of 9
Search for
b
!
u
transitions in
B
0
!
D
0
K

0
decays
B. Aubert,
1
M. Bona,
1
Y. Karyotakis,
1
J. P. Lees,
1
V. Poireau,
1
E. Prencipe,
1
X. Prudent,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
L. Lopez,
3a,3b
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
L. Sun,
4
G. S. Abrams,
5
M. Battaglia,
5
D. N. Brown,
5
R. N. Cahn,
5
R. G. Jacobsen,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
I. L. Osipenkov,
5
M. T. Ronan,
5,
*
K. Tackmann,
5
T. Tanabe,
5
C. M. Hawkes,
6
N. Soni,
6
A. T. Watson,
6
H. Koch,
7
T. Schroeder,
7
D. Walker,
8
D. J. Asgeirsson,
9
B. G. Fulsom,
9
C. Hearty,
9
T. S. Mattison,
9
J. A. McKenna,
9
M. Barrett,
10
A. Khan,
10
V. E. Blinov,
11
A. D. Bukin,
11
A. R. Buzykaev,
11
V. P. Druzhinin,
11
V. B. Golubev,
11
A. P. Onuchin,
11
S. I. Serednyakov,
11
Yu. I. Skovpen,
11
E. P. Solodov,
11
K. Yu. Todyshev,
11
M. Bondioli,
12
S. Curry,
12
I. Eschrich,
12
D. Kirkby,
12
A. J. Lankford,
12
P. Lund,
12
M. Mandelkern,
12
E. C. Martin,
12
D. P. Stoker,
12
S. Abachi,
13
C. Buchanan,
13
J. W. Gary,
14
F. Liu,
14
O. Long,
14
B. C. Shen,
14,
*
G. M. Vitug,
14
Z. Yasin,
14
L. Zhang,
14
V. Sharma,
15
C. Campagnari,
16
T. M. Hong,
16
D. Kovalskyi,
16
M. A. Mazur,
16
J. D. Richman,
16
T. W. Beck,
17
A. M. Eisner,
17
C. J. Flacco,
17
C. A. Heusch,
17
J. Kroseberg,
17
W. S. Lockman,
17
A. J. Martinez,
17
T. Schalk,
17
B. A. Schumm,
17
A. Seiden,
17
M. G. Wilson,
17
L. O. Winstrom,
17
C. H. Cheng,
18
D. A. Doll,
18
B. Echenard,
18
F. Fang,
18
D. G. Hitlin,
18
I. Narsky,
18
T. Piatenko,
18
F. C. Porter,
18
R. Andreassen,
19
G. Mancinelli,
19
B. T. Meadows,
19
K. Mishra,
19
M. D. Sokoloff,
19
P. C. Bloom,
20
W. T. Ford,
20
A. Gaz,
20
J. F. Hirschauer,
20
M. Nagel,
20
U. Nauenberg,
20
J. G. Smith,
20
K. A. Ulmer,
20
S. R. Wagner,
20
R. Ayad,
21,
A. Soffer,
21,
W. H. Toki,
21
R. J. Wilson,
21
D. D. Altenburg,
22
E. Feltresi,
22
A. Hauke,
22
H. Jasper,
22
M. Karbach,
22
J. Merkel,
22
A. Petzold,
22
B. Spaan,
22
K. Wacker,
22
M. J. Kobel,
23
W. F. Mader,
23
R. Nogowski,
23
K. R. Schubert,
23
R. Schwierz,
23
A. Volk,
23
D. Bernard,
24
G. R. Bonneaud,
24
E. Latour,
24
M. Verderi,
24
P. J. Clark,
25
S. Playfer,
25
J. E. Watson,
25
M. Andreotti,
26a,26b
D. Bettoni,
26a
C. Bozzi,
26a
R. Calabrese,
26a,26b
A. Cecchi,
26a,26b
G. Cibinetto,
26a,26b
P. Franchini,
26a,26b
E. Luppi,
26a,26b
M. Negrini,
26a,26b
A. Petrella,
26a,26b
L. Piemontese,
26a
V. Santoro,
26a,26b
R. Baldini-Ferroli,
27
A. Calcaterra,
27
R. de Sangro,
27
G. Finocchiaro,
27
S. Pacetti,
27
P. Patteri,
27
I. M. Peruzzi,
27,
x
M. Piccolo,
27
M. Rama,
27
A. Zallo,
27
A. Buzzo,
28a,28b
R. Contri,
28a,28b
M. Lo Vetere,
28a,28b
M. M. Macri,
28a
M. R. Monge,
28a,28b
S. Passaggio,
28a
C. Patrignani,
28a,28b
E. Robutti,
28a
A. Santroni,
28a,28b
S. Tosi,
28a,28b
K. S. Chaisanguanthum,
29
M. Morii,
29
A. Adametz,
30
J. Marks,
30
S. Schenk,
30
U. Uwer,
30
V. Klose,
31
H. M. Lacker,
31
D. J. Bard,
32
P. D. Dauncey,
32
J. A. Nash,
32
M. Tibbetts,
32
P. K. Behera,
33
X. Chai,
33
M. J. Charles,
33
U. Mallik,
33
J. Cochran,
34
H. B. Crawley,
34
L. Dong,
34
W. T. Meyer,
34
S. Prell,
34
E. I. Rosenberg,
34
A. E. Rubin,
34
Y. Y. Gao,
35
A. V. Gritsan,
35
Z. J. Guo,
35
C. K. Lae,
35
N. Arnaud,
36
J. Be
́
quilleux,
36
A. D’Orazio,
36
M. Davier,
36
J. Firmino da Costa,
36
G. Grosdidier,
36
A. Ho
̈
cker,
36
V. Lepeltier,
36
F. Le Diberder,
36
A. M. Lutz,
36
S. Pruvot,
36
P. Roudeau,
36
M. H. Schune,
36
J. Serrano,
36
V. Sordini,
36,
k
A. Stocchi,
36
G. Wormser,
36
D. J. Lange,
37
D. M. Wright,
37
I. Bingham,
38
J. P. Burke,
38
C. A. Chavez,
38
J. R. Fry,
38
E. Gabathuler,
38
R. Gamet,
38
D. E. Hutchcroft,
38
D. J. Payne,
38
C. Touramanis,
38
A. J. Bevan,
39
C. K. Clarke,
39
K. A. George,
39
F. Di Lodovico,
39
R. Sacco,
39
M. Sigamani,
39
G. Cowan,
40
H. U. Flaecher,
40
D. A. Hopkins,
40
S. Paramesvaran,
40
F. Salvatore,
40
A. C. Wren,
40
D. N. Brown,
41
C. L. Davis,
41
A. G. Denig,
42
M. Fritsch,
42
W. Gradl,
42
G. Schott,
42
K. E. Alwyn,
43
D. Bailey,
43
R. J. Barlow,
43
Y. M. Chia,
43
C. L. Edgar,
43
G. Jackson,
43
G. D. Lafferty,
43
T. J. West,
43
J. I. Yi,
43
J. Anderson,
44
C. Chen,
44
A. Jawahery,
44
D. A. Roberts,
44
G. Simi,
44
J. M. Tuggle,
44
C. Dallapiccola,
45
X. Li,
45
E. Salvati,
45
S. Saremi,
45
R. Cowan,
46
D. Dujmic,
46
P. H. Fisher,
46
G. Sciolla,
46
M. Spitznagel,
46
F. Taylor,
46
R. K. Yamamoto,
46
M. Zhao,
46
P. M. Patel,
47
S. H. Robertson,
47
A. Lazzaro,
48a,48b
V. Lombardo,
48a
F. Palombo,
48a,48b
J. M. Bauer,
49
L. Cremaldi,
49
R. Godang,
49,
{
R. Kroeger,
49
D. A. Sanders,
49
D. J. Summers,
49
H. W. Zhao,
49
M. Simard,
50
P. Taras,
50
F. B. Viaud,
50
H. Nicholson,
51
G. De Nardo,
52a,52b
L. Lista,
52a
D. Monorchio,
52a,52b
G. Onorato,
52a,52b
C. Sciacca,
52a,52b
G. Raven,
53
H. L. Snoek,
53
C. P. Jessop,
54
K. J. Knoepfel,
54
J. M. LoSecco,
54
W. F. Wang,
54
G. Benelli,
55
L. A. Corwin,
55
K. Honscheid,
55
H. Kagan,
55
R. Kass,
55
J. P. Morris,
55
A. M. Rahimi,
55
J. J. Regensburger,
55
S. J. Sekula,
55
Q. K. Wong,
55
N. L. Blount,
56
J. Brau,
56
R. Frey,
56
O. Igonkina,
56
J. A. Kolb,
56
M. Lu,
56
R. Rahmat,
56
N. B. Sinev,
56
D. Strom,
56
J. Strube,
56
E. Torrence,
56
G. Castelli,
57a,57b
N. Gagliardi,
57a,57b
M. Margoni,
57a,57b
M. Morandin,
57a
M. Posocco,
57a
M. Rotondo,
57a
F. Simonetto,
57a,57b
R. Stroili,
57a,57b
C. Voci,
57a,57b
P. del Amo Sanchez,
58
E. Ben-Haim,
58
H. Briand,
58
G. Calderini,
58
J. Chauveau,
58
P. David,
58
L. Del Buono,
58
O. Hamon,
58
Ph. Leruste,
58
J. Ocariz,
58
A. Perez,
58
J. Prendki,
58
S. Sitt,
58
L. Gladney,
59
M. Biasini,
60a,60b
R. Covarelli,
60a,60b
E. Manoni,
60a,60b
C. Angelini,
61a,61b
G. Batignani,
61a,61b
S. Bettarini,
61a,61b
M. Carpinelli,
61a,61b,
**
A. Cervelli,
61a,61b
F. Forti,
61a,61b
M. A. Giorgi,
61a,61b
A. Lusiani,
61a,61c
G. Marchiori,
61a,61b
M. Morganti,
61a,61b
N. Neri,
61a,61b
E. Paoloni,
61a,61b
G. Rizzo,
61a,61b
J. J. Walsh,
61a
D. Lopes Pegna,
62
C. Lu,
62
J. Olsen,
62
A. J. S. Smith,
62
A. V. Telnov,
62
F. Anulli,
63a
E. Baracchini,
63a,63b
G. Cavoto,
63a
D. del Re,
63a,63b
E. Di Marco,
63a,63b
R. Faccini,
63a,63b
F. Ferrarotto,
63a
F. Ferroni,
63a,63b
M. Gaspero,
63a,63b
P. D. Jackson,
63a
L. Li Gioi,
63a
M. A. Mazzoni,
63a
S. Morganti,
63a
PHYSICAL REVIEW D
80,
031102(R) (2009)
RAPID COMMUNICATIONS
1550-7998
=
2009
=
80(3)
=
031102(9)
031102-1
Ó
2009 The American Physical Society
G. Piredda,
63a
F. Polci,
63a,63b
F. Renga,
63a,63b
C. Voena,
63a
M. Ebert,
64
T. Hartmann,
64
H. Schro
̈
der,
64
R. Waldi,
64
T. Adye,
65
B. Franek,
65
E. O. Olaiya,
65
F. F. Wilson,
65
S. Emery,
66
M. Escalier,
66
L. Esteve,
66
S. F. Ganzhur,
66
G. Hamel de Monchenault,
66
W. Kozanecki,
66
G. Vasseur,
66
Ch. Ye
`
che,
66
M. Zito,
66
X. R. Chen,
67
H. Liu,
67
W. Park,
67
M. V. Purohit,
67
R. M. White,
67
J. R. Wilson,
67
M. T. Allen,
68
D. Aston,
68
R. Bartoldus,
68
P. Bechtle,
68
J. F. Benitez,
68
R. Cenci,
68
J. P. Coleman,
68
M. R. Convery,
68
J. C. Dingfelder,
68
J. Dorfan,
68
G. P. Dubois-Felsmann,
68
W. Dunwoodie,
68
R. C. Field,
68
A. M. Gabareen,
68
S. J. Gowdy,
68
M. T. Graham,
68
P. Grenier,
68
C. Hast,
68
W. R. Innes,
68
J. Kaminski,
68
M. H. Kelsey,
68
H. Kim,
68
P. Kim,
68
M. L. Kocian,
68
D. W. G. S. Leith,
68
S. Li,
68
B. Lindquist,
68
S. Luitz,
68
V. Luth,
68
H. L. Lynch,
68
D. B. MacFarlane,
68
H. Marsiske,
68
R. Messner,
68
D. R. Muller,
68
H. Neal,
68
S. Nelson,
68
C. P. O’Grady,
68
I. Ofte,
68
A. Perazzo,
68
M. Perl,
68
B. N. Ratcliff,
68
A. Roodman,
68
A. A. Salnikov,
68
R. H. Schindler,
68
J. Schwiening,
68
A. Snyder,
68
D. Su,
68
M. K. Sullivan,
68
K. Suzuki,
68
S. K. Swain,
68
J. M. Thompson,
68
J. Va’vra,
68
A. P. Wagner,
68
M. Weaver,
68
C. A. West,
68
W. J. Wisniewski,
68
M. Wittgen,
68
D. H. Wright,
68
H. W. Wulsin,
68
A. K. Yarritu,
68
K. Yi,
68
C. C. Young,
68
V. Ziegler,
68
P. R. Burchat,
69
A. J. Edwards,
69
S. A. Majewski,
69
T. S. Miyashita,
69
B. A. Petersen,
69
L. Wilden,
69
S. Ahmed,
70
M. S. Alam,
70
J. A. Ernst,
70
B. Pan,
70
M. A. Saeed,
70
S. B. Zain,
70
S. M. Spanier,
71
B. J. Wogsland,
71
R. Eckmann,
72
J. L. Ritchie,
72
A. M. Ruland,
72
C. J. Schilling,
72
R. F. Schwitters,
72
B. W. Drummond,
73
J. M. Izen,
73
X. C. Lou,
73
F. Bianchi,
74a,74b
D. Gamba,
74a,74b
M. Pelliccioni,
74a,74b
M. Bomben,
75a,75b
L. Bosisio,
75a,75b
C. Cartaro,
75a,75b
G. Della Ricca,
75a,75b
L. Lanceri,
75a,75b
L. Vitale,
75a,75b
V. Azzolini,
76
N. Lopez-March,
76
F. Martinez-Vidal,
76
D. A. Milanes,
76
A. Oyanguren,
76
J. Albert,
76
Sw. Banerjee,
76
B. Bhuyan,
76
H. H. F. Choi,
76
K. Hamano,
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
H. R. Band,
78
X. Chen,
78
S. Dasu,
78
K. T. Flood,
78
Y. Pan,
78
M. Pierini,
79
R. Prepost,
79
C. O. Vuosalo,
79
and S. L. Wu
79
(
B
A
B
AR
Collaboration)
1
Laboratoire de Physique des Particules, IN2P3/CNRS et Universite
́
de Savoie, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartmento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
University of Birmingham, Birmingham, B15 2TT, United Kingdom
7
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
8
University of Bristol, Bristol BS8 1TL, United Kingdom
9
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
10
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
11
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
12
University of California at Irvine, Irvine, California 92697, USA
13
University of California at Los Angeles, Los Angeles, California 90024, USA
14
University of California at Riverside, Riverside, California 92521, USA
15
University of California at San Diego, La Jolla, California 92093, USA
16
University of California at Santa Barbara, Santa Barbara, California 93106, USA
17
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
18
California Institute of Technology, Pasadena, California 91125, USA
19
University of Cincinnati, Cincinnati, Ohio 45221, USA
20
University of Colorado, Boulder, Colorado 80309, USA
21
Colorado State University, Fort Collins, Colorado 80523, USA
22
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
23
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
24
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
25
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
26a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
26b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
27
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
28a
INFN Sezione di Genova, I-16146 Genova, Italy
28b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
29
Harvard University, Cambridge, Massachusetts 02138, USA
30
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
B. AUBERT
et al.
PHYSICAL REVIEW D
80,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-2
31
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstr. 15, D-12489 Berlin, Germany
32
Imperial College London, London, SW7 2AZ, United Kingdom
33
University of Iowa, Iowa City, Iowa 52242, USA
34
Iowa State University, Ames, Iowa 50011-3160, USA
35
Johns Hopkins University, Baltimore, Maryland 21218, USA
36
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
37
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
38
University of Liverpool, Liverpool L69 7ZE, United Kingdom
39
Queen Mary, University of London, 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
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
43
University of Manchester, Manchester M13 9PL, United Kingdom
44
University of Maryland, College Park, Maryland 20742, USA
45
University of Massachusetts, Amherst, Massachusetts 01003, USA
46
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
47
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
48a
INFN Sezione di Milano, I-20133 Milano, Italy
48b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
49
University of Mississippi, University, Mississippi 38677, USA
50
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
51
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
52a
INFN Sezione di Napoli, I-80126 Napoli, Italy
52b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
53
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
54
University of Notre Dame, Notre Dame, Indiana 46556, USA
55
Ohio State University, Columbus, Ohio 43210, USA
56
University of Oregon, Eugene, Oregon 97403, USA
57a
INFN Sezione di Padova, I-35131 Padova, Italy
57b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
58
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
59
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
60a
INFN Sezione di Perugia, I-06100 Perugia, Italy
60b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
61a
INFN Sezione di Pisa, I-56127 Pisa, Italy
61b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
61c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
62
Princeton University, Princeton, New Jersey 08544, USA
63a
INFN Sezione di Roma, I-00185 Roma, Italy
63b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
64
Universita
̈
t Rostock, D-18051 Rostock, Germany
65
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
66
CEA, Irfu, SPP, Centre de 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
74a
INFN Sezione di Torino, I-10125 Torino, Italy
k
Also with Universita
`
di Roma La Sapienza, I-00185 Roma, Italy.
**
Also with Universita
`
di Sassari, Sassari, Italy.
x
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
Now at Tel Aviv University, Tel Aviv, 69978, Israel.
Now at Temple University, Philadelphia, PA 19122, USA.
{
Now at University of South Alabama, Mobile, AL 36688, USA
*
Deceased.
SEARCH FOR
b
!
u
TRANSITIONS IN
...
PHYSICAL REVIEW D
80,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-3
74b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
75a
INFN Sezione di Trieste, I-34127 Trieste, Italy
75b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
76
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
77
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
78
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
79
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 15 April 2009; published 5 August 2009)
We present a study of the decays
B
0
!
D
0
K

0
and
B
0
!

D
0
K

0
with
K

0
!
K
þ


. The
D
0
and the

D
0
mesons are reconstructed in the final states
f
¼
K
þ


,
K
þ



0
,
K
þ



þ


, and their charge
conjugates. Using a sample of
465

10
6
B

B
pairs collected with the
BABAR
detector at the PEP-II
asymmetric-energy
e
þ
e

collider at SLAC, we measure the ratio
R
ADS

ð

B
0
f

D

K

0
Þþ

ð
B
0

f

D
K

0
Þ
=
½

ð

B
0

f

D

K

0
Þþ

ð
B
0
f

D
K

0
Þ
for the three final states. We do not find significant
evidence for a signal and set the following limits at 95% probability:
R
ADS
ð
K
Þ
<
0
:
244
,
R
ADS
ð
K
0
Þ
<
0
:
181
, and
R
ADS
ð
K
Þ
<
0
:
391
. From the combination of these three results, we find that the ratio
r
S
between the
b
!
u
and the
b
!
c
amplitudes lies in the range [0.07,0.41] at 95% probability.
DOI:
10.1103/PhysRevD.80.031102
PACS numbers: 13.25.Hw, 14.40.Nd
Various methods have been proposed to determine the
unitarity triangle angle

[
1
3
] of the Cabibbo-Kobayashi-
Maskawa (CKM) quark mixing matrix [
4
] using
B

!
~
D
ðÞ
0
K
ðÞ
decays, where the symbol
~
D
ðÞ
0
indicates either
a
D
ðÞ
0
or a

D
ðÞ
0
meson. A
B

meson can decay into a
~
D
ðÞ
0
K
ðÞ
final state via a
b
!
c
or a
b
!
u
process.
CP
violation may occur due to interference between the am-
plitudes when the
D
ðÞ
0
and

D
ðÞ
0
decay to the same final
state. These processes are thus sensitive to

¼
arg
f
V

ub
V
ud
=V

cb
V
cd
g
. The sensitivity to

is proportional
to the ratio between the
b
!
u
and
b
!
c
transition am-
plitudes (
r
B
), which depends on the
B
decay channel and
needs to be determined experimentally.
In this paper we consider an alternative approach, based
on neutral
B
mesons, which is similar to the Atwood-
Dunietz-Soni (ADS) method [
2
] originally proposed for
charged
B

!
~
D
ðÞ
0
K
ðÞ
decays. We consider the decay
channel
B
0
!
~
D
0
K

0
with
K

0
!
K
þ


[charge conju-
gate processes are assumed throughout the paper and
K

0
refers to the
K

ð
892
Þ
0
]. This final state can be reached
through
b
!
c
and
b
!
u
processes as shown in Fig.
1
.
The flavor of the
B
meson is identified by the charge of the
kaon produced in the
K

0
decay. The neutral
D
mesons are
reconstructed in three final states,
f
¼
K
þ


,
K
þ



0
,
K
þ



þ


. We search for
B
0

f

D
½
K
þ



K

0
events,
where the CKM-favored
B
0
!

D
0
K

0
decay, followed by
the doubly Cabibbo-suppressed

D
0
!

f
decay, interferes
with the CKM-suppressed
B
0
!
D
0
K

0
decay, followed
by the Cabibbo-favored
D
0
!

f
decay. These are called
‘‘opposite-sign’’ events because the two kaons in the final
state have opposite charges. We also reconstruct a larger
sample of ‘‘same-sign’’ events, which mainly arise from
CKM-favored
B
0
!

D
0
K

0
decays followed by Cabibbo-
favored

D
0
!
f
decays.
In order to reduce the systematic uncertainties, we mea-
sure ratios of decay rates
R
ADS


ð

B
0
f

D

K

0
Þþ

ð
B
0

f

D
K

0
Þ

ð

B
0

f

D

K

0
Þþ

ð
B
0
f

D
K

0
Þ
;
(1)
A
ADS


ð

B
0
f

D

K

0
Þ

ð
B
0

f

D
K

0
Þ

ð

B
0
f

D

K

0
Þþ

ð
B
0

f

D
K

0
Þ
;
(2)
where
R
ADS
is the ratio between opposite- and same-sign
events.
The
K

0
resonance has a natural width (
50 MeV
=c
2
) that
is larger than the experimental resolution. This introduces a
phase difference between the various amplitudes. We
therefore introduce effective variables
r
S
,
k
, and

S
[
5
],
obtained by integrating over the region of the
B
0
!
~
D
0
K
þ


Dalitz plot dominated by the
K

0
resonance,
defined as follows:
r
2
S


ð
B
0
!
D
0
K
þ


Þ

ð
B
0
!

D
0
K
þ


Þ
¼
R
dpA
2
u
ð
p
Þ
R
dpA
2
c
ð
p
Þ
;
(3)
ke
i
S

R
dpA
c
ð
p
Þ
A
u
ð
p
Þ
e
i
ð
p
Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
R
dpA
2
c
ð
p
Þ
R
dpA
2
u
ð
p
Þ
q
:
(4)
From their definition,
0

k

1
and

S
0
;
2


. The
amplitudes for the
b
!
c
and
b
!
u
transitions,
A
c
ð
p
Þ
and
A
u
ð
p
Þ
, are real and positive and

ð
p
Þ
is the relative strong
phase. The variable
p
indicates the position in the
FIG. 1. Feynman diagrams for
B
0
!

D
0
K

0
(left,

b
!

c
tran-
sition) and
B
0
!
D
0
K

0
(right,

b
!

u
transition).
B. AUBERT
et al.
PHYSICAL REVIEW D
80,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-4
~
D
0
K
þ


Dalitz plot. The parameter
k
accounts for con-
tributions, in the
K

0
mass region, of higher-mass reso-
nances. In the case of a two-body
B
decay,
r
S
and

S
become
r
B
¼
A
u
=A
c
and

B
(the strong phase difference
between
A
u
and
A
c
) with
k
¼
1
. As shown in [
6
], the
distribution of
k
can be obtained by simulation studies
based on realistic models for the different resonance con-
tributions to the decays of neutral
B
mesons into
~
D
0
K



final states. When considering the region in the
B
0
!
~
D
0
K
þ


Dalitz plane where the invariant mass of the
kaon and the pion is within
48 MeV
=c
2
of the nominal
K

0
mass [
7
], the distribution of
k
is narrow, and is centered
at 0.95 with a root-mean-square width of 0.03.
Because of CKM factors and the fact that both diagrams
in Fig.
1
are color-suppressed, the average amplitude ratio
r
S
in
B
0
!
~
D
0
K

0
is expected to be of order 0.3, larger than
the analogous ratio for the charged
B

!
D
0
ðÞ
K
ðÞ
de-
cays, which is of order 0.1 [
8
,
9
]. This implies better
sensitivity to

for the same number of events, an expec-
tation that applies to all
B
0
!
D
0
ðÞ
K
ðÞ
0
decays, and that
motivates the use of neutral
B
meson decays to determine

. Currently, the experimental knowledge of
r
S
[
6
,
10
]is
r
S
<
0
:
54
at 95% probability.
The ratios
R
ADS
and
A
ADS
are related to
r
S
,

,
k
, and

S
through the following relations:
R
ADS
¼
r
2
S
þ
r
2
D
þ
2
kk
D
r
S
r
D
cos

cos
ð

S
þ

D
Þ
;
(5)
A
ADS
¼
2
kk
D
r
S
r
D
sin

sin
ð

S
þ

D
Þ
=R
ADS
;
(6)
where
r
2
D


ð
D
0
!
f
Þ

ð
D
0
!

f
Þ
¼
R
dmA
2
DCS
ð
m
Þ
R
dmA
2
CF
ð
m
Þ
;
(7)
k
D
e
i
D

R
dmA
CF
ð
m
Þ
A
DCS
ð
m
Þ
e
i
ð
m
Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
R
dmA
2
CF
ð
m
Þ
R
dmA
2
DCS
ð
m
Þ
q
;
(8)
with
0

k
D

1
,

D
0
;
2


,
A
CF
ð
m
Þ
and
A
DCS
ð
m
Þ
the
magnitudes of the Cabibbo-favored and the doubly
Cabibbo-suppressed amplitudes,

ð
m
Þ
the relative strong
phase, and the variable
m
the position in the
D
Dalitz plot.
In the case of a two-body
D
decay,
k
D
¼
1
,
r
D
is the ratio
between the doubly Cabibbo-suppressed and the Cabibbo-
favored decay amplitudes and

D
is the relative strong
phase.
Determining
r
S
,

, and

S
from the measurements of
R
ADS
and
A
ADS
, with the factor
k
fixed, requires knowledge
of the parameters (
k
D
,
r
D
,

D
), which depend on the
specific neutral
D
meson final states. The ratios
r
D
for
the three
D
decay modes have been measured [
7
], as has
the strong phase

D
for the
K
mode [
11
]. In addition,
experimental information is available on
k
D
and

D
for the
K
0
and
K
modes [
12
]. The smallness of the
r
D
ratios implies good sensitivity to
r
S
from a measurement of
R
ADS
. For the same reason, and since, with the present
statistics, the asymmetries
A
ADS
cannot be extracted from
data, the sensitivity to

is reduced. The aim of this
analysis is therefore the measurement of
r
S
. In the future,
good knowledge of all the
r
D
,
k
D
and

D
parameters, and a
precise measurement of the
R
ADS
ratios for the three chan-
nels, will allow

and

S
to be determined from this
method as well.
The results presented here are obtained with
423 fb

1
of
data collected at the

ð
4
S
Þ
resonance with the
BABAR
detector at the PEP-II
e
þ
e

collider at SLAC [
13
], corre-
sponding to
465

10
6
B

B
events. An additional ‘‘off-
resonance’’ data sample of
41
:
3fb

1
, collected at a
center-of-mass (CM) energy 40 MeV below the

ð
4
S
Þ
resonance, is used to study backgrounds from continuum
events,
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
,or
c
). The
BABAR
detec-
tor is described elsewhere [
14
].
The event selection is based on studies of off-resonance
data and Monte Carlo (MC) simulations of continuum and
e
þ
e

!

ð
4
S
Þ!
B

B
events. All the selection criteria are
optimized by maximizing the function
S=
ffiffiffiffiffiffiffiffiffiffiffiffiffi
S
þ
B
p
on
opposite-sign events, where
S
and
B
are the expected
numbers of opposite-sign signal and background events,
respectively.
The neutral
D
mesons are reconstructed from a charged
kaon and one or three charged pions and, in the
K
0
mode, a neutral pion. The

0
candidates are reconstructed
from pairs of photon candidates, each with energy greater
than 70 MeV, total energy greater than 200 MeV, and
invariant mass in the interval
½
118
;
145

MeV
=c
2
. The

0
candidate’s mass is subsequently constrained to its nominal
value [
7
].
The invariant mass of the particles used to reconstruct
the
D
is required to lie within
14 MeV
=c
2
(
1
:
9

),
20 MeV
=c
2
(
1
:
5

), and
9 MeV
=c
2
(
1
:
6

) of the
nominal
D
0
mass, for the
K
,
K
0
, and
K
modes,
respectively. For the
K
mode we also require that the
tracks originate from a single vertex with a probability
greater than 0.1%.
The tracks used to reconstruct the
K

0
are constrained to
originate from a common vertex and their invariant mass is
required to lie within
48 MeV
=c
2
of the nominal
K

0
mass
[
7
]. We define

H
as the angle between the direction of
flight of the
K
and
B
in the
K

0
rest frame. The distribution
of
cos

H
is proportional to
cos
2

H
for signal events and is
expected to be flat for background events. We require
j
cos

H
j
>
0
:
3
. The charged kaons used to reconstruct the
~
D
0
and
K

0
mesons are required to satisfy kaon identifica-
tion criteria, based on Cherenkov angle and
dE=dx
mea-
surements and are typically 85% efficient, depending on
momentum and polar angle. Misidentification rates are at
the 2% level.
The
B
0
candidates are reconstructed by combining a
~
D
0
and
K

0
candidate, constraining them to originate from a
common vertex with a probability greater than 0.1%. In
forming the
B
, the
D
mass is constrained to its nominal
value [
7
]. The distribution of the cosine of the
B
polar
SEARCH FOR
b
!
u
TRANSITIONS IN
...
PHYSICAL REVIEW D
80,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-5
angle with respect to the beam axis in the
e
þ
e

CM frame
cos

B
is expected to be proportional to
1

cos
2

B
.We
require
j
cos

B
j
<
0
:
9
. We measure two almost indepen-
dent kinematic variables: the beam-energy substituted
mass
m
ES

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
E

2
0
=
2
þ
~
p
0
~
p
B
Þ
2
=E
2
0

p
2
B
q
, and the en-
ergy difference

E

E

B

E

0
=
2
, where
E
and
p
are
energy and momentum, the subscripts
B
and
0
refer to
the candidate
B
and
e
þ
e

system, respectively, and the
asterisk denotes the
e
þ
e

CM frame. The distributions of
m
ES
and

E
peak at the
B
mass and zero, respectively, for
correctly reconstructed
B
mesons. The
B
candidates
are required to have

E
in the range
½
16
;
16

MeV
(
1
:
3

),
½
20
;
20

MeV
(
1
:
5

), and
½
19
;
19

MeV
(
1
:
4

) for the
K
,
K
0
, and
K
modes, respec-
tively. Finally we consider events with
m
ES
in the range
½
5
:
20
;
5
:
29

GeV
=c
2
.
We examine background
B
decays that have the same
final state reconstructed particles as the signal decay to
identify modes with peaking structure in
m
ES
or

E
that
can potentially mimic signal events. We identify three such
‘‘peaking background’’ modes in the opposite-sign sample:
B
0
!
D

½
K

0
K



þ
(for
K
),
B
0
!
D

½
K

0
K



þ
½

þ

0

(for
K
0
), and
B
0
!
D

½
K

0
K


a
þ
1
½

þ

þ



(for
K
). To reduce their contribution
we veto all candidates for which the invariant mass of the
K

0
and the
K

from the
D
0
lies within
6 MeV
=c
2
of the
nominal
D

mass.
After imposing the vetoes, the contributions of the peak-
ing backgrounds to the
K
,
K
0
, and
K
samples
are predicted to be less than 0.07, 0.05, and 0.12 events,
respectively, at 95% probability. Other possible sources
of peaking background are
B
0
!
D
0

0
and
B
0
!
D

½
D
0




þ
, which contribute to the three decay modes
in both the same- and opposite-sign samples. These events
could be reconstructed as signal, due to misidentification of
a

as a
K
. We impose additional restrictions on the
identification criteria of charged kaons from
K

decays to
reduce the contribution of these backgrounds to a negli-
gible level. Charmless
B
decays, like
B
0
!
K

0
K
, can
also contribute. The number of expected charmless back-
ground events, evaluated with data from the
~
D
0
mass side-
bands, is
N
peak
¼
0
:
5

0
:
5
(
0
:
1

1
:
2
) in the same
(opposite) sign samples.
In case of multiple
D
candidates (less than 1% of
events), we choose the one with reconstructed
~
D
0
mass
closest to the nominal mass [
7
]. In the case of two
B
candidates reconstructed from the same
~
D
0
, we choose
the candidate with the largest value of
j
cos

H
j
.
The overall reconstruction efficiencies for signal events
are
ð
13
:
2

0
:
1
Þ
%
,
ð
5
:
2

0
:
1
Þ
%
, and
ð
6
:
5

0
:
1
Þ
%
for the
K
,
K
0
, and
K
modes, respectively.
After applying the selection criteria described above, the
remaining background is composed of continuum events
and combinatorial
B

B
events. To discriminate against the
continuum background events (the dominant background
component), which, in contrast to
B

B
events, have a jetlike
shape, we use a Fisher discriminant
F
[
15
]. The discrimi-
nant
F
is a linear combination of four variables calculated
in the CM frame. The first discriminant variable is the
cosine of the angle between the
B
thrust axis and the thrust
axis of the rest of the event. The second and third variables
are
L
0
¼
P
i
p
i
, and
L
2
¼
P
i
p
i
j
cos

i
j
2
, where the index
i
runs over all the reconstructed tracks and energy deposits
in the calorimeter not associated with a track, the tracks
and energy deposits used to reconstruct the
B
are excluded,
p
i
is the momentum, and

i
is the angle with respect to the
thrust axis of the
B
candidate. The fourth variable is
j

t
j
,
the absolute value of the measured proper time interval
between the
B
and

B
decays, calculated from the measured
separation between the decay points of the
B
and

B
along
the beam direction.
The coefficients of
F
, chosen to maximize the separa-
tion between signal and continuum background, are deter-
mined using samples of simulated signal and continuum
events and validated using off-resonance data.
The signal and background yields are extracted, sepa-
rately for each channel, by maximizing the extended like-
lihood
L
¼ð
e

N
0
Þ
=
ð
N
!
Þ
N
0
N
Q
N
j
¼
1
f
ð
x
j
j
; N
0
Þ
. Here
x
j
¼f
m
ES
;
F
g
,

is a set of parameters,
N
is the number
of events in the selected sample, and
N
0
is the expectation
value for the total number of events. The term
f
ð
x
j
; N
0
Þ
is defined as
f
ð
x
j
; N
0
Þ
N
0
¼
R
ADS
N
DK

1
þ
R
ADS
f
OS
SIG
ð
x
j

OS
SIG
Þþ
N
DK

1
þ
R
ADS
f
SS
SIG
ð
x
j

SS
SIG
Þ
þ
N
OS
cont
f
OS
cont
ð
x
j

OS
cont
Þþ
N
SS
cont
f
SS
cont
ð
x
j

SS
cont
Þ
þ
N
OS
B
B
f
OS
B
B
ð
x
j

OS
B
B
Þþ
N
SS
B
B
f
SS
B
B
ð
x
j

SS
B
B
Þ
;
(9)
where
N
DK

is the total number of signal events,
R
ADS
is
the ratio between opposite- and same-sign signal events,
and
N
SS
cont
,
N
OS
cont
,
N
SS
B
B
, and
N
OS
B
B
are the number of same-
and opposite-sign events for continuum and
B
B
back-
grounds. The probability density functions (PDFs)
f
are
derived from MC and are defined as the product of one-
dimensional distributions of
m
ES
and
F
. The
m
ES
distri-
butions are modeled with a Gaussian for signal, and thresh-
old functions with different parameters for the continuum
and
B

B
backgrounds. The threshold function is expressed
as follows:
A
ð
x
Þ¼
x
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1


x
x
0

2
s
e
c
ð
1
x=x
0
Þ
2
Þ
;
(10)
where
x
0
represents the maximum allowed value for the
variable
x
described by
A
ð
x
Þ
and
c
accounts for the shape of
the distribution. The
F
distributions are modeled with
Gaussians.
From the fit to data we extract
N
DK

,
R
ADS
, and the
background yields (
N
SS
cont
,
N
OS
cont
,
N
SS
B

B
, and
N
OS
B

B
). We allow
B. AUBERT
et al.
PHYSICAL REVIEW D
80,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-6
the mean of the signal
m
ES
PDF and parameters of the
continuum
m
ES
PDFs to float.
The fitting procedure is validated using ensembles of
simulated events. A large number of pseudoexperiments is
generated with probability density functions and parame-
ters as obtained from the fit to the data. The fitting proce-
dure is then performed on these samples. We find no bias
on the number of fitted events for any of the components.
The results for
N
DK

,
R
ADS
, and the background yields
are summarized in Table
I
. The total number of opposite-
sign signal events in the three channels is
N
OS
SIG
¼
24
:
4
þ
13
:
7

10
:
9
(statistical uncertainty only). Projections of the fit onto the
variable
m
ES
are shown in Fig.
2
for the opposite- and
same-sign samples. To enhance the visibility of the signal,
events are required to satisfy
F
>
0
:
5
for
K
,
F
>
0
:
7
for
K
0
, and
F
>
1
for
K
. These requirements have an
efficiency of about 67%, 67%, and 50% for signal and 9%,
5%, and 3% for continuum background.
The systematic uncertainties on
R
ADS
are summarized in
Table
II
. To evaluate the contributions related to the
m
ES
and
F
PDFs, we repeat the fit by varying all the PDF
parameters that are fixed in the final fit within their statis-
tical errors, as obtained from the parametrization on simu-
lated events. To evaluate the uncertainty arising from the
assumption of negligible peaking background contribu-
tions, we repeat the fit by varying the number of these
events within their statistical errors. In this evaluation, we
consider all the possible sources of such backgrounds,
coming from charmless
B
decays and from
B
decays
with a
D
meson in the final state, as discussed above. For
the multibody
D
decays, the selection efficiency on same-
and opposite-sign events has been confirmed to be the
same, regardless of the difference in the Dalitz structure,
within a relative error of 3%. Finally, a systematic uncer-
tainty associated with cross feed between same- and
opposite-sign events is evaluated from MC studies to be
ð
3
:
5

0
:
5
Þ
%
,
ð
4
:
6

0
:
6
Þ
%
, and
ð
1
:
9

0
:
4
Þ
%
for the
K
,
K
0
, and
K
modes, respectively. The total system-
atic uncertainties are defined by adding the individual
terms in quadrature.
The final likelihood
L
ð
R
ADS
Þ
for each decay mode is
obtained by convolving the likelihood returned by the fit
with a Gaussian whose width equals the systematic uncer-
tainty. Figure
3
shows
L
ð
R
ADS
Þ
for all three channels,
where we exclude the unphysical region
R
ADS

0
. The
TABLE I. Fit results for
N
DK

,
R
ADS
and the number of
background events, for the three channels. The uncertainties
are statistical only.
channel
K
K
0
K
N
DK

74

12
146

17
101

17
R
ADS
0
:
067
þ
0
:
070

0
:
054
0
:
060
þ
0
:
055

0
:
037
0
:
137
þ
0
:
113

0
:
095
N
SS
B

B
75

16
265

33
345

35
N
OS
B

B
40

17
215

41
327

48
N
SS
cont
387

22
2497

56
2058

53
N
OS
cont
1602

41
7793

96
6372

91
]
2
[GeV/c
ES
m
5.2
5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Events / ( 0.00375 )
0
5
10
15
20
25
30
35
]
2
[GeV/c
ES
m
5.2
5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Events / ( 0.0036 )
0
10
20
30
40
50
60
]
2
[GeV/c
ES
m
5.2
5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Events / ( 0.0036 )
0
5
10
15
20
25
30
]
2
[GeV/c
ES
m
5.2
5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Events / ( 0.0036 )
0
2
4
6
8
10
12
14
]
2
[GeV/c
ES
m
5.2
5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Events / ( 0.0036 )
0
5
10
15
20
25
30
35
40
]
2
[GeV/c
ES
m
5.2
5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29
Events / ( 0.0036 )
0
2
4
6
8
10
12
14
16
18
FIG. 2 (color online). Projections of the fit onto the variable
m
ES
after a cut on
F
is applied (
>
0
:
5
for
K
,
>
0
:
7
for
K
0
, and
>
1
for
K
), to enhance the signal. The plots are shown for
K
(left),
K
0
(middle), and
K
(right), same-sign (top) and
opposite-sign (bottom) events. The points with error bars are data. The dashed, dotted, and dash-dotted lines represent the signal,
continuum background, and
B

B
background contributions, respectively. The solid line represents the sum of all the contributions.
TABLE II. Systematic uncertainties

R
ADS
, in units of
½
10

2

,
for
R
K
ADS
,
R
K
0
ADS
, and
R
K
ADS
.
Source
K
K
0
K
Sig. PDF
0.19
0.11
0.82
Cont. PDF
0.32
0.02
0.29
B

B
PDF
0.57
0.16
1.48
Peaking background
1.70
0.87
1.40

CF
=
DCS
0.17
0.39
Cross feed
0.04
0,05
0.02
TOTAL
1.8
0.91
2.2
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...
PHYSICAL REVIEW D
80,
031102(R) (2009)
RAPID COMMUNICATIONS
031102-7