Study of the reactions e + e − → π + π − π 0 π 0 π 0 γ and π + π − π 0 π 0 ηγ at center-of-mass energies from threshold to 4.35 GeV using initial-state radiation
BB A B AR -PUB-18/008SLAC-PUB-17344 Study of the reactions e + e − → π + π − π π π and π + π − π π η at center-of-massenergies 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 a r X i v : . [ h e p - e x ] D ec D. Bettoni a , C. Bozzi a , R. Calabrese ab , G. Cibinetto ab , E. Fioravanti ab , I. Garzia ab , E. Luppi ab , and V. Santoro a INFN Sezione di Ferrara a ; Dipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara b , I-44122 Ferrara, Italy A. Calcaterra, R. de Sangro, G. Finocchiaro, S. Martellotti,P. Patteri, I. M. Peruzzi, M. Piccolo, M. Rotondo, and A. Zallo
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
S. Passaggio and C. Patrignani † INFN Sezione di Genova, I-16146 Genova, Italy
H. M. Lacker
Humboldt-Universit¨at zu Berlin, Institut f¨ur Physik, D-12489 Berlin, Germany
B. Bhuyan
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
U. Mallik
University of Iowa, Iowa City, Iowa 52242, USA
C. Chen, J. Cochran, and S. Prell
Iowa State University, Ames, Iowa 50011, USA
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 f¨ur 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
S. H. Robertson ab and R. M. Seddon b Institute of Particle Physics a ; McGill University b , Montr´eal, Qu´ebec, Canada H3A 2T8 B. Dey a , N. Neri a , and F. Palombo ab INFN Sezione di Milano a ; Dipartimento di Fisica, Universit`a di Milano b , I-20133 Milano, Italy R. Cheaib, L. Cremaldi, R. Godang, ¶ and D. J. Summers University of Mississippi, University, Mississippi 38677, USA
P. Taras
Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, Canada H3C 3J7
G. De Nardo and C. Sciacca
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche,Universit`a di Napoli Federico II, I-80126 Napoli, Italy
G. Raven
NIKHEF, National Institute for Nuclear Physics and High 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. Gaz a , M. Margoni ab , M. Posocco a , G. Simi ab , F. Simonetto ab , and R. Stroili ab INFN Sezione di Padova a ; Dipartimento di Fisica, Universit`a di Padova b , I-35131 Padova, Italy S. Akar, E. Ben-Haim, M. Bomben, G. R. Bonneaud, G. Calderini, J. 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. Biasini ab , E. Manoni a , and A. Rossi a INFN Sezione di Perugia a ; Dipartimento di Fisica, Universit`a di Perugia b , I-06123 Perugia, Italy G. Batignani ab , S. Bettarini ab , M. Carpinelli ab , ∗∗ G. Casarosa ab , M. Chrzaszcz a , F. Forti ab , M. A. Giorgi ab ,A. Lusiani ac , B. Oberhof ab , E. Paoloni ab , M. Rama a , G. Rizzo ab , J. J. Walsh a , and L. Zani ab INFN Sezione di Pisa a ; Dipartimento di Fisica, Universit`a di Pisa b ; Scuola Normale Superiore di Pisa c , I-56127 Pisa, Italy A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
F. Anulli a , R. Faccini ab , F. Ferrarotto a , F. Ferroni a , †† A. Pilloni ab , and G. Piredda a ‡ INFN Sezione di Roma a ; Dipartimento di Fisica,Universit`a di Roma La Sapienza b , I-00185 Roma, Italy C. B¨unger, S. Dittrich, O. Gr¨unberg, M. Heß, T. Leddig, C. Voß, and R. Waldi
Universit¨at Rostock, D-18051 Rostock, Germany
T. Adye and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, 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,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
H. Ahmed
St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5
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. Bianchi ab , F. De Mori ab , A. Filippi a , and D. Gamba ab INFN Sezione di Torino a ; Dipartimento di Fisica, Universit`a di Torino b , I-10125 Torino, Italy L. Lanceri and L. Vitale
INFN Sezione di Trieste and Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy
F. Martinez-Vidal and A. Oyanguren
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
J. Albert b , A. Beaulieu b , F. U. Bernlochner b , G. J. King b , R. Kowalewski b ,T. Lueck b , I. M. Nugent b , J. M. Roney b , R. J. Sobie ab , and N. Tasneem b Institute of Particle Physics a ; University of Victoria b , Victoria, British Columbia, Canada V8W 3P6 T. J. Gershon, P. F. Harrison, and T. E. Latham
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
R. Prepost and S. L. Wu
University of Wisconsin, Madison, Wisconsin 53706, USA
We study the processes e + e − → π + π − π π π γ and π + π − π π ηγ in which an energetic photonis radiated from the initial state. The data were collected with the B A B AR detector at SLAC.About 14 000 and 4700 events, respectively, are selected from a data sample corresponding to anintegrated luminosity of 469 fb − . The invariant mass of the hadronic final state defines the effective e + e − center-of-mass energy. From the mass spectra, the first precise measurement of the e + e − → π + π − π π π cross section and the first measurement ever of the e + e − → π + π − π π η 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 ωπ π , ηπ + π − , and otherintermediate states are presented. We observe the J/ψ and ψ (2 S ) 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: Universit`a di Bologna and INFN Sezione di Bologna,
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 ( E c . m . ), as proposed in Ref. [1]. Thepossibility of exploiting ISR to make precise measure-ments of low-energy cross sections at high-luminosity φ and B factories is discussed in Refs. [2–4], and motivatesthe studies described in this paper. Such measurementsare of particular interest because of a ∼ g µ −
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 − → X h γ , using data from the B A B AR experi-ment at SLAC, have been previously reported. Here X h represents any of several exclusive hadronic final states.The X h studied to date include: charged hadron pairs π + π − [7], K + K − [8], and pp [9]; four or six chargedmesons [10–12]; charged mesons plus one or two π mesons [11–15]; a K S meson plus charged and neutralmesons [16]; and channels with K L mesons [17]. TheISR events are characterized by good reconstruction ef-ficiency and by well understood kinematics (see for ex-ample Ref. [13]), tracking, particle identification, and π , K S , and K L reconstruction, demonstrated in above ref-erences.This paper reports analyses of the π + π − π and π + π − π η final states produced in conjunction with ahard photon, assumed to result from ISR. While B A B AR data 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 (4 S ) 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: Universit`a di Sassari, I-07100 Sassari, Italy †† Also at: Gran Sasso Science Institute, I-67100 LAquila, Italy termediate states, including the η , ω , ρ , a (980), and a (1260) resonances. A clear J/ψ signal is observed forboth the π + π − π and π + π − π η channels, and the cor-responding J/ψ branching fractions are measured. Thedecay ψ (2 S ) → π + π − π π π is observed and its branch-ing fraction is measured.Previous measurements of the e + e − → π + π − π π π 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 B A B AR experiment pre-viously measured the e + e − → ηπ + π − reaction in the η → π + π − π [14] and η → γγ [20] decay channels. Be-low, we present the measurement of e + e − → ηπ + π − with η → π π π : this process contributes to e + e − → π + π − π π π . There are no previous results for e + e − → π + π − π π η . II. THE B A B AR DETECTOR AND DATASET
The data used in this analysis were collected with the B A B AR detector at the PEP-II asymmetric-energy e + e − storage ring. The total integrated luminosity used is468.6 fb − [21], which includes data collected at the Υ (4 S ) resonance (424.7 fb − ) and at a c.m. energy40 MeV below this resonance (43.9 fb − ).The B A B AR detector is described in detail else-where [22]. Charged particles are reconstructed using the B A B AR 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 K 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 K¨uhn and Czy˙z [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 − π π π γ events assumingproduction through the ω (782) π π 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 ωπ π system are in an S-wavestate and are described by a combination of phase spaceand f (980) → π π , based on our study of the ωπ + π − state [14]. The simulation of e + e − → π + π − π π ηγ events is similarly based on two production channels: aphase space model, and a model with an ωπ η interme-diate state with a π η 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(2 πγ , 3 πγ , 4 πγ , 5 πγ , 2 Kπγ , and π + π − π π γ ) are sim-ulated. To evaluate the background from the relevantnon-ISR processes, namely e + e − → qq ( q = u, d, s ) and e + 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 c ) , G e V / c gg m ( - (a) ), GeV/c γγ m( E v en t s / . G e V / c (b) FIG. 1: (a) The invariant mass m ( γγ ) of the third photon pairvs χ π π γγ . (b) The m ( γγ ) distribution for χ π π γγ < III. EVENT SELECTION AND KINEMATIC FIT
A relatively clean sample of π + π − π γ and π + π − π ηγ events is selected by requiring thatthere be two tracks reconstructed in the DCH, SVT, orboth, and seven or more photons, with an energy above ), GeV/c γγ π π m(2 ) , G e V / c γγ m ( (a) ), GeV/c γγ π π m(2 ) , G e V / c γγ m ( − (b) FIG. 2: (a) The third-photon-pair invariant mass m ( γγ ) vs m (2 π π γγ ) for (a) χ π π γγ <
60 and (b) 60 < χ π π γγ < 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 /c of the π mass m π . The selected combinations are subjected toa fit in which the diphoton masses of the two pairs with | m ( γγ ) − m π | <
35 MeV /c are constrained to m π . 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 ) − m π | <
35 MeV /c , wetest all possible combinations, allowing each of the threediphoton pairs in turn to be the third pair, i.e., the pairwithout the m π constraint.The above procedure allows us not only to search forevents with π → γγ in the third photon pair, but alsofor events with η → γγ .The 6C fit is performed under the signal hypothesis e + e − → π + π − π π γγγ ISR . The combination with thesmallest χ is retained, along with the obtained χ π π γγ value and the fitted three-momenta of each track andphoton. Each selected event is also subjected to a 6C fitunder the e + e − → π + π − π π γ ISR background hypoth-esis, and the χ π π value is retained. The π + π − π π process has a larger cross section than the π + π − π 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 − π FINAL STATEA. 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 χ π π γγ . Clear π and η peaks arevisible at small χ values. We require χ π π γγ < χ π π >
30 for the 2 π π background hypothesis. This requirement reduces thecontamination due to 2 π π 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 π mass value is a consequence of thekinematic fit constraint of the best two photon pairs tothe π 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 (2 π π γγ ) for events (a) in the signal region χ π π γγ <
60 and (b) in a control region defined by 60 <χ π π γγ < e + e − → π + π − π π π and π + π − π η 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 − π π π and π + π − π π η processes is to perform afit for the π and η yields in intervals of 0.05 GeV /c in the distribution of the π + π − π γγ invariant mass m ( π + π − π γγ ). ), GeV/c gg m( E v en t s / . G e V / c (a) ), GeV/c gg p p m(2 ) , G e V / c gg m ( (b) FIG. 3: The MC-simulated distribution for e + e − → ηπ + π − events of (a) the third-photon-pair invariant mass m ( γγ ), and(b) m ( γγ ) vs m ( π + π − π γγ ). B. Detection efficiency
As mentioned in Sec. II, the model used in the MCsimulation assumes that the five-pion final state resultspredominantly from ωπ π and ηπ + π − production, with ω 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 (2 π π γγ ) for the simulated ηπ + π − and ωπ π events, respectively. The π peak is not Gaus- ), GeV/c gg m( E v en t s / . G e V / c (a) ), GeV/c gg p p m(2 ) , G e V / c gg m ( (b) FIG. 4: The MC-simulated distribution for e + e − → ωπ π events of (a) the third-photon-pair invariant mass m ( γγ ), and(b) m ( γγ ) vs m ( π + π − π γγ ). sian in either reaction and is broader for ηπ + π − eventsthan for ωπ π 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 χ 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 /c . 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 π signalshape. The fitted fit function is shown by the smoothcurve in Fig. 5. We perform a fit of the π signal in every0.05 GeV /c interval in the m (2 π π γγ ) invariant massfor the two different simulated channels.Alternatively, for the ηπ + π − events, we determine thenumber of events vs the m (2 π π γγ ) invariant mass byfitting the η signal from the η → π π π 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 ωπ π events, the ω mass peak can be used. The ω mass peak in simula- ), GeV/c gg m( E v en t s / . G e V / c (a) ), GeV/c gg m( E v en t s / . G e V / c (b) FIG. 5: The background subtracted MC-simulated m ( γγ )distribution for (a) e + e − → ηπ + π − and (b) e + e − → ωπ π events. The dashed histogram shows the simulated distribu-tion from the χ 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 − π )in 0.05 GeV /c intervals of the m ( π + π − π γγ ) 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 /c 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 → π π π 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 π fit areshown in Fig. 7 by points for the ηπ + π − and by squaresfor the ωπ π 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 π fits. ), GeV/c p m(3 E v en t s / . G e V / c (a) ), GeV/c p - p + p m( E v en t s / . G e V / c (b) FIG. 6: (a) The background subtracted MC-simulated 3 π invariant mass for the e + e − → ηπ + π − events. The dasheddistribution is from the simulated χ control region, used forbackground subtraction. (b) The π + π − π invariant mass forthe MC-simulated e + e − → ωπ π 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. ), GeV/c p - p + p m( E ff i c i en cy FIG. 7: The energy-dependent reconstruction efficiency for e + e − → π + π − π π π 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 ), GeV/c gg m( E v en t s / . G e V / c (a) ), GeV/c gg m( E v en t s / . G e V / c (b) FIG. 8: (a) The third-photon-pair invariant mass m ( γγ ) fordata in the signal (solid) and χ control (dashed) regions.The dotted histogram shows the estimated background from e + e − → π + π − π π . (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 /c 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 − π events The solid histogram in Fig. 8 (a) shows the m ( γγ ) dataof Fig. 1 (b) binned in mass interval of 0.02 GeV /c . Thedashed histogram shows the distribution of data from the χ control region. The dotted histogram is the estimatedremaining background from the e + e − → π + π − π π pro-cess. No evidence for a peaking background is seen ineither of the two background distributions. We subtractthe background evaluated using the χ 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 /c . The result of the fit is shown by the solidand dashed curves in Fig. 8 (b). In total 14 390 ± qq events, which is discussed in Sect. IV D. The same fit isapplied to the corresponding m ( γγ ) distribution in each0.05 GeV /c interval in the π + π − π γγ invariant mass.The resulting number of π + π − π event candidates as afunction of m ( π + π − π ), including the peaking qq back-ground, is shown by the data points in Fig. 9. ), GeV/c p - p + p m( E v en t s / . G e V / c FIG. 9: The invariant mass distribution of π + π − π events,obtained from the fit to the π mass peak. The contributionfrom non-ISR uds background is shown by squares. D. Peaking background
The major background producing a π 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 − π π π π 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 − π π γγ ) forthe non-ISR light quark qq ( uds ) simulation: clear signalsfrom π and η are seen. Figure 10(b) shows the projec-tion plots for χ π π γγ <
60 and 60 < χ π π γγ < uds simulation, we calculate thediphoton invariant mass distribution of the ISR candi-date with all the remaining photons in the event. A π peak is observed, with approximately the same numberof events in data and simulation, leading to a normaliza-tion factor of 1 . ± .
1. The resulting uds background isshown by the squares in Fig. 9: the uds background isnegligible below 2 GeV /c , but accounts for more thanhalf the total background for around 4 GeV /c and above. ), GeV/c gg p p m(2 ) , G e V / c gg m ( - (a) ), GeV/c gg m( E v en t s / . G e V / c (b) FIG. 10: (a) The third-photon-pair invariant mass vs m ( π + π − π π γγ ) for the uds simulation. (b) The projectionplot for (a) the signal region χ π π γγ <
60 (solid histogram),and the control region 60 < χ π π γγ <
120 (dashed his-togram). , GeV c.m. E ) , nb p p p - p + pfi - e + ( e s FIG. 11: The measured e + e − → π + π − π π π cross section.The uncertainties are statistical only. E. Cross section for e + e − → π + π − π π π The e + e − → π + π − π π π Born cross section is deter-mined from σ (2 π π )( E c . m . ) = dN πγ ( E c . m . ) d L ( E c . m . ) (cid:15) corr5 π (cid:15) MC5 π ( E c . m . )(1 + δ R ) , (1)1 TABLE I: Summary of the e + e − → π + π − π π π cross section measurement. The uncertainties are statistical only. E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb1.125 0.00 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± where E c . m . is the invariant mass of the five-pion system; dN πγ is the background-subtracted number of selectedfive-pion events in the interval dE c . m . , and (cid:15) MC5 π ( E c . m . )is the corresponding detection efficiency from simula-tion. The factor (cid:15) corr5 π accounts for the difference be-tween data and simulation in the tracking (1.0 ± π (3.0 ± d L , iscalculated using the total integrated B A B AR luminosityof 469 fb − [13]. The initial- and final-state soft-photonemission is accounted for by the radiative correction fac-tor (1 + δ R ), 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 − π π π 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 /c , 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 E c . m . < E c . m . > TABLE II: Summary of the systematic uncertainties in the e + e − → π + π − π π π cross section measurement.Source Correction UncertaintyLuminosity – 1%MC-data difference ISRPhoton efficiency +1.5% 1% χ cut uncertainty – 3%Fit and background subtraction – 7% E c . m . > . E c . m . > . π losses +9% 3%Radiative corrections accuracy – 1%Acceptance from MC(model-dependent) – 5%Total (assuming no correlations) +12 .
5% 10% E c . m . > . E c . m . > . G. Overview of the intermediate structures
The e + e − → π + π − π π π process has a rich inter-nal substructure. To study this substructure, we restrictevents to m ( γγ ) < .
35 GeV /c , eliminating the regionpopulated by e + e − → π + π − π π η . We then assumethat the m ( π + π − π γγ ) invariant mass can be taken torepresent m ( π + π − π ).Figure 12(a) shows the distribution of the π π π 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 3 π invariant mass. From this plot, the ρ (770) η intermediate state is seen to dominate. Figure 12(c)presents a scatter plot of the 3 π invariant mass versus m ( π + π − π π γγ ).The distribution of the π + π − π invariant mass (threeentries per event) is shown in 13(a). A prominent ω peakfrom e + e − → ωπ π is seen. Some indications of φ and J/ψ peaks are also present. The scatter plot in Fig. 13(b)shows the π π vs the π + π − π invariant mass. A scatterplot of the π + π − π vs the π + π − π π γγ mass is shown2 ), GeV/c p m(3 E v en t s / . G e V / c (a) ), GeV/c p m(3 ) , G e V / c - p + p m ( (b) ), GeV/c gg p p m(2 ) , G e V / c p m ( (c) FIG. 12: (a) The π π π invariant mass. (b) The π + π − vs the π π π invariant mass. (c) The π π π invariant mass vs thefive-pion invariant mass. ), GeV/c p - p + p m( E v en t s / . G e V / c (a) ), GeV/c p - p + p m( ) , G e V / c p p m ( (b) ), GeV/c gg p p m(2 ) , G e V / c p - p + p m ( (c) FIG. 13: (a) The π + π − π invariant mass (three combinations per event). (b) The π π vs the π + π − π invariant mass. (c)The π + π − π invariant mass vs the five-pion invariant mass. ), GeV/c pp m( E v en t s / . G e V / c (a) ), GeV/c p + p m( ) , G e V / c p - p m ( (b) ), GeV/c γγ π π m(2 ) , G e V / c ππ m ( (c) FIG. 14: (a) The π + π (solid) and π − π (dashed) invariant masses (three combinations per event). (b) The π − π vs the π + π invariant mass. (c) The π ± π invariant mass vs the five-pion invariant mass. ), GeV/c p m(3 E v en t s / . G e V / c (a) ), GeV/c - p + p m( E v en t s / . G e V / c (b) FIG. 15: (a) The 3 π 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. ), GeV/c p - p + p m( E v en t s / . G e V / c FIG. 16: The m ( π + π − π ) invariant mass dependence ofthe selected data events for e + e − → ηπ + π − , η → π . in Fig. 13(c). A clear signal for a J/ψ peak is seen.Figure 14(a) shows the π + π (dotted) and π − π (solid)invariant masses (three entries per event). A prominent ρ (770) peak, corresponding to e + e − → πρ , is visible.The scatter plot in Fig. 14(b) shows the π − π vs the π + π invariant mass. An indication of the ρ + ρ − π in-termediate state is visible. Figure 14(c) shows the ππ invariant mass vs the five-pion invariant mass: a clearsignal for the J/ψ and an indication of the ψ (2 S ) 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 ± 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 , GeV c.m. E ) , nb h - p + pfi - e + ( e s (a) , GeV c.m. E ) , nb h - p + pfi - e + ( e s (b) FIG. 17: (a) The energy dependent e + e − → ηπ + π − crosssection obtained in the 2 π π mode. (b) Comparison of thecurrent results (squares) with previous measurements from B A B AR in the η → π + π − π (upside-down triangles) [14] and η → γγ modes (circles) [20]. Results from the SND experi-ment [32] are shown by triangles. each 0.05 GeV /c interval of m ( π + π − π ). The resultingdistribution is shown in Fig. 16.The π + π − invariant mass distribution for eventswithin ± /c 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 the e + 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 all η 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 measured4the e + e − → ηπ + π − cross section in three different η de-cay modes. ), GeV/c π - π + π m( E v en t s / . G e V / c (a) ), GeV/c p - p + p m( E v en t s / . G e V / c (b) FIG. 18: (a) The π + π − π 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 − π events inthe ω peak (circles) and estimated contribution from the ωπ background (squares). I. The ωπ π intermediate state To determine the contribution of the ωπ π 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 ± ωπ π events. The number of the ωπ π 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 /c interval of m ( π + π − π ). The resulting dis-tribution is shown by the circle symbols in Fig. 18(b).We do not observe a clear f (980) → π π signal in the π π 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 − π process [14], aclear f (980) → π + π − signal was seen.For the e + e − → ωπ π channel, there is a peakingbackground from e + e − → ωπ → π + π − π π . 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 ωπ π signal candidate distribution.The e + e − → ωπ π cross section, corrected for the ω → π + π − π branching fraction, is shown in Fig. 19 andtabulated in Table IV. The uncertainties are statisticalonly. The systematic uncertainties are about 10% for E c . m . < E c . m . ,and a clear resonance at around 1.6 GeV, possibly fromthe ω (1650). The measured e + e − → ωπ π cross sectionis around a factor of two smaller than that we observedfor e + e − → ωπ + π − [14], as is expected from isospin sym-metry. , GeV c.m. E ) , nb p pwfi - e + ( e s FIG. 19: The energy dependent e + e − → ωπ π cross sectionin the π + π − π mode. J. The ρ (770) ± π ∓ π π intermediate state A similar approach is followed to study events witha ρ ± meson in the intermediate state. Because the ρ meson 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 ∓ π π 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 ± ρ ± π ∓ π π 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 − π events, repeated from Fig. 9. It is seen thatthe number of events with a ρ ± exceeds the total numberof π + π − π events, implying that there is more than one ρ ± per event, namely a significant production of e + e − → ρ + ρ − π . To determine the rate of ρ + ρ − π events, weperform a fit to determine the number of ρ + in intervals5 ), GeV/c p – p m( E v en t s / . G e V / c (a) ), GeV/c p - p m( E v en t s / . G e V / c (b) ), GeV/c p – p m( ) , G e V / c p–r m ( (c) FIG. 20: (a) The π ± π invariant mass for data. The dashed curve shows the fit to the combinatorial background. The solidcurve is the sum of the background curve and the BW function for the ρ ± . (b) The result of the ρ + fit in bins of 0.04 GeV /c in the ρ − mass. (c) Scatter plot of the ρ ± π invariant mass vs the π ∓ π invariant mass. ), GeV/c p - p + p m( E v en t s / . G e V / c (a) ), GeV/c p - p + p m( E v en t s / . G e V / c (b) FIG. 21: (a) Number of events in bins of E c . m . from the ηπ + π − (triangles), ωπ π (upside-down triangles), and ρ → ππ (squares) intermediate states. The circles show the totalevent numbers obtained from the fit to the π peak. (b) Thecircles as are described for (a). The squares show the sums ofevent numbers with η , ω and the ρ contribution for correlated ρ + ρ − production. of 0.04 GeV /c in the π − π distribution of Fig. 14(b).The result is shown in Fig. 20(b). Indeed, a significant ρ + peak is observed.The number of e + e − → ρ + ρ − π 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 − π ) < . /c ,2 . < m ( π + π − π ) < . /c , and m ( π + π − π ) > . /c . 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 of π + π − π events with a ρ ± , decreases with the mass inter-val as 0.49 ± ± ± .
10, respectively,where the uncertainties are statistical. Thus, the ρ + ρ − π intermediate state dominates at threshold.Intermediate states with either one or two ρ (770)are expected to be produced, at least in part, through e + e − → ρ (1400 , π → a (1260) ± π ∓ π → ρ ± π ∓ π π and e + e − → ρ ± a ∓ → ρ + ρ − π , respectively.Figure 20(c) shows a scatter plot of the ρ ± π invariantmass vs the π ∓ π invariant mass. An indication of the a (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), ωπ π (triangles), and ρ ± π ∓ π π (square) intermediate state events, found as describedin the previous sections, in comparison to the total num-ber of π + π − π events (circles) found from the fit to the π 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 − π events,shown by the circular symbols.6Note that below E c . m . =2 GeV, the number of eventsis completely dominated by the ηπ + π − and ωπ π chan-nels, so the cross section of the intermediate states witha ρ can be estimated as the difference between the total e + e − → π + π − π π π cross section and the sum of the ηπ + π − and ωπ π contributions. V. THE π + π − π η FINAL STATEA. Determination of the number of events
The analogous approach to that described above for e + e − → π + π − π π π events is used to study e + e − → π + π − π π η 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. ), GeV/c gg m( E v en t s / . G e V / c (a) ), GeV/c h p - p + p m( E v en t s / . G e V / c (b) FIG. 22: (a) The third-photon-pair invariant mass for data.The dashed curve shows the fitted background. The solidcurve shows the sum of background and the two-Gaussianfit function used to obtain the number of events with an η .(b) The invariant mass distribution for the π + π − π η eventsobtained from the η signal fit. The contribution of the uds background events is shown by the squares. B. Peaking background
The major background producing an η peak is the non-ISR background, in particular e + e − → π + π − π π π η when 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 π peaks in data and uds simulation,we assign a scale factor of 1 . ± . η peak in the uds simulation in intervals of0.05 GeV /c in m ( π + π − π π γγ ). The results are shownby the squares in Fig. 22 (b). ), GeV/c gg m( E v en t s / . G e V / c (a) ), GeV/c p - p + p m( E v en t s / . G e V / c (b) FIG. 23: (a) The third-photon-pair invariant mass for sim-ulation of the e + e − → π + π − π π ηγ process. The dashedcurve shows the fitted background. The solid curve shows thesum of background and the two-Gaussian fit function usedto obtain the number of events with an η . (b) The π + π − π 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 − π π ηγ events fromthe phase space model and with the ωπ η 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 /c in m ( π + π − π π γγ ). The fit is illustratedin Fig. 23(a) using all π + π − π π γγ 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 ωπ η intermediate channel, we also de-termine the efficiency using an alternative method, byfitting the ω peak in the π + π − π 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 ωπ η channels, 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 efficiencies7are around 4%, similar to what is found for π + π − π (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%. ), GeV/c h p p - p + p m( E ff i c i en cy FIG. 24: The energy dependent detection efficiency, deter-mined in three different ways: see text. The curve shows thefit to the average of the three and is used in the cross sectiondetermination. , GeV c.m. E ) , nb h p p - p + pfi - e + ( e s FIG. 25: Energy dependent cross section for e + e − → π + π − π π η . The uncertainties are statistical only. D. Cross section for e + e − → π + π − π π η The cross section for e + e − → π + π − π π η 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 E c . m . < . E. Overview of the intermediate structures
The π + π − π η final state, like that for π + π − π , hasa rich substructure. Figure 26(a) shows the 2 π η in-variant mass distribution for events selected by requir-ing | m ( γγ ) − m ( η ) | < .
07 GeV /c 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 . < | m ( γγ ) − m ( η ) | < .
14 GeV /c . Figure 26(b)shows a scatter plot of the π + π − invariant mass vs the2 π η invariant mass. No structures are seen.Figure 27(a) shows the π + π − π mass distribution (twoentries per event). An ω signal is clearly visible, as well asa bump close to 1 GeV /c corresponding to φ → π + π − π .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 π η vs the π + π − π invariant mass. A clear correlation of ω and a (980) → π η production is seen. Figure 27(c) showshow ωπ η events are distributed over the π + π − π η in-variant mass.Figure 28(a) presents the π + π (solid) and π − π (dot-ted) mass combinations (two entries per event) for the se-lected π + π − π η 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 + π vs the π − π invariant mass is shown. Figure 28(c) displays the π ± π vs the π + π − π η invariant mass. F. The ωπ η and φπ η intermediate states To determine the contribution of the ωπ η and φπ η intermediate 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 − π η invariant mass is determinedby performing an analogous fit of events in Fig. 27(c) inintervals of 0.05 GeV /c in m ( π + π − π η ).We select events within ± . /c of the ω peak inFig. 29(a) and display the resulting π η invariant massin Fig. 29(b). A very clear signal from the a (980) isobserved, while no signal is seen in an ω sideband definedby 0 . < | m ( π + π − π ) − m ( ω ) | < .
14 GeV /c .The obtained e + e − → ωπ η cross section, corrected forthe ω → π + π − π 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 − → ωπ η cross section,resulting in a total systematic uncertainty of 13% below2.4 GeV. The results are presented in Table VI (statistical8 ), GeV/c h p m(2 E v en t s / . G e V / c (a) ), GeV/c h p m(2 ) , G e V / c - p + p m ( (b) FIG. 26: (a) The 2 π η invariant mass of the selected π + π − π η events (solid histogram), and the background determinedfrom the χ sideband (dotted histogram). (b) The π + π − vs the 2 π η mass for the selected events. ), GeV/c p - p + p m( E v en t s / . G e V / c (a) ), GeV/c p - p + p m( ) , G e V / c h p m ( (b) ), GeV/c h p p m(2 ) , G e V / c p - p + p m ( (c) FIG. 27: (a) The π + π − π invariant mass with two entries per event (solid histogram) and the background estimate from the η sideband (dotted histogram). (b) The π η vs the π + π − π invariant mass. (c) The π + π − π invariant mass vs the π + π − π η invariant mass. ), GeV/c p – p m( E v en t s / . G e V / c (a) ), GeV/c p - p m( ) , G e V / c p + p m ( (b) ), GeV/c h p p m(2 ) , G e V / c p–p m ( (c) FIG. 28: (a) the π + π (solid) and π − π (dotted) invariant mass for the selected π + π − π η events (two entries per event). (b)The π − π vs the π + π invariant mass for the selected events. (c) The π ± π invariant mass vs the π + π − π η invariant mass. ), GeV/c p - p + p m( E v en t s / . G e V / c (a) ), GeV/c h p m( E v en t s / . G e V / c (b) FIG. 29: (a) The π + π − π 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 π η invariant mass distribution for the events selected inthe ω peak (solid). The dashed histogram shows the distri-bution from the ω -peak side band. , GeV c.m. E ) , nb h pwfi - e + ( e s FIG. 30: The E c . m . dependence of the e + e − → ωπ η cross section (circles) in comparison with the SND results [31](squares). 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 ∓ π η 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 ± ρ ± π ∓ π η events. The result of the fit is shownin Fig. 31(a). The distribution of these events vs the π + π − π η 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 ), GeV/c p – p m( E v en t s / . G e V / c (a) ), GeV/c h – p m( ) , G e V / c h–p m ( (b) FIG. 31: (a) The π ± π invariant mass for data. The curvesshow the fit functions, described in the text. (b) The π ± η vsthe π ∓ π invariant mass. ), GeV/c h p - p + p m( E v en t s / . G e V / c FIG. 32: Number of events in bins of E c . m . for inclusive π + π − π η events (circles) and for the ωπ η (triangles), φπ η (upside-down triangles), and ρ ± π ∓ π η (squares) intermediatestates. states. We can deduce that an intermediate a (980) ρπ state is present: a correlated bump at the a (980) and ρ invariant masses is seen in the scatter plot of Fig. 31(b),where the π ± η invariant mass is plotted vs the π ∓ π mass. Also, there is a contribution from ρ + ρ − η : a scatterplot of the π ± π vs the π ∓ π 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 − π η events (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 − π η events,except in the region around 2 GeV.0 TABLE III: Summary of the e + e − → ηπ + π − cross section measurement. The uncertainties are statistical only. E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb1.075 0.06 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± e + e − → ωπ π cross section measurement. The uncertainties are statistical only. E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb1.125 0.04 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± e + e − → π + π − π π η cross section measurement. The uncertainties are statistical only. E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb1.625 0.01 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± e + e − → ωπ η cross section measurement. The uncertainties are statistical only. E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb E c . m . , GeV σ , nb1.525 0.02 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ), GeV/c p - p + p m( E en t s / . G e V / c (a) ), GeV/c p - p + p m( E v en t s / . G e V / c (b) FIG. 33: (a) The π + π − π mass distribution for ISR-produced e + e − → π + π − π π π events in the J/ψ – ψ (2 S ) re-gion. (b) The MC-simulated signals. The curves show the fitfunctions described in the text. VI. THE
J/ψ
REGIONA. The π + π − π 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 − π π π and ψ (2 S ) → π + π − π π π 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 ± J/ψ events and177 ± ψ (2 S ) events. Using the results for the numberof events, the detection efficiency, and the ISR luminos-ity, we determine the product: B J/ψ → π · Γ J/ψee = N ( J/ψ → π + π − π ) · m J/ψ π · d L /dE · (cid:15) MC · (cid:15) corr · C (2)= (150 ± ±
15) eV , where Γ J/ψee is the electronic width, d L /dE =180 nb − / MeV is the ISR luminosity at the
J/ψ mass m J/ψ , (cid:15) MC = 0 .
041 is the detection efficiency from sim-ulation with the corrections (cid:15) corr = 0 .
88, discussed inSec. IV F, and C = 3 . × nb MeV is a conversionconstant [27]. We estimate the systematic uncertaintyfor this region to be 10%, because no background sub-traction is needed. The subscript “5 π ” for the branchingfraction refers to the π + π − π final state exclusively.Using Γ J/ψee = 5 . ± .
14 keV [27], we obtain B J/ψ → π = (2 . ± . ± . × − : no other mea-surements for this channel exist.Using Eq.(2) and the result d L /dE = 228 nb − / MeVat the ψ (2 S ) mass, we obtain: B ψ (2 S ) → π · Γ ψ (2 S ) ee = (12 . ± . ± .
2) eV . With Γ ψ (2 S ) ee = 2 . ± .
06 keV [27] we find B ψ (2 S ) → π =(5 . ± . ± . × − . For this channel also, no previousresult exists. ), GeV/c p p m(2 ) , G e V / c p - p + p m ( (a) ), GeV/c p - p + p m( E v en t s / . G e V / c (b) FIG. 34: (a) The three-pion combination closest to the
J/ψ mass vs the five-pion mass. (b) The five-pion mass for theevents with the three-pion mass in the ±
50 MeV /c 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 (2 S ) peak partly corresponds to the decay chain ψ (2 S ) → J/ψπ π → π + π − π π π , with J/ψ decayto three pions. We select the π + π − π mass combina-tion closest to the J/ψ mass. Figure 34(a) displays this π + π − π mass vs the five-pion invariant mass. A clearsignal from the above decay chain is seen. We selectevents in a ± /c window around the J/ψ massand project the results onto m ( π + π − π ). The resultsare shown in Fig. 34(b). Performing a fit to this distribu-tion yields 142 ± ψ (2 S ) → J/ψπ π → π + π − π π π events. In conjunction with the detection efficiency andISR luminosity, this yields: B ψ (2 S ) → J/ψπ π · B J/ψ → π + π − π · Γ ψ (2 S ) ee =(10 . ± . ± .
1) eV . With Γ ψ (2 S ) ee as stated above and B ψ (2 S ) → J/ψπ π =0 . ± . B J/ψ → π + π − π = (2 . ± . ± . B J/ψ → π + π − π = (2 . ± . B J/ψ → π + π − π = (2 . ± . ), GeV/c p - p + p m( e v en t s / . G e V / c p w (a) ), GeV/c p - p + p m( e v en t s / . G e V / c p r (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 ± π combination in the ρ (770)mass region. The curves show the fit functions described inthe text. The ωπ π 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 − π mass distribution for events obtained by afit to the π + π − π mass distribution. The two-Gaussianfit, implemented as discribed above, yields 398 ±
29 and33 ±
10 events for the
J/ψ and ψ (2 S ), respectively. UsingEq.(2) we obtain: B J/ψ → ωπ π · B ω → π + π − π · Γ J/ψee =(24 . ± . ± .
5) eV ,B ψ (2 S ) → ωπ + π − · B ω → π + π − π · Γ ψ (2 S ) ee =(2 . ± . ± .
2) eV . Using B ω → π + π − π = 0 .
891 and the value of Γ ee fromRef. [27], we obtain B J/ψ → ωπ π = (5 . ± . ± . × − and B ψ (2 S ) → ωπ π = (1 . ± . ± . × − . Thevalue of B J/ψ → ωπ π listed in Ref. [27], based on theDM2 [33] result, is (3 . ± . × − . There is no pre-vious result for B ψ (2 S ) → ωπ π . Note that our result for B J/ψ → ωπ π is about a factor of two lower than our re-sult B J/ψ → ωπ + π − = (9 . ± . × − [14], as expectedfrom isospin symmetry. ), GeV/c p - p m( ) , G e V / c p + p m ( (a) ), GeV/c p - p m( E v en t s / . G e V / c (b) FIG. 36: (a) Scatter plot of the π + π vs the π − π invariantmass for the J/ψ region in Fig. 35(b). (b) Number of π + π events in bins of 0.04 GeV /c in the π − π mass. The curvesshow the fit functions for all events (solid) and the contribu-tion of the background (dashed). The ρ ± π ∓ π π intermediate state Figure 35(b) shows an expanded view of Fig. 21(a)(squares) for the π + π − π mass, for events obtainedfrom the fit to the ρ signal in the π ± π mass. The two-Gaussian fit yields 2299 ±
201 and <
88 events at 90%C.L. for the
J/ψ and ψ (2 S ), respectively.The obtained J/ψ → ρ ± π ∓ π π result exceeds thetotal number of observed J/ψ events. This is because of
J/ψ decays to ρ + ρ − π . Figure 36(a) shows a scat-ter plot of the π + π vs the π − π invariant mass for3051 events in a ± /c interval around the J/ψ peak of Fig. 35(b). To determine the rate of correlated ρ + ρ − production, we fit the π + π invariant mass witha BW and combinatorial background function in inter-vals of 0.04 GeV /c in the π − π mass distribution. Theresulting distribution exibits a clear ρ peak, shown inFig. 36(b), with a correlated ρ + ρ − yield of 703 ± ±
8% of the ρ ± π ∓ π π events.Using this value we estimate the number of J/ψ de-cays to single- and double- ρ to be 1241 ± ±
183 and529 ± ±
92, respectively. The second uncertainty isfrom the uncertainty in the fraction of ρ + ρ − events, givenabove. We obtain: B J/ψ → ρ ± π ∓ π π · Γ J/ψee = (78 ± ± ±
6) eV ,B J/ψ → ρ + ρ − π · Γ J/ψee = (33 ± ± ±
3) eV . Dividing by the value of Γ ee from Ref. [27] then yields: B J/ψ → ρ ± π ∓ π π = (1 . ± . ± . ± . × − ,B J/ψ → ρ + ρ − π = (0 . ± . ± . ± . × − , 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 − π η final state Figure 37 shows an expanded view of Fig. 32, witha clear
J/ψ signal seen in all three distributions: theinclusive π + π − π η mass distribution (Fig. 37(a)) andthe mass distributions for the ωπ η (Fig. 37(b)) and ρ ± π ∓ π η (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 (2 S )decay to π + π − π η . We determine: B J/ψ → π + π − π π η · Γ J/ψee = (12 . ± . ± .
0) eV ,B J/ψ → ωπ η · B ω → π · Γ J/ψee = (1 . ± . ± .
3) eV ,B J/ψ → ρ ± π ∓ π η · Γ J/ψee = (10 . ± . ± .
6) eV ,B ψ (2 S ) → π + π − π π η · Γ ψ (2 S ) ee < .
85 eV at 90% C . L .. Dividing by the appropriate Γ ee value from Ref. [27],we find B J/ψ → π + π − π π η = (2 . ± . ± . × − , B J/ψ → ωπ η = (3 . ± . ± . × − , B J/ψ → ρ ± π ∓ π η =(1 . ± . ± . × − , and B ψ (2 S ) → π + π − π π η < . × − 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 (2 S ) decays to π + π − π , π + π − π η and several intermediate final states have3 ), GeV/c h p p - p + p m( E v en t s / . G e V / c (a) ), GeV/c h pw m( E v en t s / . G e V / c (b) ), GeV/c h p -+ p +- r m( E v en t s / . G e V / c (c) FIG. 37: The
J/ψ region for the (a) π + π − π η , (b) ωπ η , and (c) ρ ± π ∓ π η events. The curves show the fit functionsdescribed in the text. TABLE VII: Summary of the J/ψ and ψ (2 S ) branching fractions.Measured Measured J/ψ or ψ (2 S ) Branching Fraction (10 − )Quantity Value ( eV) Calculated, this work PDG [27]Γ J/ψee ·B J/ψ → π + π − π π π ± ± ± ± J/ψee ·B J/ψ → ωπ π · B ω → π ± ± ± ± ± J/ψee ·B J/ψ → ρ ± π ∓ π π ± ± ± ± J/ψee ·B J/ψ → ρ + ρ − π ± ± ± ± J/ψee ·B J/ψ → π + π − π π η ± ± ± ± J/ψee ·B J/ψ → ωπ η · B ω → π ± ± ± ± J/ψee ·B J/ψ → ρ ± π ∓ π η ± ± ± ± ψ (2 S ) ee ·B ψ (2 S ) → π + π − π π π ± ± ± ± ψ (2 S ) ee ·B ψ (2 S ) → J/ψπ π · B J/ψ → π ± ± ± ± ± ψ (2 S ) ee ·B ψ (2 S ) → ωπ π · B ω → π ± ± ± ± ψ (2 S ) ee ·B ψ (2 S ) → ρ ± π ∓ π π <
6. 2 at 90% C.L. <
2. 6 at 90% C.L. no entryΓ ψ (2 S ) ee ·B ψ (2 S ) → π + π − π π η <
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 → ωπ π 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 B A B AR detector permit the reconstruction ofthe π + π − π and π + π − π η final states produced at loweffective center-of-mass energies via initial-state photonradiation in data collected in e + e − annihilation in the Υ (4 S ) 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 − π π π present a significant improvement on ex-isting data. The e + e − → π + π − π π η 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 − → ωπ π and e + e − → ηπ + π − cross sections provide evidence of reso-nant structures around 1.4 and 1.7 GeV /c , which werepreviously observed by DM2 and interpreted as ω (1450)and ω (1650) resonances.The initial-state radiation events allow a study of J/ψ and ψ (2 S ) production and a measurement of the corre-sponding products of the decay branching fractions and e + e − width for most of the studied channels, the major-ity of them for the first time. VIII. ACKNOWLEDGMENTS
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