Study of the process e+e−→K0SK0Sπ+π−in the c.m. energy range 1.6–2.0 GeV with the CMD-3 detector

Citation for this paper:

Akhmetshin, R.R., Amirkhanov, A.N., Anisenkov, A.V., Aulchenko, V.M., Banzarov,

V.Sh., Bashtovoy, N.S.,… Yudin, Yu.V. (2020).

Study of the process e

+

e

−

→

K

0_S

K

0_S

π

+

π

−

in the c.m. energy range 1.6–2.0 GeV with the CMD-3 detector

. Physics Letters B,

804, 135380.

https://doi.org/10.1016/j.physletb.2020.135380

UVicSPACE: Research & Learning Repository

_____________________________________________________________

Faculty of Science

Faculty Publications

_____________________________________________________________

Study of the process e

+

e

−

→

K

0_S

K

0_S

π

+

π

−

in the c.m. energy range 1.6–2.0 GeV with the

CMD-3 detector

R.R. Akhmetshin, A.N. Amirkhanov, A.V. Anisenkov, V.M. Aulchenko, V.Sh.

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, F.J.

Grancagnolo, A.A. Grebenuk, S.S. Gribanov… A.L. Sibidanov, E.P. Solodov, M.V.

Timoshenko, V.M. Titov, A.A. Talyshev, A.I. Vorobiov, I.M. Zemlyansky, Yu.V. Yudin

May 2020

© 2020 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/ ).

This article was originally published at:

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Study

of

the

process

e

+

e

−

→

K

0

_S

K

0

_S

π

+

π

−

in

the

c.m.

energy

range

1.6–2.0

GeV

with

the

CMD-3

detector

R.R. Akhmetshin

a

,

b

,

A.N. Amirkhanov

a

,

b

,

A.V. Anisenkov

a

,

b

,

V.M. Aulchenko

a

,

b

,

V.Sh. 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

,

e

,

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

,

F.J. Grancagnolo

f

,

A.A. Grebenuk

a

,

b

,

S.S. Gribanov

a

,

b

,

D.N. Grigoriev

a

,

b

,

c

,

F.V. Ignatov

a

,

b

,

V.L. Ivanov

a

,

b

,

S.V. Karpov

a

,

A.S. Kasaev

a

,

V.F. Kazanin

a

,

b

,

I.A. Koop

a

,

b

,

A.A. Korobov

a

,

b

,

A.N. Kozyrev

a

,

c

,

E.A. Kozyrev

a

,

b

,

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

,

A.P. Lysenko

a

,

K.Yu. Mikhailov

a

,

b

,

V.S. Okhapkin

a

,

E.A. Perevedentsev

a

,

b

,

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.V. Semenov}

a

,

b

_,

_{Yu.M. Shatunov}

a

_,

V.E. Shebalin

a

,

b

,

D.N. Shemyakin

a

,

b

,

B.A. Shwartz

a

,

b

,

D.B. Shwartz

a

,

b

,

A.L. Sibidanov

a

,

d

,

E.P. Solodov

a

,

b

,

∗

,

M.V. Timoshenko

a

,

V.M. Titov

a

,

A.A. Talyshev

a

,

b

,

A.I. Vorobiov

a

,

I.M. Zemlyansky

a

,

Yu.V. Yudin

a

,

b

a_{Budker Institute of Nuclear Physics, SB RAS, Novosibirsk, 630090, Russia} b_{Novosibirsk State University, Novosibirsk, 630090, Russia}

c_{Novosibirsk State Technical University, Novosibirsk, 630092, Russia} d_{University of Victoria, Victoria, BC, V8W 3P6, Canada}

e_{Lebedev Physical Institute RAS, Moscow, 119333, Russia} f_{Instituto Nazionale di Fisica Nucleare, Sezione di Lecce, Lecce, Italy}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Article history:

Received12December2019 Receivedinrevisedform3March2020 Accepted17March2020

Availableonline25March2020 Editor:L.Rolandi

Thecrosssectionoftheprocesse+e−_→K0

SK0S

π

+

π

−hasbeenmeasuredusingadatasampleof56.7

pb−1 collectedwiththeCMD-3detector attheVEPP-2000e+e− collider.596±27 and 210±18 signal eventshavebeen selectedwithsixandfivedetectedtracks,respectively,inthecenter-of-massenergy range1.6–2.0GeV.Thetotalsystematicuncertaintyofthecrosssectionisabout10%.Thestudyofthe productiondynamicsconfirmsthedominanceoftheK∗(892)+K∗(892)−intermediatestate.

©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

e+e− annihilationintohadronsbelow2GeVisrichforvarious multiparticlefinal states.Theirdetailedstudies are importantfor developmentofphenomenologicalmodelsdescribingstrong inter-actionsat low energies.One ofthe final states, K0_SK0_S

π

+

π

−,has beenstudied beforeby the BaBarcollaboration [1], based onthe Initial-StateRadiation(ISR)method.Theiranalysisshowedthat be-lowthecenter-of-massenergy(Ec.m.)of2GeVtheprocessis

dom-inatedby the K∗

(

892

)

+K∗

(

892

)

− intermediatestatewithasmall

*

Correspondingauthorat:BudkerInstituteofNuclearPhysics,SBRAS, Novosi-birsk,630090,Russia.

E-mail address:solodov@inp.nsk.su(E.P. Solodov).

contribution of the K0_SK0_S

ρ

(

770

)

reaction. As a part of the total hadronic crosssection, thecross section ofe+e−

→

K0_SK0_S

π

+

π

−

isinterestingforthecalculationsofthehadronicvacuum polariza-tion and, as a consequence, forthe hadronic contributionto the muon anomalous magnetic moment [2–4]. Until recently, of var-ious possible charge combinations of the KK

¯

π π

final state only two were measured (K+K−

π

+

π

− and K+K−

π

0

_π

0_).

Contribu-tionsfromotherKK

¯

π π

finalstates(K±K0_S

π

∓

π

0_,K0 SK

0 S

π

0

_π

0_etc.)

were taken into account using isospin relations that resulted in largeuncertainties.Themeasurementsofotherexclusivereactions, see [5] andreferencestherein, helpeddecreasingsuch uncertain-tiesandchangedthecontributionofsuchfinalstatestothemuon anomalous magneticmoment from3

.

31

±

0

.

58 to2

.

41

±

0

.

11 in unitsof 10−10 _{fortheenergyrange below2 GeV. Thedifference}

https://doi.org/10.1016/j.physletb.2020.135380

0370-2693/©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

2 R.R. Akhmetshin et al. / Physics Letters B 804 (2020) 135380

Table 1

Energyinterval,integratedluminosity,numberofsignal6-trackevents,numberof signal5-trackevents,detectionefficiency,and theobtainedcrosssectionforthe e+e−→K0SK

0

Sπ+π−reaction.Onlystatisticaluncertaintiesareshown.

Ec.m., MeV L, nb−1 N6π N5π  σK0 SK0Sπ+π−, nb 2007.0±0.5 4259 45±7 19.0±5.0 0.048 0.341±0.047 1980±1 2368 29±6 13.5±4.1 0.053 0.366±0.063 1940–1962 5230 95±10 33.8±6.7 0.055 0.484±0.047 1890–1925 5497 72±9 25.8±5.9 0.059 0.329±0.037 1870–1884 16803 218±17 61.5±10.1 0.061 0.298±0.021 1800–1860 8287 79±11 37.2±7.0 0.064 0.238±0.026 1700–1780 8728 47±8 11.5±4.8 0.066 0.111±0.018 1600–1680 7299 11±4 7.8±3.7 0.068 0.041±0.011

isratherlargeandthedetailedstudy oftheproductiondynamics canfurtherimprovetheaccuracyofthesecalculationsand under-standingoftheenergydependenceofthecrosssection.

Inthispaperwereporttheanalysisofthedatasampleof56.7 pb−1 collected at the CMD-3 detector in the 1.6–2.0 GeV Ec.m.

range. Thesedata were collected during four energy scans, with a 5–10MeV c.m. energystep each, performedat the VEPP-2000

e+e−collider [6–9] inthe2011,2012and2017experimentalruns. In2017(abouthalfofintegratedluminosity)thebeamenergywas monitored by the back-scattering laser-lightsystem [10,11], pro-viding an absolutebeam-energy monitoring withbetter than 0.1 MeV uncertainty at every 10-20 minutes of data taking. In ear-lier runs the beam energy was determined using measurements ofchargedtrackmomentainthedetectormagneticfield withan about1MeVuncertainty.Sincethecrosssectionoftheprocessis small,we combineourscannedpoints intoeightenergyintervals asshowninTable1.

Thegeneral-purposedetectorCMD-3hasbeendescribedin de-tail elsewhere [12]. Its tracking system consists of a cylindrical drift chamber (DC) [13] and double-layer multiwire proportional Z-chamber, both also used for a charged track trigger, and both inside a thin (0.2 X0) superconducting solenoid with a field of

1.3 T.The trackingsystemprovides the98-99%trackingefficiency in about 70% of the solid angle. The liquid xenon (LXe) barrel calorimeterwith a 5.4 X0 thickness has fine electrode structure,

providing 1–2 mm spatial resolution for photons independently of their energy [14], and is located in the cryostat vacuum vol-umeoutsidethesolenoid.ThebarrelCsIcrystalcalorimeterwitha thicknessof8.1 X0 surroundstheLXecalorimeter,whilethe

end-capBGO calorimeterwithathickness of13.4 X0 is placedinside

thesolenoid [15].Altogether,thecalorimeterscover0.9ofthesolid angle and amplitude signals provide information for the neutral trigger.Chargedtriggerrequirespresenceofonlyonechargedtrack inDC,therefore ithas practically 100%efficiency forourstudied processwithfiveorsixdetected tracks.Arelatively largefraction ofthese events hassufficient energy deposition inthe calorime-terforthe independent neutraltrigger: theseevents are usedto controlthechargedtriggerefficiency.The luminosityismeasured usingtheBhabhascatteringeventsatlarge angleswithabout1% systematicuncertainty [16].

Tounderstandthedetectorresponse toprocesses understudy andto obtainthe detectionefficiency, we havedeveloped Monte Carlo(MC) simulationofour detectorbasedon theGEANT4 [17] package,inwhichallsimulatedeventspassthewhole reconstruc-tionandselectionprocedure.TheMCsimulationusesprimary gen-eratorswith the matrixelements forthe K_S0K0_S

π

+

π

− final state withtheK∗

(

892

)

+K∗

(

892

)

−,K1

(

1400

)

K0S

→

K∗

(

892

)

±

π

∓KS0,and

K1

(

1270

)

K0S

→

K0S

ρ

(

770

)

K0S intermediatestates.Theprimary

gen-erator with the K0_SK0_S

π

+

π

− in the phase-space model (PS) has beenalsodeveloped. Theprimary generator includesradiation of photonsbyan initialelectronorpositron,calculatedaccordingto Ref. [20].

2. Selectionofe+e−

→

K_S0K0_S

π

+

π

−events

Theanalysisprocedureissimilartoourstudyoftheproduction of sixcharged pions described in Ref. [19]. Candidate events are requiredtohavefiveorsixcharged-particletracks,eachhaving:

•

morethanfivehitsintheDC;

•

atransversemomentumlargerthan40MeV/c;

•

a minimum distance from a track to the beam axis in the transverseplane oflessthan6cm,thatallowsreconstruction ofadecaypointofK0_S atlargedistances;

•

aminimumdistancefromatracktothecenterofthe interac-tionregionalongthebeamaxisZoflessthan15cm. Reconstructed momenta andangles of thetracks forthe five-andsix-trackeventsareusedforfurtherselection.

Inourreconstructionprocedurewecreatethelistofthe K_S0

→

π

+

π

− candidateswhichincludeseverypairofoppositelycharged tracks,assumingthemtobepions,withtheinvariantmasswithin

±

80 MeV/c2 _{fromthe K}0

S mass [22] and acommon vertexpoint

within a spacialuncertainty of theDC. We calculate momentum andenergyforeach K0_S candidatetakingthevalueoftheK0_S mass fromRef. [22].

At the first stage ofsignal event selectionwe requireatleast two K0

S candidateswithfourindependenttracks plusone ortwo

additional charged tracks originating from the collision point. If there arestill more thantwo K0_S candidates, twocandidate pairs withminimaldeviationsfromtheK0_S massareretained. Addition-ally,werequirethedistancefromthebeamaxisforthetracksnot fromK0

S tobelessthan0.35cm.

Fig.1showsthescatter plotfortheinvariantmassofthefirst

K0_S

→

π

+

π

− candidate vs the second one for data (a) and MC simulation(b).Allenergyintervalsarecombinedforthepresented histogramsindata.Thelinesshowselectionsforthesignalevents in thecentral squareandforthe backgroundlevelestimate from theeventsinothereightsquares.

Fig. 2(a) shows the scatter plot forthe invariant mass of the

K0

S

→

π

+

π

−candidatesvstheradialdistanceofthereconstructed

vertexfromthe beamaxis.Events associatedwith K0_S areclearly seenaswellasthebackgroundevents.Reddots(inthecolor ver-sion)areforsimulation.Fig.2(b)showsaradialdistancefromthe beamaxisforthetracksnotassociatedwiththe K0

S decay.The

ad-ditional requirementfor thisdistance tobe lessthan 0.35cm is shownbytheline.

The central vertical andhorizontalbandsin Fig.1 correspond totheeventswithone wronglyreconstructed K0_S,whichareseen inFig.1(b)alsoforsimulationduetoacombinatorialeffect,orif oneoftheK0_S decaystoothermodes.Fordatatheseeventscanbe also due to a possible background, like e+e−

→

K0_SK±

π

∓

π

+

π

−

witha misidentifiedormissingchargedkaon,whenonlyone K0_S

ispresentinthefinalstate:theseeventscontributetotheselected datasampleinFig.1(a).

Whilewedonotusespecialorderingforthecalculationofthe firstandsecondm

(

K0_S

)

,thebackgroundcontributiontothevertical andhorizontalbandscanbe different,andwe usethe“nine tile” method to extract the numberof signal eventsand estimate the background contribution. In this procedure the two-dimensional plot isdivided intonine tiles withequalarea asshownin Fig.1 by lines.The tiles inFig.1 arenumbered fromleft torightfrom top to bottom. The central (signal) tile contains N5 events with

twowell-reconstructed K0_S candidates,whiletheverticaland hor-izontal tiles, connectedto the central signal tile,are used foran estimate of thebackgroundcontribution to N5 fromthewrongly

Fig. 1. Scatterplotoftheinvariantmassofone

K

0

Scandidatevsinvariantmassforthesecond

K

0Scandidatefordata(a)andMCsimulation(b).Thelinesshowselectionsfor

thesignaleventsandforthebackgroundlevelestimate.

Fig. 2. (a)Scatterplotoftheinvariantmassofthe

K

0

Scandidatevstheradialdistanceofthedecayvertex(crosses):MCsimulationisshownby(redincolorversion)dots.

(b)Radialdistanceofthenot-from-kaonpionsfromthebeamaxis.Thelineshowsappliedselection.

to estimate the random background. The number of background eventsinthecentraltile,Nbkg,isthusdeterminedas

Nbkg

= (

N2

+

N4

+

N6

+

N8)/2

− (

N1

+

N3

+

N7

+

N9)/4

.

(1)

Notethat therandom backgroundfora single tileis takentwice fromtheverticalandhorizontaltiles,sotheaveragerandom back-ground,estimatedfromthecornertiles,isusedforcompensation. Atthenextstageofeventselection,we calculatetheexpected distribution of any kinematic quantity by weighting the contri-bution of the eight tiles as in Eq. (1). This is compared to the distributionobservedinthesignalregion.

Fig.3shows thehistograms fortheradial distance ofthe de-cayvertexforthe K0

S

→

π

+

π

− candidatesinthesignalregionof

Fig. 1 for data (a) and simulation at 1900 MeV (b). Points with errorsrepresentthecontributionofthebackground,estimatedby the“nine tile”methodofEq. (1).Thebackgroundfromthe beam-originatingeventsindataisseeninafewfirstbinsandiswell es-timatedbythemethod:itisnotdominating,sowedonotimpose anyrestrictions onthisdistance.Theprocedureis alsoappliedto the simulation, and Eq. (1) gives about 5% of the “background” events (Fig. 3(b)) due to only one correctly reconstructed K0_S or due to small non-linearity of events in the bands, which is as-sumed to be linearfor the method.In our analysis theseevents aretreatedinthesamewayasfordata.Thesystematic uncertain-tiesofthemethodarediscussedbelow.

Forthe six- orfive-track K0

SK0S

π

+

π

− candidates we calculate

thetotalenergyoftwo K0_S’sandtwopions:forthefive-track can-didatesthemissingmomentum isusedtocalculatetheenergyof thelostpion.Fig.4(a)showsthescatterplotofthedifference be-tween the total energyand c.m. energy, Etot

−

Ec.m., vs the total

momentum of six- (a) or five-track (b) candidates, Ptot for data.

Events fromthecentraltileof Fig.1areshown. Aclearsignal of the e+e−

→

K0_SK_S0

π

+

π

− reaction is seen in Fig. 4(a) asa clus-terofcrossesnear zero,inagreementwith theexpectationfrom the simulation shownby (redin the colorversion) dots. We re-quire Ptotto belessthan180MeV/c2,thusreducing thenumber

ofeventswithhardradiativephotons.

Theexpectedsignaloffive-trackcandidateshastheEtot

−

Ec.m.

valuenearzero,andthePtotvalueisdistributedupto500MeV/c,

as shown by the (red) dots from the signal MC simulation in Fig. 4(b). The (black) crosses show our data: signal events are clearlyseen.

Fig.5 showstheprojection plots ofFig.4, Etot

−

Ec.m., forthe

six-track(a) withappliedselection, andthe five-track(b)events: the histograms present events from the signal tile, while dots with errors are our estimate ofthe background contribution us-ingEq. (1).Allenergyintervalsaresummed.

Toobtainthenumberofsignalevents,weusedistributions of Fig.5fortheEtot

−

Ec.m. difference,i.e.Nsig

=

N5

−

Nbkg.We

six-4 R.R. Akhmetshin et al. / Physics Letters B 804 (2020) 135380

Fig. 3. Radialdistanceofthedecayvertexforthe K0

S→π+π− candidatesinthesignalregionofFig.1fordata(a)andsimulation(b).Dotswitherrorsrepresentthe

backgroundcontributionestimatedfromEq. (1).

Fig. 4. (a)Scatterplotofthedifferencebetweentheenergyof

K

0

SK0Sπ+π−candidatesandc.m.energyvstotalmomentumforeventswithsixtracks.Thecrossesarefordata,

whilethesignalsimulationisshownbyred(incolorversion)dots;thelineshowstheappliedselection.(b)Scatterplotofthedifferencebetweentheenergyof

K

0

SK

0

Sπ+π−

candidatesandc.m.energyvstotalmomentumforeventswithfivetracks.Thecrossesarefordata,whilethesignalsimulationisshownbyred(incolorversion)dots.

Fig. 5. (a)Thedifferencebetweentheenergyofthe

K

0

SK0Sπ+π− candidatesandc.m.energyafterselectionbythelineinFig.4forsix-trackevents(a)andfive-track

Fig. 6. (a)Thedifferencebetweentheenergyofthe

K

0

SKS0π+π−candidatesandc.m.energyafterbackgroundsubtractionforsix-track(a)andfive-trackevents(b)foreight

c.m.energyintervals(dots):lefttoright,toptobottomaccordingtoTable1.Histogramsshowexpectedsignalsfromsimulation,normalizedtothetotalnumberofevents ineachplot.

Fig. 7. (a)Experimental K0

Sπ− vs K

0

Sπ+ invariant massdistribution(twoentriesperevent,crosses)fortheeventsfromthesignalregionofFig.1.Dots(redincolor

version)showthesimulateddistributionforthe

K

∗(892)+K∗(892)−intermediatestate.(b)Projectionplotof(a)(fourentriesperevent)withthefitfunction(solidcurve) todeterminethenumberofeventswiththe

K

∗(892)signaloverthebackgrounddistribution(dottedcurve).Thehistogramshowsthecorrespondingnumberofsimulated eventsforthe

K

∗(892)+K∗(892)−intermediatestate.

and five-track events, and count remaining events in the

±

100 MeVregionforthesix-trackevents,andinthe

±

200MeVregion for the five-track events. The obtained differences are shown in Fig.6 by dots for six- (a)and five-track (b) events: from left to right,fromtoptobottomaccordingtoenergyintervalsofTable1. Thehistogramsshowexpectedsignalsfromthesimulation.In to-tal,we obtain 596

±

27 and210

±

18for six- andfive-track signal events,respectively.Thenumbersofselectedeventsdeterminedin eachenergyintervalarelistedinTable1.

3. Studyoftheproductiondynamics

First attempts to study the dynamics of the process e+e−

→

K0

SK0S

π

+

π

− were carried out by the BaBar Collaboration [1].

Theyreportedtheobservationofthee+e−

→

K∗

(

892

)

+K∗

(

892

)

−,

K∗

(

892

)

±

π

∓K0_S, K0_SK0_S

ρ

(

770

)

processes, which contribute to the

K0

SK0S

π

+

π

− final state, with a dominant production of the

K∗

(

892

)

+K∗

(

892

)

− intermediate state for the c.m. energies be-low 2.5 GeV. In the model of the KK

¯

π

+

π

− production the

K1

(

1400

)

K0S intermediate state decays to K∗

(

892

)

±

π

∓K0S, while

K1

(

1270

)

K_S0canbeobservedinthe K0_SK0_S

ρ

(

770

)

state.

Fig. 7(a) shows the scatter plot of the K0_S

π

− invariant mass vs K0_S

π

+ (two entries/event, all energy intervals are summed) for the K0_SK_S0

π

+

π

− six-track candidates. A clear signal of the correlated production of the pair of charged K∗

(

892

)

’s is seen (crosses),inagreementwiththeexpecteddistributionforthe sim-ulatede+e−

→

K∗

(

892

)

+K∗

(

892

)

−reaction(dots).Fig.7(b)shows the projection plot of (a) (four entries per event) which we fit with the sum ofa double-Gaussian distribution for the K∗

(

892

)

signal and a polynomial function for the background. The back-groundincludes also wrongly assigned K0_S

π

combinations. Gaus-sian parameters are taken from the simulated histogram shown

6 R.R. Akhmetshin et al. / Physics Letters B 804 (2020) 135380

Fig. 8. (a)Thebackground-subtractedπ+π−invariantmassdistribution(dots)incomparisonwiththesimulateddistribution(solidhistogram).(b)Thebackground-subtracted K0Sπ+π−(twoentriesperevent)invariantmassdistribution(dots)incomparisonwiththesimulatedone(asolidhistogram).Inbothplotsthesimulateddistributionincludes

the

K

∗(892)+K∗(892)−intermediatestateplus30%ofthe

K

1(1270)K0S,whichcontributionisshownbyadottedhistogram.

Fig. 9. (a)Thebackground-subtractedexperimental(dots)polarangledistributionincomparisonwiththesimulateddistribution(histograms)forthemissingpion(a)andall detectedpions(b).

in Fig. 7(b). The fit yields 788

±

73

±

95 events: a second uncer-tainty is from a variation of the fit functions. Each event from the K∗

(

892

)

+K∗

(

892

)

− reaction contributes twice, so a half of thisvalue should be compared to 596

±

27, thetotal number of thesix-tracksignalevents.Theobtainednumberindicatesthatthe contributionoftheK∗

(

892

)

+K∗

(

892

)

−intermediatestatedoesnot exceed66

±

11%.

With our data we cannot quantitatively extract a contribu-tionfromproductionofa single K∗

(

892

)

orfromeventswithout

K∗

(

892

)

’s.

Wecalculatethebackground-subtractedinvariantmassforthe twopionsinthesix-tracksample,notoriginatingfromK0_S,shown inFig.8(a),andforthe K_S0

π

+

π

− invariantmass(twoentriesper event), shown in Fig. 8(b). These distributions indicate that the

ρ

(

770

)

resonanceinthe

π

+

π

− invariantmass,andthe K1

(

1270

)

resonancein the K0_S

π

+

π

− invariant massdistribution cannot be excluded. The solid histograms show the simulated distributions of the K∗

(

892

)

+K∗

(

892

)

− intermediate state summed with the 30%contributionfromtheK1

(

1270

)

K0S

→

K0SK0S

ρ

(

770

)

intermedi-atestate.Thelattercontributionisshownbythedottedhistogram.

Withthecurrentdatasamplewecannotquantitativelyextractthis contribution.

4. Detectionefficiency

Inourexperiment, theacceptanceoftheDCforchargedtracks is not100%, andthe detectionefficiencydependsonthe produc-tiondynamicsofthereactionaswellasonthetrackreconstruction efficiencyintheDC.

To obtain the detection efficiency, we simulate K0_SK0_S

π

+

π

−

productionin theprimary generators,50000 eventsforeach c.m. energyintervalforeachmodel,passsimulatedeventsthroughthe CMD-3 detectorusing theGEANT4 [17] package, andreconstruct them withthesamesoftware asexperimentaldata.We calculate the detection efficiencyfrom theMC-simulated events asa ratio of events afterthe selectionsdescribed inSecs. 2,3 to the total numberofgeneratedevents.

Our selection ofsix- and five-track signal eventsallows us to estimate a differencein thetrackingefficiencyindata and simu-lation.Fig.9showsbydotsthebackground-subtractedpolarangle foramissingpion(a)andforalldetectedpions(b).Thehistogram

Fig. 10. (a)The ratioof the numberof five- to six-track eventsfor data (dots) and simulation for the different intermediatestates: phasespace model(squares), K∗(892)+K∗(892)− intermediatestate(opensquares),

K

1(1400)KS0(triangles),and K1(1270)K0S intermediatestate(open circles).(b)Detectionefficiencyobtainedfrom

theMCsimulationforthe

e

+e−→K0

SK

0

Sπ+π−reactionforthedifferentintermediatestates(symbolslegendisthesameasfor(a)).

represents the simulated distribution forthe K∗

(

892

)

+K∗

(

892

)

− intermediatestate.Weobservereasonableagreementfordataand simulation inthese distributions as well as inthe calculated ra-tioofthenumberoffive- tosix-trackeventsateach c.m.energy interval,shownin Fig.10 (a)by open squares. Thevalues ofthe ratioforthephase-spacemodel(squares), K1

(

1400

)

K0S (triangles),

andK1

(

1270

)

K0_S intermediatestate (opencircles) arealsoshown

inFig.10(a)andtheyarelesscompatiblewithdata.

Wecalculatethedetectionefficiencyforthesumofeventswith sixandfivedetectedtracks.Fig.10(b)showsthedetection efficien-cies obtained for the e+e−

→

K0

SK0S

π

+

π

− reaction fordifferent

intermediate states:markers are thesame asforFig. 10(a). The detectionefficiencies fordifferentmodesare relatively close, and the efficiencies calculated for the K∗

(

892

)

+K∗

(

892

)

− intermedi-ate state only and calculated with a 30% contribution from the

K1

(

1270

)

K0S reactiondifferbylessorabout5%.

5. Crosssectioncalculation

Ineachenergyintervalthecrosssectioniscalculatedas

σ

=

N6π

+

N5π

L

·



· (

1

+ δ)

,

where N6π , N5π are the background-subtracted numbers of

sig-naleventswithsixandfivetracks,L istheintegratedluminosity forthisenergyinterval,



is thedetection efficiency,and

(

1

+ δ)

is the radiative correction calculated according to Ref. [20,21]. To calculate the radiative correction, we use BaBar data for the

e+e−

→

K0_SK0_S

π

+

π

−reaction[1] asafirstapproximation,and ob-tain

(

1

+ δ)

=

0

.

92 withveryweakenergydependence.

Wecalculatethecrosssectionsforthee+e−

→

K_S0K0_S

π

+

π

− re-actions usingthe efficiency shownby open squaresin Fig. 10(b) for the K∗

(

892

)

+K∗

(

892

)

− intermediate state. The cross section isshownin Fig.11. Wealso calculatethe crosssection by using onlyeventswithsixdetected tracks: a lessthan5% difference is observed.

Theenergy interval,integratedluminosity, thenumberof six-andfive-trackevents,efficiency,andtheobtainedcrosssectionfor eachenergyintervalarelistedinTable1.

Fig. 11. The

e

+e−→K0

SK

0

Sπ+π−crosssectionmeasuredwiththeCMD-3detector

atVEPP-2000(circles).TheresultsoftheBaBarmeasurement [1] areshownbyopen circles.

6. Systematicuncertainties

The following sources of systematic uncertainties are consid-ered.

•

The tracking efficiencywas studied in detail inour previous papers [18,19],andthecorrectionforthetrackreconstruction efficiency compared to the MC simulation is about1.0

±

1.0% per track.Sincewe add events withonemissingtrack (from the twonot from K0_S),the MC-simulated detectionefficiency iscorrectedby(–5

±

3)%:theuncertaintyistakenasthe corre-spondingsystematicuncertainty.

•

The model dependence of the acceptance is determined by comparing efficiencies calculatedfor thedifferent production dynamics.The maximumdifference ofthe detection efficien-cies of the dominant K∗

(

892

)

+K∗

(

892

)

− intermediate state andthoseforother statesis about15%. apossibleadmixture (ofabout30%)ofother stateschangestheefficiencybyabout 5%,whatistakenasthesystematicuncertaintyestimate.

•

Sinceonlyonechargedtrackissufficientforatrigger(98–99% single track efficiency),and usinga cross check withthe in-dependentneutraltrigger,weconcludethatforthemultitrack

8 R.R. Akhmetshin et al. / Physics Letters B 804 (2020) 135380

eventsthe trigger inefficiency givesa negligible contribution tothesystematicuncertainty.

•

The systematic uncertainty due to the selection criteria is studied by varying the requirements described above and doesn’texceed5%.

•

The uncertainty on the determination of the integrated lu-minositycomes fromthe selection criteriaofBhabha events, radiativecorrectionsandcalibrations ofDCandCsI anddoes notexceed1% [16].

•

The uncertainty in the background subtraction is studied by the variation of the tile dimensions (20

×

20, 25

×

25, and 30

×

30MeV/c2 dimensionstested),andby thecomparisonof thecrosssectioncalculatedusingonlysix-trackevents.Aless than5%differenceisobserved.

•

Theradiativecorrection uncertaintyisestimatedasabout2%, mainlydue tothe uncertaintyon themaximum allowed en-ergyoftheemittedphoton,aswellasfromtheuncertaintyon thecrosssection.

Theabovesystematicuncertaintiessummedinquadraturegive anoverallsystematicerrorofabout10%.

7. Conclusion

Thetotalcrosssectionoftheprocess e+e−

→

K0_SK0_S

π

+

π

− has beenmeasuredusing56.7pb−1 _{ofintegratedluminositycollected}

by the CMD-3 detector at the VEPP-2000 e+e− collider in the 1.6–2.0GeVc.m.energyrange.Thesystematicuncertaintyisabout 10%.Fromourstudywecanconcludethattheobservedcross sec-tioncanbedescribedbythee+e−

→

K∗

(

892

)

+K∗

(

892

)

−reaction, but an about 30–35% contribution of the K1

(

1270

)

K0S

interme-diate state is not excluded. The measured cross section for the

e+e−

→

K0_SK0_S

π

+

π

− reactionagreeswiththeonlyavailable mea-surementbyBaBar [1].

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

The authorsare gratefultoA.I. Milsteinforhis helpwith the-oretical interpretation anddevelopmentof themodels.We thank theVEPP-2000teamforexcellent machineoperation.Theworkis partially supported by the Russian Foundation forBasic Research grant17-02-00897.

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