of 7
Improved Measurement of
B
þ
!

þ

0
and Determination of the Quark-Mixing Phase Angle

B. Aubert,
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
M. Battaglia,
5
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
I. L. Osipenkov,
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. J. Asgeirsson,
8
B. G. Fulsom,
8
C. Hearty,
8
T. S. Mattison,
8
J. A. McKenna,
8
M. Barrett,
9
A. Khan,
9
A. Randle-Conde,
9
V. E. Blinov,
10
A. D. Bukin,
10
A. R. Buzykaev,
10
V. P. Druzhinin,
10
V. B. Golubev,
10
A. P. Onuchin,
10
S. I. Serednyakov,
10
Yu. I. Skovpen,
10
E. P. Solodov,
10
K. Yu. Todyshev,
10
M. Bondioli,
11
S. Curry,
11
I. Eschrich,
11
D. Kirkby,
11
A. J. Lankford,
11
P. Lund,
11
M. Mandelkern,
11
E. C. Martin,
11
D. P. Stoker,
11
S. Abachi,
12
C. Buchanan,
12
H. Atmacan,
13
J. W. Gary,
13
F. Liu,
13
O. Long,
13
G. M. Vitug,
13
Z. Yasin,
13
L. Zhang,
13
V. Sharma,
14
C. Campagnari,
15
T. M. Hong,
15
D. Kovalskyi,
15
M. A. Mazur,
15
J. D. Richman,
15
T. W. Beck,
16
A. M. Eisner,
16
C. A. Heusch,
16
J. Kroseberg,
16
W. S. Lockman,
16
A. J. Martinez,
16
T. Schalk,
16
B. A. Schumm,
16
A. Seiden,
16
L. O. Winstrom,
16
C. H. Cheng,
17
D. A. Doll,
17
B. Echenard,
17
F. Fang,
17
D. G. Hitlin,
17
I. Narsky,
17
T. Piatenko,
17
F. C. Porter,
17
R. Andreassen,
18
G. Mancinelli,
18
B. T. Meadows,
18
K. Mishra,
18
M. D. Sokoloff,
18
P. C. Bloom,
19
W. T. Ford,
19
A. Gaz,
19
J. F. Hirschauer,
19
M. Nagel,
19
U. Nauenberg,
19
J. G. Smith,
19
S. R. Wagner,
19
R. Ayad,
20,
*
A. Soffer,
20,
W. H. Toki,
20
R. J. Wilson,
20
E. Feltresi,
21
A. Hauke,
21
H. Jasper,
21
M. Karbach,
21
J. Merkel,
21
A. Petzold,
21
B. Spaan,
21
K. Wacker,
21
M. J. Kobel,
22
R. Nogowski,
22
K. R. Schubert,
22
R. Schwierz,
22
A. Volk,
22
D. Bernard,
23
G. R. Bonneaud,
23
E. Latour,
23
M. Verderi,
23
P. J. Clark,
24
S. Playfer,
24
J. E. Watson,
24
M. Andreotti,
25a,25b
D. Bettoni,
25a
C. Bozzi,
25a
R. Calabrese,
25a,25b
A. Cecchi,
25a,25b
G. Cibinetto,
25a,25b
P. Franchini,
25a,25b
E. Luppi,
25a,25b
M. Negrini,
25a,25b
A. Petrella,
25a,25b
L. Piemontese,
25a
V. Santoro,
25a,25b
R. Baldini-Ferroli,
26
A. Calcaterra,
26
R. de Sangro,
26
G. Finocchiaro,
26
S. Pacetti,
26
P. Patteri,
26
I. M. Peruzzi,
26,
M. Piccolo,
26
M. Rama,
26
A. Zallo,
26
R. Contri,
27a,27b
E. Guido,
27a,27b
M. Lo Vetere,
27a,27b
M. R. Monge,
27a,27b
S. Passaggio,
27a
C. Patrignani,
27a,27b
E. Robutti,
27a
S. Tosi,
27a,27b
K. S. Chaisanguanthum,
28
M. Morii,
28
A. Adametz,
29
J. Marks,
29
S. Schenk,
29
U. Uwer,
29
F. U. Bernlochner,
30
V. Klose,
30
H. M. Lacker,
30
D. J. Bard,
31
P. D. Dauncey,
31
M. Tibbetts,
31
P. K. Behera,
32
X. Chai,
32
M. J. Charles,
32
U. Mallik,
32
J. Cochran,
33
H. B. Crawley,
33
L. Dong,
33
W. T. Meyer,
33
S. Prell,
33
E. I. Rosenberg,
33
A. E. Rubin,
33
Y. Y. Gao,
34
A. V. Gritsan,
34
Z. J. Guo,
34
N. Arnaud,
35
J. Be
́
quilleux,
35
A. D’Orazio,
35
M. Davier,
35
J. Firmino da Costa,
35
G. Grosdidier,
35
F. Le Diberder,
35
V. Lepeltier,
35
A. M. Lutz,
35
S. Pruvot,
35
P. Roudeau,
35
M. H. Schune,
35
J. Serrano,
35
V. Sordini,
35,
x
A. Stocchi,
35
G. Wormser,
35
D. J. Lange,
36
D. M. Wright,
36
I. Bingham,
37
J. P. Burke,
37
C. A. Chavez,
37
J. R. Fry,
37
E. Gabathuler,
37
R. Gamet,
37
D. E. Hutchcroft,
37
D. J. Payne,
37
C. Touramanis,
37
A. J. Bevan,
38
C. K. Clarke,
38
F. Di Lodovico,
38
R. Sacco,
38
M. Sigamani,
38
G. Cowan,
39
S. Paramesvaran,
39
A. C. Wren,
39
D. N. Brown,
40
C. L. Davis,
40
A. G. Denig,
41
M. Fritsch,
41
W. Gradl,
41
A. Hafner,
41
K. E. Alwyn,
42
D. Bailey,
42
R. J. Barlow,
42
G. Jackson,
42
G. D. Lafferty,
42
T. J. West,
42
J. I. Yi,
42
J. Anderson,
43
C. Chen,
43
A. Jawahery,
43
D. A. Roberts,
43
G. Simi,
43
J. M. Tuggle,
43
C. Dallapiccola,
44
E. Salvati,
44
S. Saremi,
44
R. Cowan,
45
D. Dujmic,
45
P. H. Fisher,
45
S. W. Henderson,
45
G. Sciolla,
45
M. Spitznagel,
45
R. K. Yamamoto,
45
M. Zhao,
45
P. M. Patel,
46
S. H. Robertson,
46
M. Schram,
46
A. Lazzaro,
47a,47b
V. Lombardo,
47a
F. Palombo,
47a,47b
S. Stracka,
47a,47b
J. M. Bauer,
48
L. Cremaldi,
48
R. Godang,
48,
k
R. Kroeger,
48
D. J. Summers,
48
H. W. Zhao,
48
M. Simard,
49
P. Taras,
49
H. Nicholson,
50
G. De Nardo,
51a,51b
L. Lista,
51a
D. Monorchio,
51a,51b
G. Onorato,
51a,51b
C. Sciacca,
51a,51b
G. Raven,
52
H. L. Snoek,
52
C. P. Jessop,
53
K. J. Knoepfel,
53
J. M. LoSecco,
53
W. F. Wang,
53
L. A. Corwin,
54
K. Honscheid,
54
H. Kagan,
54
R. Kass,
54
J. P. Morris,
54
A. M. Rahimi,
54
J. J. Regensburger,
54
S. J. Sekula,
54
Q. K. Wong,
54
N. L. Blount,
55
J. Brau,
55
R. Frey,
55
O. Igonkina,
55
J. A. Kolb,
55
M. Lu,
55
R. Rahmat,
55
N. B. Sinev,
55
D. Strom,
55
J. Strube,
55
E. Torrence,
55
G. Castelli,
56a,56b
N. Gagliardi,
56a,56b
M. Margoni,
56a,56b
M. Morandin,
56a
M. Posocco,
56a
M. Rotondo,
56a
F. Simonetto,
56a,56b
R. Stroili,
56a,56b
C. Voci,
56a,56b
P. del Amo Sanchez,
57
E. Ben-Haim,
57
H. Briand,
57
J. Chauveau,
57
O. Hamon,
57
Ph. Leruste,
57
J. Ocariz,
57
A. Perez,
57
J. Prendki,
57
S. Sitt,
57
L. Gladney,
58
M. Biasini,
59a,59b
E. Manoni,
59a,59b
C. Angelini,
60a,60b
G. Batignani,
60a,60b
S. Bettarini,
60a,60b
G. Calderini,
60a,60b,
{
M. Carpinelli,
60a,60b,
**
A. Cervelli,
60a,60b
F. Forti,
60a,60b
M. A. Giorgi,
60a,60b
A. Lusiani,
60a,60c
G. Marchiori,
60a,60b
M. Morganti,
60a,60b
N. Neri,
60a,60b
E. Paoloni,
60a,60b
G. Rizzo,
60a,60b
J. J. Walsh,
60a
D. Lopes Pegna,
61
C. Lu,
61
J. Olsen,
61
A. J. S. Smith,
61
A. V. Telnov,
61
F. Anulli,
62a
E. Baracchini,
62a,62b
G. Cavoto,
62a
R. Faccini,
62a,62b
F. Ferrarotto,
62a
F. Ferroni,
62a,62b
M. Gaspero,
62a,62b
P. D. Jackson,
62a
L. Li Gioi,
62a
M. A. Mazzoni,
62a
S. Morganti,
62a
G. Piredda,
62a
F. Renga,
62a,62b
C. Voena,
62a
M. Ebert,
63
T. Hartmann,
63
H. Schro
̈
der,
63
R. Waldi,
63
T. Adye,
64
B. Franek,
64
E. O. Olaiya,
64
F. F. Wilson,
64
S. Emery,
65
L. Esteve,
65
G. Hamel de Monchenault,
65
W. Kozanecki,
65
G. Vasseur,
65
Ch. Ye
`
che,
65
M. Zito,
65
X. R. Chen,
66
H. Liu,
66
W. Park,
66
M. V. Purohit,
66
R. M. White,
66
PRL
102,
141802 (2009)
PHYSICAL REVIEW LETTERS
week ending
10 APRIL 2009
0031-9007
=
09
=
102(14)
=
141802(7)
141802-1
Ó
2009 The American Physical Society
J. R. Wilson,
66
M. T. Allen,
67
D. Aston,
67
R. Bartoldus,
67
J. F. Benitez,
67
R. Cenci,
67
J. P. Coleman,
67
M. R. Convery,
67
J. C. Dingfelder,
67
J. Dorfan,
67
G. P. Dubois-Felsmann,
67
W. Dunwoodie,
67
R. C. Field,
67
A. M. Gabareen,
67
M. T. Graham,
67
P. Grenier,
67
C. Hast,
67
W. R. Innes,
67
J. Kaminski,
67
M. H. Kelsey,
67
H. Kim,
67
P. Kim,
67
M. L. Kocian,
67
D. W. G. S. Leith,
67
S. Li,
67
B. Lindquist,
67
S. Luitz,
67
V. Luth,
67
H. L. Lynch,
67
D. B. MacFarlane,
67
H. Marsiske,
67
R. Messner,
67
D. R. Muller,
67
H. Neal,
67
S. Nelson,
67
C. P. O’Grady,
67
I. Ofte,
67
M. Perl,
67
B. N. Ratcliff,
67
A. Roodman,
67
A. A. Salnikov,
67
R. H. Schindler,
67
J. Schwiening,
67
A. Snyder,
67
D. Su,
67
M. K. Sullivan,
67
K. Suzuki,
67
S. K. Swain,
67
J. M. Thompson,
67
J. Va’vra,
67
A. P. Wagner,
67
M. Weaver,
67
C. A. West,
67
W. J. Wisniewski,
67
M. Wittgen,
67
D. H. Wright,
67
H. W. Wulsin,
67
A. K. Yarritu,
67
K. Yi,
67
C. C. Young,
67
V. Ziegler,
67
P. R. Burchat,
68
A. J. Edwards,
68
T. S. Miyashita,
68
S. Ahmed,
69
M. S. Alam,
69
J. A. Ernst,
69
B. Pan,
69
M. A. Saeed,
69
S. B. Zain,
69
S. M. Spanier,
70
B. J. Wogsland,
70
R. Eckmann,
71
J. L. Ritchie,
71
A. M. Ruland,
71
C. J. Schilling,
71
R. F. Schwitters,
71
B. W. Drummond,
72
J. M. Izen,
72
X. C. Lou,
72
F. Bianchi,
73a,73b
D. Gamba,
73a,73b
M. Pelliccioni,
73a,73b
M. Bomben,
74a,74b
L. Bosisio,
74a,74b
C. Cartaro,
74a,74b
G. Della Ricca,
74a,74b
L. Lanceri,
74a,74b
L. Vitale,
74a,74b
V. Azzolini,
75
N. Lopez-March,
75
F. Martinez-Vidal,
75
D. A. Milanes,
75
A. Oyanguren,
75
J. Albert,
76
Sw. Banerjee,
76
B. Bhuyan,
76
H. H. F. Choi,
76
K. Hamano,
76
G. J. King,
76
R. Kowalewski,
76
M. J. Lewczuk,
76
I. M. Nugent,
76
J. M. Roney,
76
R. J. Sobie,
76
T. J. Gershon,
77
P. F. Harrison,
77
J. Ilic,
77
T. E. Latham,
77
G. B. Mohanty,
77
E. M. T. Puccio,
77
H. R. Band,
78
X. Chen,
78
S. Dasu,
78
K. T. Flood,
78
Y. Pan,
78
R. Prepost,
78
C. O. Vuosalo,
78
and S. L. Wu
78
(
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
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 British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
9
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
10
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
11
University of California at Irvine, Irvine, California 92697, USA
12
University of California at Los Angeles, Los Angeles, California 90024, USA
13
University of California at Riverside, Riverside, California 92521, USA
14
University of California at San Diego, La Jolla, California 92093, USA
15
University of California at Santa Barbara, Santa Barbara, California 93106, USA
16
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
17
California Institute of Technology, Pasadena, California 91125, USA
18
University of Cincinnati, Cincinnati, Ohio 45221, USA
19
University of Colorado, Boulder, Colorado 80309, USA
20
Colorado State University, Fort Collins, Colorado 80523, USA
21
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
22
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
23
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
24
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
25a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
25b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
26
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
27a
INFN Sezione di Genova, I-16146 Genova, Italy
27b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
28
Harvard University, Cambridge, Massachusetts 02138, USA
29
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
30
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstraße 15, D-12489 Berlin, Germany
31
Imperial College London, London, SW7 2AZ, United Kingdom
32
University of Iowa, Iowa City, Iowa 52242, USA
33
Iowa State University, Ames, Iowa 50011-3160, USA
34
Johns Hopkins University, Baltimore, Maryland 21218, USA
PRL
102,
141802 (2009)
PHYSICAL REVIEW LETTERS
week ending
10 APRIL 2009
141802-2
35
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
36
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
37
University of Liverpool, Liverpool L69 7ZE, United Kingdom
38
Queen Mary, University of London, London, E1 4NS, United Kingdom
39
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
40
University of Louisville, Louisville, Kentucky 40292, USA
41
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
42
University of Manchester, Manchester M13 9PL, United Kingdom
43
University of Maryland, College Park, Maryland 20742, USA
44
University of Massachusetts, Amherst, Massachusetts 01003, USA
45
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
46
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
47a
INFN Sezione di Milano, I-20133 Milano, Italy
47b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
48
University of Mississippi, University, Mississippi 38677, USA
49
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
50
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
51a
INFN Sezione di Napoli, I-80126 Napoli, Italy
51b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
52
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
53
University of Notre Dame, Notre Dame, Indiana 46556, USA
54
Ohio State University, Columbus, Ohio 43210, USA
55
University of Oregon, Eugene, Oregon 97403, USA
56a
INFN Sezione di Padova, I-35131 Padova, Italy
56b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
57
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
58
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
59a
INFN Sezione di Perugia, I-06100 Perugia, Italy
59b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
60a
INFN Sezione di Pisa, I-56127 Pisa, Italy
60b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
60c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
61
Princeton University, Princeton, New Jersey 08544, USA
62a
INFN Sezione di Roma, I-00185 Roma, Italy
62b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
63
Universita
̈
t Rostock, D-18051 Rostock, Germany
64
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
65
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
66
University of South Carolina, Columbia, South Carolina 29208, USA
67
SLAC National Accelerator Laboratory, Stanford, California 94309, USA
68
Stanford University, Stanford, California 94305-4060, USA
69
State University of New York, Albany, New York 12222, USA
70
University of Tennessee, Knoxville, Tennessee 37996, USA
71
University of Texas at Austin, Austin, Texas 78712, USA
72
University of Texas at Dallas, Richardson, Texas 75083, USA
73a
INFN Sezione di Torino, I-10125 Torino, Italy
73b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
74a
INFN Sezione di Trieste, I-34127 Trieste, Italy
74b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
75
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
76
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
77
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
78
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 22 January 2009; published 10 April 2009)
We present improved measurements of the branching fraction
B
, the longitudinal polarization fraction
f
L
, and the direct
CP
asymmetry
A
CP
in the
B
meson decay channel
B
þ
!

þ

0
. The data sample was
collected with the
BABAR
detector at SLAC. The results are
B
ð
B
þ
!

þ

0
Þ¼ð
23
:
7

1
:
4

1
:
4
Þ
10

6
,
f
L
¼
0
:
950

0
:
015

0
:
006
, and
A
CP
¼
0
:
054

0
:
055

0
:
010
, where the uncertainties are
PRL
102,
141802 (2009)
PHYSICAL REVIEW LETTERS
week ending
10 APRIL 2009
141802-3
statistical and systematic, respectively. Based on these results, we perform an isospin analysis and
determine the Cabibbo-Kobayashi-Maskawa phase angle

¼
arg
ð
V
td
V

tb
=V
ud
V

ub
Þ
to be
ð
92
:
4
þ
6
:
0

6
:
5
Þ

.
DOI:
10.1103/PhysRevLett.102.141802
PACS numbers: 13.25.Hw, 12.15.Hh, 11.30.Er
In the standard model (SM), the weak interaction cou-
plings of quarks are described by elements
V
ij
of the
Cabibbo-Kobayashi-Maskawa (CKM) matrix [
1
], where
i
¼
u; c; t
and
j
¼
d; s; b
are quark indices. The CKM
elements are complex, introducing violation of charge-
parity (
CP
) symmetry. Unitarity of the CKM matrix yields
a relationship between the
V
ij
that can be represented as a
triangle in the complex plane. The SM mechanism for
CP
violations can be tested through measurement of
the sides and angles of this unitarity triangle (UT) [
2
].
An approximate result

eff
for the UT angle

¼
arg
ð
V
td
V

tb
=V
ud
V

ub
Þ
can be obtained from
B
meson de-
cays to
CP
eigenstates dominated by tree-level
b
!
u

ud
amplitudes, such as
B
!

decays (see, e.g., Refs. [
2
,
3
]).
The correction


¼



eff
, which accounts for loop
amplitudes, can be extracted from an analysis of the
branching fractions and
CP
asymmetries of the full set of
isospin-related
b
!
u

ud
channels [
4
]. One of the most
favorable methods to determine

is through an isospin
analysis of the
B
!

system [
2
,
3
].
Here we present updated results for the
B
þ
!

þ

0
channel, with

þ
!

þ

0
and

0
!

þ


, leading to
an improved determination of

. Previous studies are
presented in Refs. [
5
,
6
]. We measure the branching frac-
tion
B
, the longitudinal polarization fraction
f
L
, and the
direct
CP
asymmetry
A
CP

B



B
þ
Þ
=
ð

B

þ

B
þ
Þ
,
with

B

the
B

decay width. Significant deviation of
A
CP
from the SM prediction of zero could indicate new
physics. We also search for the as-yet-unobserved decay
B
þ
!

þ
f
0
ð
980
Þ
, with
f
0
!

þ


. The use of charge
conjugate reactions is implied throughout.
The analysis is based on
ð
465

5
Þ
10
6
B

B
events
(
424 fb

1
) collected on the

ð
4
S
Þ
resonance [center-of-
mass (c.m.) energy
ffiffiffi
s
p
¼
10
:
58 GeV
] with the
BABAR
detector [
7
] at the PEP-II asymmetric energy
e
þ
e

collider
at SLAC. Compared to our previous study [
5
], the analysis
incorporates higher signal efficiency and background re-
jection, twice as much data, and improved procedures to
reconstruct charged particles and to account for correla-
tions in the backgrounds. Simulated event samples based
on Monte Carlo (MC) event generation are used to deter-
mine signal and background characteristics, optimize se-
lection criteria, and evaluate efficiencies.
B
þ
!

þ

0
decays are described by a superposition of
two transversely (helicity

1
) and one longitudinally (he-
licity 0) polarized amplitudes. Our acceptance is indepen-
dent of the angle between the two

decay planes in the
B
rest frame. We integrate over this angle to obtain an
expression for
ð
1
=

Þ
d
2

=
ð
d
cos


0
d
cos


þ
Þ
:
9
16
½
4
f
L
cos
2


0
cos
2


þ
þð
1

f
L
Þ
sin
2


0
sin
2


þ

;
(1)
with
f
L


L
=

, where

is the total decay width,

L
is
the partial width to the longitudinally polarized mode, and
the

0
(

þ
) helicity angle


0
(


þ
) is the angle between
the daughter

þ
in the

0
(

þ
) rest frame and the direction
of the boost from the
B
þ
rest frame.
A
B
meson candidate is kinematically characterized
by the beam-energy-substituted mass
m
ES

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s=
4
p

B
c
Þ
2
q
=c
2
and energy difference

E

E

B

ffiffiffi
s
p
=
2
, where
E

B
and
p

B
are the c.m. energy and momen-
tum of the
B
candidate, respectively. Signal events peak at
the nominal
B
mass for
m
ES
and at zero for

E
, with
resolutions of
3 MeV
=c
2
and 30 MeV, respectively.
The

0
mesons are reconstructed through

0
!

.
The

is required to be consistent with a single electro-
magnetic shower. The

and

0
laboratory energies must
be larger than 30 MeVand 0.2 GeV, respectively. The mass
of a

0
candidate (resolution
6 MeV
=c
2
) is required to lie
within
½
0
:
115
;
0
:
150

GeV
=c
2
and is subsequently con-
strained to its nominal value [
2
].
The

0
(


) candidate is combined with a

þ
to form a

þ
(

0
). The


are identified with measurements of
specific energy loss in the tracking chambers and radiation
angles and photon multiplicity in a ring-imaging
Cherenkov detector [
7
]. The

þ
(

0
) candidate mass
m

þ

0
(
m

þ


) must lie within
½
0
:
52
;
1
:
06

GeV
=c
2
.

þ
candidates with misreconstructed

0
mesons tend to clus-
ter near
cos


þ

1
, so we require
cos


þ
0
:
8
. The
B
þ
candidates must satisfy
5
:
26
<m
ES
<
5
:
29 GeV
=c
2
and
j

E
j
<
0
:
15 GeV
. In cases of multiple
B
þ
candidates
(about 10% of events), the candidate with the largest
B
þ
vertex [
8
] fit probability is retained.
Background from

B
!

D
ðÞ
X
decays, due to

D
0
!
K
þ


ð

0
Þ
with kaon misidentification and

D
0
!

þ



0
, is suppressed by requiring the
K
þ


ð

0
Þ
or

þ



0
invariant mass to lie outside

4

of the nominal
D
0
mass [
2
], with


9 MeV
=c
2
the
D
0
mass resolution.
The dominant background, from random combinations
of particles in continuum events (
e
þ
e

!
q

q
, with
q
¼
u; d; s; c
), is suppressed by requiring
j
cos

T
j
<
0
:
8
[
9
],
with

T
the angle between the thrust axis of the
B
candi-
date’s decay products and the thrust axis of the remaining
particles in the event (ROE), evaluated in the c.m. frame,
and by employing a neural network algorithm based on
11 variables calculated in the c.m.:
j
cos

T
j
; the cosines of
the angles with respect to the beam axis of the
B
momen-
tum and
B
thrust axis (we use the absolute value for the
latter variable); the momentum-weighted sums
L
0
and
L
2
[
9
], determined with charged and neutral particles sepa-
rately; the sum of transverse momenta of the ROE particles
with respect to the beam axis; the ratio of the second to
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141802-4
zeroth Fox-Wolfram moments [
10
]; the proper time differ-
ence between the
B
and

B
candidates divided by its uncer-
tainty; and
B
-tagging information from ROE particles [
8
].
The neural network output
NN
peaks near 0 and 1 for
continuum and signal events, respectively. We require
NN >
0
:
2
, which rejects about 5% of the signal and 60%
of the continuum events.
We examine the remaining
B
backgrounds and identify
nine channels with peaking structures in
m
ES
or

E
that
can potentially mimic signal events:
B
þ
!

0
a
þ
1
ð
1260
Þ
,

þ
a
0
1
,

0

þ

0
,

þ

þ


,



þ

þ
,

0



þ

þ
,
!
þ
,
f
0

0

þ
, and

0

þ
, with
a
1
!

,
!
!

þ


,
f
0
!

þ


, and

0
!

0
. All other
B
backgrounds are com-
bined into a ‘‘nonpeaking’’
B

B
background component.
An extended unbinned maximum likelihood (ML) fit is
applied to the selected events. The fit has 14 components:
signal

þ

0
events, taken to be
B
þ
!

þ

0
events that
are correctly reconstructed; self-cross-feed (SxF) events,
defined as misreconstructed
B
þ
!

þ

0
events (29% of
the
B
þ
!

þ

0
sample); signal
B
þ
!

þ
f
0
events, in-
cluding both correctly and incorrectly reconstructed events
to increase efficiency; nonpeaking
B

B
background; con-
tinuum background; and the nine peaking
B

B
background
channels listed above. The

þ

0
signal and SxF compo-
nents are further divided into categories with either longi-
tudinal or transverse polarization.
The likelihood function is
L
¼ð
1
=N
!
Þ
exp
ð
P
j
n
j
Þ
Q
N
i
¼
1
½
P
j
n
j
P
j
ð
x
i
Þ
, with
N
the number of events,
n
j
the
yield of component
j
,
P
j
ð
x
i
Þ
the probability density func-
tion (PDF) for event
i
to be associated with component
j
,
and
x
i
the seven experimental observables specified in
Eq. (
2
) below. The signal

þ

0
,

þ
f
0
, continuum, and
nonpeaking
B

B
background yields are allowed to vary in
the fit. The

þ

0
SxF yield is fixed to its expected value
based on the MC prediction for the SxF rate and the
B
þ
!

þ

0
branching fraction determined here (we iterate the fit
to find this result). The relative contributions of the

þ

0
longitudinal and transverse polarization components are
determined by allowing
f
L
to vary, with
f
L
common to
the signal and SxF events. The three

yields are varied
under the requirement that they have the same branching
fraction. The

0
a
þ
1
,

þ
a
0
1
,
!
þ
, and

0

þ
yields are fixed
according to their known branching fractions [
2
]. The

0



þ

þ
and
f
0

0

þ
yields are fixed assuming their
branching fractions to be
10

5
, consistent with or larger
than the limits [
11
,
12
] for
B
0
!

þ



þ

þ
and
f
0

þ


decays.
About 85% of continuum events, and 90% of nonpeak-
ing
B

B
background events, contain at least one misrecon-
structed

. For these events, we find correlations of or-
der 10% between the
NN
,
m

, and
cos


variables,
and—to account for these correlations—construct three-
dimensional (3D) PDFs of the five variables based on
conditional PDFs
P
ð
x
j
y
Þ
of variable
x
given the value
of variable
y
:
P
3D
¼½
P
ð
m

þ


j
cos


0
Þ
P
ð
cos


0
j
NN
Þ½
P
ð
m

þ

0
j
cos


þ
Þ
P
ð
cos


þ
j
NN
Þ
P
ð
NN
Þ
.
For example,
P
ð
m

þ

0
j
cos


þ
Þ
is constructed by exam-
ining the
m

þ

0
distribution in nine bins of
cos


þ
, fitting a
second-order polynomial to each bin, and parameterizing
how the coefficients of the polynomial vary between bins.
The fraction of events with a correctly reconstructed

þ
and

0
is fixed to the MC prediction for the nonpeaking
B

B
background and allowed to vary for the continuum back-
ground. For all other components, the overall PDFs are
defined as the product of seven 1D PDFs, one for each
observable. The PDFs of the

þ

0
signal and SxF helicity
angles take the form of Eq. (
1
), with detector resolution
and acceptance incorporated, by summing the longitudinal
(
L
) and transverse (
T
) components with a relative fraction
f
L

L
=
½
f
L

L
þð
1

f
L
Þ

T

, with

L
and

T
the respective
reconstruction efficiencies, leading to an effective 2D PDF
in
cos


þ
and
j
cos


0
j
:
P
j
ð
x
i
Þ¼
P
j
ð
m
i
ES
Þ
P
j
ð

E
i
Þ
P
j
ð
NN
i
Þ
P
j
ð
m
i

þ

0
Þ

P
j
ð
m
i

þ


Þ
P
j
ð
cos

i

þ
;
j
cos

i

0
:
(2)
The continuum background
m
ES
and

E
PDFs are de-
rived from a
44 fb

1
data sample collected 40 MeV below
the

ð
4
S
Þ
mass. All other PDFs are derived from simula-
tion. For
m
ES
, the PDFs of signal and continuum are
parameterized by a crystal ball [
13
] and an ARGUS func-
tion [
14
], respectively. A relativistic Breit-Wigner function
with a
p
-wave Blatt-Weisskopf form factor is used for the
m

distributions in

þ

0
signal events. For the back-
ground,
m

is modeled by a combination of a polynomial
and the signal function. Slowly varying distributions (

E
for nonpeaking backgrounds and
cos


) are modeled by
polynomials. High statistics histograms are used for the
NN
distributions. The remaining variables are parameter-
ized with sums of Gaussians; e.g., the
m

distribution in
f
0
decays is modeled with a sum of three Gaussians. A
large data control sample of
B
þ
!

D
0

þ
(

D
0
!
K
0
S

0
,
K
0
S
!

þ


) events is used to verify that the resolution
and peak position of the signal
m
ES
and

E
PDFs are
accurately simulated.
The fit is applied to the sample of 82 224 selected events.
We allow 11 parameters to vary in the fit: five parameters
of continuum background PDFs,
f
L
, and five yields as
mentioned above. We find
1122

63
ð
stat
Þ

þ

0
signal
events,
50

30
ð
stat
Þ

þ
f
0
events, and
f
L
¼
0
:
945

0
:
015
ð
stat
Þ
. The fit provides a simultaneous determination
of the number of
B
þ
!

þ

0
and
B

!



0
signal
events. These fitted yields are used to determine
A
CP
¼

0
:
054

0
:
055
ð
stat
Þ
. Figure
1
shows projections of the
m
ES
and
m

þ


distributions. To enhance the visibility of
the signal, events are required to satisfy
L
i
ð
S
Þ
=
½
L
i
ð
S
Þþ
L
i
ð
B
Þ
>
0
:
98
, where
L
i
ð
S
Þ
is the sum of the likelihood
functions for

þ

0
and

þ
f
0
signal events excluding the
PDF of the plotted variable
i
and
L
i
ð
B
Þ
is the correspond-
ing sum of all other components.
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A possible bias, from unmodeled correlations, is eval-
uated by applying the ML fit to an ensemble of simulated
experiments, where the numbers of signal and background
events in each component correspond to those observed or
fixed in the fit to data. The continuum events are drawn
from the PDFs, while events for all other components are
drawn from MC samples. The biases are determined to be
71

3
and

31

1
events for the signal

þ

0
and

þ
f
0
yields and

0
:
005

0
:
001
for
f
L
, where the uncertainties
are statistical. The signal yields and
f
L
are then corrected
by subtracting these biases.
The branching fractions are given by the bias-corrected
yields divided by the reconstruction efficiencies and initial
number of
B

B
pairs
N
B

B
. From the simulations, the

þ

0
signal efficiencies including the

0
daughter branching
fraction [
2
] are

L
¼½
9
:
12

0
:
02
ð
stat
Þ
%
and

T
¼
½
17
:
45

0
:
03
ð
stat
Þ
%
. The corresponding result for

þ
f
0
is
½
14
:
20

0
:
08
ð
stat
Þ
%
. We assume that the

ð
4
S
Þ
decays
to each of
B
þ
B

and
B
0

B
0
50% of the time.
The principal systematic uncertainties associated with
the ML fit are listed in Table
I
. Uncertainties from the fit
biases are defined by the quadratic sum of half the biases
themselves (for
f
L
, the full bias) and the statistical uncer-
tainties of the biases. The uncertainties related to the signal
and nonpeaking
B

B
background PDFs are assessed by
varying the PDF parameters within their uncertainties.
For the signal, the uncertainties of the PDF parameters
are determined from the
B
þ
!

D
0

þ
data control sample.
Variations of the

0
a
þ
1
,

þ
a
0
1
,
!
þ
, and

0

þ
branching
fractions within their measured uncertainties, and of the
assumed

þ



þ

0
and
f
0

þ

0
branching fractions by

100%
, define the systematic uncertainty associated with
the peaking
B

B
background. The uncertainty associated
with the SxF fraction is assessed by varying the fixed SxF
yield by

10%
. The other principal sources of systematic
uncertainty are the

0
reconstruction efficiency (3.0%), the
track reconstruction efficiency (1.1%), the


identifica-
tion efficiency (1.5%), the uncertainty of
N
B

B
(1.1%), and
the selection requirements on
j
cos

T
j
(1.0%). The indi-
vidual terms are added in quadrature to define the total
systematic uncertainties.
We find
B
ð
B
þ
!

þ

0
Þ¼ð
23
:
7

1
:
4

1
:
4
Þ
10

6
,
f
L
¼
0
:
950

0
:
015

0
:
006
,
A
CP
¼
0
:
054

0
:
055

0
:
010
, and
B
ð
B
þ
!

þ
f
0
Þ
B
ð
f
0
!

þ


Þ¼ð
1
:
21

0
:
44

0
:
40
Þ
10

6
, where the first (second) uncertainty
is statistical (systematic). The
B
ð

þ

0
Þ
result is larger
than in Ref. [
5
], primarily because of the improved method
used here to account for correlations in the backgrounds.
The significance of the
B
ð

þ
f
0
Þ
result without (with)
systematics is 3.2 (2.2) standard deviations. We find

0
:
15
<
A
CP
<
0
:
04
and
B
ð
B
þ
!

þ
f
0
Þ
B
ð
f
0
!

þ


Þ
<
2
:
0

10

6
, where these latter results corre-
spond to the 90% confidence level (C.L.) including
systematics.
We perform an isospin analysis of
B
!

decays by
minimizing a
2
that includes the measured quantities
expressed as the lengths of the sides of the
B
and

B
isospin
triangles [
4
]. We use the
B
þ
!

þ

0
branching fraction
and
f
L
results presented here, with the branching fractions,
polarizations, and
CP
-violating parameters in
B
0
!

þ


[
15
] and
B
0
!

0

0
[
11
] decays. We assume the uncer-
tainties to be Gaussian-distributed and neglect potential
isospin
I
¼
1
and electroweak-loop amplitudes, which
are expected to be small [
3
].
The CKM phase angle

and its correction


are found
to be

¼ð
92
:
4
þ
6
:
0

6
:
5
Þ

and

1
:
8

<

<
6
:
7

, respec-
tively, at 68% C.L., significant improvements [
16
] com-
pared to

¼ð
82
:
6
þ
32
:
6

6
:
3
Þ

and
j


j
<
15
:
7

[
11
] obtained
with the same

þ


and

0

0
measurements, but the
previous
B
þ
!

þ

0
results [
5
], or

¼ð
91
:
7

14
:
9
Þ

from the Belle Collaboration [
12
]. The improvement is
primarily due to the increase in
B
ð

þ

0
Þ
compared to
our previous result.
B
ð

þ

0
Þ
determines the length of
the common base of the isospin triangles for the
B
and

B
decays. The increase in the base length flattens both tri-
angles, making the four possible solutions [
4
] nearly
degenerate.
In summary, we have improved the precision of the
measurements of the
B
þ
!

þ

0
decay branching and
longitudinal polarization fractions, leading to a significant
improvement in the determination of the CKM phase angle

based on the favored
B
!

isospin method. We set a
TABLE I. Principal systematic uncertainties associated with
the ML fit (in events for the

þ

0
and

þ
f
0
yields).

þ

0
yield

þ
f
0
yield
f
L
A
CP
Fit biases
35.5
15.3
0.005 0.001
Signal PDFs
19.4
3.0
0.001 0.002
Nonpeaking
B

B
PDFs
7.3
2.1
0.001 0.001
Peaking
B

B
yields
16.3
21.1
0.003 0.001
SxF fraction
7.9
0.1
0.001 0.001
2
m
ES
)
(GeV/c
2
2
5.26
5.27
5.28
5.29
)
Events / ( 0.001 GeV/c
0
20
40
Data
0
ρ
+
ρ
0
f
+
ρ
Bkgs
B
B
q
q
(a)
2
2
2
0.6
0.8
)
(GeV/c
-
-
ππ
+
m
1
)
Events / ( 0.02 GeV/c
0
20
40
(b)
FIG. 1. Projections of the fit (solid curve) onto the (a)
m
ES
and
(b)
m

þ


variables. A requirement on the likelihood ratio that
retains 38% of the signal, 0.1% of the continuum background,
and 1.3% of the
B

B
background has been applied. The peak in
the
B

B
background at
m

þ



0
:
78 GeV
=c
2
is from
B
þ
!

þ
!
events with
!
!

þ


.
PRL
102,
141802 (2009)
PHYSICAL REVIEW LETTERS
week ending
10 APRIL 2009
141802-6
90% C.L. upper limit of
2
:
0

10

6
on the branching
fraction of
B
þ
!

þ
f
0
ð
980
Þ
, with
f
0
!

þ


.
We are grateful for the excellent luminosity and machine
conditions provided by our PEP-II colleagues and for the
substantial dedicated effort from the computing organiza-
tions that support
BABAR
. The collaborating institutions
thank SLAC for its support and kind hospitality. This work
is supported by DOE and NSF (USA), NSERC (Canada),
CEA and CNRS-IN2P3 (France), BMBF and DFG
(Germany), INFN (Italy), FOM (The Netherlands), NFR
(Norway), MES (Russia), MEC (Spain), and STFC (United
Kingdom). Individuals have received support from the
Marie Curie EIF (European Union) and the A. P. Sloan
Foundation.
*
Present address: Temple University, Philadelphia, PA
19122, USA.
Present address: Tel Aviv University, Tel Aviv, 69978,
Israel.
Also at Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
x
Also at Universita
`
di Roma La Sapienza, I-00185 Roma,
Italy.
k
Present address: University of South Alabama, Mobile,
AL 36688, USA.
{
Also at 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.
**
Also at Universita
`
di Sassari, Sassari, Italy.
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PRL
102,
141802 (2009)
PHYSICAL REVIEW LETTERS
week ending
10 APRIL 2009
141802-7