Study of
e
þ
e
!
p
p
via initial-state radiation at
BABAR
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
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
R. Y. So,
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
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
G. M. Vitug,
11
C. Campagnari,
12
M. Franco Sevilla,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
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
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
M. Morii,
26
A. Adametz,
27
U. Uwer,
27
H. M. Lacker,
28
T. Lueck,
28
P. D. Dauncey,
29
U. Mallik,
30
C. Chen,
31
J. Cochran,
31
W. T. Meyer,
31
S. Prell,
31
A. E. Rubin,
31
A. V. Gritsan,
32
N. Arnaud,
33
M. Davier,
33
D. Derkach,
33
G. Grosdidier,
33
F. Le Diberder,
33
A. M. Lutz,
33
B. Malaescu,
33
P. Roudeau,
33
M. H. Schune,
33
A. Stocchi,
33
G. Wormser,
33
D. J. Lange,
34
D. M. Wright,
34
J. P. Coleman,
35
J. R. Fry,
35
E. Gabathuler,
35
D. E. Hutchcroft,
35
D. J. Payne,
35
C. Touramanis,
35
A. J. Bevan,
36
F. Di Lodovico,
36
R. Sacco,
36
M. Sigamani,
36
G. Cowan,
37
D. N. Brown,
38
C. L. Davis,
38
A. G. Denig,
39
M. Fritsch,
39
W. Gradl,
39
K. Griessinger,
39
A. Hafner,
39
E. Prencipe,
39
R. J. Barlow,
40,
‡
G. D. Lafferty,
40
E. Behn,
41
R. Cenci,
41
B. Hamilton,
41
A. Jawahery,
41
D. A. Roberts,
41
C. Dallapiccola,
42
R. Cowan,
43
D. Dujmic,
43
G. Sciolla,
43
R. Cheaib,
44
P. M. Patel,
44,
§
S. H. Robertson,
44
P. Biassoni,
45a,45b
N. Neri,
45a
F. Palombo,
45a,45b
L. Cremaldi,
46
R. Godang,
46,
∥
R. Kroeger,
46
P. Sonnek,
46
D. J. Summers,
46
X. Nguyen,
47
M. Simard,
47
P. Taras,
47
G. De Nardo,
48a,48b
D. Monorchio,
48a,48b
G. Onorato,
48a,48b
C. Sciacca,
48a,48b
M. Martinelli,
49
G. Raven,
49
C. P. Jessop,
50
J. M. LoSecco,
50
K. Honscheid,
51
R. Kass,
51
J. Brau,
52
R. Frey,
52
N. B. Sinev,
52
D. Strom,
52
E. Torrence,
52
E. Feltresi,
53a,53b
N. Gagliardi,
53a,53b
M. Margoni,
53a,53b
M. Morandin,
53a
M. Posocco,
53a
M. Rotondo,
53a
G. Simi,
53a
F. Simonetto,
53a,53b
R. Stroili,
53a,53b
S. Akar,
54
E. Ben-Haim,
54
M. Bomben,
54
G. R. Bonneaud,
54
H. Briand,
54
G. Calderini,
54
J. Chauveau,
54
O. Hamon,
54
Ph. Leruste,
54
G. Marchiori,
54
J. Ocariz,
54
S. Sitt,
54
M. Biasini,
55a,55b
E. Manoni,
55a,55b
S. Pacetti,
55a,55b
A. Rossi,
55a,55b
C. Angelini,
56a,56b
G. Batignani,
56a,56b
S. Bettarini,
56a,56b
M. Carpinelli,
56a,56b,
¶
G. Casarosa,
56a,56b
A. Cervelli,
56a,56b
F. Forti,
56a,56b
M. A. Giorgi,
56a,56b
A. Lusiani,
56a,56c
B. Oberhof,
56a,56b
E. Paoloni,
56a,56b
A. Perez,
56a
G. Rizzo,
56a,56b
J. J. Walsh,
56a
D. Lopes Pegna,
57
J. Olsen,
57
A. J. S. Smith,
57
F. Anulli,
58a
R. Faccini,
58a,58b
F. Ferrarotto,
58a
F. Ferroni,
58a,58b
M. Gaspero,
58a,58b
L. Li Gioi,
58a
M. A. Mazzoni,
58a
G. Piredda,
58a
C. Bu
̈
nger,
59
O. Gru
̈
nberg,
59
T. Hartmann,
59
T. Leddig,
59
C. Voß,
59
R. Waldi,
59
T. Adye,
60
E. O. Olaiya,
60
F. F. Wilson,
60
S. Emery,
61
G. Hamel de Monchenault,
61
G. Vasseur,
61
Ch. Ye
`
che,
61
D. Aston,
62
D. J. Bard,
62
J. F. Benitez,
62
C. Cartaro,
62
M. R. Convery,
62
J. Dorfan,
62
G. P. Dubois-Felsmann,
62
W. Dunwoodie,
62
M. Ebert,
62
R. C. Field,
62
B. G. Fulsom,
62
A. M. Gabareen,
62
M. T. Graham,
62
C. Hast,
62
W. R. Innes,
62
M. H. Kelsey,
62
P. Kim,
62
M. L. Kocian,
62
D. W. G. S. Leith,
62
P. Lewis,
62
D. Lindemann,
62
B. Lindquist,
62
S. Luitz,
62
V. Luth,
62
H. L. Lynch,
62
D. B. MacFarlane,
62
D. R. Muller,
62
H. Neal,
62
S. Nelson,
62
M. Perl,
62
T. Pulliam,
62
B. N. Ratcliff,
62
A. Roodman,
62
A. A. Salnikov,
62
R. H. Schindler,
62
A. Snyder,
62
D. Su,
62
M. K. Sullivan,
62
J. Va’vra,
62
A. P. Wagner,
62
W. F. Wang,
62
W. J. Wisniewski,
62
M. Wittgen,
62
D. H. Wright,
62
H. W. Wulsin,
62
V. Ziegler,
62
W. Park,
63
M. V. Purohit,
63
R. M. White,
63
J. R. Wilson,
63
A. Randle-Conde,
64
S. J. Sekula,
64
M. Bellis,
65
P. R. Burchat,
65
T. S. Miyashita,
65
E. M. T. Puccio,
65
M. S. Alam,
66
J. A. Ernst,
66
R. Gorodeisky,
67
N. Guttman,
67
D. R. Peimer,
67
A. Soffer,
67
S. M. Spanier,
68
J. L. Ritchie,
69
A. M. Ruland,
69
R. F. Schwitters,
69
B. C. Wray,
69
J. M. Izen,
70
X. C. Lou,
70
F. Bianchi,
71a,71b
D. Gamba,
71a,71b
S. Zambito,
71a,71b
L. Lanceri,
72a,72b
L. Vitale,
72a,72b
F. Martinez-Vidal,
73
A. Oyanguren,
73
P. Villanueva-Perez,
73
H. Ahmed,
74
J. Albert,
74
Sw. Banerjee,
74
F. U. Bernlochner,
74
H. H. F. Choi,
74
G. J. King,
74
R. Kowalewski,
74
M. J. Lewczuk,
74
I. M. Nugent,
74
J. M. Roney,
74
R. J. Sobie,
74
PHYSICAL REVIEW D
87,
092005 (2013)
1550-7998
=
2013
=
87(9)
=
092005(18)
092005-1
Ó
2013 American Physical Society
N. Tasneem,
74
T. J. Gershon,
75
P. F. Harrison,
75
T. E. Latham,
75
H. R. Band,
76
S. Dasu,
76
Y. Pan,
76
R. Prepost,
76
and S. L. Wu
76
(
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 SB RAS, 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
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
28
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstrasse 15, D-12489 Berlin, Germany
29
Imperial College London, London, SW7 2AZ, United Kingdom
30
University of Iowa, Iowa City, Iowa 52242, USA
31
Iowa State University, Ames, Iowa 50011-3160, USA
32
Johns Hopkins University, Baltimore, Maryland 21218, USA
33
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
34
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
35
University of Liverpool, Liverpool L69 7ZE, United Kingdom
36
Queen Mary, University of London, London E1 4NS, United Kingdom
37
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
38
University of Louisville, Louisville, Kentucky 40292, USA
39
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
40
University of Manchester, Manchester M13 9PL, United Kingdom
41
University of Maryland, College Park, Maryland 20742, USA
42
University of Massachusetts, Amherst, Massachusetts 01003, USA
43
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
44
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
45a
INFN Sezione di Milano, I-20133 Milano, Italy
45b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
46
University of Mississippi, University, Mississippi 38677, USA
47
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
48a
INFN Sezione di Napoli, I-80126 Napoli, Italy
48b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
092005 (2013)
092005-2
49
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam,
The Netherlands
50
University of Notre Dame, Notre Dame, Indiana 46556, USA
51
Ohio State University, Columbus, Ohio 43210, USA
52
University of Oregon, Eugene, Oregon 97403, USA
53a
INFN Sezione di Padova, I-35131 Padova, Italy
53b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
54
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
55a
INFN Sezione di Perugia, I-06100 Perugia, Italy
55b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
56a
INFN Sezione di Pisa, I-56127 Pisa, Italy
56b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy
56c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
57
Princeton University, Princeton, New Jersey 08544, USA
58a
INFN Sezione di Roma, I-00185 Roma, Italy
58b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
59
Universita
̈
t Rostock, D-18051 Rostock, Germany
60
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
61
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
62
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
63
University of South Carolina, Columbia, South Carolina 29208, USA
64
Southern Methodist University, Dallas, Texas 75275, USA
65
Stanford University, Stanford, California 94305-4060, USA
66
State University of New York, Albany, New York 12222, USA
67
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
68
University of Tennessee, Knoxville, Tennessee 37996, USA
69
University of Texas at Austin, Austin, Texas 78712, USA
70
University of Texas at Dallas, Richardson, Texas 75083, USA
71a
INFN Sezione di Torino, I-10125 Torino, Italy
71b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
72a
INFN Sezione di Trieste, I-34127 Trieste, Italy
72b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
73
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
74
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
75
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
76
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 3 February 2013; published 10 May 2013)
The process
e
þ
e
!
p
p
is studied using
469 fb
1
of integrated luminosity collected with the
BABAR
detector at the SLAC National Accelerator Laboratory, at an
e
þ
e
center-of-mass energy of 10.6 GeV.
From the analysis of the
p
p
invariant mass spectrum, the energy dependence of the cross section for
e
þ
e
!
p
p
is measured from threshold to 4.5 GeV. The energy dependence of the ratio of electric and
magnetic form factors,
j
G
E
=G
M
j
, and the asymmetry in the proton angular distribution are measured for
p
p
masses below 3 GeV. The branching fractions for the decays
J=
c
!
p
p
and
c
ð
2
S
Þ!
p
p
are also
determined.
DOI:
10.1103/PhysRevD.87.092005
PACS numbers: 13.66.Bc, 13.25.Gv, 13.40.Gp, 14.20.Dh
I. INTRODUCTION
In this paper we use the initial-state-radiation
(ISR) technique to study the
e
þ
e
!
p
p
process
over a wide range of center-of-mass (c.m.) energies. The
study is an update of the results in Ref. [
1
], using
a data sample that is about twice as large and improved
analysis techniques. The Born cross section for the
ISR process
e
þ
e
!
p
p
integrated over the nucleon
momenta is
*
Now at the University of Tabuk, Tabuk 71491, Saudi Arabia.
†
Also with Universita
`
di Perugia, Dipartimento di Fisica,
Perugia, Italy.
‡
Now at the University of Huddersfield, Huddersfield HD1
3DH, UK.
§
Deceased.
∥
Now at University of South Alabama, Mobile, Alabama
36688, USA.
¶
Also with Universita
`
di Sassari, Sassari, Italy.
STUDY OF
e
þ
e
!
p
p
VIA INITIAL-
...
PHYSICAL REVIEW D
87,
092005 (2013)
092005-3
d
2
e
þ
e
!
p
p
ð
M
p
p
Þ
dM
p
p
d
cos
¼
2
M
p
p
s
W
ð
s; x;
Þ
p
p
ð
M
p
p
Þ
;
(1)
where
p
p
ð
m
Þ
is the Born cross section for the nonradiative
process
e
þ
e
!
p
p
,
M
p
p
is the
p
p
invariant mass,
ffiffiffi
s
p
is the nominal
e
þ
e
c.m. energy,
x
2
E
=
ffiffiffi
s
p
¼
1
M
2
p
p
=s
, and
E
and
are the ISR photon energy and polar
angle, respectively, in the
e
þ
e
c.m. frame.
1
The function
W
ð
s; x;
Þ
[
2
] describes the probability of ISR photon
emission. The Born cross section for
e
þ
e
!
p
p
is
p
p
ð
M
p
p
Þ¼
4
2
C
3
M
2
p
p
j
G
M
ð
M
p
p
Þj
2
þ
2
m
2
p
M
2
p
p
j
G
E
ð
M
p
p
Þj
2
;
(2)
where
m
p
is the nominal proton mass,
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
4
m
2
p
=M
2
p
p
q
,
C
¼
y=
ð
1
e
y
Þ
with
y
¼
=
is the Coulomb correc-
tion factor (see Ref. [
3
] and references therein), which
results in a nonzero cross section at threshold, and
G
M
and
G
E
are the magnetic and electric form factors, respec-
tively (
j
G
E
j¼j
G
M
j
at threshold). From measurement of
the cross section, a linear combination of the squared form
factors can be determined. We define the effective form
factor
j
F
p
ð
M
p
p
Þj¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
j
G
M
ð
M
p
p
Þj
2
þ
2
m
2
p
=M
2
p
p
j
G
E
ð
M
p
p
Þj
2
1
þ
2
m
2
p
=M
2
p
p
s
;
(3)
which is proportional to the square root of the measured
e
þ
e
!
p
p
cross section.
The proton angular distribution in
e
þ
e
!
p
p
[
4
] can be expressed as a sum of terms proportional to
j
G
M
j
2
and
j
G
E
j
2
. The angular dependences of the
G
M
and
G
E
terms are approximately
1
þ
cos
2
p
and
sin
2
p
, re-
spectively, where
p
is the angle between the proton mo-
mentum in the
p
p
rest frame and the momentum of the
p
p
system in the
e
þ
e
c.m. frame. Thus, the study of the
proton angular distribution can be used to determine the
modulus of the ratio of the electric and magnetic form
factors.
Direct measurements of the
e
þ
e
!
p
p
cross
section are available from
e
þ
e
experiments [
5
–
11
].
Most of these results assume
j
G
E
j¼j
G
M
j
. The proton
form factor was also determined in the inverse reaction
p
p
!
e
þ
e
[
12
–
14
]. In the PS170 experiment [
12
]at
LEAR, this reaction was studied in the c.m. energy
range from threshold up to 2.05 GeV. A strong dependence
of the form factor on c.m. energy near threshold was
observed. The
j
G
E
=G
M
j
ratio was found to be consistent
with unity. The E760 [
13
] and E835 [
14
] experiments at
Fermilab observed a strong decrease of the form factor for
c.m. energies above 3 GeV, in agreement with expectation
2
s
ð
m
2
Þ
=m
4
from perturbative QCD. However, a recent
result [
11
] based on
e
þ
e
data indicates that the
decrease of the form factor above 4 GeV is somewhat
more gradual.
II. THE
BABAR
DETECTOR AND
EVENT SAMPLES
The data, corresponding to an integrated luminosity of
469 fb
1
, were recorded with the
BABAR
detector at the
SLAC PEP-II asymmetric-energy
e
þ
e
collider. About
90% of the data were collected at a c.m. energy of
10.58 GeV, near the maximum of
ð
4S
Þ
resonance, while
10% were recoded at 10.54 GeV.
The
BABAR
detector is described in detail elsewhere
[
15
]. Charged-particle momenta are measured by a
combination of a five-layer silicon vertex tracker and a
40-layer drift chamber (DCH) operating in a 1.5-T sole-
noidal magnetic field. Charged-particle identification
(PID) is based on energy-loss measurements in the sili-
con vertex tracker and DCH, and information from a
ring-imaging Cherenkov detector. Photons and electrons
are detected in a CsI(Tl) electromagnetic calorimeter.
Muons are identified by resistive-plate chambers or
streamer tubes [
16
] in the instrumented magnetic flux
return.
Simulated events for signal and background ISR pro-
cesses are obtained with event generators based on
Ref. [
17
]. The differential cross section for
e
þ
e
!
p
p
is taken from Ref. [
4
]. To analyze the experimental
proton angular distribution, two samples of signal events
are generated, one with
G
E
¼
0
and the other with
G
M
¼
0
. Since the polar-angle distribution of the ISR photon is
peaked along the beam axis, the MC events are generated
with the restriction
20
<
<
160
(the corresponding
angular range in the laboratory frame is
12
<
<
146
). Additional photon radiation from the initial state
is generated by the structure function method [
18
]. To
restrict the maximum energy of the extra photons, the
invariant mass of the hadron system and the ISR photon
is required to be greater than
8GeV
=c
2
. For background
e
þ
e
!
þ
,
þ
,and
K
þ
K
processes, final-
state radiation is generated using the
PHOTOS
package
[
19
]. Background from
e
þ
e
!
q
q
is simulated with the
JETSET
[
20
] event generator;
JETSET
also generates ISR
events with a hadron invariant mass above
2GeV
=c
2
,and
therefore can be used to study the ISR background with
baryons in the final state. The dominant background pro-
cess,
e
þ
e
!
p
p
0
, is simulated separately. Its angular
and energy distributions are generated according to three-
body phase space.
The detector response is simulated using the
GEANT4
[
21
] package. The simulation takes into account the varia-
tions in the detector and beam background conditions over
the running period of the experiment.
1
Throughout this paper, the asterisk denotes quantities in the
e
þ
e
center-of-mass frame. All other variables except
p
are
defined in the laboratory frame.
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
092005 (2013)
092005-4
III. EVENT SELECTION
The preliminary selection of
e
þ
e
!
p
p
candidates
requires that all of the final-state particles be detected and
well reconstructed. Events are selected with at least two
tracks with opposite charge and a photon candidate with
E
>
3 GeV
and polar angle in the range
20
<
<
137
:
5
. Each charged-particle track must extrapolate to
the interaction region, have transverse momentum greater
than
0
:
1 GeV
=c
, have a polar angle in the range
25
:
8
<
<
137
:
5
, and be identified as a proton. Since a signifi-
cant fraction of the events contains beam-generated back-
ground photons and charged tracks, any number of extra
tracks and photons is allowed in an event.
The expected number of events from the background
processes
e
þ
e
!
þ
,
þ
, and
K
þ
K
ex-
ceeds the number of signal events by 2 to 3 orders of
magnitude. These backgrounds are significantly sup-
pressed by the requirement that both charged particles be
identified as protons. The suppression is a factor of
3
10
4
for pion and muon events, and a factor
10
4
for kaon events,
with a loss of approximately 30% of the signal events.
Further background suppression is based on kinematic
fitting. We perform a kinematic fit to the
e
þ
e
!
h
þ
h
hypothesis with requirements of energy and momentum
conservation. Here
h
can be
,
K
,or
p
, and
refers to the
photon with highest c.m. energy. In the case of events with
more than two charged tracks, the fit uses the parameters of
the two oppositely charged tracks that have the minimum
distance from the interaction point in the azimuthal plane.
Two conditions on the
2
of the kinematic fits are used:
2
p
<
30
and
2
K
>
30
, where
2
p
and
2
K
are the
2
values
for the proton and kaon mass hypotheses, respectively. The
2
p
distribution for simulated
p
p
events is shown in
Fig.
1
. The tail at high
2
is due to events with extra soft
photons emitted in the initial state. The dashed histogram
represents the
2
p
distribution for
K
þ
K
simulated
events. The
2
requirements provide additional back-
ground suppression by a factor of 50 for pion and muon
events, and a factor of 30 for kaon events, with a loss of
25% of the signal events.
The
p
p
invariant mass distribution is shown in Fig.
2
for
the 8298 selected data events. Most of the events have
p
p
mass less than
3 GeV
=c
2
. Signals from
J=
c
!
p
p
and
c
ð
2
S
Þ!
p
p
decays are clearly seen.
IV. BACKGROUND EVALUATION
Potential sources of background in the sample of
selected
e
þ
e
!
p
p
candidates are the processes
e
þ
e
!
þ
,
e
þ
e
!
K
þ
K
,
e
þ
e
!
þ
,
and
e
þ
e
!
e
þ
e
, in which the charged particles are
misidentified as protons, and processes with protons and
neutral particle(s) in the final state, such as
e
þ
e
!
p
p
0
,
p
p
0
.
The contribution of final-state radiation to the total cross
section for the process
e
þ
e
!
p
p
in the mass region of
interest (below 4.5 GeV) was estimated in Ref. [
1
] and
found to be negligible (about
10
3
of the ISR cross
section).
A. Background contributions from
e
þ
e
!
þ
,
e
þ
e
!
K
þ
K
,
e
þ
e
!
e
þ
e
, and
e
þ
e
!
þ
The background contribution from
e
þ
e
!
þ
is
estimated using Monte Carlo (MC) simulation. To study
how the simulation reproduces misidentification probabil-
ity for pions, special pion-enriched data samples are
χ
p
2
Events/(2 units)
0
20000
40000
60000
0
20
40
60
80
100
FIG. 1. The
2
p
distribution for simulated
e
þ
e
!
p
p
(solid
histogram) and
e
þ
e
!
K
þ
K
(dashed histogram, arbitrary
normalization) events.
M
pp
–
(GeV/c
2
)
Events/(20 MeV/c
2
)
0
100
200
300
400
234
FIG. 2. The
p
p
invariant mass spectrum for the selected data
p
p
candidates. The left edge of the plot corresponds to the
p
p
threshold.
STUDY OF
e
þ
e
!
p
p
VIA INITIAL-
...
PHYSICAL REVIEW D
87,
092005 (2013)
092005-5
selected with the following requirements on PID and on the
2
of the kinematic fits:
(1) one proton candidate,
2
<
20
;
(2) one proton candidate,
2
p
<
30
,
2
K
>
30
;
(3) two proton candidates,
2
<
20
.
Here
2
is the
2
for the pion mass hypothesis.
The distributions of the invariant mass calculated under
the pion-mass hypothesis (
M
) for data events selected
with criteria 2 and 3 are shown in Fig.
3
. The spectra are fit
with a sum of the mass spectra for simulated
þ
events (
-meson line shape with
!
-
interference) and a
linear background term. The numbers of
events with
0
:
5
<M
<
1 GeV
=c
2
obtained from the fits for selec-
tions 1–3 are listed in Table
I
, together with the corre-
sponding numbers of events expected from the
þ
MC simulation.
Since the simulation correctly predicts the numbers of
pion events for selections 1–3, we use it to estimate the
pion background for our standard selection. We observe no
events satisfying the standard selection criteria in the
MC sample. The corresponding upper limit on the
background in the data sample is 5.2 events at 90% con-
fidence level (C.L.). The estimated pion background is less
than 0.1% of the number of selected
p
p
candidates.
Similarly, the number of
e
þ
e
!
K
þ
K
events can be
estimated from the number of events in the
meson peak
in the distribution of invariant mass of the charged particles
calculated under the kaon hypothesis. It is found that the
K
þ
K
MC simulation predicts reasonably well the num-
bers of kaon events in the data sample with one identified
kaon and the standard
2
conditions, and in the data sample
with two identified kaons and
2
K
<
20
. Therefore we use
the MC simulation to estimate the kaon background for the
standard selection. The estimated background,
1
:
6
0
:
8
events, is significantly less than 0.1% of the number of data
events selected.
The specific kinematic properties of the
e
þ
e
!
e
þ
e
process are used to estimate the electron background. In a
significant fraction (about 50%) of detected
e
þ
e
events
the photon is emitted along the final electron direction.
These events have
e
þ
e
invariant mass in the range from
3to
7 GeV
=c
2
and can be selected by the requirement
cos
c
<
0
:
98
, where
c
is the angle between the two
charged tracks in the initial
e
þ
e
c.m. frame. In the sample
of selected
p
p
candidates we observe no events having the
above characteristics. The corresponding 90% C.L. upper
limit on the
e
þ
e
background in the data sample is 4.6
events (2 events with
M
p
p
<
4
:
5 GeV
=c
2
).
To compare MC simulation and data for the process
e
þ
e
!
þ
, we use a subsample of events selected
with the requirement that both charged particles be identi-
fied as muons. Muon identification is based on instru-
mented magnetic flux return information, and does not
use ring-imaging Cherenkov detector or
dE=dx
informa-
tion, which are necessary for proton identification. In the
data samples with one or two identified protons obtained
with the standard
2
selection, we select 86 and 2 muon-
identified events, respectively. These numbers can be com-
pared with
60
16
and zero events expected from the
e
þ
e
!
þ
simulation. Taking into account that
the ratio of the total number of
þ
events to those
with two identified muons is about two to one, we estimate
TABLE I. The numbers of
events for data and MC
simulation with
0
:
5
<M
<
1 GeV
=c
2
that satisfy different
selection criteria for data and MC simulation. The data numbers
are obtained from the fits to the
M
distributions described in
the text.
Selection
Data
MC simulation
1
15310
160
14800
180
2
400
60
460
30
3
41
848
11
M
ππ
(GeV/c
2
)
Events/(10 MeV/c
2
)
0
20
40
60
0.5
0.6
0.7
0.8
0.9
1
(a)
M
ππ
(GeV/c
2
)
Events/(10 MeV/c
2
)
0
2
4
6
0.5
0.6
0.7
0.8
0.9
1
(b)
FIG. 3. (a) The
M
spectrum for data events with
2
p
<
30
and
2
K
>
30
, and one proton candidate (selection 2 in the text);
(b) the same spectrum for data events with
2
<
20
and two
proton candidates (selection 3 in the text). The histograms are
the results of the fit described in the text.
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
092005 (2013)
092005-6
the
þ
background for the standard selection criteria
to be
4
:
0
2
:
8
events.
The combined background from the processes
e
þ
e
!
h
þ
h
,
h
¼
,
K
,
e
,
is less than 0.2% of the number of
selected
p
p
candidates, and so can be neglected.
B. Background from
e
þ
e
!
p
p
0
The main source of background for the process under
study is
e
þ
e
!
p
p
0
. The
p
p
0
events with an unde-
tected low-energy photon, or with merged photons from
the
0
decay, are kinematically reconstructed with a low
2
p
value and so cannot be separated from the signal
process. This background is studied by selecting a special
subsample of data events containing two charged particles
identified as protons and at least two photons with energy
greater than 0.1 GeV, one of which must have c.m. energy
above 3 GeV. The two-photon invariant mass
M
is
required to be in the range
0
:
07
–
0
:
20 GeV
=c
2
, which is
centered on the nominal
0
mass. A kinematic fit to the
e
þ
e
!
p
p
hypothesis is then performed. Conditions
on the
2
of the kinematic fit (
2
<
25
) and the two-photon
invariant mass (
0
:
1025
<M
<
0
:
1675 GeV
=c
2
) are im-
posed in order to select
e
þ
e
!
p
p
0
candidates.
Possible background is estimated using the
M
sidebands
0
:
0700
<M
<
0
:
1025 GeV
=c
2
and
0
:
1675
<M
<
0
:
2000 GeV
=c
2
. The
M
p
p
spectra and
cos
p
distributions
for data events from the signal and sideband
M
regions
are shown in Fig.
4
. The total number of selected events is
148 in the signal region and 12 in the sidebands. The
expected number of
e
þ
e
!
p
p
0
events in the
M
sidebands is 5.4.
To study the
e
þ
e
!
p
p
0
background, the sample of
simulated
e
þ
e
!
p
p
0
events is generated according to
three-body phase space, but with an additional weight
proportional to
ð
M
p
p
2
m
p
Þ
3
=
2
to imitate the
M
p
p
distri-
bution observed in data. The simulation well reproduces
the observed
cos
p
distribution.
In Fig.
5
the
cos
distribution for selected data and
simulated
e
þ
e
!
p
p
0
events is shown, where
is the
0
polar angle in the
e
þ
e
c.m. frame. It is seen that the
data and simulated distributions differ slightly. Since we do
not observe a significant variation of the
cos
distribution
with
M
p
p
in data, we use the data distribution averaged
over
M
p
p
(Fig.
5
) to reweight the
e
þ
e
!
p
p
0
simulation.
From the reweighted simulation, we calculate the ratio
(
K
MC
) of the
M
p
p
distribution for events selected with the
standard
p
p
criteria to that selected with the
p
p
0
crite-
ria. The value of the ratio
K
MC
varies from 3.4 near
p
p
threshold to 2.0 at
5 GeV
=c
2
. The expected
M
p
p
spectrum
for the
e
þ
e
!
p
p
0
background events satisfying the
p
p
selection criteria is evaluated as
K
MC
ð
M
p
p
Þ
ð
dN=dM
p
p
Þ
data
, where
ð
dN=dM
p
p
Þ
data
is the mass distribu-
tion for
e
þ
e
!
p
p
0
events obtained above [Fig.
4(a)
].
The spectrum is shown in Fig.
6
. The number of selected
e
þ
e
!
p
p
candidates and the expected number of
e
þ
e
!
p
p
0
background events are given for different
p
p
mass ranges in Table
II
. The background increases from
5% near
p
p
threshold to 50% at
M
p
p
4GeV
=c
2
.Above
4
:
5GeV
=c
2
, the number of observed
p
p
candidates is
consistent with expected
p
p
0
background.
C. Other sources of background
Other possible background sources are ISR processes
with higher final-state multiplicity (
e
þ
e
!
p
p
0
; p
p
2
0
;
...
), and direct
e
þ
e
annihilation pro-
cesses other than
e
þ
e
!
p
p
0
(
e
þ
e
!
p
p ; e
þ
e
!
p
p
2
0
;
...
). All of these processes are simulated by
JETSET
, which predicts the ISR background to be
55
6
events and the direct annihilation background to be
40
5
events. The total predicted background from these two
M
pp
–
(GeV/c
2
)
Events/(50 MeV/c
2
)
(a)
0
5
10
15
2345
cos
θ
p
Events/0.2
0
10
20
30
-1
-0.5
0
0.5
1
(b)
FIG. 4 (color online). (a) The
M
p
p
spectrum and (b) the
cos
p
distribution for selected
e
þ
e
!
p
p
0
candidates in data. In
each figure, the shaded histogram shows the background con-
tribution estimated from the
M
sidebands.
STUDY OF
e
þ
e
!
p
p
VIA INITIAL-
...
PHYSICAL REVIEW D
87,
092005 (2013)
092005-7
sources is about 1.2% of the number of selected
p
p
candidates. We do not perform a detailed study of these
background processes. Their contribution is estimated
from data by using the
2
sideband region, as described
below in Sec.
IV D
.
D. Background subtraction
The expected number of background events estimated in
the previous sections is summarized in Table
III
. The
‘‘Other ISR’’ and ‘‘
e
þ
e
’’ columns show the background
contributions estimated with
JETSET
that result from ISR
processes and from
e
þ
e
annihilation processes other than
e
þ
e
!
p
p
0
. Because
JETSET
has not been precisely
validated for the rare processes contributing to the
p
p
candidate sample, we use a method of background
estimation that is based on the difference in
2
distribu-
tions between signal and background events. The first and
second rows in Table
III
show the expected numbers of
signal and background events with
2
p
<
30
(
N
1
) and
30
<
2
p
<
60
(
N
2
). The last row lists the ratio
i
¼
N
2
=N
1
.
The coefficients
i
for signal events and for background
events from the ‘‘
e
þ
e
’’ and ‘‘Other ISR’’ columns are
very different. This difference is used to estimate and
subtract the background from these two sources. The num-
bers of signal and background (from ‘‘
e
þ
e
’’ and ‘‘ISR’’
sources) events with
2
p
<
30
can be calculated as
N
sig
¼
N
0
1
N
0
2
=
bkg
1
p
p
=
bkg
;N
bkg
¼
N
0
1
N
sig
;
(4)
where
N
0
1
and
N
0
2
are the numbers of data events in the
signal and sideband
2
regions after subtraction of the
p
p
0
background, and
bkg
is the
N
2
=N
1
ratio averaged
over all background processes of the
e
þ
e
and ISR types.
For this coefficient,
bkg
¼
1
:
6
0
:
3
is used; it is the
average of
e
þ
e
and
ISR
with the uncertainty
ð
e
þ
e
ISR
Þ
=
2
. The
p
p
coefficient is determined from signal
simulation and corrected for the data-simulation difference
in the
2
distribution. The data-simulation difference is
studied using
e
þ
e
!
þ
events, which are very
similar kinematically to the signal events and can be se-
lected with negligible background. The ratio of the
coefficients for
e
þ
e
!
þ
data and simulation is
independent of the
þ
mass and is equal to
1
:
008
0
:
008
. The corrected
p
p
value varies from 0.043 at
p
p
threshold to 0.048 at
4
:
5 GeV
=c
2
.
The total numbers of
e
þ
e
!
p
p
events (
N
sig
) and
background events from
e
þ
e
and ISR sources (
N
bkg
)in
M
pp
–
(GeV/c
2
)
Events/(50 MeV/c
2
)
1
10
10
2
2345
FIG. 6. The expected
M
p
p
spectrum for
e
þ
e
!
p
p
0
events
selected with the standard
p
p
criteria. The spectrum is ob-
tained by scaling the data distribution shown in Fig.
4(a)
by the
factor
K
MC
ð
M
p
p
Þ
described in the text.
cos
θ
π
*
Events/1.5
0
10
20
30
40
-0.5
0
0.5
FIG. 5. The
cos
distribution for
e
þ
e
!
p
p
0
event
candidates for data (points with error bars) and simulation
(histogram).
TABLE II. The number of selected
p
p
candidates,
N
p
p
, and
the number of background events from the
e
þ
e
!
p
p
0
process,
N
p
p
0
, for different ranges of
M
p
p
. The
p
p
mass ranges
near the
J=
c
and
c
ð
2
S
Þ
resonances are excluded.
M
p
p
(
GeV
=c
2
)
<
2
:
50
2.50–3.05 3.15–3.60 3.75–4.50
>
4
:
5
N
p
p
6695
592
76
29
9
N
p
p
0
321
37 66
15 26
917
66
3
TABLE III. The number of selected
p
p
candidates from the
mass region
M
p
p
<
4
:
5 GeV
=c
2
with
2
p
<
30
(
N
1
) and
30
<
2
p
<
60
(
N
2
) for signal and for different background processes;
i
is the ratio
N
2
=N
1
obtained from simulation. The first column
shows the numbers of
p
p
candidates selected in data. The
numbers for
e
þ
e
!
p
p
are obtained from data using the
background subtraction procedure described in the text.
Data
p
p
0
e
þ
e
Other ISR
p
p
N
1
8298
448
42
40
555
6
7741
113
N
2
560
79
776
774
7
337
16
i
0
:
175
0
:
04 1
:
88
0
:
29 1
:
34
0
:
18 0
:
0435
0
:
0020
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
092005 (2013)
092005-8
the signal region are found to be
7741
95
62
and
109
16
25
, respectively. The systematic uncertainty
on
N
sig
is dominated by the uncertainty in the
p
p
0
background. The number of background events is in
good agreement with the estimate from simulation,
ð
40
5
Þþð
55
6
Þ¼
95
8
. The total background in
the signal
2
p
region is
531
51
events, which is about
7% of the number of signal events.
The background subtraction procedure is performed in
each
p
p
mass interval. The number of selected events for
each interval after background subtraction and correction
for event migration between intervals (see Sec.
VII
)is
listed in Table
VI
below. The events from
J=
c
and
c
ð
2
S
Þ
decays are subtracted from the contents of the
corresponding intervals.
V. ANGULAR DISTRIBUTIONS
The modulus of the ratio of the electric and magnetic
form factors can be extracted from an analysis of the dis-
tribution of
p
, the angle between the proton momentum in
the
p
p
rest frame, and the momentum of the
p
p
system in
the
e
þ
e
c.m. frame. This distribution is given by
dN
d
cos
p
¼
A
H
M
ð
cos
p
;M
p
p
Þ
þ
G
E
G
M
2
H
E
ð
cos
p
;M
p
p
Þ
:
(5)
The angular dependences of the functions
H
M
ð
cos
p
;M
p
p
Þ
and
H
E
ð
cos
p
;M
p
p
Þ
are approximately
1
þ
cos
2
p
and
sin
2
p
, almost independent of
p
p
invariant mass, while
their relative normalization strongly depends on mass,
mainly due to the factor
2
m
2
p
=M
2
p
p
contained in the
G
E
term [see Eq. (
2
)].
The angular distributions are studied in six intervals of
p
p
invariant mass from threshold to
3 GeV
=c
2
. The mass
intervals, the corresponding numbers of selected events,
and the estimated numbers of background events are listed
in Table
IV
. The angular distributions are shown in Fig.
7
.
The background is subtracted in each angular bin using the
procedure described in Sec.
IV D
. The distributions are fit
to Eq. (
5
) with two free parameters:
A
(the overall normal-
ization) and
j
G
E
=G
M
j
. The functions
H
M
and
H
E
are
replaced by the histograms obtained from MC simulation
with the
p
p
selection criteria applied.
Imperfect simulation of PID, tracking, and photon effi-
ciency may lead to a data-simulation difference in the
angular dependence of the detection efficiency. The effi-
ciency corrections for the data-simulation differences are
discussed in Sec.
VI
. They are applied to the angular
distributions obtained from simulation. It should be noted
that the corrections change the shape of the angular dis-
tributions very little. This is demonstrated in Fig.
8
, where
the angular dependence of the detection efficiency before
and after the corrections is shown. The deviations from
uniform efficiency, which do not exceed 10%, arise from
the momentum dependence of proton/antiproton particle
identification efficiency. A more detailed description of the
fitting procedure can be found in Ref. [
1
].
The fit results are shown in Fig.
7
as histograms. The
obtained
j
G
E
=G
M
j
values are listed in Table
IV
and shown
in Fig.
9
. The curve in Fig.
9
[
1
þ
ax=
ð
1
þ
bx
3
Þ
, where
x
¼
M
p
p
2
m
p
GeV
=c
2
] is used to determine the detec-
tion efficiency (see Sec.
VI
). The quoted errors on
j
G
E
=G
M
j
are statistical and systematic, respectively. The
dominant contribution to the systematic error is due to the
uncertainty in the
p
p
0
background.
The only previous measurement of the
j
G
E
=G
M
j
ratio
comes from the PS170 experiment [
12
]. The ratio was
measured at five points between
1
:
92 GeV
=c
2
and
2
:
04 GeV
=c
2
with an accuracy of 30%–40% (see Fig.
9
).
For all points it was found to be consistent with unity. The
average of the PS170 measurements evaluated under the
assumption that the errors are purely statistical is
0
:
90
0
:
14
. The
BABAR
results are significantly larger for
M
p
p
<
2
:
1 GeV
=c
2
, and extend the measurements up to
3 GeV
=c
2
.
We also search for an asymmetry in the proton angular
distribution. The lowest-order one-photon mechanism for
proton-antiproton production predicts a symmetric angular
distribution. An asymmetry arises from higher-order con-
tributions, in particular from two-photon exchange. Two-
photon exchange is discussed (see, for example, Ref. [
22
])
as a possible source of the difference observed in
ep
scattering between the
G
E
=G
M
measurements obtained
with two different experimental techniques, namely the
Rosenbluth method [
23
], which uses the analysis of angu-
lar distributions, and the polarization method [
24
–
26
],
which is based on the measurement of the ratio of the
transverse and longitudinal polarization of the recoil
proton.
A search for an asymmetry using previous
BABAR
e
þ
e
!
p
p
results [
1
] is described in Ref. [
27
]. No
asymmetry was observed within the statistical error of
2%. It should be noted that the authors of Ref. [
27
] did
TABLE IV. The number of selected
p
p
candidates (
N
) and
the number of background events (
N
bkg
) for each
p
p
mass
interval;
j
G
E
=G
M
j
is the fitted ratio of form factors.
M
p
p
,
GeV
=c
2
NN
bkg
j
G
E
=G
M
j
1.877–1.950
1162
19
10
1
:
36
þ
0
:
15
þ
0
:
05
0
:
14
0
:
04
1.950–2.025
1290
53
16
1
:
48
þ
0
:
16
þ
0
:
06
0
:
14
0
:
05
2.025–2.100
1328
63
14
1
:
39
þ
0
:
15
þ
0
:
07
0
:
14
0
:
07
2.100–2.200
1444
118
28
1
:
26
þ
0
:
14
þ
0
:
10
0
:
13
0
:
09
2.200–2.400
1160
126
26
1
:
04
þ
0
:
16
þ
0
:
10
0
:
16
0
:
10
2.400–3.000
879
122
22
1
:
04
þ
0
:
24
þ
0
:
15
0
:
25
0
:
15
STUDY OF
e
þ
e
!
p
p
VIA INITIAL-
...
PHYSICAL REVIEW D
87,
092005 (2013)
092005-9
cos
θ
p
Events/0.2
0
50
100
150
-1
-0.5
0
0.5
1
(a)
cos
θ
p
Events/0.2
0
50
100
150
-1
-0.5
0
0.5
1
(b)
cos
θ
p
Events/0.2
0
50
100
150
-1
-0.5
0
0.5
1
(c)
cos
θ
p
Events/0.2
0
50
100
150
-1
-0.5
0
0.5
1
(d)
cos
θ
p
Events/0.2
0
50
100
-1
-0.5
0
0.5
1
(e)
cos
θ
p
Events/0.2
0
25
50
75
100
-1
-0.5
0
0.5
1
(f)
FIG. 7. The
cos
p
distributions for different
p
p
mass regions: (a)
1
:
877
–
1
:
950 GeV
=c
2
, (b)
1
:
950
–
2
:
025 GeV
=c
2
,
(c)
2
:
025
–
2
:
100 GeV
=c
2
, (d)
2
:
100
–
2
:
200 GeV
=c
2
, (e)
2
:
200
–
2
:
400 GeV
=c
2
,(f)
2
:
400
–
3
:
000 GeV
=c
2
. The points with
error bars show the data distributions after background subtraction. The histograms result from the fits: the dashed
histograms correspond to the magnetic form factor contributions and the dot-dashed histograms to the electric form factor
contributions.
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
092005 (2013)
092005-10
not take into account the angular asymmetry of the detec-
tion efficiency, which is seen in Fig.
8
and in a similar plot
in Ref. [
1
].
To measure the asymmetry we use the data with
p
p
mass less than
3 GeV
=c
2
. The
cos
p
distribution is fitted
as described above, and the result is shown in Fig.
10
. Since
the MC simulation uses a model with one-photon ex-
change, the asymmetry in the fitted histogram is due to
the asymmetry in the detection efficiency. To remove
detector effects we take the ratio of the data distribution
to the fitted simulated distribution. This ratio is shown in
Fig.
11
. A fit of a linear function to the data yields a slope
parameter value
0
:
041
0
:
026
0
:
005
. The systematic
error on the slope is estimated conservatively as the maxi-
mum slope given by an efficiency correction. The correc-
tion for the data-simulation difference in antiproton
nuclear interactions (see Sec.
VI
) is found to yield the
largest angular variation.
We then calculate the integral asymmetry
A
cos
p
¼
ð
cos
p
>
0
Þ
ð
cos
p
<
0
Þ
ð
cos
p
>
0
Þþ
ð
cos
p
<
0
Þ
¼
0
:
025
0
:
014
0
:
003
;
(6)
cos
θ
p
Detection efficiency
0.16
0.18
0.2
0.22
-1
-0.5
0
0.5
1
FIG. 8 (color online). The angular dependence of the detection
efficiency for simulated events with
M
p
p
<
2
:
5 GeV
=c
2
before
(open squares) and after (filled circles) correction for data-
simulation differences in detector response.
BABAR
PS170
M
pp
–
(GeV/c
2
)
|G
E
/G
M
|
0.5
1
1.5
2
2.25
2.5
2.75
3
FIG. 9 (color online). The measured
j
G
E
=G
M
j
mass depen-
dence. Filled circles depict
BABAR
data. Open circles show
PS170 data [
12
]. The curve is the the result of the fit described
in the text.
cos
θ
p
Events/0.2
0
200
400
600
800
-1
-0.5
0
0.5
1
FIG. 10. The
cos
p
distribution for the mass region from
threshold to
3 GeV
=c
2
. The points with error bars show the data
distribution after background subtraction; the solid histogram is
the fit result. The dashed and dot-dashed histograms show the
contributions of the terms corresponding to the magnetic and
electric form factors, respectively.
cos
θ
p
(d
σ
/dcos
θ
p
)
meas
/(d
σ
/dcos
θ
p
)
fit
0.9
1.0
1.1
-1
-0.5
0
0.5
1
FIG. 11. The ratio of the data distribution from Fig.
10
to the
fitted simulated distribution. The line shows the result of the fit
of a linear function to the data points.
STUDY OF
e
þ
e
!
p
p
VIA INITIAL-
...
PHYSICAL REVIEW D
87,
092005 (2013)
092005-11
where
ð
cos
p
>
0
Þ
and
ð
cos
p
<
0
Þ
are the cross sec-
tions for
e
þ
e
!
p
p
events with
M
p
p
<
3 GeV
=c
2
in-
tegrated over the angular regions with
cos
p
>
0
and
cos
p
<
0
, respectively. The fitted slope value and the
integral asymmetry are consistent with zero. The value of
the asymmetry extracted from experiment depends on the
selection criteria used, in particular, on the effective energy
limit for an extra photon emitted from the initial or final
state. In our analysis, this limit is determined by the
condition
2
p
<
30
and is about 100 MeV.
VI. DETECTION EFFICIENCY
The detection efficiency, which is determined using MC
simulation, is the ratio of true
p
p
mass distributions ob-
tained after and before applying the selection criteria.
Since the
e
þ
e
!
p
p
differential cross section depends
on two form factors, the detection efficiency cannot be
determined in a model-independent way. For
M
p
p
<
3 GeV
=c
2
, we use a model with the
j
G
E
=G
M
j
ratio ob-
tained from the fits to the experimental angular distribu-
tions (curve in Fig.
9
). The model error due to the
uncertainty in the measured
j
G
E
=G
M
j
ratio is estimated
to be below 1%. For
M
p
p
>
3 GeV
=c
2
, where the
j
G
E
=G
M
j
ratio is not measured, a model with
j
G
E
=G
M
j¼
1
is used. The model uncertainty for this mass region is
estimated as the maximum difference between the detec-
tion efficiencies obtained with
G
E
¼
0
or
G
M
¼
0
, and the
efficiency for
j
G
E
=G
M
j¼
1
. The uncertainty does not
exceed 4%. The mass dependence of the detection effi-
ciency is shown in Fig.
12
.
The efficiency determined from MC simulation (
"
MC
)
is corrected for data-simulation differences in detector
response:
"
¼
"
MC
Y
ð
1
þ
i
Þ
;
(7)
where the
i
are efficiency corrections. They are summa-
rized in Table
V
. Procedures for determining most of the
efficiency corrections are described in Ref. [
1
]. Higher
statistics and better understanding of detector performance
allow us to decrease the uncertainties on the corrections for
imperfect simulation of
2
distributions, track reconstruc-
tion, and PID. The PID procedure in this analysis differs
from that used in Ref. [
1
]. This leads to a significant change
of the PID correction value. The correction for photon
inefficiency listed in Table
V
is a sum of corrections for
calorimeter inefficiency (mainly due to dead calorimeter
channels) and photon conversion in the detector material
before the DCH. The latter correction, which is about
0
:
4%
, was determined in the previous analysis [
1
] with
the wrong sign.
A new effect studied in this analysis is track overlap in
the DCH. The effect of track overlap can be observed in the
distribution of the parameter
’
¼
’
þ
’
, where
’
þ
and
’
are the azimuthal angles at the production vertex of
positive and negative tracks, respectively. The detection
efficiency for simulated
e
þ
e
!
p
p
events as a function
of
’
is shown in Fig.
13
.
M
pp
–
(GeV/c
2
)
Detection efficiency
0.16
0.18
0.2
0.22
234
FIG. 12. The
p
p
mass dependence of the detection efficiency
obtained from MC simulation.
TABLE V. The values of the different efficiency corrections
i
for
p
p
invariant mass 1.9, 3.0, and
4
:
5 GeV
=c
2
.
Effect
i
ð
1
:
9
Þ
[%]
i
ð
3
Þ
[%]
i
ð
4
:
5
Þ
[%]
2
p
<
30
0
:
5
0
:
1
0
:
9
0
:
1
1
:
5
0
:
2
2
K
>
30
0
:
0
0
:
40
:
0
0
:
40
:
0
0
:
4
Track overlap
0
:
0
1
:
5
Nuclear interaction
0
:
8
0
:
41
:
1
0
:
41
:
0
0
:
4
Track reconstruction
0
:
0
0
:
50
:
0
0
:
50
:
0
0
:
5
PID
1
:
9
2
:
0
1
:
9
2
:
0
1
:
9
2
:
0
Photon inefficiency
1
:
9
0
:
1
1
:
7
0
:
1
1
:
7
0
:
1
Trigger and filters
0
:
7
0
:
6
0
:
1
0
:
5
0
:
1
0
:
5
Total
4
:
2
2
:
6
3
:
5
2
:
2
4
:
2
2
:
2
∆φ
±
(rad)
Detection efficiency
0.1
0.15
0.2
0.25
0.3
-1
-0.5
0
0.5
1
FIG. 13. The detection efficiency for
e
þ
e
!
p
p
events as a
function of
’
obtained from MC simulation.
J. P. LEES
et al.
PHYSICAL REVIEW D
87,
092005 (2013)
092005-12