Measurement of
B
(
B
!
X
s
), the
B
!
X
s
photon energy spectrum,
and the direct
CP
asymmetry in
B
!
X
s
þ
d
decays
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
A. Palano,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
D. J. Asgeirsson,
7
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
A. Khan,
8
V. E. Blinov,
9
A. R. Buzykaev,
9
V. P. Druzhinin,
9
V. B. Golubev,
9
E. A. Kravchenko,
9
A. P. Onuchin,
9
S. I. Serednyakov,
9
Yu. I. Skovpen,
9
E. P. Solodov,
9
K. Yu. Todyshev,
9
A. N. Yushkov,
9
M. Bondioli,
10
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
H. Atmacan,
11
J. W. Gary,
11
F. Liu,
11
O. Long,
11
G. M. Vitug,
11
C. Campagnari,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
J. Kroseberg,
13
W. S. Lockman,
13
A. J. Martinez,
13
B. A. Schumm,
13
A. Seiden,
13
L. Winstrom,
13
D. S. Chao,
14
C. H. Cheng,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
A. Y. Rakitin,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
U. Nauenberg,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
*
W. H. Toki,
17
B. Spaan,
18
K. R. Schubert,
19
R. Schwierz,
19
D. Bernard,
20
M. Verderi,
20
P. J. Clark,
21
S. Playfer,
21
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
L. Piemontese,
22a
V. Santoro,
22a
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
23
P. Patteri,
23
I. M. Peruzzi,
23,
†
M. Piccolo,
23
M. Rama,
23
A. Zallo,
23
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,
25
V. Prasad,
25
C. L. Lee,
26
M. Morii,
26
A. J. Edwards,
27
A. Adametz,
28
U. Uwer,
28
H. M. Lacker,
29
T. Lueck,
29
P. D. Dauncey,
30
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
W. T. Meyer,
32
S. Prell,
32
A. E. Rubin,
32
A. V. Gritsan,
33
Z. J. Guo,
33
N. Arnaud,
34
M. Davier,
34
D. Derkach,
34
G. Grosdidier,
34
F. Le Diberder,
34
A. M. Lutz,
34
B. Malaescu,
34
P. Roudeau,
34
M. H. Schune,
34
A. Stocchi,
34
G. Wormser,
34
D. J. Lange,
35
D. M. Wright,
35
C. A. Chavez,
36
J. P. Coleman,
36
J. R. Fry,
36
E. Gabathuler,
36
D. E. Hutchcroft,
36
D. J. Payne,
36
C. Touramanis,
36
A. J. Bevan,
37
F. Di Lodovico,
37
R. Sacco,
37
M. Sigamani,
37
G. Cowan,
38
D. N. Brown,
39
C. L. Davis,
39
A. G. Denig,
40
M. Fritsch,
40
W. Gradl,
40
K. Griessinger,
40
A. Hafner,
40
E. Prencipe,
40
R. J. Barlow,
41,
‡
G. Jackson,
41
G. D. Lafferty,
41
E. Behn,
42
R. Cenci,
42
B. Hamilton,
42
A. Jawahery,
42
D. A. Roberts,
42
C. Dallapiccola,
43
R. Cowan,
44
D. Dujmic,
44
G. Sciolla,
44
R. Cheaib,
45
D. Lindemann,
45
P. M. Patel,
45,
§
S. H. Robertson,
45
P. Biassoni,
46a,46b
N. Neri,
46a
F. Palombo,
46a,46b
S. Stracka,
46a,46b
L. Cremaldi,
47
R. Godang,
47,
k
R. Kroeger,
47
P. Sonnek,
47
D. J. Summers,
47
X. Nguyen,
48
M. Simard,
48
P. Taras,
48
G. De Nardo,
49a,49b
D. Monorchio,
49a,49b
G. Onorato,
49a,49b
C. Sciacca,
49a,49b
M. Martinelli,
50
G. Raven,
50
C. P. Jessop,
51
K. Knoepfel,
51
J. M. LoSecco,
51
W. F. Wang,
51
K. Honscheid,
52
R. Kass,
52
J. Brau,
53
R. Frey,
53
M. Lu,
53
N. B. Sinev,
53
D. Strom,
53
E. Torrence,
53
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
R. Stroili,
54a,54b
S. Akar,
55
E. Ben-Haim,
55
M. Bomben,
55
G. R. Bonneaud,
55
H. Briand,
55
G. Calderini,
55
J. Chauveau,
55
O. Hamon,
55
Ph. Leruste,
55
G. Marchiori,
55
J. Ocariz,
55
S. Sitt,
55
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,
58
J. Olsen,
58
A. J. S. Smith,
58
A. V. Telnov,
58
F. Anulli,
59a
R. Faccini,
59a,59b
F. Ferrarotto,
59a,59b
F. Ferroni,
59a,59b
M. Gaspero,
59a,59b
L. Li Gioi,
59a
M. A. Mazzoni,
59a
G. Piredda,
59a
C. Bu
̈
nger,
60
O. Gru
̈
nberg,
60
T. Hartmann,
60
T. Leddig,
60
H. Schro
̈
der,
60,
§
C. Voss,
60
R. Waldi,
60
T. Adye,
61
E. O. Olaiya,
61
F. F. Wilson,
61
S. Emery,
62
G. Hamel de Monchenault,
62
G. Vasseur,
62
Ch. Ye
`
che,
62
D. Aston,
63
D. J. Bard,
63
R. Bartoldus,
63
P. Bechtle,
63
J. F. Benitez,
63
C. Cartaro,
63
M. R. Convery,
63
J. Dorfan,
63
G. P. Dubois-Felsmann,
63
W. Dunwoodie,
63
M. Ebert,
63
R. C. Field,
63
M. Franco Sevilla,
63
B. G. Fulsom,
63
A. M. Gabareen,
63
M. T. Graham,
63
P. Grenier,
63
C. Hast,
63
W. R. Innes,
63
M. H. Kelsey,
63
P. Kim,
63
M. L. Kocian,
63
D. W. G. S. Leith,
63
P. Lewis,
63
B. Lindquist,
63
S. Luitz,
63
V. Luth,
63
H. L. Lynch,
63
D. B. MacFarlane,
63
D. R. Muller,
63
H. Neal,
63
S. Nelson,
63
M. Perl,
63
T. Pulliam,
63
B. N. Ratcliff,
63
A. Roodman,
63
A. A. Salnikov,
63
R. H. Schindler,
63
A. Snyder,
63
D. Su,
63
M. K. Sullivan,
63
J. Va’vra,
63
A. P. Wagner,
63
W. J. Wisniewski,
63
M. Wittgen,
63
D. H. Wright,
63
H. W. Wulsin,
63
C. C. Young,
63
V. Ziegler,
63
W. Park,
64
M. V. Purohit,
64
R. M. White,
64
J. R. Wilson,
64
A. Randle-Conde,
65
S. J. Sekula,
65
M. Bellis,
66
P. R. Burchat,
66
T. S. Miyashita,
66
M. S. Alam,
67
J. A. Ernst,
67
R. Gorodeisky,
68
N. Guttman,
68
D. R. Peimer,
68
A. Soffer,
68
P. Lund,
69
S. M. Spanier,
69
J. L. Ritchie,
70
A. M. Ruland,
70
R. F. Schwitters,
70
B. C. Wray,
70
J. M. Izen,
71
X. C. Lou,
71
F. Bianchi,
72a,72b
D. Gamba,
72a,72b
S. Zambito,
72a,72b
L. Lanceri,
73a,73b
L. Vitale,
73a,73b
F. Martinez-Vidal,
74
A. Oyanguren,
74
H. Ahmed,
75
J. Albert,
75
Sw. Banerjee,
75
F. U. Bernlochner,
75
H. H. F. Choi,
75
G. J. King,
75
R. Kowalewski,
75
M. J. Lewczuk,
75
I. M. Nugent,
75
J. M. Roney,
75
PHYSICAL REVIEW D
86,
112008 (2012)
1550-7998
=
2012
=
86(11)
=
112008(33)
112008-1
Ó
2012 American Physical Society
R. J. Sobie,
75
N. Tasneem,
75
T. J. Gershon,
76
P. F. Harrison,
76
T. E. Latham,
76
E. M. T. Puccio,
76
H. R. Band,
77
S. Dasu,
77
Y. Pan,
77
R. Prepost,
77
and S. L. Wu
77
(
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
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
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
10
University of California at Irvine, Irvine, California 92697, USA
11
University of California at Riverside, Riverside, California 92521, USA
12
University of California at Santa Barbara, Santa Barbara, California 93106, USA
13
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California 91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, USA
18
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
19
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
20
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
21
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
23
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
25
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
26
Harvard University, Cambridge, Massachusetts 02138, USA
27
Harvey Mudd College, Claremont, California 91711, USA
28
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
29
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstr. 15, D-12489 Berlin, Germany
30
Imperial College London, London, SW7 2AZ, United Kingdom
31
University of Iowa, Iowa City, Iowa 52242, USA
32
Iowa State University, Ames, Iowa 50011-3160, USA
33
Johns Hopkins University, Baltimore, Maryland 21218, USA
34
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
35
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
36
University of Liverpool, Liverpool L69 7ZE, United Kingdom
37
Queen Mary, University of London, London, E1 4NS, United Kingdom
38
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
39
University of Louisville, Louisville, Kentucky 40292, USA
40
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
41
University of Manchester, Manchester M13 9PL, United Kingdom
42
University of Maryland, College Park, Maryland 20742, USA
43
University of Massachusetts, Amherst, Massachusetts 01003, USA
44
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
45
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
47
University of Mississippi, University, Mississippi 38677, USA
48
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
49a
INFN Sezione di Napoli, I-80126 Napoli, Italy
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
112008 (2012)
112008-2
49b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
50
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
51
University of Notre Dame, Notre Dame, Indiana 46556, USA
52
Ohio State University, Columbus, Ohio 43210, USA
53
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
55
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
58
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
60
Universita
̈
t Rostock, D-18051 Rostock, Germany
61
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
62
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
63
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
64
University of South Carolina, Columbia, South Carolina 29208, USA
65
Southern Methodist University, Dallas, Texas 75275, USA
66
Stanford University, Stanford, California 94305-4060, USA
67
State University of New York, Albany, New York 12222, USA
68
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
69
University of Tennessee, Knoxville, Tennessee 37996, USA
70
University of Texas at Austin, Austin, Texas 78712, USA
71
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
74
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
75
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
76
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
77
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 25 July 2012; published 28 December 2012)
The photon spectrum in
B
!
X
s
decay, where
X
s
is any strange hadronic state, is studied using a data
sample of
ð
382
:
8
4
:
2
Þ
10
6
e
þ
e
!
ð
4
S
Þ!
B
B
events collected by the
BABAR
experiment at the
PEP-II collider. The spectrum is used to measure the branching fraction
B
ð
B
!
X
s
Þ¼ð
3
:
21
0
:
15
0
:
29
0
:
08
Þ
10
4
and the first, second, and third moments
h
E
i¼
2
:
267
0
:
019
0
:
032
0
:
003 GeV
,
hð
E
h
E
iÞ
2
i¼
0
:
0484
0
:
0053
0
:
0077
0
:
0005 GeV
2
, and
hð
E
h
E
iÞ
3
i¼
0
:
0048
0
:
0011
0
:
0011
0
:
0004 GeV
3
, for the range
E
>
1
:
8 GeV
, where
E
is the photon energy in the
B
-meson rest
frame. Results are also presented for narrower
E
ranges. In addition, the direct
CP
asymmetry
A
CP
ð
B
!
X
s
þ
d
Þ
is measured to be
0
:
057
0
:
063
. The spectrum itself is also unfolded to the
B
-meson rest frame;
that is the frame in which theoretical predictions for its shape are made.
DOI:
10.1103/PhysRevD.86.112008
PACS numbers: 13.25.Hw, 11.30.Er, 12.15.Hh, 13.20.He
I. INTRODUCTION
In the standard model (SM) the electromagnetic radia-
tive decay of the
b
quark,
b
!
s
or
b
!
d
, proceeds at
leading order via the loop diagram shown in Fig.
1
result-
ing in a photon and a strange or down quark. The rate for
b
!
d
relative to
b
!
s
is suppressed by a factor
j
V
td
=V
ts
j
2
where
V
td
and
V
ts
are the Cabibbo-Kobayashi-
Maskawa (CKM) matrix elements. Interest in these decays
*
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.
MEASUREMENT OF
B
(
B
!
X
s
), THE
B
!
X
s
PHOTON
...
PHYSICAL REVIEW D
86,
112008 (2012)
112008-3
is motivated by the possibility that new heavy particles
might enter into the loop at leading order, causing signifi-
cant deviations from the predicted SM decay rates. There is
an extensive theoretical literature evaluating the effects of
new physics; some examples are given in Refs. [
1
–
8
]. New
physics can also significantly enhance the direct
CP
asym-
metry for
b
!
s
and
b
!
d
decay [
9
–
13
].
The hadronic processes corresponding to the underlying
b
!
s
and
b
!
d
decays are
B
!
X
s
and
B
!
X
d
.
Here
X
s
and
X
d
are any final state resulting from the
hadronization of the
s
q
or
d
q
quark-level state, respec-
tively, where
q
is the spectator from the
B
meson. These are
predominantly resonances, including
K
ð
892
Þ
,
K
1
ð
1270
Þ
(
X
s
)or
,
!
(
X
d
) and higher-mass states, but also non-
resonant multihadron final states. Theoretical predictions
for the rates of such exclusive decays suffer from large
uncertainties associated with the form factors of the me-
sons. In contrast, the inclusive hadronic rates
ð
B
!
X
s
Þ
and
ð
B
!
X
d
Þ
can be equated with the precisely calcu-
lable partonic rates
ð
b
!
s
Þ
and
ð
b
!
d
Þ
at the level
of a few percent [
14
] (quark-hadron duality), leading to
significantly more accurate predictions. At next-to-next-to-
leading order (up to four loops), the SM prediction for the
branching fraction is
B
ð
B
!
X
s
Þ¼ð
3
:
15
0
:
23
Þ
10
4
ð
E
>
1
:
6 GeV
Þ
[
15
]. Measurements of the inclusive
rates and asymmetries are therefore powerful probes of
physics beyond the standard model.
The shape of the photon energy spectrum is determined
by the strong interaction of the
b
quark within the
B
meson
and by the hadronization process. The Fermi motion of the
quark within the
B
meson and gluon radiation lead to an
E
distribution, in the
B
-meson rest frame, that is peaked in
the range 2.2 to 2.5 GeV, with a kinematic limit at
m
B
=
2
2
:
64 GeV
and a rapidly falling low-energy tail. The shape
is insensitive to non-SM physics [
16
,
17
] and can therefore
provide information about the strong interaction dynamics
of the
b
quark. Heavy quark effective theory (HQET)
[
14
,
18
–
22
] has been used most extensively to describe
these dynamics. The shape of the photon spectrum pro-
vides information on parameters of this theory related to
the mass and momentum of the
b
quark within the
B
meson; the definitions and hence the values of these pa-
rameters differ slightly between the ‘‘kinetic scheme’’ [
23
]
and the ‘‘shape function scheme’’ [
24
]. The Heavy Flavor
Averaging Group (HFAG) [
25
] has computed world aver-
age values of the parameters in the kinetic scheme based on
previous measurements of the inclusive semileptonic
B
-meson decay
B
!
X
c
‘
(
‘
¼
e
or
) and of
B
!
X
s
. HFAG has also translated those values to the shape
function scheme. These parameters can be used to reduce
the error in the extraction of the CKM matrix elements
j
V
cb
j
and
j
V
ub
j
from the inclusive semileptonic decays,
B
!
X
c
‘
and
B
!
X
u
‘
[
26
–
29
]. The
B
!
X
s
spectral
shape may also be compared to predictions in the frame-
work of dressed gluon exponentiation [
30
].
The inclusive decay
B
!
X
s
was first measured by the
CLEO Collaboration [
31
–
33
] and has been subsequently
studied by the ALEPH [
34
], Belle [
35
–
40
], and
BABAR
[
41
–
43
] collaborations. All measurements have been made
with
B
mesons produced in
e
þ
e
collisions. The theoreti-
cal predictions, which assume that the measurement is
inclusive so that quark-hadron duality holds, are made in
the
B
-meson rest frame for photons with
E
>
1
:
6 GeV
.
This means that ideally the measurement is made for all
X
s
final states and for all photons
E
>
1
:
6 GeV
. The experi-
mental challenge is to make the measurement as inclusive
as possible while suppressing backgrounds from other
processes producing photons or fake photons. The back-
grounds arise from continuum events (
e
þ
e
to
q
q
or
þ
pairs, where
q
¼
u
,
d
,
s
,or
c
), with the photon coming
from either a
0
or
decay or from initial-state radiation,
and from other
B
B
processes. The
B
B
background arises
predominantly from
0
or
decay but also from decays of
other light mesons, misreconstructed electrons, and had-
rons. It is strongly dependent on photon energy and rises
steeply at lower
E
. This places a practical lower limit for
E
on the experimental measurements; measurements have
been made to date with
E
>
1
:
7
, 1.8, and 1.9 GeV.
Three experimental techniques have been pursued. They
differ in the extent to which the final state is reconstructed.
The first is the fully inclusive technique in which neither
the
X
s
from the signal
B
nor the recoiling
B
meson is
reconstructed. (Charge conjugates are implied throughout
this paper.) The second is the semi-inclusive technique, in
which as many exclusive
X
s
final states as possible are
reconstructed and combined. The recoiling
B
meson is not
reconstructed. The third is the reconstructed recoil-
B
tech-
nique, in which inclusive
B
events are tagged by fully
reconstructing the recoiling
B
mesons in as many final
states as possible, but
X
s
is not reconstructed. Each of
the techniques has different strengths and weaknesses.
If the
X
s
is not reconstructed, the sample includes all
X
s
final states, but there are significant backgrounds from other
B
B
decays that must be estimated. It also includes
X
d
states
from the Cabbibo-suppressed
b
!
d
process. These can
be subtracted by assuming the
b
!
d
photon spectrum to
have a similar shape to the
b
!
s
photon spectrum, but
scaled by the ratio of the CKM elements
ðj
V
td
j
=
j
V
ts
jÞ
2
¼
0
:
044
0
:
003
. This is believed to be a valid assumption.
W
–
γ
s,d
b
u,c,t
FIG. 1. The leading order Feynman diagram for the electro-
magnetic radiative decay of the
b
quark in the SM.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
112008 (2012)
112008-4
Also, if the
X
s
is not reconstructed then the signal
B
cannot
be reconstructed. The
B
mesons have a small momentum in
the
ð
4
S
Þ
rest frame. As the
B
meson is not reconstructed,
the direction of the momentum is not known. This leads to a
Doppler smearing of the photon energy. This effect, along
with the detector resolution, must be corrected for or
unfolded in order to compare to predictions made in the
B
-meson rest frame. Quantities measured in the
ð
4
S
Þ
rest
frame, i.e., the center-of-mass (CM) frame, such as the
photon energy
E
are denoted with an asterisk.
No semi-inclusive measurement to date has recon-
structed more than about 60% of
X
s
decays, due to the
high combinatoric background for higher multiplicity
decays. Uncertainties in modeling the mix of
X
s
final states
result in significant efficiency uncertainties, as well as a
large uncertainty in correcting for the final states that are
not reconstructed. However, the reconstruction of the
X
s
implies that the signal
B
can be fully reconstructed, pro-
viding kinematic constraints to strongly suppress back-
grounds, allowing the measurement to be made directly
in the
B
-meson rest frame.
In the reconstructed recoil-
B
technique, only about 1%
of
B
’s can be fully reconstructed, due to the presence of
neutrinos in semileptonic decays and combinatoric back-
grounds to higher multiplicity decays. This severely limits
the statistical precision but does allow the measurement to
be made in the
B
-meson rest frame.
This paper reports a fully inclusive analysis that super-
sedes the previous
BABAR
fully inclusive result [
42
],
which is based on a smaller data sample. The
E
photon
spectrum is measured in
B
!
X
s
þ
d
decays. It is used to
measure the branching fraction
B
ð
B
!
X
s
Þ
for
E
>
1
:
8 GeV
and for narrower energy ranges. The effects of
detector resolution and Doppler smearing are unfolded to
provide an
E
photon spectrum in the
B
-meson rest frame
that can be used to fit to theoretical predictions for the
spectral shape. The unfolded spectrum is also used to
measure the first, second, and third moments, given,
respectively, by
E
1
¼h
E
i
;E
2
¼hð
E
h
E
iÞ
2
i
;
E
3
¼hð
E
h
E
iÞ
3
i
:
(1)
Although the SM predicts quite different asymmetries
for
B
!
X
s
and
B
!
X
d
, the
X
s
and
X
d
final states
cannot be distinguished in the fully inclusive technique.
Hence the
B
!
X
d
contribution to the fully inclusive
measurement cannot be corrected for, and only the combi-
nation
A
CP
(
B
!
X
s
þ
d
) can be measured:
A
CP
¼
ð
b
!
s
þ
b
!
d
Þ
ð
b
!
s
þ
b
!
d
Þ
ð
b
!
s
þ
b
!
d
Þþ
ð
b
!
s
þ
b
!
d
Þ
:
This asymmetry is approximately
10
6
in the SM, with
nearly exact cancellation of opposite asymmetries for
b
!
s
and
b
!
d
.
A
CP
ð
B
!
X
s
þ
d
Þ
and
A
CP
ð
B
!
X
s
Þ
are sensitive to different new physics scenarios [
11
]. Thus
measurements of this joint asymmetry complement those
of
A
CP
in
b
!
s
[
32
,
36
,
44
,
45
] to constrain new physics
models.
II. DATA SETS, DETECTOR, SIMULATION,
AND SIGNAL MODELS
The results presented are based on data samples of
e
þ
e
!
ð
4
S
Þ!
B
B
collisions collected with the
BABAR
detector at the PEP-II asymmetric-energy
e
þ
e
collider.
The on-resonance integrated luminosity is
347
:
1fb
1
,cor-
responding to
382
:
8
10
6
B
B
events. The continuum
background is estimated with an off-resonance data
sample of
36
:
4fb
1
collected 40 MeV below the
ð
4
S
Þ
resonance energy.
The
BABAR
detector is described in detail in Ref. [
46
].
Charged-particle momenta are measured with a 5-layer,
double-sided silicon vertex tracker (SVT) and a 40-layer
drift chamber (DCH) inside a 1.5-T superconducting sole-
noidal magnet. A high resolution total-absorption electro-
magnetic calorimeter (EMC), consisting of 6580 CsI(Tl)
crystals, is used to measure localized electromagnetic en-
ergy deposits and hence to identify photons and electrons.
The EMC energy resolution for high-energy photons in the
current measurement is about 2.6%. A ring-imaging
Cherenkov radiation detector (DIRC), aided by measure-
ments of ionization energy loss,
dE=dx
, in the SVT and
DCH, is used for particle identification (PID) of charged
particles. Muons are identified in the instrumented flux
return (IFR), which consists of 18 layers of steel inter-
leaved with single-gap resistive-plate chambers. For the
last 38% of the data collected,
1
=
3
of these chambers in the
central region of the detector were replaced by 12 layers of
limited-streamer tubes, interspersed with 6 layers of brass
(to increase absorption).
The
BABAR
Monte Carlo (MC) simulation, based on
GEANT4 [
47
], EVTGEN [
48
], and JETSET [
49
], is used
to generate samples of
B
þ
B
and
B
0
B
0
,
q
q
(where
q
is a
u
,
d
,
s
,or
c
quark),
þ
, and signal events (
B
B
events in
which at least one
B
decays to
X
s
). To model beam
backgrounds, each simulated event is overlaid with one
of a set of random background data events collected using a
periodic trigger.
The signal models used to determine selection efficien-
cies are based on QCD calculations of Refs. [
23
] (kinetic
scheme) and [
27
] (shape function scheme) and on an ear-
lier calculation by Kagan and Neubert [
9
] (‘‘KN’’). Each
model uses an ansatz for the shape that is constrained by
calculations of the first and second moments of the spectra.
The models approximate the hadronic mass (
m
X
s
) spec-
trum, which contains a number of overlapping resonances,
as a smooth distribution. This is reasonable, except at the
lowest masses, where the
K
ð
892
Þ
dominates the spectrum.
Hence the portion of the
m
X
s
spectrum below
1
:
1 GeV
=c
2
is replaced by a Breit-Wigner
K
ð
892
Þ
distribution,
MEASUREMENT OF
B
(
B
!
X
s
), THE
B
!
X
s
PHOTON
...
PHYSICAL REVIEW D
86,
112008 (2012)
112008-5
normalized to yield the same fraction of the integrated
spectrum. A particular signal model is defined as the
theoretical spectrum for specific HQET parameters, with
this at low
m
X
s
. The photon energy in the
B
-meson rest
frame is related to
m
X
s
via
m
2
X
s
¼
m
2
B
2
m
B
E
c
2
:
(2)
High-statistics MC signal samples for the non-
K
ð
892
Þ
part
of the spectrum are generated uniformly in
E
, separately
for each of the two
B
-meson charge states, and then
weighted according to any particular model of interest.
Monte Carlo samples of
B
þ
B
and
B
0
B
0
events are
needed for background evaluation. They are produced,
with nearly 3 times the effective luminosity of the data
sample, and include all known
B
decays, except for events
in which either
B
decays via
B
!
X
s
þ
d
. Monte Carlo
samples of continuum events (
q
q
, separately for
c
c
and for
the light quarks, and
þ
) are used to optimize the event-
selection criteria but are not otherwise relied upon.
III. ANALYSIS OVERVIEW
The event selection is described in detail in Sec.
IV
.
The analysis begins by selecting hadronic events. A high-
energy photon, characteristic of
B
!
X
s
decays, is
then required, while photons from
0
and
decays are
vetoed, reducing both the continuum and
B
B
backgrounds.
The background from continuum events is significantly
suppressed by charged lepton tagging (requiring a high-
momentum lepton, as would be expected from the semi-
leptonic decay of a
B
meson) and by exploiting the more
jetlike topology of the
q
q
or
þ
events compared to the
isotropic
B
B
decays.
The continuum MC simulation does not adequately
model the actual continuum background, primarily
because it omits QED and two-photon processes. Hence
the continuum background is estimated with off-resonance
data (Sec.
V
), which limits the statistical precision of the
signal yield measurement. However, the continuum simu-
lation is used to optimize some of the event-selection
criteria (which must be done without reference to actual
data). After preliminary event selection, which reduces the
unmodeled backgrounds, a simple scaling of the contin-
uum MC predictions adequately models the event yield
distributions relevant for optimization.
The lepton tagging and event topology criteria do not
substantially reduce the
B
B
background relative to the
signal, as these processes have similar characteristics.
The remaining
B
B
background is estimated using MC
simulation. There are several different
B
-meson decays
that contribute. Section
VI
describes how each significant
component is compared to an independent data control
sample and weighted to replicate those data. The uncer-
tainty in these weighting procedures is the dominant source
of systematic uncertainty.
After the event selection, the continuum and reweighted
B
B
backgrounds are subtracted from the on-resonance data
sample, resulting in the raw
B
!
X
s
þ
d
photon spectrum
(Sec.
VII
). The analysis was done ‘‘blind’’ in the range of
reconstructed photon energy
E
from 1.8 to 2.9 GeV; that
is, the data were not looked at until all selection require-
ments were set and the corrected backgrounds determined.
The choice of signal range is limited by high
B
B
back-
grounds at low
E
. The regions
1
:
53
<E
<
1
:
8 GeV
and
2
:
9
<E
<
3
:
5 GeV
are dominated by
B
B
and continuum
backgrounds, respectively. They provide control regions to
validate the background estimation for the signal region.
The raw spectrum is used to extract the direct
CP
asymmetry (Sec.
IX
) and the partial branching fraction
for
1
:
8
<E
<
2
:
8 GeV
(Sec.
X
). Finally, in Sec.
XI
the
effects of detector resolution and Doppler smearing are
unfolded in order to measure the shape of the photon
energy spectrum in the
B
-meson rest frame.
IV. EVENT SELECTION
The event selection was developed using MC samples of
signal and background events. The model used for signal
simulation, as defined in Sec.
II
, is based on a KN spectrum
with
m
b
¼
4
:
65 GeV
=c
2
.
A. Selection of hadronic events
For each event, the analysis considers good-quality
reconstructed tracks, which have momenta transverse to
the beam direction of at least
0
:
1 GeV
=c
and originate
from the vicinity of the interaction point (point of closest
approach within 10 cm along the beam axis and 1.5 cm in
the transverse plane), and EMC clusters of at least 30 MeV
in the laboratory frame. Hadronic events are selected by
requiring at least three reconstructed charged particles and
the normalized second Fox-Wolfram moment [
50
]
R
2
to be
less than 0.90. To reduce radiative Bhabha and two-photon
backgrounds, the number of charged particles plus half the
number of photons with laboratory-frame energy above
0.08 GeV is required to be greater than 4.5.
B. Requirements on the high-energy photon
The photon selection requires at least one photon can-
didate with
1
:
53
<E
<
3
:
5 GeV
in the event. A photon
candidate is a neutral EMC energy cluster with a lateral
moment consistent with that of a single photon [
51
]. The
latter requirement rejects most background from neutral
hadrons, which at these energies is dominated by antineu-
trons that annihilate in the EMC. The photon location is
assigned at a depth of 12.5 cm in the EMC, where it is
required to be isolated by 25 cm from any other energy
deposit (the lateral dimensions of the crystals are approxi-
mately 5 cm by 5 cm). The cluster must also be well
contained in the calorimeter (
0
:
74
<
cos
<
0
:
94
,
where
is the laboratory-frame polar angle with respect
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
112008 (2012)
112008-6
to the direction of the electron beam). A likelihood variable
ð
L
0
Þ
based on the energy profile of the EMC cluster is
used to suppress the contribution of
0
’s in which the two
daughter photons are not resolved. The requirement on
L
0
retains essentially all isolated high-energy photons. These
photon quality criteria are determined from studies of
photons in
events and of
p
’s (
p
’s) from
(
)
decays. (Antiprotons are used to estimate the detector
response to background antineutrons.)
High-energy photons that are consistent with originating
from
0
!
or
!
decays are vetoed if the other
0
or
daughter is found. For the
0
ð
Þ
veto, combina-
tions are formed of the high-energy photon with all other
photon candidates that have laboratory-frame energy
greater than 30 (230) MeV; it is required that the invariant
mass not lie within a window around the nominal
0
ð
Þ
mass,
115
ð
508
Þ
<m
<
155
ð
588
Þ
MeV
=c
2
.
The simulated distributions of signal and background at
this stage of the event selection are shown in Fig.
2(a)
. The
cumulative signal efficiency up to this point is approxi-
mately 50%, while 1.6% of continuum and 0.4% of
B
B
backgrounds are retained. The remaining continuum back-
ground arises predominantly from unvetoed
0
and
decays, or initial-state radiation in
q
q
events. The
B
B
background is also dominated by unvetoed decays of
0
ð
Þ
from
B
!
X
0
ð
Þ
but also has a significant contri-
bution from misidentified electrons, and smaller compo-
nents from antineutrons and radiative
!
and
0
decays.
C. Lepton tagging
About 20% of
B
mesons decay semileptonically to either
an electron or muon, predominantly via
B
!
X
c
‘
.An
additional 4% of
B
decays result in an electron or muon via
B
!
X
c
. Since the tagging lepton comes from the
recoiling
B
meson, this requirement does not compromise
the inclusiveness of the
B
!
X
s
selection.
Electrons are identified with a likelihood algorithm
that incorporates properties of the deposited energy
and shower shapes of the EMC clusters, the Cherenkov
angles associated with th
e charged particle passing
through the DIRC, and the
dE=dx
energy loss of the
track. Muons are identified using a neural-network
selector containing variables that discriminate between
muons and electrons, primarily through differences in
EMC energy deposition, and those which discriminate
between muons and hadrons, mainly through differences
in IFR signatures.
The left plots of Fig.
3
show that leptons from hadronic
decays in continuum events tend to be at lower momentum.
Hence the tagging lepton is required to have momentum
p
e;
>
1
:
05 GeV
=c
. As seen in the right plots of Fig.
3
,
additionally requiring the cosine of the CM-frame angle
between the lepton and the high-energy photon
cos
‘
>
0
:
7
removes more continuum background, in which the
lepton and photon candidates tend to be back to back. The
peak at
cos
‘
1
:
0
for electrons in continuum events
arises predominantly from
0
ð
Þ!
decays in which
one photon satisfies the high-energy photon requirements
and the other converts to an
e
þ
e
pair. The peaks at
cos
‘
1
:
0
for the
B
B
background arise from
B
decays
in which the photon and lepton come from the same
B
.A
similar smaller peak for muon tags in signal events is due
to pions faking the muon signature. These tag selection
requirements are designed as a loose preselection; a more
stringent tag discrimination is achieved by the multivariate
selectors described in Sec.
IV D
.
The presence of a relatively high-energy neutrino in
semileptonic
B
decays is exploited by requiring the miss-
ing energy of the event (
E
miss
) to be greater than 0.7 GeV.
The lepton-tag requirements retain approximately 12% of
signal and
B
B
background events after the photon selec-
tion, while retaining only 2.2% of continuum backgrounds.
* (GeV)
γ
E
1.6
1.8
2
2.2
2.4
2.6
2.8
3
Events / 100 MeV
3
10
4
10
5
10
6
10
(a)
* (GeV)
γ
E
* (GeV)
γ
E
1.6
1.8
2
2.2
2.4
2.6
2.8
3
Events / 100 MeV
0
2
4
6
8
10
12
3
10
×
Continuum MC
MC
B
B
Signal MC
(b)
FIG. 2 (color online). Estimated signal and background yields vs photon energy in the CM frame based on MC simulation, at two
stages of the event selection: (a) after requiring an unvetoed high-energy photon (logarithmic scale); (b) after all selection requirements
(linear scale). The three contributions are shown cumulatively. The signal distribution is for a KN model with
m
b
¼
4
:
65 GeV
=c
2
,
while the continuum distribution has been scaled as described in Sec.
III
.
MEASUREMENT OF
B
(
B
!
X
s
), THE
B
!
X
s
PHOTON
...
PHYSICAL REVIEW D
86,
112008 (2012)
112008-7
D. Event topology requirement
As the continuum backgrounds are different for electron
and muon tags, each sample is divided according to the tag.
For each lepton type the continuum backgrounds are then
further suppressed by combining the
p
e;
and
cos
‘
for
the leptons with event topology variables into a neural-
network (NN) discriminant.
Several alternative choices of input variables were con-
sidered. For each alternative, the electron and muon NN’s
are trained, and the requirements on their output parameter
optimized (see below). The choice of variables is designed
to minimize the total error on the branching fraction and
spectral moment measurements, based on combining in
quadrature preliminary estimates of statistical, systematic,
and model-dependence errors. The latter refers to a varia-
tion of the event-selection efficiency with the choice of MC
spectrum (‘‘model’’ in the sense of Sec.
II
) used to compute
it. It arises primarily from the increase in efficiency as a
function of
E
; the stronger this trend, the larger the
model-dependence uncertainty. The selection strategy
aims for best signal precision, while minimizing the de-
pendence of efficiency on
E
. Since the backgrounds rise
sharply as
E
decreases, it is impossible to completely
eliminate the
E
dependence. Of several multivariate dis-
criminants (with different sets of input variables) that were
found to give approximately the same signal precision, the
one resulting in the least
E
dependence was chosen.
The eight topology variables chosen for the NN include
R
0
2
=R
2
, where
R
0
2
is the normalized second Fox-Wolfram
moment calculated in the frame recoiling against the
photon, which for ISR events is the
q
q
rest frame. Also
included are three momentum-weighted polar angle
moments,
L
j
=L
0
,
j
¼
1
, 2, 3, where
L
j
¼
X
i
j
p
i
jj
cos
i
j
j
:
(3)
Here
p
i
and
cos
i
are the momentum and angle, respec-
tively, of the
i
th reconstructed particle with respect to the
high-energy photon axis in the recoil frame. Summation
over
i
includes every reconstructed charged and neutral
CM Electron Momentum (GeV/c)
0
0.5
1
1.5
2
2.5
3
0
200
400
600
800
1000
1200
Signal MC
MC
B
B
Continuum MC
(a)
)
γ
* (e,
θ
cos
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
0
200
400
600
800
1000
1200
1400
1600
1800
(b)
CM Muon Momentum (GeV/c)
0
0.5
1
1.5
2
2.5
3
0
100
200
300
400
500
600
(c)
)
γ
,
μ
* (
θ
cos
-1
-0.8 -0.6 -0.4 -0.2
0
0.2
0.4
0.6
0.8
1
0
200
400
600
800
1000
1200
1400
1600
(d)
FIG. 3 (color online). Lepton distributions from MC simulation, after the photon selection requirements but before applying lepton-
tag and NN criteria. Plots (a) and (b) are for electron tags, plots (c) and (d) for muon tags. Plots (a) and (c) show the CM-frame
momentum distributions, with vertical lines indicating the minimum selection requirements. Plots (b) and (d) show the cosine of the
CM angle between the lepton and the high-energy photon, after applying the momentum criteria; the vertical lines show the minimum
requirement on this quantity. The signal (black dots) is from a KN model with
m
b
¼
4
:
65 GeV
=c
2
. The
B
B
background (solid blue
histogram) and continuum background (dashed red) are from the MC simulations. Each distribution is separately normalized to best
illustrate its behavior.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
112008 (2012)
112008-8
particle except the high-energy photon. The last four to-
pology variables are derived from the eigenvalues
ð
1
;
2
;
3
Þ
and eigenvectors of the momentum tensor [
52
]
P
nm
¼
P
i
p
n
i
p
m
i
=
j
p
i
j
P
i
j
p
i
j
;
(4)
where
p
n
i
is the
n
th component of the
i
th reconstructed
particle’s 3-momentum in the recoil frame. The high-
energy photon candidate is excluded. The derived quanti-
ties used as NN inputs are
1
d
¼
max
ð
1
;
2
;
3
Þ
;
2
d
¼
1
2
þ
2
3
þ
3
1
;
3
d
¼
1
2
3
;V
1
d
z
¼
z
component of
V
max
;
where
V
max
is the eigenvector associated with the largest
eigenvalue and
z
is the electron beam direction.
The electron and muon NN’s are trained with MC
samples of continuum and signal (KN model with
m
b
¼
4
:
65 GeV
=c
2
) events that contain a photon with energy in
the range
1
:
9
<E
<
2
:
7 GeV
. The
B
B
background simu-
lation sample is excluded from the training because this
sample is used for background subtraction and is topologi-
cally very similar to the signal. Training with background
and signal samples normalized to the expected event yields
at this stage of the event selection provides slightly better
statistical precision for signal (see Sec.
IV E
) than does
training with background and signal samples with the same
normalization. For a NN with equally normalized training
samples, the NN output distributions would peak toward
0 and 1, respectively, for backgroundlike and signallike
events. Neural network training based on expected event
yields, however, produces output distributions that are
qualitatively different, as demonstrated in Fig.
4
, which
shows the output distributions for signal and continuum
events, separated according to lepton tag. Events with an
electron (muon) tag are required to have a NN output
greater than 0.53 (0.47). This selection accepts 42% of
signal events (
1
:
8
<E
<
2
:
8 GeV
) that have passed the
photon and lepton selection requirements while retaining
1.7% of continuum and 27% of
B
B
background. Events
with more than one photon candidate after the NN require-
ment are discarded (0.16% of signal events).
E. Optimization of the event selection
The optimization for the selection criteria was per-
formed iteratively on five variables: the two NN outputs
(Sec.
IV D
), the minimum energy of the lower energy
photon in the
0
and
vetoes (Sec.
IV B
), and the missing
energy (Sec.
IV C
). The figure of merit (FOM) is the
anticipated ratio of the signal yield to its statistical uncer-
tainty for
E
between 1.8 and 2.8 GeV, taking into account
the limited size of the off-resonance sample used for con-
tinuum subtraction:
Statistical
FOM
¼
S
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
S
þ
B
þð
C
=f
off
Þ
p
:
(5)
Here S, B, and C are the estimated yields in the
on-resonance data of signal,
B
B
background, and
continuum background events, respectively (after event
selection), based on MC simulation, and
f
off
is the fra-
ction of total luminosity accumulated off resonance,
L
off
=
ð
L
on
þ
L
off
Þ¼
0
:
0949
.
The selection criterion for each of the five variables was
optimized in turn, while holding the criteria for the others
fixed, and the process repeated until a stable optimal
selection was found.
F. Overall signal efficiency
The probability that a signal event is observed and
survives the event-selection process is approximately
2.5%, while only 0.0005% of the continuum and 0.013%
of the
B
B
backgrounds remain in the sample. Figure
2(b)
shows the expected signal and background distributions
after all selection criteria.
NN Output for e-tagged Events
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Signal MC
Continuum MC
(a)
-tagged Events
μ
NN Output for
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0
0.05
0.1
0.15
0.2
0.25
0.3
Signal MC
Continuum MC
(b)
FIG. 4 (color online). The distribution of the NN output, from MC simulation after the photon selection and lepton-tag requirements,
for (a) electron-tagged events and (b) muon-tagged events. The vertical lines show the minimum requirement on this quantity. The
signal is from a KN model with
m
b
¼
4
:
65 GeV
=c
2
. The continuum is from the MC simulation. Normalizations are arbitrary.
MEASUREMENT OF
B
(
B
!
X
s
), THE
B
!
X
s
PHOTON
...
PHYSICAL REVIEW D
86,
112008 (2012)
112008-9
The photon spectrum is measured in bins of recon-
structed
E
. Hence the signal efficiency is presented here
in terms of that quantity. The selection efficiency for MC
signal events, i.e., the fraction of the events in a given range
of
E
that survive all the selection criteria described above,
is calculated in 100-MeV bins of reconstructed
E
and also
for wide ranges (such as 1.8–2.8 GeV). The overall signal
efficiency also includes an acceptance component, the
probability for the photon to enter the fiducial region of
the EMC. This is available only as a function of true
E
(the photon energy before resolution smearing), since
reconstructed
E
is defined only for accepted photons.
However, because the variation of the acceptance effi-
ciency is weak, it can be combined with the selection
efficiency to provide an overall efficiency in bins or ranges
of reconstructed
E
. Figure
5
shows the result.
V. CONTINUUM BACKGROUNDS
The continuum background is estimated using off-
resonance data scaled according to the ratio of the lumi-
nosity times the
e
þ
e
!
q
q
cross section for the on- and
off-resonance data sets. Since continuum data are collected
40 MeV below the
ð
4
S
Þ
resonance, the center-of-mass
energy is 0.4% lower than the center-of-mass energies for a
typical
B
B
event. In order to account for this difference, the
energy of a high-energy photon candidate in off-resonance
data is scaled by
m
ð
4
S
Þ
=
ffiffiffiffiffiffiffi
s
off
p
, where
m
ð
4
S
Þ
and
ffiffiffiffiffiffiffi
s
off
p
are
the mass of the
ð
4
S
Þ
system and the center-of-mass
energy of the off-resonance data event, respectively.
VI.
B
B
BACKGROUNDS
A. Overview
The background from nonsignal
B
B
events arises either
from real photons from the decays of low-mass mesons
(with
0
and
responsible for most of the background) or
from other particles faking photons.
The
B
B
background remaining after event selection is
estimated using the MC simulation as an approximate
starting point. Various control samples are then used to
correct most of the significant components of this back-
ground according to data/MC yield ratios measured as a
function of appropriate kinematic variables. The correc-
tions are applied in 100-MeV bins of
E
. The uncertainties
of these factors (along with small uncertainties from MC
statistics) constitute the
B
B
systematic errors. These can
be highly correlated between
E
bins. The remainder of
Sec.
VI
details the individual corrections, as well as a more
global correction to the lepton-tagging efficiency.
The event simulation tells us the true (generated)
particle that most closely corresponds to the reconstructed
high-energy photon candidate. This allows the categoriza-
tion of selected events according to the origin of that
candidate. Table
I
lists the MC fractions by category and
the corresponding correction factors averaged over two
broad
E
intervals, covering the
B
B
control region and
the signal region.
B.
0
and
corrections
About 80% of MC-predicted
B
B
background in the
signal region arises from
B
!
X
0
ð
Þ
with
0
ð
Þ!
. This contribution is dominated by highly asymmetric
0
ð
Þ
decays, in which a second photon has much lower
energy than the selected high-energy photon. To correct
MC predictions for these inclusive
B
decays in the phase
space region selected for the
B
!
X
s
analysis, inclusive
0
and
samples are defined by applying the same selec-
tion criteria but omitting the
0
and
vetoes. To enhance
statistics for these studies the minimum requirement on
E
is relaxed from 1.53 to 1.03 GeV, and for
’s the minimum
laboratory-frame energy for the low-energy photon is
relaxed from 230 to 75 MeV.
1. Scaling of MC
0
and
yields to data
The yields of
0
ð
Þ
are measured in bins of
E
0
ð
Þ
by
fitting the distributions of
mass (
m
) in simulated
B
B
background, on-resonance data and off-resonance data.
The signal shape for
0
is the sum of two Gaussian
functions (
G
1
and
G
2
) with different means (
1
and
2
)
and rms widths (
1
and
2
) plus a low-mass power-law tail
(parameters
p
and
):
f
ð
m
Þ¼
8
<
:
A
½
f
1
G
1
ð
m
Þþð
1
f
1
Þ
G
2
ð
m
Þ
m
m
0
B
½ð
p
1
=
Þ
=
ð
m
0
m
þ
p
1
=
Þ
p
m<m
0
;
(6)
where
m
0
ð
1
1
Þ
,
A
, and
f
1
govern the normal-
izations of the two Gaussian functions, and
B
is set by
requiring continuity at
m
¼
m
0
. The signal shape for
is a
(GeV)
γ
*
E
1.6
1.8
2
2.2
2.4
2.6
2.8
Efficiency
0
0.005
0.01
0.015
0.02
0.025
0.03
FIG. 5. Combined acceptance and event-selection efficiency
vs measured
E
for a KN model with
m
b
¼
4
:
65 GeV
=c
2
.
Uncertainties are from MC statistics. Corresponding efficiencies
for a kinetic scheme model with parameters set to HFAG world
average values are within 1% (relative) of the values plotted.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
112008 (2012)
112008-10