Study of the reactions e^+e^-\to2(π^+π^-)π^0π^0π^0 and e^+e^-\to2(π^+π^-)π^0π^0η at center-of-mass energies from threshold to 4.5 GeV using initial-state radiation
BB A B AR -PUB-20/004SLAC-PUB-17587 Study of the reactions e + e − → π + π − ) π π π and 2( π + π − ) π π η at center-of-massenergies from threshold to 4.5 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, 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
R. Cheaib b , 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
B. Dey, 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,D. X. Lin, T. S. Miyashita, P. Ongmongkolkul, J. Oyang, 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 ] F e b 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
B. J. Shuve
Harvey Mudd College, Claremont, California 91711, USA
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
Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, F-91405 Orsay, 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 N. Neri a and F. Palombo ab INFN Sezione di Milano a ; Dipartimento di Fisica, Universit`a di Milano b , I-20133 Milano, Italy 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, Sorbonne Universit´e,Paris Diderot Sorbonne Paris Cit´e, CNRS/IN2P3, 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
IRFU, CEA, Universit´e Paris-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 2( π + π − ) π π ηγ in which an energeticphoton is radiated from the initial state. The data were collected with the B A B AR detector atSLAC. About 14 000 and 4700 events, respectively, are selected from a data sample correspondingto an integrated luminosity of 469 fb − . The invariant mass of the hadronic final state defines theeffective e + e − center-of-mass energy. The center-of-mass energies range from threshold to 4.5 GeV.From the mass spectra, the first ever measurements of the e + e − → π + π − ) π π π and the e + e − → π + π − ) π π η cross sections are performed. The contributions from ωπ + π − π π , η π + π − ), andother intermediate states are presented. We observe the J/ψ and ψ (2 S ) in most of these final statesand measure 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
I. INTRODUCTION
The Standard Model (SM) calculation of the muonanomalous magnetic moment ( g µ −
2) requires input fromexperimental e + e − hadronic cross section data in order toaccount for hadronic vacuum polarization (HVP) terms.In particular, the calculation is most sensitive to the low-energy region, from the hadronic threshold to about 2GeV, where the inclusive hadronic cross section cannotbe measured reliably and a sum of exclusive states mustbe used. Despite the large data set accumulated in thepast years and the analysis studies performed, there isstill a ∼ e + e − center-of-mass(c.m.) energy ( E c . m . ), as proposed in Ref. [1]. Stud-ies of the ISR processes e + e − → µ + µ − γ [3, 4] and e + e − → X h γ , using data from the B A B AR experimentat SLAC, have been previously reported. Here X h rep-resents any of several exclusive hadronic final states.The X h studied to date include: charged hadron pairs π + π − [4], K + K − [5], and pp [6]; four or six chargedmesons [7–9]; charged mesons plus one or two or three π mesons [8–13]; a K S meson plus charged and neutralmesons [14]; and channels with K L mesons [15].In this paper, we report the first measurements of the2( π + π − )3 π and 2( π + π − )2 π η channels. The final statesare produced in conjunction with a hard photon, assumedto result from ISR. To reduce background from Υ (4 S )decays, the analysis is restricted to the c.m. energy be-low 4.5 GeV. As part of the analysis, we search for andobserve intermediate states, including the η , ω , and ρ resonances. In the charmonium region, we observe J/ψ and ψ (2 S ) signals in the studied final states and the cor-responding branching fractions are measured. ∗ Deceased † Now at: Wuhan University, Wuhan 430072, China ‡ Now at: Universit`a di Bologna and INFN Sezione di Bologna,I-47921 Rimini, Italy § Now at: King’s College, London, WC2R 2LS, UK ¶ 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 L’Aquila, Italy
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 − [19], 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 [20]. Charged particles are reconstructed usinga B A B AR tracking system, which is comprised of a siliconvertex tracker (SVT) and a drift chamber (DCH), bothlocated inside a 1.5 T solenoid. Separation of pions andkaons is accomplished by means of a detector of inter-nally reflected Cherenkov light (DIRC) and energy-lossmeasurements in the SVT and DCH. Photons are de-tected in an electromagnetic calorimeter (EMC). Muonidentification is provided by an instrumented 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 [21]. Multiple collinear soft-photon emission from the initial e + e − state is imple-mented with a structure function technique [22, 23], whileadditional photon radiation from final-state particles issimulated using the PHOTOS package [24]. The preci-sion of the radiative simulation is such that it contributesless than 1% to the uncertainty in the measured hadroniccross sections.To evaluate the detection efficiency we simulate e + e − → π + π − ) π π π γ events assuming productionthrough the ω (782) π η and π + π − π π η intermediatechannels, with decay of the ω to three pions and decayof the η to all its measured decay modes [25], from whichdecays to three pions are used in present analysis.A sample of 100-200k simulated events is generated foreach signal reaction and processed through the detectorresponse simulation, based on the GEANT4 package [26].These events are reconstructed using the same softwarechain as the data. Variations in the detector conditionsare taken into account. The simulation includes randomtrigger events to account for the observed distributionsof the background tracks and photons. Most of the ex-perimental events contain additional soft photons due tomachine background or interactions in the detector ma-terial, which are properly modeled in the simulation.For the purpose of background estimation, large sam-ples of events from the main relevant ISR processes(4 πγ , 5 πγ , ωηγ , and 2( π + π − ) π π γ ) are simulated. Thebackground from the relevant non-ISR processes, namely e + e − → qq ( q = u, d, s ) and e + e − → τ + τ − , are gener-ated using the jetset [27] and koralb [28] programs,respectively. The cross sections for the above processesare known with an accuracy about or better than 10%,which is sufficient for the present purpose. III. EVENT SELECTION AND KINEMATIC FIT
Candidates for the 2( π + π − )3 π γ and 2( π + π − )2 π ηγ events are selected by requiring that there be four wellmeasured tracks and seven or more detected photons,with an energy above 0.02 GeV in the EMC. We assumethat the photon with the highest energy is the ISR pho-ton, and we require its c.m. energy to be larger than3 GeV.The four tracks must have zero total charge and ex-trapolate to within 0.25 cm of the beam axis and 3.0 cmof the nominal collision point along that axis. In orderto recover a relatively small fraction of signal events thatcontain a background track from secondary decay or in-teraction, we allow for the presence of a fifth track in theevent, which however must not fulfill the above condition.The four tracks that satisfy the extrapolation criteria arefit to a vertex to determine the collision point, which isused in the calculation of the photon directions.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 use the four-momenta and covariance ma-trices of the colliding electrons and selected tracks andphotons. The fitted three-momenta of each track andphoton are then used in further kinematic calculations.
20 40 60 80 100 120 140 160 180 c ) , G e V / c gg m ( (a) ), GeV/c gg m( E v en t s / . G e V / c (b) FIG. 1: (a) Distribution of the invariant mass m ( γγ ) of thethird photon pair vs χ π π γγ . The lines define the boundariesof the signal and control regions. (b) Distribution of m ( γγ ) inthe signal region χ π π γγ <
50 with the additional selectioncriteria described in the text.
We exclude the photon with the highest c.m. energy,which is assumed to arise from ISR, and consider eachindependent set of six other photons, and combine theminto three pairs. For each set of six photons, thereare 15 independent combinations of photon pairs. Weretain those combinations in which the diphoton massof 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 , thenwe test all possible combinations, allowing each of thethree diphoton pairs in turn to be the third pair, i.e., thepair without 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 hypothe-sis e + e − → π + π − ) π π γγγ ISR . The combinationwith the smallest χ is retained, along with the ob-tained χ π π γγ value and the fitted three-momenta ofeach track and photon. Each selected event is also sub-jected to a 6C fit under the e + e − → π + π − ) π π γ ISR background hypothesis, and the χ π π value is retained.The 2( π + π − ) π π process has a larger cross section than ), GeV/c gg p )2 - p + p m(2( ) , G e V / c gg m ( (a) ), GeV/c gg p )2 - p + p m(2( ) , G e V / c gg m ( (b) FIG. 2: (a) The third-photon-pair invariant mass m ( γγ ) vs m (4 π π γγ ) for (a) χ π π γγ <
50 and (b) 50 < χ π π γγ < the 2( π + π − )3 π signal process and can contribute to thebackground when two background photons are present. IV. ADDITIONAL SELECTION CRITERIA
We require the tracks to lie within the fiducial re-gion of the DCH (0.45–2.40 radians) and to be incon-sistent with being a kaon or muon. The photon candi-dates are required to lie within the fiducial region of theEMC (0.35–2.40 radians) and to have an energy largerthan 0.035 GeV. The angular distance between the ISRphoton and the closest track must be greater than 1 ra-dian; this requirement significantly suppresses the non-ISR background, in particular reducing the backgroundfrom e + e − → τ + τ − to a negligible level. A requirementthat any extra photons in an event must have an energybelow 0.7 GeV reduces the multi-photon background by10-20%. Finally, the background from the ISR process e + e − → π + π − )2 π γ is reduced from 30% to about 1-2%, with a loss of only 5% of signal events, by requiring χ π π > ), GeV/c gg m( E v en t s / . G e V / c (a) ), GeV/c gg p )2 - p + p m(2( ) , G e V / c gg m ( (b) FIG. 3: The MC-simulated distribution for e + e − → ηπ + π − π π events of (a) the third-photon-pair invariant mass m ( γγ ), and (b) m ( γγ ) vs m (2( π + π − )2 π γγ ). Figure 1 (a) shows the invariant mass m ( γγ ) of thethird photon pair vs χ π π γγ after the above require-ments. Clear π and η peaks are visible at small χ values. The two vertical lines define the signal andcontrol regions, corresponding to χ π π γγ <
50 and50 < χ π π γγ < ), GeV/c gg m( E v en t s / . G e V / c (a) ), GeV/c gg p )2 - p + p m(2( ) , G e V / c gg m ( (b) FIG. 4: (a) Distribution of the third-photon-pair invariantmass m ( γγ ) and of (b) m ( γγ ) vs m (2( π + π − )2 π γγ ) for MC-simulated e + e − → ωπ η events. Figure 1 (b) shows the m ( γγ ) distribution for events inthe signal region after the above requirements have beenapplied. The dip in this distribution at the π mass valueis a consequence of the kinematic fit constraint of the besttwo photon pairs to the π mass, so the third photonpair is always formed from photon candidates that areless well measured.Figure 2 shows the m ( γγ ) distribution vs the invariantmass m (2( π + π − )2 π γγ ) for events in the signal (a) andcontrol (b) region. Events from the e + e − → π + π − )3 π and 2( π + π − )2 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; we usethese events to evaluate background.Our strategy to extract the signals for the e + e − → π + π − )3 π and 2( π + π − )2 π η processes is to performa fit for the π and η yields in intervals of 0.05 GeV /c in the distribution of the 2( π + π − )2 π γγ invariant mass.This mass interval is about three times wider than theexperimental resolution. V. DETECTION EFFICIENCYA. Number of signal events in simulation
As mentioned in Sec. II, the model used in the MCsimulation assumes that the seven-pion final state resultsfrom ωπ η and ηπ + π − π π production, with ω decays ), 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: Background subtracted m ( γγ ) distribution for MC-simulated (a) e + e − → ηπ + π − π π and (b) e + e − → ωπ η events. The fit function is described in the text. The dashedline shows a fit of the remaining contribution from the χ control region. to three pions and η decays to all modes. As shown be-low, these two final states dominate the observed crosssection. Also, the ISR photon is simulated to wider an-gles than the EMC acceptance, reducing the nominal effi-ciency. For each mode we have 200,000 simulated eventsfrom the primary generator.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 distribu-tion of m ( γγ ) vs m (2( π + π − )2 π γγ ) for the simulated ηπ + π − π π and ωπ η events, respectively. The π peakis not Gaussian in either reaction. Background photonsare included in the simulation. Therefore, the simulationaccounts for the combinatorial background that ariseswhen background photons are combined with photonsfrom the signal reactions.The combinatorial background is subtracted using thedata from the χ control region. We do not know howlarge the combinatorial background is in the signal re-gion, and we use a scale factor varying from 1.0 to 1.5for the subtraction to estimate the uncertainty in thenumber of signal events. The method is illustrated usingsimulation in Fig. 5, which shows the m ( γγ ) distributionwith a bin width of 0.02 GeV /c . The solid histograms show the simulated results from the signal region aftersubtraction of the simulated combinatorial backgroundwith the scale factor 1.5. The sum of three Gaussianfunctions is used to describe the π signal shape. Athird-order polynomial function is used to describe theshape of the remaining combinatorial background. Thefitted function is shown by the smooth solid curve, whilethe dashed curve is for the contribution of the remainingcombinatorial background. The remaining combinatorialbackground contribution is almost negligible for the scalefactor value 1.5. We obtaine 1122 ±
46 and 1161 ±
55 sim-ulated signal events for each mode, respectively. If thescale factor 1.0 is used, the remaining background is welldescribed by the polynomial function and the signal yielddoes not change by more than 3%.Alternatively, for the ηπ + π − π π events, we deter-mine the number of events by fitting the η signal fromthe η → π + π − π decay: the simulated distribution isshown in Fig. 6(a) (twelve entries per event). The fitfunctions are again the sum of three Gaussian functions ), 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. 6: (a) The π + π − π invariant mass distribution for theMC-simulated e + e − → ηπ + π − π π events. The dashed curveis for the combinatorial background. (b) The π + π − π invari-ant masses for the MC-simulated e + e − → ωπ η events. Thehistogram shows the π + π − π combination closest to the η mass, while the two remaining combinations (dots) exhibitthe ω meson. The curves show the fit functions used to ob-tain the number of signal (solid) events, and the combinatorialbackground (dashed) contribution. ), GeV/c p )3 - p + p m(2( A v e r age e ff i c i en cy FIG. 7: The energy-dependent reconstruction efficiency for e + e − → π + π − )3 π events, determined using five differentmethods: see text. The curve shows the results of a fit to theaverage values, which is used in the cross section calculation. and a polynomial for the combinatorial background. Intotal we obtain 1183 ±
49 events. A similar fit of the η signal is performed for the ωπ η final state simulationwith 1110 ±
54 selected events.Similarly, as an alternative for the ωπ η events, the ω mass peak can be used. To reduce the number of com-binatorial entries, we require one π + π − π combinationto have invariant mass close to the η mass, and fit theremaining two combinations to extract the numbers ofsignal events with an ω , as shown in Fig. 6(b). In total1104 ±
71 signal events are found. A Breit-Wigner (BW)function, convolved with a Gaussian distribution to ac-count for the detector resolution, is used to describe the ω signal. A second-order polynomial is used to describethe background. B. Efficiency evaluation
The mass-dependent detection efficiency is obtainedby dividing the number of fitted MC events in each0.05 GeV /c mass interval of the hadronic system by thenumber generated in the same interval. The number ofsignal events in the simulation, obtained by fitting the π , η , or ω signals, is consistent within uncertainties notonly in total, but also in every mass interval. We donot see any significant difference in mass-dependent effi-ciency between the different methods. The uncertainty inthe value of the efficiency in each mass bin is dominatedby the fluctuation of the combinatorial background. Weaverage the five efficiencies in each 0.05 GeV /c mass in-terval and fit the result with a third-order polynomialfunction, shown in Fig. 7. The result of this fit is usedfor the cross section calculation.Although the signal simulation accounts for all η decaymodes, the efficiency calculation considers the signal η → ), 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) Invariant mass m ( γγ ) for data in the χ signal(solid) and control (dashed) regions. The dotted histogramshows the estimated background from e + e − → π + π − ) π π .(b) The m ( γγ ) invariant mass for data after the backgroundsubtraction. The curves are the fit results as described in thetext. π + π − π decay mode only. This efficiency estimate takesinto account the geometrical acceptance of the detectorfor the final-state photons and the charged pions, theinefficiency of the detector subsystems, and the event lossdue to additional soft-photon emission from the initialand final states. Corrections that account for data-MCdifferences are discussed below.From Fig. 7 it is seen that the reconstruction efficiencyis about 2.7%, roughly independent of mass. By compar-ing the results of the five different methods used to eval-uate the efficiency, we conclude that the relative overallefficiency does not change by more than 5% because ofvariations of the functions used to extract the number ofevents or the use of different models. This value is takenas an estimate of the systematic uncertainty in the ac-ceptance associated with the simulation model used andwith the fit procedure.We do not simulate the 2( π + π − ) η and 2( π + π − )2 π η intermediate states, which are observed in data (see be-low) in the η → π and η → γγ decays. But our pre-vious studies [13] have demonstrated that, for these andsimilar decays, the variations in efficiency due to model0 ), GeV/c gg p )2 - p + p m(2( E v en t s / . G e V / c (a) ), GeV/c gg p )2 - p + p m(2( E v en t s / . G e V / c (b) FIG. 9: (a) The invariant-mass distribution of π + π − π events, obtained from the fit to the π mass peak. (b) Ex-panded view of (a) to show the contribution from non-ISR uds background, shown by squares. dependence do not exceed 5%. In combination with theselections above, we assign 7% as a sistematic uncertaintyto the detection efficiency. VI. THE 2( π + π − )3 π FINAL STATEA. Number of 2( π + π − )3 π events The solid histogram in Fig. 8 (a) shows the same m ( γγ )distribution of Fig. 1 (b) binned in mass intervals of0.02 GeV /c . The dashed histogram corresponds insteadto the distribution of data from the χ control region, andthe dotted histogram is the estimated remaining back-ground from e + e − → π + π − ) π π events produced viaISR. No evidence for a peaking background is seen in ei-ther of the two background distributions. We subtractthe background evaluated using the χ control regionwith the scale factor 1.0, and vary it to 1.5 to check thestability of the result. The resulting m ( γγ ) distributionis shown in Fig. 8 (b).We fit the data of Fig. 8 (b) with a combination of ), GeV/c gg p )2 - 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 (2( π + π − ) π π γγ ) for the uds simulation. (b) Projectedevents from (a) for the signal region χ π π γγ <
50 (solid his-togram), and the control region 50 < χ π π γγ <
100 (dashedhistogram). a 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. A total of 12 559 ±
174 events is ob-tained. Note that this number includes a relatively smallpeaking background component, due to qq events, whichis discussed in Sect. VI B. The same fit is applied to thecorresponding m ( γγ ) distribution in each 0.05 GeV /c interval in the 2( π + π − )2 π γγ invariant mass. The re-sulting number of 2( π + π − )3 π event candidates as afunction of m (2( π + π − )2 π γγ ), including the peaking qq background, is reported in Fig. 9 (a). B. Peaking background
The major background producing a π peak followingapplication of the selection criteria of Sect. IV.A is fromnon-ISR qq events, the most important channel being 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 the1 TABLE I: Summary of the e + e − → π + π − )3 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 , nb1.575 0.00 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± , GeV c.m. E ) , nb p p p - p + p - p + pfi - e + ( e s FIG. 11: The measured e + e − → π + π − ) π π π cross sec-tion. The uncertainties are statistical only. third-photon-pair invariant mass vs m (2( π + π − ) π π γγ )for the non-ISR light quark qq ( uds ) simulation: clearsignals from π and η are seen. Figure 10(b) shows the m ( γγ ) projection for χ π π γγ <
50 and 50 < χ π π γγ < uds simulation, we calculate thediphoton invariant mass distribution of the ISR candi-date with all the remaining candidate photon in theevent. A π peak is observed, with approximately thesame number of events in data and simulation, leadingto a normalization factor of 1 . ± .
1. The resulting uds background is shown by the squares in Fig. 9 (b), the uds background is negligible below 2 GeV /c , but ac-counts for more than half of the total event yield around4 GeV /c and above. C. Cross section for e + e − → π + π − ) π π π The e + e − → π + π − ) π π π Born cross section is de-termined from σ (4 π π )( E c . m . ) = dN πγ ( E c . m . ) d L ( E c . m . ) (cid:15) corr7 π (cid:15) MC7 π ( E c . m . )(1 + δ R ) , (1)where E c . m . is the invariant mass of the seven-pion sys-tem, dN πγ is the background-subtracted number ofselected events in the interval dE c . m . , and (cid:15) MC7 π ( E c . m . )is the corresponding detection efficiency from simula-tion. The factor (cid:15) corr7 π accounts for the difference be-tween data and simulation: the MC efficiency is largerby (1.0 ± ± π [12]. The ISR differential luminosity [10], d L , iscalculated using the total integrated B A B AR luminosityof 469 fb − [19]. 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 does notexhibit any clear structures except signals from the J/ψ and ψ (2 S ) resonances. Because we present our data inbins of width 0.050 GeV /c , compatible with the exper- 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 in ISRphoton efficiency +1.5% 1% χ cut uncertainty – 3%MC-data difference in track losses +4% 2%MC-data difference in π losses +9% 3%Radiative corrections accuracy – 1%Efficiency from MC(model-dependence) – 5%Total (assuming no correlations) +14 .
5% 10% ), 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 )2 - 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 theseven-pion invariant mass. ), GeV/c p - p + p m( E v en t s / . G e V / c (a) (b) ), GeV/c gg p )2 - p + p m(2( ) , G e V / c p - p + p m ( (c) FIG. 13: (a) The π + π − π invariant mass (twelve combinations per event). (b) The π + π − π vs the π + π − π invariant mass.(c) The π + π − π invariant mass vs the seven-pion 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 gg p )2 - p + p m(2( ) , G e V / c p + - p m ( (c) FIG. 14: (a) The π + π (solid) and π − π (dashed) invariant masses (twelve combinations per event). (b) The π − π vs the π + π invariant mass. (c) The π ± π invariant mass vs the seven-pion invariant mass. imental resolution, we do not apply an unfolding proce-dure to the data. Numerical values for the cross sectionare presented in Table I. The J/ψ region is discussedbelow.
D. Summary of systematic uncertaintes
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 14.5%. The systematic uncertainties are consideredto be uncorrelated and are added in quadrature, summingto 10%. The largest systematic uncertainty arises from3the fitting and background subtraction procedures. Itis estimated by varying the background levels and theparameters of the functions used.
E. 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 2( π + π − )2 π γγ invariant mass can be taken torepresent m (2( π + π − )3 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 − → η π + π − )reaction. Figure 12(b) presents a scatter plot of the π + π − (four entries per event) vs the 3 π invariant mass.From this plot, the ρ (770) η correlation in the intermedi-ate state is seen. Figure 12(c) presents a scatter plot ofthe 3 π invariant mass versus m (2( π + π − ) π π γγ ).The distribution of the π + π − π invariant mass (twelveentries per event) is shown in 13(a). Prominent η and ω peaks are seen. The scatter plot in Fig. 13(b) shows one π + π − π vs another π + π − π invariant mass for the sameevent. Correlated η and ω production from e + e − → ωπ η is seen. A scatter plot of the π + π − π vs the seven-pionmass is shown in Fig. 13(c). A clear signal for a J/ψ peak is also observed.Figure 14(a) shows the π + π (dotted) and π − π (solid)invariant masses (twelve 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 + π − π intermediate state is visible. Figure 14(c) shows the π ± π invariant mass vs the seven-pion invariant mass: a clearsignal for the J/ψ and an indication of the ψ (2 S ) areseen. ), GeV/c p m(3 E v en t s / . G e V / c 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] ), GeV/c gg p )2 - p + p m(2( E v en t s / . G e V / c FIG. 16: The m (2( π + π − )3 π ) invariant mass dependenceof the selected data events for e + e − → η π + π − ) , η → π (dots) in comparison with all seven-pion events (squares).The J/ψ signal is off-scale. , GeV c.m. E ) , nb h - p + p - p + pfi - e + ( e s FIG. 17: Comparison of the present results (dots) with pre-vious measurements of the e + e − → π + π − ) η cross sectionfrom B A B AR in η → γγ (triangles) [11] and from CMD-3(squares) [32] in η → π + π − π . The η π + π − ) intermediate state To determine the contribution of the η π + π − ) in-termediate state, we fit the events of Fig. 12(a) usinga triple-Gaussian function to describe the signal peak,as in Fig. 6(a), and a polynomial to describe the back-ground. The result of the fit is shown in Fig. 15(a).We obtain 1410 ± η π + π − ) events. The number of η π + π − ) events as a function of the seven-pion invari-ant mass is determined by performing an analogous fitin each 0.05 GeV /c interval of m (2( π + π − )3 π ). Theresulting distribution is shown in Fig. 16.The very rich intermediate structures in the η π + π − )mode were carefully studied in our previous paper [11]with significantly larger statistical precision.Using Eq. (1), we determine the cross section for the e + e − → η π + π − ) process. Our simulation takes intoaccount all η decays, so the cross section results, shownin Fig. 17 and listed in Table III, correspond to all η decays. Systematic uncertainties in this measurement are4 TABLE III: Summary of the e + e − → η 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 , nb1.575 0.00 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ), GeV/c p - p + p m( E v en t s / . G e V / c (a) ), GeV/c gg p )2 - p + p m(2( E v en t s / . G e V / c (b) FIG. 18: Mass plots for the ωπ η intermediate state: (a) Thesolid histogram is for the π + π − π invariant mass closest to the η mass, while the dots are for the two remaining combinationsof π + π − π . The solid curve shows the fit function for the ω signal plus the combinatorial background (dashed curve). (b)The mass distribution of the 2( π + π − )3 π events in the ω peak(circles) correlated with η production in comparison with all2( π + π − )3 π events(squares). the same as those listed in Table II. Figure 17 shows ourmeasurement in comparison to our previous result [11]and to those from the CMD-3 experiment [32]. Theseprevious results are based on different η decay modesthan those considered here. The different results are seento agree within the uncertainties. Including the resultsof the present study, we have thus now measured the e + e − → η π + π − ) cross section in three different η decay c.m. E00.511.522.533.5 ) , nb h pwfi - e + ( e s FIG. 19: Comparison of the present results (dots) with pre-vious measurements of the e + e − → ωπ η cross section from B A B AR in η → γγ (squares) [13] and from SND (triangles) [29]in η → π . modes. The ωπ η intermediate state As demonstrated in Fig. 13(a,b) we can expect ηπ + π − π π , ωπ + π − π π intermediate final states, orcorrelated η and ω production in the ωπ η mode.The solid histogram in Fig. 18(a) shows the mass distri-bution of the π + π − π combination closest to the nominal η mass, while the dotted histogram reports the invariantmass of the remaining two combinations of three pionsafter selecting the first combination within a window of ±
80 MeV /c from the nominal η mass. A fit to the dot-ted distribution with a sum of a BW for the ω signaland a combinatorial background, as shown in Sect. V,allows the extraction of the ωηπ intermediate state sig-nal, which amounts to 739 ±
51 events. The contributionof the ωπ η intermediate state to all 2( π + π − )3 π eventsis shown in Fig. 18(b).Using Eq. (1), we determine the cross section for the e + e − → ωπ η process. The energy dependence of the5 TABLE IV: Summary of the 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 , nb1.575 0.00 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ), GeV/c p - p + p m( E v en t s / . G e V / c (a) ), GeV/c gg p )2 - p + p m(2( E v en t s / . G e V / c (b) FIG. 20: (a) The π + π − π invariant mass for data with thefit function for the ω signal (solid) plus the combinatorialbackground (dashed curve). The solid histogram shows peak-ing background from the simulated e + e − → ωη ISR events.(b) The mass distribution of the 2( π + π − )3 π events in the ω peak (circles) and estimated contribution from the ωη back-ground (triangles), from ωπ η (up-down triangles), and from uds (squares). cross section is shown in Fig. 19 by the dots: we are inagreement with our previous measurement [13] and stillslightly below the SND result [29]. The numerical valuesof the cross section are listed in Table IV. Again, we havethe measurements of this reaction in three different decaymodes of η . , GeV c.m. E ) , nb w - p p p + pfi - e + ( e s FIG. 21: The energy dependent e + e − → ωπ + π − π π crosssection in the 2( π + π − )3 π mode (the J/ψ signal is off-scale).The result of CMD-3 for the e + e − → ωπ + π − π + π − cross sec-tion [32] is shown by squares. The ωπ + π − π π intermediate state To determine the contribution of the ωπ + π − π π in-termediate state, we fit the events of Fig. 13(a) using aBW function to model the signal and a polynomial tomodel the background. The BW function is convolvedwith a Gaussian distribution that accounts for the detec-tor resolution, as described for the fit of Fig. 6(b). The re-sult of the fit is shown in Fig. 20(a). We obtain 7808 ± ωπ + π − π π events. The number of ωπ + π − π π eventsas a function of the seven-pion invariant mass is deter-mined by performing an analogous fit in each 0.05 GeV /c interval of m (2( π + π − )3 π ). The resulting distribution isshown by the circle symbols in Fig. 20(b).For the e + e − → ωπ + π − π π channel, there is a peak-ing background from e + e − → ωη when ω and η decay to π + π − π . A simulation of this reaction with proper nor-malization leads to the peaking-background estimationshown by the histogram in Fig. 20(a) and by the trianglesymbols in Fig. 20(b). We also have peaking backgroundfrom the general uds reactions (also shown in Fig. 20(b)).These background contributions, as well as the events6 TABLE V: Summary of the e + e − → π + π − π π ω 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 , nb1.575 0.00 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ), GeV/c p - p + p m( E v en t s / . G e V / c (a) ), GeV/c gg p )2 - p + p m(2( E v en t s / . G e V / c (b) FIG. 22: Mass distributions for the ηπ + π − π π intermediatestate: (a) The curves show the fit function for the η signalin the π + π − π invariant mass (solid) plus the combinatorialbackground (dashed curve). The solid histogram shows es-timated contributions from the simulated e + e − → ωη ISRevents. (b) The mass distribution of the 2( π + π − )3 π eventsin the η peak (circles) and estimated contribution from the ωη background (triangles), from ωπ η (up-down triangles),and from uds (squares). from the correlated ω and η production from the ωπ η final state, are subtracted from the ωπ + π − π π signalcandidate distribution.The resulting e + e − → ωπ + π − π π cross section, cor-rected for the ω → π + π − π branching fraction, is shownin Fig. 21 and tabulated in Table V. The uncertainties are c.m. E00.511.522.5 ) , nb h p p - p + pfi - e + ( e s FIG. 23: The result of the energy dependent e + e − → ηπ + π − π π cross section in the η → π + π − π mode. Theresult of the B A B AR experiment in the η → γγ mode [13] isshown by triangles. statistical only. The systematic uncertainties are about10%. No previous measurement exists for this process.The cross section exhibits a rise at threshold, a decreaseat large E c . m . , and a possibly resonant activity at around2.3-2.5 GeV. The result by CMD-3 for the significantlylower e + e − → ωπ + π − π + π − cross section [32] is shownby squares. The ηπ + π − π π intermediate state A similar approach is used to determine the contri-bution of the ηπ + π − π π intermediate state. We fit theevents of Fig. 13(a) using the three-Gaussian function forthe signal and a polynomial to model the background.The result of the fit is shown in Fig. 22(a). The fitted ηπ + π − π π yield corresponds to 2522 ±
91 events. Thesignal distribution as a function of the seven-pion invari-ant mass is determined by performing an analogous fitin each 0.05 GeV /c interval of m (2( π + π − )3 π ), and isshown by the circle symbols in Fig. 22(b).Also in this case a peaking background arises from the7 TABLE VI: Summary of the 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 , nb1.650 0.17 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± process e + e − → ωη when ω and η decay to π + π − π . Itscontribution, estimated with MC simulation, is shown bythe histogram in Fig. 22(a) and by the triangle symbolsin Fig. 22(b).We also have peaking background from the general uds reactions, shown by squares in Fig. 22(b). And finally,we remove events from the ωπ η final state (up-downtriangles).The e + e − → ηπ + π − π π cross section, corrected forthe η → π + π − π branching fraction, is shown in Fig. 23and tabulated in 0.1 GeV bins in Table VI. The uncer-tainties are statistical only. The systematic uncertaintiesare about 10%. We are in good agreement with a recentmeasurement of this cross section [13] in the η → γγ decay mode. The ρ (770) ± π ∓ π + 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 twelve candidate ρ ± entries perevent, leading to a large combinatorial background. Toextract the contribution of the ρ ± π ∓ π + π − π π interme-diate state we fit the events in Fig. 14(a) with a BW func-tion to describe the signal and a polynomial to describethe background. The parameters of the ρ resonance aretaken from Ref. [25]. The result of the fit is shown inFig. 24(a). We obtain 9138 ± ρ ± π ∓ π + π − π π events.The distribution of these events vs the seven-pion invari-ant mass is shown by the circle symbols in Fig. 24(c),while a similar fit for the uds simulation is shown bysquares. The uds background is dominant in all energyregions except for J/ψ and ψ (2 S ).In these events more than one ρ ± per event can beexpected, indicating a significant production of J/ψ → ρ + ρ − π + π − π . To determine the rate of ρ + ρ − π + π − π events in the J/ψ decays, we perform a fit to determinethe number of ρ + in intervals of 0.02 GeV /c in the π − π distribution of Fig. 14(b) for events within ± /c of the J/ψ mass. The result is shown in Fig. 24(b). In-deed, a small ρ + peak with 415 ±
340 events is observed,compared to 2844 events in the
J/ψ peak region, corre-sponding to about 20% of all decays with one or two ρ ± .However, the uncertainty in this estimate is almost at thesame level.The charmonium region for all intermediate states is ), 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 gg p )2 - p + p m(2( E v en t s / . G e V / c (c) FIG. 24: Mass distributions for the ρ ± π ∓ π + π − π π inter-mediate state: (a) The π ± π invariant mass for data. Thedashed curve shows the fit to the combinatorial background.The solid curve is the sum of the background curve and theBW function for the ρ ± . (b) The result of the ρ + fit in binsof 0.02 GeV /c in the ρ − mass. (c) Number of events in binsof E c . m . from the ρ ± → π ± π (circles) intermediate states.The squares show the event numbers obtained from uds pro-duction. discussed below. F. The sum of intermediate states
We consider whether the 2( π + π − )3 π channel containsother intermediate state contributions. The circle sym-bols in Fig. 25 show the total number of 2( π + π − )3 π events, repeated from Fig. 9. We perform a sum of thenumber of η π + π − ), ωπ η , ηπ + π − π π , ωπ + π − π π ,and ρ ± π ∓ π + π − π π intermediate state events, found asdescribed in the previous sections, and show this sum bythe square symbols in Fig. 25. Based on the results of ourstudy of correlated ρ + ρ − production, we scale the num-8 TABLE VII: Summary of the 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 , nb2.075 0.03 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ), GeV/c gg p )2 - p + p m(2( E v en t s / . G e V / c FIG. 25: The 2( π + π − )2 π γγ mass distribution summed overthe intermediate states. The circles show the number ofevents, determined from the π fit. The squares show the sumof events with η , ω , and ρ production, the latter corrected forthe ρ + ρ − production. ber of events found from the fit to the ρ peak so that itcorresponds to the number of events with either a single ρ ± or with a ρ + ρ − pair. This summed curve is seen tobe in agreement with the total number of 2( π + π − )3 π events; we conclude there is no significant contributionfrom other (unobserved) intermediate states. VII. THE 2( π + π − )2 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. 26(a). Weobtain 1651 ±
50 events. Figure 26(b) shows the massdistribution of these events. ), GeV/c gg m( E v en t s / . G e V / c (a) ), GeV/c gg p )2 - p + p m(2( E v en t s / . G e V / c (b) FIG. 26: Mass distributions for the 2( π + π − )2 π η finalstate. (a) The third-photon-pair invariant mass for data. Thedashed curve shows the fitted background. The solid curveshows the sum of background and the two-Gaussian fit func-tion used to obtain the number of events with an η . (b)The invariant-mass distribution for the 2( π + π − )2 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. We fit the η peak in the uds simulation in intervals of 0.05 GeV /c in m (2( π + π − ) π π γγ ). The results are shown by the9 , GeV c.m. E ) , nb h p p - p + p - p + pfi - e + ( e s FIG. 27: Energy dependent cross section for e + e − → π + π − ) π π η . The uncertainties are statistical only. squares in Fig. 26 (b).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 . ± . C. 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. 27and listed in Table VII. These are the first results forthis process. The systematic uncertainties and correc-tions are the same as those presented in Table II exceptthat the uncertainty in the detection efficiency increasesto 13%.The cross section is approximately zero until well above2 GeV and so is not useful in the vacuum polarizationcalculations; we have not yet performed a study of inter-mediate states for this process. VIII. THE
J/ψ
REGIONA. The 2( π + π − )3 π final state Figure 28(a) shows an expanded view of the charmo-nium region from Fig. 9, which has large contributionsfrom the
J/ψ and ψ (2 S ) decays to seven pions. The non-resonant background distribution 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. 28(b).The sum of two Gaussians with a common mean is usedto describe each peak. We obtain 3391 ± J/ψ eventsand 290 ± ψ (2 S ) events. Using these results for thenumber of events, the detection efficiency, and the ISR ), GeV/c p )3 - p + p m(2( E en t s / . G e V / c (a) ), GeV/c p )3 - p + p m(2( E v en t s / . G e V / c (b) FIG. 28: (a) The 2( π + π − )3 π mass distribution for ISR-produced e + e − → π + π − ) π π π events in the J/ψ – ψ (2 S )region. (b) The MC-simulated signals. The curves show thefit functions described in the text. luminosity, we determine the product: B J/ψ → π · Γ J/ψee = N ( J/ψ → π + π − )3 π ) · m J/ψ π · d L /dE · (cid:15) MC · (cid:15) corr · C (2)= (345 ± ±
50) 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 . ± .
002 is the detection efficiencyfrom simulation, (cid:15) corr = 0 .
85 is the correction, discussedin Sec. VI D, and C = 3 . × nb MeV is a con-version constant [25]. We estimate the systematic un-certainty for this region to be 15%. The subscript “7 π ”for the branching fraction refers to the 2( π + π − )3 π finalstate exclusively.Using Γ J/ψee = 5 . ± .
10 keV [25], we obtain B J/ψ → π = (6 . ± . ± . × − : no other measure-ments for this channel exist. It is the largest decay modeof the J/ψ measured so far.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 = (33 ± ±
5) eV . With Γ ψ (2 S ) ee = 2 . ± .
04 keV [25] we find B ψ (2 S ) → π =(1 . ± . ± . × − . For this channel also, no previousresult exists.The ψ (2 S ) peak partly corresponds to the decay chain ψ (2 S ) → J/ψπ π or ψ (2 S ) → J/ψπ + π − , with J/ψ de-caying to five pions. We select the 2( π + π − )3 π events inthe ±
100 MeV /c window around the ψ (2 S ) mass and cal-culate 2( π + π − ) π and π + π − π invariant masses, shownin Fig. 29(a) and Fig. 29(b), respectively. Clear signalsfrom the above decay chains are seen. Performing a fit tothese distributions yields 130 ± ψ (2 S ) → J/ψπ π → π + π − )3 π events and 114 ± ψ (2 S ) → J/ψπ + π − → π + π − )3 π events. In conjunction with the detectionefficiency and ISR luminosity, this yields: B ψ (2 S ) → J/ψπ π · B J/ψ → π + π − ) π · Γ ψ (2 S ) ee =(14 . ± . ± .
2) eV ,B ψ (2 S ) → J/ψπ + π − · B J/ψ → π + π − π · Γ ψ (2 S ) ee =(19 . ± . ± .
2) eV . ), GeV/c p ) - p + p m(2( 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. 29: The 2( π + π − ) π invariant mass (a) and π + π − π invariant mass (b) for events with a seven-pion invariant masswithin ±
100 MeV /c of the ψ (2 S ). The curves show the fitfunctions for all events (solid) and the contribution of thebackground (dashed). With Γ ψ (2 S ) ee as stated above and B ψ (2 S ) → J/ψπ π =0 . ± . B ψ (2 S ) → J/ψπ + π − = 0 . ± . B J/ψ → π + π − ) π = (3 . ± . ± . B J/ψ → π + π − π = (2 . ± . ± . B J/ψ → π + π − ) π =(3 . ± . S = 1 . B J/ψ → π + π − π = (2 . ± . B A B AR measurements are listed inPDG [25] for the last channel. The ωπ + π − π π , ηπ + π − π π intermediatestates Figure 30(a) shows an expanded view of Fig. 20 withthe 2( π + π − )3 π mass distribution for events obtainedby a fit to the π + π − π mass distribution to select eventswith an ω . The two-Gaussian fit, implemented as de-scribed above, yields 1619 ±
92 and 159 ±
35 events forthe
J/ψ and ψ (2 S ), respectively. Using Eq.(2) we obtain: B J/ψ → ωπ + π − π π · B ω → π + π − π · Γ J/ψee =(165 ± ±
25) eV ,B ψ (2 S ) → ωπ + π − π π · B ω → π + π − π · Γ ψ (2 S ) ee =(18 ± ±
3) eV . ), GeV/c p )3 - p + p m(2( E v en t s / . G e V / c (a) ), GeV/c p )3 - p + p m(2( E v en t s / . G e V / c (b) FIG. 30: The seven-pion invariant mass for events with athree-pion invariant mass in the ω (792) (a) or η (b) massregions. The curves show the fit functions described in thetext. Using B ω → π + π − π = 0 .
891 and the value of Γ ee fromRef. [25], we obtain B J/ψ → ωπ + π − π π = (3 . ± . ± . × − and B ψ (2 S ) → ωπ + π − π π = (0 . ± . ± . × − .There are no other measurements of these decays.Similarly, an expanded view of Fig. 22 is shown inFig. 30(b) for 2( π + π − )3 π events with an η signal inthe π + π − π invariant mass. The fit yields 60 ±
41 eventscorresponding to B J/ψ → ηπ + π − π π · B η → π + π − π · Γ J/ψee =(6 ± ±
1) eV , which corresponds to B J/ψ → ηπ + π − π π = (4 . ± . ± . × − . We obtain reasonable agreement with theonly available result B J/ψ → ηπ + π − π π = (2 . ± . × − [13], obtained by B A B AR in the η → γγ decay mode.Note that the J/ψ decay to the ωπ η mode is almostten times smaller, (0 . ± . × − [13], and cannotbe extracted from our data. The ηπ + π − π + π − intermediate state An expanded view of Fig. 16 is shown in Fig. 31(a).The fit yields 55 ±
25 events corresponding to B J/ψ → η π + π − ) · B η → π · Γ J/ψee =(5 . ± . ± .
8) eV ,B J/ψ → η π + π − ) = (2 . ± . ± . × − . The result is in agreement with world average value(2 . ± . × − [25]. We only can set an upperlimit for the ψ (2 S ) → η π + π − ) decay: we observe < B ψ (2 S ) → η π + π − ) < . × − at 90% C.L., which is consistent with the world averagevalue 1 . ± . × − [25]. The ρ ± π ∓ π + π − π π intermediate state Figure 31(b) shows an expanded view of Fig. 25(a)(circles) for the 2( π + π − )3 π mass for events obtainedfrom the fit to the ρ signal in the π ± π mass. The two-Gaussian fit yields 2149 ±
363 and 266 ±
157 events forthe
J/ψ and ψ (2 S ), respectively.As shown in Sec. VI E 5 about 20% of these eventsarise from the J/ψ → ρ ± ρ ∓ π + π − π decays. We estimatethe number of J/ψ decays to single- and double- ρ to be1526 ± ±
279 and 312 ± ± ρ + ρ − events,given above. We obtain: B J/ψ → ρ ± π ∓ π + π − π π · Γ J/ψee = (155 ± ± ±
22) eV ,B J/ψ → ρ + ρ − π + π − π · Γ J/ψee = (32 ± ± ±
5) eV . Dividing by the value of Γ ee from Ref. [25] then yields: B J/ψ → ρ ± π ∓ π + π − π π = (2 . ± . ± . ± . × − ,B J/ψ → ρ + ρ − π + π − π = (0 . ± . ± . ± . × − , ), GeV/c p )3 - p + p m(2( 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 p r (b) ), GeV/c h p )2 - p + p m(2( E en t s / . G e V / c (c) FIG. 31: The
J/ψ region for 2( π + π − )3 π events for selection of (a) the ηπ + π − π + π − and (b) the ρ ± π ∓ π + π − π intermediatestates. (c) The J/ψ region for 2( π + π − )2 π η events. The curves show the fit functions described in the text.TABLE VIII: 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 [25]Γ J/ψee ·B J/ψ → π + π − π + π − π π π ± ± ± ± J/ψee ·B J/ψ → ωπ + π − π π · B ω → π + π − π ± ± ± ± J/ψee ·B J/ψ → ηπ + π − π π · B η → π + π − π ± ± ± ± ± J/ψee ·B J/ψ → π + π − π + π − η · B η → π π π ± ± ± ± ± J/ψee ·B J/ψ → ρ ± π ∓ π + π − π π ± ± ± ± J/ψee ·B J/ψ → ρ + ρ − π + π − π ± ± ± ± J/ψee ·B J/ψ → π + π − π + π − π π η · B η → γγ ± ± ± ± ψ (2 S ) ee ·B ψ (2 S ) → π + π − π + π − π π π ± ± ± ± ψ (2 S ) ee ·B ψ (2 S ) → J/ψπ π · B J/ψ → π + π − π + π − π ± ± ± ± ± ψ (2 S ) ee ·B ψ (2 S ) → J/ψπ + π − · B J/ψ → π + π − π π π ± ± ± ± ± ψ (2 S ) ee ·B ψ (2 S ) → ωπ + π − π π · B ω → π + π − π ± ± ± ± ψ (2 S ) ee ·B ψ (2 S ) → π + π − π + π − π π η · B η → γγ <
1. 9 at 90% C.L. <
2. 0 at 90% C.L. no entryΓ ψ (2 S ) ee ·B ψ (2 S ) → π + π − π + π − η · B η → π π π <
2. 3 at 90% C.L. <
2. 4 at 90% C.L. 1.2 ± where the third uncertainty is associated with the pro-cedure used to determine the correlated ρ + ρ − rate. Noother measurements for these processes exist.For the ψ (2 S ) → ρ ± π ∓ π + π − π π decay we find266 ±
157 events. We cannot extract and estimate thesize of the contribution of double- ρ events, so we do notcalculate branching fractions. B. The 2( π + π − )2 π η final state The expanded view of Fig. 26(b) is shown in Fig. 31(c).The fit yields 90 ±
26 for the
J/ψ → π + π − )2 π η eventscorresponding to B J/ψ → η π + π − )2 π · B η → γγ · Γ J/ψee =(9 . ± . ± .
4) eV ,B J/ψ → η π + π − )2 π = (4 . ± . ± . × − . We set an upper limit ψ (2 S ) → η π + π − )2 π decay:we observe <
18 events at 90% C.L. corresponding to B ψ (2 S ) → η π + π − )2 π < . × − . There are no previous results for these final states. C. Summary of the charmonium region study
The rates of
J/ψ and ψ (2 S ) decays to 2( π + π − )3 π ,2( π + π − )2 π η and several intermediate final states havebeen measured. The measured products and calculatedbranching fractions are summarized in Table VIII to-gether with the available PDG values for comparison. IX. SUMMARY
The excellent performance of the B A B AR detector forphoton energy and charged-particle resolution, togetherwith its strong particle identification capabilities, allowthe reconstruction of the 2( π + π − )3 π and 2( π + π − )2 π η final states from threshold up to 4.5 GeV via the ISRprocess.The analysis shows that the effective luminosity and2efficiency have been understood with 10–13% accu-racy. The cross section measurements for the e + e − → π + π − )3 π and the e + e − → π + π − )2 π η reactions hasbeen measured for the first time.The selected multi-hadronic final states in the broadrange of accessible energies provide new informationon hadron spectroscopy. The observed e + e − → ωπ + π − π π , e + e − → ηπ + π − π π , and e + e − → η π + π − ) cross sections provide additional informationfor the hadronic contribution calculation of the muon g − J/ψ and ψ (2 S ) production and a measurement of thecorresponding products of the decay branching fractionsand e + e − width for most of the studied channels, themajority of them for the first time. X. ACKNOWLEDGMENTS
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