of 16
Measurement of the
B
!

D
ðÞ
D
ðÞ
K
branching fractions
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
C. West,
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
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
V. Prasad,
26
C. L. Lee,
27
M. Morii,
27
A. Adametz,
28
J. Marks,
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
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
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
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
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
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
A. Rossi,
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,
61
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
PHYSICAL REVIEW D
83,
032004 (2011)
1550-7998
=
2011
=
83(3)
=
032004(16)
032004-1
Ó
2011 American Physical Society
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
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
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
(
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
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
032004 (2011)
032004-2
39
University of Louisville, Louisville, Kentucky 40292, USA
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-Paris6,
Universite
́
Denis Diderot-Paris7, 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, USA
77
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 17 November 2010; published 3 February 2011)
We present a measurement of the branching fractions of the 22 decay channels of the
B
0
and
B
þ
mesons
to

D
ðÞ
D
ðÞ
K
, where the
D
ðÞ
and

D
ðÞ
mesons are fully reconstructed. Summing the 10 neutral modes and
the 12 charged modes, the branching fractions are found to be
B
ð
B
0
!

D
ðÞ
D
ðÞ
K
Þ¼ð
3
:
68

0
:
10

0
:
24
Þ
%
and
B
ð
B
þ
!

D
ðÞ
D
ðÞ
K
Þ¼ð
4
:
05

0
:
11

0
:
28
Þ
%
, where the first uncertainties are statistical
*
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
MEASUREMENT OF THE
...
PHYSICAL REVIEW D
83,
032004 (2011)
032004-3
and the second systematic. The results are based on
429 fb

1
of data containing
471

10
6
B

B
pairs collected at the

ð
4
S
Þ
resonance with the
BABAR
detector at the SLAC National Accelerator
Laboratory.
DOI:
10.1103/PhysRevD.83.032004
PACS numbers: 13.25.Hw, 14.40.Nd
I. INTRODUCTION
In this article, we report on the measurement of the
branching fractions of the 22 decays of charged and neutral
B
mesons to

D
ðÞ
D
ðÞ
K
final states (Table
I
):
D
ðÞ
is either a
D
0
,
D

0
,
D
þ
,or
D
,

D
ðÞ
is the charge conjugate of
D
ðÞ
,
and
K
is either a
K
þ
or a
K
0
. Both

D
ðÞ
and
D
ðÞ
are fully
reconstructed. Charge conjugate reactions are assumed
throughout this article.
In the past, the values measured for hadronic decays of
the
B
meson were in disagreement with the expectations
based on the
B
semileptonic branching fraction due to the
inconsistency originating from the number of charmed
hadrons per
B
decay (charm counting) [
1
]. The
b
!
c

cs
transition in
B
decays was believed to be dominated by
B
!
D
s
X
,
B
c

c
Þ
X
, and
B
!

c
X
final states, where
X
represents any particles. However, it was realized [
2
]
that an enhancement in the
b
!
c

cs
transition was needed
to resolve the theoretical discrepancy with the
B
semi-
leptonic branching fraction. Buchalla
et al.
[
2
] predicted
sizeable branching fractions for decays of the form
B
!

D
ðÞ
D
ðÞ
K
ð
X
Þ
. Experimental evidence in support of
this picture soon appeared in the literature [
3
], including
a study by
BABAR
using
76 fb

1
of data where the
Collaboration reported the observations or the limits on
the 22 decays
B
!

D
ðÞ
D
ðÞ
K
[
4
]. The aggregate branching
fraction measurements were
B
ð
B
0
!

D
ðÞ
D
ðÞ
K
Þ¼ð
4
:
3

0
:
3

0
:
6
Þ
%
and
B
ð
B
þ
!

D
ðÞ
D
ðÞ
K
Þ¼ð
3
:
5

0
:
3

0
:
5
Þ
%
,
where the first uncertainties are statistical and the second
systematic. This result may be compared with the wrong-
sign
D
production (
b
!
c

cs
transition containing a

D
meson) that
BABAR
studied using inclusive
B
decays to
final states containing at least one charm particle [
5
]. The
wrong-sign
D
production was found to be
B
ð

B
0
!

DX
Þ¼
ð
10
:
4

1
:
9
Þ
%
and
B
ð
B

!

DX
Þ¼ð
11
:
1

0
:
9
Þ
%
. In ad-
dition,
BABAR
found a value of the total charm yield per
B
decay consistent with the one derived from the semilep-
tonic branching fraction, which solved the longstanding
problem of the charm counting.
Furthermore,

D
ðÞ
D
ðÞ
K
events are interesting for a vari-
ety of studies. These events can be used to investigate
isospin relations and to extract a measurement of the ratio
of

ð
4
S
Þ!
B
þ
B

and

ð
4
S
Þ!
B
0

B
0
decays [
6
]. It was
shown theoretically that the time-dependent rate for
B
0
!
D
ðÞ
D
ðÞþ
K
0
S
decays can be used to measure
sin2

and
cos2

[
7
].
BABAR
used the mode
B
0
!
D

D
K
0
S
with
209 fb

1
of data to perform a time-dependent
CP
asym-
metry measurement to determine the sign of
cos2

, under
some theoretical and resonant structure assumptions [
8
].
The Belle Collaboration also published a similar analysis
[
9
]. Although the resonant states are not studied in our
paper, it is worth recalling that many
D
ðÞ
K
and

D
ðÞ
D
ðÞ
resonant processes are at play in the studied decay chan-
nels. Using
B
!

D
ðÞ
D
ðÞ
K
final states,
BABAR
and Belle
observed and measured the properties of the resonances
D
þ
s
1
ð
2536
Þ
,
D
sJ
ð
2700
Þ
,
c
ð
3770
Þ
, and
X
ð
3872
Þ
[
10
12
].
The
B
!

D
ðÞ
D
ðÞ
K
decays can proceed through exter-
nal
W
-emission and internal
W
-emission amplitudes, also
called color-suppressed amplitudes. As Fig.
1
illustrates,
some decay modes proceed through only one of these
amplitudes, while others proceed through both.
In this paper, we update with the full
BABAR
data
sample our previous measurement [
4
] of the branching
fractions for the 22
B
!

D
ðÞ
D
ðÞ
K
0
and
B
!

D
ðÞ
D
ðÞ
K
þ
decays. We benefit from several improvements with re-
spect to this previous measurement:
(i) the integrated luminosity used for this analysis is
more than 5 times larger,
(ii) the track reconstruction and particle identification
algorithms have been improved (in purity and
efficiency),
(iii) the efficiency of the selection of signal events has
been increased,
(iv) the fit uses a more accurate signal parametrization,
(v) the peaking background is taken into account in
the fit,
(vi) we use a method that is insensitive to the possible
resonant structure in the final states.
TABLE I. The 22
B
!

D
ðÞ
D
ðÞ
K
decay modes. The modes
B
0
!
D

D
K
0
and
B
0
!
D

D
þ
K
0
are combined together
since they are not experimentally distinguishable. The same
applies to the modes
B
0
!

D
0
D

0
K
0
and
B
0
!

D

0
D
0
K
0
which
are also combined together.
Neutral
B
mode
Charged
B
mode
B
0
!
D

D
0
K
þ
B
þ
!

D
0
D
þ
K
0
B
0
!
D

D

0
K
þ
B
þ
!

D
0
D
K
0
B
0
!
D

D
0
K
þ
B
þ
!

D

0
D
þ
K
0
B
0
!
D

D

0
K
þ
B
þ
!

D

0
D
K
0
B
0
!
D

D
þ
K
0
B
þ
!

D
0
D
0
K
þ
B
0
!
D

D
K
0
þ
D

D
þ
K
0
B
þ
!

D
0
D

0
K
þ
B
þ
!

D

0
D
0
K
þ
B
0
!
D

D
K
0
B
þ
!

D

0
D

0
K
þ
B
0
!

D
0
D
0
K
0
B
þ
!
D

D
þ
K
þ
B
0
!

D
0
D

0
K
0
þ

D

0
D
0
K
0
B
þ
!
D

D
K
þ
B
þ
!
D

D
þ
K
þ
B
0
!

D

0
D

0
K
0
B
þ
!
D

D
K
þ
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
032004 (2011)
032004-4
Measuring the 22 modes altogether allows to avoid biases
in the branching fraction measurement by correctly taking
into account the cross-feed events, which are events from
one mode being reconstructed as a candidate for another
mode.
II. THE
BABAR
DETECTOR AND
DATA SAMPLE
The data were recorded by the
BABAR
detector at the
PEP-II asymmetric-energy
e
þ
e

storage ring operating at
the SLAC National Accelerator Laboratory. We analyze
the complete
BABAR
data sample collected at the

ð
4
S
Þ
resonance corresponding to an integrated luminosity of
429 fb

1
, giving
N
B

B
¼ð
470
:
9

0
:
1

2
:
8
Þ
10
6
B

B
pairs produced, where the first uncertainty is statistical
and the second systematic.
The
BABAR
detector is described in detail elsewhere
[
13
]. Charged particles are detected and their momenta
measured with a five-layer silicon vertex tracker and a
40-layer drift chamber in a 1.5 T axial magnetic field.
Charged particle identification is based on the measure-
ments of the energy loss in the tracking devices and of the
Cherenkov radiation in the ring-imaging detector. The
energies and locations of showers associated with photons
are measured in the electromagnetic calorimeter. Muons
are identified by the instrumented magnetic-flux return,
which is located outside the magnet.
We employ a Monte Carlo (MC) simulation to study the
relevant backgrounds and estimate the selection efficien-
cies. We use
EVTGEN
[
14
] to model the kinematics of
B
mesons and
JETSET
[
15
] to model continuum processes,
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
,
c
). The
BABAR
detector and its
response to particle interactions are modeled using the
GEANT4
[
16
] simulation package.
III.
B
CANDIDATE SELECTION
We reconstruct the
B
0
and
B
þ
mesons in the 22

D
ðÞ
D
ðÞ
K
modes. The level of background widely varies
among the signal channels, even within a specific
B
mode
depending on the
D
meson decay type. A different opti-
mization of the selection criteria is implemented for each
of the final states. The optimization determines the selec-
tion which maximizes
S=
ffiffiffiffiffiffiffiffiffiffiffiffiffi
S
þ
B
p
, where
S
and
B
are the
expected number of events for the signal and for the
background in the signal region, based, respectively,
on signal and background MC simulated events. The
u
b
_
u
c
_
c
d
_
d
s
_
B
+
D
(*)0
D
(*)+
K
0
W
+
u
b
_
u
s
_
c
d
_
d
c
_
B
+
K
+
D
(*)+
D
(*)-
W
+
u
b
_
u
s
_
c
u
_
u
c
_
B
+
K
+
D
(*)0
D
(*)0
+
W
+
u
b
_
u
c
_
c
u
u
_
s
_
B
+
D
(*)0
D
(*)0
K
+
W
+
d
b
_
d
c
_
c
u
_
u
s
_
B
0
D
(*)-
D
(*)0
K
+
W
+
d
b
_
d
s
_
c
u
u
_
c
_
B
0
K
0
D
(*)0
D
(*)0
W
+
d
b
_
d
s
_
c
d
_
d
c
_
B
0
K
0
D
(*)+
D
(*)-
+
W
+
d
b
_
d
c
_
c
d
_
d
s
_
B
0
D
(*)-
D
(*)+
K
0
W
+
FIG. 1. Top left: external W-emission amplitude for the decays
B
þ
!

D
ðÞ
0
D
ðÞþ
K
0
. Top center: internal W-emission amplitude for
the decays
B
þ
!
D
ðÞ
D
ðÞþ
K
þ
. Top right: external
þ
internal W-emission amplitudes for the decays
B
þ
!

D
ðÞ
0
D
ðÞ
0
K
þ
. Bottom
row: same as top row, respectively, for
B
0
!
D
ðÞ
D
ðÞ
0
K
þ
,
B
0
!

D
ðÞ
0
D
ðÞ
0
K
0
, and
B
0
!
D
ðÞ
D
ðÞþ
K
0
.
MEASUREMENT OF THE
...
PHYSICAL REVIEW D
83,
032004 (2011)
032004-5
branching fractions for the computation of
S
are taken from
our previous measurements of these channels [
4
].
We identify charged kaons using either loose or tight
criteria depending on the decay mode. The loose criterion
is typically 98% efficient with pion misidentification rates
at the 15% level, while the tight criterion is 85% efficient
with a misidentification around 2%. We use only the
K
0
S
meson when a neutral
K
meson is present in the final state.
The
K
0
S
candidates are reconstructed from two oppositely
charged tracks assumed to be pions consistent with coming
from a common vertex and having an invariant mass within

9
:
5 MeV
=c
2
of the nominal
K
0
S
mass [
17
]. The displace-
ment of the
K
0
S
vertex in the plane transverse to the beam
axis is required to be at least 0.2 cm.
The

0
candidates are reconstructed from pairs of pho-
tons with energies
E

>
30 MeV
in the laboratory frame
that have an invariant mass of
115
<m

<
150 MeV
=c
2
.
We reconstruct
D
mesons in the modes
D
0
!
K


þ
,
K


þ

0
,
K


þ



þ
, and
D
þ
!
K


þ

þ
. The
K
and

tracks are required to originate from a common vertex.
The invariant masses of the
D
candidates are required to lie
within

2
:
5

D
of the measured
D
mass, where

D
is the
D
invariant mass resolution. This resolution is measured
to be
5
:
8 MeV
=c
2
for
D
0
!
K


þ
,
9
:
5 MeV
=c
2
for
D
0
!
K


þ

0
,
4
:
7 MeV
=c
2
for
D
0
!
K


þ



þ
,
and
4
:
2 MeV
=c
2
for
D
þ
!
K


þ

þ
. To reduce the
combinatorial background, for some of the
B
decays in-
volving
D
0
!
K


þ

0
, we use the distribution of events
in the Dalitz plot of the squared invariant masses
m
2
ð
K


þ
Þ
m
2
ð
K


0
Þ
, where we select events that are
located in the enhanced regions dominated by the
K

ð
892
Þ
þ
,
K

ð
892
Þ
0
, and

ð
770
Þ
þ
resonances [
18
].
The
D

candidates are reconstructed in the decay modes
D
!
D
0

þ
,
D
!
D
þ

0
,
D

0
!
D
0

0
, and
D

0
!
D
0

. The

0
and the

þ
candidates must have a momen-
tum smaller than
450 MeV
=c
in the

ð
4
S
Þ
rest frame,
while the

energy in the laboratory frame must be larger
than 100 MeV. The mass difference between the
D
and
D
candidates is required to be within

3 MeV
=c
2
of the
nominal value [
17
]. For
D

0
meson decays, the mass
difference between the
D

0
and
D
0
candidates is required
to lie between 138 and
146 MeV
=c
2
for
D

0
!
D
0

0
and
between 130 and
150 MeV
=c
2
for
D

0
!
D
0

.
The
B
candidates are reconstructed by combining a

D
ðÞ
,
a
D
ðÞ
and a
K
candidate in one of the 22 modes. For modes
involving two
D
0
mesons, at least one of them is required
to decay to
K


þ
, except for the decay modes
D

D
K
0
,
D

D
K
þ
, and
D

D
0
K
þ
, which have
lower background and for which all combinations are
accepted. For modes containing a
D
meson, we look
only to the decay
D
!
D
0

þ
, except for the modes
containing
D

D
, where we also reconstruct
D
!
D
þ

0
. A mass-constrained kinematic fit is applied to the
intermediate particles (
D

0
,
D
,
D
0
,
D
þ
,
K
0
S
,

0
)to
improve their momentum resolution.
To suppress the continuum background, we remove
events with
R
2
>
0
:
3
(where
R
2
is the ratio of the second
to zeroth Fox-Wolfram moments of the event [
19
]) and
events with
j
cos
ð

B
Þj
>
0
:
9
(where

B
is the angle be-
tween the thrust axis of the candidate decay and the thrust
axis of the rest of the event).
Two kinematic variables are used to isolate the
B
-meson
signal. The first variable is the beam-energy-substituted
mass defined as
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

s=
2
þ
~
p
0
:
~
p
B
E
0

2
j
~
p
B
j
2
s
;
(1)
where
ffiffiffi
s
p
is the
e
þ
e

center-of-mass energy. For the
momenta
~
p
0
,
~
p
B
and the energy
E
0
, the subscripts 0 and
B
refer to the
e
þ
e

system and the reconstructed
B
meson,
respectively. The other variable is

E
, the difference be-
tween the reconstructed energy of the
B
candidate and
the beam energy in the
e
þ
e

center-of-mass frame.
Signal events have
m
ES
compatible with the known
B
-meson mass [
17
] and

E
compatible with 0 MeV, within
their respective resolutions. At this stage, we keep only
events which satisfy
m
ES
>
5
:
20 GeV
=c
2
.
We obtain a few signal
B
candidates per event on aver-
age. When the final state contains no
D

meson, we get 1.0
to 1.3 candidates per event depending on the specific mode,
1.3 to 1.9 candidates per event for final states containing
one
D

meson, and 1.7 to 2.1 candidates per event when the
final state contains two
D

mesons (except for
B
þ
!

D

0
D

0
K
þ
with 2.9 candidates per event). If more than
one candidate is selected in an event, we retain the one with
the smallest value of
j

E
j
(‘‘best candidate selection’’).
According to MC studies, this criterion finds the correct
candidate when this one is present in the candidate list in
more than 95% of the cases for final states with no
D

0
meson and more than 80% of the cases for modes with one
or two neutral
D

mesons. We keep only events with
j

E
j
<E
c
, with
E
c
varying from 7 MeV to 56 MeV
depending on the decay mode of the
B
and
D
mesons.
The resolution on

E
varies between 5.6 and 14.3 MeV for
modes with zero or one
D

0
meson in the final state and
between 11.6 and 19.5 MeV for modes containing two
neutral
D

mesons.
The efficiency for signal events varies from 0.5% to
22.2% depending on the final state (being typically in the
5%–10% range). The modes with the lowest efficiency are
the ones containing one or two charged
D

mesons.
Figure
2
presents the

E
and
m
ES
distributions after the
complete selection is applied. The

E
distributions are
presented for events in the signal region defined by
m
ES
>
5
:
27 GeV
=c
2
and are shown without applying the best
candidate selection. Signal events appear in the peak near

E

0 MeV
when reconstructed correctly, while the peak
around

160 MeV
is due to

D

DK
and

DD

K
decays
reconstructed as

DDK
and to

D

D

K
decays reconstructed
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
032004 (2011)
032004-6
as

D

DK
or

DD

K
. Both

E
and
m
ES
distributions show a
clear excess of events in the signal region.
IV. FITS OF THE DATA DISTRIBUTIONS
We present the fits used to extract the branching fractions.
For each mode, we fit the
m
ES
distribution between 5.22 and
5
:
30 GeV
=c
2
to get the signal yield. The data samples
corresponding to each
B
decay mode are disjoint and the
fits are performed independently for each mode. According
to their physical origin, four categories of events with differ-
ently shaped
m
ES
distributions are separately considered:

D
ðÞ
D
ðÞ
K
signal events, cross-feed events, combinatorial
background events, and peaking background events. The
total probability density function (PDF) is a sum of these
contributions. Event yields are obtained from extended
maximum likelihood unbinned fits.
A. Signal contribution
The shape of the signal is determined from fits to the
m
ES
distributions of signal MC samples. A Crystal Ball function
[
20
] (Gaussian modified to include a power-law tail on the
low side of the peak),
P
S
ð
m
ES
;
m
S
;
S
;
S
;n
S
Þ
, is used to
describe the signal (see Eq. (
A1
) in the Appendix
A
). The
parameters of this PDF are
m
S
and

S
, the mean and the
width of the Gaussian part, and

S
and
n
S
, the parameters
of the tail part. The signal yield,
N
S
, is determined from the
fit to the data.
B. Cross-feed contribution
We call ‘‘cross feed’’ the events from all of the

D
ðÞ
D
ðÞ
K
modes, except the one we reconstruct, that
pass the complete selection and that are reconstructed
in the given mode. The cross-feed events are a non-
negligible part of the
m
ES
peak in some of the modes,
and the signal event yield must be corrected for these
cross-feed events.
We observe from the analysis of simulated samples that
most of the cross feed originates from the combination of
an unrelated soft

0
or

with the
D
0
decayed from the
D
to form a wrong
D

0
candidate. The cross-feed pro-
portion is often in the 10% range relative to the signal yield
E (GeV)
Events/5 MeV
1000
1500
2000
2500
3000
3500
4000
4500
modes
0
B
E (GeV)
Events/5 MeV
2000
3000
4000
5000
6000
7000
modes
+
B
)
2
(GeV/c
ES
m
2
Events/1 MeV/c
0
200
400
600
800
1000
1200
1400
modes
0
B
)
2
(GeV/c
ES
m
-0.2 -0.15 -0.1 -0.05
0
0.05
0.1
0.15
0.2
-0.2 -0.15 -0.1 -0.05
0
0.05
0.1
0.15
0.2
5.22 5.23 5.24 5.25 5.26 5.27
5.28 5.29
5.3
5.22 5.23 5.24 5.25 5.26 5.27
5.28 5.29
5.3
2
Events/1 MeV/c
0
200
400
600
800
1000
1200
1400
1600
1800
modes
+
B
FIG. 2. Distributions of the

E
variable (top plots) and of the
m
ES
variable (bottom plots) for the sum of all the
B
0
!

D
ðÞ
D
ðÞ
K
modes (left-hand plots) and for the sum of all the
B
þ
!

D
ðÞ
D
ðÞ
K
modes (right-hand plots). The

E
distributions are shown after the
complete selection but before the choice of the best candidate and for
5
:
27
<m
ES
<
5
:
29 GeV
=c
2
, and the
m
ES
distributions are shown
after the complete selection, including the selection on the

E
variable.
MEASUREMENT OF THE
...
PHYSICAL REVIEW D
83,
032004 (2011)
032004-7
but can be comparable or larger than the signal contribu-
tion, especially for modes containing

D
ðÞ
0
D

0
in the final
state. To account for the cross-feed events, an iterative
procedure, described in Sec.
IV F
, is used to extract the
signal yields and the branching fractions.
Cross-feed distributions for modes containing no
D

0
meson can be described by a Gaussian function
P
peaking
CF
ð
m
ES
;
m
CF
;
CF
Þ
for the peaking part, where
m
CF
and

CF
are the mean and the width of the peaking com-
ponent [Eq. (
A2
)]. For modes containing at least one
neutral
D

meson, the peaking component is described
by a function
P
0
peaking
CF
ð
m
ES
;
m
CF
;
CF
;t
CF
Þ
which is able
to model the tail at low mass [Eq. (
A3
)]. The parameters
m
CF
and

CF
represent the position of the maximum value
and the width of the peak, and
t
CF
represents the tail
of the function. The nonpeaking part of the cross-feed
contribution is described by an Argus function [
21
]
P
nonpeaking
CF
ð
m
ES
;
m
0
;
CF
Þ
, where
m
0
represents the kine-
matic upper limit for the constrained mass and

CF
is the
Argus shape parameter [Eq. (
A4
)].
The total PDF for cross-feed events is
P
CF
ð
m
ES
;
m
CF
;
CF
;t
CF
;m
0
;
CF
Þ
¼
N
peaking
CF

P
ð0Þ
peaking
CF
þ
N
nonpeaking
CF

P
nonpeaking
CF
;
(2)
where
P
ð0Þ
peaking
CF
represents either
P
peaking
CF
or
P
0
peaking
CF
de-
pending on the number of neutral
D

meson in the final
state. The quantities
N
peaking
CF
and
N
nonpeaking
CF
are the num-
bers of events in the peaking PDF and in the nonpeaking
PDF, respectively. The values of the parameters of
the cross-feed PDF are determined by fitting signal MC
m
ES
distributions, except for the value of
m
0
which is
fixed to
5
:
2892 GeV
=c
2
. The cross-feed yield,
N
CF
¼
N
nonpeaking
CF
þ
N
peaking
CF
, is also extracted from the fit.
C. Combinatorial background contribution
The combinatorial background events are composed of
generic
B
decays and of continuum events, which account,
respectively, for about 88% and 12% of the total number of
background events. The combinatorial background events
are described by an Argus function
P
CB
ð
m
ES
;
m
0
;
CB
Þ
,
where

CB
is the shape parameter [Eq. (
A5
)]. The parame-
ter

CB
is free to float in the fit to the data while
m
0
is fixed
to
5
:
2892 GeV
=c
2
. The yield for the combinatorial back-
ground,
N
CB
, is also obtained from the data fit.
D. Peaking background contribution
We call ‘‘peaking background’’ the part of the back-
ground that is peaking in the signal region and that is not
due to cross feed. To extract the peaking background, we fit
the
m
ES
distributions from generic MC samples
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
,
c
,
b
) satisfying the

D
ðÞ
D
ðÞ
K
selection and
scale the results to the data luminosity.
The simulated distribution is fitted with an Argus func-
tion describing the nonpeaking part and a Gaussian func-
tion
P
PB
ð
m
ES
;
m
PB
;
PB
Þ
describing the peaking part,
where
m
PB
and

PB
are the mean and width of the
Gaussian [Eq. (
A6
)]. The parameters
m
PB
and

PB
are
free to float in the fits to the simulated events, except for
modes with nonconverging fits, where
m
PB
is fixed to the
B
mass. These modes are
B
0
!
D

D
þ
K
0
,
B
þ
!

D
0
D
þ
K
0
,
B
0
!
D

D
0
K
þ
,
B
þ
!

D

0
D
þ
K
0
,
B
þ
!

D
0
D
K
0
,
B
0
!
D

D

0
K
þ
,
B
0
!

D

0
D

0
K
0
, and
B
þ
!

D

0
D

0
K
þ
.
The fit also returns the value of the peaking background
yield,
N
PB
, which is shown in Table
II
. Only the peaking
part
P
PB
is used in the fit to the data, the nonpeaking part
being included in the combinatorial background.
E. Fits
We fit the
m
ES
distribution using the PDFs for the signal,
for the cross feed, for the combinatorial background, and
for the peaking background as detailed in the previous
sections. The total PDF
P
tot
can be written as
P
tot
¼
N
S

P
S
ð
m
ES
;
m
S
;
S
;
S
;n
S
Þ
þ
N
CF

P
CF
ð
m
ES
;
m
CF
;
CF
;t
CF
;m
0
;
CF
Þ
þ
N
CB

P
CB
ð
m
ES
;
m
0
;
CB
Þ
þ
N
PB

P
PB
ð
m
ES
;
m
PB
;
PB
Þ
:
(3)
The free parameters of the fit are
N
S
,
m
S
,
N
CB
, and

CB
.
All other parameters, except
m
0
, are fixed to the
values obtained from the simulation. For modes with low
signal statistics in the data, namely,
B
0
!

D
0
D
0
K
0
,
B
0
!

D
0
D

0
K
0
þ

D

0
D
0
K
0
, and
B
0
!

D

0
D

0
K
0
,we
fix
m
S
to the value obtained from the simulation.
The free parameters are extracted by maximizing the
unbinned extended likelihood
L
¼
e

N
N
n
n
!
Y
n
i
¼
1
P
tot
;
(4)
where
n
is the number of events in the sample and
N
is the
expectation value for the total number of events.
F. Iterative procedure
Because of the presence of cross-feed events, the fit for
the branching fraction for one channel uses as inputs the
branching fractions from other channels. Since these
branching fractions are in principle not known, we employ
an iterative procedure. In practice, we perform the com-
plete analysis for each
B
mode, using as a starting point the
branching fractions measured by
BABAR
in Ref. [
4
]. We
obtain new measurements of the branching fractions that
we use in the next step to fix the cross-feed proportion. We
repeat this procedure until the differences between the
actual branching fractions and the previous ones are
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
032004 (2011)
032004-8
smaller than 2% of the statistical uncertainty. Using this
criterion, four iterations are needed. We keep the last
iteration as the final result.
G. Fit results
The results of the fits are shown in Figs.
3
and
4
, and are
displayed in Table
II
. All the fits show a good description
of the data. Although we perform an unbinned fit, we can
compute a
2
value using bins of
2
:
5 MeV
=c
2
width.
We observe values of
2
=N
dof
typically close to 1, with
N
dof
¼
N
bin

N
float
, where
N
bin
is the number of bins and
N
float
is the number of floating parameters in the fit.
V. BRANCHING FRACTION MEASUREMENTS
A. Method
In this paper, we measure the branching fractions of the
22

D
ðÞ
D
ðÞ
K
modes, including nonresonant and resonant
modes. It has been shown that

D
ðÞ
D
ðÞ
K
events contain
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
2
Events/2.5 MeV/c
0
100
200
300
400
500
+
K
0
D
-
D
0
B
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
2
Events/2.5 MeV/c
0
100
200
300
400
500
600
700
+
K
*0
D
-
D
0
B
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
2
Events/2.5 MeV/c
0
100
200
300
400
500
600
700
+
K
0
D
*-
D
0
B
2
Events/2.5 MeV/c
0
100
200
300
400
500
600
700
+
K
*0
D
*-
D
0
B
2
Events/2.5 MeV/c
0
5
10
15
20
25
30
35
40
45
0
K
+
D
-
D
0
B
2
Events/2.5 MeV/c
0
20
40
60
80
100
120
140
160
180
0
K
+
D
*-
+ D
0
K
*+
D
-
D
0
B
2
Events/2.5 MeV/c
0
20
40
60
80
100
120
140
160
180
200
0
K
*+
D
*-
D
0
B
2
Events/2.5 MeV/c
0
20
40
60
80
100
120
0
K
0
D
0
D
0
B
2
Events/2.5 MeV/c
0
20
40
60
80
100
120
140
160
180
200
220
0
K
0
D
*0
D
+
0
K
*0
D
0
D
0
B
2
Events/2.5 MeV/c
0
20
40
60
80
100
120
140
160
180
200
0
K
*0
D
*0
D
0
B
FIG. 3 (color online). Fits of the
m
ES
data distributions for the neutral modes,
B
0
!

D
ðÞ
D
ðÞ
K
. The decay mode is indicated in the
plots. Points with statistical errors are data events, the red dashed line represents the signal PDF, the blue long-dashed line represents
the cross-feed event PDF, the blue dashed-dotted line represents the combinatorial background PDF, and the blue dotted line represents
the peaking background PDF. The black solid line shows the total PDF.
MEASUREMENT OF THE
...
PHYSICAL REVIEW D
83,
032004 (2011)
032004-9
resonant contributions. This was first reported by the
BABAR
Collaboration in Ref. [
4
], where it was observed
that the three-body phase-space decay model does not give
a satisfactory description of these decays. In a subsequent
study [
11
], we showed the presence of
D
þ
s
1
ð
2536
Þ
,
c
ð
3770
Þ
, and
X
ð
3872
Þ
mesons in these final states. From
Belle [
10
], we know that the
D
sJ
ð
2700
Þ
meson has a large
contribution in the mode
B
þ
!

D
0
D
0
K
þ
. This meson is
expected to be present in

D
ðÞ
D
ðÞ
K
final states containing
D
0
K
þ
and
D
þ
K
0
, as well as in the final states containing
D

0
K
þ
and
D
K
0
, since it was recently seen decaying to
D

K
[
22
]. There is in addition the possibility of having
unknown resonances in the

D
ðÞ
D
ðÞ
K
final states.
Simulations of the known resonances indicate that the
efficiencies for nonresonant modes and resonant modes
are significantly different. This is due to the fact that the
efficiency is not uniform across the phase space and that
resonant events, depending on the mass, the width, and the
spin of the resonance, populate differently the Dalitz plane.
Ignoring this effect would introduce a bias of up to 9% in
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
2
Events/2.5 MeV/c
0
20
40
60
80
100
120
140
160
180
200
220
0
K
+
D
0
D
+
B
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
2
Events/2.5 MeV/c
0
20
40
60
80
100
120
0
K
*+
D
0
D
+
B
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
)
2
(GeV/c
ES
m
5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3
2
Events/2.5 MeV/c
0
20
40
60
80
100
120
140
160
180
200
220
0
K
+
D
*0
D
+
B
2
Events/2.5 MeV/c
0
20
40
60
80
100
120
140
0
K
*+
D
*0
D
+
B
2
Events/2.5 MeV/c
0
100
200
300
400
500
600
700
+
K
0
D
0
D
+
B
2
Events/2.5 MeV/c
0
200
400
600
800
1000
+
K
*0
D
0
D
+
B
2
Events/2.5 MeV/c
0
100
200
300
400
500
600
+
K
0
D
*0
D
+
B
2
Events/2.5 MeV/c
0
200
400
600
800
1000
1200
1400
+
K
*0
D
*0
D
+
B
2
Events/2.5 MeV/c
0
10
20
30
40
50
60
+
K
+
D
-
D
+
B
2
Events/2.5 MeV/c
0
10
20
30
40
50
60
+
K
*+
D
-
D
+
B
2
Events/2.5 MeV/c
0
10
20
30
40
50
+
K
+
D
*-
D
+
B
2
Events/2.5 MeV/c
0
20
40
60
80
100
120
140
+
K
*+
D
*-
D
+
B
FIG. 4 (color online). Fits of the
m
ES
data distributions for the charged modes,
B
þ
!

D
ðÞ
D
ðÞ
K
. The decay mode is indicated in the
plots. Points with statistical errors are data events, the red dashed line represents the signal PDF, the blue long-dashed line represents
the cross-feed event PDF, the blue dashed-dotted line represents the combinatorial background PDF, and the blue dotted line represents
the peaking background PDF. The black solid line shows the total PDF.
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
032004 (2011)
032004-10