Measurement of the
B
0
→
D
−
π
þ
π
−
π
þ
branching fraction
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano,
3
G. Eigen,
4
D. N. Brown,
5
Yu. G. Kolomensky,
5
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
V. E. Blinov,
8a,8b,8c
A. R. Buzykaev,
8a
V. P. Druzhinin,
8a,8b
V. B. Golubev,
8a,8b
E. A. Kravchenko,
8a,8b
A. P. Onuchin,
8a,8b,8c
S. I. Serednyakov,
8a,8b
Yu. I. Skovpen,
8a,8b
E. P. Solodov,
8a,8b
K. Yu. Todyshev,
8a,8b
A. J. Lankford,
9
J. W. Gary,
10
O. Long,
10
A. M. Eisner,
11
W. S. Lockman,
11
W. Panduro Vazquez,
11
D. S. Chao,
12
C. H. Cheng,
12
B. Echenard,
12
K. T. Flood,
12
D. G. Hitlin,
12
J. Kim,
12
T. S. Miyashita,
12
P. Ongmongkolkul,
12
F. C. Porter,
12
M. Röhrken,
12
Z. Huard,
13
B. T. Meadows,
13
B. G. Pushpawela,
13
M. D. Sokoloff,
13
L. Sun,
13
,
†
J. G. Smith,
14
S. R. Wagner,
14
D. Bernard,
15
M. Verderi,
15
F. Betti,
16a,16b
,
‡
D. Bettoni,
16a
C. Bozzi,
16a
R. Calabrese,
16a,16b
G. Cibinetto,
16a,16b
E. Fioravanti,
16a,16b
I. Garzia,
16a,16b
E. Luppi,
16a,16b
V. Santoro,
16a
A. Calcaterra,
17
R. de Sangro,
17
G. Finocchiaro,
17
S. Martellotti,
17
P. Patteri,
17
I. M. Peruzzi,
17
M. Piccolo,
17
M. Rotondo,
17
A. Zallo,
17
S. Passaggio,
18
C. Patrignani,
18
,§
B. Bhuyan,
19
U. Mallik,
20
C. Chen,
21
J. Cochran,
21
S. Prell,
21
H. Ahmed,
22
A. V. Gritsan,
23
N. Arnaud,
24
M. Davier,
24
F. Le Diberder,
24
A. M. Lutz,
24
G. Wormser,
24
D. J. Lange,
25
D. M. Wright,
25
J. P. Coleman,
26
E. Gabathuler,
26
D. E. Hutchcroft,
26
D. J. Payne,
26
C. Touramanis,
26
A. J. Bevan,
27
F. Di Lodovico,
27
R. Sacco,
27
G. Cowan,
28
Sw. Banerjee,
29
D. N. Brown,
29
C. L. Davis,
29
A. G. Denig,
30
M. Fritsch,
30
W. Gradl,
30
K. Griessinger,
30
A. Hafner,
30
K. R. Schubert,
30
R. J. Barlow,
31
,
∥
G. D. Lafferty,
31
R. Cenci,
32
A. Jawahery,
32
D. A. Roberts,
32
R. Cowan,
33
R. Cheaib,
34
S. H. Robertson,
34
B. Dey,
35a
N. Neri,
35a
F. Palombo,
35a,35b
L. Cremaldi,
36
R. Godang,
36
,¶
D. J. Summers,
36
P. Taras,
37
G. De Nardo,
38
C. Sciacca,
38
G. Raven,
39
C. P. Jessop,
40
J. M. LoSecco,
40
K. Honscheid,
41
R. Kass,
41
A. Gaz,
42a
M. Margoni,
42a,42b
M. Posocco,
42a
G. Simi,
42a,42b
F. Simonetto,
42a,42b
R. Stroili,
42a,42b
S. Akar,
43
E. Ben-Haim,
43
M. Bomben,
43
G. R. Bonneaud,
43
G. Calderini,
43
J. Chauveau,
43
G. Marchiori,
43
J. Ocariz,
43
M. Biasini,
44a,44b
E. Manoni,
44a
A. Rossi,
44a
G. Batignani,
45a,45b
S. Bettarini,
45a,45b
M. Carpinelli,
45a,45b
,**
G. Casarosa,
45a,45b
M. Chrzaszcz,
45a
F. Forti,
45a,45b
M. A. Giorgi,
45a,45b
A. Lusiani,
45a,45c
B. Oberhof,
45a,45b
E. Paoloni,
45a,45b
M. Rama,
45a
G. Rizzo,
45a,45b
J. J. Walsh,
45a
A. J. S. Smith,
46
F. Anulli,
47a
R. Faccini,
47a,47b
F. Ferrarotto,
47a
F. Ferroni,
47a,47b
A. Pilloni,
47a,47b
G. Piredda,
47a
,*
C. Bünger,
48
S. Dittrich,
48
O. Grünberg,
48
M. Heß,
48
T. Leddig,
48
C. Voß,
48
R. Waldi,
48
T. Adye,
49
F. F. Wilson,
49
S. Emery,
50
G. Vasseur,
50
D. Aston,
51
C. Cartaro,
51
M. R. Convery,
51
J. Dorfan,
51
W. Dunwoodie,
51
M. Ebert,
51
R. C. Field,
51
B. G. Fulsom,
51
M. T. Graham,
51
C. Hast,
51
W. R. Innes,
51
P. Kim,
51
D. W. G. S. Leith,
51
S. Luitz,
51
V. Luth,
51
D. B. MacFarlane,
51
D. R. Muller,
51
H. Neal,
51
B. N. Ratcliff,
51
A. Roodman,
51
M. K. Sullivan,
51
J. Va
’
vra,
51
W. J. Wisniewski,
51
M. V. Purohit,
52
J. R. Wilson,
52
A. Randle-Conde,
53
S. J. Sekula,
53
M. Bellis,
54
P. R. Burchat,
54
E. M. T. Puccio,
54
M. S. Alam,
55
J. A. Ernst,
55
R. Gorodeisky,
56
N. Guttman,
56
D. R. Peimer,
56
A. Soffer,
56
S. M. Spanier,
57
J. L. Ritchie,
58
R. F. Schwitters,
58
J. M. Izen,
59
X. C. Lou,
59
F. Bianchi,
60a,60b
F. De Mori,
60a,60b
A. Filippi,
60a
D. Gamba,
60a,60b
L. Lanceri,
61
L. Vitale,
61
F. Martinez-Vidal,
62
A. Oyanguren,
62
J. Albert,
63
A. Beaulieu,
63
F. U. Bernlochner,
63
G. J. King,
63
R. Kowalewski,
63
T. Lueck,
63
I. M. Nugent,
63
J. M. Roney,
63
N. Tasneem,
63
T. J. Gershon,
64
P. F. Harrison,
64
T. E. Latham,
64
R. Prepost,
65
and S. L. Wu
65
(
BABAR
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
3
INFN Sezione di Bari and 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
8a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
8b
Novosibirsk State University, Novosibirsk 630090, Russia
8c
Novosibirsk State Technical University, Novosibirsk 630092, Russia
9
University of California at Irvine, Irvine, California 92697, USA
10
University of California at Riverside, Riverside, California 92521, USA
11
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
12
California Institute of Technology, Pasadena, California 91125, USA
13
University of Cincinnati, Cincinnati, Ohio 45221, USA
14
University of Colorado, Boulder, Colorado 80309, USA
15
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
16a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
16b
Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, I-44122 Ferrara, Italy
17
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
PHYSICAL REVIEW D
94,
091101(R) (2016)
2470-0010
=
2016
=
94(9)
=
091101(7)
091101-1
© 2016 American Physical Society
RAPID COMMUNICATIONS
18
INFN Sezione di Genova, I-16146 Genova, Italy
19
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
20
University of Iowa, Iowa City, Iowa 52242, USA
21
Iowa State University, Ames, Iowa 50011, USA
22
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudi Arabia
23
Johns Hopkins University, Baltimore, Maryland 21218, USA
24
Laboratoire de l
’
Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d
’
Orsay, F-91898 Orsay Cedex, France
25
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
26
University of Liverpool, Liverpool L69 7ZE, United Kingdom
27
Queen Mary, University of London, London, E1 4NS, United Kingdom
28
University of London, Royal Holloway and Bedford New College, Egham,
Surrey TW20 0EX, United Kingdom
29
University of Louisville, Louisville, Kentucky 40292, USA
30
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
31
University of Manchester, Manchester M13 9PL, United Kingdom
32
University of Maryland, College Park, Maryland 20742, USA
33
Massachusetts Institute of Technology, Laboratory for Nuclear Science,
Cambridge, Massachusetts 02139, USA
34
McGill University, Montréal, Québec, Canada H3A 2T8
35a
INFN Sezione di Milano, I-20133 Milano, Italy
35b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
36
University of Mississippi, University, Mississippi 38677, USA
37
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
38
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche,
Università di Napoli Federico II, I-80126 Napoli, Italy
39
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, The Netherlands
40
University of Notre Dame, Notre Dame, Indiana 46556, USA
41
Ohio State University, Columbus, Ohio 43210, USA
42a
INFN Sezione di Padova, I-35131 Padova, Italy
42b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
43
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS,
Université Pierre et Marie Curie-Paris6, Université Denis Diderot-Paris7,
F-75252 Paris, France
44a
INFN Sezione di Perugia, I-06123 Perugia, Italy
44b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
45a
INFN Sezione di Pisa, I-56127 Pisa, Italy
45b
Dipartimento di Fisica,Università di Pisa, I-56127 Pisa, Italy
45c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
46
Princeton University, Princeton, New Jersey 08544, USA
47a
INFN Sezione di Roma, I-00185 Roma, Italy
47b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
48
Universität Rostock, D-18051 Rostock, Germany
49
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
50
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
51
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
52
University of South Carolina, Columbia, South Carolina 29208, USA
53
Southern Methodist University, Dallas, Texas 75275, USA
54
Stanford University, Stanford, California 94305, USA
55
State University of New York, Albany, New York 12222, USA
56
Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
57
University of Tennessee, Knoxville, Tennessee 37996, USA
58
University of Texas at Austin, Austin, Texas 78712, USA
59
University of Texas at Dallas, Richardson, Texas 75083, USA
60a
INFN Sezione di Torino, I-10125 Torino, Italy
60b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
61
INFN Sezione di Trieste and Dipartimento di Fisica, Università di Trieste,
I-34127 Trieste, Italy
62
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
J. P. LEES
et al.
PHYSICAL REVIEW D
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63
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
64
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
65
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 22 September 2016; published 15 November 2016)
Using a sample of
ð
470
.
9
2
.
8
Þ
×
10
6
B
̄
B
pairs, we measure the decay branching fraction
B
ð
B
0
→
D
−
π
þ
π
−
π
þ
Þ¼ð
7
.
26
0
.
11
0
.
31
Þ
×
10
−
3
, where the first uncertainty is statistical and the
second is systematic. Our measurement will be helpful in studies of lepton universality by measuring
B
ð
B
0
→
D
−
τ
þ
ν
τ
Þ
using
τ
þ
→
π
þ
π
−
π
þ
̄
ν
τ
decays, normalized to
B
ð
B
0
→
D
−
π
þ
π
−
π
þ
Þ
.
DOI:
10.1103/PhysRevD.94.091101
The
BABAR
Collaboration measured the branching
fraction ratios for
B
semileptonic decays to
D
and
D
R
ðÞ
¼
B
ð
̄
B
→
D
ðÞ
τ
−
̄
ν
τ
Þ
B
ð
̄
B
→
D
ðÞ
l
−
̄
ν
l
Þ
;
ð
1
Þ
where
l
−
is an electron or a muon, to be in excess of
standard model (SM) predictions
[1]
. The use of charge
conjugate reactions is implied throughout this article. After
combining the results for
R
and
R
, the excess is
inconsistent with lepton universality at the
3
.
4
σ
level.
The Belle Collaboration
[2]
and the LHCb Collaboration
[3]
conducted similar measurements with comparable
results. A measurement of
B
ð
B
0
→
D
−
τ
þ
ν
τ
Þ
using
τ
þ
→
π
þ
π
−
π
þ
̄
ν
τ
decays, normalized to
B
ð
B
0
→
D
−
π
þ
π
−
π
þ
Þ
,
may yield the observation of a further deviation from
the SM. Such a measurement has not been done before
and may make use of a clean kinematic signature.
This possibility relies in part on a measurement of
B
ð
B
0
→
D
−
π
þ
π
−
π
þ
Þ
, for which the current world average
value is
ð
7
.
0
0
.
8
Þ
×
10
−
3
[4]
. The LHCb Collaboration
measured this value to be
ð
7
.
27
0
.
11
ð
stat
Þ
0
.
36
ð
syst
Þ
0
.
34
ð
norm
ÞÞ
×
10
−
3
[5]
, where the final
uncertainty is due to using
B
0
→
D
−
π
þ
decays for
normalization purposes. This measurement has not been
included in the world average value as yet. In this article,
we report on a measurement of
B
ð
B
0
→
D
−
π
þ
π
−
π
þ
Þ
.
We use data recorded with the
BABAR
detector at
the PEP-II asymmetric-energy
e
þ
e
−
collider at SLAC.
The
BABAR
detector is described in detail elsewhere
[6,7]
. The data sample corresponds to an integrated
luminosity of
424
.
2
1
.
8
fb
−
1
collected at the
Υ
ð
4
S
Þ
resonance
[8]
, which corresponds to the production of
ð
470
.
9
2
.
8
Þ
×
10
6
B
̄
B
pairs. We use Monte Carlo (MC)
simulations to understand background processes and signal
reconstruction efficiencies. The EvtGen event generator
[9]
is used to simulate particle decays. This includes a sample
of
e
þ
e
−
→
q
̄
q
ð
γ
Þ
events, where
q
is a
u
,
d
,
s
,or
c
quark,
with an equivalent luminosity of
2
;
589
fb
−
1
and a sample
of
1
;
427
×
10
6
B
̄
B
pairs. The detector response is simu-
lated with the Geant4
[10]
suite of programs.
We fully reconstruct the
B
0
→
D
−
π
þ
π
−
π
þ
decay
chain by adding the four-momenta of particle candidates.
The
D
−
mesons are reconstructed in the
D
−
→
̄
D
0
π
−
and
̄
D
0
→
K
þ
π
−
final states. A
̄
D
0
candidate is reconstructed
from two charged-particle tracks, of which one is identified
as a
K
þ
meson based on information obtained using the
tracking and Cherenkov detectors. We require
̄
D
0
candi-
dates to have an invariant-mass value within
20
MeV
=c
2
of the nominal
̄
D
0
mass
[4]
, which corresponds to 3
standard deviations in its mass resolution. Each
̄
D
0
can-
didate is combined with a charged-particle track with
momentum less than
0
.
45
GeV
=c
in the
e
þ
e
−
center-of-
mass (CM) frame to form a
D
−
candidate. We require
the difference between the reconstructed mass of the
D
−
candidate and the reconstructed mass of the
̄
D
0
candidate to
lie between 0.1435 and
0
.
1475
GeV
=c
2
. The
D
−
candi-
date is combined with three other charged-particle tracks to
form a
B
0
candidate. We do not explicitly apply particle
identification to select charged pions, but assign the pion
mass hypothesis to all tracks other than the
K
þ
daughter of
the
̄
D
0
. All other reconstructed tracks and neutral clusters in
the event are collectively referred to as the rest of the event
(ROE). We use a neural network classifier
[11]
to suppress
non-
B
̄
B
backgrounds. The classifier makes use of nine
variables, each of which is calculated in the CM frame:
(i) the cosine of the angle between the
B
0
candidate
’
s
thrust axis
[12]
and the beam axis;
(ii) the sphericity
[13]
of the
B
0
candidate;
(iii) the thrust of the ROE;
(iv) the sum over the ROE of
p
, where
p
is the
magnitude of a particle
’
s momentum;
(v) the sum over the ROE of
1
2
ð
3
cos
2
θ
−
1
Þ
p
, where
θ
is the polar angle of a particle
’
s momentum;
(vi) the cosine of the angle between the thrust axis of the
B
0
candidate and the thrust axis of the ROE;
*
Deceased.
†
Present address: Wuhan University, Wuhan 43072, China.
‡
Also at Laboratoire de l
’
Accélérateur Linéaire, F-91898
Orsay Cedex, France.
§
Present address: Università di Bologna and INFN Sezione di
Bologna, I-47921 Rimini, Italy.
∥
Present address: University of Huddersfield, Huddersfield
HD1 3DH, UK.
¶
Present address: University of South Alabama, Mobile,
Alabama 36688, USA.
**
Also at Università di Sassari, I-07100 Sassari, Italy.
MEASUREMENT OF THE
...
PHYSICAL REVIEW D
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091101(R) (2016)
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RAPID COMMUNICATIONS
(vii) the cosine of the angle between the sphericity axis of
the
B
0
candidate and the thrust axis of the ROE;
(viii) the ratio of the second-order to zeroth-order Fox-
Wolfram moment using all reconstructed particles
[14]
;
(ix) the cosine of the angle between the thrust axis
calculated using all reconstructed particles and the
beam axis.
Each of these nine variables contributes to separating
B
0
decays from non-
B
̄
B
decays. We apply a selection on the
output of the neural network classifier that rejects 69%
of reconstructed signal candidates from non-
B
̄
B
decays,
and retains 80% of correctly reconstructed
B
0
candidates.
Finally, we require the
B
0
candidate to have a CM-frame
energy within
90
MeV of
ffiffiffi
s
p
=
2
, where
ffiffiffi
s
p
is the nominal
invariant mass of the initial state. This corresponds to 4
standard deviations in the energy resolution. We retain all
B
0
candidates that pass our selection criteria instead of
selecting a best candidate for each event. In MC-simulated
signal and background events that have at least one
B
0
candidate passing all selection criteria, there are on average
1.57 and 1.37
B
0
candidates per event, respectively. We do
not apply corrections to the number of
B
0
candidates per
event, as the
B
0
candidate multiplicity in data is consistent
with the weighted average of those in the signal and
background simulation.
After applying all selection criteria, we determine the
energy-substituted mass
m
ES
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s=
4
−
p
2
B
p
for the
selected
B
0
candidates, where
p
B
is the CM-frame momen-
tum of a
B
0
. Figure
1
shows the
m
ES
distribution for the
data and for MC-simulated events. The
m
ES
distribution of
correctly reconstructed signal candidates has a peak near
the
B
0
mass.
The
m
ES
distribution of signal events is modeled using a
Crystal Ball
[15]
probability density function (PDF), with
cutoff and power-law parameters determined using MC-
simulated events. We consider only
B
0
candidates that are
correctly reconstructed. We model the background
m
ES
distribution as follows. The nonpeaking backgrounds from
e
þ
e
−
→
q
̄
q
ð
γ
Þ
events and from
B
̄
B
pairs are modeled using
an ARGUS function
[16]
. Each of the peaking backgrounds
from
B
þ
B
−
and
B
0
̄
B
0
is modeled by a Gaussian distribu-
tion for which the normalization, mean, and width, are
determined by a fit to the corresponding simulated event
sample. We perform a one-dimensional unbinned extended-
maximum-likelihood fit in order to estimate the number of
signal candidates. We allow the mean and width parameters
of the Crystal Ball function, the curvature parameter of the
ARGUS function, and the normalization of the nonpeaking
background, to vary in the fit. The cutoff parameter for
the ARGUS function is fixed to
ffiffiffi
s
p
=
2
, and the peaking
background PDF shapes and normalizations are fixed to
their MC-estimated values. The peaking background con-
tributions are estimated to be
590
120
and
1450
130
candidates from
B
þ
B
−
and
B
0
̄
B
0
decays, respectively;
some originate from signal decays where one or more
pion is misreconstructed even when there is a correctly
reconstructed
B
0
candidate. There is also a contribution
from
B
þ
→
D
−
X
and
B
0
→
D
−
X
decays, where
X
denotes any combination of
π
and
ρ
mesons other than
ρ
0
π
þ
or
π
þ
π
−
π
þ
. The fit to the
m
ES
distribution shown in
Fig.
1
results in a signal yield of
17800
300
.
The distribution for the MC signal peaks
0
.
2
MeV
=c
2
higher in
m
ES
value than the data. This arises from a value of
the simulated
B
0
mass that is different from that found in
Ref.
[4]
. We weight the simulated events in order to match
the data mass peak and we repeat the measurement of
the simulated efficiencies for the signal and the peaking
background. The change is negligible and produces a
negligiblecorrectiononthebranchingfractionmeasurement.
We define the signal region to be
5
.
273
<m
ES
<
5
.
285
GeV
=c
2
, and a sideband region to be
5
.
240
<m
ES
<
5
.
270
GeV
=c
2
. About 97.6% of signal events are contained
within the signal region. To obtain the
3
π
invariant-mass
distribution for the signal events in Fig.
2
, we subtract
the events in the sideband region of the
m
ES
in Fig.
1
,
normalized to the fitted background component in the
signal region, from the total
3
π
mass distribution. By
integrating the dashed line in Fig.
1
, we obtain 68883
events in the sideband region and 24427 background events
in the signal region. These values make use of the peaking
background estimates described in the previous paragraph.
As expected from the branching fractions in Ref.
[4]
,
the main contribution comes from
a
þ
1
ð
1260
Þ
decays, and a
contribution from the decay
D
þ
s
→
π
þ
π
−
π
þ
is also
)
2
(GeV/c
ES
m
5.24
5.25
5.26
5.27
5.28
5.29
5.3
2
Candidates / 0.001 GeV/c
0
1000
2000
3000
4000
5000
Data
Fit
Fitted Signal
Background
MC signal
0
B
0
B
-
B
+
B
c
sc
,
ds
,
ud
,
u
FIG. 1. The
m
ES
distribution of
B
0
candidates for data (points),
MC simulations (histograms), and the unbinned extended-
maximum-likelihood fit to the data (curves). The MC distribu-
tions are shown as stacked histograms. The
B
0
→
D
−
D
þ
s
with
D
þ
s
→
π
þ
π
−
π
þ
decays are part of the MC signal. The MC signal
contribution is normalized such that its stacked histogram has the
same integral as the data. The components of the MC simulations
and the fit are described in the legend. The
m
ES
peak of the MC
signal is slightly above that of the data. This shift has a negligible
effect on the signal yield.
J. P. LEES
et al.
PHYSICAL REVIEW D
94,
091101(R) (2016)
091101-4
RAPID COMMUNICATIONS
apparent. There is as well activity in the
1
.
7
–
1
.
9
GeV
=c
2
region, which may be due to the
J
P
¼
0
−
π
ð
1800
Þ
meson.
The analysis of the
a
þ
1
region is complicated and will be the
subject of a separate study.
The
D
þ
s
events result from the doubly charmed decay
B
0
→
D
−
D
þ
s
in which the
D
þ
s
decays weakly to
π
þ
π
−
π
þ
.
Since the
D
þ
s
decay results from an entirely different
B
0
decay mode, it represents a contamination of our
D
−
π
þ
π
−
π
þ
sample. We remove the
D
þ
s
contribution by
subtracting the events in the
1
.
9
–
2
.
0
GeV
=c
2
region of the
3
π
invariant-mass distribution of Fig.
2
that exceed the
interpolation of the bin contents in the
1
.
8
–
1
.
9
GeV
=c
2
and
2
.
0
–
2
.
1
GeV
=c
2
regions. The removed
D
þ
s
contribution
amounts to
233
63
events, and the remaining events in
the
1
.
9
–
2
.
0
GeV
=c
2
region total
326
35
.
We estimate the reconstruction efficiency as a function of
3
π
invariant mass using MC-simulated events. This is shown
in Fig.
3
. Since we model the
m
ES
PDF of the signal only
considering
B
0
candidates that are correctly reconstructed,
we apply exactly the same procedure of determining the
signal yield in our study of the reconstruction efficiency in
order to determine the branching fraction correctly. The
efficiency of the decay channel
D
−
a
þ
1
, where the
a
þ
1
decays
to
ρ
0
π
þ
and the
ρ
0
to
π
þ
π
−
was studied. The simulation
assumes a mass of
1
.
230
GeV
=c
2
and a width of 400 MeV
for the
a
þ
1
[4]
. The reconstruction efficiencies of
B
0
→
D
−
ρ
0
π
þ
and
B
0
→
D
−
D
þ
s
decays are consistent with
B
0
→
D
−
a
þ
1
decays. Taking into account the efficiency
as a function of the
3
π
mass, and removing the
D
þ
s
back-
ground, the total number of produced
B
0
→
D
−
π
þ
π
−
π
þ
events is estimated to be
84400
1200
.
Table
I
summarizes the systematic uncertainties for this
analysis. The uncertainties of our extended-maximum-
likelihood fit algorithm and peaking backgrounds are
estimated together by taking into account the uncertainties
of the fixed parameters in the fit. The values we used are
shown in Table
II
. These values are obtained entirely from
studies of MC-simulated background samples. Therefore,
we consider varying the mean and width of the
m
ES
distributions for the peaking
B
þ
B
−
and
B
0
̄
B
0
backgrounds,
the number of
B
0
̄
B
0
and
B
þ
B
−
peaking background events,
and the Crystal Ball PDF cutoff and power-law parameter
values for the signal. These values are sampled from an
eight-dimensional Gaussian function with means, widths,
and correlations that correspond to the fit results for the
PDFs for signal and peaking backgrounds from simulated
events. The systematic uncertainty is taken as the standard
deviation of the distribution of the number of signal events
from an ensemble of fits, and is found to be 2.4%. The
systematic uncertainty due to track finding consists of
two components: 1.54% for laboratory momenta less than
0
.
18
GeV
=c
, a region dominated by tracks from the decay
D
−
→
̄
D
0
π
−
, and 0.26% for greater than this value
[17]
.
The two components are added in quadrature. The pion
from the
D
−
→
̄
D
0
π
−
decay has momentum less than
0
.
180
GeV
=c
62% of the time. The corresponding fraction
)
2
(GeV/c
π
3
m
0.5
1
1.5
2
2.5
3
3.5
2
Candidates / 0.01 GeV/c
0
100
200
300
+
s
D
(PDG)
2
40 MeV/c
±
= 1230
+
1
a
m
1.8
1.9
2
2.1
0
50
100
150
FIG. 2. The background-subtracted invariant-mass spectrum of
the
3
π
system. The indicated mass value of the
a
þ
1
is obtained
from Ref.
[4]
. The
B
0
→
D
−
D
þ
s
,
D
þ
s
→
π
þ
π
−
π
þ
decay, which
is removed in the final result, is visible in the spectrum. The
spectrum is obtained prior to the efficiency correction. The inset
shows the distribution around the
D
þ
s
region.
)
2
(GeV/c
π
3
m
0.5
1
1.5
2
2.5
3
3.5
Efficiency
0
0.05
0.1
0.15
0.2
0.25
0.3
FIG. 3. The reconstruction efficiency as a function of
3
π
invariant mass using MC-simulated events. The uncertainties
are statistical.
TABLE I. Summary of systematic uncertainties. The uncer-
tainties are assumed to be uncorrelated, and so are added in
quadrature.
Source
Uncertainty (%)
Fit algorithm and peaking backgrounds
2.4
Track finding
2.0
π
þ
π
−
π
þ
invariant-mass modeling
1.7
D
−
and
̄
D
0
decay branching fractions
1.3
Υ
ð
4
S
Þ
→
B
0
̄
B
0
decay branching fraction
1.2
K
þ
identification
1.1
Signal efficiency MC statistics
0.9
Sideband subtraction
0.7
B
̄
B
counting
0.6
Total
4.3
MEASUREMENT OF THE
...
PHYSICAL REVIEW D
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RAPID COMMUNICATIONS
for other pions in the signal
B
0
decay is 5%. The
3
π
invariant mass of the
D
þ
s
contamination has the same mass
location and width in the data and MC-simulated events.
However, there are differences between the full recon-
structed
3
π
invariant-mass spectrum for the data and that
obtained from MC-simulated events. We studied the signal
yield before and after reweighting the
3
π
invariant-mass
spectrum in the MC-simulated events to match the data.
The observed change due to the reweighting of the
3
π
mass
distribution is 1.7%, which we assign as the associated
systematic uncertainty. This also accounts for uncertainties
in the relative contributions of the different decay modes
and the mass and width of the
a
þ
1
resonance. We use the
D
−
and
̄
D
0
decay branching fraction uncertainties from
Ref.
[4]
. We use the value of
B
ð
Υ
ð
4
S
Þ
→
B
0
̄
B
0
Þ¼
0
.
486
0
.
006
from Ref.
[4]
for the branching fraction of the decay
Υ
ð
4
S
Þ
→
B
0
̄
B
0
, which has a relative uncertainty of 1.2%.
The kaon identification uncertainty is estimated by
comparing the number of
D
−
events in data and MC
simulations with and without implementing identification
requirements. According to dedicated studies using
BABAR
data control samples, we correct for kaon-identification
efficiency differences between data and MC simulation by
a factor of
0
.
978
0
.
011
, where the uncertainty is chosen
to be half the difference from unity. The signal efficiency
MC statistical uncertainty is 0.9%. Nominally, we subtract
the
3
π
mass distribution in the sideband from that of the
signal region. However, the
3
π
mass distribution of both
peaking and nonpeaking backgrounds in the signal region
may not necessarily be the same as that in the sideband. To
estimate the associated systematic uncertainty, we test the
sideband subtraction procedure using only MC-simulated
background events. After applying efficiency corrections to
the resulting distribution, we obtain an integral of 571.
Dividing this by the number of efficiency-corrected signal
in the data, this translates to a 0.7% difference, which we
assign as the associated systematic uncertainty. The number
of
B
mesons produced is uncertain to 0.6%
[8]
. We studied
the MC modeling of decay angle correlations, and found
the associated systematic uncertainty to be negligible. As
described earlier in the text, there is a peaking background
contribution in the
m
ES
distribution due to signal events that
are misreconstructed. The rate of this background depends
on the branching fraction of signal events. Using our
measured branching fraction value, we apply corrections
to the expected number of
B
0
̄
B
0
peaking background and
repeat the signal extraction procedure on the data. There
is a small bias on the branching fraction value but it is
negligible compared to the systematic uncertainty due to
the other peaking backgrounds.
From the number of fitted signal events, corrected
for efficiency and normalized to the total number of
produced
B
0
mesons in the data sample, and taking into
account the
D
−
and
̄
D
0
branching fractions we derive
B
ð
B
0
→
D
−
π
þ
π
−
π
þ
Þ¼ð
7
.
26
0
.
11
0
.
31
Þ
×
10
−
3
, where
the first uncertainty is statistical and the second systematic.
The result is consistent with the current world average and
is 2.4 times more precise. This result can be used as input
for measurements of
R
ðÞ
using hadronic
τ
decays in the
search for deviations from the SM. The inclusive branching
fraction value without removing the
D
þ
s
contamination
is
ð
7
.
37
0
.
11
0
.
31
Þ
×
10
−
3
.
We are grateful for the extraordinary contributions of
our PEP-II colleagues in achieving the excellent luminosity
and machine conditions that have made this work possible.
The success of this project also relies critically on the
expertise and dedication of the computing organizations that
support
BABAR
. The collaborating institutions wish to thank
SLAC for its support and the kind hospitality extended to
them. This work is supported by the U.S. Department of
Energy and National Science Foundation, the Natural
Sciences and Engineering Research Council (Canada), the
Commissariat à l
’
Energie Atomique and Institut National de
Physique Nucléaire et de Physique des Particules (France),
the Bundesministerium für Bildung und Forschung and
Deutsche Forschungsgemeinschaft (Germany), the Istituto
Nazionale di Fisica Nucleare (Italy), the Foundation for
Fundamental Research on Matter (The Netherlands), the
Research Council of Norway, the Ministry of Education and
Science of the Russian Federation, Ministerio de Economía
y Competitividad (Spain), the Science and Technology
Facilities Council (U.K.), and the Binational Science
Foundation (U.S.-Israel). Individuals have received support
from the Marie-Curie IEF program (European Union) and
the A. P. Sloan Foundation (U.S.).
TABLE II. Fit parameters obtained from MC-simulated events.
These parameters are fixed to the central values in the signal
extraction procedure. We perform a toy study where we simulta-
neously vary these by the quoted uncertainties (along with their
correlations, which are not shown in the table) to study systematic
effects on the signal yield.
Parameter
Value
B
þ
B
−
peaking background
m
ES
Gaussian mean
5
.
2796
0
.
0006
GeV
=c
2
B
þ
B
−
peaking background
m
ES
Gaussian width
0
.
0036
0
.
0003
GeV
=c
2
Number of
B
þ
B
−
peaking
background
590
120
B
0
̄
B
0
peaking background
m
ES
Gaussian mean
5
.
2806
0
.
0002
GeV
=c
2
B
0
̄
B
0
peaking background
m
ES
Gaussian width
0
.
0029
0
.
0002
GeV
=c
2
Number of
B
0
̄
B
0
peaking
background
1450
130
Signal
’
s Crystal Ball PDF
cutoff value
2
.
09
0
.
08
Signal
’
s Crystal Ball PDF
power-law value
3
.
7
0
.
5
J. P. LEES
et al.
PHYSICAL REVIEW D
94,
091101(R) (2016)
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RAPID COMMUNICATIONS
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MEASUREMENT OF THE
...
PHYSICAL REVIEW D
94,
091101(R) (2016)
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