The
e
e
!
3
,
2
0
and
K
K
2
cross sections at center-of-mass energies
from production threshold to 4.5 GeV measured with initial-state radiation
B. Aubert, R. Barate, D. Boutigny, F. Couderc, Y. Karyotakis, J. P. Lees, V. Poireau, V. Tisserand, and A. Zghiche
Laboratoire de Physique des Particules, F-74941 Annecy-le-Vieux, France
E. Grauges
IFAE, Universitat Autonoma de Barcelona, E-08193 Bellaterra, Barcelona, Spain
A. Palano and M. Pappagallo
Universita
`
di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy
J. C. Chen, N. D. Qi, G. Rong, P. Wang, and Y. S. Zhu
Institute of High Energy Physics, Beijing 100039, China
G. Eigen, I. Ofte, and B. Stugu
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
G. S. Abrams, M. Battaglia, D. S. Best, D. N. Brown, J. Button-Shafer, R. N. Cahn, E. Charles, C. T. Day, M. S. Gill,
A. V. Gritsan,
*
Y. Groysman, R. G. Jacobsen, R. W. Kadel, J. A. Kadyk, L. T. Kerth, Yu. G. Kolomensky, G. Kukartsev,
G. Lynch, L. M. Mir, P. J. Oddone, T. J. Orimoto, M. Pripstein, N. A. Roe, M. T. Ronan, and W. A. Wenzel
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
M. Barrett, K. E. Ford, T. J. Harrison, A. J. Hart, C. M. Hawkes, S. E. Morgan, and A. T. Watson
University of Birmingham, Birmingham, B15 2TT, United Kingdom
M. Fritsch, K. Goetzen, T. Held, H. Koch, B. Lewandowski, M. Pelizaeus, K. Peters, T. Schroeder, and M. Steinke
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
J. T. Boyd, J. P. Burke, W. N. Cottingham, and D. Walker
University of Bristol, Bristol BS8 1TL, United Kingdom
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
A. Khan, P. Kyberd, 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, E. A. Kravchenko, 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, M. Bruinsma, M. Chao, S. Curry, I. Eschrich, D. Kirkby, A. J. Lankford, P. Lund, M. Mandelkern,
R. K. Mommsen, W. Roethel, 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, O. Long, B. C. Shen, K. Wang, and L. Zhang
University of California at Riverside, Riverside, California 92521, USA
D. del Re, H. K. Hadavand, E. J. Hill, 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, and J. D. Richman
University of California at Santa Barbara, Santa Barbara, California 93106, USA
PHYSICAL REVIEW D
73,
052003 (2006)
1550-7998
=
2006
=
73(5)
=
052003(26)$23.00
052003-1
©
2006 The American Physical Society
T. W. Beck, A. M. Eisner, C. J. Flacco, C. A. Heusch, J. Kroseberg, W. S. Lockman, G. Nesom, T. Schalk, B. A. Schumm,
A. Seiden, P. Spradlin, D. C. Williams, and M. G. Wilson
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
J. Albert, E. Chen, G. P. Dubois-Felsmann, A. Dvoretskii, D. G. Hitlin, I. Narsky, T. Piatenko, F. C. Porter,
A. Ryd, and A. Samuel
California Institute of Technology, Pasadena, California 91125, USA
R. Andreassen, G. Mancinelli, B. T. Meadows, 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, U. Nauenberg, A. Olivas, W. O. Ruddick,
J. G. Smith, K. A. Ulmer, S. R. Wagner, and J. Zhang
University of Colorado, Boulder, Colorado 80309, USA
A. Chen, E. A. Eckhart, 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, and B. Spaan
Universita
̈
t Dortmund, Institut fu
̈
r Physik, D-44221 Dortmund, Germany
T. Brandt, M. Dickopp, V. Klose, H. M. Lacker, R. Nogowski, S. Otto, A. Petzold, J. Schubert, K. R. Schubert, R. Schwierz,
J. E. Sundermann, and A. Volk
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
D. Bernard, G. R. Bonneaud, P. Grenier,
†
E. Latour, S. Schrenk, Ch. Thiebaux, G. Vasileiadis, and M. Verderi
Ecole Polytechnique, LLR, F-91128 Palaiseau, France
D. J. Bard, P. J. Clark, W. Gradl, F. Muheim, S. Playfer, and Y. Xie
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
M. Andreotti, D. Bettoni, C. Bozzi, R. Calabrese, G. Cibinetto, E. Luppi, M. Negrini, and L. Piemontese
Universita
`
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, and A. Zallo
Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy
A. Buzzo, R. Capra, R. Contri, M. Lo Vetere, M. M. Macri, M. R. Monge, S. Passaggio, C. Patrignani, E. Robutti,
A. Santroni, and S. Tosi
Universita
`
di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy
G. Brandenburg, K. S. Chaisanguanthum, M. Morii, and J. Wu
Harvard University, Cambridge, Massachusetts 02138, USA
R. S. Dubitzky, J. Marks, S. Schenk, and U. Uwer
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
W. Bhimji, D. A. Bowerman, P. D. Dauncey, U. Egede, R. L. Flack, J. R. Gaillard, J . A. Nash,
M. B. Nikolich, and W. Panduro Vazquez
Imperial College London, London, SW7 2AZ, United Kingdom
X. Chai, M. J. Charles, W. F. Mader, U. Mallik, 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
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
052003 (2006)
052003-2
G. Schott
Universita
̈
t Karlsruhe, Institut fu
̈
r Experimentelle Kernphysik, D-76021 Karlsruhe, Germany
N. Arnaud, M. Davier, G. Grosdidier, A. Ho
̈
cker, F. Le Diberder, V. Lepeltier, A. M. Lutz, A. Oyanguren, T. C. Petersen,
S. Pruvot, S. Rodier, P. Roudeau, M. H. Schune, A. Stocchi, W. F. Wang, and G. Wormser
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, F-91898 Orsay, France
C. H. Cheng, D. J. Lange, and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
A. J. Bevan, C. A. Chavez, I. J. Forster, J. R. Fry, E. Gabathuler, R. Gamet, K. A. George, D. E. Hutchcroft, D. J. Payne,
K. C. Schofield, and C. Touramanis
University of Liverpool, Liverpool L69 7ZE, United Kingdom
F. Di Lodovico, W. Menges, and R. Sacco
Queen Mary, University of London, E1 4NS, United Kingdom
C. L. Brown, G. Cowan, H. U. Flaecher, M. G. Green, D. A. Hopkins, P. S. Jackson, T. R. McMahon,
S. Ricciardi, and F. Salvatore
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, M. P. Kelly, G. D. Lafferty, M. T. Naisbit,
J. C. Williams, and J. I. Yi
University of Manchester, Manchester M13 9PL, United Kingdom
C. Chen, W. D. Hulsbergen, A. Jawahery, D. Kovalskyi, C. K. Lae, D. A. Roberts, and G. Simi
University of Maryland, College Park, Maryland 20742, USA
G. Blaylock, C. Dallapiccola, S. S. Hertzbach, R. Kofler, X. Li, T. B. Moore, S. Saremi, H. Staengle, and S. Y. Willocq
University of Massachusetts, Amherst, Massachusetts 01003, USA
R. Cowan, K. Koeneke, 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
H. Kim, P. M. Patel, C. T. Potter, and S. H. Robertson
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
A. Lazzaro, V. Lombardo, and F. Palombo
Universita
`
di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy
J. M. Bauer, L. Cremaldi, V. Eschenburg, R. Godang, R. Kroeger, J. Reidy, D. A. Sanders, D. J. Summers, and H. W. Zhao
University of Mississippi, University, Mississippi 38677, USA
S. Brunet, D. Co
ˆ
te
́
, P. Taras, and F. B. Viaud
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
H. Nicholson
Mount Holyoke College, South Hadley, Massachusetts 01075, USA
N. Cavallo,
x
G. De Nardo, F. Fabozzi,
x
C. Gatto, L. Lista, D. Monorchio, P. Paolucci, D. Piccolo, and C. Sciacca
Universita
`
di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy
M. Baak, H. Bulten, G. Raven, and H. L. Snoek
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
THE
e
e
!
3
,
2
0
AND
K
K
2
...
PHYSICAL REVIEW D
73,
052003 (2006)
052003-3
C. P. Jessop and J. M. LoSecco
University of Notre Dame, Notre Dame, Indiana 46556, USA
T. Allmendinger, G. Benelli, K. K. Gan, K. Honscheid, D. Hufnagel, P. D. Jackson, H. Kagan, R. Kass, T. Pulliam,
A. M. Rahimi, R. Ter-Antonyan, and Q. K. Wong
Ohio State University, Columbus, Ohio 43210, USA
N. L. Blount, J. Brau, R. Frey, O. Igonkina, M. Lu, R. Rahmat, N. B. Sinev, D. Strom, J. Strube, and E. Torrence
University of Oregon, Eugene, Oregon 97403, USA
F. Galeazzi, M. Margoni, M. Morandin, A. Pompili, M. Posocco, M. Rotondo, F. Simonetto, R. Stroili, and C. Voci
Universita
`
di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy
M. Benayoun, J. Chauveau, P. David, L. Del Buono, Ch. de la Vaissie
`
re, O. Hamon, B. L. Hartfiel, M. J. J. John,
Ph. Leruste, J. Malcle
`
s, J. Ocariz, L. Roos, and G. Therin
Universite
́
s Paris VI et VII, Laboratoire de Physique Nucle
́
aire et de Hautes Energies, F-75252 Paris, France
P. K. Behera, L. Gladney, and J. Panetta
University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
M. Biasini, R. Covarelli, and M. Pioppi
Universita
`
di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy
C. Angelini, G. Batignani, S. Bettarini, F. Bucci, G. Calderini, M. Carpinelli, R. Cenci, F. Forti, M. A. Giorgi, A. Lusiani,
G. Marchiori, M. A. Mazur, M. Morganti, N. Neri, E. Paoloni, M. Rama, G. Rizzo, and J. Walsh
Universita
`
di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy
M. Haire, D. Judd, and D. E. Wagoner
Prairie View A&M University, Prairie View, Texas 77446, USA
J. Biesiada, N. Danielson, P. Elmer, Y. P. Lau, C. Lu, J. Olsen, A. J. S. Smith, and A. V. Telnov
Princeton University, Princeton, New Jersey 08544, USA
F. Bellini, G. Cavoto, A. D’Orazio, E. Di Marco, R. Faccini, F. Ferrarotto, F. Ferroni, M. Gaspero, L. Li Gioi,
M. A. Mazzoni, S. Morganti, G. Piredda, F. Polci, F. Safai Tehrani, and C. Voena
Universita
`
di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy
H. Schro
̈
der and R. Waldi
Universita
̈
t Rostock, D-18051 Rostock, Germany
T. Adye, N. De Groot, B. Franek, E. O. Olaiya, and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
S. Emery, A. Gaidot, S. F. Ganzhur, G. Hamel de Monchenault, W. Kozanecki, M. Legendre, B. Mayer, G. Vasseur,
Ch. Ye
`
che, and M. Zito
DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France
W. Park, M. V. Purohit, A. W. Weidemann, and J. R. Wilson
University of South Carolina, Columbia, South Carolina 29208, USA
M. T. Allen, D. Aston, R. Bartoldus, N. Berger, A. M. Boyarski, R. Claus, J. P. Coleman, M. R. Convery, M. Cristinziani,
J. C. Dingfelder, D. Dong, J. Dorfan, D. Dujmic, W. Dunwoodie, R. C. Field, T. Glanzman, S. J. Gowdy, V. Halyo, C. Hast,
T. Hryn’ova, W. R. Innes, M. H. Kelsey, P. Kim, M. L. Kocian, D. W. G. S. Leith, J. Libby, S. Luitz, V. Luth, H. L. Lynch,
D. B. MacFarlane, H. Marsiske, R. Messner, D. R. Muller, C. P. O’Grady, V. E. Ozcan, A. Perazzo, M. Perl, B. N. Ratcliff,
A. Roodman, A. A. Salnikov, R. H. Schindler, J. Schwiening, A. Snyder, J. Stelzer, D. Su, M. K. Sullivan, K. Suzuki,
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
052003 (2006)
052003-4
S. K. Swain, J. M. Thompson, J. Va’vra, N. van Bakel, M. Weaver, A. J. R. Weinstein, 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, C. Roat, 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. Satpathy, and R. F. Schwitters
University of Texas at Austin, Austin, Texas 78712, USA
J. M. Izen, I. Kitayama, X. C. Lou, and S. Ye
University of Texas at Dallas, Richardson, Texas 75083, USA
F. Bianchi, M. Bona, F. Gallo, and D. Gamba
Universita
`
di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy
M. Bomben, L. Bosisio, C. Cartaro, F. Cossutti, G. Della Ricca, S. Dittongo, S. Grancagnolo, L. Lanceri, and L. Vitale
Universita
`
di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy
V. Azzolini and F. Martinez-Vidal
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
R. S. Panvini
k
Vanderbilt University, Nashville, Tennessee 37235, USA
Sw. Banerjee, B. Bhuyan, C. M. Brown, D. Fortin, 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, and G. B. Mohanty
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
H. R. Band, X. Chen, B. Cheng, S. Dasu, M. Datta, A. M. Eichenbaum, K. T. Flood, M. T. Graham, J. J. Hollar,
J. R. Johnson, P. E. Kutter, H. Li, R. Liu, B. Mellado, A. Mihalyi, A. K. Mohapatra, Y. Pan, M. Pierini, R. Prepost, P. Tan,
S. L. Wu, and Z. Yu
University of Wisconsin, Madison, Wisconsin 53706, USA
H. Neal
Yale University, New Haven, Connecticut 06511, USA
(Received 3 February 2006; published 7 March 2006)
We study the processes
e
e
!
3
,
2
0
and
K
K
2
, with the photon
radiated from the initial state. About 20 000, 33 000 and 4000 fully reconstructed events, respectively,
have been 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 these data can be compared with the corresponding
direct
e
e
measurements. From the
3
,
2
0
and
K
K
2
mass spectra, the cross
sections for the processes
e
e
!
3
,
e
e
!
2
0
and
e
e
!
K
K
2
are
measured for center-of-mass energies from production threshold to 4.5 GeV. The uncertainty in the cross
section measurement is typically 6% –15%. We observe a structure at 1.9 GeV in both cross sections and a
resonance structure with mass
1645
0
:
008 GeV
=
c
2
and width
0
:
114
0
:
014 GeV
when the
!
782
final state is extracted. We observe the
J=
in all these final states and measure the corresponding
branching fractions.
DOI:
10.1103/PhysRevD.73.052003
PACS numbers: 13.66.Bc, 13.25.Gv, 13.25.Jx, 14.40.Cs
THE
e
e
!
3
,
2
0
AND
K
K
2
...
PHYSICAL REVIEW D
73,
052003 (2006)
052003-5
I. INTRODUCTION
The idea of utilizing initial-state radiation (ISR) from a
high-mass state to explore electron-positron processes at
all energies below that state was outlined in Ref. [1]. The
possibility of exploiting such processes in high luminosity
- and
B
factories was discussed in Refs. [2 – 4] and
motivates the hadronic cross section measurement de-
scribed in this paper. This is of particular interest because
of the small deviation of the measured muon
g
2
value
from that predicted by the standard model [5], where
hadronic loop contributions are obtained from
e
e
ex-
periments at low center-of-mass (c.m.) energies. The study
of ISR events at
B
factories provides independent and
contiguous measurements of hadronic cross sections in
this energy region and also contributes to the investigation
of low-mass resonance spectroscopy.
The ISR cross section for a particular hadronic final state
f
is related to the corresponding
e
e
cross section
f
s
by
d
f
s;x
dx
W
s;x
f
s
1
x
;
(1)
where
x
2
E
=
s
p
;
E
is the energy of the ISR photon in
the nominal
e
e
c
:
m
:
frame;
s
p
E
c
:
m
:
is the nominal
e
e
c
:
m
:
energy; and
s
1
x
p
is the effective c.m.
energy at which the final state
f
is produced. The invariant
mass of the hadronic final state is used to measure the
effective
e
e
c
:
m
:
energy. The function
W
s;x
is calcu-
lated with better than 1% accuracy (see, for example,
Ref. [4]) and describes the probability density function
for ISR photon emission. ISR photons are produced at all
angles, with a distribution peaking at small angles with
respect to the axis of the beams, and are required to be
detected in the electromagnetic calorimeter (EMC) of the
BABAR
detector. The acceptance for such photons is 10% –
15% [4] depending on applied selections.
An important advantage of ISR data is that the entire
range of effective c.m. energies is scanned in one experi-
ment. This avoids the relative normalization uncertainties
that inevitably arise when data from different experiments,
or from different machine settings, are combined.
A disadvantage of the ISR measurement is that the mass
resolution is much poorer than can be obtained in direct
annihilation. The resolution and absolute energy scale can
be monitored directly using the measured width and mass
of the
J=
resonance produced in the reaction
e
e
!
J=
. Using a kinematic fit to this reaction, we find the
resolution to be about
9 MeV
=
c
2
for decays of
J=
in the
3
mode and about
15 MeV
=
c
2
in the
2
0
mode as will be shown later.
Studies of
e
e
!
and several multihadron
ISR processes using
BABAR
data have been reported pre-
viously [6 –8]. These demonstrated good detector effi-
ciency and particle identification capability for events of
this kind.
This
paper
reports
analyses
of
the
3
,
2
0
and
K
K
2
final states produced in
conjunction with a hard photon, assumed to result from
ISR. A clear
J=
signal is observed for each of these
hadronic final states and the corresponding
J=
branching
fractions are measured. While
BABAR
data are available at
effective c.m. energies up to 10.58 GeV, the present analy-
sis is restricted to energies below 4.5 GeV because of the
increase with energy of the backgrounds from non-ISR
multihadron production.
II. THE
BABAR
DETECTOR AND DATA SET
The data used in this analysis were collected with the
BABAR
detector at the PEP-II asymmetric
e
e
storage
ring. The total integrated luminosity used is
232 fb
1
,
which includes data collected at the
4
S
resonance
mass (
211 fb
1
), and at a c.m. energy 40 MeV lower
(
21 fb
1
).
The
BABAR
detector is described elsewhere [9].
Charged particles are reconstructed in the
BABAR
tracking
system, which comprises the silicon vertex tracker (SVT)
and the drift chamber (DCH). Separation of pions and
kaons is accomplished by means of the detector of inter-
nally reflected Cherenkov light (DIRC) and energy-loss
measurements in the SVT and DCH. The hard ISR photon
and photons from
0
decays are detected in the electro-
magnetic calorimeter (EMC). Muon identification is pro-
vided by the instrumented flux return (IFR).
The initial selection of candidate events requires that a
high-energy photon in the event with
E
c
:
m
:
>
3 GeV
be
found recoiling against six good-quality charged tracks
with zero net charge or against four good-quality charged
tracks with zero net charge and four or more photons with
energy higher than 0.02 GeV. Almost every candidate event
has extra soft photons with energy above this threshold,
mostly due to secondary hadron interactions and machine
background. Each charged track is required to originate
close to the interaction region, to have transverse momen-
tum greater than
0
:
1 GeV
=
c
and to have a polar angle in the
laboratory frame with respect to the collision axis in the
range from 0.4 to 2.45 rad. These selections guarantee the
quality of the charged tracks in the DCH. The charged-
track vertex is used as the point of origin to calculate the
angles for all detected photons. Events with electrons and
positrons are removed on the basis of associated EMC
*
Also with the Johns Hopkins University, Baltimore, MD
21218, USA.
k
Deceased.
x
Also with Universita
`
della Basilicata, Potenza, Italy.
‡
Also with Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
†
Also at Laboratoire de Physique Corpusculaire, Clermont-
Ferrand, France.
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
052003 (2006)
052003-6
energy deposition and energy-loss (
d
E=
d
x
) information
from the DCH.
In order to study the detector acceptance and efficiency,
we developed a set of simulation programs for radiative
processes. The simulation of the
3
and
2
0
final states is based on the generator devel-
oped according to the approach suggested by Ku
̈
hn and
Czyz
̇
[10]. For the acceptance study we simulate six-
charged pions in a phase space model and in a model
which assumes only one
770
per event, i.e. a
770
2
final state. The
2
0
and
K
K
2
final states are simulated according to
phase space.
Multiple soft-photon emission from the initial-state
charged particles is implemented with the structure-
function technique [11,12], while extra photon radiation
from the final-state particles is simulated by means of the
PHOTOS
package [13]. The accuracy of the radiative cor-
rections is about 1%.
A sample of about 400 000 events was generated with
these tools for each mode and passed through the detector
response simulation [14]. These events were then recon-
structed through the same software chain as the experi-
mental data. Variations in detector and background
conditions were taken into account.
For purposes of background estimation, a large sample
of events from the main ISR processes (
2
;
3
;
...
;
5
;
2
K;
...
) was simulated. This sample exceeded
the expected number of events in the data set by a factor
of about three. In addition, the expected numbers of
e
e
!
q
q
(
q
u;d;s;c
) events were generated via
JETSET
[15] and
e
e
!
via
KORALB
[16] in order
to estimate background contributions from non-ISR events.
The cross sections for the above processes are known with
about 10% accuracy or better, which is sufficient for the
background contribution study.
III. THE KINEMATIC FIT PROCEDURE
The initial sample of candidate events is subjected to a
constrained kinematic fit in conjunction with charged-
particle identification to extract events corresponding to
the final states of interest.
For each particular six-charged-particle candidate, and
for each possible combination of particle types [i.e.
3
or
K
K
2
], a one-constraint (1C) kine-
matic fit is performed without using information from the
detected photon candidate. The only constraint used is zero
photon mass. Because of the excellent resolution of the
DCH, the three-momentum vector of the photon is better
determined through momentum conservation than through
measurement in the EMC. As a consequence, the calibra-
tion accuracy of the EMC and its alignment with respect to
the DCH do not contribute to the systematic uncertainties.
The initial
e
e
and final-state charged-particle four-
momenta and their covariance matrices are taken into
account.
The fit for the six-pion final-state hypothesis is retained
for every event. If only one track is identified as a kaon, or
if two oppositely charged kaons are identified, the
K
K
2
fit is also retained.
For the
2
0
events a kinematic fit is performed
using the initial
e
e
, final-state charged-particle and
photon four-momenta and their covariance matrices. The
highest c.m. energy photon is assumed to be from ISR.
Only the direction of the photon momentum vector is used
in the fit, not the measured energy. All other photons with
energies above 20 MeV are paired. Combinations lying
within
35 MeV
=
c
2
of the
0
mass are tested, and the
event combination with the best
2
value is retained,
subject to the additional constraint that the two, two-
photon pairs are consistent with the
0
mass. In total five
constraints (5C fit) are applied. The three-momentum vec-
tors obtained from the fit for each charged track and photon
are used in further calculations.
IV. THE
3
FINAL STATE
A. Additional selection criteria
The results of the 1C fit to the six-charged-track candi-
dates are used to make the final selection of the six-pion
sample. The momentum vector of the photon reconstructed
by the fit in the laboratory frame is required to have a polar
angle
fit
in the range from 0.35 to 2.4 rad and to match the
measured polar angle
meas
of the ISR photon in the EMC
within 50 mrad. The corresponding azimuthal angles,
fit
and
meas
, are also required to agree within this same
tolerance. These angular criteria reduce the background
by a factor of about two with no noticeable loss of signal.
Finally, the polar angle
fit
ch
of each charged track obtained
from the fit has to satisfy
0
:
45
<
fit
ch
<
2
:
4 rad
in order to
fall within the acceptance of the DIRC, which provides
about 80% of the kaon identification efficiency.
The 1C-fit
2
distribution for the six-pion candidates is
shown as the upper histogram of Fig. 1, while the shaded
region is for the corresponding MC-simulated pure
6
events. The experimental distribution has a contribution
from background processes, but the pure
6
MC-
simulated distribution is also much broader than the usual
one-constraint
2
distribution. This is due to multiple soft-
photon emission (detected or not detected) in the initial
state and radiation from the final-state charged particles,
neither of which is taken into account by the constrained fit
but which exist both in the data and the MC simulation.
The MC-simulated
2
distribution of Fig. 1 is normalized
to the data in the region
2
<
1
where the background
contamination and multiple soft-photon emission due to
ISR or FSR is lowest.
The cross-hatched histogram in Fig. 1 represents the
non-ISR background contribution obtained from the
THE
e
e
!
3
,
2
0
AND
K
K
2
...
PHYSICAL REVIEW D
73,
052003 (2006)
052003-7
JETSET
simulation of quark-antiquark production and ha-
dronization and does not exceed 8%.
We require
2
6
<
20
for the six-pion hypothesis, and
that any accompanying fit to the
2
K
4
hypothesis has
2
2
K
4
>
20
. The subscripts ‘‘
6
’’ and ‘‘
2
K
4
’’ here and
below refer to the
3
and
K
K
2
final
states exclusively. We estimate that these requirements
reduce the misidentification of
2
K
4
events from 11% to
about 2%, at the cost of the loss of about 5% of the signal
6
events.
The region
20
<
2
6
<
40
is chosen as a control region
for the estimation of background from other ISR and non-
ISR multihadron reactions. The procedure followed is
described in the next section.
The signal region of Fig. 1 contains 19 683 data and
19 980 MC events, while for the control region the corre-
sponding numbers are 2021 and 875, respectively.
B. Background estimation
The non-ISR background contribution to the signal re-
gion is obtained from the
JETSET
MC simulation, normal-
ized using the integrated
e
e
luminosity. The
2
distribution for non-ISR events is shown by the cross-
hatched histogram of Fig. 1. The non-ISR background
dominates by
e
e
!
6 hadrons
0
production with a
photon from
0
mistakenly taken as an ISR photon.
MC simulation of the
final state and ISR produc-
tion of multihadron final states other than
3
show
that such states yield a background in the selected six-pion
sample that exhibits a relatively flat contribution to the
2
6
distribution. To validate these estimates of backgrounds
with the data, we subtract the MC-simulated signal distri-
bution (the shaded histogram of Fig. 1) from the unshaded
one, after the non-ISR background is subtracted. The shape
of the resulting histogram is well described by MC simu-
lation of remaining background processes. Its absolute
normalization is used to estimate the level of those back-
grounds in the signal region.
The background contribution to any distribution other
than
2
is estimated as the difference between the distri-
butions in the relevant quantity for data and MC events
from the control region of Fig. 1, normalized to the differ-
ence between the number of data and MC events in the
signal region. The non-ISR background is subtracted
separately.
For example, Fig. 2 shows the six-pion invariant-mass
distribution up to
4
:
5 GeV
=
c
2
for the signal region of
Fig. 1. The points with error bars show the ISR background
contribution obtained in the manner described from the
control region of Fig. 1. The cross-hatched histogram in
Fig. 2 represents the non-ISR background contribution
obtained from the
JETSET
MC simulation.
Both backgrounds are relatively small at low mass
(about 6% –8%), but the non-ISR background accounts
for about 20% – 25% of the observed data at approximately
4 GeV
=
c
2
.
Accounting for uncertainties in cross sections for back-
ground processes, uncertainties in normalization of events
in the control region and statistical fluctuations in the
number of simulated events, we estimate that this proce-
dure for background subtraction results in a systematic
1
10
10
2
0.5
1
1.5
2
2.5
3
3.5
4
4.5
m(3(
π
+
π
-
)) (GeV/c
2
)
Events/0.025 GeV/c
2
FIG. 2.
The six-pion invariant-mass distribution (unshaded
histogram) for the signal region of Fig. 1. The points indicate
the background estimated from the difference between data and
MC events for the control region of Fig. 1, normalized to the
difference between data and MC events in the signal region of
Fig. 1. The cross-hatched histogram corresponds to the non-ISR
background of Fig. 1.
10
10
2
10
3
10
4
0 1020304050607080
χ
2
(6
π
)
Events/unit
χ
2
FIG. 1. The one-constraint
2
distributions for data (unshaded
histogram) and MC
3
simulation (shaded histogram)
for six-charged-track events fitted to the six-pion hypothesis. The
cross-hatched histogram is the estimated background contribu-
tion from non-ISR events obtained from
JETSET
. The signal and
control regions are indicated.
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
052003 (2006)
052003-8
uncertainty of less than 3% in the number of signal events
in the
1
:
6
–
3 GeV
=
c
2
region of six-pion mass, but that it
increases to 3% –5% in the region above
3 GeV
=
c
2
.
By selecting a ‘‘background-free’’
6
sample with
only six-charged tracks and only one photon (about 5%
of events) we can compare
2
distributions for data and
MC events up to
2
1000
. We estimate that for a
2
6
<
20
selection the net signal size should be increased by
3
2
%
to allow for a slight shape difference between the MC
and experimental
2
distributions.
C. Tracking efficiency
The procedure to measure the track-finding efficiency is
described in our previous paper [8] for the four-pion final
state. The method uses events that have three charged-
particle tracks and a hard photon. These events are sub-
jected to a one-constraint fit, which uses all measured
parameters of the three tracks and the photon and yields
the three-momentum vector of the missing charged pion in
the laboratory frame assuming this is the only undetected
track. If the
2
of the fit is less than 30 and this vector lies
within the acceptance of the DCH, the event is included in
the data sample. The ratio of three- to four-charged-track
events gives the track-finding efficiency. The same proce-
dure is applied to MC-simulated events. The track-finding
efficiency is better for MC-simulated events by
0
:
8
0
:
5
%
per track independent from momentum [8].
Assuming no increase in correlations due to higher multi-
plicity, we apply an overall correction of
5
3
%
to the
observed six-pion event sample based on the previous
study.
D. Detection efficiency from simulation
The selection procedures applied to the data are also
applied to the MC-simulated event sample. The resulting
six-pion invariant-mass distribution is shown in Fig. 3(a)
for the signal and control (shaded histogram) regions. The
mass dependence of the detection efficiency is obtained by
dividing the number of reconstructed MC events in each
25 MeV
=
c
2
mass interval by the number generated in this
same interval. Note that the detection efficiency computed
that way is insensitive to the actual shape of the mass
distribution of Fig. 3(a) used in MC simulation. The result
is shown in Fig. 3(b); the curve is obtained from a 3rd-
order polynomial fit to the distribution. The efficiency falls
off gradually with increasing mass from about 20% at
1
:
6 GeV
=
c
2
to about 14% at
4
:
5 GeV
=
c
2
. This efficiency
estimate takes into account the geometrical acceptance of
the detector for the final-state photon and the charged
pions, the inefficiency of the several detector subsystems,
and event loss due to additional soft-photon emission from
the initial and final states.
As mentioned in Sec. II, the model used in the MC
simulation assumes that the six-pion final state results
predominantly from the
770
2
production pro-
cess. In general, this model describes well the distributions
in many of the kinematic variables characterizing the six-
pion final state. Some examples are shown in Figs. 4 and 5,
in which the points with error bars represent data while the
histograms are obtained from MC simulation. Figure 4(a)
shows the distribution in
min
, the minimum charged-pion-
pair opening angle for each event, while Figs. 4(b) and 4(c)
represent the distribution in polar angle,
ch
, and transverse
momentum,
p
T
, respectively, for all final-state pions. All
quantities are calculated in the laboratory frame. The over-
all agreement between MC simulation and data is very
good. Figure 5 compares the distributions in
cos
, where
1
10
10
2
0.5
1
1.5
2
2.5
3
3.5
4
4.5
m(3(
π
+
π
-
)) (GeV/c
2
)
Events/0.025 GeVc
2
0
0.1
0.2
0.3
0.4
0.5
0.5
1
1.5
2
2.5
3
3.5
4
4.5
m(3(
π
+
π
-
)) (GeV/c
2
)
Eff./0.025 GeVc
2
FIG. 3.
(a) The six-pion mass distributions from MC simula-
tion for the signal (unshaded) and control (shaded) regions of
Fig. 1. (b) The mass dependence of the net reconstruction and
selection efficiency obtained from simulation. The curve is a fit
described in the text.
FIG. 4.
(a) The distribution in the track-pair opening angle for
the minimum of the 15 values possible for each event; (b) the
distribution in polar angle; (c) the transverse momentum distri-
bution for all pions from all events. All quantities are in the
laboratory frame; the points are for data and the histograms are
obtained from MC simulation.
THE
e
e
!
3
,
2
0
AND
K
K
2
...
PHYSICAL REVIEW D
73,
052003 (2006)
052003-9
is the angle between a charged pion in the six-pion rest
frame, and the direction of the six-pion system in the
laboratory frame. Data and MC are in rather good
agreement.
In the six-pion rest frame, the angular acceptance is
rather uniform. A simulation without resonances using
only six-pion phase space does not produce discernible
deviations from the observed angular distributions, and
does not change the overall acceptance by more than 3%.
This value is taken as an estimate of the model-dependent
systematic uncertainty in the acceptance.
E. Cross section for
e
e
!
3
Data from the reaction
e
e
!
are used to
convert the invariant-mass distribution for an ISR-
produced hadronic final state to the energy dependence
of the corresponding
e
e
cross section. The invariant
mass of the muon pair
m
inv
defines an effective
e
e
c
:
m
:
collision energy,
E
c
:
m
:
. The differential lumi-
nosity,
d
L
, associated with the interval
dE
c
:
m
:
centered at
effective collision energy
E
c
:
m
:
is then obtained from
d
L
E
c
:
m
:
dN
E
c
:
m
:
1
FSR
E
c
:
m
:
1
vac
;
(2)
where
E
c
:
m
:
m
inv
;
dN
is the number of muon pairs in
the mass interval
dm
inv
dE
c
:
m
:
;
is the acceptance,
corrected for muon identification and soft-photon emis-
sion;
1
FSR
corrects for hard photon emission from
final-state muons;
E
c
:
m
:
is the
e
e
!
Born cross section at center-of-mass energy
E
c
:
m
:
; and
1
vac
is the corresponding vacuum polarization correction
[17]. The dependence of the differential luminosity on
E
c
:
m
:
is presented in our previous paper [8].
From a detailed study of the
e
e
!
detection
and identification efficiency described in Ref. [6] and
comparison of the observed invariant-mass spectrum with
theoretical calculations, we estimate the systematic uncer-
tainty associated with luminosity determination to be 3%.
The six-pion
e
e
cross section can then be calculated
from
3
E
c
:
m
:
dN
6
E
c
:
m
:
d
L
E
c
:
m
:
corr
6
MC
6
E
c
:
m
:
;
(3)
where
m
6
inv
E
c
:
m
:
with
m
6
inv
the invariant mass of the six-
charged-pion system;
dN
6
is the number of selected six-
charged-pion events after background subtraction in the
interval
dE
c
:
m
:
and
MC
6
E
c
:
m
:
is the corresponding detec-
tion efficiency obtained from the MC simulation. The
factor
corr
6
takes into account the difference between the
2
distributions for data and MC events, and the tracking-
efficiency discrepancies discussed in Sec. IV B and IV C
respectively.
The energy dependence of the cross section for the
reaction
e
e
!
3
after all corrections is shown
in Fig. 6. It shows a structure around 1.9 GeV and reaches a
0
0.5
1
1.5
2
1
1.5
2
2.5
3
3.5
4
4.5
E
c.m.
(GeV)
σ
(3(
π
+
π
-
)) (nb)
BABAR
Mark-11
DM2
FIG. 6 (color online).
The
e
e
c
:
m
:
energy dependence of
the
3
cross section measured with ISR data at
BABAR
compared with the direct
e
e
measurements by DM2 and
MARK-II. Only statistical errors are shown.
FIG. 5 (color online).
The angular distribution of the lowest-
momentum pion (left) and of the sum of the remaining five most
energetic pions (right) in the six-pion rest frame with respect to
the direction of the six-pion system in the laboratory frame for
the five regions of six-pion mass indicated in the right-hand
plots. The fourth slice is chosen to correspond to the
J=
region.
The points are data, and the histograms are MC simulation.
B. AUBERT
et al.
PHYSICAL REVIEW D
73,
052003 (2006)
052003-10
peak value of about 1.5 nb near 2.0 GeV, followed by a
monotonic decrease toward higher energies perturbed only
by a peak at the
J=
mass position. The cross section for
each 25 MeV interval is presented in Table I.
Since
d
L
has been corrected for vacuum polarization
and final-state soft-photon emission, the six-pion cross
section measured in this way includes effects due to vac-
uum polarization and final-state soft-photon emission. For
g
2
calculations, vacuum polarization contributions
should be excluded from this data.
We studied the resolution in six-pion mass with MC
simulation, finding that Gaussian fits of line shapes give
TABLE I.
Summary of the
e
e
!
3
cross section measurement. Errors are statistical only.
E
c
:
m
:
(GeV)
(nb)
E
c
:
m
:
(GeV)
(nb)
E
c
:
m
:
(GeV)
(nb)
E
c
:
m
:
(GeV)
(nb)
1.3125
0
:
01
0
:
01
2.1125
1
:
36
0
:
12
2.9125
0
:
55
0
:
08
3.7125
0
:
26
0
:
06
1.3375
0
:
01
0
:
01
2.1375
1
:
35
0
:
11
2.9375
0
:
51
0
:
08
3.7375
0
:
16
0
:
05
1.3625
0
:
01
0
:
01
2.1625
1
:
45
0
:
12
2.9625
0
:
60
0
:
08
3.7625
0
:
18
0
:
05
1.3875
0
:
01
0
:
01
2.1875
1
:
17
0
:
11
2.9875
0
:
68
0
:
08
3.7875
0
:
24
0
:
05
1.4125
0
:
00
0
:
02
2.2125
1
:
43
0
:
12
3.0125
0
:
70
0
:
07
3.8125
0
:
29
0
:
05
1.4375
0
:
02
0
:
01
2.2375
1
:
38
0
:
11
3.0375
0
:
45
0
:
07
3.8375
0
:
13
0
:
05
1.4625
0
:
01
0
:
02
2.2625
1
:
36
0
:
11
3.0625
0
:
54
0
:
07
3.8625
0
:
21
0
:
05
1.4875
0
:
03
0
:
02
2.2875
1
:
44
0
:
12
3.0875
1
:
87
0
:
10
3.8875
0
:
17
0
:
05
1.5125
0
:
05
0
:
03
2.3125
1
:
40
0
:
11
3.1125
1
:
58
0
:
10
3.9125
0
:
15
0
:
04
1.5375
0
:
10
0
:
03
2.3375
1
:
28
0
:
11
3.1375
0
:
52
0
:
07
3.9375
0
:
22
0
:
05
1.5625
0
:
12
0
:
03
2.3625
1
:
28
0
:
10
3.1625
0
:
51
0
:
07
3.9625
0
:
20
0
:
05
1.5875
0
:
17
0
:
05
2.3875
1
:
21
0
:
10
3.1875
0
:
55
0
:
06
3.9875
0
:
19
0
:
04
1.6125
0
:
19
0
:
05
2.4125
1
:
38
0
:
11
3.2125
0
:
51
0
:
07
4.0125
0
:
14
0
:
04
1.6375
0
:
24
0
:
06
2.4375
1
:
10
0
:
10
3.2375
0
:
55
0
:
07
4.0375
0
:
17
0
:
04
1.6625
0
:
35
0
:
06
2.4625
1
:
10
0
:
10
3.2625
0
:
38
0
:
06
4.0625
0
:
17
0
:
04
1.6875
0
:
62
0
:
07
2.4875
1
:
08
0
:
10
3.2875
0
:
40
0
:
06
4.0875
0
:
14
0
:
04
1.7125
0
:
72
0
:
09
2.5125
0
:
92
0
:
10
3.3125
0
:
53
0
:
06
4.1125
0
:
19
0
:
04
1.7375
0
:
98
0
:
09
2.5375
1
:
08
0
:
09
3.3375
0
:
33
0
:
06
4.1375
0
:
18
0
:
04
1.7625
0
:
96
0
:
11
2.5625
1
:
13
0
:
10
3.3625
0
:
30
0
:
06
4.1625
0
:
13
0
:
04
1.7875
1
:
31
0
:
11
2.5875
1
:
12
0
:
10
3.3875
0
:
37
0
:
06
4.1875
0
:
15
0
:
04
1.8125
1
:
33
0
:
11
2.6125
1
:
10
0
:
10
3.4125
0
:
35
0
:
06
4.2125
0
:
14
0
:
04
1.8375
1
:
44
0
:
12
2.6375
0
:
93
0
:
10
3.4375
0
:
31
0
:
06
4.2375
0
:
08
0
:
04
1.8625
1
:
35
0
:
12
2.6625
1
:
12
0
:
09
3.4625
0
:
34
0
:
06
4.2625
0
:
13
0
:
04
1.8875
1
:
09
0
:
11
2.6875
0
:
87
0
:
09
3.4875
0
:
39
0
:
05
4.2875
0
:
13
0
:
04
1.9125
1
:
08
0
:
10
2.7125
0
:
94
0
:
09
3.5125
0
:
32
0
:
05
4.3125
0
:
16
0
:
04
1.9375
0
:
91
0
:
10
2.7375
0
:
86
0
:
10
3.5375
0
:
28
0
:
05
4.3375
0
:
17
0
:
04
1.9625
1
:
14
0
:
10
2.7625
0
:
75
0
:
09
3.5625
0
:
28
0
:
06
4.3625
0
:
08
0
:
04
1.9875
1
:
01
0
:
10
2.7875
0
:
89
0
:
09
3.5875
0
:
22
0
:
06
4.3875
0
:
04
0
:
04
2.0125
1
:
19
0
:
11
2.8125
0
:
91
0
:
09
3.6125
0
:
30
0
:
05
4.4125
0
:
10
0
:
04
2.0375
1
:
54
0
:
11
2.8375
0
:
75
0
:
08
3.6375
0
:
35
0
:
05
4.4375
0
:
16
0
:
04
2.0625
1
:
49
0
:
11
2.8625
0
:
91
0
:
08
3.6625
0
:
25
0
:
05
4.4625
0
:
11
0
:
03
2.0875
1
:
48
0
:
11
2.8875
0
:
71
0
:
09
3.6875
0
:
41
0
:
05
4.4875
0
:
06
0
:
04
TABLE II.
Summary of systematic errors for the
e
e
!
3
cross section measurement.
Source
Correction applied
Systematic error
Luminosity from
3%
MC-data difference in
2
<
20
signal region
3%
2%
Background subtraction
3% for
m
6
<
3
:
0 GeV
=
c
2
5% for
m
6
>
3
:
0 GeV
=
c
2
MC-data difference in tracking efficiency
5%
3%
Radiative corrections accuracy
1%
Acceptance from MC (model-dependent)
3%
Total (assuming addition in quadrature and no correlations)
8%
6% for
m
6
<
3
:
0 GeV
=
c
2
8% for
m
6
>
3
:
0 GeV
=
c
2
THE
e
e
!
3
,
2
0
AND
K
K
2
...
PHYSICAL REVIEW D
73,
052003 (2006)
052003-11