of 9
Measurements of neutral
B
decay branching fractions to
K
0
S




final states and the charge
asymmetry of
B
0
!
K



B. Aubert,
1
R. Barate,
1
D. Boutigny,
1
F. Couderc,
1
Y. Karyotakis,
1
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
A. Zghiche,
1
E. Grauges,
2
A. Palano,
3
M. Pappagallo,
3
A. Pompili,
3
J. C. Chen,
4
N. D. Qi,
4
G. Rong,
4
P. Wang,
4
Y. S. Zhu,
4
G. Eigen,
5
I. Ofte,
5
B. Stugu,
5
G. S. Abrams,
6
M. Battaglia,
6
A. B. Breon,
6
D. N. Brown,
6
J. Button-Shafer,
6
R. N. Cahn,
6
E. Charles,
6
C. T. Day,
6
M. S. Gill,
6
A. V. Gritsan,
6
Y. Groysman,
6
R. G. Jacobsen,
6
R. W. Kadel,
6
J. Kadyk,
6
L. T. Kerth,
6
Yu. G. Kolomensky,
6
G. Kukartsev,
6
G. Lynch,
6
L. M. Mir,
6
P. J. Oddone,
6
T. J. Orimoto,
6
M. Pripstein,
6
N. A. Roe,
6
M. T. Ronan,
6
W. A. Wenzel,
6
M. Barrett,
7
K. E. Ford,
7
T. J. Harrison,
7
A. J. Hart,
7
C. M. Hawkes,
7
S. E. Morgan,
7
A. T. Watson,
7
M. Fritsch,
8
K. Goetzen,
8
T. Held,
8
H. Koch,
8
B. Lewandowski,
8
M. Pelizaeus,
8
K. Peters,
8
T. Schroeder,
8
M. Steinke,
8
J. T. Boyd,
9
J. P. Burke,
9
N. Chevalier,
9
W. N. Cottingham,
9
T. Cuhadar-Donszelmann,
10
B. G. Fulsom,
10
C. Hearty,
10
N. S. Knecht,
10
T. S. Mattison,
10
J. A. McKenna,
10
A. Khan,
11
P. Kyberd,
11
M. Saleem,
11
L. Teodorescu,
11
A. E. Blinov,
12
V. E. Blinov,
12
A. D. Bukin,
12
V. P. Druzhinin,
12
V. B. Golubev,
12
E. A. Kravchenko,
12
A. P. Onuchin,
12
S. I. Serednyakov,
12
Yu. I. Skovpen,
12
E. P. Solodov,
12
A. N. Yushkov,
12
D. Best,
13
M. Bondioli,
13
M. Bruinsma,
13
M. Chao,
13
S. Curry,
13
I. Eschrich,
13
D. Kirkby,
13
A. J. Lankford,
13
P. Lund,
13
M. Mandelkern,
13
R. K. Mommsen,
13
W. Roethel,
13
D. P. Stoker,
13
C. Buchanan,
14
B. L. Hartfiel,
14
A. J. R. Weinstein,
14
S. D. Foulkes,
15
J. W. Gary,
15
O. Long,
15
B. C. Shen,
15
K. Wang,
15
L. Zhang,
15
D. del Re,
16
H. K. Hadavand,
16
E. J. Hill,
16
D. B. MacFarlane,
16
H. P. Paar,
16
S. Rahatlou,
16
V. Sharma,
16
J. W. Berryhill,
17
C. Campagnari,
17
A. Cunha,
17
B. Dahmes,
17
T. M. Hong,
17
M. A. Mazur,
17
J. D. Richman,
17
W. Verkerke,
17
T. W. Beck,
18
A. M. Eisner,
18
C. J. Flacco,
18
C. A. Heusch,
18
J. Kroseberg,
18
W. S. Lockman,
18
G. Nesom,
18
T. Schalk,
18
B. A. Schumm,
18
A. Seiden,
18
P. Spradlin,
18
D. C. Williams,
18
M. G. Wilson,
18
J. Albert,
19
E. Chen,
19
G. P. Dubois-Felsmann,
19
A. Dvoretskii,
19
D. G. Hitlin,
19
I. Narsky,
19
T. Piatenko,
19
F. C. Porter,
19
A. Ryd,
19
A. Samuel,
19
R. Andreassen,
20
S. Jayatilleke,
20
G. Mancinelli,
20
B. T. Meadows,
20
M. D. Sokoloff,
20
F. Blanc,
21
P. Bloom,
21
S. Chen,
21
W. T. Ford,
21
J. F. Hirschauer,
21
A. Kreisel,
21
U. Nauenberg,
21
A. Olivas,
21
P. Rankin,
21
W. O. Ruddick,
21
J. G. Smith,
21
K. A. Ulmer,
21
S. R. Wagner,
21
J. Zhang,
21
A. Chen,
22
E. A. Eckhart,
22
A. Soffer,
22
W. H. Toki,
22
R. J. Wilson,
22
Q. Zeng,
22
D. Altenburg,
23
E. Feltresi,
23
A. Hauke,
23
B. Spaan,
23
T. Brandt,
24
J. Brose,
24
M. Dickopp,
24
V. Klose,
24
H. M. Lacker,
24
R. Nogowski,
24
S. Otto,
24
A. Petzold,
24
G. Schott,
24
J. Schubert,
24
K. R. Schubert,
24
R. Schwierz,
24
J. E. Sundermann,
24
D. Bernard,
25
G. R. Bonneaud,
25
P. Grenier,
25
S. Schrenk,
25
Ch. Thiebaux,
25
G. Vasileiadis,
25
M. Verderi,
25
D. J. Bard,
26
P. J. Clark,
26
W. Gradl,
26
F. Muheim,
26
S. Playfer,
26
Y. Xie,
26
M. Andreotti,
27
V. Azzolini,
27
D. Bettoni,
27
C. Bozzi,
27
R. Calabrese,
27
G. Cibinetto,
27
E. Luppi,
27
M. Negrini,
27
L. Piemontese,
27
F. Anulli,
28
R. Baldini-Ferroli,
28
A. Calcaterra,
28
R. de Sangro,
28
G. Finocchiaro,
28
P. Patteri,
28
I. M. Peruzzi,
28,
*
M. Piccolo,
28
A. Zallo,
28
A. Buzzo,
29
R. Capra,
29
R. Contri,
29
M. Lo Vetere,
29
M. Macri,
29
M. R. Monge,
29
S. Passaggio,
29
C. Patrignani,
29
E. Robutti,
29
A. Santroni,
29
S. Tosi,
29
G. Brandenburg,
30
K. S. Chaisanguanthum,
30
M. Morii,
30
E. Won,
30
J. Wu,
30
R. S. Dubitzky,
31
U. Langenegger,
31
J. Marks,
31
S. Schenk,
31
U. Uwer,
31
W. Bhimji,
32
D. A. Bowerman,
32
P. D. Dauncey,
32
U. Egede,
32
R. L. Flack,
32
J. R. Gaillard,
32
G. W. Morton,
32
J. A. Nash,
32
M. B. Nikolich,
32
G. P. Taylor,
32
W. P. Vazquez,
32
M. J. Charles,
33
W. F. Mader,
33
U. Mallik,
33
A. K. Mohapatra,
33
J. Cochran,
34
H. B. Crawley,
34
V. Eyges,
34
W. T. Meyer,
34
S. Prell,
34
E. I. Rosenberg,
34
A. E. Rubin,
34
J. Yi,
34
N. Arnaud,
35
M. Davier,
35
X. Giroux,
35
G. Grosdidier,
35
A. Ho
̈
cker,
35
F. Le Diberder,
35
V. Lepeltier,
35
A. M. Lutz,
35
A. Oyanguren,
35
T. C. Petersen,
35
M. Pierini,
35
S. Plaszczynski,
35
S. Rodier,
35
P. Roudeau,
35
M. H. Schune,
35
A. Stocchi,
35
G. Wormser,
35
C. H. Cheng,
36
D. J. Lange,
36
M. C. Simani,
36
D. M. Wright,
36
A. J. Bevan,
37
C. A. Chavez,
37
I. J. Forster,
37
J. R. Fry,
37
E. Gabathuler,
37
R. Gamet,
37
K. A. George,
37
D. E. Hutchcroft,
37
R. J. Parry,
37
D. J. Payne,
37
K. C. Schofield,
37
C. Touramanis,
37
C. M. Cormack,
38
F. Di Lodovico,
38
W. Menges,
38
R. Sacco,
38
C. L. Brown,
39
G. Cowan,
39
H. U. Flaecher,
39
M. G. Green,
39
D. A. Hopkins,
39
P. S. Jackson,
39
T. R. McMahon,
39
S. Ricciardi,
39
F. Salvatore,
39
D. Brown,
40
C. L. Davis,
40
J. Allison,
41
N. R. Barlow,
41
R. J. Barlow,
41
C. L. Edgar,
41
M. C. Hodgkinson,
41
M. P. Kelly,
41
G. D. Lafferty,
41
M. T. Naisbit,
41
J. C. Williams,
41
C. Chen,
42
W. D. Hulsbergen,
42
A. Jawahery,
42
D. Kovalskyi,
42
C. K. Lae,
42
D. A. Roberts,
42
G. Simi,
42
G. Blaylock,
43
C. Dallapiccola,
43
S. S. Hertzbach,
43
R. Kofler,
43
V. B. Koptchev,
43
X. Li,
43
T. B. Moore,
43
S. Saremi,
43
H. Staengle,
43
S. Willocq,
43
R. Cowan,
44
K. Koeneke,
44
G. Sciolla,
44
S. J. Sekula,
44
M. Spitznagel,
44
F. Taylor,
44
R. K. Yamamoto,
44
H. Kim,
45
P. M. Patel,
45
S. H. Robertson,
45
A. Lazzaro,
46
V. Lombardo,
46
F. Palombo,
46
J. M. Bauer,
47
L. Cremaldi,
47
V. Eschenburg,
47
R. Godang,
47
R. Kroeger,
47
J. Reidy,
47
D. A. Sanders,
47
D. J. Summers,
47
H. W. Zhao,
47
S. Brunet,
48
D. Co
ˆ
te
́
,
48
P. Taras,
48
B. Viaud,
48
H. Nicholson,
49
N. Cavallo,
50,†
G. De Nardo,
50
F. Fabozzi,
50,†
C. Gatto,
50
L. Lista,
50
D. Monorchio,
50
P. Paolucci,
50
D. Piccolo,
50
C. Sciacca,
50
M. Baak,
51
H. Bulten,
51
G. Raven,
51
H. L. Snoek,
51
L. Wilden,
51
C. P. Jessop,
52
J. M. LoSecco,
52
PHYSICAL REVIEW D
73,
031101(R) (2006)
RAPID COMMUNICATIONS
1550-7998
=
2006
=
73(3)
=
031101(9)$23.00
031101-1
©
2006 The American Physical Society
T. Allmendinger,
53
G. Benelli,
53
K. K. Gan,
53
K. Honscheid,
53
D. Hufnagel,
53
P. D. Jackson,
53
H. Kagan,
53
R. Kass,
53
T. Pulliam,
53
A. M. Rahimi,
53
R. Ter-Antonyan,
53
Q. K. Wong,
53
J. Brau,
54
R. Frey,
54
O. Igonkina,
54
M. Lu,
54
C. T. Potter,
54
N. B. Sinev,
54
D. Strom,
54
J. Strube,
54
E. Torrence,
54
F. Galeazzi,
55
M. Margoni,
55
M. Morandin,
55
M. Posocco,
55
M. Rotondo,
55
F. Simonetto,
55
R. Stroili,
55
C. Voci,
55
M. Benayoun,
56
H. Briand,
56
J. Chauveau,
56
P. David,
56
L. Del Buono,
56
Ch. de la Vaissie
`
re,
56
O. Hamon,
56
M. J. J. John,
56
Ph. Leruste,
56
J. Malcle
`
s,
56
J. Ocariz,
56
L. Roos,
56
G. Therin,
56
P. K. Behera,
57
L. Gladney,
57
Q. H. Guo,
57
J. Panetta,
57
M. Biasini,
58
R. Covarelli,
58
S. Pacetti,
58
M. Pioppi,
58
C. Angelini,
59
G. Batignani,
59
S. Bettarini,
59
F. Bucci,
59
G. Calderini,
59
M. Carpinelli,
59
R. Cenci,
59
F. Forti,
59
M. A. Giorgi,
59
A. Lusiani,
59
G. Marchiori,
59
M. Morganti,
59
N. Neri,
59
E. Paoloni,
59
M. Rama,
59
G. Rizzo,
59
J. Walsh,
59
M. Haire,
60
D. Judd,
60
D. E. Wagoner,
60
J. Biesiada,
61
N. Danielson,
61
P. Elmer,
61
Y. P. Lau,
61
C. Lu,
61
J. Olsen,
61
A. J. S. Smith,
61
A. V. Telnov,
61
F. Bellini,
62
G. Cavoto,
62
A. D’Orazio,
62
E. Di Marco,
62
R. Faccini,
62
F. Ferrarotto,
62
F. Ferroni,
62
M. Gaspero,
62
L. Li Gioi,
62
M. A. Mazzoni,
62
S. Morganti,
62
G. Piredda,
62
F. Polci,
62
F. Safai Tehrani,
62
C. Voena,
62
H. Schro
̈
der,
63
G. Wagner,
63
R. Waldi,
63
T. Adye,
64
N. De Groot,
64
B. Franek,
64
G. P. Gopal,
64
E. O. Olaiya,
64
F. F. Wilson,
64
R. Aleksan,
65
S. Emery,
65
A. Gaidot,
65
S. F. Ganzhur,
65
P.-F. Giraud,
65
G. Graziani,
65
G. Hamel de Monchenault,
65
W. Kozanecki,
65
M. Legendre,
65
G. W. London,
65
B. Mayer,
65
G. Vasseur,
65
Ch. Ye
`
che,
65
M. Zito,
65
M. V. Purohit,
66
A. W. Weidemann,
66
J. R. Wilson,
66
F. X. Yumiceva,
66
T. Abe,
67
M. T. Allen,
67
D. Aston,
67
N. van Bakel,
67
R. Bartoldus,
67
N. Berger,
67
A. M. Boyarski,
67
O. L. Buchmueller,
67
R. Claus,
67
J. P. Coleman,
67
M. R. Convery,
67
M. Cristinziani,
67
J. C. Dingfelder,
67
D. Dong,
67
J. Dorfan,
67
D. Dujmic,
67
W. Dunwoodie,
67
S. Fan,
67
R. C. Field,
67
T. Glanzman,
67
S. J. Gowdy,
67
T. Hadig,
67
V. Halyo,
67
C. Hast,
67
T. Hryn’ova,
67
W. R. Innes,
67
M. H. Kelsey,
67
P. Kim,
67
M. L. Kocian,
67
D. W. G. S. Leith,
67
J. Libby,
67
S. Luitz,
67
V. Luth,
67
H. L. Lynch,
67
H. Marsiske,
67
R. Messner,
67
D. R. Muller,
67
C. P. O’Grady,
67
V. E. Ozcan,
67
A. Perazzo,
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
J. Stelzer,
67
D. Su,
67
M. K. Sullivan,
67
K. Suzuki,
67
S. Swain,
67
J. M. Thompson,
67
J. Va’vra,
67
M. Weaver,
67
W. J. Wisniewski,
67
M. Wittgen,
67
D. H. Wright,
67
A. K. Yarritu,
67
K. Yi,
67
C. C. Young,
67
P. R. Burchat,
68
A. J. Edwards,
68
S. A. Majewski,
68
B. A. Petersen,
68
C. Roat,
68
M. Ahmed,
69
S. Ahmed,
69
M. S. Alam,
69
J. A. Ernst,
69
M. A. Saeed,
69
F. R. Wappler,
69
S. B. Zain,
69
W. Bugg,
70
M. Krishnamurthy,
70
S. M. Spanier,
70
R. Eckmann,
71
J. L. Ritchie,
71
A. Satpathy,
71
R. F. Schwitters,
71
J. M. Izen,
72
I. Kitayama,
72
X. C. Lou,
72
S. Ye,
72
F. Bianchi,
73
M. Bona,
73
F. Gallo,
73
D. Gamba,
73
M. Bomben,
74
L. Bosisio,
74
C. Cartaro,
74
F. Cossutti,
74
G. Della Ricca,
74
S. Dittongo,
74
S. Grancagnolo,
74
L. Lanceri,
74
L. Vitale,
74
F. Martinez-Vidal,
75
R. S. Panvini,
76,‡
Sw. Banerjee,
77
B. Bhuyan,
77
C. M. Brown,
77
D. Fortin,
77
K. Hamano,
77
R. Kowalewski,
77
J. M. Roney,
77
R. J. Sobie,
77
J. J. Back,
78
P. F. Harrison,
78
T. E. Latham,
78
G. B. Mohanty,
78
H. R. Band,
79
X. Chen,
79
B. Cheng,
79
S. Dasu,
79
M. Datta,
79
A. M. Eichenbaum,
79
K. T. Flood,
79
M. Graham,
79
J. J. Hollar,
79
J. R. Johnson,
79
P. E. Kutter,
79
H. Li,
79
R. Liu,
79
B. Mellado,
79
A. Mihalyi,
79
Y. Pan,
79
R. Prepost,
79
P. Tan,
79
J. H. von Wimmersperg-Toeller,
79
S. L. Wu,
79
Z. Yu,
79
and H. Neal
80
(
B
A
B
AR
Collaboration)
1
Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France
2
IFAE, Universitat Autonoma de Barcelona, E-08193 Bellaterra, Barcelona, Spain
3
Universita
`
di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy
4
Institute of High Energy Physics, Beijing 100039, China
5
Inst. of Physics, University of Bergen, N-5007 Bergen, Norway
6
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
7
University of Birmingham, Birmingham, B15 2TT, United Kingdom
8
Institut fu
̈
r Experimentalphysik, Ruhr Universita
̈
t Bochum, 1, D-44780 Bochum, Germany
9
University of Bristol, Bristol BS8 1TL, United Kingdom
10
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
11
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
12
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
13
University of California at Irvine, Irvine, California 92697, USA
14
University of California at Los Angeles, Los Angeles, California 90024, USA
15
University of California at Riverside, Riverside, California 92521, USA
16
University of California at San Diego, La Jolla, California 92093, USA
17
University of California at Santa Barbara, Santa Barbara, California 93106, USA
18
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
19
California Institute of Technology, Pasadena, California 91125, USA
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
031101 (2006)
RAPID COMMUNICATIONS
031101-2
20
University of Cincinnati, Cincinnati, Ohio 45221, USA
21
University of Colorado, Boulder, Colorado 80309, USA
22
Colorado State University, Fort Collins, Colorado 80523, USA
23
Institut fur Physik, Universita
̈
t Dortmund, D-44221 Dortmund, Germany
24
Institut fu
̈
r Kern- und Teilchenphysik, Technische Universita
̈
t Dresden, D-01062 Dresden, Germany
25
Ecole Polytechnique, LLR, F-91128 Palaiseau, France
26
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
27
Dipartimento di Fisica and INFN, Universita
`
di Ferrara, I-44100 Ferrara, Italy
28
Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
29
Dipartimento di Fisica and INFN, Universita
`
di Genova, I-16146 Genova, Italy
30
Harvard University, Cambridge, Massachusetts 02138, USA
31
Physikalisches Institut, Universita
̈
t Heidelberg, Philosophenweg 12, D-69120 Heidelberg, 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
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, F-91898 Orsay, France
36
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
37
University of Liverpool, Liverpool L69 72E, United Kingdom
38
Queen Mary, University of 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
University of Manchester, Manchester M13 9PL, United Kingdom
42
University of Maryland, College Park, Maryland 20742, USA
43
University of Massachusetts, Amherst, Massachusetts 01003, USA
44
Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
45
McGill University, Montre
́
al, Quebec, Canada H3A 2T8
46
Dipartimento di Fisica and INFN, Universita
`
di Milano, I-20133 Milano, Italy
47
University of Mississippi, University, Mississippi 38677, USA
48
Universite
́
de Montre
́
al, Laboratoire Rene
́
J. A. Le
́
vesque, Montre
́
al, Quebec, Canada H3C 3J7
49
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
50
Dipartimento di Scienze Fisiche and INFN, Universita
`
di Napoli Federico II, I-80126, Napoli, Italy
51
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
52
University of Notre Dame, Notre Dame, Indiana 46556, USA
53
Ohio State University, Columbus, Ohio 43210, USA
54
University of Oregon, Eugene, Oregon 97403, USA
55
Dipartimento di Fisica and INFN, Universita
`
di Padova, I-35131 Padova, Italy
56
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, Universite
́
s Paris VI et VII, F-75252 Paris, France
57
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
58
Dipartimento di Fisica and INFN, Universita
`
di Perugia, I-06100 Perugia, Italy
59
Dipartimento di Fisica, Scuola Normale Superiore and INFN, Universita
`
di Pisa, I-56127 Pisa, Italy
60
Prairie View A&M University, Prairie View, Texas 77446, USA
61
Princeton University, Princeton, New Jersey 08544, USA
62
Dipartimento di Fisica and INFN, 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
DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
66
University of South Carolina, Columbia, South Carolina 29208, USA
67
Stanford Linear Accelerator Center, 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
Dipartimento di Fisica Sperimentale and INFN, University of Texas at Dallas, Richardson, Texas 75083, USA
73
Universita
`
di Torino, I-10125 Torino, Italy
74
Dipartimento di Fisica and INFN, Universita
`
di Trieste, I-34127 Trieste, Italy
75
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
*
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy
Deceased
Also with Universita
`
della Basilicata, Potenza, Italy
MEASUREMENTS OF NEUTRAL
B
DECAY BRANCHING
...
PHYSICAL REVIEW D
73,
031101 (2006)
RAPID COMMUNICATIONS
031101-3
76
Vanderbilt University, Nashville, Tennessee 37235, USA
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
80
Yale University, New Haven, Connecticut 06511, USA
(Received 4 August 2005; published 15 February 2006)
We analyze the decay
B
0
!
K
0
S




using a sample of
232

10
6


4
S
!
B

B
decays collected with
the
BABAR
detector at the SLAC PEP-II asymmetric-energy
B
factory. A maximum likelihood fit finds the
following
branching
fractions:
B

B
0
!
K
0





43
:
0

2
:
3

2
:
3

10

6
;
B

B
0
!
f
0
!





K
0

5
:
5

0
:
7

0
:
5

0
:
3

10

6
and
B

B
0
!
K




11
:
0

1
:
5

0
:
5

0
:
5

10

6
. For these results, the first uncertainty is statistical, the second is systematic, and the third (if
present) is due to the effect of interference from other resonances. We also measure the
CP
-violating
charge asymmetry in the decay
B
0
!
K



,
A
K



0
:
11

0
:
14

0
:
05
.
DOI:
10.1103/PhysRevD.73.031101
PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Hh
Measurements of charmless three-body
B
decays, which
are dominated by their intermediate quasi-two-body de-
cays, are important in furthering our understanding of
quark couplings described by the Cabibbo-Kobayashi-
Maskawa matrix [1].
CP
violation can be probed through
the investigation of neutral
B
-meson decays to resonance
channels with the final state
K
0
S




, such as
f
0
K
0
S
[2],

0
K
0
S
[3] and
K



[4].
By measuring the charmless branching fraction of
B
0
!
K
0
S




, along with those of its dominant resonant subm-
odes, we can obtain information about the structure of the
decay Dalitz plot. Such measurements have previously
been performed by the CLEO [5], Belle [6] and
BABAR
[2 – 4] experiments.
QCD factorization models [7] have predicted branching
fractions and asymmetries for charmless
B
decays.
Predictions have also been made using flavor SU(3) sym-
metry [8]. For
B
0
!
K



, predictions [9] have been
made for the branching fractions and charge asymmetry,
A
K





B
0
!
K





B
0
!
K





B
0
!
K





B
0
!
K



;
(1)
which is a
CP
-violating quantity since the decay channel is
a flavor eigenstate.
CP
violation in charge asymmetry has
already been observed by
BABAR
and Belle in
B
0
!
K



[10].
In this paper the branching fractions of
B
0
!
K
0




,
B
0
!
K



and
B
0
!
f
0

980
!





K
0
are pre-
sented, averaged over charge-conjugate states, along with
a measurement of the charge asymmetry in
B
0
!
K



.
The selection criteria require events with a reconstructed
K
0
S
in the final state. Results are stated in terms of the
K
0
final state, taking into account the probabilities for
B

K
0
!
K
0
S

and
B

K
0
S
!





[11]. For the
B
0
!
K
0




branching fraction, the total charmless contribu-
tion to the Dalitz plot is measured (with charmed and
charmonium resonances removed), including contributions
from resonant charmless substructure.
The data used in this analysis were collected at the PEP-
II asymmetric-energy
e

e

storage ring with the
BABAR
detector [12]. The
BABAR
detector consists of a double-
sided five-layer silicon tracker, a 40-layer drift chamber, a
Cherenkov detector, an electromagnetic calorimeter and a
magnet with instrumented flux return. The data sample has
an integrated luminosity of
210 fb

1
collected at the


4S

resonance, which corresponds to

231
:
8

2
:
5

10
6
B

B
pairs. It is assumed that the


4S

decays equally to neutral
and charged
B
-meson pairs. In addition,
21
:
6fb

1
of data
collected at 40 MeV below the


4S

resonance were used
for background studies.
The reconstruction of candidate
B
mesons combines two
charged tracks and a
K
0
S
candidate, with the
K
0
S
being
reconstructed from two oppositely charged tracks consis-
tent with




. The
B
0
decay vertex is reconstructed
from the two charged tracks that were not daughters of
the
K
0
S
, with the requirements that the tracks originate from
the beam-spot, have at least 12 hits in the drift chamber and
have a transverse momentum greater than
100 MeV
=c
.
K
0
S
candidates are required to have a reconstructed mass within
15 MeV
=c
2
of the nominal
K
0
S
mass [11], at least a 5
standard deviation separation between the
B
0
decay vertex
and its own decay vertex, and a cosine of the angle between
the line joining the
B
0
and
K
0
S
decay vertices and the
K
0
S
momentum vector greater than 0.999. To identify pions we
use measurements of energy loss (
d
E=
d
x
) in the tracking
system, the number of photons detected by the Cherenkov
detector
and
the
corresponding
Cherenkov angle.
Candidate pions must fail the electron selection, which is
based on
d
E=
d
x
measurements, shower shape in the calo-
rimeter, and the ratio of energy in the calorimeter to
momentum in the drift chamber. Using simulated
Monte Carlo (MC) events, we determine an approximate
mean and width (

) of the mass distribution for the reso-
nances, and choose the resonance band to be

3

from the
mean. For the decay
B
0
!
K



we require
0
:
776
<
m
K
0
S

<
1
:
010 GeV
=c
2
and for
B
0
!
f
0
K
0
S
we require
0
:
879
<m




<
1
:
069 GeV
=c
2
.
The dominant source of background is continuum quark
production (
e

e

!
q

q
where
q

u;d;s;c
). An event-
shape variable, the cosine of the angle

T
between the
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
031101 (2006)
RAPID COMMUNICATIONS
031101-4
thrust axis of the selected
B
candidate and the thrust axis of
the rest of the event [12], is used to suppress this back-
ground. The distribution of
j
cos

T
j
is strongly peaked
towards unity for continuum background but is flat for
signal events. The requirement
j
cos

T
j
<
0
:
9
reduces the
relative amount of continuum background.
To separate signal events from the remaining back-
ground events, we use two kinematic variables and one
event-shape variable. The first kinematic variable

E
,
is the difference between the center-of-mass (CM) energy
of the
B
candidate and

s
p
=
2
, where

s
p
is the total CM
energy of the
e

e

beams. The second is the beam-
energy-substituted mass
m
ES



s=
2

p
i
p
B

2
=E
2
i

p
2
B
q
,
where
p
B
is the
B
momentum and (
E
i
;
p
i
) is the four-
momentum of the


4S

in the laboratory frame. We
require these variables to be in the ranges
j

E
j
<
0
:
1 GeV
and
5
:
22
<m
ES
<
5
:
29 GeV
=c
2
. We construct a
Fisher discriminant (
F
) [13] using a linear combination of
five event-shape variables: the cosine of the angle between
the
B
-candidate momentum and the beam axis, the cosine
of the angle between the
B
-candidate thrust axis and the
beam axis, the zeroth and second angular moments of the
energy flow about the thrust axis of the
B
[2], and the
output of the
B
-flavor tagging algorithm, which uses the
information from the other
B
[14]. This forms a more
efficient Fisher discriminant than used in our previous
measurement, Ref. [4].
Other
B
-meson decays can mimic a
K
0
S




final state.
MC events are used to identify the
B
decays that contribute
background events to the data sample, and we use the
available information on exclusive measurements [11,15]
to find how many events from this background to expect in
the data set. The largest
B
background is seen to come from
quasi two-body decays including charmonium mesons
such as
J= K
0
S
,

c
0
K
0
S
and

2
S

K
0
S
. In these cases the
charmonium meson decays to




or to




that are
misidentified as pions. Most of these events are removed
by vetoing the reconstructed




masses consistent
with
3
:
04
<m




<
3
:
16 GeV
=c
2
,
3
:
32
<m




<
3
:
51 GeV
=c
2
and
3
:
63
<m




<
3
:
74 GeV
=c
2
, identi-
fying the
J=
,

c
0
and

2
S

mesons, respectively. From
simulated data we estimate that
126

8
B
0
!
J= K
0
S
events and
6

3
B
0
!

2
S

K
0
S
events fall outside these
vetoes, and these are included in the model. We veto events
that are consistent with
B
0
!
D

!
K
0
S





by exclud-
ing those with
1
:
8
<m
K
0
S

<
1
:
91 GeV
=c
2
. However,
Monte Carlo simulation shows that
71

8
B
0
!
D

!
K
0
S





background events still remain, where the re-
constructed
D
mass falls outside the veto as a result of
using a
K
0
S
or a

from the other
B
decay in the event. Other
incorrectly reconstructed charmed decays
B
!
D

X
are
also included in the model.
After the above selection criteria are applied,
12
:
4%
of
events have more than one candidate that satisfies the
selection criteria. In a signal MC study, selecting the
candidate whose
cos

T
value is closest to zero is found
to select the true signal candidate in
69
:
2%
of such events.
These requirements result in a final sample size of approxi-
mately 80 000 events.
After all requirements, the largest charmless
B
back-
ground to the
B
0
!
K
0
S




measurement is the decay
B
0
!

0
K
0
S
;
0
!

0

770

;
0
!




, which tends to
peak in the signal region and which contributes
54

19
events. Table I shows the
B
-background modes for the
B
0
!
K


and
B
0
!
f
0
K
0
S
channels. These events are
effectively subtracted from the measured signal. To mea-
sure the nonresonant
B
0
!
K
0
S




, we select a region of
the Dalitz plot believed to be free of resonances, (
3
<
m




<
4 GeV
=c
2
and
m
K
0
S


>
1
:
91 GeV
=c
2
). Back-
grounds from other
B
decays and from continuum events
are subtracted. Assuming a uniform nonresonant distribu-
tion in the Dalitz plane, we set an upper limit of 2.1

10

6
at a
90%
confidence level on the nonresonant
B
0
!
K
0
S




branching fraction. All other branching fractions
are taken from Refs. [11,15].
We use an extended maximum likelihood fit to extract
the signal yield for each of the channels being investigated.
The likelihood function for
N
events is:
L

exp


X
j
N
j

Y
N
i

X
M
j

1
N
j
P
j

~
x
i


(2)
where
i
and
j
are integers,
M
is the number of hypotheses
(signal, continuum background and
B
background),
N
j
is
the number of events for the
j
th hypothesis determined by
maximizing the likelihood function, and
P
j

~
x
i

is a proba-
bility density function (PDF) evaluated using the vector
~
x
i
,
in this case
m
ES
,

E
, and
F
. Correlations between these
variables are small for signal and continuum background
hypotheses and the total PDF is a product
P
j

~
x
i

P
j

m
ES

P
j


E

P
j

F

. However for
B
background, it
is necessary to account for correlations observed between
TABLE I. The
B
-background modes for the channels
B
0
!
K


and
B
0
!
f
0
K
0
S
.
B
0
!

0
K
0
S
is included at a level
consistent with Ref. [3].
K

refers to heavier
K

resonances,
e.g.
K

0

1430

.
B
-background
Number Expected
Number Expected
Mode
(
B
0
!
K


)(
B
0
!
f
0
K
0
S
)
B
0
!
K


5

1
B
0
!
f
0
K
0
S
4

1
B
0
!

0
K
0
S
5

214

4
B
0
!
K


23

34

1
Nonresonant
7

15

1
B
0
!
D


16

2
0
B
0
!

0
K
0
S
1

119

7
B
0
!
J= K
0
S
6

1
0
MEASUREMENTS OF NEUTRAL
B
DECAY BRANCHING
...
PHYSICAL REVIEW D
73,
031101 (2006)
RAPID COMMUNICATIONS
031101-5
m
ES
and

E
by using a two-dimensional PDF for these
variables.
The parameters of the signal and
B
-background PDFs
are determined from MC simulation and fixed in the fit,
along with the
B
-background normalization. The contin-
uum background parameters are allowed to vary in the fit,
to help reduce systematic effects from this dominant event
type. Sideband data (which lie in the region
0
:
1
<

E<
0
:
3 GeV
and
5
:
22
<m
ES
<
5
:
29 GeV
=c
2
) are used to
model the continuum background PDFs. For the
m
ES
PDFs, a Gaussian distribution is used for signal and a
threshold function [16] for continuum. For the

E
PDFs,
a sum of two Gaussian distributions with the same means is
used for the signal and a first-order polynomial for the
continuum background. Finally, for the
F
PDFs, a sum of
two Gaussian distributions with distinct means and widths
is used for signal and a sum of two Gaussian distributions
with the same means is used to model the continuum
background. The Fisher discriminant distribution of the
B
backgrounds is modeled by an asymmetric Gaussian dis-
tribution that has different widths above and below the
modal value. We use
B
0
!
D

!
K
0
S





as a calibra-
tion mode since it exhibits a one-to-one signal to contin-
uum background ratio, allowing the signal parameters in a
fit to be floated. A fit to these data is used in order to
quantify any corrections and uncertainties due to MC.
These corrections are applied to the fits to the charmless
data sample.
To extract the branching fractions for the decay modes
B
0
!
K



and
B
0
!
f
0
K
0
we use the relation
B

N
sig
2
N
B
0

B
0
"
;
(3)
where
N
sig
is the number of signal events fitted,
"
is the
signal efficiency obtained from MC and
N
B
0

B
0
is the total
number of
B
0

B
0
pairs.
For the charmless
B
0
!
K
0




branching fraction
(and also for the nonresonant upper limit in the
B
-background studies above), it is necessary to account
for the variation in efficiency, between approximately
5%
and
40%
, across the Dalitz plot and to know how the signal
events are distributed across the Dalitz plot. To do this we
assign to the
j
th event
W
j

P
i
V
sig;i
P
i

~
x
j

=
P
k
N
k
P
k

~
x
j

where
V
sig
;i
are the signal components of the covariance
matrix obtained from the fit. This procedure projects out
the signal distributions [17] shown in Figs. 1– 4. The
branching
fraction
is
then
calculated
as
B

P
j
W
j
=

"
j
N
B
0

B
0

, where
"
j
is the efficiency, as a function
of Dalitz plot position, simulated in small bins using high
statistics MC.
Figure 1 shows the signal distributions for
B
0
!
K
0




candidates and the distributions of events for
all hypotheses. Figure 2 shows the signal distributions for
both the
B
0
!
K



and
B
0
!
f
0
K
0
channels. The fitted
signal yield and measured branching fraction are shown in
Table II for all the modes under study. The average effi-
ciency for
B
0
!
K
0
S




signal events is
16
:
8%
and the
continuum background yield is
79000

280
events.
Figure 3 shows the signal mass projections of
m
K
0
S

and
m




using
B
0
!
K
0




candidates. The
m
K
0
S

distri-
bution clearly shows a peak at
0
:
9 GeV
=c
2
, corresponding
to the
K


892

mass and there is a broad structure above
1 GeV
=c
2
that is the region where heavier kaon resonances
can occur. The
m




distribution shows evidence for
resonance structure around
1 GeV
=c
2
that corresponds to
the
f
0
and a broader structure below this that may be
attributed as the

0

770

. Figure 4 shows the efficiency
corrected signal distribution of the cosine of the helicity
angle,

H
, for
B
0
!
K



.
Table III shows the systematic uncertainties that are
assigned to the branching fraction measurements. Control
channels in data and MC are used to assign uncertainties
due to pion tracking, particle identification, and
K
0
S
recon-
struction efficiency. To calculate uncertainties due to the
fitting procedure, a large number of MC samples are
generated from the fitted PDFs, containing the amounts
of signal and continuum events that are measured in data
and the number of
B
-background events that were antici-
)
2
(GeV/c
ES
m
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
)
2
Events/(0.0007 GeV/c
0
200
400
600
800
1000
)
2
(GeV/c
ES
m
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
)
2
Events/(0.0007 GeV/c
0
200
400
600
800
1000
a)
)
2
(GeV/c
ES
m
5.23
5.24
5.25
5.26
5.27
5.28
5.29
)
2
Even
t
s /
(
0
.002 GeV
/
c
-50
0
50
100
150
200
250
300
350
)
2
(GeV/c
ES
m
5.23
5.24
5.25
5.26
5.27
5.28
5.29
)
2
Even
t
s /
(
0
.002 GeV
/
c
-50
0
50
100
150
200
250
300
350
d)
E (GeV)
-0.1 -0.08 -0.06 -0.04 -0.02
0
0.02 0.04 0.06 0.08 0.1
)
2
Events/(0.002 GeV/c
0
200
400
600
800
1000
E (GeV)
-0.1 -0.08 -0.06 -0.04 -0.02
0
0.02 0.04 0.06 0.08 0.1
)
2
Events/(0.002 GeV/c
0
200
400
600
800
1000
b)
E (GeV)
-0.1 -0.08 -0.06 -0.04 -0.02
0
0.02 0.04 0.06 0.08 0.1
Events / (0.007 GeV)
-20
0
20
40
60
80
100
120
140
160
E (GeV)
-0.1 -0.08 -0.06 -0.04 -0.02
0
0.02 0.04 0.06 0.08 0.1
Events / (0.007 GeV)
-20
0
20
40
60
80
100
120
140
160
e)
Fisher Discriminant
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
)
5
0
.
0
(
/
s
t
n
e
v
E
0
1000
2000
3000
4000
5000
Fisher Discriminant
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
)
5
0
.
0
(
/
s
t
n
e
v
E
0
1000
2000
3000
4000
5000
c)
Fisher Discriminant
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Events / (0.167)
0
50
100
150
200
250
300
Fisher Discriminant
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Events / (0.167)
0
50
100
150
200
250
300
f)
FIG. 1 (color online).
Plots of the maximum likelihood fit to
data for
B
0
!
K
0




candidates. Plots (a) –(c) show the
distributions of all events that pass the selection criteria for
(a)
m
ES
(b)

E
and (c) Fisher, with the solid (blue) line
indicating the total model, the (red) dotted line indicating shape
of the continuum background model and the (black) dashed line
indicating the signal model. Plots (d) –(f ) show the signal dis-
tributions for (d)
m
ES
, (e)

E
and (f ) Fisher, where the (black)
circles are the signal distribution [17] and the solid (blue) curve
is the signal PDF that was fitted in the maximum likelihood fit.
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
031101 (2006)
RAPID COMMUNICATIONS
031101-6
pated for the data set, as explained above. The differences
between the generated and fitted values using these
samples are used to ascertain the sizes of any biases.
Small biases of the order of a few percent are observed
that are a consequence of small correlations between fit
variables and are therefore assigned as systematic
uncertainties.
)
2
(GeV/c
ES
m
5.23
5.24
5.25
5.26
5.27
5.28
5.29
)
2
Events/(0.002 GeV/c
-20
-10
0
10
20
30
40
50
60
70
80
)
2
(GeV/c
ES
m
5.23
5.24
5.25
5.26
5.27
5.28
5.29
)
2
Events/(0.002 GeV/c
-20
-10
0
10
20
30
40
50
60
70
80
a)
)
2
(GeV/c
ES
m
5.23
5.24
5.25
5.26
5.27
5.28
5.29
)
2
Events / (0.002 GeV/c
-10
0
10
20
30
40
50
)
2
(GeV/c
ES
m
5.23
5.24
5.25
5.26
5.27
5.28
5.29
)
2
Events / (0.002 GeV/c
-10
0
10
20
30
40
50
d)
E (GeV)
-0.1 -0.08 -0.06 -0.04 -0.02
0
0.02 0.04 0.06 0.08
0.1
Events / (0.007 GeV)
-10
-5
0
5
10
15
20
25
30
35
E (GeV)
-0.1 -0.08 -0.06 -0.04 -0.02
0
0.02 0.04 0.06 0.08
0.1
Events / (0.007 GeV)
-10
-5
0
5
10
15
20
25
30
35
b)
E (GeV)
-0.1 -0.08 -0.06 -0.04 -0.02
0
0.02 0.04 0.06 0.08
0.1
Events / (0.007 GeV)
-5
0
5
10
15
20
25
30
E (GeV)
-0.1 -0.08 -0.06 -0.04 -0.02
0
0.02 0.04 0.06 0.08
0.1
Events / (0.007 GeV)
-5
0
5
10
15
20
25
30
e)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
E
ve
n
ts / (0.167)
-20
-10
0
10
20
30
40
50
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
E
ve
n
ts / (0.167)
-20
-10
0
10
20
30
40
50
c)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Eve
n
ts
/
(
0.1
6
7)
-10
-5
0
5
10
15
20
25
30
35
40
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Eve
n
ts
/
(
0.1
6
7)
-10
-5
0
5
10
15
20
25
30
35
40
f)
FIG. 2 (color online).
Maximum likelihood fits for signal dis-
tributions. For
B
0
!
K



the plots show (a)
m
ES
, (b)

E
, and
(c) the Fisher discriminant. The (black) circles are the signal
distribution extracted from the data with the method of Ref. [17]
and the solid curve is the signal PDF that resulted from the
maximum likelihood fit. For
B
0
!
f
0
K
0
, plots show the distri-
butions for (d)
m
ES
,(e

E
, and (f ) the Fisher discriminant, in an
analogous fashion.
TABLE II.
Signal yields and branching fractions for
B
0
!
K
0




,
B
0
!
K



and
B
0
!
f
0
K
0
where the first uncer-
tainty is statistical and where, in the case of the branching
fraction measurements, the second uncertainty is systematic
and any third uncertainty is due to possible interference effects.
The efficiency of selecting
B
0
!
K

!
K
0
S





and
B
0
!
f
0
!





K
0
S
events was found to be
24%
and
27%
respec-
tively, while the continuum background yields were
7300

86
events and
13000

110
events, respectively. The
B
0
!
K



branching fraction takes into account that
B

K

!
K
0



2
=
3
, assuming isospin symmetry.
Mode
Signal Events
Branching Fraction
Yield

10

6

B
0
!
K
0




860

47
43
:
0

2
:
3

2
:
3
B
0
!
f
0
!





K
0
120

16
5
:
5

0
:
7

0
:
6

0
:
3
B
0
!
K



140

19 11
:
0

1
:
5

0
:
5

0
:
4
)
H
θ
cos (
-1
-0.8
-0.6 -0.4
-0.2
-0
0.2
0.4
0.6
0.8
1
Events / (0.22)
0
50
100
150
200
)
H
θ
cos (
-1
-0.8
-0.6 -0.4
-0.2
-0
0.2
0.4
0.6
0.8
1
Events / (0.22)
0
50
100
150
200
FIG. 4.
Distribution of the efficiency corrected cosine of the
helicity angle,

H
, for
B
0
!
K


signal events.
)
2
(GeV/c
π
K
m
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
)
2
Events / (0.03 GeV/c
0
10
20
30
40
50
)
2
(GeV/c
π
K
m
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
)
2
Events / (0.03 GeV/c
0
10
20
30
40
50
a)
(892)
*
K
(1430)
0
*
K
)
2
(GeV/c
π
π
m
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
)
2
c
/
V
e
G
(
3
0
.
0
(
/
s
t
n
e
v
E
0
10
20
30
40
50
)
2
(GeV/c
π
π
m
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
)
2
c
/
V
e
G
(
3
0
.
0
(
/
s
t
n
e
v
E
0
10
20
30
40
50
b)
(980)
0
f
(770)
0
ρ
FIG. 3 (color online).
(a) shows the
m
K
0
S

signal distribution
of
B
0
!
K
0




candidates [17]. The one-dimensional distri-
bution is obtained by merging
m
2
K

and
m
2
K

into one (
m
2
K
)
by folding the Dalitz plane along the line corresponding to
m
2
K


m
2
K

in order to obtain the above
m
K
mass distribu-
tion. (b) shows the
m




signal distribution of
B
0
!
K
0




candidates [17]. The dashed lines indicate the expected mass of
the labeled resonances.
MEASUREMENTS OF NEUTRAL
B
DECAY BRANCHING
...
PHYSICAL REVIEW D
73,
031101 (2006)
RAPID COMMUNICATIONS
031101-7
The uncertainty of the
B
-background contribution to the
fit is estimated by varying the measured branching frac-
tions within their uncertainties. Each background is varied
by

1

[11] and the effect on the fitted signal yield is
added as a contribution to the uncertainty. For
B
0
!
K



there is an additional uncertainty in the
B
-background contributions due to the possible lineshapes
of the
K

0

1430

, which can alter the amount of
B
back-
ground expected. In order to assign a systematic uncer-
tainty,
fits
to
data
are
performed
using
two
parametrizations, a relativistic Breit –Wigner lineshape
and the LASS parametrization [18]. The latter is a coherent
sum of a relativistic Breit-Wigner and an effective range
term, and is used in the analysis of
B

!
K




[19].
The uncertainty due to simulated PDFs is obtained from
the channel
B
0
!
D

!
K
0
S





and by varying the
PDFs according to the precision of the parameters obtained
from MC. In order to take correlations between parameters
into account, the full correlation matrix is used when
varying parameters. All PDF parameters that are originally
fixed in the fit are then varied in turn and each difference
from the nominal fit is combined and taken as a systematic
uncertainty. The uncertainty in the efficiency is due to
limited MC statistics, where over 1 000 000 MC events
are generated for the decay
B
0
!
K
0




and over
150 000 MC events are generated for the decays
B
0
!
K



and
B
0
!
f
0
K
0
S
. The same uncertainty in the
number of
B

B
events is used for all channels.
For the quasi two-body modes, possible interference
effects between the final state modes were investigated
by simulating the Dalitz plot using the measured branching
fractions and random phases. The root-mean-squared of
the distribution of the branching fraction is taken to be the
uncertainty.
We measure the
CP
-violating charge asymmetry for the
decay
B
0
!
K



to be
A
K



0
:
11

0
:
14

0
:
05
,
where the first uncertainty is statistical and the second
uncertainty is systematic. The charge asymmetry in the
background is expected to be zero, as is the charge asym-
metry in signal and background of the self-tagging decay
B
0
!
D



. As a cross-check, these are measured to be

0
:
018

0
:
009
;

0
:
013

0
:
029
and
0
:
005

0
:
031
re-
spectively, where the uncertainties are statistical only.
The systematic uncertainty on
A
K


is calculated by
considering contributions due to track finding, particle
identification, fit biases and
B
-background asymmetry un-
certainties. Biases due to track finding and particle identi-
fication were found to be negligible. The fit-bias
contribution to the systematic uncertainty is calculated
using a large number of MC samples. The contribution
from
B
background is calculated by varying the number of
expected events within their uncertainties [11] and by
assuming a conservative
CP
-violating asymmetry of

0
:
5
as there are no available measurements for these
decays. The resulting systematic uncertainty on the asym-
metry is measured to be

0
:
05
.
In summary, the branching fractions for
B
0
!
K
0




,
B
0
!
K



, and
B
0
!
f
0
!





K
0
de-
caying to a
K
0
S




state are measured and all agree with
previous measurements [2,4 – 6]. We measure the direct
CP
-violating parameter
A
K


for the decay
B
0
!
K



, with no evidence of
CP
violation with the statis-
tics used. These results supersede the previous results of
the
BABAR
Collaboration [2,4].
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
wish to thank SLAC for its support and kind hospitality.
This work is supported by DOE and NSF (USA), NSERC
(Canada), IHEP (China), CEA and CNRS-IN2P3 (France),
BMBF and DFG (Germany), INFN (Italy), FOM (The
Netherlands), NFR (Norway), MIST (Russia), and
PPARC (United Kingdom). Individuals have received sup-
port from CONACyT (Mexico), A. P. Sloan Foundation,
Research Corporation, and Alexander von Humboldt
Foundation.
TABLE III. Summary of contributions to the systematic un-
certainty in the branching fractions measurements of
B
0
!
K
0




,
B
0
!
K



and
B
0
!
f
0
K
0
. The uncertainties
are shown as a percentage of the measured branching fraction.
Error
B
0
!
K
0




B
0
!
f
0
K
0
B
0
!
K



source
Error (
%
)
Error (
%
)
Error (
%
)
Particle ID
1.9
1.9
1.9
Tracking
1.6
1.6
1.6
K
0
S
efficiency
1.4
1.6
1.5
Fit Bias
1.7
6.1
2.6
PDF params.
0.1
0.1
0.3
B
background
4.2
5.9
2.0
Efficiency
0.9
0.1
0.1
No. of
B

B
1.1
1.1
1.1
TOTAL
5.4
9.1
4.5
Interference
-
4.7
4.0
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
031101 (2006)
RAPID COMMUNICATIONS
031101-8
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MEASUREMENTS OF NEUTRAL
B
DECAY BRANCHING
...
PHYSICAL REVIEW D
73,
031101 (2006)
RAPID COMMUNICATIONS
031101-9