Search for the rare decays
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1
Y. Karyotakis,
1
J. P. Lees,
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1
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G. Lynch,
6
L. M. Mir,
6
P. J. Oddone,
6
T. J. Orimoto,
6
M. Pripstein,
6
N. A. Roe,
6
M. T. Ronan,
6
W. A. Wenzel,
6
M. Barrett,
7
K. E. Ford,
7
T. J. Harrison,
7
A. J. Hart,
7
C. M. Hawkes,
7
S. E. Morgan,
7
A. T. Watson,
7
M. Fritsch,
8
K. Goetzen,
8
T. Held,
8
H. Koch,
8
B. Lewandowski,
8
M. Pelizaeus,
8
K. Peters,
8
T. Schroeder,
8
M. Steinke,
8
J. T. Boyd,
9
J. P. Burke,
9
W. N. Cottingham,
9
T. Cuhadar-Donszelmann,
10
B. G. Fulsom,
10
C. Hearty,
10
N. S. Knecht,
10
T. S. Mattison,
10
J. A. McKenna,
10
A. Khan,
11
P. Kyberd,
11
M. Saleem,
11
L. Teodorescu,
11
A. E. Blinov,
12
V. E. Blinov,
12
A. D. Bukin,
12
V. P. Druzhinin,
12
V. B. Golubev,
12
E. A. Kravchenko,
12
A. P. Onuchin,
12
S. I. Serednyakov,
12
Yu. I. Skovpen,
12
E. P. Solodov,
12
A. N. Yushkov,
12
M. Bondioli,
13
M. Bruinsma,
13
M. Chao,
13
S. Curry,
13
I. Eschrich,
13
D. Kirkby,
13
A. J. Lankford,
13
P. Lund,
13
M. Mandelkern,
13
R. K. Mommsen,
13
W. Roethel,
13
D. P. Stoker,
13
C. Buchanan,
14
B. L. Hartfiel,
14
S. D. Foulkes,
15
J. W. Gary,
15
O. Long,
15
B. C. Shen,
15
K. Wang,
15
L. Zhang,
15
D. del Re,
16
H. K. Hadavand,
16
E. J. Hill,
16
D. B. MacFarlane,
16
H. P. Paar,
16
S. Rahatlou,
16
V. Sharma,
16
J. W. Berryhill,
17
C. Campagnari,
17
A. Cunha,
17
B. Dahmes,
17
T. M. Hong,
17
M. A. Mazur,
17
J. D. Richman,
17
W. Verkerke,
17
T. W. Beck,
18
A. M. Eisner,
18
C. J. Flacco,
18
C. A. Heusch,
18
J. Kroseberg,
18
W. S. Lockman,
18
G. Nesom,
18
T. Schalk,
18
B. A. Schumm,
18
A. Seiden,
18
P. Spradlin,
18
D. C. Williams,
18
M. G. Wilson,
18
J. Albert,
19
E. Chen,
19
G. P. Dubois-Felsmann,
19
A. Dvoretskii,
19
D. G. Hitlin,
19
J. S. Minamora,
19
I. Narsky,
19
T. Piatenko,
19
F. C. Porter,
19
A. Ryd,
19
A. Samuel,
19
R. Andreassen,
20
G. Mancinelli,
20
B. T. Meadows,
20
M. D. Sokoloff,
20
F. Blanc,
21
P. C. Bloom,
21
S. Chen,
21
W. T. Ford,
21
J. F. Hirschauer,
21
A. Kreisel,
21
U. Nauenberg,
21
A. Olivas,
21
W. O. Ruddick,
21
J. G. Smith,
21
K. A. Ulmer,
21
S. R. Wagner,
21
J. Zhang,
21
A. Chen,
22
E. A. Eckhart,
22
J. L. Harton,
22
A. Soffer,
22
W. H. Toki,
22
R. J. Wilson,
22
F. Winklmeier,
22
Q. Zeng,
22
D. Altenburg,
23
E. Feltresi,
23
A. Hauke,
23
B. Spaan,
23
T. Brandt,
24
J. Brose,
24
M. Dickopp,
24
V. Klose,
24
H. M. Lacker,
24
R. Nogowski,
24
S. Otto,
24
A. Petzold,
24
J. Schubert,
24
K. R. Schubert,
24
R. Schwierz,
24
J. E. Sundermann,
24
D. Bernard,
25
G. R. Bonneaud,
25
P. Grenier,
25
E. Latour,
25
S. Schrenk,
25
Ch. Thiebaux,
25
G. Vasileiadis,
25
M. Verderi,
25
D. J. Bard,
26
P. J. Clark,
26
W. Gradl,
26
F. Muheim,
26
S. Playfer,
26
Y. Xie,
26
M. Andreotti,
27
D. Bettoni,
27
C. Bozzi,
27
R. Calabrese,
27
G. Cibinetto,
27
E. Luppi,
27
M. Negrini,
27
L. Piemontese,
27
F. Anulli,
28
R. Baldini-Ferroli,
28
A. Calcaterra,
28
R. de Sangro,
28
G. Finocchiaro,
28
P. Patteri,
28
I. M. Peruzzi,
28,
*
M. Piccolo,
28
A. Zallo,
28
A. Buzzo,
29
R. Capra,
29
R. Contri,
29
M. Lo Vetere,
29
M. M. Macri,
29
M. R. Monge,
29
S. Passaggio,
29
C. Patrignani,
29
E. Robutti,
29
A. Santroni,
29
S. Tosi,
29
G. Brandenburg,
30
K. S. Chaisanguanthum,
30
M. Morii,
30
J. Wu,
30
R. S. Dubitzky,
31
U. Langenegger,
31
J. Marks,
31
S. Schenk,
31
U. Uwer,
31
W. Bhimji,
32
D. A. Bowerman,
32
P. D. Dauncey,
32
U. Egede,
32
R. L. Flack,
32
J. R. Gaillard,
32
J. A. Nash,
32
M. B. Nikolich,
32
W. Panduro Vazquez,
32
X. Chai,
33
M. J. Charles,
33
W. F. Mader,
33
U. Mallik,
33
V. Ziegler,
33
J. Cochran,
34
H. B. Crawley,
34
L. Dong,
34
V. Eyges,
34
W. T. Meyer,
34
S. Prell,
34
E. I. Rosenberg,
34
A. E. Rubin,
34
J. I. Yi,
34
G. Schott,
35
N. Arnaud,
36
M. Davier,
36
X. Giroux,
36
G. Grosdidier,
36
A. Ho
̈
cker,
36
F. Le Diberder,
36
V. Lepeltier,
36
A. M. Lutz,
36
A. Oyanguren,
36
T. C. Petersen,
36
S. Plaszczynski,
36
S. Rodier,
36
P. Roudeau,
36
M. H. Schune,
36
A. Stocchi,
36
W. Wang,
36
G. Wormser,
36
C. H. Cheng,
37
D. J. Lange,
37
D. M. Wright,
37
A. J. Bevan,
38
C. A. Chavez,
38
I. J. Forster,
38
J. R. Fry,
38
E. Gabathuler,
38
R. Gamet,
38
K. A. George,
38
D. E. Hutchcroft,
38
R. J. Parry,
38
D. J. Payne,
38
K. C. Schofield,
38
C. Touramanis,
38
F. Di Lodovico,
39
W. Menges,
39
R. Sacco,
39
C. L. Brown,
40
G. Cowan,
40
H. U. Flaecher,
40
M. G. Green,
40
D. A. Hopkins,
40
P. S. Jackson,
40
T. R. McMahon,
40
S. Ricciardi,
40
F. Salvatore,
40
D. N. Brown,
41
C. L. Davis,
41
J. Allison,
42
N. R. Barlow,
42
R. J. Barlow,
42
Y. M. Chia,
42
C. L. Edgar,
42
M. C. Hodgkinson,
42
M. P. Kelly,
42
G. D. Lafferty,
42
M. T. Naisbit,
42
J. C. Williams,
42
C. Chen,
43
W. D. Hulsbergen,
43
A. Jawahery,
43
D. Kovalskyi,
43
C. K. Lae,
43
D. A. Roberts,
43
G. Simi,
43
G. Blaylock,
44
C. Dallapiccola,
44
S. S. Hertzbach,
44
R. Kofler,
44
X. Li,
44
T. B. Moore,
44
S. Saremi,
44
H. Staengle,
44
S. Y. Willocq,
44
R. Cowan,
45
K. Koeneke,
45
G. Sciolla,
45
S. J. Sekula,
45
M. Spitznagel,
45
F. Taylor,
45
R. K. Yamamoto,
45
H. Kim,
46
P. M. Patel,
46
S. H. Robertson,
46
A. Lazzaro,
47
V. Lombardo,
47
F. Palombo,
47
J. M. Bauer,
48
L. Cremaldi,
48
V. Eschenburg,
48
R. Godang,
48
R. Kroeger,
48
J. Reidy,
48
D. A. Sanders,
48
D. J. Summers,
48
H. W. Zhao,
48
S. Brunet,
49
D. Co
ˆ
te
́
,
49
P. Taras,
49
F. B. Viaud,
49
H. Nicholson,
50
N. Cavallo,
51,†
G. De Nardo,
51
F. Fabozzi,
51,†
C. Gatto,
51
L. Lista,
51
D. Monorchio,
51
P. Paolucci,
51
D. Piccolo,
51
C. Sciacca,
51
M. Baak,
52
H. Bulten,
52
G. Raven,
52
H. L. Snoek,
52
L. Wilden,
52
C. P. Jessop,
53
J. M. LoSecco,
53
T. Allmendinger,
54
G. Benelli,
54
K. K. Gan,
54
K. Honscheid,
54
D. Hufnagel,
54
P. D. Jackson,
54
H. Kagan,
54
R. Kass,
54
T. Pulliam,
54
A. M. Rahimi,
54
R. Ter-Antonyan,
54
Q. K. Wong,
54
N. L. Blount,
55
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55
N. B. Sinev,
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D. Strom,
55
J. Strube,
55
E. Torrence,
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56
M. Margoni,
56
M. Morandin,
56
M. Posocco,
56
M. Rotondo,
56
F. Simonetto,
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R. Stroili,
56
C. Voci,
56
M. Benayoun,
57
J. Chauveau,
57
P. David,
57
L. Del Buono,
57
Ch. de la Vaissie
`
re,
57
O. Hamon,
57
M. J. J. John,
57
Ph. Leruste,
57
J. Malcle
`
s,
57
J. Ocariz,
57
L. Roos,
57
G. Therin,
57
P. K. Behera,
58
L. Gladney,
58
Q. H. Guo,
58
J. Panetta,
58
M. Biasini,
59
R. Covarelli,
59
S. Pacetti,
59
M. Pioppi,
59
C. Angelini,
60
G. Batignani,
60
S. Bettarini,
60
F. Bucci,
60
G. Calderini,
60
M. Carpinelli,
60
R. Cenci,
60
F. Forti,
60
M. A. Giorgi,
60
A. Lusiani,
60
G. Marchiori,
60
M. Morganti,
60
N. Neri,
60
E. Paoloni,
60
M. Rama,
60
G. Rizzo,
60
J. Walsh,
60
M. Haire,
61
D. Judd,
61
D. E. Wagoner,
61
J. Biesiada,
62
N. Danielson,
62
P. Elmer,
62
Y. P. Lau,
62
C. Lu,
62
J. Olsen,
62
A. J. S. Smith,
62
A. V. Telnov,
62
F. Bellini,
63
G. Cavoto,
63
A. D’Orazio,
63
E. Di Marco,
63
R. Faccini,
63
F. Ferrarotto,
63
F. Ferroni,
63
M. Gaspero,
63
L. Li Gioi,
63
M. A. Mazzoni,
63
S. Morganti,
63
G. Piredda,
63
F. Polci,
63
F. Safai Tehrani,
63
C. Voena,
63
H. Schro
̈
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64
R. Waldi,
64
T. Adye,
65
N. De Groot,
65
B. Franek,
65
G. P. Gopal,
65
E. O. Olaiya,
65
F. F. Wilson,
65
R. Aleksan,
66
S. Emery,
66
A. Gaidot,
66
S. F. Ganzhur,
66
G. Graziani,
66
G. Hamel de Monchenault,
66
W. Kozanecki,
66
M. Legendre,
66
G. W. London,
66
B. Mayer,
66
G. Vasseur,
66
Ch. Ye
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66
M. Zito,
66
M. V. Purohit,
67
A. W. Weidemann,
67
J. R. Wilson,
67
T. Abe,
68
M. T. Allen,
68
D. Aston,
68
R. Bartoldus,
68
N. Berger,
68
A. M. Boyarski,
68
O. L. Buchmueller,
68
R. Claus,
68
J. P. Coleman,
68
M. R. Convery,
68
M. Cristinziani,
68
J. C. Dingfelder,
68
D. Dong,
68
J. Dorfan,
68
D. Dujmic,
68
W. Dunwoodie,
68
S. Fan,
68
R. C. Field,
68
T. Glanzman,
68
S. J. Gowdy,
68
T. Hadig,
68
V. Halyo,
68
C. Hast,
68
T. Hryn’ova,
68
W. R. Innes,
68
M. H. Kelsey,
68
P. Kim,
68
M. L. Kocian,
68
D. W. G. S. Leith,
68
J. Libby,
68
S. Luitz,
68
V. Luth,
68
H. L. Lynch,
68
H. Marsiske,
68
R. Messner,
68
D. R. Muller,
68
C. P. O’Grady,
68
V. E. Ozcan,
68
A. Perazzo,
68
M. Perl,
68
B. N. Ratcliff,
68
A. Roodman,
68
A. A. Salnikov,
68
R. H. Schindler,
68
J. Schwiening,
68
A. Snyder,
68
J. Stelzer,
68
D. Su,
68
M. K. Sullivan,
68
K. Suzuki,
68
S. K. Swain,
68
J. M. Thompson,
68
J. Va’vra,
68
N. van Bakel,
68
M. Weaver,
68
A. J. R. Weinstein,
68
W. J. Wisniewski,
68
M. Wittgen,
68
D. H. Wright,
68
A. K. Yarritu,
68
K. Yi,
68
C. C. Young,
68
P. R. Burchat,
69
A. J. Edwards,
69
S. A. Majewski,
69
B. A. Petersen,
69
C. Roat,
69
M. Ahmed,
70
S. Ahmed,
70
M. S. Alam,
70
R. Bula,
70
J. A. Ernst,
70
M. A. Saeed,
70
F. R. Wappler,
70
S. B. Zain,
70
W. Bugg,
71
M. Krishnamurthy,
71
S. M. Spanier,
71
R. Eckmann,
72
J. L. Ritchie,
72
A. Satpathy,
72
R. F. Schwitters,
72
J. M. Izen,
73
I. Kitayama,
73
X. C. Lou,
73
S. Ye,
73
F. Bianchi,
74
M. Bona,
74
F. Gallo,
74
D. Gamba,
74
M. Bomben,
75
L. Bosisio,
75
C. Cartaro,
75
F. Cossutti,
75
G. Della Ricca,
75
S. Dittongo,
75
S. Grancagnolo,
75
L. Lanceri,
75
L. Vitale,
75
V. Azzolini,
76
F. Martinez-Vidal,
76
R. S. Panvini,
77,‡
Sw. Banerjee,
78
B. Bhuyan,
78
C. M. Brown,
78
D. Fortin,
78
K. Hamano,
78
R. Kowalewski,
78
I. M. Nugent,
78
J. M. Roney,
78
R. J. Sobie,
78
J. J. Back,
79
P. F. Harrison,
79
T. E. Latham,
79
G. B. Mohanty,
79
H. R. Band,
80
X. Chen,
80
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80
S. Dasu,
80
M. Datta,
80
A. M. Eichenbaum,
80
K. T. Flood,
80
M. T. Graham,
80
J. J. Hollar,
80
J. R. Johnson,
80
P. E. Kutter,
80
H. Li,
80
R. Liu,
80
B. Mellado,
80
A. Mihalyi,
80
A. K. Mohapatra,
80
Y. Pan,
80
M. Pierini,
80
R. Prepost,
80
P. Tan,
80
S. L. Wu,
80
Z. Yu,
80
and H. Neal
81
(
B
A
B
AR
Collaboration)
1
Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France
2
IFAE, Universitat Autonoma de Barcelona, E-08193 Bellaterra, Barcelona, Spain
3
Universita
`
di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy
4
Institute of High Energy Physics, Beijing 100039, China
5
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
6
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
7
University of Birmingham, Birmingham, B15 2TT, United Kingdom
8
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
9
University of Bristol, Bristol BS8 1TL, United Kingdom
10
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
11
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
12
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
13
University of California at Irvine, Irvine, California 92697, USA
14
University of California at Los Angeles, Los Angeles, California 90024, USA
15
University of California at Riverside, Riverside, California 92521, USA
16
University of California at San Diego, La Jolla, California 92093, USA
17
University of California at Santa Barbara, Santa Barbara, California 93106, USA
18
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
19
California Institute of Technology, Pasadena, California 91125, USA
20
University of Cincinnati, Cincinnati, Ohio 45221, USA
21
University of Colorado, Boulder, Colorado 80309, USA
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
071103(R) (2006)
RAPID COMMUNICATIONS
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22
Colorado State University, Fort Collins, Colorado 80523, USA
23
Universita
̈
t Dortmund, Institut fu
̈
r Physik, D-44221 Dortmund, Germany
24
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
25
Ecole Polytechnique, LLR, F-91128 Palaiseau, France
26
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
27
Universita
`
di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
28
Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
29
Universita
`
di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
30
Harvard University, Cambridge, Massachusetts 02138, USA
31
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
32
Imperial College London, London, SW7 2AZ, United Kingdom
33
University of Iowa, Iowa City, Iowa 52242, USA
34
Iowa State University, Ames, Iowa 50011-3160, USA
35
Universita
̈
t Karlsruhe, Institut fu
̈
r Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
36
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, F-91898 Orsay, France
37
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
38
University of Liverpool, Liverpool L69 72E, United Kingdom
39
Queen Mary, University of London, E1 4NS, United Kingdom
40
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
41
University of Louisville, Louisville, Kentucky 40292, USA
42
University of Manchester, Manchester M13 9PL, United Kingdom
43
University of Maryland, College Park, Maryland 20742, USA
44
University of Massachusetts, Amherst, Massachusetts 01003, USA
45
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
46
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
47
Universita
`
di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
48
University of Mississippi, University, Mississippi 38677, USA
49
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
50
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
51
Universita
`
di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
52
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
53
University of Notre Dame, Notre Dame, Indiana 46556, USA
54
Ohio State University, Columbus, Ohio 43210, USA
55
University of Oregon, Eugene, Oregon 97403, USA
56
Universita
`
di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
57
Universite
́
s Paris VI et VII, Laboratoire de Physique Nucle
́
aire et de Hautes Energies, F-75252 Paris, France
58
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
59
Universita
`
di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy
60
Universita
`
di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
61
Prairie View A&M University, Prairie View, Texas 77446, USA
62
Princeton University, Princeton, New Jersey 08544, USA
63
Universita
`
di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
64
Universita
̈
t Rostock, D-18051 Rostock, Germany
65
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
66
DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
67
University of South Carolina, Columbia, South Carolina 29208, USA
68
Stanford Linear Accelerator Center, Stanford, California 94309, USA
69
Stanford University, Stanford, California 94305-4060, USA
70
State University of New York, Albany, New York 12222, USA
71
University of Tennessee, Knoxville, Tennessee 37996, USA
72
University of Texas at Austin, Austin, Texas 78712, USA
73
University of Texas at Dallas, Richardson, Texas 75083, USA
74
Universita
`
di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
75
Universita
`
di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
76
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
77
Vanderbilt University, Nashville, Tennessee 37235, USA
*
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy
‡
Deceased
†
Also with Universita
`
della Basilicata, Potenza, Italy
SEARCH FOR THE RARE DECAYS
B
0
!
D
s
a
0
2
PHYSICAL REVIEW D
73,
071103(R) (2006)
RAPID COMMUNICATIONS
071103-3
78
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
79
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
80
University of Wisconsin, Madison, Wisconsin 53706, USA
81
Yale University, New Haven, Connecticut 06511, USA
(Received 13 December 2005; published 27 April 2006)
We have searched for the decays
B
0
!
D
s
a
0
,
B
0
!
D
s
a
0
,
B
0
!
D
s
a
2
and
B
0
!
D
s
a
2
in a
sample of about
230
10
6
4
S
!
B
B
decays collected with the
BABAR
detector at the PEP-II
asymmetric-energy
B
Factory at SLAC. We find no evidence for these decays and set upper limits at
90% C.L. on the branching fractions:
B
B
0
!
D
s
a
0
<
1
:
9
10
5
,
B
B
0
!
D
s
a
0
<
3
:
6
10
5
,
B
B
0
!
D
s
a
2
<
1
:
9
10
4
, and
B
B
0
!
D
s
a
2
<
2
:
0
10
4
.
DOI:
10.1103/PhysRevD.73.071103
PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Hh
The time-dependent decay rates for neutral
B
mesons
into a
D
meson and a light meson provide sensitivity to the
Cabibbo-Kobayashi-Maskawa (CKM) [1] quark mixing
matrix phases
and
[2]. A
CP
-violating term emerges
through the interference between
B
0
B
0
mixing mediated
and direct decay amplitudes. The time-dependent
CP
-asymmetries in the decay modes
B
0
!
D
[3]
have been studied by
BABAR
and BELLE [4,5]. In these
modes, the
CP
-asymmetries arise due to a phase difference
between two amplitudes of very different magnitudes: one
decay amplitude is suppressed by the product of two small
CKM elements
V
ub
and
V
cd
, while the other is CKM
favored. Therefore, the decay rate is dominated by the
CKM-favored part of the amplitude, resulting in a very
small
CP
-violating asymmetry.
Recently it was proposed to consider other types of light
mesons in the two-body final states [6]. The idea is that
decay amplitudes with light scalar or tensor mesons, such
as
a
0
or
a
2
, emitted from a weak current, are significantly
suppressed because of the small coupling constants
f
a
0
2
.
In the
SU
2
limit,
f
a
0
0
(since the coupling constant of
a light scalar is proportional to the mass difference between
u
and
d
quarks), and any nonzero value of
f
a
0
is of the
order of isospin conservation breaking effects. Since the
light tensor meson
a
2
has spin 2, it cannot be emitted by a
W
-boson (i.e.
f
a
2
0
), and thus could only appear in a
V
cb
-mediated process via final state hadronic interactions
and rescattering. Therefore, the absolute values of the
CKM-suppressed and favored parts of the decay amplitude
(see Fig. 1, top two diagrams) could become comparable,
potentially resulting in a large
CP
-asymmetry. No
B
!
a
0
2
X
transitions have been observed yet. A summary of
the theoretical predictions for the values of
V
ub
and
V
cb
-mediated parts of the
B
0
!
D
a
0
2
branching frac-
tions can be found in [7].
The
V
ub
-mediated amplitudes in [7] were computed in
the factorization framework. In addition to model uncer-
tainties, significant uncertainty in the theoretical calcula-
tions is due to unknown
B
!
a
0
2
X
transition form factors.
One way to verify the numerical assumptions and test the
validity of the factorization approach experimentally is to
measure the branching fractions for the
SU
3
conjugated
decay modes
B
0
!
D
s
a
0
2
. These decays are repre-
sented by a single tree diagram (Fig. 1, bottom diagram)
with external
W
emission, without contributions from
additional tree or penguin diagrams. The
V
ub
-mediated
part of the
B
0
!
D
a
0
2
decay amplitude can be related
to
B
0
!
D
s
a
0
2
using
tan
Cabibbo
j
V
cd
=V
cs
j
and the
ratio of the decay constants
f
D
s
=f
D
.
Branching fractions of
B
0
!
D
s
a
2
are predicted to
be in the range 1.3–1.8 (2.1– 2.9) in units of
10
5
[8].
Branching fraction estimates for
B
0
!
D
s
a
0
of ap-
proximately
8
10
5
are obtained using
SU
3
symmetry
from the predictions made for
B
0
!
D
a
0
in [7].
In this paper we present the first search for the decays
B
0
!
D
s
a
0
,
B
0
!
D
s
a
0
,
B
0
!
D
s
a
2
and
B
0
!
D
s
a
2
. The analysis uses a sample of approximately
210 fb
1
, which corresponds to about
230
10
6
4
S
decays into
B
B
pairs collected in the years 1999 – 2004
with the
BABAR
detector at the asymmetric-energy
B
-factory PEP-II [9]. The
BABAR
detector is described
elsewhere [10] and only the components crucial to this
analysis are summarized here. Charged-particle tracking is
provided by a five-layer silicon vertex tracker (SVT) and a
40-layer drift chamber (DCH). For charged-particle iden-
tification, ionization energy loss (
dE=dx
) in the DCH and
SVT, and Cherenkov radiation detected in a ring-imaging
FIG. 1. Top two diagrams: tree diagrams contributing to the
decay amplitude of
B
0
!
D
a
0
2
(including the
B
0
B
0
mixing
mediated part of the amplitude). Bottom diagram: tree diagram
representing the decay amplitude of
B
0
!
D
s
a
0
2
.
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
071103(R) (2006)
RAPID COMMUNICATIONS
071103-4
device are used. Photons are identified and measured using
the electromagnetic calorimeter, which is comprised of
6580 thallium-doped CsI crystals. These systems are lo-
cated inside a 1.5 T solenoidal superconducting magnet.
We use GEANT4 [11] software to simulate interactions of
particles traversing the
BABAR
detector, taking into ac-
count the varying detector
conditions and beam
backgrounds.
The optimal selection criteria as well as the shapes of the
distributions of selection variables are determined by a
blind analysis based on Monte Carlo (MC) simulation of
both signal and background. For the calculation of the
expected signal yield we assume
B
B
0
!
D
s
a
2
to be
the mean values of the predicted intervals from [8] and an
estimate of
B
B
0
!
D
s
a
0
is obtained from
B
B
0
!
D
a
0
predicted in [7] and assuming
SU
3
symmetry.
We use MC samples of our signal modes and, to simulate
background, inclusive samples of
B
B
(
800 fb
1
),
B
0
B
0
(
782 fb
1
),
c
c
(
263 fb
1
), and
q
q
,
q
u
,
d
,
s
(
279 fb
1
).
In addition, we use large samples of simulated events of
rare background modes which have final states similar to
the signal. We have verified that our MC correctly de-
scribes real data by comparing distributions of various
selection variables.
Candidates for
D
s
mesons are reconstructed in the
modes
D
s
!
,
K
0
K
, and
K
0
S
K
, with
!
K
K
,
K
0
!
K
and
K
0
S
!
. The
K
0
S
candi-
dates are reconstructed from two oppositely-charged
tracks, with an invariant mass close to the nominal
K
0
S
mass [12], that come from a common vertex displaced
from the
e
e
interaction point. All other tracks are re-
quired to originate less than 1.5 cm away from the
e
e
interaction point in the transverse plane and less than
10 cm along the beam axis. Charged kaon candidates
must satisfy kaon identification criteria that are typically
around 95% efficient, depending on momentum and polar
angle, and have a misidentification rate at the 10% level.
The
!
K
K
,
K
0
!
K
and
K
0
S
!
candi-
dates are required to have invariant masses close to their
nominal masses [12] (we require the absolute differences
between their measured masses and the nominal values
[12] to be in the range 12 –15 MeV, 35– 60 MeV and 7–
12 MeV, respectively, depending on the
B
0
and
D
s
decay
modes). The polarizations of the
K
0
and
mesons in the
D
s
decays are used to reject backgrounds through the use
of the helicity angle
H
, defined as the angle between the
K
momentum vector and the direction of flight of the
D
s
in the
K
0
or
rest frame. The
K
0
candidates are required
to have
j
cos
H
j
greater than 0.25– 0.5 and
candidates are
required to have
j
cos
H
j
greater than 0.3– 0.5, depending
on the
B
0
decay mode. We also apply a vertex fit to the
D
s
candidates that decay into
and
K
0
K
, since all
charged daughter tracks of
D
s
are supposed to come
from a common vertex. The
2
of the vertex fit is required
to be less than 10 –16 (which corresponds to a probability
of better than 0.1% –1.9% for the 3 track vertex fit), de-
pending on the reconstructed mode.
The
D
s
candidates are reconstructed in the mode
D
s
!
D
s
. The photons are required to have an energy
greater than 100 MeV. The
D
s
and
D
s
candidates are
required to have invariant masses less than about
2
from their nominal values [12] (both
D
s
and
D
s
mass
resolutions are around
6 MeV
=c
2
). The invariant mass of
the
D
s
is calculated after the mass constraint on the
daughter
D
s
has been applied. Subsequently, all
D
s
candidates are subjected to a mass-constrained fit.
We reconstruct
a
0
and
a
2
candidates in their decay to
the
final state. For reconstructed
!
candidates
we require the energy of each photon to be greater than
250 MeV for
a
0
candidates, and greater than 300 –
400 MeV for
a
2
candidates, depending on the
D
s
mode.
The
mass is required to be within a
1
or
2
interval
of the nominal value [12], depending on the background
conditions in a particular
B
0
,
D
s
decay mode (the
mass
resolution is measured to be around
15 MeV
=c
2
). The
a
0
and
a
2
candidates are required to have a mass
m
in the
range
0
:
9
–
1
:
1 GeV
=c
2
and
1
:
2
–
1
:
5 GeV
=c
2
, respectively.
We also require that photons from
and
D
s
are incon-
sistent with
0
hypothesis when combined with any other
photon in the event (the
0
veto window varies from
10
to
15 MeV
=c
2
). Finally, the
B
0
meson candidates are
formed using the reconstructed combinations of
D
s
a
0
,
D
s
a
2
,
D
s
a
0
and
D
s
a
2
.
The background from continuum
q
q
production (where
q
u
,
d
,
s
,
c
) is suppressed based on the event topology.
We calculate the angle (
T
) between the thrust axis of the
B
meson candidate and the thrust axis of all other particles in
the event. In the center-of-mass frame (c.m.),
B
B
pairs are
produced approximately at rest and have a uniform
cos
T
distribution. In contrast,
q
q
pairs are produced in the c.m.
frame with high momentum, which results in a
j
cos
T
j
distribution peaking at 1. Depending on the background
level of each mode,
j
cos
T
j
is required to be smaller than
0.70 – 0.75. We further suppress backgrounds using a Fisher
discriminant (
F
) [13] constructed from the scalar sum of
the c.m. momenta of all tracks and photons (excluding the
B
candidate decay products) flowing into 9 concentric
cones centered on the thrust axis of the
B
candidate. The
more isotropic the event, the larger the value of
F
.We
require
F
to be larger than a threshold that retains 75% to
86% of the signal while rejecting 78% to 65% of the
background, depending on the background level. In addi-
tion, the ratio of the second and zeroth order Fox-Wolfram
moments [14] must be less than a threshold in the range
0.25– 0.40 depending on the decay mode.
We extract the signal using the kinematical variables
m
ES
E
2
b
P
i
p
i
2
q
and
E
P
i
m
2
i
p
2
i
q
E
b
,
where
E
b
is the beam energy in the c.m. frame,
p
i
is the
c.m. momentum of the daughter particle
i
of the
B
0
meson
candidate, and
m
i
is the mass hypothesis for particle
i
.For
SEARCH FOR THE RARE DECAYS
B
0
!
D
s
a
0
2
PHYSICAL REVIEW D
73,
071103(R) (2006)
RAPID COMMUNICATIONS
071103-5
signal events,
m
ES
peaks at the
B
0
meson mass with a
resolution of about
2
:
7 MeV
=c
2
and
E
peaks near zero
with a resolution of 20 MeV, indicating that the
B
0
candi-
date has a total energy consistent with the beam energy in
the c.m. frame. The
B
0
candidates are required to have
j
E
j
<
40 MeV
and
m
ES
>
5
:
2 GeV
=c
2
.
The fraction of multiple
B
0
candidates per event is
estimated using the MC simulation and found to be around
2% for
D
s
a
0
2
and 5% for
D
s
a
0
2
combinations. In each
event with more than one
B
0
candidate that passed the
selection requirements, we select the one with the lowest
j
E
j
value.
After all selection criteria are applied, we estimate the
B
0
reconstruction efficiencies, excluding the intermediate
branching fractions (see Table I).
Background events that pass these selection criteria are
mostly from
q
q
continuum, and their
m
ES
distribution is
described by a threshold function [15]:
f
m
ES
m
ES
1
x
2
p
exp
1
x
2
;
where
x
2
m
ES
=
s
p
,
s
p
is the total energy of the beams in
their center-of-mass frame, and
is the fit parameter. A
study using simulated events of
B
0
and
B
decay modes
with final states similar to our signal mode, including
D
s
and
D
s
, shows that these modes do not
peak in
m
ES
.
Figure 2 shows the
m
ES
distributions for the recon-
structed candidates
B
0
!
D
s
a
0
,
B
0
!
D
s
a
2
,
B
0
!
D
s
a
0
and
B
0
!
D
s
a
2
. For each mode, we perform
an unbinned maximum-likelihood fit to the
m
ES
distribu-
tions using the candidates from all
D
s
decay modes com-
bined. We fit the
m
ES
distributions with the sum of the
function
f
m
ES
characterizing the combinatorial back-
ground and a Gaussian function to describe the signal.
The total signal yield in each
B
0
decay mode is calculated
as a sum over
D
s
modes (
i
,
K
0
K
,
K
0
S
K
):
n
sig
B
N
B
B
X
i
B
i
i
;
where
B
is the branching fraction of the
B
0
decay mode,
N
B
B
is the number of produced
B
B
pairs,
B
i
is the product
of the intermediate branching ratios and
i
is the recon-
struction efficiency. The mean and the width of the
Gaussian function are fixed to values obtained from simu-
lated signal events for each decay mode. The threshold
shape parameter
, along with the branching ratio
B
are
free parameters of the fit. The likelihood function is given
by:
L
e
N
N
!
Y
N
i
1
n
sig
P
sig
i
N
n
sig
P
bkg
i
;
where
P
sig
i
and
P
bkg
i
are the probability density functions
for the corresponding hypotheses,
N
is the total number of
events in the fit and
i
is the index over all events in the fit.
Table II (second column) shows the signal event yields
from the
m
ES
fit. Because of a lack of entries in the signal
region for the
B
0
!
D
s
a
2
mode, the fit did not yield any
central value for the number of signal events in this mode.
Accounting for the estimated reconstruction efficiencies
and daughter particles branching fractions, we measure the
branching fractions shown in the third column of Table II.
The systematic errors include a 14% relative uncertainty
for
D
s
decay rates [16]. Uncertainties in the
m
ES
signal
and background shapes result in 11% relative error in the
measured branching fractions. The rest of the systematic
error sources, which include uncertainties in photon and
reconstruction efficiencies, the
a
0
and
a
2
masses and
1
2
3
5.2
5.23
5.26
0
1
2
0
5.2
5.23
5.26 5.29
Events/1 MeV/c
2
FIG. 2.
Distributions of
m
ES
for
B
0
!
D
s
a
0
2
candidates
overlaid with the projection of the maximum-likelihood fit.
Contributions from the three
D
s
decay modes are shown with
different hatching styles:
is cross hatched,
K
0
K
is
hatched, and
K
0
S
K
is white. The fit procedure and results are
described in the text.
TABLE II.
Signal yields, branching fractions and upper limits
on the branching fractions for
B
0
!
D
s
a
0
2
decays. Numbers
in parentheses in the third and fourth columns indicate the
branching fractions and the upper limits multiplied by the
branching fractions of the decays
D
s
!
and
a
0
2
!
.
B
0
mode
n
sig
B
10
5
10
7
U
:
L
:
10
5
D
s
a
0
0
:
9
2
:
2
1
:
7
0
:
6
1
:
4
1
:
1
0
:
1
2
:
6
6
:
6
5
:
1
0
:
5
1.9(0.09)
D
s
a
2
0
:
6
1
:
0
0
:
6
6
:
4
10
:
4
5
:
7
1
:
5
4
:
5
7
:
3
4
:
0
0
:
8
19(0.13)
D
s
a
0
1
:
5
2
:
3
1
:
8
1
:
4
2
:
1
1
:
6
0
:
3
6
:
5
10
:
1
7
:
8
1
:
2
3.6(0.17)
D
s
a
2
—
20(0.13)
TABLE I. Reconstruction efficiencies for
B
0
!
D
s
a
0
2
de-
cays (excluding the intermediate branching fractions).
Decay mode
D
s
!
D
s
!
K
0
K
D
s
!
K
0
S
K
B
0
!
D
s
a
0
4.7%
2.9%
2.5%
B
0
!
D
s
a
2
1.9%
1.1%
1.1%
B
0
!
D
s
a
0
2.2%
1.5%
1.3%
B
0
!
D
s
a
2
0.9%
0.7%
0.5%
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
071103(R) (2006)
RAPID COMMUNICATIONS
071103-6
widths, track and
K
0
S
reconstruction, charged kaon identi-
fication, range between 3% and 10%. We assume the
branching fraction for
a
0
!
to be 100% and assign
an asymmetric systematic error of
10%
to this assump-
tion. The systematic error in the number of produced
B
B
pairs is 1.1%. There is an additional
15%
systematic
error for
B
0
!
D
s
a
2
mode due to the unknown polariza-
tion state of the decay products. It was checked that the
selection of the best candidate based on
j
E
j
does not
introduce any significant bias in the
m
ES
fit. The total
relative systematic errors are estimated to be around 25%
for each mode.
We use a Bayesian approach with a flat prior above zero
to set 90% confidence level upper limits on the branching
fractions. In a given mode, the upper limit on the branching
fraction (
B
UL
) is defined by:
Z
B
UL
0
L
B
d
B
0
:
9
Z
1
0
L
B
d
B
where
L
B
is the likelihood as a function of the branching
fraction
B
as determined from the
m
ES
fit described above.
We account for systematic uncertainties by numerically
convolving
L
B
with a Gaussian distribution with a width
determined by the relative systematic uncertainty multi-
plied by the branching fraction obtained from the
m
ES
fit.
In cases with asymmetric errors we took the larger for the
width of this Gaussian function. In case of
D
s
a
2
(where
no central value was determined from the fit) we conser-
vatively estimate the absolute systematic error by taking
the numerically calculated 90% confidence level upper
limit (without the systematic uncertainties) instead of the
fitted branching fraction. The resulting upper limits are
summarized in Table II (fourth column). The likelihood
curves are shown in Fig. 3.
We have also calculated upper limits without including
the intermediate branching fractions of the decays
D
s
!
[16] and
a
0
2
!
[12]. The relative systematic
errors in this case are reduced to 18% for each of the
B
0
meson decay modes. The results are presented in Table II
(third and fourth columns, numbers in parenthesis).
In conclusion, we do not observe any evidence for the
decays
B
0
!
D
s
a
0
,
B
0
!
D
s
a
2
,
B
0
!
D
s
a
0
and
B
0
!
D
s
a
2
, and set 90% C.L. upper limits on their
branching fractions. The upper limit value for
B
0
!
D
s
a
0
is lower than the theoretical expectation, which might
indicate the need to revisit the
B
!
a
0
X
transition form
factor estimate. It might also imply the limited applicabil-
ity of the factorization approach for this decay mode. The
upper limits suggest that the branching ratios of
B
0
!
D
a
0
2
are too small for
CP
-asymmetry measurements
given the present statistics of the
B
-factories.
We are grateful for the excellent luminosity and machine
conditions provided by our PEP-II colleagues, and for the
substantial dedicated effort from the computing organiza-
tions that support
BABAR
. The collaborating institutions
wish to thank SLAC for its support and kind hospitality.
This work is supported by DOE and NSF (USA), NSERC
(Canada), IHEP (China), CEA and CNRS-IN2P3 (France),
BMBF and DFG (Germany), INFN (Italy), FOM (The
Netherlands), NFR (Norway), MIST (Russia), and
PPARC (United Kingdom). Individuals have received sup-
port from CONACyT (Mexico), Marie Curie EIF
(European Union), A. P. Sloan Foundation, Research
Corporation, and Alexander von Humboldt Foundation.
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cd
V
cb
=V
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tb
,
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ud
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ub
=V
cd
V
cb
.
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0.6
0.8
1
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0.8
0
01234
FIG. 3.
Likelihood functions of the fit for the
m
ES
distributions
of the selected
B
0
!
D
s
a
0
2
candidates. Solid curves repre-
sent the original likelihood scan from the fit, the dashed lines
show the result of the convolution with the systematic errors
Gaussian. Vertical lines indicate the 90% Bayesian C.L. upper
limit value.
SEARCH FOR THE RARE DECAYS
B
0
!
D
s
a
0
2
PHYSICAL REVIEW D
73,
071103(R) (2006)
RAPID COMMUNICATIONS
071103-7
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B. AUBERT
et al.
PHYSICAL REVIEW D
73,
071103(R) (2006)
RAPID COMMUNICATIONS
071103-8