of 17
Initial-state radiation measurement of the
e
þ
e

!

þ



þ


cross section
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
M. Martinelli,
3a,3b
D. A. Milanes,
3a
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
D. J. Asgeirsson,
7
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
A. Khan,
8
V. E. Blinov,
9
A. R. Buzykaev,
9
V. P. Druzhinin,
9
V. B. Golubev,
9
E. A. Kravchenko,
9
A. P. Onuchin,
9
S. I. Serednyakov,
9
Yu. I. Skovpen,
9
E. P. Solodov,
9
K. Yu. Todyshev,
9
A. N. Yushkov,
9
M. Bondioli,
10
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
D. P. Stoker,
10
H. Atmacan,
11
J. W. Gary,
11
F. Liu,
11
O. Long,
11
G. M. Vitug,
11
C. Campagnari,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
J. Kroseberg,
13
W. S. Lockman,
13
A. J. Martinez,
13
T. Schalk,
13
B. A. Schumm,
13
A. Seiden,
13
C. H. Cheng,
14
D. A. Doll,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
A. Y. Rakitin,
14
R. Andreassen,
15
M. S. Dubrovin,
15
Z. Huard,
15
B. T. Meadows,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
M. Nagel,
16
U. Nauenberg,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
*
W. H. Toki,
17
B. Spaan,
18
M. J. Kobel,
19
K. R. Schubert,
19
R. Schwierz,
19
D. Bernard,
20
M. Verderi,
20
P. J. Clark,
21
S. Playfer,
21
D. Bettoni,
22a
C. Bozzi,
22a
R. Calabrese,
22a,22b
G. Cibinetto,
22a,22b
E. Fioravanti,
22a,22b
I. Garzia,
22a,22b
E. Luppi,
22a,22b
M. Munerato,
22a,22b
M. Negrini,
22a,22b
L. Piemontese,
22a
V. Santoro,
22a,22b
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
23
M. Nicolaci,
23
P. Patteri,
23
I. M. Peruzzi,
23,
M. Piccolo,
23
M. Rama,
23
A. Zallo,
23
R. Contri,
24a,24b
E. Guido,
24a,24b
M. Lo Vetere,
24a,24b
M. R. Monge,
24a,24b
S. Passaggio,
24a
C. Patrignani,
24a,24b
E. Robutti,
24a
B. Bhuyan,
25
V. Prasad,
25
C. L. Lee,
26
M. Morii,
26
A. J. Edwards,
27
A. Adametz,
28
J. Marks,
28
U. Uwer,
28
F. U. Bernlochner,
29
M. Ebert,
29
H. M. Lacker,
29
T. Lueck,
29
P. D. Dauncey,
30
M. Tibbetts,
30
P. K. Behera,
31
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
W. T. Meyer,
32
S. Prell,
32
E. I. Rosenberg,
32
A. E. Rubin,
32
A. V. Gritsan,
33
Z. J. Guo,
33
N. Arnaud,
34
M. Davier,
34
G. Grosdidier,
34
F. Le Diberder,
34
A. M. Lutz,
34
B. Malaescu,
34
P. Roudeau,
34
M. H. Schune,
34
A. Stocchi,
34
G. Wormser,
34
D. J. Lange,
35
D. M. Wright,
35
I. Bingham,
36
C. A. Chavez,
36
J. P. Coleman,
36
J. R. Fry,
36
E. Gabathuler,
36
D. E. Hutchcroft,
36
D. J. Payne,
36
C. Touramanis,
36
A. J. Bevan,
37
F. Di Lodovico,
37
R. Sacco,
37
M. Sigamani,
37
G. Cowan,
38
D. N. Brown,
39
C. L. Davis,
39
A. G. Denig,
40
M. Fritsch,
40
W. Gradl,
40
A. Hafner,
40
E. Prencipe,
40
K. E. Alwyn,
41
D. Bailey,
41
R. J. Barlow,
41,
G. Jackson,
41
G. D. Lafferty,
41
E. Behn,
42
R. Cenci,
42
B. Hamilton,
42
A. Jawahery,
42
D. A. Roberts,
42
G. Simi,
42
C. Dallapiccola,
43
R. Cowan,
44
D. Dujmic,
44
G. Sciolla,
44
D. Lindemann,
45
P. M. Patel,
45
S. H. Robertson,
45
M. Schram,
45
P. Biassoni,
46a,46b
A. Lazzaro,
46a,46b
V. Lombardo,
46a
N. Neri,
46a,46b
F. Palombo,
46a,46b
S. Stracka,
46a,46b
L. Cremaldi,
47
R. Godang,
47,
§
R. Kroeger,
47
P. Sonnek,
47
D. J. Summers,
47
X. Nguyen,
48
P. Taras,
48
G. De Nardo,
49a,49b
D. Monorchio,
49a,49b
G. Onorato,
49a,49b
C. Sciacca,
49a,49b
G. Raven,
50
H. L. Snoek,
50
C. P. Jessop,
51
K. J. Knoepfel,
51
J. M. LoSecco,
51
W. F. Wang,
51
K. Honscheid,
52
R. Kass,
52
J. Brau,
53
R. Frey,
53
N. B. Sinev,
53
D. Strom,
53
E. Torrence,
53
E. Feltresi,
54a,54b
N. Gagliardi,
54a,54b
M. Margoni,
54a,54b
M. Morandin,
54a
M. Posocco,
54a
M. Rotondo,
54a
F. Simonetto,
54a,54b
R. Stroili,
54a,54b
S. Akar,
55
E. Ben-Haim,
55
M. Bomben,
55
G. R. Bonneaud,
55
H. Briand,
55
G. Calderini,
55
J. Chauveau,
55
O. Hamon,
55
Ph. Leruste,
55
G. Marchiori,
55
J. Ocariz,
55
S. Sitt,
55
M. Biasini,
56a,56b
E. Manoni,
56a,56b
S. Pacetti,
56a,56b
A. Rossi,
56a,56b
C. Angelini,
57a,57b
G. Batignani,
57a,57b
S. Bettarini,
57a,57b
M. Carpinelli,
57a,57b,
k
G. Casarosa,
57a,57b
A. Cervelli,
57a,57b
F. Forti,
57a,57b
M. A. Giorgi,
57a,57b
A. Lusiani,
57a,57c
B. Oberhof,
57a,57b
E. Paoloni,
57a,57b
A. Perez,
57a
G. Rizzo,
57a,57b
J. J. Walsh,
57a
D. Lopes Pegna,
58
C. Lu,
58
J. Olsen,
58
A. J. S. Smith,
58
A. V. Telnov,
58
F. Anulli,
59a
G. Cavoto,
59a
R. Faccini,
59a,59b
F. Ferrarotto,
59a
F. Ferroni,
59a,59b
M. Gaspero,
59a,59b
L. Li Gioi,
59a
M. A. Mazzoni,
59a
G. Piredda,
59a
C. Bu
̈
nger,
60
O. Gru
̈
nberg,
60
T. Hartmann,
60
T. Leddig,
60
H. Schro
̈
der,
60
R. Waldi,
60
T. Adye,
61
E. O. Olaiya,
61
F. F. Wilson,
61
S. Emery,
62
G. Hamel de Monchenault,
62
G. Vasseur,
62
Ch. Ye
`
che,
62
D. Aston,
63
D. J. Bard,
63
R. Bartoldus,
63
C. Cartaro,
63
M. R. Convery,
63
J. Dorfan,
63
G. P. Dubois-Felsmann,
63
W. Dunwoodie,
63
R. C. Field,
63
M. Franco Sevilla,
63
B. G. Fulsom,
63
A. M. Gabareen,
63
M. T. Graham,
63
P. Grenier,
63
C. Hast,
63
W. R. Innes,
63
M. H. Kelsey,
63
H. Kim,
63
P. Kim,
63
M. L. Kocian,
63
D. W. G. S. Leith,
63
P. Lewis,
63
S. Li,
63
B. Lindquist,
63
S. Luitz,
63
V. Luth,
63
H. L. Lynch,
63
D. B. MacFarlane,
63
D. R. Muller,
63
H. Neal,
63
S. Nelson,
63
I. Ofte,
63
M. Perl,
63
T. Pulliam,
63
B. N. Ratcliff,
63
A. Roodman,
63
A. A. Salnikov,
63
R. H. Schindler,
63
A. Snyder,
63
D. Su,
63
M. K. Sullivan,
63
J. Va’vra,
63
A. P. Wagner,
63
M. Weaver,
63
W. J. Wisniewski,
63
M. Wittgen,
63
D. H. Wright,
63
H. W. Wulsin,
63
A. K. Yarritu,
63
C. C. Young,
63
V. Ziegler,
63
W. Park,
64
M. V. Purohit,
64
R. M. White,
64
J. R. Wilson,
64
A. Randle-Conde,
65
S. J. Sekula,
65
M. Bellis,
66
J. F. Benitez,
66
P. R. Burchat,
66
T. S. Miyashita,
66
M. S. Alam,
67
J. A. Ernst,
67
R. Gorodeisky,
68
N. Guttman,
68
D. R. Peimer,
68
A. Soffer,
68
P. Lund,
69
S. M. Spanier,
69
R. Eckmann,
70
J. L. Ritchie,
70
A. M. Ruland,
70
C. J. Schilling,
70
R. F. Schwitters,
70
B. C. Wray,
70
J. M. Izen,
71
X. C. Lou,
71
F. Bianchi,
72a,72b
D. Gamba,
72a,72b
L. Lanceri,
73a,73b
L. Vitale,
73a,73b
F. Martinez-Vidal,
74
PHYSICAL REVIEW D
85,
112009 (2012)
1550-7998
=
2012
=
85(11)
=
112009(17)
112009-1
Ó
2012 American Physical Society
A. Oyanguren,
74
H. Ahmed,
75
J. Albert,
75
Sw. Banerjee,
75
H. H. F. Choi,
75
G. J. King,
75
R. Kowalewski,
75
M. J. Lewczuk,
75
I. M. Nugent,
75
J. M. Roney,
75
R. J. Sobie,
75
N. Tasneem,
75
T. J. Gershon,
76
P. F. Harrison,
76
T. E. Latham,
76
E. M. T. Puccio,
76
H. R. Band,
77
S. Dasu,
77
Y. Pan,
77
R. Prepost,
77
and S. L. Wu
77
(
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite
́
de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
10
University of California at Irvine, Irvine, California 92697, USA
11
University of California at Riverside, Riverside, California 92521, USA
12
University of California at Santa Barbara, Santa Barbara, California 93106, USA
13
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California 91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, USA
18
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
19
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
20
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
21
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
22a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy
22b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
23
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
24a
INFN Sezione di Genova, I-16146 Genova, Italy
24b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
25
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
26
Harvard University, Cambridge, Massachusetts 02138, USA
27
Harvey Mudd College, Claremont, California 91711, USA
28
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
29
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstr. 15, D-12489 Berlin, Germany
30
Imperial College London, London, SW7 2AZ, United Kingdom
31
University of Iowa, Iowa City, Iowa 52242, USA
32
Iowa State University, Ames, Iowa 50011-3160, USA
33
Johns Hopkins University, Baltimore, Maryland 21218, USA
34
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, IN2P3/CNRS et Universite
́
Paris-Sud 11,
Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, France
35
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
36
University of Liverpool, Liverpool L69 7ZE, United Kingdom
37
Queen Mary, University of London, London, E1 4NS, United Kingdom
38
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
39
University of Louisville, Louisville, Kentucky 40292, USA
40
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
41
University of Manchester, Manchester M13 9PL, United Kingdom
42
University of Maryland, College Park, Maryland 20742, USA
43
University of Massachusetts, Amherst, Massachusetts 01003, USA
44
Massachusetts Institute of Technology, Laboratory for Nuclear Science,
Cambridge, Massachusetts 02139, USA
45
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
46a
INFN Sezione di Milano, I-20133 Milano, Italy
46b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
J. P. LEES
et al.
PHYSICAL REVIEW D
85,
112009 (2012)
112009-2
47
University of Mississippi, University, Mississippi 38677, USA
48
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
49a
INFN Sezione di Napoli, I-80126 Napoli, Italy
49b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
50
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
51
University of Notre Dame, Notre Dame, Indiana 46556, USA
52
Ohio State University, Columbus, Ohio 43210, USA
53
University of Oregon, Eugene, Oregon 97403, USA
54a
INFN Sezione di Padova, I-35131 Padova, Italy
54b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
55
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
56a
INFN Sezione di Perugia, I-06100 Perugia, Italy
56b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
57a
INFN Sezione di Pisa, I-56127 Pisa, Italy
57b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
57c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
58
Princeton University, Princeton, New Jersey 08544, USA
59a
INFN Sezione di Roma, I-00185 Roma, Italy
59b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
60
Universita
̈
t Rostock, D-18051 Rostock, Germany
61
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
62
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
63
SLAC National Accelerator Laboratory, Stanford, California 94309, USA
64
University of South Carolina, Columbia, South Carolina 29208, USA
65
Southern Methodist University, Dallas, Texas 75275, USA
66
Stanford University, Stanford, California 94305-4060, USA
67
State University of New York, Albany, New York 12222, USA
68
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
69
University of Tennessee, Knoxville, Tennessee 37996, USA
70
University of Texas at Austin, Austin, Texas 78712, USA
71
University of Texas at Dallas, Richardson, Texas 75083, USA
72a
INFN Sezione di Torino, I-10125 Torino, Italy
72b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
73a
INFN Sezione di Trieste, I-34127 Trieste, Italy
73b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
74
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
75
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
76
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
77
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 10 February 2012; published 21 June 2012)
We study the process
e
þ
e

!

þ



þ



, with a photon emitted from the initial-state electron or
positron, using
454
:
3fb

1
of data collected with the
BABAR
detector at SLAC, corresponding to
approximately 260 000 signal events. We use these data to extract the nonradiative

ð
e
þ
e

!

þ



þ


Þ
cross section in the energy range from 0.6 to 4.5 GeV. The total uncertainty of the cross
section measurement in the peak region is less than 3%, higher in precision than the corresponding results
obtained from energy scan data.
DOI:
10.1103/PhysRevD.85.112009
PACS numbers: 13.66.Bc, 13.25.Gv, 13.40.Em, 13.66.Jn
*
Now at Temple University, Philadelphia, Pennsylvania 19122, USA.
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
Now at the University of Huddersfield, Huddersfield HD1 3DH, United Kingdom.
§
Now at University of South Alabama, Mobile, Alabama 36688, USA.
k
Also with Universita
`
di Sassari, Sassari, Italy.
INITIAL-STATE RADIATION MEASUREMENT OF THE
...
PHYSICAL REVIEW D
85,
112009 (2012)
112009-3
I. INTRODUCTION
While the electroweak contribution to the anomalous
magnetic moment of the muon
a

¼
1
2
ð
g


2
Þ
can be
calculated with sub-ppm precision, the hadronic contribu-
tion
a
had

cannot be evaluated by means of perturbative
techniques within quantum chromodynamics (QCD).
However, it is possible to relate
a
had

via a dispersion
relation to hadronic cross section

ð
e
þ
e

!
hadrons
Þ
data [
1
]. Thus, hadronic cross section measurements are
important for the standard model prediction of
a

, which
differs by more than three standard deviations from a
recent direct Brookhaven National Laboratory measure-
ment [
2
].
The study of initial-state radiation (ISR) events at an
e
þ
e

collider with a fixed center-of-mass (CM) energy
E
CM
allows high-precision measurements of the cross sec-
tion of exclusive hadronic channels for energies below the
nominal
E
CM
and is complementary to studies based on an
energy scan. Use of the ISR technique is discussed in
Refs. [
3
6
]. Previously, we used this technique to inves-
tigate low-multiplicity hadronic processes at effective CM
energies below 5 GeV [
7
15
].
The ISR cross section

f;
for a specific final-state
f
depends on the nonradiative cross section

f
and is given
by [
5
]
d
f;
ð
s;M
had
Þ
dM
had
¼
2
M
had
s

W
ð
s;x;C

Þ

f
ð
M
had
Þ
;
(1)
where
x
¼
2

E


=
ffiffiffi
s
p
,
ffiffiffi
s
p
is the nominal CM energy,
E


is
the energy of the ISR photon,
1
and
M
had
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s
ð
1

x
Þ
p
. The
radiator function
W
ð
s;x;C

Þ
, which describes the proba-
bility for the emission of an ISR photon in the polar angle
range
j
cos



j
<C

, is determined to next-to-leading order
(NLO) ISR with the PHOKHARA software package [
16
].


is the angle of the emitted

with respect to the direction
of the incoming
e

. Effects of final-state radiation (FSR),
which are neglected in Eq. (
1
), are studied and corrected
for as explained in Sec.
VI
.
Recently, cross section measurements with approxi-
mately 1% precision have been presented for the

þ


final state [
15
,
17
,
18
]. These measurements have led to a
significant reduction in the uncertainty of
a
had

[
19
]. As a
consequence, a large relative contribution to the uncer-
tainty of
a
had

now arises from the energy range
1 GeV
<
E<
2 GeV
[
20
]. In this energy range, the hadronic
cross section is dominated by the exclusive
e
þ
e

!

þ



þ


and

þ



0

0
channels.
This paper reports results from an ISR analysis of the
e
þ
e

!

þ



þ



process. The four-pion mass
M
4

serves as the effective hadronic
E
CM
value. It is
an update of our earlier study [
8
], based on a data sample
that is five times larger. We perform a more detailed
study of systematic effects and thereby obtain significant
improvements in both the statistical and systematic
uncertainties.
The outline of this paper is as follows. Section
II
describes the
BABAR
detector and the data set used in
this analysis. The primary event selection is presented in
Sec.
III
. After discussing the background suppression
(Sec.
IV
) and the acceptance and efficiency studies
(Sec.
V
), the extraction of the nonradiative cross section
is described in Sec.
VI
. A qualitative analysis of the
intermediate subsystems and a quantitative measurement
of the
J=
c
and
c
ð
2
S
Þ
branching fractions follows in
Sec.
VII
. A summary is given in Sec.
VIII
.
II. THE
BABAR
DETECTOR AND DATA SET
The data used in this analysis were collected with
the
BABAR
detector at the PEP-II asymmetric energy
e
þ
e

storage rings at the SLAC National Accelerator
Laboratory. A total integrated luminosity of
454
:
3fb

1
is
used, comprised of
413
:
1fb

1
collected at the

ð
4
S
Þ
resonance peak, and
41
:
2fb

1
collected 40 MeV below
the peak.
The
BABAR
detector is described in detail elsewhere
[
21
]. The reconstruction of charged-particle tracks is per-
formed with the tracking system, which is comprised of a
five-layer silicon vertex tracker and a 40-layer drift cham-
ber, both in a 1.5 T axial magnetic field. Separation of
electrons, protons, charged pions, and charged kaons is
achieved using Cherenkov angles measured with the de-
tector of internally reflected Cherenkov light in combina-
tion with specific ionization
dE=dx
measurements from
the silicon vertex tracker and drift chamber. The CsI(Tl)
electromagnetic calorimeter (EMC) measures the energy
of photons and electrons. Muon identification is provided
by the instrumented flux return.
A simulation package developed for radiative processes,
AFKQED, is used to determine detector acceptance and
reconstruction efficiencies. Hadronic final states, including

þ



þ



, are simulated based on an approach of
Czyz
̇
and Ku
̈
hn [
22
]. The underlying model assumes domi-
nance of the
a
1
ð
1260
Þ

final-state as was reported in
Refs. [
23
,
24
]. Because of the dominant decay
a
1
ð
1260
Þ!

0

, each event contains one pair of pions from

0
decay.
The simulation of multiple soft-photon emission from the
initial state is performed via a structure function technique
[
25
,
26
]. Extra radiation from the final state particles is
simulated by the PHOTOS package [
27
]. The accuracy
of the radiative corrections is about 1%. A new version
of PHOKHARA [
16
], which incorporates the results of
recent studies [
8
] on intermediate resonances, is used to
investigate the influence of these intermediate resonances
on the acceptance.
The simulated events are subjected to simulation of the
detector [
28
] and the same analysis procedures as the data.
1

refers to the nominal CM frame.
J. P. LEES
et al.
PHYSICAL REVIEW D
85,
112009 (2012)
112009-4
Variations in detector and background conditions over the
course of the experiment are modeled.
A large number of potential background processes are
simulated, including the ISR processes
K
þ
K


þ



and
K
0
S
K




. Other ISR background channels are also ex-
amined. Either the remaining number of events after the
event selection is negligible in comparison to other uncer-
tainties, or dedicated methods for background rejection are
implemented as described in Sec.
IV
. Non-ISR back-
grounds resulting from
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
,
c
) con-
tinuum events are modeled using the JETSET generator
[
29
], while those from
e
þ
e

!

þ


are modeled with
KORALB [
30
]. The cross sections of the ISR channels and
the branching fractions of the inclusive processes leading
to final states similar to our signal are known with about
10% accuracy or better, which is sufficient for the purpose
of this measurement. The contribution from

ð
4
S
Þ!

þ



þ



events is negligible.
III. PRIMARY EVENT SELECTION AND
KINEMATIC FIT
Charged tracks are selected by requiring that they origi-
nate from the collision region (transverse distance of clos-
est approach to the nominal interaction point
d
T
<
1
:
5cm
,
and in the beam direction
d
Z
<
2
:
5cm
), and that they have
a polar angle

ch
in the well-understood acceptance region
of the detector (
0
:
5 rad
<
ch
<
2
:
4 rad
). The coordinate
system has the
z
-axis in the direction of the incoming
e

beam. Tracks with transverse momenta less than
100 MeV
=c
or that are consistent with being an electron
are rejected. Photon candidates are required to have a
minimum energy
E
;
CM
>
50 MeV
. The ISR photon can-
didate is restricted to the polar angle range inside the well-
understood acceptance region of the EMC (
0
:
35 rad
<


<
2
:
4 rad
) and a minimum energy of
E
ISR
>
3 GeV
is
required.
Radiative Bhabha events are suppressed by requiring
the two most energetic tracks of the event not to be
identified as electrons. The minimum angle between a
charged track and the ISR photon

c
is required to satisfy

c
>
1
:
0 rad
, in order to select the back-to-back topol-
ogy between the charged tracks and photon typical for ISR
events.
A kinematic fit procedure with four constraints (4C) is
applied to events with four tracks satisfying these criteria.
The constrained fit uses the measured momenta and direc-
tions of the charged particles and the ISR photon and the
corresponding error matrix to solve the energy-momentum
equation. To provide accurate photon parameters to the
kinematic fit, a precise alignment and an energy calibration
of the EMC are performed using a

þ



sample. This
improves the data-simulation agreement in the goodness-
of-fit distributions (see below) of the kinematic fit. The

þ



sample is also used to identify and measure
differences between the data and the simulation (MC) in
the photon detection efficiency.
The kinematic fit is performed assuming the

þ



þ



signal hypothesis. If two tracks are identi-
fied as kaons the fit is also performed under the
K
þ
K


þ



hypothesis. The fitting routine returns a
goodness-of-fit quantity

2
4

and

2
2
K
2

, respectively,
which we use to select signal events and to suppress
K
þ
K


þ



background.
Figures
1(a)
and
1(b)
show the measured

2
4

distribu-
tion before background subtraction in comparison to the
distribution from the simulated signal sample. The results
are shown on logarithmic and linear scales. The distri-
butions are normalized to the number of events with

2
4

<
10
. Figure
1(c)
shows the

2
4

distribution for the
main backgrounds. The difference between measured and
simulated samples is shown in Fig.
1(d)
for

2
4

>
10
.For
large values of

2
4

, the difference is approximately flat,
and is consistent with the sum of backgrounds shown in
Fig.
1(c)
. At small

2
4

values, resolution effects cause the
difference to decrease. This is studied with a clean sample
of four pions and one photon where the resolution effect is
visible for

2
4

<
20
. To avoid a bias due to the resolution
difference between the data and simulation, the require-
ment

2
4

<
30
is used in the event analysis. In addition,
background channels are suppressed using dedicated
10
3
10
4
020406080100
0
5000
10000
15000
20000
25000
30000
020406080100
10
10
2
10
3
10
2
10
3
020406080100
1
10
020406080100
(a)
Data
Signal MC
χ
2
4
π
Events / unit
χ
2
(b)
Data
Signal MC
χ
2
4
π
Events / unit
χ
2
χ
2
4
π
(c)
K
s
0
K
πγ
uds
K
+
K
-
π
+
π
-
γ
ωπ
+
π
-
γ
χ
2
4
π
Events / unit
χ
2
χ
2
4
π
Events / unit
χ
2
(d)
FIG. 1 (color online). (a,b) The

2
4

distribution for data
without background subtraction (triangles) and signal MC (his-
togram) on a logarithmic and linear scale. (c) MC distributions
of the principal backgrounds. (d) The difference between the
measured and the simulated distributions from part (a,b). The
dashed and solid vertical lines indicate the boundaries with
the
0
<
2
4

<
10
region used for normalization and the

2
4

<
30
requirement, respectively.
INITIAL-STATE RADIATION MEASUREMENT OF THE
...
PHYSICAL REVIEW D
85,
112009 (2012)
112009-5
vetoes and particle identification (PID) selectors, as dis-
cussed in Sec.
IV
.
IV. BACKGROUND REJECTION
Because of large variations in the signal-to-background
ratio across different
4

mass
M
4

regions, different strat-
egies are implemented to eliminate background, depending
on the
M
4

region. Figure
2(a)
shows the
M
4

distribution
under the

þ



þ



hypothesis with the requirement

2
4

<
30
. The results are shown for the data and for
the sum of the simulated ISR channels
e
þ
e

!
K
þ
K


þ



,
e
þ
e

!
K
0
S
K




,
e
þ
e

!
!
þ



and the non-ISR continuum background. In Fig.
2(b)
, these
background contributions are shown individually. The

2
4

requirement effectively eliminates the
!
þ



back-
ground: according to simulation, only 450
!
þ



events remain after applying this restriction, in comparison
to 260 000 signal events with a very similar
M
4

distribu-
tion, leading to a relative contribution of less than

0
:
2%
.
At very low invariant masses,
M
4

<
1
:
1 GeV
=c
2
, the
background contributions from

þ



and

þ



0

are large and not included in Fig.
2
. In this threshold region,
the signal-to-background ratio is approximately
1:5
. In the
peak region,
1
:
1 GeV
=c
2
<M
4

<
2
:
2 GeV
=c
2
, the back-
ground contamination is at the level of 3–4%, dominated
by
e
þ
e

!
K
þ
K


þ



and
e
þ
e

!
K
0
S
K




.At
high
M
4

, the background level rises to about 10%, mainly
due to the additional contribution of
uds
-continuum
events.
A clear peak from
J=
c
!

þ



þ


is visible in the
distributions of Fig.
2
. In addition, the data exhibit a narrow
peak in the
c
ð
2
S
Þ
mass region, due to the decay
c
ð
2
S
Þ!

þ


J=
c
with
J=
c
!

þ


and misidentified muons.
The rejection of this background is described in
subsection
IV B
.
A. Background in the peak region
(
1
:
1 GeV
=c
2
<M
4

<
2
:
2 GeV
=c
2
)
The dominant background in the peak region is from the
ISR processes
e
þ
e

!
K
þ
K


þ



and
e
þ
e

!
K
0
S
K




. We utilize two different approaches to evalu-
ate the background and use the difference between the
methods to estimate the systematic uncertainty related to
the background subtraction. The background subtraction
itself is performed using method 2.
1. Method 1: Subtract simulated background
For background subtraction via method 1, we use recent
measurements of the most important background channels,
K
þ
K


þ



[
13
] and
K
0
S
K




[
14
]. We tune
AFKQED according to these measurements and use the
resulting predictions to evaluate the contributions of these
channels to the
M
4

spectrum.
2. Method 2: Background suppression
This method is a hybrid approach. We impose specific
requirements in order to suppress the
K
þ
K


þ



and
K
0
S
K




backgrounds: the so-called
K
þ
K


þ



and
K
0
S
K




vetoes. The remaining background is then
subtracted according to method 1.
K
0
S
K




events are vetoed if one of the tracks is
identified as a
K

. The identification algorithm has an
efficiency of 80–90% per track and a

misidentification
probability of 0.25%. In addition, we require the invariant
mass formed from two of the three remaining tracks to
lie within
35 MeV
=c
2
of the nominal
K
0
S
mass [
31
].
According to simulation, this method removes 74% of
the
K
0
S
K




background but only 1% of signal.
K
þ
K


þ



events are rejected if two oppositely-
charged tracks are identified as kaons and the requirement

2
2
K
2

<
10
is fulfilled. The
K

identification algorithm
has an identification efficiency of 85–95% per track and a

misidentification probability of 1%. This requirement
removes less than 0.1% of the signal, but 55% of the
K
þ
K


þ



background.
Comparing the results of the two methods yields
a systematic uncertainty of 1.0% on the
e
þ
e

!

þ



þ


cross section in the peak region.
B. Background at large invariant masses
(
M
4

>
2
:
2 GeV
=c
2
)
From Fig.
2(b)
it is seen that the
uds
continuum back-
ground is significant in the
M
4

>
2
:
2 GeV
=c
2
mass
region. The largest contribution is from
e
þ
e

!

þ



þ



0
events in which one of the photons from
the

0
!

decay is mistaken for the

ISR
. The similar
kinematic configuration of the
uds
-continuum events
causes a peak at small values of

2
4

. We estimate this
background by measuring the

0
yield from a fit to the

0
mass peak in the two-photon invariant mass distribution of
10
10
2
10
3
10
4
1234
0
100
200
300
400
500
600
700
1234
M
4
π
(GeV/c
2
)
Events / 25 MeV/c
2
(a)
Data
Background MC
M
4
π
(GeV/c
2
)
Events / 25 MeV/c
2
(b)
K
s
0
K
πγ
uds +
ωπ
+
π
-
γ
K
+
K
-
π
+
π
-
γ
FIG. 2 (color online). (a) The

þ



þ


invariant mass
distribution of

þ



þ



ISR events (triangles) for the
main selection and the sum of simulated
K
þ
K


þ



,
K
0
S
K




,
!
þ



and nonradiative
uds
-continuum
background (histogram). The large

þ



and

þ



0

background contribution in the threshold region (
M
4

<
1
:
1 GeV
=c
2
) is not included in the simulation. (b) The individual
simulated background channel contributions from top to bottom
as indicated in the legend.
J. P. LEES
et al.
PHYSICAL REVIEW D
85,
112009 (2012)
112009-6
the ISR photon candidate with any other photon candidate.
We then scale the MC

0
rate to give the same yield as
observed in the data. The corresponding scaling factor
is extracted with a relative uncertainty of about 22%.
The normalized
uds
-continuum MC sample is used for
background subtraction. The corresponding systematic
uncertainty on the cross section measurement is 0.5%
in the peak region and rises up to 1.5% for
M
4

>
2
:
8 GeV
=c
2
.
There is an additional peaking background contribution
in the charmonium region. Figure
3(a)
shows the invariant
mass distribution under the

þ



þ


hypothesis for
the data. Peaks corresponding to the
J=
c
and
c
ð
2
S
Þ
resonances are clearly seen. In Fig.
3(b)
, the invariant

þ


mass
M
2

distribution for events within the
c
ð
2
S
Þ
(
3
:
65 GeV
=c
2
<M
4

<
3
:
75 GeV
=c
2
) mass region
are plotted. The distribution contains four entries per event.
The
J=
c
peak is clearly visible. The
J=
c
!

þ


branching fraction is about a factor 400 smaller than that
of
J=
c
!

þ


[
31
]. No PID selector is used in the
sample selection. In addition, the kinematic fit does not
suppress

þ



þ


events, because the mass difference
between muons and pions is only
34 MeV
=c
2
, which is
negligible due to the fact that they are highly relativistic,
being emitted from the
J=
c
. Thus, the observed peak is
likely dominated by
c
ð
2
S
Þ!

þ



þ


decays. To
remove this background, we reject events that have
M
4

in the
c
ð
2
S
Þ
region and an
M
2

value consistent with the
J=
c
. The corresponding
M
4

distribution after the
c
ð
2
S
Þ
veto is shown in Fig.
3(c)
.
C. Background at small invariant masses
(
M
4

<
1
:
1 GeV
=c
2
)
Background in the threshold region, i.e., below
1
:
1 GeV
=c
2
, is dominated by two processes:

conversion
of a real photon in the detector material, and conversion of
a virtual photon at the primary interaction vertex (Dalitz
conversion). In
e
þ
e

!

þ



0

ISR
events, one of the
photons from the

0
decay can convert the detector mate-
rial into an
e
þ
e

pair, and both the
e
þ
and the
e

can be
misidentified as pions. Moreover,
e
þ
e

!

þ



ISR

events in which the non-ISR photon converts into an
e
þ
e

pair contribute a similar background. The second
source of background in this mass region is
e
þ
e

!

þ



ISR
e
þ
e

events in which the
e
þ
e

pair arises
from a Dalitz conversion process. Two methods are used
to remove these background channels.
1. Method 1: Vetoes for Dalitz conversion
and conversion in the detector
The first method vetoes events with either a primary
vertex probability less than
10

8
or with two identified
electrons. Electrons are identified using an algorithm with
an efficiency of 99% and a pion misidentification rate of
5–10% depending on the transverse momentum of the
track. The first requirement is not sufficient to reject back-
ground events with highly-energetic electrons or positrons,
which have a vertex probability similar to nonconversion
events. MC study shows that the combination of both
requirements yields a background rejection larger than
99% while removing less than 6% of signal.
2. Method 2: Pion identification
The second method requires all four tracks to be iden-
tified as pions, using a selector with an efficiency of
97–99% and an electron misidentification probability of
5–7% depending on the transverse momentum of the track.
There is, however, a difference in efficiency between the
data and MC simulation of approximately 0.5–1% per track
(2–4% shift per event). Therefore, this selector is not used
in the peak region, where the background contribution is
very low.
Both methods remove a large fraction of the conversions
and yield results that are consistent with each other. We
present our primary results using the pion selection
method, as the systematic uncertainties on its inputs are
better understood. Comparing the cross section results
using the two methods leads to a systematic uncertainty
estimate of 3%. It should be noted that the

ð
770
Þ
0
peak is
strongly suppressed, but is still visible as a shoulder after
background subtraction, as shown in Fig.
4
.
0
500
1000
1500
0.5
1
1.5
2
2.5
3
3.5
4
0
200
400
600
800
0.5
1
1.5
2
2.5
3
3.5
4
0
500
1000
1500
0.5
1
1.5
2
2.5
3
3.5
4
(a)
M
4
π
(GeV/c
2
)
Entries / 25 MeV/c
2
(b)
M
2
π
(GeV/c
2
)
Entries / 20 MeV/c
2
(c)
M
4
π
(GeV/c
2
)
Entries / 25 MeV/c
2
FIG. 3. (a) Invariant mass distribution under the

þ



þ


hypothesis for the data; (b)

þ


invariant mass distribution for
events with
M
4

in the
c
ð
2
S
Þ
mass region represented by the
vertical lines in (a) (4 entries per event); (c) Same as part (a) after
removing entries of the invariant

þ


-mass in the
J=
c
mass
region represented by the vertical lines in (b).
INITIAL-STATE RADIATION MEASUREMENT OF THE
...
PHYSICAL REVIEW D
85,
112009 (2012)
112009-7
D. Background subtraction summary
Figure
5(a)
shows the

2
4

distribution both for the data
after background subtraction and the signal simulation.
Compared to Fig.
1(a)
, the difference between the data
and the signal simulation is reduced. There is still some
remaining background at larger

2
4

values as can be seen
in Fig.
5(b)
. This is consistent with the uncertainties in the
background-subtraction methods as previously described.
To be conservative, we assume that the remaining back-
ground is uniform as a function of

2
4

. In this case, we find
that the associated uncertainty on the cross section is less
than 0.4% for
M
4

<
2
:
8 GeV
=c
2
and 4.0% for
2
:
8 GeV
=c
2
<M
4

<
4
:
5 GeV
=c
2
.
V. ACCEPTANCE AND EFFICIENCIES
The full chain of experimental requirements is applied to
the signal MC sample. We define the ratio of the number
of selected events divided by the number of events with-
out applying any requirements as the global efficiency.
Figure
6
shows the global efficiency as a function of
M
4

determined with the simulation. The decrease of efficiency
in the threshold region, which corresponds to the highest
energy ISR photons, is due to the fact that the four tracks of
the hadronic system recoil in a narrow cone opposite to the
direction of the ISR photon. Since ISR photons are pref-
erentially emitted at small polar angles, the efficiency for
detecting all four tracks within the fiducial volume of the
detector decreases accordingly. The decrease in the global
efficiency at large values of
M
4

can be explained with
similar arguments, because the opening angle of the
hadronic system increases with decreasing ISR photon
energy, increasing the probability of losing one of the
four tracks. The discontinuity at
M
4

¼
1
:
1 GeV
=c
2
is
due to the pion PID requirement for the tracks at low
invariant masses.
As mentioned in section
II
, it is assumed that the

þ



þ



hadronic final state arises from the decay
of various intermediate resonances such as
a
1
ð
1260
Þ

. The
relative contributions of intermediate states are discussed
in Sec.
VII
. Different intermediate states might exhibit
different results for the angular distributions of final-state
particles. The limited knowledge of the hadronic substruc-
ture hence corresponds to a systematic uncertainty in the
0
0.5
1
1.5
2
2.5
3
3.5
4
0.6
0.7
0.8
0.9
1
1.1
Data
Data after PID requirement
M
4
π
(GeV/c
2
)
σ[
nb
]
/ 25 MeV/c
2
FIG. 4 (color online).

þ



þ



cross section in the
threshold region for the data (squares) and for the data after
requiring each track to satisfy a dedicated pion selection algo-
rithm (triangles), corresponding to the method 2 selection crite-
rion. The indicated uncertainties are statistical.
10
3
10
4
0
20
40
6
0
80
100
0
50
100
150
200
250
300
02
04060
80
100
χ
2
4
π
Events / unit
χ
2
(a)
Data-B
ackground M
C
Signa
l MC
Bac
kgrou
nd MC
χ
2
4
π
Events / unit
χ
2
(b)
FIG. 5 (color online). (a) The

2
distribution for data after
background subtraction (points), signal MC (histogram) and the
sum of simulated background channels (hatched histogram).
(b) The difference between data with background subtraction
and signal MC. The dashed line indicates the boundary with the
0
<
2
4

<
10
region used for normalization.
M
4
π
(GeV/c
2
)
Efficiency / 25 MeV/c
2
0
0.05
0.1
0.15
0.2
0.25
1
1.5
2
2.5
3
3.5
4
4.5
FIG. 6 (color online). The efficiency as a function of the

þ



þ


invariant mass. The vertical line at
M
4

¼
1
:
1 GeV
=c
2
separates the regions with and without a pion PID
requirement for the reconstructed tracks. The curves on either
side of the vertical line are fits based on the sum of a Gaussian
and a polynomial.
J. P. LEES
et al.
PHYSICAL REVIEW D
85,
112009 (2012)
112009-8