Precision Measurement of the
B
!
X
s
Photon Energy Spectrum, Branching Fraction,
and Direct
CP
Asymmetry
A
CP
ð
B
!
X
s
þ
d
Þ
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,54b
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,
556a,56b
E. Manoni,
556a,56b
S. Pacetti,
556a,56b
A. Rossi,
556a,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
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
PRL
109,
191801 (2012)
PHYSICAL REVIEW LETTERS
week ending
9 NOVEMBER 2012
0031-9007
=
12
=
109(19)
=
191801(8)
191801-1
Ó
2012 American Physical Society
R. Kowalewski,
75
M. J. Lewczuk,
75
I. M. Nugent,
75
J. M. Roney,
75
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
PRL
109,
191801 (2012)
PHYSICAL REVIEW LETTERS
week ending
9 NOVEMBER 2012
191801-2
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
556a
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 12 July 2012; published 9 November 2012)
The photon spectrum in the inclusive electromagnetic radiative decays of the
B
meson,
B
!
X
s
plus
B
!
X
d
, is studied using a data sample of
ð
382
:
8
4
:
2
Þ
10
6
ð
4
S
Þ!
B
B
decays collected by the
BABAR
experiment at SLAC. The spectrum is used to extract the branching fraction
B
ð
B
!
X
s
Þ¼
ð
3
:
21
0
:
33
Þ
10
4
for
E
>
1
:
8 GeV
and the direct
CP
asymmetry
A
CP
ð
B
!
X
s
þ
d
Þ¼
0
:
057
0
:
063
. The effects of detector resolution and Doppler smearing are unfolded to measure the
photon energy spectrum in the
B
meson rest frame.
DOI:
10.1103/PhysRevLett.109.191801
PACS numbers: 13.20.He, 11.30.Er, 12.15.Hh
In the standard model (SM), the electromagnetic
radiative decays of the
b
quark,
b
!
s
and
b
!
d
,
proceed via a loop diagram at leading order. A wide
variety of new physics (NP) scenarios such as supersym-
metry may cause new contributions to the loop [
1
–
8
]at
the same order as the SM, resulting in significant devia-
tions for both the branching fractions and the direct
CP
asymmetry
A
CP
¼
½
b
!ð
s
þ
d
Þ
½
b
!ð
s
þ
d
Þ
½
b
!ð
s
þ
d
Þ
þ
½
b
!ð
s
þ
d
Þ
:
Inclusive hadronic branching fractions (BF)
B
ð
B
!
X
s
Þ
and
B
ð
B
!
X
d
Þ
can be equated with the perturbatively
calculable partonic BF
B
ð
b
!
s
Þ
and
B
ð
b
!
d
Þ
at the level of a few percent [
9
], allowing theoretically
clean predictions. At next-to-next-to-leading-order
(four-loop), the SM calculation gives
B
ð
B
!
X
s
Þ¼
ð
3
:
15
0
:
23
Þ
10
4
(
E
>
1
:
6 GeV
)[
10
], where
E
is
the photon energy measured in the rest frame of the
B
meson.
B
ð
B
!
X
d
Þ
is suppressed by a factor of
j
V
td
=V
ts
j
2
0
:
04
, where
V
ij
are the elements of
the Cabbibo-Kobayashi-Mashawa (CKM) quark-mixing
PRL
109,
191801 (2012)
PHYSICAL REVIEW LETTERS
week ending
9 NOVEMBER 2012
191801-3
matrix. NP with nonminimal flavor violation can also
significantly enhance
A
CP
[
11
], which is approximately
10
6
in the SM [
12
–
14
]. Consequently the precision
measurement of these decays has long been identified as
important in the search for NP. They are central to the
program of the future Super
B
factories [
15
–
17
], which
will probe NP mass scales up to 100 TeV.
In this letter, new precise measurements of
B
ð
B
!
X
s
Þ
and
A
CP
are presented. The analysis has been significantly
improved from our previous result [
18
], which it super-
sedes. In addition, the shape of the photon energy spectrum
is measured in the
B
meson rest frame. It is insensitive to
NP [
19
] but can be used to determine the heavy quark
expansion parameters
m
b
and
2
[
20
,
21
], related to the
mass and momentum of the
b
quark within the
B
meson.
These parameters are used to reduce the uncertainty in
the extraction of the CKM elements
j
V
cb
j
and
j
V
ub
j
from
semileptonic
B
meson decays [
22
–
25
].
This Letter summarizes a fully inclusive analysis of
B
!
X
s
decays collected from
e
þ
e
!
ð
4
S
Þ!
B
B
events. Full details are given in Ref. [
26
]. The photon
from the decay of one
B
meson is measured, but
X
s
is
not reconstructed. This avoids large uncertainties from
the modeling of the
X
s
system, at the cost of large back-
grounds, which need to be strongly suppressed. The prin-
cipal backgrounds are from other
B
B
decays containing a
high-energy photon and from continuum
q
q
(
q
¼
udsc
)
and
þ
events. The continuum background, including
a contribution from initial-state radiation, is suppressed
principally by requiring a high-momentum charged lepton
(‘‘lepton tag’’) from the nonsignal
B
decay, and also by
discriminating against events with a more jetlike topology.
The
B
B
background to high-energy photons, dominated
by
0
and
decays, is reduced by vetoing reconstructed
0
or
mesons. The residual continuum background is
subtracted using off-resonance data collected at a center-
of-mass (c.m.) energy 40 MeV below the
ð
4
S
Þ
, while
the remaining
B
B
background is estimated using a
Monte Carlo (MC) simulation that has been corrected
using data control samples. The photon energy spectrum
is measured in the
ð
4
S
Þ
rest frame. Quantities measured
in this frame are denoted by an asterisk, e.g.,
E
.
The data were collected with the
BABAR
detector [
27
]
at the PEP-II asymmetric-energy
e
þ
e
collider. The on-
resonance integrated luminosity is
347
:
1fb
1
, correspond-
ing to
ð
382
:
8
4
:
2
Þ
10
6
B
B
events. Additionally,
36
:
4fb
1
of off-resonance data are used. The
BABAR
MC simulation, based on
GEANT4
[
28
],
EVTGEN
[
29
], and
JETSET
[
30
], is used to generate samples of
B
þ
B
and
B
0
B
0
(excluding signal channels),
q
q
,
þ
, and signal
events. The signal models used to compute efficiencies are
based on QCD calculations in the ‘‘kinetic scheme’’ [
20
],
‘‘shape function scheme’’ [
21
], and in an earlier model
[
19
]. These calculations approximate the
X
s
resonance
structure with a smooth distribution in the hadronic mass
m
X
s
. The portion of the
m
X
s
spectrum below
1
:
1 GeV
=c
2
,
where the
K
ð
892
Þ
dominates, is replaced by a Breit-
Wigner
K
ð
892
Þ
distribution. The analysis is performed
‘‘blind’’ in the range
1
:
8
<E
<
2
:
9 GeV
; that is, the
on-resonance data are not examined until all selection
requirements are finalized and the corrected
B
B
back-
grounds determined. The signal range is limited by large
B
B
backgrounds at low
E
.
The event selection begins by requiring at least one
photon candidate with
1
:
53
<E
<
3
:
50 GeV
. A photon
candidate is an electromagnetic calorimeter (EMC) energy
cluster with a lateral profile consistent with that of a
single photon, isolated by 25 cm from any other cluster,
and well contained in the calorimeter. Photons that
are consistent with originating from an identifiable
0
or
!
decay are vetoed. Hadronic events are selected
by requiring at least three reconstructed charged particles
and the normalized second Fox-Wolfram moment
R
2
to be
less than 0.9. To reduce radiative Bhabha and two-photon
backgrounds, the number of charged particles plus half
the number of photons with energy above 0.08 GeV is
required to be at least 4.5.
About 20% of
B
mesons decay semileptonically to either
e
or
. Leptons from these decays are emitted isotropically
and tend to have higher momentum than the continuum
background in which the lepton and photon candidates
also tend to be anticollinear. To suppress the continuum
background a tagging lepton (
‘
¼
e
,
) is required to have
momentum
p
l
>
1
:
05 GeV
=c
and an angle relative to
the photon
cos
‘
>
0
:
7
. The tag requirement does not
compromise the inclusiveness of the
B
!
X
s
selection
since the lepton comes from the recoiling
B
meson. The
presence of a relatively high-energy neutrino in semilep-
tonic
B
decays is used to further suppress the background
by requiring the missing energy of the event to satisfy
E
miss
>
0
:
7 GeV
.
The sample is separated into electron and muon tags.
For each,
p
l
and
cos
‘
are then combined in a neural
network (NN) with eight event-shape variables that exploit
the difference in topology between isotropic
B
B
events and
jetlike continuum events. The NN is trained to separate
signal-like events from continuum background using MC
samples. The
B
B
background sample is excluded from the
training because it is used for background subtraction and
is topologically similar to the signal. The NN is validated
with a
B
!
X
s
0
data sample.
The selection criteria are optimized for statistical preci-
sion. This was done iteratively for five variables: the two
NN outputs, the energies of the lower-energy photon in
the
0
and
vetoes, and
E
miss
. The signal efficiency for
the entire selection depends on
E
, falling at lower values.
This effect is significantly reduced from our previous
analysis, lessening the uncertainty due to the assumed
signal model (‘‘model-dependence’’). The efficiency inte-
grated over the range
1
:
8
<E
<
2
:
8 GeV
is about 2.5%,
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while only 0.0005% of the continuum and 0.013% of the
B
B
background remain in the sample.
The remaining continuum background is estimated with
off-resonance data scaled to the on-resonance luminosity
and adjusted to account for the 40 MeV c.m. energy
difference. The
B
B
background is estimated with the
B
B
MC sample. It consists predominantly of photons originat-
ing from
0
or
decays (
80%
in the signal region),
electrons (
10%
) that are misreconstructed, not identi-
fied, or undergo hard bremsstrahlung,
!
and
0
decays
(
4%
), and
n
’s (
2%
) that fake photons by annihilating
in the EMC. Each of the significant components is cor-
rected by comparison with data control samples.
The
0
and
background simulations are compared
to data using the same selection criteria as for
B
!
X
s
but removing the
0
and
vetos. For this comparison the
high-energy photon requirement is relaxed to
E
>
1
:
03 GeV
to increase the size of the sample. The yields
of
0
and
are measured in bins of
E
0
ð
Þ
by fitting the
mass distributions in on-resonance data, off-resonance
data, and
B
B
simulation. Correction factors to the
0
and
components of the
B
B
simulation are derived from these
yields. An additional correction is applied to account for
data-MC differences in the low-energy photon detection
efficiency. This has an opposite effect on the control-
sample
0
and
selection than on the standard event
selection, where finding a
0
or
results in the event
being vetoed.
As an antineutron control sample could not be isolated,
this source of
B
B
background is corrected by comparing
simulation to data for inclusive antiproton yields in
B
decay and, using
!
p
þ
samples, for the EMC response
to
p
’s. The misreconstructed electron background is
measured using
B
!
XJ=
c
ð
e
þ
e
Þ
data. This sample
closely models the particle multiplicity in
B
!
X
s
events.
Bremsstrahlung in the detector is reliably simulated by
GEANT4
, so no correction is necessary. The small contribu-
tions from
!
and
0
decays are corrected in bins of
E
using
inclusive
B
decay data. Nearly all of the tagging leptons
arise from
B
!
X
c
‘
. The yield of such events in the
simulation is corrected as a function of lepton momentum
according to previous
BABAR
measurements [
31
,
32
].
The complete
B
B
background estimation incorporates
the correction factors and uncertainties and includes
correlations between
E
bins. The dominant uncertainties
originate from the
0
,
, and misreconstructed electron
corrections.
Figure
1
shows the measured
E
spectrum after subtract-
ing both continuum and
B
B
backgrounds. The systematic
errors are due to the
B
B
subtraction uncertainty. The region
1
:
53
<E
<
1
:
80 GeV
is dominated by
B
B
background,
while the higher-energy range
2
:
9
<E
<
3
:
5 GeV
con-
tains only continuum background. These regions are used
to validate the background subtraction procedure. In the
higher-energy range there are
100
138
ð
stat
Þ
events.
In the lower-energy region there are
1252
272
ð
stat
Þ
841
ð
syst
Þ
events. Allowing for an average of 275 signal
events from a range of plausible signal models, and for
correlations between the bins, the latter result is consistent
with zero to within 1 standard deviation (
1
).
To extract BFs and the shape of the spectrum, it is
necessary to first correct for efficiency. Theoretical predic-
tions are made for the true
E
in the
B
meson rest frame,
whereas the
E
is measured in the
ð
4
S
Þ
frame. Hence it is
also necessary to correct for the asymmetric EMC resolu-
tion and the Doppler smearing due to the motion of the
B
meson in the
ð
4
S
Þ
rest frame. The efficiency and smearing
corrections depend upon the assumed signal shape due to
the effects of bin migration. In both the kinetic and shape
function schemes, this shape is parametrized by
m
b
and
2
.
The Heavy Flavor Averaging Group (HFAG) [
33
] has
extracted values and uncertainties in the kinetic scheme
by fitting moments of inclusive distributions in
B
!
X
c
‘
decays and previous
B
!
X
s
measurements, and has also
translated them to the shape function scheme. These results
define the nominal signal model (kinetic scheme) used for
the BF measurement, along with a model-dependence un-
certainty (kinetic and shape function schemes). To provide
an independent measurement of the shape of the spectrum,
the measured spectrum is unfolded using an iterative
technique that reduces sensitivity to the signal model. In
this case the initial signal model and model-dependence
uncertainty are based on the data rather than the HFAG
parameters. The effects of efficiency and smearing cancel in
the
A
CP
measurement so it is extracted directly from the
measured
E
yield separated by lepton tag charge.
The BF is computed from
B
ð
B
!
X
s
þ
d
Þ¼
S
=
ð
2
N
B
B
sig
Þ
;
where
S
is the signal yield integrated over the
E
ranges
1.8, 1.9, 2.0 to 2.8 GeV,
sig
is the signal efficiency, and
1.5
2
2.5
3
3.5
0
500
1000
1500
* (GeV)
γ
E
Events/0.1 GeV
B
B
control
Continuum
control
FIG. 1 (color online). The measured
E
photon energy spec-
trum after background subtraction, uncorrected for efficiency
and resolution smearing. The inner error bars are statistical only,
while the outer include systematic errors added in quadrature.
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N
B
B
is the number of
B
B
pairs in the sample. The factor
,
which is close to unity, corrects for resolution and Doppler
smearing and is computed with the nominal signal model.
The model-dependence errors on the BF associated with
the efficiency and the smearing correction are fully
correlated. The results for the three energy ranges are
given in Table
I
. The BFs have been corrected by a factor
1
=
ð
1
þðj
V
td
j
=
j
V
ts
jÞ
2
Þ¼
0
:
958
0
:
003
[
34
] to remove the
contribution from
b
!
d
. The most significant systematic
error is from the corrections to the
B
B
background
simulation, which in the range
1
:
8 GeV
<E
<
2
:
8 GeV
contributes 7.8% to a total systematic uncertainty of 9.0%.
Additional contributions added in quadrature, all energy-
independent, arise from uncertainties in the selection
efficiency (3.1%), predominantly due to the high-energy
photon and NN selections, the semileptonic BF for
B
meson decays, and the modeling of the
X
s
system.
Correlations between the
B
B
and the signal efficiency
systematic errors contribute an additional 2.9% uncer-
tainty. Finally, there is a 1.1% uncertainty in
N
B
B
.
To obtain an
E
spectrum in the
B
rest frame, the
E
spectrum shown in Fig.
1
is corrected for selection effi-
ciency, and the resolution smearing and Doppler smearing
are unfolded. A simplified version [
35
] of an iterative
unfolding technique [
36
] is used. The method starts with
an initial signal model that, when passed through the
detector simulation and event selection, closely resembles
the data (shape function scheme with
m
b
¼
4
:
51 GeV
,
2
¼
0
:
46 GeV
2
). This model is used to correct for effi-
ciency and unfold the data. A fraction, determined by a
bin-dependent regularization function, of the difference
between the unfolded data and the initial signal model is
used to adjust the signal model, and the process is iterated
until it converges. Only one iteration is necessary. The
results are shown in Fig.
2
. This technique preserves fluc-
tuations in the spectrum and reduces the model error. The
model-dependence uncertainty is computed using an initial
model that is approximately
1
lower than the data in
Fig.
1
in the region with significant
B
B
background (
1
:
8
<
E
<
2
:
1 GeV
). The error is the absolute value of the
difference bin by bin after unfolding. It is small except
near the kinematic limit,
E
m
B
=
2
, where the sharply
falling edge leads to strongly anticorrelated differences in
adjacent bins. To reduce this effect, the 100-MeV bins
between 2.4 and 2.8 GeV are combined into 200-MeV
bins. The spectral shape and the full covariance matrix,
provided in Ref. [
26
], are used to compute the first and
second moments in Table
I
. They can also be used to fit
any theoretical prediction for the spectral shape. The BFs
computed from the sum of the
B
in Fig.
2
are consistent
with the values given in Table
I
[
26
].
Finally the
E
sample is divided into
B
and
B
decays,
using the charge of the lepton tag, to measure
A
meas
CP
ð
B
!
X
s
þ
d
Þ¼ð
N
þ
N
Þ
=
ð
N
þ
þ
N
Þ
, where
N
þðÞ
are the
positively (negatively) tagged signal yields.
A
CP
is then
given by
A
CP
¼
A
meas
CP
=
ð
1
2
!
Þ
, where
!
is the mistag
fraction. To maximize the statistical precision a require-
ment of
2
:
1
<E
<
2
:
8 GeV
is made. This is determined
from simulation and does not bias the SM prediction for
the asymmetry [
37
]. The yields are
N
þ
¼
2620
158
ð
stat
Þ
and
N
¼
2389
151
ð
stat
Þ
. The bias on
A
CP
due to charge asymmetry in the detector response or
B
B
background is measured to be
A
meas
CP
ð
B
!
X
s
þ
d
Þ¼
0
:
004
0
:
013
, using events in the
B
B
control region to
check for a background asymmetry, and using several
event samples (
e
þ
e
!
e
þ
e
,
e
þ
e
!
, and
B
!
K
ðÞ
J=
c
ð
‘
þ
‘
Þ
) to check for a lepton tag asymmetry.
The mistag fraction
!
¼
0
:
133
0
:
006
is dominated by
B
0
B
0
mixing, which contributes
0
:
093
0
:
001
[
34
], with
TABLE I. The measured BF, first, and second moments (
stat
syst
model
) for different ranges of
E
in the
B
rest frame.
Correlations between the energy ranges are given in Ref. [
26
].
E
Range (GeV)
B
ð
B
!
X
s
Þ
(
10
4
)
h
E
i
(GeV)
hð
E
h
E
iÞ
2
i
(
GeV
2
)
1.8 to 2.8
3
:
21
0
:
15
0
:
29
0
:
08
2
:
267
0
:
019
0
:
032
0
:
003
0
:
0484
0
:
0053
0
:
0077
0
:
0005
1.9 to 2.8
3
:
00
0
:
14
0
:
19
0
:
06
2
:
304
0
:
014
0
:
017
0
:
004
0
:
0362
0
:
0033
0
:
0033
0
:
0005
2.0 to 2.8
2
:
80
0
:
12
0
:
14
0
:
04
2
:
342
0
:
010
0
:
008
0
:
005
0
:
0251
0
:
0021
0
:
0013
0
:
0009
1.6
1.8
2
2.2
2.4
2.6
2.8
0
0.5
1
(GeV)
γ
E
per 100 MeV
-4
)/10
γ
s+d
X
→
(B
B
∆
FIG. 2 (color online). The
E
photon energy spectrum cor-
rected for efficiency, resolution, and Doppler smearing, shown as
a partial branching fraction
B
. The inner error bars are
statistical and the outer include systematic errors added in
quadrature. The vertical line shows the boundary between the
lower control region and the signal region. The curve is the
kinetic scheme model using HFAG world average parameters,
normalized to data in the range
1
:
8
<E
B
<
2
:
8 GeV
.
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191801-6
an additional
0
:
040
0
:
005
arising from wrong-sign lep-
tons from the
B
decay chain and from misidentifcation of
hadrons as leptons. After correcting for charge bias and
mistagging it is found
A
CP
¼
0
:
057
0
:
060
ð
stat
Þ
0
:
018
ð
syst
Þ
:
The systematic error includes relative uncertainties from
the
B
B
background subtraction (2.2%) and mistagging
(1.8%). The uncertainty due to differences in the
B
!
X
s
and
B
!
X
d
spectra is negligible.
In summary, the photon spectrum of
B
!
X
s
þ
d
decays
has been measuredandusedtoextract the branching fraction,
spectral moments, and
A
CP
. Previous inclusive measure-
ments of
B
!
X
s
have been presented by the CLEO [
38
],
BABAR
[
18
], and Belle [
39
] Collaborations. The measured
branching fraction
B
ð
B
!
X
s
Þ¼ð
3
:
21
0
:
15
0
:
29
0
:
08
Þ
10
4
(
1
:
8
<E
<
2
:
8GeV
) is comparable in preci-
sion to the Belle result,
ð
3
:
36
0
:
13
0
:
25
0
:
01
Þ
10
4
,
butwithadatasetthathas60%smallerintegratedluminosity.
The BF for
1
:
8
<E
<
2
:
8GeV
is extrapolated to the range
E
>
1
:
6GeV
using a factor of
1
=
ð
0
:
968
0
:
006
Þ
deter-
mined by HFAG. This results in
B
ð
B
!
X
s
Þ¼ð
3
:
31
0
:
16
0
:
30
0
:
09
Þ
10
4
for
E
>
1
:
6GeV
,ingood
agreement with the SM prediction. The extrapolated
B
ð
B
!
X
s
Þ
can be used to constrain NP. For example, in
a type-II two-Higgs-doublet model [
10
,
40
] the region
M
H
<
327 GeV
is excluded independent of
tan
at 95%
confidence level. This limit is far more stringent than that
from direct searches at the LHC [
41
,
42
]. The
A
CP
measure-
ment is the most precise to date and can be used to constrain
nonminimal flavor-violating models [
11
]. The measured
moments and spectra provide input to improve the precision
on the HFAG estimation of
m
b
and
2
, which will result in a
reduced error on
j
V
ub
j
. Finally, the improved technique
presented in this Letter can be applied with increased preci-
sion at future Super
B
factories.
We are grateful for the excellent luminosity and machine
conditions provided by our PEP-II colleagues, and for the
substantial dedicated effort from the computing organiza-
tions that support
BABAR
. The collaborating institutions
wish to thank SLAC for its support and kind hospitality.
This work is supported by DOE and NSF (USA), NSERC
(Canada), CEA and CNRS-IN2P3 (France), BMBF and
DFG (Germany), INFN (Italy), FOM (The Netherlands),
NFR (Norway), MES (Russia), MICIIN (Spain), and STFC
(United Kingdom). Individuals have received support from
the Marie Curie EIF (European Union) and the A. P. Sloan
Foundation (USA).
*
Deceased.
†
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.
k
Now at University of South Alabama, Mobile, AL 36688,
USA.
{
Also with Universita
`
di Sassari, Sassari, Italy.
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