of 16
Measurement of the
I
¼
1
=
2
K
π
S
-wave amplitude from Dalitz plot analyses
of
η
c
K
̄
K
π
in two-photon interactions
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
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
A. Zallo,
17
S. Passaggio,
18a
C. Patrignani,
18a,18b
B. Bhuyan,
19
U. Mallik,
20
C. Chen,
21
J. Cochran,
21
S. Prell,
21
H. Ahmed,
22
M. R. Pennington,
23
A. V. Gritsan,
24
N. Arnaud,
25
M. Davier,
25
F. Le Diberder,
25
A. M. Lutz,
25
G. Wormser,
25
D. J. Lange,
26
D. M. Wright,
26
J. P. Coleman,
27
E. Gabathuler,
27
D. E. Hutchcroft,
27
D. J. Payne,
27
C. Touramanis,
27
A. J. Bevan,
28
F. Di Lodovico,
28
R. Sacco,
28
G. Cowan,
29
Sw. Banerjee,
30
D. N. Brown,
30
C. L. Davis,
30
A. G. Denig,
31
M. Fritsch,
31
W. Gradl,
31
K. Griessinger,
31
A. Hafner,
31
K. R. Schubert,
31
R. J. Barlow,
32
,
G. D. Lafferty,
32
R. Cenci,
33
A. Jawahery,
33
D. A. Roberts,
33
R. Cowan,
34
R. Cheaib,
35
S. H. Robertson,
35
B. Dey,
36a
N. Neri,
36a
F. Palombo,
36a,36b
L. Cremaldi,
37
R. Godang,
37
,
D. J. Summers,
37
P. Taras,
38
G. De Nardo,
39
C. Sciacca,
39
G. Raven,
40
C. P. Jessop,
41
J. M. LoSecco,
41
K. Honscheid,
42
R. Kass,
42
A. Gaz,
43a
M. Margoni,
43a,43b
M. Posocco,
43a
M. Rotondo,
43a
G. Simi,
43a,43b
F. Simonetto,
43a,43b
R. Stroili,
43a,43b
S. Akar,
44
E. Ben-Haim,
44
M. Bomben,
44
G. R. Bonneaud,
44
G. Calderini,
44
J. Chauveau,
44
G. Marchiori,
44
J. Ocariz,
44
M. Biasini,
45a,45b
E. Manoni,
45a
A. Rossi,
45a
G. Batignani,
46a,46b
S. Bettarini,
46a,46b
M. Carpinelli,
46a,46b
G. Casarosa,
46a,46b
M. Chrzaszcz,
46a
F. Forti,
46a,46b
M. A. Giorgi,
46a,46b
A. Lusiani,
46a,46c
B. Oberhof,
46a,46b
E. Paoloni,
46a,46b
M. Rama,
46a
G. Rizzo,
46a,46b
J. J. Walsh,
46a
A. J. S. Smith,
47
F. Anulli,
48a
R. Faccini,
48a,48b
F. Ferrarotto,
48a
F. Ferroni,
48a,48b
A. Pilloni,
48a,48b
G. Piredda,
48a
C. Bünger,
49
S. Dittrich,
49
O. Grünberg,
49
M. Heß,
49
T. Leddig,
49
C. Voß,
49
R. Waldi,
49
T. Adye,
50
F. F. Wilson,
50
S. Emery,
51
G. Hamel de Monchenault,
51
G. Vasseur,
51
D. Aston,
52
C. Cartaro,
52
M. R. Convery,
52
J. Dorfan,
52
W. Dunwoodie,
52
M. Ebert,
52
R. C. Field,
52
B. G. Fulsom,
52
M. T. Graham,
52
C. Hast,
52
W. R. Innes,
52
P. Kim,
52
D. W. G. S. Leith,
52
S. Luitz,
52
V. Luth,
52
D. B. MacFarlane,
52
D. R. Muller,
52
H. Neal,
52
B. N. Ratcliff,
52
A. Roodman,
52
M. K. Sullivan,
52
J. Va
vra,
52
W. J. Wisniewski,
52
M. V. Purohit,
53
J. R. Wilson,
53
A. Randle-Conde,
54
S. J. Sekula,
54
M. Bellis,
55
P. R. Burchat,
55
E. M. T. Puccio,
55
M. S. Alam,
56
J. A. Ernst,
56
R. Gorodeisky,
57
N. Guttman,
57
D. R. Peimer,
57
A. Soffer,
57
S. M. Spanier,
58
J. L. Ritchie,
59
R. F. Schwitters,
59
J. M. Izen,
60
X. C. Lou,
60
F. Bianchi,
61a,61b
F. De Mori,
61a,61b
A. Filippi,
61a
D. Gamba,
61a,61b
L. Lanceri,
62
L. Vitale,
62
F. Martinez-Vidal,
63
A. Oyanguren,
63
J. Albert,
64
A. Beaulieu,
64
F. U. Bernlochner,
64
G. J. King,
64
R. Kowalewski,
64
T. Lueck,
64
I. M. Nugent,
64
J. M. Roney,
64
N. Tasneem,
64
T. J. Gershon,
65
P. F. Harrison,
65
T. E. Latham,
65
R. Prepost,
66
and S. L. Wu
66
(The
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
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
PHYSICAL REVIEW D
93,
012005 (2016)
2470-0010
=
2016
=
93(1)
=
012005(16)
012005-1
© 2016 American Physical Society
17
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
18a
INFN Sezione di Genova, I-16146 Genova, Italy
18b
Dipartimento di Fisica, Università 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, Saudi Arabia
23
Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
24
Johns Hopkins University, Baltimore, Maryland 21218, USA
25
Laboratoire de l
Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d
Orsay, F-91898 Orsay Cedex, France
26
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
27
University of Liverpool, Liverpool L69 7ZE, United Kingdom
28
Queen Mary, University of London, London, E1 4NS, United Kingdom
29
University of London, Royal Holloway and Bedford New College, Egham,
Surrey TW20 0EX, United Kingdom
30
University of Louisville, Louisville, Kentucky 40292, USA
31
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
32
University of Manchester, Manchester M13 9PL, United Kingdom
33
University of Maryland, College Park, Maryland 20742, USA
34
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge,
Massachusetts 02139, USA
35
McGill University, Montréal, Québec, Canada H3A 2T8
36a
INFN Sezione di Milano, I-20133 Milano, Italy
36b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
37
University of Mississippi, University, Mississippi 38677, USA
38
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
39
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche,
Università di Napoli Federico II, I-80126 Napoli, Italy
40
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, Netherlands
41
University of Notre Dame, Notre Dame, Indiana 46556, USA
42
Ohio State University, Columbus, Ohio 43210, USA
43a
INFN Sezione di Padova, I-35131 Padova, Italy
43b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
44
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie
Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France
45a
INFN Sezione di Perugia, I-06123 Perugia, Italy
45b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
46a
INFN Sezione di Pisa, I-56127 Pisa, Italy
46b
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
46c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
47
Princeton University, Princeton, New Jersey 08544, USA
48a
INFN Sezione di Roma, I-00185 Roma, Italy
48b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
49
Universität Rostock, D-18051 Rostock, Germany
50
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
51
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
52
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
53
University of South Carolina, Columbia, South Carolina 29208, USA
54
Southern Methodist University, Dallas, Texas 75275, USA
55
Stanford University, Stanford, California 94305, USA
56
State University of New York, Albany, New York 12222, USA
57
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
58
University of Tennessee, Knoxville, Tennessee 37996, USA
59
University of Texas at Austin, Austin, Texas 78712, USA
60
University of Texas at Dallas, Richardson, Texas 75083, USA
61a
INFN Sezione di Torino, I-10125 Torino, Italy
61b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
62
INFN Sezione di Trieste and Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
012005 (2016)
012005-2
63
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
64
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
65
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
66
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 8 November 2015; published 20 January 2016)
We study the processes
γγ
K
0
S
K

π
and
γγ
K
þ
K
π
0
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 observe
η
c
decays to both final states and
perform Dalitz plot analyses using a model-independent partial wave analysis technique. This allows a
model-independent measurement of the mass-dependence of the
I
¼
1
=
2
K
π
S
-wave amplitude and phase.
A comparison between the present measurement and those from previous experiments indicates similar
behavior for the phase up to a mass of
1
.
5
GeV
=c
2
. In contrast, the amplitudes show very marked
differences. The data require the presence of a new
a
0
ð
1950
Þ
resonance with parameters
m
¼
1931

14

22
MeV
=c
2
and
Γ
¼
271

22

29
MeV.
DOI:
10.1103/PhysRevD.93.012005
I. INTRODUCTION
Scalar mesons are still a puzzle in light meson spec-
troscopy: they have complex structure, and there are too
many states to be accommodated within the quark model
without difficulty
[1]
. In particular, the structure of the
I
¼
1
=
2
K
π
S
-wave is a long-standing problem. In recent
years many experiments have performed accurate studies
of the decays of heavy-fl
avored hadrons producing a
K
π
system in the final state. These studies include searches
for
CP
violation
[2]
, and searches for, and observation of,
new exotic resonances
[3]
and charmed mesons
[4]
.
However, the still poorly known structure of the
I
¼
1
=
2
K
π
S
-wave is a source of large systematic uncertain-
ties. The best source of information on the scalar structure
of the
K
π
system comes from the LASS experiment,
which studied the reaction
K
p
K
π
þ
n
[5]
. Partial
wave analysis of the
K
π
system reveals a large contribu-
tionfromthe
I
¼
1
=
2
K
π
S
-wave amplitude over the mass
range studied. In the description of the
I
¼
1
=
2
scalar
amplitude up to a
K
π
mass of about
1
.
5
GeV
=c
2
the
K

0
ð
1430
Þ
resonant amplitude is added coherently to an
effective-range description in such a way that the net
amplitude actually decreases rapidly at the resonance
mass. The
I
¼
1
=
2
S
-wave amplitude representation is
given explicitly in Ref.
[6]
. In the LASS analysis, in the
region above
1
.
82
GeV
=c
2
,the
S
-wave suffers from a
twofold ambiguity, but in both solutions it is understood in
terms of the presence of a
K

0
ð
1950
Þ
resonance. It should
be noted that the extraction of the
I
¼
1
=
2
S
-wave
amplitude is complicated by the presence of an
I
¼
3
=
2
contribution.
Further information on the
K
π
system has been extracted
from Dalitz plot analysis of the decay
D
þ
K
π
þ
π
þ
where, in order to fit the data, the presence of an additional
resonance, the
κ
ð
800
Þ
, was claimed
[7]
. Using the same
data, a model independent partial wave analysis (MIPWA)
of the
K
π
system was developed for the first time
[8]
. This
method allows the amplitude and phase of the
K
π
S
-wave
to be extracted as functions of mass (see also Refs.
[9]
and
[10]
). However in these analyses the phase space is limited
to mass values less than
1
.
6
GeV
=c
2
due to the kinematical
limit imposed by the
D
þ
mass. A similar method has been
used to extract the
π
þ
π
S
-wave amplitude in a Dalitz plot
analysis of
D
þ
s
π
þ
π
π
þ
[11]
.
In the present analysis, we consider three-body
η
c
decays
to
K
̄
K
π
and obtain new information on the
K
π
I
¼
1
=
2
S
-
wave amplitude extending up to a mass of
2
.
5
GeV
=c
2
.We
emphasize that, due to isospin conservation in the
η
c
hadronic decay to
ð
K
π
Þ
̄
K
, the
ð
K
π
Þ
amplitude must have
I
¼
1
=
2
, and there is no
I
¼
3
=
2
contribution. The
BABAR
experiment first performed a Dalitz plot analysis of
η
c
K
þ
K
π
0
and
η
c
K
þ
K
η
using an isobar model
[12]
.
The analysis reported the first observation of
K

0
ð
1430
Þ
K
η
, and observed that
η
c
decays to three pseudoscalars
are dominated by intermediate scalar mesons. A previous
search for charmonium resonances decaying to
K
0
S
K

π
in
two-photon interactions is reported in Ref.
[13]
. We con-
tinue these studies of
η
c
decays and extract the
K
π
S
-wave
amplitude by performing a MIPWA of both
η
c
K
0
S
K

π
and
η
c
K
þ
K
π
0
final states.
We describe herein studies of the
K
̄
K
π
system produced
in two-photon interactions. Two-photon events in which at
least one of the interacting photons is not quasireal are
strongly suppressed by the selection criteria described
below. This implies that the allowed
J
PC
values of any
*
Also at Thomas Jefferson National Accelerator Facility,
Newport News, Virginia 23606, USA.
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.
MEASUREMENT OF THE
I
¼
1
=
2
K
π
S
-
...
PHYSICAL REVIEW D
93,
012005 (2016)
012005-3
produced resonances are
0
,
2
,
3
þþ
,
4
...
[14]
.
Angular momentum conservation, parity conservation,
and charge conjugation invariance imply that these quan-
tum numbers also apply to the final state except that the
K
̄
K
π
state cannot be in a
J
P
¼
0
þ
state.
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 of
the
K
0
S
K

π
system. In Sec.
IV
, we describe studies of
efficiency and resolution, while in Sec.
V
we describe the
MIPWA. In Secs.
VI
and
VII
we perform Dalitz plot analyses
of
η
c
K
0
S
K

π
and
η
c
K
þ
K
π
0
decays.Section
VIII
is
devotedtodiscussionofthemeasured
K
π
S
-waveamplitude,
and finally results are summarized in Sec.
IX
.
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
e
þ
e
collider located at SLAC, and correspond to an
integrated luminosity of
519
fb
1
[15]
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
[16]
. Charged particles are detected, and their
momenta are measured, by means of a five-layer, double-
sided microstrip detector, and a 40-layer drift chamber, both
operating in the 1.5 T magnetic field of a superconducting
solenoid. Photons are measured and electrons are identified
in a CsI(Tl) crystal electromagnetic calorimeter. Charged-
particle identification is provided by the measurement of
specific energy loss in the tracking devices, and by an
internally reflecting, ring-imaging Cherenkov detector.
Muons and
K
0
L
mesons are detected in the instrumented
flux return of the magnet. Monte Carlo (MC) simulated
events
[17]
, with reconstructed sample sizes more than 10
times larger than the corresponding data samples, are used to
evaluate the signal efficiency and to determine background
features. Two-photon events are simulated using the
GamGam MC generator
[18]
.
III. RECONSTRUCTION AND SELECTION
OF
η
c
K
0
S
K

π
EVENTS
To study the reaction
γγ
K
0
S
K

π
ð
1
Þ
we select events in which the
e
þ
and
e
beam particles are
scattered at small angles, and hence are undetected in the
final state. 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 electromag-
netic calorimeter 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 which requires a
χ
2
fit probability
greater than 0.001. 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 0.001. 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 main vertex of the event 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 primary and the
K
0
S
vertex. 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
4-vector by adding the three-momenta of the pions and
computing the energy using the
K
0
S
PDG mass value
[19]
.
Background arises mainly from random combinations
of particles from
e
þ
e
annihilation, from other two-
photon processes, and from events with initial-state photon
radiation (ISR). The ISR background is dominated by
J
PC
¼
1
−−
resonance production
[20]
. We discriminate
against
K
0
S
K

π
events produced via ISR by requiring
M
2
rec
ð
p
e
þ
e
p
rec
Þ
2
>
10
GeV
2
=c
4
, where
p
e
þ
e
is the
four-momentum of the initial state and
p
rec
is the four-
momentum of the
K
0
S
K

π
system.
The
K
0
S
K

π
mass spectrum shows a prominent
η
c
signal. We define
p
T
as the magnitude of the vector sum of
the transverse momenta, in the
e
þ
e
rest frame, of the final-
state particles with respect to the beam axis. Since well-
reconstructed two-photon events are expected to have low
values of
p
T
, we optimize the selection as a function of this
variable. We produce
K
0
S
K

π
mass spectra with different
p
T
selections and fit the mass spectra to extract the number
of
η
c
signal events (
N
s
) and the number of background
events below the
η
c
signal (
N
b
). We then compute the
purity, defined as
P
¼
N
s
=
ð
N
s
þ
N
b
Þ
, and the significance
S
¼
N
s
=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
N
s
þ
N
b
p
. To obtain the best significance with
the highest purity, we optimize the selection by requiring
the maximum value of the product of purity and signifi-
cance,
P
·
S
, and find that this corresponds to the require-
ment
p
T
<
0
.
08
GeV
=c
.
Figure
1
shows the measured
p
T
distribution in compari-
son to the corresponding
p
T
distribution obtained from
simulation of the signal process. A peak at low
p
T
is
observed indicating the presence of the two-photon process.
The shape of the peak agrees well with that seen in the
MC simulation. Figure
2
shows the
K
0
S
K

π
mass spectrum
in the
η
c
mass region. A clear
η
c
signal over a background
of about 35% can be seen, together with a residual
J=
ψ
signal. Information on the fitting procedure is given at the
end of Sec.
IV
. We define the
η
c
signal region as the range
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
012005 (2016)
012005-4
2.922
3.039 GeV
=c
2
[
m
ð
η
c
Þ
1
.
5
Γ
], which contains
12849 events with a purity of
64
.
3%

0
.
4%
. Sideband
regions are defined by the ranges
2
.
785
2
.
844
GeV
=c
2
and
3
.
117
3
.
175
GeV
=c
2
(within
3
.
5
5
Γ
), respectively
as indicated (shaded) in Fig.
2
.
Details on data selection, event reconstruction, resolu-
tion, and efficiency measurement for the
η
c
K
þ
K
π
0
decay can be found in Ref.
[12]
. The
η
c
signal region for
this decay mode contains 6710 events with a purity
of (
55
.
2%

0
.
6%
).
IV. EFFICIENCY AND RESOLUTION
To compute the efficiency, MC signal events are gen-
erated using a detailed detector simulation
[17]
in which the
η
c
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. Due to the presence of long tails in the
Breit-Wigner (BW) representation of the resonance, we
apply selection criteria to restrict the generated events to the
η
c
mass region. We express the efficiency as a function of
the invariant mass,
m
ð
K
þ
π
Þ
[21]
, and cos
θ
, where
θ
is the
angle, in the
K
þ
π
rest frame, between the directions of the
K
þ
and the boost from the
K
0
S
K
þ
π
rest frame.
To smooth statistical fluctuations, this efficiency map is
parametrized as follows. First we fit the efficiency as a
function of cos
θ
in separate intervals of
m
ð
K
þ
π
Þ
, using
Legendre polynomials up to
L
¼
12
:
ε
ð
cos
θ
Þ¼
X
12
L
¼
0
a
L
ð
m
Þ
Y
0
L
ð
cos
θ
Þ
;
ð
2
Þ
where
m
denotes the
K
þ
π
invariant mass. For each value
of
L
, we fit the mass dependent coefficients
a
L
ð
m
Þ
with a
seventh-order polynomial in
m
. Figure
3
shows the result-
ing fitted efficiency map
ε
ð
m;
cos
θ
Þ
. We obtain
χ
2
=N
cells
¼
217
=
300
for this fit, where
N
cells
is the number of cells
in the efficiency map. We observe a significant decrease in
efficiency inregionsofcos
θ

1
due totheimpossibilityof
reconstructing
K

mesons with laboratory momentum less
than about
200
MeV
=c
,and
π

and
K
0
S
ð
π
þ
π
Þ
mesons
with laboratory momentum less than about
100
MeV
=c
(see
Fig. 9 of Ref.
[6]
). These effects result from energy loss in the
beampipe and inner-detector material.
The mass resolution,
Δ
m
, is measured as the difference
between the generated and reconstructed
K
0
S
K

π
invari-
ant-mass values. The distribution has a root-mean-squared
value of
10
MeV
=c
2
, and is parameterized by the sum of a
crystal ball
[22]
and a Gaussian function. We perform a
binned fit to the
K
0
S
K

π
mass spectrum in data using
the following model. The background is described by a
second-order polynomial, and the
η
c
resonance is
(GeV/c)
T
p
0
0.1
0.2
0.3
0.4
0.5
0
10000
20000
30000
40000
events/(5 MeV/c)
FIG. 1. Distributions of
p
T
for
γγ
K
0
S
K

π
. The data are
shown as (black) points with error bars, and the signal MC
simulation as a (red) histogram; the vertical dashed line indicates
the selection applied to select two-photon events.
)
2
) (GeV/c
±
π
±
K
S
0
m(K
2.8
3
3.2
)
2
events/(5 MeV/c
0
200
400
600
800
1000
FIG. 2. The
K
0
S
K

π
mass spectrum in the
η
c
mass region after
requiring
p
T
<
0
.
08
GeV
=c
. The solid curve shows the total
fitted function, and the dashed curve shows the fitted background
contribution. The shaded areas show signal and sideband regions.
0.02
0.04
0.06
0.08
0.1
0.12
2
) GeV/c
-
π
+
m(K
1
1.5
2
θ
cos
1
0.5
0
0.5
1
FIG. 3. Fitted detection efficiency in the cos
θ
vs m
ð
K
þ
π
Þ
plane. Each interval shows the average value of the fit for
that region.
MEASUREMENT OF THE
I
¼
1
=
2
K
π
S
-
...
PHYSICAL REVIEW D
93,
012005 (2016)
012005-5
represented by a nonrelativistic BW function convolved
with the resolution function. In addition, we allow for the
presence of a residual
J=
ψ
contribution modeled with a
Gaussian function. Its parameter values are fixed to
those obtained from a fit to the
K
0
S
K

π
mass spectrum
for the ISR data sample obtained by requiring
j
M
2
rec
j
<
1
GeV
2
=c
4
. The fitted
K
0
S
K

π
mass spectrum is shown in
Fig.
2
. We obtain the following
η
c
parameters:
m
¼
2980
.
8

0
.
4
MeV
=c
2
;
Γ
¼
33

1
MeV
;
N
η
c
¼
9808

164
;
ð
3
Þ
where uncertainties are statistical only. Our measured
mass value is
2
.
8
MeV
=c
2
lower than the world average
[19]
. This may be due to interference between the
η
c
amplitude and that describing the background in the signal
region
[23]
.
V. MODEL INDEPENDENT PARTIAL
WAVE ANALYSIS
We perform independent MIPWA of the
K
0
S
K

π
and
K
þ
K
π
0
Dalitz plots in the
η
c
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
;m
n
Þ
P
i
k
i
I
B
i

ð
4
Þ
where:
(i)
N
is the number of events in the signal region;
(ii) for the
n
th event,
m
n
is the
K
0
S
K

π
or the
K
þ
K
π
0
invariant mass;
(iii) for the
n
th event,
x
n
¼
m
2
ð
K
þ
π
Þ
,
y
n
¼
m
2
ð
K
0
S
π
Þ
for
K
0
S
K

π
;
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
;
(iv)
f
sig
is the mass-dependent fraction of signal ob-
tained from the fit to the
K
0
S
K

π
or
K
þ
K
π
0
mass
spectrum;
(v) for the
n
th event,
ε
ð
x
0
n
;y
0
n
Þ
is the efficiency para-
metrized as a function of
x
0
n
¼
m
ð
K
þ
π
Þ
for
K
0
S
K

π
and
x
0
n
¼
m
ð
K
þ
K
Þ
for
K
þ
K
π
0
, and
y
0
n
¼
cos
θ
(see Sec.
IV
);
(vi) for the
n
th event, the
A
i
ð
x
n
;y
n
Þ
describe the com-
plex signal-amplitude contributions;
(vii)
c
i
is the complex amplitude for 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
x
0
;y
0
Þ
d
x
d
y
and
I
B
i
¼
R
B
i
ð
x; y
Þ
d
x
d
y
are normalization integrals. Numeri-
cal integration is performed on phase space gener-
ated events with
η
c
signal and background generated
according to the experimental distributions. In case
of MIPWA or when resonances have free parame-
ters, integrals are recomputed at each minimization
step. Background integrals and fits dealing with
amplitudes having fixed resonance parameters are
computed only once.
Amplitudes are described along the lines described in
Ref.
[24]
. For an
η
c
meson decaying into three pseudoscalar
mesons via an intermediate resonance
r
of spin
J
(i.e.
η
c
Cr
,
r
AB
), each amplitude
A
i
ð
x; y
Þ
is represented
by the product of a complex Breit-Wigner (BW) function
and a real angular distribution function represented by the
spherical harmonic function
ffiffiffiffiffiffi
2
π
p
Y
0
J
ð
cos
θ
Þ
;
θ
is the angle
between the direction of
A
, in the rest frame of
r
, and the
direction of
C
in the same frame. This form of the angular
dependence results from angular momentum conservation
in the rest frame of the
η
c
, which leads to the production of
r
with helicity 0.
It follows that
A
i
ð
x; y
Þ¼
BW
ð
M
AB
Þ
ffiffiffiffiffiffi
2
π
p
Y
0
J
ð
cos
θ
Þ
:
ð
5
Þ
The function
BW
ð
M
AB
Þ
is a relativistic BW function of
the form
BW
ð
M
AB
Þ¼
F
η
c
F
M
2
r
M
2
AB
iM
r
Γ
tot
ð
M
AB
Þ
ð
6
Þ
where
M
r
is the mass of the resonance
r
, and
Γ
tot
ð
M
AB
Þ
is
its mass-dependent total width. In general, this mass
dependence cannot be specified, and a constant value should
be used. However, for a resonance such as the
K

0
ð
1430
Þ
,
which is approximately elastic, we can use the partial width
Γ
AB
, and specify the mass-dependence as:
Γ
AB
¼
Γ
r

p
AB
p
r

2
J
þ
1

M
r
M
AB

F
2
ð
7
Þ
where
p
AB
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
M
2
AB
M
2
A
M
2
B
Þ
2
4
M
2
A
M
2
B
p
2
M
AB
;
ð
8
Þ
and
p
r
is the value of
p
AB
when
M
AB
¼
M
r
.
The form factors
F
η
c
and
F
attempt to model the
underlying quark structure of the parent particle and the
intermediate resonances. We set
F
η
c
to a constant value,
while for
F
we use Blatt-Weisskopf penetration factors
[25]
(Table
I
), that depend on a single parameter
R
representing
J. P. LEES
et al.
PHYSICAL REVIEW D
93,
012005 (2016)
012005-6