arXiv:0804.0178v1 [hep-ex] 1 Apr 2008
Measurement of e+e−→ φ → K+K−cross
section with CMD-2 detector at VEPP-2M
R.R.Akhmetshina, V.M.Aulchenkoa,b, V.Sh.Banzarova,
L.M.Barkova, S.E.Barua, N.S.Bashtovoya, A.E.Bondara,b,
D.V.Bondareva, A.V.Bragina, S.I.Eidelmana,b,
D.A.Epifanova,b, G.V.Fedotovicha,b, N.I.Gabysheva,
A.A.Grebeniuka,b, D.N.Grigorieva,b, F.V.Ignatova,b,
S.V.Karpova, V.F.Kazanina,b, B.I.Khazina,b, I.A.Koopa,b,
P.P.Krokovnya,b, A.S.Kuzmina,b, I.B.Logashenkoa,
P.A.Lukina,1, A.P.Lysenkoa, K.Yu.Mikhailova, V.S.Okhapkina,
E.A. Perevedentseva,b, A.S.Popova,b, S.I. Redina, A.A.Rubana,
N.M.Ryskulova, Yu.M.Shatunova, B.A.Shwartza,b,
A.L.Sibidanova,b, I.G.Snopkova, E.P.Solodova,b, Yu.V.Yudina
aBudker Institute of Nuclear Physics, Novosibirsk, 630090, Russia
bNovosibirsk State University, Novosibirsk, 630090, Russia
The process e+e−→ φ → K+K−has been studied with the CMD-2 detector using
about 542 000 events detected in the center-of-mass energy range from 1.01 to
1.034 GeV. The systematic error of the cross section is estimated to be 2.2%. The
φ(1020) meson parameters in the φ → K+K−decay channel have been measured:
σ0(φ → K+K−) = 2016 ± 8 ± 44 nb, mφ = 1019.441 ± 0.008 ± 0.080 MeV/c2,
Γφ= 4.24 ± 0.02 ± 0.03 MeV, Be+e−BK+K− = (14.27 ± 0.05 ± 0.31) × 10−5.
A study of the process e+e−→ K+K−is of interest for a number of physical
problems. Since the K+K−final state is the main φ(1020) meson decay chan-
1contact person. e-mail:P.A.Lukin@inp.nsk.su
Preprint submitted to Elsevier2 April 2008
nel, the resonance parameters can be obtained by measuring the cross section
of the process in the energy range around the φ(1020) meson mass [1,2]. The
isovector part of the e+e−→ K¯K cross section (both K+K−and K0
states should be considered) can be related to the τ−→ K−K0ντdecay by us-
ing conservation of vector current (CVC). Finally, the process under study
is used in the calculation of the hadronic contribution to the muon anomalous
magnetic moment . In view of the increasing experimental accuracy in the
measurement of this quantity , any significant contribution like that from
the process e+e−→ K+K−should be measured with adequate precision.
At the energy around the φ(1020) meson mass low momenta kaons from the
process e+e−→ K+K−have large probabilities for a nuclear interaction, de-
cays in flight and kaon stop in a thin layer of the detector material. That
introduces large uncertainties in the detection efficiency and increases sys-
tematic errors in the cross section. Earlier measurement of the cross section
performed by the CMD-2 collaboration  at the VEPP-2M collider , was
based on a relatively small data sample and had a systematic accuracy about
4%. The SND collaboration  used significantly larger statistics to study
the reaction e+e−→ K+K−. The experiment was based on the integrated
luminosity of 8.5 pb−1, but the accuracy of the cross section was limited by
systematic errors estimated to be 7.1%.
In this work we report a measurement of the e+e−→ K+K−cross section
based on 1.0 pb−1of data collected with the CMD-2 Detector  at the VEPP-
2M collider from 1.01 to 1.034 GeV center-of-mass (Ec.m. =√s) energy. A
special procedure to extract the detection efficiency from data is developed
and the systematic uncertainty on the cross section is estimated to be 2.2%.
2Detector and experiment
The CMD-2 detector has been described in detail elsewhere . The detector
tracking system consists of the cylindrical drift chamber (DC)  surrounding
the interaction point, and proportional Z-chamber (ZC)  for a precise mea-
surement of polar angles, both also used as a charged trigger. Both chambers
are inside a thin (0.38 X0) superconducting solenoid  with a field of 1 T.
The barrel electromagnetic calorimeter  is placed outside the solenoid and
consists of 892 CsI crystals. The muon-range system  of the detector, also
located outside the solenoid, is based on streamer tubes. The end-cap electro-
magnetic calorimeter  based on the 680 BGO crystals makes the detector
almost hermetic for photons. In this experiment we require a charged-trigger
signal from at least one charged track and any (>20 MeV) energy deposition
in the barrel electromagnetic calorimeter.
The data sample used in the analysis was collected in two scans of the center-
of-mass energy range 1.01 – 1.034 GeV. In the scans the beam energy was
increased from 505 MeV to 517 MeV with a 0.5 MeV step. To determine the
detection efficiency, we simulated 50000 events  of the process e+e−→
K+K−(γ) at each energy point.
A candidate to a e+e−→ K+K−event is an event with two low-momentum
tracks and high ionization losses, originating from the interaction region. There
is a number of effects leading to the loss of a charged-kaon track: decays in
flight, nuclear interactions, track reconstruction inefficiency etc. If one track
is not reconstructed, the event can still be identified using a second detected
track. Using single-track events to study detection efficiency we can signifi-
cantly reduce various systematic errors. In our analysis we select events with
one or two “good kaons” found, where a “good kaon” is defined according to
the following criteria:
• Track polar angle is 1.0 < θK< π − 1.0 radians
• Track total momentum is Ptot< 200 MeV/c
• Track ionization loss is dE/dx > 2 · dE/dxMIP
• Track impact parameter in R − ϕ plane is ρ < 0.4 cm.
Figure 1 shows a scatter plot of the track ionization losses vs. track total
momentum for all two-track events. Lines show the boundaries of applied
selections which allow to separate events with charged kaon(s) from other
reactions. The distribution of the track impact parameter in the R − ϕ plane
is shown in Fig. 2 for the remaining events. The vertical arrow shows the
The number of events with one or two “good” kaons found is determined from
the distribution of a Z-coordinate of the point closest to the interaction region
along the beam axis. Figure 3 demonstrates the Z-coordinate distribution for
events with one “good kaon”. A background from the beam-gas and beam-pipe
interactions producing low-momentum protons or pions is clearly seen. This
background contributes about 15% to a sample of one “good” kaon events and
is significantly smaller (0.4%) if both tracks are identified as “good kaons”.
To extract the number of signal events, the distribution is fitted to a sum
of a Gaussian function describing the interaction region and a smooth func-
tion describing the background. The shape of the background distribution
was derived from the analysis of events collected at the energy point below
the threshold of charged kaon pair production. The Z-coordinate distribution
Fig. 1. The track ionization losses versus
Fig. 2. The distribution of the track im-
pact parameter in the R − ϕ plane.
obtained at the center-of-mass energy of 0.984 GeV is shown in Fig. 4 and is
fitted to a sum of three Gaussian functions. The obtained values of the fitting
parameters but the number of background events are then used for the back-
ground description at each energy point. The background is relatively small,
so that variations of these parameters or the alternative description of the
background with the “flat” distribution do not change the final number of
signal events by more than 0.4%.
After background subtraction we select 178932±432 events with one “good
kaon” and 363490±604 events with two “good kaons”. The number of selected
events for each energy point is presented in Table 1. By varying the selection
criteria we estimate the systematic error on these numbers as 1.4%.
4 Cross section
At each energy point the e+e−→ K+K−cross section is calculated according
to the formula:
εL · (1 + δrad), (1)
where N1and N2are the numbers of events with one or two “good” kaons,
ε is the detection efficiency obtained from the MC simulation  with some
corrections from data, L is the integrated luminosity calculated with a 1%
accuracy using events of large angle Bhabha scattering  and (1 + δrad)
is the correction for initial-state radiation determined with a 0.5% accuracy
according to Ref. .
-20 -15-10-505 101520
Fig. 3. The distribution of the Z-coordi-
nate of the point closest to the interac-
tion region for events with one “good”
kaon. The curve shows the result of the
fit described in the text.
Fig. 4. The distribution of the Z-coordi-
nate of the point closest to the interac-
tion region for background events. The
curve shows the results of the fit de-
scribed in the text.
The detection efficiency is determined from the following formula:
ε = εgeom· εTF· εCsI·1 + ∆SIM
1 + ∆EXP,(2)
where the acceptance εgeomis calculated as the ratio of the number of events
passing the selection criteria to the initial number of MC simulated events,
εTF· εCsIis the product of the charged-trigger efficiency and a probability to
have energy deposition in the CsI calorimeter.
The number of events with one “good” kaon is about 50% of that with two
“good” kaons. Therefore, using the sum of events with one and two “good”
kaons we increase the detection efficiency and decrease the uncertainty due
to an incorrect description of the track losses in the MC simulation. In Eq. 2
we introduce ∆EXPand ∆SIMas the corrections describing the losses of both
charged kaons for experimental and MC simulated events, respectively, taking
into account a different probability of nuclear interaction as well as the dif-
ferent number of hits for tracks of positive and negative kaons. We found no
statistically significant difference in the losses of positive and negative kaons
due to the effects mentioned above. For example, from the N1and N2values
in Table 1 at√s = 1020.1 MeV and assuming no correlations, we estimate a
probability to lose both kaons to be ∆EXP= 0.035 in good agreement with
the MC simulation. The difference in ∆EXPand ∆SIMat all energy points does
not exceed 0.7% and this value is taken as an estimate of the systematic error
in the acceptance calculation.
The charged-trigger efficiency (εTF) was estimated to be 0.920±0.003 using a
special computer code simulating CMD-2 trigger . The difference between
the trigger efficiency for experimental and Monte Carlo events is 1% and is
used as an estimate of the corresponding systematic error.
The positive trigger decision also requires the presence of at least one cluster
in the CsI calorimeter with the energy deposition greater than 20 MeV. The
efficiency εCsIis calculated in a similar way and is 0.970 ± 0.001.
The total calculated efficiency for each energy point is listed in Table 1. The
beam energy at each point was determined using a procedure described in
detail in .
The total systematic error on the cross section is estimated to be equal to 2.2%
obtained by adding in quadrature contributions from various sources listed in
The experimental points are fit with the Breit-Wigner function , which
includes the contributions from the ρ, ω and φ mesons:
3 · s5/2· q3(s)
gV γgV K+K−
where V means ρ(770),ω(782) or φ(1020) mesons. q(s) =
charged kaon momentum, DV(s) = (m2
the vector meson V , gV γis a constant describing the coupling of the meson V
with a photon and gV KK— coupling constant of the meson V with a K+K−
pair, ψV is the phase. The coupling constants gV γgV KK are related to the
product of the branching fractions B(V → e+e−)B(V → K+K−) according
s/4 − m2
K± is the
V−s−ı√sΓV(s)) is the propagator of
gV γgV KK=3m2
?mVB(V → e+e−)B(V → K+K−)
Since the ρ(770) and ω(782) mesons are below the K+K−pair production
threshold, we calculate B(ρ,ω → K+K−) using the corresponding relation
from simple quark model (see, for example, Ref. ):
The phases ψφand ψωare equal to π according to SU(3). If the phase ψρis a
free parameter of the fit, its obtained value is consistent with π in agreement
The number of events, integrated luminosity, detection efficiency, radiative correc-
tion, cross section of the e+e−→ φ → K+K−process.
(1 + δrad)
89.7 0.590 0.816
9.8 0.563 0.712
40.6 0.585 0.867
with simple quark model . We fixed ψρ at π while determining the φ
meson parameters. AK+K− is a constant complex amplitude describing possible
contributions from excited vector states. The energy dependence of the total
width for a meson V is chosen as in Ref. . The function Z(s) given by the
Z(s) = 1 + α · π ·1 + v2
2 · v,
Contributions to the systematic error of the e+e−→ K+K−cross section
describes the Coulombian interaction of charged kaons in the final state .
Masses and total widths of the ρ(770) and ω(782) resonances were taken from
The product B(φ → e+e−)B(φ → K+K−) is related to the peak cross section
σ(φ → K+K−) according to the formula:
σ(φ → K+K−) = 12πB(φ → e+e−)B(φ → K+K−)
and this parameter along with the φ meson mass and total width is determined
from the fit:
σ(φ → K+K−) = 2016 ± 8 ± 44 nb,
mφ= 1019.441 ± 0.008 ± 0.080 MeV/c2,
Γφ= 4.24 ± 0.02 ± 0.03 MeV.
And from the other fit, where instead of the peak cross section we have a
product of the branching fractions as a free parameter, we obtain:
Bφ→e+e− · Bφ→K+K− = (14.27 ± 0.05 ± 0.31) · 10−5,
where the first error is statistical and the second is systematic. If we keep
AK+K− as a free parameter, it is consistent with zero and we fixed it at this
value while determining the φ meson parameters.
The systematic error in φ meson mass and total width is dominated by the
accuracy of the beam energy determination described in Ref. .
The obtained value of σ(φ → K+K−) agrees with the results of CMD-2
2001 ± 65 ± 82 nb  and SND 1967 ± 23 ± 140 nb  and is more precise.
The values of mφand Γφobtained in this work are strongly correlated with
the corresponding values obtained in our analysis of the neutral kaon pair
production in Ref.  because they are based on almost the same data sample
and therefore should be not averaged together. The values of both φ meson
mass and width obtained in this analysis agree with the world average values
and that for the width is more precise.
The parameter Be+e− · BK+K− is in good agreement with the world average
value  (14.60 ± 0.33) × 10−5and has the same accuracy.
In Fig. 5 we show the energy dependence of the cross section obtained in this
work as well as the results of the most precise previous experiments [1,2]. The
results of all experiments are in good agreement.
∆ σ, (nb)
Fig. 5. (Top) The deviations of the measured cross section from the fitting curve.
(Bottom) The experimental cross section of the reaction e+e−→ φ → K+K−
obtained in the present analysis (squares), earlier CMD-2 experiment  (circles)
and SND experiment  (triangles)
Significant improvement of the systematic accuracy of the cross section (from
4% to 2.2%) is achieved due to additional analysis of events with only one
charged kaon. It allows to take into account a possible difference of nuclear
interactions, decays in flight and reconstruction efficiency of the charged kaons
in data and MC simulation. The trigger efficiency is also extracted directly
from the data and is in good agreement with the MC simulation.
Using this precise measurement we recalculate the contribution of the reaction
e+e−→ φ → K+K−to the hadronic part of the theoretical prediction for the
anomalous magnetic moment of muon. It can be calculated via the dispersion
dsK(s) · R(s)
where K(s) is the QED kernel , R(s) denotes the ratio of the “bare” cross-
section for e+e−annihilation into hadrons to the muon pair cross section.
Using data on the e+e−→ φ → K+K−cross section from [1,2] one obtains
the following average K+K−contribution to ahad,LO
√s = 1.011 – 1.055 GeV: (15.28±0.16±0.78)·10−10. From the results of the
present work the new value of the K+K−contribution to ahad,LO
energy range is (15.53±0.15±0.33)·10−10. It agrees with the previous one and
is more precise.
in the c.m. energy range
in the same
Using a data sample of 5.42×105reconstructed events with one or two recon-
structed charged kaons collected at CMD-2, the most precise measurement of
the cross section of the reaction e+e−→ φ → K+K−has been performed.
The estimated systematic error in the cross section is 2.2%. The following φ
meson parameters have been determined:
σ(φ → K+K−) = 2016 ± 8 ± 44 nb,
mφ= 1019.441 ± 0.008 ± 0.080 MeV/c2,
Γφ= 4.24 ± 0.02 ± 0.03 MeV,
Bee· BKK= (14.27 ± 0.05 ± 0.31) · 10−5.
The obtained results agree with and are more precise than the results of other
The authors are grateful to the staff of VEPP-2M for excellent collider per-
formance, to all engineers and technicians who participated in the design,
commissioning and operation of CMD-2.
This work is supported in part by the grants INTAS YSF 06-100014-9464,
INTAS 1000008-8328, RFBR 06-02-16156,RFBR 06-02-26590, RFBR 06-02-16445.
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