The $e^+ e^-\to K^+ K^- \pi^+\pi^-$, $K^+ K^- \pi^0\pi^0$ and $K^+ K^-
  K^+ K^-$ Cross Sections Measured with Initial-State Radiation
BABAR-PUB-07/021
SLAC-PUB-12435
Phys. Rev. D76, 012008 (2007)
The e+e− → K+K−π+π−, K+K−π0π0 and K+K−K+K− Cross Sections Measured
with Initial-State Radiation
B. Aubert, M. Bona, D. Boutigny, Y. Karyotakis, J. P. Lees, V. Poireau, X. Prudent, V. Tisserand, and A. Zghiche
Laboratoire de Physique des Particules, IN2P3/CNRS et Université de Savoie, F-74941 Annecy-Le-Vieux, France
J. Garra Tico and E. Grauges
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
L. Lopez and A. Palano
Università di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy
G. Eigen, B. Stugu, and L. Sun
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
G. S. Abrams, M. Battaglia, D. N. Brown, J. Button-Shafer, R. N. Cahn, Y. Groysman,
R. G. Jacobsen, J. A. Kadyk, L. T. Kerth, Yu. G. Kolomensky, G. Kukartsev, D. Lopes Pegna,
G. Lynch, L. M. Mir, T. J. Orimoto, M. T. Ronan,∗ K. Tackmann, and W. A. Wenzel
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
P. del Amo Sanchez, C. M. Hawkes, and A. T. Watson
University of Birmingham, Birmingham, B15 2TT, United Kingdom
T. Held, H. Koch, B. Lewandowski, M. Pelizaeus, T. Schroeder, and M. Steinke
Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany
D. Walker
University of Bristol, Bristol BS8 1TL, United Kingdom
D. J. Asgeirsson, T. Cuhadar-Donszelmann, B. G. Fulsom,
C. Hearty, N. S. Knecht, T. S. Mattison, and J. A. McKenna
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
M. Barrett, A. Khan, M. Saleem, and L. Teodorescu
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
V. E. Blinov, A. D. Bukin, V. P. Druzhinin, V. B. Golubev, A. P. Onuchin,
S. I. Serednyakov, Yu. I. Skovpen, E. P. Solodov, and K. Yu Todyshev
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
M. Bondioli, S. Curry, I. Eschrich, D. Kirkby, A. J. Lankford, P. Lund, M. Mandelkern, E. C. Martin, and D. P. Stoker
University of California at Irvine, Irvine, California 92697, USA
S. Abachi and C. Buchanan
University of California at Los Angeles, Los Angeles, California 90024, USA
S. D. Foulkes, J. W. Gary, F. Liu, O. Long, B. C. Shen, and L. Zhang
University of California at Riverside, Riverside, California 92521, USA
H. P. Paar, S. Rahatlou, and V. Sharma
University of California at San Diego, La Jolla, California 92093, USA
J. W. Berryhill, C. Campagnari, A. Cunha, B. Dahmes, T. M. Hong, D. Kovalskyi, and J. D. Richman
http://arxiv.org/abs/0704.0630v3
University of California at Santa Barbara, Santa Barbara, California 93106, USA
T. W. Beck, A. M. Eisner, C. J. Flacco, C. A. Heusch, J. Kroseberg, W. S. Lockman,
T. Schalk, B. A. Schumm, A. Seiden, D. C. Williams, M. G. Wilson, and L. O. Winstrom
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
E. Chen, C. H. Cheng, F. Fang, D. G. Hitlin, I. Narsky, T. Piatenko, and F. C. Porter
California Institute of Technology, Pasadena, California 91125, USA
G. Mancinelli, B. T. Meadows, K. Mishra, and M. D. Sokoloff
University of Cincinnati, Cincinnati, Ohio 45221, USA
F. Blanc, P. C. Bloom, S. Chen, W. T. Ford, J. F. Hirschauer, A. Kreisel, M. Nagel,
U. Nauenberg, A. Olivas, J. G. Smith, K. A. Ulmer, S. R. Wagner, and J. Zhang
University of Colorado, Boulder, Colorado 80309, USA
A. M. Gabareen, A. Soffer, W. H. Toki, R. J. Wilson, F. Winklmeier, and Q. Zeng
Colorado State University, Fort Collins, Colorado 80523, USA
D. D. Altenburg, E. Feltresi, A. Hauke, H. Jasper, J. Merkel, A. Petzold, B. Spaan, and K. Wacker
Universität Dortmund, Institut für Physik, D-44221 Dortmund, Germany
T. Brandt, V. Klose, M. J. Kobel, H. M. Lacker, W. F. Mader, R. Nogowski,
J. Schubert, K. R. Schubert, R. Schwierz, J. E. Sundermann, and A. Volk
Technische Universität Dresden, Institut für Kern- und Teilchenphysik, D-01062 Dresden, Germany
D. Bernard, G. R. Bonneaud, E. Latour, V. Lombardo, Ch. Thiebaux, and M. Verderi
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
P. J. Clark, W. Gradl, F. Muheim, S. Playfer, A. I. Robertson, and Y. Xie
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
M. Andreotti, D. Bettoni, C. Bozzi, R. Calabrese, A. Cecchi, G. Cibinetto, P. Franchini,
E. Luppi, M. Negrini, A. Petrella, L. Piemontese, E. Prencipe, and V. Santoro
Università di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy
F. Anulli, R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro,
S. Pacetti, P. Patteri, I. M. Peruzzi,† M. Piccolo, M. Rama, and A. Zallo
Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
A. Buzzo, R. Contri, M. Lo Vetere, M. M. Macri, M. R. Monge,
S. Passaggio, C. Patrignani, E. Robutti, A. Santroni, and S. Tosi
Università di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
K. S. Chaisanguanthum, M. Morii, and J. Wu
Harvard University, Cambridge, Massachusetts 02138, USA
R. S. Dubitzky, J. Marks, S. Schenk, and U. Uwer
Universität Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
D. J. Bard, P. D. Dauncey, R. L. Flack, J. A. Nash, M. B. Nikolich, and W. Panduro Vazquez
Imperial College London, London, SW7 2AZ, United Kingdom
P. K. Behera, X. Chai, M. J. Charles, U. Mallik, N. T. Meyer, and V. Ziegler
University of Iowa, Iowa City, Iowa 52242, USA
J. Cochran, H. B. Crawley, L. Dong, V. Eyges, W. T. Meyer, S. Prell, E. I. Rosenberg, and A. E. Rubin
Iowa State University, Ames, Iowa 50011-3160, USA
A. V. Gritsan, Z. J. Guo, and C. K. Lae
Johns Hopkins University, Baltimore, Maryland 21218, USA
A. G. Denig, M. Fritsch, and G. Schott
Universität Karlsruhe, Institut für Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
N. Arnaud, J. Béquilleux, M. Davier, G. Grosdidier, A. Höcker, V. Lepeltier, F. Le Diberder, A. M. Lutz, S. Pruvot,
S. Rodier, P. Roudeau, M. H. Schune, J. Serrano, V. Sordini, A. Stocchi, W. F. Wang, and G. Wormser
Laboratoire de l’Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d’Orsay, B. P. 34, F-91898 ORSAY Cedex, France
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
C. A. Chavez, I. J. Forster, J. R. Fry, E. Gabathuler, R. Gamet,
D. E. Hutchcroft, D. J. Payne, K. C. Schofield, and C. Touramanis
University of Liverpool, Liverpool L69 7ZE, United Kingdom
A. J. Bevan, K. A. George, F. Di Lodovico, W. Menges, and R. Sacco
Queen Mary, University of London, E1 4NS, United Kingdom
G. Cowan, H. U. Flaecher, D. A. Hopkins, P. S. Jackson, T. R. McMahon, F. Salvatore, and A. C. Wren
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
D. N. Brown and C. L. Davis
University of Louisville, Louisville, Kentucky 40292, USA
J. Allison, N. R. Barlow, R. J. Barlow, Y. M. Chia, C. L. Edgar, G. D. Lafferty, T. J. West, and J. I. Yi
University of Manchester, Manchester M13 9PL, United Kingdom
J. Anderson, C. Chen, A. Jawahery, D. A. Roberts, G. Simi, and J. M. Tuggle
University of Maryland, College Park, Maryland 20742, USA
G. Blaylock, C. Dallapiccola, S. S. Hertzbach, X. Li, T. B. Moore, E. Salvati, and S. Saremi
University of Massachusetts, Amherst, Massachusetts 01003, USA
R. Cowan, P. H. Fisher, G. Sciolla, S. J. Sekula, M. Spitznagel, F. Taylor, and R. K. Yamamoto
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
S. E. Mclachlin, P. M. Patel, and S. H. Robertson
McGill University, Montréal, Québec, Canada H3A 2T8
A. Lazzaro and F. Palombo
Università di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
J. M. Bauer, L. Cremaldi, V. Eschenburg, R. Godang, R. Kroeger, D. A. Sanders, D. J. Summers, and H. W. Zhao
University of Mississippi, University, Mississippi 38677, USA
S. Brunet, D. Côté, M. Simard, P. Taras, and F. B. Viaud
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
H. Nicholson
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
G. De Nardo, F. Fabozzi,‡ L. Lista, D. Monorchio, and C. Sciacca
Università di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
M. A. Baak, G. Raven, and H. L. Snoek
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
G. Benelli, L. A. Corwin, K. K. Gan, K. Honscheid, D. Hufnagel, H. Kagan, R. Kass,
J. P. Morris, A. M. Rahimi, J. J. Regensburger, R. Ter-Antonyan, and Q. K. Wong
Ohio State University, Columbus, Ohio 43210, USA
N. L. Blount, J. Brau, R. Frey, O. Igonkina, J. A. Kolb, M. Lu,
R. Rahmat, N. B. Sinev, D. Strom, J. Strube, and E. Torrence
University of Oregon, Eugene, Oregon 97403, USA
N. Gagliardi, A. Gaz, M. Margoni, M. Morandin, A. Pompili,
M. Posocco, M. Rotondo, F. Simonetto, R. Stroili, and C. Voci
Università di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
E. Ben-Haim, H. Briand, G. Calderini, J. Chauveau, P. David, L. Del Buono,
Ch. de la Vaissière, O. Hamon, Ph. Leruste, J. Malclès, J. Ocariz, and A. Perez
Laboratoire de Physique Nucléaire et de Hautes Energies,
IN2P3/CNRS, Université Pierre et Marie Curie-Paris6,
Université Denis Diderot-Paris7, F-75252 Paris, France
L. Gladney
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
M. Biasini, R. Covarelli, and E. Manoni
Università di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy
C. Angelini, G. Batignani, S. Bettarini, M. Carpinelli, R. Cenci, A. Cervelli, F. Forti, M. A. Giorgi,
A. Lusiani, G. Marchiori, M. A. Mazur, M. Morganti, N. Neri, E. Paoloni, G. Rizzo, and J. J. Walsh
Università di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
M. Haire
Prairie View A&M University, Prairie View, Texas 77446, USA
J. Biesiada, P. Elmer, Y. P. Lau, C. Lu, J. Olsen, A. J. S. Smith, and A. V. Telnov
Princeton University, Princeton, New Jersey 08544, USA
E. Baracchini, F. Bellini, G. Cavoto, A. D’Orazio, D. del Re, E. Di Marco, R. Faccini, F. Ferrarotto, F. Ferroni,
M. Gaspero, P. D. Jackson, L. Li Gioi, M. A. Mazzoni, S. Morganti, G. Piredda, F. Polci, F. Renga, and C. Voena
Università di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
M. Ebert, H. Schröder, and R. Waldi
Universität Rostock, D-18051 Rostock, Germany
T. Adye, G. Castelli, B. Franek, E. O. Olaiya, S. Ricciardi, W. Roethel, and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
R. Aleksan, S. Emery, M. Escalier, A. Gaidot, S. F. Ganzhur, G. Hamel de Monchenault,
W. Kozanecki, M. Legendre, G. Vasseur, Ch. Yèche, and M. Zito
DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
X. R. Chen, H. Liu, W. Park, M. V. Purohit, and J. R. Wilson
University of South Carolina, Columbia, South Carolina 29208, USA
M. T. Allen, D. Aston, R. Bartoldus, P. Bechtle, N. Berger, R. Claus, J. P. Coleman, M. R. Convery,
J. C. Dingfelder, J. Dorfan, G. P. Dubois-Felsmann, D. Dujmic, W. Dunwoodie, R. C. Field, T. Glanzman,
S. J. Gowdy, M. T. Graham, P. Grenier, C. Hast, T. Hryn’ova, W. R. Innes, J. Kaminski, M. H. Kelsey,
H. Kim, P. Kim, M. L. Kocian, D. W. G. S. Leith, S. Li, S. Luitz, V. Luth, H. L. Lynch, D. B. MacFarlane,
H. Marsiske, R. Messner, D. R. Muller, C. P. O’Grady, I. Ofte, A. Perazzo, M. Perl, T. Pulliam,
B. N. Ratcliff, A. Roodman, A. A. Salnikov, R. H. Schindler, J. Schwiening, A. Snyder, J. Stelzer, D. Su,
M. K. Sullivan, K. Suzuki, S. K. Swain, J. M. Thompson, J. Va’vra, N. van Bakel, A. P. Wagner,
M. Weaver, W. J. Wisniewski, M. Wittgen, D. H. Wright, A. K. Yarritu, K. Yi, and C. C. Young
Stanford Linear Accelerator Center, Stanford, California 94309, USA
P. R. Burchat, A. J. Edwards, S. A. Majewski, B. A. Petersen, and L. Wilden
Stanford University, Stanford, California 94305-4060, USA
S. Ahmed, M. S. Alam, R. Bula, J. A. Ernst, V. Jain, B. Pan, M. A. Saeed, F. R. Wappler, and S. B. Zain
State University of New York, Albany, New York 12222, USA
W. Bugg, M. Krishnamurthy, and S. M. Spanier
University of Tennessee, Knoxville, Tennessee 37996, USA
R. Eckmann, J. L. Ritchie, A. M. Ruland, C. J. Schilling, and R. F. Schwitters
University of Texas at Austin, Austin, Texas 78712, USA
J. M. Izen, X. C. Lou, and S. Ye
University of Texas at Dallas, Richardson, Texas 75083, USA
F. Bianchi, F. Gallo, D. Gamba, and M. Pelliccioni
Università di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
M. Bomben, L. Bosisio, C. Cartaro, F. Cossutti, G. Della Ricca, L. Lanceri, and L. Vitale
Università di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
V. Azzolini, N. Lopez-March, F. Martinez-Vidal, D. A. Milanes, and A. Oyanguren
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
J. Albert, Sw. Banerjee, B. Bhuyan, K. Hamano, R. Kowalewski, I. M. Nugent, J. M. Roney, and R. J. Sobie
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
J. J. Back, P. F. Harrison, T. E. Latham, G. B. Mohanty, and M. Pappagallo§
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
H. R. Band, X. Chen, S. Dasu, K. T. Flood, J. J. Hollar,
P. E. Kutter, Y. Pan, M. Pierini, R. Prepost, S. L. Wu, and Z. Yu
University of Wisconsin, Madison, Wisconsin 53706, USA
H. Neal
Yale University, New Haven, Connecticut 06511, USA
(Dated: November 4, 2018)
We study the processes e+e− → K+K−π+π−γ, K+K−π0π0γ and K+K−K+K−γ, where the
photon is radiated from the initial state. About 34600, 4400 and 2300 fully reconstructed events,
respectively, are selected from 232 fb−1 of BABAR data. The invariant mass of the hadronic final state
defines the effective e+e− center-of-mass energy, so that the K+K−π+π−γ data can be compared
with direct measurements of the e+e− → K+K−π+π− reaction; no direct measurements exist for
the e+e− → K+K−π0π0 or e+e− → K+K−K+K− reactions. Studying the structure of these
events, we find contributions from a number of intermediate states, and we extract their cross
sections where possible. In particular, we isolate the contribution from e+e− → φ(1020)f0(980)
and study its structure near threshold. In the charmonium region, we observe the J/ψ in all three
final states and several intermediate states, as well as the ψ(2S) in some modes, and measure the
corresponding branching fractions. We see no signal for the Y (4260) and obtain an upper limit of
BY (4260)→φπ+π− · Γ
ee < 0.4 eV at 90% C.L.
PACS numbers: 13.66.Bc, 14.40.Cs, 13.25.Gv, 13.25.Jx, 13.20.Jf
I. INTRODUCTION
Electron-positron annihilation at fixed center-of-mass
(c.m.) energies has long been a mainstay of research in
elementary particle physics. The idea of utilizing initial-
state radiation (ISR) to explore e+e− reactions below the
nominal c.m. energies was outlined in Ref. [1], and dis-
cussed in the context of high-luminosity φ and B facto-
ries in Refs. [2, 3, 4]. At high energies, e+e− annihilation
is dominated by quark-level processes producing two or
more hadronic jets. However, low-multiplicity exclusive
processes dominate at energies below about 2 GeV, and
the region near charm threshold, 3.0–4.5 GeV, features
a number of resonances [5]. These allow us to probe a
wealth of physics parameters, including cross sections,
spectroscopy and form factors.
Of particular current interest are the recently observed
states in the charmonium region, such as the Y (4260) [6],
and a possible discrepancy between the measured value
of the anomalous magnetic moment of the muon, gµ− 2,
and that predicted by the Standard Model [7]. Charmo-
nium and other states with JPC = 1−− can be observed
as resonances in the cross section, and intermediate states
may be present in the hadronic system. Measurements
of the decay modes and their branching fractions are im-
portant in understanding the nature of these states. For
example, the glue-ball model [8] predicts a large branch-
ing fraction for Y (4260) into φππ. The prediction for
gµ − 2 is based on hadronic-loop corrections measured
from low-energy e+e− → hadrons data, and these dom-
inate the uncertainty on the prediction. Improving this
prediction requires not only more precise measurements,
but also measurements over the entire energy range and
inclusion of all the important subprocesses in order to un-
derstand possible acceptance effects. ISR events atB fac-
tories provide independent and contiguous measurements
of hadronic cross sections from the production threshold
to about 5 GeV.
The cross section for the radiation of a photon of
energy Eγ followed by the production of a particular
hadronic final state f is related to the corresponding di-
rect e+e− → f cross section σf (s) by
dσγf (s, x)
=W (s, x) · σf (s(1− x)) , (1)
where
s is the initial e+e− c.m. energy, x = 2Eγ/
is the fractional energy of the ISR photon and Ec.m. ≡
∗Deceased
†Also with Università di Perugia, Dipartimento di Fisica, Perugia,
Italy
‡Also with Università della Basilicata, Potenza, Italy
§Also with IPPP, Physics Department, Durham University,
Durham DH1 3LE, United Kingdom
s(1− x) is the effective c.m. energy at which the fi-
nal state f is produced. The probability density function
W (s, x) for ISR photon emission has been calculated with
better than 1% precision (see e.g. Ref. [4]). It falls rapidly
as Eγ increases from zero, but has a long tail, which com-
bines with the increasing σf (s(1−x)) to produce a sizable
cross section at very low Ec.m.. The angular distribution
of the ISR photon peaks along the beam directions, but
10–15% [4] of the photons are within a typical detector
acceptance.
Experimentally, the measured invariant mass of the
hadronic final state defines Ec.m.. An important feature
of ISR data is that a wide range of energies is scanned
simultaneously in one experiment, so that no structure
is missed and the relative normalization uncertainties in
data from different experiments or accelerator parame-
ters are avoided. Furthermore, for large values of x the
hadronic system is collimated, reducing acceptance issues
and allowing measurements at energies down to produc-
tion threshold. The mass resolution is not as good as a
typical beam energy spread used in direct measurements,
but the resolution and absolute energy scale can be mon-
itored by the width and mass of well known resonances,
such as the J/ψ produced in the reaction e+e− → J/ψγ.
Backgrounds from e+e− → hadrons events at the nomi-
s and from other ISR processes can be suppressed
by a combination of particle identification and kinematic
fitting techniques. Studies of e+e− → µ+µ−γ and sev-
eral multi-hadron ISR processes using BABAR data have
been reported [9, 10, 11, 12], demonstrating the viability
of such measurements.
The K+K−π+π− final state has been measured di-
rectly by the DM1 collaboration [13] for
s < 2.2 GeV,
and we have previously published ISR measurements of
the K+K−π+π− and K+K−K+K− final states [11] for
Ec.m.< 4.5 GeV. We recently reported [14] an updated
measurement of theK+K−π+π− final state with a larger
data sample, along with the first measurement of the
K+K−π0π0 final state, in which we observed a struc-
ture near threshold in the φf0 intermediate state. In
this paper we present a more detailed study of these two
final states along with an updated measurement of the
K+K−K+K− final state. In all cases we require detec-
tion of the ISR photon and perform a set of kinematic
fits. We are able to suppress backgrounds sufficiently to
study these final states from their respective production
thresholds up to 5 GeV. In addition to measuring the
overall cross sections, we study the internal structure of
the events and measure cross sections for a number of
intermediate states. We study the charmonium region,
measure several J/ψ and ψ(2S) branching fractions, and
set limits on other states.
II. THE BABAR DETECTOR AND DATASET
The data used in this analysis were collected with the
BABAR detector at the PEP-II asymmetric energy e+e−
storage rings. The total integrated luminosity used is
232 fb−1, which includes 211 fb−1 collected at the Υ (4S)
peak,
s = 10.58 GeV, and 21 fb−1 collected below the
resonance, at
s = 10.54 GeV.
The BABAR detector is described elsewhere [15]. Here
we use charged particles reconstructed in the track-
ing system, which comprises the five-layer silicon vertex
tracker (SVT) and the 40-layer drift chamber (DCH) in
a 1.5 T axial magnetic field. Separation of charged pi-
ons, kaons and protons uses a combination of Cherenkov
angles measured in the detector of internally reflected
Cherenkov light (DIRC) and specific ionization measured
in the SVT and DCH. For the present study we use a kaon
identification algorithm that provides 90–95% efficiency,
depending on momentum, and pion and proton rejection
factors in the 20–100 range. Photon and electron energies
are measured in the CsI(Tl) electromagnetic calorimeter
(EMC). We use muon identification provided by the in-
strumented flux return (IFR) to select the µ+µ−γ final
state.
To study the detector acceptance and efficiency, we
use a simulation package developed for radiative pro-
cesses. The simulation of hadronic final states, includ-
ing K+K−π+π−γ, K+K−π0π0γ and K+K−K+K−γ,
is based on the approach suggested by Czyż and
Kühn[16]. Multiple soft-photon emission from the initial-
state charged particles is implemented with a structure-
function technique [17, 18], and photon radiation from
the final-state particles is simulated by the PHOTOS
package [19]. The accuracy of the radiative corrections
is about 1%.
We simulate the K+K−ππ final states both accord-
ing to phase space and with models that include the
φ(1020) → K+K− and/or f0(980) → ππ channels, and
the K+K−K+K− final state both according to phase
space and including the φ → K+K− channel. The
generated events go through a detailed detector simula-
tion [20], and we reconstruct them with the same software
chain as the experimental data. Variations in detector
and background conditions are taken into account.
We also generate a large number of background pro-
cesses, including the ISR channels e+e−→ π+π−π+π−γ
and π+π−π0π0γ, which can contribute due to particle
misidentification, and φηγ, φπ0γ, π+π−π0γ, which have
larger cross sections and can contribute via missing or
spurious tracks or photons. In addition, we study the
non-ISR backgrounds e+e−→qq (q = u, d, s, c) generated
by JETSET [21] and e+e−→ τ+τ− by KORALB [22].
The contribution from the Υ (4S) decays is found to be
negligible. The cross sections for these processes are
known with about 10% accuracy or better, which is suf-
ficient for these measurements.
III. EVENT SELECTION AND KINEMATIC FIT
In the initial selection of candidate events, we con-
sider photon candidates in the EMC with energy above
0.03 GeV and charged tracks reconstructed in the DCH
or SVT or both that extrapolate within 0.25 cm of the
beam axis in the transverse plane and within 3 cm of
the nominal collision point along the axis. These criteria
are looser than in our previous analysis [11], and have
been chosen to maximize efficiency. We require a high-
energy photon in the event with an energy in the initial
e+e− c.m. frame of Eγ > 3 GeV, and either exactly four
charged tracks with zero net charge and total momen-
tum roughly opposite to the photon direction, or exactly
two oppositely charged tracks that combine with a set
of other photons to roughly balance the highest-energy
photon momentum. We fit a vertex to the set of charged
tracks and use it as the point of origin to calculate the
photon direction. Most events contain additional soft
photons due to machine background or interactions in
the detector material.
We subject each of these candidate events to a set of
constrained kinematic fits, and use the fit results, along
with charged-particle identification, both to select the fi-
nal states of interest and to measure backgrounds from
other processes. We assume the photon with the highest
Eγ in the c.m. frame is the ISR photon, and the kine-
matic fits use its direction along with the four-momenta
and covariance matrices of the initial e+e− and the set
of selected tracks and photons. Because of excellent res-
olution for the momenta in the DCH and good angular
resolution for the photons in the EMC, the ISR photon
energy is determined with better resolution through four-
momentum conservation than through measurement in
the EMC. Therefore we do not use its measured energy
in the fits, eliminating the systematic uncertainty due to
the EMC calibration for high energy photons. The fitted
three-momenta for each charged track and photon are
used in further kinematical calculations.
For the four-track candidates, the fits have three con-
straints (3C). We first fit to the π+π−π+π− hypothesis,
obtaining a χ24π. If the four tracks include one identified
K+ and one K−, we fit to the K+K−π+π− hypothesis
and retain the event as a K+K−π+π− candidate. For
events with one identified kaon, we perform fits with each
of the two oppositely charged tracks given the kaon hy-
pothesis, and the combination with the lower χ2
KKπ+π−
is retained if it is lower than χ24π. If the event contains
three or four identified K±, we fit to the K+K−K+K−
hypothesis and retain the event as a K+K−K+K− can-
didate.
For the events with two charged tracks and five or more
photon candidates, we require both tracks to be identified
as kaons to suppress background from ISR π+π−π0π0
and K±K0
π∓ events. We then pair all non-ISR pho-
ton candidates and consider combinations with invariant
mass within ±30 MeV/c2 of the π0 mass as π0 candi-
dates. We perform a six-constraint (6C) fit to each set of
0 20 40 60
χ2(2K2π)
FIG. 1: Distribution of χ2 from the three-constraint fit for
K+K−π+π− candidates in the data (points). The open his-
togram is the distribution for simulated signal events, normal-
ized as described in the text. The cross-hatched (hatched) his-
togram represents the background from non-ISR events (plus
that from ISR 4π events), estimated as described in the text.
two non-overlapping π0 candidates plus the ISR photon
direction, the two tracks and the beam particles. Both
π0 candidates are constrained to the π0 mass, and we
retain the combination with the lowest χ2
KKπ0π0
IV. THE K+K−π+π− FINAL STATE
A. Final Selection and Backgrounds
The experimental χ2
KKπ+π−
distribution for the
K+K−π+π− candidates is shown in Fig. 1 as points, and
the open histogram is the distribution for the simulated
K+K−π+π− events. The simulated distribution is nor-
malized to the data in the region χ2
KKπ+π−
< 10 where
the backgrounds and radiative corrections are insignif-
icant. The experimental distribution has contributions
from background processes, but the simulated distribu-
tion is also broader than the expected 3C χ2 distribution.
This is due to multiple soft-photon emission from the ini-
tial state and radiation from the final-state charged par-
ticles, which are not taken into account by the fit, but are
present in both data and simulation. The shape of the χ2
distribution at high values was studied in detail [11, 12]
using specific ISR processes for which a very clean sample
can be obtained without any limit on the χ2 value.
The cross-hatched histogram in Fig. 1 represents the
background from e+e−→ qq events, which is based on
the JETSET simulation. It is dominated by events with
a hard π0 producing a fake ISR photon, and the similar
kinematics cause it to peak at low values of χ2
KKπ+π−
We evaluate this background in a number of Ec.m. ranges
by combining the ISR photon candidate with another
photon candidate in both data and simulated events,
and comparing the π0 signals in the resulting γγ invari-
ant mass distributions. The simulation gives an Ec.m.-
dependence consistent with the data, so we normalize
it by an overall factor. The hatched histogram repre-
sents the sum of this background and that from ISR
e+e−→π+π−π+π− events with one or two misidentified
π±, which also contributes at low χ2 values. We estimate
the contribution as a function of Ec.m. from a simulation
using the known cross section [11].
All remaining background sources are either negligible
or give a χ2
KKπ+π−
distribution that is nearly uniform
over the range shown in Fig. 1. We therefore define a
signal region χ2
KKπ+π−
<30, and estimate the sum of the
remaining backgrounds from the difference between the
number of data and simulated entries in a control region,
30<χ2
KKπ+π−
< 60. This difference is normalized to the
corresponding difference in the signal region, as described
in detail in Refs. [11, 12]. The signal region contains
34635 data and 14077 simulated events, and the control
region contains 4634 data and 723 simulated events.
1 2 3 4 5
m(K+K-π+π-) (GeV/c2)
FIG. 2: The invariant mass distribution for K+K−π+π−
candidates in the data (points): the cross-hatched, hatched
and open histograms represent, cumulatively, the non-ISR
background, the contribution from ISR π+π−π+π− events,
and the ISR background from the control region of Fig. 1.
Figure 2 shows the K+K−π+π− invariant mass dis-
tribution from threshold up to 5.0 GeV/c2 for events in
the signal region. Narrow peaks are apparent at the J/ψ
and ψ(2S) masses. The cross-hatched histogram repre-
sents the qq background, which is negligible at low mass
but becomes large at higher masses. The hatched region
represents the ISR π+π−π+π− contribution, which we es-
timate to be 2.4% of the selected events on average. The
open histogram represents the sum of all backgrounds,
including those estimated from the control region. They
total 6–8% at low mass but account for 20-25% of the ob-
served data near 4 GeV/c2 and become the largest con-
tribution near 5 GeV/c2.
We subtract the sum of backgrounds in each mass bin
to obtain a number of signal events. Considering un-
certainties in the cross sections for the background pro-
cesses, the normalization of events in the control region
and the simulation statistics, we estimate a systematic
uncertainty on the signal yield that is less than 3% in
the 1.6–3 GeV/c2 mass region, but increases to 3–5% in
the region above 3 GeV/c2.
B. Selection Efficiency
The selection procedures applied to the data are also
applied to the simulated signal samples. The resulting
K+K−π+π− invariant-mass distributions in the signal
and control regions are shown in Fig. 3(a) for the phase
space simulation. The broad, smooth mass distribution
is chosen to facilitate the estimation of the efficiency as a
function of mass, and this model reproduces the observed
distributions of kaon and pion momenta and polar angles.
We divide the number of reconstructed simulated events
in each mass interval by the number generated in that
interval to obtain the efficiency shown as the points in
Fig. 3(b). The 3rd order polynomial fit to the points is
used for further calculations. We simulate events with
the ISR photon confined to the angular range 20–160◦
with respect to the electron beam in the e+e− c.m. frame,
which is about 30% wider than the EMC acceptance.
This efficiency is for this fiducial region, but includes the
acceptance for the final-state hadrons, the inefficiencies of
the detector subsystems, and event loss due to additional
soft-photon emission.
The simulations including the φ(1020)π+π− and/or
K+K−f0(980) channels have very different mass and an-
gular distributions in the K+K−π+π− rest frame. How-
ever, the angular acceptance is quite uniform for ISR
events, and the efficiencies are consistent with those from
the phase space simulation within 3%. To study possible
mis-modeling of the acceptance, we repeat the analysis
with the tighter requirements that all charged tracks be
within the DIRC acceptance, 0.45<θch<2.4 radians, and
the ISR photon be well away from the edges of the EMC,
0.35< θISR < 2.4 radians. The fraction of selected data
events satisfying the tighter requirements differs from the
simulated ratio by 3.7%. We conservatively take the sum
in quadrature of this variation and the 3% model varia-
tion (5% total) as a systematic uncertainty due to accep-
tance and model dependence.
We correct for mis-modeling of the shape of the
KKπ+π−
distribution by (3.0±2.0)% and the track find-
ing efficiency following the procedures described in de-
tail in Ref. [11]. We use a comparison of data and sim-
ulated χ24π distributions in the much larger samples of
ISR π+π−π+π− events. We consider data and simulated
1 2 3 4
m(K+K-π+π-) (GeV/c2)
1 2 3 4
m(K+K-π+π-) (GeV/c2)
FIG. 3: (a) The invariant mass distributions for simulated
K+K−π+π− events in the phase space model, reconstructed
in the signal (open) and control (hatched) regions of Fig. 1;
(b) net reconstruction and selection efficiency as a function
of mass obtained from this simulation (the curve represents a
3rd order polynomial fit).
1 1.5 2 2.5 3 3.5 4 4.5 5
- DM1
- BaBar ISR
Ec.m. (GeV)
FIG. 4: The e+e−→K+K−π+π− cross section as a function
of the effective e+e− c.m. energy measured with ISR data at
BABAR (dots). The direct measurements from DM1 [13] are
shown as the open circles. Only statistical errors are shown.
events that contain a high-energy photon plus exactly
three charged tracks and satisfy a set of kinematical cri-
teria, including a good χ2 from a kinematic fit under the
hypothesis that there is exactly one missing track in the
event. We find that the simulated track-finding efficiency
is overestimated by (0.8 ± 0.5)% per track, so we apply
a correction of +(3± 2)% to the signal yield.
TABLE I: Measurements of the e+e−→ K+K−π+π− cross section (errors are statistical only).
Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb)
1.4125 0.00± 0.02 2.1375 2.83± 0.13 2.8625 0.50± 0.05 3.5875 0.12± 0.03 4.3125 0.04± 0.02
1.4375 0.01± 0.02 2.1625 2.71± 0.12 2.8875 0.51± 0.05 3.6125 0.13± 0.03 4.3375 0.04± 0.02
1.4625 0.00± 0.02 2.1875 2.46± 0.12 2.9125 0.54± 0.05 3.6375 0.12± 0.03 4.3625 0.03± 0.02
1.4875 0.04± 0.02 2.2125 1.84± 0.10 2.9375 0.46± 0.05 3.6625 0.11± 0.03 4.3875 0.06± 0.02
1.5125 0.03± 0.02 2.2375 1.66± 0.10 2.9625 0.45± 0.05 3.6875 0.25± 0.03 4.4125 0.01± 0.02
1.5375 0.11± 0.03 2.2625 1.59± 0.09 2.9875 0.46± 0.05 3.7125 0.07± 0.03 4.4375 0.03± 0.02
1.5625 0.15± 0.04 2.2875 1.66± 0.09 3.0125 0.36± 0.04 3.7375 0.08± 0.02 4.4625 0.06± 0.02
1.5875 0.32± 0.05 2.3125 1.50± 0.09 3.0375 0.39± 0.04 3.7625 0.11± 0.03 4.4875 0.03± 0.02
1.6125 0.48± 0.06 2.3375 1.65± 0.09 3.0625 0.31± 0.04 3.7875 0.11± 0.03 4.5125 0.04± 0.02
1.6375 0.85± 0.08 2.3625 1.56± 0.09 3.0875 2.95± 0.10 3.8125 0.10± 0.03 4.5375 0.01± 0.02
1.6625 1.42± 0.10 2.3875 1.49± 0.09 3.1125 1.51± 0.08 3.8375 0.08± 0.02 4.5625 0.02± 0.02
1.6875 1.86± 0.11 2.4125 1.46± 0.09 3.1375 0.37± 0.04 3.8625 0.12± 0.03 4.5875 0.05± 0.02
1.7125 2.36± 0.13 2.4375 1.48± 0.09 3.1625 0.35± 0.04 3.8875 0.09± 0.02 4.6125 0.02± 0.02
1.7375 2.67± 0.13 2.4625 1.17± 0.08 3.1875 0.28± 0.04 3.9125 0.09± 0.02 4.6375 0.01± 0.02
1.7625 3.51± 0.15 2.4875 1.16± 0.08 3.2125 0.35± 0.04 3.9375 0.08± 0.02 4.6625 0.04± 0.02
1.7875 3.98± 0.16 2.5125 1.21± 0.08 3.2375 0.31± 0.04 3.9625 0.10± 0.02 4.6875 0.02± 0.02
1.8125 4.10± 0.16 2.5375 0.94± 0.07 3.2625 0.30± 0.04 3.9875 0.04± 0.02 4.7125 0.03± 0.02
1.8375 4.68± 0.17 2.5625 0.95± 0.07 3.2875 0.24± 0.04 4.0125 0.06± 0.02 4.7375 0.01± 0.02
1.8625 4.49± 0.17 2.5875 0.84± 0.07 3.3125 0.22± 0.04 4.0375 0.07± 0.02 4.7625 0.02± 0.02
1.8875 4.26± 0.17 2.6125 0.85± 0.07 3.3375 0.25± 0.04 4.0625 0.05± 0.02 4.7875 0.01± 0.02
1.9125 4.30± 0.16 2.6375 0.90± 0.07 3.3625 0.16± 0.03 4.0875 0.06± 0.02 4.8125 0.00± 0.02
1.9375 4.20± 0.16 2.6625 0.82± 0.06 3.3875 0.17± 0.03 4.1125 0.06± 0.02 4.8375 0.02± 0.02
1.9625 4.13± 0.16 2.6875 0.70± 0.06 3.4125 0.18± 0.03 4.1375 0.05± 0.02 4.8625 0.00± 0.02
1.9875 3.74± 0.15 2.7125 0.86± 0.06 3.4375 0.12± 0.03 4.1625 0.06± 0.02 4.8875 0.04± 0.02
2.0125 3.45± 0.15 2.7375 0.81± 0.06 3.4625 0.17± 0.03 4.1875 0.05± 0.02 4.9125 0.05± 0.02
2.0375 3.38± 0.14 2.7625 0.76± 0.06 3.4875 0.17± 0.03 4.2125 0.05± 0.02 4.9375 0.02± 0.02
2.0625 3.17± 0.14 2.7875 0.73± 0.06 3.5125 0.21± 0.03 4.2375 0.08± 0.02 4.9625 0.00± 0.02
2.0875 3.23± 0.14 2.8125 0.64± 0.05 3.5375 0.14± 0.03 4.2625 0.04± 0.02 4.9875 0.04± 0.02
2.1125 3.15± 0.14 2.8375 0.56± 0.05 3.5625 0.16± 0.03 4.2875 0.08± 0.02
We correct the simulated kaon identification efficiency
using e+e−→φ(1020)γ→K+K−γ events. Events with a
hard ISR photon and two charged tracks, one of which is
identified as a kaon, with a K+K− invariant mass near
the φ mass provide a very clean sample, and we com-
pare the fractions of data and simulated events with the
other track also identified as a kaon, as a function of mo-
mentum. The data-simulation efficiency ratio averages
0.990 ± 0.001 in the 1–5 GeV/c momentum range with
variations at the 0.01 level. We conservatively apply a
correction of +(1.0 ± 1.0)% per kaon, or +(2.0 ± 2.0)%
to the signal yield.
C. Cross Section for e+e− → K+K−π+π−
We calculate the e+e−→K+K−π+π− cross section as
a function of the effective c.m. energy from
σKKπ+π−(Ec.m.) =
dNKKπ+π−γ(Ec.m.)
dL(Ec.m.) · ǫKKπ+π−(Ec.m.)
, (2)
where Ec.m. ≡ mKKπ+π−c2, mKKπ+π− is the measured
invariant mass of the K+K−π+π− system, dNKKπ+π−γ
is the number of selected events after background sub-
traction in the interval dEc.m., and ǫKKπ+π−(Ec.m.) is
the corrected detection efficiency. We calculate the differ-
ential luminosity, dL(Ec.m.), in each interval dEc.m. from
ISR µ+µ−γ events with the photon in the same fiducial
range used for the simulation; the procedure is described
in Refs. [11, 12]. From data-simulation comparison we
conservatively estimate a systematic uncertainty on dL
of 3%. This dL has been corrected for vacuum polar-
TABLE II: Summary of corrections and systematic uncer-
tainties on the e+e−→K+K−π+π− cross section. The total
correction is the linear sum of the components and the total
uncertainty is the sum in quadrature.
Source Correction Uncertainty
Rad. Corrections – 1%
Backgrounds – 3%, mKKπ+π−< 3 GeV/c
5%, mKKπ+π−> 3 GeV/c
Model Dependence – 5%
KKπ+π−
Distn. +3% 2%
Tracking Efficiency +3% 2%
Kaon ID Efficiency +2% 2%
ISR Luminosity – 3%
Total +8% 7%, mKKπ+π−< 3 GeV/c
9%, mKKπ+π−> 3 GeV/c
ization and final-state soft-photon emission; the former
should be excluded when using these data in calculations
of gµ−2.
For the cross section measurement we use the tighter
angular criteria on the charged tracks and the ISR pho-
ton, discussed in Sec. IVB, to exclude possible errors
from incorrect simulation of the EMC and DCH edge ef-
fects. We show the cross section as a function of Ec.m. in
Fig. 4, with statistical errors only, and provide a list of
our results in Table I. The result is consistent with the
direct measurement by DM1 [13], and with our previous
measurement of this channel [11] but has much better
statistical precision. The systematic uncertainties, sum-
marized in Table II, affect the normalization, but have
little effect on the energy dependence.
The cross section rises from threshold to a peak value
of about 4.7 nb near 1.85 GeV, then generally decreases
with increasing energy. In addition to narrow peaks at
the J/ψ and ψ(2S) masses, there are several possible
wider structures in the 1.8–2.8 GeV region. Such struc-
tures might be due to thresholds for intermediate reso-
nant states, such as φf0(980) near 2 GeV. Gaussian fits
to the simulated line shapes give a resolution on the mea-
sured K+K−π+π− mass that varies between 4.2 MeV/c2
in the 1.5–2.5 GeV/c2 region and 5.5 MeV/c2 in the 2.5–
3.5 GeV/c2 region. The resolution function is not purely
Gaussian due to soft-photon radiation, but less than 10%
of the signal is outside the 25 MeV/c2 mass bin. Since
the cross section has no sharp structure other than the
J/ψ and ψ(2S) peaks discussed in Sec. VIII below, we
apply no correction for resolution.
D. Substructure in the K+K−π+π− Final State
Our previous study [11] showed many intermediate res-
onances in the K+K−π+π− final state. With the larger
data sample used here, they can be seen more clearly
and, in some cases, studied in detail. Figure 5(a) shows
a scatter plot of the invariant mass of the K−π+ pair
versus that of the K+π− pair, and Fig. 5(b) shows the
sum of the two projections. Here we have suppressed the
contributions from φπ+π− and K+K−ρ(770) by requir-
ing |m(K+K−)−m(φ)| > 10 MeV/c2 and |m(π+π−)−
m(ρ)| > 100 MeV/c2, where m(φ) and m(ρ) values are
taken from the Particle Data Group (PDG) tables [5].
Bands and peaks corresponding to the K∗0(892) and
K∗02 (1430) are visible. In Fig. 5(c) we show the sum
of projections of the K∗0(892) bands, defined by lines in
Fig. 5(a), with events in the overlap region plotted only
once. No K∗0(892) signal is seen, confirming that the
e+e−→K∗0(892)K∗0(892) cross section is small. We ob-
serve associated K∗0(892)K∗02 (1430) production, but it
is mostly from J/ψ decays (see Sec. VIII).
We combine K∗0/K∗0 candidates within the lines in
Fig. 5(a) with the remaining pion and kaon to ob-
tain the K∗0π+− invariant mass distribution shown in
Fig. 6(a), and the K∗0π+− vs.K∗0K−+ mass scatter plot
1 1.5 2
m(K+π-) (GeV/c2)
1 1.5 2
m(K+π-, K-π+) (GeV/c2)
2000 (c)
m(K+π-,K-π+) (GeV/c2)
FIG. 5: (a) Invariant mass of the K−π+ pair versus that
of the K+π− pair; (b) sum of projections of (a); (c) sum of
projections of the K∗0 bands of (a), with events in the overlap
region taken only once. The φπ+π− and KKρ are vetoed.
in Fig. 6(b). The bulk of Fig. 6(b) shows a strong posi-
tive correlation, characteristic ofK∗0Kπ final states with
no higher resonances. The horizontal band in Fig. 6(b)
corresponds to the peak region in Fig. 6(a), and is consis-
tent with contributions from the K1(1270) and K1(1400)
resonances. There is also an indication of a vertical band
in Fig. 6(b), perhaps corresponding to a K∗0K resonance
at ∼1.5 GeV/c2.
1 1.5 2 2.5 3
m(K*π+-) (GeV/c2)
1 1.5 2 2.5 3
m(K*K+-) (GeV/c2)
FIG. 6: (a) The K∗0π invariant mass distribution; (b) the
K∗0π mass versus K∗0K mass.
We now suppress K∗0Kπ by considering only events
outside the lines in Fig. 5(a). In Fig. 7 we show the
K±π+π− invariant mass (two entries per event) vs. that
of the π+π− pair, along with its two projections. There
is a strong ρ(770)→π+π− signal, and theK±π+π− mass
projection shows further indications of the K1(1270) and
K1(1400) resonances, both of which decay into Kρ(770).
There are suggestions of additional structure in the π+π−
mass distribution, including possible f0(980) shoulder
and a possible enhancement near the f2(1270), however
the current statistics do not allow us to make definitive
statements.
The separation of all these, and any other, intermedi-
0.5 1
m(π+π− ) (GeV/c2)
m(Kππ) (GeV/c2)
(b)(a)
0.2 1 1.8
m(π+π− ) (GeV/c2)
FIG. 7: (a) Invariant mass of the K±π+π− combinations
versus that of the π+π− pair; (b) the K±π+π− and (c) π+π−
mass projections of (a).
ate states involving relatively wide resonances requires a
partial wave analysis. This is beyond the scope of this
paper. Here we present the cross section for the sum of
all states including a K∗0(892), and study intermediate
states that include a narrow φ or f0 resonance.
E. The e+e−→K∗0Kπ Cross Section
Signals for theK∗0(892) andK∗02 (1430) are clearly vis-
ible in the K±π∓ mass distributions in Fig. 5(b) and,
with a different bin size, in Fig. 8(a). We perform a
fit to this distribution using P-wave Breit-Wigner (BW)
functions for the K∗0 and K∗02 signals and a third-order
polynomial function for the remainder of the distribu-
tion taking into account the Kπ threshold. The result
is shown in Fig. 8(a). The fit yields a K∗0 signal of
19738 ± 266 events with m(Kπ) = 896.2 ± 0.3 MeV/c2
and Γ(Kπ) = 50.6 ± 0.9 MeV, and a K∗02 signal of
1786±127 events withm(Kπ) = 1428.5±3.9 MeV/c2 and
Γ(Kπ) = 113.7± 9.2 MeV. These values are consistent
with current world averages [5], and the fit describes the
data well, indicating that contributions from any other
resonances decaying into K±π∓ are small.
We perform a similar fit to the data in bins of the
K+K−π+π− invariant mass, with the resonance masses
and widths fixed to the values obtained by the overall fit.
Since there is at most one K∗0 per event, we convert the
resultingK∗0 yield in each bin into an “inclusive” e+e−→
K∗0Kπ cross section, following the procedure described
in Sec. IVC. This cross section is shown in Fig. 8(b) and
listed in Table III for the effective c.m. energies from
threshold up to 3.5 GeV. At higher energies the signals
are small and contain an unknown, but possibly large,
contribution from e+e−→qq events. There is a rapid rise
from threshold to a peak value of about 4 nb at 1.84 GeV,
0.75 1 1.25 1.5 1.75
m(K+-π-+) (GeV/c2)
1.5 2 2.5 3 3.5
Ec.m. (GeV)
FIG. 8: (a) The K±π∓ mass distribution (two entries per
event) for all selected K+K−π+π− events: the solid line rep-
resents a fit including two resonances and a polynomial func-
tion (see text), shown separately as the dashed line; (b) the
e+e−→K∗0Kπ cross section obtained from the K∗0(892) sig-
nal by a similar fit in each 25 MeV/c2 mass bin.
followed by a very rapid decrease with increasing energy.
There are suggestions of narrow structure in the peak
region, but the only statistically significant structure is
the J/ψ peak, which is discussed below.
The e+e−→K∗0Kπ contribution is a large fraction of
the total K+K−π+π− cross section at all energies above
its threshold, and dominates in the 1.8–2.0 GeV region.
We are unable to extract a meaningful measurement of
the K∗02 Kπ cross section from this data sample because
it is more than ten times smaller. The K+K−ρ0(770) in-
termediate state makes up the majority of the remainder
of the cross section and it can be estimated as a difference
of the values in Table I and Table III for theK+K−π+π−
and K∗0Kπ final states.
F. The φ(1020)π+π− Intermediate State
Intermediate states containing relatively narrow reso-
nances can be studied more easily. Figure 9(a) shows
a scatter plot of the invariant mass of the π+π− pair
versus that of the K+K− pair. Horizontal and vertical
bands corresponding to the ρ0(770) and φ, respectively,
are visible, and there is a concentration of entries on the
φ band corresponding to the correlated production of φ
and f0(980). The φ signal is also visible in the K
mass projection, Fig. 9(c). The large contribution from
the ρ(770), coming from the K1 decay, is nearly uniform
in the K+K− mass, and the cross-hatched histogram
shows the non-K+K−π+π− background estimated from
the control region in χ2
KKπ+π−
. The cross-hatched his-
TABLE III: Measurements of the e+e− → K∗0(892)Kπ cross section (errors are statistical only).
Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb)
1.5875 0.16 ± 0.11 2.0875 2.36 ± 0.16 2.5875 0.54 ± 0.07 3.0875 1.73 ± 0.10
1.6125 0.31 ± 0.08 2.1125 1.92 ± 0.16 2.6125 0.63 ± 0.06 3.1125 0.92 ± 0.07
1.6375 0.81 ± 0.13 2.1375 1.99 ± 0.14 2.6375 0.57 ± 0.06 3.1375 0.21 ± 0.04
1.6625 0.79 ± 0.12 2.1625 1.19 ± 0.15 2.6625 0.46 ± 0.06 3.1625 0.24 ± 0.04
1.6875 1.33 ± 0.15 2.1875 1.24 ± 0.14 2.6875 0.46 ± 0.06 3.1875 0.08 ± 0.03
1.7125 1.63 ± 0.15 2.2125 1.25 ± 0.11 2.7125 0.64 ± 0.06 3.2125 0.15 ± 0.03
1.7375 1.87 ± 0.14 2.2375 0.90 ± 0.10 2.7375 0.56 ± 0.06 3.2375 0.14 ± 0.04
1.7625 2.12 ± 0.17 2.2625 0.79 ± 0.11 2.7625 0.46 ± 0.06 3.2625 0.16 ± 0.03
1.7875 2.51 ± 0.20 2.2875 1.15 ± 0.10 2.7875 0.36 ± 0.06 3.2875 0.13 ± 0.03
1.8125 2.96 ± 0.21 2.3125 0.99 ± 0.09 2.8125 0.31 ± 0.05 3.3125 0.12 ± 0.03
1.8375 4.35 ± 0.20 2.3375 0.91 ± 0.11 2.8375 0.35 ± 0.05 3.3375 0.14 ± 0.03
1.8625 4.11 ± 0.20 2.3625 1.11 ± 0.09 2.8625 0.27 ± 0.04 3.3625 0.12 ± 0.06
1.8875 3.26 ± 0.23 2.3875 0.83 ± 0.09 2.8875 0.27 ± 0.05 3.3875 0.09 ± 0.03
1.9125 3.90 ± 0.20 2.4125 0.87 ± 0.09 2.9125 0.34 ± 0.05 3.4125 0.10 ± 0.03
1.9375 3.53 ± 0.20 2.4375 1.00 ± 0.09 2.9375 0.29 ± 0.04 3.4375 0.11 ± 0.03
1.9625 3.42 ± 0.21 2.4625 0.86 ± 0.08 2.9625 0.25 ± 0.04 3.4625 0.10 ± 0.05
1.9875 2.81 ± 0.18 2.4875 0.88 ± 0.09 2.9875 0.38 ± 0.05 3.4875 0.08 ± 0.03
2.0125 2.47 ± 0.17 2.5125 0.69 ± 0.07 3.0125 0.21 ± 0.04
2.0375 2.26 ± 0.16 2.5375 0.62 ± 0.07 3.0375 0.24 ± 0.04
2.0625 2.00 ± 0.16 2.5625 0.55 ± 0.07 3.0625 0.22 ± 0.04
togram also shows a φ peak, but this is a small fraction
of the events. Subtracting this background and fitting
the remaining data gives 1706±56 events produced via
the φπ+π− intermediate state.
To study the φπ+π− channel, we select candidate
events with a K+K− invariant mass within 10 MeV/c2
of the φ mass, indicated by the inner vertical lines in
Figs. 9(a,c), and estimate the non-φ contribution from
the mass sidebands between the inner and outer verti-
cal lines. In Fig. 9(b) we show the π+π− invariant mass
distributions for φ candidate events, sideband events and
χ2 control region events as the open, hatched and cross-
hatched histograms, respectively, and in Fig. 9(d) we
show the numbers of entries from the candidate events
minus those from the sideband and control region. There
is a clear f0 peak over a broad mass distribution, with
no indication of associated ρ0 production.
A coherent sum of two Breit-Wigner functions is suf-
ficient to describe the invariant mass distribution of the
π+π− pair recoiling against a φ in Fig. 9(d). We fit with
the function:
F (m) =
1− 4m2π/m2 · |A1(m) + eiψA2(m)|2 , (3)
Ai(m) = miΓi
Ni/(m
i −m2 + imiΓi) ,
where m is the π+π− invariant mass, mi and Γi are the
parameters of the ith resonance, ψ is their relative phase
and Ni are normalization parameters, corresponding to
the number of events under each BW. One BW corre-
sponds to the f0(980), but a wide range of values of the
other parameters can describe the data. Fixing the rela-
tive phase to ψ = π and the parameters of the first BW
to m1 = 0.6 GeV/c
2 and Γ1 = 0.45 GeV (which could be
interpreted as the f0(600) [5]), we obtain the fit shown in
Fig. 9(d). It describes the data well and gives an f0(980)
0.98 1 1.02 1.04 1.06
m(K-K+) (GeV/c2)
0.4 0.6 0.8 1 1.2
m(π+π-) (GeV/c2)
0.98 1 1.02 1.04 1.06
m(K+K-) (GeV/c2)
0.4 0.6 0.8 1 1.2
m(π+π-) (GeV/c2)
FIG. 9: (a) The π+π− vs. the K+K− invariant masses
for all selected K+K−π+π− events; (b) the π+π− invari-
ant mass projections for events in the φ peak (open his-
togram), sidebands (hatched) and background control region
(cross-hatched); (c) theK+K− mass projections for all events
(open) and control region (cross-hatched); (d) the difference
between the open and the sum of the other histograms in (b).
signal of 262±30 events, withm2 = 0.973±0.003 GeV/c2
and Γ2 = 0.065 ± 0.013 GeV, consistent with the PDG
values [5]. There is a suggestion of an f2(1270) peak in
the data, but it is much smaller than the f0 peak and we
do not consider it further.
We obtain the number of e+e− → φπ+π− events in
bins of φπ+π− invariant mass by fitting the K+K− in-
variant mass projection in that bin after subtracting non-
K+K−π+π− background. Each projection is a subset of
Fig. 9(c), where the curve represent a fit to the full sam-
ple. In each mass bin, all parameters are fixed to the
values obtained from the overall fit except the numbers
of events in the φ peak and the non-φ component.
The efficiency may depend on the details of the pro-
duction mechanism. Using the two-pion mass distribu-
tion in Fig. 9(d) as input, we simulate the π+π− system
as an S-wave comprising two scalar resonances, with pa-
rameters set to the values given above. To describe the
φπ+π− mass distribution we use a simple model with one
resonance, the φ(1680), of mass 1.68 GeV/c2 and width
0.2 GeV, decaying to φf0. The simulated reconstructed
spectrum is shown in Fig. 10(a). There is a sharp in-
crease at about 2 GeV/c2 due to the φf0(980) threshold.
All other structure is determined by phase space and a
m−2 falloff with increasing mass.
1 2 3 4
m(K+K-π+π-) (GeV/c2)
1 2 3 4
m(K+K-π+π-) (GeV/c2)
FIG. 10: (a) The K+K−π+π− invariant mass distributions
from the φπ+π− simulation described in the text, recon-
structed in the signal (open) and control (hatched) regions;
(b) net reconstruction and selection efficiency as a function
of mass: the solid line represents a cubic fit, and the dashed
line the corresponding fit for the space phase model shown in
Fig. 3.
Dividing the number of reconstructed events in each
bin by the number of generated ones, we obtain the effi-
ciency as a function of φπ+π− mass shown in Fig. 10(b).
The solid line represents a fit to a third order polyno-
mial, and the dashed line the corresponding fit to the
phase space model from Fig. 3. The model dependence
is weak, giving confidence in the efficiency calculation.
We calculate the e+e− → φπ+π− cross section as de-
scribed in Sec. IVC but using the efficiency from the fit
to Fig. 10(b) and dividing by the φ→K+K− branching
fraction of 0.491 [5]. We show our results as a func-
tion of energy in Fig. 11 and list them in Table IV.
The cross section has a peak value of about 0.6 nb at
about 1.7 GeV, then decreases with increasing energy
until φ(1020)f0(980) threshold, around 2.0 GeV. From
this point it rises, falls sharply at about 2.2 GeV, and
then decreases slowly. Except in the charmonium region,
the results at energies above 2.9 GeV are not meaningful
due to small signals and potentially large backgrounds,
and are omitted from Table IV. Figure 11 displays the
cross-section up to 4.5 GeV to show the signals from the
J/ψ and ψ(2S) decays. They are discussed in Sec. VIII.
There are no previous measurements of this cross section,
and our results are consistent with the upper limits given
in Ref. [13].
1.5 2 2.5 3 3.5 4
Ec.m. (GeV)
FIG. 11: The e+e−→ φπ+π− cross section as a function of
the effective e+e− c.m. energy.
We perform a study of the angular distributions in the
φ(1020)π+π− final state by considering all K+K−π+π−
candidate events with mass below 3 GeV/c2, binning
them in terms of the cosine of the angles defined below,
and fitting the background-subtracted K+K− mass pro-
jections. The efficiency is nearly uniform in these angles,
so we study the number of events in each bin. We define
the φ production angle, Θφ as the angle between the φ
momentum and the e− beam direction in the rest frame
of the φπ+π− system. The distribution of cosΘφ, shown
in Fig. 12(a), is consistent with the uniform distribution
expected if S-wave two-body channels φX , X → π+π−
dominate the φπ+π− system. We define the pion and
kaon helicity angles, Θπ+ and ΘK+ as those between the
π+ and the π+π−-system momenta in the π+π− rest
frame and between the K+ and ISR photon momenta
in the φ rest frame, respectively. The distributions of
cosΘπ+ and cosΘK+ , shown in Figs. 12(b) and 12(c), re-
spectively, are consistent with those expected from scalar
and vector meson decays.
TABLE IV: Measurements of the e+e− → φ(1020)π+π− cross section (errors are statistical only).
Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb)
1.4875 0.01 ± 0.02 1.8375 0.39 ± 0.10 2.1875 0.32 ± 0.06 2.5375 0.09 ± 0.03
1.5125 0.03 ± 0.03 1.8625 0.44 ± 0.10 2.2125 0.22 ± 0.05 2.5625 0.03 ± 0.02
1.5375 0.09 ± 0.04 1.8875 0.23 ± 0.08 2.2375 0.15 ± 0.04 2.5875 0.06 ± 0.02
1.5625 0.13 ± 0.04 1.9125 0.34 ± 0.09 2.2625 0.10 ± 0.03 2.6125 0.07 ± 0.02
1.5875 0.21 ± 0.06 1.9375 0.37 ± 0.08 2.2875 0.11 ± 0.04 2.6375 0.08 ± 0.03
1.6125 0.23 ± 0.06 1.9625 0.31 ± 0.08 2.3125 0.08 ± 0.03 2.6625 0.06 ± 0.02
1.6375 0.54 ± 0.08 1.9875 0.36 ± 0.07 2.3375 0.13 ± 0.03 2.6875 0.04 ± 0.02
1.6625 0.61 ± 0.09 2.0125 0.38 ± 0.07 2.3625 0.10 ± 0.04 2.7125 0.08 ± 0.03
1.6875 0.64 ± 0.10 2.0375 0.29 ± 0.07 2.3875 0.13 ± 0.04 2.7375 0.06 ± 0.02
1.7125 0.38 ± 0.09 2.0625 0.42 ± 0.07 2.4125 0.12 ± 0.04 2.7625 0.07 ± 0.02
1.7375 0.64 ± 0.10 2.0875 0.30 ± 0.06 2.4375 0.15 ± 0.04 2.7875 0.02 ± 0.02
1.7625 0.55 ± 0.11 2.1125 0.49 ± 0.07 2.4625 0.06 ± 0.03 2.8125 0.06 ± 0.02
1.7875 0.55 ± 0.11 2.1375 0.30 ± 0.06 2.4875 0.09 ± 0.03 2.8375 0.04 ± 0.02
1.8125 0.31 ± 0.09 2.1625 0.49 ± 0.07 2.5125 0.09 ± 0.03 2.8625 0.03 ± 0.01
-1 -0.5 0 0.5 1
cos(Θφ)
-1 -0.5 0 0.5 1
cos(Θπ+)
-1 -0.5 0 0.5 1
cos(ΘK+)
FIG. 12: Distributions of the cosines of (a) the φ production angle, (b) the pion helicity angle, and (c) the kaon helicity angle
(see text) for e+e−→φπ+π− events: the lines represent the distributions expected if the π+π− system recoiling against a vector
φ meson is produced in an S-wave, normalized to the number of events in the data.
G. The φ(1020)f0(980) Intermediate State
The narrow f0(980) peak seen in Fig. 9(d) allows the
selection of a fairly clean sample of φf0 events. We re-
peat the analysis just described with the additional re-
quirement that the π+π− invariant mass be in the range
0.85–1.10 GeV/c2. The fit to the full sample yields about
700 events; all of these contain a true φ, but about 10%
are from e+e− → φπ+π− events where the pion pair is
not produced through the f0(980).
We convert the numbers of fitted events in each mass
bin into a measurement of the e+e−→ φ(1020)f0(980)
cross section as described above and dividing by the
f0→ π+π− branching fraction of two-thirds. The cross
section is shown in Fig. 13 as a function of the effective
c.m. energy and is listed in Table V. Its behavior near
threshold does not appear to be smooth, but is more
consistent with a steep rise to a value of about 0.3 nb at
1.95 GeV followed by a slow decrease that is interrupted
by a structure around 2.175 GeV. Possible interpreta-
tions of this structure are discussed in Sec. VII. Again,
the values are not meaningful for the effective c.m. above
about 2.9 GeV/c2, except for the J/ψ and ψ(2S) signals,
discussed in Sec. VIII.
V. THE K+K−π0π0 FINAL STATE
A. Final Selection and Backgrounds
The K+K−π0π0 sample contains background from
the ISR processes e+e− → K+K−π0γ and K+K−ηγ,
in which two soft photon candidates from machine- or
detector-related background combine with the relatively
energetic photons from the π0 or η to form two fake π0
candidates. We reduce this background using the helic-
ity angle between each reconstructed π0 direction and the
direction of its higher-energy photon daughter calculated
in its rest frame. If the cosines of both helicity angles are
higher than 0.85, we remove the event.
Figure 14 shows the distribution of χ2KKπ0π0 for
the remaining candidates together with the simulated
TABLE V: Summary of the e+e− → φ(1020)f0(980) cross section measurement. Errors are statistical only.
Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb)
1.8875 0.02 ± 0.02 2.1625 0.56 ± 0.08 2.4375 0.13 ± 0.04 2.7125 0.05 ± 0.02
1.9125 0.07 ± 0.04 2.1875 0.38 ± 0.07 2.4625 0.09 ± 0.04 2.7375 0.02 ± 0.01
1.9375 0.30 ± 0.07 2.2125 0.21 ± 0.06 2.4875 0.08 ± 0.03 2.7625 0.06 ± 0.02
1.9625 0.27 ± 0.07 2.2375 0.17 ± 0.05 2.5125 0.09 ± 0.03 2.7875 0.03 ± 0.02
1.9875 0.25 ± 0.07 2.2625 0.12 ± 0.04 2.5375 0.07 ± 0.03 2.8125 0.04 ± 0.02
2.0125 0.25 ± 0.07 2.2875 0.13 ± 0.05 2.5625 0.02 ± 0.02 2.8375 0.05 ± 0.02
2.0375 0.28 ± 0.07 2.3125 0.12 ± 0.04 2.5875 0.06 ± 0.03 2.8625 0.02 ± 0.02
2.0625 0.43 ± 0.08 2.3375 0.14 ± 0.04 2.6125 0.07 ± 0.03 2.8875 0.01 ± 0.01
2.0875 0.28 ± 0.07 2.3625 0.13 ± 0.05 2.6375 0.06 ± 0.03 2.9125 0.02 ± 0.01
2.1125 0.54 ± 0.09 2.3875 0.13 ± 0.04 2.6625 0.05 ± 0.03 2.9375 0.00 ± 0.00
2.1375 0.46 ± 0.08 2.4125 0.14 ± 0.05 2.6875 0.03 ± 0.02 2.9625 0.02 ± 0.01
1.5 2 2.5 3 3.5 4
Ec.m. (GeV)
FIG. 13: The e+e− → φ(1020)f0(980) cross section as a
function of the effective e+e− c.m. energy obtained from the
K+K−π+π− final state.
K+K−π0π0 events. Again, the distributions are broader
than those for a typical 6C χ2 due to higher order ISR,
and we normalize the histogram to the data in the region
χ2KKπ0π0 < 10. The cross-hatched histogram in Fig. 14
represents background from e+e−→qq events, evaluated
in the same way as for the K+K−π+π− final state. The
hatched histogram represents the sum of this background
and that from ISR π+π−π0π0 events with both charged
pions misidentified as kaons, evaluated using the simula-
tion.
The dominant background in this case is from resid-
ual ISR K+K−π0 and K+K−η events, as well as ISR
K+K−π0π0π0 events. Their simulated contribution,
shown as the dashed histogram in Fig. 14, is consistent
with the data in the high χ2
KKπ0π0
region. All other back-
grounds are either negligible or distributed uniformly in
KKπ0π0
. We define a signal region, χ2
KKπ0π0
<50, con-
taining 4425 data and 6948 simulated events, and a con-
trol region, 50 < χ2
KKπ0π0
< 100, containing 1751 data
0 20 40 60 80 100
χ2(2K2π0)
FIG. 14: Distribution of χ2 from the six-constraint fit for
K+K−π0π0 candidates in the data (points). The open his-
togram is the distribution for simulated signal events, nor-
malized as described in the text. The cross-hatched, hatched
and dashed histograms represent, cumulatively, the back-
grounds from non-ISR events, ISR π+π−π0π0 events, and ISR
K+K−π0, K+K−η and K+K−π0π0π0 events.
and 848 simulated events.
Figure 15 shows the K+K−π0π0 invariant mass dis-
tribution from threshold up to 5 GeV/c2 for events in
the signal region. The qq background (cross-hatched his-
togram) is negligible at low masses but forms a large frac-
tion of the selected events above about 4 GeV/c2. The
ISR π+π−π0π0 contribution (hatched region) is negligi-
ble except in the 1.5–2.5 GeV/c2 region. The sum of all
other backgrounds, estimated from the control region,
is the dominant contribution below 1.6 GeV/c2 and non
negligible everywhere. The total background in the 1.6–
2.5 GeV/c2 region is 15–20% (open histogram).
We subtract the sum of backgrounds from the number
of selected events in each mass bin to obtain a number
of signal events. Considering uncertainties in the cross
sections for the background processes, the normalization
1 2 3 4 5
m(K+K-π0π0) (GeV/c2)
FIG. 15: Invariant mass distribution for K+K−π0π0 candi-
dates in the data (points). The cross-hatched, hatched and
open histograms represent, cumulatively, the non-ISR back-
ground, the contribution from ISR π+π−π0π0 events, and the
ISR background from the control region of Fig. 14.
of events in the control region and the simulation statis-
tics, we estimate a systematic uncertainty on the signal
yield after background subtraction as less than 5% in the
1.6–3.0 GeV/c2 region, but increases to 10% in the region
above 3 GeV/c2.
B. Selection Efficiency
The detection efficiency is determined in the same
manner as in Sec. IVB. Figure 16(a) shows the sim-
ulated K+K−π0π0 invariant mass distributions in the
signal and control regions from the phase space model.
We divide the number of reconstructed events in each
40 MeV/c2 mass interval by the number generated ones
in that interval to obtain the efficiency shown as the
points in Fig. 16(b); a third order polynomial fit to the
efficiency is used to calculate the cross section. Again,
the simulation of the ISR photon covers a limited angu-
lar range, about 30% wider than EMC acceptance, and
shown efficiency is factor 0.7 lower than for the hadronic
system alone. Simulations assuming dominance of the
φ→K+K− and/or f0→π0π0 channels give consistent re-
sults, and we apply the same 5% systematic uncertainty
for possible model dependence as in Sec. IVB.
We correct for mis-modeling of the track finding and
kaon identification efficiencies as in Sec. IVB, and for
the shape of the χ2
KKπ0π0
distribution analogously, using
the result in Ref. [12], (0 ± 6)%. We correct the π0-
finding efficiency using the procedure described in detail
in Ref. [12]. From ISR e+e−→ωπ0γ→π+π−π0π0γ events
selected with and without the π0 from the ω decay, we
1 2 3 4
m(K+K-π0π0) (GeV/c2)
1 2 3 4
m(K+K-π0π0) (GeV/c2)
FIG. 16: (a) Invariant mass distribution for simulated
K+K−π0π0 events in the signal (open) and control (hatched)
regions (see Fig. 14); (b) net reconstruction and selection ef-
ficiency as a function of mass obtained from this simulation
(the curve represents a third order polynomial fit).
find that the simulated efficiency for one π0 is too high
by (2.8±1.4)%. Conservatively we apply a correction of
+(5.6± 2.8)% for two π0 in the event.
C. Cross Section for e+e− → K+K−π0π0
We calculate the cross section for e+e− → K+K−π0π0
in 40 MeV Ec.m. intervals from the analog of Eq. 2, using
the invariant mass of the K+K−π0π0 system to deter-
mine the effective c.m. energy. We show the first mea-
surement of this cross section in Fig. 17 and list the re-
sults obtained in Table VI. The cross section rises to a
peak value near 1 nb at 2 GeV, falls sharply at 2.2 GeV,
then decreases slowly. The only statistically significant
structure is the J/ψ peak. The drop at 2.2 GeV is sim-
ilar to that seen in the K+K−π+π− mode. Again, dL
includes corrections for vacuum polarization that should
be omitted from calculations of gµ−2.
The simulated K+K−π0π0 invariant mass resolution
is 8.8 MeV/c2 in the 1.5–2.5 GeV/c2 mass range, and in-
creases with mass to 11.2 MeV/c2 in the 2.5–3.5 GeV/c2
range. Since less than 20% of the events in a 40 MeV/c2
bin are reconstructed outside that bin and the cross sec-
tion has no sharp structure other than the J/ψ peak, we
again make no correction for resolution. The point-to-
point systematic errors are much smaller than statistical
ones, and the errors on the normalization are summa-
rized in Table VII, along with the corrections that were
applied to the measurements. The total correction is
+9.2%, and the total systematic uncertainty is 10% at
low mass, increasing to 14% above 3 GeV/c2.
TABLE VI: Measurements of the e+e− → K+K−π0π0 cross section (errors are statistical only).
Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb)
1.4200 0.00 ± 0.05 2.3400 0.35 ± 0.06 3.2600 0.13 ± 0.03 4.1800 0.02 ± 0.01
1.4600 0.12 ± 0.07 2.3800 0.29 ± 0.06 3.3000 0.09 ± 0.03 4.2200 0.03 ± 0.01
1.5000 0.00 ± 0.07 2.4200 0.38 ± 0.06 3.3400 0.09 ± 0.03 4.2600 0.03 ± 0.01
1.5400 0.01 ± 0.08 2.4600 0.38 ± 0.06 3.3800 0.08 ± 0.02 4.3000 0.03 ± 0.01
1.5800 0.03 ± 0.09 2.5000 0.22 ± 0.05 3.4200 0.11 ± 0.03 4.3400 0.03 ± 0.01
1.6200 0.09 ± 0.09 2.5400 0.25 ± 0.05 3.4600 0.06 ± 0.02 4.3800 0.01 ± 0.01
1.6600 0.31 ± 0.11 2.5800 0.25 ± 0.05 3.5000 0.04 ± 0.02 4.4200 0.05 ± 0.01
1.7000 0.35 ± 0.11 2.6200 0.25 ± 0.05 3.5400 0.06 ± 0.02 4.4600 0.03 ± 0.01
1.7400 0.49 ± 0.11 2.6600 0.28 ± 0.05 3.5800 0.07 ± 0.02 4.5000 0.04 ± 0.01
1.7800 0.51 ± 0.12 2.7000 0.16 ± 0.04 3.6200 0.04 ± 0.02 4.5400 0.00 ± 0.01
1.8200 0.84 ± 0.12 2.7400 0.22 ± 0.04 3.6600 0.06 ± 0.02 4.5800 0.02 ± 0.01
1.8600 0.94 ± 0.11 2.7800 0.21 ± 0.04 3.7000 0.08 ± 0.02 4.6200 0.02 ± 0.01
1.9000 0.95 ± 0.12 2.8200 0.13 ± 0.04 3.7400 0.09 ± 0.02 4.6600 0.02 ± 0.01
1.9400 0.80 ± 0.11 2.8600 0.21 ± 0.04 3.7800 0.02 ± 0.02 4.7000 0.04 ± 0.01
1.9800 0.87 ± 0.11 2.9000 0.11 ± 0.03 3.8200 0.05 ± 0.01 4.7400 0.02 ± 0.01
2.0200 1.00 ± 0.10 2.9400 0.12 ± 0.04 3.8600 0.04 ± 0.01 4.7800 0.01 ± 0.01
2.0600 0.96 ± 0.10 2.9800 0.12 ± 0.04 3.9000 0.03 ± 0.02 4.8200 0.01 ± 0.01
2.1000 0.90 ± 0.10 3.0200 0.21 ± 0.04 3.9400 0.02 ± 0.01 4.8600 0.01 ± 0.01
2.1400 0.82 ± 0.10 3.0600 0.16 ± 0.04 3.9800 0.03 ± 0.01 4.9000 0.03 ± 0.01
2.1800 0.58 ± 0.08 3.1000 0.92 ± 0.07 4.0200 0.05 ± 0.01 4.9400 0.04 ± 0.02
2.2200 0.56 ± 0.08 3.1400 0.19 ± 0.04 4.0600 0.04 ± 0.01 4.9800 0.04 ± 0.02
2.2600 0.37 ± 0.07 3.1800 0.12 ± 0.03 4.1000 0.03 ± 0.01
2.3000 0.43 ± 0.07 3.2200 0.14 ± 0.03 4.1400 0.03 ± 0.01
TABLE VII: Summary of corrections and systematic uncer-
tainties on the e+e−→K+K−π0π0 cross section. The total
correction is the linear sum of the components and the total
uncertainty is the sum in quadrature.
Source Correction Uncertainty
Rad. Corrections – 1%
Backgrounds – 5%, mKKπ0π0< 3 GeV/c
10%, mKKπ0π0> 3 GeV/c
Model Dependence – 5%
χ2KKπ0π0 Distn. 0% 6%
Tracking Efficiency +1.6% 0.8%
Kaon ID Efficiency +2% 2%
π0 Efficiency +5.6% 2.8%
ISR Luminosity – 3%
Total +9.2% 10%, mKKπ0π0< 3 GeV/c
14%, mKKπ0π0> 3 GeV/c
D. Substructure in the K+K−π0π0 Final State
A scatter plot of the invariant mass of the K−π0 versus
that of the K+π0 pair is shown in Fig. 18(a) with two en-
tries per event selected in the χ2 signal region. Horizontal
and vertical bands corresponding to the K∗+(892) and
K∗−(892), respectively, are visible. Figure 18(b) shows
as points the sum of the two projections of Fig. 18(a);
a large K∗±(892) signal is evident. Fitting this distri-
bution with the function discussed in Sec. IVE gives
a good χ2 and the curve shown on Fig. 18(b). The
K∗±(1430):K∗±(892) ratio is consistent with that for
1 2 3 4 5
Ec.m. (GeV)
FIG. 17: The e+e−→K+K−π0π0 cross section as a function
of the effective e+e− c.m. energy measured with ISR data at
BABAR. The errors are statistical only.
neutral K∗ seen in the K+K−π+π− channel, and the
number of K∗±(892) in the peak is consistent with one
per selected event. The hatched histogram in Fig. 18(b)
represents theK±π0 mass in events with the otherK∓π0
mass within the lines in Fig. 18(a), but with events in the
overlap region used only once, and shows no K∗±(892)
signal. These results indicate that the e+e−→K∗±K∗∓
cross section is small and that the K∗±(892)K∓π0 chan-
1 1.5 2
m(K+π0) (GeV/c2)
1 1.5 2
m(K+π0, K-π0) (GeV/c2)
FIG. 18: (a) Invariant mass of the K−π0 pair versus that
of the K+π0 pair in selected K+K−π0π0 events (two entries
per event); (b) sum of projections of (a) (dots, four entries per
event). The curve represents the result of the fit described in
the text. The hatched histogram is the K±π0 distribution
for events in which the other K∓π0 combination is within the
K∗±(892) bands indicated in (a), with events in the overlap
region taken only once.
nels dominate the overall cross section.
We find no signals for resonances in the K+K−π0 or
K±π0π0 decay modes. Since the K∗±(892)K∓π0 chan-
nels dominate and the statistics are low in any mass bin,
we do not attempt to extract a separate K∗±(892)K∓π0
cross section. The total K+K−π0π0 cross section is
roughly a factor of four lower than the K∗0(892)K±π∓
cross section observed in the K+K−π+π− final state.
This is consistent with what one might expect from
isospin and the charged vs. neutral K∗ branching frac-
tions into charged kaons.
E. The φ(1020)π0π0 Intermediate State
The selection of events containing a φ(1020)→K+K−
decay follows that in Section IVF. Figure 19(a) shows a
scatter plot of the invariant mass of the π0π0 pair versus
that of the K+K− pair. A vertical band corresponding
to the φ is visible, whose intensity decreases with increas-
ing π0π0 mass except for an enhancement in the f0(980)
region. The φ signal is also visible in the K+K− invari-
ant mass projection shown in Fig. 19(c). The relative
non-φ background is smaller than in the K+K−π+π−
mode, but there is a large background from ISR φπ0,
φη and/or φπ0π0π0 events, as indicated by the control
region histogram (hatched) in Fig. 19(c). The contribu-
tions from non-ISR and ISR π+π−π0π0 events are negli-
gible. Selecting φ candidate and side band events as for
the K+K−π+π− mode (vertical lines in Figs. 19(a,c)),
we obtain the π0π0 mass projections shown as the open
and cross-hatched histograms, respectively, in Fig. 19(b).
Control region events (hatched histogram) are concen-
trated at low masses. A peak corresponding to the
f0(980) is visible over a relatively low background.
In Fig. 19(d) we show the numbers of entries from
the candidate events minus those from the sideband and
control regions. A sum of two Breit-Wigner functions
is again sufficient to describe the data. Fitting Eq. 3
0.98 1 1.021.041.06
m(K-K+) (GeV/c2)
0.4 0.6 0.8 1 1.2 1.4
m(π0π0) (GeV/c2)
0.98 1 1.021.041.06
m(K+K-) (GeV/c2)
0.4 0.6 0.8 1 1.2 1.4
m(π0π0) (GeV/c2)
FIG. 19: (a) Scatter plot of the π0π0 invariant mass vs.
the K+K− invariant mass for all selected K+K−π0π0 events;
(b) the π0π0 invariant mass projections for events in the φ
peak (open histogram), sidebands (cross-hatched) and control
region (hatched); (c) the K+K− mass projection for events in
the signal (open) and control (hatched) regions; (d) difference
between the open and other histograms in (b).
with the parameters of one BW fixed to the values given
in Sec. IVF, corresponding to the f0(600), we obtain a
good fit, shown as the curve in Fig. 19(d). This fit yields
a f0(980) signal of 54±9 events with a massm = 0.970±
0.007 GeV/c2 and width Γ = 0.081± 0.021 GeV consis-
tent with PDG values [5]. Due to low statistics and high
backgrounds, we do not extract an e+e− → φ(1020)π0π0
cross section.
F. The φ(1020)f0(980) Intermediate State
Since the background under the f0(980) peak in
Figs. 19(b,d) is relatively low we are able to extract the
φ(1020)f0(980) contribution. As in Sec. IVG, we require
the dipion mass to be in the range 0.85–1.10 GeV/c2 and
fit the background-subtractedK+K− mass projection in
each bin of K+K−π0π0 mass to obtain a number of φf0
events. Again, about 10% of these are φπ0π0 events in
which the π0π0 pair is not produced through the f0, but
this does not affect the conclusions.
We convert the number of fitted events in each mass
bin into a measurement of the e+e−→ φ(1020)f0(980)
cross section as described above and dividing by the
f0(980)→ π0π0 branching fraction of one-third. The
cross section is shown in Fig. 20 as a function of Ec.m.
and is listed in Table VIII. Due to smaller number
of events, we have used larger bins at higher energies.
The overall shape is consistent with that obtained in the
K+K−π+π− mode (see Fig. 13), and there is a sharp
TABLE VIII: Measurements of the e+e− → φ(1020)f0(980) cross section (f0 → π
0π0, errors are statistical only).
Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb)
1.88-1.92 0.078+0.082−0.053 2.12-2.16 0.397
+0.164
−0.137 2.44-2.52 0.120
+0.053
−0.042
1.92-1.96 0.220+0.114−0.085 2.16-2.20 0.408
+0.143
−0.118 2.52-2.68 0.050
+0.024
−0.019
1.96-2.00 0.136+0.104−0.075 2.20-2.24 0.070
+0.064
−0.042 2.68-2.84 0.026
+0.017
−0.012
2.00-2.04 0.446+0.160−0.131 2.24-2.28 0.174
+0.095
−0.071 2.84-3.00 0.026
+0.015
−0.011
2.04-2.08 0.315+0.142−0.113 2.28-2.36 0.069
+0.042
−0.030 3.00-3.16 0.032
+0.017
−0.013
2.08-2.12 0.519+0.169−0.141 2.36-2.44 0.112
+0.051
−0.040 3.16-3.32 0.012
+0.012
−0.008
1.5 2 2.5 3 3.5 4
Ec.m. (GeV)
FIG. 20: Cross section for the reaction e+e− →
φ(1020)f0(980) as a function of effective e
+e− c.m. energy
obtained from the K+K−π0π0 final state.
drop near 2.2 GeV/c2, but the statistical errors are large
and no conclusion can be drawn from this mode alone.
Possible interpretations are discussed in Section VII.
VI. THE K+K−K+K− FINAL STATE
A. Final Selection and Background
Figure 21 shows the distribution of χ24K for the
K+K−K+K− candidates as points, and the open his-
togram is the distribution for simulated K+K−K+K−
events, normalized to the data in the region χ24K < 5
where the backgrounds and radiative corrections are
small. The hatched histogram represents the back-
ground from e+e− → qq events, evaluated as for the
other modes. The cross-hatched histogram represents
the background from simulated ISR K+K−π+π− events
with both charged pions misidentified as kaons.
We define signal and control regions of χ24K < 20 and
20< χ24K < 40, respectively. The signal region contains
2,305 data and 20,616 simulated events, and the con-
trol region contains 463 data and 1,601 simulated events.
0 20 40 60
χ2(4K)
FIG. 21: Distribution of χ2 from the three-constraint fit
for K+K−K+K− candidates in the data (points). The open
histogram is the distribution for simulated signal events, nor-
malized as described in the text. The hatched histogram rep-
resents the background from non-ISR events, estimated as
described in the text. The cross-hatched histograms is for
simulated ISR K+K−π+π− events.
Figure 22 shows the K+K−K+K− invariant mass distri-
bution from threshold up to 5 GeV/c2 for events in the
signal region as points with errors. The qq background
(hatched histogram) is small at low masses, but dominant
above about 4.5 GeV/c2. Since the ISR K+K−π+π−
background does not peak at low χ24K values, we in-
clude it in the background evaluated from the control
region, according to the method explained in Sec. IVA.
It dominates this background, which is 10% or lower at
all masses. The total background is shown as the open
histogram in Fig. 22.
We subtract the sum of backgrounds from the number
of selected events in each mass bin to obtain a number
of signal events. Considering uncertainties in the cross
sections for the background processes, the normalization
of events in the control region, and the simulation statis-
tics, we estimate a systematic uncertainty on the signal
yield of less than 5% in the 2–3 GeV/c2 region, increasing
to 10% in the region above 3 GeV/c2.
2 3 4 5
m(K+K-K+K-) (GeV/c2)
FIG. 22: Invariant mass distribution for K+K−K+K− can-
didates in the data (points). The hatched and open his-
tograms represent, cumulatively, the non-ISR background and
the ISR background from the control region, which is domi-
nated by the contribution from ISR K+K−π+π− events.
2 3 4
m(K+K-K+K-) (GeV/c2)
2 3 4
m(K+K-K+K-) (GeV/c2)
FIG. 23: (a) Invariant mass distributions for simulated
K+K−K+K− events in the signal (open) and control
(hatched) regions (see Fig. 21); (b) net reconstruction and
selection efficiency as a function of mass obtained from this
simulation (the curve represents a 3rd order polynomial fit).
B. Selection Efficiency
The detection efficiency is determined as for the other
two final states. Figure 23(a) shows the simulated
K+K−K+K− invariant-mass distributions in the signal
and control regions from the phase space model. We di-
vide the number of reconstructed events in each mass
interval by the number of generated ones in that interval
to obtain the efficiency shown as the points in Fig. 23(b).
It is quite uniform, and we fit a third order polynomial,
which we use to extract the cross section. A factor of 0.7
is again applicable for only hadronic system efficiency due
to the limited angular coverage of the ISR photon simula-
tion. A simulation assuming dominance of the φK+K−
channel, with the K+K− pair in an S-wave, gives con-
sistent results, and we apply the same 5% systematic
uncertainty as for the other final states. We correct for
mis-modeling of the track finding and kaon identifica-
tion efficiencies as in Sec. IVB, and for the shape of the
χ24K distribution analogously, using the result in Ref. [11],
(3.0± 2.0)%.
C. Cross Section for e+e− → K+K−K+K−
We calculate the e+e−→K+K−K+K− cross section
in 40 MeV Ec.m. intervals from the analog of Eq. 2, us-
ing the invariant mass of the K+K−K+K− system to
determine the effective c.m. energy. We show this cross
section in Fig. 24 and list it in Table IX. It rises to a
peak value near 0.1 nb in the 2.3–2.7 GeV region, then
decreases slowly with increasing energy. The only sta-
tistically significant narrow structure is the J/ψ peak.
Again, dL includes corrections for vacuum polarization
that should be omitted from calculations of gµ−2. This
supersedes our previous result [11].
2 3 4 5
Ec.m. (GeV)
FIG. 24: The e+e−→K+K−K+K− cross section as a func-
tion of the effective e+e− c.m. energy measured with ISR data
at BABAR. The errors are statistical only.
The simulated K+K−K+K− invariant mass resolu-
tion is 3.0 MeV/c2 in the 2.0–2.5 GeV/c2 range, increas-
ing with mass to 4.7 MeV/c2 in the 2.5–3.5 GeV/c2 range.
Since the cross section has no sharp structure except for
the J/ψ peak, we again make no correction for resolution.
TABLE IX: Measurements of the e+e− → K+K−K+K− cross section (errors are statistical only).
Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb) Ec.m. (GeV) σ (nb)
2.02 0.006 ± 0.004 2.66 0.075 ± 0.015 3.30 0.025 ± 0.009 3.94 0.012 ± 0.006
2.06 0.011 ± 0.006 2.70 0.102 ± 0.015 3.34 0.025 ± 0.009 3.98 0.012 ± 0.006
2.10 0.019 ± 0.007 2.74 0.069 ± 0.014 3.38 0.024 ± 0.010 4.02 0.010 ± 0.006
2.14 0.034 ± 0.011 2.78 0.063 ± 0.014 3.42 0.034 ± 0.010 4.06 0.009 ± 0.005
2.18 0.040 ± 0.013 2.82 0.051 ± 0.012 3.46 0.036 ± 0.009 4.10 0.006 ± 0.005
2.22 0.087 ± 0.016 2.86 0.024 ± 0.011 3.50 0.032 ± 0.009 4.14 0.008 ± 0.006
2.26 0.064 ± 0.018 2.90 0.054 ± 0.012 3.54 0.025 ± 0.009 4.18 0.011 ± 0.005
2.30 0.082 ± 0.017 2.94 0.045 ± 0.013 3.58 0.031 ± 0.009 4.22 0.011 ± 0.005
2.34 0.079 ± 0.018 2.98 0.045 ± 0.011 3.62 0.014 ± 0.007 4.26 0.012 ± 0.005
2.38 0.084 ± 0.017 3.02 0.063 ± 0.013 3.66 0.019 ± 0.008 4.30 0.004 ± 0.005
2.42 0.070 ± 0.016 3.06 0.049 ± 0.012 3.70 0.028 ± 0.008 4.34 0.003 ± 0.006
2.46 0.092 ± 0.018 3.10 0.287 ± 0.024 3.74 0.008 ± 0.005 4.38 0.013 ± 0.005
2.50 0.082 ± 0.015 3.14 0.050 ± 0.012 3.78 0.026 ± 0.007 4.42 0.012 ± 0.005
2.54 0.091 ± 0.015 3.18 0.054 ± 0.011 3.82 0.020 ± 0.007 4.46 0.006 ±-0.004
2.58 0.077 ± 0.017 3.22 0.049 ± 0.011 3.86 0.007 ± 0.006 4.50 -0.001 ±-0.004
2.62 0.095 ± 0.015 3.26 0.045 ± 0.010 3.90 0.012 ± 0.006 4.54 0.000 ± 0.004
The errors shown in Fig. 24 and Table IX are statisti-
cal only. The point-to-point systematic errors are much
smaller than this, and the errors on the normalization are
summarized in Table X, along with the corrections ap-
plied to the measurement. The total correction is +10%,
and the total systematic uncertainty is 9% at low mass,
increasing to 13% above 3 GeV/c2.
TABLE X: Summary of corrections and systematic uncer-
tainties on the e+e−→K+K−K+K− cross section. The total
correction is the linear sum of the components and the total
uncertainty is the sum in quadrature.
Source Correction Uncertainty
Rad. Corrections – 1%
Backgrounds – 5% m4K < 3 GeV/c
10% m4K > 3 GeV/c
Model Dependence – 5%
χ24K Distribution +3% 2%
Tracking Efficiency +3% 2%
Kaon ID Efficiency +4% 4%
ISR Luminosity – 3%
Total +10% 9% m4K < 3 GeV/c
13% m4K > 3 GeV/c
D. The φ(1020)K+K− Intermediate State
Figure 25 shows the invariant mass distribution for all
K+K− pairs in the selected K+K−K+K− events (4 en-
tries per event) as the open histogram. A prominent
φ peak is visible, along with possible peaks at 1.5, 1.7
and 2.0 GeV/c2. The hatched histogram is for the pair
in each event with mass closest to the nominal φ mass,
and indicates that the φK+K− channel dominates the
K+K−K+K− final state. Our previous finding of very
1 1.5 2
m(K+K-) (GeV/c2)
FIG. 25: Invariant mass distributions for all K+K− pairs in
selected e+e−→K+K−K+K− events (open histogram) and
for the combination in each event closest to the φ-meson mass
(hatched).
little φ signal [11] was incorrect due to an error in the
analysis algorithm.
If the pair mass closest to the φ mass is within
10 MeV/c2 of the φ mass, then we include the invariant
mass of the other K+K− combination in Fig. 26. The
contribution from events in the J/ψ peak is shown as the
hatched histogram which is in agreement with the BES
experiment [24] which studied the structures around 1.5,
1.7 and 2.0 GeV/c2 in detail. There is no evidence for
the φf0 channel, but there is an enhancement at thresh-
old that can be interpreted as the tail of the f0(980).
This is expected in light of the φf0 cross sections mea-
sured above in the K+K−π+π− and K+K−π0π0 final
1 1.2 1.4 1.6 1.8 2 2.2 2.4
m(K+K-) (GeV/c2)
FIG. 26: Invariant mass distribution for K+K− pairs in
events in which the other K+K− pair has mass closest to and
within 10 MeV/c2 of the nominal φ mass (open histogram).
The hatched histogram is for the subset with a K+K−K+K−
mass in the J/ψ peak.
states. However the statistics and uncertainties in the
f0(980) → K+K− lineshape do not allow a meaningful
extraction of the cross section in this final state.
We observe no significant structure in the K+K−K±
mass distribution. We use these events to study the pos-
sibility that part of our φπ+π− signal is due to φK+K−
events with the two kaons not from the φ taken as pions.
No structure is present in the reconstructedK+K−π+π−
invariant mass distribution from these events.
VII. e+e− → φf0 NEAR THRESHOLD
The behavior of the e+e− → φf0 cross section near
threshold shows a structure near 2150 MeV/c2, and we
have published this result in Ref. [14]. Here we pro-
vide a more detailed study of this cross section in the
1.8–3 GeV region. In Fig. 27 we superimpose the cross
sections measured in the K+K−π+π− and K+K−π0π0
final states (shown in Figs. 13 and 20); they are con-
sistent with each other. The K+K−K+K− cross section
(Sec. VID) is also consistent with the presence of a struc-
ture near 2150 MeV/c2 and shows a contribution from
the φf0 channel, but since we cannot extract a meaning-
ful φf0 cross section, we do not discuss this final state
further.
First, we attempt to reproduce this spectrum with a
smooth threshold function. In the absence of resonances,
the only theoretical constraint on the cross section well
above threshold is that it should decrease smoothly with
increasing Ec.m.. However the form of the cutoff at
threshold is determined by the properties of the interme-
1.8 2 2.2 2.4 2.6 2.8 3
Ec.m. (GeV)
FIG. 27: The e+e−→φ(1020)f0(980) cross section measured
in the K+K−π+π− (circles) and K+K−π0π0 (squares) final
states. The hatched histogram shows the simulated cross sec-
tion, assuming no resonant structure. The solid (dashed) line
represents the result of the one-resonance (no-resonance) fit
described in the text.
diate resonances and the final state particle spins, phase
space and detector resolution. The model discussed in
Sec. IVF takes the φ and f0(980) lineshapes, the spins
of all particles and their phase space into account, and
postulates a simple E−4c.m. dependence of the cross section.
For the e+e−→φf0 reaction, it predicts the cross section
shown as the hatched histogram in Fig. 27, normalized
to the same total area as the data. It shows a sharp rise
from the threshold with a peak near 2070 MeV and is
inconsistent with the data.
To account for uncertainties in the f0 width and the
shape of the cross section well above threshold, we seek a
functional form that describes the simulation and whose
parameters can be varied to cover a reasonable range of
possibilities. This can be achieved by the product of a
phase space term, an exponential rise and a second order
polynomial:
σnr(µ) = P (µ) ·Anr(µ), (4)
Anr(µ) = σ0 · (1 − e−(µ/a1)
) · (1 + a2µ+ a3µ2),
P (µ) =
1−m20/(m0 + µ)2, µ = Ec.m.−m0,
where the ai are free parameters, σ0 is a normalization
factor, and P (µ) is a good approximation of the two-body
phase space for particles with similar masses. Both the
φ(1020) and f0(980) have small but finite widths, and
our selection criterion of m(ππ) > 0.85 GeV/c2 defines
an effective minimum mass, m0 = 1.8 GeV/c
2. Fitting
Eq. 4 to the simulated cross section yields the ai values
listed in the first column of Table XI. Fitting to the data
with all ai fixed to these values and σ0 floating yields
χ2/n.d.f.= 86/(56 − 2). Floating a2 and a3 in addition,
we obtain χ2/n.d.f.=85/(56− 4) with a confidence level
(C.L.) of 0.0025. If we float all parameters in Eq. 4,
the fit yields χ2/n.d.f.= 80/(56− 5) with C.L. of 0.0053.
The results of these fits are listed in Table XI, and the
latter is shown as the dashed curve on Fig. 27; all fits are
inconsistent with the data.
TABLE XI: Parameter values, χ2 values and confidence levels
from the fits of Eq. 4 to the data described in the text. An
asterisk denotes a value that was fixed in that fit.
Fit All ai fixed Only a1 fixed All ai free
σ0 1.19±0.03 1.23±0.03 1.09±0.01
a1 0.218* 0.218* 0.174±0.012
a2 −1.68* −1.51±0.15 −1.49±0.12
a3 0.81* 0.66±0.14 0.63±0.11
χ2/n.d.f. 86.4/54 85.3/52 80.5/51
P(χ2) 0.0035 0.0025 0.0053
We now add a resonance and fit the data with the
function
σ1r(µ) =
P (µ)
P (m1)
∣Anr(µ)e
iψ1 +Ar1(µ)
, (5)
Ar1(µ) =
σ1m1Γ1
m21 − E2c.m.− iEc.m.Γ1
where m1 and Γ1 are the mass and width of the reso-
nance, σ1 is its peak cross section, and ψ1 is its phase rela-
tive to the non-resonant component. We obtain good fits
both assuming no interference between the two compo-
nents, ψ1=π, and with ψ1 floating. The result of the lat-
ter fit is shown as the solid curve on Fig. 27. The data are
somewhat above this curve near 2.4 GeV/c2 and a fit with
two resonances can also describe the data. Due to the
sharp drop near 2.2 GeV/c2, the single-resonance fit with
interference gives a resonance mass about 30 MeV/c2
higher than the other two fits. All these fits, with or with-
out resonances, give a peak non-resonant cross section in
the range 0.3–0.4 nb, which is of independent theoretical
interest, because it can be related to the φ → f0(980)γ
decay studied at the φ-factory [25].
Under the hypothesis of one resonance interfering with
the non-resonant component, the fit gives the resonance
parameters
σ1 = 0.13± 0.04 nb,
m1 = 2.175± 0.010 GeV/c2,
Γ1 = 0.058± 0.016 GeV, and
ψ1 = −0.57± 0.30 radians,
along with χ2/n.d.f.=37.6/(56− 9) (C.L. 0.84). We can
estimate the product of its electronic width and branch-
ing fraction to φf0 as
Bφf0 · Γee =
Γ1σ1m
= (2.5± 0.8± 0.4) eV ,
where we fit the product Γ1σ1 to reduce correlations, and
the conversion constant C = 0.389 mb(GeV/c2)2. The
second error is systematic and corresponds to the nor-
malization errors on the cross section.
The significance of the structure calculated from the
change in χ2 between the best fit and the null hypothe-
sis is 6.2 standard deviations. Since this calculation can
be unreliable in the case of low statistics and functions
that vary rapidly on the scale of the bin size, we per-
form a set of simulations in which we generate a number
of events according to a Poisson distribution about the
number observed in the data and with a mass distribu-
tion given by either the simulation or fitted function in
Fig. 27 without resonant structure. On each sample, we
perform fits to Eqs. 4 and 5 and calculate the difference
in χ2. The fraction of trials giving a χ2 difference larger
than that seen in the data corresponds to a significance
of approximately 5 standard deviations.
We search for this structure in other submodes with
different and/or fewer intermediate resonances. The to-
tal cross sections are dominated by K∗Kπ channels, and
the K∗0K+π− cross section is shown in Fig. 8. There
is no significant structure in the 2.1–2.5 GeV region, but
the point-to-point statistical uncertainties are large. If we
remove events within the bands in Figs. 5 and 18, then
most of the events containing a K∗ are eliminated and
we obtain the raw mass distributions shown as the points
with errors in Figs. 28 and 29, respectively. Both distri-
bution show evidence of a structure around 2.15 GeV/c2
and the K+K−π+π− distribution also shows a structure
near 2.4 GeV/c2. We cannot exclude the presence of these
structures in events with a K∗, but we can conclude that
they do not dominate those events, whereas they com-
prise a substantial fraction of the remaining events in
that mass region.
Applying the further requirement that the dipion mass
be in the range 0.85–1.10 GeV/c2, we remove most of
the events without an f0, and obtain the mass distribu-
tions shown as the hatched histograms in Figs. 28 and 29.
Peaks are visible at both 2.15 GeV/c2 and 2.4 GeV/c2 in
both distributions, and they contain enough events to
account for the corresponding structures in the distribu-
tions for all non-K∗ events. These peaks contain at least
as many events as are present in the φf0 samples, but
the non-resonant components are higher and there is a
substantial kinematic overlap between K+K−f0 events
and K∗Kπ events in this mass range.
Since this f0(980) band appears to contain a large frac-
tion of the events within the structure, we now consider
all selected events with a dipion mass inside or outside
this range. Figure 31 shows the mass distribution for all
selected K+K−π0π0 events as the open histogram, and
the subsets of events with π0π0 mass inside and outside
the range 0.85–1.10 GeV/c2 as the hatched and cross-
hatched histograms, respectively. It is evident that the
K+K−f0 channel contains the majority of the structure
in the 2.0–2.6 GeV/c2 range.
We show the corresponding distributions for the
1 1.5 2 2.5 3 3.5 4 4.5 5
m(K+K-π+π-) (GeV/c2)
FIG. 28: Invariant mass distribution for all selected
K+K−π+π− events lying outside the K∗0(892) bands of
Fig. 5 (points), and the subset of these events with 0.85 <
m(π+π−) < 1.10 GeV/c2 (hatched).
1 1.5 2 2.5 3 3.5 4 4.5 5
m(K+K-π0π0) (GeV/c2)
FIG. 29: Invariant mass distribution for all selected
K+K−π0π0 events lying outside the K∗0(892) bands of
Fig. 18 (points), and the subset of these events with 0.85 <
m(π0π0) < 1.10 GeV/c2 (hatched).
K+K−π+π− events in Fig. 30. Due to the presence of
the ρ0, the relative f0 contribution is much smaller in this
final state, but the events in the f0 band show clear in-
dications of structure in the 2.0–2.4 GeV/c2 region. The
remaining events may also have structure in this region,
but the statistical significance is marginal and it could
be due to other sources, such as the φf2(1270) threshold
at 2.3 GeV/c2.
Figures 32 and 33 show enlarged views of the mass
distributions within the f0 bands from Figs. 30 and 31,
respectively. The two-peak structure is more evident
1 1.5 2 2.5 3 3.5 4 4.5 5
m(K+K-π+π-) (GeV/c2)
FIG. 30: The K+K−π+π− invariant mass distribution for all
selected events (open histogram), and for those with a π+π−
mass inside (cross-hatched) or outside (hatched) the f0 band
as defined in the text.
1 1.5 2 2.5 3 3.5 4 4.5 5
m(K+K-π0π0) (GeV/c2)
FIG. 31: The K+K−π0π0 invariant mass distribution for all
selected events (open histogram), and for those with a π0π0
mass inside (cross-hatched) or outside (hatched) the f0 band
as defined in the text.
here than in the φf0 events. The 0.85 < m(ππ) <
1.10 GeV/c2 requirement gives enough phase space for
K+K− invariant mass to cover the region from threshold
to ∼1.3 GeV/c2 for m(K+K−ππ) ≈ 2.15 GeV/c2. From
the measured kaon form factor we expect to find only
about two-thirds of K+K− P-wave in our fitted φ peak.
Since the non-ISR and ISR ππππ backgrounds have not
been subtracted and the samples contain an unknown
mixture of intermediate states, we fit them with a modi-
TABLE XII: Summary of parameters obtained from the fits described in the text to the K+K−π+π− and K+K−π0π0 events
with dipion mass in the f0(980) band. An asterisk denotes a value that was fixed in that fit.
No Resonance One Resonance Two Resonances
Fit K+K−π+π− K+K−π0π0 K+K−π+π− K+K−π0π0 K+K−π+π− K+K−π0π0
Nnr 7204±775 991±202 8466±334 722±112 6502±476 117±89
a1 0.181±0.012 0.134±0.017 0.224±0.024 0.197±0.048 0.201±0.035 0.143±0.053
a2 −0.75±0.21 −1.47±0.38 −0.89±0.17 −0.36±0.10 −0.44±0.15 5.80±2.36
a3 0.09±0.17 0.75±0.35 0.17±0.08 −0.28±0.14 −0.15±0.12 −5.26±1.75
a4 0.75* 0.50* 0.75* 0.50* 0.75* 0.50*
N1 0* 0* 116±95 149±36 163±70 192±44
m1 (GeV/c
2) – – 2.192±0.014 2.169±0.020 2.187±0.013 2.154±0.029
Γ1 (GeV) – – 0.071±0.021 0.102±0.027 0.066±0.018 0.110±0.022
ψ1 (rad) – – −0.60±0.41 −1.02±0.19 −1.10±0.14 −1.04±0.23
N2 0* 0* 0* 0* 16±16 6±5
m2 (GeV/c
2) – – – – 2.47±0.07 2.45±0.04
Γ2 (GeV) – – – – 0.077±0.065 0.062±0.102
ψ2 (rad) – – – – 0.28±1.06 1.41±1.29
χ2/n.d.f. 62.8/41 38.1/21 35.6/37 13.0/17 31.4/34 9.7/13
P(χ2) 0.016 0.012 0.54 0.74 0.60 0.72
fied version of Eq. 5 that allows up to two resonances,
F (µ) = (a4 · Anr)2 (6)
+ |(1 − a4)Anr +Ar1eiψ1 +Ar2eiψ2 |2.
Here, the normalization is in terms of events rather than
cross section (σi → Ni) and a fraction a4 of the non-
resonant component does not interfere with the reso-
nances. We first fit the distribution with no resonances
(and a4 =1). The results are shown as the dashed lines
in Figs. 32 and 33 and listed in Table XII; both are in-
consistent with the data.
We next include one resonance in the fit. The param-
eter a4 is not well constrained by the data and its value
has a small influence on all other fit parameters except
for the number of events assigned to the resonance, so we
present results with a4 fixed to the reasonable values of
0.75 and 0.50 for theK+K−π+π− andK+K−π0π0 data,
respectively. The results are shown as the solid lines in
Figs. 32 and 33 and listed in Table XII. The fit quality is
good in both cases, the fitted resonance parameters are
consistent with those from the φf0 study, and the cal-
culated significance of the structure for the K+K−π+π−
data is similar, 5.2 standard deviations. TheK+K−π0π0
data show much more pronounced structure than in the
φf0 study, allowing a full fit to this sample with a signif-
icance of 5.0 standard deviations.
We then add a second resonance to the fit, keeping a4
fixed and floating all other parameters. The results are
shown as the dotted lines in Figs. 32 and 33, and listed
in Table XII. These fits are also of good quality, but
do not change the χ2 CL or the parameters of the first
resonance significantly. We also perform fits with no in-
terference between the non-resonant component and any
resonance (a4 = 1), obtaining good quality fits for both
one resonance and two resonances with relative phase
π/2. The fitted resonance parameters are consistent in
all cases, except that the mass of the first resonance is
lower by about 50 MeV/c2, similar to the 30 MeV/c2 shift
seen in the φf0 study.
From these studies we conclude that we have observed
a new vector structure at a mass of about 2150 MeV/c2
with a significance of over six standard deviations. It
decays into K+K−f0(980), with the K
+K− pair pro-
duced predominantly via the φ(1020). There is an ad-
ditional structure at about 2400 MeV/c2, and the two
structures can be described by either two resonances or
a single resonance that interferes with the non-resonant
K+K−f0(980) process. More data and searches in other
final states are needed to understand the nature of these
structures.
If the main structure is due to a resonance, then it
is relatively narrow and might be interpreted as the
strange analog of the recently observed charmed Y(4260)
state [6], which decays to J/ψπ+π−. The value of
Bφf0 ·Γee = (2.5± 0.8± 0.4) eV measured here is similar
to the value of BY→J/ψπ+π− · ΓYee = (5.5± 1.0± 0.8) eV
reported in Ref. [6].
VIII. THE CHARMONIUM REGION
The data at masses above 3 GeV/c2 can be used to
measure or set limits for the branching fractions of nar-
row resonances, such as charmonia, and the narrow J/ψ
and ψ(2S) peaks allow measurements of our mass scale
and resolution. Figures 34, 35 and 36 show the in-
variant mass distributions for the selected K+K−π+π−,
K+K−π0π0 and K+K−K+K− events, respectively, in
this region, with finer binning than in the corresponding
Figs. 2, 15 and 22. We do not subtract any background
FIG. 32: The K+K−π+π− invariant mass distribution in
the K+K−f0(980) threshold region for events with a π
mass inside the f0 band. The lines represent the results of
the fits including no (dashed), one (solid) and two (dotted)
resonances described in the text.
FIG. 33: The K+K−π0π0 invariant mass distribution in the
K+K−f0(980) threshold region for events with a π
0π0 mass
inside the f0 band. The lines represent the results of the
fits including no (dashed), one (solid) and two (dotted) reso-
nances described in the text.
from the K+K−π+π− or K+K−K+K− data, since it is
small and nearly uniformly distributed, but we use the
KKπ0π0
control region to subtract part of the ISR back-
ground from the K+K−π0π0 data. Signals from the J/ψ
are visible in all three distributions, and the ψ(2S) is vis-
ible in the K+K−π+π− mode.
We fit each of these distributions using a sum of two
Gaussian functions to describe the J/ψ and ψ(2S) signals
plus a polynomial to describe the remainder of the dis-
3 3.25 3.5 3.75
m(K+K-π+π-) (GeV/c2)
FIG. 34: Raw invariant mass distribution for all selected
e+e−→K+K−π+π− events in the charmonium region. The
line represents the result of the fit described in the text.
tribution. We take the signal function parameters from
the simulation, but let the overall mean and width float
in the fit, along with the amplitude and the coefficients
of the polynomial. The fits are of good quality and are
shown as the curves on Figs. 34, 35 and 36. In all cases,
the fitted mean value is within 1 MeV/c2 of the PDG [5]
J/ψ or ψ(2S) mass, and the width is consistent within
10% with the simulated resolution discussed in Sec. IVC,
VC or VIC.
The fits yield 1586± 58 events in the J/ψ peak for the
K+K−π+π− final state, 203± 16 events for K+K−π0π0
and 156±15 events for K+K−K+K−. From these num-
bers of observed events in each final state f , NJ/ψ→f , we
calculate the product of the J/ψ branching fraction to f
and the J/ψ electronic width:
BJ/ψ→f · ΓJ/ψee =
NJ/ψ→f ·m2J/ψ
6π2 · dL/dE · ǫf(mJ/ψ) · C
, (7)
where dL/dE = 89.8 nb−1/MeV and ǫf (mJ/ψ) are the
ISR luminosity and corrected selection efficiency, respec-
tively, at the J/ψ mass and C is the conversion constant.
We estimate ǫK+K−π+π− =0.202, ǫK+K−π0π0 =0.069 and
ǫK+K−K+K− =0.176.
Using Γ
ee = 5.40 ± 0.18 keV [5], we obtain the
branching fractions listed in Table XIII, along with
the measured products and the current PDG val-
ues. The systematic errors include a 3% uncertainty
ee . The branching fractions to K
+K−π+π−
and K+K−K+K− are more precise than the current
PDG values, which were dominated by our previous
results of (6.25±0.80)×10−3 and (7.4±1.8)×10−4, re-
spectively [11]. This is the first measurement of the
K+K−π0π0 branching fraction.
3 3.25 3.5 3.75
m(K+K-π0π0) (GeV/c2)
FIG. 35: Invariant mass distribution for e+e−→K+K−π0π0
events in the charmonium region, after partial background
subtraction. The line represents the result of the fit described
in the text.
3 3.25 3.5 3.75
m(K+K-K+K-) (GeV/c2)
FIG. 36: Raw invariant mass distribution for all selected
e+e−→K+K−K+K− events in the charmonium region. The
line represents the result of the fit described in the text.
These fits also yield 91±15 K+K−π+π− events in the
ψ(2S) peak, but no other significant signals. We expect
6.3 events from ψ(2S)→J/ψπ+π−→K+K−π+π− from
the relevant branching fractions [5], which is less than
the statistical error. Subtracting this contribution and
using a calculation analogous to Eq. 7, with dL/dE =
115.3 nb−1/MeV, we obtain the product of the ψ(2S)→
K+K−π+π− branching fraction and its electronic width.
Dividing by the world average value of Γ
ψ(2S)
ee [5], we
obtain the branching fraction listed in Table XIII; it is
consistent with the current PDG value [5].
As noted in Sec. IVD and shown in Fig. 5,
the K+K−π+π− final state is dominated by the
K∗0(892)Kπ channels, with a small fraction seen in the
K∗0(892)K∗02 (1430) + c.c. channels. Figure 37 shows a
scatter plot of the invariant mass of a K±π∓ pair ver-
sus that of the K+K−π+π− system in events with the
other K∓π± pair near the K∗0(892) mass, i.e. within
the bands in Fig. 5(a) with overlapped region taken only
once. There is a large concentration of entries in the
J/ψ band with K±π∓ masses near 1430 MeV/c2, but
no solid evidence for a horizontal band corresponding
to K∗02 (1430) production other than in J/ψ decays. We
show the K±π∓ mass projection for the subset of events
with a K+K−π+π− mass within 50 MeV/c2 of the J/ψ
mass in Fig. 38 as the open histogram. The hatched his-
togram is the projection for events with a K+K−π+π−
mass between 50 and 100 MeV/c2 below the J/ψ mass.
2 3 4
m(K+K-π+π-) (GeV/c2)
FIG. 37: The K±π∓ invariant mass versus K+K−π+π−
invariant mass for events with the other K∓π± combination
in the K∗0(892) bands of Fig. 5(a). The overlapped region is
taken only once.
The J/ψ component appears to be dominated by the
K∗02 (1430). Also seen is a small signal from K
∗0(892)
indicating the K∗0(892)K̄∗0(892) decay of J/ψ: this is
also seen as an enhancement in the vertical J/ψ band in
Fig. 37. The enhancement at 1.8 GeV/c2 of Fig. 38 can be
explained by the J/ψ decay into K∗0(892)K2(1770)+c.c.
(or K∗0(892)K2(1820)+ c.c.), a mode which has not pre-
viously been reported. Subtracting the number of side-
band events from the number in the J/ψ mass window,
we obtain 317±23 events with a K±π∓ mass in the range
1200–1700 MeV/c2, which we take as a measure of J/ψ
decays into K∗0(892)K∗02 (1430), 25 ± 8 events in the
0.8–1.0 GeV/c2 window for the K∗0(892)K̄∗0(892) de-
cay and 110 ± 14 events for the K∗0(892)K2(1770) or
K∗0(892)K2(1830) final state in the 1.7–2.0 GeV/c
2 re-
gion. We convert these to branching fractions using Eq. 7
and dividing by the known branching fractions of excited
1 2 3
m(K+π-,K-π+) (GeV/c2)
FIG. 38: The K±π∓ mass projection from Fig. 37 for events
with a K+K−π+π− mass within 50 MeV/c2 of the J/ψ mass
(open histogram) and 50–100 MeV/c2 below (hatched).
kaons [5]. The results are listed in Table XIII: they
are considerably more precise than the PDG values. We
cannot calculate BJ/ψ→K∗0K2(1770) because no branching
fractions of K2(1770) or K2(1830) to Kπ are reported.
We study decays into φπ+π− and φπ0π0 using the
mass distributions shown in Figs. 39 and 40, respectively.
The open histograms are for the events with a K+K−
mass within the φ bands of Figs. 9(c) and 19(c). The
cross-hatched histogram in Fig. 39 is from the φ side-
bands of Fig. 9(c) and represents the dominant back-
ground in the φπ+π− mode. The hatched histogram in
Fig. 40 is from the χ2KKπ0π0 control region and represents
the dominant background in the φπ0π0 mode. Subtract-
ing these backgrounds, we find 103±12 J/ψ → φπ+π−
events, 23±6 J/ψ → φπ0π0 events, and 10±4 ψ(2S) →
φπ+π− events. We convert these to branching fractions
and list them in Table XIII. This is the first measure-
ment of the J/ψ → φπ0π0 branching fraction, and the
other two are consistent with current PDG values.
If the Y (4260) has a substantial branching fraction into
φπ+π−, then we would expect to see a signal in Fig. 39.
In the mass range |m(φπ+π−) − m(Y )| < 0.1 GeV/c2,
we find 10 events, and assuming a uniform distribu-
tion we estimate 9.2 background events from the 3.8–
5.0 GeV/c2 region. This corresponds to a signal of
0.8± 3.3 events or a limit of < 5 events at the 90% C.L.
Using dL/dE = 147.7 nb−1/MeV at the Y (4260) mass,
we calculate BY→φπ+π− ·ΓYee<0.4 eV which is well below
the value of BY→J/ψπ+π− ·ΓYee = (5.5± 1.0± 0.8) eV [6].
No Y (4260) signal is seen in any other mode studied here.
Figures 41(a) and 42 show the corresponding mass dis-
tributions for φf0 events, i.e. the subsets of the events in
Figs. 39 and 40 with a dipion mass in the range 0.85–
1.10 GeV/c2. Signals at the J/ψ mass are visible in
3 3.5 4 4.5 5
m(K+K-π+π-) (GeV/c2)
FIG. 39: Raw invariant mass distributions for candidate
e+e− → φπ+π− events (open histogram) and events in the
φ side bands of Fig. 9(c) (cross-hatched) in the charmonium
region. The vertical lines indicate the region used for the
Y (4260) search.
3 3.5 4 4.5 5
m(K+K-π0π0) (GeV/c2)
FIG. 40: Raw invariant mass distributions for candidate
e+e− → φπ0π0 events (open histogram) and events in the
χ2KKπ0π0 control region (hatched) in the charmonium region.
both cases, but φf0 is not the dominant mode of the
J/ψ→ φπ+π− decay. Figure 41(b) shows the π+π− in-
variant mass distribution for events in the J/ψ peak of
Fig. 39, 3.05<m(K+K−π+π−)< 3.15 GeV/c2. A two-
peak structure is visible that can interpreted as due to
the f0(980) and f2(1270) resonances. Fitting the dis-
tribution in Fig. 41(b) with a sum of two Breit-Wigner
functions with parameters fixed to PDG values [5], we
find 19.5 ± 4.5 J/ψ→φf0 events and 44 ± 7 J/ψ→φf2
events. From Fig. 42 we estimate 7.0± 2.8 φf0 events in
the π0π0 mode.
TABLE XIII: Summary of the J/ψ and ψ(2S) branching fractions measured in this article.
Measured Measured J/ψ or ψ(2S) Branching Fraction (10−3)
Quantity Value ( eV) Calculated, this work PDG2006
ee ·BJ/ψ→K+K−π+π− 36.3 ±1.3 ±2.1 6.72±0.24±0.40 6.2 ±0.7
ee ·BJ/ψ→K+K−π0π0 13.6 ±1.1 ±1.3 2.52±0.20±0.25 no entry
ee ·BJ/ψ→K+K−K+K− 4.11±0.39±0.30 0.76±0.07±0.06 0.78 ±0.14
ee ·BJ/ψ→K∗0K∗0
· BK∗0→Kπ · BK∗0
→Kπ 7.3 ±0.5 ±0.6 2.7 ±0.2 ±0.2 6.7 ±2.6
ee ·BJ/ψ→K∗0K̄∗0 · BK∗0→Kπ · BK̄∗0→Kπ 0.57±0.18±0.05 0.11±0.04±0.01 <0. 5 at 90% C.L.
ee ·BJ/ψ→K∗0K2(1770) · BK∗0→Kπ · BK2→Kπ 2.5 ±0.3 ±0.2 – no entry
ee ·BJ/ψ→φπ+π− · Bφ→K+K− 2.61±0.30±0.18 0.98±0.11±0.07 0.94 ±0.15
ee ·BJ/ψ→φπ0π0 · Bφ→K+K− 1.54±0.40±0.16 0.58±0.15±0.06 no entry
ee ·BJ/ψ→φf0 · Bφ→K+K− · Bf0→π+π−
0.50±0.11±0.04 0.28±0.07±0.02 0.32 ±0.09 (s=1.9)
ee ·BJ/ψ→φf0 · Bφ→K+K− · Bf0→π0π0
0.47±0.19±0.05 0.54±0.21±0.05 0.32 ±0.09 (s=1.9)
ee ·BJ/ψ→φf2 · Bφ→K+K− · Bf2→π+π−
1.12±0.18±0.09 0.50±0.08±0.04 <0. 37 at 90% C.L.
ψ(2S)
ee ·Bψ(2S)→K+K−π+π− 2.56±0.42±0.16 1.2 ±0.2 ±0.08 0.72 ±0.05
ψ(2S)
ee ·Bψ(2S)→φπ+π− · Bφ→K+K− 0.28±0.11±0.02 0.27±0.11±0.02 0.113 ±0.029
ψ(2S)
ee ·Bψ(2S)→φf0 · Bφ→K+K− · Bf0→π+π−
0.17±0.08±0.02 0.26±0.12±0.03 0.090 ±0.033
3 3.5 4 4.5 5
m(φ f0) (GeV/c
0.5 1 1.5
m(π+π-) (GeV/c2)
FIG. 41: (a) Raw invariant mass distribution for candidate
φf0, f0→π
+π− events (open histogram) and events in the φ
side bands (cross-hatched) in the charmonium region; (b) the
π+π− invariant mass distribution for φπ+π− events from the
J/ψ peak of Fig. 39. The line represents the result of the fit
described in the text.
Using Eq. 7 and dividing by the appropriate branching
fractions, we obtain the J/ψ branching fractions listed in
Table XIII. The measurements of BJ/ψ→φf0 in the π+π−
and π0π0 decay modes of the f0 are consistent with each
other and with the PDG value, and combined they have
roughly the same precision as listed in the PDG [5]. This
is the first measurement of BJ/ψ→φf2 , and the value is
consistent with the previous upper limit [5]. We also
3 3.5 4 4.5 5
m(φ f0) (GeV/c
FIG. 42: Raw invariant mass distribution for candidate φf0,
0π0 events (open histogram) and events in the χ2KKπ0π0
control region (hatched) in the charmonium region.
observe 6 ± 3 ψ(2S)→φf0, f0→π+π− events, which we
convert to the branching fraction listed in Table XIII; it is
consistent with the PDG value [5], assuming Bf0→π+π− =
In the Y (4260) region we have 4 events with an esti-
mated background of about 1 event. This corresponds to
3±2 events, or a 90% CL upper limit of 5.6 events. We
convert this to the limits
BY→φf0 · ΓYee · Bφ→K+K− · Bf0→π+π− < 0.14 eV ,
BY→φf0 · ΓYee < 0.43 eV, 90%CL,
which is again much lower than the corresponding quan-
tity for the Y (4260)→J/ψπ+π− decay.
IX. SUMMARY
We use the excellent charged particle tracking and
identification, and photon detection of the BABAR
detector to fully reconstruct events of the type
e+e− → γe+e− → γK+K−π+π−, γK+K−π0π0 and
γK+K−K+K−, where the γ is radiated from the ini-
tial state e+ or e−. Such events are equivalent to direct
e+e− annihilation at an effective c.m. energy correspond-
ing to the mass of the hadronic system, and we study
the annihilation into these three final states at low Ec.m.,
from their respective production thresholds up to 5 GeV.
The K+K−π+π− and K+K−K+K− measurements are
consistent with, and supersede, our previous results [11].
This is the first measurement of the K+K−π0π0 final
state, although some of the results were also presented in
Ref. [14].
The systematic uncertainties on the normaliza-
tion of the e+e− → K+K−π+π−, K+K−π0π0 and
K+K−K+K− cross sections are 8%, 10% and 9%, re-
spectively, for Ec.m.<3 GeV, and 10%, 14% and 13% in
the 3–5 GeV range. The obtained cross sections are con-
siderably more precise than previous measurements and
cover this low energy range completely, so they provide
important input to calculations of the hadronic correc-
tions to the anomalous magnetic moment of the muon
and the fine structure constant at the Z0 mass.
These final states exhibit complex resonant substruc-
ture. In the K+K−π+π− mode we measure the cross
sections for the first time for the specific channels e+e−→
K∗0(890)K−π+, φπ+π− and φf0. We also observe sig-
nals for the ρ0(770), K1(1270), K1(1400), K
2 (1430)
and f∗02 (1270) resonances. It is difficult to disentangle
these contributions to the final state, and we make no
attempt to do so in this paper. We note that the ρ0
signal is consistent with being due entirely to K1 de-
cays, and the total cross section is dominated by the
K∗0(892)K−π+ + c.c. channels, but there is no signifi-
cant signal for e+e−→K∗0(892)K∗0(892).
In the K+K−π0π0 mode we measure cross sections
for e+e− → φf0 and observe signals for the K∗±(892)
and K∗±2 (1430) resonances. Again, the total cross sec-
tion is dominated by the K∗±(892)K∓π0 channels, and
there is no signal for e+e−→K∗+(892)K∗−(892). The
K+K−π0π0 final state is not accessible to intermediate
states containing K1 resonances, and we note that the
cross section is roughly a factor of four smaller over most
of the range than the K+K−π+π− cross section, consis-
tent with K∗Kπ dominance with a factor of two isospin
suppression of the π0π0 final state and another factor of
two for the relative branching fractions of the neutral and
charged K∗ to charged kaons.
In the K+K−K+K− mode we find e+e−→φK+K− to
be the dominant channel. With the current data sample
we can say little about the other K+K− combination,
except that there is an enhancement near threshold, con-
sistent with the φf0 channel, and that in J/ψ decays
there is structure in the 1.5–2.0 GeV region, consistent
with that observed by BES [24].
The φf0 cross section measured in the K
+K−π+π−
final state shows structure around 2.15 GeV and pos-
sibly 2.4 GeV, and the corresponding measurement in
the K+K−π0π0 final state is consistent, as reported in
Ref. [14]. Further investigation here reveals consistent re-
sults in the K+K−K+K− final state and clear signals in
the K+K−f0 channels, with f0→π+π− and π0π0. The
signals are predominantly from φf0, but the relaxation
of the K+K− mass requirement reveals a strong signal
in the K+K−π0π0 final state. This structure can be in-
terpreted as a strange partner (with c-quarks replaced
by s-quarks) of the recently observed Y (4260), which has
the analogous decay mode J/ψπ+π−, or as an ssss state
that decays predominantly to φf0.
We also study charmonium decays into these final
states and their intermediate channels. All nine of the
J/ψ branching fractions and one of the three ψ(2S)
branching fractions listed in Table XIII are as precise or
more precise than the current world averages. We do not
observe the Y (4260) in any decay mode. In particular, we
find that the branching fraction for the Y (4260)→φπ+π−
decay, that a glueball model [8] predicts, is less than one-
tenth of that to J/ψπ+π−.
X. ACKNOWLEDGMENTS
We are grateful for the extraordinary contributions of
our PEP-II colleagues in achieving the excellent luminos-
ity and machine conditions that have made this work pos-
sible. The success of this project also relies critically on
the expertise and dedication of the computing organiza-
tions that support BABAR. The collaborating institutions
wish to thank SLAC for its support and the kind hospi-
tality extended to them. This work is supported by the
US Department of Energy and National Science Foun-
dation, the Natural Sciences and Engineering Research
Council (Canada), the Commissariat à l’Energie Atom-
ique and Institut National de Physique Nucléaire et de
Physique des Particules (France), the Bundesministerium
für Bildung und Forschung and Deutsche Forschungsge-
meinschaft (Germany), the Istituto Nazionale di Fisica
Nucleare (Italy), the Foundation for Fundamental Re-
search on Matter (The Netherlands), the Research Coun-
cil of Norway, the Ministry of Education and Science of
the Russian Federation, Ministerio de Educación y Cien-
cia (Spain), and the Science and Technology Facilities
Council (United Kingdom). Individuals have received
support from the Marie-Curie IEF program (European
Union) and the A. P. Sloan Foundation.
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	Introduction
	The BABAR detector and dataset
	Event Selection and Kinematic Fit
	The K+ K- +- final state
	Final Selection and Backgrounds
	Selection Efficiency
	Cross Section for e+e-  K+ K- +- 
	Substructure in the K+ K- +-  Final State
	The e+e-  K*0 K  Cross Section
	The (1020)+- Intermediate State
	The (1020) f0(980) Intermediate State
	The K+ K-00 Final State
	Final Selection and Backgrounds
	Selection Efficiency
	Cross Section for e+e-  K+ K- 00
	Substructure in the K+ K- 00 Final State
	The (1020)00 Intermediate State
	The (1020) f0(980) Intermediate State
	The K+ K- K+ K-  Final State
	Final Selection and Background
	Selection Efficiency
	Cross Section for e+e-  K+ K- K+ K-
	The (1020) K+ K-  Intermediate State
	e+e-  f0 Near Threshold
	The Charmonium Region
	Summary
	Acknowledgments
	References
