Measurement of Branching Fractions and Resonance Contributions
for
B
0
!
D
0
K
and Search for
B
0
!
D
0
K
Decays
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
D. Best,
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
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
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
J. S. Minamora,
19
I. Narsky,
19
T. Piatenko,
19
F. C. Porter,
19
A. Ryd,
19
A. Samuel,
19
R. Andreassen,
20
G. Mancinelli,
20
B. T. Meadows,
20
M. D. Sokoloff,
20
F. Blanc,
21
P. C. Bloom,
21
S. Chen,
21
W. T. Ford,
21
J. F. Hirschauer,
21
A. Kreisel,
21
U. Nauenberg,
21
A. Olivas,
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
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
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. 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
J . A. Nash,
32
M. B. Nikolich,
32
W. Panduro Vazquez,
32
X. Chai,
33
M. J. Charles,
33
W. F. Mader,
33
U. Mallik,
33
V. Ziegler,
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. I. Yi,
34
G. Schott,
35
N. Arnaud,
36
M. Davier,
36
X. Giroux,
36
G. Grosdidier,
36
A. Ho
̈
cker,
36
F. Le Diberder,
36
V. Lepeltier,
36
A. M. Lutz,
36
A. Oyanguren,
36
T. C. Petersen,
36
S. Plaszczynski,
36
S. Rodier,
36
P. Roudeau,
36
M. H. Schune,
36
A. Stocchi,
36
G. Wormser,
36
C. H. Cheng,
37
D. J. Lange,
37
M. C. Simani,
37
D. M. Wright,
37
A. J. Bevan,
38
C. A. Chavez,
38
I. J. Forster,
38
J. R. Fry,
38
E. Gabathuler,
38
R. Gamet,
38
K. A. George,
38
D. E. Hutchcroft,
38
R. J. Parry,
38
D. J. Payne,
38
K. C. Schofield,
38
C. Touramanis,
38
C. M. Cormack,
39
F. Di Lodovico,
39
W. Menges,
39
R. Sacco,
39
C. L. Brown,
40
G. Cowan,
40
H. U. Flaecher,
40
M. G. Green,
40
D. A. Hopkins,
40
P. S. Jackson,
40
T. R. McMahon,
40
S. Ricciardi,
40
F. Salvatore,
40
D. N. Brown,
41
C. L. Davis,
41
J. Allison,
42
N. R. Barlow,
42
R. J. Barlow,
42
C. L. Edgar,
42
M. C. Hodgkinson,
42
M. P. Kelly,
42
G. D. Lafferty,
42
M. T. Naisbit,
42
J. C. Williams,
42
C. Chen,
43
W. D. Hulsbergen,
43
A. Jawahery,
43
D. Kovalskyi,
43
C. K. Lae,
43
D. A. Roberts,
43
G. Simi,
43
G. Blaylock,
44
C. Dallapiccola,
44
S. S. Hertzbach,
44
R. Kofler,
44
X. Li,
44
T. B. Moore,
44
S. Saremi,
44
H. Staengle,
44
S. Y. Willocq,
44
R. Cowan,
45
K. Koeneke,
45
G. Sciolla,
45
S. J. Sekula,
45
M. Spitznagel,
45
F. Taylor,
45
R. K. Yamamoto,
45
H. Kim,
46
P. M. Patel,
46
S. H. Robertson,
46
A. Lazzaro,
47
V. Lombardo,
47
F. Palombo,
47
J. M. Bauer,
48
L. Cremaldi,
48
V. Eschenburg,
48
R. Godang,
48
R. Kroeger,
48
J. Reidy,
48
D. A. Sanders,
48
D. J. Summers,
48
H. W. Zhao,
48
S. Brunet,
49
D. Co
ˆ
te
́
,
49
P. Taras,
49
F. B. Viaud,
49
H. Nicholson,
50
N. Cavallo,
51
G. De Nardo,
51
F. Fabozzi,
51,†
C. Gatto,
51
L. Lista,
51
D. Monorchio,
51
P. Paolucci,
51
D. Piccolo,
51
C. Sciacca,
51
M. Baak,
52
H. Bulten,
52
G. Raven,
52
H. L. Snoek,
52
L. Wilden,
52
PRL
96,
011803 (2006)
PHYSICAL REVIEW LETTERS
week ending
13 JANUARY 2006
0031-9007
=
06
=
96(1)
=
011803(7)$23.00
011803-1
©
2006 The American Physical Society
C. P. Jessop,
53
J. M. LoSecco,
53
T. Allmendinger,
54
G. Benelli,
54
K. K. Gan,
54
K. Honscheid,
54
D. Hufnagel,
54
P. D. Jackson,
54
H. Kagan,
54
R. Kass,
54
T. Pulliam,
54
A. M. Rahimi,
54
R. Ter-Antonyan,
54
Q. K. Wong,
54
N. L. Blount,
55
J. Brau,
55
R. Frey,
55
O. Igonkina,
55
M. Lu,
55
C. T. Potter,
55
R. Rahmat,
55
N. B. Sinev,
55
D. Strom,
55
J. Strube,
55
E. Torrence,
55
F. Galeazzi,
56
M. Margoni,
56
M. Morandin,
56
M. Posocco,
56
M. Rotondo,
56
F. Simonetto,
56
R. Stroili,
56
C. Voci,
56
M. Benayoun,
57
H. Briand,
57
J. Chauveau,
57
P. David,
57
L. Del Buono,
57
Ch. de la Vaissie
`
re,
57
O. Hamon,
57
M. J. J. John,
57
Ph. Leruste,
57
J. Malcle
`
s,
57
J. Ocariz,
57
L. Roos,
57
G. Therin,
57
P. K. Behera,
58
L. Gladney,
58
Q. H. Guo,
58
J. Panetta,
58
M. Biasini,
59
R. Covarelli,
59
S. Pacetti,
59
M. Pioppi,
59
C. Angelini,
60
G. Batignani,
60
S. Bettarini,
60
F. Bucci,
60
G. Calderini,
60
M. Carpinelli,
60
R. Cenci,
60
F. Forti,
60
M. A. Giorgi,
60
A. Lusiani,
60
G. Marchiori,
60
M. Morganti,
60
N. Neri,
60
E. Paoloni,
60
M. Rama,
60
G. Rizzo,
60
J. Walsh,
60
M. Haire,
61
D. Judd,
61
D. E. Wagoner,
61
J. Biesiada,
62
N. Danielson,
62
P. Elmer,
62
Y. P. Lau,
62
C. Lu,
62
J. Olsen,
62
A. J. S. Smith,
62
A. V. Telnov,
62
F. Bellini,
63
G. Cavoto,
63
A. D’Orazio,
63
E. Di Marco,
63
R. Faccini,
63
F. Ferrarotto,
63
F. Ferroni,
63
M. Gaspero,
63
L. Li Gioi,
63
M. A. Mazzoni,
63
S. Morganti,
63
G. Piredda,
63
F. Polci,
63
F. Safai Tehrani,
63
C. Voena,
63
H. Schro
̈
der,
64
R. Waldi,
64
T. Adye,
65
N. De Groot,
65
B. Franek,
65
G. P. Gopal,
65
E. O. Olaiya,
65
F. F. Wilson,
65
R. Aleksan,
66
S. Emery,
66
A. Gaidot,
66
S. F. Ganzhur,
66
G. Graziani,
66
G. Hamel de Monchenault,
66
W. Kozanecki,
66
M. Legendre,
66
G. W. London,
66
B. Mayer,
66
G. Vasseur,
66
Ch. Ye
`
che,
66
M. Zito,
66
M. V. Purohit,
67
A. W. Weidemann,
67
J. R. Wilson,
67
F. X. Yumiceva,
67
T. Abe,
68
M. T. Allen,
68
D. Aston,
68
R. Bartoldus,
68
N. Berger,
68
A. M. Boyarski,
68
O. L. Buchmueller,
68
R. Claus,
68
J. P. Coleman,
68
M. R. Convery,
68
M. Cristinziani,
68
J. C. Dingfelder,
68
D. Dong,
68
J. Dorfan,
68
D. Dujmic,
68
W. Dunwoodie,
68
S. Fan,
68
R. C. Field,
68
T. Glanzman,
68
S. J. Gowdy,
68
T. Hadig,
68
V. Halyo,
68
C. Hast,
68
T. Hryn’ova,
68
W. R. Innes,
68
M. H. Kelsey,
68
P. Kim,
68
M. L. Kocian,
68
D. W. G. S. Leith,
68
J. Libby,
68
S. Luitz,
68
V. Luth,
68
H. L. Lynch,
68
H. Marsiske,
68
R. Messner,
68
D. R. Muller,
68
C. P. O’Grady,
68
V. E. Ozcan,
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
J. Stelzer,
68
D. Su,
68
M. K. Sullivan,
68
K. Suzuki,
68
S. K. Swain,
68
J. M. Thompson,
68
J. Va’vra,
68
N. van Bakel,
68
M. Weaver,
68
A. J. R. Weinstein,
68
W. J. Wisniewski,
68
M. Wittgen,
68
D. H. Wright,
68
A. K. Yarritu,
68
K. Yi,
68
C. C. Young,
68
P. R. Burchat,
69
A. J. Edwards,
69
S. A. Majewski,
69
B. A. Petersen,
69
C. Roat,
69
M. Ahmed,
70
S. Ahmed,
70
M. S. Alam,
70
R. Bula,
70
J. A. Ernst,
70
M. A. Saeed,
70
F. R. Wappler,
70
S. B. Zain,
70
W. Bugg,
71
M. Krishnamurthy,
71
S. M. Spanier,
71
R. Eckmann,
72
J. L. Ritchie,
72
A. Satpathy,
72
R. F. Schwitters,
72
J. M. Izen,
73
I. Kitayama,
73
X. C. Lou,
73
S. Ye,
73
F. Bianchi,
74
M. Bona,
74
F. Gallo,
74
D. Gamba,
74
M. Bomben,
75
L. Bosisio,
75
C. Cartaro,
75
F. Cossutti,
75
G. Della Ricca,
75
S. Dittongo,
75
S. Grancagnolo,
75
L. Lanceri,
75
L. Vitale,
75
V. Azzolini,
76
F. Martinez-Vidal,
76
R. S. Panvini,
77,‡
Sw. Banerjee,
78
B. Bhuyan,
78
C. M. Brown,
78
D. Fortin,
78
K. Hamano,
78
R. Kowalewski,
78
J. M. Roney,
78
R. J. Sobie,
78
J. J. Back,
79
P. F. Harrison,
79
T. E. Latham,
79
G. B. Mohanty,
79
H. R. Band,
80
X. Chen,
80
B. Cheng,
80
S. Dasu,
80
M. Datta,
80
A. M. Eichenbaum,
80
K. T. Flood,
80
M. T. Graham,
80
J. J. Hollar,
80
J. R. Johnson,
80
P. E. Kutter,
80
H. Li,
80
R. Liu,
80
B. Mellado,
80
A. Mihalyi,
80
A. K. Mohapatra,
80
Y. Pan,
80
M. Pierini,
80
R. Prepost,
80
P. Tan,
80
S. L. Wu,
80
Z. Yu,
80
and H. Neal
81
(The
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
University of Bergen, Institute of Physics, 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
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 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
Institute for Particle Physics, University of California at Santa Cruz, Santa Cruz, California 95064, USA
PRL
96,
011803 (2006)
PHYSICAL REVIEW LETTERS
week ending
13 JANUARY 2006
011803-2
19
California Institute of Technology, Pasadena, California 91125, USA
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
Universita
̈
t Dortmund, Institut fu
̈
r Physik, D-44221 Dortmund, Germany
24
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
25
Ecole Polytechnique, LLR, F-91128 Palaiseau, France
26
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
27
Universita
`
di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
28
Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
29
Universita
`
di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
30
Harvard University, Cambridge, Massachusetts 02138, USA
31
Universita
̈
t Heidelberg, Physikalisches Institut, 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
Universita
̈
t Karlsruhe, Institut fu
̈
r Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
36
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, F-91898 Orsay, France
37
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
38
University of Liverpool, Liverpool L69 72E, United Kingdom
39
Queen Mary, University of London, E1 4NS, United Kingdom
40
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
41
University of Louisville, Louisville, Kentucky 40292, USA
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
Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
46
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
47
Universita
`
di Milano, Dipartimento di Fisica and INFN, 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
51
Universita
`
di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, 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
56
Universita
`
di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
57
Universite
́
s Paris VI et VII, Laboratoire de Physique Nucle
́
aire et de Hautes Energies, F-75252 Paris, France
58
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
59
Universita
`
di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy
60
Dipartimento di Fisica, Scuola Normale Superiore, Universita
`
di Pisa and INFN, I-56127 Pisa, Italy
61
Prairie View A&M University, Prairie View, Texas 77446, USA
62
Princeton University, Princeton, New Jersey 08544, USA
63
Universita
`
di Roma La Sapienza, Dipartimento di Fisica and INFN, 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/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, 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
74
Dipartimento di Fisica Sperimentale, Universita
`
di Torino and INFN, I-10125 Torino, Italy
75
Dipartimento di Fisica, Universita
`
di Trieste and INFN, I-34127 Trieste, Italy
76
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
77
Vanderbilt University, Nashville, Tennessee 37235, USA
78
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
79
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
PRL
96,
011803 (2006)
PHYSICAL REVIEW LETTERS
week ending
13 JANUARY 2006
011803-3
80
University of Wisconsin, Madison, Wisconsin 53706, USA
81
Yale University, New Haven, Connecticut 06511, USA
(Received 23 September 2005; published 11 January 2006)
Using
226
10
6
4
S
!
B
B
events collected with the
BABAR
detector at the PEP-II
e
e
storage
ring at the Stanford Linear Accelerator Center, we measure the branching fraction for
B
0
!
D
0
K
,
excluding
B
0
!
D
K
,tobe
B
B
0
!
D
0
K
88
15
9
10
6
. We observe
B
0
!
D
0
K
892
0
and
B
0
!
D
2
2460
K
contributions. The ratio of branching fractions
B
B
0
!
D
K
=
B
B
0
!
D
7
:
76
0
:
34
0
:
29
%
is measured separately. The branching fraction
for the suppressed mode
B
0
!
D
0
K
is
B
B
0
!
D
0
K
<
19
10
6
at the 90% confidence level.
DOI:
10.1103/PhysRevLett.96.011803
PACS numbers: 13.25.Hw
A theoretically clean method for measuring the angle
arg
V
ud
V
ub
=V
cd
V
cb
in the unitarity triangle of the
Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing ma-
trix [1] in the standard model of particle physics utilizes
decay modes of the type
B
!
DK
. Several methods have
been proposed [2 – 4] to extract
from these decays
using interference effects between
b
!
u
cs
and
b
!
c
us
processes. However, the
b
!
u
cs
amplitude is suppressed
by a color factor in addition to the CKM factor
j
V
ub
V
cs
=V
cb
V
us
j’
0
:
4
, and the extraction of
with pre-
vious methods in Refs. [2,3] is subject to an eightfold
ambiguity due to unknown strong phases.
Three-body
B
!
DK
decays have been proposed [5,6]
as an alternative method for measuring
. In these modes,
the CKM-suppressed
b
!
u
cs
processes include color-
allowed diagrams; thus larger decay rates and more sig-
nificant
CP
violation effects are possible. In addition, a
DK
Dalitz plot analysis can resolve the strong phase and
reduce the ambiguity to twofold, similar to Ref. [4]. The
sensitivity to
in these decays is determined by the size of
the overlapping
b
!
c
us
and
b
!
u
cs
amplitudes in the
Dalitz plot.
In this Letter, we report the measurements of the branch-
ing fraction for the CKM-favored
B
0
!
D
0
K
[7]
decay and dominant resonance contributions, and the
search for the CKM-suppressed
B
0
!
D
0
K
decays.
The flavor of the
B
meson is tagged by the charge of the
prompt kaon. The favored mode has been previously ob-
served through its dominant resonances
D
K
[8] and
D
0
K
892
0
[9]. Since
D
K
occupies only a very small
region of the allowed phase space, we treat it separately
and measure the ratio
r
B
B
0
!
D
K
=
B
B
0
!
D
, which can be used to test factorization and
flavor-SU(3) symmetry.
Signal events are selected from
226
10
6
B
B
pairs col-
lected with the
BABAR
detector [10] at the PEP-II
asymmetric-energy storage ring. Charged tracks are de-
tected by a five-layer silicon vertex tracker and a 40-layer
drift chamber. Hadrons are identified based on the ioniza-
tion energy loss in the tracking system and the opening
angle of the Cherenkov radiation in a ring-image detector
[11]. Photons are measured by an electromagnetic calo-
rimeter. These systems are mounted inside a 1.5 T sole-
noidal superconducting magnet.
The
D
0
candidate is reconstructed through
K
,
K
0
, and
K
channels, where the measured
invariant mass is required to be within 20, 35, and 20
MeV
=c
2
, respectively, of the nominal
D
0
mass [12], cor-
responding to 3.0, 2.5, and 3.0
. A vertex fit is performed
with the mass constrained to the nominal value. The
0
candidate is formed from two photon candidates with
invariant mass between 115 and
150 MeV
=c
2
.
For the measurement of the ratio
r
, the
D
0
is combined
with a low momentum
to form a
D
candidate, with its
vertex constrained to the interaction point (beam spot).
Candidates with mass difference
m
D
0
m
D
0
between
144 and
147 MeV
=c
2
are retained. A charged track, as-
sumed to have the pion mass, is combined with the
D
to
form a
B
0
candidate. The
2
probabilities for both the
D
and
B
0
vertex fits are required to be greater than 0.1%. To
reject jetlike continuum background, the normalized Fox-
Wolfram second moment
R
2
[13], computed with charged
tracks and neutral clusters, is required to be less than 0.5,
and
j
cos
T
j
less than 0.85, where
T
is the thrust angle
between the
B
0
candidate and the rest of the event in the
e
e
center-of-mass (c.m.) frame.
For
B
0
!
D
0
K
and
D
0
K
measurements, the
B
0
candidate is formed by combining a
D
0
candidate with
oppositely charged pion and kaon candidates. We select
candidates outside the
D
K
region (
142
:
5
<m
D
0
m
D
0
<
148
:
5 MeV
=c
2
,a
6
window). The measured
D
0
invariant mass must be within 12, 28, and
8
:
5 MeV
=c
2
of
the nominal
D
0
mass for
K
,
K
0
, and
K
modes,
respectively. Candidates are rejected if the
D
0
!
K
0
decay probability, computed with the Dalitz parameters
measured in Ref. [14], is less than 6% of the maximum
value. The
2
probability of the
D
0
(
B
0
) vertex fit is
required to be greater than 0.5% (2%). All charged tracks
are required to have at least 12 hits in the drift chamber and
transverse momentum greater than
100 MeV
=c
. Both kaon
candidates are required to be consistent with the kaon
hypothesis. Prompt pion candidates consistent with the
kaon hypothesis are rejected.
To further reduce the continuum background,
j
cos
B
j
must be less than 0.9, where
B
is the polar angle of the
B
0
candidate in the c.m. frame. A Fisher discriminant
F
is
formed based on
R
2
,
cos
T
,
B
, and two moments
L
0
and
L
2
, where
L
i
P
j
p
j
j
cos
j
j
i
, summed over the remaining
PRL
96,
011803 (2006)
PHYSICAL REVIEW LETTERS
week ending
13 JANUARY 2006
011803-4
particles
j
in the event, where
j
and
p
j
are the angle with
respect to the
B
0
thrust and the momentum in the c.m.
frame. Different cuts on
F
are applied for each mode to
optimize the signal significance based on simulated event
samples. Candidates used in the subsequent fits have beam-
energy
substituted
mass
m
ES
s
p
=
2
2
p
2
q
>
5
:
2 GeV
=c
2
and energy difference
j
E
jj
E
s
p
=
2
j
<
150 MeV
, where
E
and
p
are the energy and momentum
of the
B
0
candidate and
s
p
is the total energy in the c.m.
frame.
We study five samples separately: (a)
B
0
!
D
0
K
excluding the
D
K
contribution, (b)
B
0
!
D
0
K
,
(c)
B
0
!
D
0
K
892
0
, (d)
B
0
!
D
2
2460
K
, and
(e)
B
0
!
D
h
, where
h
is a pion or kaon.
Samples (c) and (d) are subsets of (a), where the reso-
nances are selected within 1.5 times their full widths [12].
For samples (a) –(d), a two-dimensional (
m
ES
,
E
)
unbinned-maximum-likelihood fit is used to determine
the signal yields. The signal component is the product of
a Gaussian in
m
ES
centered at the
B
0
mass and a Crystal
Ball line shape [15] in
E
centered near zero. The com-
binatorial background component is modeled with an
Argus threshold function [16] in
m
ES
and a second-order
polynomial in
E
. Two background components peak in
m
ES
: peaking background
A
describes the
B
0
!
D
contribution, which also peaks in
E
but the peak is shifted
by about
50 MeV
because the pion is misidentified as a
kaon; peaking background
B
uses a second-order polyno-
mial in
E
to accommodate events such as
D
K
, and
D
, where one or more pions or photons are missed in
the reconstruction and/or a pion is misidentified as a kaon.
The probability density function (PDF) is the sum of the
signal and three background components. A large
B
0
!
D
data control sample is used to determine the signal
shape in both
E
and
m
ES
, and the peaking background
A
in
E
, where we assign the kaon mass to the pion candi-
date. We use the same parameters for signal and peaking
backgrounds in
m
ES
since they are consistent in simula-
tion. The
E
distributions and yields for the four compo-
nents in the signal region are shown in Fig. 1 and Table I,
respectively.
The signal yield for
B
0
!
D
0
K
is corrected for
variations in signal efficiency across the
DK
Dalitz
plot. Each event
k
with variables
~
q
k
m
ES
;k
;
E
k
is
assigned a signal weight [17]
w
sig
~
q
k
P
4
j
1
V
sig
;j
P
j
~
q
k
P
4
j
1
N
j
P
j
~
q
k
;
calculated from the four PDF components
P
j
, their yields
N
j
from the fit, and the covariance matrix elements
V
sig
;j
between
N
sig
and
N
j
. The efficiency-corrected signal yield
is then
P
k
w
sig
~
q
k
="
k
, where the efficiency
"
k
is estimated
from the simulated events in the vicinity of each data point
in the Dalitz plot.
Figure 2 shows the signal weight distribution as a func-
tion of
m
K
and
m
D
0
. The peaks near
m
K
892
0
and
m
D
2
2460
are clearly visible. We use the
m
ES
;
E
fit
Events / ( 0.0125 GeV )
100
200
300
Events / ( 0.0125 GeV )
100
200
300
(a)
200
400
600
200
400
600
(b)
E (GeV)
∆
-0.1
0
0.1
Events / ( 0.0125 GeV )
0
20
40
60
E (GeV)
∆
-0.1
0
0.1
Events / ( 0.0125 GeV )
0
20
40
60
(c)
E (GeV)
∆
-0.1
0
0.1
0
10
20
30
E (GeV)
∆
-0.1
0
0.1
0
10
20
30
(d)
FIG. 1 (color online).
E
distributions and PDF projections
with
m
ES
>
5
:
27 GeV
=c
2
for (a)
B
0
!
D
0
K
excluding
D
K
candidates, (b)
B
0
!
D
0
K
, (c)
B
0
!
D
0
K
892
0
,
and (d)
B
0
!
D
2
2460
K
, for the three
D
0
modes combined.
Circles with error bars are data points. Four curves from top to
bottom represent the total PDF (solid line), total background
(dashed line), combinatorial background plus peaking back-
ground
B
described in the text (dot-dashed line), and combina-
torial background only (dotted line). In (a) –(c), the middle two
curves overlap because the peaking background
A
is negligible.
TABLE I. The yields of signal, combinatorial (comb.), and peaking (peak
A
, peak
B
) background PDFs of the samples (a) –
(d) described in the text; values and errors are rescaled to represent the yields in the signal region (
m
ES
>
5
:
27 GeV
=c
2
,
j
E
j
<
40 MeV
). The bottom row shows the branching fractions with statistical errors.
(a)
B
0
!
D
0
K
(b)
B
0
!
D
0
K
(c)
B
0
!
D
0
K
892
0
(d)
B
0
!
D
2
2460
K
D
0
mode
K
K
0
K
K
K
0
K K K
0
K K K
0
K
Signal
101
17 58
20 69
19
17
13 34
24 8
22 35
721
731
715
615
616
5
Comb.
229
4 500
5 528
5 608
5 918
6 989
617
129
130
116
116
122
1
Peak
A
5
60
10
20
00
00
00
00
00
02
25
22
1
Peak
B
45
976
12 42
10 50
11 54
14 45
13 6
310
33
32
37
30
1
B
10
6
88
15
4
12
38
618
:
3
4
:
0
PRL
96,
011803 (2006)
PHYSICAL REVIEW LETTERS
week ending
13 JANUARY 2006
011803-5
results and signal efficiencies estimated from simulated
B
0
!
D
0
K
892
0
and
B
0
!
D
2
2460
K
samples to
compute corresponding branching fractions. For the
B
0
!
D
0
K
mode, we assume a flat distribution on the Dalitz
plot when determining the signal efficiency.
For modes in which we do not observe a significant
signal, the 90% confidence level (C.L.) branching frac-
tion upper limit (UL) is determined by integrating the
product of the PDFs for the three
D
0
modes as a function
of branching fraction from 0 to
B
UL
so that
R
B
UL
0
L
d
B
0
:
9
R
1
0
L
d
B
, where
L
is the likelihood function.
To measure
r
, we select
events with
m
ES
>
5
:
27 GeV
=c
2
from sample (e). A two-dimensional PDF
of
E
and
C
(the reconstructed Cherenkov-light angle of
the prompt track) is used to separate
D
K
from
D
decays. Tracks with an estimated
C
uncertainty
C
>
4 mrad
or
n
;s
=
n
;s
n
;b
p
<
3
are removed, where
n
;s
and
n
;b
are the numbers of signal and background photons
determined from a likelihood fit to the ring of Cherenkov
photons associated with the track [11]. Finally, events are
rejected if
C
is smaller than the predicted Cherenkov
angle for kaons by more than
4
C
, in order to remove
particles heavier than kaon.
The
E
signal peak PDF is a Crystal Ball line shape and
the background is a linear function plus a Gaussian peaked
near
150 MeV
to accommodate background events such
as
D
and
D
where a soft
is missed in the
reconstruction.The distribution of
C
C
=
C
is mod-
eled by Gaussian functions. For the pion component, we
use three Gaussian functions centered near zero. For the
kaon component, a single Gaussian function centered near
K
C
C
=
C
is sufficient, where
K
C
and
C
are the
expected Cherenkov angle for kaon and pion, respectively,
based on the measured momentum. Most of the parameters
are obtained from a fit to the pion or kaon tracks in a large
c
c
!
D
X
!
D
0
X
,
D
0
!
K
data control sample,
except the total width of the distribution, which is free in
the final fit to accommodate a small difference in width due
to differences in momentum spectra between signal and
control samples.
Figure 3 shows the
E
and
C
C
=
C
distributions
and PDF projections for
B
0
!
D
h
(
h
or
K
) can-
didates. We find 13 400 signal events, of which
f
6
:
80
0
:
28
%
are
D
K
events, and 4850 background
events in the sample. The ratio
r
f=
1
f
is corrected
by the signal efficiency ratio
r
"
"
D
K="
D
94
:
0
2
:
3
%
obtained from simulation. This ratio is smaller than
unity because
C
for kaons is smaller (resulting in fewer
Cherenkov photons) and more kaons than pions decay in
flight within the tracking volume. The uncertainty on
r
"
includes simulation statistics and systematic uncertainties
due to the two aforementioned effects.
For samples (a) –(d), the systematic uncertainties on the
signal efficiency are studied with large
lepton decay
samples (for track reconstruction efficiency) and compari-
sons between signal simulation and the
B
0
!
D
data
control sample. The fractional uncertainty, common to all
four samples, on signal efficiency is 5% including the
uncertainties on the number of
B
B
events and the
D
0
branching fractions. For the
B
0
!
D
0
K
mode, the
uncertainty of efficiency variation on the Dalitz plot con-
tributes an additional systematic error of 8%. In addition,
we vary the control sample shapes in each fit by one
standard error and sum the changes in signal yield in
quadrature. The total signal yield variations are 8, 2.0,
3.4, and 2.6 events for
D
0
K
,
D
0
K
,
D
0
K
892
0
,
and
D
2
2460
K
,
respectively.
For
the
B
0
!
D
0
K
892
0
and
D
2
2460
K
measurements, we con-
sider possible contamination from each other and from
the nonresonance contribution. Using the signal yields
for
B
0
!
D
0
K
892
0
and
D
2
2460
K
, and the cross-
feed efficiencies determined from simulation, we find that
six events in each of these two
B
0
modes could be attrib-
uted to the other mode and to nonresonance contributions.
This contributes a 6% uncertainty for
B
0
!
D
0
K
892
0
and 11% for
B
0
!
D
2
2460
K
. The uncertainty due to
the full width of the
D
2
2460
and
K
892
0
resonances is
8% for
B
0
!
D
2
2460
K
and less than 1% for
B
0
!
D
0
K
892
0
.
E (GeV)
∆
-0.1
0
0.1
)
V
e
G
3
0
0
.
0
(
/
s
t
n
e
v
E
0
200
400
600
800
E (GeV)
∆
-0.1
0
0.1
)
V
e
G
3
0
0
.
0
(
/
s
t
n
e
v
E
0
200
400
600
800
(a)
C
σ
)/
π
C
θ
-
C
θ
(
-20
-10
0
10
)
5
.
0
(
/
s
t
n
e
v
E
1
10
2
10
3
10
C
σ
)/
π
C
θ
-
C
θ
(
-20
-10
0
10
)
5
.
0
(
/
s
t
n
e
v
E
1
10
2
10
3
10
(b)
FIG. 3 (color online).
(a)
E
and (b) Cherenkov angle
C
C
=
C
distributions for
D
h
candidates and PDF projec-
tions. Circles with error bars are data points. Shaded distribution
is the combinatorial background, the dotted curve adds the
D
contribution, and the solid curve is the full PDF. The dashed
curve represents the
D
K
contribution only.
E
for
D
is
centered near zero, while for
D
K
it is shifted to lower values
because the prompt track is assumed to be a pion.
)
2
(GeV/c
π
K
m
0.5
1
1.5
2
2.5
3
3.5
)
2
Events / ( 0.1 GeV/c
0
20
40
60
(a)
)
2
(GeV/c
π
D
m
2
2.5
3
3.5
4
4.5
(b)
FIG. 2 (color online).
The signal weight distribution as a
function of
m
K
and
m
D
0
. The shaded histograms include
only events with (a)
j
m
D
0
2460 MeV
=c
2
j
<
75 MeV
=c
2
,
and (b)
j
m
K
896 MeV
=c
2
j
<
150 MeV
=c
2
.
PRL
96,
011803 (2006)
PHYSICAL REVIEW LETTERS
week ending
13 JANUARY 2006
011803-6
The largest systematic uncertainties cancel in the
branching ratio measurement [sample (e)]. The remaining
systematic errors are from PDF shapes, control sample
distributions and contaminations (1.9%), residual uncer-
tainties in the signal efficiency ratio (2.4%), and potential
fit bias (2.1%). The last item has been evaluated with
simulation samples including background.
In conclusion, we have measured the branching fraction
for the
B
0
!
D
0
K
decay excluding
D
K
,
B
B
0
!
D
0
K
88
15
9
10
6
;
as well as its two significant resonances,
B
B
0
!
D
0
K
892
0
B
K
892
0
!
K
38
6
4
10
6
;
and
B
B
0
!
D
2
2460
K
B
D
2
2460
!
D
0
18
:
3
4
:
0
3
:
1
10
6
:
The signal significances are 8.7, 8.3, and 5.0 standard
deviations, respectively, determined from the change in
the likelihood between the best fit and a fit with the sig-
nal yield fixed to zero (the first case) or the possible cross
feed from other sources (six events for the latter two cases).
From a fit excluding the observed resonances, assuming
flat distriubtion on the Dalitz plot, we find
B
B
0
!
D
0
K
26
8
4
10
6
, whose signal signifi-
cance is
3
:
1
and 90% confidence level upper limit is
37
10
6
. We do not observe a significant signal for the CKM-
suppressed
B
0
!
D
0
K
mode. The 90% confidence
level upper limit is
B
B
0
!
D
0
K
<
19
10
6
.
The event yields in this channel are lower than anticipated
[5], indicating that a significantly larger data sample is
required to constrain
through this method.
The ratio of branching fractions for
B
0
!
D
K
to
B
0
!
D
is measured to be
r
7
:
76
0
:
34
0
:
29
%
;
a nearly fourfold improvement compared to the previous
result [8]. This ratio is consistent with
f
K
=f
2
tan
2
Cab
’
0
:
072
[18], expected at tree level if factorization and flavor-
SU(3) symmetry hold, where
Cab
is the Cabibbo angle and
f
K
and
f
are the decay constants of the kaon and pion,
respectively.
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.
*Also at Dipartimento di Fisica, Universita
`
di Perugia,
Perugia, Italy.
†
Also at Universita
`
della Basilicata, Potenza, Italy.
‡
Deceased.
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PRL
96,
011803 (2006)
PHYSICAL REVIEW LETTERS
week ending
13 JANUARY 2006
011803-7