Measurement of
CP
observables for the decays
B
!
D
0
CP
K
B. Aubert,
1
R. Barate,
1
D. Boutigny,
1
F. Couderc,
1
Y. Karyotakis,
1
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
A. Zghiche,
1
E. Grauges,
2
A. Palano,
3
M. Pappagallo,
3
J. C. Chen,
4
N. D. Qi,
4
G. Rong,
4
P. Wang,
4
Y. S. Zhu,
4
G. Eigen,
5
I. Ofte,
5
B. Stugu,
5
G. S. Abrams,
6
M. Battaglia,
6
D. S. Best,
6
D. N. Brown,
6
J. Button-Shafer,
6
R. N. Cahn,
6
E. Charles,
6
C. T. Day,
6
M. S. Gill,
6
A. V. Gritsan,
6,
*
Y. Groysman,
6
R. G. Jacobsen,
6
R. W. Kadel,
6
J. A. Kadyk,
6
L. T. Kerth,
6
Yu. G. Kolomensky,
6
G. Kukartsev,
6
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
D. Walker,
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
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
K. Yu Todyshev,
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
S. Abachi,
14
C. Buchanan,
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
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
J. D. Richman,
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
A. Soffer,
22
W. H. Toki,
22
R. J. Wilson,
22
F. Winklmeier,
22
Q. Zeng,
22
D. D. Altenburg,
23
E. Feltresi,
23
A. Hauke,
23
H. Jasper,
23
B. Spaan,
23
T. Brandt,
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
A. Volk,
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
S. Pacetti,
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
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
G. Schott,
35
N. Arnaud,
36
M. Davier,
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. Pruvot,
36
S. Rodier,
36
P. Roudeau,
36
M. H. Schune,
36
A. Stocchi,
36
W. F. 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
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. P. Kelly,
42
G. D. Lafferty,
42
M. T. Naisbit,
42
J. C. Williams,
42
J. I. Yi,
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
C. T. Potter,
46
S. H. Robertson,
46
A. Lazzaro,
47
V. Lombardo,
47
F. 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,
x
G. De Nardo,
51
F. Fabozzi,
51,
x
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
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
J. Brau,
55
R. Frey,
55
O. Igonkina,
55
M. Lu,
55
R. Rahmat,
55
N. B. Sinev,
55
D. Strom,
55
J. Strube,
55
E. Torrence,
55
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73,
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F. Galeazzi,
56
M. Margoni,
56
M. Morandin,
56
A. Pompili,
56
M. Posocco,
56
M. Rotondo,
56
F. Simonetto,
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R. Stroili,
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C. Voci,
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M. Benayoun,
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J. Chauveau,
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P. David,
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L. Del Buono,
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Ch. de la Vaissie
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O. Hamon,
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B. L. Hartfiel,
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M. J. J. John,
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Ph. Leruste,
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J. Malcle
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s,
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J. Ocariz,
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L. Roos,
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G. Therin,
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L. Gladney,
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J. Panetta,
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M. Biasini,
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R. Covarelli,
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M. Pioppi,
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C. Angelini,
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G. Batignani,
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S. Bettarini,
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G. Calderini,
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M. Carpinelli,
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R. Cenci,
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F. Forti,
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M. A. Giorgi,
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A. Lusiani,
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G. Marchiori,
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M. A. Mazur,
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M. Morganti,
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E. Paoloni,
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M. Rama,
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E. Di Marco,
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R. Faccini,
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F. Ferrarotto,
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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,
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C. Voena,
63
H. Schro
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R. Waldi,
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T. Adye,
65
N. De Groot,
65
B. Franek,
65
E. O. Olaiya,
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F. F. Wilson,
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S. Emery,
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A. Gaidot,
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S. F. Ganzhur,
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G. Hamel de Monchenault,
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W. Kozanecki,
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M. Legendre,
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B. Mayer,
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G. Vasseur,
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Ch. Ye
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M. H. Kelsey,
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D. W. G. S. Leith,
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H. L. Lynch,
68
D. B. MacFarlane,
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R. Messner,
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D. R. Muller,
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C. P. O’Grady,
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V. E. Ozcan,
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A. Perazzo,
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M. Perl,
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A. Roodman,
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A. A. Salnikov,
68
R. H. Schindler,
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J. Schwiening,
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A. Snyder,
68
J. Stelzer,
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D. Su,
68
M. K. Sullivan,
68
K. Suzuki,
68
S. K. Swain,
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J. M. Thompson,
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J. Va’vra,
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N. van Bakel,
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M. Weaver,
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A. J. R. Weinstein,
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W. J. Wisniewski,
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M. Wittgen,
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D. H. Wright,
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M. Bomben,
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R. J. Sobie,
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P. Tan,
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S. L. Wu,
80
Z. Yu,
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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,
051105 (2006)
RAPID COMMUNICATIONS
051105-2
22
Colorado State University, Fort Collins, Colorado 80523, USA
23
Universita
̈
t Dortmund, Institut fur 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 7ZE, 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
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 27 December 2005; published 15 March 2006)
MEASUREMENT OF
CP
OBSERVABLES FOR THE DECAYS
B
!
D
0
CP
K
PHYSICAL REVIEW D
73,
051105 (2006)
RAPID COMMUNICATIONS
051105-3
We present a study of the decay
B
!
D
0
CP
K
and its charge conjugate, where
D
0
CP
is reconstructed
in
CP
-even,
CP
-odd, and non-
CP
flavor eigenstates, based on a sample of
232
10
6
4
S
!
B
B
decays
collected with the
BABAR
detector at the PEP-II
e
e
storage ring. We measure the partial-rate charge
asymmetries
A
CP
and the ratios
R
CP
of the
B
!
D
0
K
decay branching fractions as measured in
CP
and
non-
CP D
0
decays:
A
CP
0
:
35
0
:
13
stat
0
:
04
syst
,
A
CP
0
:
06
0
:
13
stat
0
:
04
syst
,
R
CP
0
:
90
0
:
12
stat
0
:
04
syst
, and
R
CP
0
:
86
0
:
10
stat
0
:
05
syst
.
DOI:
10.1103/PhysRevD.73.051105
PACS numbers: 11.30.Er, 13.25.Hw, 14.40.Nd
A theoretically clean measurement of the angle
arg
V
ud
V
ub
=V
cd
V
cb
of
the
Cabibbo-Kobayashi-
Maskawa matrix
V
can be obtained from the study of
B
!
D
0
K
decays [1] by exploiting the interference
between the
b
!
c
us
and
b
!
u
cs
decay amplitudes [2,3].
Among the proposed methods, the one originally suggested
by Gronau, London, and Wyler (GLW) exploits the inter-
ference between
B
!
D
0
K
and
B
!
D
0
K
when the
D
0
and
D
0
mesons decay to the same
CP
eigenstate.
The results of the GLW analyses are usually expressed in
terms of the ratios
R
CP
of charge-averaged partial rates
and of the partial-rate charge asymmetries
A
CP
,
R
CP
B
!
D
0
CP
K
B
!
D
0
CP
K
B
!
D
0
K
B
!
D
0
K
=
2
;
(1)
A
CP
B
!
D
0
CP
K
B
!
D
0
CP
K
B
!
D
0
CP
K
B
!
D
0
CP
K
:
(2)
Here,
D
0
CP
D
0
D
0
=
2
p
are the
CP
eigenstates of
the neutral
D
meson system, and we have followed the
notation used in [4]. Neglecting
D
0
D
0
mixing [5], the
observables
R
CP
and
A
CP
are related to the angle
, the
magnitude
r
of the ratio of the amplitudes for the processes
B
!
D
0
K
and
B
!
D
0
K
, and the relative strong
phase
between these two amplitudes, through the rela-
tions
R
CP
1
r
2
2
r
cos
cos
and
A
CP
2
r
sin
sin
=R
CP
[2]. Theoretical expectations for
r
are in the range
0
:
1
–
0
:
2
[2,6], in agreement with the
90% C.L. upper limits on
r
set by
BABAR
(
r<
0
:
23
) and
Belle (
r<
0
:
18
) through the study of
B
!
DK
,
D
!
K
decays [7].
In this paper we present the measurements of
R
CP
and
A
CP
. The ratios
R
CP
are computed using the relations
R
CP
R
=R
, where the quantities
R
are defined as
R
B
B
!
D
0
CP
K
B
B
!
D
0
CP
K
B
B
!
D
0
CP
B
B
!
D
0
CP
:
(3)
Several systematic uncertainties cancel out in the measure-
ment of these double ratios. We also express the
CP
-sensitive observables in terms of three independent
quantities:
x
R
CP
1
A
CP
R
CP
1
A
CP
4
;
(4)
r
2
x
2
y
2
R
CP
R
CP
2
2
;
(5)
where
x
r
cos
and
y
r
sin
are the
same
CP
parameters as were measured by the
BABAR
Collaboration with
B
!
DK
,
D
!
K
0
S
decays
[8]. This choice allows the results of the two measurements
to be expressed in a consistent manner.
The measurements use a sample of 232 million
4
S
decays into
B
B
pairs collected with the
BABAR
detector at
the PEP-II asymmetric-energy
B
factory. Since the
BABAR
detector is described in detail elsewhere [9], only the
components that are crucial to this analysis are summa-
rized here. Charged-particle tracking is provided by a five-
layer silicon vertex tracker (SVT) and a 40-layer drift
chamber (DCH). For charged-particle identification, ion-
ization energy loss in the DCH and SVT, and Cherenkov
radiation detected in a ring-imaging device (DIRC) are
used. Photons are identified by the electromagnetic calo-
rimeter (EMC), which comprises 6580 thallium-doped CsI
crystals. These systems are mounted inside a 1.5-T sole-
noidal superconducting magnet. We use the
GEANT
[10]
software to simulate interactions of particles traversing the
detector, taking into account the varying accelerator and
detector conditions.
We reconstruct
B
!
D
0
h
decays, where the prompt
track
h
is a kaon or a pion.
D
0
candidates are recon-
structed in the
CP
-even eigenstates
and
K
K
(
D
0
CP
), in the
CP
-odd eigenstates
K
0
S
0
,
K
0
S
and
K
0
S
!
(
D
0
CP
), and in the non-
CP
, flavor eigenstate
K
.
candidates are reconstructed in the
K
K
channel and
!
candidates in the
0
channel. We optimize our event
selection to minimize the statistical error on the
B
!
D
0
CP
K
signal yield, determined for each
D
0
decay chan-
nel using simulated signal and background events.
k
Deceased.
x
Also with Universita
`
della Basilicata, Potenza, Italy.
‡
Also with Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
†
Also at Laboratoire de Physique Corpusculaire, Clermont-
Ferrand, France.
*
Also with the Johns Hopkins University, Baltimore, MD
21218, USA.
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
051105 (2006)
RAPID COMMUNICATIONS
051105-4
The prompt particle
h
is required to have a momentum
greater than
1
:
4 GeV
=c
and the number of photons asso-
ciated to its Cherenkov ring is required to be greater than
four to improve the quality of the reconstruction. We reject
a candidate track if its Cherenkov angle does not agree
within 4 standard deviations (
) with either the pion or
kaon hypothesis, or if it is identified as an electron by the
DCH and the EMC. Particle identification (PID) informa-
tion from the drift chamber and, when available, from the
DIRC, must be consistent with the kaon hypothesis for the
K
meson candidate in
D
0
!
K
,
D
0
!
K
K
, and
!
K
K
decays and with the pion hypothesis for the
meson candidates in
D
0
!
and
!
!
0
decays.
Neutral pions are reconstructed by combining pairs
of photon candidates with energy deposits larger
than 70 MeV that are not matched to charged tracks. The
invariant mass is required to be in the range
115
–
150 MeV
=c
2
and the total
0
energy must be greater
than 200 MeV. To improve momentum resolution, the
invariant mass of the two photons from candidate
0
’s
used in the
B
meson reconstruction is constrained to the
nominal
0
mass [11].
Neutral kaons are reconstructed from pairs of oppositely
charged tracks with invariant mass within
7
:
8 MeV
=c
2
(
3
) of the nominal
K
0
mass. We also require that the ratio
between the flight length in the plane transverse to the
beam direction and its error be greater than 2. The
mesons are reconstructed from two oppositely
charged kaons with invariant mass in the range
1
:
008
<
M
K
K
<
1
:
032 GeV
=c
2
.
We
also
require
j
cos
hel
j
>
0
:
4
, where
hel
is the angle between
the flight direction of one of the
daughters and the
D
0
flight direction, in the
rest frame. The
!
mesons are
reconstructed from
0
combinations with invariant
mass in the range
0
:
763
<M
0
<
0
:
799 GeV
=c
2
.
We define
N
as the angle between the normal to the
!
decay plane and the
D
0
momentum in the
!
rest frame, and
as the angle between the flight direction of one of the
three pions in the
!
rest frame and the flight direction of
one of the other two pions in their center-of-mass (CM)
frame. The quantities
cos
N
and
cos
follow
cos
2
N
and
sin
2
distributions for the signal and are almost flat for
wrongly reconstructed or false
!
candidates. We require
the product
cos
2
N
sin
2
>
0
:
08
. The invariant mass of a
D
0
candidate,
M
D
0
, must be within
2
:
5
of the mean
fitted mass, with resolution
ranging from 4 to
20 MeV
=c
2
depending on the
D
0
decay mode. For
D
0
!
, the invariant mass of the (
h
) system, where
is the pion from
D
0
, and
h
is the prompt track from
B
taken with the kaon mass hypothesis, must be greater
than
1
:
9 GeV
=c
2
to reject background from
B
!
D
0
,
D
0
!
K
and
B
!
K
0
,
K
0
!
K
decays.
To improve the
D
0
momentum resolution, for all the
D
0
decay channels the candidate invariant mass is constrained
to the nominal
D
0
mass [11].
We reconstruct
B
meson candidates by combining a
D
0
candidate with a track
h
. For the
D
0
!
K
mode,
the charge of the track
h
must match that of the kaon
from the
D
0
meson decay. We select
B
meson
candidates using the beam-energy-substituted mass
m
ES
E
2
i
=
2
p
i
p
B
2
=E
2
i
p
2
B
q
and the energy difference
E
E
B
E
i
=
2
, where the subscripts
i
and
B
refer to
the initial
e
e
system and the
B
candidate, respectively,
and the asterisk denotes the CM [
4
S
] frame. The
m
ES
distributions for
B
!
D
0
h
signals are Gaussian func-
tions centered at the
B
mass with a resolution of
2
:
6 MeV
=c
2
, which do not depend on the decay mode or
on the nature of the prompt track. In contrast, the
E
distributions depend on the mass assigned to the prompt
track and on the
D
0
momentum resolution. We evaluate
E
with the kaon mass hypothesis so that the distributions
are Gaussian and centered near zero for
B
!
D
0
K
events and shifted by approximately 50 MeV for
B
!
D
0
events. The
B
!
D
0
K
E
resolution is about
17 MeV for all the
D
0
decay modes. All
B
candidates are
selected with
m
ES
within
3
of the mean value and with
E
in the range
0
:
16
<
E<
0
:
23 GeV
.
To reduce background from continuum production of
light quarks, we construct a linear Fisher discriminant [12]
based on the following quantities: (i)
L
0
P
i
p
i
and
L
2
P
i
p
i
cos
2
i
, evaluated in the CM frame, where
p
i
is the
momentum, and
i
is the angle with respect to the thrust
axis of the
B
candidate of charged tracks and neutral
clusters not used to reconstruct the
B
; (ii)
j
cos
T
j
, where
T
is the angle between the thrust axes of the
B
candidate
and of the remaining tracks and clusters, evaluated in the
CM frame; (iii)
j
cos
B
j
, where
B
is the polar angle of the
B
candidate in the CM frame.
For events with multiple
B
!
D
0
h
candidates (1% –
7% of the selected events, depending on the
D
0
decay
mode), we choose that with the smallest
2
formed from
the differences of the measured and true masses of the
candidate
B
,
D
0
,
0
(only for
D
0
!
K
0
S
0
,
K
0
S
!
),
D
0
!
K
0
S
,
!
D
0
!
K
0
S
!
, scaled by the mass spread. The total
reconstruction efficiencies, based on simulated signal
events, are 39% (
K
), 31% (
K
K
), 30% (
),
17% (
K
0
S
0
), 20% (
K
0
S
), and 7% (
K
0
S
!
).
The main contributions to the background from
B
B
events come from the processes
B
!
D
h
h
; K
,
B
!
D
0
, misreconstructed
B
!
D
0
h
, and from
charmless
B
decays to the same final state as the signal:
for instance, the process
B
!
K
K
K
is a background
for
B
!
D
0
K
,
D
0
!
K
K
. These charmless back-
grounds have similar
E
and
m
ES
distribution as the
D
0
K
signal
and
we
call
them
‘‘peaking
B
B
backgrounds.’’
For each
D
0
decay mode an extended unbinned maxi-
mum likelihood fit to the selected data events determines
yields for two signal channels,
B
!
D
0
and
B
!
D
0
K
, and four kinds of backgrounds: candidates selected
MEASUREMENT OF
CP
OBSERVABLES FOR THE DECAYS
B
!
D
0
CP
K
PHYSICAL REVIEW D
73,
051105 (2006)
RAPID COMMUNICATIONS
051105-5
either from continuum or from
B
B
events, in which the
prompt track is either a pion or a kaon.
The fit uses as input
E
and a particle identification
probability for the prompt track based on the Cherenkov
angle
C
, the momentum
p
, and the polar angle
of the
track.
The extended likelihood function
L
is defined as
L
exp
X
6
i
1
n
i
Y
N
j
1
X
6
i
1
n
i
P
i
~
x
j
;
~
i
;
(6)
where
N
is the total number of observed events and
n
i
is the
yield of the
i
th event category. The six functions
P
i
~
x
j
;
~
i
are the probability density functions (PDFs) for the varia-
bles
~
x
j
, given the set of parameters
~
i
. They are evaluated
as a product
P
i
P
1
i
E
P
2
i
C
.
The
E
distribution for
B
!
D
0
K
signal events is
parametrized with a Gaussian function. The
E
distribu-
tion for
B
!
D
0
is parametrized with the same
Gaussian function used for
B
!
D
0
K
with an addi-
tional shift, computed event by event as a function of the
prompt track momentum, arising from the wrong mass
assignment to the prompt track. The offset and width of
the Gaussian functions are determined from data together
with the yields.
The
E
distribution for the continuum background is
parametrized with a linear function whose slope is deter-
mined from off-resonance data. The
E
distribution for the
nonpeaking
B
B
background is empirically parametrized
with the sum of a Gaussian function and an exponential
function when the prompt track is a pion, and with an
exponential function when the prompt track is a kaon.
The parameters are determined from simulated events.
The
E
distribution for the peaking charmless
B
B
back-
ground is parametrized with the same Gaussian function
used for the
B
!
D
0
K
signal. The yield of the
B
B
peaking background is estimated from the sidebands of
the
D
0
invariant mass distribution and fixed in the fit.
The parametrization of the particle identification PDF is
performed by fitting with two Gaussian functions the
background-subtracted distribution of the difference be-
tween the reconstructed and expected Cherenkov angles
of kaon and pion samples. The parametrization is per-
formed as a function of the momentum and polar angle
of the track. Pions and kaons are selected from a pure
D
!
D
0
,
D
0
!
K
control sample.
The results of the fit are summarized in Table I. Figure 1
shows the distributions of
E
for the
K
,
CP
and
CP
modes after enhancing the
B
!
D
0
K
purity by re-
quiring that the prompt track be consistent with the kaon
hypothesis. The total PDF, normalized by the fitted signal
TABLE I. Yields from the maximum likelihood fit. The quoted
uncertainties are statistical.
D
0
mode
N
D
N
D
N
DK
N
DK
K
8151
95 7899
93 649
29 611
28
K
K
705
28
690
28
26
970
10
256
18
219
17
18
717
7
K
0
S
0
707
29
677
29
39
942
9
K
0
S
176
14
157
13
15
513
4
K
0
S
!
235
17
230
17
25
714
6
E (GeV)
∆
-0.1
0
0.1
0.2
Events/(0.01 GeV)
0
100
200
300
DATA
K
0
D
→
B
π
0
D
→
B
background
E (GeV)
∆
-0.1
0
0.1
0.2
Events/(0.01 GeV)
0
20
40
DATA
K
CP+
0
D
→
B
π
CP+
0
D
→
B
background
E (GeV)
∆
-0.1
0
0.1
0.2
Events/(0.01 GeV)
0
20
40
60
DATA
K
CP-
0
D
→
B
π
CP-
0
D
→
B
background
FIG. 1. Distributions of
E
for events enhanced in the
B
!
D
0
K
signal. Top:
B
!
D
0
K
,
D
0
!
K
; middle:
B
!
D
0
CP
K
; bottom:
B
!
D
0
CP
K
. Solid curves represent pro-
jections of the maximum likelihood fit; dashed, dash-dotted and
dotted curves represent the
B
!
D
0
K
,
B
!
D
0
and back-
ground contributions.
TABLE II.
Measured ratios
R
CP
and
A
CP
for
CP
-even and
CP
-odd
D
decay modes. The first error is statistical, the second
is systematic.
R
CP
and
A
CP
are corrected for the
CP
-even
dilution described in the text.
D
0
mode
R
CP
A
CP
CP
0
:
90
0
:
12
0
:
04
0
:
35
0
:
13
0
:
04
CP
0
:
86
0
:
10
0
:
05
0
:
06
0
:
13
0
:
04
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
051105 (2006)
RAPID COMMUNICATIONS
051105-6