of 20
Measurements of the semileptonic decays

B
!
D‘


and

B
!
D



using a global fit
to
DX‘


final states
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. 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
B. G. Fulsom,
9
C. Hearty,
9
T. S. Mattison,
9
J. A. McKenna,
9
M. Barrett,
10
A. Khan,
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
P. C. Bloom,
20
W. T. Ford,
20
A. Gaz,
20
J. F. Hirschauer,
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
J. Marks,
30
S. Schenk,
30
U. Uwer,
30
V. Klose,
31
H. M. Lacker,
31
D. J. Bard,
32
P. D. Dauncey,
32
J. A. Nash,
32
W. Panduro Vazquez,
32
M. Tibbetts,
32
P. K. Behera,
33
X. Chai,
33
M. J. Charles,
33
U. Mallik,
33
J. Cochran,
34
H. B. Crawley,
34
L. Dong,
34
W. T. Meyer,
34
S. Prell,
34
E. I. Rosenberg,
34
A. E. Rubin,
34
Y. Y. Gao,
35
A. V. Gritsan,
35
Z. J. Guo,
35
C. K. Lae,
35
A. G. Denig,
36
M. Fritsch,
36
G. Schott,
36
N. Arnaud,
37
J. Be
́
quilleux,
37
A. D’Orazio,
37
M. Davier,
37
J. Firmino da Costa,
37
G. Grosdidier,
37
A. Ho
̈
cker,
37
V. Lepeltier,
37
F. Le Diberder,
37
A. M. Lutz,
37
S. Pruvot,
37
P. Roudeau,
37
M. H. Schune,
37
J. Serrano,
37
V. Sordini,
37,
k
A. Stocchi,
37
G. Wormser,
37
D. J. Lange,
38
D. M. Wright,
38
I. Bingham,
39
J. P. Burke,
39
C. A. Chavez,
39
J. R. Fry,
39
E. Gabathuler,
39
R. Gamet,
39
D. E. Hutchcroft,
39
D. J. Payne,
39
C. Touramanis,
39
A. J. Bevan,
40
C. K. Clarke,
40
K. A. George,
40
F. Di Lodovico,
40
R. Sacco,
40
M. Sigamani,
40
G. Cowan,
41
H. U. Flaecher,
41
D. A. Hopkins,
41
S. Paramesvaran,
41
F. Salvatore,
41
A. C. Wren,
41
D. N. Brown,
42
C. L. Davis,
42
K. E. Alwyn,
43
D. Bailey,
43
R. J. Barlow,
43
Y. M. Chia,
43
C. L. Edgar,
43
G. Jackson,
43
G. D. Lafferty,
43
T. J. West,
43
J. I. Yi,
43
J. Anderson,
44
C. Chen,
44
A. Jawahery,
44
D. A. Roberts,
44
G. Simi,
44
J. M. Tuggle,
44
C. Dallapiccola,
45
X. Li,
45
E. Salvati,
45
S. Saremi,
45
R. Cowan,
46
D. Dujmic,
46
P. H. Fisher,
46
K. Koeneke,
46
G. Sciolla,
46
M. Spitznagel,
46
F. Taylor,
46
R. K. Yamamoto,
46
M. Zhao,
46
P. M. Patel,
47
S. H. Robertson,
47
A. Lazzaro,
48a,48b
V. Lombardo,
48a
F. Palombo,
48a,48b
J. M. Bauer,
49
L. Cremaldi,
49
V. Eschenburg,
49
R. Godang,
49,
{
R. Kroeger,
49
D. A. Sanders,
49
D. J. Summers,
49
H. W. Zhao,
49
M. Simard,
50
P. Taras,
50
F. B. Viaud,
50
H. Nicholson,
51
G. De Nardo,
52a,52b
L. Lista,
52a
D. Monorchio,
52a,52b
G. Onorato,
52a,52b
C. Sciacca,
52a,52b
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
S. Sitt,
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
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
PHYSICAL REVIEW D
79,
012002 (2009)
1550-7998
=
2009
=
79(1)
=
012002(20)
012002-1
Ó
2009 The American Physical Society
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
F. F. Wilson,
65
S. Emery,
66
M. Escalier,
66
L. Esteve,
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
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
29
Harvard University, Cambridge, Massachusetts 02138, USA
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
012002 (2009)
012002-2
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
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
Johns Hopkins University, Baltimore, Maryland 21218, USA
36
Universita
̈
t Karlsruhe, Institut fu
̈
r Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
37
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
38
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
39
University of Liverpool, Liverpool L69 7ZE, United Kingdom
40
Queen Mary, University of London, London, E1 4NS, United Kingdom
41
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
42
University of Louisville, Louisville, Kentucky 40292, USA
43
University of Manchester, Manchester M13 9PL, United Kingdom
44
University of Maryland, College Park, Maryland 20742, USA
45
University of Massachusetts, Amherst, Massachusetts 01003, USA
46
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
47
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
48a
INFN Sezione di Milano, I-20133 Milano, Italy
48b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
49
University of Mississippi, University, Mississippi 38677, USA
50
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
51
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
52a
INFN Sezione di Napoli, I-80126 Napoli, Italy
52b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
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, I-56127 Pisa, Italy
61c
Universita
`
di Pisa, 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/Irfu, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, 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
**
Also with Universita
`
di Sassari, Sassari, Italy.
{
Now at University of South Alabama, Mobile, AL 36688, USA.
k
Also with Universita
`
di Roma La Sapienza, I-00185 Roma, Italy.
x
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
Now at Tel Aviv University, Tel Aviv, 69978, Israel.
Now at Temple University, Philadelphia, PA 19122, USA.
*
Deceased.
MEASUREMENTS OF THE SEMILEPTONIC DECAYS
...
PHYSICAL REVIEW D
79,
012002 (2009)
012002-3
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
79
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 8 September 2008; published 15 January 2009)
Semileptonic

B
decays to
DX‘


(
¼
e
or

) are selected by reconstructing
D
0
and
D
þ
combina-
tions from a sample of
230

10
6

ð
4
S
Þ!
B

B
decays recorded with the
BABAR
detector at the PEP-II
e
þ
e

collider at SLAC. A global fit to these samples in a three-dimensional space of kinematic variables
is used to determine the branching fractions
B
ð
B

!
D
0


Þ¼ð
2
:
34

0
:
03

0
:
13
Þ
%
and
B
ð
B

!
D

0


Þ¼ð
5
:
40

0
:
02

0
:
21
Þ
%
where the errors are statistical and systematic, respectively. The fit also
determines form-factor parameters in a parametrization based on heavy quark effective theory, resulting in

2
D
¼
1
:
20

0
:
04

0
:
07
for

B
!
D‘


and

2
D

¼
1
:
22

0
:
02

0
:
07
for

B
!
D



. These values are
used to obtain the product of the Cabibbo-Kobayashi-Maskawa matrix element
j
V
cb
j
times the form factor
at the zero recoil point for both

B
!
D‘


decays,
G
ð
1
Þj
V
cb
j¼ð
43
:
1

0
:
8

2
:
3
Þ
10

3
, and for

B
!
D



decays,
F
ð
1
Þj
V
cb
j¼ð
35
:
9

0
:
2

1
:
2
Þ
10

3
.
DOI:
10.1103/PhysRevD.79.012002
PACS numbers: 13.25.Hw, 12.15.Hh, 11.30.Er
I. INTRODUCTION
The study of semileptonic decays of heavy quarks pro-
vides the cleanest avenue for the determination of several
elements of the Cabibbo-Kobayashi-Maskawa matrix [
1
],
which are fundamental parameters in the standard model of
particle physics. The coupling strength of the weak
b
!
c
transition is proportional to
j
V
cb
j
, which has been mea-
sured in both inclusive semileptonic
B
decays [
2
] and in the
exclusive transitions

B
!
D‘


[
3
6
] and

B
!
D



[
3
,
6
10
](
¼
e
or

and charge conjugate modes are implied).
The inclusive and exclusive determinations of
j
V
cb
j
rely on
different theoretical calculations. The former employs a
parton-level calculation of the decay rate organized in a
double expansion in

S
and in inverse powers of
m
b
, the
b
-quark mass. The latter relies on a parametrization of the
decay form factors using heavy quark symmetry and a
nonperturbative calculation of the form-factor normaliza-
tion at the zero recoil (maximum squared momentum
transfer) point. The theoretical uncertainties in these two
approaches are independent. The inclusive and exclusive
experimental measurements use different techniques and
have negligible statistical overlap, and thus have largely
uncorrelated uncertainties. This independence makes the
comparison of
j
V
cb
j
from inclusive and exclusive decays a
powerful test of our understanding of semileptonic decays.
The latest determinations [
11
] differ by more than 2 stan-
dard deviations (

), and the inclusive determination is
currently more than twice as precise as the exclusive
determination. Improvements in the measurements of ex-
clusive decays will strengthen this test. This is particularly
true for the

B
!
D‘


decay, where the experimental un-
certainties dominate the determination of
j
V
cb
j
. For the
decay

B
0
!
D


, the experimental situation needs
clarification, as existing measurements are in poor agree-
ment with each other [
11
]. Finally, precise measurements
of semileptonic
B
decays to charm are needed to further
improve determinations of
j
V
ub
j
, where

B
!
D
ðÞ


de-
cays are the principal background.
Semileptonic
b
!
c
transitions result in the production
of a charm system that cascades down to the ground state
D
0
or
D
þ
mesons. Most previous analyses have focused on
reconstructing separately the exclusive decays

B
!
D



[
3
,
7
10
] and

B
!
D‘


[
3
5
]. The

B
!
D



analyses
involve reconstruction of the soft transition pion from the
decay
D

!
D
, which is at the limit of detector accep-
tance; determination of the reconstruction efficiency for
these pions introduces significant systematic uncertainty.
Studies of the exclusive decay

B
!
D‘


suffer from large
feed-down background from

B
!
D



decays where the
transition pion is undetected.
In this analysis we reconstruct
D
0
and
D
þ
pairs and
use a global fit to their kinematic properties to determine
the branching fractions and form-factor parameters of the
dominant semileptonic decays

B
!
D‘


and

B
!
D



.
The reconstructed
D‘
samples contain, by design, the feed-
down from all the higher mass states (apart from decays of
the type

B
!
D
þ
s
X‘


[
12
]). Kinematic restrictions are
imposed to reduce the contribution of backgrounds from
semileptonic decays to final state hadronic systems more
massive than
D

and from other sources of
D‘
combina-
tions. Distributions from selected events are binned in the
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
012002 (2009)
012002-4
three-dimensional space described below. The electron and
muon samples are input into separate fits, in which isospin
symmetry is assumed for the semileptonic decay rates.
Semileptonic decays are produced via a spectator diagram
in which the heavy quark decays independently; strong
interaction corrections to this process conserve isospin.
As a result, we constrain semileptonic decay rates for
B

and

B
0
to be equal, e.g.,

ð
B

!
D
0
l



Þ¼

ð

B
0
!
D
þ
l



Þ
. This substantially reduces statistical uncertainties
on the fitted parameters. Systematic uncertainties associ-
ated with the modeling of the signal and background
processes, the detector response, and uncertainties on input
parameters are determined, along with their correlations
between the electron and muon samples. The fitted results
are then combined using the full covariance matrix of
statistical and systematic errors. For both

B
!
D‘


and

B
!
D



decays, the fitted branching fractions and form-
factor parameters are used to determine the products
G
ð
1
Þj
V
cb
j
and
F
ð
1
Þj
V
cb
j
. These measurements, along
with theoretical input on the form-factor normalizations
G
ð
1
Þ
and
F
ð
1
Þ
at the zero recoil point, allow determina-
tions of
j
V
cb
j
.
The approach taken in this study has some similarity to
that of Ref. [
6
], where the branching fractions for

B
!
D‘


and

B
!
D



are measured simultaneously.
However, Ref. [
6
] reconstructs semileptonic
B
decays in
events in which the second
B
meson is fully reconstructed.
That approach allows the use of the missing mass squared
as a powerful discriminant. This analysis provides modest
discrimination between the different semileptonic decays
on an event-by-event basis, but results in a much larger
statistical sample and enables the measurement of form-
factor parameters.
The remaining sections of this paper are organized as
follows. In Sec.
II
we describe the
BABAR
detector and the
samples of
BABAR
data and simulated events used in the
analysis. The event selection and the distributions that are
input to the global fit are discussed in Sec.
III
. We give the
parametrization of the form factors of

B
!
D
ðÞ


decays
and the modeling of semileptonic

B
decays to
D
ðÞ

and
D
ðÞ

states in Sec.
IV
. The global fit strategy and results
are given in Sec.
V
, and the evaluation of systematic
uncertainties is detailed in Sec.
VI
. Section
VII
presents
the determination of
j
V
cb
j
from the fitted results. The final
section, Sec.
VIII
, discusses the results and provides aver-
ages with previous
BABAR
measurements.
II. THE
BABAR
DETECTOR AND DATA SET
The data used in this analysis were collected with the
BABAR
detector at the PEP-II storage ring between 1999
and 2004. PEP-II is an asymmetric collider; the center of
mass (CM) of the colliding
e
þ
e

moves with velocity

¼
0
:
49
along the beam axis in the laboratory rest frame. The
data collected at energies near the peak of the

ð
4
S
Þ
resonance (on peak) correspond to
207 fb

1
or
230

10
6
B

B
decays. Data collected just below the
B

B
threshold
(off peak), corresponding to
21
:
5fb

1
, are used to subtract
the
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
,
c
) background under the

ð
4
S
Þ
resonance.
The
BABAR
detector is described in detail elsewhere
[
13
]. It consists of a silicon vertex tracker (SVT), a drift
chamber (DCH), a detector of internally reflected
Cherenkov light (DIRC), an electromagnetic calorimeter
(EMC), and an instrumented flux return (IFR). The SVT
and DCH operate in an axial magnetic field of 1.5 T and
provide measurements of the positions and momenta of
charged particles, as well as of their ionization energy loss
(
dE=dx
). Energy and shower shape measurements for
photons and electrons are provided by the EMC. The
DIRC measures the angle of Cherenkov photons emitted
by charged particles traversing the fused silica radiator
bars. Charged particles that traverse the EMC and shower-
ing hadrons are measured in the IFR as they penetrate
successive layers of the return yoke of the magnet.
Simulated events used in the analysis are generated
using the
EVTGEN
[
14
] program, and the generated particles
are propagated through a model of the
BABAR
detector
with the
GEANT4
[
15
] program and reconstructed using the
same algorithms used on
BABAR
data. The form-factor
parametrization [
16
] used in the simulation for

B
!
D



decays is based on heavy quark effective theory
(HQET) [
17
], while the ISGW2 model [
18
] is used for

B
!
D‘


and

B
!
D



decays, where
D

is one of the four
P
-wave charm mesons as described in Sec.
III B
. These are
subsequently reweighted to the forms given in Sec.
IV
.For
nonresonant

B
!
D
ðÞ
‘


decays, the Goity-Roberts
model [
19
] is used. In order to saturate the inclusive semi-
leptonic
b
!
c‘


decay rate, we include a contribution
from

B
!
D
ðÞ
‘


decays; a variety of models are con-
sidered for this purpose. The branching fractions for
B
and
charm decays in the simulation are rescaled to the values in
Ref. [
11
]. In addition, the momentum spectra for
D
0
and
D
þ
from
B
!
DX
and

B
!
DX
decays are adjusted to
agree with the corresponding measured spectra from
Ref. [
20
]. This adjustment is done only for background
processes.
The simulation of the detector response provided by the
GEANT4
-based program is further adjusted by comparing
with
BABAR
data control samples. In particular, the effi-
ciency of charged track reconstruction is modified by 1%–
2%, depending on momenta and event multiplicity, based
on studies of multihadron events and 1-versus-3 prong
e
þ
e

!

þ


events. The efficiencies and misidentifica-
tion probabilities of the particle identification (PID) algo-
rithms used to select pions, kaons, electrons, and muons
(see Sec.
III
) are adjusted based on studies of samples of
e
þ
e

!
e
þ
e

and
e
þ
e

!

þ


, and several
samples reconstructed without particle identification: 1-
versus-3 prong
e
þ
e

!

þ


events,
K
0
S
!

þ


,
D
!
D
0

þ
K


þ
Þ

þ
, and
!
p

.
MEASUREMENTS OF THE SEMILEPTONIC DECAYS
...
PHYSICAL REVIEW D
79,
012002 (2009)
012002-5
III. EVENT SELECTION
A. Preselection of
D‘
candidates
We select multihadron events by requiring at least three
good-quality charged tracks, a total reconstructed energy in
the event exceeding 4.5 GeV, the second normalized Fox-
Wolfram moment [
21
]
R
2
<
0
:
5
, and the distance between
the interaction point and the primary vertex of the
B
decay
to be less than 0.5 cm (6.0 cm) in the direction transverse
(parallel) to the beam line. In these events an identified
electron or muon candidate must be present, along with a
candidate
D
meson decay. Candidate electrons are identi-
fied using a likelihood ratio based on the shower shape in
the EMC,
dE=dx
in the tracking detectors, the Cherenkov
angle, and the ratio of EMC energy to track momentum.
The electron identification efficiency is 94% within the
acceptance of the calorimeter, and the pion misidentifica-
tion rate is 0.1%. Muon candidates are identified using a
neural network that takes input information from the track-
ing detectors, EMC, and IFR. The muon identification
efficiency rises with momentum to reach a plateau of
70% for laboratory momenta above
1
:
4 GeV
=c
, and the
pion misidentification rate is 3%.
Kaon candidates are required to satisfy particle identi-
fication criteria based on the
dE=dx
measured in the track-
ing detectors and the Cherenkov angle measured in the
DIRC. Each kaon candidate is combined with one or two
charged tracks of opposite sign to form a
D
0
!
K


þ
or
D
þ
!
K


þ

þ
candidate. Those combinations with in-
variant masses in the range
1
:
840
<m
K
<
1
:
888 GeV
=c
2
are considered as
D
0
candidates and those in the range
1
:
845
<m
K
<
1
:
893 GeV
=c
2
as
D
þ
candidates, respec-
tively. Combinations in the ‘‘sideband’’ mass regions
1
:
816
<m
K
<
1
:
840 GeV
=c
2
and
1
:
888
<m
K
<
1
:
912 GeV
=c
2
(
1
:
821
<m
K
<
1
:
845 GeV
=c
2
and
1
:
893
<m
K
<
1
:
917 GeV
=c
2
) are used to estimate the
combinatorial background.
The charge of the kaon candidate is required to have the
same sign as that of the candidate lepton. Each
D
-lepton
combination in an event is fitted to both

B
!
D‘
and
D
!
K


þ
ð

þ
Þ
vertices using the algorithm described in
Ref. [
22
]. The fit probabilities are required to exceed
0.01 for the

B
!
D
0
and

B
!
D
þ
vertices and 0.001
for the
D
0
and
D
þ
decay vertices. We require the absolute
value of the cosine of the angle between the
D‘
momentum
vector and the thrust axis of the remaining particles in the
event to be smaller than 0.92 to further reduce background,
most of which comes from
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
,
c
)
events.
The signal yields are determined by subtracting the
estimated combinatorial background from the number of
D
candidates in the peak region. The combinatorial back-
ground is estimated using the number of candidates in the
D
mass sideband regions scaled by the ratio of the widths
of the signal and sideband regions. This is equivalent to
assuming a linear dependence of the combinatorial back-
ground on invariant mass. The change in the yields is
negligible when using other assumptions for the back-
ground shape. Candidates from
e
þ
e

!
q

q
events are
statistically removed from the data sample by subtracting
the distribution of candidates observed in the data collected
at energies below the
B

B
threshold (off peak), after scaling
these data by the factor
r
L
¼ð
L
on
s
off
Þ
=
ð
L
off
s
on
Þ
to ac-
count for the difference in luminosity and the dependence
of the annihilation cross section on energy. The selection
criteria listed above were determined using simulated
B

B
events and off-peak data to roughly maximize the statisti-
cal significance of the
D‘
signal yields in
e
þ
e

!
B

B
events. They have an overall efficiency of 80% (76%) for

B
!
D
0
X‘


(

B
!
D
þ
X‘


) decays with
p

, the lepton
momentum magnitude in the CM frame, in the range
0
:
8
2
:
8 GeV
=c
.
The invariant mass distributions for the
D
0
and
D
þ
candidates, after off-peak subtraction, are shown in Fig.
1
for two kinematic subsets representing regions with good
and poor signal-to-background ratios. The small differ-
ences in peak position and combinatorial background level
have a negligible impact on the analysis due to the side-
band subtraction described above and the wide signal
window.
The
D
0
and
D
þ
candidates are binned in three kine-
matic variables:
(i)
p

D
, the
D
momentum in the CM frame;
(ii)
p

, the lepton momentum in the CM frame;
(iii)
cos
B

D‘
2
E

B
E

D‘

m
2
B

m
2
D‘
Þ
=
ð
2
p

B
p

D‘
Þ
;
,
the cosine of the angle between the

B
and
D‘
momentum vectors in the CM frame under the
assumption that the

B
decayed to
D‘


. If the
D‘
pair is not from a

B
!
D‘


decay,
j
cos
B

D‘
j
can
exceed unity. The
B
energy and momentum are not
measured event by event; they are calculated from
the CM energy determined by the PEP-II beams as
E

B
¼
ffiffiffi
s
p
=
2
and
p

B
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E

2
B

m
2
B
q
, where
m
B
is the
B
0
meson mass. The energy, momentum, and in-
variant mass corresponding to the sum of the
D
and
lepton four-vectors in the CM frame are denoted
E

D‘
,
p

D‘
, and
m
D‘
, respectively.
The binning in these three variables is discussed in
Sec.
III C
.
B. Sources of
D‘
candidates
There are several sources of
D‘
candidates that survive
the
D
-mass sideband and off-peak subtractions. In both the
D
0
and
D
þ
samples we group them as follows (

B
repre-
sents both
B

and

B
0
):
(i)

B
!
D‘


,
(ii)

B
!
D



,
(iii)

B
!
D
ðÞ
ð
n
Þ


, which includes the following:
(a) The
P
-wave
D

charm mesons. In the frame-
work of HQET, the
P
-wave charm mesons are
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
012002 (2009)
012002-6
categorized by the angular momentum of the
light constituent,
j
, namely,
j
P
¼
1
=
2

dou-
blet
D

0
and
D
0
1
and
j
P
¼
3
=
2

doublet
D
1
and
D

2
[
23
].
(b) Nonresonant

B
!
D
ðÞ
‘


.
(c) Decays of the type

B
!
D
ðÞ
‘


; the model-
ing of these is discussed in Sec.
IV D
.
(iv) Background from
B

B
events in which the lepton
and
D
candidates do not arise from a single semi-
leptonic

B
decay. These include (in order of im-
portance)
(a) Direct leptons from

B
!
X‘


decays combined
with a
D
from the decay of the other
B
meson in
the event. Roughly one-third of this background
comes from events in which
B
0

B
0
mixing re-
sults in the decay of two

B
0
mesons. Most of the
remaining contribution comes from Cabibbo-
Kobayashi-Maskawa-suppressed
B
!
DX
transitions.
(b) Uncorrelated cascade decays. In this case the
lepton mostly comes from the decay of an anti-
charm meson produced in the
B
decay and the
D
arises from the decay of the other

B
meson in
the event.
(c) Correlated cascade decays, in which the lepton
and
D
candidates come from the same parent

B
meson. These are mainly

B
!
D

D
ð
X
Þ
and

B
!
D
ð
X
Þ

decays, with the lepton coming from
the decay of an anticharm meson or tau.
(d) Misidentified lepton background. The probabil-
ity of a hadron being misidentified as a lepton is
negligible for electrons but not for muons.
As mentioned previously, the same decay widths are im-
posed for the semileptonic transitions of

B
0
and
B

.For
the background processes (source iv) no such requirement
is imposed.
C. Kinematic restrictions
Despite the use of the best available information for
calculating the background and

B
!
D
ðÞ
ð
n
Þ


distribu-
tions, these components suffer from significant uncertain-
ties. We therefore restrict the kinematic range of the
variables used in the fit to reduce the impact of these
Candidates/2MeV
2000
4000
6000
(a)
(b)
)
2
) (GeV/c
π
m(K
1.82
1.84
1.86
1.88
1.9
Candidates/2MeV
0
500
1000
1500
2000
2500
(c)
)
2
) (GeV/c
π
π
m(K
1.84
1.86
1.88
1.9
(d)
FIG. 1 (color online). The invariant mass distributions (data points) for selected candidates. Scaled off-peak data have been
subtracted to remove contributions from
e
þ
e

!
q

q
annihilation. Plots (a, c) show
K


þ
combinations and (b, d) show
K


þ

þ
combinations. In each case the
D‘
candidates are required to satisfy

2
:
0
<
cos
B

D‘
<
1
:
1
. The further kinematic requirements are
1
:
6
<p

<
1
:
8 GeV
=c
,
1
:
6
<p

D
<
2
:
0 GeV
=c
for plots (a, b) and
2
:
0
<p

<
2
:
35 GeV
=c
,
0
:
8
<p

D
<
1
:
2 GeV
=c
for plots (c, d).
The histograms show the contribution from simulated
B

B
events scaled to the data luminosity. The arrows indicate the boundaries
between signal and sideband regions.
MEASUREMENTS OF THE SEMILEPTONIC DECAYS
...
PHYSICAL REVIEW D
79,
012002 (2009)
012002-7
uncertainties while preserving sensitivity to the

B
!
D‘


and

B
!
D



branching fractions and form-factor pa-
rameters. We require

2
<
cos
B

D‘
<
1
:
1
and place re-
strictions on
p

D
and
p

, rejecting regions where the signal
decays are not dominant. This results in the ranges
1
:
2 GeV
=c < p

<
2
:
35 GeV
=c
and
0
:
8 GeV
=c < p

D
<
2
:
25 GeV
=c
. The yield within this region is
4
:
79

10
5
(
2
:
95

10
5
) candidates in the
D
0
(
D
þ
) sample with a
statistical uncertainty of 0.26% (0.66%).
The data are binned finely enough to have good sensi-
tivity to the fit parameters while maintaining adequate
statistics per bin. Table
I
gives the binning used in the fit.
We avoid setting a bin edge at
cos
B

D‘
¼
1
to reduce our
sensitivity to the modeling of the resolution in this variable,
since the

B
!
D‘


decay distribution has a sharp cutoff at
this point.
Two-dimensional projections of the signal, background,
and data distributions for the
D
0
e
sample are shown in
Fig.
2
to illustrate the separation power in these variables.
The distributions for the
D
0

sample (not shown) are
similar. The one-dimensional projections of the
De
and
D
samples are shown in Figs.
3
and
4
. The difference in
the size of the

B
!
D



components in
D
0
and
D
þ
distributions is due to the fact that
D

0
does not decay
to
D
þ
.
IV. MODELING OF SEMILEPTONIC
B
DECAYS
In our fully simulated event samples

B
!
D‘


and

B
!
D



decays were generated using the ISGW2 model
[
18
]. For

B
!
D



decays, a HQET model was used
with a linear form-factor parametrization. We reweight
TABLE I. Definitions of bins used for kinematic variables.
Quantity
Number of bins
Bin edges
cos
B

D‘
3

2
:
0
,

1
:
0
, 0.0, 1.1
p

ð
GeV
=c
Þ
10
1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.35
p

D
ð
GeV
=c
Þ
8
0.8, 1.1, 1.35, 1.5, 1.65, 1.8, 1.95, 2.1, 2.25
* (GeV/c)
D
p
1
1.5
2
(a)
(b)
* (GeV/c)
l
p
1.5
2
* (GeV/c)
D
p
1
1.5
2
(c)
* (GeV/c)
l
p
1.5
2
(d)
FIG. 2 (color online). Distribution of
p

D
vs
p

for
D
0
e
candidates after sideband subtraction. The shaded boxes have area
proportional to the number of entries. The plots show simulated candidates for (a)

B
!
De


, (b)

B
!
D

e


, and (c) other (sources
iii and iv combined), and for data after off-peak subtraction (d). The binning given in Table
I
is used, and only candidates that satisfy
0
:
0
<
cos
B

D‘
<
1
:
1
are plotted.
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
012002 (2009)
012002-8
all these decays using the formulas given in the following
subsections. The histograms in Figs.
3
and
4
are
reweighted.
A.

B
!
D‘


decays
The differential decay rate is given by [
17
]
d

ð

B
!
D‘


Þ
dw
¼
G
2
F
j
V
cb
j
2
m
5
B
48

3
r
3
ð
w
2

1
Þ
3
=
2
½ð
1
þ
r
Þ
h
þ
ð
w
Þð
1

r
Þ
h

ð
w
Þ
2
;
(1)
where
G
F
is the Fermi constant,
h
þ
ð
w
Þ
and
h

ð
w
Þ
are the
form factors,
r

m
D
=m
B
is the mass ratio, and
m
B
and
m
D
are the
B
and
D
meson masses, respectively. The velocity
transfer
w
is defined as
w

v
B

v
D
;
(2)
where
v
B
and
v
D
are the four-velocities of the
B
and
D
mesons, respectively. In the
B
rest frame
w
corresponds to
the Lorentz boost of the
D
meson. In the HQET model, the
form factors are given by [
16
]
h
þ
ð
w
Þ¼
G
ð
1
Þ½
1

8

2
D
z
þð
51

2
D

10
Þ
z
2
252

2
D

84
Þ
z
3

(3)
and
Candidates/100MeV
10 000
20 000
30 000
(a)
* (GeV/c)
l
p
1.5
2
0.9
0.95
1
1.05
1.1
Candidates/100MeV
10 000
20 000
(d)
0.9
1
1.1
Candidates/100MeV
10 000
20 000
(b)
* (GeV/c)
D
p
11.52
0.9
0.95
1
1.05
1.1
Candidates/100MeV
5000
10 000
(e)
0.9
1
1.1
Candidates/1.0
3
10
×
50
100
(c)
B-Dl
Θ
cos
-2
-1
0
1
0.9
0.95
1
1.05
1.1
Candidates/1.0
20 000
40 000
60 000
(f)
* (GeV/c)
l
p
1.5
2
* (GeV/c)
D
p
11.52
B-Dl
Θ
cos
-2
-1
0
1
0.9
1
1.1
FIG. 3 (color online). Projections onto individual kinematic variables of the data after off-peak subtraction and the results of the fit:
(a, d) lepton and (b, e)
D
momentum in the CM frame, and (c, f)
cos
B

D‘
. The points show data for accepted
D
0
e
(a, b, c) and
D
þ
e
(d, e, f) candidates, and the histograms show the individual fit components (from top to bottom):

B
!
De


,

B
!
D

e


,

B
!
D
ðÞ
ð
n
Þ
e


, and other
B

B
background. The ratio of data to the sum of the fitted yields is shown below each plot.
MEASUREMENTS OF THE SEMILEPTONIC DECAYS
...
PHYSICAL REVIEW D
79,
012002 (2009)
012002-9
h

ð
w
Þ¼
0
;
(4)
where
z
¼ð
ffiffiffiffiffiffiffiffiffiffiffiffiffi
w
þ
1
p

ffiffiffi
2
p
Þ
=
ð
ffiffiffiffiffiffiffiffiffiffiffiffiffi
w
þ
1
p
þ
ffiffiffi
2
p
Þ
and

2
D
and
G
ð
1
Þ
are, respectively, the form-factor slope and normal-
ization at
w
¼
1
.
The above formulas neglect the lepton mass
m
. Muon
mass effects need to be included to achieve precision at the
few percent level on the form-factor parameters. Allowing
for nonzero lepton mass introduces additional terms in the
phase space and form-factor expressions [
24
] that can be
included by multiplying the decay rate formula by the
following factor:
W
D
¼

1

1
1
þ
r
2

2
rw
m
2
m
2
B

2

1
þ
K
D
ð
w
Þ
m
2
m
2
B

(5)
where
K
D
ð
w
Þ

1
þ
3

1

r
1
þ
r

2

w
þ
1
w

1

1
2
ð
1
þ
r
2

2
rw
Þ
:
(6)
Candidates/100MeV
10 000
20 000
30 000
(a)
* (GeV/c)
l
p
1.5
2
0.9
0.95
1
1.05
1.1
Candidates/100MeV
10 000
20 000
(d)
* (GeV/c)
l
p
1.5
2
0.9
1
1.1
Candidates/100MeV
10 000
20 000
(b)
* (GeV/c)
D
p
1
1.5
2
0.9
0.95
1
1.05
1.1
Candidates/100MeV
5000
10 000
(e)
* (GeV/c)
D
p
1
1.5
2
0.9
1
1.1
Candidates/1.0
50
100
3
10
×
(c)
B-Dl
Θ
cos
-2
-1
0
1
0.9
0.95
1
1.05
1.1
Candidates/1.0
20 000
40 000
60 000
(f)
B-Dl
Θ
cos
-2
-1
0
1
0.9
1
1.1
FIG. 4 (color online). Projections onto individual kinematic variables of the data after off-peak subtraction and the results of the fit:
(a, d) lepton and (b, e)
D
momentum in the CM frame, and (c, f)
cos
B

D‘
. The points show data for accepted
D
0

(a, b, c) and
D
þ

(d, e, f) candidates, and the histograms show the individual fit components (from top to bottom):

B
!
D


,

B
!
D




,

B
!
D
ðÞ
ð
n
Þ



, and other
B

B
background. The ratio of data to the sum of the fitted yields is shown below each plot.
B. AUBERT
et al.
PHYSICAL REVIEW D
79,
012002 (2009)
012002-10
B.

B
!
D



decays
We need three additional kinematic variables to describe
this decay. A common choice is
,
V
, and
, shown in
Fig.
5
, and defined as
(i)
: the angle between the lepton and the direction
opposite the
B
meson in the
W
rest frame.
(ii)
V
: the angle between the
D
meson and the direc-
tion opposite the
B
meson in the
D

rest frame.
(iii)
: the azimuthal angle between the planes formed
by the
W
-
and
D


D
systems in the
B
rest
frame.
The differential decay rate is given by [
17
]
d

ð

B
!
D



Þ
dwd
cos
V
d
cos
d
¼
3
G
2
F
4
ð
4

Þ
4
j
V
cb
j
2
m
B
m
2
D

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
w
2

1
p
ð
1
þ
r

2

2
r

w
Þ½ð
1

cos
Þ
2
sin
2
V
j
H
þ
ð
w
Þj
2
þð
1
þ
cos
Þ
2
sin
2
V
j
H

ð
w
Þj
2
þ
4sin
2
cos
2
V
j
H
0
ð
w
Þj
2

4 sin
ð
1

cos
Þ
sin
V
cos
V
cos
H
þ
ð
w
Þ
H
0
ð
w
Þ
þ
4 sin
ð
1
þ
cos
Þ
sin
V
cos
V
cos
H

ð
w
Þ
H
0
ð
w
Þ
2sin
2
sin
2
V
cos 2
H
þ
ð
w
Þ
H

ð
w
Þ
;
(7)
where
H
i
ð
w
Þ
are form factors,
r

¼
m
D

=m
B
, and
m
D

is
the
D

meson mass. The
H
i
ð
w
Þ
are usually written in terms
of one form factor
h
A
1
ð
w
Þ
and two form-factor ratios,
R
1
ð
w
Þ
and
R
2
ð
w
Þ
, as follows:
H
i
¼
m
B
R

ð
1

r

2
Þð
w
þ
1
Þ
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
þ
r

2

2
r

w
p
h
A
1
ð
w
Þ
~
H
i
ð
w
Þ
;
(8)
where
R

¼ð
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m
B
m
D

p
Þ
=
ð
m
B
þ
m
D

Þ
and
~
H

ð
w
Þ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
þ
r

2

2
r

w
p
1

r


1

ffiffiffiffiffiffiffiffiffiffiffiffiffi
w

1
w
þ
1
s
R
1
ð
w
Þ

;
~
H
0
ð
w
Þ¼
1
þ
w

1
1

r

ð
1

R
2
ð
w
ÞÞ
:
(9)
The form-factor ratios have a modest dependence on
w
,
estimated [
16
]as
R
1
ð
w
Þ¼
R
1

0
:
12
ð
w

1
Þþ
0
:
05
ð
w

1
Þ
2
;
R
2
ð
w
Þ¼
R
2
þ
0
:
11
ð
w

1
Þ
0
:
06
ð
w

1
Þ
2
:
(10)
The form used for
h
A
1
ð
w
Þ
is [
16
]
h
A
1
ð
w
Þ¼
F
ð
1
Þ½
1

8

2
D

z
þð
53

2
D


15
Þ
z
2
231

2
D


91
Þ
z
3

;
(11)
where

2
D

and
F
ð
1
Þ
are, respectively, the form-factor
slope and normalization at
w
¼
1
.
Nonzero lepton mass is accounted for by multiplying the
decay rate formula by the factor
W
D

¼

1

1
1
þ
r

2

2
r

w
m
2
m
2
B

2

1
þ
K
D

ð
w
Þ
m
2
m
2
B

;
(12)
where
K
D

ð
w
Þ

1
þ
3
2
~
H
2
t
~
H
2
þ
þ
~
H
2

þ
~
H
2
0

1
2
ð
1
þ
r

2

2
r

w
Þ
:
(13)
Here,
~
H
t
is expressed, using another form-factor ratio
R
3
ð
w
Þ
,by
~
H
t
ð
w
Þ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
w
2

1
p
1

r


1
þ
r


w
w
þ
1
R
3

1
þ
r

2

2
r

w
r

ð
w
þ
1
Þ
R
2

:
(14)
We take
R
3
ð
w
Þ¼
1
; this approximation has a negligible
impact on our fit results.
C.

B
!
D
ðÞ
‘


decays
The four
P
-wave
D

states have been measured in
semileptonic decays [
25
28
]. The decays

B
!
D



are
modeled following a HQET-inspired form-factor parame-
trization given in Ref. [
23
]. Detailed formulas are given in
the Appendix. We use the approximation
B
1
of this model
for our main fit and use the approximation
B
2
to evaluate
the uncertainty due to the approximation. The slope of the
FIG. 5. Definition of the three angles
,
V
, and
for the
decay

B
!
D



.
MEASUREMENTS OF THE SEMILEPTONIC DECAYS
...
PHYSICAL REVIEW D
79,
012002 (2009)
012002-11