Cross sections for the reactions $e^+ e^-\to K^0_S K^0_L\pi^0$, $K^0_S K^0_L\eta$, and $K^0_S K^0_L\pi^0\pi^0$ from events with initial-state radiation

0.55 MB·

by  The BABAR Collaboration

BABAR-PUB-16/004
SLAC-PUB-16918
Cross sections for the reactions e+e− → K0K0π0, K0K0η, and K0K0π0π0 from
S L S L S L
events with 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-Vieux, France
E. Grauges
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
7
1
0 A. Palano
2 INFN Sezione di Bari and Dipartimento di Fisica, Universit`a di Bari, I-70126 Bari, Italy

n
a G. Eigen
J University of Bergen, Institute of Physics, N-5007 Bergen, Norway

8
2 D. N. Brown and Yu. G. Kolomensky
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA

]
x
e M. Fritsch, H. Koch, and T. Schroeder
- Ruhr Universita¨t Bochum, Institut fu¨r Experimentalphysik 1, D-44780 Bochum, Germany
p
e
h C. Heartyab, T. S. Mattisonb, J. A. McKennab, and R. Y. Sob
[ Institute of Particle Physicsa; University of British Columbiab,

Vancouver, British Columbia, Canada V6T 1Z1
1
v
V. E. Blinovabc, A. R. Buzykaeva, V. P. Druzhininab, V. B. Golubevab, E. A. Kravchenkoab,
7
9 A. P. Onuchinabc, S. I. Serednyakovab, Yu. I. Skovpenab, E. P. Solodovab, and K. Yu. Todyshevab
2 Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090a,
8 Novosibirsk State University, Novosibirsk 630090b,
0 Novosibirsk State Technical University, Novosibirsk 630092c, Russia
.
1
0 A. J. Lankford
7 University of California at Irvine, Irvine, California 92697, USA
1
:
v J. W. Gary and O. Long
i University of California at Riverside, Riverside, California 92521, USA
X
r A. M. Eisner, W. S. Lockman, and W. Panduro Vazquez
a
University of California at Santa Cruz, Institute for Particle 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. Ro¨hrken
California Institute of Technology, Pasadena, California 91125, USA
Z. Huard, B. T. Meadows, B. G. Pushpawela, M. D. Sokoloff, and L. Sun∗
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. Bettonia, C. Bozzia, R. Calabreseab, G. Cibinettoab, E. Fioravantiab, I. Garziaab, E. Luppiab, and V. Santoroa
INFN Sezione di Ferraraa; Dipartimento di Fisica e Scienze della Terra, Universita` di Ferrarab, 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, Italy
S. Passaggio and C. Patrignani†
INFN Sezione di Genova, I-16146 Genova, Italy
H. M. Lacker
Humboldt-Universita¨t zu Berlin, Institut fu¨r 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, Kingdom 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, California 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 Kingdom
G. Cowan
University of London, Royal Holloway and Bedford New College, 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. Schubert
Johannes Gutenberg-Universit¨at Mainz, Institut fu¨r Kernphysik, D-55099 Mainz, Germany
R. J. Barlow§ and G. D. Lafferty
University of Manchester, Manchester M13 9PL, United Kingdom
R. Cenci, A. Jawahery, and D. A. Roberts
University of Maryland, College Park, Maryland 20742, USA
R. Cowan
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
3
S. H. Robertson
Institute of Particle Physics and McGill University, Montr´eal, Qu´ebec, Canada H3A 2T8
B. Deya, N. Neria, and F. Palomboab
INFN Sezione di Milanoa; Dipartimento di Fisica, Universita` di Milanob, 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,
Universita` di Napoli Federico II, I-80126 Napoli, Italy
G. Raven
NIKHEF, National Institute for Nuclear Physics and High Energy 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. Gaza, M. Margoniab, M. Posoccoa, G. Simiab, F. Simonettoab, and R. Stroiliab
INFN Sezione di Padovaa; Dipartimento di Fisica, Universita` di Padovab, I-35131 Padova, Italy
S. Akar, E. Ben-Haim, M. Bomben, G. R. Bonneaud, G. Calderini, J. Chauveau, 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. Biasiniab, E. Manonia, and A. Rossia
INFN Sezione di Perugiaa; Dipartimento di Fisica, Universita` di Perugiab, I-06123 Perugia, Italy
G. Batignaniab, S. Bettariniab, M. Carpinelliab,∗∗ G. Casarosaab, M. Chrzaszcza, F. Fortiab,
M. A. Giorgiab, A. Lusianiac, B. Oberhofab, E. Paoloniab, M. Ramaa, G. Rizzoab, and J. J. Walsha
INFN Sezione di Pisaa; Dipartimento di Fisica, Universita` di Pisab; Scuola Normale Superiore di Pisac, I-56127 Pisa, Italy
A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
F. Anullia, R. Facciniab, F. Ferrarottoa, F. Ferroniab, A. Pilloniab, and G. Pireddaa‡
INFN Sezione di Romaa; Dipartimento di Fisica,
Universita` di Roma La Sapienzab, I-00185 Roma, Italy
C. Bu¨nger, S. Dittrich, O. Gru¨nberg, M. Heß, T. Leddig, C. Voß, and R. Waldi
Universita¨t Rostock, D-18051 Rostock, Germany
T. Adye and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
S. Emery and G. Vasseur
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
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. Luitz, D. B. MacFarlane,
4
D. R. Muller, H. Neal, B. N. Ratcliff, A. Roodman, M. K. Sullivan, J. Va’vra, and W. J. Wisniewski
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
M. V. Purohit and J. R. Wilson
University of South Carolina, Columbia, South Carolina 29208, 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 Aviv, 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. Bianchiab, F. De Moriab, A. Filippia, and D. Gambaab
INFN Sezione di Torinoa; Dipartimento di Fisica, Universita` di Torinob, I-10125 Torino, Italy
L. Lanceri and L. Vitale
INFN Sezione di Trieste and Dipartimento di Fisica, Universita` di Trieste, I-34127 Trieste, Italy
F. Martinez-Vidal and A. Oyanguren
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
J. Albertb, A. Beaulieub, F. U. Bernlochnerb, G. J. Kingb, R. Kowalewskib,
T. Lueckb, I. M. Nugentb, J. M. Roneyb, R. J. Sobieab, and N. Tasneemb
Institute of Particle Physicsa; University of Victoriab, 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
We study the processes e+e− → K0K0π0γ, K0K0ηγ, and K0K0π0π0γ, where the photon is
S L S L S L
radiated from the initial state, providing cross section measurements for the hadronic final states
overacontinuumofcenter-of-massenergies. Theresultsarebasedon469 fb−1 ofdatacollected at
orneartheΥ(4S) resonancewiththeBABARdetectoratSLAC.Wepresentthefirstmeasurements
of the e+e− → K0K0π0, K0K0η, and K0K0π0π0 cross sections up to a center-of-mass energy of
S L S L S L
4 GeV, and study their intermediate resonance structures. We observe J/ψ decays to all of these
finalstatesforthefirsttime,presentmeasurementsoftheirJ/ψ branchingfractions, andsearch for
ψ(2S) decays.
PACSnumbers: 13.66.Bc,14.40.-n,13.25.Jx
∗Nowat: WuhanUniversity,Wuhan43072,China
†Now at: Universit`a di Bologna and INFN Sezione di Bologna,
5
e+e− → γK0K0π0π0 processes, which are forbidden by
S S
C-parity conservation, and we see no indication of them
I. INTRODUCTION at the level of single background events. Together with
our previous measurements [8, 11, 16], these results pro-
Electron-positronannihilationeventswithinitial-state vide a much more complete understanding of the KKπ,
radiation (ISR) can be used to study processes over a KKη and KKππ final states in e+e− annihilation.
widerangeofenergiesbelowthenominale+e− center-of-
mass (c.m.) energy (Ec.m.), as demonstrated in Ref. [1].
The possibility of exploiting ISR to make precise mea-
surementsoflow-energycrosssectionsathigh-luminosity
φ and B factories is discussed in Refs. [2–4], and mo- II. THE BABAR DETECTOR AND DATA SET
tivates the studies described in this paper. Such mea-
surements are of particular current interest because of a
three-standard-deviation discrepancy between the mea- The data used in this analysis were collected with the
sured value of the muon anomalous magnetic moment BABAR detector at the PEP-II asymmetric-energy e+e−
(g −2) and that computed in the Standard Model [5], storage ring. The total integrated luminosity used is
whµerethehadronicloopcontributionsrequireexperimen- 468.6 fb−1 [17], which includes data collected at the
tal e+e− annihilation crosssections as input. The calcu- Υ(4S) resonance (424.7 fb−1) and at a c.m. energy
lation is most sensitive to the low-energy region, where 40 MeV below this resonance (43.9 fb−1).
the inclusive hadronic cross section cannot be measured The BABAR detector is described in detail else-
reliably,andasumofexclusivestatesmustbe used. Not where [18]. Charged particles are reconstructed using
all accessible states have been measured yet, and new the BABAR tracking system, which comprises the silicon
measurements will improve the reliability of the calcu- vertex tracker (SVT) and the drift chamber (DCH) in-
lation. In addition, studies of ISR events at B facto- side the 1.5 T solenoid. Separation of pions and kaons
ries provide information on resonance spectroscopy for is accomplished by means of the detector of internally
masses up through the charmonium region. reflected Cherenkov light (DIRC) and energy-loss mea-
StudiesoftheISRprocessese+e− →µ+µ−γ [6,7]and surements in the SVT and DCH. The hard ISR photon,
e+e− →Xhγ, where Xh represents any of several exclu- photons from π0 and η decays, and K0 are detected in
sivemultihadronfinalstates,usingdataoftheBABARex- the electromagnetic calorimeter (EMCL). Muon identifi-
periment at SLAC, have been reported previously. The cation,providedby the instrumentedflux return,isused
Xhstudiedsofarinclude: chargedhadronpairsπ+π−[7], to select the µ+µ−γ final state.
K+K−[8],andpp[9];fourorsixchargedmesons[10–12];
chargedmesonsplus oneortwoπ0 mesons[11–14]; a K0 To study the detector acceptance and efficiency, we
S havedevelopedaspecialpackageofsimulationprograms
plus charged and neutral mesons [15]; and the first ISR
measurement from BABAR that includes K0 mesons [16]. for radiative processes based on the approach suggested
L by Ku¨hn and Czyz˙ [19]. Multiple collinear soft-photon
Together, they demonstrate good detector efficiency for
emissionfromtheinitial e+e− stateis implementedwith
eventsofthiskind,andwellunderstoodtracking,particle
identification, and π0, K0 and K0 reconstruction. thestructure-functiontechnique[20,21],whileadditional
S L photon radiation from the final-state particles is simu-
Inthis paperwereportmeasurementsofthe K0K0π0,
S L lated using the PHOTOS package [22]. The precision of
K0K0η, and K0K0π0π0 final states, produced in con-
S L S L the radiative simulation contributes less than 1% to the
junction with a hard photon that is assumed to result
uncertainty of the measured hadronic cross sections.
from ISR. Candidate K0 mesons are reconstructed in
S
the π+π− decay mode, candidate π0 and η mesons are In addition to the signal channels K0K0π0, K0K0η,
S L S L
reconstructed in the γγ decay mode, and K0 mesons and K0K0π0π0, we simulate ISR processes which result
L S L
are detected via their nuclear interactions in the elec- inhighbackgrounds,K0K0,K0K±π∓,andK0K±π∓π0,
S L S S
tromagnetic calorimeter. For these final states, we mea- with cross sections and mass dependences based on our
sure cross sections from threshold to Ec.m. = 4 GeV, previousmeasurementsandisospinrelations. TheKS0KL0
studytheir internalstructure,performthe firstmeasure- and K0K0η channels are dominated by e+e− →γφ and
S L
ments of J/ψ branching fractions, and search for ψ(2S) γφη,respectively. Samplesofthreetofivetimesthenum-
decays. We also search for the e+e− → γK0K0π0 and ber of expected events are generated for each final state
S S
and processed through the detector response simulation
[23]. Theseeventsarethenreconstructedusingthe same
software chain as the data.
I-47921Rimini,Italy We also simulate several non-ISR backgrounds, in-
‡Deceased cluding e+e− → qq (q = u,d,s,c) events using the
§Nowat: UniversityofHuddersfield,HuddersfieldHD13DH,UK Jetset7.4 [24] generator, and e+e− → τ+τ− events us-
¶Now at: University of South Alabama, Mobile, Alabama 36688,
ing the KORALB [25] generator. Variations in detector
USA
∗∗Alsoat: Universit`adiSassari,I-07100Sassari,Italy and background conditions are taken into account.
6
3 cm along the axis from the nominal interaction point.
2
c
V/105 Any number of additional tracks and EMC clusters is
e allowed. We consider all clusters with reconstructed en-
G
7 ergy above 0.1 GeV as photon candidates, and calculate
0 the invariant mass of each pair. Every pair with a mass
0
0 within 30 (50) MeV/c2 of the nominal π0 (η) mass is
/0. considered a π0 (η) candidate. The efficiency of π0 and
s
t
n η reconstruction in these events is about 97%.
ve104 The decay length of the K0 meson is large, and the
E L
probability to detect a K0 decay in the DCH is low. In-
L
stead,welookforaclusterintheEMCresultingfromthe
interactionof a K0 with a nucleus in the EMC material.
L
Such clusters are indistinguishable from photon-induced
clusters,andgivepoorresolutionontheK0 energy. The
L
103 characteristics of these clusters were studied in detail in
our previous publication [16], where it was shown using
e+e− → φγ events that K0 clusters are detected with
0.47 0.48 0.49 0.5 0.51 0.52 L
m(π+π-) GeV/c2 highefficiency andgoodangularresolution. Background
from low-energy clusters is high, and the requirement of
FIG. 1: The π+π− invariant mass distribution for the se- at least 0.2 GeV in cluster energy yields a clean sample
lectedK0 candidatesinthedata(points)andsimulation(his- with 48% efficiency. Here, we apply the same energy re-
S
togram). The vertical lines indicate thesignal region. quirement, and use the efficiency and angular resolution
measured as a function of polar and azimuthal angles in
Ref. [16].
III. EVENT SELECTION AND
RECONSTRUCTION IV. THE KINEMATIC FIT PROCEDURE
We begin with events containing at least two charged EacheventselectedasdescribedinSec.IIIissubjected
particles and at least four clusters of energy deposits to a set of constrained kinematic fits, in which the four-
in contiguous crystals in the EMC. We then consider momentaandcovariancematricesoftheinitiale+e−,the
the cluster in the event with the highest energy in the ISRphoton,thebestK0 candidate,andzero,twoorfour
e+e− c.m. frame as the ISR photon candidate, and re- relevant photon candidSates are taken into account. The
quire Ecγ.m. > 3 GeV. Since the ISR photons are pro- direction and angular resolution, but not the energy, of
ducedmostlyalongthebeamline,thisacceptsonlyabout the K0 candidate is also used, and the K0 momentum
L L
10% of the signal events, but in the selected events, the is determined in the fit. The three-momentum vectors
hadronic system is fully contained and can be studied for all other particles, including the photons, are also
reliably. determined with better accuracy from the fits, and the
In these events, we reconstruct candidate K0 decays fitted values are used in further calculations.
S
to two charged pions from pairs of oppositely charged For every event, we first perform kinematic fits under
tracksnot identified as electrons. They must havea well the K0K0γ hypothesis, considering the ISR photon and
S L
reconstructed vertex between 0.1 and 40.0 cm in radial K0 candidates, along with each cluster with energy over
S
distance from the beam axis, and their total momentum 0.2 GeVinturnastheK0 candidate. Eachfithas3con-
L
must be consistent with the assumption that they origi- straints, and we consider the combination with the best
nate from the interaction region. The m(π+π−) invari- χ2 value, denoted χ2(K0K0). This variable is useful in
S L
ant mass distribution for these K0 candidates is shown suppressing the large background arising from combina-
S
in Fig. 1 for both data (points) and the e+e− → γφ → tions of background photons with a mass near the π0 or
γK0K0 simulation(histogram). Thesignalisveryclean, η mass.
S L
and requiring 482 < m(π+π−) < 512 MeV/c2 (vertical Next, we consider each π0 and η candidate, and per-
lines in Fig. 1) accepts 98% of the signal events. We use formasetoffitstotheK0K0π0γ andK0K0ηγ hypothe-
S L S L
the sidebands 472–482 and 512–522 MeV/c2 to estimate sis,includingtheISRphoton,K0,andtwophotoncandi-
S
the contributions from non-K0 backgrounds, which are dates, along with each K0 candidate not included in the
S L
found to be negligible in all cases after final selection. π0 or η candidate. These fits have four constraints, in-
A few thousand events (about 1% of the total) have cludingoneontheπ0 orηcandidatemass. Weretainthe
more than one selected K0 candidate, and we use only π0K0 andηK0 candidatecombinationsyieldingthe best
S L L
the candidate with m(π+π−) closest to the nominal [26] values of χ2(K0K0π0) and χ2(K0K0η), respectively.
S L S L
K0 mass. We also require the event to contain no other Similarly, for events with six or more clusters, we con-
S
tracksthatextrapolatewithin2cmofthebeamaxisand sidereachpairofnon-overlappingπ0candidates,andper-
7
form a set of five-constraint fits under the K0K0π0π0γ 4C χ2 distributions due to higher-order ISR, which is
S L
hypothesis. Both π0 masses are constrained, and we re- present in both data and simulation, but not taken into
taintheπ0π0K0 candidatecombinationyieldingthelow- account in the fit. The reliability of the simulated dis-
L
est value of χ2(K0K0π0π0). tributionhasbeendemonstratedinourpreviousstudies,
S L
Finally, we perform similar fits for all the other sim- and is discussed below. In the figure, the simulated sig-
ulated signal and background processes discussed in nal distribution is normalized to the data in the region
Sec.II,givingusadditionalχ2 variablesthatcanbeused χ2(K0K0π0)<3,wherethecontributionofhigher-order
S L
to select (or suppress) these processes. ISRissmallandthebackgroundcontaminationislowest,
but still amounts to about 5% of the signal. The differ-
ence between the two distributions at high values gives
V
e an indication of the level of background.
G We define a signal region χ2(K0K0π0) < 25 and a
x S L
a control region 25 < χ2(K0K0π0) < 50 (vertical lines in
m S L
γ 2 10 Fig. 3(a)), from which we estimate backgrounds in the
E
signal region. The signal region contains 5441 data and
3402signal-MCevents, while the controlregioncontains
2733 and 632 events, respectively.
1 B. Background subtraction
Weestimate knownISRbackgroundsfromsimulation,
and normalize the simulated non-ISR background us-
ing the π0 peak, as described in Ref. [16]. The largest
1
backgrounds we can evaluate in this way are shown in
0 Fig. 3(a): the shaded, cross-hatched, and hatched ar-
0 0.1 0.2 0.3
m GeV/c2 eas represent the simulated backgrounds from non-ISR
γγ qq¯, ISR K0K0(φ), and ISR φη events, respectively. The
S L
FIG. 2: Two-dimensional distribution of the higher clus- shapes of these three distributions are consistent with
ter energy in a photon-candidate pair vs. the corresponding each other and quite distinct from that expected for
diphotonmassmγγ forallpairsofEMCclustersinKS0KL0π0γ signal events. However, these backgrounds account for
eventscontainingneither theISR photon,theK0 candidate,
L less than half of the observed difference between data
nor either photon in the π0 candidate. and simulation at large χ2 values. We assume the re-
maining background is from other ISR processes, with
a χ2(K0K0π0) distribution similar in shape to those
S L
shown.
To obtain any distribution of the K0K0π0 signal
V. THE K0K0π0 FINAL STATE S L
S L events, we use the control region to estimate the sum
of all backgrounds, following the procedure described in
A. Additional selection criteria detailinRef.[16]. Ineachbinofthedistributioninques-
tion, the background contribution is estimated as the
For the K0K0π0 final state, a few additional selec- difference between the numbers of data and signal-MC
S L
tion criteria are applied. Considering all pairs of EMC events in the control region (see Fig. 3(a)), normalized
clustersnotassignedtotheISRphoton,π0,orK0 candi- to the corresponding difference in the signal region.
L
dates,weobservealargesignalfromextraπ0’s,shownin The K0K0π0 invariant mass distribution of events in
S L
Fig.2. Itisespeciallystrongwhenoneoftheclustershas the signal region is shown in Fig. 3(b) as the points.
highenergy,sowerequireEmax <0.5 GeV. Thisreduces The shaded, cross-hatched, and hatched areas represent
γ
backgrounds from several sources with a loss of 3% in the same simulated backgrounds as in Fig. 3(a). The
simulatedsignalefficiency. However,manyISRφγevents sum of all backgrounds, estimated from the control re-
with a false π0, formed by accidential photons, remain. gion, is shown as the open histogram in Fig. 3(b), and
To reduce this background, we require χ2(K0K0) > 15 the extracted mass distribution for e+e− → K0K0π0
S L S L
if the fitted K0K0 invariant mass m(K0K0) is smaller signal events is shown as the filled points in Fig. 3(c).
S L S L
than 1.04 GeV/c2. We observe 3669 events in the mass range from thresh-
The 4C χ2 distribution for the remaining events un- old to 4.0 GeV/c2. In addition to a main peak around
der the K0K0π0γ hypothesis is shown as the points in 1.8 GeV/c2, a J/ψ signal is visible.
S L
Fig. 3(a), with the corresponding distribution for MC- Thisprocedurereliesongoodagreementbetweendata
simulated pure K0K0π0γ events shown as the open his- and simulation in the χ2(K0K0π0) distribution. Con-
S L S L
togram. Both distributions are broader than typical sidering our previous studies of χ2 distributions [16],
8
2χ 2c 2c
nit eV/400 eV/400
u G G
nts/ 05 05
ve 0. 0.300
E102 ents/300 ents/
v v
E E
200
200
100
100
10
0 0
0 10 20 30 40 50 60 70 1 2 3 4 1 2 3 4
χ2(K K π0) m(K K π0) (GeV/c2) m(K K π0) (GeV/c2)
S L S L S L
FIG.3: (a)Thefour-constraintχ2 distributionsfordata(points)andMC-simulatedK0K0π0γ events(openhistogram). The
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shaded, cross-hatched, and hatched areas represent the simulated backgrounds from non-ISR qq¯, ISR φ, and ISR φη events,
respectively. (b) The K0K0π0 invariant mass distribution for data events in the signal region (points). The shaded, cross-
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hatched, and hatched areas represent the simulated contributions from non-ISR qq¯, ISR φ, and ISR φη events, respectively,
while theopen histogram representsthetotal background estimated from thecontrol region. (c) The K0K0π0 invariant mass
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distribution after background subtraction (points). The open circles represent the contribution from the resonant process
e+e− →K∗(892)0K0+c.c.→K0K0π0 (see text).
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along with simulation and normalization statistics, we C. Detection efficiency
estimatetherelativesystematicuncertaintyontheback-
ground to be 30%. This results in an uncertainty
The selection procedures applied to the data are also
on the background-subtracted signal of about 10% for
m(K0K0π0) < 2.2 GeV/c2, increasing roughly linearly applied to the MC-simulated event sample. The result-
withSmaLss to about 40% at 3.2 GeV/c2 and above. ing distribution of the reconstructed KS0KL0π0 invariant
mass is shown in Fig. 4(a) for events with χ2(K0K0π0)
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in the signal (open histogram) and control (hatched) re-
gions. Thereconstructionefficiencyasafunctionofmass
2
c is obtained by dividing the number of reconstructedMC
/
V300 events in each 50 MeV/c2 mass interval by the number
e
G generated in that interval, and is shown in Fig. 4(b).
5 200 The effects of detector resolution, about 25 MeV/c2, are
0
0. included in this efficiency. Below 1.5 GeV/c2 the effi-
/100
ts ciency becomes very large, due to the rapidly changing
n
ve 0 crosssectionnearthreshold. Sincethe resolutionismea-
E 1 2 3 4 sured from the data and the shape of the threshold rise
m(K K π0) (GeV/c2)
S L is well simulated, we apply no correction. Nevertheless,
2 the backgrounds and the resolution-effect uncertainties
c0.08
V/ arehighinthisregion,sowedonotquoteacrosssection
Ge0.06 measurement below 1.4 GeV/c2, and we assign an addi-
5 tional 50% (30%) relative systematic uncertainty for the
0.00.04 mass bin at 1.425(1.475) GeV/c2.
f./0.02 Thisefficiencyiscorrectedforthedata-MCdifferences
f
E 0 evaluatedinourpreviousstudies. TheISRphotondetec-
1 2 3 4 tion efficiency has been studied using µ+µ−γ events [7],
m(K K π0) (GeV/c2)
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FIG. 4: (a) The reconstructed KS0KL0π0 invariant mass dis- ically −1.5±0.5% to the simulated efficiency. The KS0
tribution for MC-simulated signal events in the signal (open detection efficiency has been studied very carefully at
histogram) and control (hatched) regions of Fig. 3(a). (b) BABAR, with data-MC differences in the efficiency deter-
The net reconstruction efficiency from thesimulation. mined asa function ofthe K0 directionandmomentum.
S
We apply a correction event by event, which introduces
anoverallcorrectionof+1.1±1.0%totheefficiency. The
π0 reconstruction efficiency has been studied in BABAR
usingωγ andωπ0γ events,andthecorrectionisfoundto
9
be (−3±1)%. The K0 detection requires a (−6.1±0.6)% bybackgroundcontributions,andamountstoabout10%
L
correction [16]. In total, there is a (−9.5±1.6)% correc- near the peak of the cross section (1.7 GeV), increasing
tion; this systematic uncertainty is small compared with roughly lineary with decreasing cross section to about
that due to the backgrounds, described above. 30% in the 2.5–3 GeV region, always similar in size to
the statistical uncertainty. Above the J/ψ mass, statis-
tics dominate the ∼40% systematic uncertainty.
)
b
n
(
0) 3 2 2
π c c
L / /
K V V
S e e
K G G
σ( 3 3 600
2 .0600 .0
0 0
/ /
s s
t t
n n
e e
v v
E E400
400
1
200
200
0
1 2 3 4
E (GeV)
c.m.
FIG.5: Thee+e− →K0K0π0 cross section. Theerrorbars
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0 0
are statistical only. 1 2 1 2
m(K π0) (GeV/c2) m(K π0) (GeV/c2)
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FIG.6: Thebackground-subtracted(a)K0π0 and(b)K0π0
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invariantmassdistributionsine+e− →K0K0π0 events. The
D. The e+e− →KS0KL0π0 cross section curves represent the results of the fits desScriLbed in the text,
withthehatchedareasrepresentingthenon-resonantcompo-
The cross section for e+e− annihilation into K0K0π0 nents.
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is calculated from
σ(KS0KL0π0)(Ec.m.)= dLd(NEKc.Sm0K.)L0·πǫ0(γE(Ec.cm.m.).)·R, (1)
where Ec.m. ≡ m(KS0KL0π0); dNKS0KL0π0γ is the number E. The K∗(892)0 and K2∗(1430)0 contributions
ofselected,background-subtractedK0K0π0eventsinthe
interval dEc.m.; ǫ(Ec.m.) =ǫMC(Ec.m.S)·L(1+δcorr) is the Figure6showsthedistributionsofthefittedKS0π0and
simulateddetection efficiency correctedfor data-MCdif- K0π0invariantmassesintheselectedK0K0π0events,af-
L S L
ferences, as described above. The radiative correction R ter backgroundsubtraction. Clear signals corresponding
is unity within 1%, with an estimated precisionof about to the K∗(892)0 resonance are visible, as well as indica-
1%. ThedifferentialISRluminositydL(Ec.m.)associated tions of K2∗(1430)0 production.
with the interval dEc.m. centered at an effective collision We fit these distributions with a sum of two inco-
energy of Ec.m. is calculated using the leading order for- herent Breit-Wigner functions and a function describ-
mula(see,forexample,Ref.[13]),andthesystematicun- ing the non-resonant contribution, yielding 1750 ± 84
certaintyassociatedwiththeluminositydeterminationis K∗(892)0 →K0π0 decays, 1795±56 K∗(892)0 →K0π0
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estimated to be 0.5%. decays, and a total of 145±54 K∗(1430)0 decays. The
2
The cross section is shown as a function of energy in sumoftheseK∗0decaysisconsistentwiththetotalnum-
Fig. 5, and listed in Table I. There are no previous mea- ber of K0K0π0 events, indicating that the process is
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surements for this final state. We do not quote the cross dominated by K∗0K0+c.c., and mostly K∗(892)0K0+
section from threshold (1.13 GeV) to 1.4 GeV, where it c.c., production.
shows a sharp rise to a maximum value of about 3 nb Indeed, if we perform fits similar to those shown in
near 1.7 GeV, presumably dominated by the φ(1680) Fig. 6 for events in each 0.05 GeV/c2 interval of the
resonance, and a slow decrease toward higher energies, K0K0π0 invariant mass, and sum the K∗(892)0K0 and
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perturbed by the J/ψ signal. Only statistical uncertain- K∗(892)0K0 yields, we obtain the K0K0π0 mass distri-
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ties areshown. The systematicuncertaintyis dominated butionshowninFig.3(c)bythe opencircles. Theerrors
10
TABLE I: Summaryof thee+e− →K K π0 cross section measurement. Uncertainties are statistical only.
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E (GeV) σ (nb) E (GeV) σ (nb) E (GeV) σ (nb) E (GeV) σ (nb)
c.m. c.m. c.m. c.m.
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
are statistical only, and the difference between the num-
b
berofK0K0π0 eventsandtheK∗(892)0K0 contribution n
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,
ineachbinislessthanthesystematicuncertaintydueto )
0
π
the background subtraction procedure.
φ
(
σ
2c 0.2
/
V
e
G

4
0 40
0
.
0
/
s 0.1
t
n
e
v
E
20
0
1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8
E , GeV
c.m.
FIG.8: Thee+e− →φπ0crosssectionfromthiswork(dots)
compared with that obtained in the K+K−π0 channel [15]
0 (circles). The error bars are statistical only.
1 1.025 1.05 1.075 1.1
2
m(K K ) (GeV/c )
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FIG. 7: The K0K0 invariant mass distribution in selected
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K0K0π0 events (dots), and the background estimated from but not in the background. A fit with a Gaussian plus
thSecoLntrolregion(hatchedhistogram)ofFig.3(a). Thesolid polynomial function yields a total of 29±9 φ → KS0KL0
line represents theresult of thefit described in the text. decays in K0K0π0 events.
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Fitting the m(K0K0) distribution in 0.1 GeV/c2 bins
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of the K0K0π0 mass, we obtain a φπ0 invariant mass
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spectrum for the K0K0π0 final state. Using Eq. 1 and
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the φ → K0K0 branching fraction [26], we calculate a
F. The φ(1020)π0 contribution cross sectionSfoLr this intermediate state, shown in Fig. 8
(dots) and listed in Table II. Only statistical uncertain-
Figure 7 shows the distribution ofthe fitted K0K0 in- ties are shown. The systematic uncertainties of 10–30%
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variantmassfortheselectedK0K0π0eventsbeforeback- relativeinthismassrangearesmallerthanthestatistical
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ground subtraction (dots), along with the background uncertainties.
(histogram) estimated from the χ2(K0K0π0) control re- The results are consistent with those observed in our
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gion. A φ(1020) signal is visible in the K0K0π0 signal, previous study of the K+K−π0 final state [15], also
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