of 49
Precise measurement of the
e
þ
e

!

þ


ð

Þ
cross section with the initial-state
radiation method at
B
A
B
AR
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
A. Palano,
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
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
B. A. Schumm,
13
A. Seiden,
13
D. S. Chao,
14
C. H. Cheng,
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
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
U. Nauenberg,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
W. H. Toki,
17
B. Spaan,
18
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
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
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
U. Uwer,
28
H. M. Lacker,
29
T. Lueck,
29
P. D. Dauncey,
30
P. K. Behera,
31
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
W. T. Meyer,
32
S. Prell,
32
A. E. Rubin,
32
A. V. Gritsan,
33
Z. J. Guo,
33
N. Arnaud,
34
M. Davier,
34
D. Derkach,
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
L. L. Wang,
34,
§
G. Wormser,
34
D. J. Lange,
35
D. M. Wright,
35
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
K. Griessinger,
40
A. Hafner,
40
E. Prencipe,
40
R. J. Barlow,
41,
k
G. Jackson,
41
G. D. Lafferty,
41
E. Behn,
42
R. Cenci,
42
B. Hamilton,
42
A. Jawahery,
42
D. A. Roberts,
42
C. Dallapiccola,
43
R. Cowan,
44
D. Dujmic,
44
G. Sciolla,
44
R. Cheaib,
45
D. Lindemann,
45
P. M. Patel,
45
S. H. Robertson,
45
P. Biassoni,
46a,46b
N. Neri,
46a
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
M. Simard,
48
P. Taras,
48
G. De Nardo,
49a,49b
D. Monorchio,
49a,49b
G. Onorato,
49a,49b
C. Sciacca,
49a,49b
M. Martinelli,
50
G. Raven,
50
C. P. Jessop,
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
G. Simi,
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,
**
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
J. Olsen,
58
A. J. S. Smith,
58
A. V. Telnov,
58
F. Anulli,
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,
*
C. Voss,
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
J. F. Benitez,
63
C. Cartaro,
63
M. R. Convery,
63
J. Dorfan,
63
G. P. Dubois-Felsmann,
63
W. Dunwoodie,
63
M. Ebert,
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
P. Kim,
63
M. L. Kocian,
63
D. W. G. S. Leith,
63
P. Lewis,
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
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
W. J. Wisniewski,
63
M. Wittgen,
63
D. H. Wright,
63
H. W. Wulsin,
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
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
J. L. Ritchie,
70
A. M. Ruland,
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
86,
032013 (2012)
1550-7998
=
2012
=
86(3)
=
032013(49)
032013-1
Ó
2012 American Physical Society
A. Oyanguren,
74
H. Ahmed,
75
J. Albert,
75
Sw. Banerjee,
75
F. U. Bernlochner,
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
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
47
University of Mississippi, University, Mississippi 38677, USA
48
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032013 (2012)
032013-2
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 14 May 2012; published 28 August 2012)
A precise measurement of the cross section of the process
e
þ
e

!

þ


ð

Þ
from threshold to an
energy of 3 GeV is obtained with the initial-state radiation (ISR) method using
232 fb

1
of data collected
with the
BABAR
detector at
e
þ
e

center-of-mass energies near 10.6 GeV. The ISR luminosity is
determined from a study of the leptonic process
e
þ
e

!

þ


ð

Þ

ISR
, which is found to agree with
the next-to-leading-order QED prediction to within 1.1%. The cross section for the process
e
þ
e

!

þ


ð

Þ
is obtained with a systematic uncertainty of 0.5% in the dominant

resonance region. The
leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured

cross section from threshold to 1.8 GeV is
ð
514
:
1

2
:
2
ð
stat
Þ
3
:
1
ð
syst
ÞÞ
10

10
.
DOI:
10.1103/PhysRevD.86.032013
PACS numbers: 13.40.Em, 13.60.Hb, 13.66.Bc, 13.66.Jn
I. INTRODUCTION
A. The physics context
The theoretical precision of observables like the running
of the quantum electrodynamic (QED) fine structure
constant

ð
s
Þ
or the anomalous magnetic moment of the
muon is limited by second-order loop effects from had-
ronic vacuum polarization (VP). Theoretical calculations
*
Deceased.
Now at the University of Tabuk, Tabuk 71491, Saudi Arabia.
Also with Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
§
Now at Institute of High Energy Physics, Beijing, China.
k
Now at the University of Huddersfield, Huddersfield HD1
3DH, UK.
{
Now at University of South Alabama, Mobile, AL 36688,
USA.
**
Also with Universita
`
di Sassari, Sassari, Italy.
PRECISE MEASUREMENT OF THE
...
PHYSICAL REVIEW D
86,
032013 (2012)
032013-3
are related to hadronic production rates in
e
þ
e

annihila-
tion via dispersion relations. As perturbative quantum
chromodynamic theory fails in the energy regions where
resonances occur, measurements of the
e
þ
e

!
hadrons
cross section are necessary to evaluate the dispersion in-
tegrals. Of particular interest is the contribution
a
had

to the
muon magnetic moment anomaly
a

, which requires data
in a region dominated by the process
e
þ
e

!

þ


ð

Þ
.
The accuracy of the theoretical prediction for
a

is linked
to the advances in
e
þ
e

measurements. A discrepancy of
roughly 3 standard deviations (

) including systematic
uncertainties between the measured [
1
] and predicted
[
2
4
] values of
a

persisted for years before the results
of this analysis became available [
5
], possibly hinting at
new physics. An independent approach using

decay data
leads to a smaller difference of
1
:
8

[
6
] in the same
direction, with enlarged systematic uncertainties due to
isospin-breaking corrections.
The kernel in the integrals involved in vacuum polariza-
tion calculations strongly emphasizes the low-energy part
of the spectrum. About 73% of the lowest-order hadronic
contribution is provided by the

þ


ð

Þ
final state, and
about 60% of its total uncertainty stems from that mode
[
7
]. To improve on present calculations, the precision on
the VP dispersion integrals is required to be better than 1%.
More precise experimental data in the

þ


ð

Þ
channel
are needed, such that systematic uncertainties on the cross
sections that are correlated over the relevant mass range are
kept well below the percent level.
In this paper an analysis of the process
e
þ
e

!

þ


ð

Þ

based on data collected with the
BABAR
ex-
periment is presented. In addition, as a cross-check of the
analysis, we measure the
e
þ
e

!

þ


ð

Þ

cross sec-
tion on the same data and compare it to the QED predic-
tion. The reported results and their application to the

contribution to the muon magnetic anomaly have been
already published in shorter form [
5
].
B. The ISR approach
The initial-state radiation (ISR) method has been pro-
posed [
8
11
] as a novel way to study
e
þ
e

annihilation
processes instead of the standard point-by-point energy-
scan measurements. The main advantage of the ISR
approach is that the final-state mass spectrum is obtained
in a single configuration of the
e
þ
e

storage rings and of
the detection apparatus, thus providing a cross section
measurement over a wide mass range starting at threshold.
Consequently, a better control of the systematic errors can
be achieved compared to the energy-scan method, which
necessitates different experiments and colliders to cover
the same range. The disadvantage is the reduction of the
measured cross section, which is suppressed by one order
of

. This is offset by the availability of high-luminosity
e
þ
e

storage rings, primarily designed as
B
and
K
facto-
ries in order to study
CP
violation.
In the ISR method, the cross section for
e
þ
e

!
X
at
the reduced energy
ffiffiffiffi
s
0
p
¼
m
X
, where
X
can be any final
state, is deduced from a measurement of the radiative
process
e
þ
e

!
X
, where the photon is emitted by the
initial
e
þ
or
e

particle. The reduced energy is related to
the energy
E


of the ISR photon in the
e
þ
e

center-of-
mass (c.m.) frame by
s
0
¼
s
ð
1

2
E


=
ffiffiffi
s
p
Þ
, where
s
is the
square of the
e
þ
e

c.m. energy. In this analysis,
s

ð
10
:
58 GeV
Þ
2
and
ffiffiffiffi
s
0
p
ranges from the two-pion produc-
tion threshold to 3 GeV. Two-body ISR processes
e
þ
e

!
X
with
X
¼

þ


ð

Þ
and
X
¼

þ


ð

Þ
are measured,
where the ISR photon is detected at large angle to the
beams, and the charged particle pair can be accompanied
by a final-state radiation (FSR) photon.
Figure
1
shows the Feynman diagrams relevant to this
study. The lowest-order (LO) radiated photon can be either
from ISR or FSR. In the muon channel, ISR is dominant in
the measurement range, but the LO FSR contribution needs
to be subtracted using QED. In the pion channel, the LO
FSR calculation is model-dependent, but the contribution
is strongly suppressed due to the large
s
value. In both
channels, interference between ISR and FSR amplitudes
vanishes for a charge-symmetric detector.
In order to control the overall efficiency to high
precision, it is necessary to consider higher-order radia-
tion. The next-to-leading-order (NLO) correction in

amounts to about 4% [
12
] with the selection used for this
analysis, while the next-to-next-to-leading-order (NNLO)
correction is expected to be at least 1 order of magnitude
smaller than NLO. Most of the higher-order contributions
come from ISR and hence are independent of the final
state. As the cross section is measured through the
=
ratio, as explained below, most higher-order
radiation effects cancel and NLO is sufficient to reach
precisions of
10

3
. As a result, the selection keeps

(

) as well as

(

) final states, where the
additional photon can be either ISR or FSR.
FIG. 1. The generic Feynman diagrams for the processes rele-
vant to this study with one or two real photons: lowest-order
(LO) ISR (top left), LO FSR (top right), next-to-leading order
(NLO) ISR with additional ISR (bottom left), NLO with addi-
tional FSR (bottom right).
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032013 (2012)
032013-4
C. Cross section measurement through
the
=
ratio
The cross section for the process
e
þ
e

!
X
is related to
the
ffiffiffiffi
s
0
p
spectrum of
e
þ
e

!
X
ISR
events through
dN
X
ISR
d
ffiffiffiffi
s
0
p
¼
dL
eff
ISR
d
ffiffiffiffi
s
0
p
"
X
ð
ffiffiffiffi
s
0
p
Þ

0
X
ð
ffiffiffiffi
s
0
p
Þ
;
(1)
where
dL
eff
ISR
=d
ffiffiffiffi
s
0
p
is the effective ISR luminosity,
"
X
is
the full acceptance for the event sample, and

0
X
is the
‘‘bare’’ cross section for the process
e
þ
e

!
X
(including
additional FSR photons), in which the leptonic and had-
ronic vacuum polarization effects are removed.
Equation (
1
) applies equally to
X
¼

ð

Þ
and
X
¼

ð

Þ
final states, so that the ratio of cross sections
is directly related to the ratio of the pion to muon spectra as
a function of
ffiffiffiffi
s
0
p
. Specifically, the ratio
R
exp
ð
ffiffiffiffi
s
0
p
Þ
of the
produced

ð

Þ

ISR
and

ð

Þ

ISR
spectra, obtained
from the measured spectra corrected for full acceptance,
can be expressed as
R
exp
ð
ffiffiffiffi
s
0
p
Þ¼
dN
prod

ð

Þ

ISR
d
ffiffiffi
s
0
p
dN
prod

ð

Þ

ISR
d
ffiffiffi
s
0
p
(2)
¼

0

ð

Þ
ð
ffiffiffiffi
s
0
p
Þ
ð
1
þ


FSR
Þ

0

ð

Þ
ð
ffiffiffiffi
s
0
p
Þ
(3)
¼
R
0
ð
ffiffiffiffi
s
0
p
Þ
ð
1
þ


FSR
Þð
1
þ


add
:
FSR
Þ
:
(4)
The ‘‘bare’’ ratio
R
0
(no vacuum polarization, but addi-
tional FSR included), which enters the VP dispersion in-
tegrals, is given by
R
0
ð
ffiffiffiffi
s
0
p
Þ¼

0

ð

Þ
ð
ffiffiffiffi
s
0
p
Þ

pt
ð
ffiffiffiffi
s
0
p
Þ
;
(5)
where

pt
¼
4

2
=
3
s
0
is the cross section for pointlike
charged fermions. The factor (
1
þ


FSR
) corrects for the
lowest-order FSR contribution, including possibly addi-
tional soft photons, to the
e
þ
e

!

þ



final state, as
is explicitly given in Eq. (
18
). No such factor is included
for pions because of the negligible LO FSR contribution
(see Sec.
IX H 1
). The factor (
1
þ


add
:
FSR
) corrects for
additional FSR in the
e
þ
e

!

þ


process at
ffiffiffiffi
s
0
p
,as
is explicitly given in Eq. (
19
).
In this analysis, we use a procedure strictly equivalent to
taking the ratio
R
exp
ð
ffiffiffiffi
s
0
p
Þ
, namely, we measure the

0

ð

Þ
ð
ffiffiffiffi
s
0
p
Þ
cross section using Eq. (
1
) in which the effec-
tive ISR luminosity is obtained from the mass spectrum of
produced

ð

Þ

ISR
events divided by the

0

ð

Þ
ð
ffiffiffiffi
s
0
p
Þ
cross section computed with QED. The ISR luminosity
measurement is described in detail in Sec.
VIII F
.
This way of proceeding considerably reduces the un-
certainties related to the effective ISR luminosity function
when determined through
dL
eff
ISR
d
ffiffiffiffi
s
0
p
¼
L
ee
dW
d
ffiffiffiffi
s
0
p


ð
s
0
Þ

ð
0
Þ

2
"

ISR
ð
ffiffiffiffi
s
0
p
Þ
"
MC

ISR
ð
ffiffiffiffi
s
0
p
Þ
:
(6)
Equation (
6
) relies on the
e
þ
e

luminosity measurement
(
L
ee
) and on the theoretical radiator function
dW=d
ffiffiffiffi
s
0
p
.
The latter describes the probability to radiate an ISR
photon (with possibly additional ISR photons) so that the
produced final state (excluding ISR photons) has a mass
ffiffiffiffi
s
0
p
. It depends on
ffiffiffi
s
p
,on
ffiffiffiffi
s
0
p
, and on the angular range
ð

min
;

max
Þ
of the ISR photon in the
e
þ
e

c.m. system. For
convenience, two factors that are common to the muon and
pion channels are included in the effective luminosity
definition of Eq. (
6
): (i) the ratio of
"

ISR
, the efficiency
to detect the main ISR photon, to the same quantity
"
MC

ISR
in
simulation, and (ii) the vacuum polarization correction
ð

ð
s
0
Þ
=
ð
0
ÞÞ
2
. The latter factor is implicitly included in
the effective luminosity deduced from

ð

Þ

ISR
data
using Eq. (
1
), while the former, which cancels out in the

to

ratio, is ignored in Eq. (
1
). As an important
cross-check of the analysis, hereafter called the QED test,
we use Eq. (
6
), together with Eq. (
1
), to measure the muon
cross section and compare it to the QED prediction.
Many advantages follow from taking the
R
exp
ð
ffiffiffiffi
s
0
p
Þ
ratio:
(i) the result is independent of the
BABAR
luminosity
L
ee
measurement;
(ii) the determination of the ISR luminosity comes from
the muon data, independently of the number of
additional ISR photons, and thus does not depend
on a theoretical calculation;
(iii) the ISR photon efficiency cancels out;
(iv) the vacuum polarization also cancels out.
Furthermore the Monte Carlo generator and the detector
simulation are only used to compute the acceptance of the
studied
X
ISR
processes, with
X
¼

ð

Þ
,

ð

Þ
. The
overall systematic uncertainty on the

cross section is
reduced, because some individual uncertainties cancel be-
tween pions and muons.
II. ANALYSIS OUTLINE
A. The
BABAR
detector and data samples
The analysis is based on
232 fb

1
of data collected
with the
BABAR
detector at the SLAC PEP-II
asymmetric-energy
e
þ
e

storage rings operated at the

ð
4
S
Þ
resonance. The
BABAR
detector is described in
detail elsewhere [
13
]. Charged-particle tracks are mea-
sured with a five-layer double-sided silicon vertex tracker
(SVT) together with a 40-layer drift chamber (DCH) inside
a 1.5 T superconducting solenoid magnet. Photons are
assumed to originate from the primary vertex defined by
PRECISE MEASUREMENT OF THE
...
PHYSICAL REVIEW D
86,
032013 (2012)
032013-5
the charged tracks of the event and their energy is mea-
sured in a CsI(Tl) electromagnetic calorimeter (EMC).
Charged-particle identification (PID) uses the ionization
losses
d
E=
d
x
in the SVT and DCH, the Cherenkov radia-
tion detected in a ring-imaging device (DIRC), the shower
energy deposit in the EMC (
E
cal
) and the shower shape in
the instrumented flux return (IFR) of the magnet. The IFR
system is constructed from modules of resistive plate
chambers interspaced with iron slabs, arranged in a con-
figuration with a barrel and two endcaps.
B. Monte Carlo generators and simulation
Signal and background ISR processes
e
þ
e

!
X
are
simulated with a Monte Carlo (MC) event generator called
AfkQed, which is based on the formalism of Ref. [
14
]. The
main ISR (or main FSR in the case of

) photon is
generated within the angular range [

min
¼
20
0
,

max
¼
160
0
] in the c.m. system, bracketing the photon detection
range with a margin to account for finite resolution.
Additional ISR photons are generated with the structure
function method [
15
], and additional FSR photons with
PHOTOS [
16
]. Additional ISR photons are emitted along
the
e
þ
or
e

beam particle direction. A minimum mass
m
X
ISR
>
8 GeV
=c
2
is imposed at generation, which places
an upper bound on the additional ISR photon energy.
Samples corresponding to 5 to 10 times the number of
data events are generated for the signal channels. The more
accurate Phokhara generator [
17
] is used at the 4-vector
level to study some effects (defined in Sec.
IX D
) related to
additional ISR photons. Background processes
e
þ
e

!
q

q
(
q
¼
u
,
d
,
s
,
c
) are generated with JETSET [
18
], and
e
þ
e

!

þ


with KORALB [
19
]. The response of the
BABAR
detector is simulated with GEANT4 [
20
].
C. Analysis method
The

ð

Þ

ISR
and

ð

Þ

ISR
processes are measured
independently with full internal checks and the ratio
R
exp
ð
ffiffiffiffi
s
0
p
Þ
, which yields the measured

0

ð

Þ
ð
ffiffiffiffi
s
0
p
Þ
cross
section, is only examined after these checks are success-
fully passed. One of the most demanding tests is the
absolute comparison of the

ð

Þ

ISR
cross section,
which uses the
BABAR
L
ee
luminosity, with the NLO
QED prediction (QED test).
After preliminary results were presented from the blind
analysis [
21
], a few aspects of the analysis were revisited to
refine some effects that had been initially overlooked,
mostly affecting the correlated loss of muon identification
for both tracks. While the final measurement is not a
strictly blind analysis, all studies are again made indepen-
dently for muons and pions and combined at the very end.
The selected events correspond to a final state with two
tracks and the ISR candidate, all within the detector accep-
tance, as described in Sec.
III
. Kinematic fits provide
discrimination of the channels under study from other
processes. However the separation between the different
two-prong final states (including
K
þ
K

ð

Þ

ISR
)relies
exclusively on the identification of the charged particles.
Thus particle identification plays a major role in the analy-
sis. This is the subject of Sec.
IV D
. Background reduction
and control of the remaining background contributions are
another challenge of the analysis, in particular, in the pion
channel away from the

resonance. This is discussed
in Sec.
VI
.
The determination of the
ffiffiffiffi
s
0
p
spectrum is described in
Sec.
VII
. The relevant final-state mass is
m

(
m

) when
there is additional ISR or no additional radiation, or
m

(
m

) in the case of additional FSR. The
ffiffiffiffi
s
0
p
spectrum is
obtained from the observed
m

(
m

) distributions
through unfolding (Sec.
VII A
).
Although selection of the final state of two-body ISR
processes is rather simple, the main difficulty of the analy-
sis resides in the full control of all involved efficiencies.
Relying on the simulation alone cannot provide the re-
quired precision. The simulation is used in a first step in
order to incorporate in a consistent way all effects entering
the final event acceptance. Corrections for data-to-MC
differences are obtained for each efficiency using dedi-
cated studies performed on the data and simulation
samples. The main contributions for these corrections
originate from trigger, tracking, particle identification,
and the
2
selection of the kinematic fits, so that the
corrected efficiency is
"
¼
"
MC
0
@
"
data
trig
"
MC
trig
1
A
0
@
"
data
track
"
MC
track
1
A
0
@
"
data
PID
"
MC
PID
1
A
0
@
"
data
2
"
MC
2
1
A
:
(7)
The corrections
C
i
¼ð
"
data
i
"
MC
i
Þ
are reviewed in turn in the
following sections (Sec.
IV
and
V
). They are applied as
mass-dependent corrections to the MC efficiency. They
amount to at most a few percent and are known to a few
permil level or better. Efficiency measurements are de-
signed to avoid correlations between the
C
i
. Further data-
to-MC corrections deal with second-order effects related to
the description of additional ISR in the generator, which
was found inadequate at the level of precision required for
this analysis. As outlined in Sec.
IB
the chosen approach
guarantees that radiative corrections are at a very small
level. Residual effects are studied in Sec.
IX D
.
III. EVENT SELECTION
A. Topological selection
Two-body ISR events are selected by requiring a photon
candidate with
E


>
3 GeV
and laboratory polar angle in
the range 0.35–2.4 rad, and exactly two tracks of opposite
charge, each with momentum
p>
1 GeV
c
1
and within the
1
Unless otherwise stated, starred quantities are measured in
the
e
þ
e

c.m. and unstarred quantities in the laboratory.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032013 (2012)
032013-6
angular range 0.40–2.45 rad. A photon candidate is defined
as a cluster in the EMC, with energy larger than 0.02 GeV,
not associated to a charged track. If several photons are
detected, the main ISR photon is assumed to be that with the
highest
E


; this results in an incorrectly assigned ISR
photon in less than

10

4
of the events, mostly due to
the ISR photon loss in inactive areas of the EMC. The track
momentum requirement is dictated by the falloff of the
muon-identification efficiency at low momenta. The tracks
are required to have at least 15 hits in the DCH, and
originate within 5 mm of the collision axis (distance of
closest approach
doca
xy
<
5mm
) and within 6 cm from the
beam spot along the beam direction (
j

z
j
<
6cm
). They
are required to extrapolate to the DIRC active area, whose
length further restricts the minimum track polar angle to

0
:
45 rad
. Tracks are also required to extrapolate to the
IFR active areas that exclude low-efficiency regions. An
additional veto based on a combination of
E
cal
and
d
E=
d
x
,
ðð
E
cal
=p

1
Þ
=
0
:
15
Þ
2
þðð
d
E=
d
x
DCH

690
Þ
=
150
Þ
2
<
1
), re-
duces electron contamination. Events can be accompanied
by any number of ‘‘bad’’ tracks, not satisfying the above
criteria, and any number of additional photons. To ensure a
rough momentum balance at the preselection level (here-
after called ‘‘preselection cut’’), the ISR photon is required
to lie within 0.3 rad of the missing momentum of the tracks
(or of tracks plus other photons).
B. Kinematic fit description and

2
selection
For both the

and

processes, the event defi-
nition is enlarged to include the radiation of one photon in
addition to the already-required ISR photon. Two types of
fits are considered, according to the following situations:
(i) The additional photon is detected in the EMC, in
which case its energy and angles can be readily used
in the fit: we call this a 3-constraint (3C) FSR fit,
although the extra photon can be either from FSR or
from ISR at large angle to the beams. The threshold
for the additional photon is kept low (20 MeV). This
can introduce some background, but with little effect
as the fit in that case would not be different in
practice from a standard fit to the

ð

Þ

ISR
(

ð

Þ

ISR
) hypothesis.
(ii) The additional photon is assumed to be from ISR at a
small angle to the beams. Since further information
2
is not available, it is presumed that the extra photon is
perfectly aligned with either the
e
þ
or the
e

beam.
The corresponding so-called 2C ISR fit ignores addi-
tional photons measured in the EMC and determines
the energy of the fitted collinear ISR photon.
In both cases the constrained fit procedure uses the ISR
photon direction and the measured momenta and angles of
the two tracks with their covariance matrix in order to solve
the four energy-momentum conservation equations. The
measured energy of the primary ISR photon is not used in
either fit, as it adds little information for the relatively low
masses involved.
Each event is characterized by two
2
values,
2
FSR
and
2
ISR
from the FSR and ISR fits, respectively, which are
examined on a two-dimensional (2D) plot. In practice the
quantities
ln
ð
2
þ
1
Þ
are used so that the long tails can be
properly visualized (Figs.
2
and
3
). Events without any
extra measured photons have only the
2
ISR
value and they
are plotted separately on a line above the
2
FSR
overflow.
In case several extra photons are detected, FSR fits are
0
2.5
5
7.5
10
0
2.5
5
7.5
10
1
10
10
2
10
3
ln(
χ
2
ISR
+1)
ln(
χ
2
FSR
+1)
γμ
+
μ
(data)
FIG. 3 (color online). The 2D-
2
distribution for

ð

Þ

ISR
(data) for
0
:
5
<m

<
1
:
0 GeV
=c
2
, where the signal and back-
ground regions are indicated.
0
2.5
5
7.5
10
0
2.5
5
7.5
10
1
10
10
2
10
3
ln(
χ
2
ISR
+1)
ln(
χ
2
FSR
+1)
no
γ
2
γπ
+
π
(data)
add.ISR
add.‘FSR’
no add.Rad.
2D-
χ
2
cut
(BG region)
trk rec + interactions + more add. rad.
FIG. 2 (color online). The 2D-
2
distribution for

ð

Þ

ISR
(data) for
0
:
5
<m

<
1
:
0 GeV
=c
2
, where different interesting
regions are defined.
2
This is not strictly true as the missing photon could be
completely reconstructed if the ISR photon energy were used
in the kinematic fit. However tests have shown that the relative
quality of this new information does not permit a significant
improvement for the fitted direction of the additional ISR photon
over the collinear assumption.
PRECISE MEASUREMENT OF THE
...
PHYSICAL REVIEW D
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032013 (2012)
032013-7
performed using each photon in turn and the fit with the
smallest
2
FSR
is retained. The muon (pion) mass is assumed
for the two charged particles, according to the selected
channel, and in the following studies and final distributions,
the

(

) mass is obtained using the fitted parameters of
the two charged particles from the ISR fit if
2
ISR
<
2
FSR
and from the FSR fit in the reverse case.
It is easy to visualize the different interesting regions in
the 2D-
2
plane, as illustrated in Fig.
2
for

ð

Þ

ISR
data.
Most of the events peak at small values of both
2
, but the
tails along the axes clearly indicate events with additional
radiation: small-angle ISR along the
2
FSR
axis (with large
ISR energies at large values of
2
FSR
), or FSR or large-angle
ISR along the
2
ISR
axis (with large additional radiation
energies at large values of
2
ISR
). Events along the diagonal
do not satisfy either hypothesis and result from resolution
effects for the pion tracks (also secondary interactions) or
the primary ISR photon, or possibly additional radiation of
more than one photon. Multibody background populates the
region where both
2
are large and consequently a back-
ground region is defined in the 2D-
2
plane. This region is
optimized as a compromise between efficiency and back-
ground contamination in the signal sample, aiming at best
control of the corresponding systematic uncertainties.
The
2
criteria used in the pion analysis depend on the

mass region considered. The
m

region between 0.5
and
1 GeV
=c
2
is dominated by the

resonance. The
corresponding large cross section provides a dominant
contribution to vacuum-polarization dispersion integrals,
so it has to be known with small systematic uncertainties.
Also background is expected to be at a small level in this
region. These two considerations argue for large efficien-
cies, in order to keep systematic uncertainties sufficiently
low. Therefore a loose
2
criterion is used, where the
physical (accepted) region corresponds to the left of the
contour outlined in Fig.
2
, excluding the BG-labeled
region. The same loose
2
criterion is applied for the

ð

Þ

ISR
analysis (Fig.
3
).
The pion form factor decreases rapidly away from the

peak, while the backgrounds vary slowly with the

mass. The multihadronic background in the physical sam-
ple becomes excessively large if the
2
criterion as used in
the

region is applied, and it is necessary to tighten the
selection of

ð

Þ

ISR
events. Figure
4
shows the tight
2
selection boundary
ln
ð
2
ISR
þ
1
Þ
<
3
chosen to reduce
multihadronic background, and the 2D-
2
distributions
for masses below and above the central

region. The tight
2
criterion retains events with additional ISR since this
region in the
2
plane is free of multihadronic background.
The reduced efficiency on signal from the tight selection
results in a larger relative uncertainty, but this is still
acceptable considering the much smaller contribution
from the

tails to the dispersion integral.
Efficiencies and systematic uncertainties resulting from
the loose and tight
2
selection criteria are discussed in
Sec.
VB
.
IV. EFFICIENCY STUDIES (I)
To achieve the required precision for the cross section
measurement, efficiencies are validated with data at every
step of the event processing, and mass-dependent data/MC
corrections are determined. This necessitates specific stud-
ies on data control samples whose selection criteria are
designed to minimize biases on efficiency measurements.
Residual effects are estimated and included in the system-
atic errors.
A. Efficiency-dedicated event selection
and kinematic fit
For trigger and tracking efficiency studies, a dedicated
selection of

þ



ISR
and

þ



ISR
events is devised
0
2.5
5
7.5
10
0
2.5
5
7.5
10
1
10
10
2
ln(
χ
2
ISR
+1)
ln(
χ
2
FSR
+1)
m
ππ
<
0.5GeV/c
2
,
ππγ(γ)
data
0
2.5
5
7.5
10
0
2.5
5
7.5
10
1
10
10
2
ln(
χ
2
ISR
+1)
ln(
χ
2
FSR
+1)
1
<
m
ππ
<
2GeV/c
2
,
ππγ(γ)
data
FIG. 4 (color online). The 2D-
2
distributions in

ð

Þ

ISR
data: (left) below the central

region (
m

<
0
:
5 GeV
=c
2
); (right)
above the central

region (
1
:<m

<
2
:
GeV
=c
2
). The line indicates the boundary for the tight
2
selection.
J. P. LEES
et al.
PHYSICAL REVIEW D
86,
032013 (2012)
032013-8
that only requires one reconstructed track (called ‘‘pri-
mary’’), identified as a muon or pion, and the ISR photon.
A 1Ckinematicfitisperformedandthemomentumvector of
the second muon (pion) is predicted from 4-momentum
conservation. Standard track selection is applied to the
primary track and the predicted track is required to be in
the acceptance.
B. Trigger and filtering
A number of trigger conditions are imposed at the hard-
ware (L1) and online software (L3) levels, as well as in a
final filtering, before an event is fully reconstructed and
stored in the
BABAR
data sample. They are common to all
BABAR
analyses, and hence are not specifically designed
to select ISR events. Since individual trigger and filter line
responses are stored for every recorded event, efficiencies
can be computed by comparing the response of trigger
lines, after choosing lines that are as orthogonal and as
efficient as possible. Trigger efficiencies are determined on
data and simulation samples, after applying identical event
selections and measurement methods, and data/MC cor-
rections
C
trig
are computed from the comparison of mea-
sured efficiencies on background-subtracted data and
signal MC. Once the physics origins of inefficiencies are
identified, uncertainties are estimated through studies of
biases and data-to-MC comparison of distributions of rele-
vant quantities. Efficiencies and data/MC corrections are
measured separately for the pion and muon channels.
Trigger efficiencies are determined on samples unbiased
with respect to the number of tracks actually reconstructed,
to avoid correlations between trigger and tracking effi-
ciency measurements. In practice, one- and two-track
samples are sufficient and consequently the trigger control
samples are selected through the dedicated 1C kinematic fit
described above. Because of the loose requirement with
respect to tracking, the data samples contain backgrounds
with potentially different trigger efficiencies to that of the
signal. These backgrounds are studied with simulation and
are then subtracted. To obtain data samples that are as pure
as possible, criteria tighter than the standard track selection
are applied to the primary track, including tight PID iden-
tification. Possible biases resulting from the tighter selec-
tion are studied and accounted for in the systematic errors.
Background contributions are subtracted from the data
spectra using properly-normalized simulated samples,
and, if necessary, with data/MC correction of the trigger
efficiencies in an iterative procedure.
The data/MC corrections for the L1 trigger are found to
be at a few

10

4
level for muon and pion events. The L3
level involves a track trigger (at least one track is required)
and a calorimetric trigger (demanding at least one high-
energy cluster and one low-energy cluster). Both of them
are efficient for

ISR
events. For

ISR
events, the
small efficiency of the calorimetric trigger limits the sta-
tistical precision of the track-trigger and overall efficiency
measurements. Furthermore, a correlated change of the
two trigger line responses for close-by tracks induces
both a nonuniformity in the efficiency and a bias in the
efficiency measurement. This originates from the overlap
of tracks in the drift chamber and of showers in the EMC,
which induces a simultaneous decrease in the track-trigger
efficiency and an increase in the calorimetric-trigger effi-
ciency. Overlap is a major source of overall inefficiency
and difference between data and simulation, necessitating
specific studies. The correction to the MC L3 trigger
efficiency is small for pions, about
2

10

3
at the

peak, and known to a precision better than
10

3
. The
data/MC correction
C
trig
is larger in the

ð

Þ

ISR
chan-
nel, due to the dominant role of the track trigger, about 1%
at a

mass of
0
:
7 GeV
=c
2
, and known to a precision of
3

10

3
(Fig.
5
top). Uncertainties, which increase to
5

10

3
at the maximum overlap (
m


0
:
4 GeV
=c
2
),
are mostly statistical in nature.
0.95
0.975
1
1.025
1.05
0
0.5
1
1.5
2
2.5
m
μμ
(GeV/c
2
)
ε
data
/
ε
MC
0.9
0.95
1
1.05
0
0.5
1
1.5
m
ππ
(GeV/c
2
)
ε
data
/
ε
MC
FIG. 5. The data/MC event trigger and filter correction
C
trig
for
the

ð

Þ

ISR
(top) and

ð

Þ

ISR
(bottom) cross sections as a
function of the

and

masses, respectively. Statistical
errors only.
PRECISE MEASUREMENT OF THE
...
PHYSICAL REVIEW D
86,
032013 (2012)
032013-9