Observation of a fine structure in e+e−→hadrons production at the nucleon-antinucleon threshold

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).

Observation of a fine

structure in

e+e−→

hadrons production at the nucleon-antinucleon threshold

.

Physics Letters B, 794, 64-68.

https://doi.org/10.1016/j.physletb.2019.05.032

UVicSPACE: Research & Learning Repository

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_____________________________________________________________

Observation of a fine structure in

e+e−→

hadrons production at the

nucleon-antinucleon threshold

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

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:

R.R. Akhmetshin

,

A.N. Amirkhanov

,

A.V. Anisenkov

,

V.M. Aulchenko

,

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

_,

_{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

,

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

,

∗

,

A.A. Talyshev

a

,

b

_,

_{V.M. Titov}

a

_,

_{S.S. Tolmachev}

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_{LebedevPhysicalInstitute,RAS,Moscow,119333,Russia}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received12April2019

Receivedinrevisedform13May2019 Accepted20May2019

Availableonline27May2019 Editor:L.Rolandi

Astudyofhadronproductionatthenucleon-antinucleonthresholdhasbeenperformedwiththeCMD-3 detectorattheVEPP-2000e+e−collider.Theveryfastrisewithabout1MeVwidthhasbeenobserved inthee+e−_→pp cross¯ section.Asharpdropinthee+e−_→3(

π

+

π

−)crosssectionhasbeenconfirmed andfoundtohavealessthan2MeVwidth,inagreementwiththeobservedfastriseofthee+e−→pp¯ crosssection.Forthefirsttimeasimilarsharpdropisdemonstratedinthee+e−→K+K−

π

+

π

−cross section.Thebehaviorofthee+e−_→3(

π

+

π

−), K+K−

π

+

π

−crosssectionscannotbeexplainedbyan interferenceofanyresonanceamplitudewithcontinuum,thereforethisphenomenoncannotbedueto anarrownear-thresholdresonance.Nosuchstructurehasbeenobservedinthee+e−→2(

π

+

π

−)cross section.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

Production of sixpions in e+e− annihilation,studied at DM2 [1–3],showeda “dip”inthe crosssectionatabout1.9GeV, con-firmed later by the Fermilab E687 experiment in photoproduc-tion [4,5], andwitha muchlarger effectiveintegratedluminosity

*

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

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

atBaBar [6] usinginitial-stateradiation(ISR). Evenearlier,a nar-row structure near theproton-antiproton threshold was also ob-servedinthetotalcrosssectionofe+e−annihilationintohadrons inthe FENICEexperiment [7]. AmeasurementoftheCMD-3 Col-laboration [8] confirmedtheseobservationsanddemonstratedthat the drop in the e+e−

→

3

(

π

+

π

−

)

cross section occurredin the narrow energy range of less than 10 MeV width. The origin of the “dip” remains unclear, but one of the explanations suggests the presence of a below-threshold proton-antiproton (pp)

¯

reso-nance [9].Alternatively,accordingtoRefs. [10–13] the“dip”isdue

https://doi.org/10.1016/j.physletb.2019.05.032

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

Fig. 1. Thee+e−→3(π+π−)BorncrosssectionmeasuredwiththeCMD-3detector inthe2017run(squares).TheresultsofthepreviousCMD-3measurement [8] are shownbydotsandthoseofBaBar [6] byopencircles.Theinsetshowsthevisible crosssectionwiththefitresultofastep-likefunction,shownbydot-dashedcurve, convolutedwiththeresolutionandradiativeeffectsasdescribedinthetext.The verticallinesshowtheNN thresholds.¯ Hereandthroughoutthepaperallerrorsin thefiguresarestatisticalonly.

tothestronginteractioninvirtual nucleon-antinucleon(NN )

¯

pro-duction,andisrelatedtothefastriseofthee+e−

→

NN cross

¯

sec-tionandNN annihilation

¯

tohadrons.Thishypothesisissupported by the fast increase of the pp [

¯

14,15] and nn [

¯

16] form factors nearthreshold,andexplains a similar dropin the

η



(

958

)

π

+

π

−

spectrum, observed by the BES-III Collaboration in the J

/ψ

→

η



(

958

)

π

+

π

−

γ

decay [17]. Theauthors ofRef. [10] considerthe two-stepprocess e+e−

→

NN

¯

→

multipions andevaluate the to-talreactionamplitudeforvariousintermediatemechanismsofthe

e+e−

→

5

π

,

6

π

reactions. In Refs. [11–13] the authors go even furthertakingintoaccounttheproton-neutronmassdifferenceand

¯

p p Coulombinteraction.

However, the mass-energy resolution of the previous experi-ments does not allow a study of the fine structure of the “dip” or the rise of the e+e−

→

NN cross

¯

section. Therefore we de-cided to repeat a scan of this energy range with a larger data sample and a fine step in an attempt to measure the width of thedip. In thispaper we presentthe analysisof 50 pb−1 _of

in-tegratedluminositycollected withtheCMD-3detector [18] at29 c.m.energypointsattheVEPP-2000colliderwiththeupgraded in-jectioncomplex [19–22].Whilethedatahavebeencollectedinthe 1.5–2.0GeVcenter-of-massenergy(Ec.m.) range,thescope ofthis paperisadetailedstudyofthe NN threshold

¯

region.Thescanof the NN-threshold

¯

energy range was performed witha fine step, corresponding to the c.m. energy spread. The beam energy and energyspread havebeen monitored by the back-scattering-laser-light system [23,24], providing an absolute energy measurement withbetterthan0.1MeVuncertaintyineverysinglemeasurement. DuringdatatakingtheEc.m.variations arounda centralvaluedid not exceed 0.1MeV ateach energy point: this value is taken as the systematicuncertainty estimate. The energy spread,

σ

Ec.m.,is measured to be 0.95

±

0.10MeV at the NN threshold:

¯

the added uncertaintyisourestimateofasystematiceffectwithanegligible contributionofthestatistics.

TheluminositywasmeasuredusingeventsofBhabhascattering atlargeangles [25].

2. Thee+e−

→

3

(

π

+

π

−

)

crosssection

Theanalysisofthee+e−

→

3

(

π

+

π

−

)

processwasdescribedin detailinRef. [8]. Forthe newdatawe havereproduced all steps

Fig. 2. Thee+e−→K+K−π+π−BorncrosssectionmeasuredwiththeCMD-3 de-tectorinthe2017run(squares).TheresultsoftheBaBar [27] measurementsare shownbyopencircles.Theinsetshowsthevisiblecrosssectionwiththefitresult ofastep-likefunction,shownbydashedcurve,convolutedwiththeresolutionand radiativeeffectsasdescribedinthetext.TheverticallinesshowtheNN thresholds.¯ forselectionoffiveandsixchargedtracks,andthecalculation of the efficiencyandradiative corrections. As inRef. [8], we havea background-freesampleofthesix-tracksignalevents,andusethe ratioofthefive- andsix-trackeventstocorrecttheefficiency.With thenewdatasample,thenumberofsignaleventswithsixcharged tracks increased to 10155(comparedto 2887events in the pre-vious analysis) andthat withone missingtrack to 17822(5069) events. The cross section obtained from the new data is shown inFig.1 bysquares,whilethe BaBar [6] andprevious CMD-3 [8] dataare shownbyopen andclosedcircles,respectively.Our pre-vious resultis confirmedwith betterstatistical accuracy, whilea systematicuncertainty is estimatedat the same6% level, mostly dominated by theuncertainties inthe efficiencyand background estimate. The“dip” atthe NN threshold

¯

isalso confirmedandis studiedinmoredetail(seebelow).

3. Thee+e−

→

K+K−

π

+

π

−crosssection

The analysis of the e+e−

→

K+K−

π

+

π

− process was de-scribedindetailinRef. [26].Forthenewdatawehavereproduced all steps for selection of four charged tracks, pion-kaon separa-tionprocedure,andthecalculation oftheefficiencyandradiative corrections.Aspeciallydesignedlikelihoodfunctionisusedto sep-aratekaonsandpions.Inthisanalysisweuseeventswithexactly fourchargedtrackswhichhavepracticallynobackground.In con-trast to the previous analysis, the eventswith one missing kaon or events with a missing pion are not used to reduce the un-certainty in the background subtraction. Nevertheless, the same overall statistical accuracy isachieved since the scan around the

NN threshold

¯

is performedwithlarge integratedluminosity that allowsustoselectabout1500signaleventsperenergypoint.The cross section obtainedfrom the new data is shownin Fig. 2 by squares,whiletheBaBar [27] dataareshownbyopen circles.Our previousresultisconfirmedwithbetterstatisticalaccuracy,while asystematicuncertaintyremainsatthesame6%level,dominated bythatintheefficiencyestimate.Evidenceforthe“dip”attheNN

¯

thresholdisobtainedforthefirsttimeinthischannelandis stud-iedinmoredetailbelow.

4. Thee+e−

→

pp cross

¯

sectionattheNN threshold

¯

The analysis procedure is described in our previous publica-tion [15]. At the energies near threshold,for Ec.m.

<

1900 MeV,

Fig. 3. Thee+e−→pp visible¯ crosssection measuredwiththe CMD-3detector. Thesolidcurveshowstheresultofthefittoanexponentiallysaturatedfunctionof Eq. (3) (shownbydashedcurve,Ethrisfixedat1876.54MeV)convolvedwiththe

0.95MeVenergyspreadandradiationfunctions.Theverticallinesshowthepp and¯ nn thresholds.¯ Theinsetshowstheexpandedviewofthevisiblecrosssection.

protons and antiprotons from the reaction e+e−

→

pp stop

¯

in the material of the beam pipe because of very low momentum. Toselectsuch events,welookforthe productsofantiproton an-nihilation with more than two charged tracks coming from the aluminumbeampipe.Comparisonofthecalorimeterresponsefor sucheventsbelowandabovethe NN threshold

¯

yieldsthenumber of pp events.

¯

Points belowthe production thresholds,where we assumenosignalfromthee+e−

→

pp reaction,

¯

areusedfor back-groundnormalizationandwe obtain490

±

30signal eventsinthe energyrangefromtheproductionthresholdto1900MeV.Starting from Ec.m.=1900 MeV, protons have enough energy to penetrate thebeampipe,andabove thisenergynoannihilationof antipro-tons at the beam pipe is observed. Protons and antiprotons are detectedascollineartrackswithlargespecificenergylosses,dE/dx, in the drift chamber (DC) of the CMD-3: we detect 4770 signal events.Ateach energya visiblecrosssection iscalculatedasthe numberofselectedeventsdividedbythedetectionefficiencyand integratedluminosity.Theobtainede+e−

→

pp visible

¯

cross sec-tionisshowninFig.3.Weestimatethesystematicuncertaintyas about10%,dominatedbytheuncertaintyintheefficiency calcula-tion:aspecialstudywasperformedtoestimatedata-MCdifference inthereconstructionefficiency.

5. TheNN threshold

¯

region

ThecrosssectioninFig.3exhibitsverysharpstep-like behav-ior close tothe NN threshold.

¯

The Born crosssection cannot be obtainedwithouttakingintoaccountitssmearingduetoradiation ofrealphotonsby initialelectrons andpositrons,andthe energy spreadofthecollision energywith

σ

Ec.m.

=

0

.

95

±

0

.

10 MeV.The visiblecrosssection isdescribed byaconvolutionoftheradiative crosssection,

σ

fγ

(

Ec.m.

)

,withthec.m.energyspreadfunction:

σ

vis

(

Ec.m.

)

=

1

√

2

π σ

Ec.m.



dE_c.m.

σ

fγ

(

Ec.m.

)

·

exp



−

(

Ec.m.

−

Ec.m.

)

2 2

σ

2 Ec.m.



,

(1)

where

σ

fγ

(

Ec.m.

)

is a convolution of the Born cross section with theradiatorfunctionF

(

Ec.m.

,

Eγ

)

[28,29]:

A andA

+

B (B

=

0 forEc.m.

<

Ethr) givetheasymptoticvaluesof

thecrosssectionbelowandabovethepp threshold.

¯

First, the e+e−

→

pp visible

¯

cross section is fit to Eq. (3) with all parameters floating except the A value fixed at zero, assuming no signal below the threshold. The fit yields Ethr

=

1877

.

1

±

0

.

2 MeV, consistent with the pp production

¯

threshold withinuncertaintiesintheenergymeasurement,and

σ

thr

=

0

.

18

±

0

.

27 MeV.Since no pp events

¯

are expectedbelowthethreshold, Ethr is fixed at1876.54 MeV (the doubled protonmass), andthe

fityields

σ

thr

=

0

.

76

±

0

.

28 MeV.Inbothcasesthe

σ

thrvalueand

itsuncertaintyaresmallerthantheenergydifferencebetweenthe neutron andproton productionthresholds. Fig.3 showsthe visi-blee+e−

→

pp cross

¯

sectionwiththefitresult(solidcurve)when Ethr inBorncrosssection(dashedcurve)isfixedat1876.54 MeV.

Lines showthe pp and

¯

nn threshold

¯

positions.Anexpandedview ofthe visiblee+e−

→

pp cross

¯

section aroundthe NN threshold

¯

isshownintheinsetinFig.3.

Similarly, the e+e−

→

3

(

π

+

π

−

)

visiblecross section is fit to the above functions with all parameters floating in the energy rangeEc.m.=1834–1944MeV,wherethecrosssectioncanbe con-sideredrelativelyflat. Thefityields Ethr

=

1875

.

8

±

0

.

2 MeV,and

σ

thr

=

0

.

18

±

0

.

67 MeV. The fit with fixed Ethr

=

1876

.

54 MeV

yields

σ

thr

=

0

.

0

±

2

.

5 MeV,witha good

χ

2

/

ndf

=

18

/

21 value:

ourstatisticalaccuracyandenergyspreadallowadropwithazero width. TheresultofthelatterfitisshownasaninsetinFig.1by asolidline,whileadot-dashedlineshowstheBorncrosssection. The obtained

σ

thr value is consistent with that obtained for the

e+e−

→

pp reaction.

¯

Variationof the “flat” region inreasonable scalechangestheB value,buthassmallinfluenceonthe“dip” pa-rameters.

Then we fit the e+e−

→

K+K−

π

+

π

− visiblecross section to the above functions with all parameters floating in the energy range Ec.m.= 1850–1970 MeV, where the cross section can be considered relatively flat. The fityields Ethr

=

1878

.

8

±

0

.

2 MeV:

the value iscloseto thenn threshold.

¯

The obtainedvalue

σ

thr

=

0

.

35

±

2

.

69 MeV indicates that the observed effectis dominated by thestatisticaluncertainty,andis consistentwithazero-width drop in theBorn cross section. The fit withfixed Ethr

=

1876

.

54

MeV yields

σ

thr

=

2

.

36

±

2

.

01 MeV, witha good

χ

2

/

ndf

=

8

/

11

value. TheresultofthelatterfitisshownasaninsetinFig.2by asolidline,whileadashedlineshowstheBorncrosssection.

The resultsof thefit are summarizedin Table1,and demon-stratethat theobservedbehaviorofthecrosssectionshassimilar origin, and the “dip” in the hadronic cross section can be in-terpreted asdue to opening of the direct production of the NN

¯

channel.NotethatwhenEthrisfloating,theobtainedvalueincase

of 3

(

π

+

π

−

)

is close to the pp threshold

¯

energy, while for the

K+K−

π

+

π

− channel thisvalue isconsistentwiththenn thresh-

¯

old(1879.13MeV).

Weperformasimultaneousfitofallthreechannelswith com-mon Ethr and

σ

thr values, and the fit yields 1876

.

87

±

0

.

10

∓

Table 1

Resultsofthefittotheexponentiallyrisingfunction.Onlystatisticaluncertainties areshown.

Reac. A, nb B, nb Ethr, MeV σthr, MeV χ2/ndf

p¯p 0 – fxd 0.91±0.02 1877.1±0.2 0.18±0.27 29/26 p¯p 0 – fxd 0.91±0.02 1876.54-fxd 0.76±0.28 31/27 6π 1.55±0.02 –0.42±0.03 1875.8±0.2 0.18±0.67 17/20 6π 1.54±0.02 –0.41±0.03 1876.54–fxd 0.0±2.5 18/21 2K 2π 4.69±0.08 –0.44±0.12 1878.8±0.2 0.35±2.69 7/10 2K 2π 4.70±0.08 –0.45±0.12 1876.54–fxd 2.36±2.01 8/11

Fig. 4. Thee+e−→pp Born¯ crosssectionmeasuredwithCMD-3(dots[15] and squares)andBaBar(opencircles).Thesolidcurveshowstheresultoftheprediction fromRefs. [11–13].Theinsetshowstheexpandedviewofthetheoreticalfunction forthe Born(solidline),and forthe visiblecross sectionafterexperimental ef-fects(dashedline)incomparisonwiththeCMD-3data.Theverticallinesshowthe

p¯p andnn thresholds.¯

0

.

11 MeVand0

.

31

±

0

.

25

∓

0

.

15 MeV,respectively,with

χ

2

_/

_ndf

₌

66

/(

67

−

7

)

value.Thesecond uncertaintyissystematicand anti-correlated with the systematic uncertainty in the energy spread 0

.

95

±

0

.

10 MeV.

Unfortunately,theaccelerator-inducedenergyspreadand rela-tivelylow statisticalaccuracy donot allowusto directlyobserve apossiblestructure ofthisrise (drop)duetothe proton-neutron interaction,whichcouldbeexpectedinthestudiedreactions.

In a recently published paper [13], the authors use the opti-cal potential and experimental data of the nucleon interactions tomake a predictionofthe pp and

¯

nn cross

¯

section behaviorat very small energies above the production thresholds. The calcu-latedtheoreticale+e−

→

pp Born

¯

crosssectionisshowninFig.4 bysolid curve andis ingoodagreement withavailable data.But fora comparisonof thetheoretical curve anddata atvery small deviationsfromthethreshold,energyspreadandradiativeeffects mustbe takenintoaccount.Theresultofthisconvolutionforthe theoreticalfunctionisshownintheinset(dashedcurve),andalso isingoodagreementwithourvisiblecrosssection.Note,the sug-gestedmodelofthefinal-stateinteractionofaveryslowNN pair

¯

predicts a nonzero cross section atthe pp threshold

¯

due to the Coulombinteraction,butexperimentaleffectsandlimitedaccuracy donotallowustoprovethat.

6. Thee+e−

→

2

(

π

+

π

−

)

crosssectionattheNN threshold

¯

As suggested in Ref. [13], the total hadronic cross section is stronglyaffectedbyvirtualproductionandannihilationoftheNN

¯

pairs.Thecalculationpredictsa7nb“bump”inthetotalcross sec-tion,whichisabout40nbatthisenergy,andshouldbeseeninall

e+e−

→

hadrons finalstates.Anaiveexpectationsuggeststhatthe

Fig. 5. The e+e−→2(π+π−) cross section measured with CMD-3 (dots) and BaBar [31] (opencircles).Theverticallinesshowthepp and¯ nn thresholds.¯ effectcould be proportional tothe probabilityof pp annihilation

¯

intothestudiedfinalstate.

Totestthat,weanalyzedataattheNN threshold

¯

by selecting eventsforthereactione+e−

→

2

(

π

+

π

−

)

accordingtothe proce-duredescribedinRef. [30],andshowtheobtainedcrosssectionin Fig.5together withthemostprecisemeasurementbyBaBar [31]. Whiletheoverallsystematicuncertaintiesonthecrosssectionare still under investigation,the relative point-to-point errors donot exceed0.1-0.2nb.Nostructureexceedingthelevelof0.1nbis ob-served atthe NN threshold

¯

ineithermeasurement. According to Ref. [32],the probabilityof pp annihilation

¯

(withisospinone)to fourchargedpionsisabout14%,while forsixchargedpionsit is about6%.Ifacrosssectiondropinthehadronicchannelisrelated tovirtual NN annihilation [

¯

13],forfour-pionproductiononecould expectanabout0.5–0.8nbdropinthecrosssection,whichisnot supported byourdata.Notethat accordingtoRef. [32] the prob-abilityofNN annihilation

¯

tothe K+K−

π

+

π

− finalstate ismuch lowerthanthatforsix- orfour-pionstates,andobservationofthe “dip”inthischannelindicatesacomplicatedproductiondynamics.

7. Conclusion

Using the improved performance of VEPP-2000, the scan of the e+e− c.m. energy in the 1680 – 2007 MeV range has been carried out. A detailed study of the NN threshold

¯

region con-firms a fast drop (rise) in the e+e−

→

3

(

π

+

π

−

)

(e+e−

→

pp)

¯

cross section observed previously. For the first time a width of thisstructureismeasuredinthee+e−

→

pp reaction:

¯

the

σ

thr

=

0

.

76

±

0

.

28 MeVvalueissmallerthanthedifferencebetweenthe

pp and

¯

nn production

¯

thresholds.Theenergypositionofthe“dip” inthee+e−

→

K+K−

π

+

π

− crosssections,observed forthe first time, is consistent with the nn production

¯

threshold, while that for the e+e−

→

3

(

π

+

π

−

)

reaction is closeto the pp threshold.

¯

No structures in the e+e−

→

2

(

π

+

π

−

)

cross section have been foundatthe NN threshold

¯

suggestingforamorecomplicated dy-namicsatthemicroscopic level,whichcannot besummarizedby thesimpleriseofthevirtualnucleon-antinucleonproduction.

Afterthisworkwassubmitted tothearXiv,thepaper [33] ap-pearedin whichthe authoranalyzes variousfinal states ofe+e−

annihilation around the NN threshold.

¯

Based on the earlier data withatypicalc.m.energystepof10MeVorlarger,heclaimsthe existenceofthe

ρ

(

1900

)

resonanceresidingabove thenn thresh-

¯

oldwithawidthofabout10MeV.Incontrast,ournewdatashow thattheobservedstructureisconsistentwithopeningNN thresh-

¯

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