Search for
B
þ
!
D
þ
K
0
and
B
þ
!
D
þ
K
0
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,
1,
*
W. H. Toki,
1
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
M. Morii,
27
A. Adametz,
28
J. Marks,
28
S. Schenk,
28
U. Uwer,
28
F. U. Bernlochner,
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
H. W. Zhao,
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
M. Ebert,
60
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
R. H. Schindler,
63
J. Schwiening,
63
A. Snyder,
63
D. Su,
63
M. K. Sullivan,
63
PHYSICAL REVIEW D
82,
092006 (2010)
1550-7998
=
2010
=
82(9)
=
092006(11)
092006-1
Ó
2010 The American Physical Society
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
X. Chen,
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,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
1
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,
092006 (2010)
092006-2
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, IN
2
P
3
/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
77
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 4 May 2010; published 19 November 2010)
We report a search for the rare decays
B
þ
!
D
þ
K
0
and
B
þ
!
D
þ
K
0
in an event sample of
approximately
465
10
6
B
B
pairs collected with the
B
A
B
AR
detector at the PEP-II asymmetric-energy
e
þ
e
collider at SLAC National Accelerator Laboratory. We find no significant evidence for either mode
*
Now at Temple University, Philadelphia, Pennsylvania 19122, USA
†
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy
‡
Also with Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
x
Present address: University of South Alabama, Mobile, Alabama 36688, USA
k
Also with Universita
`
di Sassari, Sassari, Italy
SEARCH FOR
B
þ
!
D
þ
K
0
AND
...
PHYSICAL REVIEW D
82,
092006 (2010)
092006-3
and we set 90% probability upper limits on the branching fractions of
B
ð
B
þ
!
D
þ
K
0
Þ
<
2
:
9
10
6
and
B
ð
B
þ
!
D
þ
K
0
Þ
<
3
:
0
10
6
.
DOI:
10.1103/PhysRevD.82.092006
PACS numbers: 13.25.Hw, 14.40.Nd
I. INTRODUCTION
Charged
B
meson decays in which neither constituent
quark appears in the final state, such as
B
þ
!
D
þ
K
ðÞ
0
, are
expected to be dominated by weak-annihilation diagrams
with the
bu
pair annihilating into a
W
þ
boson. Such
processes therefore can provide insight into the internal
dynamics of
B
mesons, in particular, the overlap between
the
b
and the
u
quark wave functions. Annihilation ampli-
tudes cannot be evaluated with the commonly used facto-
rization approach [
1
]. As a consequence, there are no
reliable estimates for the corresponding decay rates.
Annihilation amplitudes are expected to be proportional
to
f
B
=m
B
where
m
B
is the mass of the
B
meson and
f
B
is
the pseudoscalar
B
meson decay constant. The quantity
f
B
represents the probability amplitude for the two quark
wave functions to overlap. Numerically,
f
B
=m
B
is approxi-
mately equal to
2
, where
is the sine of the Cabibbo
angle [
1
,
2
]. In addition, these amplitudes are also
suppressed by the Cabibbo-Kobayashi-Maskawa quark-
mixing matrix (CKM) factor
j
V
ub
j
3
. So far, there
has been no observation of a hadronic
B
meson decay
that proceeds purely through weak-annihilation diagrams,
although evidence for the leptonic decay
B
!
has been
found [
3
]. In theoretical calculations of nonleptonic de-
cays, the assumption is often made that these amplitudes
may be neglected.
Some studies indicate that the branching fractions of
weak-annihilation processes could be enhanced by so-
called rescattering effects, in which long-range strong
interactions between
B
decay products, rather than the
decay amplitudes, lead to the final state of interest [
2
].
Figure
1
shows the Feynman diagram for the decays
B
þ
!
D
þ
K
ðÞ
0
and
B
þ
!
D
þ
s
0
[
4
], and the hadron-level
diagram for the rescattering of
D
þ
s
0
into
D
þ
K
ðÞ
0
.
Significant rescattering could thus mimic a large weak-
annihilation amplitude. It has been argued [
2
] that rescat-
tering effects might be suppressed by only
4
, compared to
5
for the weak-annihilation amplitudes, rendering the
B
þ
!
D
þ
K
ðÞ
0
decay rate due to rescattering comparable
to the isospin-related color-suppressed
B
0
!
D
0
K
ðÞ
0
decay rate of approximately
5
10
6
.
B
þ
!
D
þ
K
ðÞ
0
decays are also of interest because
their decay rates can be used to constrain the annihilation
amplitudes in phenomenological fits [
1
,
5
]. This allows the
translation of the measurements of the
B
þ
!
D
0
K
ðÞþ
amplitudes into estimations of the
j
V
ub
j
suppressed ampli-
tudes
B
0
!
D
0
K
ðÞ
0
[
5
,
6
]. None of the modes studied here
has been observed so far, and a 90% confidence level upper
limit on the branching fraction
B
ð
B
þ
!
D
þ
K
0
Þ
<
5
10
6
has been established by
B
A
B
AR
[
7
]. No study of
B
þ
!
D
þ
K
0
has previously been published.
The results presented here are obtained with
426 fb
1
of
data collected at the
ð
4
S
Þ
resonance with the
B
A
B
AR
detector at the PEP-II asymmetric
e
þ
e
collider corre-
sponding to
465
10
6
B
B
pairs (
N
B
B
). An additional
44
:
4fb
1
of data (‘‘off-resonance’’) collected at a
center-of-mass (CM) energy 40 MeV below the
ð
4
S
Þ
resonance is used to study backgrounds from
e
þ
e
!
q
q
(
q
¼
u
,
d
,
s
,or
c
) processes, which we refer to as contin-
uum events.
The
B
A
B
AR
detector is described in detail elsewhere [
8
].
Charged-particle tracking is provided by a five-layer sili-
con vertex tracker (SVT) and a 40 layer drift chamber
(DCH). In addition to providing precise position informa-
tion for tracking, the SVT and DCH measure the specific
ionization, which is used for particle identification of
low-momentum charged particles. At higher momenta
(
p>
0
:
7 GeV
=c
) pions and kaons are identified by
Cherenkov radiation detected in a ring-imaging device
(DIRC). The position and energy of photons are measured
with an electromagnetic calorimeter (EMC) consisting of
6580 thallium-doped CsI crystals. These systems are
mounted inside a 1.5 T solenoidal superconducting mag-
net. Muons are identified by the instrumented magnetic-
flux return, which is located outside the magnet.
II. EVENT RECONSTRUCTION AND SELECTION
The event selection criteria are determined using
Monte Carlo (MC) simulations of
e
þ
e
!
ð
4
S
Þ!
B
B
(‘‘
B
B
’’ in the following) and continuum events, and the
off-resonance data. The selection criteria are optimized by
B
+
b
u
W
D
K
s
d
d
+
(*)0
+
b
u
B
W
c
s
u
+
+
D
s
0
+
B
+
K
D
K
D
*0
(*)0
0
s
+
+
FIG. 1. Annihilation diagram for the decay
B
þ
!
D
þ
K
ðÞ
0
(top). Tree diagram (bottom left) for the decay
B
þ
!
D
þ
s
0
and hadron-level diagram (bottom right) for the rescattering
contribution to
B
þ
!
D
þ
K
ðÞ
0
via
B
þ
!
D
þ
s
0
.
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
82,
092006 (2010)
092006-4
maximizing the quantity
S=
ffiffiffiffiffiffiffiffiffiffiffiffiffi
S
þ
B
p
, where
S
and
B
are
the expected numbers of signal and background events,
respectively. We assume the signal branching fraction to be
5
10
6
in the optimization procedure.
The charged-particle candidates are required to have
transverse momenta above
100 MeV
=c
and at least 12
hits in the DCH.
Candidate
D
þ
mesons are reconstructed in the
D
þ
!
K
þ
þ
(
K
in the following),
D
þ
!
K
0
S
þ
(
K
0
S
),
D
þ
!
K
þ
þ
0
(
K
0
) and
D
þ
!
K
0
S
þ
0
(
K
0
S
0
) modes for the
B
þ
!
D
þ
K
0
decay channel
(
DK
). Only the first two modes are used for the
B
þ
!
D
þ
K
0
decay channel (
DK
in the following) since we find
that including the
K
0
and
K
0
S
0
modes in this
channel does not appreciably improve the sensitivity of
the analysis.
The
D
þ
candidates are reconstructed by combining
kaons (either charged or neutral depending on the channel)
and the appropriate number of pions. The charged kaons
used to reconstruct the
D
þ
and
K
0
candidates are required
to satisfy kaon identification criteria obtained using a like-
lihood technique based on the opening angle of the
Cherenkov light measured in the ring-imaging device
(DIRC) and the ionization energy loss measured in the
SVT and DCH. These criteria are typically 85% efficient,
depending on the momentum and polar angle, with mis-
identification rates at the 2% level. Kaons and pions from
D
decays are required to have momenta in the laboratory
frame greater than
200 MeV
=c
and
150 MeV
=c
, respec-
tively. The reconstructed
D
þ
candidates are required to
satisfy the invariant mass (
M
D
) selection criteria given in
Table
I
.
The
K
0
S
candidates are reconstructed from pairs of
oppositely-charged pions with invariant mass within
5
–
7 MeV
=c
2
of the nominal
K
0
S
mass [
9
]. This mass cut
corresponds to 2–2.8 standard deviations of the experimen-
tal resolution and varies slightly among channels due to
the different amounts of background per channel. For the
prompt
K
0
S
candidates from the
B
þ
!
D
þ
K
0
S
decay, we
require
ln
ð
1
cos
K
0
S
ð
B
þ
ÞÞ
<
8
, where
K
0
S
ð
B
þ
Þ
is the
angle between the momentum vector of the
K
0
S
candidate
and the vector connecting the
B
þ
and
K
0
S
decay vertices.
For
K
0
S
daughters of a
D
þ
decay, we require
ln
ð
1
cos
K
0
S
ð
D
þ
ÞÞ
<
6
, where
K
0
S
ð
D
þ
Þ
is defined in a similar
way.
The
0
candidates are reconstructed from pairs of pho-
ton candidates each with an energy greater than 70 MeV,
and a lateral shower profile in the electromagnetic calo-
rimeter (EMC) consistent with a single electromagnetic
deposit. These pairs must have a total energy greater than
200 MeV, a CM momentum greater than
400 MeV
=c
, and
an invariant mass within
10 MeV
=c
2
(for the
K
0
mode) or
12 MeV
=c
2
(for the
K
0
S
0
mode) of the nomi-
nal
0
mass [
9
].
The
K
0
candidates are reconstructed in the decay chan-
nel
K
0
!
K
þ
. These charged tracks are constrained to
originate from a common vertex. The reconstructed invari-
ant mass, whose width is dominated by the
K
0
natural
width, is required to lie within
40 MeV
=c
2
of the nominal
K
0
mass [
9
]. We define
H
as the angle between the
direction of flight of the charged
K
and the direction of
flight of the
B
in the
K
0
rest frame. The probability
distribution of
cos
H
is proportional to
cos
2
H
for longi-
tudinally polarized
K
0
mesons from
B
!
DK
0
decays,
due to angular momentum conservation, and is approxi-
mately flat for fake (random combinations of tracks) or
unpolarized background
K
0
candidates. To suppress fake
and background
K
0
candidates we require
j
cos
H
j
>
0
:
5
.
The
B
þ
candidates are reconstructed by combining one
D
þ
and one
K
0
S
or
K
0
candidate, constraining them to
originate from a common vertex. The probability distribu-
tion of the cosine of the
B
polar angle with respect to
the beam axis in the CM frame,
cos
B
, is expected to
be proportional to
1
cos
2
B
. Selection criteria on
j
cos
B
j
are channel dependent and are summarized in
Table
I
.
We measure two almost independent kinematic
variables: the beam-energy substituted mass
m
ES
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðð
E
2
0
=c
2
Þ
=
2
þ
~
p
0
~
p
B
=c
2
Þ
2
=
ð
E
2
0
=c
2
Þð
p
B
=c
Þ
2
q
, and the
energy 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 to the
e
þ
e
system, respectively, and
the asterisk denotes a calculation made in the CM frame.
Signal events are expected to peak at the
B
meson mass for
m
ES
and at zero for
E
. Channel-dependent selection
criteria on
j
E
j
are given in Table
I
. We retain candidates
with
m
ES
in the range
½
5
:
20
;
5
:
29
GeV
=c
2
for subsequent
analysis.
In less than 1% of the cases, multiple
B
þ
candidates are
present in the same event, and in those cases we choose the
TABLE I. Main selection criteria used to distinguish between signal and background events.
M
D;
PDG
is the nominal mass of the
D
þ
meson [
9
].
B
þ
!
D
þ
K
0
B
þ
!
D
þ
K
0
Selection criteria
K
K
0
K
0
S
K
0
S
0
K
K
0
S
j
M
D;
PDG
j
(
MeV
=c
2
)
<
12
ð’
1
:
8
Þ
<
18
ð’
1
:
5
Þ
<
14
ð’
1
:
6
Þ
<
22
ð’
1
:
6
Þ
<
10
ð’
1
:
6
Þ
<
10
ð’
1
:
4
Þ
j
cos
B
j
<
0
:
76
<
0
:
77
<
0
:
87
<
0
:
85
<
0
:
82
<
0
:
84
j
E
j
(MeV)
<
20
ð’
1
:
3
Þ
<
23
ð’
1
:
5
Þ
<
25
ð’
1
:
5
Þ
<
24
ð’
1
:
5
Þ
<
19
ð’
1
:
3
Þ
<
19 MeV
ð’
1
:
3
Þ
SEARCH FOR
B
þ
!
D
þ
K
0
AND
...
PHYSICAL REVIEW D
82,
092006 (2010)
092006-5
one with the reconstructed
D
þ
mass closest to the nominal
mass value [
9
]. If more than one
B
þ
candidate shares the
same
D
þ
candidate, then we choose the
B
þ
candidate with
E
closest to zero.
III. BACKGROUND CHARACTERIZATION
After applying the selection criteria described above,
the remaining background is composed of nonsignal
B
B
events and continuum events, the latter being the dominant
contribution. Continuum background events, in contrast to
B
B
events, are characterized by a jetlike shape, which can
be used in a Fisher discriminant
F
[
10
] to reduce this
background component. The discriminant
F
is a linear
combination of four variables trained to peak at 1 for signal
and at
1
for continuum background. The first variable is
the cosine of the angle between the
B
thrust axis and the
thrust axis of all the other reconstructed charged tracks and
neutral energy deposits (rest of the event), where the thrust
axis is defined as the direction that maximizes the sum of
the longitudinal momenta of all the particles. The second
and third variables are the event shape moments
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 tracks and energy deposits in the rest of the event;
p
i
is the momentum and
i
is the angle with respect to the
thrust axis of the
B
candidate. These three variables are
calculated in the CM. Finally we use
j
t
j
, the absolute
value of the measured proper time interval between the two
B
decays [
11
]. It is calculated using the measured separa-
tion along the beam direction
z
between the decay points
of the reconstructed
B
and the other
B
, and the Lorentz boost
between the laboratory and CM frames. The other
B
decay
point is obtained from the tracks that do not belong to the
reconstructed
B
, with constraints from the reconstructed
B
momentum and the beam-spot location. The coefficients
of
F
, chosen to maximize the separation between signal
and continuum background, are determined with samples
of simulated signal and continuum events, and validated
using off-resonance data. We denote two regions: the
fit region, defined as
5
:
20
<m
ES
<
5
:
29 GeV
=c
2
and
5
<
F
<
5
, and the signal region, defined as
5
:
27
<
m
ES
<
5
:
29 GeV
=c
2
and
0
<
F
<
5
.
To reduce the importance of the continuum background
in the final sample we divide the events according to their
flavor-tagging category [
11
]. We define the following
exclusive tagging categories:
(i)
lepton category
, events contain at least one lepton in
the decay of the other
B
meson;
(ii)
kaon category
, events contain at least one kaon in
the decay of the other
B
meson, which do not belong
to the first category;
(iii)
other category
contains all the events not included
in the two previous categories.
The first two categories are expected to be less contami-
nated by continuum background. We fit all three categories
simultaneously. Studies of simulated events show that
using the tagging categories reduces the statistical uncer-
tainty on the measured branching fraction for the
K
mode by 5%, but leads to little gain for the other modes
(which are less statistically significant themselves). Hence,
we use tagging information only for the
K
channel.
The
B
B
background is divided into two components:
nonpeaking (combinatorial) and peaking. The latter can
occur when one or several particles of a background chan-
nel are replaced by a low-momentum charged
þ
and the
resulting candidate still contributes to the signal region.
The largest contributions to the
B
B
peaking background
for the
B
þ
!
D
þ
K
0
channel arise from the following
decays:
B
0
!
D
þ
with
D
þ
decaying into signal chan-
nels,
B
0
!
D
0
K
0
and
B
0
!
D
0
K
0
. To further reduce the
contribution from the
B
0
!
D
þ
background, the vari-
able
j
cos
K
0
S
j
has been introduced, where
K
0
S
is the
K
0
S
helicity angle, i.e., the angle between one of the two pions
TABLE II. Reconstruction efficiencies and expected numbers of events in the fit and signal region assuming
B
ð
B
þ
!
D
þ
K
0
Þ¼
B
ð
B
þ
!
D
þ
K
0
Þ¼
5
10
6
.
B
þ
!
D
þ
K
0
B
þ
!
D
þ
K
0
region
K
K
0
K
0
S
K
0
S
0
K
K
0
S
Signal efficiency
fit
18.4%
5.2%
21.3%
6.2%
10.6%
10.5%
signal
12.4%
3.8%
14.7%
4.9%
7.6%
7.4%
Signal
fit
14
:
1
0
:
22
:
5
0
:
11
:
81
0
:
03 2
:
4
0
:
115
:
8
0
:
31
:
70
0
:
04
signal
9
:
6
0
:
21
:
8
0
:
11
:
21
0
:
03 1
:
9
0
:
111
:
3
0
:
31
:
20
0
:
03
Combinatorial
B
B
background
fit
67
4
157
412
236
3
400
10
42
:
8
4
signal
7
220
23
18
230
26
:
4
1
Peaking
B
B
background
fit
2
:
0
0
:
23
:
3
0
:
41
:
1
0
:
21
:
8
0
:
526
22
:
4
0
:
3
signal
0
:
3
0
:
11
:
0
0
:
20
:
3
0
:
10
:
6
0
:
25
:
4
10
:
7
0
:
2
Continuum background
fit
2840
40 4860
50
640
20
1600
30 6100
50
630
20
signal
63
6
104
812
345
5
129
813
3
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
82,
092006 (2010)
092006-6
from the
K
0
S
and the
D
þ
in the
K
0
S
rest frame. We reject
events with
j
cos
K
0
S
j
greater than 0.8 for the
K
mode
and 0.9 for all other modes. Based on MC studies, we
expect no more than 1
B
B
peaking background event per
mode in the signal region, after applying all selection
criteria (see Table
II
). A similar study is performed for
the
B
þ
!
D
þ
K
0
decay modes. The main peaking back-
grounds arise from
B
0
!
D
þ
,
B
0
!
D
þ
K
, and
B
0
!
D
þ
a
1
. In all cases, the
D
þ
decays into the signal decay
modes. The number of
B
B
peaking background events
expected in the signal region for the
DK
mode are shown
in Table
II
.
Charmless
B
decays may also contribute to the peaking
background. These decays can produce
and
K
mesons
with characteristics similar to those of signal events
without forming a real
D
meson. The charmless back-
ground is evaluated from data using the
D
þ
sidebands:
events are required to satisfy the criteria
1
:
774
<M
D
<
1
:
840 GeV
=c
2
or
1
:
900
<M
D
<
1
:
954 GeV
=c
2
.We
obtain
1
:
7
1
:
0
events for
DK
decays and
0
:
7
2
:
1
events for
DK
decays. We estimate the charmless peaking
background contribution to be negligible and assign a
systematic uncertainty based on this assumption.
The overall reconstruction and selection efficiencies for
signal events, as well as the numbers of expected events for
each background category, are given in Table
II
.
IV. FIT PROCEDURE
The signal and background yields are extracted by max-
imizing the unbinned extended likelihood
L
¼ð
e
N
0
=N
!
Þ
N
0
N
Y
N
j
¼
1
f
ð
x
j
j
; N
0
Þ
:
(1)
Here
x
j
¼f
m
ES
;
F
g
,
is a set of parameters,
N
is the
number of events in the selected sample,
N
0
is the expec-
tation value for the total number of events, and
f
ð
x
j
; N
0
Þ¼
N
sig
f
sig
ð
x
j
Þþ
P
i
N
B
i
f
B
i
ð
x
j
Þ
N
0
;
(2)
with
f
sig
ð
x
j
Þ
and
f
B
i
ð
x
j
Þ
the probability density func-
tions (PDFs) for the hypothesis that the event is a signal
or a background event, respectively. The
B
i
are the differ-
ent background categories used in the fit: continuum
background, combinatorial
B
B
background, and peaking
B
B
background.
N
sig
is the number of signal events,
and
N
B
i
is the number of events for each background
species
B
i
.
The individual probability density functions are defined
by the product of the one-dimensional distributions of
m
ES
and
F
. Absence of the correlations between these distri-
butions is checked using the MC samples. The signal
m
ES
distribution is modeled with a Gaussian function.
The continuum and nonpeaking
B
B
background
m
ES
distributions are modeled with two different threshold
ARGUS functions defined [
12
] as follows:
A
ð
x
Þ¼
x
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
x
x
0
2
s
e
c
ð
1
ð
x=x
0
Þ
2
Þ
;
(3)
where
x
0
represents the maximum allowed value for the
variable
x
and
c
accounts for the shape of the distribution.
The
m
ES
distribution of the peaking
B
B
background is
modeled with a Crystal Ball (CB) function [
13
]. The CB
function is a Gaussian modified to include a power-law
tail on the low side of the peak. The
F
distributions are
modeled as the sum of two asymmetric Gaussians for
signal and continuum background events, and with a
Gaussian for the combinatorial
B
B
background. For the
peaking
B
B
background we use a Gaussian distribution for
the
DK
mode. For the
DK
mode, an asymmetric Gaussian
is used for the
K
mode and a sum of two asymmetric
Gaussians for the
K
0
S
mode. The shape parameters of the
threshold function for continuum background are deter-
mined from data. All other PDF parameters are derived
from the simulated events.
In the fits we fix the numbers of peaking
B
B
back-
ground events, which are estimated from the Particle
Data Group (PDG) branching fractions [
9
] and MC effi-
ciency evaluations.
The number of signal events determined by the fit (
N
sig
)
is used to calculate the branching fraction as
B
ð
B
þ
!
D
þ
K
0
Þ¼
N
sig
N
B
þ
sig
2
B
D
B
K
0
S
;
TABLE III. Expected errors on the branching fractions from
toy MC studies depending on the branching fractions generated.
The combined errors are obtained as results of likelihood com-
bination per each toy (see text for details). All the numbers are
given in units of
10
6
.
B
¼
5
B
¼
0
Decay mode Mean error [95% range] Mean error [95% range]
B
þ
!
D
þ
K
0
K
þ
3
:
3
[2.7, 4.0]
þ
2
:
8
[2.2, 3.6]
3
:
0
[2.2, 3.6]
2
:
4
[1.6, 3.2]
K
0
þ
20
[14, 25]
þ
19
[13, 24]
17
[10, 23]
17
[9.4, 22]
K
0
S
þ
12
[7.3, 16]
þ
11
[7.1, 16]
8
[4.6, 14]
8
[4.5, 14]
K
0
S
0
þ
14
[8.9, 18]
þ
13
[8.3, 17]
12
[6.2, 16]
11
[5.6, 15]
combined
2
:
9
[2.1, 3.6]
2
:
5
[1.5, 3.2]
B
þ
!
D
þ
K
0
K
þ
3
:
5
[2.5, 4.0]
þ
3
:
3
[2.5, 4.0]
3
:
2
[1.8, 3.6]
2
:
8
[1.6, 3.8]
K
0
S
þ
15
[9.8, 19]
þ
14
[7.9, 17]
11
[5.8, 16]
7
:
7
[3.8, 14]
combined
3
:
3
[2.1, 4.2]
3
:
0
[1.8, 3.9]
SEARCH FOR
B
þ
!
D
þ
K
0
AND
...
PHYSICAL REVIEW D
82,
092006 (2010)
092006-7