Dalitz plot analyses of
J
=
ψ
→
π
+
π
−
π
0
,
J
=
ψ
→
K
+
K
−
π
0
, and
J
=
ψ
→
K
0
s
K
π
∓
produced via
e
+
e
−
annihilation with initial-state radiation
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
M. Fritsch,
6
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7a,7b
T. S. Mattison,
7b
J. A. McKenna,
7b
R. Y. So,
7b
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
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
,§
H. M. Lacker,
19
B. Bhuyan,
20
A. P. Szczepaniak,
21
,
†
U. Mallik,
22
C. Chen,
23
J. Cochran,
23
S. Prell,
23
H. Ahmed,
24
M. R. Pennington,
25
A. V. Gritsan,
26
N. Arnaud,
27
M. Davier,
27
F. Le Diberder,
27
A. M. Lutz,
27
G. Wormser,
27
D. J. Lange,
28
D. M. Wright,
28
J. P. Coleman,
29
E. Gabathuler,
29
,*
D. E. Hutchcroft,
29
D. J. Payne,
29
C. Touramanis,
29
A. J. Bevan,
30
F. Di Lodovico,
30
R. Sacco,
30
G. Cowan,
31
Sw. Banerjee,
32
D. N. Brown,
32
C. L. Davis,
32
A. G. Denig,
33
W. Gradl,
33
K. Griessinger,
33
A. Hafner,
33
K. R. Schubert,
33
R. J. Barlow,
34
,
∥
G. D. Lafferty,
34
R. Cenci,
35
A. Jawahery,
35
D. A. Roberts,
35
R. Cowan,
36
S. H. Robertson,
37
B. Dey,
38a
N. Neri,
38a
F. Palombo,
38a,38b
R. Cheaib,
39
L. Cremaldi,
39
R. Godang,
39
,**
D. J. Summers,
39
P. Taras,
40
G. De Nardo,
41
C. Sciacca,
41
G. Raven,
42
C. P. Jessop,
43
J. M. LoSecco,
43
K. Honscheid,
44
R. Kass,
44
A. Gaz,
45a
M. Margoni,
45a,45b
M. Posocco,
45a
G. Simi,
45a,45b
F. Simonetto,
45a,45b
R. Stroili,
45a,45b
S. Akar,
46
E. Ben-Haim,
46
M. Bomben,
46
G. R. Bonneaud,
46
G. Calderini,
46
J. Chauveau,
46
G. Marchiori,
46
J. Ocariz,
46
M. Biasini,
47a,47b
E. Manoni,
47a
A. Rossi,
47a
G. Batignani,
48a,48b
S. Bettarini,
48a,48b
M. Carpinelli,
48a,48b
,
††
G. Casarosa,
48a,48b
M. Chrzaszcz,
48a
F. Forti,
48a,48b
M. A. Giorgi,
48a,48b
A. Lusiani,
48a,48c
B. Oberhof,
48a,48b
E. Paoloni,
48a,48b
M. Rama,
48a
G. Rizzo,
48a,48b
J. J. Walsh,
48a
A. J. S. Smith,
49
F. Anulli,
50a
R. Faccini,
50a,50b
F. Ferrarotto,
50a
F. Ferroni,
50a,50b
A. Pilloni,
50a,50b
G. Piredda,
50a
,*
C. Bünger,
51
S. Dittrich,
51
O. Grünberg,
51
M. Heß,
51
T. Leddig,
51
C. Voß,
51
R. Waldi,
51
T. Adye,
52
F. F. Wilson,
52
S. Emery,
53
G. Vasseur,
53
D. Aston,
54
C. Cartaro,
54
M. R. Convery,
54
J. Dorfan,
54
W. Dunwoodie,
54
M. Ebert,
54
R. C. Field,
54
B. G. Fulsom,
54
M. T. Graham,
54
C. Hast,
54
W. R. Innes,
54
P. Kim,
54
D. W. G. S. Leith,
54
S. Luitz,
54
D. B. MacFarlane,
54
D. R. Muller,
54
H. Neal,
54
B. N. Ratcliff,
54
A. Roodman,
54
M. K. Sullivan,
54
J. Va
’
vra,
54
W. J. Wisniewski,
54
M. V. Purohit,
55
J. R. Wilson,
55
A. Randle-Conde,
56
S. J. Sekula,
56
M. Bellis,
57
P. R. Burchat,
57
E. M. T. Puccio,
57
M. S. Alam,
58
J. A. Ernst,
58
R. Gorodeisky,
59
N. Guttman,
59
D. R. Peimer,
59
A. Soffer,
59
S. M. Spanier,
60
J. L. Ritchie,
61
R. F. Schwitters,
61
J. M. Izen,
62
X. C. Lou,
62
F. Bianchi,
63a,63b
F. De Mori,
63a,63b
A. Filippi,
63a
D. Gamba,
63a,63b
L. Lanceri,
64
L. Vitale,
64
F. Martinez-Vidal,
65
A. Oyanguren,
65
J. Albert,
66b
A. Beaulieu,
66b
F. U. Bernlochner,
66b
G. J. King,
66b
R. Kowalewski,
66b
T. Lueck,
66b
I. M. Nugent,
66b
J. M. Roney,
66b
R. J. Sobie,
66a,66b
N. Tasneem,
66b
T. J. Gershon,
67
P. F. Harrison,
67
T. E. Latham,
67
R. Prepost,
68
and S. L. Wu
68
(
B
A
B
AR
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
7a
Institute of Particle Physics, Vancouver, British Columbia, Canada V6T 1Z1
7b
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
PHYSICAL REVIEW D
95,
072007 (2017)
2470-0010
=
2017
=
95(7)
=
072007(19)
072007-1
© 2017 American Physical Society
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
18
INFN Sezione di Genova, I-16146 Genova, Italy
19
Humboldt-Universität zu Berlin, Institut für Physik, D-12489 Berlin, Germany
20
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
21
Indiana University, Bloomington, Indiana 47405, USA
22
University of Iowa, Iowa City, Iowa 52242, USA
23
Iowa State University, Ames, Iowa 50011, USA
24
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudi Arabia
25
Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
26
Johns Hopkins University, Baltimore, Maryland 21218, USA
27
Laboratoire de l
’
Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d
’
Orsay, F-91898 Orsay Cedex, France
28
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
29
University of Liverpool, Liverpool L69 7ZE, United Kingdom
30
Queen Mary, University of London, London E1 4NS, United Kingdom
31
University of London, Royal Holloway and Bedford New College, Egham,
Surrey TW20 0EX, United Kingdom
32
University of Louisville, Louisville, Kentucky 40292, USA
33
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
34
University of Manchester, Manchester M13 9PL, United Kingdom
35
University of Maryland, College Park, Maryland 20742, USA
36
Massachusetts Institute of Technology, Laboratory for Nuclear Science,
Cambridge, Massachusetts 02139, USA
37
Institute of Particle Physics and McGill University, Montréal, Québec, Canada H3A 2T8
38a
INFN Sezione di Milano, I-20133 Milano, Italy
38b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
39
University of Mississippi, University, Mississippi 38677, USA
40
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
41
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche, Università di Napoli Federico II,
I-80126 Napoli, Italy
42
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, The Netherlands
43
University of Notre Dame, Notre Dame, Indiana 46556, USA
44
Ohio State University, Columbus, Ohio 43210, USA
45a
INFN Sezione di Padova, I-35131 Padova, Italy
45b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
46
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie
Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France
47a
INFN Sezione di Perugia, I-06123 Perugia, Italy
47b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
48a
INFN Sezione di Pisa, I-56127 Pisa, Italy
48b
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
48c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
49
Princeton University, Princeton, New Jersey 08544, USA
50a
INFN Sezione di Roma, I-00185 Roma, Italy
50b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
51
Universität Rostock, D-18051 Rostock, Germany
52
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
53
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
54
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
55
University of South Carolina, Columbia, South Carolina 29208, USA
56
Southern Methodist University, Dallas, Texas 75275, USA
57
Stanford University, Stanford, California 94305, USA
58
State University of New York, Albany, New York 12222, USA
59
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
60
University of Tennessee, Knoxville, Tennessee 37996, USA
61
University of Texas at Austin, Austin, Texas 78712, USA
62
University of Texas at Dallas, Richardson, Texas 75083, USA
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
072007 (2017)
072007-2
63a
INFN Sezione di Torino, I-10125 Torino, Italy
63b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
64
INFN Sezione di Trieste and Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
65
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
66a
Institute of Particle Physics, Victoria, British Columbia, Canada V8W 3P6
66b
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
67
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
68
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 6 February 2017; published 10 April 2017)
We study the processes
e
þ
e
−
→
γ
ISR
J=
ψ
, where
J=
ψ
→
π
þ
π
−
π
0
,
J=
ψ
→
K
þ
K
−
π
0
, and
J=
ψ
→
K
0
S
K
π
∓
using a data sample of
519
fb
−
1
recorded with the
BABAR
detector operating at the SLAC
PEP-II asymmetric-energy
e
þ
e
−
collider at center-of-mass energies at and near the
Υ
ð
nS
Þ
(
n
¼
2
;
3
;
4
)
resonances. We measure the ratio of branching fractions
R
1
¼
B
ð
J=
ψ
→
K
þ
K
−
π
0
Þ
B
ð
J=
ψ
→
π
þ
π
−
π
0
Þ
and
R
2
¼
B
ð
J=
ψ
→
K
0
S
K
π
∓
Þ
B
ð
J=
ψ
→
π
þ
π
−
π
0
Þ
.We
perform Dalitz plot analyses of the three
J=
ψ
decay modes and measure fractions for resonances
contributing to the decays. We also analyze the
J=
ψ
→
π
þ
π
−
π
0
decay using the Veneziano model. We
observe structures compatible with the presence of
ρ
ð
1450
Þ
in all three
J=
ψ
decay modes and measure the
relative branching fraction:
R
ð
ρ
ð
1450
ÞÞ ¼
B
ð
ρ
ð
1450
Þ
→
K
þ
K
−
Þ
B
ð
ρ
ð
1450
Þ
→
π
þ
π
−
Þ
¼
0
.
307
0
.
084
ð
stat
Þ
0
.
082
ð
sys
Þ
.
DOI:
10.1103/PhysRevD.95.072007
I. INTRODUCTION
Charmonium decays, in particular radiative and hadronic
decays of the
J=
ψ
meson, have been studied extensively
[1,2]
. One of the motivations for these studies is to search
for non-
q
̄
q
mesons such as glueballs or molecular states
that are predicted by QCD to populate the low mass region
of the hadron mass spectrum
[3]
.
Previous studies of
J=
ψ
decays to
π
þ
π
−
π
0
show a clear
signal of
ρ
ð
770
Þ
production
[4,5]
. In addition there is an
indication of higher mass resonance production in
ψ
ð
2
S
Þ
decays
[5]
. This is not necessarily the case in
J=
ψ
decays,
but neither does the
ρ
ð
770
Þ
contribution saturate the
spectrum. Attempts have been made to describe the
J=
ψ
decay distribution with additional partial waves
[6]
.Itwas
found that interference effects are strong and even after
adding
ππ
interactions up to
≈
1
.
6
GeV
=c
2
the description
remained quite poor. Continuing to expand the partial wave
basis to cover an even higher mass region would lead to a
rather unconstrained analysis. On the other hand with the
amplitudes developed in the Veneziano model, all partial
waves are related to the same Regge trajectory, which gives
a very strong constraint on the amplitude analysis
[7]
.
While large samples of
J=
ψ
decays exist, some branch-
ing fractions remain poorly measured. In particular the
J=
ψ
→
K
þ
K
−
π
0
branching fraction has been measured by
Mark II
[8]
using only 25 events.
Only a preliminary result exists, to date, on a Dalitz
plot analysis of
J=
ψ
decays to
π
þ
π
−
π
0
[9]
. The BESII
experiment
[10]
has performed an angular analysis of
J=
ψ
→
K
þ
K
−
π
0
. The analysis requires the presence of a
broad
J
PC
¼
1
−−
state in the
K
þ
K
−
threshold region, which
is interpreted as a multiquark state. However Refs.
[11,12]
explain it by the interference between the
ρ
ð
1450
Þ
and
ρ
ð
1700
Þ
. On the other hand, the decay
ρ
ð
1450
Þ
→
K
þ
K
−
appears as
“
not seen
”
according to the PDG listing
[13]
.No
Dalitz plot analysis has been performed to date on the
J=
ψ
→
K
0
S
K
π
∓
decay.
We describe herein a study of the
J=
ψ
→
π
þ
π
−
π
0
,
J=
ψ
→
K
þ
K
−
π
0
, and
J=
ψ
→
K
0
S
K
π
∓
decays produced
in
e
þ
e
−
annihilation via initial-state radiation (ISR), where
only resonances with
J
PC
¼
1
−−
can be produced.
This article is organized as follows. In Sec.
II
, a brief
description of the
BABAR
detector is given. Section
III
is
devoted to the event reconstruction and data selection. In
Sec.
IV
, we describe the study of efficiency and resolution,
while Sec.
V
is devoted to the measurement of the
J=
ψ
branching fractions. Section
VI
describes the Dalitz plot
analyses while in Sec.
VII
, we report the measurement of
the
ρ
ð
1450
Þ
branching fraction. Finally we summarize the
results in Sec.
VIII
.
II. THE
BABAR
DETECTOR AND DATA SET
The results presented here are based on data collected
with the
BABAR
detector at the PEP-II asymmetric-energy
*
Deceased.
†
Also at Thomas Jefferson National Accelerator Facility,
Newport News, Virginia 23606, USA.
‡
Present address: Wuhan University, Wuhan 43072, China.
§
Present address: Università di Bologna and INFN Sezione di
Bologna, I-47921 Rimini, Italy.
¶
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.
DALITZ PLOT ANALYSES OF
...
PHYSICAL REVIEW D
95,
072007 (2017)
072007-3
e
þ
e
−
collider located at SLAC. The data sample corre-
sponds to an integrated luminosity of
519
fb
−
1
[14]
recorded
at center-of-mass energies at and near the
Υ
ð
nS
Þ
(
n
¼
2
;
3
;
4
) resonances. The
BABAR
detector is described
in detail elsewhere
[15]
. Charged particles are detected, and
their momenta are measured, by means of a five-layer,
double-sided microstrip detector, and a 40-layer drift cham-
ber, both operating in the 1.5 T magnetic field of a super-
conducting solenoid. Photons are measured and electrons
are identified in a CsI(Tl) crystal electromagnetic calorim-
eter (EMC). Charged-particle identification is provided
by the specific energy loss in the tracking devices, and by
an internally reflecting ring-imaging Cherenkov detector.
Muons are detected in the instrumented flux return of the
magnet. Monte Carlo (MC) simulated events
[16]
, with
sample sizes more than 10 times larger than the correspond-
ing datasamples,are usedtoevaluatesignalefficiencyand to
determine background features.
III. EVENT RECONSTRUCTION AND
DATA SELECTION
We study the following reactions:
e
þ
e
−
→
γ
ISR
π
þ
π
−
π
0
;
ð
1
Þ
e
þ
e
−
→
γ
ISR
K
þ
K
−
π
0
;
ð
2
Þ
e
þ
e
−
→
γ
ISR
K
0
S
K
π
∓
;
ð
3
Þ
where
γ
ISR
indicates the ISR photon.
For reactions
(1)
and
(2)
, we consider only events for
which the number of well-measured charged-particle tracks
with transverse momenta greater than
0
.
1
GeV
=c
is exactly
equal to 2. The charged-particle tracks are fitted to a
common vertex with the requirements that they originate
from the interaction region and that the
χ
2
probability of
the vertex fit be greater than 0.1%. We observe prominent
J=
ψ
signals in both reactions and optimize the signal-to-
background ratio using the data by retaining only selection
criteria that do not remove significant
J=
ψ
signal. We require
the energy of the less-energetic photon from
π
0
decays to be
greater than 100 MeV. Each pair of photons is kinematically
fitted to a
π
0
requiring it to emanate from the primary vertex
of the event, and with the diphoton mass constrained to the
nominal
π
0
mass
[13]
. Due to the soft-photon background,
we do not impose a veto on the presence of additional
photons in the final state but we require exactly one
π
0
candidate in each event. Particle identification is used in two
different ways. For reaction
(1)
, we require two oppositely
charged particles to be loosely identified as pions. For
reaction
(2)
, we loosely identify one kaon and require that
neither track be a well-identified pion, electron, or muon.
For reaction
(3)
, we consider only events for which the
number of well-measured charged-particle tracks with
transverse momentum greater than
0
.
1
GeV
=c
is exactly
equal to 4, and for which there are no more than five photon
candidates with reconstructed energy in the EMC greater
than 100 MeV. We obtain
K
0
S
→
π
þ
π
−
candidates by means
of a vertex fit of pairs of oppositely charged tracks, for
which we require a
χ
2
fit probability greater than 0.1%.
Each
K
0
S
candidate is then combined with two oppositely
charged tracks, and fitted to a common vertex, with the
requirements that the fitted vertex be within the
e
þ
e
−
interaction region and have a
χ
2
fit probability greater than
0.1%. We select kaons and pions by applying high-
efficiency particle identification criteria. We do not apply
any particle identification requirements to the pions from
the
K
0
S
decay. We accept only
K
0
S
candidates with decay
lengths from the
J=
ψ
candidate decay vertex greater than
0.2 cm, and require cos
θ
K
0
S
>
0
.
98
, where
θ
K
0
S
is defined as
the angle between the
K
0
S
momentum direction and the line
joining the
J=
ψ
and
K
0
S
vertices. A fit to the
π
þ
π
−
mass
spectrum using a linear function for the background and a
Gaussian function with mean
m
and width
σ
gives
m
¼
497
.
24
MeV
=c
2
and
σ
¼
2
.
9
MeV
=c
2
. We select the
K
0
S
signal region to be within
2
σ
of
m
and reconstruct the
K
0
S
four-vector by summing the three-momenta of the pions
and computing the energy using the known
K
0
S
mass
[13]
.
The ISR photon is preferentially emitted at small angles
with respect to the beam axis (see Fig.
1
), and escapes
detection in the majority of ISR events. Consequently, the
ISR photon is treated as a missing particle.
We define the squared mass
M
2
rec
recoiling against the
π
þ
π
−
π
0
,
K
þ
K
−
π
0
, and
K
0
S
K
π
∓
systems using the four-
momenta of the beam particles (
p
e
) and of the recon-
structed final state particles:
M
2
rec
≡
ð
p
e
−
þ
p
e
þ
−
p
h
1
−
p
h
2
−
p
h
3
Þ
2
;
ð
4
Þ
where the
h
i
indicate the three hadrons in the final states.
This quantity should peak near zero for both ISR events and
(deg)
ISR
θ
0
50
100
events/(2 deg)
0
2000
4000
6000
8000
FIG. 1. (a) Distribution of
θ
ISR
for events in the
J=
ψ
→
π
þ
π
−
π
0
ISR signal region. The dashed line indicates the
θ
ISR
¼
23
0
angle.
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
072007 (2017)
072007-4
for exclusive production of
e
þ
e
−
→
h
1
h
2
h
3
. However, in
the exclusive production the
h
1
h
2
h
3
mass distribution
peaks at the kinematic limit. We select the ISR reactions
(in the following also defined as ISR regions) requiring
j
M
2
rec
j
<
2
GeV
2
=c
4
ð
5
Þ
for reaction
(1)
and
(2)
and
j
M
2
rec
j
<
1
.
5
GeV
2
=c
4
ð
6
Þ
for reaction
(3)
.
We reconstruct the three-momentum of the ISR photon
from momentum conservation as
p
ISR
¼
p
e
−
þ
p
e
þ
−
p
h
1
−
p
h
2
−
p
h
3
:
ð
7
Þ
Table
I
gives the ranges used to define the ISR signal regions
for the three
J=
ψ
decay modes. We show in Fig.
1
, for events
in the
J=
ψ
→
π
þ
π
−
π
0
ISR signal region, the distribution of
θ
ISR
, the angle of the reconstructed ISR photon with respect
to the
e
−
beam direction in the laboratory system. We
observe a narrow peak close to zero with a tail extending up
to
140
0
while background events from
J=
ψ
sidebands are
distributed over the full angular range. Since angular cover-
age of the EMC starts at
θ
>
23
0
, we improve the signal to
background ratio for
J=
ψ
events where
θ
ISR
>
23
0
,by
removing events for which no photon shower is found in
the EMC in the expected angular region. Therefore, we
require the difference between the predicted polar and
azimuthal angles from
p
ISR
and the closest photon shower
to be
j
Δ
θ
j
<
0
.
1
rad and
j
Δ
φ
j
<
0
.
05
rad. We do not use the
information on the energy since some photons may not be
fully contained in the EMC.
For reaction
(1)
we define the helicity angle
θ
h
as the
angle in the
π
þ
π
−
rest frame between the direction of the
π
þ
and the boost from the
π
þ
π
−
. We observe that residual
background from
e
þ
e
−
→
γπ
þ
π
−
is concentrated at
j
cos
θ
π
j
≈
1
and therefore we remove events having
j
cos
θ
π
j
>
0
.
95
. A very small
J=
ψ
signal is observed in
the events removed by this selection. No evidence is found
for background from the ISR reaction
e
þ
e
−
→
γ
ISR
K
þ
K
−
.
Figure
2
shows the
M
2
rec
distributions for the three
reactions in the
J=
ψ
signal regions, in comparison to the
corresponding
M
2
rec
distributions obtained from simulation.
A peak at zero is observed in all distributions indicating the
presence of the ISR process. We observe some discrepancy
for reactions
(1)
and
(2)
due to some inaccuracy in
reconstructing slow
π
0
in the EMC. Figure
3
shows the
π
þ
π
−
π
0
,
K
þ
K
−
π
0
, and
K
0
S
K
π
∓
mass spectra in the ISR
region, before applying the efficiency correction. We
observe strong
J=
ψ
signals over relatively small back-
grounds and no more than one candidate per event. We
perform a fit to the
π
þ
π
−
π
0
,
K
þ
K
−
π
0
, and
K
0
S
K
π
∓
mass
spectra. Backgrounds are described by first-order poly-
nomials, and each resonance is represented by a simple
TABLE I. Ranges used to define the
J=
ψ
signal regions, event
yields, and purities for the three
J=
ψ
decay modes.
J=
ψ
Signal region
Event
Purity
decay mode
(GeV
=c
2
)
yields
%
π
þ
π
−
π
0
3.028
–
3.149
20417
91
.
3
0
.
2
K
þ
K
−
π
0
3.043
–
3.138
2102
88
.
8
0
.
7
K
0
S
K
π
∓
3.069
–
3.121
3907
93
.
1
0
.
4
)
4
/c
2
(GeV
2
rec
M
−
10
−
50 510
))
4
/c
2
events/(0.2 (GeV
0
200
400
600
800
1000
1200
1400
0
π
-
π
+
π
→
ψ
(a) J/
)
4
/c
2
(GeV
2
rec
M
−
10
−
50 510
))
4
/c
2
events/(0.2 (GeV
0
50
100
150
200
250
0
π
-
K
+
K
→
ψ
(b) J/
)
4
/c
2
(GeV
2
rec
M
−
10
−
50 510
))
4
/c
2
events/(0.2 (GeV
0
100
200
300
400
500
600
700
±
π
±
K
S
0
K
→
ψ
(c) J/
FIG. 2. Distributions of
M
2
rec
for
e
þ
e
−
→
γ
ISR
J=
ψ
, where (a)
J=
ψ
→
π
þ
π
−
π
0
, (b)
J=
ψ
→
K
þ
K
−
π
0
, and (c)
J=
ψ
→
K
0
S
K
π
∓
.
In each figure the data are shown as points with error bars, and the
MC simulation is shown as a histogram.
DALITZ PLOT ANALYSES OF
...
PHYSICAL REVIEW D
95,
072007 (2017)
072007-5
Breit-Wigner function convolved with the corresponding
resolution function (see Sec.
IV
). Figure
3
shows the fit
result, and Table
II
summarizes the mass values and yields.
We observe (not taking into account systematic uncertain-
ties) a
J=
ψ
mass shift of
þ
2
.
9
,
þ
4
.
1
, and
−
2
.
2
MeV
=c
2
for
the three decay modes.
IV. EFFICIENCY AND RESOLUTION
To compute the efficiency,
J=
ψ
MC signal events for the
three channels are generated using a detailed detector
simulation
[16]
in which the
J=
ψ
decays uniformly in
phase space. These simulated events are reconstructed and
analyzed in the same manner as data. The efficiency is
computed as the ratio of reconstructed to generated events.
We express the efficiency as a function of the
m
12
mass
(
π
þ
π
−
for
J=
ψ
→
π
þ
π
−
π
0
,
K
þ
K
−
for
J=
ψ
→
K
þ
K
−
π
0
,
and
K
0
S
K
for
J=
ψ
→
K
0
S
K
π
∓
) and cos
θ
h
defined in
Sec.
III
. To smooth statistical fluctuations, this efficiency is
then parametrized as follows
[17]
.
First we fit the efficiency as a function of cos
θ
h
in
separate intervals of
m
12
, in terms of Legendre polynomials
up to
L
¼
12
:
ε
ð
cos
θ
h
Þ¼
X
12
L
¼
0
a
L
ð
m
12
Þ
Y
0
L
ð
cos
θ
h
Þ
:
ð
8
Þ
For each value of
L
, we fit the mass dependent coefficients
a
L
ð
m
12
Þ
with a seventh-order polynomial in
m
12
. Figure
4
shows the resulting fitted efficiency
ε
ð
m
12
;
cos
θ
h
Þ
for each
of the three reactions. We observe a significant decrease
in efficiency at low
m
12
for cos
θ
∼
1
and
1
.
1
<
m
ð
K
þ
K
−
Þ
<
1
.
5
GeV
=c
2
due to the difficulty of recon-
structing low-momentum tracks (
p<
200
MeV
=c
in the
laboratory frame), which arise because of significant
energy losses in the beampipe and inner-detector material.
The mass resolution,
Δ
m
, is measured as the difference
between the generated and reconstructed
π
þ
π
−
π
0
,
K
þ
K
−
π
0
, and
K
0
S
K
π
∓
invariant-mass values. These dis-
tributions, for the
J=
ψ
decays having a
π
0
in the final state,
deviate from Gaussian shapes due to a low-energy tail
caused by the response of the CsI calorimeter to photons.
We fit the distributions using the sum of a Crystal Ball
function
[18]
and a Gaussian function. The root-mean-
squared values are 24.4 and
22
.
7
MeV
=c
2
for the
J=
ψ
→
π
þ
π
−
π
0
and
J=
ψ
→
K
þ
K
−
π
0
final states, respectively. The
mass resolution for
J=
ψ
→
K
0
S
K
π
∓
is well described by a
single Gaussian having a
σ
¼
9
.
7
MeV
=c
2
.
V.
J
=
ψ
BRANCHING RATIOS
We compute the ratio of the branching fractions for
J=
ψ
→
K
þ
K
−
π
0
and
J=
ψ
→
π
þ
π
−
π
0
according to
R
1
¼
B
ð
J=
ψ
→
K
þ
K
−
π
0
Þ
B
ð
J=
ψ
→
π
þ
π
−
π
0
Þ
¼
N
K
þ
K
−
π
0
N
π
þ
π
−
π
0
ε
π
þ
π
−
π
0
ε
K
þ
K
−
π
0
;
ð
9
Þ
)
2
) (GeV/c
0
π
-
π
+
π
m(
2.8
3
3.2
)
2
events/(5 MeV/c
0
200
400
600
800
1000
1200
1400
1600
1800
)
2
) (GeV/c
0
π
-
K
+
m(K
2.9
3
3.1
3.2
3.3
)
2
events/(5 MeV/c
0
50
100
150
200
250
)
2
) (GeV/c
±
π
±
K
S
0
m(K
3
3.05
3.1
3.15
3.2
)
2
events/(2.5 MeV/c
0
100
200
300
400
FIG. 3. (a) The
π
þ
π
−
π
0
, (b)
K
þ
K
−
K
0
, and
K
0
S
K
π
∓
mass
spectra in the ISR region. In each figure, the solid curve shows
the total fit function and the dashed curve shows the fitted
background contribution.
TABLE II. Results from the fits to the mass spectra and
efficiency corrections. Errors are statistical only.
J=
ψ
decay
mode
χ
2
=NDF
J=
ψ
mass
(MeV
=c
2
) Signal yield
1
=
ε
π
þ
π
−
π
0
90
=
105 3099
.
8
0
.
2 19560
164 15
.
57
1
.
05
K
þ
K
−
π
0
129
=
95 3101
.
0
0
.
2 2002
48 18
.
31
0
.
63
K
0
S
K
π
∓
127
=
96 3094
.
7
0
.
2 3694
64 15
.
15
0
.
33
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
072007 (2017)
072007-6
where
N
π
þ
π
−
π
0
and
N
K
þ
K
−
π
0
represent the fitted yields for
J=
ψ
in the
π
þ
π
−
π
0
and
K
þ
K
−
π
0
mass spectra, while
ε
π
þ
π
−
π
0
and
ε
K
þ
K
−
π
0
are the corresponding efficiencies. We
estimate
ε
π
þ
π
−
π
0
and
ε
K
þ
K
−
π
0
for the
J=
ψ
signals by making
use of the 2D efficiency distributions described in Sec.
IV
.
To remove the dependence of the fit quality on the
efficiency functions we make use of the unfitted efficiency
distributions. Due to the presence of non-negligible back-
grounds in the
J=
ψ
signals, which have different distribu-
tions in the Dalitz plot, we perform a sideband subtraction
by assigning a weight
w
¼
f=
ε
ð
m
12
;
cos
θ
Þ
, where
f
¼
1
for events in the
J=
ψ
signal region and
f
¼
−
1
for events
in the sideband regions. The size of the sum of the two
sidebands is taken to be the same as that of the signal
region. Therefore we obtain the weighted efficiencies as
ε
h
þ
h
−
π
0
¼
P
N
i
¼
1
f
i
P
N
i
¼
1
f
i
=
ε
ð
m
12
;
cos
θ
i
Þ
;
ð
10
Þ
where
N
indicates the number of events in the signal
þ
sidebands regions. The resulting yields and efficiencies are
reported in Table
II
.
We note that in Eq.
(9)
the number of charged-particle
tracks and
γ
’
s is the same in the numerator and in the
denominator of the ratio, so that several systematic uncer-
tainties cancel. We estimate the systematic uncertainties as
follows. We modify the signal fitting function, describing
the
J=
ψ
signals using the sum of two Gaussian functions.
The uncertainty due to efficiency weighting is evaluated by
computing 1000 new weights obtained by randomly
modifying the weight in each cell of the
ε
ð
m
12
;
cos
θ
Þ
plane according to its statistical uncertainty. The widths of
the resulting Gaussian distributions yield the estimate of the
systematic uncertainty for the efficiency weighting pro-
cedure. These values are reported as the uncertainties on
1
=
ε
in Table
II
. We assign a 1% systematic uncertainty for
the identification of each of the two kaons, from studies
performed using high statistics control samples. The con-
tributions to the systematic uncertainties from different
sources are given in Table
III
and combined in quadrature.
We obtain
R
1
¼
B
ð
J=
ψ
→
K
þ
K
−
π
0
Þ
B
ð
J=
ψ
→
π
þ
π
−
π
0
Þ
¼
0
.
120
0
.
003
ð
stat
Þ
0
.
009
ð
sys
Þ
:
ð
11
Þ
The PDG reports
B
ð
J=
ψ
→
π
þ
π
−
π
0
Þ¼ð
2
.
11
0
.
07
Þ
×
10
−
2
,
while the branching fraction
B
ð
J=
ψ
→
K
þ
K
−
π
0
Þ
has
been measured by Mark II
[8]
using 25 events, to be
ð
2
.
8
0
.
8
Þ
×
10
−
3
. These values give a ratio
R
PDG
1
¼
0
.
133
0
.
038
, in agreement with our measurement.
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
2
) GeV/c
-
π
+
π
m(
0.5
1
1.5
2
2.5
h
θ
cos
0
-1
-0.5
0.5
1
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
2
) GeV/c
-
K
+
m(K
1
1.5
2
2.5
h
θ
cos
-1
-0.5
0
0.5
1
0.05
0.06
0.07
0.08
0.09
0.1
2
) GeV/c
±
K
S
0
m(K
1
1.5
2
2.5
3
h
θ
cos
-1
-0.5
0
0.5
1
(a)
(b)
(c)
FIG. 4. Fitted detection efficiency in the cos
θ
h
vs
m
12
plane for
(a)
J=
ψ
→
π
þ
π
−
π
0
, (b)
J=
ψ
→
K
þ
K
−
π
0
, and (c)
J=
ψ
→
K
0
S
K
π
∓
.
Each bin shows the average value of the fit in that region.
TABLE III. Fractional systematic uncertainties in the evalu-
ation of the ratios of branching fractions.
Effect
R
1
(%)
R
2
(%)
Efficiency
7.5
7.0
Background subtraction
1.3
1.0
Particle identification
2.0
1.8
K
0
S
reconstruction
1.1
π
0
reconstruction
3.0
Mass fits
0.8
0.8
Total
7.9
8.0
DALITZ PLOT ANALYSES OF
...
PHYSICAL REVIEW D
95,
072007 (2017)
072007-7
We perform a test of the
R
1
measurement using a
minimum bias procedure. We remove all the selections
used to separate reactions
(1)
and
(2)
, except for the
requirements on
M
2
rec
and obtain the events yield for
J=
ψ
→
π
þ
π
−
π
0
. To obtain the
J=
ψ
→
K
þ
K
−
π
0
yield,
we apply very loose identifications of the two kaons to
remove the large background and the strong cross feed
from the
J=
ψ
→
π
þ
π
−
π
0
final state. We observe a loss of
the
J=
ψ
signal which is estimated by MC to be 3.6%. The
ratios between the two minimum bias yields, corrected for
the above efficiency loss gives directly the ratio of the two
branching fractions which is in good agreement with the
previous estimate.
Using a similar procedure as for the measurement of
R
1
,
correcting for unseen
K
0
S
decay modes, we compute the
ratio of the branching fractions for
J=
ψ
→
K
0
S
K
π
∓
and
J=
ψ
→
π
þ
π
−
π
0
according to
R
2
¼
B
ð
J=
ψ
→
K
0
S
K
π
∓
Þ
B
ð
J=
ψ
→
π
þ
π
−
π
0
Þ
¼
N
K
0
S
K
π
∓
N
π
þ
π
−
π
0
ε
π
þ
π
−
π
0
ε
K
0
S
K
π
∓
¼
0
.
265
0
.
005
ð
stat
Þ
0
.
021
ð
sys
Þ
:
ð
12
Þ
Systematic uncertainties on the evaluation of
R
2
include
0.46% per track for charged tracks reconstruction, 3% and
1.1% for
π
0
and
K
0
S
reconstruction, and 0.5% and 1% for
the identification of pions and kaons, respectively. The
contributions to the total systematic uncertainty are sum-
marized in Table
III
.
The branching fraction
B
ð
J=
ψ
→
K
0
S
K
π
∓
Þ
has been
measured by Mark I
[19]
, using 126 events, to be
ð
26
7
Þ
×
10
−
4
. Using the above measurements we obtain
an estimate of
R
2
:
R
PDG
2
¼
0
.
123
0
.
033
;
ð
13
Þ
which deviates by
3
.
6
σ
from our measurement.
As a cross-check, using the above
R
1
and
R
2
measure-
ments and adding in quadrature statistical and systematic
uncertainties, we compute
R
3
¼
B
ð
J=
ψ
→
K
0
S
K
π
∓
Þ
B
ð
J=
ψ
→
K
þ
K
−
π
0
Þ
¼
2
.
21
0
.
24
ð
14
Þ
in agreement with the expected value of 2.
VI. DALITZ PLOT ANALYSIS
We perform Dalitz plot analyses of the
J=
ψ
→
π
þ
π
−
π
0
,
J=
ψ
→
K
þ
K
−
π
0
, and
J=
ψ
→
K
0
S
K
π
∓
candidates in the
J=
ψ
mass region using unbinned maximum likelihood fits.
The likelihood function is written as
L
¼
Y
N
n
¼
1
f
sig
ð
m
n
Þ
·
ε
ð
x
0
n
;y
0
n
Þ
P
i;j
c
i
c
j
A
i
ð
x
n
;y
n
Þ
A
j
ð
x
n
;y
n
Þ
P
i;j
c
i
c
j
I
A
i
A
j
þð
1
−
f
sig
ð
m
n
ÞÞ
P
i
k
i
B
i
ð
x
n
;y
n
Þ
P
i
k
i
I
B
i
;
ð
15
Þ
where
(i)
N
is the number of events in the signal region;
(ii) for the
n
th event,
m
n
is the
π
þ
π
−
π
0
,
K
þ
K
−
π
0
,or
K
0
S
K
π
∓
invariant mass;
(iii) for the
n
th event,
x
n
¼
m
2
ð
π
þ
π
0
Þ
,
y
n
¼
m
2
ð
π
−
π
0
Þ
for
π
þ
π
−
π
0
;
x
n
¼
m
2
ð
K
þ
π
0
Þ
,
y
n
¼
m
2
ð
K
−
π
0
Þ
for
K
þ
K
−
π
0
;
x
n
¼
m
2
ð
K
π
∓
Þ
,
y
n
¼
m
2
ð
K
0
S
π
∓
Þ
for
K
0
S
K
π
∓
;
(iv)
f
sig
is the mass-dependent fraction of signal ob-
tained from the fits to the
π
þ
π
−
π
0
,
K
þ
K
−
π
0
, and
K
0
S
K
π
∓
mass spectra;
(v) for the
n
th event,
ε
ð
x
0
n
;y
0
n
Þ
is the efficiency para-
metrized as a function
x
0
n
¼
m
12
and
y
0
n
¼
cos
θ
h
(see Sec.
IV
);
(vi) for the
n
th event, the
A
i
ð
x
n
;y
n
Þ
represent the complex
signal-amplitude contributions described below;
(vii)
c
i
is the complex amplitude of the
i
th signal
component; the
c
i
parameters are allowed to vary
during the fit process;
(viii) for the
n
th event, the
B
i
ð
x
n
;y
n
Þ
describe the back-
ground probability-density functions assuming that
interference between signal and background ampli-
tudes can be ignored;
(ix)
k
i
is the magnitude of the
i
th background compo-
nent; the
k
i
parameters are obtained by fitting the
sideband regions;
(x)
I
A
i
A
j
¼
R
A
i
ð
x; y
Þ
A
j
ð
x; y
Þ
ε
ð
m
12
;
cos
θ
Þ
d
x
d
y
and
I
B
i
¼
R
B
i
ð
x; y
Þ
d
x
d
y
are normalization integrals;
numerical integration is performed on phase-space-
generated events with
J=
ψ
signal and background
generated according to the experimental distributions.
Parity conservation in
J=
ψ
→
π
þ
π
−
π
0
restricts the pos-
sible spin-parity of any intermediate two-body resonance
to be
J
PC
¼
1
−−
;
3
−−
;
...
. Amplitudes are parametrized
using Zemach
’
s tensors
[20,21]
. Except as noted, all fixed
resonance parameters are taken from the Particle Data
Group averages
[13]
.
For reaction
(1)
, we label the decay particles as
J=
ψ
→
π
þ
1
π
−
2
π
0
3
:
ð
16
Þ
Indicating with
p
i
the momenta of the particles in the
J=
ψ
center-of-mass rest frame, for a resonance
R
jk
decaying as
R
jk
→
j
þ
k
we also define the three-vectors
t
i
as the vector
part of
t
μ
i
¼
p
μ
j
−
p
μ
k
−
ð
p
μ
j
þ
p
μ
k
Þ
m
2
j
−
m
2
k
m
2
jk
;
ð
17
Þ
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
072007 (2017)
072007-8