of 13
Search for mixing-induced
CP
violation using partial reconstruction
of
̄
B
0
D
X
l
̄
ν
l
and kaon tagging
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
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,
9a,9b,9c
A. R. Buzykaev,
9a
V. P. Druzhinin,
9a,9b
V. B. Golubev,
9a,9b
E. A. Kravchenko,
9a,9b
A. P. Onuchin,
9a,9b,9c
S. I. Serednyakov,
9a,9b
Yu.I.Skovpen,
9a,9b
E. P. Solodov,
9a,9b
K. Yu. Todyshev,
9a,9b
A. J. Lankford,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
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
J. Kim,
14
T. S. Miyashita,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
M. Röhrken,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
B. G. Pushpawela,
15
M. D. Sokoloff,
15
L. Sun,
15
W. T. Ford,
16
A. Gaz,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17
,
W. H. Toki,
17
B. Spaan,
18
D. Bernard,
19
M. Verderi,
19
S. Playfer,
20
D. Bettoni,
21a
C. Bozzi,
21a
R. Calabrese,
21a,21b
G. Cibinetto,
21a,21b
E. Fioravanti,
21a,21b
I. Garzia,
21a,21b
E. Luppi,
21a,21b
L. Piemontese,
21a
V. Santoro,
21a
A. Calcaterra,
22
R. de Sangro,
22
G. Finocchiaro,
22
S. Martellotti,
22
P. Patteri,
22
I. M. Peruzzi,
22
M. Piccolo,
22
A. Zallo,
22
R. Contri,
23a,23b
M. R. Monge,
23a,23b
S. Passaggio,
23a
C. Patrignani,
23a,23b
E. Robutti,
23a
B. Bhuyan,
24
V. Prasad,
24
A. Adametz,
25
U. Uwer,
25
H. M. Lacker,
26
U. Mallik,
27
C. Chen,
28
J. Cochran,
28
S. Prell,
28
H. Ahmed,
29
A. V. Gritsan,
30
N. Arnaud,
31
M. Davier,
31
D. Derkach,
31
G. Grosdidier,
31
F. Le Diberder,
31
A. M. Lutz,
31
B. Malaescu,
31
,
P. Roudeau,
31
A. Stocchi,
31
G. Wormser,
31
D. J. Lange,
32
D. M. Wright,
32
J. P. Coleman,
33
J. R. Fry,
33
E. Gabathuler,
33
D. E. Hutchcroft,
33
D. J. Payne,
33
C. Touramanis,
33
A. J. Bevan,
34
F. Di Lodovico,
34
R. Sacco,
34
G. Cowan,
35
D. N. Brown,
36
C. L. Davis,
36
A. G. Denig,
37
M. Fritsch,
37
W. Gradl,
37
K. Griessinger,
37
A. Hafner,
37
K. R. Schubert,
37
R. J. Barlow,
38
G. D. Lafferty,
38
R. Cenci,
39
B. Hamilton,
39
A. Jawahery,
39
D. A. Roberts,
39
R. Cowan,
40
R. Cheaib,
41
P. M. Patel,
41
,*
S. H. Robertson,
41
N. Neri,
42a
F. Palombo,
42a,42b
L. Cremaldi,
43
R. Godang,
43
,
D. J. Summers,
43
M. Simard,
44
P. Taras,
44
G. De Nardo,
45a,45b
G. Onorato,
45a,45b
C. Sciacca,
45a,45b
G. Raven,
46
C. P. Jessop,
47
J. M. LoSecco,
47
K. Honscheid,
48
R. Kass,
48
M. Margoni,
49a,49b
M. Morandin,
49a
M. Posocco,
49a
M. Rotondo,
49a
G. Simi,
49a,49b
F. Simonetto,
49a,49b
R. Stroili,
49a,49b
S. Akar,
50
E. Ben-Haim,
50
M. Bomben,
50
G. R. Bonneaud,
50
H. Briand,
50
G. Calderini,
50
J. Chauveau,
50
Ph. Leruste,
50
G. Marchiori,
50
J. Ocariz,
50
M. Biasini,
51a,51b
E. Manoni,
51a
A. Rossi,
51a
C. Angelini,
52a,52b
G. Batignani,
52a,52b
S. Bettarini,
52a,52b
M. Carpinelli,
52a,52b
G. Casarosa,
52a,52b
M. Chrzaszcz,
52a
F. Forti,
52a,52b
M. A. Giorgi,
52a,52b
A. Lusiani,
52a,52c
B. Oberhof,
52a,52b
E. Paoloni,
52a,52b
M. Rama,
52a
G. Rizzo,
52a,52b
J. J. Walsh,
52a
D. Lopes Pegna,
53
J. Olsen,
53
A. J. S. Smith,
53
F. Anulli,
54a
R. Faccini,
54a,54b
F. Ferrarotto,
54a
F. Ferroni,
54a,54b
M. Gaspero,
54a,54b
A. Pilloni,
54a,54b
G. Piredda,
54a
C. Bünger,
55
S. Dittrich,
55
O. Grünberg,
55
M. Hess,
55
T. Leddig,
55
C. Voß,
55
R. Waldi,
55
T. Adye,
56
E. O. Olaiya,
56
F. F. Wilson,
56
S. Emery,
57
G. Vasseur,
57
D. Aston,
58
D. J. Bard,
58
C. Cartaro,
58
M. R. Convery,
58
J. Dorfan,
58
G. P. Dubois-Felsmann,
58
W. Dunwoodie,
58
M. Ebert,
58
R. C. Field,
58
B. G. Fulsom,
58
M. T. Graham,
58
C. Hast,
58
W. R. Innes,
58
P. Kim,
58
D. W. G. S. Leith,
58
S. Luitz,
58
V. Luth,
58
D. B. MacFarlane,
58
D. R. Muller,
58
H. Neal,
58
T. Pulliam,
58
B. N. Ratcliff,
58
A. Roodman,
58
R. H. Schindler,
58
A. Snyder,
58
D. Su,
58
M. K. Sullivan,
58
J. Va
vra,
58
W. J. Wisniewski,
58
H. W. Wulsin,
58
M. V. Purohit,
59
J. R. Wilson,
59
A. Randle-Conde,
60
S. J. Sekula,
60
M. Bellis,
61
P. R. Burchat,
61
E. M. T. Puccio,
61
M. S. Alam,
62
J. A. Ernst,
62
R. Gorodeisky,
63
N. Guttman,
63
D. R. Peimer,
63
A. Soffer,
63
S. M. Spanier,
64
J. L. Ritchie,
65
R. F. Schwitters,
65
J. M. Izen,
66
X. C. Lou,
66
F. Bianchi,
67a,67b
F. De Mori,
67a,67b
A. Filippi,
67a
D. Gamba,
67a,67b
L. Lanceri,
68a,68b
L. Vitale,
68a,68b
F. Martinez-Vidal,
69
A. Oyanguren,
69
J. Albert,
70
Sw. Banerjee,
70
A. Beaulieu,
70
F. U. Bernlochner,
70
H. H. F. Choi,
70
G. J. King,
70
R. Kowalewski,
70
M. J. Lewczuk,
70
T. Lueck,
70
I. M. Nugent,
70
J. M. Roney,
70
R. J. Sobie,
70
N. Tasneem,
70
T. J. Gershon,
71
P. F. Harrison,
71
T. E. Latham,
71
H. R. Band,
72
S. Dasu,
72
Y. Pan,
72
R. Prepost,
72
and S. L. Wu
72
(The
B
A
B
A
R
Collaboration)
1
Laboratoire d
Annecy-le-Vieux de Physique des Particules (LAPP), Université de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento di Fisica, Università di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universität Bochum, Institut für 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
PHYSICAL REVIEW D
93,
032001 (2016)
2470-0010
=
2016
=
93(3)
=
032001(13)
032001-1
© 2016 American Physical Society
9a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
9b
Russia Novosibirsk State University, Novosibirsk 630090, Russia
9c
Russia Novosibirsk State Technical University, Novosibirsk 630092, 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 Universität Dortmund, Fakultät 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
21a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
21b
Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, I-44122 Ferrara, Italy
22
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
23a
INFN Sezione di Genova, I-16146 Genova, Italy
23b
Dipartimento di Fisica, Università di Genova, I-16146 Genova, Italy
24
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
25
Universität Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
26
Humboldt-Universität zu Berlin, Institut für Physik, D-12489 Berlin, Germany
27
University of Iowa, Iowa City, Iowa 52242, USA
28
Iowa State University, Ames, Iowa 50011-3160, USA
29
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudi Arabia
30
Johns Hopkins University, Baltimore, Maryland 21218, USA
31
Laboratoire de l
Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d
Orsay, F-91898 Orsay Cedex, France
32
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
33
University of Liverpool, Liverpool L69 7ZE, United Kingdom
34
Queen Mary, University of London, London E1 4NS, United Kingdom
35
University of London, Royal Holloway and Bedford New College,
Egham, Surrey TW20 0EX, United Kingdom
36
University of Louisville, Louisville, Kentucky 40292, USA
37
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
38
University of Manchester, Manchester M13 9PL, United Kingdom
39
University of Maryland, College Park, Maryland 20742, USA
40
Massachusetts Institute of Technology, Laboratory for Nuclear Science,
Cambridge, Massachusetts 02139, USA
41
McGill University, Montréal, Québec, Canada H3A 2T8
42a
INFN Sezione di Milano, I-20133 Milano, Italy
42b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
43
University of Mississippi, University, Mississippi 38677, USA
44
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
45a
INFN Sezione di Napoli, I-80126 Napoli, Italy
45b
Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy
46
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, The Netherlands
47
University of Notre Dame, Notre Dame, Indiana 46556, USA
48
Ohio State University, Columbus, Ohio 43210, USA
49a
INFN Sezione di Padova, I-35131 Padova, Italy
49b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
50
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS,
Université Pierre et Marie Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France
51a
INFN Sezione di Perugia, I-06123 Perugia, Italy
51b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
52a
INFN Sezione di Pisa, I-56127 Pisa, Italy
52b
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
52c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
53
Princeton University, Princeton, New Jersey 08544, USA
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
032001 (2016)
032001-2
54a
INFN Sezione di Roma, I-00185 Roma, Italy
54b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
55
Universität Rostock, D-18051 Rostock, Germany
56
Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom
57
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
58
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
59
University of South Carolina, Columbia, South Carolina 29208, USA
60
Southern Methodist University, Dallas, Texas 75275, USA
61
Stanford University, Stanford, California 94305-4060, USA
62
State University of New York, Albany, New York 12222, USA
63
Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
64
University of Tennessee, Knoxville, Tennessee 37996, USA
65
University of Texas at Austin, Austin, Texas 78712, USA
66
University of Texas at Dallas, Richardson, Texas 75083, USA
67a
INFN Sezione di Torino, I-10125 Torino, Italy
67b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
68a
INFN Sezione di Trieste, I-34127 Trieste, Italy
68b
Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
69
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
70
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
71
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
72
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 8 June 2015; revised manuscript received 23 December 2015; published 8 February 2016)
We describe in detail a previously published measurement of
CP
violation in
B
0
-
̄
B
0
oscillations, based
on an integrated luminosity of
425
.
7
fb
1
collected by the
BABAR
experiment at the PEPII collider.
We apply a novel technique to a sample of about 6 million
̄
B
0
D
l
̄
ν
l
decays selected with partial
reconstruction of the
D
meson. The charged lepton identifies the flavor of one
B
meson at its decay time,
the flavor of the other
B
is determined by kaon tagging. We determine a
CP
violating asymmetry
A
CP
¼ð
N
ð
B
0
B
0
Þ
N
ð
̄
B
0
̄
B
0
ÞÞ
=
ð
N
ð
B
0
B
0
Þþ
N
ð
̄
B
0
̄
B
0
ÞÞ¼ð
0
.
06

0
.
17
þ
0
.
38
0
.
32
Þ
%
corresponding to
Δ
CP
¼
1
j
q=p
j¼ð
0
.
29

0
.
84
þ
1
.
88
1
.
61
Þ
×
10
3
. This measurement is consistent and competitive with those
obtained at the
B
factories with dilepton events.
DOI:
10.1103/PhysRevD.93.032001
I. INTRODUCTION
The time evolution of neutral
B
mesons is governed by
the Schrödinger equation:
i
t
Ψ
¼
H
Ψ
ð
1
Þ
where
Ψ
¼
ψ
1
j
B
0
ψ
2
j
̄
B
0
i
and
B
0
¼ð
̄
bd
Þ
and
̄
B
0
¼
ð
b
̄
d
Þ
are flavor eigenstates. Hamiltonian
H
¼
M
i
2
Γ
is
the combination of two
2
×
2
Hermitian matrices,
M
¼
M
,
Γ
¼
Γ
expressing dispersive and absorptive
contributions respectively. The two eigenstates of
H
, with
well-defined values of mass (
m
L
,
m
H
) and decay width
(
Γ
L
,
Γ
H
), are expressed in terms of
B
0
and
̄
B
0
,as
j
B
L
p
j
B
0
q
j
̄
B
0
i
j
B
H
p
j
B
0
i
q
j
̄
B
0
i
;
ð
2
Þ
where
q
p
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
M

12
i
Γ

12
=
2
M
12
i
Γ
12
=
2
s
:
ð
3
Þ
The process of
B
0
-
̄
B
0
flavor mixing is therefore governed
by two real parameters,
j
M
12
j
,
j
Γ
12
j
and by the phase
φ
12
¼
arg
ð
Γ
12
=M
12
Þ
.
The value of
j
M
12
j
is related to the frequency of
B
0
-
̄
B
0
oscillations,
Δ
m
, by the relation
Δ
m
¼
m
H
m
L
¼
2
j
M
12
j
;
ð
4
Þ
*
Deceased.
Present address: University of Tabuk, Tabuk 71491, Saudi
Arabia.
Present address: Laboratoire de Physique Nucléaire et de
Hautes Energies, IN2P3/CNRS, F-75252 Paris, France.
§
Present address: University of Huddersfield, Huddersfield
HD1 3DH, United Kingdom.
Present address: University of South Alabama, Mobile,
Alabama 36688, USA.
Also at Università di Sassari, I-07100 Sassari, Italy.
SEARCH FOR MIXING-INDUCED
CP
VIOLATION
...
PHYSICAL REVIEW D
93,
032001 (2016)
032001-3
whereas the following expression relates the decay width
difference
ΔΓ
to
j
Γ
12
j
and
φ
12
:
ΔΓ
¼
Γ
L
Γ
H
¼
2
j
Γ
12
j
cos
φ
12
:
ð
5
Þ
A third observable probing mixing is the
CP
mixing
asymmetry
A
CP
¼
̄
P
P
̄
P
þ
P
2

1




q
p





¼
ΔΓ
Δ
m
tan
φ
12
;
ð
6
Þ
where
P
¼
prob
ð
B
0
̄
B
0
Þ
is the probability that a state,
produced as a
B
0
, decays as a
̄
B
0
;
̄
P
¼
prob
ð
̄
B
0
B
0
Þ
is
the probability for the
CP
conjugate oscillation; the second
equality holds if
j
q=p
j
1
; and the last if
j
Γ
12
=M
12
j
1
.
In the Standard Model the dispersive term
M
12
is
dominated by box diagrams involving two top quarks.
Owing to the large top mass, a sizable value of
Δ
m
is
expected. The measured value
Δ
m
¼
0
.
510

0
.
004
ps
1
[1]
is consistent with the SM expectation. The period
corresponds to about eight times the
B
0
average lifetime.
As only the few final states common to
B
0
and
̄
B
0
contribute to
j
Γ
12
j
, small values of
ΔΓ
and
A
CP
are
expected. One of the most recent theoretical calculations
based on the SM
[2]
, including NLO QCD correction,
predicts
Δ
CP
¼
1
j
q=p
j
1
2
A
CP
¼
ð
2
.
4
þ
0
.
5
0
.
6
Þ
×
10
4
:
ð
7
Þ
Sizable deviations from zero would therefore be a clear
indication of new physics (NP). A detailed review of
possible NP contributions to
CP
violation in
B
0
-
̄
B
0
mixing can be found in
[3]
. In this paper, we describe
the measurement of
A
CP
performed by the
BABAR
Collaboration with a novel technique, previously published
in
[4]
, which, due to the analysis complexity, requires a
more detailed description.
This article is organized as follows. An overview of the
current experimental situation and the strategy of this
measurement are reported in Sec.
II
. The
BABAR
detector is described briefly in Sec.
III
. Event selection
and sample composition are then described in Sec.
IV
.
Tagging the flavor of the
B
meson is described in Sec.
V
.
The measurement of
A
CP
is described in Sec.
VI
, the fit
validation is described in Sec.
VII
, and the discussion of
the systematic uncertainties follows in Sec.
VIII
, while
we summarize the results and draw our conclusions in
Secs.
IX
and
X
.
II. EXPERIMENTAL OVERVIEW AND
DESCRIPTION OF THE MEASUREMENT
In hadron collider experiments,
b
̄
b
pairs produced at the
parton level hadronize generating the
b
hadrons, which
eventually decay weakly. In
B
factories, pairs of opposite
flavor
B
-mesons are produced through the process
e
þ
e
Υ
ð
4
S
Þ
B
̄
B
in an entangled quantum state. Because of
flavor mixing, decays of two
B
0
or
̄
B
0
mesons are observed.
If
CP
is violated in mixing,
P
̄
P
and a different number
of
B
0
B
0
events with respect to
̄
B
0
̄
B
0
is expected. The
asymmetry is measured by selecting flavor tagged final
states
f
, for which the decay
B
0
f
is allowed and the
decay
̄
B
0
f
is forbidden. Inclusive semileptonic decays
B
0
l
þ
ν
l
X
have been used in the past, due to the large
branching fraction and high selection efficiency (unless
the contrary is explicitly stated, we always imply charge
conjugated processes;
lepton
l
means either electron or
muon). Assuming
CPT
symmetry for semileptonic decays
[
Γ
ð
B
0
l
þ
ν
l
X
Þ¼
Γ
ð
̄
B
0
l
̄
ν
l
̄
X
Þ
], the observed
asymmetry is directly related to
CP
violation in mixing:
N
ð
l
þ
l
þ
Þ
N
ð
l
l
Þ
N
ð
l
þ
l
þ
Þþ
N
ð
l
l
Þ
¼
A
CP
ð
8
Þ
where
N
ð
l

l

Þ
is the efficiency-corrected number of
equal charge dilepton events after background subtraction.
Published results from CLEO
[5]
and the
B
factory
experiments of Belle
[6]
and
BABAR
[7,8]
, based on the
analysis of dilepton events, are consistent with the SM
expectation. The
D
0
Collaboration
[9]
, using a dimuon
sample, obtained a more precise measurement, which
however includes contributions from both
B
0
and
B
0
s
mixing. They observe a deviation larger than three standard
deviations from the SM expectation. Measurements based
on the reconstruction of
̄
B
0
s
D
ðÞþ
s
l
̄
ν
l
decays
[10,11]
and of
̄
B
0
D
ðÞþ
l
̄
ν
l
decays
[12,13]
are compatible both
with the SM and with
D
0
.
The dilepton measurements benefit from the large
number of events that can be selected at
B
factories or
at hadron colliders. 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 uncertainties asso-
ciated with the corrections for these effects constitute a
severe limitation of the precision of the measurements.
Particularly obnoxious is the case when a lepton from a
direct
B
semileptonic decay is combined with a lepton of
equal charge from a charm meson produced in the decay of
the other
B
. As the mixing probability is rather low, this
background process is enhanced with respect to the signal,
so that stringent kinematic selections need to be applied.
Authors of
[14]
suggest that at least a part of the
D
0
dilepton discrepancy could be due to charm decays.
Herein we present in detail a measurement which over-
comes these difficulties with a new approach. To reduce the
background dilution from
B
þ
B
or from light quark
events, we reconstruct
̄
B
0
D
l
̄
ν
l
decays with a very
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
032001 (2016)
032001-4
efficient selection using only the charged lepton and the
low-momentum pion (
π
s
) from the
D
D
0
π
s
decay. A
state decaying as a
B
0
(
̄
B
0
) meson produces
l
þ
π
s
(
l
π
s
þ
). We use charged kaons from decays of the other
B
0
to tag its flavor (
K
T
). Kaons are mostly produced in the
Cabibbo-favored (CF) process
B
0
̄
DX
,
̄
D
K
þ
X
0
,so
that a state decaying as a
B
0
(
̄
B
0
) meson results most often
in a
K
þ
ð
K
Þ
. If mixing takes place, the
l
and the
K
will
have the same charge. Kaons produced in association with
the
l
π
s
pair are used to measure the large instrumental
asymmetry in kaon identification.
The observed asymmetry between the number of
positive-charge and negative-charge leptons can be
approximated as
A
l
A
r
l
þ
A
CP
·
χ
d
;
ð
9
Þ
where
χ
d
¼
0
.
1862

0
.
0023
[1]
is the integrated mixing
probability for
B
0
mesons, and
A
r
l
is the charge asym-
metry in the reconstruction of
̄
B
0
D
l
̄
ν
l
decays.
With the same approximations as before, the observed
asymmetry in the rate of kaon-tagged mixed events is
A
T
¼
N
ð
l
þ
K
þ
T
Þ
N
ð
l
K
T
Þ
N
ð
l
þ
K
þ
T
Þþ
N
ð
l
K
T
Þ
A
r
l
þ
A
K
þ
A
CP
;
ð
10
Þ
where
A
K
is the charge asymmetry in kaon reconstruction.
A kaon with the same charge as the
l
might also come from
the 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
¼
N
ð
l
þ
K
þ
R
Þ
N
ð
l
K
R
Þ
N
ð
l
þ
K
þ
R
Þþ
N
ð
l
K
R
Þ
A
r
l
þ
A
K
þ
A
CP
·
χ
d
:
ð
11
Þ
Equations
(9)
,
(10)
, and
(11)
, defining quantities computed
in terms of the observed number of events integrated over
time, can be inverted to extract
A
CP
and the detector
induced asymmetries. It is not possible to distinguish a
K
T
from a
K
R
in each event. They are separated on a statistical
basis, using kinematic features and proper-time difference
information.
III. THE
BABAR
DETECTOR
A detailed description of the
BABAR
detector and
the algorithms used for charged and neutral particle
reconstruction and identification is provided elsewhere
[15,16]
. A brief summary is given here. The momentum
of charged particles is measured by the tracking system,
which consists of a silicon vertex tracker (SVT) and a drift
chamber (DCH) in a 1.5 T magnetic field. The positions of
points along the trajectories of charged particles measured
with the SVT are used for vertex reconstruction and for
measuring the momentum of charged particles, including
those particles with low transverse momentum that do not
reach the DCH due to the bending in the magnetic field.
The energy loss in the SVT is used to discriminate low-
momentum pions from electrons.
Higher-energy electrons are identified from the ratio of
the energy of their associated shower in the electromagnetic
calorimeter (EMC) to their momentum, the transverse
profile of the shower, the energy loss in the DCH, and
the information from the Cherenkov detector (DIRC). The
electron identification efficiency is 93%, and the misiden-
tification rate for pions and kaons is less than 1%.
Muons are identified on the basis of the energy deposited
in the EMC and the penetration in the instrumented flux
return (IFR) of the superconducting coil, which contains
resistive plate chambers and limited streamer tubes inter-
spersed with iron. Muon candidates compatible with the
kaon hypothesis in the DIRC are rejected. The muon
identification efficiency is about 80%, and the misidenti-
fication rate for pions and kaons is
3%
.
We select kaons from charged particles with momenta
larger than
0
.
2
GeV
=c
using a standard algorithm which
combines DIRC information with the measurements of the
energy losses in the SVT and DCH. True kaons are
identified with
85%
efficiency and a
3%
pion mis-
identification rate.
IV. EVENT SELECTION
The data sample used in this analysis consists of 468
million
B
̄
B
pairs, corresponding to an integrated luminosity
of
425
.
7
fb
1
collected at the
Υ
ð
4
S
Þ
resonance (on-
resonance) and
45
fb
1
collected 40 MeV below the
resonance (off-resonance) by the
BABAR
detector
[17]
.
The off-resonance events are used to describe the non-
B
̄
B
(continuum) background. A simulated sample of
B
̄
B
events
with integrated luminosity equivalent to approximately
three times the size of the data sample, based on
E
VT
G
EN
[18]
and GEANT4
[19]
with full detector
response and event reconstruction, is used to test the
analysis procedure.
We preselect a sample of hadronic events with at least
four charged particles. To reduce continuum background
we require the ratio of the second to the zeroth order
Fox-Wolfram variables
[20]
to be less than 0.6. We then
select a sample of partially reconstructed
B
mesons in the
channel
̄
B
0
D
X
l
̄
ν
l
, by retaining events containing a
charged lepton (
l
¼
e
,
μ
) and a low-momentum pion
(soft pion,
π
þ
s
) from the decay
D
D
0
π
þ
s
. The lepton
momentum must be in the range
1
.
4
<p
l
<
2
.
3
GeV
=c
and the soft pion candidate must satisfy
60
<p
π
þ
s
<
190
MeV
=c
. Throughout this paper the momentum, energy
and direction of all particles are determined in the
e
þ
e
rest
frame. The two tracks must be consistent with originating
SEARCH FOR MIXING-INDUCED
CP
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PHYSICAL REVIEW D
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032001 (2016)
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from a common vertex, constrained to the beam-spot in the
plane transverse to the
e
þ
e
collision axis. Finally, we
combine
p
l
,
p
π
þ
s
and the probability from the vertex fit
into a likelihood ratio variable (
η
). A cut on
η
is optimized
to reject background from other
B
̄
B
events. If more than
one combination is found in an event, we keep the one with
the largest value of
η
.
The squared missing mass is
M
miss
2
ð
E
beam
E
D

E
l
Þ
2
ð
p
D

þ
p
l
Þ
2
;
ð
12
Þ
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
þ
e
center-of-mass frame;
E
l
and
p
l
are the energy and momentum of the lepton and
p
D

is the
estimated momentum of the
D

. As a consequence of the
limited phase space available in the
D
decay, the soft
pion is emitted in a direction close to that of the
D
and a
strong correlation holds between the energy of the two
particles in the
B
0
center-of-mass frame. The
D
four-
momentum can, therefore, be estimated by approximating
its direction as that of the soft pion, and parametrizing its
momentum as a linear function of the soft-pion momentum
using simulated events. We select pairs of tracks with
opposite charge for the signal (
l
π
s

) and we use same-
charge pairs (
l

π
s

) for background studies.
Several processes where
D
and
l
originate from the
same
B
-meson produce a peak near zero in the
M
miss
2
distribution. The signal consists of (a)
̄
B
0
D
l
̄
ν
l
decays (primary); (b)
̄
B
0
D
ð
n
π
Þ
l
̄
ν
l
(
D

), and
(c)
̄
B
0
D
τ
̄
ν
τ
,
τ
l
̄
ν
l
ν
τ
. The main source of
peaking background is due to charged-
B
decays to resonant
or nonresonant charm excitations,
B
þ
D
ð
n
π
Þ
l
̄
ν
l
,or
to
τ
leptons, and
B
D
h
X
, where the hadron (
h
¼
π
,
K
,
D
) is erroneously identified as, or decays to, a charged
lepton. We also include radiative events, where photons
with energy above 1 MeV are emitted by any charged
particle, as described in the simulation by
PHOTOS
[21]
.We
define the signal region
M
miss
2
>
2
GeV
2
=c
4
, and the
sideband
10
<
M
miss
2
<
4
GeV
2
=c
4
.
Continuum events and random combinations of a low-
momentum pion and an opposite-charge lepton from
combinatorial
B
̄
B
events contribute to the nonpeaking
background. We determine the number of signal events
in the sample with a minimum-
χ
2
fit to the
M
miss
2
distribution in the interval
10
<
M
miss
2
<
2
.
5
GeV
2
=c
4
.
In the fit, the continuum contribution is obtained from
off-peak events, normalized by the on-peak to off-peak
luminosity ratio; the other contributions are taken from the
simulation. The number of events from combinatorial
B
̄
B
background, primary decays and
D

[(a) and (b) categories
described previously] is allowed to vary in the fit, while the
other peaking contributions are fixed to the simulation
expectations (few percent). The number of
B
0
mesons in
the sample is then obtained assuming that
2
=
3
of the fitted
number of
D

events are produced by
B
þ
decays, as
suggested by simple isospin considerations. We find a total
of
ð
5
.
945

0
.
007
Þ
×
10
6
signal events, where the uncer-
tainty is only statistical. In the full range signal events
account for about 30% of the sample and continuum
background for about 15%. The result of the fit is shown
in Fig.
1
.
V. KAON TAG
We indicate with
K
R
(
K
T
) kaons produced from the
decay of the
D
0
from the partially reconstructed
B
0
(
B
R
), or
in any step of the decay of the other
B
(
B
T
). We exploit the
relation between the charge of the lepton and that of the
K
T
to define an event as
mixed
or
unmixed
. When an
oscillation takes place, and the two
B
0
mesons in the event
have the same flavor at decay time, a
K
T
from a CF decay
has the same charge as the
l
. Equal-charge combinations
are also observed from Cabibbo-suppressed (CS)
K
T
production in unmixed events, and from CF
K
R
production.
Unmixed CF
K
T
, mixed CS
K
T
, and CS
K
R
result in
opposite-charge combinations. Other charged particles
wrongly identified as kaons contribute both to equal and
opposite charge events with comparable rates.
We distinguish
K
T
from
K
R
using proper-time difference
information. We define
Δ
Z
¼
Z
rec
Z
tag
,where
Z
rec
is the
projectionalong thebeam directionofthe
B
R
decay point, and
Z
tag
is the projection along the same direction of the
FIG. 1.
M
miss
2
distribution for the selected events. The data are
represented by the points with error bars. The fitted contributions
from
̄
B
0
D
l
̄
ν
l
plus
̄
B
0
D
τ
̄
ν
l
, peaking background,
D

events (
1
=
3
from
̄
B
0
and
2
=
3
from
B
þ
decays),
B
̄
B
combinatorial, and rescaled off-peak events are shown (see text
for details).
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
032001 (2016)
032001-6
intersection of the
K
track trajectory with the beam-spot. In
the boost approximation
[22]
we measure the proper-time
difference between the two
B
meson decays using the relation
Δ
t
¼
Δ
Z=
ð
βγ
c
Þ
, where the parameters
β
,
γ
express the
Lorentz boost from the laboratory to the
Υ
ð
4
S
Þ
rest frame.
We reject events if the uncertainty
σ
ð
Δ
t
Þ
exceeds 3 ps.
Due to the short lifetime and small boost of the
D
0
meson, small values of
Δ
t
are expected for the
K
R
. Much
larger values are instead expected for CF mixed
K
T
, due to
the long period of the
B
0
oscillation. Figure
2
shows the
Δ
t
distributions for
K
T
and
K
R
events, as obtained from the
simulation. To improve the separation between
K
T
and
K
R
,
we also exploit kinematics. In the rest frame of the
B
0
, the
l
and the
D
are emitted at large angles. Therefore the angle
θ
l
K
between the
l
and the
K
R
has values close to
π
, and
cos
θ
l
K
close to
1
. The corresponding distribution for
K
T
is instead uniform, as shown in Fig.
3
.
In about 20% of the cases, our events contain more than
one kaon: most often we find both a
K
T
and a
K
R
candidate.
As these two carry different information, we accept
multiple candidate events. Using several simulated pseu-
doexperiments, we assess the effect of this choice on the
statistical uncertainty.
VI. EXTRACTION OF
Δ
CP
The measurement proceeds in two stages.
First we measure the sample composition of the eight
tagged samples grouped by lepton kind, lepton charge and
K
charge, with the fit to
M
miss
2
previously described. We
also fit the four inclusive lepton samples to determine the
charge asymmetries at the reconstruction stage [see
Eq.
(9)
]. At this point of the analysis we use the total
number of collected events.
The results of the first stage are used in the second stage,
where we fit simultaneously the cos
θ
l
K
and
Δ
t
distribu-
tions in the eight tagged samples.
The
Δ
t
distributions for
B
̄
B
,
BB
and
̄
B
̄
B
events are
parametrized as the convolutions of the theoretical distri-
butions
F
i
ð
Δ
t
0
j
~
Θ
Þ
with the resolution function
R
ð
Δ
t;
Δ
t
0
Þ
:
G
i
ð
Δ
t
Þ¼
R
þ
−∞
F
i
ð
Δ
t
0
j
~
Θ
Þ
R
ð
Δ
t;
Δ
t
0
Þ
d
ð
Δ
t
0
Þ
, where
Δ
t
0
is
the actual difference between the times of decay of the
two mesons and
~
Θ
is the vector of the physical parameters.
The decays of the
B
þ
mesons are parametrized by an
exponential function,
F
B
þ
¼
Γ
þ
e
j
Γ
þ
Δ
t
0
j
, where the
B
þ
decay width is the inverse of the lifetime
Γ
1
þ
¼
τ
þ
¼
1
.
641

0
.
008
ps
[1]
. According to Ref.
[23]
, the decays of
the
B
0
mesons are described by the following expressions:
F
̄
B
0
B
0
ð
Δ
t
0
Þ¼
E
ð
Δ
t
0
Þ

1
þ




q
p




2
r
0
2

cosh
ð
ΔΓΔ
t
0
=
2
Þ
þ

1




q
p




2
r
0
2

cos
ð
Δ
m
Δ
t
0
Þ




q
p




ð
b
þ
c
Þ
sin
ð
Δ
m
Δ
t
0
Þ

ð
13
Þ
F
B
0
̄
B
0
ð
Δ
t
0
Þ¼
E
ð
Δ
t
0
Þ

1
þ




p
q




2
r
0
2

cosh
ð
ΔΓΔ
t
0
=
2
Þ
þ

1




p
q




2
r
0
2

cos
ð
Δ
m
Δ
t
0
Þ
þ




p
q




ð
b
c
Þ
sin
ð
Δ
m
Δ
t
0
Þ

ð
14
Þ
FIG. 2.
Δ
t
distributions for (a)
K
T
and for (b)
K
R
, as predicted
by the simulation.
FIG. 3. cos
ð
θ
l
K
Þ
distributions for (a)
K
T
and for (b)
K
R
,as
predicted by the simulation.
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CP
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PHYSICAL REVIEW D
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032001 (2016)
032001-7
F
̄
B
0
̄
B
0
ð
Δ
t
0
Þ¼
E
ð
Δ
t
0
Þ

1
þ




p
q




2
r
0
2

cosh
ð
ΔΓΔ
t
0
=
2
Þ

1




p
q




2
r
0
2

cos
ð
Δ
m
Δ
t
0
Þ




p
q




ð
b
c
Þ
sin
ð
Δ
m
Δ
t
0
Þ





q
p




2
ð
15
Þ
F
B
0
B
0
ð
Δ
t
0
Þ¼
E
ð
Δ
t
0
Þ

1
þ




q
p




2
r
0
2

cosh
ð
ΔΓΔ
t
0
=
2
Þ

1




q
p




2
r
0
2

cos
ð
Δ
m
Δ
t
0
Þ
þ




q
p




ð
b
þ
c
Þ
sin
ð
Δ
m
Δ
t
0
Þ





p
q




2
E
ð
Δ
t
0
Þ¼
Γ
0
2
ð
1
þ
r
0
2
Þ
e
Γ
0
j
Δ
t
0
j
;
ð
16
Þ
where the first index refers to the flavor of the
B
R
and
the second index to that of the
B
T
. In Eqs.
(13)
(16)
,
Γ
0
¼
τ
B
0
1
is the average width of the two
B
0
mass
eigenstates,
Δ
m
and
ΔΓ
are respectively their mass and
width differences,
r
0
is a parameter resulting from the
interference of CF and doubly Cabibbo-suppressed
(DCS) decays on the
B
T
side, and
b
and
c
are two
parameters expressing the
CP
violation arising from
that interference. In the Standard Model the value of
r
0
is rather small,
O
ð
1%
Þ
,
b
¼
2
r
0
sin
ð
2
β
þ
γ
Þ
cos
δ
0
, and
c
¼
2
r
0
cos
ð
2
β
þ
γ
Þ
sin
δ
0
, where
β
and
γ
are angles of
the unitary triangle
[24]
, and
δ
0
is a strong phase. Besides
j
q=p
j
, also
Δ
m
,
τ
B
0
, sin
ð
2
β
þ
γ
Þ
,
b
, and
c
are determined as
effective parameters to reduce the systematic uncertainty.
The value of
ΔΓ
is fixed to zero, and then varied within its
allowed range
[1]
when computing the systematic uncer-
tainty. Neglecting the tiny contribution from DCS decays,
the main contribution to the asymmetry is time independent
and due to the normalization factors in Eqs.
(15)
and
(16)
.
When the
K
T
comes from the decay of the
B
0
meson to a
CP
eigenstate [as, for instance
B
0
D
ðÞ
D
ðÞ
], a different
expression applies:
F
CP
ð
Δ
t
0
Þ¼
Γ
0
4
e
Γ
0
j
Δ
t
0
j
½
1

S
sin
ð
Δ
m
Δ
t
0
Þ

C
cos
ð
Δ
m
Δ
t
0
Þ
;
ð
17
Þ
where the sign plus is used if the
B
R
decaysasa
B
0
and the
sign minus otherwise. This sample contains several compo-
nents and is strongly biased by the selection cuts; therefore
we take the values of
S
and
C
, and the fraction of these
events in each sample (about 1%) from the simulation.
The resolution function
R
ð
Δ
t;
Δ
t
0
Þ
accounts for the
uncertainties in the measurement of
Δ
t
, for the effect of
the boost approximation, and for the displacement of the
K
T
production point from the
B
T
decay position due to the
motion of the charm meson. It consists of the superposition
of several Gaussian functions convolved with exponentials.
We determine
Δ
CP
with two different inputs for
G
K
R
ð
Δ
t
Þ
,
describing the
Δ
t
distribution for
K
R
events, and take the
mean value of the two determinations as the nominal result.
As first input, we use the distribution obtained from a high
purity selectionof
K
R
events on data,
G
Data
K
R
ð
Δ
t
Þ
HP
. Assecond
input,weusethedistributionfor
K
R
events as predicted bythe
simulation,
G
MC
K
R
ð
Δ
t
Þ
, corrected using Eq.
(18)
:
G
Data
K
R
ð
Δ
t
Þ¼
G
MC
K
R
ð
Δ
t
Þ
×

G
Data
K
R
ð
Δ
t
Þ
G
MC
K
R
ð
Δ
t
Þ

HP
:
ð
18
Þ
To select thehighpurity
K
R
sample, we requirethe lepton and
the kaon to have the same charge. As discussed above, this
sample consists of about 75% genuine
K
R
, where the residual
number of events with a
K
T
is mostly due to mixing.
Therefore we select events with a second high-momentum
lepton, with charge opposite to that of the first lepton.
According to the simulation, this raises the
K
R
purity in
the sample to about 87%. Finally, we use topological
variables, correlating the kaon momentum-vector to those
of the two leptons, to raise the
K
R
purity in the sample to
about 95%.
Due to the large number of events, the fit complexity, and
the high number offloated parameters, the time needed for an
unbinned fit to reach convergence is too large; therefore we
perform a binned maximum likelihood fit. Events belonging
to each of the eight categories are grouped into
100
Δ
t
bins;
25
σ
ð
Δ
t
Þ
bins;
4
cos
θ
l
;K
bins; and
5
M
miss
2
bins. We further
split the data into five binsof
K
momentum,
p
K
,toaccountfor
the dependencies of several parameters, describing the
Δ
t
resolution function, the cos
ð
θ
l
K
Þ
distributions, the fractions
of
K
T
events, etc., observed in the simulation.
Accounting for events with wrong flavor assignment and
K
R
events, the peaking
B
0
contributions to the equal and
opposite charge samples in each bin
j
are
G
B
0
l
þ
K
þ
ð
j
Þ¼ð
1
þ
A
r
l
Þð
1
þ
A
K
Þfð
1
f
þþ
K
R
Þ½ð
1
ω
þ
Þ
G
B
0
B
0
ð
j
Þþ
ω
G
B
0
̄
B
0
ð
j
Þ þ
f
þþ
K
R
ð
1
ω
Þ
G
K
R
ð
j
Þð
1
þ
χ
d
A
CP
Þg
G
B
0
l
K
ð
j
Þ¼ð
1
A
r
l
Þð
1
A
K
Þfð
1
f
−−
K
R
Þ½ð
1
ω
Þ
G
̄
B
0
̄
B
0
ð
j
Þþ
ω
þ
G
̄
B
0
B
0
ð
j
Þ þ
f
−−
K
R
ð
1
ω
0
Þ
G
K
R
ð
j
Þð
1
χ
d
A
CP
Þg
G
B
0
l
þ
K
ð
j
Þ¼ð
1
þ
A
r
l
Þð
1
A
K
Þfð
1
f
þ
K
R
Þ½ð
1
ω
Þ
G
B
0
̄
B
0
ð
j
Þþ
ω
þ
G
B
0
B
0
ð
j
Þ þ
f
þ
K
R
ω
G
K
R
ð
j
Þð
1
þ
χ
d
A
CP
Þg
G
B
0
l
K
þ
ð
j
Þ¼ð
1
A
r
l
Þð
1
þ
A
K
Þfð
1
f
þ
K
R
Þ½ð
1
ω
þ
Þ
G
̄
B
0
B
0
ð
j
Þþ
ω
G
̄
B
0
̄
B
0
ð
j
Þ þ
f
þ
K
R
ω
0
G
K
R
ð
j
Þð
1
χ
d
A
CP
Þg
ð
19
Þ
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
032001 (2016)
032001-8
where the probability density functions (PDFs)
G
B
0
B
0
ð
Δ
t
Þ
,
G
B
0
̄
B
0
ð
Δ
t
Þ
,
G
̄
B
0
B
0
ð
Δ
t
Þ
and
G
̄
B
0
̄
B
0
ð
Δ
t
Þ
are the convolutions of
the theoretical distributions in Eqs.
(13)
(16)
with the
resolution function. The reconstruction asymmetries
A
r
l
are determined separately for the
e
and
μ
samples. Wrong-
flavor assignments are described by the probabilities
ω

for
B
T
and
ω
0
for
B
R
. They are different because
K
T
s come
from a mixture of
D
mesons, while
K
R
s are produced by
D
0
decays only. The parameters
f

K
R
ð
p
K
Þ
describe the
fractions of
K
R
tags in each sample as a function of the
kaon momentum. Due to the different charge asymmetry of
the
K
T
and the
K
R
events [see Eqs.
(10)
and
(11)
], the fitted
values of
f

K
R
ð
p
K
Þ
and
j
q=p
j
are strongly correlated. The
f

K
R
ð
p
K
Þ
fractions can be factorized as
f

K
R
ðj
q=p
jÞ ¼
f

K
R
ðj
q=p
1
Þ
×
g

ðj
q=p
ð
20
Þ
where the
f

K
R
ðj
q=p
1
Þ
parameters are left free in the fit
and
g

ðj
q=p
are analytical functions. In order to limit
the number of free parameters in the fit, the fractions of
K
R
events in the
B
þ
sample are computed from the corre-
sponding fractions in the
B
0
samples:
f

K
R
ð
B
þ
Þ¼
f

K
R
ðj
q=p
1
Þ
×
R

ð
21
Þ
where
R

are correction factors obtained from the
simulation.
The combinatorial background consists of
B
þ
and
̄
B
0
decays with comparable contributions. A non-negligible
fraction of
̄
B
0
combinatorial events is obtained when the
lepton in
B
D

X
l
ν
decay is combined with a soft pion
from the decay of a tag-side
D
. As the two particles must
have opposite charges, the fraction of mixed events in the
̄
B
0
combinatorial background is larger than for peaking
events. In the simulation we find that the effective mixing
rate of the combinatorial events depends linearly on the
kaon momentum according to the relation
χ
comb
d
¼
χ
comb
0
ð
a
þ
b
·
p
K
Þ
;
ð
22
Þ
where
χ
comb
0
¼
x
2
comb
2
ð
1
þ
x
2
comb
Þ
ð
23
Þ
and
x
comb
¼
Δ
m
comb
τ
comb
B
0
. In this expression,
Δ
m
comb
and
τ
comb
B
0
are the mass difference and lifetime measured in
combinatorial events. To account for this effect, we use for
the
̄
B
0
combinatorial background the same expressions as
for the signal [see Eq.
(19)
], with the replacements
G
comb
̄
B
0
̄
B
0
¼
G
̄
B
0
̄
B
0
χ
comb
d
χ
comb
0
;
G
comb
B
0
B
0
¼
G
B
0
B
0
χ
comb
d
χ
comb
0
;
G
comb
̄
B
0
B
0
¼
G
̄
B
0
B
0
1
χ
comb
d
1
χ
comb
0
;
G
comb
B
0
̄
B
0
¼
G
B
0
̄
B
0
1
χ
comb
d
1
χ
comb
0
:
ð
24
Þ
The parameters
a
and
b
in Eq.
(22)
,
Δ
m
comb
and
τ
comb
B
0
are
determined in the fit.
The probabilities to assign a wrong flavor to
B
T
in the
combinatorial sample are found to be different in mixed and
unmixed events.
Different sets of parameters are used for peaking and
for combinatorial events, including lifetimes, frequencies
of
̄
B
0
oscillation, and detector-related asymmetries,
whereas the same value of
j
q=p
j
is used. For
B
þ
combinatorial events, the same PDFs as for peaking
B
þ
background are employed, with different sets of
parameters.
The distribution
G
cont
ð
Δ
t
Þ
of continuum events is rep-
resented by a decaying exponential, convolved with a
resolution function similar to that used for
B
events. The
effective lifetime and resolution parameters are determined
by fitting simultaneously the off-peak data.
We rely on the simulation to parametrize the cos
θ
l
K
distributions. The individual cos
θ
l
K
shapes for the eight
B
̄
B
tagged samples are obtained from the histograms of the
corresponding simulated distributions, separately for
K
T
and
K
R
events, whereas we interpolate off-peak data to
describe the continuum.
The normalized
Δ
t
distributions for each tagged sample
are then expressed as the sum of the predicted contributions
from peaking,
B
̄
B
combinatorial, and continuum back-
ground events:
F
l
K
ð
Δ
t;
σ
Δ
t
;
M
miss
2
;
cos
θ
l
;K
;p
K
j
τ
B
0
;
Δ
m;
j
q=p
¼ð
1
f
B
þ
ð
M
miss
2
Þ
f
CP
ð
M
miss
2
Þ
f
comb
ð
M
miss
2
Þ
f
cont
ð
M
miss
2
ÞÞ
G
B
0
l
K
ð
Δ
t;
σ
Δ
t
;
cos
θ
l
;K
;p
K
Þ
þ
f
B
þ
ð
M
miss
2
Þ
G
B
þ
l
K
ð
Δ
t;
σ
Δ
t
;
cos
θ
l
;K
;p
K
Þþ
f
CP
ð
M
miss
2
Þ
G
CP
l
K
ð
Δ
t;
σ
Δ
t
;
cos
θ
l
;K
;p
K
Þ
þ
f
0
comb
ð
M
miss
2
Þ
G
B
0
comb
l
K
ð
Δ
t;
σ
Δ
t
;
cos
θ
l
;K
;p
K
Þþ
f
þ
comb
ð
M
miss
2
Þ
G
B
þ
comb
l
K
ð
Δ
t;
σ
Δ
t
;
cos
θ
l
;K
;p
K
Þ
þ
f
cont
ð
M
miss
2
Þ
G
cont
l
K
ð
Δ
t;
σ
Δ
t
;
cos
θ
l
;K
;p
K
Þð
25
Þ
SEARCH FOR MIXING-INDUCED
CP
VIOLATION
...
PHYSICAL REVIEW D
93,
032001 (2016)
032001-9
where the fractions of peaking
B
þ
(
f
B
þ
),
CP
eigenstates
(
f
CP
), combinatorial
B
̄
B
(
f
comb
), and continuum (
f
cont
)
events in each
M
miss
2
interval are taken from the results of
the first stage. The fraction of
B
0
(
f
0
comb
) and of
B
þ
events
(
f
þ
comb
¼
f
comb
f
0
comb
) in the combinatorial background
have been determined from a simulation. The functions
G
B
0
l
K
ð
j
Þ
for peaking
B
0
events are defined in Eq.
(19)
; the
functions
G
B
þ
l
K
ð
j
Þ
,
G
CP
l
K
ð
j
Þ
,
G
B
0
comb
l
K
ð
j
Þ
,
G
B
þ
comb
l
K
ð
j
Þ
and
G
cont
l
K
ð
j
Þ
are the corresponding PDFs for the other samples.
For a sample of
B
0
signal events tagged by a kaon from
the
B
T
meson decay, the expected fraction
P
exp
m
of mixed
events in each
p
K
bin depends on
Δ
m
,
τ
B
0
, and
ω

, and
reads
P
exp
m
¼
G
B
0
T
l
þ
K
þ
þ
G
B
0
T
l
K
G
B
0
T
l
þ
K
þ
þ
G
B
0
T
l
K
þ
G
B
0
T
l
þ
K
þ
G
B
0
T
l
K
þ
;
ð
26
Þ
where the functions
G
B
0
T
l
K
are obtained from Eq.
(19)
taking
into account only the contributions from
B
0
T
events.
We estimate this fraction by multiplying the likelihood
by the binomial factor
C
B
0
T
m
¼
N
!
N
m
!
N
u
!
ð
P
exp
m
Þ
N
m
ð
1
P
exp
m
Þ
N
u
;
ð
27
Þ
where
N
m
and
N
u
are the number of mixed and unmixed
events, respectively, in a given
p
K
bin for each subsample.
These are obtained as the sums of the numbers of mixed
events tagged by a kaon of a given charge,
N
m
¼
N
m;K
þ
þ
N
m;K
ð
28
Þ
N
u
¼
N
u;K
þ
þ
N
u;K
:
ð
29
Þ
Finally,
N
¼
N
m
þ
N
u
.
The corresponding value of
P
exp
m;
comb
for the sample of
B
0
combinatorial events tagged by a kaon from the
B
T
meson
decay depends on
Δ
m
comb
,
τ
comb
B
0
, and the wrong flavor
assignment probability for the mixed and unmixed
subsamples.
For a sample of
B
0
events tagged by a kaon from the
B
T
meson decay, the expected fraction of mixed and unmixed
events, tagged by a positive charge kaon, depends on
A
CP
and the detector charge asymmetries. For the
B
0
signal
sample this fraction reads
P
exp
m
ð
u
Þ
;K
þ
¼
G
B
0
T
l
þ
ð
l
Þ
K
þ
G
B
0
T
l
þ
ð
l
Þ
K
þ
þ
G
B
0
T
l
ð
l
þ
Þ
K
:
ð
30
Þ
We estimate this quantity by multiplying the likelihood
by the binomial factor
C
B
0
T
m
ð
u
Þ
;K
þ
¼
N
m
ð
u
Þ
!
N
m
ð
u
Þ
;K
þ
!
N
m
ð
u
Þ
;K
!
×
ð
P
exp
m
ð
u
Þ
K
þ
Þ
N
m
ð
u
Þ
K
þ
×
ð
1
P
exp
m
ð
u
Þ
K
þ
Þ
N
m
ð
u
Þ
K
:
ð
31
Þ
For a sample of
B
0
events tagged by a kaon from the
B
R
meson decay, the fraction of mixed events depends on
ω
0
.
The fraction of mixed and unmixed events, tagged by a
positive charge kaon, depends on the detector charge
asymmetries and on
A
CP
. Analogously, the corresponding
fractions for a sample of
B
þ
events tagged by a kaon from
the
B
T
or
B
R
meson decay give information on the detector
charge asymmetries.
The same values of
A
CP
and
A
K
are shared between
signal and combinatorial
B
0
samples. The values of
P
exp
m
and
P
exp
m
ð
u
Þ
;K
þ
for all the subsamples are obtained from the
ratio of integrals of the corresponding observed PDFs.
We maximize the likelihood
L
¼

Y
N
m;K
þ
i
¼
1
F
l
þ
K
þ
i

Y
N
m;K
j
¼
1
F
l
K
j

×

Y
N
u;K
þ
m
¼
1
F
l
K
þ
m

Y
N
u;K
n
¼
1
F
l
þ
K
n

×

Y
5
k
¼
1
Y
8
l
¼
1
C
l
m
ð
k
Þ
C
l
m;K
þ
ð
k
Þ
C
l
u;K
þ
ð
k
Þ

where the indices
i
,
j
,
m
and
n
denote the mixed (unmixed)
events, tagged by a kaon of a given charge; the index
k
denotes the
p
K
bin; and the index
l
denotes the signal
(combinatorial background) subsample, according to the
B
meson charge (
B
0
or
B
þ
), and the tagging kaon category
(
K
T
or
K
R
).
A total of 168 parameters are determined in the fit. To
reach the convergence of the fit, we use a three-step
approach. In the first step we fit only the parameters
describing the
B
R
event fractions, whereas all the other
parameters are fixed to the values obtained on simulated
events. In the second step we fix the
B
R
fractions to the
values obtained in the first step and we float only the
parameters describing the resolution function. In the last
step we fix the resolution parameters to the values obtained
in the second step and we float again all the other
parameters together with
Δ
CP
.
VII. FIT VALIDATION
Several tests are performed to validate the result. We
analyze simulated events with the same procedure we use
for data, first considering only the
B
0
signal and adding step
by step all the other samples. At each stage, the fit
reproduces the generated values of
Δ
CP
(zero), and of
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
032001 (2016)
032001-10
the other most significant parameters (
A
r
l
,
A
K
,
Δ
m
,
and
τ
B
0
).
We then repeat the test, randomly rejecting
B
0
or
̄
B
0
events in order to produce samples of simulated events with
Δ
CP
¼
0
.
005
,

0
.
01
,

0
.
025
. Also in this case the
generated values are well reproduced by the fit. By
removing events we also vary artificially
A
r
l
or
A
K
,
testing values in the range of

10%
. In each case, the
input values are correctly determined, and an unbiased
value of
Δ
CP
is always obtained. A total of 67 different
simulated event samples are used to check for biases.
Pseudoexperiments are used to check the result and its
statistical uncertainty. We perform 173 pseudoexperiments,
each with the same number of events as the data. We obtain
a value of the likelihood larger than in the data in 23% of
the cases.
The distribution of the fit results for
Δ
CP
, obtained using
the
MIGRAD
minimizer of the
MINUIT
[25]
physics analysis
tool for function minimization, is described by a Gaussian
function with a central value biased by
3
.
6
×
10
4
(
0
.
4
σ
)
with respect to the nominal result. We quote this discrep-
ancy as a systematic uncertainty related to the analysis bias.
The pull distribution is described by a Gaussian function,
with a central value
0
.
48

0
.
11
and rms width of
1
.
44

0
.
08
. The statistical uncertainty, is, therefore, some-
what underestimated. As a cross-check, by fitting the
negative log likelihood profile near the minimum with a
parabola, we obtain an estimate of the statistical uncertainty
from the
Δ
CP
values for which
log
L
¼
log
L
min
þ
0
.
5
[1]
. This result is in good agreement with the rms width of
the distribution of the pseudoexperiments results, which we
take as the statistical uncertainty of the measurement.
VIII. SYSTEMATIC UNCERTAINTIES AND
CONSISTENCY CHECKS
We consider several sources of systematic uncertainty.
We vary each quantity by its error, as discussed below; we
repeat the measurement; and we consider the variation of
the result as the corresponding systematic uncertainty. We
then add in quadrature all the contributions to determine the
overall systematic uncertainty.
Peaking sample composition:
We vary the sample
composition in the second-stage fit by the statistical
uncertainties obtained in the first stage; the corresponding
variation is added in quadrature to the systematic uncer-
tainty. We then vary the fraction of
B
0
to
B
þ
in the
D

peaking sample in the range
ð
50

25
Þ
%
to account for
(large) violation of isospin symmetry. The fraction of the
peaking contributions fixed to the simulation expectations
is varied by

20%
. Finally we conservatively vary the
fraction of
CP
eigenstates by

50%
.
B
̄
B
combinatorial sample composition:
The fraction of
B
þ
and
B
0
in the
B
̄
B
combinatorial background is
determined by the simulation. A difference between
B
þ
and
B
0
is expected when mixing takes place and the lepton
is coupled to the tag side
π
s
from
̄
B
0
D
X
decay. We
then vary the fraction of
B
0
to
B
þ
events in the combina-
torial sample by

4
.
5%
, which corresponds to the uncer-
tainty in the inclusive branching fraction
̄
B
0
D
X
.
Δ
t
resolution model:
In order to reduce the time in the fit
validation, all the parameters describing the resolution
function, which show a weak correlation with
j
q=p
j
, are
fixed to the values obtained using an iterative procedure.
We perform a fit by leaving free all the parameters and we
quote the difference between the two results as a systematic
uncertainty.
K
R
fraction:
We vary the fraction of
B
þ
K
R
X
to
B
0
K
R
X
by

6
.
8%
, which corresponds to the uncertainty on
the ratio
BR
ð
D

0
K
X
Þ
=BR
ð
D
K
X
Þ
.
K
R
Δ
t
distribution:
We use half the difference between
the results obtained using the two different strategies to
describe the
K
R
Δ
t
distribution as a systematic uncertainty.
Fit bias:
We consider two contributions: the statistical
uncertainty on the validation test using the detailed sim-
ulation, and the difference between the nominal result and
the central result determined from the ensemble of para-
metrized simulations, described in Sec.
VII
.
CP
eigenstate description:
We vary the
S
and
C
parameters describing the
CP
eigenstates by their statistical
uncertainty as obtained from simulation.
Physical parameters:
We repeat the fit, setting the value
of
ΔΓ
to
0
.
02
ps
1
instead of zero. The lifetime of the
B
0
and
B
þ
mesons and
Δ
m
are floated in the fit. Alternatively,
we check the effect of fixing each parameter in turn to the
world average.
By adding in quadrature all the contributions described
above, and summarized in Table
I
, we determine an overall
systematic uncertainty of
þ
1
.
88
1
.
61
×
10
3
.
IX. RESULTS
We perform a blind analysis: the value of
Δ
CP
is kept
masked until the study of the systematic uncertainties is
completed and all the consistency checks are successfully
TABLE I. Breakdown of the main systematic uncertainties on
Δ
CP
.
Source
δ
Δ
CP
ð
10
3
Þ
Peaking sample composition
þ
1
.
50
1
.
17
Combinatorial sample composition

0
.
39
Δ
t
resolution model

0
.
60
K
R
fraction

0
.
11
K
R
Δ
t
distribution

0
.
65
Fit bias
þ
0
.
58
0
.
46
CP
eigenstate description
0
Physical parameters
þ
0
0
.
28
Total
þ
1
.
88
1
.
61
SEARCH FOR MIXING-INDUCED
CP
VIOLATION
...
PHYSICAL REVIEW D
93,
032001 (2016)
032001-11