of 19
arXiv:1704.05009v1 [hep-ex] 17 Apr 2017
B
A
B
AR
-PUB-15/005
SLAC-PUB-16940
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, V. Poireau, and V. Tisserand
Laboratoire d’Annecy-le-Vieux de Physique des Particules
(LAPP),
Universit ́e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vie
ux, France
E. Grauges
Universitat de Barcelona, Facultat de Fisica, Departament
ECM, E-08028 Barcelona, Spain
A. Palano
INFN Sezione di Bari and Dipartimento di Fisica, Universit`
a di Bari, I-70126 Bari, Italy
G. Eigen
University of Bergen, Institute of Physics, N-5007 Bergen,
Norway
D. N. Brown and Yu. G. Kolomensky
Lawrence Berkeley National Laboratory and University of Ca
lifornia, Berkeley, California 94720, USA
M. Fritsch, H. Koch, and T. Schroeder
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphys
ik 1, D-44780 Bochum, Germany
C. Hearty
ab
, T. S. Mattison
b
, J. A. McKenna
b
, and R. Y. So
b
Institute of Particle Physics
a
; University of British Columbia
b
,
Vancouver, British Columbia, Canada V6T 1Z1
V. E. Blinov
abc
, A. R. Buzykaev
a
, V. P. Druzhinin
ab
, V. B. Golubev
ab
, E. A. Kravchenko
ab
, P. A. Lukin
ab
,
A. P. Onuchin
abc
, S. I. Serednyakov
ab
, Yu. I. Skovpen
ab
, E. P. Solodov
ab
, and K. Yu. Todyshev
ab
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630
090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 6300
92
c
, Russia
A. J. Lankford
University of California at Irvine, Irvine, California 926
97, USA
J. W. Gary and O. Long
University of California at Riverside, Riverside, Califor
nia 92521, USA
A. M. Eisner, W. S. Lockman, and W. Panduro Vazquez
University of California at Santa Cruz, Institute for Parti
cle Physics, Santa Cruz, California 95064, USA
D. S. Chao, C. H. Cheng, B. Echenard, K. T. Flood, D. G. Hitlin, J. Kim
,
T. S. Miyashita, P. Ongmongkolkul, F. C. Porter, and M. R ̈ohrken
California Institute of Technology, Pasadena, California
91125, USA
Z. Huard, B. T. Meadows, B. G. Pushpawela, M. D. Sokoloff, and L. S
un
University of Cincinnati, Cincinnati, Ohio 45221, USA
J. G. Smith and S. R. Wagner
University of Colorado, Boulder, Colorado 80309, USA
D. Bernard and M. Verderi
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS
/IN2P3, F-91128 Palaiseau, France
2
D. Bettoni
a
, C. Bozzi
a
, R. Calabrese
ab
, G. Cibinetto
ab
, E. Fioravanti
ab
, I. Garzia
ab
, E. Luppi
ab
, and V. Santoro
a
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a
di Ferrara
b
, I-44122 Ferrara, Italy
A. Calcaterra, R. de Sangro, G. Finocchiaro, S. Martellotti,
P. Patteri, I. M. Peruzzi, M. Piccolo, M. Rotondo, and A. Zallo
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, I
taly
S. Passaggio and C. Patrignani
INFN Sezione di Genova, I-16146 Genova, Italy
H. M. Lacker
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, D-
12489 Berlin, Germany
B. Bhuyan
Indian Institute of Technology Guwahati, Guwahati, Assam,
781 039, India
U. Mallik
University of Iowa, Iowa City, Iowa 52242, USA
C. Chen, J. Cochran, and S. Prell
Iowa State University, Ames, Iowa 50011, USA
H. Ahmed
Physics Department, Jazan University, Jazan 22822, Kingdo
m of Saudi Arabia
A. V. Gritsan
Johns Hopkins University, Baltimore, Maryland 21218, USA
N. Arnaud, M. Davier, F. Le Diberder, A. M. Lutz, and G. Wormser
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et
Universit ́e Paris-Sud 11,
Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, Calif
ornia 94550, USA
J. P. Coleman, E. Gabathuler,
D. E. Hutchcroft, D. J. Payne, and C. Touramanis
University of Liverpool, Liverpool L69 7ZE, United Kingdom
A. J. Bevan, F. Di Lodovico, and R. Sacco
Queen Mary, University of London, London, E1 4NS, United Kin
gdom
G. Cowan
University of London, Royal Holloway and Bedford New Colleg
e, Egham, Surrey TW20 0EX, United Kingdom
Sw. Banerjee, D. N. Brown, and C. L. Davis
University of Louisville, Louisville, Kentucky 40292, USA
A. G. Denig, W. Gradl, K. Griessinger, A. Hafner, and K. R. Schuber
t
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Ker
nphysik, D-55099 Mainz, Germany
R. J. Barlow
§
and G. D. Lafferty
University of Manchester, Manchester M13 9PL, United Kingd
om
R. Cenci, A. Jawahery, and D. A. Roberts
University of Maryland, College Park, Maryland 20742, USA
R. Cowan
Massachusetts Institute of Technology, Laboratory for Nuc
lear Science, Cambridge, Massachusetts 02139, USA
3
S. H. Robertson
Institute of Particle Physics and McGill University, Montr
́eal, Qu ́ebec, Canada H3A 2T8
B. Dey
a
, N. Neri
a
, and F. Palombo
ab
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
R. Cheaib, L. Cremaldi, R. Godang,
and D. J. Summers
University of Mississippi, University, Mississippi 38677
, USA
P. Taras
Universit ́e de Montr ́eal, Physique des Particules, Montr ́
eal, Qu ́ebec, Canada H3C 3J7
G. De Nardo and C. Sciacca
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II, I-80126 Napoli, Italy
G. Raven
NIKHEF, National Institute for Nuclear Physics and High Ene
rgy Physics, NL-1009 DB Amsterdam, The Netherlands
C. P. Jessop and J. M. LoSecco
University of Notre Dame, Notre Dame, Indiana 46556, USA
K. Honscheid and R. Kass
Ohio State University, Columbus, Ohio 43210, USA
A. Gaz
a
, M. Margoni
ab
, M. Posocco
a
, G. Simi
ab
, F. Simonetto
ab
, and R. Stroili
ab
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
S. Akar, E. Ben-Haim, M. Bomben, G. R. Bonneaud, G. Calderini, J. C
hauveau, G. Marchiori, and J. Ocariz
Laboratoire de Physique Nucl ́eaire et de Hautes Energies,
IN2P3/CNRS, Universit ́e Pierre et Marie Curie-Paris6,
Universit ́e Denis Diderot-Paris7, F-75252 Paris, France
M. Biasini
ab
, E. Manoni
a
, and A. Rossi
a
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
G. Batignani
ab
, S. Bettarini
ab
, M. Carpinelli
ab
,
∗∗
G. Casarosa
ab
, M. Chrzaszcz
a
, F. Forti
ab
,
M. A. Giorgi
ab
, A. Lusiani
ac
, B. Oberhof
ab
, E. Paoloni
ab
, M. Rama
a
, G. Rizzo
ab
, and J. J. Walsh
a
INFN Sezione di Pisa
a
; Dipartimento di Fisica, Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
F. Anulli
a
, R. Faccini
ab
, F. Ferrarotto
a
, F. Ferroni
ab
, A. Pilloni
ab
, and G. Piredda
a
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
C. B ̈unger, S. Dittrich, O. Gr ̈unberg, M. Heß, T. Leddig, C. Voß,
and R. Waldi
Universit ̈at Rostock, D-18051 Rostock, Germany
T. Adye and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX
11 0QX, United Kingdom
S. Emery and G. Vasseur
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, F
rance
D. Aston, C. Cartaro, M. R. Convery, J. Dorfan, W. Dunwoodie, M
. Ebert, R. C. Field, B. G. Fulsom,
M. T. Graham, C. Hast, W. R. Innes, P. Kim, D. W. G. S. Leith, S. Luit
z, D. B. MacFarlane,
4
D. R. Muller, H. Neal, B. N. Ratcliff, A. Roodman, M. K. Sullivan, J. Va’vr
a, and W. J. Wisniewski
SLAC National Accelerator Laboratory, Stanford, Californ
ia 94309 USA
M. V. Purohit and J. R. Wilson
University of South Carolina, Columbia, South Carolina 292
08, USA
A. Randle-Conde and S. J. Sekula
Southern Methodist University, Dallas, Texas 75275, USA
M. Bellis, P. R. Burchat, and E. M. T. Puccio
Stanford University, Stanford, California 94305, USA
M. S. Alam and J. A. Ernst
State University of New York, Albany, New York 12222, USA
R. Gorodeisky, N. Guttman, D. R. Peimer, and A. Soffer
Tel Aviv University, School of Physics and Astronomy, Tel Av
iv, 69978, Israel
S. M. Spanier
University of Tennessee, Knoxville, Tennessee 37996, USA
J. L. Ritchie and R. F. Schwitters
University of Texas at Austin, Austin, Texas 78712, USA
J. M. Izen and X. C. Lou
University of Texas at Dallas, Richardson, Texas 75083, USA
F. Bianchi
ab
, F. De Mori
ab
, A. Filippi
a
, and D. Gamba
ab
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
L. Lanceri and L. Vitale
INFN Sezione di Trieste and Dipartimento di Fisica, Univers
it`a di Trieste, I-34127 Trieste, Italy
F. Martinez-Vidal and A. Oyanguren
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spa
in
J. Albert
b
, A. Beaulieu
b
, F. U. Bernlochner
b
, G. J. King
b
, R. Kowalewski
b
,
T. Lueck
b
, I. M. Nugent
b
, J. M. Roney
b
, R. J. Sobie
ab
, and N. Tasneem
b
Institute of Particle Physics
a
; University of Victoria
b
, Victoria, British Columbia, Canada V8W 3P6
T. J. Gershon, P. F. Harrison, and T. E. Latham
Department of Physics, University of Warwick, Coventry CV4
7AL, United Kingdom
R. Prepost and S. L. Wu
University of Wisconsin, Madison, Wisconsin 53706, USA
The processes
e
+
e
K
0
S
K
±
π
π
0
and
e
+
e
K
0
S
K
±
π
η
are studied over a continuum of
energies from threshold to 4 GeV with the initial-state phot
on radiation method. Using 454 fb
1
of data collected with the
B
A
B
AR
detector at the SLAC PEP-II storage ring, the first measureme
nts
of the cross sections for these processes are obtained. The i
ntermediate resonance structures from
K
0
(
)
0
,
K
(892)
±
(
)
and
K
0
S
K
±
ρ
are studied. The
J/ψ
is observed in all of these channels,
and corresponding branching fractions are measured.
PACS numbers: 13.66.Bc, 14.40.-n, 13.25.Jx
Now at: Wuhan University, Wuhan 43072, China
Now at: Universit`a di Bologna and INFN Sezione di Bologna,
5
I. INTRODUCTION
Measurements of low-energy
e
+
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
+
e
collider, a continuous spectrum of collision en-
ergies below the nominal
e
+
e
center-of-mass (c.m.) en-
ergy can be attained by selecting events with initial-state
radiation (ISR), as proposed in Ref. [2] and discussed in
Refs. [3–5].
At energies below a few GeV, individual exclusive fi-
nal states must be studied in order to understand the
experimental acceptance. The cross section
σ
γf
for an
incoming
e
+
e
pair colliding at a c.m. energy
s
to ra-
diate a photon of energy E
γ
and then annihilate into a
specific final state
f
is related to the corresponding direct
e
+
e
f
cross section
σ
f
by:
γf
(
s,x
)
dx
=
W
(
s,x
)
σ
f
(
E
c
.
m
.
)
,
(1)
where
x
= 2
E
γ
/
s
and
E
c
.
m
.
=
s
(1
x
) is the ef-
fective center-of-mass energy at which the state
f
is pro-
duced. The radiator function
W
(
s,x
), or probability den-
sity 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
=
K
+
K
[7],
K
+
K
π
+
π
[8],
K
0
S
K
0
L
,
K
0
S
K
0
L
π
+
π
,
K
0
S
K
0
S
π
+
π
and
K
0
S
K
0
S
K
+
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 re-
port measurements of the
e
+
e
K
0
S
K
±
π
π
0
and
K
0
S
K
±
π
η
channels, including studies of the interme-
diate resonant substructure.
II. THE
B
A
B
AR
DETECTOR AND DATA SET
The results presented in this analysis are based on a
sample of
e
+
e
annihilation data collected at
E
c
.
m
.
=
10.58 GeV with the
B
A
B
AR
detector [12] at the SLAC
PEP-II storage ring, and correspond to an integrated lu-
minosity of 454 fb
1
[13].
Charged-particle momenta are measured in a track-
ing system consisting of a five-layer double-sided sili-
con vertex tracker (SVT) and a 40-layer central drift
I-47921 Rimini, Italy
Deceased
§
Now at: University of Huddersfield, Huddersfield HD1 3DH, UK
Now at: University of South Alabama, Mobile, Alabama 36688,
USA
∗∗
Also at: Universit`a di Sassari, I-07100 Sassari, Italy
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 electromag-
netic calorimeter (EMC) is used to detect and identify
photons and electrons. Muons are identified in the in-
strumented 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 elec-
tromagnetic 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 tech-
nique [15, 16], while extra photon radiation from final-
state particles is simulated with the PHOTOS [17] pack-
age.
Large samples of signal
e
+
e
K
0
S
K
±
π
π
0
γ
and
K
0
S
K
±
π
ηγ
events are generated with this program,
as well as samples of events from the principal ISR
background sources,
e
+
e
K
0
S
K
±
π
γ
and
e
+
e
K
0
S
K
±
π
π
0
π
0
γ
. The
K
0
S
K
±
π
γ
generator is tuned to
reproduce our measured [10]
E
c
.
m
.
dependence and res-
onant 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 distributions observed in the data,
and we study the effect of resonances on the efficiency in
each case below. In addition to the ISR sources, back-
ground arises from the non-ISR processes
e
+
e
q
q
and
τ
+
τ
. These events are simulated with the JETSET [18]
and KORALB [19] event generators, respectively. All
simulated events are processed through a detector simu-
lation based on the GEANT4 [20] package and are ana-
lyzed in the same manner as the data.
III. EVENT SELECTION AND KINEMATICS
We require events to contain at least three photon can-
didates and at least four charged tracks, including at least
one
K
0
S
π
+
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 eval-
uated in the
e
+
e
c.m. frame. To reduce background
from machine-induced soft photons, at least one addi-
tional photon candidate must have
E
>
100 MeV and
another
E
>
60 MeV. We calculate the invariant mass
6
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
+
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
+
π
de-
cay 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 their reconstructed total
momentum and the line joining their vertex with the pri-
mary vertex position must satisfy cos(
θ
K
0
S
)
>
0
.
99.
Each of these events is subjected to a set of 5-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
+
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
.
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 5-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 simula
ted
signal and
q
q
background events, respectively, normalized as
described in the text. The signal and control regions are in-
dicated.
IV. THE
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
+
e
K
0
S
K
±
π
π
0
γ
events is shown in Fig. 1, after subtrac-
tion 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 con-
tributions 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 Section 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.
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
+
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).
Figure 2(a) compares the
γγ
invariant-mass distribu-
tion of the
π
0
candidate for data events in the signal
region with the prediction of the signal-event simulation.
The
π
0
peak in the simulation is shifted with respect to
the data by
0
.
6
±
0.2 MeV/c
2
, while the standard devia-
tions are consistent with each other (
σ
DATA
= 6
.
65
±
0
.
14
MeV/c
2
and
σ
MC
= 6
.
70
±
0
.
12 MeV/c
2
).
The corresponding distributions of the
π
+
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
= 2
.
40
±
0
.
03 MeV/c
2
and
σ
MC
= 2
.
30
±
0
.
03 MeV/c
2
. Our selec-
7
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.
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 back-
grounds evaluated from ISR and
q
q
events, respectively.
Cross sections for backgrounds from
q
q
processes are
poorly known. In simulation, the dominant such process
is
e
+
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 combined with another photon in the event. Follow-
ing 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 sub-
tracted.
The remaining background arises from ISR processes,
dominated by
e
+
e
K
0
S
K
±
π
γ
events combined with
random photons, and by
e
+
e
K
0
S
K
±
π
π
0
π
0
γ
events.
These have broad distributions in
χ
2
, and can be esti-
mated 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
dis-
tributions of Fig. 1. Assuming good signal simulation
and low ISR backround 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
back-
ground 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
back-
ground also has a 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 ob-
tain the simulated distribution shown as the histogram
in Fig. 4. This demonstrates sufficient understanding
of the shape of the background distribution, and we as-
sume that all remaining background has the simulated
shape. The genuine signal and the ISR background in
0
20
40
60
0
10
20
30
40
50
60
70
80
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
+
e
K
0
S
K
±
π
γ
and
e
+
e
K
0
S
K
±
π
π
0
π
0
γ
(open histogram) described in the
text.
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 sub-
traction 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
=
α
= 6
.
59
±
0
.
24, and from the ISR
background simulation
N
1
B
/N
2
B
=
β
= 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
=
α
·
N
1
β
·
N
2
α
β
,
(2)
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
= 6430
±
90, where the uncertainty is
8
statistical. The systematic uncertainty in the
q
q
back-
ground estimate is taken to be 50%, to account for the
limited knowledge of the
q
q
cross section. The system-
atic uncertainty in the ISR background estimate is, more
conservatively, taken to be 100%. The total system-
atic 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 efficien-
cies for charged-track, photon, and
K
0
S
reconstruction de-
pend 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
detection efficiency from the simulation, including the
K
0
S
π
+
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
+
e
ωγ
π
+
π
π
0
γ
events, yield-
ing 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 +2
±
1%, independent of
E
c
.
m
.
. Similarly, we incor-
porate corrections to the charged-track and
K
0
S
recon-
struction efficiencies making use of the results found in
our previous studies of
e
+
e
π
+
π
π
+
π
γ
[23] and
e
+
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
+0
.
8
±
1
.
0% for each of the
π
±
and
K
±
, and +1
.
1
±
1
.
0%
for the
K
0
S
, are derived, again independent of
E
c
.
m
.
. Sim-
ilar corrections to the pion and kaon identification effi-
ciencies 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 +3
.
7
±
4
.
6%.
As a cross-check, using a fast simulation of the detec-
tor response for computational simplicity, we compare
the 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, specifi-
cally
e
+
e
K
(892)
±
K
0
S
π
and
K
0
K
±
π
. No differ-
ence in efficiency larger than 0.5% is seen, and we assign a
systematic uncertainty of 0.5% to account both for possi-
ble model dependence and for the choice of parametriza-
tion of the efficiency as a function of
E
c
.
m
.
. These cor-
rections and uncertainties are listed in Table I. The total
correction is +8.6%
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
+
e
K
0
S
K
±
π
π
0
events as a function of the hadronic invariant mass
E
c
.
m
.
=
m
(
K
0
S
K
±
π
π
0
). The solid curve shows a fitted parametriza-
tion.
C. The cross section for
e
+
e
K
0
S
K
±
π
π
0
The
e
+
e
K
0
S
K
±
π
π
0
cross section is obtained
from:
σ
(
E
c
.
m
.
) =
dN
K
0
S
K
±
π
π
0
(
E
c
.
m
.
)
d
L
(
E
c
.
m
.
)
ε
(
E
c
.
m
.
)
R
(
E
c
.
m
.
)
,
(3)
where
E
c
.
m
.
is the invariant mass of the
K
0
S
K
±
π
π
0
sys-
tem,
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
(
E
c
.
m
.
) is the differential
luminosity,
ε
(
E
c
.
m
.
) is the corrected efficiency discussed
in Section IV B, and
R
(
E
c
.
m
.
) is the correction to ac-
count for additional soft radiative photon emission from
the initial state.
The differential luminosity
d
L
(
m
) is calculated using
the total PEP-II integrated luminosity
L
= 454 fb
1
and
the probability density function for ISR photon emission.
To first order it can be written as:
d
L
dm
=
α
πx
(
(2
2
x
+
x
2
) log
1 +
C
1
C
x
2
C
)
2
m
s
L
.
(4)
Here
m
=
m
(
K
0
S
K
±
π
π
0
),
x
= 1
m
2
/s
,
C
= cos
θ
0
,
and
θ
0
defines the acceptance of the analysis in the polar
angle of the ISR photon in the
e
+
e
c.m. frame,
θ
0
<
θ
γ
<
180
o
θ
0
. Here,
θ
0
= 20
o
.
The radiative correction
R
(
E
c
.
m
.
) 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 de-
termine
R
= 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
+
e
K
0
S
K
±
π
π
0
cross section
is shown in Fig. 6 and listed in Table II, with statistical
9
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.
TABLE I: Summary of the corrections to, and systematic un-
certainties in the
e
+
e
K
0
S
K
±
π
π
0
cross section.
Source
Correction Systematic
(%)
uncertainty (%)
π
0
reconstruction
+2.0
1.0
K
±
,
π
±
reconstruction
+1.6
2.0
K
0
S
reconstruction
+1.1
1.0
PID efficiency
0.0
2.0
χ
2
selection
+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 Rad.Corr.
1.4
Total
+8.6
6.3,
<
2.0 GeV
7.1, 2.0-3.0 GeV
11.5,
>
3.0 GeV
0
1
2
3
1
1.5
2
2.5
3
3.5
4
E
c.m.
(GeV)
σ
(nb)
FIG. 6: Cross section for the process
e
+
e
K
0
S
K
±
π
π
0
.
The uncertainties are statistical.
D. Substructure in the
K
0
S
K
±
π
π
0
final state
Previously, we studied single
K
(892) production in
the processes
e
+
e
K
0
S
K
±
π
and
K
+
K
π
0
[10], and
double
K
(892) production, as well as
φ
,
ρ
, and
f
0
pro-
duction, in
e
+
e
K
+
K
π
+
π
,
K
+
K
π
0
π
0
[8] and
K
0
S
K
0
L
π
+
π
[9]. Here, we expect single
K
(892), double
K
(892),
ρ
, and possibly other resonance contributions,
but the statistical precision of the data sample is insuf-
ficient for competitive measurements of such processes.
Since it is important to confirm, as far as possible, reso-
nant cross sections measured in different final states, and
to verify expected isospin relations, we perform a simple
study of those resonant subprocesses accessible with our
data.
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
+
e
K
0
S
K
±
π
π
0
events.
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 scat-
ter plot of the
K
0
S
π
0
vs.
K
±
π
invariant masses in the
selected data sample, corrected for backgrounds as de-
scribed above, while Fig. 7(b) shows the
K
±
π
0
vs.
K
0
S
π
masses. Clear signals for charged and neutral
K
(892)
0
states are seen. Figure 8(a) is the projection of Fig. 7(a)
onto the vertical axis, and shows a large
K
(892)
0
peak
as well as possible structure near 1.43 GeV
/c
2
. This could
arise from the
K
2
(1430) or
K
0
(1430) 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 non-resonant (NR) component. The
K
(892)
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 nomi-
nal values [21] for
K
2
(1430) or
K
0
(1430). The narrower
K
2
(1430) 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
(892)
0
K
±
π
events and
85
±
24
K
2
(1430)
K
±
π
events, where the uncertain-
ties 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
(892)
K
±
π
events
are produced through the
K
0
(892)
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
(892)
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
(892)
K
0
(892) subtraction,
10
TABLE II: Measurements of the
e
+
e
K
0
S
K
±
π
π
0
cross section versus
E
c
.
m
.
=
m
(
K
0
S
K
±
π
π
0
). The uncertainties are
statistical only; systematic uncertainties are given in Ta
ble I.
E
c.m.
σ
E
c.m.
σ
E
c.m.
σ
E
c.m.
σ
E
c.m.
σ
(GeV)
(nb)
(GeV)
(nb)
(GeV)
(nb)
(GeV)
(nb)
(GeV)
(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
yields 454
±
60
K
(892)
0
K
0
S
π
0
and 20
±
25
K
2
(1430)
K
0
S
π
0
events, respectively.
Corresponding fits to the projections of Fig. 7(b),
shown in Figs.
8(c) and 8(d), followed by
K
(892)
+
K
(892)
subtraction, yield 1173
±
64
K
(892)
±
K
π
0
events, 157
±
50
K
(892)
±
K
0
S
π
events, 187
±
25
K
2
(1430)
K
π
0
events, and 141
±
27
K
2
(1430)
K
0
S
π
events. The uncertainties are statistical
only; systematic uncertainties are discussed below.
Repeating these fits in 0.2 GeV bins of
E
c
.
m
.
, and us-
ing Eq. (3), we extract the cross sections for the pro-
cesses
e
+
e
K
(892)
0
K
±
π
,
K
(892)
0
K
0
S
π
0
,
and
e
+
e
K
(892)
0
K
0
S
π
0
,
K
(892)
0
K
±
π
shown
in Fig. 9(a), as well as for the processes
e
+
e
K
(892)
±
K
0
S
π
,
K
(892)
±
K
±
π
0
and
e
+
e
K
(892)
±
K
π
0
,
K
(892)
±
K
0
S
π
shown in Fig. 9(b).
They are similar in size and shape, except that the
K
0
K
0
S
π
0
cross section is a factor of 2 – 3 lower.
Accounting for the
K
(892) branching fractions, the
K
(892)
0
K
±
π
and
K
(892)
±
K
π
0
cross sections are
consistent with those we measured previously [8] in the
K
+
K
π
+
π
and
K
+
K
π
0
π
0
final states, respectively,
and the
K
(892)
±
K
0
S
π
cross section is consistent with
our previous measurement [9] in the
K
0
S
K
0
S
π
+
π
final
state.
We investigate the correlated production of
K
0
and
K
0
directly by repeating the fit of the
K
±
π
invariant
mass distribution in 0.05 GeV
/c
2
bins of the
K
0
S
π
0
in-
variant mass. The resulting numbers of
K
(892)
0
decays
in each bin are shown in Fig. 10(a), and there is a sub-
stantial peak near 892 MeV
/c
2
. Fitting these points with
the same NR function plus a single BW function yields
138
±
16
e
+
e
K
0
K
0
events. Similarly, fitting the
K
0
S
π
±
invariant-mass distribution in bins of the
K
±
π
0
invariant mass yields the results for
K
(892)
±
decays
shown in Fig. 10(b), and a single-resonance plus NR fit to
those results yields 814
±
36
e
+
e
K
(892)
+
K
(892)
events. Repeating this procedure in 0.2 GeV
/c
2
bins
of
E
c
.
m
.
, and applying Eq. (3) provides the cross sec-
tions for
e
+
e
K
0
K
0
K
0
S
K
±
π
π
0
and
e
+
e
K
(892)
±
K
(892)
K
0
S
K
±
π
π
0
shown in Figs. 9(a)
and 9(b), respectively.
The
K
(892)
+
K
(892)
intermediate state dominates
both
K
(892)
±
K
0
S
π
and
K
(892)
±
K
π
0
production,
whereas the
K
0
K
0
intermediate state (Fig. 9(a)) pro-
vides a significant fraction of
K
(892)
0
produc-
tion only near 2.1 GeV. Accounting for the
K
(892)
branching fractions, the
K
(892)
+
K
(892)
cross sec-
tion is consistent with our previous measurement [8]
in the
K
+
K
π
0
π
0
final state, where it also dominated
K
(892)
±
K
π
0
production, and the
K
0
K
0
cross sec-
tion is consistent with our previous measurement [8] in
the
K
+
K
π
+
π
final state, where it also represented
only a small fraction of
K
(892)
0
K
+
π
and
K
0
K
π
+
production.
Figure 11(a) shows the distribution of the
π
±
π
0