arXiv:1810.11962v2 [hep-ex] 10 Dec 2018 · BABAR-PUB-18/008 SLAC-PUB-17344 Study of the reactions...

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B A B AR-PUB-18/008 SLAC-PUB-17344 Study of the reactions e + e - π + π - π 0 π 0 π 0 and π + π - π 0 π 0 η at center-of-mass energies from threshold to 4.35 GeV 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-Vieux, 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 California, Berkeley, California 94720, USA M. Fritsch, H. Koch, and T. Schroeder Ruhr Universit¨ at Bochum, Institut f¨ ur Experimentalphysik 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. Kozyrev ab , E. A. Kravchenko 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 630090 a , Novosibirsk State University, Novosibirsk 630090 b , Novosibirsk State Technical University, Novosibirsk 630092 c , Russia A. J. Lankford University of California at Irvine, Irvine, California 92697, USA J. W. Gary and O. Long University of California at Riverside, Riverside, California 92521, USA A. M. Eisner, W. S. Lockman, and W. Panduro Vazquez 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, Y. Li, 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. 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 arXiv:1810.11962v2 [hep-ex] 10 Dec 2018

Transcript of arXiv:1810.11962v2 [hep-ex] 10 Dec 2018 · BABAR-PUB-18/008 SLAC-PUB-17344 Study of the reactions...

Page 1: arXiv:1810.11962v2 [hep-ex] 10 Dec 2018 · BABAR-PUB-18/008 SLAC-PUB-17344 Study of the reactions e+e !ˇ+ˇ ˇ0ˇ0ˇ0 and ˇ+ˇ ˇ0ˇ0 at center-of-mass energies from threshold to

BABAR-PUB-18/008SLAC-PUB-17344

Study of the reactions e+e− → π+π−π0π0π0 and π+π−π0π0η at center-of-massenergies from threshold to 4.35 GeV using initial-state radiation

J. P. Lees, V. Poireau, and V. TisserandLaboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),

Universite de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France

E. GraugesUniversitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain

A. PalanoINFN Sezione di Bari and Dipartimento di Fisica, Universita di Bari, I-70126 Bari, Italy

G. EigenUniversity of Bergen, Institute of Physics, N-5007 Bergen, Norway

D. N. Brown and Yu. G. KolomenskyLawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA

M. Fritsch, H. Koch, and T. SchroederRuhr Universitat Bochum, Institut fur Experimentalphysik 1, D-44780 Bochum, Germany

C. Heartyab, T. S. Mattisonb, J. A. McKennab, and R. Y. Sob

Institute of Particle Physics a; University of British Columbiab,Vancouver, British Columbia, Canada V6T 1Z1

V. E. Blinovabc, A. R. Buzykaeva, V. P. Druzhininab, V. B. Golubevab, E. A. Kozyrevab, E. A. Kravchenkoab,

A. P. Onuchinabc, S. I. Serednyakovab, Yu. I. Skovpenab, E. P. Solodovab, and K. Yu. Todyshevab

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090a,Novosibirsk State University, Novosibirsk 630090b,

Novosibirsk State Technical University, Novosibirsk 630092c, Russia

A. J. LankfordUniversity of California at Irvine, Irvine, California 92697, USA

J. W. Gary and O. LongUniversity of California at Riverside, Riverside, California 92521, USA

A. M. Eisner, W. S. Lockman, and W. Panduro VazquezUniversity 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,

Y. Li, T. S. Miyashita, P. Ongmongkolkul, F. C. Porter, and M. RohrkenCalifornia 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. WagnerUniversity of Colorado, Boulder, Colorado 80309, USA

D. Bernard and M. VerderiLaboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France

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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. ZalloINFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy

S. Passaggio and C. Patrignani†

INFN Sezione di Genova, I-16146 Genova, Italy

H. M. LackerHumboldt-Universitat zu Berlin, Institut fur Physik, D-12489 Berlin, Germany

B. BhuyanIndian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India

U. MallikUniversity of Iowa, Iowa City, Iowa 52242, USA

C. Chen, J. Cochran, and S. PrellIowa State University, Ames, Iowa 50011, USA

A. V. GritsanJohns Hopkins University, Baltimore, Maryland 21218, USA

N. Arnaud, M. Davier, F. Le Diberder, A. M. Lutz, and G. WormserLaboratoire de l’Accelerateur Lineaire, IN2P3/CNRS et Universite Paris-Sud 11,

Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France

D. J. Lange and D. M. WrightLawrence Livermore National Laboratory, Livermore, California 94550, USA

J. P. Coleman, E. Gabathuler,‡ D. E. Hutchcroft, D. J. Payne, and C. TouramanisUniversity of Liverpool, Liverpool L69 7ZE, United Kingdom

A. J. Bevan, F. Di Lodovico, and R. SaccoQueen Mary, University of London, London, E1 4NS, United Kingdom

G. CowanUniversity of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom

Sw. Banerjee, D. N. Brown, and C. L. DavisUniversity of Louisville, Louisville, Kentucky 40292, USA

A. G. Denig, W. Gradl, K. Griessinger, A. Hafner, and K. R. SchubertJohannes Gutenberg-Universitat Mainz, Institut fur Kernphysik, D-55099 Mainz, Germany

R. J. Barlow§ and G. D. LaffertyUniversity of Manchester, Manchester M13 9PL, United Kingdom

R. Cenci, A. Jawahery, and D. A. RobertsUniversity of Maryland, College Park, Maryland 20742, USA

R. CowanMassachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA

S. H. Robertsonab and R. M. Seddonb

Institute of Particle Physics a; McGill Universityb, Montreal, Quebec, Canada H3A 2T8

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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. SummersUniversity of Mississippi, University, Mississippi 38677, USA

P. TarasUniversite de Montreal, Physique des Particules, Montreal, Quebec, Canada H3C 3J7

G. De Nardo and C. SciaccaINFN Sezione di Napoli and Dipartimento di Scienze Fisiche,

Universita di Napoli Federico II, I-80126 Napoli, Italy

G. RavenNIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands

C. P. Jessop and J. M. LoSeccoUniversity of Notre Dame, Notre Dame, Indiana 46556, USA

K. Honscheid and R. KassOhio 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. OcarizLaboratoire de Physique Nucleaire et de Hautes Energies,IN2P3/CNRS, Universite Pierre et Marie Curie-Paris6,Universite 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, J. J. Walsha, and L. Zaniab

INFN Sezione di Pisaa; Dipartimento di Fisica, Universita di Pisab; Scuola Normale Superiore di Pisac, I-56127 Pisa, Italy

A. J. S. SmithPrinceton University, Princeton, New Jersey 08544, USA

F. Anullia, R. Facciniab, F. Ferrarottoa, F. Ferronia,†† A. Pilloniab, and G. Pireddaa‡

INFN Sezione di Romaa; Dipartimento di Fisica,Universita di Roma La Sapienzab, I-00185 Roma, Italy

C. Bunger, S. Dittrich, O. Grunberg, M. Heß, T. Leddig, C. Voß, and R. WaldiUniversitat Rostock, D-18051 Rostock, Germany

T. Adye and F. F. WilsonRutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom

S. Emery and G. VasseurCEA, 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,

D. R. Muller, H. Neal, B. N. Ratcliff, A. Roodman, M. K. Sullivan, J. Va’vra, and W. J. WisniewskiSLAC National Accelerator Laboratory, Stanford, California 94309 USA

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M. V. Purohit and J. R. WilsonUniversity of South Carolina, Columbia, South Carolina 29208, USA

A. Randle-Conde and S. J. SekulaSouthern Methodist University, Dallas, Texas 75275, USA

H. AhmedSt. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5

M. Bellis, P. R. Burchat, and E. M. T. PuccioStanford University, Stanford, California 94305, USA

M. S. Alam and J. A. ErnstState University of New York, Albany, New York 12222, USA

R. Gorodeisky, N. Guttman, D. R. Peimer, and A. SofferTel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel

S. M. SpanierUniversity of Tennessee, Knoxville, Tennessee 37996, USA

J. L. Ritchie and R. F. SchwittersUniversity of Texas at Austin, Austin, Texas 78712, USA

J. M. Izen and X. C. LouUniversity 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. VitaleINFN Sezione di Trieste and Dipartimento di Fisica, Universita di Trieste, I-34127 Trieste, Italy

F. Martinez-Vidal and A. OyangurenIFIC, 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 Physics a; University of Victoriab, Victoria, British Columbia, Canada V8W 3P6

T. J. Gershon, P. F. Harrison, and T. E. LathamDepartment of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

R. Prepost and S. L. WuUniversity of Wisconsin, Madison, Wisconsin 53706, USA

We study the processes e+e− → π+π−π0π0π0γ and π+π−π0π0ηγ in which an energetic photonis radiated from the initial state. The data were collected with the BABAR detector at SLAC.About 14 000 and 4700 events, respectively, are selected from a data sample corresponding to anintegrated luminosity of 469 fb−1. The invariant mass of the hadronic final state defines the effectivee+e− center-of-mass energy. From the mass spectra, the first precise measurement of the e+e− →π+π−π0π0π0 cross section and the first measurement ever of the e+e− → π+π−π0π0η cross sectionare performed. The center-of-mass energies range from threshold to 4.35 GeV. The systematicuncertainty is typically between 10 and 13%. The contributions from ωπ0π0, ηπ+π−, and otherintermediate states are presented. We observe the J/ψ and ψ(2S) in most of these final states andmeasure the corresponding branching fractions, many of them for the first time.

PACS numbers: 13.66.Bc, 14.40.Cs, 13.25.Gv, 13.25.Jx, 13.20.Jf

∗Now at: Wuhan University, Wuhan 430072, China †Now at: Universita di Bologna and INFN Sezione di Bologna,

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I. INTRODUCTION

Electron-positron annihilation events with initial-stateradiation (ISR) can be used to study processes over awide range of energies below the nominal e+e− center-of-mass (c.m.) energy (Ec.m.), as proposed in Ref. [1]. Thepossibility of exploiting ISR to make precise measure-ments of low-energy cross sections at high-luminosity φand B factories is discussed in Refs. [2–4], and motivatesthe studies described in this paper. Such measurementsare of particular interest because of a ∼3.5 standard-deviation discrepancy between the measured value of themuon anomalous magnetic moment (gµ−2) and the Stan-dard Model value [5], where the Standard Model calcu-lation requires input from experimental e+e− hadroniccross section data in order to account for hadronic vac-uum polarization (HVP) terms. The calculation is mostsensitive to the low-energy region, where the inclusivehadronic cross section cannot be measured reliably and asum of exclusive states must be used. Not all accessiblestates have yet been measured, and new measurementswill improve the reliability of the calculation. In addi-tion, studies of ISR events at B factories are interestingin their own right, because they provide information onresonance spectroscopy for masses up to the charmoniumregion.

Studies of the ISR processes e+e− → µ+µ−γ [6, 7]and e+e− → Xhγ, using data from the BABAR experi-ment at SLAC, have been previously reported. Here Xh

represents any of several exclusive hadronic final states.The Xh studied to date include: charged hadron pairsπ+π− [7], K+K− [8], and pp [9]; four or six chargedmesons [10–12]; charged mesons plus one or two π0

mesons [11–15]; a K0S meson plus charged and neutral

mesons [16]; and channels with K0L mesons [17]. The

ISR events are characterized by good reconstruction ef-ficiency and by well understood kinematics (see for ex-ample Ref. [13]), tracking, particle identification, and π0,K0

S , and K0L reconstruction, demonstrated in above ref-

erences.

This paper reports analyses of the π+π−3π0 andπ+π−2π0η final states produced in conjunction with ahard photon, assumed to result from ISR. While BABARdata are available at effective c.m. energies up to 10.58GeV, the present analysis is restricted to energies below4.35 GeV because of backgrounds from Υ (4S) decays.As part of the analysis, we search for and observe in-

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: Universita di Sassari, I-07100 Sassari, Italy††Also at: Gran Sasso Science Institute, I-67100 LAquila, Italy

termediate states, including the η, ω, ρ, a0(980), anda1(1260) resonances. A clear J/ψ signal is observed forboth the π+π−3π0 and π+π−2π0η channels, and the cor-responding J/ψ branching fractions are measured. Thedecay ψ(2S)→ π+π−π0π0π0 is observed and its branch-ing fraction is measured.

Previous measurements of the e+e− → π+π−π0π0π0

cross section were reported by the M3N [18] andMEA [19] experiments, but with very limited preci-sion, leading to a large uncertainty in the correspond-ing HVP contribution. The BABAR experiment pre-viously measured the e+e− → ηπ+π− reaction in theη → π+π−π0 [14] and η → γγ [20] decay channels. Be-low, we present the measurement of e+e− → ηπ+π−

with η → π0π0π0: this process contributes to e+e− →π+π−π0π0π0. There are no previous results for e+e− →π+π−π0π0η.

II. THE BABAR DETECTOR AND DATASET

The data used in this analysis were collected with theBABAR detector at the PEP-II asymmetric-energy e+e−

storage ring. The total integrated luminosity used is468.6 fb−1 [21], which includes data collected at theΥ (4S) resonance (424.7 fb−1) and at a c.m. energy40 MeV below this resonance (43.9 fb−1).

The BABAR detector is described in detail else-where [22]. Charged particles are reconstructed using theBABAR tracking system, which is comprised of the siliconvertex tracker (SVT) and the drift chamber (DCH), bothlocated inside the 1.5 T solenoid. Separation of pions andkaons is accomplished by means of the detector of inter-nally reflected Cherenkov light (DIRC) and energy-lossmeasurements in the SVT and DCH. Photons and K0

L

mesons are detected in the electromagnetic calorimeter(EMC). Muon identification is provided by the instru-mented flux return.

To evaluate the detector acceptance and efficiency, wehave developed a special package of Monte Carlo (MC)simulation programs for radiative processes based on theapproach of Kuhn and Czyz [23]. Multiple collinear soft-photon emission from the initial e+e− state is imple-mented with the structure function technique [24, 25],while additional photon radiation from final-state parti-cles is simulated using the PHOTOS package [26]. Theprecision of the radiative simulation is such that it con-tributes less than 1% to the uncertainty in the measuredhadronic cross sections.

We simulate e+e− → π+π−π0π0π0γ events assumingproduction through the ω(782)π0π0 and ηρ(770) inter-mediate channels, with decay of the ω to three pions anddecay of the η to all its measured decay modes [27]. Thetwo neutral pions in the ωπ0π0 system are in an S-wavestate and are described by a combination of phase spaceand f0(980) → π0π0, based on our study of the ωπ+π−

state [14]. The simulation of e+e− → π+π−π0π0ηγevents is similarly based on two production channels: a

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phase space model, and a model with an ωπ0η interme-diate state with a π0η S-wave system.

A sample of 100-200k simulated events is generated foreach signal reaction and processed through the detectorresponse simulation, based on the GEANT4 package [28].These events are reconstructed using the same softwarechain as the data. Variations in detector and backgroundconditions are taken into account.

For the purpose of background estimation, large sam-ples of events from the main relevant ISR processes(2πγ, 3πγ, 4πγ, 5πγ, 2Kπγ, and π+π−π0π0γ) are sim-ulated. To evaluate the background from the relevantnon-ISR processes, namely e+e− → qq (q = u, d, s) ande+e− → τ+τ−, simulated samples with integrated lumi-nosities about twice that of the data are generated usingthe jetset [29] and koralb [30] programs, respectively.The cross sections for the above processes are known withan accuracy slightly better than 10%, which is sufficientfor the present purposes.

20 40 60 80 100 120 140

6C2χ

0

0.1

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0.72),

GeV

/cγγ

m(

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.72), GeV/cγγm(

0

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400

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700

800

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2E

vent

s/0.

0025

GeV

/c

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FIG. 1: (a) The invariant mass m(γγ) of the third photon pairvs χ2

2π2π0γγ . (b) The m(γγ) distribution for χ22π2π0γγ < 60

and with additional selection criteria applied as described inthe text.

III. EVENT SELECTION AND KINEMATIC FIT

A relatively clean sample of π+π−3π0γ andπ+π−2π0ηγ events is selected by requiring thatthere be two tracks reconstructed in the DCH, SVT, orboth, and seven or more photons, with an energy above

1 1.5 2 2.5 3 3.5 42), GeV/cγγ0π2πm(2

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m(

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FIG. 2: (a) The third-photon-pair invariant mass m(γγ) vsm(2π2π0γγ) for (a) χ2

2π2π0γγ < 60 and (b) 60 < χ22π2π0γγ <

120.

0.02 GeV, in the EMC. We assume the photon with thehighest energy to be the ISR photon, and we require itsc.m. energy to be larger than 3 GeV.

We allow either exactly two or exactly three tracks inan event, but only two that extrapolate to within 0.25 cmof the beam axis and 3.0 cm of the nominal collision pointalong that axis. The reason a third track is allowed is tocapture a relatively small fraction of signal events thatcontain a background track. The two tracks that satisfythe extrapolation criteria are fit to a vertex, which is usedas the point of origin in the calculation of the photondirections.

We subject each candidate event to a set of constrainedkinematic fits and use the fit results, along with charged-particle identification, to select the final states of inter-est and evaluate backgrounds from other processes. Thekinematic fits make use of the four-momenta and covari-ance matrices of the initial e+, e−, and the set of selectedtracks and photons. The fitted three-momenta of eachtrack and photon are then used in further kinematicalcalculations.

Excluding the photon with the highest c.m. energy,which is assumed to arise from ISR, six other photonsare combined into three pairs. For each set of six pho-tons, there are 15 independent combinations of photonpairs. We retain those combinations in which the dipho-ton mass of at least two pairs lies within 35 MeV/c2 of theπ0 mass mπ0 . The selected combinations are subjected toa fit in which the diphoton masses of the two pairs with

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|m(γγ)−mπ0 | < 35 MeV/c2 are constrained to mπ0 . Incombination with the constraints due to four-momentumconservation, there are thus six constraints (6C) in the fit.The photons in the remaining (“third”) pair are treatedas being independent. If all three photon pairs in thecombination satisfy |m(γγ) − mπ0 | < 35 MeV/c2, wetest all possible combinations, allowing each of the threediphoton pairs in turn to be the third pair, i.e., the pairwithout the mπ0 constraint.

The above procedure allows us not only to search forevents with π0 → γγ in the third photon pair, but alsofor events with η → γγ.

The 6C fit is performed under the signal hypothesise+e− → π+π−π0π0γγγISR. The combination with thesmallest χ2 is retained, along with the obtained χ2

2π2π0γγvalue and the fitted three-momenta of each track andphoton. Each selected event is also subjected to a 6C fitunder the e+e− → π+π−π0π0γISR background hypoth-esis, and the χ2

2π2π0 value is retained. The π+π−π0π0

process has a larger cross section than the π+π−3π0 sig-nal process and can contribute to the background whentwo background photons are present. Most events con-tain additional soft photons due to machine backgroundor interactions in the detector material.

IV. THE π+π−3π0 FINAL STATE

A. Additional selection criteria

The results of the 6C fit to events with two tracks andat least seven photon candidates are used to perform thefinal selection of the five-pion sample. We require thetracks to lie within the fiducial region of the DCH (0.45-2.40 radians) and to be inconsistent with being a kaon ormuon. The photon candidates are required to lie withinthe fiducial region of the EMC (0.35-2.40 radians) andto have an energy larger than 0.035 GeV. A requirementthat there be no charged tracks within 1 radian of theISR photon reduces the τ+τ− background to a negligiblelevel. A requirement that any extra photons in an eventeach have an energy below 0.7 GeV slightly reduces themulti-photon background.

Figure 1 (a) shows the invariant mass m(γγ) of thethird photon pair vs χ2

2π2π0γγ . Clear π0 and η peaks are

visible at small χ2 values. We require χ22π2π0γγ < 60

for the signal hypothesis and χ22π2π0 > 30 for the 2π2π0

background hypothesis. This requirement reduces thecontamination due to 2π2π0 events from 30% to about1-2% while reducing the signal efficiency by only 5%.

Figure 1 (b) shows the m(γγ) distribution after theabove requirements have been applied. The dip in thisdistribution at the π0 mass value is a consequence of thekinematic fit constraint of the best two photon pairs tothe π0 mass. Also, because of this constraint, the thirdphoton pair is sometimes formed from photon candidatesthat are less well measured.

Figure 2 shows the m(γγ) distribution vs the invari-ant mass m(2π2π0γγ) for events (a) in the signal regionχ22π2π0γγ < 60 and (b) in a control region defined by 60 <

χ22π2π0γγ < 120. Events from the e+e− → π+π−π0π0π0

and π+π−2π0η processes are clearly seen in the signalregion, as well as J/ψ decays to these final states. In thecontrol region no significant structures are seen and weuse these events to evaluate background.

Our strategy to extract the signals for the e+e− →π+π−π0π0π0 and π+π−π0π0η processes is to perform afit for the π0 and η yields in intervals of 0.05 GeV/c2

in the distribution of the π+π−2π0γγ invariant massm(π+π−2π0γγ).

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events of (a) the third-photon-pair invariant mass m(γγ), and(b) m(γγ) vs m(π+π−2π0γγ).

B. Detection efficiency

As mentioned in Sec. II, the model used in the MCsimulation assumes that the five-pion final state resultspredominantly from ωπ0π0 and ηπ+π− production, withω decays to three pions and η decays to all modes. Asshown below, these two final states dominate the ob-served cross section.

The selection procedure applied to the data is alsoapplied to the MC-simulated events. Figures 3 and 4show (a) the m(γγ) distribution and (b) the distributionof m(γγ) vs m(2π2π0γγ) for the simulated ηπ+π− andωπ0π0 events, respectively. The π0 peak is not Gaus-

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events of (a) the third-photon-pair invariant mass m(γγ), and(b) m(γγ) vs m(π+π−2π0γγ).

sian in either reaction and is broader for ηπ+π− eventsthan for ωπ0π0 events because the photon energies arelower. Background photons are included in the simula-tion. Thus these distributions include simulation of thecombinatoric background that arises when backgroundphotons are combined with photons from the signal re-actions.

The combinatoric background is subtracted using thedata from the χ2 control region. The method is illus-trated using simulation in Fig. 5, which shows the m(γγ)distribution with a bin width of 0.02 GeV/c2. The dashedhistograms show the simulated combinatoric background.The solid histograms show the simulated results from thesignal region after subtraction of the simulated combina-toric background. The sum of three Gaussian functionswith a common mean is used to describe the π0 signalshape. The fitted fit function is shown by the smoothcurve in Fig. 5. We perform a fit of the π0 signal in every0.05 GeV/c2 interval in the m(2π2π0γγ) invariant massfor the two different simulated channels.

Alternatively, for the ηπ+π− events, we determine thenumber of events vs the m(2π2π0γγ) invariant mass byfitting the η signal from the η → π0π0π0 decay: thesimulated background-subtracted distribution is shownin Fig. 6(a). The fit function is again the sum of threeGaussian functions with a common mean.

Similarly, as an alternative for the ωπ0π0 events, theω mass peak can be used. The ω mass peak in simula-

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FIG. 5: The background subtracted MC-simulated m(γγ)distribution for (a) e+e− → ηπ+π− and (b) e+e− → ωπ0π0

events. The dashed histogram shows the simulated distribu-tion from the χ2 control region, used for subtraction. The fitfunction is described in the text.

tion is shown in Fig. 6(b), with three entries per event.We obtain the number of events by fitting m(π+π−π0)in 0.05 GeV/c2 intervals of the m(π+π−2π0γγ) invariantmass. A Breit-Wigner (BW) function, convoluted witha Gaussian distribution to account for the detector reso-lution, is used to describe the ω signal. A second-orderpolynomial is used to describe the background.

The mass-dependent detection efficiency is obtainedby dividing the number of fitted MC events in each0.05 GeV/c2 mass interval by the number generated inthe same interval. Although the signal simulation ac-counts for all η decay modes, the efficiency calculationconsiders the signal η → π0π0π0 decay mode only. Thisefficiency estimate takes into account the geometrical ac-ceptance of the detector for the final-state photons andthe charged pions, the inefficiency of the detector sub-systems, and the event loss due to additional soft-photonemission from the initial and final states. Correctionsthat account for data-MC differences are discussed be-low.

The mass-dependent efficiencies from the π0 fit areshown in Fig. 7 by points for the ηπ+π− and by squaresfor the ωπ0π0 intermediate states, respectively. The ef-ficiencies determined from the η and ω fits are shown inFig. 7 by the triangles and upside-down triangles, respec-tively. These results are very similar to those obtainedfrom the π0 fits.

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invariant mass for the e+e− → ηπ+π− events. The dasheddistribution is from the simulated χ2 control region, used forbackground subtraction. (b) The π+π−π0 invariant mass forthe MC-simulated e+e− → ωπ0π0 events (three entries perevent). The solid curve shows the fit function used to ob-tain number of signal events. The dashed curve shows the fitfunction for the combinatorial background.

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FIG. 7: The energy-dependent reconstruction efficiency fore+e− → π+π−π0π0π0 events, determined using four differentmethods: see text. The curve shows the results of a fit to theaverage values, which is used in the cross section calculation.

From Fig. 7 it is seen that the reconstruction efficiencyis about 4%, roughly independent of mass. By comparingthe results of the four different methods used to evaluatethe efficiency, we conclude that the overall acceptancedoes not change by more than 5% because of variationsof the functions used to extract the number of events or

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FIG. 8: (a) The third-photon-pair invariant mass m(γγ) fordata in the signal (solid) and χ2 control (dashed) regions.The dotted histogram shows the estimated background frome+e− → π+π−π0π0. (b) The m(γγ) invariant mass for dataafter background subtraction. The curves are the fit resultsas described in the text.

the use of different models. This value is taken as anestimate of the systematic uncertainty in the acceptanceassociated with the simulation model used and with thefit procedure. We average the four efficiencies in each0.05 GeV/c2 mass interval and fit the result with a thirdorder polynomial function, shown in Fig. 7. The resultof this fit is used for the cross section calculation.

C. Number of π+π−3π0 events

The solid histogram in Fig. 8 (a) shows the m(γγ) dataof Fig. 1 (b) binned in mass interval of 0.02 GeV/c2. Thedashed histogram shows the distribution of data from theχ2 control region. The dotted histogram is the estimatedremaining background from the e+e− → π+π−π0π0 pro-cess. No evidence for a peaking background is seen ineither of the two background distributions. We subtractthe background evaluated using the χ2 control region.The resulting m(γγ) distribution is shown in Fig. 8 (b).

We fit the data of Fig. 8 (b) with a combination ofa signal function, taken from simulation, and a back-ground function, taken to be a third-order polynomial.The fit is performed in the m(γγ) mass range from 0.0to 0.5 GeV/c2. The result of the fit is shown by the solidand dashed curves in Fig. 8 (b). In total 14 390 ± 182

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events are obtained. Note that this number includes arelatively small peaking background component, due toqq events, which is discussed in Sect. IV D. The same fit isapplied to the corresponding m(γγ) distribution in each0.05 GeV/c2 interval in the π+π−2π0γγ invariant mass.The resulting number of π+π−3π0 event candidates as afunction of m(π+π−3π0), including the peaking qq back-ground, is shown by the data points in Fig. 9.

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FIG. 9: The invariant mass distribution of π+π−3π0 events,obtained from the fit to the π0 mass peak. The contributionfrom non-ISR uds background is shown by squares.

D. Peaking background

The major background producing a π0 peak follow-ing application of the selection criteria of Sect. IV.A isfrom non-ISR qq events, the most important channel be-ing e+e− → π+π−π0π0π0π0 in which one of the neutralpions decays asymmetrically, yielding a high energy pho-ton that mimics an ISR photon. Figure 10 (a) shows thethird-photon-pair invariant mass vs m(π+π−π0π0γγ) forthe non-ISR light quark qq (uds) simulation: clear signalsfrom π0 and η are seen. Figure 10(b) shows the projec-tion plots for χ2

2π2π0γγ < 60 and 60 < χ22π2π0γγ < 120.

To normalize the uds simulation, we calculate thediphoton invariant mass distribution of the ISR candi-date with all the remaining photons in the event. A π0

peak is observed, with approximately the same numberof events in data and simulation, leading to a normaliza-tion factor of 1.0± 0.1. The resulting uds background isshown by the squares in Fig. 9: the uds background isnegligible below 2 GeV/c2, but accounts for more thanhalf the total background for around 4 GeV/c2 and above.

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2π2π0γγ < 60 (solid histogram),

and the control region 60 < χ22π2π0γγ < 120 (dashed his-

togram).

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b0 π0 π0 π- π

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FIG. 11: The measured e+e− → π+π−π0π0π0 cross section.The uncertainties are statistical only.

E. Cross section for e+e− → π+π−π0π0π0

The e+e− → π+π−π0π0π0 Born cross section is deter-mined from

σ(2π3π0)(Ec.m.) =dN5πγ(Ec.m.)

dL(Ec.m.)εcorr5π εMC5π (Ec.m.)(1 + δR)

,

(1)

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TABLE I: Summary of the e+e− → π+π−π0π0π0 cross section measurement. The uncertainties are statistical only.

Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb1.125 0.00 ± 0.02 1.775 2.20 ± 0.23 2.425 0.92 ± 0.10 3.075 4.36 ± 0.13 3.725 0.29 ± 0.051.175 0.00 ± 0.03 1.825 2.03 ± 0.17 2.475 0.61 ± 0.09 3.125 2.66 ± 0.11 3.775 0.15 ± 0.041.225 –0.03 ± 0.05 1.875 1.65 ± 0.15 2.525 0.45 ± 0.08 3.175 0.60 ± 0.06 3.825 0.20 ± 0.041.275 0.21 ± 0.12 1.925 1.23 ± 0.15 2.575 0.71 ± 0.10 3.225 0.33 ± 0.05 3.875 0.18 ± 0.041.325 0.51 ± 0.12 1.975 1.46 ± 0.19 2.625 0.45 ± 0.08 3.275 0.31 ± 0.05 3.925 0.14 ± 0.041.375 1.17 ± 0.20 2.025 1.41 ± 0.14 2.675 0.56 ± 0.09 3.325 0.20 ± 0.05 3.975 0.22 ± 0.041.425 1.68 ± 0.15 2.075 1.42 ± 0.14 2.725 0.22 ± 0.08 3.375 0.35 ± 0.05 4.025 0.14 ± 0.041.475 2.10 ± 0.26 2.125 1.30 ± 0.12 2.775 0.40 ± 0.08 3.425 0.22 ± 0.05 4.075 0.14 ± 0.031.525 1.92 ± 0.28 2.175 1.12 ± 0.13 2.825 0.29 ± 0.08 3.475 0.19 ± 0.05 4.125 0.04 ± 0.031.575 2.49 ± 0.27 2.225 1.16 ± 0.13 2.875 0.62 ± 0.08 3.525 0.26 ± 0.05 4.175 0.08 ± 0.031.625 2.36 ± 0.27 2.275 1.03 ± 0.12 2.925 0.55 ± 0.08 3.575 0.12 ± 0.05 4.225 0.09 ± 0.031.675 2.81 ± 0.20 2.325 0.82 ± 0.11 2.975 0.60 ± 0.09 3.625 0.38 ± 0.05 4.275 0.12 ± 0.031.725 2.20 ± 0.25 2.375 0.68 ± 0.10 3.025 0.85 ± 0.10 3.675 0.41 ± 0.06 4.325 0.09 ± 0.03

where Ec.m. is the invariant mass of the five-pion system;dN5πγ is the background-subtracted number of selectedfive-pion events in the interval dEc.m., and εMC

5π (Ec.m.)is the corresponding detection efficiency from simula-tion. The factor εcorr5π accounts for the difference be-tween data and simulation in the tracking (1.0±1.0%/pertrack) [10] and π0 (3.0±1.0% per pion) [15] reconstruc-tion efficiencies. The ISR differential luminosity, dL, iscalculated using the total integrated BABAR luminosityof 469 fb−1 [13]. The initial- and final-state soft-photonemission is accounted for by the radiative correction fac-tor (1 + δR), which is close to unity for our selectioncriteria. The cross section results contain the effect ofvacuum polarization because this effect is not accountedfor in the luminosity calculation.

Our results for the e+e− → π+π−π0π0π0 cross sec-tion are shown in Fig. 11. The cross section exhibits astructure around 1.7 GeV with a peak value of about2.5 nb, followed by a monotonic decrease toward higherenergies. Because we present our data in bins of width0.050 GeV/c2, compatible with the experimental resolu-tion, we do not apply an unfolding procedure to the data.Numerical values for the cross section are presented inTable I. The J/ψ region is discussed later.

F. Summary of the systematic studies

The systematic uncertainties, presented in the previ-ous sections, are summarized in Table II, along with thecorrections that are applied to the measurements.

The three corrections applied to the cross sections sumup to 12.5%. The systematic uncertainties vary from 10%for Ec.m. < 2.5 GeV to 50% for Ec.m. > 3.5 GeV. Thelargest systematic uncertainty arises from the fitting andbackground subtraction procedures. It is estimated byvarying the background levels and the parameters of thefunctions used.

TABLE II: Summary of the systematic uncertainties in thee+e− → π+π−π0π0π0 cross section measurement.Source Correction UncertaintyLuminosity – 1%MC-data difference ISRPhoton efficiency +1.5% 1%χ2 cut uncertainty – 3%Fit and background subtraction – 7%

Ec.m. > 2.5 GeV – 20%Ec.m. > 3.5 GeV – 50%

MC-data difference in track losses +2% 2%MC-data difference in π0 losses +9% 3%Radiative corrections accuracy – 1%Acceptance from MC(model-dependent) – 5%Total (assuming no correlations) +12.5% 10%

Ec.m. > 2.5 GeV 21%Ec.m. > 3.5 GeV 50%

G. Overview of the intermediate structures

The e+e− → π+π−π0π0π0 process has a rich inter-nal substructure. To study this substructure, we restrictevents to m(γγ) < 0.35 GeV/c2, eliminating the regionpopulated by e+e− → π+π−π0π0η. We then assumethat the m(π+π−2π0γγ) invariant mass can be taken torepresent m(π+π−3π0).

Figure 12(a) shows the distribution of the π0π0π0 in-variant mass. The distribution is seen to exhibit a promi-nent η peak, which is due to the e+e− → ηπ+π− reac-tion. Figure 12(b) presents a scatter plot of the π+π−

vs the 3π0 invariant mass. From this plot, the ρ(770)ηintermediate state is seen to dominate. Figure 12(c)presents a scatter plot of the 3π0 invariant mass versusm(π+π−π0π0γγ).

The distribution of the π+π−π0 invariant mass (threeentries per event) is shown in 13(a). A prominent ω peakfrom e+e− → ωπ0π0 is seen. Some indications of φ andJ/ψ peaks are also present. The scatter plot in Fig. 13(b)shows the π0π0 vs the π+π−π0 invariant mass. A scatterplot of the π+π−π0 vs the π+π−π0π0γγ mass is shown

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FIG. 14: (a) The π+π0 (solid) and π−π0 (dashed) invariant masses (three combinations per event). (b) The π−π0 vs theπ+π0 invariant mass. (c) The π±π0 invariant mass vs the five-pion invariant mass.

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FIG. 15: (a) The 3π0 invariant mass for data. The curvesshow the fit functions. The solid curve shows the η peak(based on MC simulation) plus the non-η continuum back-ground (dashed). (b) The π+π− invariant mass for eventsselected in the η peak region. The dashed histogram showsthe continuum events in the η-peak sidebands.

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in Fig. 13(c). A clear signal for a J/ψ peak is seen.Figure 14(a) shows the π+π0(dotted) and π−π0(solid)

invariant masses (three entries per event). A prominentρ(770) peak, corresponding to e+e− → 3πρ, is visible.The scatter plot in Fig. 14(b) shows the π−π0 vs theπ+π0 invariant mass. An indication of the ρ+ρ−π0 in-termediate state is visible. Figure 14(c) shows the ππ0

invariant mass vs the five-pion invariant mass: a clearsignal for the J/ψ and an indication of the ψ(2S) areseen.

H. The ηπ+π− intermediate state

To determine the contribution of the ηπ+π− inter-mediate state, we fit the events of Fig. 12(a) using atriple-Gaussian function to describe the signal peak, as inFig. 6(a), and a polynomial to describe the background.The result of the fit is shown in Fig. 15(a). We obtain2102± 112 ηπ+π− events. The number of ηπ+π− eventsas a function of the five-pion invariant mass is determinedby performing an analogous fit of events in Fig. 12(c) in

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each 0.05 GeV/c2 interval of m(π+π−3π0). The resultingdistribution is shown in Fig. 16.

The π+π− invariant mass distribution for eventswithin ±0.7 GeV/c2 of the η peak in Fig. 15(a) is shownin Fig. 15(b). A clear signal from ρ(770) is observed,supporting the statement that the reaction is dominatedby the ρ(770)η intermediate state. The distribution ofevents from η-peak sidebands is shown by the dashedhistogram.

Using Eq. (1), we determine the cross section for thee+e− → ηπ+π− process. Our simulation takes into ac-count all η decays, so the cross section results, shownin Fig. 17(a) and listed in Table III, correspond to allη decays. Systematic uncertainties in this measurementare the same as those listed in Table II. Figure 17(b)shows our measurement in comparison to our previous re-sults [14, 20] and to those from the SND experiment [32].These previous results are based on different η decaymodes than that considered here. The different resultsare seen to agree within the uncertainties. Including theresults of the present study, we have thus now measured

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the e+e− → ηπ+π− cross section in three different η de-cay modes.

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FIG. 18: (a) The π+π−π0 invariant mass for data. Thesolid curve shows the fit function for signal (based onMC-simulation) plus the combinatorial background (dashedcurve). (b) The mass distribution of the π+π− 3π0 events inthe ω peak (circles) and estimated contribution from the ωπ0

background (squares).

I. The ωπ0π0 intermediate state

To determine the contribution of the ωπ0π0 interme-diate state, we fit the events of Fig. 13(a) using a BWfunction to model the signal and a polynomial to modelthe background. The BW function is convoluted with aGaussian distribution that accounts for the detector res-olution, as described for the fit of Fig. 6(b). The resultof the fit is shown in Fig. 18(a). We obtain 3960 ± 146ωπ0π0 events. The number of the ωπ0π0 events as afunction of the five-pion invariant mass is determined byperforming an analogous fit of events in Fig. 13(c) in each0.05 GeV/c2 interval of m(π+π−3π0). The resulting dis-tribution is shown by the circle symbols in Fig. 18(b).We do not observe a clear f0(980) → π0π0 signal in theπ0π0 invariant mass, perhaps because of a large combi-natorial background. In contrast, in our previous studyof the e+e− → ωπ+π− → π+π−π+π−π0 process [14], aclear f0(980)→ π+π− signal was seen.

For the e+e− → ωπ0π0 channel, there is a peakingbackground from e+e− → ωπ0 → π+π−π0π0. A simula-tion of this reaction with proper normalization leads to

the peaking-background estimation shown by the squaresymbols in Fig. 18(b). This background is subtractedfrom the ωπ0π0 signal candidate distribution.

The e+e− → ωπ0π0 cross section, corrected for theω → π+π−π0 branching fraction, is shown in Fig. 19 andtabulated in Table IV. The uncertainties are statisticalonly. The systematic uncertainties are about 10% forEc.m. < 2.4 GeV, as discussed in Sec. IV F. No previousmeasurement exists for this process. The cross sectionexhibits a rise at threshold, a decrease at large Ec.m.,and a clear resonance at around 1.6 GeV, possibly fromthe ω(1650). The measured e+e− → ωπ0π0 cross sectionis around a factor of two smaller than that we observedfor e+e− → ωπ+π− [14], as is expected from isospin sym-metry.

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J. The ρ(770)±π∓π0π0 intermediate state

A similar approach is followed to study events witha ρ± meson in the intermediate state. Because the ρmeson is broad, a BW function is used to describe thesignal shape. There are six ρ± entries per event, leadingto a large combinatoric background. To extract the con-tribution of the ρ±π∓π0π0 intermediate state we fit theevents in Fig. 14(a) with a BW function to describe thesignal and a polynomial to describe the background. Theparameters of the ρ resonance are taken from Ref. [27].The result of the fit is shown in Fig. 20(a). We obtain14 894± 501 ρ±π∓π0π0 events. The distribution of theseevents vs the five-pion invariant mass is shown by thesquare symbols in Fig. 21(a).

The circle symbols in Fig. 21(a) show the total numberof π+π−3π0 events, repeated from Fig. 9. It is seen thatthe number of events with a ρ± exceeds the total numberof π+π−3π0 events, implying that there is more than oneρ± per event, namely a significant production of e+e− →ρ+ρ−π0. To determine the rate of ρ+ρ−π0 events, weperform a fit to determine the number of ρ+ in intervals

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in the ρ− mass. (c) Scatter plot of the ρ±π0 invariant mass vs the π∓π0 invariant mass.

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FIG. 21: (a) Number of events in bins of Ec.m. from theηπ+π− (triangles), ωπ0π0 (upside-down triangles), and ρ →ππ0 (squares) intermediate states. The circles show the totalevent numbers obtained from the fit to the π0 peak. (b) Thecircles as are described for (a). The squares show the sums ofevent numbers with η, ω and the ρ contribution for correlatedρ+ρ− production.

of 0.04 GeV/c2 in the π−π0 distribution of Fig. 14(b).The result is shown in Fig. 20(b). Indeed, a significantρ+ peak is observed.

The number of e+e− → ρ+ρ−π0 events is determined

by fitting the data of Fig. 20(b) with the sum of aBW function and a polynomial. The sample is dividedinto three mass intervals: m(π+π−3π0) < 2.5 GeV/c2,2.5 < m(π+π−3π0) < 3.0 GeV/c2, and m(π+π−3π0) >3.0 GeV/c2. For each mass interval we determine thenumber of ρ+ events. We find that the fraction of cor-related ρ+ρ− events, relative to the total number ofπ+π−3π0 events with a ρ±, decreases with the mass inter-val as 0.49±0.05, 0.37±0.07, and 0.23±0.10, respectively,where the uncertainties are statistical. Thus, the ρ+ρ−π0

intermediate state dominates at threshold.

Intermediate states with either one or two ρ(770)are expected to be produced, at least in part, throughe+e− → ρ(1400, 1700)0π0 → a1(1260)±π∓π0 →ρ±π∓π0π0 and e+e− → ρ±a∓1 → ρ+ρ−π0, respectively.Figure 20(c) shows a scatter plot of the ρ±π0 invariantmass vs the π∓π0 invariant mass. An indication of thea1(1260) is seen, but it is not statistically significant.

K. The sum of intermediate states

Figure 21(a) shows the number of ηπ+π− (upside-down triangles), ωπ0π0 (triangles), and ρ±π∓π0π0

(square) intermediate state events, found as describedin the previous sections, in comparison to the total num-ber of π+π−3π0 events (circles) found from the fit to theπ0 mass peak. The results for the η and ω are repeatedfrom Figs. 16 and 18, respectively. As noted above, a sig-nificant excess of events with a ρ is observed. Based onthe results of our study of correlated ρ+ρ− production,we scale the number of events found from the fit to therho peak so that it corresponds to the number of eventswith either a single ρ± or with a ρ+ρ− pair. We thensum this latter result with the eta and omega curves inFig. 21(a). The result of this sum is shown by the squaresymbols in Fig. 21(b). This summed curve is seen to bein agreement with the total number of π+π−3π0 events,shown by the circular symbols.

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Note that below Ec.m. =2 GeV, the number of eventsis completely dominated by the ηπ+π− and ωπ0π0 chan-nels, so the cross section of the intermediate states witha ρ can be estimated as the difference between the totale+e− → π+π−π0π0π0 cross section and the sum of theηπ+π− and ωπ0π0 contributions.

V. THE π+π−2π0η FINAL STATE

A. Determination of the number of events

The analogous approach to that described above fore+e− → π+π−π0π0π0 events is used to study e+e− →π+π−π0π0η events. We fit the η signal in the third-photon-pair invariant mass distribution (cf., Fig. 1) withthe sum of two Gaussians with a common mean, while therelatively smooth background is described by a second-order polynomial function, as shown in Fig. 22(a). Weobtain 4700 ± 84 events. Figure 22(b) shows the massdistribution of these events.

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B. Peaking background

The major background producing an η peak is the non-ISR background, in particular e+e− → π+π−π0π0π0ηwhen one of the neutral pions decays asymmetrically,producing a photon interpreted as ISR. The η peak fromthe uds simulation is visible in Fig. 10.

To normalize the uds simulation, we form the diphotoninvariant mass distribution of the ISR candidate with allthe remaining photons in the event. Comparing the num-ber of events in the π0 peaks in data and uds simulation,we assign a scale factor of 1.5 ± 0.2 to the simulation.We fit the η peak in the uds simulation in intervals of0.05 GeV/c2 in m(π+π−π0π0γγ). The results are shownby the squares in Fig. 22 (b).

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invariant mass for simulation. The solid curve shows a two-Gaussian fit function for the ω signal plus the combinatorialbackground (dashed).

C. Detection efficiency

We use simulated e+e− → π+π−π0π0ηγ events fromthe phase space model and with the ωπ0η intermediatestate to determine the efficiency. As for the data, we fitto find the η signal in the third photon pair in intervalsof 0.05 GeV/c2 in m(π+π−π0π0γγ). The fit is illustratedin Fig. 23(a) using all π+π−π0π0γγ candidates. The effi-ciency is determined as the ratio of the number of fittedevents in each interval to the number generated in thatinterval. For the ωπ0η intermediate channel, we also de-termine the efficiency using an alternative method, byfitting the ω peak in the π+π−π0 invariant mass distri-bution, shown in Fig. 23(b).

The efficiencies obtained for the three methods areshown in Fig. 24. The circles and squares show the resultsfrom the fit to the η peak for the phase space and ωπ0ηchannels, respectively. The triangles show the results forthe fit to the ω peak. The efficiencies are calculated as-suming the η → γγ mode only. The obtained efficiencies

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are around 4%, similar to what is found for π+π−3π0

(Fig. 7). The results from the three methods are consis-tent with each other, and are averaged. The average isfit with a third-order polynomial, shown by the curve inFig. 24. The result of the fit is used for the cross sectiondetermination.

We estimate the systematic uncertainty in the effi-ciency due to the fit procedure and the model dependenceto be not more than 10%.

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D. Cross section for e+e− → π+π−π0π0η

The cross section for e+e− → π+π−π0π0η is deter-mined using Eq. (1). The results are shown in Fig. 25and listed in Table V. These are the first results for thisprocess. The systematic uncertainties and corrections arethe same as those presented in Table II except there isan increase in the uncertainty in the detection efficiency.The total systematic uncertainty for Ec.m. < 2.5 GeV is13%.

E. Overview of the intermediate structures

The π+π−2π0η final state, like that for π+π−3π0, hasa rich substructure. Figure 26(a) shows the 2π0η in-variant mass distribution for events selected by requir-ing |m(γγ) −m(η)| < 0.07 GeV/c2 in Fig. 22(a). Thereis a small but clear signal for η(1285) production. Thedotted histogram shows the background distribution, de-termined using an η sideband control region defined by0.07 < |m(γγ) − m(η)| < 0.14 GeV/c2. Figure 26(b)shows a scatter plot of the π+π− invariant mass vs the2π0η invariant mass. No structures are seen.

Figure 27(a) shows the π+π−π0 mass distribution (twoentries per event). An ω signal is clearly visible, as well asa bump close to 1 GeV/c2 corresponding to φ→ π+π−π0.The dotted histogram shows the estimate of the back-ground, evaluated using the η sideband described above.The scatter plot in Fig. 27(b) shows the π0η vs theπ+π−π0 invariant mass. A clear correlation of ω anda0(980) → π0η production is seen. Figure 27(c) showshow ωπ0η events are distributed over the π+π−2π0η in-variant mass.

Figure 28(a) presents the π+π0 (solid) and π−π0 (dot-ted) mass combinations (two entries per event) for the se-lected π+π−2π0η events. Signals from the ρ± are clearlyvisible, but they can also come from events with a ρ+ρ−

pair. The fraction of ρ+ρ− events is extracted from thedistribution in Fig. 28(b), where the π+π0 vs the π−π0

invariant mass is shown. Figure 28(c) displays the π±π0

vs the π+π−2π0η invariant mass.

F. The ωπ0η and φπ0η intermediate states

To determine the contribution of the ωπ0η and φπ0ηintermediate states, we fit the events in Fig. 27(a) withtwo Gaussian functions, one to describe the ω peak andthe other the φ peak, and a polynomial function, whichdescribes the background. The results of the fit are shownin Fig. 29(a). We obtain 1676 ± 22 and 269 ± 68 eventsfor the ω and φ, respectively. The number of events as afunction of the π+π−2π0η invariant mass is determinedby performing an analogous fit of events in Fig. 27(c) inintervals of 0.05 GeV/c2 in m(π+π−2π0η).

We select events within ±0.7 GeV/c2 of the ω peak inFig. 29(a) and display the resulting π0η invariant massin Fig. 29(b). A very clear signal from the a0(980) isobserved, while no signal is seen in an ω sideband definedby 0.07 < |m(π+π−π0)−m(ω)| < 0.14 GeV/c2.

The obtained e+e− → ωπ0η cross section, corrected forthe ω → π+π−π0 branching fraction, is shown in Fig. 30in comparison to previous results from SND [31]. TheSND results, which are available only for energies below2 GeV, are seen to lie systematically above our data.All systematic uncertainties discussed in section IV F areapplied to the measured e+e− → ωπ0η cross section,resulting in a total systematic uncertainty of 13% below2.4 GeV. The results are presented in Table VI (statistical

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FIG. 29: (a) The π+π−π0 invariant mass for data. Thedashed curve describes the non-resonant background. Thesolid curve shows the sum of the background and the fit func-tions for the ω and φ contributions, described in the text. (b)The π0η invariant mass distribution for the events selected inthe ω peak (solid). The dashed histogram shows the distri-bution from the ω-peak side band.

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uncertainties only) in bin widths of 0.05 GeV. Above 3.5GeV, the cross section measurements are consistent withzero within the experimental accuracy.

G. The ρ(770)±π∓π0η intermediate state

The approach described in Sec. IV J is used to studyevents with a ρ± meson in the intermediate state. Wefit the events in Fig. 28(a) using a BW function to de-scribe the ρ signal and a polynomial function to describethe background (four entries per event). The fit yields2908±202 ρ±π∓π0η events. The result of the fit is shownin Fig. 31(a). The distribution of these events vs theπ+π−2π0η invariant mass is shown by the squares inFig. 32.

The size of our data sample is not sufficient to justifya sophisticated amplitude analysis, as would be neededto extract detailed information on all the intermediate

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FIG. 31: (a) The π±π0 invariant mass for data. The curvesshow the fit functions, described in the text. (b) The π±η vsthe π∓π0 invariant mass.

2 3 42), GeV/cη0π2-π+πm(

0

20

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60

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100

120

140

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180

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FIG. 32: Number of events in bins of Ec.m. for inclusiveπ+π−2π0η events (circles) and for the ωπ0η (triangles), φπ0η(upside-down triangles), and ρ±π∓π0η (squares) intermediatestates.

states. We can deduce that an intermediate a0(980)ρπstate is present: a correlated bump at the a0(980) and ρinvariant masses is seen in the scatter plot of Fig. 31(b),where the π±η invariant mass is plotted vs the π∓π0

mass. Also, there is a contribution from ρ+ρ−η: a scatterplot of the π±π0 vs the π∓π0 invariant mass is presentedin Fig. 28(b), from which an enhancement correspondingto correlated ρ+ρ− production is visible.

H. The sum of intermediate states

Figure 32 displays the number of events obtained fromthe fits described above to the ω (triangles), φ (upside-down triangles), and ρ (square) peaks. The results areshown in comparison to the total number of π+π−2π0ηevents (circles) obtained from the fit to the third pho-ton pair invariant mass distribution. The sum of eventsfrom the intermediate states is seen to agree within theuncertainties with the total number of π+π−2π0η events,except in the region around 2 GeV.

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TABLE III: Summary of the e+e− → ηπ+π− cross section measurement. The uncertainties are statistical only.

Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb1.075 0.06 ± 0.03 1.475 3.74 ± 0.43 1.875 1.16 ± 0.21 2.275 0.35 ± 0.10 2.675 0.27 ± 0.071.125 0.29 ± 0.23 1.525 4.14 ± 0.44 1.925 1.00 ± 0.19 2.325 0.22 ± 0.09 2.725 0.11 ± 0.051.175 0.00 ± 0.12 1.575 3.48 ± 0.40 1.975 0.65 ± 0.16 2.375 0.33 ± 0.09 2.775 0.09 ± 0.051.225 0.23 ± 0.25 1.625 2.67 ± 0.36 2.025 0.78 ± 0.16 2.425 0.22 ± 0.07 2.825 0.03 ± 0.041.275 0.57 ± 0.27 1.675 2.52 ± 0.32 2.075 0.51 ± 0.13 2.475 0.51 ± 0.10 2.875 0.05 ± 0.041.325 1.15 ± 0.34 1.725 2.20 ± 0.30 2.125 0.50 ± 0.13 2.525 0.27 ± 0.09 2.925 0.02 ± 0.041.375 1.83 ± 0.36 1.775 2.38 ± 0.29 2.175 0.75 ± 0.13 2.575 0.08 ± 0.05 2.975 0.09 ± 0.051.425 2.74 ± 0.40 1.825 1.39 ± 0.23 2.225 0.23 ± 0.11 2.625 0.12 ± 0.06 3.025 0.05 ± 0.05

TABLE IV: Summary of the e+e− → ωπ0π0 cross section measurement. The uncertainties are statistical only.

Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb1.125 0.04 ± 0.08 1.775 0.88 ± 0.16 2.425 0.07 ± 0.05 3.075 0.83 ± 0.07 3.725 0.06 ± 0.021.175 0.03 ± 0.10 1.825 0.62 ± 0.14 2.475 0.12 ± 0.05 3.125 0.52 ± 0.05 3.775 0.03 ± 0.021.225 –0.02 ± 0.10 1.875 0.96 ± 0.14 2.525 0.21 ± 0.05 3.175 0.11 ± 0.03 3.825 0.03 ± 0.011.275 0.13 ± 0.11 1.925 0.61 ± 0.13 2.575 0.15 ± 0.04 3.225 0.08 ± 0.02 3.875 0.02 ± 0.011.325 0.41 ± 0.13 1.975 0.45 ± 0.11 2.625 0.13 ± 0.04 3.275 0.08 ± 0.02 3.925 0.03 ± 0.021.375 0.69 ± 0.18 2.025 0.47 ± 0.10 2.675 0.12 ± 0.04 3.325 0.07 ± 0.02 3.975 0.04 ± 0.011.425 0.29 ± 0.18 2.075 0.33 ± 0.09 2.725 0.17 ± 0.04 3.375 0.06 ± 0.02 4.025 0.03 ± 0.011.475 0.68 ± 0.19 2.125 0.29 ± 0.09 2.775 0.10 ± 0.04 3.425 0.07 ± 0.02 4.075 0.02 ± 0.011.525 1.05 ± 0.21 2.175 0.26 ± 0.08 2.825 0.11 ± 0.04 3.475 0.03 ± 0.02 4.125 0.03 ± 0.011.575 1.44 ± 0.22 2.225 0.40 ± 0.08 2.875 0.18 ± 0.04 3.525 0.07 ± 0.02 4.175 0.02 ± 0.011.625 1.40 ± 0.21 2.275 0.31 ± 0.07 2.925 0.10 ± 0.03 3.575 0.04 ± 0.02 4.225 0.01 ± 0.011.675 1.55 ± 0.20 2.325 0.21 ± 0.06 2.975 0.14 ± 0.06 3.625 0.06 ± 0.02 4.275 0.01 ± 0.011.725 0.96 ± 0.18 2.375 0.23 ± 0.06 3.025 0.25 ± 0.04 3.675 0.11 ± 0.03 4.325 0.02 ± 0.01

TABLE V: Summary of the e+e− → π+π−π0π0η cross section measurement. The uncertainties are statistical only.

Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb1.625 0.01 ± 0.10 2.175 1.59 ± 0.16 2.725 1.07 ± 0.13 3.275 0.26 ± 0.09 3.825 0.02 ± 0.071.675 –0.05 ± 0.08 2.225 1.66 ± 0.18 2.775 0.97 ± 0.14 3.325 0.15 ± 0.11 3.875 0.08 ± 0.081.725 0.20 ± 0.10 2.275 1.29 ± 0.16 2.825 0.68 ± 0.14 3.375 0.50 ± 0.10 3.925 0.12 ± 0.071.775 0.51 ± 0.12 2.325 1.27 ± 0.15 2.875 1.00 ± 0.13 3.425 0.15 ± 0.11 3.975 –0.02 ± 0.081.825 0.71 ± 0.14 2.375 1.70 ± 0.18 2.925 0.81 ± 0.13 3.475 0.34 ± 0.10 4.025 –0.04 ± 0.081.875 0.73 ± 0.14 2.425 1.30 ± 0.15 2.975 0.96 ± 0.13 3.525 0.30 ± 0.08 4.075 0.10 ± 0.061.925 1.22 ± 0.16 2.475 1.27 ± 0.16 3.025 0.61 ± 0.14 3.575 0.18 ± 0.09 4.125 0.14 ± 0.071.975 2.22 ± 0.20 2.525 1.00 ± 0.13 3.075 1.21 ± 0.16 3.625 0.20 ± 0.11 4.175 –0.06 ± 0.072.025 2.01 ± 0.19 2.575 0.95 ± 0.15 3.125 1.06 ± 0.15 3.675 0.18 ± 0.09 4.225 0.05 ± 0.062.075 1.61 ± 0.18 2.625 1.11 ± 0.16 3.175 0.50 ± 0.12 3.725 0.28 ± 0.09 4.275 0.10 ± 0.062.125 1.90 ± 0.18 2.675 0.67 ± 0.14 3.225 0.52 ± 0.11 3.775 0.06 ± 0.09 4.325 0.04 ± 0.06

TABLE VI: Summary of the e+e− → ωπ0η cross section measurement. The uncertainties are statistical only.

Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb Ec.m., GeV σ, nb1.525 0.02 ± 0.10 2.125 1.26 ± 0.17 2.725 0.35 ± 0.07 3.325 0.13 ± 0.04 3.925 0.08 ± 0.031.575 0.03 ± 0.07 2.175 1.06 ± 0.14 2.775 0.29 ± 0.07 3.375 0.11 ± 0.03 3.975 0.00 ± 0.031.625 0.24 ± 0.10 2.225 0.83 ± 0.13 2.825 0.25 ± 0.06 3.425 0.13 ± 0.04 4.025 0.05 ± 0.021.675 0.20 ± 0.10 2.275 0.74 ± 0.12 2.875 0.22 ± 0.06 3.475 0.09 ± 0.03 4.075 0.00 ± 0.031.725 0.30 ± 0.11 2.325 0.47 ± 0.10 2.925 0.25 ± 0.06 3.525 0.06 ± 0.03 4.125 0.04 ± 0.021.775 0.76 ± 0.15 2.375 0.68 ± 0.11 2.975 0.18 ± 0.05 3.575 0.10 ± 0.03 4.175 0.03 ± 0.021.825 0.96 ± 0.16 2.425 0.58 ± 0.10 3.025 0.15 ± 0.05 3.625 0.02 ± 0.02 4.225 0.03 ± 0.021.875 0.88 ± 0.16 2.475 0.41 ± 0.09 3.075 0.35 ± 0.07 3.675 0.06 ± 0.03 4.275 0.00 ± 0.031.925 1.46 ± 0.18 2.525 0.45 ± 0.09 3.125 0.20 ± 0.05 3.725 0.05 ± 0.03 4.325 0.02 ± 0.011.975 1.62 ± 0.20 2.575 0.48 ± 0.09 3.175 0.14 ± 0.04 3.775 0.08 ± 0.022.025 1.54 ± 0.19 2.625 0.41 ± 0.08 3.225 0.13 ± 0.04 3.825 0.04 ± 0.032.075 1.16 ± 0.16 2.675 0.39 ± 0.08 3.275 0.09 ± 0.03 3.875 0.07 ± 0.02

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2.5 3 3.5 42), GeV/c0π3-π+πm(

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FIG. 33: (a) The π+π−3π0 mass distribution for ISR-produced e+e− → π+π−π0π0π0 events in the J/ψ–ψ(2S) re-gion. (b) The MC-simulated signals. The curves show the fitfunctions described in the text.

VI. THE J/ψ REGION

A. The π+π−3π0 final state

Figure 33(a) shows an expanded view of the J/ψ massregion from Fig. 9 for the five-pion data sample. Signalsfrom J/ψ → π+π−π0π0π0 and ψ(2S) → π+π−π0π0π0

are clearly seen. The non-resonant background distribu-tion is flat in this region.

The observed peak shapes are not purely Gaussian be-cause of radiation effects and resolution, as is also seenin the simulated signal distributions shown in Fig. 33(b).The sum of two Gaussians with a common mean is usedto describe them. We obtain 2389 ± 63 J/ψ events and177± 27 ψ(2S) events. Using the results for the numberof events, the detection efficiency, and the ISR luminos-ity, we determine the product:

BJ/ψ→5π · ΓJ/ψee =N(J/ψ → π+π−3π0) ·m2

J/ψ

6π2 · dL/dE · εMC · εcorr · C(2)

= (150± 4± 15) eV ,

where ΓJ/ψee is the electronic width, dL/dE =

180 nb−1/MeV is the ISR luminosity at the J/ψ massmJ/ψ, εMC = 0.041 is the detection efficiency from sim-ulation with the corrections εcorr = 0.88, discussed inSec. IV F, and C = 3.894× 1011 nb MeV2 is a conversionconstant [27]. We estimate the systematic uncertaintyfor this region to be 10%, because no background sub-traction is needed. The subscript “5π” for the branchingfraction refers to the π+π−3π0 final state exclusively.

Using ΓJ/ψee = 5.55 ± 0.14 keV [27], we obtain

BJ/ψ→5π = (2.70 ± 0.07 ± 0.27) × 10−2: no other mea-surements for this channel exist.

Using Eq.(2) and the result dL/dE = 228 nb−1/MeVat the ψ(2S) mass, we obtain:

Bψ(2S)→5π · Γψ(2S)ee = (12.4± 1.9± 1.2) eV .

With Γψ(2S)ee = 2.34±0.06 keV [27] we find Bψ(2S)→5π =

(5.2±0.8±0.5)×10−3. For this channel also, no previousresult exists.

3.4 3.5 3.6 3.7 3.8 3.92), GeV/c0π3πm(2

2.9

2.95

3

3.05

3.1

3.15

3.2

3.25

3.32),

GeV

/c0 π- π

+ πm

(

(a)

3.4 3.5 3.6 3.7 3.8 3.9 42), GeV/c0π2-π+πm(

0

5

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(b)

FIG. 34: (a) The three-pion combination closest to the J/ψmass vs the five-pion mass. (b) The five-pion mass for theevents with the three-pion mass in the ±50 MeV/c2 inter-val around the J/ψ mass. The curves show the fit functionsfor all events (solid) and the contribution of the background(dashed).

The ψ(2S) peak partly corresponds to the decay chainψ(2S) → J/ψπ0π0 → π+π−π0π0π0, with J/ψ decayto three pions. We select the π+π−π0 mass combina-tion closest to the J/ψ mass. Figure 34(a) displays thisπ+π−π0 mass vs the five-pion invariant mass. A clearsignal from the above decay chain is seen. We selectevents in a ±0.05 GeV/c2 window around the J/ψ massand project the results onto m(π+π−3π0). The resultsare shown in Fig. 34(b). Performing a fit to this distribu-tion yields 142 ± 21 ψ(2S) → J/ψπ0π0 → π+π−π0π0π0

events. In conjunction with the detection efficiency andISR luminosity, this yields:

Bψ(2S)→J/ψπ0π0 ·BJ/ψ→π+π−π0 · Γψ(2S)ee =

(10.1± 1.5± 1.1) eV .

With Γψ(2S)ee as stated above and Bψ(2S)→J/ψπ0π0 =

0.1817 ± 0.0031 [27], we obtain BJ/ψ→π+π−π0 = (2.29 ±0.28±0.23)%, in agreement with our direct measurementBJ/ψ→π+π−π0 = (2.18 ± 0.19)% [13] as well as with thePDG value BJ/ψ→π+π−π0 = (2.11±0.07)%. This gives usconfidence that our normalization procedure is correct.

3 3.52), GeV/c0π3-π+πm(

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0 π2ω

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π3ρ

(b)

FIG. 35: (a) The five-pion mass for events with the three-pion combination in the ω(782) mass region. (b) The five-pion mass for events with π±π0 combination in the ρ(770)mass region. The curves show the fit functions described inthe text.

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1. The ωπ0π0 intermediate state

The J/ψ → ηπ+π− branching fraction is very small, aswe observed in our previous publication [20], and there isnot a statistically significant signal in our sample, shownin Fig. 16. We do not attempt to extract a J/ψ branchingfraction for this channel.

Figure 35(a) shows an expanded view of Fig. 18 withthe π+π−3π0 mass distribution for events obtained by afit to the π+π−π0 mass distribution. The two-Gaussianfit, implemented as discribed above, yields 398± 29 and33±10 events for the J/ψ and ψ(2S), respectively. UsingEq.(2) we obtain:

BJ/ψ→ωπ0π0 ·Bω→π+π−π0 · ΓJ/ψee =

(24.9± 1.8± 2.5) eV ,

Bψ(2S)→ωπ+π− ·Bω→π+π−π0 · Γψ(2S)ee =

(2.3± 0.7± 0.2) eV .

Using Bω→π+π−π0 = 0.891 and the value of Γee fromRef. [27], we obtain BJ/ψ→ωπ0π0 = (5.04± 0.37± 0.50)×10−3 and Bψ(2S)→ωπ0π0 = (1.1± 0.3± 0.1)× 10−3. Thevalue of BJ/ψ→ωπ0π0 listed in Ref. [27], based on the

DM2 [33] result, is (3.4± 0.8)× 10−3 . There is no pre-vious result for Bψ(2S)→ωπ0π0 . Note that our result forBJ/ψ→ωπ0π0 is about a factor of two lower than our re-

sult BJ/ψ→ωπ+π− = (9.7 ± 0.9) × 10−3 [14], as expectedfrom isospin symmetry.

0.5 1 1.5 22), GeV/c0π-πm(

0.5

1

1.5

2

2),

GeV

/c0 π

+ πm

(

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(b)

FIG. 36: (a) Scatter plot of the π+π0 vs the π−π0 invariantmass for the J/ψ region in Fig. 35(b). (b) Number of π+π0

events in bins of 0.04 GeV/c2 in the π−π0 mass. The curvesshow the fit functions for all events (solid) and the contribu-tion of the background (dashed).

2. The ρ±π∓π0π0 intermediate state

Figure 35(b) shows an expanded view of Fig. 21(a)(squares) for the π+π−3π0 mass, for events obtainedfrom the fit to the ρ signal in the π±π0 mass. The two-Gaussian fit yields 2299 ± 201 and < 88 events at 90%C.L. for the J/ψ and ψ(2S), respectively.

The obtained J/ψ → ρ±π∓π0π0 result exceeds thetotal number of observed J/ψ events. This is because

of J/ψ decays to ρ+ρ−π0. Figure 36(a) shows a scat-ter plot of the π+π0 vs the π−π0 invariant mass for3051 events in a ±0.1 GeV/c2 interval around the J/ψpeak of Fig. 35(b). To determine the rate of correlatedρ+ρ− production, we fit the π+π0 invariant mass witha BW and combinatorial background function in inter-vals of 0.04 GeV/c2 in the π−π0 mass distribution. Theresulting distribution exibits a clear ρ peak, shown inFig. 36(b), with a correlated ρ+ρ− yield of 703 ± 153events, corresponding to 46±8% of the ρ±π∓π0π0 events.Using this value we estimate the number of J/ψ de-cays to single- and double-ρ to be 1241± 109± 183 and529 ± 46 ± 92, respectively. The second uncertainty isfrom the uncertainty in the fraction of ρ+ρ− events, givenabove. We obtain:

BJ/ψ→ρ±π∓π0π0 · ΓJ/ψee = (78± 7± 8± 6) eV ,

BJ/ψ→ρ+ρ−π0 · ΓJ/ψee = (33± 3± 3± 3) eV .

Dividing by the value of Γee from Ref. [27] then yields:

BJ/ψ→ρ±π∓π0π0 = (1.40± 0.12± 0.14± 0.10)× 10−2,

BJ/ψ→ρ+ρ−π0 = (0.60± 0.05± 0.06± 0.05)× 10−2,

where the third uncertainty is associated with the uncer-tainty arising from the procedure used to determine thecorrelated ρ+ρ− rate. No other measurements for theseprocesses exist.

B. The π+π−2π0η final state

Figure 37 shows an expanded view of Fig. 32, witha clear J/ψ signal seen in all three distributions: theinclusive π+π−2π0η mass distribution (Fig. 37(a)) andthe mass distributions for the ωπ0η (Fig. 37(b)) andρ±π∓π0η (Fig. 37(c)) intermediate states. Our fits yield203±29, 27±14, and 168±62 events for the J/ψ decaysinto these final states, respectively. Only an upper limitwith < 12 events at 90% C.L. is obtained for the ψ(2S)decay to π+π−2π0η. We determine:

BJ/ψ→π+π−π0π0η · ΓJ/ψee = (12.8± 1.8± 2.0) eV ,

BJ/ψ→ωπ0η ·Bω→3π · ΓJ/ψee = (1.7± 0.8± 0.3) eV ,

BJ/ψ→ρ±π∓π0η · ΓJ/ψee = (10.5± 4.1± 1.6) eV ,

Bψ(2S)→π+π−π0π0η · Γψ(2S)ee < 0.85 eV at 90% C.L..

Dividing by the appropriate Γee value from Ref. [27],we find BJ/ψ→π+π−π0π0η = (2.30 ± 0.33 ± 0.35) × 10−3,

BJ/ψ→ωπ0η = (3.4± 1.6± 0.6)× 10−4, BJ/ψ→ρ±π∓π0η =

(1.9± 0.7± 0.3)× 10−3, and Bψ(2S)→π+π−π0π0η < 3.5×10−4 at 90% C.L.. There are no previous results for thesefinal states.

C. Summary of the charmonium region study

The rates of J/ψ and ψ(2S) decays to π+π−3π0,π+π−2π0η and several intermediate final states have

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2.5 3 3.52), GeV/cη0π0π-π+πm(

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FIG. 37: The J/ψ region for the (a) π+π−2π0η, (b) ωπ0η, and (c) ρ±π∓π0η events. The curves show the fit functionsdescribed in the text.

TABLE VII: Summary of the J/ψ and ψ(2S) branching fractions.

Measured Measured J/ψ or ψ(2S) Branching Fraction (10−3)Quantity Value ( eV) Calculated, this work PDG [27]

ΓJ/ψee ·BJ/ψ→π+π−π0π0π0 150.0±4.0±15.0 27.0 ±0.7 ±2.7 no entry

ΓJ/ψee ·BJ/ψ→ωπ0π0 · Bω→3π 24.8±1.8±2.5 5.04±0.37±0.50 3.4±0.8

ΓJ/ψee ·BJ/ψ→ρ±π∓π0π0 78.0±9.0±8.0 14.0 ±1.2 ±1.4 no entry

ΓJ/ψee ·BJ/ψ→ρ+ρ−π0 33.0±5.0±3.3 6.0 ±0.9 ±0.6 no entry

ΓJ/ψee ·BJ/ψ→π+π−π0π0η 12.8±1.8±2.0 2.30±0.33±0.35 no entry

ΓJ/ψee ·BJ/ψ→ωπ0η · Bω→3π 1.7±0.8±0.3 0.34±0.16±0.06 no entry

ΓJ/ψee ·BJ/ψ→ρ±π∓π0η 10.5±4.1±1.6 1.7 ±0.7 ±0.3 no entry

Γψ(2S)ee ·Bψ(2S)→π+π−π0π0π0 12.4±1.8±1.2 5.2 ±0.8 ±0.5 no entry

Γψ(2S)ee ·Bψ(2S)→J/ψπ0π0 · BJ/ψ→3π 10.1±1.5±1.1 22.9 ±2.8 ±2.3 21.1±0.7

Γψ(2S)ee ·Bψ(2S)→ωπ0π0 · Bω→3π 2.3±0.7±0.2 1.1 ±0.3 ±0.1 no entry

Γψ(2S)ee ·Bψ(2S)→ρ±π∓π0π0 <6. 2 at 90% C.L. <2. 6 at 90% C.L. no entry

Γψ(2S)ee ·Bψ(2S)→π+π−π0π0η <0. 85 at 90% C.L. <0. 35 at 90% C.L. no entry

been measured. A small discrepancy with only one avail-able current PDG value, measured by the DM2 experi-ment [33], is observed for the J/ψ → ωπ0π0 decay rate.The measured products and calculated branching frac-tions are summarized in Table VII together with theavailable PDG values for comparison.

VII. SUMMARY

The photon-energy and charged-particle momentum res-olutions together with the particle identification capabil-ities of the BABAR detector permit the reconstruction ofthe π+π−3π0 and π+π−2π0η final states produced at loweffective center-of-mass energies via initial-state photonradiation in data collected in e+e− annihilation in theΥ (4S) mass region.

The analysis shows that the effective luminosity andefficiency have been understood with 10–13% accuracy.The cross section measurements for the reaction e+e− →π+π−π0π0π0 present a significant improvement on ex-isting data. The e+e− → π+π−π0π0η cross section hasbeen measured for the first time.

The selected multi-hadronic final states in the broadrange of accessible energies provide new information onhadron spectroscopy. The observed e+e− → ωπ0π0 ande+e− → ηπ+π− cross sections provide evidence of reso-nant structures around 1.4 and 1.7 GeV/c2, which werepreviously observed by DM2 and interpreted as ω(1450)and ω(1650) resonances.

The initial-state radiation events allow a study of J/ψand ψ(2S) production and a measurement of the corre-sponding products of the decay branching fractions ande+e− width for most of the studied channels, the major-ity of them for the first time.

VIII. ACKNOWLEDGMENTS

We are grateful for the extraordinary contributions ofour PEP-II colleagues in achieving the excellent luminos-ity and machine conditions that have made this work pos-sible. The success of this project also relies critically onthe expertise and dedication of the computing organiza-tions that support BABAR. The collaborating institutionswish to thank SLAC for its support and the kind hospi-

Page 24: arXiv:1810.11962v2 [hep-ex] 10 Dec 2018 · BABAR-PUB-18/008 SLAC-PUB-17344 Study of the reactions e+e !ˇ+ˇ ˇ0ˇ0ˇ0 and ˇ+ˇ ˇ0ˇ0 at center-of-mass energies from threshold to

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tality extended to them. This work is supported by theUS Department of Energy and National Science Foun-dation, the Natural Sciences and Engineering ResearchCouncil (Canada), the Commissariat a l’Energie Atom-ique and Institut National de Physique Nucleaire et dePhysique des Particules (France), the Bundesministeriumfur Bildung und Forschung and Deutsche Forschungsge-meinschaft (Germany), the Istituto Nazionale di FisicaNucleare (Italy), the Foundation for Fundamental Re-

search on Matter (The Netherlands), the Research Coun-cil of Norway, the Ministry of Education and Science ofthe Russian Federation, Ministerio de Economıa y Com-petitividad (Spain), the Science and Technology Facili-ties Council (United Kingdom), and the Binational Sci-ence Foundation (U.S.-Israel). Individuals have receivedsupport from the Marie-Curie IEF program (EuropeanUnion) and the A. P. Sloan Foundation (USA).

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