of 16
Exclusive measurements of
b
!
s
transition rate and photon energy spectrum
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
A. Palano,
3a,3b
G. Eigen,
3
B. Stugu,
3
D. N. Brown,
4
L. T. Kerth,
4
Yu. G. Kolomensky,
4
G. Lynch,
4
H. Koch,
5
T. Schroeder,
5
D. J. Asgeirsson,
6
C. Hearty,
6
T. S. Mattison,
6
J. A. McKenna,
6
A. Khan,
7
V. E. Blinov,
8
A. R. Buzykaev,
8
V. P. Druzhinin,
8
V. B. Golubev,
8
E. A. Kravchenko,
8
A. P. Onuchin,
8
S. I. Serednyakov,
8
Yu. I. Skovpen,
8
E. P. Solodov,
8
K. Yu. Todyshev,
8
A. N. Yushkov,
8
M. Bondioli,
9
D. Kirkby,
9
A. J. Lankford,
9
M. Mandelkern,
9
H. Atmacan,
10
J. W. Gary,
10
F. Liu,
10
O. Long,
10
G. M. Vitug,
10
C. Campagnari,
11
T. M. Hong,
11
D. Kovalskyi,
11
J. D. Richman,
11
C. A. West,
11
A. M. Eisner,
12
J. Kroseberg,
12
W. S. Lockman,
12
A. J. Martinez,
12
B. A. Schumm,
12
A. Seiden,
12
D. S. Chao,
13
C. H. Cheng,
13
D. A. Doll,
13
B. Echenard,
13
K. T. Flood,
13
D. G. Hitlin,
13
P. Ongmongkolkul,
13
F. C. Porter,
13
A. Y. Rakitin,
13
R. Andreassen,
14
Z. Huard,
14
B. T. Meadows,
14
M. D. Sokoloff,
14
L. Sun,
14
P. C. Bloom,
15
W. T. Ford,
15
A. Gaz,
15
U. Nauenberg,
15
J. G. Smith,
15
S. R. Wagner,
15
R. Ayad,
16,
*
W. H. Toki,
16
B. Spaan,
17
K. R. Schubert,
18
R. Schwierz,
18
D. Bernard,
19
M. Verderi,
19
P. J. Clark,
20
S. Playfer,
20
D. Bettoni,
22a
C. Bozzi,
22a
R. Calabrese,
22a,22b
G. Cibinetto,
22a,22b
E. Fioravanti,
22a,22b
I. Garzia,
22a,22b
E. Luppi,
22a,22b
M. Munerato,
22a,22b
M. Negrini,
22a,22b
L. Piemontese,
22a
V. Santoro,
22a
R. Baldini-Ferroli,
21
A. Calcaterra,
21
R. de Sangro,
21
G. Finocchiaro,
21
P. Patteri,
21
I. M. Peruzzi,
21,
M. Piccolo,
21
M. Rama,
21
A. Zallo,
21
R. Contri,
24a,24b
E. Guido,
24a,24b
M. Lo Vetere,
24a,24b
M. R. Monge,
24a,24b
S. Passaggio,
24a
C. Patrignani,
24a,24b
E. Robutti,
24a
B. Bhuyan,
22
V. Prasad,
22
C. L. Lee,
23
M. Morii,
23
A. J. Edwards,
23
A. Adametz,
24
U. Uwer,
25
H. M. Lacker,
26
T. Lueck,
26
P. D. Dauncey,
27
P. K. Behera,
28
U. Mallik,
28
C. Chen,
29
J. Cochran,
29
W. T. Meyer,
29
S. Prell,
29
A. E. Rubin,
29
A. V. Gritsan,
29
Z. J. Guo,
30
N. Arnaud,
31
M. Davier,
31
D. Derkach,
31
G. Grosdidier,
31
F. Le Diberder,
31
A. M. Lutz,
31
B. Malaescu,
31
P. Roudeau,
31
M. H. Schune,
31
A. Stocchi,
31
G. Wormser,
31
D. J. Lange,
32
D. M. Wright,
32
C. A. Chavez,
33
J. P. Coleman,
33
J. R. Fry,
33
E. Gabathuler,
33
D. E. Hutchcroft,
33
D. J. Payne,
33
C. Touramanis,
33
A. J. Bevan,
34
F. Di Lodovico,
34
R. Sacco,
34
M. Sigamani,
34
G. Cowan,
35
D. N. Brown,
36
C. L. Davis,
36
A. G. Denig,
37
M. Fritsch,
37
W. Gradl,
37
K. Griessinger,
37
A. Hafner,
37
E. Prencipe,
37
D. Bailey,
38
R. J. Barlow,
38,
G. Jackson,
38
G. D. Lafferty,
38
E. Behn,
39
R. Cenci,
39
B. Hamilton,
39
A. Jawahery,
39
D. A. Roberts,
39
C. Dallapiccola,
40
R. Cowan,
41
D. Dujmic,
41
G. Sciolla,
41
R. Cheaib,
42
D. Lindemann,
42
P. M. Patel,
42,
§
S. H. Robertson,
42
P. Biassoni,
46a,46b
N. Neri,
46a
F. Palombo,
46a,46b
S. Stracka,
46a,46b
L. Cremaldi,
43
R. Godang,
43,
k
R. Kroeger,
43
P. Sonnek,
43
D. J. Summers,
43
X. Nguyen,
44
M. Simard,
44
P. Taras,
44
G. De Nardo,
49a,49b
D. Monorchio,
49a,49b
G. Onorato,
49a,49b
C. Sciacca,
49a,49b
M. Martinelli,
45
G. Raven,
45
C. P. Jessop,
46
J. M. LoSecco,
46
W. F. Wang,
46
K. Honscheid,
47
R. Kass,
47
J. Brau,
48
R. Frey,
48
N. B. Sinev,
48
D. Strom,
48
E. Torrence,
48
E. Feltresi,
54a,54b
N. Gagliardi,
54a,54b
M. Margoni,
54a,54b
M. Morandin,
54a
M. Posocco,
54a
M. Rotondo,
54a
G. Simi,
54a
F. Simonetto,
54a,54b
R. Stroili,
54a,54b
S. Akar,
49
E. Ben-Haim,
49
M. Bomben,
49
G. R. Bonneaud,
49
H. Briand,
49
G. Calderini,
49
J. Chauveau,
49
O. Hamon,
49
Ph. Leruste,
49
G. Marchiori,
49
J. Ocariz,
49
S. Sitt,
49
M. Biasini,
56a,56b
E. Manoni,
56a,56b
S. Pacetti,
56a,56b
A. Rossi,
56a,56b
C. Angelini,
57a,57b
G. Batignani,
57a,57b
S. Bettarini,
57a,57b
M. Carpinelli,
57a,57b,
{
G. Casarosa,
57a,57b
A. Cervelli,
57a,57b
F. Forti,
57a,57b
M. A. Giorgi,
57a,57b
A. Lusiani,
57a,57c
B. Oberhof,
57a,57b
E. Paoloni,
57a,57b
A. Perez,
57a
G. Rizzo,
57a,57b
J. J. Walsh,
57a
D. Lopes Pegna,
50
J. Olsen,
50
A. J. S. Smith,
50
A. V. Telnov,
50
F. Anulli,
59a
R. Faccini,
59a,59b
F. Ferrarotto,
59a
F. Ferroni,
59a,59b
M. Gaspero,
59a,59b
L. Li Gioi,
59a
M. A. Mazzoni,
59a
G. Piredda,
59a
C. Bu
̈
nger,
51
O. Gru
̈
nberg,
51
T. Hartmann,
51
T. Leddig,
51
H. Schro
̈
der,
51,
§
C. Voss,
51
R. Waldi,
51
T. Adye,
52
E. O. Olaiya,
52
F. F. Wilson,
52
S. Emery,
53
G. Hamel de Monchenault,
53
G. Vasseur,
53
Ch. Ye
`
che,
53
D. Aston,
54
D. J. Bard,
54
R. Bartoldus,
54
C. Cartaro,
54
M. R. Convery,
54
J. Dorfan,
54
G. P. Dubois-Felsmann,
54
W. Dunwoodie,
54
M. Ebert,
54
R. C. Field,
54
M. Franco Sevilla,
54
B. G. Fulsom,
54
A. M. Gabareen,
54
M. T. Graham,
54
P. Grenier,
54
C. Hast,
54
W. R. Innes,
54
M. H. Kelsey,
54
P. Kim,
54
M. L. Kocian,
54
D. W. G. S. Leith,
54
P. Lewis,
54
B. Lindquist,
54
S. Luitz,
54
V. Luth,
54
H. L. Lynch,
54
D. B. MacFarlane,
54
D. R. Muller,
54
H. Neal,
54
S. Nelson,
54
M. Perl,
54
T. Pulliam,
54
B. N. Ratcliff,
54
A. Roodman,
54
A. A. Salnikov,
54
R. H. Schindler,
54
A. Snyder,
54
D. Su,
54
M. K. Sullivan,
54
J. Va’vra,
54
A. P. Wagner,
54
W. J. Wisniewski,
54
M. Wittgen,
54
D. H. Wright,
54
H. W. Wulsin,
54
C. C. Young,
54
V. Ziegler,
54
W. Park,
55
M. V. Purohit,
55
R. M. White,
55
J. R. Wilson,
55
A. Randle-Conde,
56
S. J. Sekula,
56
M. Bellis,
57
J. F. Benitez,
57
P. R. Burchat,
57
T. S. Miyashita,
57
M. S. Alam,
58
J. A. Ernst,
58
R. Gorodeisky,
59
N. Guttman,
59
D. R. Peimer,
59
A. Soffer,
59
P. Lund,
60
S. M. Spanier,
60
R. Eckmann,
61
J. L. Ritchie,
61
A. M. Ruland,
61
R. F. Schwitters,
61
B. C. Wray,
61
J. M. Izen,
62
X. C. Lou,
62
F. Bianchi,
72a,72b
D. Gamba,
72a,72b
L. Lanceri,
73a,73b
L. Vitale,
73a,73b
F. Martinez-Vidal,
63
A. Oyanguren,
63
H. Ahmed,
64
J. Albert,
64
Sw. Banerjee,
64
F. U. Bernlochner,
64
H. H. F. Choi,
64
G. J. King,
64
R. Kowalewski,
64
M. J. Lewczuk,
64
I. M. Nugent,
64
J. M. Roney,
64
R. J. Sobie,
64
N. Tasneem,
64
T. J. Gershon,
65
P. F. Harrison,
65
T. E. Latham,
65
E. M. T. Puccio,
65
H. R. Band,
66
S. Dasu,
66
Y. Pan,
66
R. Prepost,
66
and S. L. Wu
66
PHYSICAL REVIEW D
86,
052012 (2012)
1550-7998
=
2012
=
86(5)
=
052012(16)
052012-1
Ó
2012 American Physical Society
(
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite
́
de Savoie,
CNRS/IN2P3, 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
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
3
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
4
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
5
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
6
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
7
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
8
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
9
University of California at Irvine, Irvine, California 92697, USA
10
University of California at Riverside, Riverside, California 92521, USA
11
University of California at Santa Barbara, Santa Barbara, California 93106, USA
12
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
13
California Institute of Technology, Pasadena, California 91125, USA
14
University of Cincinnati, Cincinnati, Ohio 45221, USA
15
University of Colorado, Boulder, Colorado 80309, USA
16
Colorado State University, Fort Collins, Colorado 80523, USA
17
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
18
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
19
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
20
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
22a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
22b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
21
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
24a
INFN Sezione di Genova, I-16146 Genova, Italy
24b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
22
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
23
Harvard University, Cambridge, Massachusetts 02138, USA
24
Harvey Mudd College, Claremont, California 91711, USA
25
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
26
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstrasse 15, D-12489 Berlin, Germany
27
Imperial College London, London, SW7 2AZ, United Kingdom
28
University of Iowa, Iowa City, Iowa 52242, USA
29
Iowa State University, Ames, Iowa 50011-3160, USA
30
Johns Hopkins University, Baltimore, Maryland 21218, USA
31
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
32
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
33
University of Liverpool, Liverpool L69 7ZE, United Kingdom
34
Queen Mary, University of London, London, E1 4NS, United Kingdom
35
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
36
University of Louisville, Louisville, Kentucky 40292, USA
37
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
38
University of Manchester, Manchester M13 9PL, United Kingdom
39
University of Maryland, College Park, Maryland 20742, USA
40
University of Massachusetts, Amherst, Massachusetts 01003, USA
41
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
42
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
46a
INFN Sezione di Milano, I-20133 Milano, Italy
46b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
43
University of Mississippi, University, Mississippi 38677, USA
44
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
49a
INFN Sezione di Napoli, I-80126 Napoli, Italy
49b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
45
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, Netherlands
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
052012 (2012)
052012-2
46
University of Notre Dame, Notre Dame, Indiana 46556, USA
47
The Ohio State University, Columbus, Ohio 43210, USA
48
University of Oregon, Eugene, Oregon 97403, USA
54a
INFN Sezione di Padova, I-35131 Padova, Italy
54b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
49
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
56a
INFN Sezione di Perugia, I-06100 Perugia, Italy
56b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
57a
INFN Sezione di Pisa, I-56127 Pisa, Italy
57b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
57c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
50
Princeton University, Princeton, New Jersey 08544, USA
59a
INFN Sezione di Roma, I-00185 Roma, Italy
59b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
51
Universita
̈
t Rostock, D-18051 Rostock, Germany
52
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
53
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
54
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
55
University of South Carolina, Columbia, South Carolina 29208, USA
56
Southern Methodist University, Dallas, Texas 75275, USA
57
Stanford University, Stanford, California 94305-4060, USA
58
State University of New York, Albany, New York 12222, USA
59
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
60
University of Tennessee, Knoxville, Tennessee 37996, USA
61
University of Texas at Austin, Austin, Texas 78712, USA
62
University of Texas at Dallas, Richardson, Texas 75083, USA
72a
INFN Sezione di Torino, I-10125 Torino, Italy
72b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
73a
INFN Sezione di Trieste, I-34127 Trieste, Italy
73b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
63
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
64
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
65
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
66
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 11 July 2012; published 26 September 2012)
We use
429 fb

1
of
e
þ
e

collision data collected at the

ð
4
S
Þ
resonance with the
BABAR
detector to
measure the radiative transition rate of
b
!
s
with a sum of 38 exclusive final states. The inclusive
branching fraction with a minimum photon energy of 1.9 GeV is found to be
B
ð

B
!
X
s

Þ¼ð
3
:
29

0
:
19

0
:
48
Þ
10

4
where the first uncertainty is statistical and the second is systematic. We also
measure the first and second moments of the photon energy spectrum and extract the best-fit values for the
heavy-quark parameters,
m
b
and

2

, in the kinetic and shape function models.
DOI:
10.1103/PhysRevD.86.052012
PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Hh
I. INTRODUCTION
Flavor changing neutral current processes such as
b
!
s
, forbidden at the tree level in the standard model
(SM), occur at leading order through radiative loop
diagrams. Since these diagrams are the dominant contri-
butions to this decay, the effects of many new physics
scenarios, either enhancing or suppressing this transition
rate by introducing new mediators within the loop, can be
constrained by precision measurements of the total
b
!
s
transition rate [
1
5
].
In the context of the SM, the first order radiative penguin
diagram for the
b
!
s
transition has a
W
boson and
t
,
c
,
or
u
quark in the loop. The SM calculation for the corre-
sponding
B
meson branching fraction has been performed
at next-to-next-to-leading order in the perturbative term,
yielding
B
ð

B
!
X
s

Þ¼ð
3
:
15

0
:
23
Þ
10

4
for a pho-
ton energy of
E

>
1
:
6 GeV
, measured in the
B
meson rest
frame [
6
,
7
]. Experiments perform this measurement at
*
Now at the University of Tabuk, Tabuk 71491, Saudi Arabia.
Also with Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
Now at the University of Huddersfield, Huddersfield HD1
3DH, United Kingdom.
§
Deceased.
k
Now at University of South Alabama, Mobile, AL 36688,
USA.
{
Also with Universita
`
di Sassari, Sassari, Italy.
EXCLUSIVE MEASUREMENTS OF
b
!
s
...
PHYSICAL REVIEW D
86,
052012 (2012)
052012-3
higher minimum photon energies, generally between 1.7
and 2.0 GeV, to limit the background from other
B
sources.
The results are then extrapolated to the lower energy cut-
off,
E

>
1
:
6 GeV
, based on different photon spectrum
shape functions. The current world average is in good
agreement with the SM calculation and is measured to be
B
ð

B
!
X
s

Þ¼ð
3
:
55

0
:
24

0
:
09
Þ
10

4
, for
E

>
1
:
6 GeV
[
8
]. The second uncertainty is attributable to the
photon spectrum shape function used to extrapolate to the
1.6 GeV photon energy cutoff.
The photon energy spectrum is also of interest, as it
gives insight into the momentum distribution function of
the
b
quark inside the
B
meson. Precise knowledge of the
function is useful in determining
j
V
ub
j
from inclusive
semileptonic
B
!
X
u
l
measurements [
9
13
]. We fit the
measured spectrum to two classes of models: the ‘‘shape
function’’ scheme [
13
] and the ‘‘kinetic’’ scheme [
14
]. The
photon energy spectra predicted by these models are pa-
rametrized to find the best values for the heavy-quark
effective theory (HQET) parameters,
m
b
and

2

[
10
].
Our measurement uses a ‘‘sum-of-exclusives’’ ap-
proach, in which we reconstruct the final state of the
s
quark hadronic system,
X
s
, in 38 different modes. For this
article we update a former
BABAR
analysis [
15
] with about
5 times the integrated luminosity of the previous measure-
ment, as well as an improved analysis procedure. By
reconstructing the
X
s
system, we access the photon energy
through
E
B

¼
m
2
B

m
2
X
s
2
m
B
;
(1)
where
E
B

is the energy of the transition photon in the
B
rest
frame,
m
B
is the mass of the
B
meson, and
m
X
s
is the
invariant mass of the
X
s
hadronic system. Measuring
m
X
s
,
with a resolution of around
5 MeV
=c
2
, gives better reso-
lution on
E

than measuring the transition photon directly.
We are also able to measure the energy of the transition
photon in the rest frame of the
B
meson rather than
correcting for the boost of the
B
meson with respect to
the center of mass (CM) as is required for a direct mea-
surement of the transition photon. We perform this mea-
surement over the range
0
:
6
<m
X
s
<
2
:
8 GeV
=c
2
in 14
bins with a width of
100 MeV
=c
2
for
m
X
s
<
2
:
0 GeV
=c
2
,
and 4 bins with a width of
200 MeV
=c
2
for
m
X
s
>
2
:
0 GeV
=c
2
. To evaluate a total branching fraction for
B
ð

B
!
X
s

Þ
with
E

>
1
:
9 GeV
, we sum the partial
branching fractions from each
m
X
s
bin. This minimizes
our dependence on the underlying photon spectrum struc-
ture and is a departure from our previous procedure [
15
],
which combined the entire range
0
:
6
<m
X
s
<
2
:
8 GeV
=c
2
and used a single fit to the signal yield to determine the
total branching fraction.
II. DETECTOR AND DATA
Our results are based on the entire

ð
4
S
Þ
data set col-
lected with the
BABAR
detector [
16
] at the PEP-II
asymmetric-energy
B
factory at the SLAC National
Accelerator Laboratory. The data sample has an integrated
luminosity of
429 fb

1
collected at the

ð
4
S
Þ
resonance,
with a CM energy
ffiffiffi
s
p
¼
10
:
58 GeV
, and contains
471

10
6
B

B
pairs. We refer to this sample as the ‘‘on-peak’’
sample. An ‘‘off-peak’’ sample with an integrated luminos-
ity of
44
:
8fb

1
was recorded about 40 MeV below the

ð
4
S
Þ
resonance and is used for the study of backgrounds
consisting of
e
þ
e

production of light
q

q
(
q
¼
u
,
d
,
s
,
c
)
or

þ


states.
The
BABAR
detector is described in detail in [
16
].
Charged-particle momenta are measured by the combina-
tion of a silicon vertex tracker (SVT), consisting of five
layers of double-sided silicon strip detectors, and a 40-
layer central drift chamber (DCH) having a combination of
axial and stereo wires.
Charged-particle identification is provided by the com-
bination of the average energy loss (
dE=dx
) measured in
the tracking devices and the Cherenkov-radiation informa-
tion measured by an internally reflecting ring-imaging
Cherenkov detector (DIRC).
Photon and electron energies are measured by a CsI(Tl)
electromagnetic calorimeter (EMC). The SVT, DCH,
DIRC, and EMC operate inside of a 1.5 T magnet.
Charged
=
separation is done using the instrumented
flux return of the magnetic field, originally instrumented
with resistive plate chambers [
16
] and later with limited
streamer tubes [
17
].
III. SIGNAL AND BACKGROUND SIMULATION
To avoid experimental biases, we use Monte Carlo (MC)
simulations to model both the expected signal and back-
ground events and to define selection criteria before look-
ing at the data. We have produced MC samples for
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
,
c
) and
e
þ
e

!

þ


events,
each at 2 times the on-peak luminosity, as well as
B

B
MC
events, excluding decays of the
B
meson to an
X
s

final
state, at 3 times the on-peak luminosity. We also consider
‘‘cross-feed’’ backgrounds. We define cross feed as signal
events in which we wrongly reconstruct the
B
candidate.
This occurs because the
X
s
final state is not one of the 38
reconstructed modes, not all of the particles in the true final
state are detected, or the procedure for selecting the cor-
rectly reconstructed
B
from several potential
B
candidates
fails in some cases.
Two types of signal MC events are generated, one for the
K

ð
892
Þ
region (
m
X
s
<
1
:
1 GeV
=c
2
) in which the
b
!
s
transition proceeds exclusively through
B
!
K

ð
892
Þ

,
and one for the region above the
K

ð
892
Þ
resonance (
1
:
1
<
m
X
s
<
2
:
8 GeV
=c
2
, the upper bound being the limit of our
ability to adequately reject
B
backgrounds). While there
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
052012 (2012)
052012-4
are several known
X
s
resonances above the
K

ð
892
Þ
, and
evidence for even more [
18
], these resonances are broad
and overlapping. We therefore take only the
K

ð
892
Þ
reso-
nance explicitly into account when simulating the signal
events, as recommended by [
19
].
The quarks in inclusive region signal MC events shower
using the ‘‘phase-space hadronization model,’’ as opposed
to the well-known ‘‘Lund string model,’’ with our default
JETSET
[
20
] settings. The most important
JETSET
parame-
ters that influence the fragmentation of the
X
s
system in
this inclusive region are the probabilities of forming a
spin-1 state for the
s
quark or
u=d
quarks (the correspond-
ing
JETSET
parameters are
PARJ(12)
and
PARJ(11)
). These
probabilities are set to 0.60 and 0.40, respectively.
We generate the inclusive signal MC events with a flat
photon spectrum with bounds corresponding to the
m
X
s
boundaries, which we then reweight to match whichever
spectrum model we choose. We do not take any explicit
photon model into account when evaluating signal effi-
ciency within a given
X
s
mass bin. However, to evaluate
the optimal background-rejection requirements, we do
need to specify the expected shape of the spectrum. For
this, we use the model settings for the kinetic scheme
models [
14
] found to be consistent with the previous
BABAR
sum-of-exclusive analysis (
m
b
¼
4
:
65 GeV
=c
2
,

2

¼
0
:
20 GeV
2
)[
15
].
GEANT4
[
21
] is used to model the response of the detec-
tor for all MC samples. Time-dependent detector ineffi-
ciencies, monitored during data taking, are also included.
IV.
B
MESON RECONSTRUCTION AND
BACKGROUND REJECTION
We reconstruct the
B
meson in one of 38 final states of
the
X
s
plus a high energy photon, as listed in Table
I
[
22
].
These modes consist of one or three kaons, at most one

,
and at most four pions, of which no more than two can be
neutral pions. The method of particle identification (PID)
has improved over the run of the experiment. In particular
for charged
K
identification, we use a multiclass classifier
procedure of error correcting output code (ECOC) [
23
].
The kaon identification efficiency is roughly 90% for the
momentum range considered for this analysis.
The
K
0
S
mesons are reconstructed as
K
0
S
!

þ


can-
didates with an invariant

þ


mass within
9 MeV
=c
2
of
the nominal
K
0
S
mass [
18
], a flight distance greater than
0.2 cm from the primary event vertex, and a flight signifi-
cance (measurement of flight distance divided by the un-
certainty on the measured distance) greater than 3. We do
not include
K
0
L
mesons or
K
0
S
!

0

0
decays in our
reconstructed final states.
Charged
K
candidates are identified based on the ECOC
algorithms [
23
], which use information from the tracking
system, the DIRC, and the EMC to identify particle species
using multivariate classifiers. All remaining charged tracks
are assumed to originate from charged pions.
The

0
and

candidates are reconstructed from photon
candidates with an energy greater than 60 MeV as mea-
sured in the laboratory frame and must have an invariant
mass between 115 and
150 MeV
=c
2
for the

0
, and 470
and
620 MeV
=c
2
for the

. We also require a minimum
momentum
p

0
;
>
200 MeV
=c
in the lab frame.
Although we do not explicitly reconstruct the

!

þ



0
decay mode, this mode is implicitly included
in the final states if there is at most one other pion in the
event. We combine these charged and neutral particles to
form different
X
s
candidates in the event.
We require that an event contain at least one photon
candidate with
1
:
6
<E


<
3
:
0 GeV
(where ‘‘

’’ hence-
forth indicates variables measured in the CM), which is
consistent with the signal photon of the decay
b
!
s
. The
distance to the closest cluster in the EMC is required to be
greater than 25 cm from this signal photon cluster. We also
require the angle between the signal photon candidate and
the thrust axis of the rest of the event to satisfy
j
cos


T
j
<
0
:
85
, and the ratio of event shape angular moments to
satisfy
L
12
=L
10
<
0
:
46
[
24
] (the signal peaks at slightly
lower values than the background). These two preliminary
requirements on the event topology are especially effective
at reducing the large amount of more jetlike light
q

q
backgrounds, and together decrease this background
source by about 50% (while only removing 10% of the
signal).
We combine the
X
s
candidates and the signal photon
candidates to form
B
candidates in the event. We define the
TABLE I. The 38
X
s
decay modes used for
B
meson recon-
struction in this analysis.
Mode no.
Final state
Mode no.
Final state
1
K
0
S

þ
20
K
0
S

þ



þ


2
K
þ

0
21
K
þ

þ





0
3
K
þ


22
K
0
S

þ



0

0
4
K
0
S

0
23
K
þ

5
K
þ

þ


24
K
0
S

6
K
0
S

þ

0
25
K
0
S

þ
7
K
þ

0

0
26
K
þ

0
8
K
0
S

þ


27
K
þ


9
K
þ



0
28
K
0
S

0
10
K
0
S

0

0
29
K
þ

þ


11
K
0
S

þ



þ
30
K
0
S

þ

0
12
K
þ

þ



0
31
K
0
S

þ


13
K
0
S

þ

0

0
32
K
þ



0
14
K
þ

þ




33
K
þ
K

K
þ
15
K
0
S

0

þ


34
K
þ
K

K
0
S
16
K
þ



0

0
35
K
þ
K

K
0
S

þ
17
K
þ

þ



þ


36
K
þ
K

K
þ

0
18
K
0
S

þ



þ

0
37
K
þ
K

K
þ


19
K
þ

þ



0

0
38
K
þ
K

K
0
S

0
EXCLUSIVE MEASUREMENTS OF
b
!
s
...
PHYSICAL REVIEW D
86,
052012 (2012)
052012-5
beam-energy substituted mass,
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
ffiffiffi
s
p
=
2
Þ
2
p

B
Þ
2
q
,
and require
m
ES
>
5
:
24 GeV
=c
2
. We also require the
difference between the expected
B
energy and the recon-
structed
B
energy,
j

E
j¼j
E

B

ffiffiffi
s
p
=
2
j
, to satisfy
j

E
j
<
0
:
15 GeV
. For these quantities,
p

B
and
E

B
are the momen-
tum and energy of the reconstructed
B
meson in the CM
system.
With these loose preliminary requirements in place, each
event still typically has several
B
meson candidates. We
construct a random forest classifier [
25
] [a signal selecting
classifier (SSC)] to find the best candidate in an event. This
classifier is built using the variables

E=
E
(where

E
is
the uncertainty on the total energy of the reconstructed
B
),
the thrust of the reconstructed
B
, the

0
momentum in the
CM (if the candidate has a

0
), the invariant mass of the
X
s
candidate, and the zeroth and fifth Fox-Wolfram moments
of the event [
26
]. We choose to include the fifth Fox-
Wolfram moment because our MC simulation indicates
that this variable improves the performance of our classi-
fier. The selected
B
candidate in an event is the candidate
with the highest response to this classifier. We find that
applying this classifier to select the best candidate, after
placing a loose requirement on
j

E
j
, rather than selecting
the candidate with the smallest
j

E
j
, improves the signal
efficiency by a factor of about 2. We also find that placing a
requirement on the SSC response is effective at further
removing
B
backgrounds.
To further reduce the background from events in which a
photon from a high energy

0
decay is mistaken as the
signal photon candidate, we construct a dedicated

0
veto
using a random forest classifier [
25
]. If the signal photon
candidate in an event can be combined with any other
photon to form a candidate with an invariant mass in the
range
115
<m

<
150 MeV
=c
2
, we evaluate the

0
veto
classifier response based on the invariant mass of the two
photons and the energy of the lower energy photon. The
response of the

0
veto classifier is used as input to a more
general background rejecting classifier (BRC).
The BRC is constructed to remove continuum (lighter
q

q
) backgrounds. To construct this classifier, we use infor-
mation from the

0
veto,
j
cos


T
j
,
j
cos


T
j
(the angle
between the thrust axis of
B
and the thrust axis of the
rest of the event),
j
cos


B
j
(the CM polar angle of the
B
flight direction), the zeroth, first, and second angular mo-
ments [
24
] computed along the signal photon candidate’s
axis as well as the ratio
L
12
=L
10
(which exhibits slightly
different signal and background shapes), and the 10

mo-
mentum flow cones around the
B
flight direction.
To effectively remove background while maintaining
signal efficiency, we evaluate optimal requirements for
the responses of the BRC and SSC in four mass regions,
[0.6–1.1], [1.1–2.0], [2.0–2.4], and
½
2
:
4
2
:
8

GeV
=c
2
, op-
timizing the figure of merit
S=
ffiffiffiffiffiffiffiffiffiffiffiffiffi
S
þ
B
p
, where
S
is the
expected signal yield and
B
is the expected background
yield evaluated using MC simulation.
V. SIGNAL YIELD EXTRACTION
We extract the signal yield by performing fits to the
m
ES
distribution in each bin of
m
X
s
. The signal distribution is
described by a crystal ball function (CB) [
27
]:
f
ð
m
ES
Þ¼
e
ð
ð
m
ES

m
0
Þ
2
2

2
Þ
;








m
ES

m
0









< ;
f
ð
m
ES
Þ¼
ð
n
CB
Þ
n
CB
e
ð
2
2
Þ
ð
n
CB


m
ES

m
0

Þ
n
CB
;








m
ES

m
0









> ;
(2)
where
m
0
and

are the peak position and width, respec-
tively, and the parameters
and
n
CB
take account of
the non-Gaussian tail. This distribution takes into account
the asymmetry of the
m
ES
distribution for these events. The
backgrounds are described by ARGUS functions [
28
] for
the combinatorial components:
f
ð
m
ES
Þ¼
m
ES

1


m
ES
m

2

ð
1
=
2
Þ

e
ð
c
m
ES
m
Þ
;
(3)
where
m
is the end point,
c
is the slope, and Novosibirsk
functions [
29
] for both the peaking
B

B
contribution and
peaking cross-feed contribution (‘‘peaking’’ meaning ap-
parently resonant behavior similar to the signal distribution
in
m
ES
).
The signal CB distribution is parametrized based on a fit
to correctly reconstructed signal MC events over the full
hadronic mass range,
0
:
6
2
:
8 GeV
=c
2
, as we find little
X
s
mass dependence of the signal shape parameters. The CB
parameters take the values
¼
1
:
12
,
m
0
¼
5
:
28 GeV
=c
2
,

¼
2
:
84 MeV
=c
2
, and
n
CB
¼
145
for every mass bin. In
Sec.
VII
we evaluate the uncertainties introduced by fixing
the CB shape parameters.
The cross-feed shape has both a peaking component and a
combinatoric tail. The peaking component is described by a
Novosibirsk function, parametrized over five different mass
regions, [0.6–1.1], [1.1–1.5], [1.5–2.0], [2.0–2.4], and
½
2
:
4
2
:
8

GeV
=c
2
, based on MC distributions over these
regions. The combinatoric cross-feed tail is described by an
ARGUS function with the slope
c
fit to the MC events in
each mass bin and fixed in the fits to data. We fix the fraction
of peaking cross-feed MC events, the fraction of signal to
signal
þ
cross-feed events, and the shapes of the cross-feed
Novosibirsk and ARGUS functions, in each bin of
m
X
s
,
based on the MC events. We allow the total signal
þ
cross-feed yield to float in each mass bin in the fits to data.
A second ARGUS function is used to parametrize the
combinatoric background from continuum and other
B

B
sources. We fix the end point
m
of the ARGUS function to
the kinematic limit (
5
:
29 GeV
=c
2
) of the
m
ES
variable and
allow the yield to float.
The
B

B
background also has a peaking component,
which becomes more significant at higher
X
s
mass, is
also described by a Novosibirsk function, and is parame-
trized over three mass ranges, [0.6–2.0], [2.0–2.4], and
½
2
:
4
2
:
8

GeV
=c
2
. We fix the total number and shape of
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
052012 (2012)
052012-6
the peaking
B

B
events based on a fit to the
B

B
MC events
in each mass bin.
We perform a minimum
2
fit to the
m
ES
distribution in
each bin of
m
X
s
, allowing the slope of the combinatoric
ARGUS and the fractional yield of signal
þ
cross feed to
float (the complementary fractional yield, once the peaking
B

B
is accounted for, reflects the normalization of the
combinatoric ARGUS function). Figure
1
shows an ex-
ample for
m
X
s
bin
1
:
4
1
:
5 GeV
=c
2
. We fix all other shape
parameters, and evaluate systematic uncertainties associ-
ated with fixing these parameters in Sec.
VII
. We perform
MC simulations (‘‘toy studies’’) to ensure that we do not
introduce any biases attributable to the fitting procedure.
VI.
X
s
FRAGMENTATION AND
MISSING FRACTION
The fragmentation of the hadronic system in the inclu-
sive region,
1
:
1
<m
X
s
<
2
:
8 GeV
=c
2
, is modeled with
JETSET
with a phase-space hadronization model. The dif-
ferences between fragmentation in the MC sample and in
the data influence the measurement in two ways. First,
since the efficiencies for the 38 modes are not the same,
an incorrect modeling of their relative fractions will lead to
an incorrect expected total efficiency for reconstructing the
38 final states (
38
). Second, the simulation of the frag-
mentation process can introduce incorrect estimates of the
fraction of the total inclusive
b
!
s
transition rate re-
flected by the 38 modes (
incl
). The fraction of final states
in each of the mass bins that is not included in our 38
modes is referred to as the ‘‘missing fraction,’’ and is
equivalent to
1

incl
.
We are able to evaluate and correct
38
for the first effect,
and we use these results to estimate the uncertainty on the
second effect, our uncertainty on
incl
, by performing a
fragmentation study comparing the frequency of groups of
modes in the MC sample to the data. For this study, we
compare the frequency of ten groups of modes, each con-
taining two to ten final states, in the MC sample to the
frequency for these groups found in the data. We perform
this study in four different mass regions, [1.1–1.5],
[1.5–2.0], [2.0–2.4], and
½
2
:
4
2
:
8

GeV
=c
2
.
The procedure for the study involves reweighting the
relative contribution of each of the groups of modes in our
MC sample based on the relative amount found in the
data. The efficacy of the procedure is checked on MC
events by ensuring we can find the
38
in each mass bin
for the Lund string model when starting with the default
phase-space hadronization model [
20
], as well as find the
38
in each mass bin for the phase-space hadronization
model when starting with the Lund string model. The
different groups of modes we use to compare data and
the MC samples, along with the results of the compari-
sons in each mass bin, are given in Table
II
, obtained with
the default phase-space hadronization model as the start-
ing point.
To perform this study, we combine the mass bins into the
four mass regions and fit the signal
þ
cross-feed contribu-
tion for each subset of modes in each mass region in the
data. We then use the ratio of the yield of each subset found
5.24 5.245 5.25 5.255 5.26 5.265 5.27 5.275 5.28 5.285 5.29
0
50
100
150
200
250
)
2
(GeV/c
ES
m)
2
(GeV/c
ES
m
5.24 5.245 5.25 5.255 5.26 5.265 5.27 5.275 5.28 5.285 5.29
2
Events / 1 MeV/c
2
Events / 1 MeV/c
0
50
100
150
200
250
(a)
5.24 5.245 5.25 5.255 5.26 5.265 5.27 5.275 5.28 5.285 5.29
0
10
20
30
40
50
60
70
)
2
(GeV/c
ES
m)
2
(GeV/c
ES
m
5.24 5.245 5.25 5.255 5.26 5.265 5.27 5.275 5.28 5.285 5.29
2
Events / 1 MeV/c
2
Events / 1 MeV/c
0
10
20
30
40
50
60
70
(b)
5.24 5.245 5.25 5.255 5.26 5.265 5.27 5.275 5.28 5.285 5.29
0
2
4
6
8
10
12
)
2
(GeV/c
ES
m)
2
(GeV/c
ES
m
5.24 5.245 5.25 5.255 5.26 5.265 5.27 5.275 5.28 5.285 5.29
2
Events / 1 MeV/c
2
Events / 1 MeV/c
0
2
4
6
8
10
12
(c)
5.24 5.245 5.25 5.255 5.26 5.265 5.27 5.275 5.28 5.285 5.29
0
50
100
150
200
250
300
350
)
2
(GeV/c
ES
m)
2
(GeV/c
ES
m
5.24 5.245 5.25 5.255 5.26 5.265 5.27 5.275 5.28 5.285 5.29
2
Events / 1 MeV/c
2
Events / 1 MeV/c
0
50
100
150
200
250
300
350
(d)
FIG. 1. Thefitinmassbin
1
:
4
<m
X
s
<
1
:
5GeV
=c
2
to(a)signal
MC events, (b) cross-feed MC events, (c) peaking
B

B
MC events,
and (d) the data. The signal (thick dashed curve), cross-feed (two
dot-dashed curves, one ARGUS function, and one Novosibirsk
function), peaking
B

B
(dotted curve), and combinatoric back-
ground (thin dashed curve) component functions are shown.
EXCLUSIVE MEASUREMENTS OF
b
!
s
...
PHYSICAL REVIEW D
86,
052012 (2012)
052012-7
in data to the amount found in the MC sample to reweight
the MC sample to better reflect the data in the mass region.
We use the statistical uncertainty in fitting each subset in
data as the uncertainty on the ratio.
After correcting the signal and cross-feed MC events
based on these comparisons, we evaluate the value of
38
for each mass bin, reported in Table
III
.Forthe
inclusive region, the uncertainty on
38
is calculated
using the uncertainties in the fragmentation corrections,
as described later in Sec.
VII
. Since the fragmentation
in the
K

ð
892
Þ
region is considered well modeled, we
do not perform a fragmentation correction on these
mass bins.
We base the uncertainty on the fraction of the inclusive
b
!
s
transitions measured by the 38 final states,
incl
,on
the range of values predicted by competing fragmentation
models in the MC samples. We consider many settings of
JETSET
using both the default phase-space and the Lund
string hadronization mechanism, as well as a thermody-
namical model [
30
]. Other models in
JETSET
(Field-
Feynman model [
31
] of the showering quark system,
etc.) are found to yield results consistent with the Lund
string model and are not further considered.
As mentioned above, we identify the probabilities for
forming a spin-1 hadron with the
s
quark or
u=d
quarks to
be the
JETSET
parameters that have the largest impact on
the breakdown of final states. We try many settings for
these parameters in both the phase-space hadronization
mechanism and the Lund string model mechanism in
JETSET
. By varying the spin-1 probabilities and using
both of these fragmentation mechanisms, we are able to
identify a range of models that, taken together, accounts for
the breakdown of final states found in the data in the
TABLE II. The subsets of modes and the ratio of yields found in each
m
X
s
region when comparing the data to the MC events. The
error is statistical only.
Data subset
Definition
Modes used
1
2 bodies without

0
1,3
2
2 bodies with 1

0
2,4
3
3 bodies without

0
5,8
4
3 bodies with 1

0
6,9
5
4 bodies without

0
11,14
6
4 bodies with 1

0
12,15
7
3
=
4
bodies with 2

0
7,10,13,16
8
5 bodies with 0–2

0
17–22
9

!

23–32
10
3K modes
33–38
Data
subset
1
:
1
<m
X
s
<
1
:
5 GeV
=c
2
(data/MC)
1
:
5
<m
X
s
<
2
:
0 GeV
=c
2
(data/MC)
2
:
0
<m
X
s
<
2
:
4 GeV
=c
2
(data/MC)
2
:
4
<m
X
s
<
2
:
8 GeV
=c
2
(data/MC)
1
0
:
65

0
:
03
0
:
38

0
:
03
0
:
05

0
:
05
0
:
18

0
:
13
2
0
:
53

0
:
05
0
:
28

0
:
06
0
:
32

0
:
12
0
:
15
þ
0
:
25

0
:
15
3
1
:
20

0
:
03
1
:
01

0
:
04
0
:
72

0
:
11
0
:
25

0
:
25
4
1
:
70

0
:
05
1
:
03

0
:
06
0
:
33

0
:
13
1
:
00
þ
0
:
47

1
:
00
5
0
:
34

0
:
08
1
:
34

0
:
10
1
:
12

0
:
23
2
:
29

0
:
74
6
1
:
24

0
:
13
1
:
16

0
:
11
1
:
28

0
:
27
0
:
10
þ
0
:
39

0
:
10
7
0
:
56

0
:
19
1
:
37

0
:
30
0
:
83

0
:
53
2
:
06

1
:
64
8
1
:
00
þ
1
:
05

1
:
00
0
:
57

0
:
16
0
:
74

0
:
28
0
:
29
þ
1
:
27

0
:
29
9
0
:
94

0
:
15
1
:
70

0
:
20
2
:
47

0
:
50
1
:
09
þ
1
:
03

1
:
09
10
0
:
00

0
:
00
0
:
62

0
:
11
0
:
74

0
:
31
0
:
83
þ
1
:
11

0
:
83
TABLE III. The value of
38
before and after the fragmenta-
tion corrections are performed on the inclusive region. The
uncertainty on the corrected value in the inclusive region reflects
the uncertainty of the fits to the data.
m
X
s
(
GeV
=c
2
)
38
original (%)
38
final (%)
0.6–0.7
15.0
15.0
0.7–0.8
16.5
16.5
0.8–0.9
17.3
17.3
0.9–1.0
18.3
18.3
1.0–1.1
16.0
16.0
1.1–1.2
11.5
10
:
4

0
:
4
1.2–1.3
11.6
10
:
6

0
:
3
1.3–1.4
10.7
9
:
9

0
:
3
1.4–1.5
9.5
8
:
9

0
:
5
1.5–1.6
8.4
7
:
5

0
:
5
1.6–1.7
7.2
6
:
5

0
:
4
1.7–1.8
5.5
5
:
0

0
:
4
1.8–1.9
4.5
4
:
2

0
:
4
1.9–2.0
3.3
3
:
0

0
:
4
2.0–2.2
4.0
3
:
2

0
:
4
2.2–2.4
3.1
2
:
4

0
:
4
2.4–2.6
2.3
1
:
9

0
:
7
2.6–2.8
2.3
2
:
1

0
:
9
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
052012 (2012)
052012-8
fragmentation study (Table
II
). We vary the probability for
forming a spin-1 hadron with the
s
quark between zero and
one, and with the
u=d
quark between 0.2 and 0.8. When
comparing to our default MC settings, the models we
consider predict both higher and lower ratios than those
found in the data, but no single model matches every ratio
in every mass region.
We also find that no single mechanism or
JETSET
setting
perfectly reproduces the fragmentation in the data; how-
ever, the models chosen bound the data. The fact that spin-
1 probability settings need to be varied to account for data
and MC differences is expected, as a variety of resonances
exist in the inclusive region. The maximum, minimum, and
default values for
incl
that we find are reported in Table
IV
.
We account for what is seen in data in the fragmentation
study through a variety of settings of both the Lund string
mechanism and phase-space hadronization mechanism,
and therefore base our uncertainty on
incl
on these same
models. The statistics model and the default
JETSET
set-
tings predict values for
incl
that lie between those pre-
dicted by other settings of
JETSET
that we try. As we find
that no model exactly describes the fragmentation we
observe in the data, but together the models considered
bound the data, we count each model as equally probable,
take the systematic uncertainty on the correct value for
incl
as the difference between the maximum and minimum
values of
incl
relative to the default MC value, and divide
by
ffiffiffiffiffiffi
12
p
, reflecting the standard deviation of a uniform
distribution.
VII. SYSTEMATIC UNCERTAINTIES
We present the
X
s
mass-bin-dependent uncertainties in
Table
V
. The uncertainty on the total number of
B
mesons
produced at
BABAR
is evaluated at 1.1%.
The uncertainty on the efficiency of the requirements on
the two multivariate classifiers are evaluated in signallike
data sidebands, regions in parameter space similar to, but
not overlapping with, the signal region, by comparing the
efficiency of the requirements on MC events and the
efficiency of these requirements on data. We define our
sidebands as the inverse of the requirements we place on
the classifiers. Therefore if we require the SSC response to
be greater than 0.5 for a mass region, we evaluate the BRC
uncertainty in the SSC sideband defined by requiring an
SSC response less than 0.5 (and similarly for evaluating
the SSC uncertainty in the BRC-defined sideband). The
relative difference between the two efficiencies is taken
as the systematic uncertainty. The sideband produced by
taking the inverse of the requirements on the SSC is used to
evaluate the uncertainty on the requirements on the BRC.
To evaluate the uncertainty on the SSC requirement, the
events that are identified by the

0
-veto classifier to con-
tain a

0
candidate are used with the further requirement
m
ES
>
5
:
27 GeV
=c
2
. This gives a more signallike sample
of events that have a high energy

0
in place of the signal
transition photon. The efficiency of the SSC requirement is
compared between data and the MC events with the use of
this sideband.
To evaluate fitting uncertainties related to fixing many of
the parameters in the signal and cross-feed probability
density functions (PDFs), we use the
K

ð
892
Þ
region
(
m
X
s
<
1
:
1 GeV
=c
2
) to determine reasonable shifts in
these parameters. We assign the systematic uncertainty as
the change in signal yield in the fit to data when we use the
shifted shape parameters. For the uncertainty on the frac-
tion of signal to signal
þ
cross feed, which is also fixed in
the fit to data, we fix the total yield and slope of this
ARGUS function (these are the two parameters that we
float in the fits to data) and allow this fraction to float in
each mass bin. We take the change in signal yield when we
fix the signal fraction to this new value as the systematic
uncertainty.
To evaluate the uncertainty on the peaking
B

B
back-
ground PDF shape, we use the change in signal yield when
changing the parameter values by the uncertainty in the fits
to MC events.
The uncertainty on the number of peaking
B

B
events,
generally the largest source of
B

B
fitting error in Table
V
,is
again evaluated based on the

0
-veto sideband. In this
sideband, we evaluate the
B

B
MC predictions for the
number of peaking events and compare this to the number
of peaking
B

B
events we find in data. We find these values
to agree within 1 standard deviation for the three mass
regions over which we have parametrized the peaking
B

B
Novosibirsk function (see Sec.
V
). We determine the
TABLE IV. The minimum, maximum, and default values of
incl
found for the range of models that account for the differ-
ences seen between the default MC events and data in the
inclusive region. We include the
K

ð
892
Þ
region default values
as well, though these mass bins are not modeled by the inclusive
MC sample.
m
X
s
(
GeV
=c
2
) Minimum
incl
Maximum
incl
Default
incl
0.6–0.7


0.75
0.7–0.8


0.74
0.8–0.9


0.74
0.9–1.0


0.75
1.0–1.1


0.74
1.1–1.2
0.71
0.74
0.73
1.2–1.3
0.71
0.74
0.72
1.3–1.4
0.70
0.74
0.72
1.4–1.5
0.69
0.73
0.71
1.5–1.6
0.66
0.73
0.68
1.6–1.7
0.59
0.72
0.66
1.7–1.8
0.57
0.72
0.63
1.8–1.9
0.52
0.71
0.59
1.9–2.0
0.47
0.68
0.54
2.0–2.2
0.41
0.64
0.48
2.2–2.4
0.33
0.60
0.39
2.4–2.6
0.27
0.56
0.31
2.6–2.8
0.23
0.51
0.25
EXCLUSIVE MEASUREMENTS OF
b
!
s
...
PHYSICAL REVIEW D
86,
052012 (2012)
052012-9
mass-region-dependent uncertainty on the measurement of
peaking
B

B
yield in the

0
-veto sideband in data. We use
this uncertainty added in quadrature with the uncertainty
from the fits to the
B

B
MC sample as the uncertainty on the
number of peaking
B

B
events in each mass bin. Unlike the
other systematic uncertainties, which are multiplicative in
nature, this uncertainty is additive since we are subtracting
out peaking
B

B
events we would otherwise fit as signal
þ
cross feed in the fits to data.
The detector response uncertainties associated with PID,
photon detection both from the transition photon and from

0
=
decay, and tracking of charged particles are approxi-
mately 2.5%–2.9% in every mass bin.
The uncertainty on
38
from the fragmentation study is
taken from the change in
38
when modifying the weights
given in Table
II
by the uncertainty on these values indi-
vidually. We also account for the differences in statistics
between the mass regions over which these uncertainties
were determined and the individual mass bins. Since our
fragmentation study procedure groups bins together before
evaluating appropriate weights, the weights we identify
tend to reflect the bins with higher numbers of events,
and the uncertainty on the bins with fewer events needs
to be increased. We therefore increase the uncertainty in
each
m
X
s
bin by a factor of
ffiffiffiffiffiffiffiffiffiffiffiffiffi
N
region
p
=
ffiffiffiffiffiffiffiffiffi
N
bin
p
, where
N
region
(
N
bin
) refers to the number of events in the region (bin).
This correction ensures that if an
m
X
s
bin has few events
compared to its corresponding region, then the uncertainty
for this bin will be larger. The total fragmentation uncer-
tainty is found by summing in quadrature the changes for
each of the ten subset amounts. Where asymmetric uncer-
tainties are reported in Table
II
, we take the average change
in
38
when fluctuating the weights by the indicated
amounts. For the mass bin
1
:
0
<m
X
s
<
1
:
1 GeV
=c
2
,itis
unknown if the fragmentation in the data is modeled more
effectively by the
K

ð
892
Þ
MC sample or the inclusive MC
sample. We take the average of the two predictions to be
the value for
38
, and the uncertainty is the difference
divided by
ffiffiffiffiffiffi
12
p
, consistent with the standard deviation of
a uniform distribution.
The uncertainty on the missing fraction was covered in
Sec.
VI
for the inclusive region. The competing fragmen-
tation models give an uncertainty on the missing fraction
from 1.3% to 32.7%, getting larger at higher mass. For the
K

ð
892
Þ
region, we take the uncertainty to be the differ-
ence between the default
K

ð
892
Þ
MC prediction for the
missing fraction and the hypothesis of exclusively missing
K
0
L
final states, which would be a missing fraction of 25%
for this region.
We take each of these systematic uncertainties to be
uncorrelated within an
m
X
s
bin. However, there are corre-
lations in the errors between the mass bins. The
B

B
count-
ing, classifier requirements, non-
B

B
fitting for signal and
cross-feed PDF shapes, and detector response systematic
TABLE V. List of systematic uncertainties described in the text. These subcomponent system-
atic uncertainties are assumed to be uncorrelated within a given mass bin, and the total
uncertainty reflects their addition in quadrature. All uncertainties are given in percent. Many
of these uncertainties are taken to be completely correlated over
m
X
s
regions, and we have
indicated the correlated uncertainties with horizontal lines defining the regions.
Mass bin
(
GeV
=c
2
)
B

B
counting
Classifier
selection
Non-
B

B
fitting
B

B
fitting
Detector
response Frag.
Missing
fraction Total
0.6–0.7
1.1
1.0
14.9
21.3
2.5

0.6
26.2
0.7–0.8
1.1
1.0
2.7
3.1
2.6

0.9
5.1
0.8–0.9
1.1
1.0
1.7
0.6
2.6

1.3
3.8
0.9–1.0
1.1
1.0
1.7
0.7
2.7

0.0
3.6
1.0–1.1
1.1
1.0
5.1
2.5
2.7
13.1
0.9
14.6
1.1–1.2
1.1
0.7
5.7
0.9
2.7
3.9
1.3
7.7
1.2–1.3
1.1
0.7
4.7
0.4
2.7
3.0
1.3
6.4
1.3–1.4
1.1
0.7
4.6
0.3
2.7
3.0
1.6
6.4
1.4–1.5
1.1
0.7
4.7
0.6
2.7
5.7
1.8
8.2
1.5–1.6
1.1
0.7
3.7
1.5
2.7
6.1
3.1
8.5
1.6–1.7
1.1
0.7
4.3
1.3
2.7
6.3
5.9
10.2
1.7–1.8
1.1
0.7
4.9
1.5
2.7
7.9
6.9
12.1
1.8–1.9
1.1
0.7
3.4
13.1
2.7
10.0
9.6
19.6
1.9–2.0
1.1
0.7
5.3
4.2
2.7
13.4
11.1
18.9
2.0–2.2
1.1
1.9
4.5
6.6
2.9
11.0
13.9
19.8
2.2–2.4
1.1
1.9
4.9
22.0
2.9
18.4
19.7
35.3
2.4–2.6
1.1
2.8
4.7
23.8
2.8
36.7
26.8
51.7
2.6–2.8
1.1
2.8
49.3
154.1
2.8
45.7
32.7
171.3
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
052012 (2012)
052012-10
uncertainties are taken to be completely correlated be-
tween all mass bins. As we parametrize the peaking
B

B
Novosibirsk function in three different regions, we evalu-
ate the uncertainties over the same regions, taking the
uncertainties to be independent from one region to the
other (indicated by the horizontal lines in Table
V
).
Similarly, the fragmentation uncertainty and missing frac-
tion uncertainty are evaluated using different samples and
strategies in different mass regions; we take the uncertainty
on these mass regions to be uncorrelated with one another,
but completely correlated between the mass bins within a
mass region.
VIII. BRANCHING FRACTIONS
We measure the signal yield in
100 MeV
=c
2
wide bins
of the
X
s
mass over the range
0
:
6
<m
X
s
<
2
:
0 GeV
=c
2
,
and
200 MeV
=c
2
wide bins over the mass range
2
:
0
<
m
X
s
<
2
:
8 GeV
=c
2
. We report the measured signal yield
in Table
VI
, where we have included the
2
per degree of
freedom (dof) from the fits.
We use the efficiencies reported in Tables
III
and
IV
to
derive the total number of
b
!
s
events,
N
b
!
s
, based on
the yields,
N
yield
, reported in Table
VI
, according to
N
b
!
s
¼
N
yield
38
incl
:
(4)
The partial branching fraction (PBF) for each mass bin is
reported in Table
VII
. In this table, we also report the total
branching fraction, with a minimum photon energy of
E

>
1
:
9 GeV
, reflecting the sum of the 18 bins,
B
ð

B
!
X
s

Þ¼ð
3
:
29

0
:
19

0
:
48
Þ
10

4
;
(5)
where the first uncertainty is statistical and the second is
systematic. This result is consistent with the previous
BABAR
sum-of-exclusive results of
B
ð

B
!
X
s

Þ¼
ð
3
:
27

0
:
18
þ
0
:
55
þ
0
:
04

0
:
40

0
:
09
Þ
10

4
[
15
], where the first uncer-
tainty is statistical, the second systematic, and the third
from theory. The total statistical uncertainty on our result
reflects the sum in quadrature of the statistical uncertainty
of the 18 uncorrelated statistical uncertainties in the mass
bins. This method ensures reduced spectrum-model depen-
dence when quoting a branching fraction. An alternate
method of measuring the transition rate based on larger
mass bins yields similar results. This alternative method is
similar to the method used in the previous analysis [
15
], in
which one measurement of the signal yield over the entire
mass range was used to determine the total transition rate.
However, that method introduces additional model depen-
dence owing to the uncertainty in the spectrum shape, and
we instead decide to take the total transition rate as the sum
of the transition rates in each of the
m
X
s
bins. The total
systematic uncertainty reported in our study takes the
correlations, indicated in Table
V
, into account. The corre-
lation coefficients between the total uncertainties in each
bin are included in the Appendix. The partial branching
fractions per
100 MeV
=c
2
in
X
s
mass are illustrated in
Fig.
2
, with the previous
BABAR
sum-of-exclusive results
also shown.
TABLE VI. Signal yields from fits to the on-peak data and
corresponding
2
=
dof
from the fits (the uncertainties are
statistical only).
m
X
s
(
GeV
=c
2
)
N
yield
(events)
Data fit
2
=
dof
0.6–0.7
5
:
9

12
:
2
0.8
0.7–0.8
114
:
7

24
:
0
0.9
0.8–0.9
2627
:
4

50
:
2
1.0
0.9–1.0
2249
:
5

53
:
1
0.9
1.0–1.1
380
:
4

36
:
1
0.9
1.1–1.2
393
:
7

37
:
1
0.8
1.2–1.3
1330
:
5

47
:
1
0.6
1.3–1.4
1501
:
0

54
:
7
1.0
1.4–1.5
1479
:
6

58
:
3
1.0
1.5–1.6
1039
:
6

55
:
7
0.9
1.6–1.7
929
:
1

56
:
7
0.9
1.7–1.8
736
:
5

48
:
6
1.2
1.8–1.9
585
:
8

50
:
8
1.0
1.9–2.0
272
:
0

37
:
4
1.0
2.0–2.2
684
:
4

68
:
2
1.1
2.2–2.4
277
:
5

64
:
6
1.0
2.4–2.6
159
:
7

54
:
4
0.8
2.6–2.8

34
:
4

62
:
0
1.1
TABLE VII. The partial branching fractions in each mass bin
reflecting branching fractions per 100 or
200 MeV
=c
2
, and the
total branching fraction for
b
!
s
with
E

>
1
:
9 GeV
. The
uncertainties quoted are statistical and systematic.
m
X
s
(
GeV
c
2
)
Branching fraction
per 100 or
200 MeV
=c
2
(

10

6
)
0.6–0.7
0
:
1

0
:
1

0
:
0
0.7–0.8
1
:
0

0
:
2

0
:
1
0.8–0.9
21
:
8

0
:
4

0
:
8
0.9–1.0
17
:
4

0
:
4

0
:
6
1.0–1.1
3
:
4

0
:
3

0
:
5
1.1–1.2
5
:
5

0
:
5

0
:
4
1.2–1.3
18
:
4

0
:
7

1
:
2
1.3–1.4
22
:
5

0
:
8

1
:
5
1.4–1.5
24
:
9

1
:
0

2
:
0
1.5–1.6
21
:
5

1
:
2

1
:
8
1.6–1.7
23
:
0

1
:
4

2
:
3
1.7–1.8
24
:
6

1
:
6

3
:
0
1.8–1.9
25
:
4

2
:
2

5
:
0
1.9–2.0
17
:
9

2
:
5

3
:
4
2.0–2.2
24
:
0

2
:
4

4
:
7
2.2–2.4
16
:
2

3
:
8

5
:
7
2.4–2.6
14
:
1

4
:
8

7
:
3
2.6–2.8

3
:
5

6
:
4

6
:
1
0.6–2.8
329

19

48
EXCLUSIVE MEASUREMENTS OF
b
!
s
...
PHYSICAL REVIEW D
86,
052012 (2012)
052012-11
IX. FITS TO SPECTRUM MODELS
AND MOMENTS
Since we measure the hadronic mass spectrum in bins of
100 or
200 MeV
=c
2
, we are able to fit directly different
models of this spectrum to obtain the best-fit values of
different HQET parameters. We choose to fit two such
classes of models: the kinetic model, using an exponential
distribution function [
14
], and the shape function model,
also using an exponential distribution function [
13
]. The
choice of distribution function is not expected to have a
large impact on the values determined for the underlying
HQET parameters for each model, but the parameters
themselves are not immediately comparable between mod-
els (for example, the models are evaluated at different
energy scales).
To fit the measured spectrum to these models, we need to
take special account of the
K

ð
892
Þ
resonance, as the
models assume quark-hadron duality in their spectra.
Consequently, the models smooth over this resonance.
We fit a relativistic Breit-Wigner (RBW) [
32
] to the
K

ð
892
Þ
MC sample at the generator level to extract the
parameters of this curve. Fits to the transition point be-
tween the RBW curve of the
K

ð
892
Þ
resonance and
the remaining spectrum indicate a value close to
m
X
s
¼
1
:
17 GeV
=c
2
, which we take to be the location of this
transition. Furthermore, we require that the integral
of the RBW used to parametrize the
K

ð
892
Þ
region
(
m
X
s
<
1
:
17 GeV
=c
2
) be equivalent to the integral of this
region in the spectrum models. For the hadronic mass bin
containing the transition from the
K

ð
892
Þ
resonance to the
nonresonant-spectrum models (
1
:
1
<m
X
s
<
1
:
2 GeV
=c
2
),
we assign the value of the integral of the RBW up to the
transition point (
1
:
10
<m
X
s
<
1
:
17 GeV
=c
2
) plus the in-
tegral of the spectrum model from the transition point to
the bin boundary (
1
:
17
<m
X
s
<
1
:
20 GeV
=c
2
).
We perform a fit to the different spectrum models by
minimizing the quantity
2
¼
X
i;j
ð
PBF
th

PBF
exp
Þ
i
C

1
ij
ð
PBF
th

PBF
exp
Þ
j

i

j
;
(6)
where
PBF
th
and
PBF
exp
are the PBF predicted by the
spectrum model in the mass bin and the PBF we measured
in the mass bin, respectively. The matrix
C

1
ij
is the inverse
of the matrix of correlation coefficients between the un-
certainties on bins
i
and
j
, reported in the Appendix,
having taken the correlated systematic uncertainties and
uncorrelated statistical uncertainties into account. The

i
and

j
are the total uncertainties (statistical and systematic
added in quadrature) on the branching fractions determined
for bins
i
and
j
.
We find the best HQET parameter values based on the
measured hadronic mass spectrum for two quantities for
each model we fit. For the kinetic model, we fix the
chromomagnetic operator (

2
G
)to
0
:
35 GeV
2
and the ex-
pectation values of Darwin (
3
D
¼
0
:
2 GeV
3
) and spin-
orbit (
3
LS
¼
0
:
09 GeV
3
) terms; we allow
m
b
and

2

to take values between 4.45 and
4
:
75 GeV
=c
2
and 0.2 and
0
:
7 GeV
2
, respectively. We have points on the
m
b
-

2

plane at which the spectrum has been evaluated exactly.
These points are spaced every
0
:
05 GeV
=c
2
for
m
b
and
every
0
:
05 GeV
2
for

2

. We interpolate the spectrum mass
bin predictions between these points using
F
ð
m
b
;
2

Þ¼
A
þ
B
m
b

4
:
45
Þþ
C

2


0
:
2
Þ
þ
D
m
b

4
:
45
Þð

2


0
:
2
Þ
;
(7)
where we solve this equation for [
A
,
B
,
C
,
D
]. The values
4.45 and 0.2 in Eq. (
7
) are changed to the different values
for which we have exact spectra provided. This strategy
ensures continuity in the value of the spectrum predic-
tions for each hadronic mass bin across the
m
b
-

2

plane.
The shape function models use two variables to parame-
trize the spectrum,
b
and
[
13
], that may be converted to
values of
m
b
and

2

, evaluated at a single energy scale of
1.5 GeV. Similar to the kinetic model fits, we interpolate
between points on the
b
-
plane at which we have exact
spectrum predictions (for
2
:
0

b

5
:
0
in increments of
0.25, and
0
:
4


0
:
9 GeV
in increments of 0.05 GeV).
2
)
(GeV/c
s
X
m
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
6
) x10
2
PBF/(100 MeV/c
-20
-10
0
10
20
30
40
50
(a)
(GeV)
γ
E
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
6
) x10
s
X
in m
2
PBF/(100 MeV/c
-20
-10
0
10
20
30
40
50
(b)
FIG. 2 (color online). The partial branching fractions binned
in (a)
X
s
mass and (b) the corresponding
E

bins, with the
statistical and systematic uncertainties added in quadrature. The
current results (solid lines) and former
BABAR
results [
15
]
(dashed lines) are shown.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
052012 (2012)
052012-12