Study of the process e+ e− → π+ π− π0 η in the c.m. energy range 1394–2005 MeV with the CMD-3 detector

(1)

Citation for this paper:

Akhmetshin et al., (2017). Study of the process

e

+

_e

−

→

π

+

π

−

π

0

η

in the c.m.

energy range 1394–2005 MeV with the CMD-3 detector. Physics Letters B,

773(October), 150-158. https://doi.org/10.1016/j.physletb.2017.08.019

UVicSPACE: Research & Learning Repository

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Faculty Publications

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Study of the process

e

+

_e

−

→

π

+

π

−

π

0

η

in the c.m. energy range 1394–2005 MeV

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, F.V. Ignatov, V.L. Ivanov, S.V. Karpov,

V.F. Kazanin, I.A. Koop, A.N. Kirpotin, A.A. Korobov, A.N. Kozyrev, E.A. Kozyrev,

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,

Yu.A. Rogovsky, A.A. Ruban, N.M. Ryskulov, A.E. Ryzhenenkov, A.I. Senchenko,

Yu.M. Shatunov, P.Yu. Shatunov, V.E. Shebalin, D.N. Shemyakin, B.A. Shwartz,

D.B. Shwartz, A.L. Sibidanov, E.P. Solodov, V.M. Titov, A.A. Talyshev, A.I.

Vorobiov, I.M. Zemlyansky, Yu.V. Yudin

October 2017

©2017 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:

(2)

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Study

of

the

process

e

+

e

−

→

π

+

π

−

π

0

η

in

the

c.m. energy

range

1394–2005 MeV

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

,

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_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

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received22June2017

Receivedinrevisedform3August2017 Accepted5August2017

Availableonline18August2017 Editor:L.Rolandi

Thecrosssectionoftheprocesse+e−_→

π

+

π

−

π

0

_η

_has_been_measured_using_a_data_sample_of₂₁_._{8 pb}−1 collectedwiththeCMD-3detectorattheVEPP-2000 e+e− collider.2769±95 signaleventshavebeen selectedinthecenter-of-massenergyrange1394–2005 MeV.Theproductiondynamicsisdominatedby the

ω

(782)

η

and φ(1020)

η

intermediatestatesinthe lowerenergy range,and bythea0(980)

ρ

(770) intermediatestateathigherenergies.

1. Introduction

Theproductiondynamicsofthe

π

+

π

−

π

0

_η

_ﬁnal_state_in_e+_e− annihilation has been never studied before. Only the e+e−

→

ω

(

782

)

η

cross section was measured by the BaBar Collabora-tion [1] with a relatively low statistical accuracy using

η

→

π

+

π

−

π

0 _decay,_and_by _the_SND_{Collaboration}_[2]_(with

_η

_→

_{γ γ}

decay). The e+e−

→

π

+

π

−

π

0

_η

_cross _section _contributes _a _not negligible value (upto 15%of thetotal hadroniccross section in

*

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

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

some energy range)to the calculationsofthe hadronic contribu-tiontothemuonanomalousmagneticmoment[3],andadetailed study of the production dynamics can further improve the ac-curacy of these calculationsas well as our understanding of the spectroscopyoflightmesons.

In thispaperwereport theanalysisofthe datasample based on21

.

8 pb−1oftheintegratedluminosity collectedattheCMD-3 detector in the 1394–2005 MeV center-of-mass energy (Ec.m.) range.Weidentifythe

π

+

π

−

π

0

_η

_candidate_events_using

_η

_→

_{γ γ}

decay, andobservenocandidateeventsbelow Ec.m.

=

1400 MeV. Thesedatahavebeencollectedinthreeenergyscansat40c.m. en-ergy points,performedattheVEPP-2000collider[4]in2011and 2012.

http://dx.doi.org/10.1016/j.physletb.2017.08.019

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Thegeneral-purposedetectorCMD-3hasbeendescribedin de-tail elsewhere [5]. Its tracking system consists of a cylindrical drift chamber (DC) [6] and double-layer multiwire proportional Z-chamber, both also used for a trigger, and both inside a thin (0.2 X0)superconductingsolenoidwithaﬁeldof1.3 T.Thetracking systemallowstodetectchargedtrackswithaminimumpolar an-gleabout0.5radiansrelativetothebeamaxis(about90%of4

π

). Thebarrelliquid-xenon(LXe)calorimeterwitha 5.4 X0 thickness hasﬁne electrode structure, providing a 1–2 mm spatial resolu-tionforphotons[7],andsharesthecryostatvacuumvolumewith thesuperconductingsolenoid. ThebarrelCsI-crystalcalorimeteris placedoutsidethe LXe calorimeter,andincreasesthe total thick-nessto 13.5 X0.TheendcapBGO calorimeterwithathicknessof 13.4 X0 isplacedinsidethesolenoid[8].Ourcombined calorime-terallows to detect photons with a minimum polarangle down to0.25radians relative tothe beamaxis(about 98%of 4

π

). The luminosityismeasuredusingeventsofBhabhascatteringatlarge angleswithabout1%accuracy[9].

Thebeamenergyhasbeenmonitoredbymeasuringthecurrent inthedipolemagnetsofthemainring,andatafewenergypoints by usingthe Back-Scattering-Laser-Light system [10]. Using mea-suredaveragemomentumofBhabhaevents,andaverage momen-tumofproton–antiprotonpairsfromtheprocesse+e−

→

pp

¯

[11], wedetermineEc.m. ateachenergypointwithabout1 MeV accu-racy.

Tounderstandthedetectorresponse toprocessesunder study and to obtain a detection eﬃciency, we have developed Monte Carlo(MC)simulation ofourdetectorbased onthe GEANT4 [12]

package,inwhichallsimulatedeventspassthewhole reconstruc-tionandselectionprocedure.TheMCsimulationusesprimary gen-eratorswithmatrix elementsforthe studiedprocesses,including softphotonradiationbyinitialelectronorpositron,calculated ac-cordingtoRef.[13].Forthebackgroundstudywe havedeveloped a special MC generator to simulate generically e+e−

→

hadrons,

whichincludesthemajority(

>

30)ofexclusivechannelsweighted withtheir known cross sections, and perform analysisof events basedonit.

2. Selectionofe+e−

→

π

+

π

−

π

0

_η

_events

Candidates for the process under study are required to have two good tracks of charged particles with opposite charges,and

fourormoreclustersinthecalorimeters,notrelatedtothetracks, assumedtobephotons.We requireionization lossesofatrackin theDCtobeconsistentwiththepionhypothesis,atrack momen-tumlargerthan40 MeV

/

c,aminimumdistancefromatracktothe beamaxisinthetransverseplane lessthan 0.25 cm,anda mini-mumdistancefromatracktothecenteroftheinteractionregion along the beamaxisZ lessthan 12 cm.The photon candidate is requiredto haveenergydeposition in thecalorimetersexceeding 25 MeV.

Reconstructed momenta and angles of the detected charged tracks as well as energyand angles of four photonsare subject to thekinematic ﬁtforthe e+e−

→

π

+

π

−

π

0

_{γ γ}

_hypothesis, as-sumingthatthetotalenergyisequaltoEc.m.andtotalmomentum isequaltozero.First,welookforonephotonpairwiththe invari-ant mass closest to the

π

0 _mass _inside _the

_±

_{55 MeV}

_/

_c2 _(about

±

3

.

5 standarddeviations)window,andweusethe

π

0 _mass_as_an additional fifth constraint in the fit (5Cfit) for thisphoton pair. No additional constraints are applied to the second photon pair. The covariancematricesforchargedtracks andphotonsareused inthe fitandprovidea

χ

2 _value _for_each _event._{A large} _fraction of theevent candidates hasmore than fourphotons: we test all possiblecombinations,andtwophotonpairswiththesmallest

χ

2 valueareretainedforfurtheranalysis.Asaresultoftheﬁt,we ob-tain improvedvaluesofthemomenta,energiesandanglesforall particles.

Fig. 1(a) shows the obtained

χ

2 _{distributions} _for _the exper-imental (dots) and simulated e+e−

→

π

+

π

−

π

0

_η

_(histogram) events,when the invariant mass ofthe second photon pair is in the

±

50 MeV

/

c2_window_around_the

_η

_mass._{A vertical}_line_shows theappliedselection.

Each event is also subject to the 4C ﬁt under a e+e−

→

π

+

π

−

γ γ

hypothesis: all photon pairs are tested to get the best

χ

2 _value, _and _a _requirement

_χ

2

π+π−γ γ

>

40 suppresses the

background from the processes e+e−

→

π

+

π

−

π

0 _and _e+_e−

_→

π

+

π

−

η

byafactorof10–20toanegligiblelevelwitha1.5%loss ofthesignal events.Tostudytheremaining backgroundwe ana-lyze events fromthegeneric e+e−

→

hadrons MCgeneratorwith theexcludedsignalprocess.

Fig. 1(b) presents the invariant mass distributions for the second photon pair before (dashed histogram) and after (solid histogram) the 5C kinematic ﬁt for events in the Ec.m.

=

1600–1800 MeV energy rangeand applied

χ

2 _selection. _{A signal}

Fig. 1. (a)The5C-ﬁtχ2_distribution_for_events_with_two_tracks,_π0_,_and_two_photons_for_the_e+_e−_→_π+_π−_π0_{γ γ}_hypothesis_for_data_(dots)_and_{corresponding}_simulation (histograms).(b) Theexperimentaltwo-photoninvariantmassdistributionsbefore(dashedhistogram)andafter(solidhistogram)akinematicﬁt.A shadedhistogramisfor thegenerice+e−→hadrons MCsimulationwithexcludedsignalprocess.

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Fig. 2. Two-photoninvariantmassdistributionsandﬁtfunctionstodeterminethenumberofπ+π−π0_η_events_at_E

c.m.=1680 MeV (a)andEc.m.=1600 MeV (b).Dashed

curvesshowthebackgroundcontribution.Histogramsarefortheexpectedsignaleventsfromsimulation.

Fig. 3. Thebackground-subtractedπ+π−π0_invariant_mass_distribution_for_events_in_the_E

c.m.=1400–1550 MeV (a),1600–1800 MeV (b),1800–2000 MeV (c)energyranges.

Thelinesshowresultsoftheﬁtswiththeω(782)andφ(1020)signals(solid),andthebackgroundcontribution(dashed).HistogramsshowexpectedMC-simulatedsignals fromtheω(782)ηandφ(1020)ηintermediatestates.

fromthe

η

→

γ γ

decayisclearlyseen,andanimprovementinthe resolutionisobtained.Theshadedhistogramshowsabackground fromotherprocesses, dominatedbythe e+e−

→

π

+

π

−

π

0

_π

0 re-action with wrong-assigned photons. No peaking background is observed.

The

η

peak in the invariant mass distribution of the sec-ond photon pair is used to obtain the inclusive number of the

π

+

π

−

π

0

_η

_events._We_ﬁt_the_{distributions}_of_{Fig. 1}_(b)_at_each en-ergy witha sumoffunctions toseparate signal and background. Theshapeofthe

η

signalistakenfromtheMCsimulation(shown byshaded histograms),while asecond-order polynomialfunction isusedforthebackground.Twoexamplesoftheﬁtareshownin

Fig. 2atEc.m.

=

1680 MeV (a)andEc.m.

=

1600 MeV (b). The to-talnumberofeventsevaluatedbythisprocedureis2769

±

95.We donot observe anysignal eventsfor Ec.m. below 1400 MeV, and presentourdatastartingfromEc.m.

=

1394 MeV.

The observed

π

+

π

−

π

0

_η

_events _contain _several _intermediate states.Ourdatasampleistoosmallforstandardamplitude analy-sis.Instead,weﬁrstextractacontributionofthenarrow interme-diateresonances,

ω

(

782

)

and

φ (

1020

)

,andtheninvestigateother

contributions, assuming low interference with the narrow states above.

3. Thee+e−

→

ω

(

782

)

η

,e+e−

→ φ(

1020

)

η

intermediatestates

To study intermediate states we select signal candidates by requiring

|

mγ γ

−

mη

|

<

65 MeV

/

c2_, _see _{Fig. 1}_(b), _and _subtract the sideband background using events with 65

<

|

mγ γ

−

mη

|

<

130 MeV

/

c2 for any experimental distribution. Fig. 3 shows the background-subtracted

π

+

π

−

π

0 _invariant _mass _{distributions} _for the selected

π

+

π

−

π

0

_η

_candidates _combined _in _three _energy ranges: Ec.m.

=

1400–1550 MeV (a), Ec.m.

=

1600–1800 MeV (b), and Ec.m.

=

1800–2000 MeV (c).A signal from the

ω

(

782

)

dom-inates atlow energies, signalsfromthe

ω

(

782

)

and

φ (

1020

)

are well seen in the second range, and they are relatively small at higherenergies,whereotherintermediatestatesdominate.To de-termine the number of

ω

and

φ

events, we ﬁt distributions at each energy with a sum of the signal and combinatorial back-ground functions. For the signal peaks we use double-Gaussian functionswithallparameters, exceptthenumberofevents,ﬁxed fromtheMC-simulation.A smoothfunctionisusedtodescribethe

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Fig. 4. Thebackground-subtractedπ+η,π−η,π0_η_invariant _mass_{distributions}_for _events_in_the _{1800–2000 MeV}_(a)_and_{1600–1800 MeV}_(b)_E

c.m. rangefromtheη

peakofFig. 1(b).HistogramscumulativelyshowtheMC-simulatedcontributionsfromtheρ(1450,1700)π (shaded),ω(782)η(crosshatched),φ(1020)η(hatched),and

a0(980)ρ(770)(open)intermediatestates.Linesshowaﬁtwiththea0(980)signalandbackgroundcontribution(dashed).

Fig. 5. Thebackground-subtractedπ+π0_,_π−_π0_,_π+_π−_invariant_mass_{distributions}_for_events_in_the_{1800–2000 MeV}_(a)_and_{1600–1800 MeV}_(b)_E_c

.m. rangesfromthe

ηpeakofFig. 1(b).HistogramscumulativelyshowtheMC-simulatedcontributionsfromtheρ(1450,1700)π (shaded),ω(782)η(crosshatched),φ(1020)η(hatched),and

a0(980)ρ(770)(open)ﬁnalstates.Thedashedhistogramin(b)correspondstothecasewhenthephasespace3π ηsimulationisusedinsteadoftheρ(1450,1700)πﬁnal state.

combinatorialbackgroundfromotherﬁnalstates(seeSec.4). His-tograms in Fig. 3 show the expectedMC-simulated signalsfrom the

ω

(

782

)

η

and

φ (

1020

)

η

intermediate states. In total, for all energy points we obtain 824

±

41 and 214

±

46 events for the

ω

(

782

)

η

and

φ (

1020

)

η

intermediate states,respectively. By vari-ation of the polynomial order ofthe background function or re-movingsidebandbackgroundsubtraction,weestimateasystematic uncertaintyonthenumberofsignaleventsatabout5%.

4. Thee+e−

→

a0

(

980

)

ρ

(

770

)

intermediatestate

Thecombinatorial backgroundforthe

ω

(

782

)

η

and

φ (

1020

)

η

ﬁnal states is relatively large andother intermediate resonances arethusexpected:mostprobablearea0

(

980

)

ρ

(

770

)

and

ρ

(

1450

,

1700

)

π

which have

π

+

π

−

π

0

_η

_at _the _end _of _the _decay _chains. The a0

(

980

)

is relatively narrow and should be seen in the

ηπ

invariant mass. Fig. 4 shows the background-subtracted

π

+

η

,

π

−

η

,

π

0

_η

_invariant _mass _distribution _(three _entries _per _event) for the events in the Ec.m.

=

1800–2000 MeV (a) and Ec.m.

=

1600–1800 MeV (b)ranges.A clearsignalassociatedwitha0

(

980

)

is seen in both energy ranges: while events in Fig. 4(b) are below the nominal a0

(

980

)

ρ

(

770

)

threshold, a0

(

980

)

is still visible due to the large width of the

ρ

(

770

)

. Histograms cu-mulatively show MC-simulated contributions from the expected

ρ

(

1450

,

1700

)

π

(shaded,seediscussioninSec.5),

ω

(

782

)

η

(cross hatched),

φ (

1020

)

η

(hatched), and a0

(

980

)

ρ

(

770

)

(open) inter-mediate states. Lines show a ﬁt with the a0

(

980

)

signal and the contribution of the combinatorial background (dashed). We tunebackground-descriptionfunctionwiththesimulation,andthe “Fermi”stepforthethresholdbehaviorconvolvedwiththe third-orderpolynomialfunctiongivesthebestresult.

Wealsoobservea clearsignal fromthe

ρ

(

770

)

inthe

π

+

π

−,

π

−

π

0_,

_π

+

_π

0_{corresponding}_mass_{combinations,}_shown_in_{Fig. 5}_(a) for the Ec.m.

=

1800–2000 MeV range, where the a0

(

980

)

ρ

(

770

)

ﬁnal state dominates. We ﬁt the distributions of Fig. 4 at each energy with a sum of functions describing signal, combinato-rial and other backgrounds, shown by the lines in Fig. 4. The

a0

(

980

)

signalisﬁttedwithaBreit-Wignerfunctionusing55 MeV width[16]convolvedwiththedetectorresolution(

≈

50 MeV).We obtain 1072

±

116 events corresponding to the process e+e−

→

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Fig. 6. (a)Thenumberofe+e−→π+π−π0_η_events_with_an_excluded_contribution_from_the_ω₍₇₈₂₎_η_,_φ(₁₀₂₀₎_η_,_and_a

0(980)ρ(770)intermediatestates.Blackandblue colorsareforthe2011and2012data,respectively.(b)Thebackground-subtractedπ+−0η(threeentriesperevent)invariantmassdistributionwithexcluded ω(782)η

andφ(1020)ηintermediatestates.Short-dashed,solid,andlong-dashedhistogramsshowsasimulatedsignalfromasumofthea0(980)ρ(770)andρ(1450,1700)π inter-mediatestatesincaseofconstructive,no-interference,anddestructiveinterferenceoftheiramplitudes,respectively.Theshadedhistogramshowsthecontributionofthe

ρ(1450,1700)πintermediatestateonly.(Forinterpretationofthereferencestocolorinthisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

a0

(

980

)

ρ

(

770

)

. We vary the shape of the function used for the combinatorial background subtraction and estimate a systematic uncertaintyonthenumberofsignaleventsasabout15%.

5. Thee+e−

→

π

+

π

−

π

0

_η

₍

_no

_ω

_,

_φ,

_a

0

)

intermediatestate

IntheEc.m.

=

1900–2000 MeV energyrangethenumberofthe

π

+

π

−

π

0

_η

_events_determined_from_the

_η

_peak_in_Sec.₂_is_almost completelydominatedbythea0

(

980

)

ρ

(

770

)

channel.Theobtained numberof

π

+

π

−

π

0

_η

_events_in _the _Ec

.m.

=

1600–1800 MeV en-ergyrange exceededthat expectedfromthesumof thee+e−

→

ω

(

782

)

η

(33%),

φ (

1020

)

η

(7%), and a0

(

980

)

ρ

(

770

)

(29%) reac-tions.

At each Ec.m. energy we subtract events obtained for the

ω

,

φ,

a0 signalsfromthetotalnumberofeventsobtainedfromthe

η

signalofFig. 1(b),andshow thedifferencevsEc.m. inFig. 6(a). A resonantstructureisobservedaroundEc.m.

=

1700 MeV.The dif-ference(about31%)canbe,forexample,explainedbythepresence ofthee+e−

→

ω

(

1650

)

→

ρ

(

1450

,

1700

)

π

→

ρ

(

770

)

ηπ

reaction. Inthiscasean additionalsignal fromthe

ρ

(

770

)

shouldbe seen intwo-pionmasses.FortheEc.m.

=

1600–1800 MeV energyrange we show thebackground-subtracted

π

+

π

0

_,

_π

−

_π

0

_,

_π

+

_π

− invari-ant mass distribution (three entries per event) in Fig. 5(b). His-togramscumulatively show the MC-simulated contributions from the

ρ

(

1450

,

1700

)

π

(shaded),

ω

(

782

)

η

(cross hatched),

φ (

1020

)

η

(hatched),anda0

(

980

)

ρ

(

770

)

(open)ﬁnal states.The dashed his-togram in Fig. 5(b) presents simulation when the phase-space modelisusedinsteadof

ρ

(

1450

,

1700

)

π

,indicatingsomedata ex-cessaround the

ρ

(

770

)

mass.Our data donot contradictto the presenceofthee+e−

→

ω

(

1650

)

→

ρ

(

1450

,

1700

)

π

→

ρ

(

770

)

ηπ

reaction, but an additional

ρ

(

770

)

contribution cannot be quan-titatively extracted from the mass distributions with reasonable accuracy.Notethatthe

ρ

(

770

)

signalfromthea0

(

980

)

ρ

(

770

)

in-termediate state is also diluted below 1750 GeV due to limited phasespace.

Moreover, the expected

ρ

(

1450

,

1700

)

π

→

ρ

(

770

)

ηπ

decay chain anda0

(

980

)

ρ

(

770

)

both contain a relatively broad

ρ

(

770

)

resonance, and can interfere at the amplitude level. To exam-ine an interference effect we sum two equal amplitudes of the aboveintermediatestatesattheprimarygeneratorlevel,and per-formsimulationwithpositiveandnegativerelativesigns.Fig. 6(b)

showsthebackground-subtractedexperimental

π

+−0

η

(three en-tries per event) invariant massdistribution (points) with the ex-cluded contributionfrom the

ω

(

782

)

η

and

φ (

1020

)

η

intermedi-ate states (using MC-simulation). Short-dashed, solid, and long-dashed histograms show a simulatedsignal fromthe sumof the

a0

(

980

)

ρ

(

770

)

and

ρ

(

1450

,

1700

)

π

intermediatestatesincaseof constructive, no-interference, and destructive interference of the amplitudes, respectively. The shaded histogram shows a contri-bution of the

ρ

(

1450

,

1700

)

π

intermediate state only. When we ﬁt the a0

(

980

)

signal peak as described above, the number of eventschangesby

±

50% fromthevaluewithnointerference. Be-cause of that, we should add at least a 50% model-dependent systematic error to the number of a0

(

980

)

ρ

(

770

)

(and hence to

ρ

(

1450

,

1700

)

π

) events in the Ec.m.

=

1650–1750 MeV energy range,whereoverlapisthelargest.

6. Detectioneﬃciency

As demonstrated above,the

π

+

π

−

π

0

_η

_ﬁnal _state _is_produced viaseveralintermediateresonantstates:weobservethe

ω

(

782

)

η

,

φ (

1020

)

η

, a0

(

980

)

ρ

(

770

)

, and, possibly,

ρ

(

1450

,

1700

)

π

→

ρ

(

770

)

ηπ

intermediate states.Our detector doesnot have 100% acceptance, and due to different angular distributions of ﬁnal particles, we observe variations in the detection eﬃciency for different intermediate states. Fig. 7(a) shows the MC-simulated

e+e−

→

π

+

π

−

π

0

_η

_detection _eﬃciency ₍

₎ _for _different produc-tion modes determined as a ratio of events that passed recon-struction andselection criteriato the total number of simulated events.

As shown in Sec. 3, the

π

+

π

−

π

0

_η

_ﬁnal _state _below _E c.m.

=

1600 MeV is dominatedbythe process e+e−

→

ω

(

782

)

η

,an ad-mixture ofthe

φ (

1020

)

η

,a0

(

980

)

ρ

(

770

)

, and

ρ

(

1450

,

1700

)

π

→

ρ

(

770

)

ηπ

intermediatestatesarisesintheEc.m.

=

1600–1800 MeV range, and the a0

(

980

)

ρ

(

770

)

state dominates above Ec.m.

=

1800 MeV.

Toestimatethedetectioneﬃciencyforchargedandneutral par-ticles,weuseaprocedurewithselectingacleansample ofevents with one missingparticle, predict momentumand angles ofthis particleusingkinematics,andcheck howoftenthisparticleis de-tected withour detector.By applyingthisprocedure to dataand MC simulationwe can obtaina correction forthecalculated eﬃ-ciency. Forthispurposewe usethee+e−

→

π

+

π

−

π

0

_π

0 _process

(7)

Fig. 7. (a)MC-calculatedeﬃciencyfordifferentintermediatestates:ω(782)η(circles),φ(1020)η(squares),a0(980)ρ(770)(trianglesup),ρ(1450,1700)π(opencircles),phase space(trianglesdown);theshadedareashowsanaverageeﬃciencywithestimatedsystematicerrors.(b)Radiativecorrections(1+ δR)forthee+e−→π+π−π0ηcross

section.

Fig. 8. Thee+e−→π+π−π0_η_cross_section_obtained_with_the_CMD-3_detector._Black_and_blue_colors_are_for_the₂₀₁₁_and₂₀₁₂_data,_{respectively.}_(For_{interpretation}_of_the referencestocolorinthisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

whichhasamuchhighercrosssectioninthestudiedenergyrange andlowbackground.

The correction tothe MC-calculated eﬃciency of

−

1

.

5

±

1

.

0% forachargedand

−

1

±

1% for aneutralpionhasbeen obtained. Assuming similar eﬃciency for

η

→

γ γ

decay, we estimate the data-MC difference in the detection eﬃciency as a sum of cor-rections for two charged pions and two

π

0_’s:

corr

=

0

.

95. The uncertaintyofthisnumber,3%,obtainedasaquadraticsumof2% fromchargedand2%fromneutralpions,istakenasasystematic uncertainty.

OurdetectioneﬃciencyisobtainedfromMCsimulationwhich includes a radiative photon from initial particles according to Ref.[13],takingintoaccounttheenergydependenceofeach chan-nel.

7.Thecrosssectioncalculation

Using events of the process e+e−

→

π

+

π

−

π

0

_η

_or _events _of theintermediatestatesdiscussedabove,wecalculatethecross sec-tionsateachenergyas

σ

(

π

+

π

−

π

0

η

)

=

N

L

· · (

1

+ δ

R

)

·

corr

,

(1)

where N isthenumberofselectedevents,L istheintegrated lu-minosity,

is the detection eﬃciency shown in Fig. 7(a) for all studiedchannels, and

(

1

+ δ

R

)

isaradiative correction.SinceMC

simulation does not perfectly describe the experimental resolu-tions,weapplyasmallcorrection,

corr,determinedfromthedata asdiscussedintheSec.6.

Tocalculatetheinclusivecrosssectionfortheprocesse+e−

→

π

+

π

−

π

0

_η

_,_we _use_events_obtained_from_the

_η

_peak _of_{Fig. 1}_(b), andweighteﬃciencies calculatedfordifferentmodes, takinginto account the relative contribution of each channel. For this com-bined eﬃciency we introduce a systematic uncertainty of about 10%,shownasashadedareainFig. 7(a).Theenergydependenceof the

(

1

+δ

R

)

valuesisshownforthisprocessinFig. 7(b):thevalues

areobtainedaccordingtoRef.[13],takingintoaccounttheenergy dependenceoftheobservedcrosssection(byiteration),presented inFig. 8 andlistedinTable 2.Itis theﬁrstmeasurement ofthis crosssection.

UsingEq.(1)we calculatethecrosssectionsforthe processes

e+e−

→

ω

(

782

)

η

ande+e−

→ φ(

1020

)

η

.Radiativecorrectionsfor the

ω

(

782

)

η

and

φ (

1020

)

η

ﬁnalstatesarecalculatedaccordingto Ref.[13].Eﬃcienciesforthesetwoprocessesaredeterminedfrom the simulation (see discussion in Sec. 6) and shownin Fig. 7(a).

Fig. 9showstheobtainedcrosssectionsfortheprocessese+e−

→

(8)

pre-Fig. 9. Thee+e−→ω(782)η(a)ande+e−→ φ(1020)η(b)crosssectionsobtainedattheCMD-3detectorintheπ+π−π0_η_mode_(circles)._Black_and_blue_colors_are_for the2011and2012data,respectively.AlsoshownarecorrespondingmeasurementsbyBaBar(opencircles),SND(opensquares),andCMD-3intheK+K−ηmode(open triangles).(Forinterpretationofthereferencestocolorinthisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

Fig. 10. (a) The e+e−→a0(980)ρ(770) cross sections obtained at the CMD-3 detector in the π+π−π0η mode. (b) The cross section for the process e+e−→

π+π−π0_η

(noω,φ,a0),obtainedattheCMD-3detector.

vious measurements by BaBar [1], SND [2], and CMD-3 [14] for the

φ (

1020

)

η

in the K+K−

η

mode. The branching fractions of the

ω

(

782

)

→

π

+

π

−

π

0 _and

_{φ (}

₁₀₂₀

₎

_→

_π

+

_π

−

_π

0 _decays _[16] are taken into account. Our data forthe e+e−

→

ω

(

782

)

η

cross section, listed in Table 2, are in good agreement with the SND experiment, and conﬁrm a discrepancywiththe BaBar data.The numberofthe

ω

(

782

)

η

eventsintheenergyrangebelowEc.m.

=

1600 MeV isequivalent to thenumberof

π

+

π

−

π

0

_η

_events dis-cussed in Sec. 2. The cross section for the

φ (

1020

)

η

mode is compatiblewiththepreviousmeasurements, buthasmuchlower statistical precision because of a small

φ

→

π

+

π

−

π

0 _branching fraction.

Fig. 10(a)showsthe e+e−

→

a0

(

980

)

ρ

(

770

)

crosssection cal-culatedaccordingtoEq.(1)witheﬃcienciesfromFig. 7(b) (trian-glesup).Itistheﬁrstmeasurementofthiscrosssection,listedin

Table 2.

UsingtheeﬃciencyshowninFig. 7(a)(opencircles)andthe ra-diativecorrectionsimilartothoseshowninFig. 7(b),wecalculate a cross section for the process e+e−

→

π

+

π

−

π

0

_η

₍

_no

_ω

_,

_φ,

_a

0

)

, presentedinFig. 10(b)andlistedinTable 2.Thecrosssectionhas resonant behavior with a mass around Ec.m.

=

1700 MeV, but is

consistent withzerobelow 1600 MeVandabove 1800 MeV. The

e+e−

→

ω

(

1650

)

→

ρ

(

1450

,

1700

)

π

→

ρ

(

770

)

ηπ

→

π

+

π

−

π

0

_η

reactionchaincanberesponsibleforthiscrosssection.

8. Systematicerrorsandcorrections

Allcrosssectionsabovehavea1%systematicuncertaintyfrom theluminosity measurement[9],3%fromineﬃciency forcharged and neutral pions (see Sec. 6), and 1% from uncertainty on the radiative correction.Using twoindependent triggersbased onDC orcalorimeterinformation,thetriggereﬃciencyisestimatedtobe closetounitywitha1%systematicuncertainty.

The uncertainties above shouldbe combinedwitha 5% (15%) uncertainty from variation of the signal and background shapes in the ﬁtting procedure to extract

ω

(

782

)

η

(

φ (

1020

)

η

,

a0

(

980

)

ρ

(

770

)

) signals. We sum these errors in quadrature, and the 6.5% (16%) value is an overall systematic error forthe mea-suredexclusivecrosssections.

For the inclusive process e+e−

→

π

+

π

−

π

0

_η

_we _add _a _10% (11% total) systematicuncertainty dueto variation of eﬃciencies ofcontributingchannels.

(9)

Fig. 11. Thee+e−→ω(782)ηcrosssectionsobtainedwiththeCMD-3detectorintheπ+π−π0_η_mode._Lines_show_{Fit 1}_(dashed_line)_and_{Fit 2}_(solid_line)_described_in_the text.

Table 1

Summaryofparametersobtainedfromthefitsdescribedinthetext.Thevalueswithouterrorswere fixedinthatfit. Fit 1 2 ωη[2] ωπ+π−[15] PDG[16] BeeBωf·107 0.32±0.06 0.50±0.26 0.16₋₀+0..0907 1.3±0.4 – eeBωf (eV) 7.1±1.2 5.3±1.6 – 17.5±5.4 – mw(MeV/c2₎ ₁₄₂₀ ₁₄₁₈_±₃₀ ₁₄₂₀ ₁₃₈₂_±₂₃ _1400–1450 ω(MeV) 220 104±35 220 133±48 180–250 φω(rad.) π π π π – BeeBωf·107 4.7±0.3 4.5±0.3 4.4±0.5 4.7±0.4 – eeBωf (eV) 59±3 51±3 – 103.5±8.3 – mω(MeV/c2) 1679±5 1671±6 1660±10 1667±13 1670±30 ω(MeV) 121±9 113±9 110±20 222±25 315±35 χ2_/n.d.f. _23/35 _18/33 _14.5/9 _34.9/48 _–

And ﬁnally, for the process e+e−

→

π

+

π

−

π

0

_η

₍

_no

_ω

_,

_φ,

_a 0

)

, assuming e+e−

→

ρ

(

1450

,

1700

)

π

reaction, we estimate the uncertainty on the cross section as about 50% due to possi-ble interference with the process e+e−

→

a0

(

980

)

ρ

(

770

)

in the Ec.m.

=

1650–1750 MeV energyrange,wherethelatterisalso de-terminedwiththesameuncertainty.

9. Fittothee+e−

→

ω

(

782

)

η

reaction

UsingtheproceduresuggestedinRef.[2,15],weﬁtthee+e−

→

ω

(

782

)

η

crosssectionwiththesumoftwo

ω

-likeinterfering res-onances.Theparametersofthe

ω

(

1420

)

(denotedbelowas

ω

)are notwelldetermined[16],andinourfirstfitwefixthemat aver-agevalues,similarly toRef. [2].A relative phaseis fixed at

π

to describetheasymmetryofthepeakinthemeasuredcrosssection. OurresultsshowninFig. 11byadashedlineandlistedinTable 1

(Fit 1),areconsistentwiththatinRef.[2](alsoshowninTable 1). Theobtainedwidthofthe

ω

(

1650

)

(denotedas

ω

)issigniﬁcantly differentfromthevaluesinPDG[16],butclosetothatinRef.[15]

fortheprocesse+e−

→

ω

(

782

)

π

+

π

−(alsoshowninTable 1),and agreeswith

ω

=

114

±

14 MeV,obtainedinRef.[1].Ourdata

al-lowustoperformaﬁtwithﬂoating

ω

(

1420

)

parameters,andthe ﬁt(Fit 2inTable 1 andthesolid linein Fig. 11) yieldthewidth smallerthan estimated inPDG,but consistent withthe resultof Ref.[15].

In addition to the products of the

ω

,

ω

branching fractions toe+e− andthestudiedﬁnal state,

B

ee

B

ωf

,

B

ee

B

ωf inTable 1,

we also calculate the products of electron width and branching

fractiontoﬁnalstate,

ee

B

ωf

,

ee

B

ωf,whichlessdependonthe

uncertaintyontheresonancewidths.

10. Conclusion

We report the ﬁrst measurement of the e+e−

→

π

+

π

−

π

0

_η

(

η

→

γ γ

)crosssectionwiththeCMD-3detectorattheVEPP-2000 collider. We also present the cross sections for the intermediate states

ω

(

782

)

η

,

φ (

1020

)

η

,anda0

(

980

)

ρ

(

770

)

.

Theprocess e+e−

→

ω

(

782

)

η

iswell describedby thesumof the

ω

(

1420

)

resonance andthe resonance withm

=

1671

±

4

±

10 MeV

/

c2,

=

113

±

9

±

10 MeV,whichcouldbeassociatedwith the

ω

(

1650

)

,buthasawidthsmallerthansuggestedbyPDG[16]. We observea contribution tothe process e+e−

→

π

+

π

−

π

0

_η

from the process not associated with the

ω

(

782

),

φ (

1020

)

, or

a0

(

980

)

intermediate states,whichcan beexplained bythe reac-tione+e−

→

ω

(

1650

)

→

ρ

(

1450

,

1700

)

π

→

ρ

(

770

)

ηπ

.

Acknowledgements

We thankthe VEPP-2000personnel forexcellent machine op-eration. Part of this work related to the photon reconstruction algorithm inthe electromagneticcalorimeteris supported by the Russian Science Foundation (project #14-50-00080). The work is partially supported by the Russian Foundation for Basic Re-search (grants RFBR 14-02-00580-a, RFBR 15-02-05674-a, RFBR 16-02-00160-a).

(10)

Table 2

Numberofsignaleventsandthee+e−→π+π−π0_η_,_ω₍₇₈₂₎_η_{, a}

0(980)ρ(770),andπ+π−π0η(noω,φ,a0)crosssections vsEc.m.,measuredwiththeCMD-3detector.Onlystatisticalerrorsareshown.

Ec.m., MeV N(π+π−π0η) σ(π+π−π0η), nb σ(ωη), nb σ(a0ρ), nb σ(noω, φ,a0), nb 2005 10±7 0.27±0.25 0.09±0.10 0.10±0.41 0.13±0.39 1989 41±12 0.81±0.30 0.00±0.16 0.70±0.37 0.45±0.53 1978 25±8 0.68±0.28 0.12±0.13 0.55±0.38 0.00±0.39 1967 44±11 0.76±0.23 0.13±0.08 0.30±0.29 0.67±0.47 1953 22±9 0.68±0.33 0.08±0.12 0.40±0.83 0.61±0.79 1945 63±12 1.00±0.24 0.07±0.07 0.82±0.37 0.56±0.72 1927 42±10 1.06±0.30 0.00±0.09 1.73±0.60 −0.35±0.54 1926 44±10 0.80±0.22 0.00±0.07 1.01±0.36 0.07±0.46 1903 79±13 1.44±0.28 0.06±0.05 0.75±0.39 0.93±0.72 1901 40±10 1.19±0.34 0.10±0.09 0.72±0.46 0.25±0.52 1893 45±11 1.26±0.34 0.12±0.11 1.77±0.59 −0.36±0.61 1874 108±14 1.77±0.26 0.00±0.07 2.17±0.46 −0.01±0.73 1871 60±12 1.31±0.28 0.00±0.09 1.28±0.53 0.17±0.48 1849 39±9 1.29±0.32 0.05±0.09 1.51±0.55 −0.05±0.53 1840 102±15 1.85±0.30 0.09±0.07 2.04±0.55 −0.05±0.64 1826 39±12 1.15±0.37 0.24±0.12 1.08±0.57 −0.28±0.6 1798 103±15 1.67±0.25 0.38±0.10 1.61±0.44 −0.19±0.99 1793 60±12 2.13±0.43 0.45±0.15 1.16±0.68 0.33±0.69 1774 74±13 2.08±0.36 0.50±0.15 1.60±0.68 −0.05±0.62 1758 139±17 2.28±0.27 0.48±0.11 2.15±0.52 −0.07±0.94 1742 96±14 2.82±0.39 0.87±0.16 0.57±0.80 1.43±0.71 1723 152±16 4.61±0.45 1.02±0.22 1.93±0.92 1.73±0.74 1716 203±20 3.40±0.30 1.09±0.16 1.02±0.58 2.81±1.18 1693 204±17 6.24±0.47 2.10±0.33 1.08±0.90 2.84±0.83 1674 273±21 5.05±0.34 2.18±0.25 2.38±0.96 1.91±1.12 1669 189±17 5.27±0.41 2.22±0.27 0.55±1.08 2.42±0.73 1643 156±16 5.30±0.47 2.05±0.30 1.00±1.19 2.66±0.82 1623 82±13 2.62±0.33 1.82±0.26 1.19±1.16 0.11±0.73 1595 75±14 1.34±0.20 1.07±0.16 0.54±0.55 −0.01±0.70 1594 52±10 1.84±0.29 0.83±0.24 1.41±1.09 −0.12±0.66 1572 30±10 0.87±0.24 0.95±0.18 – 0.00±0.24 1543 22±8 0.63±0.19 0.69±0.16 – 0.02±0.21 1522 10±7 0.29±0.17 0.44±0.15 – −0.28±0.20 1515 15±9 0.45±0.22 0.56±0.18 – −0.05±0.25 1494 19±9 0.54±0.21 0.59±0.17 – 0.02±0.22 1471 21±9 0.63±0.24 0.54±0.19 – 0.18±0.25 1443 10±6 0.36±0.18 0.71±0.21 – −0.23±0.28 1435 12±8 0.18±0.11 0.46±0.12 – −0.38±0.31 1423 21±7 0.61±0.17 0.28±0.15 – 0.37±0.19 1394 0±9 0.00±0.23 0.27±0.16 – −0.23±0.21 References

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