B
A
B
AR
-PUB-13/015
SLAC-PUB-15947
Measurements of Direct
CP
Asymmetries in
B
→
X
s
γ
decays
using Sum of Exclusive Decays
J. P. Lees, V. Poireau, and V. Tisserand
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),
Universit ́e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
E. Grauges
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
A. Palano
ab
INFN Sezione di Bari
a
; Dipartimento di Fisica, Universit`a di Bari
b
, I-70126 Bari, Italy
G. Eigen and B. Stugu
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
D. N. Brown, L. T. Kerth, Yu. G. Kolomensky, M. J. Lee, and G. Lynch
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
H. Koch and T. Schroeder
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphysik 1, D-44780 Bochum, Germany
C. Hearty, T. S. Mattison, J. A. McKenna, and R. Y. So
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
A. Khan
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
V. E. Blinov
ac
, A. R. Buzykaev
a
, V. P. Druzhinin
ab
, V. B. Golubev
ab
, E. A. Kravchenko
ab
, A. P. Onuchin
ac
,
S. I. Serednyakov
ab
, Yu. I. Skovpen
ab
, E. P. Solodov
ab
, K. Yu. Todyshev
ab
, and A. N. Yushkov
a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 630092
c
, Russia
D. Kirkby, A. J. Lankford, and M. Mandelkern
University of California at Irvine, Irvine, California 92697, USA
B. Dey, J. W. Gary, and O. Long
University of California at Riverside, Riverside, California 92521, USA
C. Campagnari, M. Franco Sevilla, T. M. Hong, D. Kovalskyi, J. D. Richman, and C. A. West
University of California at Santa Barbara, Santa Barbara, California 93106, USA
A. M. Eisner, W. S. Lockman, B. A. Schumm, and A. Seiden
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
D. S. Chao, C. H. Cheng, B. Echenard, K. T. Flood, D. G. Hitlin, P. Ongmongkolkul, and F. C. Porter
California Institute of Technology, Pasadena, California 91125, USA
R. Andreassen, Z. Huard, B. T. Meadows, B. G. Pushpawela, M. D. Sokoloff, and L. Sun
University of Cincinnati, Cincinnati, Ohio 45221, USA
P. C. Bloom, W. T. Ford, A. Gaz, U. Nauenberg, J. G. Smith, and S. R. Wagner
University of Colorado, Boulder, Colorado 80309, USA
arXiv:1406.0534v1 [hep-ex] 2 Jun 2014
2
R. Ayad
∗
and W. H. Toki
Colorado State University, Fort Collins, Colorado 80523, USA
B. Spaan
Technische Universit ̈at Dortmund, Fakult ̈at Physik, D-44221 Dortmund, Germany
R. Schwierz
Technische Universit ̈at Dresden, Institut f ̈ur Kern- und Teilchenphysik, D-01062 Dresden, Germany
D. Bernard and M. Verderi
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
S. Playfer
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
D. Bettoni
a
, C. Bozzi
a
, R. Calabrese
ab
, G. Cibinetto
ab
, E. Fioravanti
ab
,
I. Garzia
ab
, E. Luppi
ab
, L. Piemontese
a
, and V. Santoro
a
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara
b
, I-44122 Ferrara, Italy
R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro,
S. Martellotti, P. Patteri, I. M. Peruzzi,
†
M. Piccolo, M. Rama, and A. Zallo
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
R. Contri
ab
, E. Guido
ab
, M. Lo Vetere
ab
, M. R. Monge
ab
, S. Passaggio
a
, C. Patrignani
ab
, and E. Robutti
a
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
B. Bhuyan and V. Prasad
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
M. Morii
Harvard University, Cambridge, Massachusetts 02138, USA
A. Adametz and U. Uwer
Universit ̈at Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
H. M. Lacker
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, D-12489 Berlin, Germany
P. D. Dauncey
Imperial College London, London, SW7 2AZ, United Kingdom
U. Mallik
University of Iowa, Iowa City, Iowa 52242, USA
C. Chen, J. Cochran, W. T. Meyer, and S. Prell
Iowa State University, Ames, Iowa 50011-3160, USA
H. Ahmed and H. Ahmed
Jazan University, Jazan 22822, Kingdom of Saudi Arabia
A. V. Gritsan
Johns Hopkins University, Baltimore, Maryland 21218, USA
N. Arnaud, M. Davier, D. Derkach, G. Grosdidier, F. Le Diberder,
A. M. Lutz, B. Malaescu,
‡
P. Roudeau, A. Stocchi, and G. Wormser
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et Universit ́e Paris-Sud 11,
Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France
3
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
J. P. Coleman, J. R. Fry, E. Gabathuler, D. E. Hutchcroft, D. J. Payne, and C. Touramanis
University of Liverpool, Liverpool L69 7ZE, United Kingdom
A. J. Bevan, F. Di Lodovico, and R. Sacco
Queen Mary, University of London, London, E1 4NS, United Kingdom
G. Cowan
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
J. Bougher, D. N. Brown, and C. L. Davis
University of Louisville, Louisville, Kentucky 40292, USA
A. G. Denig, M. Fritsch, W. Gradl, K. Griessinger, A. Hafner, E. Prencipe, and K. R. Schubert
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Kernphysik, D-55099 Mainz, Germany
R. J. Barlow
§
and G. D. Lafferty
University of Manchester, Manchester M13 9PL, United Kingdom
E. Behn, R. Cenci, B. Hamilton, A. Jawahery, and D. A. Roberts
University of Maryland, College Park, Maryland 20742, USA
R. Cowan, D. Dujmic, and G. Sciolla
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
R. Cheaib, P. M. Patel,
¶
and S. H. Robertson
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
P. Biassoni
ab
, N. Neri
a
, and F. Palombo
ab
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
L. Cremaldi, R. Godang,
∗∗
P. Sonnek, and D. J. Summers
University of Mississippi, University, Mississippi 38677, USA
M. Simard and P. Taras
Universit ́e de Montr ́eal, Physique des Particules, Montr ́eal, Qu ́ebec, Canada H3C 3J7
G. De Nardo
ab
, D. Monorchio
ab
, G. Onorato
ab
, and C. Sciacca
ab
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
M. Martinelli and G. Raven
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
C. P. Jessop and J. M. LoSecco
University of Notre Dame, Notre Dame, Indiana 46556, USA
K. Honscheid and R. Kass
Ohio State University, Columbus, Ohio 43210, USA
J. Brau, R. Frey, N. B. Sinev, D. Strom, and E. Torrence
University of Oregon, Eugene, Oregon 97403, USA
E. Feltresi
ab
, M. Margoni
ab
, M. Morandin
a
, M. Posocco
a
, M. Rotondo
a
, G. Simi
a
, F. Simonetto
ab
, and R. Stroili
ab
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
4
S. Akar, E. Ben-Haim, M. Bomben, G. R. Bonneaud, H. Briand,
G. Calderini, J. Chauveau, Ph. Leruste, G. Marchiori, J. Ocariz, and S. Sitt
Laboratoire de Physique Nucl ́eaire et de Hautes Energies,
IN2P3/CNRS, Universit ́e Pierre et Marie Curie-Paris6,
Universit ́e Denis Diderot-Paris7, F-75252 Paris, France
M. Biasini
ab
, E. Manoni
a
, S. Pacetti
ab
, and A. Rossi
a
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
C. Angelini
ab
, G. Batignani
ab
, S. Bettarini
ab
, M. Carpinelli
ab
,
††
G. Casarosa
ab
, A. Cervelli
ab
, F. Forti
ab
,
M. A. Giorgi
ab
, A. Lusiani
ac
, B. Oberhof
ab
, E. Paoloni
ab
, A. Perez
a
, G. Rizzo
ab
, and J. J. Walsh
a
INFN Sezione di Pisa
a
; Dipartimento di Fisica, Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
D. Lopes Pegna, J. Olsen, and A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
R. Faccini
ab
, F. Ferrarotto
a
, F. Ferroni
ab
, M. Gaspero
ab
, L. Li Gioi
a
, and G. Piredda
a
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
C. B ̈unger, O. Gr ̈unberg, T. Hartmann, T. Leddig, C. Voß, and R. Waldi
Universit ̈at Rostock, D-18051 Rostock, Germany
T. Adye, E. O. Olaiya, and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
S. Emery, G. Hamel de Monchenault, G. Vasseur, and Ch. Y`eche
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
F. Anulli,
‡‡
D. Aston, D. J. Bard, J. F. Benitez, C. Cartaro, M. R. Convery, J. Dorfan, G. P. Dubois-Felsmann,
W. Dunwoodie, M. Ebert, R. C. Field, B. G. Fulsom, A. M. Gabareen, M. T. Graham, C. Hast,
W. R. Innes, P. Kim, M. L. Kocian, D. W. G. S. Leith, P. Lewis, D. Lindemann, B. Lindquist, S. Luitz,
V. Luth, H. L. Lynch, D. B. MacFarlane, D. R. Muller, H. Neal, S. Nelson, M. Perl, T. Pulliam,
B. N. Ratcliff, A. Roodman, A. A. Salnikov, R. H. Schindler, A. Snyder, D. Su, M. K. Sullivan, J. Va’vra,
A. P. Wagner, W. F. Wang, W. J. Wisniewski, M. Wittgen, D. H. Wright, H. W. Wulsin, and V. Ziegler
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
W. Park, M. V. Purohit, R. M. White,
§§
and J. R. Wilson
University of South Carolina, Columbia, South Carolina 29208, USA
A. Randle-Conde and S. J. Sekula
Southern Methodist University, Dallas, Texas 75275, USA
M. Bellis, P. R. Burchat, T. S. Miyashita, and E. M. T. Puccio
Stanford University, Stanford, California 94305-4060, USA
M. S. Alam and J. A. Ernst
State University of New York, Albany, New York 12222, USA
R. Gorodeisky, N. Guttman, D. R. Peimer, and A. Soffer
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
S. M. Spanier
University of Tennessee, Knoxville, Tennessee 37996, USA
J. L. Ritchie, A. M. Ruland, R. F. Schwitters, and B. C. Wray
University of Texas at Austin, Austin, Texas 78712, USA
5
J. M. Izen and X. C. Lou
University of Texas at Dallas, Richardson, Texas 75083, USA
F. Bianchi
ab
, F. De Mori
ab
, A. Filippi
a
, D. Gamba
ab
, and S. Zambito
ab
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
L. Lanceri
ab
and L. Vitale
ab
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, I-34127 Trieste, Italy
F. Martinez-Vidal, A. Oyanguren, and P. Villanueva-Perez
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
J. Albert, Sw. Banerjee, F. U. Bernlochner, H. H. F. Choi, G. J. King, R. Kowalewski,
M. J. Lewczuk, T. Lueck, I. M. Nugent, J. M. Roney, R. J. Sobie, and N. Tasneem
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
T. J. Gershon, P. F. Harrison, and T. E. Latham
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
H. R. Band, S. Dasu, Y. Pan, R. Prepost, and S. L. Wu
University of Wisconsin, Madison, Wisconsin 53706, USA
We measure the direct
CP
violation asymmetry,
A
CP
, in
B
→
X
s
γ
and the isospin difference of the
asymmetry, ∆
A
CP
, using 429 fb
−
1
of data collected at
Υ
(4
S
) resonance with the
B
A
B
AR
detector
at the PEP-II asymmetric-energy
e
+
e
−
storage rings operating at the SLAC National Accelerator
Laboratory.
B
mesons are reconstructed from 10 charged
B
final states and 6 neutral
B
final states.
We find
A
CP
= +(1
.
7
±
1
.
9
±
1
.
0)%, which is in agreement with the Standard Model prediction
and provides an improvement on the world average. Moreover, we report the first measurement of
the difference between
A
CP
for charged and neutral decay modes, ∆
A
CP
= +(5
.
0
±
3
.
9
±
1
.
5)%.
Using the value of ∆
A
CP
, we also provide 68% and 90% confidence intervals on the imaginary
part of the ratio of the Wilson coefficients corresponding to the chromo-magnetic dipole and the
electromagnetic dipole transitions.
PACS numbers: 13.20.-v,13.25.Hw
I. INTRODUCTION
The flavor-changing neutral current decay
B
→
X
s
γ
,
where
X
s
represents any hadronic system with one unit of
strangeness, is highly suppressed in the standard model
(SM), as is the direct
CP
asymmetry,
A
CP
=
Γ
B
0
/B
−
→
X
s
γ
−
Γ
B
0
/B
+
→
X
s
γ
Γ
B
0
/B
−
→
X
s
γ
+ Γ
B
0
/B
+
→
X
s
γ
,
(1)
∗
Now at the University of Tabuk, Tabuk 71491, Saudi Arabia
†
Also with Universit`a di Perugia, Dipartimento di Fisica, Perugia,
Italy
‡
Now at Laboratoire de Physique Nucl ́aire et de Hautes Energies,
IN2P3/CNRS, Paris, France
§
Now at the University of Huddersfield, Huddersfield HD1 3DH,
UK
¶
Deceased
∗∗
Now at University of South Alabama, Mobile, Alabama 36688,
USA
††
Also with Universit`a di Sassari, Sassari, Italy
‡‡
Also with INFN Sezione di Roma, Roma, Italy
§§
Now at Universidad T ́ecnica Federico Santa Maria, Valparaiso,
Chile 2390123
due to the combination of CKM and GIM suppres-
sions [1]. New physics effects could enhance the asym-
metry to a level as large as 15% [2][3][4]. The current
world average of
A
CP
based on the results from
B
A
B
AR
[5],
Belle [6] and CLEO [7] is
−
(0
.
8
±
2
.
9)%[8]. The SM pre-
diction for the asymmetry was found in a recent study
to be long-distance-dominated [9] and to be in the range
−
0
.
6%
< A
SM
CP
<
2
.
8%.
Benzke
et al.
[9] predict a difference in direct
CP
asym-
metry for charged and neutral
B
mesons:
∆
A
X
s
γ
=
A
B
±
→
X
s
γ
−
A
B
0
/
B
0
→
X
s
γ
,
(2)
which suggests a new test of the SM. The difference,
∆
A
X
s
γ
, arises from an interference term in
A
CP
that
depends on the charge of the spectator quark. The mag-
nitude of ∆
A
X
s
γ
is proportional to Im (
C
8
g
/C
7
γ
) where
C
7
γ
and
C
8
g
are Wilson coefficients corresponding to the
electromagnetic dipole and the chromo-magnetic dipole
transitions, respectively. The two coefficients are real in
the SM; therefore ∆
A
X
s
γ
=0. New physics contributions
from the enhancement of the
CP
-violating phase or of the
magnitude of the two Wilson coefficients [1][10], or the
introduction of new operators [11] could enhance ∆
A
X
s
γ
to be as large as 10% [9]. Unlike
C
7
γ
,
C
8
g
currently does
6
not have a strong experimental constraint [12]. Thus a
measurement of ∆
A
X
s
γ
together with the existing con-
straints on
C
7
γ
can provide a constraint on
C
8
g
.
Experimental studies of
B
→
X
s
γ
are approached in
one of two ways. The inclusive approach relies entirely
on observation of the high-energy photon from these de-
cays without reconstruction of the hadronic system
X
s
.
By ignoring the
X
s
system, this approach is sensitive to
the full
b
→
sγ
decay rate and is robust against final
state fragmentation effects. The semi-inclusive approach
reconstructs the
X
s
system in as many specific final state
configurations as practical. This approach provides ad-
ditional information, but since not all
X
s
final states can
be reconstructed without excessive background, fragmen-
tation model-dependence is introduced if semi-inclusive
measurements are extrapolated to the complete ensem-
ble of
B
→
X
s
γ
decays.
B
A
B
AR
has recently published
results on the
B
→
X
s
γ
branching fraction and photon
spectrum for both approaches [13][14]. The inclusive ap-
proach has also been used to search for direct
CP
viola-
tion, but since the inclusive method does not distinguish
hadronic final states, decays due to
b
→
dγ
transitions
are included.
We report herein a measurement of
A
CP
and the
first measurement of ∆
A
X
s
γ
using the semi-inclusive ap-
proach with the full
B
A
B
AR
data set. We reconstruct 38
exclusive
B
-decay modes, listed in Table I, but for use
in this analysis a subset of 16 modes (marked with an
asterisk in Table I) is chosen for which high statistical
significance is achieved. Also, for this analysis, modes
must be flavor self-tagging (i.e., the bottomness can be
determined from the reconstructed final state). The 16
modes include ten charged
B
and six neutral
B
decays.
After all event selection criteria are applied, the mass
of the hadronic
X
s
system (
m
X
s
) in this measurement
covers the range of about 0.6 to 2.0 GeV
/c
2
. The up-
per edge of this range approximately corresponds to a
minimum photon energy in the
B
rest frame of 2.3 GeV.
For
B
→
X
s
γ
decays with 0
.
6
< m
X
s
<
2
.
0 GeV
/c
2
, the
10 charged
B
modes used account for about 52% of all
B
+
→
X
s
γ
decays and the six neutral modes account for
about 34% of all neutral
B
0
→
X
s
γ
decays [15]. In this
analysis it is assumed that
A
CP
and ∆
A
X
s
γ
are indepen-
dent of final state fragmentation. That is, it is assumed
that
A
CP
and ∆
A
X
s
γ
are independent of the specific
X
s
final states used for this analysis and independent of the
m
X
s
distribution of the selected events.
II. ANALYSIS OVERVIEW
With data from the
B
A
B
AR
detector (Section III), we
reconstructed
B
candidates from various final states (Sec-
tion IV). We then trained two multivariate classifiers
(Section V): one to separate correctly reconstructed
B
decays from mis-reconstructed events and the other to
reject the continuum background,
e
+
e
−
→
q
q
, where
q
=
u,d,s,c
. The output of the first classifier is used
TABLE I: The 38 final states we reconstruct in this analysis.
Charge conjugation is implied. The 16 final states used in the
CP
measurement are marked with an asterisk.
# Final State
# Final State
1*
B
+
→
K
S
π
+
γ
20
B
0
→
K
S
π
+
π
−
π
+
π
−
γ
2*
B
+
→
K
+
π
0
γ
21
B
0
→
K
+
π
+
π
−
π
−
π
0
γ
3*
B
0
→
K
+
π
−
γ
22
B
0
→
K
S
π
+
π
−
π
0
π
0
γ
4
B
0
→
K
S
π
0
γ
23*
B
+
→
K
+
ηγ
5*
B
+
→
K
+
π
+
π
−
γ
24
B
0
→
K
S
ηγ
6*
B
+
→
K
S
π
+
π
0
γ
25
B
+
→
K
S
ηπ
+
γ
7*
B
+
→
K
+
π
0
π
0
γ
26
B
+
→
K
+
ηπ
0
γ
8
B
0
→
K
S
π
+
π
−
γ
27*
B
0
→
K
+
ηπ
−
γ
9*
B
0
→
K
+
π
−
π
0
γ
28
B
0
→
K
S
ηπ
0
γ
10
B
0
→
K
S
π
0
π
0
γ
29
B
+
→
K
+
ηπ
+
π
−
γ
11*
B
+
→
K
S
π
+
π
−
π
+
γ
30
B
+
→
K
S
ηπ
+
π
0
γ
12*
B
+
→
K
+
π
+
π
−
π
0
γ
31
B
0
→
K
S
ηπ
+
π
−
γ
13*
B
+
→
K
S
π
+
π
0
π
0
γ
32
B
0
→
K
+
ηπ
−
π
0
γ
14*
B
0
→
K
+
π
+
π
−
π
−
γ
33*
B
+
→
K
+
K
−
K
+
γ
15
B
0
→
K
S
π
0
π
+
π
−
γ
34
B
0
→
K
+
K
−
K
S
γ
16*
B
0
→
K
+
π
−
π
0
π
0
γ
35
B
+
→
K
+
K
−
K
S
π
+
γ
17
B
+
→
K
+
π
+
π
−
π
+
π
−
γ
36
B
+
→
K
+
K
−
K
+
π
0
γ
18
B
+
→
K
S
π
+
π
−
π
+
π
0
γ
37*
B
0
→
K
+
K
−
K
+
π
−
γ
19
B
+
→
K
+
π
+
π
−
π
0
π
0
γ
38
B
0
→
K
+
K
−
K
S
π
0
γ
to select the best
B
candidate for each event. Then,
the outputs from both classifiers are used to reject back-
grounds. We use the remaining events to determine the
asymmetries.
We use identical procedures to extract three asymme-
tries: the asymmetries of charged and neutral B mesons,
and of the combined sample, and the difference, ∆
A
X
s
γ
.
The bottomness of the
B
meson is determined by the
charge of the kaon for
B
0
and
B
0
, and by the total charge
of the reconstructed
B
meson for
B
+
and
B
−
.
We can decompose
A
CP
into three components:
A
CP
=
A
peak
−
A
det
+
D
(3)
where
A
peak
is the fitted asymmetry of the events in the
peak of the
m
ES
distribution (Section VI),
A
det
is the
detector asymmetry due to the difference in
K
+
and
K
−
efficiency (Section VII), and
D
is the bias due to peaking
background contamination (Section VIII). In this anal-
ysis we establish upper bounds on the magnitude of
D
,
and then treat those as systematic errors.
III. DETECTOR AND DATA
We use a data sample of 429 fb
−
1
[16] collected at the
Υ
(4
S
) resonance,
√
s
= 10
.
58 GeV
/c
2
, with the
B
A
B
AR
detector at the PEP-II asymetric-energy
B
factory at
the SLAC National Accelerator Laboratory. The data
corresponds to 471
×
10
6
produced
B
B
pairs.
The
B
A
B
AR
detector and its operation are described
in detail elsewhere [17][18]. The charges and momenta
7
of charged particles are measured by a five-layer double-
sided silicon strip detector (SVT) and a 40-layer drift
chamber (DCH) operated in a 1.5 T solenoidal field.
Charged
K/π
separation is achieved using
dE/dx
infor-
mation from the trackers and by a detector of internally
reflected Cherenkov light (DIRC), which measures the
angle of the Cherenkov radiation cone. An electromag-
netic calorimeter (EMC) consisting of an array of CsI(Tl)
crystals measures the energy of photons and electrons.
We use a Monte Carlo (MC) simulation based on Evt-
Gen [19] to optimize the event selection criteria. We
model the background as
e
+
e
−
→
q
q
,
e
+
e
−
→
τ
+
τ
−
and
B
B
. We generate signal
B
→
X
s
γ
with a uniform
photon spectrum and then weight signal MC events so
that the photon spectrum matches the kinematic-scheme
model [20] with parameter values consistent with the pre-
vious
B
A
B
AR
B
→
X
s
γ
photon spectrum analysis (
m
b
=
4
.
65 GeV
/c
2
and
μ
2
π
= 0
.
20 GeV
2
) [21]. We use JET-
SET [22] as the fragmentation model and GEANT4 [23]
to simulate the detector response.
IV.
B
RECONSTRUCTION
We reconstructed
B
meson candidates from 38 final
states listed in Table I. The 16 modes marked with an
asterisk (*) in Table I are used in the
CP
measurement.
The other final states are either not flavor-specific final
states or are low in yield. We reconstruct the unused
modes in order to veto them after selecting the best can-
didate. In total, we use 10 charged
B
final states and 6
neutral
B
final states in the
A
CP
measurement. These fi-
nal states are the same as those used in a previous
B
A
B
AR
analysis [5].
Charged kaons and pions are selected from tracks
classified with an error-correcting output code algo-
rithm [18][25]. The classification uses SVT, DIRC, DCH,
and EMC information. The kaon particle identification
(PID) algorithm has approximately 90% efficiency and
a pion-as-kaon misidentification rate of about 1%. Pion
identification is roughly 99% efficient with a 15% kaon-
as-pion misidentification rate.
Neutral kaons are reconstructed from the decay
K
0
S
→
π
+
π
−
. The invariant mass of the two oppositely charged
tracks is required to be between 489 and 507 MeV. The
flight distance of the
K
0
S
must be greater than 0.2 cm
from the interaction point. The flight significance (de-
fined as the flight distance divided by the uncertainty in
the flight distance) of the
K
0
S
must be greater than three.
K
0
L
and
K
0
S
→
π
0
π
0
decays are not reconstructed for this
analysis.
The neutral
π
0
and
η
mesons are reconstructed from
two photons. We require each photon to have energy of
at least 30 MeV for
π
0
and at least 50 MeV for
η
. The
invariant mass of the two photons must be in the range
of [115,150] MeV for
π
0
candidates and in the range of
[470,620] MeV for
η
candidates. Only
π
0
and
η
candi-
dates with momentum greater than 200 MeV are used.
We do not reconstruct
η
→
π
+
π
−
π
0
decays explicitly, but
some are included in final states that contain
π
+
π
−
π
0
.
Each event is required to have at least one photon with
energy 1
.
6
< E
∗
γ
<
3
.
0 GeV, where the asterisk denotes
variables measured in the
Υ
(4
S
) center-of-mass (CM)
frame. These photons are used as the primary photon
in reconstructing
B
mesons. Such a photon must have a
lateral moment [26] less than 0.8 and the nearest EMC
cluster must be at least 15 cm away. The angle of the
photon momentum with respect to the beam axis must
satisfy
−
0
.
74
<
cos
θ <
0
.
93.
The invariant mass of
X
s
(all daughters of the
B
can-
didate excluding the primary photon) must satisfy 0
.
6
<
m
X
s
<
3
.
2 GeV
/c
2
. The
X
s
candidate is then com-
bined with the primary photon to form a
B
candidate,
which is required to have an energy-substituted mass
m
ES
=
√
s/
4
−
p
∗
B
2
, where
p
∗
B
is the momentum of
B
in the CM frame, greater than 5.24 GeV
/c
2
. We also
require the difference between half of the beam total
energy and the energy of the reconstructed
B
in the
CM frame,
|
∆
E
|
=
|
E
∗
beam
/
2
−
E
∗
B
|
, to be less than
0.15 GeV. The angle between the thrust axis of the rest
of the event(ROE) and the primary photon must satisfy
|
cos
θ
∗
Tγ
|
<
0
.
85.
V. EVENT AND CANDIDATE SELECTION
There are three main sources of background. The
dominant source is continuum background,
e
+
e
−
→
q
q
.
These events are more jet-like than the
e
+
e
−
→
Υ
(4
S
)
→
B
B
. Thus, event shape variables provide discrimination.
The continuum
m
ES
distribution does not peak at the
B
meson mass. The second background source is
B
B
de-
cays to final states other than
X
s
γ
; hereafter we refer to
these as generic
B
B
decays. The third source is cross-
feed background which comes from actual
B
→
X
s
γ
de-
cays in which we fail to reconstruct the
B
in the correct
final state. The
e
+
e
−
→
τ
+
τ
−
contribution is negligibly
small.
We first place a preliminary selection on the ratio of
angular moments [27][28],
L
12
/L
10
<
0
.
46 to reduce the
number of the continuum background events. This ratio
measures the jettiness of the event. Since the mass of
the
B
meson is close to half the mass of the
Υ
(4
S
), the
kinetic energy that the
B
meson can have is less than
that available to
e
+
e
−
→
light quark pairs. Therefore,
the signal peaks at a lower value of
L
12
/L
10
than does
the continuum background.
The
B
meson reconstruction typically yields multiple
B
candidates per event. To select the best candidate,
we train a random forest classifier [29] based on ∆
E/σ
E
,
where
σ
E
is the uncertainty on the
B
candidate energy,
the thrust of the reconstructed
B
candidate [30],
π
0
mo-
mentum, the invariant mass of the
X
s
system, and the
zeroth and fifth Fox-Wolfram moments [31]. This Signal
Selecting Classifier (SSC) is trained on a large MC event
8
sample to separate correctly reconstructed
B
→
X
s
γ
de-
cays from mis-reconstructed ones. For each event, the
candidate with the maximum classifier output is chosen
as the best candidate. This is the main difference from
a previous
B
A
B
AR
analysis [5] which chose the event with
the smallest
|
∆
E
|
as the best candidate. This method
increases the efficiency by a factor of approximately two
for the same misidentification rate.
It should be emphasized that the best candidate selec-
tion procedure also selects final states in which the bot-
tomness of the
B
cannot be deduced from the final decay
products (flavor-ambiguous final states). After selecting
the best candidate, we keep only events in which the best
candidate is reconstructed with the final states marked
with an asterisk in Table I. This removes events which are
flavor-ambiguous final states from the
A
CP
measurement.
Furthermore, because of the way the SSC was trained
to discriminate against mis-reconstructed
B
candidates,
SSC also provides good discriminating power against the
generic
B
B
background.
To further reduce the continuum background we build
another random forest classifier, the Background Reject-
ing Classifier (BRC), using the following variables:
•
π
0
score: the output from a random forest classi-
fier using the invariant mass of the primary pho-
ton with all other photons in the event and the en-
ergy of the other photons, which is trained to reject
high-energy photons that come from the
π
0
→
γγ
decays.
•
Momentum flow [32] in 10
◦
increments about the
reconstructed
B
direction.
•
Zeroth, first and second order angular moments
along the primary photon axis computed in the CM
frame of the ROE.
•
The ratio of the second and the zeroth angular mo-
ments described above.
• |
cos
θ
∗
B
|
: the cosine of the angle between the
B
flight direction and the beam axis in the CM frame.
• |
cos
θ
∗
T
|
: the cosine of the angle between the thrust
axis of the
B
candidate and the thrust axis of the
ROE in the CM frame.
• |
cos
θ
∗
Tγ
|
: the cosine of the angle between the pri-
mary photon momentum and the thrust axis of the
ROE in the CM frame.
To obtain the best sensitivity, we simultaneously op-
timize, using MC samples, the SSC and BRC selections
in four
X
s
mass ranges ([0.6-1.1], [1.1-2.0], [2.0-2.4], and
[2.4-2.8] GeV
/c
2
), maximizing
S/
√
S
+
B
, where
S
is the
number of expected signal events and
B
is the number
of expected background events with
m
ES
>
5.27 GeV
/c
2
.
The optimized selection values are the same for both
B
and
B
.
VI. FITTED ASYMMETRY
For each
B
flavor, we describe the
m
ES
distribution
with a sum of an ARGUS distribution [33][34] and a two-
piece normal distribution (
G
) [35]:
PDF
b
(
m
ES
) =
T
cont
2
(1 +
A
cont
)ARGUS(
m
ES
;
c
b
,χ
b
,p
b
)+
T
peak
2
(1 +
A
peak
)
G
(
m
ES
;
μ
b
,σ
b
L
,σ
b
R
)
,
(4)
PDF
b
(
m
ES
) =
T
cont
2
(1
−
A
cont
)ARGUS(
m
ES
;
c
b
,χ
b
,p
b
)+
T
peak
2
(1
−
A
peak
)
G
(
m
ES
;
μ
b
,σ
b
L
,σ
b
R
) (5)
where
T
cont
=
n
b
cont
+
n
b
cont
,
(6)
T
peak
=
n
b
peak
+
n
b
peak
(7)
are the total number of events of both flavors described
by the ARGUS distribution and the two-piece normal
distribution and
A
cont
=
n
b
cont
−
n
b
cont
n
b
cont
+
n
b
cont
,
(8)
A
peak
=
n
b
peak
−
n
b
peak
n
b
peak
+
n
b
peak
(9)
are the flavor asymmetries of events described by the AR-
GUS distribution and the two-piece normal distribution,
respectively. The superscript
b
and
b
indicate whether
the parameter belongs to the
b
-quark containing
B
me-
son (
B
0
and
B
−
) distribution or the
b
-quark containing
B
meson distribution (
B
0
and
B
+
), respectively. In par-
ticular,
n
b
peak
and
n
b
peak
are the numbers of events in the
peaking (Gaussian) part of the distribution. Similarly,
n
b
cont
and
n
b
cont
are the numbers of events in the contin-
uum (ARGUS) part of the distribution. The shape pa-
rameters for ARGUS distributions are the curvatures (
χ
b
and
χ
b
), the powers (
p
b
and
p
b
), and the endpoint ener-
gies (
c
b
and
c
b
). The shape parameters for two-piece nor-
mal distribution are the peak locations (
μ
b
and
μ
b
), the
left-side widths (
σ
b
L
and
σ
b
L
), and the right-side widths
(
σ
b
R
and
σ
b
R
).
It should be noted that
A
peak
is related to
A
CP
de-
fined in Eq. 1 by the relation shown in Eq. 3. To obtain
A
peak
, we perform a simultaneous binned likelihood fit for
both
B
flavors. The ARGUS endpoint energies
c
b
and
c
b
are fixed at 5.29 GeV
/c
2
. All other shape parameters for
the ARGUS distributions and the two-piece normal dis-
tributions are allowed to float separately. Fig. 1 shows
the
m
ES
distributions, along with fitted shapes. Table II
summarizes the results for
A
peak
.
9
5.24
5.25
5.26
5.27
5.28
5.29
m
ES
(GeV/
c
2
)
0
50
100
150
200
250
300
350
400
Events per 0.25 MeV/
c
2
B
0
and
B
−
Total PDF
Peaking
Continuum
Data
5.24
5.25
5.26
5.27
5.28
5.29
m
ES
(GeV/
c
2
)
0
50
100
150
200
250
300
350
400
Events per 0.25 MeV/
c
2
B
0
and
B
+
5.24
5.25
5.26
5.27
5.28
5.29
m
ES
(GeV/
c
2
)
0
50
100
150
200
250
Events per 0.25 MeV/
c
2
B
−
5.24
5.25
5.26
5.27
5.28
5.29
m
ES
(GeV/
c
2
)
0
50
100
150
200
250
Events per 0.25 MeV/
c
2
B
+
5.24
5.25
5.26
5.27
5.28
5.29
m
ES
(GeV/
c
2
)
0
50
100
150
200
250
Events per 0.25 MeV/
c
2
B
0
5.24
5.25
5.26
5.27
5.28
5.29
m
ES
(GeV/
c
2
)
0
50
100
150
200
250
Events per 0.25 MeV/
c
2
B
0
FIG. 1: The
m
ES
distributions along with fitted probability density functions, for:
B
0
and
B
−
sample (top left),
B
0
and
B
+
sample (top right),
B
−
sample (middle left),
B
+
sample (middle right),
B
0
sample (bottom left), and
B
0
sample (bottom right).
Data are shown as points with error bars. The ARGUS distribution component, two-piece normal distribution component and
the total probability density function are shown with dotted lines, dashed lines, and solid lines, respectively.
VII. DETECTOR ASYMMETRY
Part of the difference between
A
peak
and
A
CP
comes
from the difference in
K
+
and
K
−
efficiencies. The
K
+
PID efficiency is slightly higher than the
K
−
PID effi-
ciency; the difference also varies with the track momen-
tum. The cause of this difference is the fact that the
cross-section for
K
−
-hadron interactions is higher than
that for
K
+
-hadron interactions. This translates to the
K
−
having a greater probability of interacting before it
reaches the DIRC, thereby lowering the quality of the
K
−
Cherenkov cone angle measurement, which affects
the PID performance.
The first order correction to
A
CP
from
K
+
/
K
−
effi-
ciency differences is given by
A
det
=
ν
b
−
ν
b
ν
b
+
ν
b
(10)
where
ν
b
and
ν
b
are the number of events for each flavor
after all selections, assuming the underlying physics has
no flavor asymmetry.
We use a sideband region (
m
ES
<
5
.
27 GeV
/c
2
) which
consists mostly of
e
+
e
−
→
q
q
events to measure
A
det
.
We do not expect a flavor asymmetry in the underlying
physics in this region. We count the number of events
in the sideband region for each flavor and use Eq. 10 to
determine
A
sideband
det
.
However, since the difference in
K
−
and
K
+
hadron
cross section depends on
K
momentum and the
K
momentum distributions of the side band region and
10
the peaking region (
m
ES
>
5
.
27 GeV
/c
2
) slightly differ,
A
sideband
det
and
A
det
need not be identical. The variation of
A
det
for any
K
momentum distribution can be bounded
by the maximum and minimum value of the ratio between
K
+
and
K
−
efficiencies (
K
+
/
K
−
) in the
K
momentum
range of interest:
1
2
(
min
p
K
K
+
K
−
−
1
)
≤
A
det
≤
1
2
(
max
p
K
K
+
K
−
−
1
)
.
(11)
The final states with no charged
K
can be considered
as having a special value of
p
K
where
K
+
and
K
−
are
identical.
We use highly pure samples of charged kaons from the
decay
D
∗
+
→
D
0
π
+
, followed by
D
0
→
K
−
π
+
, and its
charge conjugate, to measure the ratio of efficiencies for
K
+
and
K
−
. We find that the deviation from unity of
K
+
/
K
−
varies from 0 to 2.5% depending on the track
momentum.
The bound given in Eq. 11 implies that the distribution
of the differences between any two detector asymmetries
chosen uniformly within the bound is a triangle distribu-
tion with the base width of 2.5%.
The standard deviation of such a distribution is
2
.
5%
/
√
24 = 0
.
5%. We use
A
sideband
det
as the central value
for
A
det
and this standard deviation as the systematic un-
certainty associated with detector asymmetry. Table II
lists the results of
A
det
.
VIII. PEAKING BACKGROUND
CONTAMINATION
Our fitting procedure does not explicitly separate the
cross-feed and generic
B
B
backgrounds from the signal.
Both backgrounds have small peaking components, as
shown in Figure 2, so the yield for each flavor used in
calculating
A
peak
contains both signal and these peaking
backgrounds. We quantify the effect and include it as a
source of systematic uncertainty.
Let the number of signal events for
b
-quark contain-
ing
B
mesons and
b
-quark containing
B
mesons be
n
b
and
n
b
and the number of contaminating peaking back-
ground events misreconstructed as
b
-quark containing
B
mesons and
b
-quark containing
B
mesons be
β
b
and
β
b
.
The difference between
A
peak
and
A
CP
due to peaking
background contamination is given by:
D
=
R
×
δA,
(12)
where
R
is the ratio of the number of peaking background
events to the total number of events in the peaking re-
gion, given by
R
=
β
b
+
β
b
n
b
+
n
b
+
β
b
+
β
b
,
(13)
and
δA
is the difference between the true signal asym-
metry and the peaking background asymmetry, given by
δA
=
n
b
−
n
b
n
b
+
n
b
−
β
b
−
β
b
β
b
+
β
b
.
(14)
We estimate
R
using the MC sample. We use the sum
of the expected number of cross-feed background events
and expected number of generic
B
B
events with
m
ES
>
5
.
27 GeV
/c
2
for each flavor as
β
b
and
β
b
. We obtain
n
b
and
n
b
from the total number of expected signal events
for each flavor.
Since the peaking background events are from mis-
reconstructed
B
mesons, the
m
ES
distribution of the
peaking background has a very long tail. It resembles
the sum of an ARGUS distribution and a small peaking
part. The fit to the total
m
ES
distribution is the sum of
a two-piece normal distribution and an ARGUS distri-
bution. A significant portion of peaking background is
absorbed into the ARGUS distribution causing our esti-
mate of
R
to be overestimated.
We bound the difference in asymmetry,
δA
, us-
ing the range of values predicted by the SM:
−
0
.
6 %
< A
SM
CP
<
2
.
8 %. This gives
|
δA
|
<
3
.
4%.
This value is also very conservative, since the amount
of cross-feed background in the signal region is approxi-
mately five times the amount of generic
B
B
background,
and we expect the flavor asymmetry of the cross-feed
events to be similar to that of the signal.
We validate our estimates by extracting
A
peak
from
pseudo MC experiments with varying amounts of cross-
feed background asymmetry and observe the shift from
the true value of the signal asymmetry. The shift is about
half the value estimated using the method described; we
use the more conservative estimate as our systematic un-
certainty. For
A
CP
of the charged and neutral
B
, this
estimate is conservative enough to cover a large possi-
ble range of
|
∆
A
X
s
γ
|
<
15% that could shift the value
of
A
peak
via the cross-feed of the type
B
0
→
X
s
γ
mis-
reconstructed as
B
−
→
X
s
γ
(
B
0
⇒
B
−
) and
B
−
→
X
s
γ
misreconstructed as
B
0
→
X
s
γ
(
B
−
⇒
B
0
). Table III
lists the values of
R
,
δA
and
D
.
IX. RESULTS
Following Eq. 3, we subtract
A
det
from
A
peak
to obtain
A
CP
. The statistical uncertainties are added in quadra-
ture. Systematic uncertainties from peaking background
contamination and from detector asymmetry are added
in quadrature to obtain the total systematic uncertainty.
We find
A
CP
= +(1
.
7
±
1
.
9
±
1
.
0)%
(15)
where the uncertainties are statistical and systematic, re-
spectively. Compared to the current world average, the
statistical uncertainty is smaller by approximately 1/3
due to the improved rejection of peaking background de-
scribed above.
The measurement of
A
CP
is based on the ratio of the
number of events, but
A
CP
is defined as the ratio of
widths. In order to make the two definitions of
A
CP
equivalent, we make two assumptions. First, we assume