Study of the process e+e− → 3(π+π−)π0 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, Y.V.(2019). Study of the process e

+

_e

−

_→ 3(π

+

_π

−

_)π

0

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

792, 419-423.

https://doi.org/10.1016/j.physletb.2019.04.007

UVicSPACE: Research & Learning Repository

_____________________________________________________________

Faculty of Science

Faculty Publications

_____________________________________________________________

Study of the process e

+

_e

−

_→ 3(π

+

_π

−

_)π

0

_{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, A.A. Grebenuk, S.S.

Gribanov, D.N. Grigoriev, …Yu.V. Yudin

May 2019

©2019 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:

V.Sh. Banzarov

,

N.S. Bashtovoy

,

D.E. Berkaev

,

A.E. Bondar

,

A.V. Bragin

,

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

,

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

_,

_{V.F. Kazanin}

a

,

b

_,

_{I.A. Koop}

a

,

b

_,

_{A.N. Kirpotin}

a

_,

_{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

,

K.Yu. Mikhailov

a

,

V.S. Okhapkin

a

,

A.V. Otboev

a

,

Yu.N. Pestov

a

,

A.S. Popov

a

,

b

,

G.P. Razuvaev

a

,

b

,

Yu.A. Rogovsky

a

,

A.A. Ruban

a

,

N.M. Ryskulov

a

,

A.E. Ryzhenenkov

a

,

b

,

A.I. Senchenko

a

,

Yu.M. Shatunov

a

,

P.Yu. 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

,

∗

,

V.M. Titov

a

,

A.A. Talyshev

a

,

b

,

A.I. Vorobiov

a

,

I.M. Zemlyansky

a

,

Yu.V. Yudin

a

,

b

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

c_{NovosibirskStateTechnicalUniversity,Novosibirsk,630092,Russia} d_{UniversityofVictoria,Victoria,BC,V8W3P6,Canada}

e_{LebedevPhysicalInstituteRAS,Moscow,119333,Russia}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received19February2019

Receivedinrevisedform12March2019 Accepted5April2019

Availableonline9April2019 Editor: L.Rolandi

The cross sectionof the processe+e−_→3(

π

+

π

−)

π

0 _{hasbeen measured forthe first time usinga}

data sampleof56.7pb−1collectedwiththeCMD-3detectorattheVEPP-2000e+e− collider.632±32 signaleventshavebeenselectedinthecenter-of-massenergyrange1.6–2.0GeV.Astudyofdynamicsof seven-pionproductionallowsonetoextractcontributionsofthedominated2(

π

+

π

−)

ω

and2(

π

+

π

−)

η

intermediatestates.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Production of seven pions in e+e− annihilation has not been studied before. A partial estimate of the cross section is pos-sible from the BaBar measurement of the cross section of the

e+e−

→

2

(

π

+

π

−

)

η

,

η

→

γ γ

[1] reaction, based on the Initial-StateRadiation(ISR)method.Usingthewell-known

η

→

π

+

π

−

π

0

decayrate, acontribution tothe seven-pion crosssection can be calculated.Asapartofthetotal hadroniccross section,thecross sectionofe+e−

→

3

(

π

+

π

−

)

π

0 _{isinteresting forthe calculations}

*

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

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

ofthehadroniccontributiontothemuonanomalousmagnetic mo-ment [2–4]. The detailed study of the production dynamics can further improve the accuracy of thesecalculations and can help explainenergydependenceofthecrosssection.

Inthispaperwe report theanalysisofthedata samplebased on56.7pb−1 _{oftheintegratedluminositycollectedattheCMD-3}

detector in the 1.6–2.0 GeV center-of-mass (c.m.) energy range. Thesedatawerecollectedinfourenergyscans,about50c.m. en-ergypointseach,performedattheVEPP-2000e+e−collider [5–8] in the 2011, 2012and 2017 experimental runs. In the 2017 ex-perimentalrunthebeamenergyhasbeenmonitoredbythe back-scattering-laser-light system [9,10], providing an absolute energy measurementwithbetterthan0.1MeVuncertaintyineverysingle measurement. In earlier runsbeam energy hasbeen determined https://doi.org/10.1016/j.physletb.2019.04.007

0370-2693/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

420 R.R. Akhmetshin et al. / Physics Letters B 792 (2019) 419–423

Fig. 1. (a)Scatterplotofthedifferencebetweentheenergyofsevenpionsandc.m.energy(E)vstotalmomentum.Thelineshowstheboundaryoftheappliedselection, wheredatapoints areshownbyincreasedcircles,andseven-pionsignalsimulationisshownbyred crosses;(b)Projectionplotof(a).Thesolidhistogramsshow the normalizedMC-simulateddistributionfortheexpectedseven-pionsignal(leftpeak)andsix-pionbackground(rightpeak).

usingchargetrackmomentaindetectormagneticfieldwithabout 1MeVuncertainty.Sincethecrosssectionoftheprocessissmall, we combine our scanned points into eight energy intervals as showninTable1.

Thegeneral-purposedetectorCMD-3hasbeendescribedin de-tail elsewhere [11]. Its tracking system consists of a cylindrical drift chamber (DC) [12] and double-layer multiwire proportional Z-chamber, both also used for a trigger, and both inside a thin (0.2 X0) superconducting solenoid with a field of 1.3 T. The

liq-uid xenon (LXe) barrel calorimeter with a 5.4 X0 thickness has

fineelectrodestructure,providing1–2mmspatialresolution [13], and shares the cryostat vacuum volume with the superconduct-ing solenoid. The barrel CsI crystal calorimeter with a thickness of 8.1 X0 is placed outside the LXe calorimeter, and the

end-cap BGO calorimeter with a thickness of 13.4 X0 is placed

in-side the solenoid [14]. The luminosity is measured using events ofBhabhascatteringatlargeangleswithabout1%systematic un-certainty [15].

2. Selectionofe+e−

→

3

(

π

+

π

−

)

π

0_events

The analysis procedure is based on our study of the six-charged-pionreactiondescribed inRef. [18].Candidateeventsare requiredtohavesixcharged-particletracks,eachonehaving:

•

morethanfivehitsintheDC.

•

amomentumislargerthan40MeV/c.

•

a minimum distance from a track to the beam axis in the transverseplaneislessthan0.5cm.

•

aminimumdistancefromatracktothecenterofthe interac-tionregionalongthebeamaxisZislessthan10cm.

•

apolaranglelargeenoughtocrosshalfoftheDCradius. Reconstructed momenta andangles ofthe tracks forsix-track eventswereusedforfurtherselection.

Theanalysisstrategyisbasedonthereconstructionofthe six-charged-pion system, assuming a missing

π

0 _{particle. The total}

energyEtotofthesevenpionfinalstateiscalculatedfromthetotal

momentumPtotofchargedtracks:

Ptot

= |

6



i=1

¯

pi

|,

Etot

=

6



i=1



p2 i

+

m2π

+



P2 tot

+

m2_π0

.

We donot usecalorimeterresponse for thephotonsfromthe

π

0 _{decay due to large number of extra soft clusters from the}

charge pion nuclear interactions. Theseclusters are not properly reproducedinsimulation.

Fig. 1(a) shows a scatter plot of the difference between the total energy andc.m. energy,



E

=

Etot

−

Ec.m., vs the total

mo-mentum Ptot for the six-track candidates. A clear signal of the e+e−

→

3

(

π

+

π

−

)

reactionisseenin dataasa clusterofdots at



E

=

135 MeVandthetotal momentumnearzero.Theexpected seven-pionsignalhasthe



E valuenearzero,andthePtotvalueis

distributedup to 400MeV/c,asshownby the(red)crossesfrom the Monte Carlo(MC) signal simulation. The enlarged (blue) cir-cles show data in the region where we search for signal events. Fig. 1(b)showstheprojection plotof(a): circlesare forthedata and the histograms show the normalized to data MC-simulated distributionsfortheseven-pionsignalandsix-pionbackground.

Toreduceacontributionfromsix-pionevents,weselectevents belowthelineshowninFig.1(a).The



E distributionoftheevent candidatesafterselectionisshowninFig.2(a)bycircles,whilethe histogramshowstheremainingcontributionofthesix-pionevents. The observed signal of six-pion eventsateach energy interval is used to normalizetheMC simulation. Wesubtract this contribu-tionfromtheexperimentaldistributionofFig.2(a),andshowthe resultinFig.2(b)togetherwiththefitfunctionsusedtodetermine the numberofseven-pioneventsandremaining background.The signal lineshape is taken fromthe MC simulation of the seven-pion process, shownby the histogram, and is well described by the double-Gaussian function. All parameters of the signal func-tion arefixed accordingto MCsimulationateach energyinterval exceptforthenumberofeventsandthemainGaussianresolution. A third-orderpolynomial isusedto describetheremaining back-grounddistributionshownbythedashedlineinFig.2(b).

Avariation ofthepolynomialparameters forthe experimental andMC-simulated signal distributions aswell asvariation of ap-pliedselectionsleadtoanabout10%uncertaintyonthenumberof signal events,whichistakenasanestimate ofthesystematic un-certainty.Thebackgroundcontributionincreaseswithenergy,and forthehighestenergyintervalweestimatethisuncertaintyas15%. We apply this procedure to the eventsample in each energy interval, andintotalfind632

±

32signalevents,corresponding to theprocesse+e−

→

3

(

π

+

π

−

)

π

0_{inthestudiedenergyrange.The}

numbersofselectedeventsdeterminedineachenergyintervalare listedinTable1.

Fig. 2. (a)Thedifferencebetweentheenergyofsevenpionsandc.m.energy(E)afterselectionbythelineinFig.1(a).Allenergyintervalsaresummed.Thehistogram showsthenormalizedtothedataofFig.1(b)MC-simulateddistributionfortheremainingsix-pionbackground.(b)Exampleofthefittotheseven-pionsignal(solidline) andremainingbackground(dashedline)afterthesix-pionbackgroundsubtraction.ThehistogramshowstheexpectedsignalfromtheMCsimulation.

Fig. 3. (a)Experimentalπ+π−π0_{invariantmassdistribution(nineentriesperevent)fortheeventsfromthesignalpeakofFig.2(b).Thesolidlineshowsthefitfunctions} describingthe signalsfromη,ω,and thecombinatorialbackground(dashedcurve).Thehistogram representsMCsimulationinthe phase-spacemodel.(b)Detection efficiencyobtainedfromtheMCsimulationforthe2(π+π−)ωmodel(squares),andforthe2(π+π−)ηone(circles)incaseofextractingeventsfromtheE peakof Fig.2(b),orfromtheηandtheωsignalsinthethree-pionmassdistribution(trianglesandup-downtriangles,respectively).

3. Firststudyoftheproductiondynamics

Thedynamicsoftheprocesse+e−

→

3

(

π

+

π

−

)

π

0_hasnotbeen

studiedpreviously.TheBaBarCollaboration [1] reportedthe obser-vation of the e+e−

→

2

(

π

+

π

−

)

η

,

η

→

γ γ

process, which con-tributes to seven final-state pions if the

η

decays to

π

+

π

−

π

0_.

Weinvestigatetheproductionmechanismsusingtheeventsinthe signal region of Fig. 2(b)using the requirement

|

E

| <

60 MeV. Fig. 3(a) shows an invariant mass distribution for all

π

+

π

−

π

0

combinations(nineentriesperevent)forselectedevents.The sig-nal from the

η

meson is clearly seen, as well as presence of the

ω

(

782

)

resonance in the intermediate state with the

ω

→

π

+

π

−

π

0 _{decay. To obtain the number of events with}

_η

_and

_ω

inthe intermediate states, we fit this distribution withthe sum of functions describing combinatorial background and the peaks from the

η

and the

ω

signals as shown by the solid curve in Fig.3(a).Ourresolution issignificantly largerthan theresonance widths(about20MeV),andweusetheGaussian functionforthe peaks,whilethepolynomialfunctionisusedforthecombinatorial background(thedashed lineinFig.3(a)).Thecombinatorial back-groundis welldescribed by theMC-simulateddistribution inthe

phase-space model without any intermediate resonances, shown by thehistograminFig.3(a).Intotal,we obtain280

±

36 events forthee+e−

→

2

(

π

+

π

−

)

η

,

η

→

π

+

π

−

π

0 _{process and204}

_±

₃₇

eventsfore+e−

→

2

(

π

+

π

−

)

ω

,

ω

→

π

+

π

−

π

0_{.Notethat the}

to-talnumberofthe3

(

π

+

π

−

)

π

0 _events(632

_±

_{32)exceedsthesum}

ofthe eventsfromthe

η

and

ω

peaks(484

±

52) by about32%: thisisdiscussedbelow.

Weapplythisfittoeveryenergyintervalandlisttheobtained numberofeventsinTable1.

Wecalculatethe invariantmassesforthecombinations ofthe two(totalcharge

±

1 orzero),thefour(totalchargezero),andthe five(totalchargezero)pionsfromtheselectedevents,andfindno signalfromthe

ρ

(

770

)

resonanceorfromanyotherresonancesin our rangeof the c.m. energies. In general, all thesedistributions arewelldescribedbythephase-spacemodel.

4. Detectionefficiency

Inourexperiment,theacceptanceoftheDCforchargedtracks isnot 100%,andthedetectionefficiencydependson the produc-tion dynamics of seven pions. We have developed the primary generators for the seven-pion final-state production in the e+e−

422 R.R. Akhmetshin et al. / Physics Letters B 792 (2019) 419–423

Fig. 4. (a)Thee+e−→2(π+π−)ηcrosssectionmeasuredwiththeCMD-3detectoratVEPP-2000(circles).TheresultsoftheBaBarmeasurement [1] areshownbyopen circles.(b)Thee+e−→2(π+π−)ωcrosssectionmeasuredwiththeCMD-3detectoratVEPP-2000.

collisionforthe phase-spacemodel,andforthe modelswiththe intermediate2

(

π

+

π

−

)

η

and2

(

π

+

π

−

)

ω

states.Inourmodelthe 2

(

π

+

π

−

)

η

intermediate state is described as the

ρ

(

1450

)

η

pro-ductionwiththe

ρ

(

1450

)

decayeithertofourpionsintheP-wave ortothea1

(

1260

)

π

state.The2

(

π

+

π

−

)

ω

stateismodeledas

pro-duction ofthe f0

(

1370

)

ω

state, followed by fourpions fromthe f0

(

1370

)

decayintheS-wave.

Toobtainthedetectionefficiency,wesimulateseven-pion pro-ductionintheprimary generators,passsimulatedeventsthrough the CMD-3 detector using the GEANT4 [16] package, and recon-struct them with the same reconstruction software as experi-mental data.We calculate the detection efficiencyfrom the MC-simulatedeventsasaratioofeventsaftertheselectionsdescribed inSecs.2,3tothetotalnumberofgeneratedevents.

Fig. 4(b) shows the detection efficiency obtained for the 2

(

π

+

π

−

)

ω

(squares) andfor the 2

(

π

+

π

−

)

η

(circles) intermedi-ate states when the number of signal events is obtained from the fit ofthe



E peak of Fig. 2(b).Due to the difference inthe angularand momentum distributions ofthe pions, the efficiency for the 2

(

π

+

π

−

)

η

intermediate state is lower compared to the 2

(

π

+

π

−

)

ω

model:about10%and13%,respectively.Variations of the dynamics or resonance parameters inside the initial “vector-pseudo-scalar”stateforthe2

(

π

+

π

−

)

η

production,andinsidethe “scalar-vector”state forthe2

(

π

+

π

−

)

ω

productiondonot change theobtaineddetectionefficiencybymorethan3–5%.

IfwedeterminethenumberoftheMC-simulatedeventsusing the

η

and

ω

peaksfromthehistogramsimilarlytothatinFig.3(a), the detection efficiencydecreases additionallyby 20–40% dueto the

|

E

| <

60MeV requirement. Theseefficiencies are shown in Fig. 3(b) by triangles and up-down triangles for the 2

(

π

+

π

−

)

η

and2

(

π

+

π

−

)

ω

states,respectively.

5. Crosssectioncalculation

Ineachenergyintervalthecrosssectioniscalculatedas

σ

=

N

L

·

· (

1

+ δ)

,

where N is the number of signal events, L is the integrated lu-minosityforthisenergyinterval,

isthedetectionefficiency,and

(

1

+ δ)

istheradiativecorrectioncalculatedaccordingtoRef. [19, 20]. To calculate the radiative correction, we use BaBar data for thee+e−

→

2

(

π

+

π

−

)

η

reaction[1] asa firstapproximation,and obtain

(

1

+ δ)

=

0

.

92 withveryweakenergydependence.

Fig. 5. Thee+e−→3(π+π−)π0_{crosssectionmeasuredwiththeCMD-3detector} atVEPP-2000(dots).Thecontributionfromthee+e−→2(π+π−)ηande+e−→ 2(π+π−)ωreactionsareshownbytrianglesandopencircles,respectively.

Wecalculatethecrosssectionsforthee+e−

→

2

(

π

+

π

−

)

η

and

e+e−

→

2

(

π

+

π

−

)

ω

reactionsusingtheefficienciesshownby tri-anglesandup-downtrianglesinFig.3(b),respectively.Thesecross sections are shown in Fig. 4(a,b): the branching fractions of the

η

→

π

+

π

−

π

0 _and

_ω

_→

_π

+

_π

−

_π

0 _{decays aretakeninto account}

usingvaluesfromRef. [21].Weobserverelativelygoodagreement withtheBaBarmeasurementofthee+e−

→

2

(

π

+

π

−

)

η

reaction, while no other measurements exist for the e+e−

→

2

(

π

+

π

−

)

ω

crosssection.

As mentioned in Secs. 2, 3, the total numberof 3

(

π

+

π

−

)

π

0

events is about32% larger than the sum ofthe individual chan-nels withthe

η

and

ω

intermediate states. Thisdifference is al-most eliminated after taking into account the difference in the efficiency obtained by the fit of



E or by the fit of the

η

and

ω

signals where cut

|

E

<

60

|

MeV is applied: the average ra-tios are about 1.35–1.37 for both channels. The obtained num-berNeff

= ((

280

±

36

)

+ (

204

±

37

))

·

1

.

36

=

658

±

70 isconsistent

withthetotalnumberofthe3

(

π

+

π

−

)

π

0_events(632

_±

_32)within

the statistical uncertainty. We come to the conclusion that the inclusive e+e−

→

3

(

π

+

π

−

)

π

0 _{crosssection is completely}

domi-nated bythesumofthetwointermediatestateswithinthe mea-suredaccuracy.

To calculate the inclusive cross section for the e+e−

→

uncertaintyduetostatisticalfluctuationsoftheratio.

Forcomparison, we show in Fig. 5 the contribution fromthe

e+e−

→

2

(

π

+

π

−

)

η

and e+e−

→

2

(

π

+

π

−

)

ω

reactions by trian-glesandopencircles,respectively:onlydecaysof

η

and

ω

tothree pionsare taken. The e+e−

→

π

+

π

−

η



(

958

)

reaction,reportedin Ref. [1], contributes about 0.1 nb to the total cross section at

Ec.m.

=

2

.

0 GeV, butthe decay rateof

η



(

958

)

→

2

(

π

+

π

−

)

η

→

3

(

π

+

π

−

)

π

0 _{to the studied final state reduces the visible cross}

section to 0.01 nb, what is lessthan a sensitivityof our experi-ment.

The integrated luminosity, the number of the seven-pion events,thenumberofeventsforthe 2

(

π

+

π

−

)

η

and2

(

π

+

π

−

)

ω

intermediate states, and obtained cross sections for each energy intervalarelistedinTable1.

6. Systematicuncertainties

The following sources of systematic uncertainties are consid-ered.

•

The trackingefficiency was studied in detail in our previous papers [17,18],andthecorrectionforthetrackreconstruction efficiency compared to the MC simulation is about 1.5

±

1.0% per track:the MC-simulated detection efficiencyis corrected by -6%while3%istakenasthecorrespondingsystematic un-certainty.

•

The model dependence of the acceptance is determined us-ing the comparisonofefficiencies calculatedforthedifferent productiondynamicsfore+e−

→

2

(

π

+

π

−

)

η

andthee+e−

→

2

(

π

+

π

−

)

ω

reactions.Itisestimatedas3–5%.

•

Sinceonlyonechargedtrackissufficientforatrigger(98–99% efficiency), we assume that forthe multitrack events consid-eredinthisanalysisthetriggerinefficiency givesanegligible contributiontothesystematicuncertainty.

•

Asystematicuncertaintyduetotheselection criteriais stud-ied by varyingthe requirementsdescribed aboveanddoesn’t exceed5%.

•

The uncertainty on the determination of the integrated lu-minosity comes fromtheselection criteriaof Bhabhaevents, radiative correctionsandcalibrations ofDCandCsI anddoes notexceed1% [15].

•

The uncertainty in the background subtractionis studied by thevariationofthefunctionsusedforthebackground descrip-tioninthefit,showninFig.2(b)andisestimatedas10%(15% for Ec.m.

=

2

.

0 GeV).

•

The radiativecorrectionuncertaintyisestimatedasabout2%, mainly dueto the uncertaintyonthe maximum allowed

en-differenceintheefficiencyforthe2

(

π

+

π

−

)

η

and2

(

π

+

π

−

)

ω

intermediatestates.

Theabovesystematicuncertaintiessummedinquadraturegive anoverallsystematicerrorofabout13%,increasingto20%forthe inclusivecrosssection.

7. Conclusion

Thetotalcrosssectionoftheprocesse+e−

→

3

(

π

+

π

−

)

π

0 _has

beenmeasuredforthefirsttimeusing56.7pb−1 ofintegrated lu-minositycollectedbytheCMD-3detectorattheVEPP-2000e+e−

colliderinthe1.6–2.0GeVc.m. energyrange.From ourstudywe canconcludethattheobserved crosssection canbe describedby the e+e−

→

2

(

π

+

π

−

)

η

and the e+e−

→

2

(

π

+

π

−

)

ω

reactions. The measured cross section for the e+e−

→

2

(

π

+

π

−

)

η

reaction is in good agreement with the only available measurement by BaBar [1].

Acknowledgements

The authorsaregratefulto A.I. Milsteinforhishelp with the-oretical interpretationanddevelopment ofthe models.We thank the VEPP-2000 team for excellent machine operation. This work ispartially supported bythe RussianFoundation ofthe Basic Re-searchgrant18-32-01020.

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