. Dubois-Felsmann,
68
W. Dunwoodie,
68
R. C. Field,
68
A. M. Gabareen,
68
S. J. Gowdy,
68
M. T. Graham,
68
P. Grenier,
68
C. Hast,
68
W. R. Innes,
68
J. Kaminski,
68
M. H. Kelsey,
68
H. Kim,
68
P. Kim,
68
M. L. Kocian,
68
D. W. G. S. Leith,
68
S. Li,
68
B. Lindquist,
68
S. Luitz,
68
V. Luth,
68
H. L. Lynch,
68
D. B. MacFarlane,
68
H. Marsiske,
68
R. Messner,
68
D. R. Muller,
68
H. Neal,
68
S. Nelson,
68
C. P. O’Grady,
68
I. Ofte,
68
A. Perazzo,
68
M. Perl,
68
B. N. Ratcliff,
68
A. Roodman,
68
A. A. Salnikov,
68
R. H. Schindler,
68
J. Schwiening,
68
A. Snyder,
68
D. Su,
68
M. K. Sullivan,
68
K. Suzuki,
68
S. K. Swain,
68
J. M. Thompson,
68
J. Va’vra,
68
A. P. Wagner,
68
M. Weaver,
68
C. A. West,
68
W. J. Wisniewski,
68
M. Wittgen,
68
D. H. Wright,
68
H. W. Wulsin,
68
A. K. Yarritu,
68
K. Yi,
68
C. C. Young,
68
V. Ziegler,
68
P. R. Burchat,
69
A. J. Edwards,
69
S. A. Majewski,
69
T. S. Miyashita,
69
B. A. Petersen,
69
L. Wilden,
69
S. Ahmed,
70
M. S. Alam,
70
J. A. Ernst,
70
B. Pan,
70
M. A. Saeed,
70
S. B. Zain,
70
S. M. Spanier,
71
B. J. Wogsland,
71
R. Eckmann,
72
J. L. Ritchie,
72
A. M. Ruland,
72
C. J. Schilling,
72
R. F. Schwitters,
72
B. W. Drummond,
73
J. M. Izen,
73
X. C. Lou,
73
F. Bianchi,
74a,74b
D. Gamba,
74a,74b
M. Pelliccioni,
74a,74b
M. Bomben,
75a,75b
L. Bosisio,
75a,75b
C. Cartaro,
75a,75b
G. Della Ricca,
75a,75b
L. Lanceri,
75a,75b
L. Vitale,
75a,75b
V. Azzolini,
76
N. Lopez-March,
76
F. Martinez-Vidal,
76
D. A. Milanes,
76
A. Oyanguren,
76
J. Albert,
77
Sw. Banerjee,
77
B. Bhuyan,
77
H. H. F. Choi,
77
K. Hamano,
77
R. Kowalewski,
77
M. J. Lewczuk,
77
I. M. Nugent,
77
J. M. Roney,
77
R. J. Sobie,
77
T. J. Gershon,
78
P. F. Harrison,
78
J. Ilic,
78
T. E. Latham,
78
G. B. Mohanty,
78
H. R. Band,
79
X. Chen,
79
S. Dasu,
79
K. T. Flood,
79
Y. Pan,
79
M. Pierini,
79
R. Prepost,
79
C. O. Vuosalo,
79
and S. L. Wu
79
(
B
A
B
AR
Collaboration)
1
Laboratoire de Physique des Particules, IN2P3/CNRS et Universite
́
de Savoie, 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
Dipartmento 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
University of Birmingham, Birmingham, B15 2TT, United Kingdom
7
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
8
University of Bristol, Bristol BS8 1TL, United Kingdom
9
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
10
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
11
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
12
University of California at Irvine, Irvine, California 92697, USA
13
University of California at Los Angeles, Los Angeles, California 90024, USA
14
University of California at Riverside, Riverside, California 92521, USA
15
University of California at San Diego, La Jolla, California 92093, USA
16
University of California at Santa Barbara, Santa Barbara, California 93106, USA
17
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
18
California Institute of Technology, Pasadena, California 91125, USA
19
University of Cincinnati, Cincinnati, Ohio 45221, USA
20
University of Colorado, Boulder, Colorado 80309, USA
21
Colorado State University, Fort Collins, Colorado 80523, USA
22
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
23
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
24
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
25
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
26a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
26b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
27
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
28a
INFN Sezione di Genova, I-16146 Genova, Italy
28b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
29
Harvard University, Cambridge, Massachusetts 02138, USA
30
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
B. AUBERT
et al.
PHYSICAL REVIEW D
78,
112001 (2008)
112001-2
31
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstr. 15, D-12489 Berlin, Germany
32
Imperial College London, London, SW7 2AZ, United Kingdom
33
University of Iowa, Iowa City, Iowa 52242, USA
34
Iowa State University, Ames, Iowa 50011-3160, USA
35
Johns Hopkins University, Baltimore, Maryland 21218, USA
36
Universita
̈
t Karlsruhe, Institut fu
̈
r Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
37
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
38
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
39
University of Liverpool, Liverpool L69 7ZE, United Kingdom
40
Queen Mary, University of London, London, E1 4NS, United Kingdom
41
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
42
University of Louisville, Louisville, Kentucky 40292, USA
43
University of Manchester, Manchester M13 9PL, United Kingdom
44
University of Maryland, College Park, Maryland 20742, USA
45
University of Massachusetts, Amherst, Massachusetts 01003, USA
46
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
47
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
48a
INFN Sezione di Milano, I-20133 Milano, Italy
48b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
49
University of Mississippi, University, Mississippi 38677, USA
50
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
51
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
52a
INFN Sezione di Napoli, I-80126 Napoli, Italy
52b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
53
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
54
University of Notre Dame, Notre Dame, Indiana 46556, USA
55
Ohio State University, Columbus, Ohio 43210, USA
56
University of Oregon, Eugene, Oregon 97403, USA
57a
INFN Sezione di Padova, I-35131 Padova, Italy
57b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
58
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
59
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
60a
INFN Sezione di Perugia, I-06100 Perugia, Italy
60b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
61a
INFN Sezione di Pisa, I-56127 Pisa, Italy
61b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
61c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
62
Princeton University, Princeton, New Jersey 08544, USA
63a
INFN Sezione di Roma, I-00185 Roma, Italy
63b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
64
Universita
̈
t Rostock, D-18051 Rostock, Germany
65
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
66
DSM/Irfu, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, France
67
University of South Carolina, Columbia, South Carolina 29208, USA
68
Stanford Linear Accelerator Center, Stanford, California 94309, USA
69
Stanford University, Stanford, California 94305-4060, USA
70
State University of New York, Albany, New York 12222, USA
71
University of Tennessee, Knoxville, Tennessee 37996, USA
72
University of Texas at Austin, Austin, Texas 78712, USA
73
University of Texas at Dallas, Richardson, Texas 75083, USA
{
Now at University of South Alabama, Mobile, AL 36688, USA.
k
Also with Universita
`
di Roma La Sapienza, I-00185 Roma, Italy.
x
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
Now at Tel Aviv University, Tel Aviv, 69978, Israel.
+
Now at Temple University, Philadelphia, PA 19122, USA.
**
Also with Universita
`
di Sassari, Sassari, Italy.
*
Deceased.
MEASUREMENTS OF BRANCHING FRACTIONS FOR
...
PHYSICAL REVIEW D
78,
112001 (2008)
112001-3
74a
INFN Sezione di Torino, I-10125 Torino, Italy
74b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
75a
INFN Sezione di Trieste, I-34127 Trieste, Italy
75b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
76
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
77
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
78
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
79
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 9 August 2008; published 1 December 2008)
We present branching fraction measurements for the radiative decays
B
þ
!

þ

,
B
0
!

0

, and
B
0
!
!
. The analysis is based on a data sample of
465

10
6
B

B
events collected with the
BABAR
detector at the PEP-II asymmetric-energy
B
Factory located at the Stanford Linear Accelerator Center. We
find
B
ð
B
þ
!

þ

Þ¼ð
1
:
20
þ
0
:
42

0
:
37

0
:
20
Þ
10

6
,
B
ð
B
0
!

0

Þ¼ð
0
:
97
þ
0
:
24

0
:
22

0
:
06
Þ
10

6
, and a
90% C.L. upper limit
B
ð
B
0
!
!
Þ
<
0
:
9

10

6
, where the first error is statistical and the second is
systematic. We also measure the isospin-violating quantity

ð
B
þ
!

þ

Þ
=
2
ð
B
0
!

0

Þ
1
¼

0
:
43
þ
0
:
25

0
:
22

0
:
10
.
DOI:
10.1103/PhysRevD.78.112001
PACS numbers: 12.15.Hh, 13.25.Hw
I. INTRODUCTION
Within the standard model (SM), the radiative decays
B
þ
!

þ

,
B
0
!

0

, and
B
0
!
!
1
proceed mainly
through a
b
!
d
electroweak penguin amplitude with a
virtual top quark in the loop. Hence, the decay rates depend
on the magnitude of the Cabibbo-Kobayashi-Maskawa
(CKM) matrix element
V
td
. The branching fraction results
from recent next-to-leading order calculations are listed in
Table
I
. While these exclusive decay rates have a large
theoretical uncertainty dominated by the imprecise knowl-
edge of the form factors, some of this uncertainty cancels
in the ratio of
B
!

ð
!
Þ

to
B
!
K


branching frac-
tions. This ratio provides a constraint on the ratio of the
CKM matrix elements
j
V
td
=V
ts
j
, which can also be ob-
tained from the ratio of
B
d
and
B
s
mixing frequencies [
4
].
Physics beyond the SM could affect differently
B
!

ð
!
Þ

and
B
d
=B
s
mixing, and hence create inconsisten-
cies between the results obtained from the two methods.
The ratio of
B
!

ð
!
Þ

to
B
!
K


branching frac-
tions is related to
j
V
td
=V
ts
j
[
5
] via
B
½
B
!

ð
!
Þ


B
ð
B
!
K


Þ
¼
S








V
td
V
ts








2

1

m
2

ð
!
Þ
=m
2
B
1

m
2
K

=m
2
B

3

2

ð
!
Þ
1
þ

R

ð
!
Þ

:
(1)
The coefficient
S
is 1 for

þ
and
1
2
for

0
or
!
,
m
is the
particle mass,


ð
!
Þ
is the ratio of the form factors for the
decays
B
!

ð
!
Þ

and
B
!
K


, and

R

ð
!
Þ
accounts
for differences in decay dynamics, including weak annihi-
lation contributions. The precision of the
j
V
td
=V
ts
j
deter-
mination can be improved by using an average branching
fraction for
B
!

ð
!
Þ

decays. Within the SM, the isospin
asymmetry between
B
þ
!

þ

and
B
0
!

0

is domi-
nated by weak annihilation contributions, and is expected
to be small; on the other hand, the asymmetry between
B
0
!

0

and
B
0
!
!
can be sizable, due to the differ-
ence in the form factors [
1
,
3
].
We report an updated study of the decays
B
þ
!

þ

,
B
0
!

0

, and
B
0
!
!
based on
465

10
6
B

B
events,
corresponding to an integrated luminosity of
423 fb

1
,a
data sample 25% larger than that used in our previous
publication [
6
]. In addition, we reduce backgrounds con-
siderably by using a multivariate algorithm based on
bootstrap-aggregated (bagged) decision trees (BDTs) [
7
]
and additional discriminating variables to separate signal
from background.
II. THE
BABAR
DETECTOR AND DATA SET
The data sample is collected with the
BABAR
detector at
the PEP-II asymmetric-energy
e
þ
e

storage ring at a
center-of-mass (CM) energy near
ffiffiffi
s
p
¼
10
:
58 GeV
, corre-
sponding to the

ð
4
S
Þ
resonance (on resonance). Charged
particle trajectories and energy loss (
dE=dx
) are measured
with a five-layer silicon vertex tracker (SVT) and a 40-
layer drift chamber (DCH) in a 1.5 T magnetic field.
Photons and electrons are detected in a CsI(Tl) crystal
electromagnetic calorimeter (EMC) with photon energy
resolution

E
=E
¼
0
:
023
ð
E=
GeV
Þ

1
=
4

0
:
019
. A ring-
imaging Cherenkov detector based on the detection of
internally reflected Cherenkov light (DIRC) provides in-
formation for charged particle identification. The
K
-

TABLE I. Recent predictions of the branching fractions.
Mode
Branching fraction (

10

6
)
Reference [
1
] Reference [
2
] Reference [
3
]
B
þ
!

þ

1
:
41

0
:
27
1
:
58
þ
0
:
53

0
:
46
1
:
16

0
:
26
B
0
!

0

0
:
69

0
:
12
0
:
76
þ
0
:
26

0
:
23
0
:
55

0
:
13
B
0
!
!
0
:
55

0
:
09
0
:
44

0
:
10
1
Charge conjugate modes are implied throughout.
B. AUBERT
et al.
PHYSICAL REVIEW D
78,
112001 (2008)
112001-4
separation in the DIRC is above
4

at laboratory momenta
up to
3 GeV
=c
. In order to identify muons, the magnetic
flux return is instrumented with resistive plate chambers
and limited streamer tubes. A detailed description of the
detector can be found elsewhere [
8
].
We use a
GEANT4
-based [
9
] Monte Carlo (MC) simula-
tion to model the
BABAR
detector response, taking into
account the varying accelerator and detector conditions.
Dedicated signal and background MC samples are used to
optimize selection criteria, to obtain signal efficiencies,
and to validate the analysis. Data control samples, includ-
ing
41 fb

1
of data collected about 40 MeV below the
B

B
production threshold (off resonance), are used to study
backgrounds coming from continuum
e
þ
e

!
q

q
, with
q
¼
u
,
d
,
s
,
c
.
III. EVENT RECONSTRUCTION AND
BACKGROUND SUPPRESSION
The decays
B
!

ð
!
Þ

are reconstructed by combining
a high-energy photon with a vector meson reconstructed in
the decay modes

þ
!

þ

0
,

0
!

þ


, and
!
!

þ



0
. The dominant source of background is coming
from continuum events that contain a high-energy photon
from

0
or

decays or from initial-state radiation (ISR).
There are also significant backgrounds from
B
meson
decays. The decays
B
!
K


,
K

!
K
can mimic the
signal when the kaon is misidentified as a pion. Decays of
B
=!
Þð

0
=
Þ
with a high-energy photon from the

0
or

decay also mimic the signal. In addition, there are
other
B
backgrounds originating mainly from
B
!
X
s

and
B
!
X
ð

0
=
Þ
decays.
The event selection and background suppression are
performed in two steps. We apply a set of loose selection
criteria to select well-measured photons and charged pions
and to reject background events that are kinematically very
different from the signal events. For events that pass the
loose event selection criteria, we then use the BDT tech-
nique to further reduce background.
A. Loose selection
We reduce background contributions from continuum
processes by considering only events for which the ratio
R
2
of second-to-zeroth Fox-Wolfram moments [
10
], calcu-
lated using the momenta of all charged and neutral parti-
cles in the event, is less than 0.7.
A photon candidate is identified as a cluster of energy
deposited in contiguous EMC crystals, and not associated
with any charged track. The high-energy photon must have
energy
1
:
5
<E

<
4
:
4 GeV
in the laboratory frame and
1
:
5
<E


<
3
:
5 GeV
in the CM frame, be well contained
within the EMC acceptance with polar angle

0
:
74
<
cos
<
0
:
93
, and be isolated by at least 25 cm at the
entrance of the EMC from any other photon candidate or
charged track. The distribution of the energy deposition is
required to be consistent with that of a photon shower.
Charged-pion candidates are selected from well-
reconstructed tracks that have at least 12 DCH hits used
in the track fit and a minimum momentum transverse to the
beam direction of
100 MeV
=c
. The tracks are required to
originate near the interaction point (IP): the distance of
closest approach to the IP must be less than 10 cm along
the beam direction and less than 2 cm in the plane perpen-
dicular to the beam direction. The


identification is
based on a likelihood
L
i
computed for particle hypothesis
i
ð¼
; K; p
Þ
using
dE=dx
measured in the SVT and DCH
and the information of Cherenkov photons detected by the
DIRC. The selection criteria are optimized to reject
charged kaons produced in
B
!
K


decays. The pion
candidates in
B
0
!
!
must have
L
K
=
ð
L
K
þ
L

Þ
<
0
:
5
and
L
p
=
ð
L
p
þ
L

Þ
<
0
:
98
and must not be consistent with
being an electron. The pion candidates in
B
!

must
have
L
K
=
ð
L
K
þ
L

Þ
<
0
:
2
and
L
p
=
ð
L
p
þ
L

Þ
<
0
:
5
and
must not be consistent with either an electron or a muon
candidate hypothesis; in addition, for all candidates with
laboratory momenta above
0
:
6 GeV
=c
, the number of
photons observed in the DIRC is required to be consistent
with the number that is expected for the pion hypothesis.
The performance of the pion identification requirements is
evaluated with the decay
D
!
D
0
ð!
K


þ
Þ

þ
, which
provides a large, clean sample of


and
K

. Using the
results shown in Fig.
1
, we find that the pion identification
requirement retains 85% of the pions from
B
!

decays
and rejects 99% of the kaons from
B
!
K


decays.
We form

0
candidates from pairs of photons with
energies greater than 50 MeV in the laboratory frame and
an invariant mass
m

in the range
115
150 MeV
=c
2
.We
combine the identified pions into vector-meson candidates
requiring
630
<m

þ


<
960MeV
=c
2
,
640
<m

þ

0
<
930 MeV
=c
2
, and
760
<m

þ



0
<
790 MeV
=c
2
for

0
,

þ
, and
!
, respectively. The charged-pion pairs are
required to originate from a common vertex.
The photon and
=!
candidates are combined to form
the
B
meson candidates. We define

E

E

B

ffiffiffi
s
p
=
2
,
where
E

B
¼
E

=!
þ
E


is the CM energy of the
B
meson
candidate. The

E
distributions of signal events are ex-
pected to peak near zero with a resolution of about 50 MeV
dominated by the photon energy resolution, and to have a
tail in the negative region due to photon energy loss in the
detector. We also define the beam-energy-substituted mass
m
ES

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s=
4

p
0
2
B
q
, where
p
0
B
is the CM momentum of
the
B
candidate modified by scaling the photon momentum
so that
E

=!
þ
E
0


ffiffiffi
s
p
=
2
¼
0
. This procedure improves
the
m
ES
resolution for the signal events in the

E
negative
tail. Signal events are expected to have an
m
ES
distribution
centered at the mass of the
B
meson
m
B
with a resolution of
3 MeV
=c
2
. We consider candidates with
m
ES
>
5
:
22 GeV
=c
2
and

0
:
3
<

E<
0
:
3 GeV
for further
analysis. This region includes sidebands that allow the
continuum background yields to be extracted from a fit to
the data.
MEASUREMENTS OF BRANCHING FRACTIONS FOR
...
PHYSICAL REVIEW D
78,
112001 (2008)
112001-5
The signal efficiencies for the loose selection described
above are 22% for
B
þ
!

þ

, 25% for
B
0
!

0

, and
17% for
B
0
!
!
.
B. Bagged decision tree
The bagged decision trees are trained separately for the
B
þ
!

þ

,
B
0
!

0

, and
B
0
!
!
channels with MC
simulated signal and background samples of about 60 000
and 90 000 events, respectively, and then validated with
independent samples of the same size. The background
sample consists of a
B

B
MC sample that is about 3 times
larger than the data and of a continuum MC sample that is
about 1.5 times larger. For the input classifiers, we choose
approximately 60 event quantities that characterize the
kinematics of the

0
candidates, the high-energy photon,
the vector meson, the
B
meson, and the rest of the event
(ROE), which are the particles that are not used to recon-
struct the
B
candidate. These quantities all have distribu-
tions that agree well between off-resonance data and
continuum MC events.
To reduce combinatorial background in the recon-
structed

0
candidates, we use in the BDT the invariant
mass
m

and
cos


, the cosine of the opening angle
between the photons in the laboratory frame.
We associate the high-energy photon candidate

with
each of the other photons

0
in the event and calculate the
likelihood ratio
LR
i
¼
P
ð
m

0
;E

0
j
i
Þ
P
ð
m

0
;E

0
j
signal
Þþ
P
ð
m

0
;E

0
j
i
Þ
;
(2)
where
i
¼

0
,

and
P
is the probability density function
(PDF) defined in terms of the energy of the second photon
in the laboratory frame
E

0
and the invariant mass of the
pair
m

0
. The PDFs are determined from simulated signal
and continuum background events. The likelihood ratios
LR

0
and
LR

are used in the BDT to reject high-energy
photons from

0
and

decays.
To reject background events from
B
!

ð

0
=
Þ
and
B
!
!
ð

0
=
Þ
, we also use the vector-meson helicity
angle

H
, which is defined as the angle between the
B
momentum vector and the

þ
track calculated in the

rest
frame for a

meson, or the angle between the
B
momen-
tum vector and the normal to the
!
decay plane for an
!
meson. This variable is useful because in signal events the
vector meson is transversely polarized, while in the back-
ground events it is longitudinally polarized.
Variables used in the BDT to reduce continuum back-
ground include
R
2
, the significance of the separation of the
two
B
vertices along the beam axis (
S

z
), the polar angle of
the
B
candidate momentum in the CM frame with respect
to the beam axis (


B
), and
R
0
2
, which is
R
2
in the frame
recoiling against the photon momentum. We compute the
moments
M
i

P
j
p

j
j
cos


j
j
i
=
P
j
p

j
with
i
¼
1
,2,3,
where
p

j
is the momentum of each particle
j
in the ROE
and


j
is the angle of the momentum with respect to an
axis. We use the
M
i
with respect to the photon direction
and the ROE thrust axis. We also include flavor-tagging
variables [
11
] to exploit the differences in lepton and kaon
production between background and
B
decays.
While we find that all the variables contribute to the
sensitivity of the analysis, the most effective ones are
S

z
,
cos


,
R
2
,
cos


B
,
M
3
with respect to the photon direction,
the missing mass of the ROE,
cos

H
, and
LR

0
;
. The
distribution of the BDT output for the decay
B
0
!

0

is
shown in Fig.
2
. We require the BDT output to be greater
than 0.94 (0.93) for
B
!

(
B
0
!
!
). These selection
requirements have been optimized for maximum statistical
signal significance with assumed signal branching frac-
tions of
1
:
0

10

6
and
0
:
5

10

6
for the charged and
neutral modes, respectively. The signal significance is
determined from a fit described in the next section. For
the signal events that pass the loose selection criteria, the
BDT requirements have an efficiency of 19% for
B
þ
!

þ

, 31% for
B
0
!

0

, and 34% for
B
0
!
!
.
Momentum (GeV/c)
01234
Efficiency
±
π
0.5
0.6
0.7
0.8
0.9
1
mis-ID Rate
±
K
0
0.02
0.04
0.06
0.08
0.1
Efficiency
±
π
mis-ID Rate
±
K
Momentum (GeV/c)
01234
Efficiency
±
π
0.5
0.6
0.7
0.8
0.9
1
mis-ID Rate
±
K
0
0.02
0.04
0.06
0.08
0.1
Efficiency
±
π
mis-ID Rate
±
K
FIG. 1. Performance of the charged-pion identification requirement applied to
B
!

decays, evaluated using the
D

control
sample. Filled circles are for


efficiency and use the left-hand scale. Open circles are for
K

misidentification and use the right-hand
scale. The plot on the left shows results for continuum MC events and the plot on the right shows results for data.
B. AUBERT
et al.
PHYSICAL REVIEW D
78,
112001 (2008)
112001-6
In events where multiple candidates are present, we
select the one with the reconstructed vector-meson mass
closest to the nominal mass. This criterion is chosen be-
cause the mass of the vector meson is found to be uncorre-
lated with the variables used in the fit. After applying all
the selection criteria described above to signal MC
samples, we find signal efficiencies of 4.2% for
B
þ
!

þ

, 7.7% for
B
0
!

0

, and 5.2% for
B
0
!
!
[taking
into account the branching fraction
B
ð
!
!

þ



0
Þ¼
0
:
892

0
:
007
[
12
]], while backgrounds are reduced by
O
ð
10

5
Þ
.
IV. MAXIMUM LIKELIHOOD FIT
We determine signal yields from an unbinned maximum
likelihood fit to
m
ES
and

E
. The likelihood function for a
signal mode
k
(
¼

þ

,

0

,
!
) with a sample of
N
k
events is defined as
L
k
¼
exp


X
N
hyp
i
¼
1
n
i

Y
N
k
j
¼
1

X
N
hyp
i
¼
1
n
i
P
i
ð
~
x
j
;
~
i
Þ

;
(3)
where
N
hyp
is the number of event hypotheses, and
n
i
is the
yield for each. For
B
0
!
!
, three event hypotheses are
considered: signal, continuum background, and combina-
torial
B
backgrounds. For
B
0
!

0

,a
B
0
!
K

0

back-
ground hypothesis is also included, while for
B
þ
!

þ

,a
combined
B
þ
!
K
=
þ

0
hypothesis is included.
Since the correlations between
m
ES
and

E
are found to
be negligible in MC event samples, we define the proba-
bility density function
P
i
ð
~
x
j
;
~
i
Þ
as the product of individ-
ual PDFs for each observable
x
j
¼
m
ES
,

E
, given the set
of parameters
~
i
.
The individual PDFs are determined from fits to dedi-
cated MC event samples. The signal
m
ES
PDFs are pa-
rametrized by a Crystal Ball (CB) function [
13
] and the

E
PDFs are parametrized as
f
ð

E
Þ/
exp


E

Þ
2
2

2
L;R
þ
L;R
ð

E

Þ
2

;
(4)
where
is the peak position of the distribution,

L
and

R
are the widths on the left and right of the peak, and
L
and
R
are measures of the tails on the left and right of the
peak, respectively. The peak positions and widths of the
signal
m
ES
and

E
PDFs are corrected for the observed
difference between data and MC samples of
B
!
K


decays. The PDFs for the remaining
B
0
!
K

0

and com-
bined
B
þ
!
K
=B
þ
!

þ

0
backgrounds are deter-
mined from dedicated MC samples that are 100 times
larger than the data. These PDFs are described by a CB
function for
m
ES
with a peak position the same as that of
the signal PDF—but with a much larger width—and a CB
function for

E
with a peak position near

80 MeV
. The
negative

E
peak position is due either to a kaon mis-
identified as a pion in
B
!
K


or to a single missing
photon in
B
þ
!

þ

0
. The
m
ES
and

E
PDFs for all other
B
backgrounds are determined from the
B

B
MC sample.
The
m
ES
spectra peak slightly in the signal region, and
therefore are parametrized by a CB function, while the

E
spectra are parametrized by an exponential function. The
continuum
m
ES
and

E
PDFs are parametrized by an
ARGUS threshold function [
14
] and a first order polyno-
mial, respectively.
The fit to the data determines the signal yield
n
sig
, the
continuum yield, and the shape parameters of the contin-
uum PDFs. The shape parameters of the signal and
B
background PDFs are fixed in the fit. The relative yield
between the peaking and the other
B
backgrounds is fixed
to the value obtained from known branching fractions [
12
]
and selection efficiencies determined from MC event
samples. The overall yields of the
B
backgrounds are
also fixed. All fixed parameters are later varied to evaluate
systematic errors in
n
sig
.
We validate the fitting procedure using ensembles of
signal and background events, with signal contributions
of zero, 1, and 2 times the rate expected from previous
measurements of the

þ

,

0

, and
!
branching frac-
tions. Two types of ensembles are produced: one with both
signal and background events generated using the PDFs
described above, and the other with signal events randomly
sampled from the
GEANT4
MC events and background
events generated using the corresponding PDFs. No bias
is found in the fit to these event samples.
Figure
3
shows the data points and the projections of the
fit results for

E
and
m
ES
separately for each decay mode.
0.0
0.2
0.4
0.6
0.8
1.0
1e−04
5e−04
1e−03
5e−03
1e−02
5e−02
1e−01
5e−01
fraction of events
FIG. 2 (color online). Distributions of the BDT output for
B
0
!

0

in signal (dashed line) and background (dotted line)
MC samples. The distributions are normalized to the same area.
MEASUREMENTS OF BRANCHING FRACTIONS FOR
...
PHYSICAL REVIEW D
78,
112001 (2008)
112001-7
The signal yields are reported in Table
II
. The significance
is computed as
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 ln
L
p
, where
ln
L
is the log-
likelihood difference between the best fit and the null-
signal hypothesis. To take into account the systematic error
in
n
sig
, the likelihood function is convolved with a
Gaussian distribution that has a width equal to the system-
atic error.
V. SYSTEMATIC UNCERTAINTIES
Table
III
gives the contributions to the systematic un-
certainties. The systematic error affecting the signal effi-
ciency includes uncertainties on tracking, particle
identification,

and

0
reconstruction, and BDT selection.
The modeling of signal and background in the fit contrib-
utes to the uncertainties on the signal yields.
TABLE II. The signal yield
n
sig
, significance

in standard
deviations including the systematic error in
n
sig
, efficiency
, and
branching fraction
B
for each mode. The first error is statistical
and the second is systematic. The branching fractions for
B
!
ð
=!
Þ

and
B
!

are obtained with the assumption of
isospin and
SU
ð
3
Þ
F
symmetries; see Sec. VI.
Mode
n
sig

ð
%
Þ
B
ð
10

6
Þ
B
þ
!

þ

23
:
3
þ
8
:
1

7
:
3

3
:
13
:
2

4.2
1
:
20
þ
0
:
42

0
:
37

0
:
20
B
0
!

0

34
:
9
þ
8
:
6

7
:
9

1
:
25
:
4

7.7
0
:
97
þ
0
:
24

0
:
22

0
:
06
B
0
!
!
12
:
4
þ
6
:
6

5
:
7

2
:
02
:
2

5.2
0
:
50
þ
0
:
27

0
:
23

0
:
09
B
=!
Þ

6
:
5

1
:
63
þ
0
:
30

0
:
28

0
:
16
B
!

6
:
0

1
:
73
þ
0
:
34

0
:
32

0
:
17
)
2
(GeV/c
ES
m
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
5.3
)
2
Events / ( 0.004 GeV/c
0
5
10
15
20
25
)
2
(GeV/c
ES
m
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
5.3
)
2
Events / ( 0.004 GeV/c
0
5
10
15
20
25
E (GeV)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Events / ( 0.03 GeV )
0
2
4
6
8
10
12
14
16
18
E (GeV)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Events / ( 0.03 GeV )
0
2
4
6
8
10
12
14
16
18
)
2
(GeV/c
ES
m
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
5.3
)
2
Events / ( 0.004 GeV/c
0
5
10
15
20
25
30
)
2
(GeV/c
ES
m
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
5.3
)
2
Events / ( 0.004 GeV/c
0
5
10
15
20
25
30
E (GeV)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Events / ( 0.03 GeV )
0
2
4
6
8
10
12
14
16
18
E (GeV)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Events / ( 0.03 GeV )
0
2
4
6
8
10
12
14
16
18
)
2
(GeV/c
ES
m
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
5.3
)
2
Events / ( 0.004 GeV/c
0
2
4
6
8
10
12
14
16
18
)
2
(GeV/c
ES
m
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
5.3
)
2
Events / ( 0.004 GeV/c
0
2
4
6
8
10
12
14
16
18
E (GeV)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Events / ( 0.03 GeV )
0
2
4
6
8
10
E (GeV)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Events / ( 0.03 GeV )
0
2
4
6
8
10
FIG. 3 (color online).

E
and
m
ES
projections of the fits for the decay modes
B
þ
!

þ

(top panels),
B
0
!

0

(middle panels),
and
B
0
!
!
(bottom panels). For illustrative purposes only, these plots are made by requiring

0
:
2
<

E<
0
:
1 GeV
for the
m
ES
projections and
m
ES
>
5
:
27 GeV
=c
2
for the

E
projections. The points are data, the solid line is the fit result, the dashed line is the
sum of
B
backgrounds, and the dash-dotted and dotted lines are the contributions from continuum background and signal, respectively.
TABLE III. Fractional systematic errors (in %) of the mea-
sured branching fractions.
Source of error

þ

0
!
ð
=!
Þ

Tracking efficiency
0.4
0.4 0.4 0.4
0.4
Particle identification 1.0
2.0 1.0 1.4
1.2
Photon selection
2.8
2.8 2.8 2.8
2.8

0
reconstruction
3.0

3.0 1.7
2.0
BDT efficiency
9.3
4.2 5.1 7.0
7.5
Signal model
7.1
2.1 16.3 3.0
3.0
Background model
10.9
2.8 2.7 4.3
3.6
B

B
counting
1.1
1.1 1.1 1.1
1.1
B
ð
!
!

þ



0
Þ
0.8

0.1
Sum in quadrature
16.7
6.6 17.9 9.5
9.5
B. AUBERT
et al.
PHYSICAL REVIEW D
78,
112001 (2008)
112001-8
The errors in BDT selections are determined from a
control sample of the decay
B
0
!
K

0
ð!
K
þ


Þ

for
the

0
mode and a sample of
B
þ
!
K
ð!
K
þ

0
Þ

for
the

þ
and
!
modes. These
B
!
K


decays are kine-
matically similar to
B
=!
Þ

decays. The events are
required to pass all applicable loose selection criteria,
except the pion identification requirements. We also re-
quire the invariant mass
0
:
80
<m
K
þ


<
1
:
0 GeV
=c
2
and
0
:
82
<m
K
þ

0
<
0
:
96 GeV
=c
2
. The BDT output classifiers
are computed from the decision trees trained for the cor-
responding signal modes. The differences in the BDT
selection efficiencies between the
B
!
K


data and MC
samples are used to correct the signal efficiencies. The
efficiency correction factor is
0
:
88

0
:
09
for
B
þ
!

þ

,
0
:
91

0
:
04
for
B
0
!

0

, and
0
:
90

0
:
05
for
B
0
!
!
. The uncertainty of the correction is taken as
the systematic error. The large BDT systematic error for
the decay
B
þ
!

þ

is due to the limited size of the
B
þ
!
K
ð!
K
þ

0
Þ

sample. As a means of validating
the BDT technique, we apply the same analysis technique
to the
B
!
K


data control samples and measure the
branching fractions for
B
!
K


. The results are consis-
tent with the world averages [
12
].
The error in the pion identification requirements is esti-
mated using the
D

control sample as shown in Fig.
1
.
Based on the difference of a momentum-weighted effi-
ciency between the continuum MC sample and data, a
1% systematic error per charged pion is assigned to the
B
!

decays. The MC sample is in better agreement
with data for the looser pion identification criteria applied
to
B
0
!
!
, and a 0.5% error per charged pion is assigned.
The uncertainties from tracking,

0
reconstruction, and
photon selection are also determined from suitable inde-
pendent data control samples.
To estimate the uncertainty related to the modeling of
the signal and background, we vary the parameters of the
PDFs that are fixed in the fit within their errors. We vary the
relative and absolute normalizations of
B
background
components that are fixed in the fit based on a kaon mis-
identification study using the
D

control sample as shown
in Fig.
1
. We find that the difference in the momentum-
weighted kaon misidentification rates between the data and
MC samples is 23%, and we conservatively vary the
B
!
K


background yield by 30%. The effect of the uncer-
tainty of
B
ð
B
þ
!

þ

0
Þ
[
12
] is also considered for the
decay
B
þ
!

þ

. For all the variations, the corresponding
changes in the extracted signal yield are taken as system-
atic uncertainties, which are then combined, taking into
account correlations. The error on background modeling
for
B
þ
!

þ

is dominated by uncertainties in
B
back-
ground PDFs.
VI. RESULTS
To calculate the branching fractions from the measured
signal yields, we assume
B
ð

ð
4
S
Þ!
B
0

B
0
Þ¼
B
ð

ð
4
S
Þ!
B
þ
B

Þ¼
0
:
5
. The results are listed in
Table
II
.For
B
0
!
!
, we also compute the 90% C.L.
upper limit
B
ð
B
0
!
!
Þ
<
0
:
9

10

6
using a Bayesian
technique, assuming a prior that is flat in the branching
fraction and taking into account the systematic uncertainty.
We test the hypothesis of isospin symmetry by measur-
ing the quantity


¼

ð
B
þ
!

þ

Þ
2
ð
B
0
!

0

Þ

1
¼
0
:
43
þ
0
:
25

0
:
22

0
:
10
:
Most theoretical calculations [
1
3
,
15
] predict small


.
For example, the estimate in Ref. [
3
]is

0
:
05

0
:
03
for

¼
60
and

0
:
10

0
:
02
for

¼
70
, where

is the
phase of
V

ub
. Our result is consistent with these predictions
within the large experimental errors. However, it is worth
noting that a recent calculation [
16
] indicated that non-
perturbative charming penguin contributions can accom-
modate large


. We also measure the
SU
ð
3
Þ
F
-violating
quantity

!
¼

ð
B
0
!
!
Þ

ð
B
0
!

0

Þ

1
¼
0
:
49
þ
0
:
30

0
:
27

0
:
10
;
which is consistent with the theoretical calculations.
We extract average branching fractions using a simulta-
neous fit to all the relevant decay modes with the con-
straints on the widths of the decay modes:

B
þ
!

þ

¼
2
B
0
!

0

¼
2
B
0
!
!
. The average branching
fractions are defined as
B
ð
B
!

Þ
1
2

B
ð
B
þ
!

þ

Þ
þ
2
B
þ
B
0
B
ð
B
0
!

0

Þ

(5)
and
B
½
B
=!
Þ


1
2

B
ð
B
þ
!

þ

Þþ
B
þ
B
0
½
B
ð
B
0
!

0

Þ
þ
B
ð
B
0
!
!
Þ

;
(6)
where
B
þ
=
B
0
is the measured ratio between the charged
and neutral
B
meson lifetimes, for which the current world
average is
1
:
071

0
:
009
[
12
]. Our measurements of the
individual branching fractions are consistent with this hy-
pothesis, with a
2
of 2.3 for 2 degrees of freedom. We find
B
ð
B
!

Þ¼ð
1
:
73
þ
0
:
34

0
:
32

0
:
17
Þ
10

6
;
B
½
B
=!
Þ

¼ð
1
:
63
þ
0
:
30

0
:
28

0
:
16
Þ
10

6
:
Using the world average value of
B
ð
B
þ
!
K

Þ¼
ð
4
:
03

0
:
26
Þ
10

5
,
B
ð
B
0
!
K

0

Þ¼ð
4
:
01

0
:
2
Þ
10

5
[
12
], and the isospin averaged branching fraction
B
ð
B
!
K


Þ¼ð
4
:
16

0
:
17
Þ
10

5
, we calculate
MEASUREMENTS OF BRANCHING FRACTIONS FOR
...
PHYSICAL REVIEW D
78,
112001 (2008)
112001-9
R

þ
¼
B
ð
B
þ
!

þ

Þ
B
ð
B
þ
!
K

Þ
¼
0
:
030
þ
0
:
012

0
:
011
;
R

0
¼
B
ð
B
0
!

0

Þ
B
ð
B
0
!
K

0

Þ
¼
0
:
024

0
:
006
;
R
!
¼
B
ð
B
0
!
!
Þ
B
ð
B
0
!
K

0

Þ
¼
0
:
012
þ
0
:
007

0
:
006
;
R

¼
B
ð
B
!

Þ
B
ð
B
!
K


Þ
¼
0
:
042

0
:
009
;
R
=!
¼
B
½
B
=!
Þ


B
ð
B
!
K


Þ
¼
0
:
039

0
:
008
:
These ratios of branching fractions can be used to calculate
j
V
td
=V
ts
j
[
3
,
5
,
17
]. Following Eq. (
1
) and using
1
=

¼
1
:
17

0
:
09
,
1
=
!
¼
1
:
30

0
:
10
[
3
],

R

þ
¼
0
:
057
þ
0
:
057

0
:
055
,

R

0
¼
0
:
006
þ
0
:
046

0
:
043
, and

R
!
¼

0
:
002
þ
0
:
046

0
:
043
[
1
] , we obtain
j
V
td
=V
ts
j

þ
¼
0
:
198
þ
0
:
039

0
:
035

0
:
016
;
j
V
td
=V
ts
j

0
¼
0
:
254
þ
0
:
033

0
:
031

0
:
021
;
j
V
td
=V
ts
j
!
¼
0
:
202
þ
0
:
058

0
:
050

0
:
016
;
where the first error is experimental and the second is
theoretical. Using the average branching fractions and
following Ref. [
1
], we obtain
j
V
td
=V
ts
j

¼
0
:
235
þ
0
:
026

0
:
025

0
:
020
;
j
V
td
=V
ts
j
=!
¼
0
:
233
þ
0
:
025
þ
0
:
022

0
:
024

0
:
021
:
Similar values are found following Ref. [
3
]. These results
are consistent with the value of this ratio,
0
:
208

0
:
002
ð
exp
Þ
þ
0
:
008

0
:
006
ð
theory
Þ
[
12
], obtained from the studies
of
B
d
and
B
s
mixing by the CDF and D0 Collaborations.
VII. SUMMARY
We report the updated measurements of the branching
fractions for the radiative decays
B
þ
!

þ

,
B
0
!

0

,
and
B
0
!
!
,
B
ð
B
þ
!

þ

Þ¼ð
1
:
20
þ
0
:
42

0
:
37

0
:
20
Þ
10

6
;
B
ð
B
0
!

0

Þ¼ð
0
:
97
þ
0
:
24

0
:
22

0
:
06
Þ
10

6
;
B
ð
B
0
!
!
Þ
<
0
:
9

10

6
ð
90% C
:
L
:
Þ
:
We test the hypothesis of isospin symmetry by measuring
the quantity


¼
0
:
43
þ
0
:
25

0
:
22

0
:
10
. We also measure
the averaged branching fractions
B
ð
B
!

Þ¼
ð
1
:
73
þ
0
:
34

0
:
32

0
:
17
Þ
10

6
and
B
½
B
=!
Þ

ð
1
:
63
þ
0
:
30

0
:
28

0
:
16
Þ
10

6
. These results are in good
agreement with, and supersede, the previous published
BABAR
measurement [
6
], which uses a subsample of the
data used for this analysis. These results are also consistent
with the measurements from Belle [
18
]. These branching
fraction measurements are used to extract
j
V
td
=V
ts
j
in a
way that is complementary to the approach using
B
mixing
[
4
].
ACKNOWLEDGMENTS
We are grateful for the extraordinary contributions of
our PEP-II2 colleagues in achieving the excellent luminos-
ity and machine conditions that have made this work
possible. The success of this project also relies critically
on the expertise and dedication of the computing organ-
izations that support
BABAR
. The collaborating institutions
wish to thank SLAC for its support and the kind hospitality
extended to them. This work is supported by the U.S.
Department of Energy and National Science Foundation,
the Natural Sciences and Engineering Research Council
(Canada), the Commissariat a
`
l’Energie Atomique and
Institut National de Physique Nucle
́
aire et de Physique
des Particules (France), the Bundesministerium fu
̈
r
Bildung und Forschung and Deutsche Forschungs-
gemeinschaft (Germany), the Istituto Nazionale di Fisica
Nucleare (Italy), the Foundation for Fundamental Research
on Matter (The Netherlands), the Research Council of
Norway, the Ministry of Education and Science of the
Russian Federation, Ministerio de Educacio
́
n y Ciencia
(Spain), and the Science and Technology Facilities
Council (United Kingdom). Individuals have received sup-
port from the Marie-Curie IEF program (European Union)
and the A. P. Sloan Foundation.
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