B
A
B
AR
-PUB-13/005
SLAC-PUB-15448
Search for
CP
Violation in
B
0
B
0
Mixing using Partial Reconstruction of
B
0
→
D
∗−
X`
+
ν
`
and a Kaon Tag
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
ac
,
9
A. R. Buzykaev
a
,
9
V. P. Druzhinin
ab
,
9
V. B. Golubev
ab
,
9
E. A. Kravchenko
ab
,
9
A. P. Onuchin
ac
,
9
S. I. Serednyakov
ab
,
9
Yu. I. Skovpen
ab
,
9
E. P. Solodov
ab
,
9
K. Yu. Todyshev
ab
,
9
A. N. Yushkov
a
,
9
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
G. M. Vitug,
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
A. J. Martinez,
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
P. Ongmongkolkul,
14
F. C. Porter,
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
S. Playfer,
21
D. Bettoni
a
,
22
C. Bozzi
a
,
22
R. Calabrese
ab
,
22
G. Cibinetto
ab
,
22
E. Fioravanti
ab
,
22
I. Garzia
ab
,
22
E. Luppi
ab
,
22
L. Piemontese
a
,
22
V. Santoro
a
,
22
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
23
S. Martellotti,
23
P. Patteri,
23
I. M. Peruzzi,
23,
†
M. Piccolo,
23
M. Rama,
23
A. Zallo,
23
R. Contri
ab
,
24
E. Guido
ab
,
24
M. Lo Vetere
ab
,
24
M. R. Monge
ab
,
24
S. Passaggio
a
,
24
C. Patrignani
ab
,
24
E. Robutti
a
,
24
B. Bhuyan,
25
V. Prasad,
25
M. Morii,
26
A. Adametz,
27
U. Uwer,
27
H. M. Lacker,
28
P. D. Dauncey,
29
U. Mallik,
30
C. Chen,
31
J. Cochran,
31
W. T. Meyer,
31
S. Prell,
31
A. E. Rubin,
31
A. V. Gritsan,
32
N. Arnaud,
33
M. Davier,
33
D. Derkach,
33
G. Grosdidier,
33
F. Le Diberder,
33
A. M. Lutz,
33
B. Malaescu,
33
P. Roudeau,
33
A. Stocchi,
33
G. Wormser,
33
D. J. Lange,
34
D. M. Wright,
34
J. P. Coleman,
35
J. R. Fry,
35
E. Gabathuler,
35
D. E. Hutchcroft,
35
D. J. Payne,
35
C. Touramanis,
35
A. J. Bevan,
36
F. Di Lodovico,
36
R. Sacco,
36
G. Cowan,
37
J. Bougher,
38
D. N. Brown,
38
C. L. Davis,
38
A. G. Denig,
39
M. Fritsch,
39
W. Gradl,
39
K. Griessinger,
39
A. Hafner,
39
E. Prencipe,
39
R. J. Barlow,
40,
‡
G. D. Lafferty,
40
E. Behn,
41
R. Cenci,
41
B. Hamilton,
41
A. Jawahery,
41
D. A. Roberts,
41
R. Cowan,
42
D. Dujmic,
42
G. Sciolla,
42
R. Cheaib,
43
P. M. Patel,
43,
§
S. H. Robertson,
43
P. Biassoni
ab
,
44
N. Neri
a
,
44
F. Palombo
ab
,
44
L. Cremaldi,
45
R. Godang,
45,
¶
P. Sonnek,
45
D. J. Summers,
45
X. Nguyen,
46
M. Simard,
46
P. Taras,
46
G. De Nardo
ab
,
47
D. Monorchio
ab
,
47
G. Onorato
ab
,
47
C. Sciacca
ab
,
47
M. Martinelli,
48
G. Raven,
48
C. P. Jessop,
49
J. M. LoSecco,
49
K. Honscheid,
50
R. Kass,
50
J. Brau,
51
R. Frey,
51
N. B. Sinev,
51
D. Strom,
51
E. Torrence,
51
E. Feltresi
ab
,
52
M. Margoni
ab
,
52
M. Morandin
a
,
52
M. Posocco
a
,
52
M. Rotondo
a
,
52
G. Simi
a
,
52
F. Simonetto
ab
,
52
R. Stroili
ab
,
52
S. Akar,
53
E. Ben-Haim,
53
M. Bomben,
53
G. R. Bonneaud,
53
H. Briand,
53
G. Calderini,
53
J. Chauveau,
53
Ph. Leruste,
53
G. Marchiori,
53
J. Ocariz,
53
S. Sitt,
53
M. Biasini
ab
,
54
E. Manoni
a
,
54
S. Pacetti
ab
,
54
A. Rossi
a
,
54
C. Angelini
ab
,
55
G. Batignani
ab
,
55
S. Bettarini
ab
,
55
M. Carpinelli
ab
,
55,
∗∗
G. Casarosa
ab
,
55
A. Cervelli
ab
,
55
F. Forti
ab
,
55
M. A. Giorgi
ab
,
55
A. Lusiani
ac
,
55
B. Oberhof
ab
,
55
E. Paoloni
ab
,
55
A. Perez
a
,
55
G. Rizzo
ab
,
55
J. J. Walsh
a
,
55
D. Lopes Pegna,
56
J. Olsen,
56
A. J. S. Smith,
56
R. Faccini
ab
,
57
F. Ferrarotto
a
,
57
F. Ferroni
ab
,
57
M. Gaspero
ab
,
57
L. Li Gioi
a
,
57
G. Piredda
a
,
57
C. B ̈unger,
58
O. Gr ̈unberg,
58
T. Hartmann,
58
T. Leddig,
58
C. Voß,
58
R. Waldi,
58
T. Adye,
59
E. O. Olaiya,
59
F. F. Wilson,
59
S. Emery,
60
G. Hamel de Monchenault,
60
G. Vasseur,
60
Ch. Y`eche,
60
F. Anulli
a
,
61
D. Aston,
61
D. J. Bard,
61
J. F. Benitez,
61
C. Cartaro,
61
M. R. Convery,
61
J. Dorfan,
61
G. P. Dubois-Felsmann,
61
W. Dunwoodie,
61
M. Ebert,
61
R. C. Field,
61
B. G. Fulsom,
61
A. M. Gabareen,
61
M. T. Graham,
61
C. Hast,
61
W. R. Innes,
61
P. Kim,
61
M. L. Kocian,
61
D. W. G. S. Leith,
61
P. Lewis,
61
D. Lindemann,
61
B. Lindquist,
61
S. Luitz,
61
V. Luth,
61
H. L. Lynch,
61
D. B. MacFarlane,
61
D. R. Muller,
61
H. Neal,
61
S. Nelson,
61
M. Perl,
61
T. Pulliam,
61
B. N. Ratcliff,
61
A. Roodman,
61
A. A. Salnikov,
61
R. H. Schindler,
61
A. Snyder,
61
D. Su,
61
M. K. Sullivan,
61
J. Va’vra,
61
A. P. Wagner,
61
W. F. Wang,
61
W. J. Wisniewski,
61
M. Wittgen,
61
D. H. Wright,
61
H. W. Wulsin,
61
V. Ziegler,
61
W. Park,
62
M. V. Purohit,
62
R. M. White,
62,
††
J. R. Wilson,
62
A. Randle-Conde,
63
S. J. Sekula,
63
M. Bellis,
64
P. R. Burchat,
64
T. S. Miyashita,
64
E. M. T. Puccio,
64
M. S. Alam,
65
J. A. Ernst,
65
R. Gorodeisky,
66
N. Guttman,
66
D. R. Peimer,
66
A. Soffer,
66
S. M. Spanier,
67
J. L. Ritchie,
68
A. M. Ruland,
68
R. F. Schwitters,
68
B. C. Wray,
68
J. M. Izen,
69
X. C. Lou,
69
F. Bianchi
ab
,
70
F. De Mori
ab
,
70
A. Filippi
a
,
70
D. Gamba
ab
,
70
S. Zambito
ab
,
70
L. Lanceri
ab
,
71
L. Vitale
ab
,
71
F. Martinez-Vidal,
72
A. Oyanguren,
72
P. Villanueva-Perez,
72
arXiv:1305.1575v4 [hep-ex] 1 Aug 2013
2
H. Ahmed,
73
J. Albert,
73
Sw. Banerjee,
73
F. U. Bernlochner,
73
H. H. F. Choi,
73
G. J. King,
73
R. Kowalewski,
73
M. J. Lewczuk,
73
T. Lueck,
73
I. M. Nugent,
73
J. M. Roney,
73
R. J. Sobie,
73
N. Tasneem,
73
T. J. Gershon,
74
P. F. Harrison,
74
T. E. Latham,
74
H. R. Band,
75
S. Dasu,
75
Y. Pan,
75
R. Prepost,
75
and S. L. Wu
75
(The
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),
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
Technische Universit ̈at Dresden, Institut f ̈ur 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
22
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara
b
, I-44122 Ferrara, Italy
23
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
24
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
25
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
26
Harvard University, Cambridge, Massachusetts 02138, USA
27
Universit ̈at Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
28
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, D-12489 Berlin, Germany
29
Imperial College London, London, SW7 2AZ, United Kingdom
30
University of Iowa, Iowa City, Iowa 52242, USA
31
Iowa State University, Ames, Iowa 50011-3160, USA
32
Johns Hopkins University, Baltimore, Maryland 21218, USA
33
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
34
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
35
University of Liverpool, Liverpool L69 7ZE, United Kingdom
36
Queen Mary, University of London, London, E1 4NS, United Kingdom
37
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
38
University of Louisville, Louisville, Kentucky 40292, USA
39
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Kernphysik, D-55099 Mainz, Germany
40
University of Manchester, Manchester M13 9PL, United Kingdom
41
University of Maryland, College Park, Maryland 20742, USA
42
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
43
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
44
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
45
University of Mississippi, University, Mississippi 38677, USA
46
Universit ́e de Montr ́eal, Physique des Particules, Montr ́eal, Qu ́ebec, Canada H3C 3J7
47
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
48
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
49
University of Notre Dame, Notre Dame, Indiana 46556, USA
50
Ohio State University, Columbus, Ohio 43210, USA
51
University of Oregon, Eugene, Oregon 97403, USA
52
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
53
Laboratoire de Physique Nucl ́eaire et de Hautes Energies,
3
IN2P3/CNRS, Universit ́e Pierre et Marie Curie-Paris6,
Universit ́e Denis Diderot-Paris7, F-75252 Paris, France
54
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
55
INFN Sezione di Pisa
a
; Dipartimento di Fisica,
Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
56
Princeton University, Princeton, New Jersey 08544, USA
57
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
58
Universit ̈at Rostock, D-18051 Rostock, Germany
59
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
60
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
61
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
62
University of South Carolina, Columbia, South Carolina 29208, USA
63
Southern Methodist University, Dallas, Texas 75275, USA
64
Stanford University, Stanford, California 94305-4060, USA
65
State University of New York, Albany, New York 12222, USA
66
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
67
University of Tennessee, Knoxville, Tennessee 37996, USA
68
University of Texas at Austin, Austin, Texas 78712, USA
69
University of Texas at Dallas, Richardson, Texas 75083, USA
70
INFN Sezione di Torino
a
; Dipartimento di Fisica Sperimentale, Universit`a di Torino
b
, I-10125 Torino, Italy
71
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, I-34127 Trieste, Italy
72
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
73
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
74
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
75
University of Wisconsin, Madison, Wisconsin 53706, USA
We present results of a search for
CP
violation in
B
0
B
0
mixing with the
B
A
B
AR
detector. We
select a sample of
B
0
→
D
∗−
X`
+
ν
decays with a partial reconstruction method and use kaon
tagging to assess the flavor of the other
B
meson in the event. We determine the
CP
violating
asymmetry
A
CP
≡
N
(
B
0
B
0
)
−
N
(
B
0
B
0
)
N
(
B
0
B
0
)+
N
(
B
0
B
0
)
= (0
.
06
±
0
.
17
+0
.
38
−
0
.
32
)%, corresponding to ∆
CP
= 1
−|
q/p
|
=
(0
.
29
±
0
.
84
+1
.
88
−
1
.
61
)
×
10
−
3
.
PACS numbers: 13.25.Ft, 13.20.He, 13.20.Gd
Experiments at
B
factories have observed
CP
violation
in direct
B
0
decays [1] and in the interference between
B
0
mixing and decay [2].
CP
violation in mixing has so
far eluded observation.
The weak-Hamiltonian eigenstates are related to the
flavor eigenstates of the strong interaction Hamiltonian
by
|
B
L,H
〉
=
p
|
B
0
〉 ±
q
|
B
0
〉
. The value of the ratio
|
q/p
|
can be determined from the asymmetry between
the two oscillation probabilities
P
=
P
(
B
0
→
B
0
) and
̄
P
=
P
(
B
0
→
B
0
) through
A
CP
= (
̄
P −P
)
/
(
̄
P
+
P
) =
1
−|
q/p
|
4
1+
|
q/p
|
4
≈
2∆
CP
, where ∆
CP
= 1
−|
q/p
|
and the Stan-
dard Model (SM) prediction is
A
CP
=
−
(4
.
0
±
0
.
6)
×
10
−
4
[3]. Any observation with the present experimen-
tal sensitivity (
O
(10
−
3
)) would therefore reveal physics
beyond the SM.
Experiments measure
A
CP
from the dilepton asym-
metry,
A
``
=
N
(
`
+
`
+
)
−
N
(
`
−
`
−
)
N
(
`
+
`
+
)+
N
(
`
−
`
−
)
, where an
`
+
(
`
−
) tags
a
B
0
(
B
0
) meson, and
`
refers either to an electron
or a muon [4]. These measurements benefit from the
large number of produced dilepton events. However,
they rely on the use of control samples to subtract the
charge-asymmetric background originating from hadrons
wrongly identified as leptons or leptons from light hadron
decays, and to compute the charge-dependent lepton
identification asymmetry that may produce a false signal.
The systematic uncertanties associated with the correc-
tions for these effects constitute a severe limitation to the
precision of the measurements.
Using a sample of dimuon events, the
D
∅
Collabora-
tion measured a value of
A
CP
for a mixture of
B
s
and
B
0
decays that deviates from the SM by 3.9 standard
deviations [5]. Measurements of
A
CP
for
B
s
mesons
performed by the
D
∅
Collaboration with
B
s
→
D
s
μX
decays are consistent with the SM [7].
We present a measurement of
A
CP
(
B
0
) with a new
analysis technique.
We reconstruct a sample of
B
0
mesons (hereafter called
B
R
; charge conjugate states are
implied unless otherwise stated) from the semileptonic
transition
B
0
→
D
∗−
X`
+
ν
, with a partial reconstruction
of the
D
∗−
→
π
−
D
0
decay (see Ref. [8] and references
therein). The observed asymmetry between the number
of events with an
`
+
compared to those with an
`
−
is
then:
A
`
≈A
r`
+
A
CP
χ
d
,
(1)
where
χ
d
= 0
.
1862
±
0
.
0023 [9] is the integrated mix-
ing probability for
B
0
mesons and
A
r`
is the detector-
4
induced charge asymmetry in the
B
R
reconstruction.
We identify (“tag”) the flavor of the other
B
0
meson
(labeled
B
T
) using events with a charged kaon (
K
T
). An
event with a
K
+
(
K
−
) usually arises from a state that
decays as a
B
0
(
B
0
) meson. When mixing takes places,
the
`
and the
K
T
then have the same electric charge. The
observed asymmetry in the rate of mixed events is:
A
T
=
N
(
`
+
K
+
T
)
−
N
(
`
−
K
−
T
)
N
(
`
+
K
+
T
) +
N
(
`
−
K
−
T
)
≈A
r`
+
A
K
+
A
CP
,
(2)
where
A
K
is the detector charge asymmetry in kaon re-
construction. A kaon with the same charge as the
`
might
also arise from the Cabibbo-Favored (CF) decays of the
D
0
meson produced with the lepton from the partially
reconstructed side (
K
R
). The asymmetry observed for
these events is:
A
R
=
N
(
`
+
K
+
R
)
−
N
(
`
−
K
−
R
)
N
(
`
+
K
+
R
) +
N
(
`
−
K
−
R
)
≈A
r`
+
A
K
+
A
CP
χ
d
.
(3)
Eqs. 1, 2, and 3 can be used to extract
A
CP
and the
detector induced asymmetries (
A
r`
and
A
K
).
A detailed description of the
B
A
B
AR
detector is pro-
vided elsewhere [10]. We use a sample with an inte-
grated luminosity of 425.7 fb
−
1
[11] collected on the
peak of the
Υ
(4
S
) resonance. A 45 fb
−
1
sample col-
lected 40 MeV below the resonance (“off-peak”) is used
for background studies. We also use a simulated sample
of
B
B
events [12] with an integrated luminosity equiva-
lent to approximately three times the data.
We preselect a sample of hadronic events requiring the
number of charged particles to be at least four. We re-
duce non-
B
B
(continuum) background by requiring the
ratio of the second to the zeroth order Fox-Wolfram mo-
ments [13] to be less than 0.6.
We select the
B
R
sample by searching for combi-
nations of a charged lepton (in the momentum range
1
.
4
< p
`
<
2
.
3 GeV
/c
) and a low momentum pion
π
−
s
(60
< p
π
−
s
<
190 MeV
/c
), which is taken to arise from
D
∗−
→
D
0
π
−
s
decay. Here and elsewhere momenta are
calculated in the-center-of-mass frame. The
`
+
and the
π
−
s
must have opposite electric charge. Their tracks must
be consistent with originating from a common vertex,
which is constrained to the beam collision point in the
plane transverse to the beam axis. Finally, we combine
p
`
,
p
π
−
s
, and the probability of the vertex fit in a likeli-
hood ratio variable (
η
) optimized to reject combinatorial
B
B
events. If more than one candidate is found in the
event, we choose the one with the largest value of
η
.
We determine the square of the unobserved neutrino
mass as:
M
2
ν
= (
E
beam
−
E
D
∗
−
E
`
)
2
−
(
p
D
∗
+
p
`
)
2
,
where we neglect the momentum of the
B
0
(p
B
≈
340 MeV
/c
) and identify the
B
0
energy with the beam
energy
E
beam
in the
e
+
e
−
center-of-mass frame;
E
`
and
p
`
are the energy and momentum of the lepton and
p
D
∗
is the estimated momentum of the
D
∗
. As a conse-
quence of the limited phase space available in the
D
∗
+
decay, the soft pion is emitted nearly at rest in the
D
∗
+
rest frame. The
D
∗
+
four-momentum can therefore be
computed by approximating its direction as that of the
soft pion, and parametrizing its momentum as a linear
function of the soft-pion momentum. All
B
0
semilep-
tonic decays with
M
2
ν
near zero are considered to be
signal events, including
B
0
→
D
∗−
X
0
`
+
ν
`
(primary),
B
0
→
D
∗−
X
0
τ
+
ν
τ
, τ
+
→
`
+
ν
`
̄
ν
τ
(cascade), and
B
0
→
D
∗−
h
+
(misidentified), where the hadron (
h
=
π,K
)
is erroneously identified as a lepton (in most cases, a
muon).
B
0
decays to flavor-insensitive
CP
eigenstates,
B
0
→
D
∗±
DX,D
→
`
∓
X
, and
B
+
→
D
∗−
X
+
`
+
ν
`
de-
cays accumulate around zero as the signal events (“peak-
ing background”). The uncorrelated background consists
of continuum and combinatorial
B
B
events. The latter
category includes events where a genuine
D
∗−
is com-
bined with an
`
+
from the other
B
meson.
We identify charged kaons in the momentum range
0
.
2
< p
K
<
4 GeV
/c
with an average efficiency of about
85% and a
∼
3% pion misidentification rate. We deter-
mine the
K
production point from the intersection of the
K
track and the beam spot, and then determine the dis-
tance ∆
z
between the
`
+
π
−
s
and
K
vertices coordinates
along the beam axis. Finally, we define the proper time
difference ∆
t
between the
B
R
and the
B
T
in the so called
“Lorentz boost approximation” [14], ∆
t
=
∆
z
βγ
, where
the product
βγ
= 0
.
56 is the average Lorentz boost of
the
Υ
(4
S
) in the laboratory frame. Since the
B
mesons
are not at rest in the
Υ
(4
S
) rest frame, and in addi-
tion the
K
is usually produced in the cascade process
B
T
→
DX,D
→
KY
, ∆
t
is in fact only an approxima-
tion of the actual proper time difference between the
B
R
and the
B
T
. We reject events if the uncertainty
σ
(∆
t
) ex-
ceeds 3 ps. This selection reduces to a negligible level the
contamination from protons produced in the scattering
of primary particles with the beam pipe or the detector
material and wrongly identified as kaons, which would
otherwise constitute a large charge-asymmetric source of
background.
We define an event as “mixed” if the
K
and the
`
have
the same electric charge and as “unmixed” otherwise. In
about 20% of the cases, the
K
has the wrong charge cor-
relation with respect to the
B
T
, and the event is wrongly
defined (mistags).
About 95% of the
K
R
candidates have the same elec-
tric charge as the
`
; they constitute 75% of the mixed
event sample. Due to the small lifetime of the
D
0
meson,
the separation in space between the
K
R
and the
`π
s
pro-
duction points is much smaller than for
K
T
. Therefore,
we use ∆
t
as a first discriminant variable. Kaons in the
K
R
sample are usually emitted in the hemisphere oppo-
site to the
`
, while genuine
K
T
are produced randomly,
5
so we use in addition the cosine of the angle
θ
`K
between
the
`
and the
K
.
In about 20% of the cases, the events contain more
than one
K
; most often we find both a
K
T
and a
K
R
can-
didate. As these two carry different information, we ac-
cept multiple-candidate events. Using ensembles of sim-
ulated samples of events, we find that this choice does
not affect the statistical uncertainty.
The
M
2
ν
distribution of all signal candidates in shown
in Fig. 1. We determine the signal fraction by fitting
the
M
2
ν
distribution in the interval [
−
10
,
2
.
5] GeV
2
/c
4
with the sum of continuum,
B
B
combinatorial, and
B
B
peaking events. We split peaking
B
B
into direct (
B
0
→
D
∗−
`
+
ν
), “
D
∗∗
” (
B
→
D
∗−
X
0
`
+
ν
`
), cascade, hadrons
wrongly identified as leptons, and
CP
eigenstates. In the
fit, we float the fraction of direct,
D
∗∗
, and
B
B
combi-
natorial background, while we fix the continuum contri-
bution to the expectation from off-peak events, rescaled
by the on-peak to off-peak luminosity ratio, and the rest
(less than 2% of the total) to the level predicted by the
Monte Carlo simulation. Based on the assumption of
isospin conservation, we attribute 66% of the
D
∗∗
events
to
B
+
decays and the rest to
B
0
decays. We use the
result of the fit to compute the fractions of continuum,
combinatorial, and peaking
B
+
background,
CP
eigen-
states, and
B
0
signal in the sample, as a function of
M
2
ν
.
We find a total of (5
.
945
±
0
.
007)
×
10
6
peaking events
(see Fig. 1).
We then repeat the fit after dividing events in the
four lepton categories (
e
±
,μ
±
) and eight tagged samples
(
e
±
K
±
,
μ
±
K
±
).
We measure
A
CP
with a binned four-dimensional fit
to ∆
t
(100 bins),
σ
(∆
t
)(20), cos
θ
`k
(4), and
p
K
(5). Fol-
lowing Ref. [15] and neglecting resolution effects, the ∆
t
distributions for signal events with a
K
T
are represented
by the following expressions:
F
B
0
B
0
(∆
t
) =
Γ
0
e
−
Γ
0
|
∆
t
|
2(1 +
r
′
2
)
[
(
1 +
∣
∣
∣
∣
q
p
∣
∣
∣
∣
2
r
′
2
)
cosh(∆Γ∆
t/
2) +
(
1
−
∣
∣
∣
∣
q
p
∣
∣
∣
∣
2
r
′
2
)
cos(∆
m
d
∆
t
)
−
∣
∣
∣
∣
q
p
∣
∣
∣
∣
(
b
+
c
) sin(∆
m
d
∆
t
)
]
,
F
B
0
B
0
(∆
t
) =
Γ
0
e
−
Γ
0
|
∆
t
|
2(1 +
r
′
2
)
[
(
1 +
∣
∣
∣
∣
p
q
∣
∣
∣
∣
2
r
′
2
)
cosh(∆Γ∆
t/
2) +
(
1
−
∣
∣
∣
∣
p
q
∣
∣
∣
∣
2
r
′
2
)
cos(∆
m
d
∆
t
) +
∣
∣
∣
∣
p
q
∣
∣
∣
∣
(
b
−
c
) sin(∆
m
d
∆
t
)
]
,
F
B
0
B
0
(∆
t
) =
Γ
0
e
−
Γ
0
|
∆
t
|
2(1 +
r
′
2
)
[
(
1 +
∣
∣
∣
∣
p
q
∣
∣
∣
∣
2
r
′
2
)
cosh(∆Γ∆
t/
2)
−
(
1
−
∣
∣
∣
∣
p
q
∣
∣
∣
∣
2
r
′
2
)
cos(∆
m
d
∆
t
)
−
∣
∣
∣
∣
p
q
∣
∣
∣
∣
(
b
−
c
) sin(∆
m
d
∆
t
)
]
∣
∣
∣
∣
q
p
∣
∣
∣
∣
2
,
F
B
0
B
0
(∆
t
) =
Γ
0
e
−
Γ
0
|
∆
t
|
2(1 +
r
′
2
)
[
(
1 +
∣
∣
∣
∣
q
p
∣
∣
∣
∣
2
r
′
2
)
cosh(∆Γ∆
t/
2)
−
(
1
−
∣
∣
∣
∣
q
p
∣
∣
∣
∣
2
r
′
2
)
cos(∆
m
d
∆
t
) +
∣
∣
∣
∣
q
p
∣
∣
∣
∣
(
b
+
c
) sin(∆
m
d
∆
t
)
]
∣
∣
∣
∣
p
q
∣
∣
∣
∣
2
,
where the first index of
F
refers to the flavor of the
B
R
and the second to the
B
T
, Γ
0
=
τ
−
1
B
0
is the average width
of the two
B
0
mass eigenstates, ∆
m
d
and ∆Γ are re-
spectively their mass and width difference, the param-
eter
r
′
results from the interference of CF and Doubly
Cabibbo Suppressed (DCS) decays on the
B
T
side [15]
and has a very small value (
O
(1%)), and
b
and
c
are
two parameters expressing the
CP
violation arising from
that interference. In the SM,
b
= 2
r
′
sin(2
β
+
γ
) cos
δ
′
and
c
=
−
2
r
′
cos(2
β
+
γ
) sin
δ
′
, where
β
and
γ
are angles
of the Unitary Triangle and
δ
′
is a strong phase. The
quantities ∆
m
d
,
τ
B
0
,
b
,
c
, and sin(2
β
+
γ
) are left free in
the fit to reduce the systematic uncertainty. The value
of ∆Γ is fixed to zero. Neglecting the tiny contribution
from DCS decays, the main contribution to the asym-
metry is time independent and due to the normalization
factors of the two mixed terms.
The ∆
t
distribution for the decays of the
B
+
mesons is parametrized by an exponential function,
F
B
+
= Γ
+
e
−|
Γ
+
∆
t
|
, where the
B
+
decay width is com-
puted as the inverse of the lifetime Γ
−
1
+
=
τ
B
+
=
(1
.
641
±
0
.
008) ps.
When the
K
T
comes from the decay of the
B
0
meson
to a
CP
eigenstate (as, for example
B
0
→
D
(
∗
)
D
(
∗
)
[9]),
a different expression applies:
F
CPe
(∆
t
) =
Γ
0
4
e
−
Γ
0
|
∆
t
|
[1
±
S
sin(∆
m
d
∆
t
)
±
C
cos(∆
m
d
∆
t
)]
,
where the plus sign is used if the
B
R
decays as a
B
0
and
the minus sign otherwise. The fraction of these events
(about 1%) and the parameters
S
and
C
are fixed in the
fits and are taken from simulation.
We obtain the ∆
t
distributions for
K
T
in
B
B
events,
G
i
(∆
t
), by convolving the theoretical ones with a resolu-
tion function, which consists of the superposition of sev-
eral Gaussian functions, convolved with exponentials to
take into account the finite lifetime of charmed mesons in
the cascade decay
b
→
c
→
K
. Different sets of param-
eters are used for peaking and for combinatorial back-
ground events.
To describe the ∆
t
distributions for
K
R
events,
G
K
R
(∆
t
), we select a subsample of data containing fewer
than 5%
K
T
decays, and use background-subtracted his-
tograms in our likelihood functions. As an alternative,
6
FIG. 1: (color online).
M
2
ν
distribution for selected events.
The data are represented by the points with error bars. The
fitted contributions from
B
0
→
D
∗
+
`
−
̄
ν
`
, other peaking
background,
D
∗∗
events,
B
B
combinatorial background, and
rescaled off-peak events are overlaid.
we apply the same selection to the simulation and cor-
rect the ∆
t
distribution predicted by the Monte Carlo
by the ratio of the histograms extracted from data and
simulated events. The cos
θ
`K
shapes are obtained from
the histograms of the simulated distributions for
B
B
events. The ∆
t
distribution of continuum events is rep-
resented by a decaying exponential convolved with Gaus-
sians parametrized by fitting simultaneously the off-peak
data.
The rate of events in each bin (
j
) and for each tagged
sample are then expressed as the sum of the predicted
contributions from peaking events,
B
B
combinatorial,
and continuum background. Accounting for mistags and
K
R
events, the peaking
B
0
contributions to the same-
sign samples are:
G
`
+
K
+
(
j
) = (1 +
A
r`
)(1 +
A
K
)
{
(1
−
f
++
K
R
)[(1
−
ω
+
)
G
B
0
B
0
(
j
) +
ω
−
G
B
0
B
0
(
j
)]
+
f
++
K
R
(1
−
ω
′
+
)
G
K
R
(
j
)(1 +
χ
d
A
``
)
}
,
G
`
−
K
−
(
j
) = (1
−A
r`
)(1
−A
K
)
{
(1
−
f
−−
K
R
)[(1
−
ω
−
)
G
B
0
B
0
(
j
) +
ω
+
G
B
0
B
0
(
j
)]
+
f
−−
K
R
(1
−
ω
′−
)
G
K
R
(
j
)(1
−
χ
d
A
``
)
}
,
where the reconstruction asymmetries have separate val-
ues for the
e
and
μ
samples. We allow for different mistag
probabilities for
K
T
(
ω
±
) and
K
R
(
ω
′±
). The parame-
ters
f
±±
K
R
(
p
k
) describe the fractions of
K
R
tags in each
sample as a function of the kaon momentum.
A total of 168 parameters are determined in the fit. By
analyzing simulated events as data, we observe that the
fit reproduces the generated values of 1
−|
q/p
|
(zero) and
of the other most significant parameters (
A
r`
,
A
K
, ∆
m
d
,
and
τ
B
0
). We then produce samples of simulated events
with ∆
CP
=
±
0
.
005
,
±
0
.
010
,
±
0
.
025 and
A
r`
or
A
K
in
the range of
±
10%, by removing events. A total of 67
different simulated event samples are used to check for
biases. In each case, the input values are correctly deter-
mined, and an unbiased value of
|
q/p
|
is always obtained.
TABLE I: Principal sources of systematic uncertainties.
Source
σ
(∆
CP
)
Peaking Sample Composition
+1
.
50
−
1
.
17
×
10
−
3
Combinatorial Sample Composition
±
0
.
39
×
10
−
3
∆
t
Resolution Model
±
0
.
60
×
10
−
3
K
R
Fraction
±
0
.
11
×
10
−
3
K
R
∆
t
Distribution
±
0
.
65
×
10
−
3
Fit Bias
+0
.
58
−
0
.
46
×
10
−
3
CP
eigenstate Description
±
0
Physical Parameters
+0
−
0
.
28
×
10
−
3
Total
+1
.
88
−
1
.
61
×
10
−
3
FIG. 2: (color online). Distribution of ∆
t
for the continuum-
subtracted data (points with error bars) and fitted contribu-
tions from
K
R
(dark) and
K
T
(light), for: (a)
`
+
K
+
events;
(b)
`
−
K
−
events; (c)
`
−
K
+
events; (d)
`
+
K
−
events; (e) raw
asymmetry between
`
+
K
+
and
`
−
K
−
events.
The fit to the data yields ∆
CP
= (0
.
29
±
0
.
84
+1
.
88
−
1
.
61
)
×
10
−
3
,
where the first uncertainty is statistical and the second
7
systematic. The values of the detector charge asymme-
tries are
A
r,e
= (3
.
0
±
0
.
4)
×
10
−
3
,
A
r,μ
= (3
.
1
±
0
.
5)
×
10
−
3
, and
A
K
= (13
.
7
±
0
.
3)
×
10
−
3
. The frequency of the
oscillation ∆
m
d
= 508
.
5
±
0
.
9 ns
−
1
is consistent with the
world average, while
τ
B
0
= 1
.
553
±
0
.
002 ps is somewhat
larger than the world average, which we account for in
the evaluation of the systematic uncertainties. Figures 2
and 3 show the fit projections for ∆
t
and cos
θ
`K
.
The systematic uncertainty is computed as the sum in
quadrature of several contributions, described below and
summarized in Table I:
-
Peaking Sample Composition
: we vary the sample
composition by the statistical uncertainty of the
M
2
ν
fit,
the fraction of
B
0
to
B
+
in the
D
∗∗
peaking sample in
the range 50
±
25% to account for possible violation of
isospin symmetry, the fraction of the peaking contribu-
tions (taken from the simulation) by
±
20%, and the frac-
tion of
CP
eigenstates by
±
50%.
-
B
B
combinatorial sample composition
: we vary the
fraction of
B
+
events in the
B
B
combinatorial sample
by
±
4
.
5%, which corresponds to the uncertainty in the
inclusive branching fraction for
B
0
→
D
∗−
X
.
-∆
t
resolution model
: we quote the difference between
the result when all resolution parameters are determined
in the fit and those obtained when those that exhibit a
weak correlation with
|
q/p
|
are fixed.
-
K
R
fraction
: we vary the ratio of
B
+
→
K
R
X
to
B
0
→
K
R
X
by
±
6
.
8%, which corresponds to the uncer-
tainty of the fraction
BR
(
D
∗
0
→
K
−
X
)
BR
(
D
∗
+
→
K
−
X
)
.
-
K
R
∆
t
distribution
: we use half the difference between
the results obtained using the two different strategies to
describe the
K
R
∆
t
distribution.
-
Fit bias
: parametrized simulations are used to check
the estimate of the result and its statistical uncertainty.
We add the statistical uncertainty on the validation test
using the detailed simulation and the difference between
the nominal result and the central result determined from
the ensemble of parametrized simulations.
-
CP
eigenstates description
: we vary the
S
and
C
parameters describing the
CP
eigenstates by their statis-
tical uncertainties as obtained from simulation.
-
Physical parameters
: we repeat the fit setting the
value of ∆Γ to 0.02 ps
−
1
. The lifetimes of the
B
0
and
B
+
mesons and ∆
m
d
are floated in the fit. Alternatively, we
check the effect of fixing each parameter in turn to the
world average.
In summary, we present a new measurement of the
parameter governing
CP
violation in
B
0
B
0
oscillations.
With a partial
B
0
→
D
∗−
X`
+
ν
reconstruction and kaon
tagging, we find ∆
CP
= (0
.
29
±
0
.
84
+1
.
88
−
1
.
61
)
×
10
−
3
,
and
A
CP
= (0
.
06
±
0
.
17
+0
.
38
−
0
.
32
)%
.
These results are consistent
with, and more precise than, dilepton-based results from
B factories [4]. No deviation is observed from the SM
expectation [3].
We are grateful for the excellent luminosity and ma-
chine conditions provided by our PEP-II colleagues, and
for the substantial dedicated effort from the comput-
ing organizations that support
B
A
B
AR
. The collaborat-
ing institutions wish to thank SLAC for its support and
kind hospitality. This work is supported by DOE and
NSF (USA), NSERC (Canada), IHEP (China), CEA and
CNRS-IN2P3 (France), BMBF and DFG (Germany),
INFN (Italy), FOM (The Netherlands), NFR (Norway),
MIST (Russia), MEC (Spain), and PPARC (United
Kingdom). Individuals have received support from the
Marie Curie EIF (European Union) and the A. P. Sloan
Foundation.
FIG. 3: (color online).
Distributions of cos
θ
`K
for the
continuum-subtracted data (points with error bars) and fitted
contributions from
B
R
(dark) and
B
T
(light), for: (a)
`
+
K
+
events; (b)
`
−
K
−
events; (c)
`
−
K
+
events; (d)
`
+
K
−
events.
∗
Now at the University of Tabuk, Tabuk 71491, Saudi
Arabia
†
Also with Universit`a di Perugia, Dipartimento di Fisica,
Perugia, Italy
‡
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
††
Now at Universidad T ́ecnica Federico Santa Maria, Val-
paraiso, Chile 2390123
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