Measurement of ratios of branching fractions and
CP
-violating asymmetries
of
B
!
D
K
decays
B. Aubert,
1
M. Bona,
1
Y. Karyotakis,
1
J. P. Lees,
1
V. Poireau,
1
E. Prencipe,
1
X. Prudent,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
L. Lopez,
3a,3b
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
L. Sun,
4
G. S. Abrams,
5
M. Battaglia,
5
D. N. Brown,
5
R. N. Cahn,
5
R. G. Jacobsen,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Kukartsev,
5
G. Lynch,
5
I. L. Osipenkov,
5
M. T. Ronan,
5,
*
K. Tackmann,
5
T. Tanabe,
5
C. M. Hawkes,
6
N. Soni,
6
A. T. Watson,
6
H. Koch,
7
T. Schroeder,
7
D. Walker,
8
D. J. Asgeirsson,
9
T. Cuhadar-Donszelmann,
8
B. G. Fulsom,
9
C. Hearty,
9
T. S. Mattison,
9
J. A. McKenna,
9
M. Barrett,
10
A. Khan,
10
L. Teodorescu,
10
V. E. Blinov,
11
A. D. Bukin,
11
A. R. Buzykaev,
11
V. P. Druzhinin,
11
V. B. Golubev,
11
A. P. Onuchin,
11
S. I. Serednyakov,
11
Yu. I. Skovpen,
11
E. P. Solodov,
11
K. Yu. Todyshev,
11
M. Bondioli,
12
S. Curry,
12
I. Eschrich,
12
D. Kirkby,
12
A. J. Lankford,
12
P. Lund,
12
M. Mandelkern,
12
E. C. Martin,
12
D. P. Stoker,
12
S. Abachi,
13
C. Buchanan,
13
J. W. Gary,
14
F. Liu,
14
O. Long,
14
B. C. Shen,
14,
*
G. M. Vitug,
14
Z. Yasin,
14
L. Zhang,
14
V. Sharma,
15
C. Campagnari,
16
T. M. Hong,
16
D. Kovalskyi,
16
M. A. Mazur,
16
J. D. Richman,
16
T. W. Beck,
17
A. M. Eisner,
17
C. J. Flacco,
17
C. A. Heusch,
17
J. Kroseberg,
17
W. S. Lockman,
17
T. Schalk,
17
B. A. Schumm,
17
A. Seiden,
17
L. Wang,
17
M. G. Wilson,
17
L. O. Winstrom,
17
C. H. Cheng,
18
D. A. Doll,
18
B. Echenard,
18
F. Fang,
18
D. G. Hitlin,
18
I. Narsky,
18
T. Piatenko,
18
F. C. Porter,
18
R. Andreassen,
19
G. Mancinelli,
19
B. T. Meadows,
19
K. Mishra,
19
M. D. Sokoloff,
19
F. Blanc,
20
P. C. Bloom,
20
W. T. Ford,
20
A. Gaz,
20
J. F. Hirschauer,
20
A. Kreisel,
20
M. Nagel,
20
U. Nauenberg,
20
J. G. Smith,
20
K. A. Ulmer,
20
S. R. Wagner,
20
R. Ayad,
21,
+
A. Soffer,
21,
‡
W. H. Toki,
21
R. J. Wilson,
21
D. D. Altenburg,
22
E. Feltresi,
22
A. Hauke,
22
H. Jasper,
22
M. Karbach,
22
J. Merkel,
22
A. Petzold,
22
B. Spaan,
22
K. Wacker,
22
M. J. Kobel,
23
W. F. Mader,
23
R. Nogowski,
23
K. R. Schubert,
23
R. Schwierz,
23
J. E. Sundermann,
23
A. Volk,
23
D. Bernard,
24
G. R. Bonneaud,
24
E. Latour,
24
Ch. Thiebaux,
24
M. Verderi,
24
P. J. Clark,
25
W. Gradl,
25
S. Playfer,
25
J. E. Watson,
25
M. Andreotti,
26a,26b
D. Bettoni,
26a
C. Bozzi,
26a
R. Calabrese,
26a,26b
A. Cecchi,
26a,26b
G. Cibinetto,
26a,26b
P. Franchini,
26a,26b
E. Luppi,
26a,26b
M. Negrini,
26a,26b
A. Petrella,
26a,26b
L. Piemontese,
26a
V. Santoro,
26a,26b
R. Baldini-Ferroli,
27
A. Calcaterra,
27
R. de Sangro,
27
G. Finocchiaro,
27
S. Pacetti,
27
P. Patteri,
27
I. M. Peruzzi,
27,
x
M. Piccolo,
27
M. Rama,
27
A. Zallo,
27
A. Buzzo,
28a
R. Contri,
28a,28b
M. Lo Vetere,
28a,28b
M. M. Macri,
28a
M. R. Monge,
28a,28b
S. Passaggio,
28a
C. Patrignani,
28a,28b
E. Robutti,
28a
A. Santroni,
28a,28b
S. Tosi,
28a,28b
K. S. Chaisanguanthum,
29
M. Morii,
29
R. S. Dubitzky,
30
J. Marks,
30
S. Schenk,
30
U. Uwer,
30
V. Klose,
31
H. M. Lacker,
31
G. De Nardo,
32a,32b
L. Lista,
32a
D. Monorchio,
32a,32b
G. Onorato,
32a,32b
C. Sciacca,
32a,32b
D. J. Bard,
33
P. D. Dauncey,
33
J. A. Nash,
33
W. Panduro Vazquez,
33
M. Tibbetts,
33
P. K. Behera,
34
X. Chai,
34
M. J. Charles,
34
U. Mallik,
34
J. Cochran,
35
H. B. Crawley,
35
L. Dong,
35
W. T. Meyer,
35
S. Prell,
35
E. I. Rosenberg,
35
A. E. Rubin,
35
Y. Y. Gao,
36
A. V. Gritsan,
36
Z. J. Guo,
36
C. K. Lae,
36
A. G. Denig,
37
M. Fritsch,
37
G. Schott,
37
N. Arnaud,
38
J. Be
́
quilleux,
38
A. D’Orazio,
38
M. Davier,
38
J. Firmino da Costa,
38
G. Grosdidier,
38
A. Ho
̈
cker,
38
V. Lepeltier,
38
F. Le Diberder,
38
A. M. Lutz,
38
S. Pruvot,
38
P. Roudeau,
38
M. H. Schune,
38
J. Serrano,
38
V. Sordini,
38,
k
A. Stocchi,
38
G. Wormser,
38
D. J. Lange,
39
D. M. Wright,
39
I. Bingham,
40
J. P. Burke,
40
C. A. Chavez,
40
J. R. Fry,
40
E. Gabathuler,
40
R. Gamet,
40
D. E. Hutchcroft,
40
D. J. Payne,
40
C. Touramanis,
40
A. J. Bevan,
41
K. A. George,
41
F. Di Lodovico,
41
R. Sacco,
41
M. Sigamani,
41
G. Cowan,
42
H. U. Flaecher,
42
D. A. Hopkins,
42
S. Paramesvaran,
42
F. Salvatore,
42
A. C. Wren,
42
D. N. Brown,
43
C. L. Davis,
43
K. E. Alwyn,
44
N. R. Barlow,
44
R. J. Barlow,
44
Y. M. Chia,
44
C. L. Edgar,
44
G. D. Lafferty,
44
T. J. West,
44
J. I. Yi,
44
J. Anderson,
45
C. Chen,
45
A. Jawahery,
45
D. A. Roberts,
45
G. Simi,
45
J. M. Tuggle,
45
C. Dallapiccola,
46
S. S. Hertzbach,
46
X. Li,
46
E. Salvati,
46
S. Saremi,
46
R. Cowan,
47
D. Dujmic,
47
P. H. Fisher,
47
K. Koeneke,
47
G. Sciolla,
47
M. Spitznagel,
47
F. Taylor,
47
R. K. Yamamoto,
47
M. Zhao,
47
S. E. Mclachlin,
48,
*
P. M. Patel,
48
S. H. Robertson,
48
A. Lazzaro,
49a,49b
V. Lombardo,
49a
F. Palombo,
49a,49b
J. M. Bauer,
50
L. Cremaldi,
50
V. Eschenburg,
50
R. Godang,
50,
{
R. Kroeger,
50
D. A. Sanders,
50
D. J. Summers,
50
H. W. Zhao,
50
M. Simard,
51
P. Taras,
51
F. B. Viaud,
51
H. Nicholson,
52
M. A. Baak,
53
G. Raven,
53
H. L. Snoek,
53
C. P. Jessop,
54
K. J. Knoepfel,
54
J. M. LoSecco,
54
W. F. Wang,
54
G. Benelli,
55
L. A. Corwin,
55
K. Honscheid,
55
H. Kagan,
55
R. Kass,
55
J. P. Morris,
55
A. M. Rahimi,
55
J. J. Regensburger,
55
S. J. Sekula,
55
Q. K. Wong,
55
N. L. Blount,
56
J. Brau,
56
R. Frey,
56
O. Igonkina,
56
J. A. Kolb,
56
M. Lu,
56
R. Rahmat,
56
N. B. Sinev,
56
D. Strom,
56
J. Strube,
56
E. Torrence,
56
G. Castelli,
57a,57b
N. Gagliardi,
57a,57b
M. Margoni,
57a,57b
M. Morandin,
57a
M. Posocco,
57a
M. Rotondo,
57a
F. Simonetto,
57a,57b
R. Stroili,
57a,57b
C. Voci,
57a,57b
P. del Amo Sanchez,
58
E. Ben-Haim,
58
H. Briand,
58
G. Calderini,
58
J. Chauveau,
58
P. David,
58
L. Del Buono,
58
O. Hamon,
58
Ph. Leruste,
58
J. Ocariz,
58
A. Perez,
58
J. Prendki,
58
L. Gladney,
59
M. Biasini,
60a,60b
R. Covarelli,
60a,60b
E. Manoni,
60a,60b
C. Angelini,
61a,61b
G. Batignani,
61a,61b
S. Bettarini,
61a,61b
M. Carpinelli,
61a,61b,
**
A. Cervelli,
61a,61b
F. Forti,
61a,61b
M. A. Giorgi,
61a,61b
A. Lusiani,
61a,61c
G. Marchiori,
61a,61b
M. Morganti,
61a,61b
N. Neri,
61a,61b
E. Paoloni,
61a,61b
G. Rizzo,
61a,61b
J. J. Walsh,
61a
J. Biesiada,
62
PHYSICAL REVIEW D
78,
092002 (2008)
1550-7998
=
2008
=
78(9)
=
092002(13)
092002-1
Ó
2008 The American Physical Society
D. Lopes Pegna,
62
C. Lu,
62
J. Olsen,
62
A. J. S. Smith,
62
A. V. Telnov,
62
F. Anulli,
63a
E. Baracchini,
63a,63b
G. Cavoto,
63a
D. del Re,
63a,63b
E. Di Marco,
63a,63b
R. Faccini,
63a,63b
F. Ferrarotto,
63a
F. Ferroni,
63a,63b
M. Gaspero,
63a,63b
P. D. Jackson,
63a
L. Li Gioi,
63a
M. A. Mazzoni,
63a
S. Morganti,
63a
G. Piredda,
63a
F. Polci,
63a,63b
F. Renga,
63a,63b
C. Voena,
63a
M. Ebert,
64
T. Hartmann,
64
H. Schro
̈
der,
64
R. Waldi,
64
T. Adye,
65
B. Franek,
65
E. O. Olaiya,
65
W. Roethel,
65
F. F. Wilson,
65
S. Emery,
66
M. Escalier,
66
L. Esteve,
66
A. Gaidot,
66
S. F. Ganzhur,
66
G. Hamel de Monchenault,
66
W. Kozanecki,
66
G. Vasseur,
66
Ch. Ye
`
che,
66
M. Zito,
66
X. R. Chen,
67
H. Liu,
67
W. Park,
67
M. V. Purohit,
67
R. M. White,
67
J. R. Wilson,
67
M. T. Allen,
68
D. Aston,
68
R. Bartoldus,
68
P. Bechtle,
68
J. F. Benitez,
68
R. Cenci,
68
J. P. Coleman,
68
M. R. Convery,
68
J. C. Dingfelder,
68
J. Dorfan,
68
G. P. Dubois-Felsmann,
68
W. Dunwoodie,
68
R. C. Field,
68
A. M. Gabareen,
68
S. J. Gowdy,
68
M. T. Graham,
68
P. Grenier,
68
C. Hast,
68
W. R. Innes,
68
J. Kaminski,
68
M. H. Kelsey,
68
H. Kim,
68
P. Kim,
68
M. L. Kocian,
68
D. W. G. S. Leith,
68
S. Li,
68
B. Lindquist,
68
S. Luitz,
68
V. Luth,
68
H. L. Lynch,
68
D. B. MacFarlane,
68
H. Marsiske,
68
R. Messner,
68
D. R. Muller,
68
H. Neal,
68
S. Nelson,
68
C. P. O’Grady,
68
I. Ofte,
68
A. Perazzo,
68
M. Perl,
68
B. N. Ratcliff,
68
A. Roodman,
68
A. A. Salnikov,
68
R. H. Schindler,
68
J. Schwiening,
68
A. Snyder,
68
D. Su,
68
M. K. Sullivan,
68
K. Suzuki,
68
S. K. Swain,
68
J. M. Thompson,
68
J. Va’vra,
68
A. P. Wagner,
68
M. Weaver,
68
C. A. West,
68
W. J. Wisniewski,
68
M. Wittgen,
68
D. H. Wright,
68
H. W. Wulsin,
68
A. K. Yarritu,
68
K. Yi,
68
C. C. Young,
68
V. Ziegler,
68
P. R. Burchat,
69
A. J. Edwards,
69
S. A. Majewski,
69
T. S. Miyashita,
69
B. A. Petersen,
69
L. Wilden,
69
S. Ahmed,
70
M. S. Alam,
70
R. Bula,
70
J. A. Ernst,
70
B. Pan,
70
M. A. Saeed,
70
S. B. Zain,
70
S. M. Spanier,
71
B. J. Wogsland,
71
R. Eckmann,
72
J. L. Ritchie,
72
A. M. Ruland,
72
C. J. Schilling,
72
R. F. Schwitters,
72
B. W. Drummond,
73
J. M. Izen,
73
X. C. Lou,
73
F. Bianchi,
74a,74b
D. Gamba,
74a,74b
M. Pelliccioni,
74a,74b
M. Bomben,
75a,75b
L. Bosisio,
75a,75b
C. Cartaro,
75a,75b
G. Della Ricca,
75a,75b
L. Lanceri,
75a,75b
L. Vitale,
75a,75b
V. Azzolini,
76
N. Lopez-March,
76
F. Martinez-Vidal,
76
D. A. Milanes,
76
A. Oyanguren,
76
J. Albert,
77
Sw. Banerjee,
77
B. Bhuyan,
77
H. H. F. Choi,
77
K. Hamano,
77
R. Kowalewski,
77
M. J. Lewczuk,
77
I. M. Nugent,
77
J. M. Roney,
77
R. J. Sobie,
77
T. J. Gershon,
78
P. F. Harrison,
78
J. Ilic,
78
T. E. Latham,
78
G. B. Mohanty,
78
H. R. Band,
79
X. Chen,
79
S. Dasu,
79
K. T. Flood,
79
Y. Pan,
79
M. Pierini,
79
R. Prepost,
79
C. O. Vuosalo,
79
and S. L. Wu
79
(
B
A
B
AR
Collaboration)
1
Laboratoire de Physique des Particules, IN2P3/CNRS et Universite
́
de Savoie, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartmento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
University of Birmingham, Birmingham, B15 2TT, United Kingdom
7
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
8
University of Bristol, Bristol BS8 1TL, United Kingdom
9
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
10
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
11
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
12
University of California at Irvine, Irvine, California 92697, USA
13
University of California at Los Angeles, Los Angeles, California 90024, USA
14
University of California at Riverside, Riverside, California 92521, USA
15
University of California at San Diego, La Jolla, California 92093, USA
16
University of California at Santa Barbara, Santa Barbara, California 93106, USA
17
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
18
California Institute of Technology, Pasadena, California 91125, USA
19
University of Cincinnati, Cincinnati, Ohio 45221, USA
20
University of Colorado, Boulder, Colorado 80309, USA
21
Colorado State University, Fort Collins, Colorado 80523, USA
22
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
23
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
24
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
25
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
26a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
26b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
27
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
28a
INFN Sezione di Genova, I-16146 Genova, Italy
28b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
B. AUBERT
et al.
PHYSICAL REVIEW D
78,
092002 (2008)
092002-2
29
Harvard University, Cambridge, Massachusetts 02138, USA
30
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
31
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstr. 15, D-12489 Berlin, Germany
32a
INFN Sezione di Napoli, I-80126 Napoli, Italy;
32b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
33
Imperial College London, London, SW7 2AZ, United Kingdom
34
University of Iowa, Iowa City, Iowa 52242, USA
35
Iowa State University, Ames, Iowa 50011-3160, USA
36
Johns Hopkins University, Baltimore, Maryland 21218, USA
37
Universita
̈
t Karlsruhe, Institut fu
̈
r Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
38
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
39
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
40
University of Liverpool, Liverpool L69 7ZE, United Kingdom
41
Queen Mary, University of London, E1 4NS, United Kingdom
42
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
43
University of Louisville, Louisville, Kentucky 40292, USA
44
University of Manchester, Manchester M13 9PL, United Kingdom
45
University of Maryland, College Park, Maryland 20742, USA
46
University of Massachusetts, Amherst, Massachusetts 01003, USA
47
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
48
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
49a
INFN Sezione di Milano, I-20133 Milano, Italy
49b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
50
University of Mississippi, University, Mississippi 38677, USA
51
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
52
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
53
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
54
University of Notre Dame, Notre Dame, Indiana 46556, USA
55
Ohio State University, Columbus, Ohio 43210, USA
56
University of Oregon, Eugene, Oregon 97403, USA
57a
INFN Sezione di Padova, I-35131 Padova, Italy
57b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
58
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie-Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
59
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
60a
INFN Sezione di Perugia, I-06100 Perugia, Italy
60b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
61a
INFN Sezione di Pisa, I-56127 Pisa, Italy
61b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
61c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
62
Princeton University, Princeton, New Jersey 08544, USA
63a
INFN Sezione di Roma, I-00185 Roma, Italy
63b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
64
Universita
̈
t Rostock, D-18051 Rostock, Germany
65
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
66
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
74a
INFN Sezione di Torino, I-10125 Torino, Italy
74b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
75a
INFN Sezione di Trieste, I-34127 Trieste, Italy
75b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
76
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
77
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
78
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
MEASUREMENT OF RATIOS OF BRANCHING FRACTIONS
...
PHYSICAL REVIEW D
78,
092002 (2008)
092002-3
79
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 16 July 2008; published 10 November 2008)
We report a study of
B
!
D
K
decays with
D
decaying to
D
0
or
D
, using
383
10
6
B
B
pairs
collected at the
ð
4
S
Þ
resonance with the
BABAR
detector at the SLAC PEP-II
B
Factory. The
D
meson
decays under study include a non-
CP
mode
ð
K
Þ
,
CP
-even modes
ð
K
K
;
Þ
, and
CP
-odd
modes
ð
K
0
S
0
;K
0
S
; K
0
S
!
Þ
. We measure ratios (
R
CP
) of branching fractions of decays to
CP
eigenmode
states and to flavor-specific states as well as
CP
asymmetries (
A
CP
). These measurements are sensitive to
the unitarity triangle angle
. We obtain
A
CP
þ
¼
0
:
11
0
:
09
0
:
01
,
R
CP
þ
¼
1
:
31
0
:
13
0
:
04
, and
A
CP
¼
0
:
06
0
:
10
0
:
02
,
R
CP
¼
1
:
10
0
:
12
0
:
04
, where the first error is statistical and the
second error is systematic. Translating our results into an alternative parametrization, widely used for
related measurements, we obtain
x
þ
¼
0
:
11
0
:
06
0
:
02
and
x
¼
0
:
00
0
:
06
0
:
02
. No significant
CP
-violating charge asymmetry is found in either the flavor-specific mode
D
!
K
or in
B
!
D
decays.
DOI:
10.1103/PhysRevD.78.092002
PACS numbers: 14.40.Nd, 11.30.Er, 12.15.Hh, 13.25.Hw
I. INTRODUCTION
In the standard model (SM),
CP
-violating phenomena
are a consequence of a single complex phase in the
Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing ma-
trix [
1
]. The
B
!
D
ðÞ
K
ðÞ
decay modes provide a theo-
retically clean determination of the unitarity triangle angle
, since the latter is equal to the relative phase between the
CKM- and color-favored
b
!
c
and the CKM- and color-
suppressed
b
!
u
decay amplitudes that are dominant in
the considered decays. The method proposed by Gronau,
London, and Wyler (GLW) makes use of the direct
CP
violation in the interference between the amplitudes for
B
!
D
0
K
and
B
!
D
0
K
decays when the
D
0
and
D
0
mesons decay to the same
CP
eigenstate [
2
,
3
]. The
same approach is equally applicable when the
D
and/or the
K
meson is replaced with its excited state. In this paper we
use the
B
!
D
K
decay. We use the notation
D
0
,
D
0
,
D
0
, and
D
0
to denote states with definite flavor, while
D
CP
þ
and
D
CP
þ
denote
CP
-even eigenstates,
D
CP
and
D
CP
denote
CP
-odd eigenstates, and
D
and
D
denote
any state of the
D
ð
1864
Þ
0
and
D
ð
2007
Þ
0
mesons, respec-
tively. With the integrated luminosity presently available, it
is not possible to make a precise
measurement with the
GLW method alone, but the combination of several meth-
ods and of several modes allows an improvement of the
overall precision [
4
].
In the case of
B
!
D
K
decays, one defines the
CP
-violating charge asymmetry
A
CP
B
ð
B
!
D
CP
K
Þ
B
ð
B
þ
!
D
CP
K
þ
Þ
B
ð
B
!
D
CP
K
Þþ
B
ð
B
þ
!
D
CP
K
þ
Þ
;
(1)
and the ratio of branching fractions for the decays to
CP
eigenmodes and flavor-specific states,
R
CP
B
ð
B
!
D
CP
K
Þþ
B
ð
B
þ
!
D
CP
K
þ
Þ
½
B
ð
B
!
D
0
K
Þþ
B
ð
B
þ
!
D
0
K
þ
Þ
=
2
:
(2)
We refer to the companion of the charmed meson in the
final state as the prompt track. Experimentally, it is conve-
nient to normalize the branching fractions of the decays
with a prompt kaon in the final state to those of the similar
decays with a prompt pion that have a larger branching
fraction. The ratio
R
CP
can then be expressed as
R
CP
R
R
;
(3)
where
R
and
R
are the
K=
ratios
R
B
ð
B
!
D
CP
K
Þþ
B
ð
B
þ
!
D
CP
K
þ
Þ
B
ð
B
!
D
CP
Þþ
B
ð
B
þ
!
D
CP
þ
Þ
(4)
and
R
B
ð
B
!
D
0
K
Þþ
B
ð
B
þ
!
D
0
K
þ
Þ
B
ð
B
!
D
0
Þþ
B
ð
B
þ
!
D
0
þ
Þ
:
(5)
The ratio
R
is predicted to be of the order of
½ð
f
K
=f
Þ
j
V
us
=V
ud
j
2
¼
0
:
080
0
:
002
[
5
], where
f
K
and
f
are the
form factors of the mesons. Equation (
3
) would be an
equality if
CP
violation was completely absent in
B
!
D
decays. Defining the charge asymmetry
A
h
B
ð
B
!
D
h
Þ
B
ð
B
þ
!
D
h
þ
Þ
B
ð
B
!
D
h
Þþ
B
ð
B
þ
!
D
h
þ
Þ
(6)
(noted
A
and
A
K
when referring to
h
¼
and
h
¼
K
,
respectively), this approximation implies that the pion
charge asymmetry
A
should be compatible with zero, as
*
Deceased.
+
Now at Temple University, Philadelphia, PA 19122, USA.
‡
Now at Tel Aviv University, Tel Aviv, 69978, Israel.
x
Also with Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
k
Also with Universita
`
di Roma La Sapienza, I-00185 Roma,
Italy.
{
Now at University of South Alabama, Mobile, AL 36688,
USA.
**
Also with Universita
`
di Sassari, Sassari, Italy.
B. AUBERT
et al.
PHYSICAL REVIEW D
78,
092002 (2008)
092002-4
should be the kaon charge asymmetry
A
K
for the flavor-
specific modes
D
!
K
. The possible bias induced
by this approximation is expected to be small since the
ratio of the amplitudes of the
B
!
D
0
and
B
!
D
0
processes is predicted to be of the order of 1% [
6
]
in the SM, and will be accounted for in the systematic
uncertainties.
Most experimental systematic uncertainties, such as
those related to the reconstruction of the
D
, and the
uncertainties on the
D
decay branching fractions, cancel
in the
K=
ratios
R
and
R
. By neglecting the small [
7
,
8
]
D
0
-
D
0
mixing [
9
] and
CP
violation in
D
0
decays,
R
CP
and
A
CP
are related to
through
R
CP
¼
1
þ
r
2
B
2
r
B
cos
B
cos
(7)
and
A
CP
¼
2
r
B
sin
B
sin
1
þ
r
2
B
2
r
B
cos
B
cos
;
(8)
where
r
B
is the magnitude of the ratio of the amplitudes for
the processes
B
!
D
0
K
and
B
!
D
0
K
, and
B
is
the relative strong phase between these two amplitudes.
The ratio
r
B
involves a CKM factor
j
V
ub
V
cs
=V
cb
V
us
j
0
:
44
0
:
05
[
5
] and a color suppression factor that has
been estimated to lie between
0
:
26
0
:
07
0
:
05
[
10
]
and 0.44 [
6
], so that
r
B
is predicted to be in the range
0.1–0.2. More recent calculations that take into account
final state interactions [
11
] yield predictions of
r
B
¼
0
:
09
0
:
02
.
The latest results by
BABAR
and Belle are reported in
Refs. [
12
–
14
], respectively.
BABAR
used
123
10
6
B
B
pairs with
D
!
D
0
and
D
reconstructed in the
CP
-even
modes
K
þ
K
and
þ
, and non-
CP
modes
K
,
K
þ
, and
K
0
. Belle used
275
10
6
B
B
pairs with
D
!
D
0
and
D
reconstructed in the
CP
-even
modes
K
þ
K
and
þ
,
CP
-odd modes
K
0
S
0
,
K
0
S
!
,
K
0
S
, and non-
CP
modes
K
[
13
]. The results are
summarized in Table
I
. Similar studies have been per-
formed on the channels
B
!
DK
[
13
,
15
,
16
] and
B
!
DK
[
17
].
The
BABAR
[
18
] and Belle [
19
] experiments have re-
cently obtained estimates of
r
B
and
B
parameters from the
overlap of the
D
0
and
D
0
decays in the Dalitz planes of
some three-body
D
decays.
BABAR
obtains
r
B
¼
0
:
135
0
:
051
and
B
¼ð
63
þ
28
30
Þ
, while Belle obtains
r
B
¼
0
:
21
0
:
08
0
:
02
0
:
05
and
B
¼ð
342
þ
21
23
4
23
Þ
(where the first error is statistical, the second is the experi-
mental systematic uncertainty, and the third reflects the
uncertainty on the
D
decay Dalitz models).
In this paper, by using
ð
383
4
Þ
10
6
B
B
pairs, we
update the results of our previous study of
B
!
D
K
decays [
12
] for
D
decays to the
CP
-even modes
K
þ
K
,
þ
and to the flavor-specific modes
K
, and we
extend it to the
CP
-odd modes
K
0
S
0
,
K
0
S
!
, and
K
0
S
, and
to
D
!
D
. Because of parity and angular-momentum
conservation, the
CP
eigenvalue of the
D
is inferred from
that of the
D
, when the
CP
eigenvalue of the neutral
companion (
or
0
) is taken into account [
20
]:
CP
ð
D
Þ¼
CP
ð
D
Þ
when
D
!
D
0
, and
CP
ð
D
Þ¼
CP
ð
D
Þ
when
D
!
D
.
Experimental results can also be presented using the
‘‘Cartesian coordinates’’
ð
x
;y
Þð
r
B
cos
ð
B
Þ
;r
B
sin
ð
B
ÞÞ
;
(9)
which have the advantage of having Gaussian uncertain-
ties, and of being uncorrelated and unbiased (
r
B
, being
positive, is biased towards larger values in low precision
measurements, whereas
x
and
y
show no such bias)
[
21
]. The parameters
x
can be obtained from
R
CP
and
A
CP
,
x
¼
R
CP
þ
ð
1
A
CP
þ
Þ
R
CP
ð
1
A
CP
Þ
4
:
(10)
The measurements presented in this paper have no direct
sensitivity to
y
, in contrast to Dalitz analyses. However,
an indirect constraint can be obtained using
ð
r
B
Þ
2
¼
x
2
þ
y
2
¼
R
CP
þ
þ
R
CP
2
2
:
(11)
Note that there are four observables in these pa-
rametrizations, either
ð
A
CP
þ
;R
CP
þ
;A
CP
;R
CP
Þ
or
ð
x
þ
;y
þ
;x
;y
Þ
, while there are only three indepen-
dent fundamental parameters,
ð
; r
B
;
B
Þ
. The set of pa-
rameters must therefore fulfill one constraint, which can
be
¼
0
, where
R
CP
þ
A
CP
þ
þ
A
CP
R
CP
:
(12)
II. THE DATA SET AND DETECTOR
The results presented in this paper are based on data
collected with the
BABAR
detector at the PEP-II
asymmetric-energy
e
þ
e
storage ring of the Stanford
Linear Accelerator Center. At PEP-II, 9.0 GeV electrons
and 3.1 GeV positrons collide at a center-of-mass energy of
10.58 GeV, which corresponds to the mass of the
ð
4
S
Þ
TABLE I. Past measurements of parameters related to the measurement of
in
B
!
D
K
decays by the GLW method.
A
CP
þ
A
CP
R
CP
þ
R
CP
R
BABAR
[
12
]
0
:
10
0
:
23
þ
0
:
03
0
:
04
1
:
06
0
:
26
þ
0
:
10
0
:
09
0
:
0813
0
:
0040
þ
0
:
0042
0
:
0031
Belle [
13
,
14
]
0
:
20
0
:
22
0
:
04 0
:
13
0
:
30
0
:
08 1
:
41
0
:
25
0
:
06 1
:
15
0
:
31
0
:
12 0
:
078
0
:
019
0
:
009
MEASUREMENT OF RATIOS OF BRANCHING FRACTIONS
...
PHYSICAL REVIEW D
78,
092002 (2008)
092002-5
resonance. The asymmetric beam energies result in a boost
from the laboratory to the center-of-mass frame of
0
:
56
. The data set analyzed in this paper corresponds to an
integrated luminosity of
347 fb
1
at the
ð
4
S
Þ
resonance.
The
BABAR
detector is described in detail elsewhere
[
22
]. Surrounding the interaction point is a five-layer
double-sided silicon vertex tracker (SVT), which measures
the trajectories of charged particles. A 40-layer drift cham-
ber (DCH) provides measurements of the momenta of
charged particles. Both the SVT and DCH are located in-
side a 1.5 T magnetic field provided by a solenoid magnet.
Charged hadron identification is achieved through mea-
surements of particle energy loss in the tracking system
and the Cherenkov angle obtained from a detector of in-
ternally reflected Cherenkov light (DIRC). A CsI(Tl) elec-
tromagnetic calorimeter (EMC) provides photon detection,
electron identification, and
0
reconstruction. Finally, the
instrumented flux return (IFR) of the magnet enables dis-
crimination of muons from pions. For the most recent
134 fb
1
of data, a fraction of the resistive plate chambers
constituting the muon system has been replaced by limited
streamer tubes [
23
].
We use Monte Carlo (MC) simulation to study the
detector acceptance and backgrounds. The MC simulation
uses the
EVTGEN
generator [
24
] and
GEANT4
[
25
] to simu-
late the passage of particles through matter.
III. RECONSTRUCTION OF
B
CANDIDATES
We perform an exclusive reconstruction of the full
B
meson decay chain, in the modes described in the Intro-
duction, starting from the final stable products (charged-
particle tracks and neutral electromagnetic deposits in
the EMC).
The
0
candidates used to form an
!
,a
D
,ora
D
candidate are reconstructed from pairs of photons with
energies larger than 30 MeV, and shower shapes consistent
with electromagnetic showers, with invariant mass in the
range
115
<m
<
150 MeV
=c
2
. In addition, the
0
can-
didates used to form a
D
candidate are required to have
center-of-mass frame momenta
p
<
450 MeV
=c
. The
!
candidates are reconstructed in the three-body decay
!
!
þ
0
, with an invariant mass within
50 MeV
=c
2
of the
world average [
5
]. We reconstruct
K
0
S
!
þ
candidates
from pairs of oppositely charged tracks that are consistent
with having originated from a common vertex position and
with an invariant mass within
25 MeV
=c
2
of the world
average [
5
]. We reconstruct
!
K
þ
K
candidates from
pairs of oppositely charged tracks with particle identifica-
tion inconsistent with a pion hypothesis, that are consistent
with having originated from a common vertex position, and
that have invariant mass within
30 MeV
=c
2
of the world
average [
5
].
Only two-body
D
decays are considered in this study.
The
D
candidates are reconstructed from their two daugh-
ters that are required to be consistent with having origi-
nated from a common vertex position. In the case of
D
!
K
0
S
0
, in which vertexing of the
K
0
S
0
system would
yield a poor geometrical constraint, a beam spot constraint
is added to the fit in order to force the
D
daughters to
originate from the interaction region.
The
D
candidates are formed from
D
and
0
or
candidates. These photon candidates are required to have
energies larger than 100 MeVand shower shapes consistent
with electromagnetic showers. The
D
candidates are
required to fulfill
130
<
m<
170 MeV
=c
2
and
80
<
m<
180 MeV
=c
2
, respectively, where
m
is the invari-
ant mass difference between the
D
and the
D
candidate.
The
0
,
K
0
S
,
D
, and
D
candidates are refitted with mass
constraints before their four-momenta are used to recon-
struct the
B
decay chain. We form
B
candidates from
D
candidates and charged tracks, fitted with a beam spot
constraint. We characterize
B
candidates by two kinematic
variables: the difference between the reconstructed energy
of the
B
candidate and the beam energy in the center-of-
mass frame
E
K
E
B
ffiffiffi
s
p
=
2
, and the beam-energy sub-
stituted mass
m
ES
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
s=
2
þ
p
0
p
B
Þ
2
=E
2
0
p
2
B
q
, where
ð
E
0
;
p
0
Þ
and
ð
E
B
;
p
B
Þ
are the four-momenta of the
ð
4
S
Þ
and
B
meson candidate, respectively, the asterisk denotes
the
ð
4
S
Þ
rest frame, and
ffiffiffi
s
p
is the total energy in the
ð
4
S
Þ
rest frame. The subscript
K
in
E
K
indicates that
the kaon hypothesis has been assumed for the prompt track
in the computation of
E
. For a correctly reconstructed
B
meson having decayed to a
D
K
final state,
E
K
is
expected to peak near zero, with an R.M.S. of about
16 MeV, and
m
ES
is expected to peak near the
B
meson
mass
5
:
279 GeV
=c
2
, with an R.M.S. that is almost inde-
pendent of the channel and close to
3 MeV
=c
2
.Fora
B
!
D
decay reconstructed as
B
!
D
K
with a correctly
identified
D
, the
E
K
peak is shifted by approximately
þ
50 MeV
. At reconstruction level, the loose requirements
5
:
2
<m
ES
<
5
:
3 GeV
=c
2
and
j
E
K
j
<
0
:
2 GeV
are ap-
plied to the
B
meson candidate.
We form a Fisher discriminant
F
[
26
] to distinguish
signal events from the significant background due to
e
þ
e
!
q
q
(
q
¼
u
,
d
,
s
,
c
) continuum events. Six varia-
bles are used:
(i)
L
0
and
L
2
, the zeroth and second angular moments
of the energy flow around the
B
thrust axis. They
are defined as
P
i
p
i
and
P
i
p
i
cos
2
i
, respectively,
where
p
i
is the momentum and
i
is the angle with
respect to the thrust axis of the
B
candidate, both in
the center-of-mass frame, for all tracks and neutral
clusters not used to reconstruct the
B
meson.
(ii)
R
2
, the ratio of the second to the zeroth Fox-
Wolfram moment [
27
] of charged tracks and neu-
tral clusters in the center-of-mass frame.
(iii)
j
cos
B
j
, where
B
is the angle between the mo-
mentum of the
B
candidate and the boost direction
of the
e
þ
e
center-of-mass frame.
B. AUBERT
et al.
PHYSICAL REVIEW D
78,
092002 (2008)
092002-6
(iv)
j
cos
Thrust
j
, where
Thrust
is the angle between the
B
candidate thrust vector and the beam axis in the
center-of-mass frame.
(v)
j
cos
T
j
, where
T
is the angle between the
B
can-
didate thrust axis and the thrust axis of the rest of
the event in the center-of-mass frame (where the
rest of the event corresponds to reconstructed par-
ticles not associated with the
B
candidate).
IV. SELECTION OF
B
CANDIDATES
After the preliminary event reconstruction, a large
amount of background remains in the signal candidate
sample. In this section we describe the additional selection
criteria used to reduce the background.
The selection of each
B
!
D
K
decay mode is opti-
mized separately, by the maximization of the sensitivity
S=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
S
þ
B
þ
1
p
, where
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
S
þ
B
þ
1
p
is a symmetrized ap-
proximation of the Poisson uncertainty on the measure-
ment of
S
þ
B
. The numbers
S
and
B
of signal and
background expected events are estimated from, respec-
tively, high-statistics exclusive MC samples, and a cocktail
of generic
B
þ
B
(with signal events removed),
B
0
B
0
, and
q
q
MC samples.
In the optimization procedure, we include requirements
on all variables, including those that will be relaxed during
the fit, and including tightening requirements that have
been made in the reconstruction stage. Our optimization
procedure is similar to that used in Ref. [
28
], and allows us
to determine the optimal set of variables as well as the
optimal requirements on those variables, by the examina-
tion of the signal-to-background ratio distributions [
29
].
The final set of variables on which we apply selection
optimization is as follows:
(i) The
B
candidate-related variables
m
ES
and
E
K
introduced above.
(ii) The mass
m
D
0
of the
D
candidate before the mass
constraint is applied, and the mass difference
m
.
(iii) Likelihood ratios for the prompt track that are
evaluated making use of the Cherenkov angle in-
formation from the DIRC, and of the
dE=dx
infor-
mation provided by the tracking system. Explicitly,
we compute likelihoods
L
h
for particle identifi-
cation (PID) hypotheses
h
¼
K
,
,
p
and make
requirements on the ratios
L
K
=
ð
L
K
þ
L
Þ
and
L
K
=
ð
L
K
þ
L
p
Þ
. We also require that the track is
not identified as an electron or a muon.
(iv) Likelihood ratios for pion and kaon candidates that
are daughters of two-body
D
decays.
(v) The value of the Fisher variable
F
.
(vi) The invariant masses of the
K
0
S
,
,
0
, and
!
candidates, when relevant, and before the mass
constraints. Furthermore, for decays involving
K
0
S
candidates, we include the ratio of the flight length
of
K
0
S
candidates in the transverse plane divided
by its uncertainty, and require it to be larger than 2.
For decays involving
!
candidates, we include
j
cos
ð
!
Þj
, where
!
is the angle between the nor-
mal to the pion decay plane and the
D
direction in
the
!
rest frame.
The selection requirements applied to these variables are
mode dependent, except for the prompt-track PID require-
ments
L
K
=
ð
L
K
þ
L
Þ
>
0
:
9
and
L
K
=
ð
L
K
þ
L
p
Þ
>
0
:
2
that are applied to all
B
!
D
K
channels. The selection
of the
B
!
D
modes is identical to that of the
B
!
D
K
modes, except for the prompt-track PID that is
reversed [
L
K
=
ð
L
K
þ
L
Þ
<
0
:
2
].
A fraction of the events have several
B
candidates se-
lected: the average multiplicity varies from 1.07 to 1.66 for
D
!
D
0
and from 1.00 to 1.25 for
D
!
D
, depend-
ing on the channel. We select the
B
candidate that has the
B
vertex fit with the largest probability. This best-candidate
procedure is used during the optimization of the selection
that we have described above. The probability of selection
of the well-reconstructed signal candidate is mode depen-
dent and is in the range 56%–72% for
D
!
D
0
decays
and in the range 68%–81% for
D
!
D
decays.
V. MAXIMUM LIKELIHOOD FIT
The dominant contribution to the remaining background
after event selection is from
B
decays, including a signifi-
cant amount of feed-across from
B
!
D
decays.
Therefore the measurement is performed with an unbinned
likelihood fit [
30
,
31
] based on two variables that best dis-
criminate this background, namely,
E
K
and a PID vari-
able
T
R
defined below.
As the prompt-track PID likelihood ratio
R
L
K
=
ð
L
K
þ
L
Þ
is very strongly peaked near zero for
pions and near 1 for kaons, we use a pseudologarithmic
change of variable
T
R
¼
log
10
R
þ
1
R
þ
:
(13)
We include a small positive number
¼
10
7
, so that
T
R
is always defined, with
T
R
¼þ
7
for
R
¼
1
(‘‘perfect
kaons’’) and
T
R
¼
7
for
R
¼
0
(‘‘perfect pions’’).
The measurement is performed with an extended un-
binned maximum likelihood function
L
¼
e
N
0
ð
N
0
Þ
N
N
!
Y
N
i
¼
1
P
i
;
(14)
where
N
is the number of events in the sample to fit,
N
0
is
the expected number, and for event
i
P
i
¼
1
N
0
X
j
N
j
P
j
i
;
(15)
where
j
¼
D
K
,
D
,
B
K
,
B
is one of four event cate-
gories: signal kaon and pion, and background kaon and
pion, respectively, where the background is a combination
MEASUREMENT OF RATIOS OF BRANCHING FRACTIONS
...
PHYSICAL REVIEW D
78,
092002 (2008)
092002-7
of continuum,
B
þ
B
, and
B
0
B
0
events. The quantity
P
j
i
is
the probability density function (PDF) for event
i
and cate-
gory
j
, and
N
j
is the number of events in category
j
.
For the signal categories, the distance between the kaon
and pion
E
K
peaks provides powerful separation between
pions and kaons, in addition to PID. For the background
categories, we use mutually exclusive likelihood-based
pion and kaon selectors, that, in particular, contain require-
ments of
R
>
0
:
9
(kaon) and
R
<
0
:
1
(pion), respectively.
For consistency and symmetry reasons, the whole region
0
:
1
<
R
<
0
:
9
is removed for all categories, including the
signal categories used in the fit.
The correlations between
T
R
and
E
K
are found to
be small (compatible with zero for the signal
K
and for
the background categories, and with
6%
for the
signal
category); therefore, a factorized approximation is used:
P
j
i
ð
E
K
;
T
R
Þ¼
P
j
i
ð
E
K
Þ
P
j
i
ð
T
R
Þ
:
(16)
We have checked that no bias is introduced by this ap-
proximation by simulating a large number of experiments
in which the signal is taken from the large statistics ex-
clusive MC samples used for estimating these correlations.
The PDFs used in the fit are determined from MC sam-
ples. The signal
E
K
PDFs are parametrized with double
Gaussian functions. The background PDFs are mode-
dependent functions chosen to best represent the MC back-
ground distributions: they include Gaussian, exponential,
and third-order Chebyshev polynomial functions. The
complicated shape of the
E
K
distribution of the
B
category arises from the contributions from several distinct
components: at low
E
K
values,
B
!
D
decays
dominate; in the signal region, the background is mainly
composed of
$
0
cross feed and of
B
!
D
0
, the
latter of which dominates at high
E
K
values. The
T
R
PDFs are histograms, determined from MC samples, with a
binning
T
R
¼
0
:
5
and, therefore, 28 bins. MC-based
studies have shown that the results of such fits do not
depend on the number of bins
n
b
as long as
n
b
>
2
.
We correct for a small discrepancy in PID efficiencies
between data and MC samples, using high-statistics high-
purity kaon and pion samples from inclusive
D
!
D
,
D
!
K
data. The difference in track momentum spec-
tra between these control samples and the exclusive modes
studied in the present analysis is accounted for in the
correction procedure. This is achieved by weighting the
control sample
T
R
PDF by the ratio of the MC to control
sample prompt-track momentum distributions for both
cases of the prompt track being a kaon or a pion. An
example of the PDFs used for the channel
D
!
D
0
,
D
!
K
is shown in Fig.
1
.
For signal events with a pion prompt track, for which
E
(the subscript
indicates that the pion hypothesis has
been assumed for the prompt track in the computation of
E
) is close to zero, the relation
E
K
E
1
2
p
E
ð
4
S
Þ
m
ð
4
S
Þ
ð
m
2
K
m
2
Þ
(17)
introduces a mild dependence of
E
K
on the momentum
p
of the prompt track. The parameters
E
ð
4
S
Þ
and
m
ð
4
S
Þ
,
m
K
,
m
denote the energy of the
e
þ
e
system in the laboratory
frame and the masses of the mesons, respectively. Fits tak-
ing this dependence into account do not show any signifi-
cant improvement, nor degradation.
Fits performed on the
B
þ
B
,
B
0
B
0
, and
q
q
background
MC samples show no significant bias. Similar fits with
either pion or kaon signal events removed yield numbers
of signal events compatible with zero for the removed
category. This indicates that the factorization approxima-
z
z
z
z
FIG. 1 (color online). Distributions of
E
K
(upper plots) and the PID variable
T
R
(lower plots) from MC simulations of the
categories (from left to right)
D
K
,
D
,
B
K
, and
B
(the latter two from
B
þ
B
,
B
0
B
0
, and
q
q
MC samples), for the mode
D
!
D
0
,
D
!
K
. In the upper plots, the dots represent the MC sample spectrum, and the curves show the PDFs. Note the vertical log
scale in the lower plots.
B. AUBERT
et al.
PHYSICAL REVIEW D
78,
092002 (2008)
092002-8