Measurement of the
e
+
e
−
→
K
0
s
K
π
∓
π
0
and
K
0
s
K
π
∓
η
cross sections
using 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
P. A. Lukin,
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
(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
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,
092005 (2017)
2470-0010
=
2017
=
95(9)
=
092005(17)
092005-1
© 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, 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,
092005 (2017)
092005-2
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 19 April 2017; published 30 May 2017)
The processes
e
þ
e
−
→
K
0
S
K
π
∓
π
0
and
e
þ
e
−
→
K
0
S
K
π
∓
η
are studied over a continuum of energies
from threshold to 4 GeV with the initial-state photon radiation method. Using
454
fb
−
1
of data collected
with the
BABAR
detector at the SLAC PEP-II storage ring, the first measurements of the cross sections for
these processes are obtained. The intermediate resonance structures from
K
0
ð
K
π
Þ
0
,
K
ð
892
Þ
ð
K
π
Þ
∓
, and
K
0
S
K
ρ
∓
are studied. The
J=
ψ
is observed in all of these channels, and corresponding branching fractions
are measured.
DOI:
10.1103/PhysRevD.95.092005
I. INTRODUCTION
Measurements of low-energy
e
þ
e
−
hadronic cross sec-
tions are important ingredients for the standard model
prediction of the muon anomalous magnetic moment
[1]
and provide a wealth of spectroscopic information. At an
e
þ
e
−
collider, a continuous spectrum of collision energies
below the nominal
e
þ
e
−
c.m. energy can be attained by
selecting events with initial-state radiation (ISR), as pro-
posed in Ref.
[2]
and discussed in Refs.
[3
–
5]
.
At energies below a few GeV, individual exclusive final
states must be studied in order to understand the experimental
acceptance. The cross section
σ
γ
f
for an incoming
e
þ
e
−
pair
colliding at a c.m. energy
ffiffiffi
s
p
toradiateaphotonofenergy
E
γ
and then annihilate into a specific final state
f
is related to the
corresponding direct
e
þ
e
−
→
f
cross section
σ
f
by
d
σ
γ
f
ð
s; x
Þ
dx
¼
W
ð
s; x
Þ
σ
f
ð
E
c
:
m
:
Þ
;
ð
1
Þ
where
x
¼
2
E
γ
=
ffiffiffi
s
p
and
E
c
:
m
:
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s
ð
1
−
x
Þ
p
is the effective
center-of-mass energy at which the state
f
is produced. The
radiator function
W
ð
s; x
Þ
, or probability density for photon
emission, can be evaluated to better than 1% accuracy
[6]
.
Previously, we presented measurements of low-energy
cross sections for many exclusive hadronic reactions using
the ISR method, including a number of final states with two
kaons in the final state, such as
f
¼
K
þ
K
−
[7]
,
K
þ
K
−
π
þ
π
−
[8]
,
K
0
S
K
0
L
,
K
0
S
K
0
L
π
þ
π
−
,
K
0
S
K
0
S
π
þ
π
−
and
K
0
S
K
0
S
K
þ
K
−
[9]
,
K
0
S
K
π
∓
[10]
,
K
0
S
K
0
L
π
0
, and
K
0
S
K
0
L
π
0
π
0
[11]
. Here, we
extend our program and report measurements of the
e
þ
e
−
→
K
0
S
K
π
∓
π
0
and
K
0
S
K
π
∓
η
channels, including
studies of the intermediate resonant substructure.
II.
BABAR
DETECTOR AND DATA SET
The results presented in this analysis are based on a
sample of
e
þ
e
−
annihilation data collected at
E
c
:
m
:
¼
10
.
58
GeV with the
BABAR
detector
[12]
at the SLAC
PEP-II2 storage ring and correspond to an integrated
luminosity of
454
fb
−
1
[13]
.
Charged-particle momenta are measured in a tracking
system consisting of a five-layer double-sided silicon vertex
tracker (SVT) and a 40-layer central drift chamber (DCH),
immersed in a 1.5 T axial magnetic field. An internally
reflecting ring-imaging Cherenkov detector (DIRC) with
fused silica radiators provides charged-particle identification
(PID). A CsI electromagnetic calorimeter (EMC) is used to
detect and identify photons and electrons. Muons are
identified in the instrumented magnetic flux-return system.
Charged pion and kaon candidates are selected using a
likelihood function based on the specific ionization in
the DCH and SVT and the Cherenkov angle measured in
the DIRC. Photon candidates are defined as clusters in the
EMC that have a shape consistent with an electromagnetic
shower and no associated charged track.
To study the signal efficiency as well as backgrounds
from other ISR processes, a special package of Monte Carlo
(MC) simulation programs for radiative processes has been
developed. Algorithms for generating hadronic final states
via ISR are derived from Ref.
[14]
. Multiple soft-photon
emission from initial-state charged particles is implemented
by means of the structure-function technique
[15,16]
, while
extra photon radiation from final-state particles is simulated
with the
PHOTOS
[17]
package.
Large samples of signal
e
þ
e
−
→
K
0
S
K
π
∓
π
0
γ
and
K
0
S
K
π
∓
ηγ
events are generated with this program, as
are samples of events from the principal ISR background
sources,
e
þ
e
−
→
K
0
S
K
π
∓
γ
and
e
þ
e
−
→
K
0
S
K
π
∓
π
0
π
0
γ
.
*
Now at Wuhan University, Wuhan 43072, China.
†
Now at Università di Bologna and INFN Sezione di Bologna,
I-47921 Rimini, Italy.
‡
Deceased.
§
Now at University of Huddersfield, Huddersfield HD1 3DH,
UK.
∥
Now at University of South Alabama, Mobile, AL 36688,
USA.
¶
Also at Università di Sassari, I-07100 Sassari, Italy.
MEASUREMENT OF THE
...
PHYSICAL REVIEW D
95,
092005 (2017)
092005-3
The
K
0
S
K
π
∓
γ
generator is tuned to reproduce our mea-
sured
[10]
E
c
:
m
:
dependence and resonant substructure. The
other modes use smooth
E
c
:
m
:
dependences and phase space
for the final-state hadrons. The signal and
K
0
S
K
π
∓
generators reproduce the kaon and pion kinematic distri-
butions observed in the data, and we study the effect of
resonances on the efficiency in each case below. In addition
to the ISR sources, background arises from the non-ISR
processes
e
þ
e
−
→
q
̄
q
and
τ
þ
τ
−
. These events are simu-
lated with the JETSET
[18]
and KORALB
[19]
event
generators, respectively. All simulated events are processed
through a detector simulation based on the GEANT4
[20]
package and are analyzed in the same manner as the data.
III. EVENT SELECTION AND KINEMATICS
We require events to contain at least three photon
candidates and at least four charged tracks, including at
least one
K
0
S
→
π
þ
π
−
candidate.
Photon candidates must lie within the acceptance of the
EMC, defined by
0
.
35
<
θ
<
2
.
4
radians, where
θ
is the
polar angle relative to the
e
−
beam direction. The photon
candidate with highest energy is assumed to be the ISR
photon and is required to have energy
E
>
3
GeV, where
the asterisk indicates a quantity evaluated in the
e
þ
e
−
c.m.
frame. To reduce background from machine-induced soft
photons, at least one additional photon candidate must have
E
>
100
MeV, and another must have
E
>
60
MeV.
We calculate the invariant mass
m
γγ
of each pair of
photon candidates and consider a pair to be a
π
0
candidate if
0
.
09
<m
γγ
<
0
.
18
GeV
=c
2
and an
η
candidate
if
0
.
47
<m
γγ
<
0
.
62
GeV
=c
2
. Events with at least one
π
0
or
η
candidate are retained.
We require at least two charged tracks in an event, of
opposite charge, one identified as a kaon and one as a pion,
that appear in the polar angle range
0
.
45
<
θ
<
2
.
40
radians. Each track must extrapolate to within 0.25 cm
of the nominal
e
þ
e
−
collision point in the plane
perpendicular to the beam axis and to within 3 cm along
the axis.
The
K
0
S
candidates are reconstructed in the
π
þ
π
−
decay mode from pairs of oppositely charged tracks not
identified as electrons. They must have an invariant mass
within
15
MeV
=c
2
of the nominal
K
0
S
mass and a well-
reconstructed vertex at least 2 mm away from the beam
axis. The angle
θ
K
0
S
between reconstructed total momentum
of these tracks and the line joining their vertex with the
primary vertex position must satisfy cos
ð
θ
K
0
S
Þ
>
0
.
99
.
Each of these events is subjected to a set of five-
constraint (5C) kinematic fits, in which the four-momentum
of the
K
0
S
K
π
∓
γ
ISR
γγ
system is required to equal that of the
initial
e
þ
e
−
system and the invariant mass of the two non-
ISR photon candidates is constrained to the nominal
π
0
or
η
mass. The fits employ the full covariance matrices and
provide
χ
2
values and improved determinations of the
particle momenta and angles, which are used in the
subsequent analysis. Fits are performed for every
π
0
and
η
candidate in the event, and we retain the combinations
giving the lowest values of
χ
2
K
0
S
K
π
∓
π
0
and
χ
2
K
0
S
K
π
∓
η
.
IV.
K
0
S
K
π
∓
π
0
FINAL STATE
A. Event selection
The
χ
2
K
0
S
K
π
∓
π
0
distribution for the selected
e
þ
e
−
→
K
0
S
K
π
∓
π
0
γ
events is shown in Fig.
1
, after subtraction of
the small background from
q
̄
q
events, which is discussed
below and shown in the figure as the cross-hatched
histogram. The corresponding distribution for simulated,
selected signal events is shown as the open histogram. It is
normalized to the data integrated over the first five bins,
where the lowest ISR background contributions are
expected. These distributions are broader than a typical
5C
χ
2
distribution because of multiple soft-photon emission
from the initial state, which is not taken into account in the
fit but is present in both the data and simulation. Previous
studies have found these effect to be well simulated, and we
assign a systematic uncertainty in Sec.
IV B
. The remaining
differences can be explained by ISR backgrounds, which
we discuss in this subsection.
Signal event candidates are selected by requiring
χ
2
K
0
S
K
π
∓
π
0
<
20
. Events with
20
<
χ
2
K
0
S
K
π
∓
π
0
<
40
are used
as a control sample to evaluate background. The signal and
control samples contain 6859 (5656) and 1257(870)
experimental (simulation) events, respectively.
Figure
2(a)
compares the
γγ
invariant-mass distribution
of the
π
0
candidate for data events in the signal region
with the prediction of the signal-event simulation. The
π
0
1
10
10
2
10
3
10
20
30
40
50
60
Signal
Control
region
region
χ
2
(K
S
K
ππ
0
)
Events/Unit
χ
2
FIG. 1. Distribution of
χ
2
from the five-constraint fit for
K
0
S
K
π
∓
π
0
γ
candidates in the data (points). The open and
cross-hatched histograms are the distributions for simulated
signal and
q
̄
q
background events, respectively, normalized as
described in the text. The signal and control regions are indicated.
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
092005 (2017)
092005-4
peak in the simulation is shifted with respect to the
data by
−
0
.
6
0
.
2
MeV
=c
2
, while the standard deviations
are consistent with each other (
σ
DATA
¼
6
.
65
0
.
14
MeV
=c
2
and
σ
MC
¼
6
.
70
0
.
12
MeV
=c
2
).
The corresponding distributions of the
π
þ
π
−
invariant
mass of the
K
0
S
candidate are shown in Fig.
2(b)
. In this
case, a shift in the peak values of
0
.
23
0
.
05
MeV
=c
2
is observed between data and simulation. The widths
are found to be somewhat different:
σ
DATA
¼
2
.
40
0
.
03
MeV
=c
2
and
σ
MC
¼
2
.
30
0
.
03
MeV
=c
2
. Our selec-
tion criteria on the
π
0
and
K
0
S
masses are unrestrictive
enough to ensure the shifts do not affect the result.
The distribution of the invariant mass of the final-state
hadronic system for all data events in the signal region is
shown as the open histogram in Fig.
3
. A narrow peak due
to
J=
ψ
→
K
0
S
K
π
∓
π
0
decays is clearly visible.
Cross sections for backgrounds from
q
̄
q
processes are
poorly known. In simulation, the dominant such process is
e
þ
e
−
→
K
0
S
K
π
∓
π
0
π
0
, in which an energetic photon from
one of the
π
0
decays is erroneously taken as the ISR photon.
These events have kinematic properties similar to signal
events and yield a
χ
2
distribution peaked at low values. This
component can be evaluated from the data, since such
events produce a peak at the
π
0
invariant mass when the
photon erroneously identified as the ISR photon is com-
bined with another photon in the event. Following the
procedure described in Ref.
[10]
, we use the MC mass
distribution and normalize it to the data in the region
2
<m<
4
GeV, where the
π
0
peak is prominent. A
consistent normalization factor is obtained from the
4
–
6
GeV
=c
2
region. For lower masses, we see no signifi-
cant
π
0
peak in the data, and we use the very small MC
prediction with the same normalization. The normalized
contribution of the
q
̄
q
background to the distributions of
Figs.
1
and
3
is shown by the cross-hatched histograms. For
subsequent distributions, the
q
̄
q
background is subtracted.
The remaining background arises from ISR processes,
dominated by
e
þ
e
−
→
K
0
S
K
π
∓
γ
events combined with
random photons and by
e
þ
e
−
→
K
0
S
K
π
∓
π
0
π
0
γ
events.
These have broad distributions in
χ
2
and can be estimated
from the control region of the
χ
2
distribution. The points
with errors in Fig.
4
show the difference between the data
and the normalized simulated
χ
2
K
0
S
K
π
∓
π
0
distributions of
Fig.
1
. Assuming good signal simulation and low ISR
background at low
χ
2
, this gives an estimate of the shape
of the distribution for the total remaining background.
The simulation of the ISR
K
0
S
K
π
∓
background shows a
consistent shape and, when normalized to our previous
measurement
[10]
, accounts for about 10% of the entries.
The simulated ISR
K
0
S
K
π
∓
π
0
π
0
background also has a
0
500
1000
0.08
0.1
0.12
0.14
0.16
0.18
0.2
m(
γγ
) (GeV/c
2
)
Events/0.0025 GeV/c
2
(a)
0
200
400
600
800
0.485
0.49
0.495
0.5
0.505
0.51
m(
π
+
π
-
) (GeV/c
2
)
Events/0.0006 GeV/c
2
(b)
FIG. 2. The (a)
γγ
and (b)
π
þ
π
−
invariant-mass distributions of
the
π
0
and
K
0
S
candidates, respectively, in
K
0
S
K
π
∓
π
0
events in
the
χ
2
K
0
S
K
π
∓
π
0
signal region, for the selected data (points) and the
signal simulation (histograms).
1
10
10
2
1
1.5
2
2.5
3
3.5
4
m(K
S
K
ππ
0
) (GeV/c
2
)
Events/0.02 GeV/c
2
FIG. 3. Distribution of the fitted
K
0
S
K
π
∓
π
0
invariant mass
for data events in the
K
0
S
K
π
∓
π
0
signal region. The hatched
and cross-hatched distributions show the estimated backgrounds
evaluated from ISR and
q
̄
q
events, respectively.
0
20
40
60
0 1020304050607080
χ
2
(K
S
K
ππ
0
)
Events/6
χ
2
Units
FIG. 4. The
χ
2
K
0
S
K
π
∓
π
0
distributions of the ISR background
determined from the data (points with errors) and the sum of MC
simulations for the processes
e
þ
e
−
→
K
0
S
K
π
∓
γ
and
e
þ
e
−
→
K
0
S
K
π
∓
π
0
π
0
γ
(open histogram) described in the text.
MEASUREMENT OF THE
...
PHYSICAL REVIEW D
95,
092005 (2017)
092005-5
consistent shape and is expected to be much larger.
Normalizing to a cross section nine times larger and adding
the ISR
K
0
S
K
π
∓
prediction, we obtain the simulated
distribution shown as the histogram in Fig.
4
. This
demonstrates sufficient understanding of the shape of the
background distribution, and we assume that all remaining
background has the simulated shape. The genuine signal
and the ISR background in any distribution other than the
χ
2
are estimated bin by bin using the numbers of selected
events in that bin in the signal and control regions,
N
1
and
N
2
, after subtraction of the respective
q
̄
q
backgrounds.
We take
N
1
(
N
2
) to be the sum of the numbers of genuine
signal
N
1
S
(
N
2
S
) and ISR background events
N
1
B
(
N
2
B
)in
the signal (control) region. From the signal simulation,
we obtain
N
1
S
=N
2
S
¼
α
¼
6
.
59
0
.
24
, and from the ISR
background simulation,
N
1
B
=N
2
B
¼
β
¼
0
.
49
0
.
07
.
The observed values of
N
1
and
N
2
are
6509
81
and
1146
34
, respectively. We then solve for
N
1
S
¼
α
·
N
1
−
β
·
N
2
α
−
β
ð
2
Þ
and
N
1
B
in that bin.
The ISR background evaluated in this manner is shown
by the hatched histogram in Fig.
3
.
We find
N
1
S
¼
6430
90
, where the uncertainty is
statistical. The systematic uncertainty in the
q
̄
q
background
estimate is taken to be 50%, to account for the limited
knowledge of the
q
̄
q
cross section. The systematic uncer-
tainty in the ISR background estimate is, more conserva-
tively, taken to be 100%. The total systematic uncertainty is
evaluated in three regions of
E
c
:
m
:
. This yields relative
uncertainties in
N
1
S
of 2.5% for
E
c
:
m
:
<
2
GeV, 6.25% for
2
<E
c
:
m
:
<
3
GeV, and 10% for
E
c
:
m
:
>
3
GeV.
B. Detection efficiency
The reconstruction and selection efficiency for signal
events is determined from the signal simulation, corrected
for known differences with respect to data. The efficiencies
for charged-track, photon, and
K
0
S
reconstruction depend
on the momentum and polar angle of the particle. The
distributions of these variables are well described by the
simulation for all relevant particles. The total event detec-
tion efficiency from the simulation, including the
K
0
S
→
π
þ
π
−
branching fraction of 0.692
[21]
, is shown as a
function of
E
c
:
m
:
in Fig.
5
. A smooth parametrization,
shown by the solid line, is used.
The
π
0
detection efficiency was studied in our previous
analysis
[22]
of
e
þ
e
−
→
ωγ
→
π
þ
π
−
π
0
γ
events, yielding
corrections to the simulation as a function of the
π
0
momentum and polar angle. Applying these event by event
to the signal simulation yields an overall correction of
þ
2
1%
, independent of
E
c
:
m
:
. Similarly, we incorporate
corrections to the charged-track and
K
0
S
reconstruction
efficiencies, making use of the results found in our previous
studies of
e
þ
e
−
→
π
þ
π
−
π
þ
π
−
γ
[23]
and
e
þ
e
−
→
K
0
S
K
0
L
γ
[9]
events, respectively, where the latter corrections also
depend on the flight length of the
K
0
S
meson transverse to
the beam direction. Corrections of
þ
0
.
8
1
.
0%
for each of
the
π
and
K
, and
þ
1
.
1
1
.
0%
for the
K
0
S
, are derived,
again independent of
E
c
:
m
:
. Similar corrections to the pion
and kaon identification efficiencies amount to
0
2%
.
We study a possible data-MC difference in the shape of
the
χ
2
distribution using the
J=
ψ
signal, which has
negligible non-ISR background. The increase in the
J=
ψ
yield when loosening the
χ
2
requirement from 20 to 200 is
consistent with the expectation from simulation, and we
estimate a correction of
þ
3
.
7
4
.
6%
.
As a cross-check, using a fast simulation of the detector
response for computational simplicity, we compare the
0
0.01
0.02
0.03
1.5
2
2.5
3
3.5
4
E
c.m.
(GeV)
ε
FIG. 5. Detection efficiency for
e
þ
e
−
→
K
0
S
K
π
∓
π
0
events
as a function of the hadronic invariant mass
E
c
:
m
:
¼
m
ð
K
0
S
K
π
∓
π
0
Þ
. The solid curve shows a fitted parametrization.
TABLE I. Summary of the corrections to and systematic
uncertainties in the
e
þ
e
−
→
K
0
S
K
π
∓
π
0
cross section.
Source
Correction (%)
Systematic
uncertainty (%)
π
0
reconstruction
þ
2
.
0
1.0
K
,
π
reconstruction
þ
1
.
6
2.0
K
0
S
reconstruction
þ
1
.
1
1.0
PID efficiency
0.0
2.0
χ
2
selection
þ
3
.
7
4.6
Background subtraction
—
2.5,
<
2
.
0
GeV
4.2, 2.0
–
3.0 GeV
10.0,
>
3
.
0
GeV
Model acceptance
—
0.5
Luminosity and
radiative corrections
—
1.4
Total
þ
8
.
6
6.3,
<
2
.
0
GeV
7.1, 2.0
–
3.0 GeV
11.5,
>
3
.
0
GeV
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
092005 (2017)
092005-6
results obtained for signal events generated with a phase-
space model to those obtained for signal events generated
with intermediate
K
0
S
π
∓
resonances, specifically
e
þ
e
−
→
K
ð
892
Þ
K
0
S
π
∓
and
K
0
K
π
∓
. No difference in efficiency
larger than 0.5% is seen, and we assign a systematic
uncertainty of 0.5% to account both for possible model
dependence and for the choice of parametrization of the
efficiency as a function of
E
c
:
m
:
. These corrections and
uncertainties are listed in Table
I
. The total correction
is
þ
8
.
6%
.
C. Cross section for
e
+
e
−
→
K
0
S
K
π
∓
π
0
The
e
þ
e
−
→
K
0
S
K
π
∓
π
0
cross section is obtained from
σ
ð
E
c
:
m
:
Þ¼
dN
K
0
S
K
π
∓
π
0
ð
E
c
:
m
:
Þ
d
L
ð
E
c
:
m
:
Þ
ε
ð
E
c
:
m
:
Þ
R
ð
E
c
:
m
:
Þ
;
ð
3
Þ
where
E
c
:
m
:
is the invariant mass of the
K
0
S
K
π
∓
π
0
system,
dN
K
0
S
K
π
∓
π
0
is the number of signal
K
0
S
K
π
∓
π
0
events in
the interval
dE
c
:
m
:
,
d
L
ð
E
c
:
m
:
Þ
is the differential luminosity,
ε
ð
E
c
:
m
:
Þ
is the corrected efficiency discussed in Sec.
IV B
,
and
R
ð
E
c
:
m
:
Þ
is the correction to account for additional soft
radiative photon emission from the initial state.
The differential luminosity
d
L
ð
m
Þ
is calculated using the
total PEP-II integrated luminosity
L
¼
454
fb
−
1
and the
probability density function for ISR photon emission. To
first order, it can be written as
d
L
dm
¼
α
π
x
ð
2
−
2
x
þ
x
2
Þ
log
1
þ
C
1
−
C
−
x
2
C
2
m
s
L
:
ð
4
Þ
Here,
m
¼
m
ð
K
0
S
K
π
∓
π
0
Þ
,
x
¼
1
−
m
2
=s
,
C
¼
cos
θ
0
,
and
θ
0
defines the acceptance of the analysis in the
polar angle of the ISR photon in the
e
þ
e
−
c.m. frame,
θ
0
<
θ
γ
<
180
o
−
θ
0
. Here,
θ
0
¼
20
°.
The radiative correction
R
ð
E
c
:
m
:
Þ
is determined using
generator-level MC (without simulation of the detector
response) as the ratio of the
K
0
S
K
π
∓
π
0
spectrum with soft-
photon emission to that at the Born level. We determine
R
¼
1
.
0029
0
.
0065
, independent of
E
c
:
m
:
. The combined
systematic uncertainty in the luminosity and radiative
correction is estimated to be 1.4%.
The fully corrected
e
þ
e
−
→
K
0
S
K
π
∓
π
0
cross section is
shown in Fig.
6
and listed in Table
II
, with statistical
uncertainties. The relative systematic uncertainties are
summarized in Table
I
; their total ranges from 6.2% for
E
c
:
m
:
<
2
GeV to 11.6% for
E
c
:
m
:
>
3
GeV.
D. Substructure in the
K
0
S
K
π
∓
π
0
final state
Previously, we studied single
K
ð
892
Þ
production in the
processes
e
þ
e
−
→
K
0
S
K
π
∓
and
K
þ
K
−
π
0
[10]
and double
K
ð
892
Þ
production, as well as
φ
,
ρ
, and
f
0
production, in
e
þ
e
−
→
K
þ
K
−
π
þ
π
−
,
K
þ
K
−
π
0
π
0
[8]
, and
K
0
S
K
0
L
π
þ
π
−
[9]
.
Here, we expect single
K
ð
892
Þ
, double
K
ð
892
Þ
,
ρ
, and
possibly other resonance contributions, but the statistical
precision of the data sample is insufficient for competitive
measurements of such processes. Since it is important to
confirm, as far as possible, resonant cross sections mea-
sured in different final states and to verify expected isospin
relations, we perform a simple study of those resonant
subprocesses accessible with our data.
Decays of the
J=
ψ
are discussed below (Sec.
VI
), and for
the study presented in this section, we exclude the region
3
.
0
<E
c
:
m
:
<
3
.
2
GeV. Figure
7(a)
shows a scatter plot of
the
K
0
S
π
0
vs
K
π
∓
invariant masses in the selected data
sample,correctedforbackgroundsasdescribedabove,while
Fig.
7(b)
shows the
K
π
0
vs
K
0
S
π
∓
masses. Clear signals for
charged and neutral
K
ð
892
Þ
0
states are seen. Figure
8(a)
is
the projection of Fig.
7(a)
onto the vertical axis and
shows a large
K
ð
892
Þ
0
peak as well as possible structure
near
1
.
43
GeV
=c
2
. This could arise from the
K
2
ð
1430
Þ
or
K
0
ð
1430
Þ
resonances, or any combination. We cannot study
this structure in detail but must take it into account in any fit.
We fit this distribution with a sum of two incoherent
resonances and a nonresonant (NR) component. The
K
ð
892
Þ
0
is described by a relativistic P-wave Breit-
Wigner (BW) function with a threshold term, with mass
and width fixed to the world-average values
[21]
. The NR
function is the product of a fifth-order polynomial in the
inverse of the mass and an exponential cutoff at threshold.
The second peak is described by a relativistic D- or S-wave
BW with parameters fixed to the nominal values
[21]
for
K
2
ð
1430
Þ
or
K
0
ð
1430
Þ
. The narrower
K
2
ð
1430
Þ
gives
better fits here and in most cases below, so we use it
everywhere. The result of the fit is shown as the line in
Fig.
8(a)
, with the NR component indicated by the
hatched area.
The fit yields
1671
60
K
ð
892
Þ
0
K
π
∓
events and
85
24
K
2
ð
1430
Þ
⋆
K
π
∓
events, where the uncertainties
0
1
2
3
11.522.533.5
4
E
c.m.
(GeV)
σ
(nb)
FIG. 6. Cross section for the process
e
þ
e
−
→
K
0
S
K
π
∓
π
0
. The
uncertainties are statistical.
MEASUREMENT OF THE
...
PHYSICAL REVIEW D
95,
092005 (2017)
092005-7
are statistical only. We do not claim observation of any
particular state near
1
.
43
GeV
=c
2
, but we quote a generic
number of events from this fit and those below for
completeness. Some of the
K
0
ð
892
Þ
K
π
∓
events are
produced through the
K
0
ð
892
Þ
̄
K
0
channel, which we
study below. In order to avoid double counting, we subtract
the latter yield to obtain
1533
60
quasi-three-body
K
ð
892
Þ
0
K
π
∓
events.
The projection of Fig.
7(a)
onto the horizontal axis
is shown in Fig.
8(b)
, along with the results of a corre-
sponding fit, which, after
K
0
ð
892
Þ
̄
K
0
ð
892
Þ
subtraction,
yields
454
60
K
ð
892
Þ
0
K
0
S
π
0
and
20
25
K
2
ð
1430
Þ
K
0
S
π
0
events, respectively.
TABLE II. Measurements of the
e
þ
e
−
→
K
0
S
K
π
∓
π
0
cross section vs
E
c
:
m
:
¼
m
ð
K
0
S
K
π
∓
π
0
Þ
. The uncertainties are statistical only;
systematic uncertainties are given in Table
I
.
E
c
:
m
:
(GeV)
σ
(nb)
E
c
:
m
:
(GeV)
σ
(nb)
E
c
:
m
:
(GeV)
σ
(nb)
E
c
:
m
:
(GeV)
σ
(nb)
E
c
:
m
:
(GeV)
σ
(nb)
1.51
0
.
05
0
.
03
2.01
1
.
65
0
.
16
2.51
0
.
65
0
.
09
3.01
0
.
47
0
.
07
3.61
0
.
14
0
.
03
1.53
0
.
05
0
.
03
2.03
1
.
67
0
.
16
2.53
0
.
77
0
.
10
3.03
0
.
26
0
.
05
3.63
0
.
07
0
.
02
1.55
0
.
02
0
.
02
2.05
1
.
62
0
.
16
2.55
0
.
83
0
.
10
3.05
0
.
33
0
.
06
3.65
0
.
15
0
.
04
1.57
0
.
06
0
.
04
2.07
1
.
91
0
.
17
2.57
0
.
71
0
.
09
3.07
0
.
39
0
.
06
3.67
0
.
11
0
.
03
1.59
0
.
19
0
.
06
2.09
1
.
44
0
.
15
2.59
0
.
85
0
.
10
3.09
2
.
69
0
.
16
3.69
0
.
17
0
.
04
1.61
0
.
16
0
.
06
2.11
1
.
90
0
.
17
2.61
0
.
56
0
.
08
3.11
1
.
61
0
.
13
3.71
0
.
16
0
.
04
1.63
0
.
36
0
.
09
2.13
1
.
78
0
.
16
2.63
0
.
43
0
.
07
3.13
0
.
38
0
.
06
3.73
0
.
07
0
.
02
1.65
0
.
53
0
.
10
2.15
1
.
73
0
.
16
2.65
0
.
56
0
.
08
3.15
0
.
30
0
.
05
3.75
0
.
08
0
.
02
1.67
0
.
52
0
.
10
2.17
1
.
36
0
.
14
2.67
0
.
64
0
.
09
3.17
0
.
25
0
.
05
3.77
0
.
08
0
.
03
1.69
0
.
72
0
.
12
2.19
1
.
49
0
.
14
2.69
0
.
46
0
.
07
3.19
0
.
16
0
.
04
3.79
0
.
05
0
.
02
1.71
0
.
70
0
.
12
2.21
1
.
42
0
.
14
2.71
0
.
63
0
.
08
3.21
0
.
21
0
.
04
3.81
0
.
09
0
.
03
1.73
1
.
09
0
.
14
2.23
1
.
36
0
.
14
2.73
0
.
49
0
.
07
3.23
0
.
18
0
.
04
3.83
0
.
07
0
.
02
1.75
0
.
91
0
.
13
2.25
1
.
36
0
.
14
2.75
0
.
59
0
.
08
3.25
0
.
19
0
.
04
3.85
0
.
04
0
.
02
1.77
1
.
11
0
.
14
2.27
1
.
15
0
.
12
2.77
0
.
37
0
.
06
3.27
0
.
23
0
.
05
3.87
0
.
04
0
.
02
1.79
1
.
48
0
.
16
2.29
0
.
99
0
.
12
2.79
0
.
51
0
.
07
3.29
0
.
16
0
.
04
3.89
0
.
11
0
.
03
1.81
1
.
35
0
.
15
2.31
0
.
95
0
.
11
2.81
0
.
35
0
.
06
3.31
0
.
19
0
.
04
3.51
0
.
05
0
.
02
1.83
1
.
67
0
.
17
2.33
1
.
25
0
.
13
2.83
0
.
30
0
.
06
3.33
0
.
07
0
.
03
3.53
0
.
17
0
.
04
1.85
1
.
73
0
.
17
2.35
0
.
98
0
.
11
2.85
0
.
36
0
.
06
3.35
0
.
15
0
.
04
3.55
0
.
09
0
.
03
1.87
1
.
98
0
.
18
2.37
0
.
98
0
.
11
2.87
0
.
42
0
.
07
3.37
0
.
13
0
.
03
3.57
0
.
08
0
.
03
1.89
2
.
12
0
.
19
2.39
0
.
61
0
.
09
2.89
0
.
28
0
.
05
3.39
0
.
12
0
.
03
3.59
0
.
13
0
.
03
1.91
1
.
99
0
.
18
2.41
1
.
08
0
.
12
2.91
0
.
44
0
.
07
3.41
0
.
14
0
.
03
3.91
0
.
08
0
.
02
1.93
2
.
31
0
.
19
2.43
0
.
84
0
.
10
2.93
0
.
37
0
.
06
3.43
0
.
15
0
.
04
3.93
0
.
08
0
.
03
1.95
2
.
05
0
.
18
2.45
1
.
03
0
.
11
2.95
0
.
23
0
.
05
3.45
0
.
18
0
.
04
3.95
0
.
05
0
.
02
1.97
2
.
32
0
.
19
2.47
0
.
93
0
.
11
2.97
0
.
29
0
.
06
3.47
0
.
09
0
.
03
3.97
0
.
10
0
.
03
1.99
2
.
00
0
.
18
2.49
0
.
77
0
.
10
2.99
0
.
42
0
.
07
3.49
0
.
14
0
.
04
3.99
0
.
08
0
.
02
0.5
1
1.5
2
2.5
0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5
1
10
10
2
m(K
π
) (GeV/c
2
)
m(K
S
π
0
) (GeV/c
2
)
(a)
0.5
1
1.5
2
2.5
0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5
1
10
10
2
m(K
S
π
) (GeV/c
2
)
m(K
π
0
) (GeV/c
2
)
(b)
FIG. 7. Scatter plots of (a) the
K
0
S
π
0
vs
K
π
∓
and (b)
K
π
0
vs
K
0
S
π
∓
invariant masses in
e
þ
e
−
→
K
0
S
K
π
∓
π
0
events.
0
200
400
600
0.5
1
1.5
2
2.5
3
m(K
S
π
0
) (GeV/c
2
)
Events/0.02 GeV/c
2
(a)
0
100
200
300
0.5
1
1.5
2
2.5
3
m(K
+-
π
-+
) (GeV/c
2
)
Events/0.02 GeV/c
2
(b)
0
200
400
600
0.5
1
1.5
2
2.5
3
m(K
S
π
+-
) (GeV/c
2
)
Events/0.02 GeV/c
2
(c)
0
200
400
0.5
1
1.5
2
2.5
3
m(K
+-
π
0
) (GeV/c
2
)
Events/0.02 GeV/c
2
(d)
FIG. 8. The (a)
K
0
S
π
0
and (b)
K
π
∓
invariant-mass projections
of Fig.
7(a)
and the (c)
K
0
S
π
and (d)
K
π
0
invariant-mass
projections of Fig.
7(b)
. The lines represent the results of the
fits described in the text, with the hatched areas denoting their
nonresonant components.
J. P. LEES
et al.
PHYSICAL REVIEW D
95,
092005 (2017)
092005-8