Measurement of
B
!
X
Decays and Determination of
j
V
td
=V
ts
j
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
A. J. Martinez,
17
T. Schalk,
17
B. A. Schumm,
17
A. Seiden,
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
A. Volk,
23
D. Bernard,
24
G. R. Bonneaud,
24
E. Latour,
24
M. Verderi,
24
P. J. Clark,
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
A. Adametz,
30
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
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
N. Arnaud,
36
J. Be
́
quilleux,
36
A. D’Orazio,
36
M. Davier,
36
J. Firmino da Costa,
36
G. Grosdidier,
36
A. Ho
̈
cker,
36
V. Lepeltier,
36
F. Le Diberder,
36
A. M. Lutz,
36
S. Pruvot,
36
P. Roudeau,
36
M. H. Schune,
36
J. Serrano,
36
V. Sordini,
36,
k
A. Stocchi,
36
G. Wormser,
36
D. J. Lange,
37
D. M. Wright,
37
I. Bingham,
38
J. P. Burke,
38
C. A. Chavez,
38
J. R. Fry,
38
E. Gabathuler,
38
R. Gamet,
38
D. E. Hutchcroft,
38
D. J. Payne,
38
C. Touramanis,
38
A. J. Bevan,
39
C. K. Clarke,
39
K. A. George,
39
F. Di Lodovico,
39
R. Sacco,
39
M. Sigamani,
39
G. Cowan,
40
H. U. Flaecher,
40
D. A. Hopkins,
40
S. Paramesvaran,
40
F. Salvatore,
40
A. C. Wren,
40
D. N. Brown,
41
C. L. Davis,
41
A. G. Denig,
42
M. Fritsch,
42
W. Gradl,
42
G. Schott,
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
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
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
E. Di Marco,
63a,63b
R. Faccini,
63a,63b
PRL
102,
161803 (2009)
PHYSICAL REVIEW LETTERS
week ending
24 APRIL 2009
0031-9007
=
09
=
102(16)
=
161803(7)
161803-1
Ó
2009 The American Physical Society
F. Ferrarotto,
63a,63b
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,63b
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,
68
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
PRL
102,
161803 (2009)
PHYSICAL REVIEW LETTERS
week ending
24 APRIL 2009
161803-2
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
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
37
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
38
University of Liverpool, Liverpool L69 7ZE, United Kingdom
39
Queen Mary, University of London, 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
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
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, 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
CEA, Irfu, SPP, Centre de 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
79
University of Wisconsin, Madison, Wisconsin 53706, USA
PRL
102,
161803 (2009)
PHYSICAL REVIEW LETTERS
week ending
24 APRIL 2009
161803-3
(Received 1 August 2008; published 23 April 2009)
Using a sample of
383
10
6
B
B
events collected by the
BABAR
experiment, we measure sums of seven
exclusive final states
B
!
X
d
ð
s
Þ
, where
X
d
ð
X
s
Þ
is a nonstrange (strange) charmless hadronic system in the
mass range
0
:
6
–
1
:
8 GeV
=c
2
. After correcting for unmeasured decay modes in this mass range, we obtain a
branching fraction for
b
!
d
of
ð
7
:
2
2
:
7
ð
stat
Þ
2
:
3
ð
syst
Þ
Þ
10
6
. Taking the ratio of
X
d
to
X
s
we
find
ð
b
!
d
Þ
=
ð
b
!
s
Þ¼
0
:
033
0
:
013
ð
stat
Þ
0
:
009
ð
syst
Þ
, from which we determine
j
V
td
=V
ts
j¼
0
:
177
0
:
043
.
DOI:
10.1103/PhysRevLett.102.161803
PACS numbers: 13.20.He, 12.15.Hh
The decays
b
!
d
and
b
!
s
are flavor-changing
neutral current processes. They are forbidden at tree level
in the standard model (SM), but can occur via one-loop
electroweak penguin diagrams involving the top quark. In
the SM, the inclusive rate for
b
!
d
is suppressed com-
pared to
b
!
s
by
j
V
td
=V
ts
j
2
, where
V
td
and
V
ts
are
Cabibbo-Kobayashi-Maskawa matrix elements. Measure-
ments of
j
V
td
=V
ts
j
from
B
!ð
;!
Þ
and
B
!
K
[
1
]
have theoretical uncertainties of 7% from weak annihila-
tion and hadronic form factors [
2
]. A measurement of the
inclusive decay
b
!
d
relative to
b
!
s
could deter-
mine
j
V
td
=V
ts
j
with reduced theoretical uncertainties com-
pared to the exclusive modes [
3
]. In theories beyond the
SM [
4
], new particles may appear differently in the pen-
guin loop diagrams for
b
!
d
and
b
!
s
compared to
the box diagrams responsible for
B
d
and
B
s
mixing [
5
],
leading to differences in
j
V
td
=V
ts
j
.
This Letter presents the first measurement of
j
V
td
=V
ts
j
from
b
!
d
and
b
!
s
inclusive decays including the
region above the
=!
resonances, with systematic uncer-
tainties largely independent of those from the measure-
ment provided by the exclusive reconstruction of the
B
!ð
;!
Þ
and
B
!
K
decay channels.
We present measurements of the rare decays
B
!
X
d
using seven exclusive final states
B
0
!
þ
,
B
þ
!
þ
0
,
B
þ
!
þ
þ
,
B
0
!
þ
0
,
B
0
!
þ
þ
,
B
þ
!
þ
þ
0
and
B
þ
!
þ
[
6
], in the hadronic mass range
0
:
6
–
1
:
0 GeV
=c
2
(which
contains the
and
!
resonances), and in the previously
unmeasured region
1
:
0
–
1
:
8 GeV
=c
2
. We combine the re-
sults and correct for decay modes that are not reconstructed
to obtain the inclusive branching fraction for
b
!
d
in
the mass range
0
:
6
–
1
:
8 GeV
=c
2
. A parallel analysis of
B
!
X
s
using these modes with a
K
þ
replacing the
first
þ
allows us to measure the ratio of inclusive rates
ð
b
!
d
Þ
=
ð
b
!
s
Þ
in the same mass range.
This analysis uses
383
10
6
B
B
pairs collected at the
ð
4
S
Þ
resonance with the
BABAR
detector [
7
] at the PEP-II
B
factory. The high-energy
is defined as an isolated
energy cluster in the CsI(Tl) calorimeter, with a shape
consistent with a single
, and energy
1
:
15
<E
<
3
:
5 GeV
in the center-of-mass (c.m.) frame. We remove
s forming a
0
(
) candidate with another
of energy
greater than 30(250) MeV, if the two-photon invariant mass
is in the range
105
<m
<
155 MeV
=c
2
(
500
<m
<
590 MeV
=c
2
).
Charged particle tracks are reconstructed by means of a
5-layer silicon vertex detector and a 40-layer drift chamber
coaxial with a 1.5 T magnetic field; a minimum laboratory
momentum of
300 MeV
=c
is required. To distinguish
þ
s
from
K
þ
s we combine information from the detector of
internally reflected Cherenkov light with specific ionisa-
tion energy loss measured in the tracking system. At a
typical
þ
energy of 1 GeV,
þ
selection efficiency is
85% with
K
þ
misidentification rate 3%.
K
þ
s are selected
by inverting the pion selection criteria. We reconstruct a
0
ð
Þ
candidate with laboratory momentum greater than
300 MeV
=c
from a pair of
s, each with energy
>
20 MeV
and satisfying
107
<m
<
145 MeV
=c
2
(
470
<m
<
620 MeV
=c
2
). The
0
ð
Þ
candidate, the high-energy
and the selected charged tracks are combined to form a
B
meson candidate consistent with one of the decay modes.
For a
B
!
X
s
decay one
K
þ
is required, with all other
tracks required to be
þ
s. For
B
!
X
d
decays, all tracks
are required to be identified as
þ
s. The charged particles
are combined to form a common vertex for which the
vertex fit probability is required to be greater than 2%.
The backgrounds encountered in this analysis arise
mostly from continuum
e
þ
e
!
q
q
events,
q
¼
ð
u;d;s;c
Þ
, in which an energetic
comes from either
initial state radiation or the decay of a
0
ð
Þ
. We require
R
2
<
0
:
9
and
j
cos
T
j
<
0
:
8
, where
R
2
is the ratio of the
2nd to 0th Fox-Wolfram moments [
8
], and
T
is the angle
between the
and the thrust axis of the rest of the event
(ROE) in the c.m. frame. The ROE includes all the charged
tracks and neutral energy in the calorimeter, excluding the
B
candidate.
The quantity
cos
T
and 12 other variables that distin-
guish signal from continuum events are combined in a
neural network (NN). These include the ratio
R
0
2
, which
is
R
2
calculated in the frame recoiling against the
mo-
mentum, the
B
meson production angle
B
in the c.m.
frame with respect to the beam axis, and five Legendre
polynomial moments of the ROE with respect to both the
thrust axis of the ROE and the direction of the high-energy
. Differences in lepton and kaon production between
background and
B
decays are exploited by including five
flavor-tagging variables applied to the ROE [
9
]. We opti-
mize the NN configuration for maximal discrimination
between signal and background; this gives 50% signal
efficiency and 0.5% misidentification of continuum, based
on a Monte Carlo (MC) simulation.
PRL
102,
161803 (2009)
PHYSICAL REVIEW LETTERS
week ending
24 APRIL 2009
161803-4
We use the kinematic variables
E
¼
E
B
E
beam
and
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E
2
beam
j
~
p
2
B
j
q
, where
E
B
and
~
p
B
are the c.m.
energy and momentum of the
B
candidate, and
E
beam
is
the c.m. beam energy. Signal events should have a
E
distribution centered at zero with a resolution
30 MeV
,
and an
m
ES
distribution centered at the
B
meson mass with
a resolution
3 MeV
=c
2
. We retain candidates with
0
:
3 GeV
<
E<
0
:
2 GeV
and
m
ES
>
5
:
22 GeV
=c
2
to
allow the combinatorial background yield to be extracted
from a fit to the data. After all selection criteria are applied
there are, on average, 1.75 candidates per event. In events
with multiple candidates we select the one with the best
0
ð
Þ
mass, or, where there is no
0
ð
Þ
, we select the
candidate with the best vertex fit probability.
The signal yield in each
B
decay category is determined
from a two-dimensional unbinned maximum likelihood fit
to the (
E
,
m
ES
) distributions of the sums of all seven final
states. We consider the following contributions: signal,
combinatorial backgrounds from continuum processes,
B
!
X
0
=
decays, backgrounds from other
B
decays,
and cross-feed from misreconstructed signal
B
!
X
de-
cays. The fit to the
B
!
X
d
sample contains a component
from misidentified
B
!
X
s
decays, but we neglect the
small
B
!
X
d
background in the
B
!
X
s
sample. The
B
background yields are determined from MC simulation,
whereas the continuum background yield is free to vary in
the fit.
Each background contribution is modeled by a proba-
bility density function (PDF) determined from MC events.
Each signal PDF is the product of one-dimensional
m
ES
and
E
distributions determined from fits to the
B
!
K
data. For the signal cross-feed component, and the
B
!
X
s
background in the
B
!
X
d
fit, MC studies indicate
that two-dimensional histogram PDFs are required to ac-
count for correlations that are not present in signal MC
events. The contributions from
B
!
X
0
=
are modeled
by a Gaussian peak in each of
E
and
m
ES
, where
E
is
displaced by
80 MeV
due to the missing photon. The
B
!
X
s
background in the
B
!
X
d
sample also peaks,
with
E
displaced by
50 MeV
due to
K
þ
misidentifica-
tion. Continuum and other nonpeaking backgrounds are
described by an ARGUS shape [
10
]in
m
ES
and a second-
order polynomial in
E
.
We perform separate fits for
B
!
X
d
and
B
!
X
s
,in
the two hadronic mass ranges. The signal and continuum
yields, the continuum ARGUS shape parameter and the
continuum polynomial shape parameters are allowed to
vary. We scale the cross-feed contribution proportionally
to the fitted signal yield, refit, and iterate until the fit
converges. The fit projections for
B
!
X
s
and
B
!
X
d
are shown in Fig.
1
.
The fit results are summarized in Table
I
. The recon-
struction efficiency depends on the distribution of the
signal yield among the final states. For
X
s
we obtain this
distribution from the data, but for
X
d
this is not possible
and so we use the phase space fragmentation model im-
plemented in
JETSET
[
11
] for this purpose.
The branching fractions in Table
II
are obtained after
correcting for missing final states. In the low mass region
for both channels we assume that there are no nonresonant
decays, an assumption consistent with our data in the
B
!
X
s
channel. Our low mass
B
!
X
s
measurement agrees
with previous rate measurements for
B
!
K
[
12
], after
accounting for the 50% of decays to neutral kaons. For the
X
d
modes at low mass, the fraction of nonreconstructed
and
!
decays is small, and we find a branching fraction of
FIG. 1 (color online). Projections of the fits to data in the
hadronic mass range
0
:
6
–
1
:
0 GeV
=c
2
(a)–(d) and
1
:
0
–
1
:
8 GeV
=c
2
(e)–(h). Projections of
E
with
5
:
275
<m
ES
<
5
:
286 GeV
=c
2
for (a),(e)
B
!
X
s
and (c),(f)
B
!
X
d
, and of
m
ES
with
0
:
1
<
E<
0
:
05 GeV
for (b),(g)
B
!
X
s
and (d),
(h)
B
!
X
d
. Data (points) are compared with the sum of all the
fit contributions (solid curve) including the signal (dashed curve)
and the
B
!
X
s
contribution in the
B
!
X
d
fit (dotted curve).
TABLE I. Signal yield (
N
S
), average efficiency (
) and partial
branching fraction (
B
) for the measured decay modes. The first
error is statistical, the second systematic.
M
ð
X
Þ½
GeV
=c
2
N
S
B
ð
10
6
Þ
0
:
6
<M
ð
X
s
Þ
<
1
:
0 1543
46
8.5%
23
:
7
0
:
7
1
:
7
0
:
6
<M
ð
X
d
Þ
<
1
:
066
26
7.0%
1
:
2
0
:
5
0
:
1
1
:
0
<M
ð
X
s
Þ
<
1
:
8 2279
75
6.1%
48
:
7
1
:
6
4
:
1
1
:
0
<M
ð
X
d
Þ
<
1
:
8
107
47
5.2%
2
:
7
1
:
2
0
:
4
PRL
102,
161803 (2009)
PHYSICAL REVIEW LETTERS
week ending
24 APRIL 2009
161803-5
ð
1
:
2
0
:
5
Þ
10
6
, in agreement with previous measure-
ments of
B
ð
B
!ð
;!
Þ
Þ
[
1
]. In the high mass region for
both channels, we correct for missing final states with
5
stable particles, or with multiple
0
s, by using the frag-
mentation model described above. Alternative fragmenta-
tion models are used to estimate the associated uncertainty,
as described below.
The sources of systematic uncertainty in the measure-
ment of the branching fractions are listed in Table
III
.
These include uncertainty in track reconstruction effi-
ciency,
and
0
=
reconstruction, the
0
=
veto, the
NN selection, and the number of
B
B
pairs. The 2% uncer-
tainty in
K
þ
=
þ
particle identification and the 20% un-
certainty in
K
þ
misidentification, which affects the fixed
B
!
X
s
contribution to the
B
!
X
d
fits, do not cancel
in the ratio. The systematic errors associated with the
variation of the fit PDFs also do not cancel because of
the very different signal to background ratios in the two
samples. We vary the signal PDF parameters within the
range allowed by the fit to the
B
!
K
data. The normal-
ization of the signal cross-feed is varied by
30%
, and the
contribution of
B
!
X
0
=
by
100%
, in accordance
with MC studies. The remaining peaking
B
backgrounds,
including the
B
!
X
s
contribution to the
B
!
X
d
fits,
are varied by
20%
. We use simulated signal and back-
ground event samples to assign a systematic uncertainty
due to possible bias in the fit method.
There is an additional systematic error on the efficiency
due to the uncertainties in the measured fragmentation of
the
X
s
hadronic system into the seven
B
!
X
s
final states.
The equivalent error for
B
!
X
d
is obtained by compar-
ing our fragmentation model for
B
!
X
d
to the fragmen-
tation observed for
B
!
X
s
data. We assume that these
errors are independent and so do not cancel in the ratio of
branching fractions.
Table
III
also shows the systematic errors associated
with corrections for the missing final states. There is no
information from the data on the missing fraction of high
multiplicity final states with
5
stable hadrons, or on the
missing fraction of other final states with
1
0
or
mesons. We vary these fractions by
50%
relative to their
default phase space fragmentation values. Our choice of a
50%
variation is motivated by studies of alternative MC
signal models in which we replace half of the nonresonant
width in the
1
:
0
–
1
:
8 GeV
=c
2
mass range with a mix of
X
d
or
X
s
resonances. The missing fraction errors partially
cancel in the ratio when the
50%
variations are made
in the same direction for
b
!
d
and
b
!
s
.
We take the spectral shape of the high-energy
from
Ref. [
13
] using the values
ð
m
b
;
2
Þ¼ð
4
:
65 GeV
=c
2
;
0
:
52 GeV
2
Þ
extracted from fits to
b
!
s
and
b
!
c‘
data [
14
]. We vary these shape parameters in a correlated
way between
ð
m
b
;
2
Þ¼ð
4
:
60 GeV
=c
2
;
0
:
60 GeV
2
Þ
and
ð
m
b
;
2
Þ¼ð
4
:
70 GeV
=c
2
;
0
:
45 GeV
2
Þ
. Systematic
errors on the branching fractions result from these varia-
tions, but they are small and cancel in the ratio. The
fraction of the spectrum in the mass range
0
:
6
–
1
:
8 GeV
=c
2
is estimated to be
ð
51
4
Þ
%
for
b
!
d
and
ð
50
4
Þ
%
for
b
!
s
. We do not extrapolate the
ratio of branching fractions to
M
X
>
1
:
8 GeV
=c
2
, and so
these errors, which mostly cancel in the ratio, are not
included in Table
III
. If we make this correction, we ob-
tain
B
ð
b
!
d
Þ¼ð
1
:
4
0
:
5
0
:
4
0
:
1
Þ
10
5
and
B
ð
b
!
s
Þ¼ð
4
:
3
0
:
3
0
:
7
0
:
2
Þ
10
4
, where the
first error is statistical, the second systematic and the third
accounts for the uncertainty in extrapolating to the mass
TABLE III. Systematic errors on the measured partial and total
branching fractions
B
. The final column shows systematic errors
that do not cancel in the ratio of rates.
Systematic
M
ð
X
s
Þ
M
ð
X
d
Þ
X
d
=X
s
Error Source
0.6–1.0 1.0–1.8 0.6–1.0 1.0–1.8 Ratio
Tracking
1.7% 1.7% 1.7% 1.7%
High-energy photon 2.5% 2.5% 2.5% 2.5%
0
=
reconstruction 1.7% 1.7% 1.7% 1.7%
0
=
veto
1.0% 1.0% 1.0% 1.0%
K=
identification 2.0% 2.0% 2.0% 2.0% 2.0%
Neural network
5.0% 5.0% 5.0% 5.0%
B
B
pair counting
1.1% 1.1% 1.1% 1.1%
Fit PDFs
2.4% 3.6% 7.0% 8.3% 8.7%
Backgrounds
0.3% 0.4% 2.4% 6.1% 5.4%
Fit bias
0.4% 1.7% 0.4% 3.3% 3.0%
Fragmentation
3.6%
7.7% 8.5%
Partial
B
7.0% 11.4% 10.0% 14.8% 13.8%
Missing
5
body
5.6%
25.8% 21.0%
Other missing states
17.0%
23.8% 7.1%
Spectrum Model
1.8%
1.6%
Total
B
7.0% 21.2% 10.0% 38.1% 26.1%
TABLE II. Branching fractions
B
ð
10
6
Þ
and their ratio in the two mass regions of
M
ð
X
Þ
½
GeV
=c
2
, after correcting for missing final states. The first error is statistical and the second
systematic.
M
ð
X
Þ
B
ð
b
!
d
Þ
B
ð
b
!
s
Þ
B
ð
b
!
d
Þ
=
B
ð
b
!
s
Þ
0.6–1.0
1
:
2
0
:
5
0
:
147
1
30
:
026
0
:
011
0
:
002
1.0–1.8
6
:
0
2
:
6
2
:
3
168
14
33
0
:
036
0
:
015
0
:
009
0.6–1.8
7
:
2
2
:
7
2
:
3
215
14
33
0
:
033
0
:
013
0
:
009
PRL
102,
161803 (2009)
PHYSICAL REVIEW LETTERS
week ending
24 APRIL 2009
161803-6
range. The result for
B
!
X
s
is consistent with the mea-
sured inclusive
b
!
s
branching fraction of
ð
3
:
55
0
:
24
Þ
10
4
[
12
].
We convert the ratio of partial widths from the full
mass range
0
:
6
–
1
:
8 GeV
=c
2
,
ð
b
!
d
Þ
=
ð
b
!
s
Þ¼
0
:
033
0
:
013
0
:
009
, into a value for
j
V
td
=V
ts
j
using
Table
I
and Eq. (26) of Ref. [
3
]. We obtain
j
V
td
=V
ts
j¼
0
:
177
0
:
043
0
:
001
, where the first error is experimen-
tal, including systematic errors, and the second error is
from theory. The theory error includes uncertainties in the
CKM parameters
and
, and on
1
=m
2
c
and
1
=m
2
b
correc-
tions, but includes no uncertainty for the restriction to the
region below
1
:
8 GeV
=c
2
.
As a check, we use the low mass region to determine
j
V
td
=V
ts
j
using predictions for exclusive
B
!ð
;!
Þ
and
B
!
K
from [
2
]. We find
j
V
td
=V
ts
j¼
0
:
214
0
:
046
0
:
028
where the errors are as before. This is in good
agreement with previously published results [
1
].
In summary, we have made the first measurement of
B
!
X
d
decays in the hadronic mass range up to
1
:
8 GeV
=c
2
, and have extracted
j
V
td
=V
ts
j
from an inclu-
sive model with small theoretical uncertainties. These
results are consistent with the measurements of
j
V
td
=V
ts
j
from the exclusive decays
B
!ð
;!
Þ
[
1
], and with
B
s
=B
d
oscillations [
5
]. Future studies applying this method
to larger data sets could provide a substantial improvement
in the determination of this quantity via radiative
B
meson
decays. This offers the possibility that new physics effects
could be revealed by the comparison of this determination
with that from
B
d
=B
s
oscillations. A measurement of the
CP
-violating parameters for inclusive
b
!
d
may also be
possible.
We are grateful for the excellent luminosity and machine
conditions provided by our PEP-II colleagues, and for the
substantial dedicated effort from the computing organiza-
tions that support
BABAR
. The collaborating institutions
wish to thank SLAC for its support and kind hospitality.
This work is supported by DOE and NSF (USA), NSERC
(Canada), CEA and CNRS-IN2P3 (France), BMBF and
DFG (Germany), INFN (Italy), FOM (The Netherlands),
NFR (Norway), MES (Russia), MEC (Spain), and STFC
(United Kingdom). Individuals have received support from
the Marie Curie EIF (European Union) and the A. P. Sloan
Foundation.
*
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.
[1] B. Aubert
et al.
(
BABAR
Collaboration), Phys. Rev. Lett.
98
, 151802 (2007); D. Mohapatra
et al.
(Belle
Collaboration), Phys. Rev. Lett.
96
, 221601 (2006).
[2] P. Ball, G. Jones, and R. Zwicky, Phys. Rev. D
75
, 054004
(2007).
[3] A. Ali, H. Asatrian, and C. Greub, Phys. Lett. B
429
,87
(1998).
[4] S. Bertolini, F. Borzumati, and A. Masiero, Nucl. Phys. B
294
, 321 (1987); H. Baer and M. Brhlik, Phys. Rev. D
55
,
3201 (1997); J. Hewett and J. Wells, Phys. Rev. D
55
, 5549
(1997); M. Carena
et al.
, Phys. Lett. B
499
, 141 (2001).
[5] W.-M. Yao
et al.
(Particle Data Group), J. Phys. G
33
,1
(2006).
[6] Charge conjugate states are implied throughout this paper.
[7] B. Aubert
et al.
(
BABAR
Collaboration), Nucl. Instrum.
Methods Phys. Res., Sect. A
479
, 1 (2002).
[8] G. C. Fox and S. Wolfram, Nucl. Phys.
B149
, 413 (1979).
[9] B. Aubert
et al.
(
BABAR
Collaboration), Phys. Rev. Lett.
89
, 201802 (2002).
[10] The ARGUS function is defined as:
P
ð
x
Þ¼
x
½
1
ð
x
m
Þ
2
P
exp
ð
c
½
1
ð
x
m
Þ
2
Þ
, H. Albrecht
et al.
(ARGUS
Collaboration), Phys. Lett. B
185
, 218 (1987).
[11] T. Sjostrand, arXiv:hep-ph/9508391; T. Sjostrand,
Comput. Phys. Commun.
82
, 74 (1994).
[12] E. Barberio
et al.
(Heavy Flavor Averaging Group),
arXiv:0704.3575.
[13] A. L. Kagan and M. Neubert, Phys. Rev. D
58
, 094012
(1998).
[14] O. Buchmu
̈
ller and H. Fla
̈
cher, Phys. Rev. D
73
, 073008
(2006).
PRL
102,
161803 (2009)
PHYSICAL REVIEW LETTERS
week ending
24 APRIL 2009
161803-7