Cross sections for the reactions
e
þ
e
−
→
K
0
S
K
0
L
π
0
,
K
0
S
K
0
L
η
,and
K
0
S
K
0
L
π
0
π
0
from
events 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
U. Mallik,
21
C. Chen,
22
J. Cochran,
22
S. Prell,
22
H. Ahmed,
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
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
S. H. Robertson,
35
B. Dey,
36a
N. Neri,
36a
F. Palombo,
36a,36b
R. Cheaib,
37
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
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. 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
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,
64b
A. Beaulieu,
64b
F. U. Bernlochner,
64b
G. J. King,
64b
R. Kowalewski,
64b
T. Lueck,
64b
I. M. Nugent,
64b
J. M. Roney,
64b
R. J. Sobie,
64a,64b
N. Tasneem,
64b
T. J. Gershon,
65
P. F. Harrison,
65
T. E. Latham,
65
R. Prepost,
66
and S. L. Wu
66
(
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
16a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
PHYSICAL REVIEW D
95,
052001 (2017)
2470-0010
=
2017
=
95(5)
=
052001(16)
052001-1
© 2017 American Physical Society
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
University of Iowa, Iowa City, Iowa 52242, USA
22
Iowa State University, Ames, Iowa 50011, USA
23
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudi Arabia
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
Institute of Particle Physics and McGill University, Montréal, Québec H3A 2T8, Canada
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 H3C 3J7, Canada
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
95,
052001 (2017)
052001-2
63
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
64a
Institute of Particle Physics, Victoria, British Columbia V8W 3P6, Canada
64b
University of Victoria, Victoria, British Columbia V8W 3P6, Canada
65
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
66
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 2 February 2017; published 6 March 2017)
We study the processes
e
þ
e
−
→
K
0
S
K
0
L
π
0
γ
,
K
0
S
K
0
L
ηγ
, and
K
0
S
K
0
L
π
0
π
0
γ
, where the photon is radiated from
the initial state, providing cross section measurements for the hadronic final states over a continuum of
center-of-mass energies. The results are based on
469
fb
−
1
of data collected at or near the
Υ
ð
4
S
Þ
resonance
with the
BABAR
detector at SLAC. We present the first measurements of the
e
þ
e
−
→
K
0
S
K
0
L
π
0
,
K
0
S
K
0
L
η
, and
K
0
S
K
0
L
π
0
π
0
cross sections up to a center-of-mass energy of 4 GeV and study their intermediate resonance
structures. We observe
J=
ψ
decays to all of these final states for the first time, present measurements of
their
J=
ψ
branching fractions, and search for
ψ
ð
2
S
Þ
decays.
DOI:
10.1103/PhysRevD.95.052001
I. INTRODUCTION
Electron-positron annihilation events with initial-
state radiation (ISR) can be used to study processes over
a wide range of energies below the nominal
e
þ
e
−
center-of-
mass (c.m.) energy (
E
c
:
m
:
), as demonstrated in Ref.
[1]
. The
possibility of exploiting ISR to make precise measurements
of low-energy cross sections at high-luminosity
φ
and
B
factories is discussed in Refs.
[2
–
4]
and motivates the
studies described in this paper. Such measurements are of
particular current interest because of a three-standard-
deviation discrepancy between the measured value of the
muon anomalous magnetic moment (
g
μ
−
2
) and that
computed in the Standard Model
[5]
, where the hadronic
loop contributions require experimental
e
þ
e
−
annihilation
cross sections as input. The calculation is most sensitive to
the low-energy region, where the inclusive hadronic cross
section cannot be measured reliably, and a sum of exclusive
states must be used. Not all accessible states have been
measured yet, and new measurements will improve the
reliability of the calculation. In addition, studies of ISR
events at
B
factories provide information on resonance
spectroscopy for masses up through the charmonium
region.
Studies of the ISR processes
e
þ
e
−
→
μ
þ
μ
−
γ
[6,7]
and
e
þ
e
−
→
X
h
γ
, where
X
h
represents any of several exclusive
multihadron final states, using data of the
BABAR
experi-
ment at SLAC, have been reported previously. The
X
h
studied so far include charged hadron pairs
π
þ
π
−
[7]
,
K
þ
K
−
[8]
, and
p
̄
p
[9]
; four or six charged mesons
[10
–
12]
;
charged mesons plus one or two
π
0
mesons
[11
–
14]
;a
K
0
S
plus charged and neutral mesons
[15]
; and the first ISR
measurement from
BABAR
that includes
K
0
L
mesons
[16]
.
Together, they demonstrate good detector efficiency for
events of this kind and well-understood tracking, particle
identification, and
π
0
,
K
0
S
and
K
0
L
reconstruction.
In this paper we report measurements of the
K
0
S
K
0
L
π
0
,
K
0
S
K
0
L
η
, and
K
0
S
K
0
L
π
0
π
0
final states, produced in conjunc-
tion with a hard photon that is assumed to result from ISR.
Candidate
K
0
S
mesons are reconstructed in the
π
þ
π
−
decay
mode, candidate
π
0
and
η
mesons are reconstructed in the
γγ
decay mode, and
K
0
L
mesons are detected via their
nuclear interactions in the electromagnetic calorimeter. For
these final states, we measure cross sections from threshold
to
E
c
:
m
:
¼
4
GeV, study their internal structure, perform
the first measurements of
J=
ψ
branching fractions, and
search for
ψ
ð
2
S
Þ
decays. We also search for the
e
þ
e
−
→
γ
K
0
S
K
0
S
π
0
and
e
þ
e
−
→
γ
K
0
S
K
0
S
π
0
π
0
processes, which are
forbidden by
C
-parity conservation, and we see no indi-
cation of them at the level of single background events.
Together with our previous measurements
[8,11,16]
, these
results provide a much more complete understanding of the
K
̄
K
π
,
K
̄
K
η
and
K
̄
K
ππ
final states in
e
þ
e
−
annihilation.
II. THE
BABAR
DETECTOR AND DATA SET
The data used in this analysis were collected with
the
BABAR
detector at the PEP-II2 asymmetric-energy
e
þ
e
−
storage ring. The total integrated luminosity used is
468
.
6
fb
−
1
[17]
, which includes data collected at the
Υ
ð
4
S
Þ
resonance (
424
.
7
fb
−
1
) and at a c.m. energy 40 MeV below
this resonance (
43
.
9
fb
−
1
).
The
BABAR
detector is described in detail elsewhere
[18]
. Charged particles are reconstructed using the
BABAR
tracking system, which comprises the silicon vertex tracker
(SVT) and the drift chamber (DCH) inside the 1.5 T
solenoid. Separation of pions and kaons is accomplished by
*
Present address: Wuhan University, Wuhan 43072, China.
†
Present address: Università di Bologna and INFN Sezione di
Bologna, I-47921 Rimini, Italy.
‡
Deceased.
§
Present address: University of Huddersfield, Huddersfield
HD1 3DH, United Kingdom.
∥
Present address: University of South Alabama, Mobile, AL
36688, USA.
**
Also at Università di Sassari, I-07100 Sassari, Italy.
CROSS SECTIONS FOR THE REACTIONS
...
PHYSICAL REVIEW D
95,
052001 (2017)
052001-3
means of the detector of internally reflected Cherenkov
light and energy-loss measurements in the SVT and DCH.
The hard ISR photon, photons from
π
0
and
η
decays, and
K
0
L
are detected in the electromagnetic calorimeter (EMC).
Muon identification, provided by the instrumented flux
return, is used to select the
μ
þ
μ
−
γ
final state.
To study the detector acceptance and efficiency, we have
developed a special package of simulation programs for
radiative processes based on the approach suggested by
Kühn and Czy
ż
[19]
. Multiple collinear soft-photon emis-
sion from the initial
e
þ
e
−
state is implemented with the
structure-function technique
[20,21]
, while additional pho-
ton radiation from the final-state particles is simulated
using the
PHOTOS
package
[22]
. The precision of the
radiative simulation contributes less than 1% to the uncer-
tainty of the measured hadronic cross sections.
In addition to the signal channels
K
0
S
K
0
L
π
0
,
K
0
S
K
0
L
η
, and
K
0
S
K
0
L
π
0
π
0
, we simulate ISR processes which result in high
backgrounds,
K
0
S
K
0
L
,
K
0
S
K
π
∓
, and
K
0
S
K
π
∓
π
0
, with cross
sections and mass dependences based on our previous
measurements and isospin relations. The
K
0
S
K
0
L
and
K
0
S
K
0
L
η
channels are dominated by
e
þ
e
−
→
γφ
and
γφη
, respec-
tively. Samples of 3
–
5 times the number of expected events
are generated for each final state and processed through the
detector response simulation
[23]
. These events are then
reconstructed using the same software chain as the data.
We also simulate several non-ISR backgrounds, includ-
ing
e
þ
e
−
→
q
̄
q
(
q
¼
u
,
d
,
s
,
c
) events using the J
etset7.4
[24]
generator and
e
þ
e
−
→
τ
þ
τ
−
events using the
KORALB
[25]
generator. Variations in detector and back-
ground conditions are taken into account.
III. EVENT SELECTION AND RECONSTRUCTION
We begin with events containing at least two charged
particles and at least four clusters of energy deposits in
contiguous crystals in the EMC. We then consider the cluster
in the event with the highest energy in the
e
þ
e
−
c.m. frame as
the ISR photon candidate and require
E
γ
c
:
m
:
>
3
GeV. Since
the ISR photons are produced mostly along the beam
line, this accepts only about 10% of the signal events, but
in the selected events, the hadronic system is fully contained
and can be studied reliably.
In these events, we reconstruct candidate
K
0
S
decays to
two charged pions from pairs of oppositely charged tracks
not identified as electrons. They must have a well-recon-
structed vertex between 0.1 and 40.0 cm in radial distance
from the beam axis, and their total momentum must be
consistent with the assumption that they originate from the
interaction region. The
m
ð
π
þ
π
−
Þ
invariant mass distribu-
tion for these
K
0
S
candidates is shown in Fig.
1
for both data
(points) and the
e
þ
e
−
→
γφ
→
γ
K
0
S
K
0
L
simulation (histo-
gram). The signal is very clean, and requiring
482
<
m
ð
π
þ
π
−
Þ
<
512
MeV
=c
2
(vertical lines in Fig.
1
) accepts
98% of the signal events. We use the sidebands 472
–
482
and
512
–
522
MeV
=c
2
to estimate the contributions from
non-
K
0
S
backgrounds, which are found to be negligible in
all cases after final selection.
A few thousand events (about 1% of the total) have more
than one selected
K
0
S
candidate, and we use only the
candidate with
m
ð
π
þ
π
−
Þ
closest to the nominal
[26]
K
0
S
mass. We also require the event to contain no other tracks
that extrapolate within 2 cm of the beam axis and 3 cm
along the axis from the nominal interaction point.
Any number of additional tracks and EMC clusters is
allowed. We consider all clusters with reconstructed energy
above 0.1 GeV as photon candidates and calculate the
invariant mass of each pair. Every pair with a mass within
30
ð
50
Þ
MeV
=c
2
of the nominal
π
0
(
η
) mass is considered a
π
0
(
η
) candidate. The efficiency of
π
0
and
η
reconstruction
in these events is about 97%.
The decay length of the
K
0
L
meson is large, and the
probability to detect a
K
0
L
decay in the DCH is low.
Instead, we look for a cluster in the EMC resulting from
the interaction of a
K
0
L
with a nucleus in the EMC
material. Such clusters are indistinguishable from photon-
induced clusters and give poor resolution on the
K
0
L
energy. The characteristics of these clusters were studied
in detail in our previous publication
[16]
, where it was
shown using
e
þ
e
−
→
φγ
events that
K
0
L
clusters are
detected with high efficiency and good angular resolu-
tion. Background from low-energy clusters is high, and
the requirement of at least 0.2 GeV in cluster energy
yields a clean sample with 48% efficiency. Here, we
apply the same energy requirement and use the efficiency
and angular resolution measured as a function of polar
and azimuthal angles in Ref.
[16]
.
10
3
10
4
10
5
0.47
0.48
0.49
0.5
0.51
0.52
m(
π
+
π
-
) GeV/c
2
Events/0.0007 GeV/c
2
FIG. 1. The
π
þ
π
−
invariant mass distribution for the selected
K
0
S
candidates in the data (points) and simulation (histogram).
The vertical lines indicate the signal region.
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
052001 (2017)
052001-4
IV. THE KINEMATIC FIT PROCEDURE
Each event selected as described in Sec.
III
is subjected
to a set of constrained kinematic fits, in which the four-
momenta and covariance matrices of the initial
e
þ
e
−
, the
ISR photon, the best
K
0
S
candidate, and zero, two or four
relevant photon candidates are taken into account. The
direction and angular resolution, but not the energy, of the
K
0
L
candidate is also used, and the
K
0
L
momentum is
determined in the fit. The three-momentum vectors for all
other particles, including the photons, are also determined
with better accuracy from the fits, and the fitted values are
used in further calculations.
For every event, we first perform kinematic fits under the
K
0
S
K
0
L
γ
hypothesis, considering the ISR photon and
K
0
S
candidates, along with each cluster with energy over
0.2 GeV in turn as the
K
0
L
candidate. Each fit has three
constraints, and we consider the combination with the best
χ
2
value, denoted
χ
2
ð
K
0
S
K
0
L
Þ
. This variable is useful in
suppressing the large background arising from combina-
tions of background photons with a mass near the
π
0
or
η
mass.
Next, we consider each
π
0
and
η
candidate and perform a
set of fits to the
K
0
S
K
0
L
π
0
γ
and
K
0
S
K
0
L
ηγ
hypothesis,
including the ISR photon,
K
0
S
, and two photon candidates,
along with each
K
0
L
candidate not included in the
π
0
or
η
candidate. These fits have four constraints, including one
on the
π
0
or
η
candidate mass. We retain the
π
0
K
0
L
and
η
K
0
L
candidate combinations yielding the best values of
χ
2
ð
K
0
S
K
0
L
π
0
Þ
and
χ
2
ð
K
0
S
K
0
L
η
Þ
, respectively.
Similarly, for events with six or more clusters, we
consider each pair of nonoverlapping
π
0
candidates and
perform a set of five-constraint fits under the
K
0
S
K
0
L
π
0
π
0
γ
hypothesis. Both
π
0
masses are constrained, and we retain
the
π
0
π
0
K
0
L
candidate combination yielding the lowest
value of
χ
2
ð
K
0
S
K
0
L
π
0
π
0
Þ
.
Finally, we perform similar fits for all the other simulated
signal and background processes discussed in Sec.
II
,
giving us additional
χ
2
variables that can be used to select
(or suppress) these processes.
V. THE
K
0
S
K
0
L
π
0
FINAL STATE
A. Additional selection criteria
For the
K
0
S
K
0
L
π
0
final state, a few additional selection
criteriaare applied. Considering all pairs of EMC clusters not
assigned to the ISR photon,
π
0
,or
K
0
L
candidates, we observe
a large signal from extra
π
0
’
s, shown in Fig.
2
. It is especially
strong whenone oftheclustershas high energy, sowerequire
E
max
γ
<
0
.
5
GeV. This reduces backgrounds from several
sources with a loss of 3% in simulated signal efficiency.
However, many ISR
φγ
events with a false
π
0
,formedby
accidental photons, remain. To reduce this background, we
require
χ
2
ð
K
0
S
K
0
L
Þ
>
15
if the fitted
K
0
S
K
0
L
invariant mass
m
ð
K
0
S
K
0
L
Þ
is smaller than
1
.
04
GeV
=c
2
.
The 4C
χ
2
distribution for the remaining events under the
K
0
S
K
0
L
π
0
γ
hypothesis is shown as the points in Fig.
3(a)
,
with the corresponding distribution for MC-simulated pure
K
0
S
K
0
L
π
0
γ
events shown as the open histogram. Both
distributions are broader than typical 4C
χ
2
distributions
due to higher-order ISR, which is present in both data and
simulation but not taken into account in the fit. The
reliability of the simulated distribution has been demon-
strated in our previous studies and is discussed below. In
the figure, the simulated signal distribution is normalized to
the data in the region
χ
2
ð
K
0
S
K
0
L
π
0
Þ
<
3
, where the con-
tribution of higher-order ISR is small and the background
contamination is lowest, but still amounts to about 5% of
the signal. The difference between the two distributions at
high values gives an indication of the level of background.
We define a signal region
χ
2
ð
K
0
S
K
0
L
π
0
Þ
<
25
and a
control region
25
<
χ
2
ð
K
0
S
K
0
L
π
0
Þ
<
50
[vertical lines in
Fig.
3(a)
], from which we estimate backgrounds in the
signal region. The signal region contains 5441 data and
3402 signal-MC events, while the control region contains
2733 and 632 events, respectively.
B. Background subtraction
We estimate known ISR backgrounds from simulation
and normalize the simulated non-ISR background using the
π
0
peak, as described in Ref.
[16]
. The largest backgrounds
we can evaluate in this way are shown in Fig.
3(a)
: the
shaded, cross-hatched, and hatched areas represent the
simulated backgrounds from non-ISR
q
̄
q
, ISR
K
0
S
K
0
L
ð
φ
Þ
,
and ISR
φη
events, respectively. The shapes of these three
0
1
2
0
0.1
0.2
0.3
1
10
m
γγ
GeV/c
2
E
γ
max GeV
FIG. 2. Two-dimensional distribution of the higher cluster
energy in a photon-candidate pair vs the corresponding diphoton
mass
m
γγ
for all pairs of EMC clusters in
K
0
S
K
0
L
π
0
γ
events
containing neither the ISR photon, the
K
0
L
candidate, nor either
photon in the
π
0
candidate.
CROSS SECTIONS FOR THE REACTIONS
...
PHYSICAL REVIEW D
95,
052001 (2017)
052001-5
distributions are consistent with each other and quite distinct
from that expected for signal events. However, these
backgrounds account for less than half of the observed
difference between data and simulation at large
χ
2
values.
We assume the remaining background is from other ISR
processes, with a
χ
2
ð
K
0
S
K
0
L
π
0
Þ
distribution similar in shape
to those shown.
To obtain any distribution of the
K
0
S
K
0
L
π
0
signal events,
we use the control region to estimate the sum of all
backgrounds, following the procedure described in detail
in Ref.
[16]
. In each bin of the distribution in question, the
background contribution is estimated as the difference
between the numbers of data and signal-MC events in
the control region [see Fig.
3(a)
], normalized to the
corresponding difference in the signal region.
The
K
0
S
K
0
L
π
0
invariant mass distribution of events in
the signal region is shown in Fig.
3(b)
as the points. The
shaded, cross-hatched, and hatched areas represent the same
simulated backgrounds as in Fig.
3(a)
. The sum of all
backgrounds, estimated from the control region, is shown as
the open histogram in Fig.
3(b)
, and the extracted mass
distribution for
e
þ
e
−
→
K
0
S
K
0
L
π
0
signal events is shown as
the filled points in Fig.
3(c)
. We observe 3669 events in the
mass range from threshold to
4
.
0
GeV
=c
2
. In addition to a
main peak around
1
.
8
GeV
=c
2
,a
J=
ψ
signal is visible.
Thisprocedurerelieson goodagreementbetweendataand
simulation in the
χ
2
ð
K
0
S
K
0
L
π
0
Þ
distribution. Considering our
previous studies of
χ
2
distributions
[16]
, along with simu-
lation and normalization statistics, we estimate the relative
systematic uncertainty on the background to be 30%. This
results in an uncertainty on the background-subtracted signal
of about 10% for
m
ð
K
0
S
K
0
L
π
0
Þ
<
2
.
2
GeV
=c
2
, increasing
roughly linearly with mass to about 40% at
3
.
2
GeV
=c
2
and above.
C. Detection efficiency
The selection procedures applied to the data are also
applied to the MC-simulated event sample. The resulting
distribution of the reconstructed
K
0
S
K
0
L
π
0
invariant mass is
shown in Fig.
4(a)
for events with
χ
2
ð
K
0
S
K
0
L
π
0
Þ
in the signal
(open histogram) and control (hatched) regions. The
reconstruction efficiency as a function of mass is obtained
by dividing the number of reconstructed MC events in each
50
MeV
=c
2
mass interval by the number generated in that
interval and is shown in Fig.
4(b)
. The effects of detector
10
10
2
0 10203040506070
χ
2
(K
S
K
L
π
0
)
Events/unit
χ
2
0
100
200
300
400
(a)
(b)
(c)
1234
m(K
S
K
L
π
0
) (GeV/c
2
)
Events/0.05 GeV/c
2
0
100
200
300
400
1234
m(K
S
K
L
π
0
) (GeV/c
2
)
Events/0.05 GeV/c
2
FIG. 3. (a) The four-constraint
χ
2
distributions for data (points) and MC-simulated
K
0
S
K
0
L
π
0
γ
events (open histogram). The shaded,
cross-hatched, and hatched areas represent the simulated backgrounds from non-ISR
q
̄
q
, ISR
φ
, and ISR
φη
events, respectively. (b) The
K
0
S
K
0
L
π
0
invariant mass distribution for data events in the signal region (points). The shaded, cross-hatched, and hatched areas represent
the simulated contributions from non-ISR
q
̄
q
, ISR
φ
, and ISR
φη
events, respectively, while the open histogram represents the total
background estimated from the control region. (c) The
K
0
S
K
0
L
π
0
invariant mass distribution after background subtraction (points). The
open circles represent the contribution from the resonant process
e
þ
e
−
→
K
ð
892
Þ
0
̄
K
0
þ
c
:
c
:
→
K
0
S
K
0
L
π
0
(see text).
0
100
200
300
(a)
(b)
1234
m(K
S
K
L
π
0
) (GeV/c
2
)
Events/0.05 GeV/c
2
0
0.02
0.04
0.06
0.08
1234
m(K
S
K
L
π
0
) (GeV/c
2
)
Eff./0.05 GeV/c
2
FIG. 4. (a) The reconstructed
K
0
S
K
0
L
π
0
invariant mass distribu-
tion for MC-simulated signal events in the signal (open histo-
gram) and control (hatched) regions of Fig.
3(a)
. (b) The net
reconstruction efficiency from the simulation.
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
052001 (2017)
052001-6
resolution,about
25
MeV
=c
2
,areincludedinthis efficiency.
Below
1
.
5
GeV
=c
2
theefficiencybecomes very large, due to
the rapidly changing cross section near threshold. Since the
resolution is measured from the data and the shape of the
threshold rise is well simulated, we apply no correction.
Nevertheless, the backgrounds and the resolution-effect
uncertainties are high in this region, so we do not quote a
cross section measurement below
1
.
4
GeV
=c
2
, and we
assign an additional 50% (30%) relative systematic uncer-
tainty for the mass bin at
1
.
425
ð
1
.
475
Þ
GeV
=c
2
.
This efficiency is corrected for the data-MC differences
evaluated in our previous studies. The ISR photon detection
efficiency has been studied using
μ
þ
μ
−
γ
events
[7]
, and we
apply a polar-angle-dependent correction of typically
−
1
.
5
0
.
5%
to the simulated efficiency. The
K
0
S
detection
efficiency has been studied very carefully at
BABAR
, with
data-MC differences in the efficiency determined as a
function of the
K
0
S
direction and momentum. We apply a
correction event by event, which introduces an overall
correction of
þ
1
.
1
1
.
0%
to the efficiency. The
π
0
reconstruction efficiency has been studied in
BABAR
using
ωγ
and
ωπ
0
γ
events, and the correction is found to be
ð
−
3
1
Þ
%
. The
K
0
L
detection requires a
ð
−
6
.
1
0
.
6
Þ
%
correction
[16]
. In total, there is a
ð
−
9
.
5
1
.
6
Þ
%
correc-
tion; this systematic uncertainty is small compared with
that due to the backgrounds, described above.
D. The
e
þ
e
−
→
K
0
S
K
0
L
π
0
cross section
The cross section for
e
þ
e
−
annihilation into
K
0
S
K
0
L
π
0
is
calculated from
σ
ð
K
0
S
K
0
L
π
0
Þð
E
c
:
m
:
Þ¼
dN
K
0
S
K
0
L
π
0
γ
ð
E
c
:
m
:
Þ
d
L
ð
E
c
:
m
:
Þ
·
ε
ð
E
c
:
m
:
Þ
·
R
;
ð
1
Þ
where
E
c
:
m
:
≡
m
ð
K
0
S
K
0
L
π
0
Þ
;
dN
K
0
S
K
0
L
π
0
γ
is the number of
selected, background-subtracted
K
0
S
K
0
L
π
0
events in the inter-
val
dE
c
:
m
:
;
ε
ð
E
c
:
m
:
Þ¼
ε
MC
ð
E
c
:
m
:
Þ
·
ð
1
þ
δ
corr
Þ
is the simu-
lated detection efficiency corrected for data-MC differences,
as described above. The radiative correction
R
is unity within
1%, with an estimated precision of about 1%. The differential
ISR luminosity
d
L
ð
E
c
:
m
:
Þ
associated with the interval
dE
c
:
m
:
centered at an effective collision energy of
E
c
:
m
:
is calculated
using the leading-order formula (see, for example, Ref.
[13]
),
and the systematic uncertainty associated with the luminosity
determination is estimated to be 0.5%.
The cross section is shown as a function of energy in
Fig.
5
and listed in Table
I
. There are no previous
measurements for this final state. We do not quote the
cross section from threshold (1.13 GeV) to 1.4 GeV, where
it shows a sharp rise to a maximum value of about 3 nb near
1.7 GeV, presumably dominated by the
φ
ð
1680
Þ
resonance,
and a slow decrease toward higher energies, perturbed by
the
J=
ψ
signal. Only statistical uncertainties are shown.
The systematic uncertainty is dominated by background
contributions and amounts to about 10% near the peak of
0
1
2
3
1234
E
c.m.
(GeV)
σ
(K
S
K
L
π
0
) (nb)
FIG. 5. The
e
þ
e
−
→
K
0
S
K
0
L
π
0
cross section. The error bars are
statistical only.
TABLE I. Summary of the
e
þ
e
−
→
K
S
K
L
π
0
cross section measurement. Uncertainties are statistical only.
E
c
:
m
:
(GeV)
σ
(nb)
E
c
:
m
:
(GeV)
σ
(nb)
E
c
:
m
:
(GeV)
σ
(nb)
E
c
:
m
:
(GeV)
σ
(nb)
1.425
0
.
28
0
.
07
2.075
0
.
55
0
.
11
2.725
0
.
12
0
.
05
3.375
0
.
03
0
.
04
1.475
0
.
94
0
.
15
2.125
0
.
44
0
.
09
2.775
0
.
12
0
.
08
3.425
0
.
02
0
.
01
1.525
1
.
68
0
.
22
2.175
0
.
42
0
.
09
2.825
0
.
10
0
.
06
3.475
0
.
05
0
.
03
1.575
2
.
60
0
.
28
2.225
0
.
36
0
.
08
2.875
0
.
15
0
.
10
3.525
0
.
01
0
.
03
1.625
2
.
89
0
.
26
2.275
0
.
48
0
.
09
2.925
0
.
04
0
.
03
3.575
0
.
04
0
.
03
1.675
3
.
15
0
.
30
2.325
0
.
31
0
.
07
2.975
0
.
10
0
.
10
3.625
0
.
03
0
.
03
1.725
2
.
79
0
.
29
2.375
0
.
18
0
.
07
3.025
0
.
06
0
.
03
3.675
0
.
00
0
.
01
1.775
1
.
96
0
.
23
2.425
0
.
26
0
.
07
3.075
0
.
31
0
.
09
3.725
0
.
04
0
.
04
1.825
1
.
30
0
.
18
2.475
0
.
25
0
.
08
3.125
0
.
24
0
.
12
3.775
0
.
01
0
.
01
1.875
1
.
12
0
.
18
2.525
0
.
19
0
.
06
3.175
0
.
05
0
.
04
3.825
0
.
03
0
.
02
1.925
0
.
79
0
.
12
2.575
0
.
09
0
.
04
3.225
0
.
02
0
.
03
3.875
0
.
00
0
.
01
1.975
0
.
55
0
.
10
2.625
0
.
14
0
.
05
3.275
0
.
04
0
.
03
3.925
0
.
02
0
.
02
2.025
0
.
58
0
.
11
2.675
0
.
07
0
.
03
3.325
0
.
05
0
.
04
3.975
0
.
01
0
.
01
CROSS SECTIONS FOR THE REACTIONS
...
PHYSICAL REVIEW D
95,
052001 (2017)
052001-7
the cross section (1.7 GeV), increasing roughly linearly
with decreasing cross section to about 30% in the 2.5
–
3 GeV region, always similar in size to the statistical
uncertainty. Above the
J=
ψ
mass, statistics dominate the
∼
40%
systematic uncertainty.
E. The
K
ð
892
Þ
0
and
K
2
ð
1430
Þ
0
contributions
Figure
6
shows the distributions of the fitted
K
0
S
π
0
and
K
0
L
π
0
invariant masses in the selected
K
0
S
K
0
L
π
0
events, after
background subtraction. Clear signals corresponding to the
K
ð
892
Þ
0
resonance are visible, as well as indications of
K
2
ð
1430
Þ
0
production.
We fit these distributions with a sum of two incoherent
Breit-Wigner functions and a function describing the non-
resonant contribution, yielding
1750
84
K
ð
892
Þ
0
→
K
0
S
π
0
decays,
1795
56
K
ð
892
Þ
0
→
K
0
L
π
0
decays, and
a total of
145
54
K
2
ð
1430
Þ
0
decays. The sum of these
K
0
decaysisconsistentwith the total numberof
K
0
S
K
0
L
π
0
events,
indicating that the process is dominated by
K
0
̄
K
0
þ
c
:
c
:
,
and mostly
K
ð
892
Þ
0
̄
K
0
þ
c
:
c
:
, production.
Indeed, if we perform fits similar to those shown in Fig.
6
for events in each
0
.
05
GeV
=c
2
interval of the
K
0
S
K
0
L
π
0
invariant mass and sum the
K
ð
892
Þ
0
K
0
S
and
K
ð
892
Þ
0
K
0
L
yields, we obtain the
K
0
S
K
0
L
π
0
mass distribution shown in
Fig.
3(c)
by the open circles. The errors are statistical only,
andthedifference between thenumber of
K
0
S
K
0
L
π
0
events and
the
K
ð
892
Þ
0
̄
K
0
contribution in each bin is less than the
systematic uncertainty due to the background subtraction
procedure.
F. The
φ
ð
1020
Þ
π
0
contribution
Figure
7
shows the distribution of the fitted
K
0
S
K
0
L
invariant mass for the selected
K
0
S
K
0
L
π
0
events before
background subtraction (dots), along with the background
(histogram) estimated from the
χ
2
ð
K
0
S
K
0
L
π
0
Þ
control region.
0
200
400
600
12
m(K
S
π
0
) (GeV/c
2
)
Events/0.03 GeV/c
2
0
200
400
600
12
m(K
L
π
0
) (GeV/c
2
)
Events/0.03 GeV/c
2
(a)
(b)
FIG. 6. The background-subtracted (a)
K
0
S
π
0
and (b)
K
0
L
π
0
invariant mass distributions in
e
þ
e
−
→
K
0
S
K
0
L
π
0
events. The
curves represent the results of the fits described in the text, with
the hatched areas representing the nonresonant components.
0
20
40
1
1.025
1.05
1.075
1.1
m(K
S
K
L
) (GeV/c
2
)
Events/0.004 GeV/c
2
FIG. 7. The
K
0
S
K
0
L
invariant mass distribution in selected
K
0
S
K
0
L
π
0
events (dots) and the background estimated from the
control region (hatched histogram) of Fig.
3(a)
. The solid line
represents the result of the fit described in the text.
0
0.1
0.2
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
E
c.m.
, GeV
σ
(
φπ
0
), nb
FIG. 8. The
e
þ
e
−
→
φπ
0
cross section from this work (dots)
compared with that obtained in the
K
þ
K
−
π
0
channel
[15]
(circles). The error bars are statistical only.
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
052001 (2017)
052001-8
A
φ
ð
1020
Þ
signal is visible in the
K
0
S
K
0
L
π
0
signal but not in
the background. A fit with a Gaussian plus polynomial
function yields a total of
29
9
φ
→
K
0
S
K
0
L
decays in
K
0
S
K
0
L
π
0
events.
Fitting the
m
ð
K
0
S
K
0
L
Þ
distribution in
0
.
1
GeV
=c
2
bins of
the
K
0
S
K
0
L
π
0
mass, we obtain a
φπ
0
invariant mass spectrum
for the
K
0
S
K
0
L
π
0
final state. Using Eq.
(1)
and the
φ
→
K
0
S
K
0
L
branching fraction
[26]
, we calculate a cross section
for this intermediate state, shown in Fig.
8
(dots) and listed
in Table
II
. Only statistical uncertainties are shown. The
systematic uncertainties of 10%
–
30% relative in this mass
range are smaller than the statistical uncertainties.
The results are consistent with those observed in our
previous study of the
K
þ
K
−
π
0
final state
[15]
, also shown
in Fig.
8
(circles). Together, our measurements suggest a
possible resonant structure near
1
.
6
GeV
=c
2
with isospin
I
¼
1
. The low cross section is expected, as the
φπ
0
channels are suppressed by the OZI rule.
VI. THE
K
0
S
K
0
L
η
FINAL STATE
A. Final selection and backgrounds
We apply the same requirements on extra
π
0
’
s and
χ
2
ð
K
0
S
K
0
L
Þ
as for the
K
0
S
K
0
L
π
0
final state (see Sec.
V
) and
consider the
η
−
K
0
L
combination in each event with the best
χ
2
under the
K
0
S
K
0
L
ηγ
hypothesis. Figure
9(a)
shows the
χ
2
ð
K
0
S
K
0
L
η
Þ
distribution of the remaining events in the data
(dots) compared with that of the signal simulation (open
histogram). The simulated distribution is normalized to the
data in the region
χ
2
ð
K
0
S
K
0
L
η
Þ
<
3
, where the contribution of
higher-order ISR is small and the background contamination
is lowest, but still amounts to about 10% of the signal. The
cross-hatched and hatched areas represent the simulated
contributions from non-ISR
q
̄
q
events and the sum of ISR
K
0
S
K
0
L
π
0
, ISR
K
0
S
K
0
L
, and ISR
K
0
S
K
0
L
π
0
π
0
events, respec-
tively; together, they account for about half of the excess of
data over signal events at high values of
χ
2
.
We define a signal region
χ
2
ð
K
0
S
K
0
L
η
Þ
<
20
and a control
region
20
<
χ
2
ð
K
0
S
K
0
L
η
Þ
<
40
[vertical lines in Fig.
9(a)
],
containing 1829 data and 2518 signal-MC events and
1473 data and 495 signal-MC events, respectively. The
m
ð
K
0
S
K
0
L
η
Þ
distribution for the events in the signal region is
shown in Fig.
9(b)
as points, along with the sum of the
simulated background processes as the cross-hatched and
hatched areas. Using events from the control region (see
Sec.
VB
) we calculate the total background contribution,
assumedto be dominated by ISR channels, and show it as the
open histogram in Fig.
9(b)
.
We fit the total background with a smooth function to
reduce fluctuations and use the result [curve in Fig.
9(b)
]for
the background subtraction. This yields a total of
864
43
TABLE II. Summary of the
e
þ
e
−
→
φπ
0
cross section meas-
urement. Uncertainties are statistical only.
E
c
:
m
:
(GeV)
σ
(nb)
E
c
:
m
:
(GeV)
σ
(nb)
1.25
0
.
00
0
.
02
2.15
0
.
00
0
.
01
1.35
0
.
00
0
.
02
2.25
0
.
01
0
.
01
1.45
0
.
06
0
.
06
2.35
0
.
02
0
.
02
1.55
0
.
17
0
.
06
2.45
0
.
02
0
.
01
1.65
0
.
04
0
.
03
2.55
0
.
00
0
.
01
1.75
0
.
05
0
.
03
2.65
0
.
01
0
.
01
1.85
0
.
02
0
.
02
2.75
0
.
00
0
.
01
1.95
0
.
00
0
.
01
2.85
0
.
00
0
.
01
2.05
0
.
03
0
.
02
1
10
10
(a)
(b)
(c)
2
0204060
χ
2
(K
S
K
L
η
)
Events/unit
χ
2
0
20
40
60
1234
m(K
S
K
L
η
) (GeV/c
2
)
Events/0.05 GeV/c
2
0
20
40
60
1234
m(K
S
K
L
η
) (GeV/c
2
)
Events/0.05 GeV/c
2
FIG. 9. (a) The four-constraint
χ
2
distributions for data (points) and MC-simulated
K
0
S
K
0
L
ηγ
events (open histogram). The cross-
hatched and hatched areas represent the simulated backgrounds from non-ISR
q
̄
q
events and the sum of ISR
K
0
S
K
0
L
π
0
,
K
0
S
K
0
L
, and
K
0
S
K
0
L
π
0
π
0
events, respectively. (b) The
K
0
S
K
0
L
η
invariant mass distribution for data events in the signal region (points). The cross-
hatched and hatched areas represents simulated backgrounds from non-ISR
q
̄
q
and the sum of known ISR events, respectively, while the
open histogram represents the total background, estimated from the control region. The curve shows the empirical fit used for
background subtraction. (c) The
K
0
S
K
0
L
η
invariant mass distribution after background subtraction (points). The open circles represent the
contribution from the resonant process
e
þ
e
−
→
φη
→
K
0
S
K
0
L
η
(see text).
CROSS SECTIONS FOR THE REACTIONS
...
PHYSICAL REVIEW D
95,
052001 (2017)
052001-9
signal events with masses between threshold and
4
.
0
GeV
=c
2
, with the mass distribution shown in Fig.
9(c)
.
Again, we estimate the relative systematic uncertainty on the
background as 30%, corresponding to an uncertainty on the
cross section of about 15% for
m
ð
K
0
S
K
0
L
η
Þ
<
2
.
2
GeV
=c
2
,
increasing roughly linearly to 30% at
3
.
0
GeV
=c
2
, and over
100% above 3.2 GeV
=c
2
.
B. Cross section for
e
þ
e
−
→
K
0
S
K
0
L
η
We calculate the
e
þ
e
−
→
K
0
S
K
0
L
η
cross section as a
function of the effective c.m. energy using Eq.
(1)
.The
simulatedefficiencyis1.6%andshowsnodependenceonthe
K
0
S
K
0
L
η
invariant mass. All efficiency corrections discussed
in Sec.
VD
are applied; in particular, the same correction is
applied to the
η
reconstruction efficiency as for the
π
0
.
The fully corrected cross section is shown in Fig.
10
and
listedinTable
III
,withstatisticaluncertaintiesonly.Thereare
no other measurements for this final state. The cross section
shows a steep rise from threshold at 1.6 GeV, a maximum
value of about 1 nb near 1.7 GeV, and a decrease with
increasing energy, punctuated by a clear
J=
ψ
signal (dis-
cussed in Sec.
VIII
). The relative systematic uncertainty is
dominated by the uncertainty of the backgrounds, totals 15%
at the peak of the cross section, increases roughly linearly to
about 30% at 3 GeV, and exceeds 100% at higher energies.
C. The
φ
ð
1020
Þ
η
contribution
Figure
11
shows the background-subtracted
K
0
S
K
0
L
invari-
ant mass distribution in
e
þ
e
−
→
K
0
S
K
0
L
η
events (dots),
compared with that of simulated ISR
φη
events (histogram).
The two distributions are consistent at low mass values, and
we simply take the number of events with
m
ð
K
0
S
K
0
L
Þ
<
1
.
05
GeV
=c
2
as an estimate of the
φη
contribution. It totals
386
20
events, withthe
K
0
S
K
0
L
η
invariant mass distribution
shown in Fig.
9(c)
as the open circles. The
φη
channel
dominates
K
0
S
K
0
L
η
production for masses below about
2
GeV
=c
2
, but its contribution decreases rapidly for higher
masses and shows no significant
J=
ψ
signal.
Using these events, we calculate the
e
þ
e
−
→
φη
cross
section, which is shown in Fig.
12
as the points. It is
consistent with our previous measurement
[15]
in the
K
þ
K
−
η
final state (circles). Again, only statistical uncer-
tainties are shown, and they are larger than the 15%
–
30%
systematic uncertainties. We observe no significant struc-
tures in the
K
0
S
η
or in the
K
0
L
η
invariant mass distributions.
VII. THE
K
0
S
K
0
L
π
0
π
0
FINAL STATE
A. Final selection and backgrounds
From all events with a
K
0
S
,a
K
0
L
and at least two
nonoverlapping
π
0
candidates, we consider the combina-
tion with the best value of
χ
2
ð
K
0
S
K
0
L
π
0
π
0
Þ
, as described in
Sec.
IV
. Since background candidates are not well sup-
pressed using additional photon or
π
0
, no additional
requirements are imposed. Figure
13(a)
shows the
χ
2
ð
K
0
S
K
0
L
π
0
π
0
Þ
distribution of the data (dots), compared
0
0.5
1
1234
E
c.m.
(GeV)
σ
(K
S
K
L
η
) (nb)
FIG. 10. The
e
þ
e
−
→
K
0
S
K
0
L
η
cross section.
TABLE III. Summary of the
e
þ
e
−
→
K
S
K
L
η
cross section measurement. Uncertainties are statistical only.
E
c
:
m
:
(GeV)
σ
(nb)
E
c
:
m
:
(GeV)
σ
(nb)
E
c
:
m
:
(GeV)
σ
(nb)
E
c
:
m
:
(GeV)
σ
(nb)
2.075
0
.
41
0
.
12
2.725
0
.
15
0
.
06
3.375
0
.
01
0
.
02
2.125
0
.
45
0
.
12
2.775
0
.
10
0
.
05
3.425
0
.
02
0
.
03
2.175
0
.
44
0
.
11
2.825
0
.
08
0
.
05
3.475
0
.
01
0
.
02
1.575
0
.
12
0
.
14
2.225
0
.
49
0
.
12
2.875
0
.
14
0
.
06
3.525
0
.
02
0
.
02
1.625
0
.
52
0
.
14
2.275
0
.
30
0
.
11
2.925
0
.
05
0
.
04
3.575
−
0
.
01
0
.
02
1.675
0
.
78
0
.
18
2.325
0
.
31
0
.
09
2.975
0
.
05
0
.
06
3.625
−
0
.
01
0
.
01
1.725
1
.
01
0
.
23
2.375
0
.
30
0
.
10
3.025
0
.
14
0
.
06
3.675
0
.
07
0
.
03
1.775
0
.
50
0
.
14
2.425
0
.
32
0
.
10
3.075
0
.
22
0
.
06
3.725
0
.
04
0
.
03
1.825
0
.
53
0
.
14
2.475
0
.
19
0
.
07
3.125
0
.
09
0
.
05
3.775
0
.
07
0
.
04
1.875
0
.
41
0
.
12
2.525
0
.
12
0
.
06
3.175
0
.
03
0
.
04
3.825
0
.
01
0
.
02
1.925
0
.
36
0
.
12
2.575
0
.
29
0
.
09
3.225
−
0
.
01
0
.
03
3.875
0
.
01
0
.
02
1.975
0
.
28
0
.
09
2.625
0
.
11
0
.
06
3.275
0
.
04
0
.
04
3.925
0
.
01
0
.
02
2.025
0
.
46
0
.
11
2.675
0
.
19
0
.
08
3.325
0
.
05
0
.
03
3.975
0
.
02
0
.
02
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
052001 (2017)
052001-10