B
A
B
AR
-PUB-14/006
SLAC-PUB-15983
Study of
CP
asymmetry in
B
0
-
B
0
mixing with inclusive dilepton events
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano
ab
,
3
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
M. J. Lee,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
A. Khan,
8
V. E. Blinov
abc
,
9
A. R. Buzykaev
a
,
9
V. P. Druzhinin
ab
,
9
V. B. Golubev
ab
,
9
E. A. Kravchenko
ab
,
9
A. P. Onuchin
abc
,
9
S. I. Serednyakov
ab
,
9
Yu. I. Skovpen
ab
,
9
E. P. Solodov
ab
,
9
K. Yu. Todyshev
ab
,
9
A. J. Lankford,
10
M. Mandelkern,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
C. Campagnari,
12
M. Franco Sevilla,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
W. S. Lockman,
13
W. Panduro Vazquez,
13
B. A. Schumm,
13
A. Seiden,
13
D. S. Chao,
14
C. H. Cheng,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
T. S. Miyashita,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
M. R ̈ohrken,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
B. G. Pushpawela,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17, a
W. H. Toki,
17
B. Spaan,
18
D. Bernard,
19
M. Verderi,
19
S. Playfer,
20
D. Bettoni
a
,
21
C. Bozzi
a
,
21
R. Calabrese
ab
,
21
G. Cibinetto
ab
,
21
E. Fioravanti
ab
,
21
I. Garzia
ab
,
21
E. Luppi
ab
,
21
L. Piemontese
a
,
21
V. Santoro
a
,
21
A. Calcaterra,
22
R. de Sangro,
22
G. Finocchiaro,
22
S. Martellotti,
22
P. Patteri,
22
I. M. Peruzzi,
22, b
M. Piccolo,
22
M. Rama,
22
A. Zallo,
22
R. Contri
ab
,
23
M. Lo Vetere
ab
,
23
M. R. Monge
ab
,
23
S. Passaggio
a
,
23
C. Patrignani
ab
,
23
E. Robutti
a
,
23
B. Bhuyan,
24
V. Prasad,
24
A. Adametz,
25
U. Uwer,
25
H. M. Lacker,
26
P. D. Dauncey,
27
U. Mallik,
28
C. Chen,
29
J. Cochran,
29
S. Prell,
29
H. Ahmed,
30
A. V. Gritsan,
31
N. Arnaud,
32
M. Davier,
32
D. Derkach,
32
G. Grosdidier,
32
F. Le Diberder,
32
A. M. Lutz,
32
B. Malaescu,
32, c
P. Roudeau,
32
A. Stocchi,
32
G. Wormser,
32
D. J. Lange,
33
D. M. Wright,
33
J. P. Coleman,
34
J. R. Fry,
34
E. Gabathuler,
34
D. E. Hutchcroft,
34
D. J. Payne,
34
C. Touramanis,
34
A. J. Bevan,
35
F. Di Lodovico,
35
R. Sacco,
35
G. Cowan,
36
J. Bougher,
37
D. N. Brown,
37
C. L. Davis,
37
A. G. Denig,
38
M. Fritsch,
38
W. Gradl,
38
K. Griessinger,
38
A. Hafner,
38
K. R. Schubert,
38
R. J. Barlow,
39, d
G. D. Lafferty,
39
R. Cenci,
40
B. Hamilton,
40
A. Jawahery,
40
D. A. Roberts,
40
R. Cowan,
41
G. Sciolla,
41
R. Cheaib,
42
P. M. Patel,
42, e
S. H. Robertson,
42
N. Neri
a
,
43
F. Palombo
ab
,
43
L. Cremaldi,
44
R. Godang,
44, f
P. Sonnek,
44
D. J. Summers,
44
M. Simard,
45
P. Taras,
45
G. De Nardo
ab
,
46
G. Onorato
ab
,
46
C. Sciacca
ab
,
46
M. Martinelli,
47
G. Raven,
47
C. P. Jessop,
48
J. M. LoSecco,
48
K. Honscheid,
49
R. Kass,
49
E. Feltresi
ab
,
50
M. Margoni
ab
,
50
M. Morandin
a
,
50
M. Posocco
a
,
50
M. Rotondo
a
,
50
G. Simi
ab
,
50
F. Simonetto
ab
,
50
R. Stroili
ab
,
50
S. Akar,
51
E. Ben-Haim,
51
M. Bomben,
51
G. R. Bonneaud,
51
H. Briand,
51
G. Calderini,
51
J. Chauveau,
51
Ph. Leruste,
51
G. Marchiori,
51
J. Ocariz,
51
M. Biasini
ab
,
52
E. Manoni
a
,
52
S. Pacetti
ab
,
52
A. Rossi
a
,
52
C. Angelini
ab
,
53
G. Batignani
ab
,
53
S. Bettarini
ab
,
53
M. Carpinelli
ab
,
53, g
G. Casarosa
ab
,
53
A. Cervelli
ab
,
53
M. Chrzaszcz
a
,
53
F. Forti
ab
,
53
M. A. Giorgi
ab
,
53
A. Lusiani
ac
,
53
B. Oberhof
ab
,
53
E. Paoloni
ab
,
53
A. Perez
a
,
53
G. Rizzo
ab
,
53
J. J. Walsh
a
,
53
D. Lopes Pegna,
54
J. Olsen,
54
A. J. S. Smith,
54
R. Faccini
ab
,
55
F. Ferrarotto
a
,
55
F. Ferroni
ab
,
55
M. Gaspero
ab
,
55
L. Li Gioi
a
,
55
A. Pilloni
ab
,
55
G. Piredda
a
,
55
C. B ̈unger,
56
S. Dittrich,
56
O. Gr ̈unberg,
56
M. Hess,
56
T. Leddig,
56
C. Voß,
56
R. Waldi,
56
T. Adye,
57
E. O. Olaiya,
57
F. F. Wilson,
57
S. Emery,
58
G. Vasseur,
58
F. Anulli,
59, h
D. Aston,
59
D. J. Bard,
59
C. Cartaro,
59
M. R. Convery,
59
J. Dorfan,
59
G. P. Dubois-Felsmann,
59
W. Dunwoodie,
59
M. Ebert,
59
R. C. Field,
59
B. G. Fulsom,
59
M. T. Graham,
59
C. Hast,
59
W. R. Innes,
59
P. Kim,
59
D. W. G. S. Leith,
59
P. Lewis,
59
D. Lindemann,
59
S. Luitz,
59
V. Luth,
59
H. L. Lynch,
59
D. B. MacFarlane,
59
D. R. Muller,
59
H. Neal,
59
M. Perl,
59, e
T. Pulliam,
59
B. N. Ratcliff,
59
A. Roodman,
59
A. A. Salnikov,
59
R. H. Schindler,
59
A. Snyder,
59
D. Su,
59
M. K. Sullivan,
59
J. Va’vra,
59
W. J. Wisniewski,
59
H. W. Wulsin,
59
M. V. Purohit,
60
R. M. White,
60, i
J. R. Wilson,
60
A. Randle-Conde,
61
S. J. Sekula,
61
M. Bellis,
62
P. R. Burchat,
62
E. M. T. Puccio,
62
M. S. Alam,
63
J. A. Ernst,
63
R. Gorodeisky,
64
N. Guttman,
64
D. R. Peimer,
64
A. Soffer,
64
S. M. Spanier,
65
J. L. Ritchie,
66
A. M. Ruland,
66
R. F. Schwitters,
66
B. C. Wray,
66
J. M. Izen,
67
X. C. Lou,
67
F. Bianchi
ab
,
68
F. De Mori
ab
,
68
A. Filippi
a
,
68
D. Gamba
ab
,
68
L. Lanceri
ab
,
69
L. Vitale
ab
,
69
F. Martinez-Vidal,
70
A. Oyanguren,
70
P. Villanueva-Perez,
70
J. Albert,
71
Sw. Banerjee,
71
A. Beaulieu,
71
F. U. Bernlochner,
71
H. H. F. Choi,
71
G. J. King,
71
R. Kowalewski,
71
M. J. Lewczuk,
71
T. Lueck,
71
I. M. Nugent,
71
J. M. Roney,
71
R. J. Sobie,
71
N. Tasneem,
71
T. J. Gershon,
72
P. F. Harrison,
72
T. E. Latham,
72
H. R. Band,
73
S. Dasu,
73
Y. Pan,
73
R. Prepost,
73
and S. L. Wu
73
(The
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),
arXiv:1411.1842v1 [hep-ex] 7 Nov 2014
2
Universit ́e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3
INFN Sezione di Bari
a
; Dipartimento di Fisica, Universit`a di Bari
b
, 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 Universit ̈at Bochum, Institut f ̈ur 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 SB RAS, Novosibirsk 630090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 630092
c
, 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 Universit ̈at Dortmund, Fakult ̈at Physik, D-44221 Dortmund, Germany
19
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
20
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
21
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara
b
, I-44122 Ferrara, Italy
22
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
23
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
24
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
25
Universit ̈at Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
26
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, D-12489 Berlin, Germany
27
Imperial College London, London, SW7 2AZ, United Kingdom
28
University of Iowa, Iowa City, Iowa 52242, USA
29
Iowa State University, Ames, Iowa 50011-3160, USA
30
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudia Arabia
31
Johns Hopkins University, Baltimore, Maryland 21218, USA
32
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
33
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
34
University of Liverpool, Liverpool L69 7ZE, United Kingdom
35
Queen Mary, University of London, London, E1 4NS, United Kingdom
36
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
37
University of Louisville, Louisville, Kentucky 40292, USA
38
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Kernphysik, D-55099 Mainz, Germany
39
University of Manchester, Manchester M13 9PL, United Kingdom
40
University of Maryland, College Park, Maryland 20742, USA
41
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
42
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
43
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
44
University of Mississippi, University, Mississippi 38677, USA
45
Universit ́e de Montr ́eal, Physique des Particules, Montr ́eal, Qu ́ebec, Canada H3C 3J7
46
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
47
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
48
University of Notre Dame, Notre Dame, Indiana 46556, USA
49
Ohio State University, Columbus, Ohio 43210, USA
50
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
51
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
52
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
53
INFN Sezione di Pisa
a
; Dipartimento di Fisica,
Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
54
Princeton University, Princeton, New Jersey 08544, USA
55
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
56
Universit ̈at Rostock, D-18051 Rostock, Germany
3
57
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
58
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
59
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
60
University of South Carolina, Columbia, South Carolina 29208, USA
61
Southern Methodist University, Dallas, Texas 75275, USA
62
Stanford University, Stanford, California 94305-4060, USA
63
State University of New York, Albany, New York 12222, USA
64
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
65
University of Tennessee, Knoxville, Tennessee 37996, USA
66
University of Texas at Austin, Austin, Texas 78712, USA
67
University of Texas at Dallas, Richardson, Texas 75083, USA
68
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
69
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, I-34127 Trieste, Italy
70
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
71
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
72
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
73
University of Wisconsin, Madison, Wisconsin 53706, USA
We present a measurement of the asymmetry
A
CP
between same-sign inclusive dilepton samples
`
+
`
+
and
`
−
`
−
(
`
=
e, μ
) from semileptonic
B
decays in
Υ
(4
S
)
→
B
B
events, using the complete
data set recorded by the
B
A
B
AR
experiment near the
Υ
(4
S
) resonance, corresponding to 471 million
B
B
pairs. The asymmetry
A
CP
allows comparison between the mixing probabilities
P
(
B
0
→
B
0
)
and
P
(
B
0
→
B
0
), and therefore probes
CP
and
T
violation. The result,
A
CP
= (
−
3
.
9
±
3
.
5(stat
.
)
±
1
.
9(syst
.
))
×
10
−
3
, is consistent with the Standard Model expectation.
PACS numbers: 13.20.He, 11.30.Er
A neutral
B
meson can transform to its antiparticle
through the weak interaction. A difference between the
probabilities
P
(
B
0
→
B
0
) and
P
(
B
0
→
B
0
) is allowed
by the Standard Model (SM), and is a signature of vi-
olations of both
CP
and
T
symmetries. This type of
CP
violation, called
CP
violation in mixing, was first ob-
served in the neutral kaon system [1], but has not been
observed in the neutral
B
system, where the SM predicts
an asymmetry of the order of 10
−
4
[2]. The current ex-
perimental average of
CP
asymmetry in mixing measured
in the
B
0
system alone is
A
CP
= (+2
.
3
±
2
.
6)
×
10
−
3
[3],
dominated by the
B
A
B
AR
[4, 5], DØ [6], and Belle [7]
experiments
1
. A recent measurement in a mixture of
B
0
and
B
0
s
mesons by the DØ collaboration deviates from
the SM expectation by more than three standard devia-
tions [8]. Improving the experimental precision is crucial
for understanding the source of this apparent discrep-
ancy.
The neutral
B
meson system can be described by an ef-
fective Hamiltonian
H
=
M
−
i
Γ
/
2 for the two states
|
B
0
〉
and
|
B
0
〉
. Assuming
CPT
symmetry, the mass eigenstates
can be written as
|
B
L/H
〉
=
p
|
B
0
〉±
q
|
B
0
〉
. If
|
q/p
| 6
= 1,
both
CP
and
T
symmetries are violated. Details of the
formalism can be found in Refs. [10, 11].
The
B
0
B
0
pair created in the
Υ
(4
S
) decay evolves
coherently until one
B
meson decays. In this analysis,
we use the charge of the lepton (electron or muon) in
1
The quoted average excludes the DØ inclusive dimuon result [8]
and the recently published LHCb result [9].
semileptonic
B
decays to identify the flavor of the
B
me-
son at the time of its decay. If the second
B
meson has
oscillated to its antiparticle, it will produce a lepton that
has the same charge as the lepton from the first
B
de-
cay. The
CP
asymmetry
A
CP
between
P
(
B
0
→
B
0
) and
P
(
B
0
→
B
0
) can be measured by the charge asymmetry
of the same-sign dilepton event rate
P
±±
``
:
A
CP
=
P
++
``
−P
−−
``
P
++
``
+
P
−−
``
=
1
−|
q/p
|
4
1 +
|
q/p
|
4
.
(1)
This asymmetry is independent of the
B
decay time.
We present herein an updated measurement of
A
CP
using inclusive dilepton events collected by the
B
A
B
AR
detector at the PEP-II asymmetric-energy
e
+
e
−
storage
rings at SLAC National Accelerator Laboratory. The
data set consists of 471
×
10
6
B
B
pairs produced at the
Υ
(4
S
) resonance peak (on-peak) and 44 fb
−
1
of data col-
lected at a center-of-mass (CM) energy 40 MeV below the
peak (off-peak) [12]. Monte Carlo (MC) simulated
B
B
events equivalent to 10 times the data set based on Evt-
Gen [13] and GEANT4 [14] with full detector response
and event reconstruction are used to test the analysis
procedure. The main changes with respect to the previ-
ous
B
A
B
AR
analysis [4] include doubling the data set, a
higher signal selection efficiency, improved particle iden-
tification algorithms, and a time-independent approach
instead of a time-dependent analysis.
The
B
A
B
AR
detector is described in detail else-
where [15].
Events are selected if the two highest-
momentum particles in the event are consistent with the
electron or muon hypotheses. All quantities are evaluated
4
in the CM frame unless stated otherwise. The higher-
momentum and lower-momentum lepton candidates are
labeled as 1 and 2, respectively. Four lepton combina-
tions are allowed:
`
1
`
2
=
{
ee,eμ,μe,μμ
}
, as are four
charge combinations, for a total of 16 subsamples. We
assume
e
-
μ
universality, i.e., equal
A
CP
for all
`
1
`
2
combi-
nations. The time-integrated signal yields can be written
as [16]
N
±±
`
1
`
2
=
1
2
N
0
`
1
`
2
(1
±
a
`
1
±
a
`
2
±
A
CP
)
χ
`
1
`
2
d
,
(2)
N
±∓
`
1
`
2
=
1
2
N
0
`
1
`
2
(1
±
a
`
1
∓
a
`
2
)(1
−
χ
`
1
`
2
d
+
r
B
)
,
(3)
in the limit of
A
CP
1 and
a
`
j
1, where
a
`
j
=
(
+
`
j
−
−
`
j
)
/
(
+
`
j
+
−
`
j
) is the average charge asymmetry
of the detection efficiency for lepton
j
,
r
B
is the
B
+
/
B
0
event ratio,
χ
`
1
`
2
d
is the effective mixing probability of
neutral
B
mesons including efficiency corrections, and
N
0
`
1
`
2
is the neutral
B
signal yield for the
`
1
`
2
flavor
combination.
A small fraction of the background comes from
e
+
e
−
→
f
̄
f
(
γ
) continuum events (
f
∈{
u,d,s,c,e,μ,τ
}
).
This contribution is subtracted using the off-peak data
and the integrated luminosity ratio [12] between the on-
peak and off-peak data sets. The remaining background
comes from
B
B
events, where at least one lepton candi-
date originates from
B
→
X
→
`Y
cascade decays, or
from a hadron misidentified as a lepton.
Including the background, we expand Eqs.(2,3) to pa-
rameterize the total observed numbers of events as
M
±±
`
1
`
2
=
1
2
N
0
`
1
`
2
(1 +
R
±±
`
1
`
2
)
[
1
±
a
`
1
±
a
`
2
±
1 +
δ
`
1
`
2
R
±±
`
1
`
2
1 +
R
±±
`
1
`
2
A
CP
]
χ
`
1
`
2
d
,
(4)
M
±∓
`
1
`
2
=
1
2
N
0
`
1
`
2
(1 +
R
±∓
`
1
`
2
)(1
±
a
`
1
∓
a
`
2
)(1
−
χ
`
1
`
2
d
+
r
B
)
,
(5)
where
R
±±
`
1
`
2
and
R
±∓
`
1
`
2
are background-to-signal ratios un-
der the condition
A
CP
= 0, and
δ
`
1
`
2
is the probability
of a same-sign background event being consistent with
the flavors of the neutral
B
pairs at the time of their
decay after
B
0
-
B
0
mixing, i.e.,
`
+
`
+
(
`
−
`
−
) for
B
0
B
0
(
B
0
B
0
), minus the probability of the opposite case, i.e.,
`
+
`
+
(
`
−
`
−
) for
B
0
B
0
(
B
0
B
0
). The detailed derivation
can be found in the supplemental material [16]. For
the opposite-sign events, signal is
CP
symmetric. The
background originating from
B
0
B
0
(
B
0
B
0
) preferably
contributes to
`
+
`
−
(
`
−
`
+
) because a primary lepton
tends to have a higher momentum than a cascade lep-
ton. Therefore, the background yield is also a function
of
A
CP
. However, the coefficient of
A
CP
is less than 0.01
for the final data sample, so it is ignored in the fits.
Events with
≥
1 lepton (single-lepton sample) are used
to constrain the charge asymmetry of the detector effi-
ciency
a
`
≡
(
a
`
1
+
a
`
2
)
/
2. The inclusive single-lepton
asymmetry
a
on
in on-peak data can be expressed as [16]
a
on
=
α
+
βχ
d
A
CP
+
γa
`
,
(6)
where parameters
α
,
β
, and
γ
are functions of the fol-
lowing quantities: the fractions and asymmetries of the
continuum background, misidentified leptons, and cas-
cade leptons; the
B
0
/B
+
ratio; and
w
casc
B
0
the probability
of the cascade-lepton’s charge incorrectly identifying the
B
flavor at the time of the
B
decay.
We build a
χ
2
fit using the 8+8+1 equations repre-
sented by Eqs. (4)–(6) to extract
A
CP
. For the single-
lepton sample, we use only electrons since the purity is
much higher than that of muons.
The event selection requires
≥
4 charged particle
tracks and the normalized second-order Fox-Wolfram mo-
ment [17]
R
2
<
0
.
6. The leptons should satisfy 0
.
6 GeV
<
p
`
2
≤
p
`
1
<
2
.
2 GeV. The polar angle
θ
of the electron
(muon) candidate in the laboratory frame is required to
satisfy
−
0
.
788
<
cos
θ <
0
.
961 (
−
0
.
755
<
cos
θ <
0
.
956).
The lepton is rejected if, when combined with another
lepton of opposite charge, the invariant mass is consis-
tent with that of a
J/ψ
or a
ψ
(2
S
) meson, or when arising
from a photon conversion. The lepton tracks must pass
a set of quality requirements. For dilepton events, the
invariant mass of the lepton pair must be greater than
150 MeV. The proper decay time difference ∆
t
of the two
B
mesons can be determined from the distance along the
collision axis between the points of closest approach of
the lepton tracks to the beam spot, and the boost factor
(
'
0
.
56) of the CM frame. We require
|
∆
t
|
<
15 ps and
its uncertainty
σ
∆
t
<
3 ps.
Electrons and muons are identified by two sepa-
rate multivariate algorithms that predominately use the
shower shape and energy deposition in the electromag-
netic calorimeter for electrons, and the track path length
and cluster shape in the instrumented flux return for
muons.
The electron (muon) identification efficiency
is approximately 93% (40%–80% depending on momen-
tum). The probability of a hadron being identified as an
electron (muon) is
<
0
.
1% (
∼
1%).
To further suppress background, we use random for-
est multivariate classifiers [18]. Off-peak data are used
to represent continuum events, and simulated events are
used for signal and
B
B
background. In the dilepton sam-
5
ple, we use six variables:
p
`
1
,
p
`
2
, thrust and spheric-
ity [19] of the rest of the event, the opening angle
θ
12
of
the two tracks in the CM frame, and ∆
t
. Separate classi-
fiers are trained on the same-sign and opposite-sign sam-
ples. The
ee
,
eμ
,
μe
, and
μμ
samples are also trained sep-
arately. The dilepton signal probability distributions of
the classifiers are shown in Fig. 1. We select events with a
probability
>
0
.
7 to minimize the statistical uncertainty
based on fits to the
B
B
MC sample. The final on-peak
data sample includes 2
.
5% continuum background for all
dilepton samples, and 35% (8%)
B
B
background in the
same-sign (opposite-sign) sample.
0.5
0.6
0.7
0.8
0.9
0
5
10
15
(a)
0.5
0.6
0.7
0.8
0.9
1.0
0.9
1.0
1.1
Ratio
0.5
0.6
0.7
0.8
0.9
1.0
Multivariate output
0
40
80
120
(b)
0.5
0.6
0.7
0.8
0.9
1.0
0.9
1.0
1.1
Ratio
Entries / 0.005 (
×
10
3
)
FIG. 1. (Color online) Signal probability distributions from
the dilepton multivariate algorithm for (a) the same-sign sam-
ple and (b) the opposite-sign sample; all lepton flavors are
combined. Points are continuum-subtracted data; shaded re-
gions from bottom to top are for signal,
B
B
background with
≥
1 misidentified lepton, and
B
B
background with both real
leptons. Hatched region is rejected. Data/MC ratios are
shown in inset plots. Regions below 0.45 are not shown.
Approximately 0.1% (3%) of selected electrons
(muons) in dilepton samples are misidentified. According
to the simulation, nearly 98% of the misidentified elec-
trons come from pions and 87% (12%) of the misidentified
muons come from pions (kaons). To correct for the dif-
ference in the muon misidentification rates between data
and MC samples, we study the muon identification effi-
ciency in clean kaon and pion control samples from the
process
D
∗
+
→
D
0
π
+
followed by
D
0
→
K
−
π
+
(and
the charge-conjugate process). The ratios of the efficien-
cies between data and MC samples are used to scale the
misidentified muon component in the MC sample. The
corrections to
μ
+
(
μ
−
) is 0
.
792
±
0
.
012 (0
.
797
±
0
.
013).
Since the misidentification rate is very low for elec-
trons, we use a much larger pion control sample from
K
0
S
→
π
+
π
−
decays. This control sample has a lower
momentum spectrum and does not cover the region of
p >
2
.
5 GeV in the laboratory frame, which accounts for
less than 8% of the misidentified leptons. The correc-
tions to misidentified
e
+
(
e
−
) is 1
.
00
±
0
.
10 (0
.
56
±
0
.
10).
The quoted uncertainties are conservative estimates that
result from mismatched momentum spectra and from a
small fraction of kaons and protons among misidentified
electrons.
For the single-lepton sample, the random forest algo-
rithm uses the number of tracks, the event thrust,
R
2
, the
difference between the observed energy in the event and
the sum of the
e
+
e
−
beam energies, the cosines of the an-
gles between the lepton and the axes of the thrust and the
sphericity of the rest of the event, and the zeroth-order
and second-order polynomial moments
L
0
and
L
2
, where
L
n
=
∑
p
i
(cos
θ
i
)
n
,
p
i
is the momentum of a particles
in the rest of the event and
θ
i
is the angle between that
particle and the single-lepton candidate. We optimize
the selection requirement by minimizing the uncertainty
of the charge asymmetry after the continuum component
is subtracted from the on-peak data. A total of 8
.
5
×
10
7
single electrons are selected in the on-peak data, of which
approximately 63% are from direct semileptonic
B
de-
cays. Finally, the single electrons are randomly sampled
so that the signal momentum spectrum matches that of
the dilepton events.
Raw asymmetries of the single electrons in the on- and
off-peak data are found to be
a
on
= (4
.
16
±
0
.
14)
×
10
−
3
and
a
off
= (11
.
1
±
1
.
4)
×
10
−
3
. The larger asymme-
try in the off-peak data is primarily due to the radiative
Bhabha background and the larger detector acceptance
in the backward (positron-beam) direction. The contin-
uum fraction
f
cont
= (10
.
32
±
0
.
02)% is obtained from the
ratio of the selected single electrons and the integrated
luminosities in off- and on-peak data [12]. The neutral
B
fraction in the
B
B
component
f
B
0
= (48
.
5
±
0
.
6)%
is the
Υ
(4
S
)
→
B
0
B
0
branching fraction [20] corrected
for the selection efficiency.
The cascade event frac-
tions
f
casc
B
0
= 19
.
8% and
f
casc
B
±
= 15
.
3% are obtained
from simulation, with negligible statistical uncertain-
ties. The fraction of the misidentified electron is 0.19%,
and the asymmetry is approximately 35%. The differ-
ence between direct and cascade electron asymmetries
is (
−
1
.
16
±
0
.
25)
×
10
−
3
in MC. The probability
w
casc
B
0
in MC is found to be (73
.
8
±
0
.
1)%. Using these nu-
merical values, we determine the coefficients in Eq. (6):
a
on
−
α
= (2
.
60
±
0
.
20)
×
10
−
3
,
βχ
d
= 0
.
057
±
0
.
001, and
γ
= 0
.
8951
±
0
.
0002.
The fitting procedure is tested on the
B
B
MC sam-
ple; the result
A
MC
CP
= (
−
1
.
00
±
1
.
04)
×
10
−
3
is consistent
with the
CP
-symmetric simulation model. We artificially
create a non-zero
A
CP
by reweighing mixed events in the
MC sample, and confirm that the fitting procedure tracks
the change in the
A
CP
without bias. The continuum-
subtracted event yields are shown in Table I and are used
in Eqs. (4–5) for the fit. The result of the fit to data, after
correcting for the small bias (
−
1
.
0
×
10
−
3
) in the simula-
6
TABLE I. Continuum-subtracted number of events.
`
+
`
+
`
+
`
−
`
−
`
+
`
−
`
−
ee
82 303
±
320 426 296
±
783 425 309
±
782 81 586
±
323
eμ
55 277
±
263 384 552
±
684 378 261
±
660 55 878
±
264
μe
67 399
±
290 467 591
±
737 475 363
±
744 67 152
±
290
μμ
47 384
±
243 277 936
±
619 278 691
±
618 48 145
±
247
tion, is
A
CP
= (
−
3
.
9
±
3
.
5)
×
10
−
3
,
a
e
1
= (3
.
4
±
0
.
6)
×
10
−
3
,
a
e
2
= (3
.
0
±
0
.
6)
×
10
−
3
,
a
μ
1
= (
−
5
.
6
±
1
.
1)
×
10
−
3
, and
a
μ
2
= (
−
6
.
5
±
1
.
1)
×
10
−
3
. The remaining free parame-
ters are
N
0
`
1
`
2
and
χ
`
1
`
2
d
. The
χ
2
value is 6.2 for 4 degrees
of freedom. The correlations between
A
CP
and
a
e
1
,
a
e
2
,
a
μ
1
, and
a
μ
2
are
−
0
.
41,
−
0
.
47,
−
0
.
54, and
−
0
.
51, respec-
tively. Correlations among other parameters are negligi-
ble. Figure 2 shows the fit results for the six data-taking
periods and the four flavor subsamples.
1
2
3
4
5
6
1-4
5-6
ee
eμ
μe
μμ
Subsample
40
30
20
10
0
10
A
CP
(
10
−
3
)
FIG. 2. (Color online)
A
CP
of the six data-taking periods
(dots), the first four and the last two periods (squares), and
the four flavor subsamples (rhombuses). The horizontal band
is the
±
1
σ
region of the final fit result. All error bars are
statistical only.
The systematic uncertainties are summarized in Ta-
ble II. The branching fractions in the
B
decay chain par-
tially determine the background-to-signal ratio. We cor-
rect the MC samples so that important branching frac-
tions are consistent with the world average [20]. These
branching fractions correspond to inclusive
B
semilep-
tonic decays,
B
→
τν
τ
X
, charm production (
D
0
,
D
0
,
D
±
,
D
±
s
,
Λ
+
c
, and
Λ
−
c
) from
B
decays, and inclusive
charm semileptonic decays. The corrections vary for
most decays between 0.57 and 1.32, depending on the
channel.
We estimate the systematic uncertainty by
varying the corrections over their uncertainties, which
are dominated by the errors of the world averages.
The systematic uncertainties due to misidentified lep-
tons are estimated by varying the uncertainties of the
corrections to
e
+
,
e
−
,
μ
+
, and
μ
−
individually, and sep-
arately for the dilepton and single-electron samples.
In the single-electron MC sample, the charge asymme-
try of the electron in
B
0
B
0
is slightly different from that
in
B
+
B
−
by (0
.
46
±
0
.
18)
×
10
−
3
. Since we cannot sep-
arate
B
+
B
−
electrons from
B
0
B
0
electrons in data, the
single-electron asymmetry measurement is the average
of the two asymmetries, which is half the difference away
from the
B
0
B
0
electron charge asymmetry. The system-
atic uncertainty is determined by the change in
A
CP
af-
ter shifting the asymmetry in the signal component of
the single-electron sample by half the charge asymmetry
difference .
The difference in charge asymmetry between the direct
and the cascade electrons is found to be
a
casc
e
−
a
dir
e
=
(
−
1
.
16
±
0
.
25)
×
10
−
3
in the single-electron MC sam-
ple. The difference between the lower-momentum and
the higher-momentum electron asymmetries is negative.
This trend is consistent with the result of the fit to
the dilepton data:
a
e
2
−
a
e
1
= (
−
0
.
4
±
0
.
7)
×
10
−
3
.
For muons, the corresponding values are
a
casc
μ
−
a
dir
μ
=
(
−
0
.
47
±
0
.
28)
×
10
−
3
and
a
μ
2
−
a
μ
1
= (
−
0
.
9
±
1
.
2)
×
10
−
3
.
In each case, we set the cascade lepton charge asymmetry
to that of the direct lepton, and use the change in
A
CP
as a systematic uncertainty.
The background-to-signal ratios
R
±±
`
1
`
2
and
R
±∓
`
1
`
2
(un-
der the condition
A
CP
=0) in the dilepton sample are
determined from the MC sample. The correction for
the misidentified lepton background has been dealt with
above. The real lepton portion of the ratio is in prin-
ciple the same between
`
+
`
+
and
`
−
`
−
samples because
the particle identification efficiencies cancel between the
background and the signal. In the MC sample, they are
consistent within 1
σ
. Varying
R
++
`
1
`
2
and
R
−−
`
1
`
2
or
R
+
−
`
1
`
2
and
R
−
+
`
1
`
2
simultaneously in the same direction results
in negligible changes in
A
CP
. If they are varied indepen-
dently, the quadratic sum of the changes in
A
CP
is larger.
We use the latter as a systematic uncertainty.
The random forest output distribution in the data
could be different from that in the MC sample. The
selection efficiency in the MC
B
B
dilepton events is ap-
proximately 2% larger than that in the data. We move
the dilepton random forest selection for the MC sample,
while keeping data the same, so that the selected MC
events are reduced by up to 6%. We take the average
change in
A
CP
as a systematic uncertainty.
Several other sources of systematic uncertainties are
studied and found to be negligible. These include the
overall dilepton signal fraction estimate, the kinematic
difference between on-peak and off-peak data due to dif-
ferent CM energies, the continuum component fraction,
the probability
w
casc
B
0
, the neutral-to-charged
B
ratio, the
same-sign background dilution factors
δ
`
1
`
2
, and the over-
all cascade event fraction.
In conclusion, we measure the
CP
asymmetry
A
CP
=
(
−
3
.
9
±
3
.
5
±
1
.
9)
×
10
−
3
in
B
0
-
B
0
mixing using inclu-
sive dilepton decays. This result is consistent with the
SM prediction and the world average [3]. This measure-
ment represents a significant improvement with respect
to our previous result [4] (superseded by this result), and
is among the most precise measurements [9, 20]. A Com-
parison of experimental results and averages is shown in
Fig. 3.
We are grateful for the excellent luminosity and ma-