of 32
arXiv:1306.3600v1 [hep-ex] 15 Jun 2013
B
A
B
AR
-PUB-13/006
SLAC-PUB-15487
arXiv:wwwwwwww [hep-ex]
Precision measurement of the cross section for
e
+
e
K
+
K
(
γ
) with the
initial-state radiation method at
B
A
B
AR
J. P. Lees, V. Poireau, and V. Tisserand
Laboratoire d’Annecy-le-Vieux de Physique des Particules
(LAPP),
Universit ́e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vie
ux, France
E. Grauges
Universitat de Barcelona, Facultat de Fisica, Departament
ECM, E-08028 Barcelona, Spain
A. Palano
ab
INFN Sezione di Bari
a
; Dipartimento di Fisica, Universit`a di Bari
b
, I-70126 Bari, Italy
G. Eigen and B. Stugu
University of Bergen, Institute of Physics, N-5007 Bergen,
Norway
D. N. Brown, L. T. Kerth, Yu. G. Kolomensky, M. J. Lee, and G. Lyn
ch
Lawrence Berkeley National Laboratory and University of Ca
lifornia, Berkeley, California 94720, USA
H. Koch and T. Schroeder
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphys
ik 1, D-44780 Bochum, Germany
C. Hearty, T. S. Mattison, J. A. McKenna, and R. Y. So
University of British Columbia, Vancouver, British Columb
ia, Canada V6T 1Z1
A. Khan
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kin
gdom
V. E. Blinov
ac
, A. R. Buzykaev
a
, V. P. Druzhinin
ab
, V. B. Golubev
ab
, E. A. Kravchenko
ab
, A. P. Onuchin
ac
,
S. I. Serednyakov
ab
, Yu. I. Skovpen
ab
, E. P. Solodov
ab
, K. Yu. Todyshev
ab
, and A. N. Yushkov
a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630
090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 6300
92
c
, Russia
D. Kirkby, A. J. Lankford, and M. Mandelkern
University of California at Irvine, Irvine, California 926
97, USA
B. Dey, J. W. Gary, O. Long, and G. M. Vitug
University of California at Riverside, Riverside, Califor
nia 92521, USA
C. Campagnari, M. Franco Sevilla, T. M. Hong, D. Kovalskyi, J. D. Rich
man, and C. A. West
University of California at Santa Barbara, Santa Barbara, C
alifornia 93106, USA
A. M. Eisner, W. S. Lockman, A. J. Martinez, B. A. Schumm, and A. S
eiden
University of California at Santa Cruz, Institute for Parti
cle Physics, Santa Cruz, California 95064, USA
D. S. Chao, C. H. Cheng, B. Echenard, K. T. Flood, D. G. Hitlin, P. On
gmongkolkul, and F. C. Porter
California Institute of Technology, Pasadena, California
91125, USA
R. Andreassen, Z. Huard, B. T. Meadows, B. G. Pushpawela, M. D.
Sokoloff, and L. Sun
University of Cincinnati, Cincinnati, Ohio 45221, USA
P. C. Bloom, W. T. Ford, A. Gaz, U. Nauenberg, J. G. Smith, and S. R
. Wagner
University of Colorado, Boulder, Colorado 80309, USA
2
R. Ayad
and W. H. Toki
Colorado State University, Fort Collins, Colorado 80523, U
SA
B. Spaan
Technische Universit ̈at Dortmund, Fakult ̈at Physik, D-44
221 Dortmund, Germany
R. Schwierz
Technische Universit ̈at Dresden, Institut f ̈ur Kern- und T
eilchenphysik, D-01062 Dresden, Germany
D. Bernard and M. Verderi
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS
/IN2P3, F-91128 Palaiseau, France
S. Playfer
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
D. Bettoni
a
, C. Bozzi
a
, R. Calabrese
ab
, G. Cibinetto
ab
, E. Fioravanti
ab
,
I. Garzia
ab
, E. Luppi
ab
, L. Piemontese
a
, and V. Santoro
a
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a
di Ferrara
b
, I-44122 Ferrara, Italy
R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro,
S. Martellotti, P. Patteri, I. M. Peruzzi,
M. Piccolo, M. Rama, and A. Zallo
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, I
taly
R. Contri
ab
, E. Guido
ab
, M. Lo Vetere
ab
, M. R. Monge
ab
, S. Passaggio
a
, C. Patrignani
ab
, and E. Robutti
a
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
B. Bhuyan and V. Prasad
Indian Institute of Technology Guwahati, Guwahati, Assam,
781 039, India
M. Morii
Harvard University, Cambridge, Massachusetts 02138, USA
A. Adametz and U. Uwer
Universit ̈at Heidelberg, Physikalisches Institut, D-691
20 Heidelberg, Germany
H. M. Lacker
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, D-
12489 Berlin, Germany
P. D. Dauncey
Imperial College London, London, SW7 2AZ, United Kingdom
U. Mallik
University of Iowa, Iowa City, Iowa 52242, USA
C. Chen, J. Cochran, W. T. Meyer, S. Prell, and A. E. Rubin
Iowa State University, Ames, Iowa 50011-3160, USA
A. V. Gritsan
Johns Hopkins University, Baltimore, Maryland 21218, USA
N. Arnaud, M. Davier, D. Derkach, G. Grosdidier, F. Le Diberder, A
. M. Lutz,
B. Malaescu,
P. Roudeau, A. Stocchi, L. L. Wang,
§
and G. Wormser
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et
Universit ́e Paris-Sud 11,
Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, Calif
ornia 94550, USA
3
J. P. Coleman, J. R. Fry, E. Gabathuler, D. E. Hutchcroft, D. J. P
ayne, and C. Touramanis
University of Liverpool, Liverpool L69 7ZE, United Kingdom
A. J. Bevan, F. Di Lodovico, and R. Sacco
Queen Mary, University of London, London, E1 4NS, United Kin
gdom
G. Cowan
University of London, Royal Holloway and Bedford New Colleg
e, Egham, Surrey TW20 0EX, United Kingdom
J. Bougher, D. N. Brown, and C. L. Davis
University of Louisville, Louisville, Kentucky 40292, USA
A. G. Denig, M. Fritsch, W. Gradl, K. Griessinger, A. Hafner, E. Pre
ncipe, and K. Schubert
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Ker
nphysik, D-55099 Mainz, Germany
R. J. Barlow
and G. D. Lafferty
University of Manchester, Manchester M13 9PL, United Kingd
om
E. Behn, R. Cenci, B. Hamilton, A. Jawahery, and D. A. Roberts
University of Maryland, College Park, Maryland 20742, USA
R. Cowan, D. Dujmic, and G. Sciolla
Massachusetts Institute of Technology, Laboratory for Nuc
lear Science, Cambridge, Massachusetts 02139, USA
R. Cheaib, P. M. Patel,
∗∗
and S. H. Robertson
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
P. Biassoni
ab
, N. Neri
a
, and F. Palombo
ab
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
L. Cremaldi, R. Godang,
††
P. Sonnek, and D. J. Summers
University of Mississippi, University, Mississippi 38677
, USA
X. Nguyen, M. Simard, and P. Taras
Universit ́e de Montr ́eal, Physique des Particules, Montr ́
eal, Qu ́ebec, Canada H3C 3J7
G. De Nardo
ab
, D. Monorchio
ab
, G. Onorato
ab
, and C. Sciacca
ab
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
M. Martinelli and G. Raven
NIKHEF, National Institute for Nuclear Physics and High Ene
rgy Physics, NL-1009 DB Amsterdam, The Netherlands
C. P. Jessop and J. M. LoSecco
University of Notre Dame, Notre Dame, Indiana 46556, USA
K. Honscheid and R. Kass
Ohio State University, Columbus, Ohio 43210, USA
J. Brau, R. Frey, N. B. Sinev, D. Strom, and E. Torrence
University of Oregon, Eugene, Oregon 97403, USA
E. Feltresi
ab
, M. Margoni
ab
, M. Morandin
a
, M. Posocco
a
, M. Rotondo
a
, G. Simi
a
, F. Simonetto
ab
, and R. Stroili
ab
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
S. Akar, E. Ben-Haim, M. Bomben, G. R. Bonneaud, H. Briand,
G. Calderini, J. Chauveau, Ph. Leruste, G. Marchiori, J. Ocariz, an
d S. Sitt
Laboratoire de Physique Nucl ́eaire et de Hautes Energies,
4
IN2P3/CNRS, Universit ́e Pierre et Marie Curie-Paris6,
Universit ́e Denis Diderot-Paris7, F-75252 Paris, France
M. Biasini
ab
, E. Manoni
a
, S. Pacetti
ab
, and A. Rossi
a
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
C. Angelini
ab
, G. Batignani
ab
, S. Bettarini
ab
, M. Carpinelli
ab
,
‡‡
G. Casarosa
ab
, A. Cervelli
ab
, F. Forti
ab
,
M. A. Giorgi
ab
, A. Lusiani
ac
, B. Oberhof
ab
, E. Paoloni
ab
, A. Perez
a
, G. Rizzo
ab
, and J. J. Walsh
a
INFN Sezione di Pisa
a
; Dipartimento di Fisica, Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
D. Lopes Pegna, J. Olsen, and A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
R. Faccini
ab
, F. Ferrarotto
a
, F. Ferroni
ab
, M. Gaspero
ab
, L. Li Gioi
a
, and G. Piredda
a
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
C. B ̈unger, O. Gr ̈unberg, T. Hartmann, T. Leddig, C. Voß, and R
. Waldi
Universit ̈at Rostock, D-18051 Rostock, Germany
T. Adye, E. O. Olaiya, and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX
11 0QX, United Kingdom
S. Emery, G. Hamel de Monchenault, G. Vasseur, and Ch. Y`eche
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, F
rance
F. Anulli, D. Aston, D. J. Bard, J. F. Benitez, C. Cartaro, M. R. Con
very, J. Dorfan, G. P. Dubois-Felsmann,
W. Dunwoodie, M. Ebert, R. C. Field, B. G. Fulsom, A. M. Gabareen, M
. T. Graham, C. Hast,
W. R. Innes, P. Kim, M. L. Kocian, D. W. G. S. Leith, P. Lewis, D. Linde
mann, B. Lindquist, S. Luitz,
V. Luth, H. L. Lynch, D. B. MacFarlane, D. R. Muller, H. Neal, S. Nels
on, M. Perl, T. Pulliam,
B. N. Ratcliff, A. Roodman, A. A. Salnikov, R. H. Schindler, A. Snyder
, D. Su, M. K. Sullivan, J. Va’vra,
A. P. Wagner, W. F. Wang, W. J. Wisniewski, M. Wittgen, D. H. Wright,
H. W. Wulsin, and V. Ziegler
SLAC National Accelerator Laboratory, Stanford, Californ
ia 94309 USA
W. Park, M. V. Purohit, R. M. White,
§§
and J. R. Wilson
University of South Carolina, Columbia, South Carolina 292
08, USA
A. Randle-Conde and S. J. Sekula
Southern Methodist University, Dallas, Texas 75275, USA
M. Bellis, P. R. Burchat, T. S. Miyashita, and E. M. T. Puccio
Stanford University, Stanford, California 94305-4060, US
A
M. S. Alam and J. A. Ernst
State University of New York, Albany, New York 12222, USA
R. Gorodeisky, N. Guttman, D. R. Peimer, and A. Soffer
Tel Aviv University, School of Physics and Astronomy, Tel Av
iv, 69978, Israel
S. M. Spanier
University of Tennessee, Knoxville, Tennessee 37996, USA
J. L. Ritchie, A. M. Ruland, R. F. Schwitters, and B. C. Wray
University of Texas at Austin, Austin, Texas 78712, USA
J. M. Izen and X. C. Lou
University of Texas at Dallas, Richardson, Texas 75083, USA
5
F. Bianchi
ab
, F. De Mori
ab
, A. Filippi
a
, D. Gamba
ab
, and S. Zambito
ab
INFN Sezione di Torino
a
; Dipartimento di Fisica Sperimentale, Universit`a di Tori
no
b
, I-10125 Torino, Italy
L. Lanceri
ab
and L. Vitale
ab
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, I-34127 Trieste, Italy
F. Martinez-Vidal, A. Oyanguren, and P. Villanueva-Perez
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spa
in
H. Ahmed, J. Albert, Sw. Banerjee, F. U. Bernlochner, H. H. F. Ch
oi, G. J. King, R. Kowalewski,
M. J. Lewczuk, T. Lueck, I. M. Nugent, J. M. Roney, R. J. Sobie, a
nd N. Tasneem
University of Victoria, Victoria, British Columbia, Canad
a V8W 3P6
T. J. Gershon, P. F. Harrison, and T. E. Latham
Department of Physics, University of Warwick, Coventry CV4
7AL, United Kingdom
H. R. Band, S. Dasu, Y. Pan, R. Prepost, and S. L. Wu
University of Wisconsin, Madison, Wisconsin 53706, USA
(Dated: June 12, 2013)
A precise measurement of the cross section for the process
e
+
e
K
+
K
(
γ
) from threshold to
an energy of 5 GeV is obtained with the initial-state radiati
on (ISR) method using 232 fb
1
of data
collected with the
B
A
B
AR
detector at
e
+
e
center-of-mass energies near 10
.
6 GeV. The measurement
uses the effective ISR luminosity determined from the
e
+
e
μ
+
μ
(
γ
)
γ
ISR
process with the same
data set. The corresponding lowest-order contribution to t
he hadronic vacuum polarization term
in the muon magnetic anomaly is found to be
a
KK,
LO
μ
= (22
.
93
±
0
.
18
stat
±
0
.
22
syst
)
×
10
10
. The
charged kaon form factor is extracted and compared to previo
us results. Its magnitude at large
energy significantly exceeds the asymptotic QCD prediction
, while the measured slope is consistent
with the prediction.
PACS numbers: 13.40Em, 13.60.Hb, 13.66.Bc, 13.66.Jn
I. INTRODUCTION
The measurement of the
e
+
e
K
+
K
(
γ
) cross
section presented in this paper takes place in the con-
text of a precision measurement of
R
=
σ
(
e
+
e
hadrons)
(
e
+
e
μ
+
μ
) at low energy. Integrals in-
volving
R
enter the calculations of the hadronic contribu-
tion to vacuum polarization (VP). Uncertainties on VP
are a limiting factor in precise comparisons of data with
the Standard Model (SM) expectations, such as the value
of the muon magnetic moment anomaly
a
μ
. The analysis
makes use of several data-driven techniques to measure
Now at the University of Tabuk, Tabuk 71491, Saudi Arabia
Also with Universit`a di Perugia, Dipartimento di Fisica, P
erugia,
Italy
Now at Laboratoire de Physique Nucl ́eaire et de Hautes Energ
ies,
IN2P3/CNRS, Paris, France
§
Also with Institute of High Energy Physics, Beijing, China
Now at the University of Huddersfield, Huddersfield HD1 3DH,
UK
∗∗
Deceased
††
Now at University of South Alabama, Mobile, Alabama 36688,
USA
‡‡
Also with Universit`a di Sassari, Sassari, Italy
§§
Now at Universidad T ́ecnica Federico Santa Maria, Valparai
so,
Chile 2390123
efficiencies and constrain systematic uncertainties below
the 1% level. Accurate parameters for the
φ
resonance
are determined and the charged kaon form factor is ex-
tracted for the first time in a large energy range, from
the
K
+
K
production threshold to 5 GeV.
Unlike previous measurements, which were performed
through energy scans, the present analysis uses the
initial-state radiation (ISR) method [1–4]. The
e
+
e
K
+
K
(
γ
) cross section at the reduced energy
s
is deduced from the measured spectrum of
e
+
e
K
+
K
(
γ
)
γ
ISR
events produced at the center-of-mass
(c.m.) energy
s
. The reduced energy is related to the
energy
E
γ
of the ISR photon in the
e
+
e
c.m. frame by
s
=
s
(1
2
E
γ
/
s
), and it is equal to the mass
m
KK
of
the hadronic final state, or
m
KKγ
if an additional pho-
ton from final-state radiation (FSR) has been emitted.
The cross section for the process
e
+
e
K
+
K
(
γ
) is
related to the
s
spectrum of
e
+
e
K
+
K
(
γ
)
γ
ISR
events through
dN
K
+
K
(
γ
)
γ
ISR
d
s
=
dL
eff
ISR
d
s
ε
KKγ
(
s
)
σ
0
KK
(
γ
)
(
s
)
,
(1)
where
dL
eff
ISR
/d
s
is the effective ISR luminosity,
ε
KKγ
is the full acceptance for the event sample, and
σ
0
KK
(
γ
)
is
the ‘bare’ cross section for the process
e
+
e
K
+
K
(
γ
)
(including final-state radiative effects), from which the
6
leptonic and hadronic vacuum polarization contributions
are excluded. In contrast to most measurements based
on the ISR method, the effective ISR luminosity does
not rely on the theoretical radiator function [1–4], which
describes the probability to emit an ISR photon of en-
ergy
E
γ
in a given angular acceptance, or on the external
measurement of the data luminosity. Instead, the effec-
tive ISR luminosity is determined from the measurement
of the
e
+
e
μ
+
μ
(
γ
)
γ
ISR
spectrum with the same
data sample, through a relation similar to Eq. (1) where
the
e
+
e
μ
+
μ
cross section is given by Quantum
Electrodynamics (QED). In this manner several system-
atic uncertainties cancel. In particular, the cross section
measurement is mostly insensitive to higher-order ISR
corrections and other theoretical uncertainties that af-
fect the kaon and muon channels equally. The method
used in this analysis has been developed for the precision
measurement of the
e
+
e
π
+
π
(
γ
) cross section and
is expounded in Ref. [5].
This paper is organized as follows. In Sec. II, we de-
scribe the data samples used in the analysis and the event
selection. In Sec. III, selection efficiencies and the corre-
sponding corrections based on differences between data
and Monte Carlo (MC) simulation are presented. Sec. IV
describes backgrounds. Sec. V is dedicated to the un-
folding of the mass spectrum, while Sec. VI describes the
acceptance corrections applied to the cross section. Fi-
nally, Sec. VII reports the results for the cross section and
kaon form-factor from threshold to 5 GeV, and includes
the
K
+
K
contribution to the anomalous magnetic mo-
ment of the muon.
II. SAMPLES AND EVENT SELECTION
Signal events are characterized by two charged-particle
tracks and a high energy photon, all required to lie within
the detector acceptance. In addition, in order to con-
trol the overall efficiency to high precision, it is found
necessary to include higher-order radiation. The next-
to-leading-order (NLO) is sufficient to reach accuracies
of 10
3
, so the analysis considers
KKγγ
as well as
KKγ
final states, where the additional photon can be either
ISR or FSR.
The data were produced at the SLAC National Accel-
erator Laboratory at the PEP-II
e
+
e
collider, operated
at and 40 MeV below the peak of the
Υ
(4
S
) resonance,
s
= 10
.
58 GeV. The analysis is based on 232 fb
1
of data collected with the
B
A
B
AR
detector, described
in detail in Ref. [6]. Charged-particle tracks are mea-
sured with a five-layer double-sided silicon vertex tracker
(SVT) together with a 40-layer drift chamber (DCH),
both inside a 1.5 T superconducting solenoid magnet.
Photons are assumed to originate from the primary ver-
tex defined by the charged tracks of the event, and their
energy and position are measured in a CsI(Tl) electro-
magnetic calorimeter (EMC). Charged-particle identifi-
cation (PID) uses the ionization energy loss (d
E/
d
x
) in
the SVT and DCH, the Cherenkov radiation detected in
a ring-imaging device (DIRC), the shower energy deposit
in the EMC (
E
cal
), and the shower shape in the instru-
mented flux return (IFR) of the magnet. The IFR system
is composed of modules of resistive-plate chambers inter-
spaced with iron slabs, arranged in a layout with a barrel
and two endcaps.
Signal and background ISR processes are simulated
with the AfkQed event generator based on Ref. [7]. The
signal
KK
(
γ
)
γ
ISR
sample corresponds to about 30 times
the integrated luminosity of the data. The main ISR pho-
ton,
γ
ISR
, is generated within the angular range [
θ
min
=
20
,
θ
max
= 160
] in the c.m. system
1
, wider than the
geometrical acceptance of the detector. Additional radi-
ation from the initial state is generated with the struc-
ture function method [8] in the collinear approximation,
while additional final-state photons are generated with
the
PHOTOS
[9] program. A minimum-mass requirement
m
K
+
K
γ
ISR
>
8 GeV
/c
2
, applied at generation, limits the
emission of a second hard photon in simulation. Back-
ground processes
e
+
e
q
q
(
q
=
u,d,s,c
) are gener-
ated with the
JETSET
[10] generator, and
e
+
e
τ
+
τ
with the
KORALB
[11] program. The response of the
B
A
B
AR
detector is simulated using the
GEANT
4 [12] pack-
age. In addition, since the additional ISR generated
by AfkQed is inadequate, large samples of Monte Carlo
(MC) events at the four-momentum level, dedicated to
specific ISR studies, are produced with the nearly-exact
NLO Phokhara [13] generator.
A. Topological selection
Two-charged-particle ISR events are selected by re-
quiring a photon with an energy
E
γ
>
3 GeV in the
e
+
e
c.m. and laboratory polar angle with respect to
the
e
beam in the range [0.35–2.4] rad, and exactly
two tracks of opposite charge, each with momentum
p >
1 GeV
/c
and within the angular range [0.40–2.45] rad.
If more than one photon is detected, the ISR photon is
assumed to be the candidate with the highest
E
γ
. The
charged-particle tracks are required to have at least 15
hits in the DCH, to originate within 5 mm of the colli-
sion axis (distance of closest approach doca
xy
<
5 mm)
and within 6 cm from the beam spot along the beam di-
rection (
|
z
|
<
6 cm), and to extrapolate to the DIRC
and IFR active areas, in order to exclude low-efficiency
regions. Events can be accompanied by any number of re-
constructed tracks not satisfying the above criteria, and
any number of additional photons. To ensure a rough
momentum balance at the preselection level (hereafter
called ‘preselection cut’), the ISR photon is required to
lie within 0
.
3 rad of the missing momentum of all the
1
Unless otherwise stated, starred quantities are measured i
n the
e
+
e
c.m. and un-starred quantities in the laboratory.
7
tracks (or of the tracks plus the other photons).
B. Kaon identification
To select
KKγ
candidates, the two tracks are required
to be identified as kaons. Kaon identification (
K
-ID)
proceeds from an optimization between efficiency and
misidentification of particles of other types (
e,μ,π,p
) as
kaons. Electron contamination is strongly reduced by a
criterion based on a combination of
E
cal
and d
E/
d
x
. In
addition, kaons are positively selected through a likeli-
hood estimator
L
based on the d
E/
d
x
in the DCH and
SVT and on the Cherenkov angle in the DIRC. Tracks
whose number of associated photons in the DIRC is not
sufficient to define a Cherenkov ring (
N
DIRC
<
3) are re-
jected. Pions and protons are rejected through selection
criteria on likelihood ratios:
L
K
/
(
L
K
+
L
π
)
>
0
.
9 and
L
K
/
(
L
K
+
L
p
)
>
0
.
2, respectively. Kaons are further re-
quired to fail muon identification. To maximize the
K
-ID
efficiency, the veto against the muon background relies on
a tight muon selector, where muons are identified by an
energy deposit in the EMC consistent with a minimum
ionizing particle (MIP), and topological requirements in
the IFR (penetration, number of hits, and shower width).
A
K
-ID efficiency of 80% is achieved. The probabilities
to misidentify a muon or pion as a kaon are below 10%
and are measured in the data, as described in Sec. III C 2.
The proton misidentification probability is 5% or less and
is taken from simulation.
C. ISR Kinematic fit with an additional photon
Following the method described in Ref. [5] for the anal-
ysis of the
μμγ
and
ππγ
processes, the event definition is
enlarged to include the radiation of one photon in addi-
tion to the already required ISR photon. Two kinematic
fits to the
e
+
e
KK
(
γ
)
γ
ISR
hypothesis are performed:
If an additional photon is detected in the EMC
with energy
E
γ
>
20 MeV, its energy and angles
are used in a three-constraint (3C) fit. We call this
an ‘FSR’ fit, although the extra photon can be ei-
ther from FSR or from ISR at large angle. In case
multiple extra photons are detected, the FSR fit
is performed using each photon in turn and the fit
with the smallest
χ
2
FSR
is retained.
For every event, an additional photon from ISR
at small angle is assumed to be emitted along ei-
ther the
e
+
or the
e
beam direction. The cor-
responding so-called 2C ISR fit ignores additional
photons measured in the EMC and returns the en-
ergy
E
γ
add
.
ISR
of the fitted collinear ISR photon.
In both cases, the constrained fit uses the measured
γ
ISR
direction, and momenta and angles of the two tracks,
0
2
4
6
8
10
12
0
2
4
6
8
10
12
1
10
10
2
10
3
ln(
χ
2
ISR
+1)
ln(
χ
2
FSR
+1)
no add. photon
add.‘FSR’
add.ISR
no add.Rad.
BG region
trk rec + interactions + more add. rad.
FIG. 1: (color online). The 2D-
χ
2
distribution for the
KK
(
γ
)
γ
ISR
data sample in the [0.98–5] GeV
/c
2
range of the
fitted
KK
mass, where different interesting regions are de-
fined. The line labeled ‘no add. photon’ corresponds to event
s
with no detected additional photon, which are characterize
d
by the
χ
2
ISR
value only.
along with their covariance matrix, to solve the four-
momentum conservation equations. The kaon mass is
assumed for the two charged particles. The energy of the
primary ISR photon is not used in either fit. Each event
is characterized by the
χ
2
values of the two kinematic
fits, except for the 12.5% of the candidates with no extra
measured photons, for which only the
χ
2
from the ISR
fit (
χ
2
ISR
) is available. The
K
+
K
invariant mass
m
KK
is obtained using the fitted parameters of the two kaons
from the ISR fit if
χ
2
ISR
< χ
2
FSR
, and from the FSR fit in
the reverse case.
Most events appear at small values of both
χ
2
ISR
and
χ
2
FSR
, as shown on the 2D-
χ
2
distribution (Fig. 1), but
the tails along the axes clearly indicate events with addi-
tional radiation: small-angle ISR along the
χ
2
FSR
axis
(with large fitted photon energies at large values of
χ
2
FSR
), and FSR or large-angle ISR along the
χ
2
ISR
axis
(with large measured photon energies at large values of
χ
2
ISR
). Events along the diagonal do not satisfy either
hypothesis and result from either the finite resolution of
the kaon track measurement or the direction of the pri-
mary ISR photon, or possibly from additional radiation
of more than one photon. Events affected by secondary
interactions also lie along the diagonal. Multibody back-
ground is expected to populate the region where both
χ
2
are large, and, consequently, a background (‘BG’) region
is defined in the 2D-
χ
2
plane, as indicated in Fig. 1.
For the cross section measurement, the
KK
(
γ
)
γ
ISR
candidates are required to satisfy a ‘tight’ selection
ln(
χ
2
ISR
+ 1)
<
3. In order to study efficiencies, back-
grounds and mass resolution, we define a ‘loose’ selection,
given by the full 2D-
χ
2
plane except for the BG-labeled
region. We refer to the region within the loose selection
8
but excluded by the tight selection as the ‘intermediate’
region.
D. Raw mass spectrum and angular distribution in
the
K
+
K
frame
Figure 2 shows the
K
+
K
mass spectrum measured in
the data with the tight
χ
2
selection, without background
subtraction or correction for acceptance. The spectrum
exhibits distinct features. Besides the prominent
φ
reso-
nance at 1.02 GeV
/c
2
, other structures are visible in the
[1.6–2.5] GeV
/c
2
mass region, as well as signals at the
J/ψ
and
ψ
(2
S
) resonances. These features are examined in
Sec. VII.
Since the background is small in the
φ
region, as dis-
cussed in Sec. IV, one can readily verify that the angular
distribution in the
KK
center-of-mass frame behaves as
expected for a decaying vector-particle with helicity one.
Figure 3 shows the distributions of the cosine of the angle
θ
γ
trk
between the ISR photon and the charged tracks in
the
KK
center-of-mass frame, for data and MC. The two
distributions are consistent with each other and follow
the expected sin
2
θ
γ
trk
shape.
III. EFFICIENCY AND DATA-MC
CORRECTIONS FOR DETECTOR SIMULATION
The mass-dependent overall acceptance
ε
KKγ
is deter-
mined with the full AfkQed plus
GEANT4
simulation,
with corrections applied to account for observed differ-
ences between data and MC. Through specific studies, we
determine the ratios of the efficiencies
ε
i
obtained with
the same methods in data and simulation for the trigger,
tracking, PID, and
χ
2
selection, and we apply them as
mass-dependent corrections to the measured
m
KK
spec-
trum. Corrections to the geometrical acceptance are
treated separately in Sec. VI, as most corrections can-
cel in the
KK
(
γ
) cross section measurement using the
effective luminosity from
μμ
(
γ
)
γ
ISR
data.
The event efficiency corrected for detector effects is
thus
ε
=
ε
MC
(
ε
data
trig
ε
MC
trig
)
(
ε
data
track
ε
MC
track
) (
ε
data
PID
ε
MC
PID
)
(
ε
data
χ
2
ε
MC
χ
2
)
.
(2)
The mass-dependent corrections
C
i
=
(
ε
data
i
MC
i
)
are
discussed below. Most trigger, tracking, and PID in-
efficiencies arise from a geometrical effect, namely the
overlap of the two tracks in the DCH, EMC, or IFR. To
avoid correlations between the
C
i
terms, the efficiencies
are determined sequentially, with minimal requirements
on the subsequent step. Trigger efficiency is measured on
enlarged signal samples selected without a requirement
on the actual number of reconstructed tracks. Tracking
efficiency is measured with events that have passed the
triggers. PID efficiencies and misidentification probabil-
ities are measured with two-track events. Biases associ-
ated with the efficiency determination, which result from
the measurement method, are studied with MC and are
normalized to data through data-to-MC comparison of
characteristic distributions once the physics origin of the
bias is identified. Since the data sample in the
φ
peak re-
gion is so pure, efficiencies are measured in the restricted
mass range 1
.
0
< m
KK
<
1
.
05 GeV
/c
2
and extrapolated
to higher mass regions, where large backgrounds preclude
direct measurements. Extrapolation is performed using
the
KK
(
γ
)
γ
ISR
MC to sample the corrections
C
i
deter-
mined in the restricted phase space as functions of the
relevant variables. Details of the procedure applied to
determine each
C
i
correction term are given below.
A. Trigger and filter efficiency corrections
Trigger and filter efficiencies are determined in data
and MC using complementary triggers. Several sets of
criteria (triggers) are applied to each of three levels, hard-
ware (L1), software (L3) and event filter (EF), and the
response of each is recorded with the event. In addition,
a prescaled sample is retained regardless of whether any
trigger is satisfied. The efficiencies of all triggers can
therefore be cross calibrated with the others. These are
all multipurpose triggers common to
B
A
B
AR
, with none
specifically designed to retain two-track ISR events.
Events for the trigger studies are selected through the
1C fit designed for tracking studies (see below) applied
to the one- or two-prong sample. The ‘primary’ track
is required to be identified as a kaon with momentum
p >
1 GeV
/c
, but otherwise minimal requirements are
imposed on track quality to avoid correlations with the
tracking efficiency measurement.
Inefficiencies of the hardware (L1) and software (L3)
triggers are found to be below 10
4
and (3
.
5
±
0
.
2)%, re-
spectively, for data in the vicinity of the
φ
peak. They are
well reproduced by simulation, and the deviation from
unity of the data/MC ratio for the L3 trigger efficiency
is found to be (
0
.
3
±
1
.
6)
×
10
3
, with no significant
variation with
m
KK
. The online event filter introduces
an inefficiency of (1
.
2
±
0
.
1)
×
10
3
in data, slightly un-
derestimated by MC; a correction of (0
.
6
±
0
.
2)
×
10
3
is applied. Biases on L3 and filter efficiency measure-
ments are observed in MC at a few per mil level. They
are due to pairs of non-interacting, minimum-ionizing
kaons, whose tracks overlap both in the DCH and EMC.
For such events, the tracking-based triggers are degraded
while, simultaneouly, the triggers based on EMC deposits
are enhanced. The biases are calibrated with data us-
ing the fractions of double-MIP deposits in the EMC.
They are maximal at the
φ
mass due to the kinematics
of the
φ
resonance. The related uncertainties on
C
trig
are 0
.
7
×
10
3
under the
φ
peak and are extrapolated to
about 0
.
5
×
10
3
at larger masses. At threshold, the un-
certainties related to the muon background subtraction
9
1
10
10
2
10
3
0.98
1
1.02
1.04
1.06
1.08
1.1
m
KK
(GeV/c
2
)
Events / (0.5 MeV/c
2
)
1
10
10
2
10
3
1.5
2
2.5
3
3.5
4
4.5
5
m
KK
(GeV/c
2
)
Events / (20 MeV/c
2
)
FIG. 2: The
K
+
K
invariant mass spectrum for the data sample, after the tight
χ
2
selection:
φ
mass region (left), masses
above
m
φ
(right).
0
200
400
600
800
1000
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
|cos
θ
γ
trk
|
Events / 0.01
FIG. 3: Distributions of the absolute value of the cosine of
the angle between the ISR photon and the charged tracks in
the
KK
center-of-mass, for data (black points) and MC (blue
histogram). The
KK
mass range is from 1.01 to 1.03 GeV
/c
2
.
The MC is normalized to the number of events in the data.
in the data sample dominate, and the systematic error
on
C
trig
reaches 1
.
0
×
10
3
.
B. Tracking efficiency correction
A 1C kinematic fit is used to select
K
+
K
γ
ISR
events
for tracking efficiency studies. The fit is performed on an
enlarged tracking sample that includes events with one or
two tracks. The fit uses as input only one kaon-identified
good track (called ‘primary’) and the ISR photon, and
the momentum vector of the second kaon is predicted
(rad)
φδ
-0.15
-0.1 -0.05
0
0.05
0.1
0.15
MC
track
ε
/
data
track
ε
0.7
0.75
0.8
0.85
0.9
0.95
1
FIG. 4: Fit of the data/MC correction for the tracking ef-
ficiency (per event, i.e., for the two tracks) as a function of
δφ
. The function for the fit is a constant plus two Gaussians.
The central values of the Gaussians are fixed at 0
.
1 rad. The
red band indicates the errors computed from the covariance
matrix of the fit parameters.
from four-momentum conservation. The predicted kaon
is required to lie within the tracking acceptance. Only
kinematically reconstructed
K
+
K
masses in the
φ
reso-
nance region (1
.
00
< m
KK
<
1
.
05 GeV
/c
2
) are selected in
order to reduce the non-kaon background in the tracking
sample to the 1% level.
The rate of in-acceptance predicted tracks that are ac-
tually reconstructed in the tracking system, with a charge
opposite to that of the primary kaon, determines the kaon
10
)
2
(GeV/c
KK
m
1
1.5
2
2.5
3
3.5
4
4.5
5
MC
track
ε
/
data
track
ε
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Stat. Error MC KK
Total Error
)
2
(GeV/c
KK
m
1
1.02
1.04
1.06
1.08
1.1
MC
track
ε
/
data
track
ε
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Stat. Error MC KK
Total Error
FIG. 5: (color online). The data/MC correction for the track
ing-efficiency as a function of
m
KK
. The red error bars show the
(small) statistical errors from the sampling, whereas the b
lue ones show the total errors (including the errors from the
fit). The
figure on the right is a zoom of the figure on the left in the
φ
resonance region.
tracking efficiency. The method yields the intrinsic track-
ing inefficiency, which is mostly due to interactions in the
detector material or kaon decays in flight. In addition to
the uncorrelated track loss, a local reduction of the in-
dividual track efficiency is induced by the overlap of the
tracks in the DCH. The tracking efficiency as a function
of the signed angular difference between the positive and
negative tracks in the transverse plane
δφ
=
φ
+
φ
exhibits a dip at small positive values of
δφ
both in data
and MC, which is characteristic of track overlap. This ef-
fect has been studied in detail in data and simulation for
the
μ
+
μ
and
π
+
π
final states [5]. The same features
are observed for
K
+
K
, although the
φ
mass selection
applied to the kaon tracking sample precludes
δφ
from
reaching values larger than 0.15 rad.
Some difference between data and MC is observed in
the magnitude of the effect, as seen in Fig. 4. The
δφ
dependence of the data/MC correction is fitted with the
functional form observed over the full
δφ
range for muons
and pions: besides a flat component due to the intrinsic
inefficiency, a double Gaussian is used to describe the
sharp asymmetric structure related to the track overlap,
located at
δφ
0
.
1 rad. As the magnitude of the overlap
effect varies with mass, studies of the peak inefficiency
are performed with MC on the kaon sample, and, in par-
allel, on the muon (pion) samples of
μμγ
(
ππγ
) data and
MC events. The general mass dependence of the peak
inefficiency is similar for all two-track ISR channels: a
maximum of about 1
2% around the region of maxi-
mum overlap, and a slow decrease to a plateau at higher
masses. In the muon sample, where efficiencies can be
measured both in data and MC over the full mass range,
the data/MC ratio of peak inefficiencies is found to be
independent of mass. This validates the extrapolation of
the track overlap effect in
KKγ
, measured at the
φ
mass,
to higher masses according to the mass dependence of the
peak inefficiency in MC. The latter is obtained in wide
mass ranges, and the resulting
C
track
correction is shown
in Fig. 5 as a function of mass, where discontinuities re-
flect the statistical fluctuations of the peak inefficiency
values, and errors are fully correlated within the wide
mass bins. The correction increases from 3
.
0% at thresh-
old to about 4
.
5% in the
φ
region, and it decreases to
around 1
.
5% at high masses.
The probability of losing the two tracks in a correlated
way, also induced by the track overlap, and the proba-
bility for having an extra reconstructed track, are found
to be well reproduced by MC in this analysis and small
data/MC differences of 0
.
8
×
10
3
and 1
.
2
×
10
3
, re-
spectively, are included in the systematic uncertainties.
Uncertainties on the bias from the primary-track tagging
induce a systematic error of 1
.
1
×
10
3
. Together with
the uncertainties on the mass dependence of the overlap
correction, the dominant contribution to the systematic
error is related to the model used to describe the cor-
rection as a function of
δφ
. The total systematic un-
certainty for the
C
track
correction is smaller than 0
.
3%
below 1.05 GeV
/c
2
, increasing to about 1% at high mass.
C. Particle ID efficiency corrections
Separation of ISR two-body processes
e
+
e
x
+
x
(
γ
)
γ
ISR
(
x
=
e,μ,π,K,p
) from each other relies
on PID. The specific studies conducted to determine
the kaon-ID efficiency for data and MC, as well as the
μ
K
’ and
π
K
’ misidentification probabilities, are
described below. Electron misidentification as a kaon