of 18
Search for
b
!
u
transitions in
B

!
DK

and
D

K

decays
P. del Amo Sanchez,
1
J. P. Lees,
1
V. Poireau,
1
E. Prencipe,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
M. Martinelli,
3a,3b
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
L. Sun,
4
M. Battaglia,
5
D. N. Brown,
5
B. Hooberman,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
I. L. Osipenkov,
5
T. Tanabe,
5
C. M. Hawkes,
6
A. T. Watson,
6
H. Koch,
7
T. Schroeder,
7
D. J. Asgeirsson,
8
C. Hearty,
8
T. S. Mattison,
8
J. A. McKenna,
8
A. Khan,
9
A. Randle-Conde,
9
V. E. Blinov,
10
A. R. Buzykaev,
10
V. P. Druzhinin,
10
V. B. Golubev,
10
A. P. Onuchin,
10
S. I. Serednyakov,
10
Yu. I. Skovpen,
10
E. P. Solodov,
10
K. Yu. Todyshev,
10
A. N. Yushkov,
10
M. Bondioli,
11
S. Curry,
11
D. Kirkby,
11
A. J. Lankford,
11
M. Mandelkern,
11
E. C. Martin,
11
D. P. Stoker,
11
H. Atmacan,
12
J. W. Gary,
12
F. Liu,
12
O. Long,
12
G. M. Vitug,
12
C. Campagnari,
13
T. M. Hong,
13
D. Kovalskyi,
13
J. D. Richman,
13
A. M. Eisner,
14
C. A. Heusch,
14
J. Kroseberg,
14
W. S. Lockman,
14
A. J. Martinez,
14
T. Schalk,
14
B. A. Schumm,
14
A. Seiden,
14
L. O. Winstrom,
14
C. H. Cheng,
15
D. A. Doll,
15
B. Echenard,
15
D. G. Hitlin,
15
P. Ongmongkolkul,
15
F. C. Porter,
15
A. Y. Rakitin,
15
R. Andreassen,
16
M. S. Dubrovin,
16
G. Mancinelli,
16
B. T. Meadows,
16
M. D. Sokoloff,
16
P. C. Bloom,
17
W. T. Ford,
17
A. Gaz,
17
J. F. Hirschauer,
17
M. Nagel,
17
U. Nauenberg,
17
J. G. Smith,
17
S. R. Wagner,
17
R. Ayad,
18,
*
W. H. Toki,
18
H. Jasper,
19
T. M. Karbach,
19
J. Merkel,
19
A. Petzold,
19
B. Spaan,
19
K. Wacker,
19
M. J. Kobel,
20
K. R. Schubert,
20
R. Schwierz,
20
D. Bernard,
21
M. Verderi,
21
P. J. Clark,
22
S. Playfer,
22
J. E. Watson,
22
M. Andreotti,
23a,23b
D. Bettoni,
23a
C. Bozzi,
23a
R. Calabrese,
23a,23b
A. Cecchi,
23a,23b
G. Cibinetto,
23a,23b
E. Fioravanti,
23a,23b
P. Franchini,
23a,23b
E. Luppi,
23a,23b
M. Munerato,
23a,23b
M. Negrini,
23a,23b
A. Petrella,
23a,23b
L. Piemontese,
23a
R. Baldini-Ferroli,
24
A. Calcaterra,
24
R. de Sangro,
24
G. Finocchiaro,
24
M. Nicolaci,
24
S. Pacetti,
24
P. Patteri,
24
I. M. Peruzzi,
24,
M. Piccolo,
24
M. Rama,
24
A. Zallo,
24
R. Contri,
25a,25b
E. Guido,
25a,25b
M. Lo Vetere,
25a,25b
M. R. Monge,
25a,25b
S. Passaggio,
25a
C. Patrignani,
25a,25b
E. Robutti,
25a
S. Tosi,
25a,25b
B. Bhuyan,
26
C. L. Lee,
27
M. Morii,
27
A. Adametz,
28
J. Marks,
28
S. Schenk,
28
U. Uwer,
28
F. U. Bernlochner,
29
M. Ebert,
29
H. M. Lacker,
29
T. Lueck,
29
A. Volk,
29
P. D. Dauncey,
30
M. Tibbetts,
30
P. K. Behera,
31
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
H. B. Crawley,
32
L. Dong,
32
W. T. Meyer,
32
S. Prell,
32
E. I. Rosenberg,
32
A. E. Rubin,
32
Y. Y. Gao,
33
A. V. Gritsan,
33
Z. J. Guo,
33
N. Arnaud,
34
M. Davier,
34
D. Derkach,
34
J. Firmino da Costa,
34
G. Grosdidier,
34
F. Le Diberder,
34
A. M. Lutz,
34
B. Malaescu,
34
A. Perez,
34
P. Roudeau,
34
M. H. Schune,
34
J. Serrano,
34
V. Sordini,
34,
A. Stocchi,
34
L. Wang,
34
G. Wormser,
34
D. J. Lange,
35
D. M. Wright,
35
I. Bingham,
36
J. P. Burke,
36
C. A. Chavez,
36
J. P. Coleman,
36
J. R. Fry,
36
E. Gabathuler,
36
R. Gamet,
36
D. E. Hutchcroft,
36
D. J. Payne,
36
C. Touramanis,
36
A. J. Bevan,
37
F. Di Lodovico,
37
R. Sacco,
37
M. Sigamani,
37
G. Cowan,
38
S. Paramesvaran,
38
A. C. Wren,
38
D. N. Brown,
39
C. L. Davis,
39
A. G. Denig,
40
M. Fritsch,
40
W. Gradl,
40
A. Hafner,
40
K. E. Alwyn,
41
D. Bailey,
41
R. J. Barlow,
41
G. Jackson,
41
G. D. Lafferty,
41
T. J. West,
41
J. Anderson,
42
R. Cenci,
42
A. Jawahery,
42
D. A. Roberts,
42
G. Simi,
42
J. M. Tuggle,
42
C. Dallapiccola,
43
E. Salvati,
43
R. Cowan,
44
D. Dujmic,
44
P. H. Fisher,
44
G. Sciolla,
44
M. Zhao,
44
D. Lindemann,
45
P. M. Patel,
45
S. H. Robertson,
45
M. Schram,
45
P. Biassoni,
46a,46b
A. Lazzaro,
46a,46b
V. Lombardo,
46a
F. Palombo,
46a,46b
S. Stracka,
46a,46b
L. Cremaldi,
47
R. Godang,
47,
x
R. Kroeger,
47
P. Sonnek,
47
D. J. Summers,
47
X. Nguyen,
48
M. Simard,
48
P. Taras,
48
G. De Nardo,
49a,49b
D. Monorchio,
49a,49b
G. Onorato,
49a,49b
C. Sciacca,
49a,49b
G. Raven,
50
H. L. Snoek,
50
C. P. Jessop,
51
K. J. Knoepfel,
51
J. M. LoSecco,
51
W. F. Wang,
51
L. A. Corwin,
52
K. Honscheid,
52
R. Kass,
52
J. P. Morris,
52
A. M. Rahimi,
52
N. L. Blount,
53
J. Brau,
53
R. Frey,
53
O. Igonkina,
53
J. A. Kolb,
53
R. Rahmat,
53
N. B. Sinev,
53
D. Strom,
53
J. Strube,
53
E. Torrence,
53
G. Castelli,
54a,54b
E. Feltresi,
54a,54b
N. Gagliardi,
54a,54b
M. Margoni,
54a,54b
M. Morandin,
54a
M. Posocco,
54a
M. Rotondo,
54a
F. Simonetto,
54a,54b
R. Stroili,
54a,54b
E. Ben-Haim,
55
G. R. Bonneaud,
55
H. Briand,
55
G. Calderini,
55
J. Chauveau,
55
O. Hamon,
55
Ph. Leruste,
55
G. Marchiori,
55
J. Ocariz,
55
J. Prendki,
55
S. Sitt,
55
M. Biasini,
56a,56b
E. Manoni,
56a,56b
C. Angelini,
57a,57b
G. Batignani,
57a,57b
S. Bettarini,
57a,57b
M. Carpinelli,
57a,57b,
k
G. Casarosa,
57a,57b
A. Cervelli,
57a,57b
F. Forti,
57a,57b
M. A. Giorgi,
57a,57b
A. Lusiani,
57a,57c
N. Neri,
57a,57b
E. Paoloni,
57a,57b
G. Rizzo,
57a,57b
J. J. Walsh,
57a
D. Lopes Pegna,
58
C. Lu,
58
J. Olsen,
58
A. J. S. Smith,
58
A. V. Telnov,
58
F. Anulli,
59a
E. Baracchini,
59a,59b
G. Cavoto,
59a
R. Faccini,
59a,59b
F. Ferrarotto,
59a
F. Ferroni,
59a,59b
M. Gaspero,
59a,59b
L. Li Gioi,
59a
M. A. Mazzoni,
59a
G. Piredda,
59a
F. Renga,
59a,59b
T. Hartmann,
60
T. Leddig,
60
H. Schro
̈
der,
60
R. Waldi,
60
T. Adye,
61
B. Franek,
61
E. O. Olaiya,
61
F. F. Wilson,
61
S. Emery,
62
G. Hamel de Monchenault,
62
G. Vasseur,
62
Ch. Ye
`
che,
62
M. Zito,
62
M. T. Allen,
63
D. Aston,
63
D. J. Bard,
63
R. Bartoldus,
63
J. F. Benitez,
63
C. Cartaro,
63
M. R. Convery,
63
J. Dorfan,
63
G. P. Dubois-Felsmann,
63
W. Dunwoodie,
63
R. C. Field,
63
M. Franco Sevilla,
63
B. G. Fulsom,
63
A. M. Gabareen,
63
M. T. Graham,
63
P. Grenier,
63
C. Hast,
63
W. R. Innes,
63
M. H. Kelsey,
63
H. Kim,
63
P. Kim,
63
M. L. Kocian,
63
D. W. G. S. Leith,
63
S. Li,
63
B. Lindquist,
63
S. Luitz,
63
V. Luth,
63
H. L. Lynch,
63
D. B. MacFarlane,
63
H. Marsiske,
63
D. R. Muller,
63
H. Neal,
63
S. Nelson,
63
C. P. O’Grady,
63
I. Ofte,
63
M. Perl,
63
T. Pulliam,
63
B. N. Ratcliff,
63
A. Roodman,
63
A. A. Salnikov,
63
V. Santoro,
63
PHYSICAL REVIEW D
82,
072006 (2010)
1550-7998
=
2010
=
82(7)
=
072006(18)
072006-1
Ó
2010 The American Physical Society
R. H. Schindler,
63
J. Schwiening,
63
A. Snyder,
63
D. Su,
63
M. K. Sullivan,
63
S. Sun,
63
K. Suzuki,
63
J. M. Thompson,
63
J. Va’vra,
63
A. P. Wagner,
63
M. Weaver,
63
C. A. West,
63
W. J. Wisniewski,
63
M. Wittgen,
63
D. H. Wright,
63
H. W. Wulsin,
63
A. K. Yarritu,
63
C. C. Young,
63
V. Ziegler,
63
X. R. Chen,
64
W. Park,
64
M. V. Purohit,
64
R. M. White,
64
J. R. Wilson,
64
S. J. Sekula,
65
M. Bellis,
66
P. R. Burchat,
66
A. J. Edwards,
66
T. S. Miyashita,
66
S. Ahmed,
67
M. S. Alam,
67
J. A. Ernst,
67
B. Pan,
67
M. A. Saeed,
67
S. B. Zain,
67
N. Guttman,
68
A. Soffer,
68
P. Lund,
69
S. M. Spanier,
69
R. Eckmann,
70
J. L. Ritchie,
70
A. M. Ruland,
70
C. J. Schilling,
70
R. F. Schwitters,
70
B. C. Wray,
70
J. M. Izen,
71
X. C. Lou,
71
F. Bianchi,
72a,72b
D. Gamba,
72a,72b
M. Pelliccioni,
72a,72b
M. Bomben,
73a,73b
L. Lanceri,
73a,73b
L. Vitale,
73a,73b
N. Lopez-March,
74
F. Martinez-Vidal,
74
D. A. Milanes,
74
A. Oyanguren,
74
J. Albert,
75
Sw. Banerjee,
75
H. H. F. Choi,
75
K. Hamano,
75
G. J. King,
75
R. Kowalewski,
75
M. J. Lewczuk,
75
I. M. Nugent,
75
J. M. Roney,
75
R. J. Sobie,
75
T. J. Gershon,
76
P. F. Harrison,
76
J. Ilic,
76
T. E. Latham,
76
E. M. T. Puccio,
76
H. R. Band,
77
S. Dasu,
77
K. T. Flood,
77
Y. Pan,
77
R. Prepost,
77
C. O. Vuosalo,
77
and S. L. Wu
77
(The
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite
́
de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
University of Birmingham, Birmingham, B15 2TT, United Kingdom
7
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
8
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
9
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
10
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
11
University of California at Irvine, Irvine, California 92697, USA
12
University of California at Riverside, Riverside, California 92521, USA
13
University of California at Santa Barbara, Santa Barbara, California 93106, USA
14
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
15
California Institute of Technology, Pasadena, California 91125, USA
16
University of Cincinnati, Cincinnati, Ohio 45221, USA
17
University of Colorado, Boulder, Colorado 80309, USA
18
Colorado State University, Fort Collins, Colorado 80523, USA
19
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
20
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
21
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
22
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
23a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
23b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
24
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
25a
INFN Sezione di Genova, I-16146 Genova, Italy
25b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
26
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
27
Harvard University, Cambridge, Massachusetts 02138, USA
28
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
29
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstr. 15, D-12489 Berlin, Germany
30
Imperial College London, London, SW7 2AZ, United Kingdom
31
University of Iowa, Iowa City, Iowa 52242, USA
32
Iowa State University, Ames, Iowa 50011-3160, USA
33
Johns Hopkins University, Baltimore, Maryland 21218, USA
34
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
35
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
36
University of Liverpool, Liverpool L69 7ZE, United Kingdom
37
Queen Mary, University of London, London, E1 4NS, United Kingdom
38
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
39
University of Louisville, Louisville, Kentucky 40292, USA
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
82,
072006 (2010)
072006-2
40
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
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
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
45
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
46a
INFN Sezione di Milano, I-20133 Milano, Italy
46b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
47
University of Mississippi, University, Mississippi 38677, USA
48
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
49a
INFN Sezione di Napoli, I-80126 Napoli, Italy
49b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
50
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
51
University of Notre Dame, Notre Dame, Indiana 46556, USA
52
Ohio State University, Columbus, Ohio 43210, USA
53
University of Oregon, Eugene, Oregon 97403, USA
54a
INFN Sezione di Padova, I-35131 Padova, Italy
54b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
55
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie Curie-Paris 6,
Universite
́
Denis Diderot-Paris 7, F-75252 Paris, France
56a
INFN Sezione di Perugia, I-06100 Perugia, Italy
56b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
57a
INFN Sezione di Pisa, I-56127 Pisa, Italy
57b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
57c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
58
Princeton University, Princeton, New Jersey 08544, USA
59a
INFN Sezione di Roma, I-00185 Roma, Italy
59b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
60
Universita
̈
t Rostock, D-18051 Rostock, Germany
61
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
62
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
63
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
64
University of South Carolina, Columbia, South Carolina 29208, USA
65
Southern Methodist University, Dallas, Texas 75275, USA
66
Stanford University, Stanford, California 94305-4060, USA
67
State University of New York, Albany, New York 12222, USA
68
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
69
University of Tennessee, Knoxville, Tennessee 37996, USA
70
University of Texas at Austin, Austin, Texas 78712, USA
71
University of Texas at Dallas, Richardson, Texas 75083, USA
72a
INFN Sezione di Torino, I-10125 Torino, Italy
72b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
73a
INFN Sezione di Trieste, I-34127 Trieste, Italy
73b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
74
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
75
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
76
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
77
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 23 June 2010; published 11 October 2010)
We report results from an updated study of the suppressed decays
B

!
DK

and
B

!
D

K

followed by
D
!
K
þ


, where
D
ðÞ
indicates a
D
ðÞ
0
or a

D
ðÞ
0
meson, and
D

!
D
0
or
D

!
D
.
These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity triangle angle

due to
interference between the
b
!
c
transition
B

!
D
ðÞ
0
K

followed by the doubly Cabibbo-suppressed
*
Now at Temple University, Philadelphia, PA 19122, USA
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy
Also with Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
x
Now at University of South Alabama, Mobile, AL 36688, USA
k
Also with Universita
`
di Sassari, Sassari, Italy
SEARCH FOR
b
!
u
TRANSITIONS IN
...
PHYSICAL REVIEW D
82,
072006 (2010)
072006-3
decay
D
0
!
K
þ


, and the
b
!
u
transition
B

!

D
ðÞ
0
K

followed by the Cabibbo-favored
decay

D
0
!
K
þ


. We also report an analysis of the decay
B

!
D
ðÞ


with the
D
decaying
into the doubly Cabibbo-suppressed mode
D
!
K
þ


. Our results are based on
467

10
6

ð
4
S
Þ!
B

B
decays collected with the
BABAR
detector at SLAC. We measure the ratios
R
ðÞ
of
the suppressed (
½
K
þ



D
K

=

) to favored (
½
K


þ

D
K

=

) branching fractions as
well as the
CP
asymmetries
A
ðÞ
of those modes. We see indications of signals for the
B

!
DK

and
B

!
D

D
0
K

suppressed modes, with statistical significances of 2.1 and
2
:
2

, respectively, and
we measure:
R
DK
¼ð
1
:
1

0
:
6

0
:
2
Þ
10

2
;
A
DK
¼
0
:
86

0
:
47
þ
0
:
12

0
:
16
,
R

ð
D
0
Þ
K
¼ð
1
:
8

0
:
9

0
:
4
Þ
10

2
;
A

ð
D
0
Þ
K
¼þ
0
:
77

0
:
35

0
:
12
;
R

ð
D
Þ
K
¼ð
1
:
3

1
:
4

0
:
8
Þ
10

2
;
A

ð
D
Þ
K
¼þ
0
:
36

0
:
94
þ
0
:
25

0
:
41
, where the first uncertainty is statistical and the second is systematic. We use a frequentist
approach to obtain the magnitude of the ratio
r
B
j
A
ð
B

!

D
0
K

Þ
=A
ð
B

!
D
0
K

Þj ¼ ð
9
:
5
þ
5
:
1

4
:
1
Þ
%
,
with
r
B
<
16
:
7%
at 90% confidence level. In the case of
B

!
D

K

we find
r

B
j
A
ð
B

!

D

0
K

Þ
=A
ð
B

!
D

0
K

Þj ¼ ð
9
:
6
þ
3
:
5

5
:
1
Þ
%
, with
r

B
<
15
:
0%
at 90% confidence level.
DOI:
10.1103/PhysRevD.82.072006
PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Hh, 14.40.Nd
I. INTRODUCTION
The standard model accommodates
CP
violation
through a single phase in the Cabibbo-Kobayashi-
Maskawa (CKM) quark mixing matrix
V
[
1
]. In the
Wolfenstein parameterization [
2
], the angle

¼
arg
ð
V
ud
V

ub
=V
cd
V

cb
Þ
of the unitarity triangle is related
to the complex phase of the CKM matrix element
V
ub
through
V
ub
¼j
V
ub
j
e

i
. A theoretically clean source of
information on the angle

is provided by
B

!
D
ðÞ
K

decays, where
D
ðÞ
represents an admixture of
D
ðÞ
0
and

D
ðÞ
0
states. These decays exploit the interference
between
B

!
D
ðÞ
0
K

and
B

!

D
ðÞ
0
K

(Fig.
1
) that
occurs when the
D
ðÞ
0
and the

D
ðÞ
0
decay to common final
states.
In the Atwood-Dunietz-Soni (ADS) method [
3
], the
D
0
from the favored
b
!
c
amplitude is reconstructed in the
doubly Cabibbo-suppressed decay
K
þ


, while the

D
0
from the
b
!
u
suppressed amplitude is reconstructed in
the favored decay
K
þ


. The product branching fractions
for these final states, which we denote as
½
K
þ



D
K

(
B

!
DK

) and
½
K
þ



D

K

(
B

!
D

K

), are small
(

10

7
), but the two interfering amplitudes are of the
same order of magnitude, and large
CP
asymmetries are
therefore possible. The favored decay mode
B

!
½
K


þ

D
ðÞ
K

is used to normalize the measurement and
cancel many systematic uncertainties. Thus, ignoring
possible small effects due to
D
mixing and assuming no
CP
violation in the normalization modes, we define the
charge-specific ratios for
B
þ
and
B

decay rates to the
ADS final states as
R

DK


ð½
K




D
K

Þ

ð½
K




D
K

Þ
¼
r
2
B
þ
r
2
D
þ
2
r
B
r
D
cos
ð

þ

Þ
;
(1)
where
r
B
¼j
A
ð
B

!

D
0
K

Þ
=A
ð
B

!
D
0
K

Þj
10%
[
4
7
] and
r
D
¼j
A
ð
D
0
!
K
þ


Þ
=A
ð
D
0
!
K


þ
Þj ¼
ð
5
:
78

0
:
08
Þ
%
[
8
] are the suppressed to favored
B
and
D
amplitude ratios. The rates in Eq. (
1
) depend on the
relative weak phase

and the relative strong phase



B
þ

D
between the interfering amplitudes, where

B
and

D
are the strong phase differences between the two
B
and
D
decay amplitudes, respectively. The value of

D
has
been measured to be

D
¼ð
201
:
9
þ
11
:
3

12
:
4
Þ
[
8
], where we
have accounted for a phase shift of 180
in the definition
of

D
between Ref. [
8
] and this analysis.
The main experimental observables are the charge-
averaged decay rate and the direct
CP
asymmetry, which
can be written as
R
DK

1
2
ð
R
þ
DK
þ
R

DK
Þ¼
r
2
B
þ
r
2
D
þ
2
r
B
r
D
cos

cos
;
(2)
A
DK

R

DK

R
þ
DK
R

DK
þ
R
þ
DK
¼
2
r
B
r
D
sin

sin
=
R
DK
:
(3)
The treatment for the
D

K
mode is identical to the
DK
one,
but the parameters
r

B
and


B
are not expected to be
numerically the same as those of the
DK
mode. Taking
into account the effective strong phase difference of

between the
D

decays to
D
and
D
0
[
9
], we define the
charge-specific ratios for
D

as
R

ð
D
0
Þ
K


ð½
K




D

!
D
0
K

Þ

ð½
K




D

!
D
0
K

Þ
¼
r

2
B
þ
r
2
D
þ
2
r

B
r
D
cos
ð

þ


Þ
;
(4)
FIG. 1. Feynmandiagramsfor
B

!
D
ðÞ
0
K
ðÞ
and

D
ðÞ
0
K
ðÞ
.
The latter is CKM and color-suppressed with respect to the
former.
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
82,
072006 (2010)
072006-4
R

ð
D
Þ
K


ð½
K




D

!
D
K

Þ

ð½
K




D

!
D
K

Þ
¼
r

2
B
þ
r
2
D

2
r

B
r
D
cos
ð

þ


Þ
;
(5)
with
r

B
¼j
A
ð
B

!

D

0
K

Þ
=A
ð
B

!
D

0
K

Þj
and





B
þ

D
, where


B
is the strong phase difference between
the two
B
decay amplitudes. The charge-averaged ratios
for
D

!
D
0
and
D

!
D
are then:
R

ð
D
0
Þ
K

1
2
ð
R
ð
D
0
Þ
K
þ
R

ð
D
0
Þ
K
Þ
¼
r

2
B
þ
r
2
D
þ
2
r

B
r
D
cos

cos


;
(6)
R

ð
D
Þ
K

1
2
ð
R
ð
D
Þ
K
þ
R

ð
D
Þ
K
Þ
¼
r

2
B
þ
r
2
D

2
r

B
r
D
cos

cos


:
(7)
Definitions of the direct
CP
asymmetries
A

ð
D
0
Þ
K
and
A

ð
D
Þ
K
follow Eq. (
3
).
This paper is an update of our previous ADS analysis
in Ref. [
4
], which used
232

10
6
B

B
pairs and set
90% C.L. upper limits
R
DK
<
0
:
029
,
R

ð
D
0
Þ
K
<
0
:
023
and
R

ð
D
Þ
K
<
0
:
045
. In addition to an increased data
sample, new features in the analysis include a multidimen-
sional fit involving the neural network output used to
discriminate the signal from the continuum background,
rather than a simple cut on this variable as was done in the
previous analysis. We also include measurements of the
ratios of the doubly Cabibbo-suppressed to Cabibbo-
favored
D
ðÞ

decay rates,
R
ðÞ
D


ð
B

K




D
ðÞ


Þ

ð
B

K




D
ðÞ


Þ
;
(8)
and of the corresponding asymmetries. These measure-
ments are used as a check for the
B

K
þ



D
ðÞ
K

ADS analysis. In the
D
ðÞ

case, we expect that the ratio
r
ðÞð
D
Þ
B
of the
V
ub
to
V
cb
amplitudes is suppressed by a
factor
j
V
cd
V
us
=V
ud
V
cs
j
compared to the
D
ðÞ
K
case, if
we assume the same color suppression factor for both
decays. One expects therefore
r
ðÞð
D
Þ
B
r
ðÞ
B

tan
2

c
5

10

3
r
D
, where

c
is the Cabibbo angle and where
we have assumed
r
ðÞ
B
¼
10%
. Neglecting higher order
terms,
R
ðÞ
D
r
2
D
and
A
ðÞ
D
2
r
ðÞ
B
tan
2

c
sin

sin

ðÞ
=r
D
.
Hence, the maximum asymmetry possible for
D
ðÞ

ADS
decays is
2
r
ðÞ
B
tan
2

c
=r
D
18%
.
II. THE
BABAR
DETECTOR AND DATA SET
The results presented in this paper are based on
467

10
6

ð
4
S
Þ!
B

B
decays, corresponding to an inte-
grated luminosity of
426 fb

1
(on-peak data). The data
were collected between 1999 and 2007 with the
BABAR
detector [
10
] at the PEP-II
e
þ
e

collider at SLAC. In
addition, a
44 fb

1
data sample, with center-of-mass
(CM) energy 40 MeV below the

ð
4
S
Þ
resonance
(off-peak data), is used to study backgrounds from contin-
uum events,
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
,or
c
).
The
BABAR
detector response to various physics
processes as well as to varying beam and environmental
conditions is modeled with simulation software based on
the
GEANT4
[
11
] tool kit. We use
EVTGEN
[
12
] to model the
kinematics of
B
meson decays and
JETSET
[
13
] to model
continuum processes
e
þ
e

!
q

q
.
III. ANALYSIS METHOD
A. Basic requirements
We reconstruct
B

!
D
ðÞ
K

and
B

!
D
ðÞ


with
the
D
decaying to
K


þ
(right-sign [RS] decays) and
K
þ


(wrong-sign [WS] decays). Charge conjugate reac-
tions are assumed throughout this paper. For decays in-
volving a
D

, both
D

!
D
0
and
D

!
D
modes are
reconstructed. Charged kaon and pion candidates must
satisfy identification criteria that are typically 85% effi-
cient, depending on momentum and polar angle. The mis-
identification rates are at the few percent level. We select
D
candidates with an invariant mass within
20 MeV
=c
2
(about 3 standard deviations) of the known
D
0
mass [
14
].
All
D
candidates are mass and vertex constrained. For
modes with
D

!
D
0
or
D

!
D
, the mass difference

m
between the
D

and the
D
must be within
4 MeV
=c
2
(
4

)or
15 MeV
=c
2
(
2

), respectively, of the nomi-
nal mass difference [
14
].
For the WS decays
B

K




D
K

, two important
sources of background arise: the first from
B

!
½


K


D
K

(in which the
K
and

in the
D
decay are
misidentified as

and
K
) and the second from
B

!
½
K

K


D


(when the
K



pair has an invariant
mass within
20 MeV
=c
2
of the nominal
D
0
mass). To
eliminate the first background, we recompute the invariant
mass (
M
switch
) of the
h
þ
h
0
pair in
D
0
!
h
þ
h
0
switching
the mass assumptions on the
h
þ
and the
h
0
. We veto
candidates with
M
switch
within
20 MeV
=c
2
of the
D
0
mass [
14
]. To eliminate the second background, we also
veto any candidate where the
KK
invariant mass is within
20 MeV
=c
2
of the
D
0
mass. To ensure the same selection
efficiencies, these criteria are applied both to
B

!
½
K




D
ðÞ
K

and to
B

K




D
ðÞ
K

candidates.
These veto cuts are 88% efficient on signal decays, while
removing approximately 90% of the
½


K


D
K

and
½
K

K


D


peaking background. Other possible back-
ground contributions faking the signal, like
B

!
½
K




0

D
K

, are found to be negligible, thanks to the

E
and
D
mass cuts.
We identify
B
candidates using two nearly indepen-
dent kinematic variables that are customarily used
when reconstructing
B
-meson decays at the

ð
4
S
Þ
.
These variables are the energy-substituted mass,
m
ES

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
s
2
þ
~
p
0
~
p
B
Þ
2
=E
2
0

p
2
B
q
and energy difference

E

E

B

1
2
ffiffiffi
s
p
, where
E
and
p
are energy and momentum,
SEARCH FOR
b
!
u
TRANSITIONS IN
...
PHYSICAL REVIEW D
82,
072006 (2010)
072006-5
the asterisk denotes the CM frame, the subscripts 0 and
B
refer to the

ð
4
S
Þ
and
B
candidate, respectively, and
s
is
the square of the CM energy. For signal events
m
ES
¼
m
B
þ
[
14
] and

E
¼
0
within the resolutions of about
2
:
6 MeV
=c
2
and 17 MeV, respectively. We require that
all candidates have
j

E
j
<
40 MeV
and we use
m
ES
in
the fit to extract the number of signal events.
The average number of
B
!
D
ðÞ
K
candidates recon-
structed per selected event is about 1.4 in
B
!
DK
signal
Monte Carlo (MC) simulation events and about 2 for
B
!
D

K
signal MC events. This is mostly due to the cross-feed
between the
DK
and the
D

K
final states. For all events
with multiple
B
!
D
ðÞ
K
candidates, we retain only one
candidate per event, based on the smallest value of
j

E
j
.
This method does not bias the sample since

E
is not used
to extract the number of signal events. After this arbitra-
tion, less than 0.4% (0.5%) of the
B
!
DK
(
B
!
D

K
)
signal MC events selected are reconstructed as
B
!
D

K
(
B
!
DK
). About 10% of the
B
!
D

D
0
K
events selected
are reconstructed as
B
!
D

D
K
and about 2% of the
B
!
D

D
K
events selected are reconstructed as
B
!
D

D
0
K
.
The
B
!
D
ðÞ

analysis is performed independently of
the
B
!
D
ðÞ
K
analysis, but uses the same multiple candi-
date selection algorithm. A summary of the selection effi-
ciencies for the WS modes
½
K




D
ðÞ
h

(
h
¼
K
,

) and
the RS modes
½


K


D
ðÞ
h

is given in Table
I
.
B. Neural network
After these initial requirements, backgrounds domi-
nantly arise from continuum events, especially
e
þ
e

!
c

c
, with

c
!

D
0
X
,

D
0
!
K
þ


and
c
!
D
0
X
,
D
0
!
K

þ
anything. The continuum background is reduced by
using a multilayer perceptron artificial neural network with
2 hidden layers, available in the framework of the
TMVA
package [
15
]. To select the discriminating variables used in
the neural network, we rely on a study performed for the
previous version of this analysis [
4
], and we consider the
seven quantities listed below:
(1) Two event shape moments
L
0
¼
P
i
p
i
, and
L
2
¼
P
i
p
i
cos
2

i
, calculated in the CM frame. Here,
p
i
is
the momentum and

i
is the angle with respect to the
thrust axis of the
B
candidate; the index
i
runs over
all tracks and clusters not used to reconstruct the
B
meson (rest of the event). These variables are sensi-
tive to the shape of the event, separating jetlike
continuum events from more spherical
B

B
events.
(2) The absolute value of the cosine of the angle in
the CM frame between the thrust axes of the
B
candidate and the detected remainder of the event,
j
cos

T
j
. The distribution of
j
cos

T
j
is approxi-
mately uniform for signal and strongly peaked at
one for continuum background.
(3) The absolute value of the cosine of the CM angle
between the
B
candidate momentum and the beam
axis,
j
cos

B
j
. In this variable, the signal follows a
1

cos
2

B
distribution, while the background is
approximately uniform.
(4) The charge difference

Q
between the sum of the
charges of tracks in the
D
ðÞ
hemisphere and the sum
of the charges of the tracks in the opposite hemi-
sphere, excluding the tracks used in the recon-
structed
B
, and where the partitioning of the event
into two hemispheres is done in the CM frame. This
variable exploits the correlation occurring in
c

c
events between the charge of the
c
(or

c
) in a given
hemisphere and the sum of the charges of all parti-
cles in that hemisphere. For signal events, the
average charge difference is
h

Q
0
, whereas
for the
c

c
background
h

Q
i
7
3

Q
B
, where
Q
B
is the charge of the
B
candidate.
(5) The product
Q
B
Q
K
, where
Q
K
is the sum of the
charges of all kaons in the rest of the event. In many
signal events, there is a charged kaon among the
decay products of the other
B
in the event. The
charge of this kaon tends to be highly correlated
with the charge of the
B
. Thus, signal events tend to
have
Q
B
Q
K

1
. On the other hand, most con-
tinuum events have no kaons outside of the recon-
structed
B
, and therefore
Q
K
¼
0
.
(6) A quantity
M
K‘
, defined to be zero if there are no
leptons (
e
or

) in the event, and, if a lepton is
found, taken to be equal to the invariant mass of this
lepton and the kaon from
B
(bachelor
K
). This
quantity differentiates between continuum back-
ground and signal because continuum events have
fewer leptons than
B

B
events. Furthermore, a large
fraction of leptons in
c

c
background events are from
D
!
K‘
, where the kaon becomes the bachelor
kaon candidate, so that the average
M
K‘
in
c

c
events is lower than in
B
signal events.
(7) The absolute value of the measured proper time
interval between the two
B
decays,
j

t
j
. This is
calculated from the measured separation,

z
, be-
tween the decay points of the reconstructed
B
and
the other
B
along the beam direction, and the known
Lorentz boost of the initial
e
þ
e

state. For contin-
uum background,
j

t
j
is peaked at 0, with most
TABLE I. Selection efficiencies, after correction for known
data/MC differences, for
B

K




D
ðÞ
h

(

WS
) and
B

!
½
K




D
ðÞ
h

(

RS
), and efficiency ratio

WS
=
RS
.
Channel

WS
(%)

RS
(%)

WS
=
RS
(
10

2
)
DK
26
:
5

0
:
126
:
6

0
:
199
:
6

0
:
5
D

D
0
K
13
:
3

0
:
113
:
2

0
:
1
100
:
6

1
:
1
D

D
K
17
:
4

0
:
117
:
5

0
:
199
:
8

0
:
8
D
26
:
0

0
:
126
:
5

0
:
197
:
9

0
:
5
D

D
0

14
:
3

0
:
114
:
8

0
:
196
:
4

0
:
9
D

D

18
:
8

0
:
119
:
5

0
:
196
:
3

0
:
7
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
82,
072006 (2010)
072006-6