of 16
Study of the
e
þ
e
K
þ
K
reaction in the energy range from 2.6 to 8.0 GeV
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
M. J. Lee,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
7
A. Khan,
8
V. E. Blinov,
9a,9b,9c
A. R. Buzykaev,
9a
V. P. Druzhinin,
9a,9b
V. B. Golubev,
9a,9b
E. A. Kravchenko,
9a,9b
A. P. Onuchin,
9a,9b,9c
S. I. Serednyakov,
9a,9b
Yu. I. Skovpen,
9a,9b
E. P. Solodov,
9a,9b
K. Yu. Todyshev,
9a,9b
A. J. Lankford,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
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
W. Panduro Vazquez,
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
J. Kim,
14
T. S. Miyashita,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
M. Röhrken,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
B. G. Pushpawela,
15
M. D. Sokoloff,
15
L. Sun,
15
W. T. Ford,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17
,
W. H. Toki,
17
B. Spaan,
18
D. Bernard,
19
M. Verderi,
19
S. Playfer,
20
D. Bettoni,
21a
C. Bozzi,
21a
R. Calabrese,
21a,21b
G. Cibinetto,
21a,21b
E. Fioravanti,
21a,21b
I. Garzia,
21a,21b
E. Luppi,
21a,21b
L. Piemontese,
21a
V. Santoro,
21a
A. Calcaterra,
22
R. de Sangro,
22
G. Finocchiaro,
22
S. Martellotti,
22
P. Patteri,
22
I. M. Peruzzi,
22
M. Piccolo,
22
A. Zallo,
22
R. Contri,
23a,23b
M. R. Monge,
23a,23b
S. Passaggio,
23a
C. Patrignani,
23a,23b
B. Bhuyan,
24
V. Prasad,
24
A. Adametz,
25
U. Uwer,
25
H. M. Lacker,
26
U. Mallik,
27
C. Chen,
28
J. Cochran,
28
S. Prell,
28
H. Ahmed,
29
A. V. Gritsan,
30
N. Arnaud,
31
M. Davier,
31
D. Derkach,
31
G. Grosdidier,
31
F. Le Diberder,
31
A. M. Lutz,
31
B. Malaescu,
31
,
P. Roudeau,
31
A. Stocchi,
31
G. Wormser,
31
D. J. Lange,
32
D. M. Wright,
32
J. P. Coleman,
33
J. R. Fry,
33
E. Gabathuler,
33
D. E. Hutchcroft,
33
D. J. Payne,
33
C. Touramanis,
33
A. J. Bevan,
34
F. Di Lodovico,
34
R. Sacco,
34
G. Cowan,
35
D. N. Brown,
36
C. L. Davis,
36
A. G. Denig,
37
M. Fritsch,
37
W. Gradl,
37
K. Griessinger,
37
A. Hafner,
37
K. R. Schubert,
37
R. J. Barlow,
38
G. D. Lafferty,
38
R. Cenci,
39
B. Hamilton,
39
A. Jawahery,
39
D. A. Roberts,
39
R. Cowan,
40
R. Cheaib,
41
P. M. Patel,
41
,*
S. H. Robertson,
41
N. Neri,
42a
F. Palombo,
42a,42b
L. Cremaldi,
43
R. Godang,
43
D. J. Summers,
43
M. Simard,
44
P. Taras,
44
G. De Nardo,
45a,45b
G. Onorato,
45a,45b
C. Sciacca,
45a,45b
G. Raven,
46
C. P. Jessop,
47
J. M. LoSecco,
47
K. Honscheid,
48
R. Kass,
48
M. Margoni,
49a,49b
M. Morandin,
49a
M. Posocco,
49a
M. Rotondo,
49a
G. Simi,
49a,49b
F. Simonetto,
49a,49b
R. Stroili,
49a,49b
S. Akar,
50
E. Ben-Haim,
50
M. Bomben,
50
G. R. Bonneaud,
50
H. Briand,
50
G. Calderini,
50
J. Chauveau,
50
Ph. Leruste,
50
G. Marchiori,
50
J. Ocariz,
50
M. Biasini,
51a,51b
E. Manoni,
51a
A. Rossi,
51a
C. Angelini,
52a,52b
G. Batignani,
52a,52b
S. Bettarini,
52a,52b
M. Carpinelli,
52a,52b
,**
G. Casarosa,
52a,52b
M. Chrzaszcz,
52a
F. Forti,
52a,52b
M. A. Giorgi,
52a,52b
A. Lusiani,
52a,52c
B. Oberhof,
52a,52b
E. Paoloni,
52a,52b
M. Rama,
52a
G. Rizzo,
52a,52b
J. J. Walsh,
52a
D. Lopes Pegna,
53
J. Olsen,
53
A. J. S. Smith,
53
F. Anulli,
54a
R. Faccini,
54a,54b
F. Ferrarotto,
54a
F. Ferroni,
54a,54b
M. Gaspero,
54a,54b
A. Pilloni,
54a,54b
G. Piredda,
54a
C. Bünger,
55
S. Dittrich,
55
O. Grünberg,
55
M. Hess,
55
T. Leddig,
55
C. Voß,
55
R. Waldi,
55
T. Adye,
56
E. O. Olaiya,
56
F. F. Wilson,
56
S. Emery,
57
G. Vasseur,
57
D. Aston,
58
D. J. Bard,
58
C. Cartaro,
58
M. R. Convery,
58
J. Dorfan,
58
G. P. Dubois-Felsmann,
58
M. Ebert,
58
R. C. Field,
58
B. G. Fulsom,
58
M. T. Graham,
58
C. Hast,
58
W. R. Innes,
58
P. Kim,
58
D. W. G. S. Leith,
58
S. Luitz,
58
V. Luth,
58
D. B. MacFarlane,
58
D. R. Muller,
58
H. Neal,
58
T. Pulliam,
58
B. N. Ratcliff,
58
A. Roodman,
58
R. H. Schindler,
58
A. Snyder,
58
D. Su,
58
M. K. Sullivan,
58
J. Va
vra,
58
W. J. Wisniewski,
58
H. W. Wulsin,
58
M. V. Purohit,
59
J. R. Wilson,
59
A. Randle-Conde,
60
S. J. Sekula,
60
M. Bellis,
61
P. R. Burchat,
61
E. M. T. Puccio,
61
M. S. Alam,
62
J. A. Ernst,
62
R. Gorodeisky,
63
N. Guttman,
63
D. R. Peimer,
63
A. Soffer,
63
S. M. Spanier,
64
J. L. Ritchie,
65
R. F. Schwitters,
65
J. M. Izen,
66
X. C. Lou,
66
F. Bianchi,
67a,67b
F. De Mori,
67a,67b
A. Filippi,
67a
D. Gamba,
67a,67b
L. Lanceri,
68a,68b
L. Vitale,
68a,68b
F. Martinez-Vidal,
69
A. Oyanguren,
69
J. Albert,
70
Sw. Banerjee,
70
A. Beaulieu,
70
F. U. Bernlochner,
70
H. H. F. Choi,
70
G. J. King,
70
R. Kowalewski,
70
M. J. Lewczuk,
70
T. Lueck,
70
I. M. Nugent,
70
J. M. Roney,
70
R. J. Sobie,
70
N. Tasneem,
70
T. J. Gershon,
71
P. F. Harrison,
71
T. E. Latham,
71
H. R. Band,
72
S. Dasu,
72
Y. Pan,
72
R. Prepost,
72
and S. L. Wu
72
(The
B
A
B
AR
Collaboration)
1
Laboratoire d
Annecy-le-Vieux de Physique des Particules (LAPP), Université 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, Università 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 Universität Bochum, Institut für 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
9a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
9b
Novosibirsk State University, Novosibirsk 630090, Russia
9c
Novosibirsk State Technical University, Novosibirsk 630092, Russia
10
University of California at Irvine, Irvine, California 92697, USA
PHYSICAL REVIEW D
92,
072008 (2015)
1550-7998
=
2015
=
92(7)
=
072008(16)
072008-1
© 2015 American Physical Society
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 Universität Dortmund, Fakultät Physik, D-44221 Dortmund, Germany
19
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
20
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
21a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
21b
Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, I-44122 Ferrara, Italy
22
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
23a
INFN Sezione di Genova, I-16146 Genova, Italy
23b
Dipartimento di Fisica, Università di Genova, I-16146 Genova, Italy
24
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
25
Universität Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
26
Humboldt-Universität zu Berlin, Institut für Physik, D-12489 Berlin, Germany
27
University of Iowa, Iowa City, Iowa 52242, USA
28
Iowa State University, Ames, Iowa 50011-3160, USA
29
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudi Arabia
30
Johns Hopkins University, Baltimore, Maryland 21218, USA
31
Laboratoire de l
Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d
Orsay, F-91898 Orsay Cedex, France
32
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
33
University of Liverpool, Liverpool L69 7ZE, United Kingdom
34
Queen Mary University of London, London E1 4NS, United Kingdom
35
University of London, Royal Holloway and Bedford New College,
Egham, Surrey TW20 0EX, United Kingdom
36
University of Louisville, Louisville, Kentucky 40292, USA
37
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
38
University of Manchester, Manchester M13 9PL, United Kingdom
39
University of Maryland, College Park, Maryland 20742, USA
40
Massachusetts Institute of Technology, Laboratory for Nuclear Science,
Cambridge, Massachusetts 02139, USA
41
McGill University, Montréal, Québec, Canada H3A 2T8
42a
INFN Sezione di Milano, I-20133 Milano, Italy
42b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
43
University of Mississippi, University, Mississippi 38677, USA
44
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
45a
INFN Sezione di Napoli, I-80126 Napoli, Italy
45b
Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy
46
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, Netherlands
47
University of Notre Dame, Notre Dame, Indiana 46556, USA
48
Ohio State University, Columbus, Ohio 43210, USA
49a
INFN Sezione di Padova, I-35131 Padova, Italy
49b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
50
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie
Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France
51a
INFN Sezione di Perugia, I-06123 Perugia, Italy
51b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
52a
INFN Sezione di Pisa, I-56127 Pisa, Italy
52b
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
52c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
53
Princeton University, Princeton, New Jersey 08544, USA
54a
INFN Sezione di Roma, I-00185 Roma, Italy
54b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
55
Universität Rostock, D-18051 Rostock, Germany
56
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
J. P. LEES
et al.
PHYSICAL REVIEW D
92,
072008 (2015)
072008-2
57
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
58
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
59
University of South Carolina, Columbia, South Carolina 29208, USA
60
Southern Methodist University, Dallas, Texas 75275, USA
61
Stanford University, Stanford, California 94305-4060, USA
62
State University of New York, Albany, New York 12222, USA
63
Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
64
University of Tennessee, Knoxville, Tennessee 37996, USA
65
University of Texas at Austin, Austin, Texas 78712, USA
66
University of Texas at Dallas, Richardson, Texas 75083, USA
67a
INFN Sezione di Torino, I-10125 Torino, Italy
67b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
68a
INFN Sezione di Trieste, I-34127 Trieste, Italy
68b
Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
69
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
70
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
71
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
72
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 17 July 2015; published 20 October 2015)
The
e
þ
e
K
þ
K
cross section and charged-kaon electromagnetic form factor are measured in the
e
þ
e
center-of-mass energy range (
E
) from 2.6 to 8.0 GeV using the initial-state radiation technique with
an undetected photon. The study is performed using
469
fb
1
of data collected with the
BABAR
detector at
the PEP-II2
e
þ
e
collider at center-of-mass energies near 10.6 GeV. The form factor is found to decrease
with energy faster than
1
=E
2
and approaches the asymptotic QCD prediction. Production of the
K
þ
K
final
state through the
J=
ψ
and
ψ
ð
2
S
Þ
intermediate states is observed. The results for the kaon form factor are
used together with data from other experiments to perform a model-independent determination of the
relative phases between electromagnetic (single-photon) and strong amplitudes in
J=
ψ
and
ψ
ð
2
S
Þ
K
þ
K
decays. The values of the branching fractions measured in the reaction
e
þ
e
K
þ
K
are shifted
relative to their true values due to interference between resonant and nonresonant amplitudes. The values of
these shifts are determined to be about

5%
for the
J=
ψ
meson and

15%
for the
ψ
ð
2
S
Þ
meson.
DOI:
10.1103/PhysRevD.92.072008
PACS numbers: 13.66.Bc, 13.25.Gv, 13.40.Gp, 14.40.Df
I. INTRODUCTION
The timelike charged-kaon form factor
F
K
has been
measured precisely in the threshold/
φ
-meson region
[1
3]
and by several experiments
[3
7]
in the center-of-mass
(c.m.) energy range 1.1
2.4 GeV, where substantial struc-
ture is evident. At higher energies, there are precise
measurements at 3.671,
[8]
, 3.772, and 4.170 GeV
[9]
,
and there is a scan that extends to 5 GeV
[3]
. The energy
dependence of these higher-energy data is consistent with
the asymptotic form predicted by perturbative quantum
chromodynamics (pQCD), but their magnitude is about a
factor of 4 higher than the predicted asymptotic value
[10]
M
2
K
þ
K
j
F
K
ð
M
K
þ
K
Þj¼
8
πα
s
f
2
K
;
ð
1
Þ
where
M
K
þ
K
is the
K
þ
K
invariant mass,
α
s
is the strong
coupling constant, and
f
K
¼
156
.
2

0
.
7
MeV [
[11]
p. 1027] is the charged-kaon decay constant.
1
It is expected
that the difference between the data and the asymptotic
QCD prediction will decrease with increasing energy.
Precise measurements at higher energies are needed to test
this expectation.
In this paper we analyze the initial-state radiation (ISR)
process
e
þ
e
K
þ
K
γ
. The
K
þ
K
mass spectrum mea-
sured in this process is related to the cross section of the
nonradiative process
e
þ
e
K
þ
K
. Our previous meas-
urement of
F
K
[3]
used the
large-angle
(LA) ISR
technique, in which the radiated photon is detected and
the
e
þ
e
K
þ
K
γ
event is fully reconstructed. This gives
good precision near threshold, but the cross section
decreases rapidly with increasing energy, limiting that
measurement to energies below 5 GeV. In this paper we
*
Deceased.
Now at University of Tabuk, Tabuk 71491, Saudi Arabia.
Now at Laboratoire de Physique Nucléaire et de Hautes
Energies, IN2P3/CNRS, F-75252 Paris, France.
§
Now at University of Huddersfield, Huddersfield HD1 3DH,
UK.
Now at University of South Alabama, Mobile, Alabama
36688, USA.
**
Also at Università di Sassari, I-07100 Sassari, Italy.
1
We note that this value is larger by a factor of
ffiffiffi
2
p
than that
used in Eq. (22) of Ref.
[3]
.
STUDY OF THE
e
þ
e
K
þ
K
...
PHYSICAL REVIEW D
92,
072008 (2015)
072008-3
utilize small-angle (SA) ISR events, in which the ISR
photon is emitted close to the
e
þ
e
collision axis and so is
undetected. This allows us to perform an independent and
complementary measurement of the charged-kaon form
factor, which has better precision in the range 2.6
5 GeV,
and extends the measurements up to 8 GeV.
The Born cross section for the ISR process integrated
over the kaon momenta and the photon polar angle is
d
σ
K
þ
K
γ
ð
M
K
þ
K
Þ
d
M
K
þ
K
¼
2
M
K
þ
K
s
W
ð
s; x
Þ
σ
K
þ
K
ð
M
K
þ
K
Þ
;
ð
2
Þ
where
s
is the
e
þ
e
c.m. energy squared,
x
2
E

γ
=
ffiffiffi
s
p
¼
1
M
2
K
þ
K
=s
, and
E

γ
is the ISR photon energy in
the
e
þ
e
c.m. frame.
2
The function
W
ð
s; x
Þ
, describing the
probability for single ISR emission at lowest order in
quantum electrodynamics, is known to an accuracy better
than 0.5%
[12
14]
. The
e
þ
e
K
þ
K
cross section is
given in terms of the form factor by
σ
K
þ
K
ð
M
K
þ
K
Þ¼
πα
2
β
3
C
3
M
2
K
þ
K
j
F
K
ð
M
K
þ
K
Þj
2
;
ð
3
Þ
where
α
is the fine-structure constant,
β
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
4
m
2
K
=M
2
K
þ
K
q
, and
C
is the final-state correction,
which, in particular, takes into account extra photon
radiation from the final state (see, e.g., Ref.
[15]
). In the
mass region under study the factor
C
is close to unity, and
varies from 1.008 at
2
.
6
GeV
=c
2
to 1.007 at
8
GeV
=c
2
.
In addition to the form factor, we measure the branching
fractions for the decays
J=
ψ
K
þ
K
and
ψ
ð
2
S
Þ
K
þ
K
. For the latter we study the interference between
the resonant and nonresonant
e
þ
e
K
þ
K
amplitudes,
and between the single-photon and strong
ψ
K
̄
K
ampli-
tudes (with
ψ
¼
J=
ψ
,
ψ
ð
2
S
Þ
). As a result, we extract the
interference corrections to the
J=
ψ
K
þ
K
and
ψ
ð
2
S
Þ
K
þ
K
branching fractions, which were not taken into
account in previous measurements and determine the
values of the phase difference between the single-photon
and strong amplitudes in
J=
ψ
K
̄
K
and
ψ
ð
2
S
Þ
K
̄
K
decays. In contrast to previous determinations of this phase
[16
18]
, we use a model-independent approach, calculat-
ing the single-photon decay amplitudes from our data on
the charged-kaon form factor.
II. THE
BABAR
DETECTOR, DATA,
AND SIMULATED SAMPLES
We analyze a data sample corresponding to an integrated
luminosity of
469
fb
1
[19]
recorded with the
BABAR
detector at the SLAC PEP-II2 asymmetric-energy (9-GeV
e
and 3.1-GeV
e
þ
) collider. About 90% of the data were
collected at an
e
þ
e
c.m. energy of 10.58 GeV (the
Υ
ð
4
S
Þ
mass) and 10% at 10.54 GeV.
The
BABAR
detector is described in detail elsewhere
[20]
. Charged-particle tracking is provided by a five-layer
silicon vertex tracker (SVT) and a 40-layer drift chamber
(DCH), operating in the 1.5 T magnetic field of a super-
conducting solenoid. The position and energy of a
photon-produced cluster are measured with a CsI(Tl)
electromagnetic calorimeter (EMC). Charged-particle iden-
tification (PID) is provided by specific ionization (d
E=
d
x
)
measurements in the SVT and DCH, and by an internally
reflecting ring-imaging Cherenkov detector (DIRC).
Muons are identified in the solenoid
s instrumented flux
return (IFR).
Simulated samples of signal events, and background
e
þ
e
π
þ
π
γ
and
μ
þ
μ
γ
events, are generated with the
Phokhara
[21]
Monte Carlo (MC) event generator, which
takes into account next-to-leading-order radiative correc-
tions. To obtain realistic estimates for the pion and kaon
cross sections, the experimental values of the pion and kaon
electromagnetic form factors measured in the CLEO
experiment at
ffiffiffi
s
p
¼
3
.
67
GeV
[8]
are used in the event
generator. The mass dependence of the form factors is
assumed to be
1
=m
2
, as predicted by asymptotic QCD
[10]
.
The process
e
þ
e
e
þ
e
γ
is simulated with the
BHWIDE event generator
[22]
.
Two-photon background from the process
e
þ
e
e
þ
e
K
þ
K
is simulated with the GamGam event generator
[23]
. Background contributions from
e
þ
e
q
̄
q
ð
γ
ISR
Þ
,
where
q
represents a
u
,
d
,
s
or
c
quark, are simulated
with the JETSET event generator
[24]
.
The detector response is simulated using the
G
eant
4
package
[25]
. The simulation takes into account the
variations in the detector and beam-background conditions
over the running period of the experiment.
III. EVENT SELECTION
We select events with two tracks of opposite charge
originating from the interaction region. The tracks must lie
in the polar angle range
25
.
8
°
<
θ
<
137
.
5
° and be
identified as kaons. The selected kaon candidates are fitted
to a common vertex with a beam-spot constraint. The
χ
2
probability for this fit is required to be greater than 0.1%.
Conditions on the
K
þ
K
transverse momentum
(
p
T
;K
þ
K
) and the missing-mass squared (
M
2
miss
) recoiling
against the
K
þ
K
system are used for further selection. The
p
T
;K
þ
K
distribution for simulated
e
þ
e
K
þ
K
γ
events
is shown in Fig.
1
. The peak near zero corresponds to ISR
photons emitted along the collision axis, while the long tail
is due to photons emitted at large angles. We apply the
condition
p
T
;K
þ
K
<
0
.
15
GeV
=c
, which removes large-
angle ISR and suppresses backgrounds from
e
þ
e
K
þ
K
π
0
and ISR processes with extra
π
0
mesons.
2
Throughout this paper, an asterisk denotes a quantity that is
evaluated in the
e
þ
e
c.m. frame, while quantities without
asterisks are evaluated in the laboratory frame.
J. P. LEES
et al.
PHYSICAL REVIEW D
92,
072008 (2015)
072008-4
The region of low
K
þ
K
invariant mass cannot be
studied with small-angle ISR due to limited detector
acceptance. A
K
þ
K
pair with
p
T
;K
þ
K
<
0
.
15
GeV
=c
is
detected in
BABAR
when its invariant mass is larger than
2.5
ð
4
.
2
Þ
GeV
=c
2
for an ISR photon emitted along the
electron (positron) beam direction. The average values of
the kaon momentum for the two photon directions are
about 2.5 and
5
GeV
=c
, respectively. Since the probability
for particle misidentification increases strongly with
increasing momentum, we reject events with an ISR photon
along the positron direction.
The
M
2
miss
distribution for simulated signal events is
shown in Fig.
2
. The signal distribution is peaked at zero,
while the background distributions are shifted to negative
values for
e
þ
e
e
þ
e
γ
and
μ
þ
μ
γ
events and to positive
values for
p
̄
p
γ
, two-photon and other ISR events. The
condition
j
M
2
miss
j
<
1
GeV
2
=c
4
is applied to suppress
background. Sideband regions in
M
2
miss
and
p
T
;K
þ
K
are
used to estimate the remaining background from these
sources, as described in Sec.
IV
.
The
K
þ
K
invariant-mass spectrum for events selected
with the criteria described above is shown in Fig.
3
. A clear
J=
ψ
signal is seen in the spectrum, and there are also
indications of small
ψ
ð
2
S
Þ
and
χ
c
0
peaks. The
χ
c
0
mesons
are produced in the reaction
e
þ
e
ψ
ð
2
S
Þ
γ
χ
c
0
γγ
. The
increase in the number of events for
M
K
þ
K
>
6
GeV
=c
2
is
due to background from the
e
þ
e
μ
þ
μ
γ
process. To
suppress the muon background, we apply the additional
condition that neither kaon candidate be identified as a
muon. Muon identification is based mainly on IFR infor-
mation, and does not make use of the DIRC and d
E=
d
x
measurements used for charged-kaon PID. For
μ
þ
μ
γ
background events, the probability for at least one of the
charged particles to be identified as a muon is about 88%
(see subsection
IVA
). The shaded histogram in Fig.
3
shows events with at least one identified muon candidate.
The large muon background for larger values of
M
K
þ
K
prevents us from providing results for
M
K
þ
K
>
8
GeV
=c
2
.
The mass spectrum with finer binning in the region of the
charmonium resonances (
3
.
0
4
.
5
GeV
=c
2
) is presented in
the Supplemental Material
[26]
, together with the mass
resolution functions obtained from MC simulation with
M
K
þ
K
near the
J=
ψ
and
ψ
ð
2
S
Þ
masses.
IV. BACKGROUND ESTIMATION AND
SUBTRACTION
Sources of background in the selected sample include the
following: other two-body ISR processes
e
þ
e
e
þ
e
γ
,
μ
þ
μ
γ
,
π
þ
π
γ
, and
p
̄
p
γ
; ISR processes containing addi-
tional neutral particles, e.g.,
e
þ
e
K
þ
K
π
0
γ
and
e
þ
e
ψ
ð
2
S
Þ
γ
χ
cJ
γγ
K
þ
K
γγ
; the two-photon
M
2
miss
(GeV
2
/c
4
)
Events/(0.1 GeV
2
/c
4
)
0
1000
2000
3000
-20246
FIG. 2. The
M
2
miss
distribution for simulated
e
þ
e
K
þ
K
γ
events. The arrows indicate
j
M
2
miss
1
GeV
2
=c
4
.
p
T,K
+
K
(GeV/c)
Events/(10 MeV/c)
0
2000
4000
6000
8000
0
0.2
0.4
0.6
0.8
1
FIG. 1. The
p
T
;K
þ
K
distribution for simulated
e
þ
e
K
þ
K
γ
events. The arrow indicates
p
T
;K
þ
K
¼
0
.
15
GeV
=c
.
M
K
+
K
(GeV/c
2
)
Events/(50 MeV/c
2
)
0
100
200
300
468
FIG. 3 (color online). The
K
þ
K
mass spectrum for selected
K
þ
K
γ
candidates. The peaks near 3.1, 3.4, and
3
.
7
GeV
=c
2
are
from
J=
ψ
,
χ
c
0
, and
ψ
ð
2
S
Þ
decays to
K
þ
K
, respectively. The
shaded histogram shows events with at least one identified muon
candidate.
STUDY OF THE
e
þ
e
K
þ
K
...
PHYSICAL REVIEW D
92,
072008 (2015)
072008-5
process
e
þ
e
e
þ
e
K
þ
K
; and nonradiative
e
þ
e
q
̄
q
events containing a
K
þ
K
pair plus neutrals, e.g.,
e
þ
e
K
þ
K
π
0
. The background from the process
e
þ
e
K
þ
K
π
0
, which was dominant in our LA
analysis
[3]
, is strongly suppressed by the requirement
on
p
T
;K
þ
K
, and is found to be negligible in the SA analysis.
The cross section for
e
þ
e
p
̄
p
γ
[27,28]
is smaller
than that for
e
þ
e
K
þ
K
γ
in the mass region of
interest, and this background is reduced to a negligible
level by the requirement
j
M
2
miss
j
<
1
GeV
2
=c
4
. The other
categories of background are discussed in the following
subsections.
A. Background from
e
þ
e
e
þ
e
γ
,
μ
þ
μ
γ
, and
π
þ
π
γ
To be selected and, thus, to represent background for this
analysis, both final-state charged tracks in
e
þ
e
e
þ
e
γ
,
μ
þ
μ
γ
, and
π
þ
π
γ
events must be misidentified as kaons,
and the missing-mass squared must be poorly determined.
The probability to misidentify a pion as a kaon has been
measured as a function of charge, momentum, and polar
angle using a control sample of pions from
K
S
π
þ
π
decays. Using the measured misidentification probabilities,
we calculate weights for simulated
e
þ
e
π
þ
π
γ
events
(see Sec.
II
) to be identified as
K
þ
K
γ
events and estimate
a
π
þ
π
γ
background rate relative to the signal
K
þ
K
γ
rate
ranging from
5
×
10
5
at
3
GeV
=c
2
to about
5
×
10
3
at
7
.
5
GeV
=c
2
.
A similar approach is used to estimate the
e
þ
e
e
þ
e
γ
background. The electron misidentification rate has
been measured using
e
þ
e
e
þ
e
γ
events with the
photon detected at large angles. From MC simulation we
estimate the electron contamination to be at most 0.5%. The
PID requirements suppress
e
þ
e
e
þ
e
γ
events by a
factor of about
10
8
. We have verified this suppression by
analyzing a sample of LA
K
þ
K
γ
candidates with the
photon detected in the EMC. In this data sample, surviving
e
þ
e
e
þ
e
γ
events can be identified by requiring a
small opening angle between the photon direction and that
of one of the charged-particle tracks.
In the subsequent analysis, we disregard possible back-
grounds from
e
þ
e
γ
and
π
þ
π
γ
events since their con-
tributions are expected to be negligible.
The
e
þ
e
μ
þ
μ
γ
background is non-negligible for
large values of
M
K
þ
K
.For
M
K
þ
K
>
5
.
5
GeV
=c
2
,we
estimate the numbers of signal and background events in
each of the five mass intervals listed in Table
I
by fitting the
M
2
miss
distributions in the range
½
2
;
þ
1

GeV
2
=c
4
,as
shown in Fig.
4
, using three components: signal events,
the
μ
þ
μ
γ
background, and the ISR
þ
two-photon back-
ground. The
M
2
miss
interval is extended to negative values to
TABLE I. The number of selected
K
þ
K
candidates (
N
data
), number of signal events (
N
sig
), and estimated numbers of background
events from
e
þ
e
μ
þ
μ
γ
(
N
μμγ
), from the two-photon process
e
þ
e
e
þ
e
K
þ
K
(
N
γγ
), and from ISR processes with extra neutral
particle(s) such as
e
þ
e
K
þ
K
π
0
γ
and
K
þ
K
2
π
0
γ
(
N
ISR
). In the last column,
N
ψ
;
χ
refers to the background from
J=
ψ
K
þ
K
events for
3
.
0
<M
K
þ
K
<
3
.
2
GeV
=c
2
, from
ψ
ð
2
S
Þ
K
þ
K
events for
3
.
6
<M
K
þ
K
<
3
.
8
GeV
=c
2
, and from
ψ
ð
2
S
Þ
χ
cJ
γ
K
þ
K
γ
events for
3
.
2
<M
K
þ
K
<
3
.
4
and
3
.
4
<M
K
þ
K
<
3
.
6
GeV
=c
2
(see Fig.
6
). Events with
M
K
þ
K
>
5
.
5
GeV
=c
2
are selected
with the looser condition
2
<M
2
miss
<
1
GeV
2
=c
4
. For
N
sig
, the first uncertainty is statistical and the second is systematic. For the
numbers of background events, the combined uncertainty is quoted.
M
K
þ
K
(GeV
=c
2
)
N
data
N
sig
N
μμγ
N
γγ
N
ISR
N
ψ
;
χ
2.6
2.7
76
75

9

2
<
0
.
1
<
20
.
6

0
.
5
2.7
2.8
123
121

11

2
<
0
.
1
<
21
.
6

1
.
0
2.8
2.9
160
157

13

2
<
0
.
12
.
6

1
.
90
.
9

0
.
7
2.9
3.0
157
152

13

2
<
0
.
13
.
7

2
.
11
.
3

0
.
9
3.0
3.2
614
297

22

3
<
0
.
17
.
3

2
.
82
.
3

1
.
6
307
.
1

21
.
3
3.2
3.4
290
279

17

2
<
0
.
15
.
1

2
.
11
.
8

1
.
34
.
6

1
.
6
3.4
3.6
237
194

16

2
<
0
.
16
.
1

1
.
83
.
1

2
.
033
.
7

13
.
8
3.6
3.8
212
162

16

1
<
0
.
13
.
2

0
.
91
.
5

1
.
045
.
8

11
.
0
3.8
4.0
156
152

13

1
<
0
.
12
.
6

0
.
61
.
4

1
.
0
4.0
4.2
108
105

11

1
<
0
.
12
.
8

0
.
50
.
3

0
.
4
4.2
4.4
84
81

9

10
.
2

0
.
11
.
2

0
.
21
.
7

1
.
0
4.4
4.6
47
44
.
7

6
.
9

0
.
60
.
1

0
.
11
.
2

0
.
21
.
0

0
.
7
4.6
4.8
43
41
.
2

6
.
6

0
.
30
.
1

0
.
11
.
5

0
.
30
.
2

0
.
3
4.8
5.0
38
36
.
2

6
.
2

0
.
50
.
5

0
.
30
.
8

0
.
20
.
5

0
.
4
5.0
5.2
28
26
.
8

5
.
3

0
.
30
.
2

0
.
10
.
6

0
.
10
.
4

0
.
4
5.2
5.5
47
45
.
2

6
.
9

0
.
60
.
9

0
.
50
.
6

0
.
20
.
3

0
.
3
5.5
6.0
42
35
.
3

6
.
7

0
.
76
.
0

3
.
70
.
4

0
.
30
.
7

0
.
5
6.0
6.5
25
10
.
9

4
.
6

1
.
211
.
4

4
.
30
.
3

0
.
22
.
0

1
.
1
6.5
7.0
34
13
.
8

5
.
4

0
.
718
.
5

5
.
6
<
0
.
30
.
8

0
.
6
7.0
7.5
44
7
.
5

5
.
3

1
.
933
.
3

6
.
9
<
0
.
53
.
4

1
.
8
7.5
8.0
91
0
.
0

7
.
0

2
.
087
.
6

10
.
5
<
0
.
53
.
5

1
.
9
J. P. LEES
et al.
PHYSICAL REVIEW D
92,
072008 (2015)
072008-6
increase the sensitivity to
e
þ
e
μ
þ
μ
γ
background and
thus to better determine its contribution. The distribution
for signal events is taken from simulation and is centered at
zero. The distribution for the
μ
þ
μ
γ
background is obtained
using data events with at least one identified muon, and is
shifted to negative
M
2
miss
values because of the muon-kaon
mass difference. We also include the small contributions
from ISR and two-photon events estimated as described
below in Secs.
IV B
and
IV C
. The fitted parameters are the
numbers of signal (
N
sig
) and muon-background (
N
μμγ
)
events.
The results of the fits are listed in the last five rows of
Table
I
and are shown in Fig.
4
for three representative
intervals of
M
K
þ
K
. The first uncertainty in
N
sig
is
statistical, while the second, systematic, uncertainty,
accounts for the uncertainty in the numbers of ISR and
two-photon background events. The
N
sig
results in Table
I
for
M
K
þ
K
>
5
.
5
GeV
=c
2
are obtained with the condition
2
<M
2
miss
<
1
GeV
2
=c
4
. They can be scaled into our
standard selection
j
M
2
miss
j
<
1
GeV
2
=c
4
by multiplying the
results in the
5
.
5
6
.
5
GeV
=c
2
and
6
.
5
7
.
5
GeV
=c
2
mass
ranges by 0.98 and 0.99, respectively. For
M
K
þ
K
>
7
.
5
GeV
=c
2
the scaling factor is consistent with 1.0. The
scale factors are determined using simulated signal events.
Below
5
.
5
GeV
=c
2
, where the muon background is
small, we adopt a simpler approach and estimate the
number of
μ
þ
μ
γ
background events in each mass interval
using the number of selected events
N
1
μ
with at least one
charged track identified as a muon. The number of back-
ground events is estimated as
N
μμγ
¼
C
μ
ð
N
1
μ
k
1
μ
N
data
Þ
;
ð
4
Þ
where
C
μ
, evaluated as described below, is the ratio of the
number of selected
μ
þ
μ
γ
events with no identified muon
to the number of events with at least one identified muon,
k
1
μ
is the fraction of selected
K
þ
K
γ
events with at least
one identified muon, and
N
data
is the number of events in
the respective
M
K
þ
K
interval. The value of
k
1
μ
is taken
from simulated signal events and varies from 0.006 at
M
K
þ
K
¼
2
.
6
GeV
=c
2
to 0.01 at
M
K
þ
K
¼
5
.
5
GeV
=c
2
.
Very few simulated
μ
þ
μ
γ
events have both tracks
identified as kaons and neither identified as a muon, so
C
μ
is studied as a function of
M
K
þ
K
using the probability
for an individual muon to be identified as both a kaon and a
muon, assuming the probabilities for the two tracks to be
independent. We find that
C
μ
does not exhibit a significant
dependence on mass within the range of our measurements,
2
.
6
8
.
0
GeV
=c
2
. Therefore,
C
μ
used in Eq.
(4)
is estimated
from the fitted numbers of
μ
þ
μ
γ
events above
5
.
5
GeV
=c
2
. We find
C
μ
¼
0
.
14

0
.
01

0
.
08
, where
the first uncertainty is from the fits and the second accounts
for the full range of values in different mass intervals in data
and simulation (for purposes of information, the MC result
is
C
μ
¼
0
.
11
). The resulting estimated numbers of
μ
þ
μ
γ
background events are listed in Table
I
. For masses below
4
.
2
GeV
=c
2
,
ð
N
1
μ
k
1
μ
N
data
Þ
is consistent with zero, and
we take 0.1 as both an upper limit and uncertainty.
B. Multibody ISR background
Background ISR events containing a
K
þ
K
pair and one
or more
π
0
and/or
η
mesons are distinguishable by their
nonzero values of
M
2
miss
and
p
T
;K
þ
K
, but some events with
a small number of neutral particles still can enter the
selected data sample. Figure
5(a)
shows the two-
dimensional distribution of
M
2
miss
versus
p
T
;K
þ
K
for data
events before the requirements on these two variables,
indicated by the lines, are applied. The bottom left
rectangle is the signal region. The same distribution for
simulated signal events is shown in Fig.
5(b)
, and is similar
in structure except for a deficit in the upper right rectangle,
which we take as a sideband region. The distribution for
ISR background events produced by
JETSET
is shown in
Fig.
5(c)
. It should be noted that most (98%) simulated
M
2
miss
(GeV
2
/c
4
)
Events/(0.5 GeV
2
/c
4
)
(a)
0
5
10
15
-2
-1
0
1
M
2
miss
(GeV
2
/c
4
)
Events/(0.5 GeV
2
/c
4
)
(b)
0
5
10
-2
-1
0
1
M
2
miss
(GeV
2
/c
4
)
Events/(0.5 GeV
2
/c
4
)
(c)
0
10
20
30
-2
-1
0
1
FIG. 4 (color online). The
M
2
miss
distributions for data (points with error bars) in three
M
K
þ
K
intervals: (a)
5
.
5
6
.
0
GeV
=c
2
,
(b)
6
.
5
7
.
0
GeV
=c
2
, and (c)
7
.
5
8
.
0
GeV
=c
2
. The solid histogram is the result of the fit described in the text. The dashed blue, dotted
red, and shaded histograms show the contributions of signal, muon background, and ISR
þ
two-photon background, respectively.
STUDY OF THE
e
þ
e
K
þ
K
...
PHYSICAL REVIEW D
92,
072008 (2015)
072008-7
background events in the signal region are from the process
e
þ
e
K
þ
K
π
0
γ
, while the fraction in the sideband
region is about 80%.
The number of data events in the sideband region
N
2
is
used to estimate the ISR background in the signal region
using
N
ISR
¼
N
2
β
sig
N
1
β
bkg
β
sig
;
ð
5
Þ
where
N
1
is the number of data events in the signal region,
and
β
sig
and
β
bkg
are the
N
2
=N
1
ratios from signal and
background simulation, respectively. The coefficient
β
sig
increases linearly from
0
.
046

0
.
005
at
M
K
þ
K
¼
2
.
6
GeV
=c
2
to
0
.
074

0
.
005
at
8
.
0
GeV
=c
2
, where the
uncertainty is statistical, whereas
β
bkg
¼
7
.
6

1
.
0

4
.
0
is
independent of
M
K
þ
K
. The first uncertainty in
β
bkg
is
statistical, and the second is systematic. The latter takes into
account possible differences between data and simulation
in the background composition, and in the kinematic
distributions of
e
þ
e
K
þ
K
π
0
γ
events.
The regions 3.0
3.2 and
3
.
6
3
.
8
GeV
=c
2
contain reso-
nant contributions from the decays
J=
ψ
K
þ
K
and
ψ
ð
2
S
Þ
K
þ
K
, respectively. The resonant and nonreso-
nant contributions are determined by the fits described in
Sec.
VII
, and such fits are also applied to the sideband
regions. The resulting numbers of nonresonant events,
N
1
and
N
2
, are used to estimate the ISR background.
Similarly,the
M
K
þ
K
regions 3.2
3.4 and
3
.
4
3
.
6
GeV
=c
2
contain
χ
c
0
and
χ
c
2
decays, as seen in Fig.
6
.The
χ
cJ
states
are produced in the reaction
e
þ
e
ψ
ð
2
S
Þ
γ
, followed by
ψ
ð
2
S
Þ
χ
cJ
γ
. A similar set of fits is used to determine
N
1
,
N
2
, and the background contribution from the
χ
cJ
states, and
the fit results are shown in Fig.
6
. The estimated numbers of
ISR background events are listed in Table
I
along with the
fitted numbers of
ψ
and
χ
cJ
decays in the relevant mass
intervals.
p
T,K
+
K
(GeV/c)
M
2
miss
(GeV
2
/c
4
)
(a)
-1
0
1
2
3
0
0.2
0.4
0.6
0.8
1
p
T,K
+
K
(GeV/c)
M
2
miss
(GeV
2
/c
4
)
(b)
-1
0
1
2
3
0
0.2
0.4
0.6
0.8
1
p
T,K
+
K
(GeV/c)
M
2
miss
(GeV
2
/c
4
)
(c)
-1
0
1
2
3
0
0.2
0.4
0.6
0.8
1
FIG. 5. The distributions of
M
2
miss
versus
p
T
;K
þ
K
for (a) data events, (b) simulated signal events, and (c) simulated ISR background
events. Events in the
J=
ψ
and
χ
c
0
mass regions,
3
.
05
<M
K
þ
K
<
3
.
15
GeV
=c
2
and
3
.
38
<M
K
þ
K
<
3
.
46
GeV
=c
2
, are excluded from
the distributions; regions near the
χ
c
2
and
ψ
ð
2
S
Þ
are not excluded, since their signal content is quite small. The lines indicate the
boundaries of the signal region (bottom left rectangle) and the sideband region (top right rectangle).
M
K
+
K
-
(GeV/c
2
)
Events/(20 MeV/c
2
)
0
20
40
3.2
3.3
3.4
3.5
3.6
(a)
M
K
+
K
-
(GeV/c
2
)
Events/(20 MeV/c
2
)
0
5
10
15
20
3.2
3.3
3.4
3.5
3.6
(b)
FIG. 6. The
M
K
þ
K
spectra for data (points with error bars) in the vicinity of the
χ
c
0
and
χ
c
2
resonances for the
M
2
miss
p
T
;K
þ
K
(a) signal region and (b) sideband region. The solid histograms result from the fits described in the text. The dashed histograms represent
the nonresonant contributions.
J. P. LEES
et al.
PHYSICAL REVIEW D
92,
072008 (2015)
072008-8
C. Two-photon background
Two-photon events corresponding to the process
e
þ
e
e
þ
e
γ

γ

e
þ
e
K
þ
K
are distinguished by their larger
values of
M
2
miss
. Figure
7
shows the
M
2
miss
distribution for
data events in the range
2
.
8
<M
K
þ
K
<
3
.
0
GeV
=c
2
that
satisfy all the criteria in Sec.
III
except for that on
M
2
miss
. The
two-photon events, which dominate the large
j
M
2
miss
j
region,
aregenerally seen to bewell separated from signal events but
to nonetheless have a tail that extends into the signal region
j
M
2
miss
j
<
1
GeV
2
=c
4
. The exact shape of this tail depends
on the unknown kaon angular distribution. Therefore, we
reweight our simulation (generated with a uniform distri-
bution) to reproduce the cos
θ
K
distribution observed in the
data in each
M
K
þ
K
interval; here
θ
K
is the angle between the
K
þ
momentum in the
K
þ
K
rest frame and the
e
beam
direction in the
e
þ
e
c.m. frame. The data and reweighted
simulated cos
θ
K
distributions are compared in Fig.
8
. The
simulated
M
2
miss
distribution is shown in Fig.
7
, where it is
seen to reproduce the data well.
The two-photon background in each
M
K
þ
K
interval is
estimated from the number of data events with
M
2
miss
>d
and
a scale factor from the simulation. The
M
2
miss
distribution
changes with
M
K
þ
K
, and the value of
d
is
20
GeV
2
=c
4
for
M
K
þ
K
<
4
.
4
GeV
=c
2
,
10
GeV
2
=c
4
for
M
K
þ
K
>
6
.
5
GeV
=c
2
, and varies linearly in-between. The scale factor
ranges from
10
4
in the
2
.
6
2
.
7
GeV
=c
2
interval to about
10
2
in the
7
.
0
7
.
5
GeV
=c
2
interval. However, the number
of two-photon events decreases with increasing
M
K
þ
K
.The
estimated background event contributions are listed in Table
I
.
The numbers of signal events obtained after background
subtraction are listed in Table
I
. The first uncertainty in
N
sig
is statistical and the second is systematic. The systematic
term accounts for the uncertainties in the numbers of
e
þ
e
μ
þ
μ
γ
and two-photon background events, and
the uncertainties in the coefficients
β
sig
and
β
bkg
in the ISR
background subtraction procedure.
V. DETECTION EFFICIENCY
The detection efficiency,
ε
MC
, determined using MC
simulation, is shown in Fig.
9
as a function of
M
K
þ
K
. The
nonmonotonic behavior observed for
M
K
þ
K
>
5
.
5
GeV
=c
2
is introduced by filters designed to reduce background
before the event-reconstruction stage.
Corrections are applied to
ε
MC
to account for data-MC
simulation differences in detector response
M
2
miss
(GeV
2
/c
4
)
Events/(1 GeV
2
/c
4
)
0
500
1000
0204060
0
50
100
150
200
0
2.5
5
7.5
10
FIG. 7 (color online). The
M
2
miss
distribution fordata (points with
error bars) with
2
.
8
<M
K
þ
K
<
3
.
0
GeV
=c
2
selected with all the
criteria described in Sec.
III
except for the requirement
j
M
2
miss
j
<
1
GeV
2
=c
4
. The solid histogram is a sum of signal
and background distributions obtained from MC simulation. The
dashed histogram shows the distribution for two-photon events,
and the shaded (almost invisible) histogram shows the small
contribution of all other background processes. The inset shows
an enlarged view of the region
2
<M
2
miss
<
10
GeV
2
=c
4
. Above
10
GeV
2
=c
4
thesolidand dashedhistograms areindistinguishable.
cos
θ
K
Events/0.1
0
250
500
750
1000
-0.5
0
0.5
FIG. 8. The cos
θ
K
distribution for data (points with error bars)
and reweighted simulated events (histogram) with
M
2
miss
>
20
GeV
2
=c
4
from the
K
þ
K
mass range
2
.
8
3
.
0
GeV
=c
2
.
M
K
+
K
-
(GeV/c
2
)
Detection efficiency
0
0.05
0.1
0.15
34567
FIG. 9. The
K
þ
K
mass dependence of the detection efficiency
for simulated
e
þ
e
K
þ
K
γ
events.
STUDY OF THE
e
þ
e
K
þ
K
...
PHYSICAL REVIEW D
92,
072008 (2015)
072008-9