Study of the process e+e−→K0SK0L in the center-of-mass energy range 1004–1060 MeV with the CMD-3 detector at the VEPP-2000 e+e− collider

Citation for this paper:

Kozyrev, E.A., Solodov, E.P., Amirkhanov, A.N., Anisenkov, A.V., Aulchenko, V.M.,

Banzarov, V.S. & Yudin, Yu.V. (2016). Study of the process e

+

_e

−

_→K

0

S

K

0L

in the

center-of-mass energy range 1004–1060 MeV with the CMD-3 detector at the

VEPP-2000 e

+

_e

−

_{collider. Physics Letters B, 760, 314-319.}

http://dx.doi.org/10.1016/j.physletb.2016.07.003

UVicSPACE: Research & Learning Repository

_____________________________________________________________

Faculty of Science

Faculty Publications

_____________________________________________________________

Study of the process e

+

_e

−

_→K

0

S

K

0L

in the center-of-mass energy range 1004–1060

MeV with the CMD-3 detector at the VEPP-2000 e

+

_e

−

_collider

E.A. Kozyrev, E.P. Solodov, A.N. Amirkhanov, A.V. Anisenkov, V.M. Aulchenko, V.S.

Banzarov, N.S. Bashtovoy, D.E. Berkaev, A.E. Bondar, A.V. Bragin, S.I. Eidelman,

D.A. Epifanov, L.B. Epshteyn, A.L. Erofeev, G.V. Fedotovich, S.E. Gayazov, A.A.

Grebenuk, S.S. Gribanov, D.N. Grigoriev, F.V. Ignatov, V.L. Ivanov, S.V. Karpov,

A.S. Kasaev, V.F. Kazanin, A.N. Kirpotin, A.A. Korobov, O.A. Kovalenko, A.N.

Kozyrev, I.A. Koop, P.P. Krokovny, A.E. Kuzmenko, A.S. Kuzmin, I.B. Logashenko,

P.A. Lukin, K.Yu. Mikhailov, V.S. Okhapkin, A.V. Otboev, Yu.N. Pestov, A.S. Popov,

G.P. Razuvaev, A.A. Ruban, N.M. Ryskulov, A.E. Ryzhenenkov, A.I. Senchenko, V.E.

Shebalin, D.N. Shemyakin, B.A. Shwartz, D.B. Shwartz, A.L. Sibidanov, P.Yu.

Shatunov, Yu.M. Shatunov, V.M. Titov, A.A. Talyshev, A.I. Vorobiov, Yu.V. Yudin

2016

©2016 The Author(s). Published by Elsevier B.V. This is an open access article

under the CC BY license (

http://creativecommons.org/licenses/by/4.0/

). Funded by

SCOAP3

This article was originally published at:

http://dx.doi.org/10.1016/j.physletb.2016.07.003

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Study

of

the

process

e

+

e

−

→

K

0

_S

K

_L

0

in

the

center-of-mass

energy

range

1004–1060 MeV

with

the

CMD-3

detector

at

the

VEPP-2000

e

+

e

−

collider

E.A. Kozyrev

a

,

b

,

∗

,

E.P. Solodov

a

,

b

,

A.N. Amirkhanov

a

,

b

,

A.V. Anisenkov

a

,

b

,

V.M. Aulchenko

a

,

b

,

V.S. Banzarov

a

,

N.S. Bashtovoy

a

,

D.E. Berkaev

a

,

b

,

A.E. Bondar

a

,

b

,

A.V. Bragin

a

,

S.I. Eidelman

a

,

b

,

D.A. Epifanov

a

,

b

,

L.B. Epshteyn

a

,

b

,

c

,

A.L. Erofeev

a

,

b

,

G.V. Fedotovich

a

,

b

,

S.E. Gayazov

a

,

b

,

A.A. Grebenuk

a

,

b

,

S.S. Gribanov

a

,

b

,

D.N. Grigoriev

a

,

b

,

c

,

F.V. Ignatov

a

,

V.L. Ivanov

a

,

b

,

S.V. Karpov

a

,

A.S. Kasaev

a

,

V.F. Kazanin

a

,

b

,

A.N. Kirpotin

a

,

A.A. Korobov

a

,

b

,

O.A. Kovalenko

a

,

b

,

A.N. Kozyrev

a

,

b

,

I.A. Koop

a

,

P.P. Krokovny

a

,

b

,

A.E. Kuzmenko

a

,

b

_,

_{A.S. Kuzmin}

a

,

b

_,

_{I.B. Logashenko}

a

,

b

_,

_{P.A. Lukin}

a

,

b

_,

_{K.Yu. Mikhailov}

a

,

b

_,

V.S. Okhapkin

a

,

A.V. Otboev

a

,

Yu.N. Pestov

a

,

A.S. Popov

a

,

b

,

G.P. Razuvaev

a

,

b

,

A.A. Ruban

a

,

N.M. Ryskulov

a

,

A.E. Ryzhenenkov

a

,

b

,

A.I. Senchenko

a

,

V.E. Shebalin

a

,

b

,

D.N. Shemyakin

a

,

b

,

B.A. Shwartz

a

,

b

,

D.B. Shwartz

a

,

b

,

A.L. Sibidanov

d

,

P.Yu. Shatunov

a

,

Yu.M. Shatunov

a

,

V.M. Titov

a

,

A.A. Talyshev

a

,

b

,

A.I. Vorobiov

a

,

Yu.V. Yudin

a

,

b

a_{BudkerInstituteofNuclearPhysics,SBRAS,Novosibirsk,630090,Russia} b_{NovosibirskStateUniversity,Novosibirsk,630090,Russia}

c_{NovosibirskStateTechnicalUniversity,Novosibirsk,630092,Russia}

d_{DepartmentofPhysicsandAstronomy,P.O.Box3055Victoria,B.C.,V8W3P6,Canada}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received14April2016

Receivedinrevisedform27June2016 Accepted2July2016

Availableonline9July2016 Editor:L.Rolandi

Thee+e−→K0

SK0L crosssectionhasbeenmeasuredinthecenter-of-massenergyrange1004–1060MeV

at25energypointsusing6.1×105eventswithK0_S→

π

+

π

−decay.Theanalysisisbasedon5.9 pb−1 ofanintegratedluminositycollectedwiththeCMD-3detectorattheVEPP-2000e+e−collider.Toobtain

φ(1020)mesonparametersthemeasuredcrosssectionisapproximatedaccordingtotheVectorMeson Dominancemodelasasumofthe

ρ

,

ω

,φ-likeamplitudesandtheirexcitations.Thisisthemostprecise measurementofthee+e−→K0

SK0Lcrosssectionwitha1.8%systematicuncertainty.

©2016TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Investigation ofe+e− annihilation intohadronsat low energy provides unique information about interactions of light quarks. High-precision studies of various hadronic cross sections are of greatinterestinconnectionwiththeproblemofthemuon anoma-lous magnetic moment [1] and constitute the main goal of ex-periments with the CMD-3 and SND detectors at the upgraded VEPP-2000collider[2,3].

*

Correspondingauthor.

E-mailaddress:e.a.kozyrev@inp.nsk.su(E.A. Kozyrev).

In particular, e+e−

→

K0_SK_L0 is one of the processes with a ratherlargecrosssectioninthecenter-of-massenergyrangefrom 1to2 GeV.A precisemeasurementofthiscrosssection,dominated bythecontributionofthe

φ (

1020

)

and

φ (

1680

)

resonances,is re-quiredtoimproveourknowledgeofthehadroniccontributionsto

(

g

−

2

)

μ and

α

(

M2Z

)

.Additionalmotivationforhigh-precision

mea-surementsofthee+e−

→

K0_SK_L0ande+e−

→

K+K−crosssections around the

φ

meson peak comes from a significant deviation of theratioofthecouplingconstants gφ→K+ K−

gφ→K S KL fromtheoretical pre-dictions[4].

The most precise previous studies of the process have been performed at the CMD-2 [5], SND [6] and BaBar [7] detectors.

http://dx.doi.org/10.1016/j.physletb.2016.07.003

0370-2693/©2016TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Inthispaper we presentresultsofthe newmeasurement ofthe e+e−

→

K0_SK_L0crosssectionbasedonahigh-statisticsdatasample collected at25energypoints in thecenter-of-massenergy (c.m.) Ec.m.range1004–1060 MeVwiththeCMD-3detector.

2. CMD-3detectoranddataset

The Cryogenic Magnetic Detector (CMD-3) described else-where [8] is installed in one of the two interaction regions of the VEPP-2000 e+e− collider [9]. The detector tracking system consists of the cylindrical drift chamber (DC) and double-layer cylindricalmultiwireproportionalZ-chamber,bothinstalledinside a thin (0.085 X0) superconducting solenoid with 1.3 T magnetic

field. DCcontains 1218hexagonal cells and provides a measure-ment of charged particle momentum and of the polar (

θ

) and azimuthal(

φ

)angles.AnamplitudeinformationfromtheDCwires isusedtomeasuretheionizationlossesdE

/

dx ofchargedparticles with

σ

dE/dx

≈

11–14% accuracy for minimumionization particles

(m.i.p.). A barrel electromagnetic calorimeter placed outside the solenoidconsistsoftwo subsystems:an inner liquidxenon(LXe) calorimeter(5.4 X0 thick) surroundedby a scintillation CsI

crys-tal calorimeter (8.1 X0 thick) [10]. BGO crystals with 13.4 X0

are used as an endcap calorimeter. The detector has two trig-gers: neutral and charged. A signal for neutral one is generated by the information from calorimeters, while the charged trigger comes from the tracking system. The return yoke of the detec-tor is surrounded by scintillation counters which veto cosmic events.

Toobtain a detection efficiency, MonteCarlo (MC) simulation ofthedetectorbasedontheGEANT4[11]packagehasbeen devel-oped.Simulatedeventsaresubjecttothesamereconstructionand selection procedures asthe data. MC simulation includes photon jetradiation byinitial electrons calculatedaccording toRefs. [12, 13].BackgroundwasestimatedusingamultihadronicMonteCarlo generator[14] based on experimental datafor all measured pro-cessesintheenergyrangeupto2 GeV.

The analysis uses 5

.

9 pb−1 of an integrated luminosity col-lectedintwoscansofthe

φ (

1020

)

resonanceregionat25energy points in the Ec.m.

=

1004–1060 MeV range. The beam energy

EbeamhasbeenmonitoredbyusingtheBack-Scattering-Laser-Light

system[15,16] whichdetermines Ec.m. ateachenergypoint with

about0.06 MeVaccuracy.

3. Eventselection

Signal identification is based on detection of two pions from theK0_S

→

π

+

π

− decay.Foreachpairofoppositelychargedtracks a constrainedfit toa common vertexis performedto determine trackparameters.Assuming tracks tobe pions, thepair withthe best

χ

2 _{from the vertex fit and with the invariant mass in the}

range420–580 MeV

/

c2 isselectedasa K0_S candidate.The follow-ing requirements are applied to events with a found K0

S

candi-date:

•

Thelongitudinaldistanceandthetransversecoordinateofthe vertex shouldhave

|

Z_K0

S

|

<

10 cm and

|

ρ

K0S

|

<

6 cm,

respec-tively;

•

Pions from K0_S decay are required to have polar angles 1

<

θ

π+,π−

<

π

−

1 radians;

•

Each track has momentum 130 MeV

/

c

<

Pπ±

<

320 MeV

/

c corresponding to the kinematically allowed region for pions fromthe K0_S decayanditsionization lossesinDCare within threestandarddeviationsfromtheaveragevalue,expectedfor pions. The last requirement rejects chargedkaons and

back-Fig. 1. Ionizationlossesvsmomentumforpositive(a)andnegative(b)tracksfor dataatEbeam=505 MeV.ThelinesshowselectionsofpionsfromtheK0Sdecay.

Fig. 2. TotalmomentumPK0

S(a)andcosineoftheangleψbetweenthetwocharged

pions(b)fortheK0

Scandidatesafterpreliminaryselectionfordata(openhistogram) andMCsimulation(shadedhistogram)at Ebeam=505 MeV.Thearrowsshow ad-ditionalselectionrequirements.

groundprotons,asshowninFig. 1forpositive(a)andnegative (b)tracks,respectively,atEbeam

=

505 MeV;

•

ThemomentumoftheK0_S candidate,P_K0

S

= |

Pπ+

+ 

Pπ−

|

,is

re-quiredtobenotlargerthanfivestandarddeviationsfromthe nominalmomentum P_K0 S

=



E2 c.m.

/

4

−

m2_K0 S ateachenergy,as shownbythearrowsinFig. 2(a);

•

The cosine of the angle

ψ

between the tracks should be smallerthanthecosineoftheminimalanglebetweentwo pi-ons originating from the two-body decay of the K_S0 meson, shiftedbyfivestandard deviations,asshownbythearrowin Fig. 2(b).

Fig. 3. ReconstructedpolarangleoftheK0

Smeson(a)andthetransversedistance ofthe K0

S decayvertexfromthebeam(b)at Ebeam=505 MeV fordata(points) andsignalsimulation(shadedhistogram).Thedarkshadedhistogramsrepresent theestimatedcontributionfromthebackgroundprocesses.

Thereconstructedpolarangleofthe K0

S mesonandthe

trans-verse distance of the K0_S decay vertex from the e+e− interac-tion point are shown in Fig. 3 after above selections for data (points) andMC-simulation (shadedhistogram). The darkshaded histograms show a sum of the background contributions from the MC-simulated hadronic processes (predominantly e+e−

→

π

+

π

−2

π

0_{)andacontributionfromcosmicmuonsestimated}

us-ingeventsfromthe

|

Z_K0

S

|

sideband(10

<

|

ZK0S

|

<

15 cm).

Wedeterminethenumberofsignaleventsfordataand simu-lationfromabinnedmaximumlikelihoodfitoftwo-pioninvariant mass shown in Fig. 4. The signal shape is described by a sum offour Gaussianfunctions withparameters fixedfrom the simu-lation andwith additional Gaussian smearing to account forthe differenceindata-MCdetectorresponses.Thebackgroundindata, describedbyasecond-orderpolynomialfunction,constitutesabout 30%outside the

φ

mesonpeak and0.5% underit.Bytoy MC ex-perimentswithfixed signalandbackgroundprofilesaswell asby varying thebackground shape andapproximation rangeused we estimatean uncertaintyonthenumberofextractedsignal events aslessthan1.1%.The numberofobtainedsignalevents, Nexp,for

eachenergyislistedinTable 3.

4. Crosssectionofe+e−

→

K0_SK0_L

The Borncross section ofthe processe+e−

→

K0_SK0_L is calcu-latedateachenergyfromtheexpression:

σ

Born

=

Nexp



reg



trigL

(

1

+ δ

rad.

)

(

1

+ δ

en.spr.

),

(1)

where



regisadetectionefficiency,



trigisatriggerefficiency, L is

an integrated luminosity, 1

+ δ

rad. is a radiative correction, and 1

+ δ

en.spr. _{represents a correction due to the spread of the}

col-lisionenergy.

Thedetection efficiency



reg isobtainedby dividingthe

num-ber of MC simulated events after reconstruction and selection described above by the total number of generated K0_SK_L0 pairs takingintoaccount thebranchingfraction B_K0

S→π+π−

= (

69

.

20

±

Fig. 4. ApproximationoftheinvariantmassoftwopionsatEbeam=505 MeV for simulation(a)anddata (b).Thesolidlinecorrespondstothesignal,thelong-dotted linetothebackground.

Fig. 5. DetectionefficiencyoftheK0

SK0L pairsvsenergyfromsimulation(triangles). Thegeometricalefficiencyisshownbysquares(seetext).

0

.

05

)

% [17].Fig. 5showstheobtaineddetectionefficiency (trian-gles)vsc.m.energyincomparisonwiththeexpectedgeometrical efficiency(squares).Thegeometricalefficiencyiscalculatedasthe probability of pionsto be inthe polaranglerange 1

< θ

π+,π−

<

π

−

1 radiansatthegeneratorlevel.

The trigger efficiency is studied usingresponses of two inde-pendent triggers, charged andneutral, for selected signal events, andisfoundtobeclosetounity,



trig

=

0

.

998

±

0

.

001.

The integratedluminosity L isdetermined usingeventsofthe processes e+e−

→

e+e− (Bhabha events)withabout1%[18] sys-tematicaccuracy.

Theinitial-stateradiativecorrection1

+ δ

rad.,shownbysquares inFig. 6,iscalculatedusingthestructurefunctionmethodwithan accuracybetterthan0.1%[19].

Thespreadofcollisionenergyisabout350 keV,thatis signifi-cantincomparisonwiththe

φ

mesonwidth,andweintroducethe correction of the crosssection, shown by points in Fig. 6, which hasamaximumvalueof1

.

028

±

0

.

004 atthepeakofthe

φ

reso-nance.

The resultingcrosssection islistedinTable 3 foreachenergy andshowninFig. 8.The presentederrorsarestatisticalonlyand include fluctuations of signal and Bhabha events as well as the error

δ

Ec.m. dueto the statistical uncertainty of the c.m. energy

measurement.Thelastpartwascalculatedas

|

∂σBorn

Fig. 6. Radiativecorrections1+ δrad._{(squares,leftscale)andcorrections1+ δ}en.spr. forthespreadofcollisionenergy(points,rightscale).

Fig. 7. PiondetectionefficiencyinDCvsmomentumfordata(circles)andsimulation (squares).

5. Systematicuncertainties

MC simulation may not exactly reproduce all detector re-sponses, so an additional studywas performed to obtain correc-tionsfordata-MCdifferenceinthedetectionefficiency.

The data-MC difference in the charged pion detection by DC is studied using the process e+e−

→ φ →

π

+

π

−

π

0_{. Three-pion}

eventscanbefullyreconstructedfromonedetectedchargedtrack andtwo detected photons fromthe

π

0 _{decay, anda probability}

todetectanother chargedtrackcanbe determined.Forthepolar anglerequirement1

< θ

_π+,π−

<

π

−

1 radians,theaverage detec-tion inefficiency is about 1% per track for highmomentum, and decreaseswithpionmomentum,asshowninFig. 7.Theriseof ef-ficiencyvsmomentumis explainedby the decreasingnumberof pionsthatdecayedorinteractedin DC.Good data-MCagreement isobservedforchargedpiondetection,sonoefficiencycorrection isintroduced andtheuncertaintyinthedetectionisestimatedas 0.5%.

DCcalibrationischeckedusingsignalsoftheBhabhaevents[18] inthe DC and Z-chamber, and forpions from the K0_S decay the uncertaintyduetothe polarangleselection inthe rangeofpolar angleschosenisestimatedas0.4%.

By variation of corresponding selection criteria we estimate theuncertaintydueto thedata-MCdifferenceinthe angularand momentumresolutionsas0.5%,whileotherselectioncriteria con-tributeanother 0.6%.

Thetotaluncertaintyofthedetectionefficiencyiscalculatedas aquadraticsumofuncertainties fromthedifferentsources andis estimatedtobe 1.0%.

The systematic uncertainties of the e+e−

→

K0_SK0_L cross sec-tion discussed above are summarized in Table 1 giving 1.8% in total.

6. Fittingofthee+e−

→

K0_SK_L0crosssection

Toobtain

φ (

1020

)

parameterswe approximatetheenergy de-pendenceofthecrosssectionaccordingtothevectormeson

dom-Table 1

Summaryofsystematicuncertaintiesinthee+e−→K0

SKL0crosssection measure-ment.

Source Uncertainty, %

Signal extraction by fit 1.1

Detection efficiency 1.0

Radiative correction 0.1

Energy spread correction 0.3

Trigger efficiency 0.1

Luminosity 1.0

Total 1.8

inance(VMD)modelasasumofthe

ρ

,

ω

,

φ

-likeamplitudes[20]:

σ

_e+e−→K0 SKL0

(

s

)

=

8π α 3s5/2p 3 K0

|

gργgρKK Dρ

(

s

)

+

gωγgωKK Dω

(

s

)

+

gφγgφKK Dφ

(

s

)

+

Aρ,ω,φ

|

2

,

(2) wheres

=

E2

c.m., pK0 isaneutralkaonmomentum, DV

(

s

)

=

m2_V

−

s

−

i

√

s



V

(

s

)

, mV, and



V are mass andwidthof the major

in-termediate resonances: V

=

ρ

(

770

)

,

ω

(

782

)

,

φ (

1020

)

.Theenergy dependenceofthe decaywidthisexpressed via asumof partial widths multipliedby a factor ofphase spaceenergy dependence PV→f

(

s

)

ofeachdecaymodeas:



V

(

s

)

= 

V



V→f BV→f PV→f

(

s

)

PV→f

(

m2V

)

.

The coupling constants of the intermediate vector meson V withinitialandfinalstatescanbepresentedas:

|

gVγ

| =



3m3 V



Vee 4π α

; |

gVKK

| =









6πm2V



VBVKK p3 K0

(

mV

)

,

where



Vee and BVKK are electronicwidthandbranching fraction

ofthe V mesondecaytoapairofkaons.

Inourapproximationweusetheworld-averagevaluesofmass, total width and electronic width of the

ρ

(

770

)

and

ω

(

782

)

:



ρ→ee

=

7

.

04

±

0

.

06 keV,



ω→ee

=

0

.

60

±

0

.

02 keV [17]. The

branching fractions of the

ρ

(

770

)

and

ω

(

782

)

to a kaon pair are unknown, and we use the relation g_ωK0

SK 0 L

= −

gρK 0 SK 0 L

=

−

g_φK0 SK0L

/

√

2,basedon thequark modelwith“ideal”mixingand exactSU(3)symmetryofu-,d-,s-quarks[20].

The amplitude Aρ,ω,φ denotes a contribution of excited

ρ

(

1450

)

,

ω

(

1420

)

and

φ (

1680

)

vectormesonstatesinthe

φ (

1020

)

massregion.UsingBaBar[7]dataabove1.06 GeV fortheprocess e+e−

→

K0

SK0L we found a relatively small contribution of these

states in the studied energy range in comparisonwith nonreso-nant

ρ

and

ω

contributions.

We perform a fit to the e+e−

→

K0

SK0L cross section with

floatingmφ,



φ,and



φ→ee

×

B_φ→K0 SK 0 L (oralternatively Bφ→ee

×

B_φ→K0 SK 0

L) parameters: the fit yields

χ

2

_/

_ndf

₌

₂₀

_/

_{22 ( P}

₍

_χ

2

₎

₌

58%). The contributions of the

ρ

and

ω

intermediate states are non-negligibleandweperformedafitwhereweintroducean ad-ditional floating parameter gρ,ω , which is a multiplicative factor for both g_ωK0

SK0L and gρK0SKL0 coupling constants in Eq. (2). The

fityields

χ

2

_/

_ndf

₌

₁₅

_/

_{21 ( P}

₍

_χ

2

₎

₌

_82%)with

gρ,ω

=

0

.

80

±

0

.

09. This is the first quantitative estimate ofthe

ρ

and

ω

amplitude contributions inthe

φ

mesonregion. Theobtainedparameters of the

φ

mesonincomparisonwiththevaluesofothermeasurements are presented inTable 2 andthe fit resultis shownin Fig. 8(a). Fig. 8(b)showstherelative differencebetweenthe obtaineddata

Table 2

Theresultsoftheapproximationprocedureincomparisonwithpreviousexperiments.

Parameter CMD-3 Other measurements

mφ, MeV 1019.457±0.006±0.060±0.010 1019.461±0.019 (PDG2014) φ, MeV 4.240±0.012±0.005±0.010 4.266±0.031 (PDG2014) φ→eeBφ→K0 SKL0, keV 0.428±0.001±0.008±0.005 0.4200±0.0127 (BaBar) Bφ→eeBφ→K0 SKL0,10 −5 _{10.078±0.025±0.188±0.118 10.06±0.16 (PDG2014)} Table 3

Thec.m.energyEc.m.,numberofselectedsignaleventsN,detectionefficiencyMC,radiative-correctionfactor1+ δrad.,integratedluminosityL,andBorncrosssectionσof theprocesse+e−→K0

SK0L.Statisticalerrorsonlyareshown.

Ec.m., MeV N events MC 1 +δrad. 1+ δen.spr. L, nb−1 σ, nb 1 1004.066±0.008 315±19 0.321 0.72 0.994 195.35±0.67 6.87±0.42 2 1010.466±0.010 9083±100 0.312 0.73 0.992 936.05±1.44 42.16±0.47 3 1012.955±0.007 10639±108 0.308 0.72 0.988 485.35±1.04 96.74±1.00 4 1015.068±0.012 2347±50 0.307 0.71 0.987 47.91±0.33 219.53±5.02 5 1016.105±0.010 15574±130 0.304 0.71 0.978 192.11±0.66 366.33±3.33 6 1017.155±0.012 65612±264 0.303 0.70 0.983 478.99±1.04 628.15±2.95 7 1017.156±0.013 5525±77 0.302 0.70 0.985 40.76±0.3 624.76±9.89 8 1018.046±0.021 102233±334 0.301 0.70 0.992 478.34±1.04 996.62±4.28 9 1019.118±0.016 98014±326 0.3 0.72 1.028 328.62±0.86 1413.65±6.02 10 1019.214±0.019 16059±132 0.299 0.72 1.022 52.75±0.34 1433.05±15.03 11 1019.421±0.028 11066±110 0.299 0.73 1.024 36.04±0.28 1434.84±18.40 12 1019.902±0.012 140758±386 0.299 0.75 1.016 472.34±1.04 1341.91±4.74 13 1021.222±0.021 47552±225 0.299 0.83 0.994 228.34±0.72 833.20±4.89 14 1021.309±0.009 9545±102 0.299 0.83 0.994 46.85±0.33 807.54±10.36 15 1022.078±0.021 31323±183 0.297 0.88 0.989 201.61±0.68 582.93±4.03 16 1022.744±0.019 14517±126 0.297 0.93 0.989 116.71±0.52 443.71±4.38 17 1023.264±0.025 6876±86 0.297 0.96 0.992 62.91±0.38 377.77±5.31 18 1025.320±0.031 2319±51 0.294 1.08 0.996 36.32±0.28 199.26±4.97 19 1027.956±0.015 8150±94 0.294 1.21 0.997 195.83±0.67 115.93±1.70 20 1029.090±0.014 1911±45 0.293 1.26 0.998 52.94±0.35 96.96±3.00 21 1033.907±0.011 3704±64 0.292 1.43 0.999 175.55±0.64 50.12±1.26 22 1040.028±0.035 2839±56 0.289 1.6 1 195.91±0.68 31.27±1.01 23 1049.864±0.011 4291±70 0.284 1.78 1 499.59±1.09 16.93±0.50 24 1050.862±0.031 1310±39 0.285 1.79 1 146.31±0.59 17.47±0.94 25 1059.947±0.015 1271±38 0.276 1.91 1 198.86±0.69 12.09±0.71

Fig. 8. (a) Measurede+e−→K0

SK0L crosssectionincomparisonwithprevious ex-periments.Thedotsareexperimentaldata,thecurveisthefitdescribedinthetext. (b) Relativedifferencebetweenthedataandfit.Comparisonwithother experimen-taldataisshown.Statisticaluncertaintiesonlyareincludedfordata.Thewidthof thebandshowsthesystematicuncertaintiesinourexperiment.

and the fit curve. Only statistical uncertainties are shown. The widthofthe bandshowsthe systematicuncertaintyinour mea-surement.A slopeoftheCMD-2points[5]canbeexplainedbyan

Fig. 9. Contributionsoflower- andhigher-massresonancestothefitofthee+e−→ K0SK

0

L crosssectioninthestudiedenergyrange.

about 80 keV difference betweenthe used valuesof c.m. energy intheprevious workandthisexperiment,that iswithin declared systematicuncertaintiesoftheenergymeasurements.

The contributions of the

ρ

and

ω

intermediate states are demonstratedinFig. 9bythedottedlines,whilethelong-dashed lineshowsacontributionfromhigherexcitations.Thefirst uncer-taintiespresentedinTable 2arestatistical,andthesecondarethe

Fig. 10. Relativedifferencebetweenthedataandfitforthe Ec.m.=1.00–1.25 GeV range.Thedashedlineisthecontributionoftheφmesonamplitudeonly.

systematicuncertainties. Twoeffects were taken into account in theestimationof thelatter: theaccuracy ofthemeasurement of thec.m.s.energyEc.m.of60 keVandthesystematicuncertaintyof

thecross section measurementof 1.8%(Table 1). Tostudymodel dependence of the results, several additional fits are performed. Other fits use Eq. (2)without the Aφ,ρ,ω amplitude and intro-duceanadditionalfloatingphaseofthe

φ

mesonamplitudeorthe both

ρ

and

ω

amplitudes.Thevariations inthe

φ

meson param-etersareusedasanestimate ofthemodel-dependentuncertainty presentedas a third uncertainty in Table 2. The obtainedvalues agreewithresultsofothermeasurementsandsomearemore pre-cise.

Fig. 10 shows available experimental data up to Ec.m.

=

1250 MeV anddemonstrates that theobtained fitparameters do not contradict other measurements at higher Ec.m. values. The

dashedlineshowsthecontributionofthe

φ

mesononly,whenthe amplitudesfromthe

ρ

(

770

)

and

ω

(

782

)

areexcluded demonstrat-ing that thedestructive interference withthese statesdominates intheshownenergyregion.

7.Conclusion

Usingthe K0_S

→

π

+

π

− decaywe observe6

.

1

×

105 eventsof the process e+e−

→

K0

SK0L in the 1004–1060 MeV c.m. energy

range,andmeasure the crosssection with a 1.8%systematic un-certainty.The following values of the

φ

meson parameters have beenobtained:

mφ

=

1019

.

457

±

0

.

061 MeV

/

c2



φ

=

4

.

240

±

0

.

017 MeV



φ→eeB_φ→K0

SKL0

=

0

.

428

±

0

.

009 keV

.

Theobtainedparametersareingoodagreementwithprevious ex-periments.Thevaluesof



φ and



φ→eeBφ→K0

SK0L arethemost

pre-ciseamongall existingmeasurements.Highprecisioninthecross section measurementallows thefirst quantitativeestimate ofthe contributionsfrom

ρ

and

ω

mesonstothestudiedc.m.region.

Acknowledgements

We thankthe VEPP-2000personnel forexcellent machine op-eration. Thiswork is supported inpartby the RussianEducation andbytheRussianFoundationforBasicRFBR14-02-00580-a,RFBR 14-02-91332,RFBR15-02-05674-aandRFBR16-02-00160-a.

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