Study of the Dalitz decay $\phi \rightarrow \eta e^{+}e^{-}$ with the KLOE detector

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Study of the Dalitz decay φ → η e ⁺ e ⁻ with the KLOE detector

The KLOE-2 Collaboration

D. Babusci

^h

, I. Balwierz-Pytko

^g

, G. Bencivenni

^h

, C. Bloise

^h

, F. Bossi

^h

, P. Branchini

^r

, A. Budano

^q,r

, L. Caldeira Balkeståhl

^u

, F. Ceradini

^q,r

, P. Ciambrone

^h

, F. Curciarello

^i,d

, E. Czerwi ´nski

^g

, E. Danè

^h

, V. De Leo

^i,d

, E. De Lucia

^h

, G. De Robertis

^b

, A. De Santis

^h

, P. De Simone

^h

, A. Di Cicco

^q,r

, A. Di Domenico

^m,n

, R. Di Salvo

^p

, D. Domenici

^h

,

O. Erriquez

^a,b

, G. Fanizzi

^a,b

, A. Fantini

^o,p

, G. Felici

^h

, S. Fiore

^s,n

, P. Franzini

^m,n

, A. Gajos

^g

, P. Gauzzi

^m,n

, G. Giardina

^i,d

, S. Giovannella

^h,∗

, E. Graziani

^r

, F. Happacher

^h

,

L. Heijkenskjöld

^u

, B. Höistad

^u

, T. Johansson

^u

, D. Kami ´nska

^g

, W. Krzemien

^g

, A. Kupsc

^u

, J. Lee-Franzini

^h,t

, F. Loddo

^b

, S. Loffredo

^q,r

, G. Mandaglio

^i,d,c

, M. Martemianov

^j

,

M. Martini

^h,l

, M. Mascolo

^o,p

, R. Messi

^o,p

, S. Miscetti

^h,∗

, G. Morello

^h

, D. Moricciani

^p

, P. Moskal

^g

, A. Palladino

^h

, A. Passeri

^r

, V. Patera

^k,h

, I. Prado Longhi

^q,r

, A. Ranieri

^b

, P. Santangelo

^h

, I. Sarra

^h,∗

, M. Schioppa

^e,f

, B. Sciascia

^h

, M. Silarski

^g

, L. Tortora

^r

, G. Venanzoni

^h

, W. Wi´slicki

^v

, M. Wolke

^u

aDipartimentodiFisicadell’UniversitàdiBari,Bari,Italy bINFNSezionediBari,Bari,Italy

cCentroSicilianodiFisicaNucleareeStrutturadellaMateria,Catania,Italy dINFNSezionediCatania,Catania,Italy

eDipartimentodiFisicadell’UniversitàdellaCalabria,Cosenza,Italy fINFNGruppocollegatodiCosenza,Cosenza,Italy

gInstituteofPhysics,JagiellonianUniversity,Cracow,Poland hLaboratoriNazionalidiFrascatidell’INFN,Frascati,Italy

iDipartimentodiFisicaeScienzedellaTerradell’UniversitàdiMessina,Messina,Italy jInstituteforTheoreticalandExperimentalPhysics(ITEP),Moscow,Russia

kDipartimentodiScienzediBaseedApplicateperl’Ingegneriadell’Università“LaSapienza”,Roma,Italy lDipartimentodiScienzeeTecnologieApplicate,Università“GuglielmoMarconi”,Roma,Italy mDipartimentodiFisicadell’Università“LaSapienza”,Roma,Italy

nINFNSezionediRoma,Roma,Italy

oDipartimentodiFisicadell’Università“TorVergata”,Roma,Italy pINFNSezionediRomaTorVergata,Roma,Italy

qDipartimentodiMatematicaeFisicadell’Università“RomaTre”,Roma,Italy rINFNSezionediRomaTre,Roma,Italy

sENEAUTTMAT-IRR,CasacciaR.C.,Roma,Italy

tPhysicsDepartment,StateUniversityofNewYorkatStonyBrook,NY,USA uDepartmentofPhysicsandAstronomy,UppsalaUniversity,Uppsala,Sweden vNationalCentreforNuclearResearch,Warsaw,Poland

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received16September2014

Receivedinrevisedform17December2014 Accepted10January2015

Availableonline13January2015 Editor:L.Rolandi

We have studied the vector to pseudoscalarconversion decayφ→ηe⁺e⁻,with η_→π⁰π⁰π⁰, with theKLOEdetectoratDAΦNE.Thedatasetof1.7 fb⁻¹ ofe⁺e⁻ collisionsat√

s∼^Mφ containsaclear conversion decaysignal of ∼³¹,000 events fromwhich wemeasured a value of BR(φ→ηe⁺e⁻)= (1.075±⁰.007±⁰.038)×^{10−4.Thesamesampleisusedtodeterminethetransitionformfactorbyafit}

*

Correspondingauthors.

E-mailaddresses:simona.giovannella@lnf.infn.it(S. Giovannella),stefano.miscetti@lnf.infn.it(S. Miscetti),ivano.sarra@lnf.infn.it(I. Sarra).

http://dx.doi.org/10.1016/j.physletb.2015.01.011

0370-2693/©^{2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

Keywords:

e⁺e⁻collisions Conversiondecay Transitionformfactor

tothee⁺e⁻invariantmassspectrum,obtainingbφη= (¹.28±⁰.10⁺₋⁰₀^._.⁰⁹₀₈)GeV⁻²,thatimprovesbyafactor offivetheprecisionofthepreviousmeasurementandisingoodagreementwithVMDexpectations.

©^{2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

We report the study of the vector to pseudoscalar conver- sion decay φ→

η

e⁺e⁻ with

η

→

π

⁰

π

⁰

π

⁰. In conversion de- cays, A→^B

γ

^∗_→Be⁺e⁻,the radiatedphoton isvirtual andthe squareddilepton invariant mass, M_ee²,corresponds tothe photon 4-momentum transferred, q². The probability of having a lepton pairofgiveninvariantmassisdetermined bytheelectromagnetic dynamicalstructureofthetransitionA→^B

γ

^∗.Thedifferentialde- cayrate,normalizedtotheradiativewidth,is[1]:

1

Γ (φ → ηγ )

d

Γ (φ → η

e⁺e⁻

)

dq²

= α

3

π

|

^Fφη

(

q²

) |

² q²



1

−

^4M2 q²



1

+

^2M2 q²



×



1

+

^q2 M²_φ

−

^M_η²



2

−

^4M

2 φq²

(

M²_φ

−

^M2_η

)

²



3/2

,

(1)

whereM isthemassoftheelectronand Mφ, Mη arethemasses oftheφand

η

mesons,respectively. Fφη(q²)isthetransitionform factor, TFF, that describes the coupling of the mesons to virtual photons and provides information on its nature and underlying structure. The slope ofthe transitionform factor,b_φη ,is defined as:

b_φη

≡

^dF dq²

 

q²=⁰

.

(2)

IntheVectorMesonDominancemodel,VMD, thetransitionform factorisparametrizedas:

F_φη



q²

=

¹

1

−

^q2

/Λ

²_φη

→

^bφη

≈ Λ

⁻_φη²

.

(3)

The VMD successfully describes some transitions, such as

η

_→

γ μ

⁺

μ

⁻, while is failing for others, as in the case of

ω

→

π

⁰

μ

⁺

μ

⁻[2].Recently,newmodelshavebeendevelopedtoover- come such a kind of discrepancies [3,4] and they should be validated with the experimental data from other channels. The only existing data on φ→

η

e⁺e⁻ come from the SND [5] and CMD-2[6]experiments.Theirmeasurementsofthebranching ra- tio,BR(φ→

η

e⁺e⁻),are (1.19±⁰.19±⁰.07)×^{10−4 and}(1.14± 0.10±⁰.06)×^10−4,respectively.TheVMDexpectationisBR(φ→

η

e⁺e⁻)=¹.1×^{10−4 [7]. The SND experiment has also mea-} suredtheslopeofthetransitionformfactorfromthe Mee invari- ant mass distribution, on the basis of 213 events: b_φη= (³.8± 1.8)GeV⁻² [5].TheVMDexpectationisb_φη=^{1 GeV−2[7].}

Duetothelargedatasample, wehaveperformedthreediffer- entmeasurements:

(1) thedeterminationofthebranchingfractionoftheφ→

η

e⁺e⁻ decay;

(2) thedirectmeasurementofthetransitionformfactorslopebφη withafittothedileptoninvariantmassspectrum;

(3) theextraction ofthe |^Fφη|^{2 asa functionof thedilepton in-} variantmass.

2. TheKLOEdetector

DAΦNE, the Frascati φ-factory, is an e⁺e⁻ collider running at center of mass energy of ∼^{1020 MeV. Positron and electron} beams collide at an angle of

π

-25 mrad, producing φ mesons nearlyatrest.TheKLOEexperimentoperatedatthiscolliderfrom 2000to2006, collecting2.5 fb⁻¹.The KLOEapparatusconsistsof alargecylindricalDriftChambersurroundedbyalead-scintillating fiberelectromagneticcalorimeterbothinsertedinsideasupercon- ducting coil, providinga 0.52 Taxial field.The beampipe atthe interactionregionisaspherewith10cmradius,madeofa0.5 mm thickBeryllium–Aluminumalloy.Thedriftchamber[8],4 mindi- ameterand3.3 mlong,has12,582 all-stereotungstensensewires and 37,746 aluminum field wires, with a shell made of carbon fiber-epoxycompositewithan internalwallof∼1 mm thickness.

The gas used is a 90% helium, 10% isobutane mixture. The mo- mentumresolutionis

σ

(p_⊥)/p_⊥≈⁰.4%.Verticesarereconstructed with a spatial resolution of ∼^{3 mm. The} calorimeter [9], with a readout granularity of ∼ (⁴.4×⁴.4)cm², for a total of 2440 cells arranged in five layers, covers 98% of the solid angle. Each cell is read out atboth ends by photomultipliers,both inampli- tude andtime. The energydeposits areobtained fromthesignal amplitude whilethe arrival times andthe particles positions are obtainedfromthe timedifferences. Cellscloseintime andspace are groupedintoenergyclusters. Energyandtimeresolutions are

σ

E/E =⁵.7%/√

E (GeV) and

σ

t =^{57 ps}/√

E (GeV)⊕^{100 ps, re-} spectively.Thetrigger[10]usesbothcalorimeterandchamberin- formation.Inthisanalysistheeventsareselectedbythecalorime- tertrigger,requiringtwoenergydepositswithE>50 MeV forthe barrelandE>150 MeV fortheendcaps.

Machineparametersaremeasuredonlinebymeansoflargean- gle Bhabha scatteringevents. The average value ofthe center of mass energy isevaluated witha precision of about30 keV each 200 nb⁻¹ofintegratedluminosity.Collecteddataareprocessedby aneventclassificationalgorithm[11],whichstreamsvariouscate- goriesofeventsindifferentoutputfiles.

3. Branchingratio

Theanalysisofthedecaychainφ→

η

e⁺e⁻,

η

→³

π

⁰,hasbeen performed ona data sample of about1.7 fb⁻¹. The Monte Carlo (MC) simulation forthe signal has beenproduced with dΓ (φ→

η

e⁺e⁻)/dM_ee accordingtoVMDmodel.Thesignalproductioncor- responds to an integrated luminosity one hundred times larger than collected data. Final state radiation has been included us- ing PHOTOSMonte Carlo generator [12]. For the background, all φ decays andthe not resonant e⁺e⁻→

ωπ

⁰ process have been simulatedwithastatisticstwotimeslargerthandata.

AllMCproductionstakeintoaccountchangesinDAΦNEoper- ation andbackground conditionsona run-by-runbasis. Data-MC correctionsforclusterenergiesandtrackingefficienciesareevalu- atedwithradiativeBhabhaandφ→

ρπ

samples,respectively.The mainstepsoftheanalysisare:

(1) apreselection requiring two tracks ofopposite signextrapo- latedtoacylinderaroundtheinteractionpointand6prompt photoncandidates;

(2) aloose cut on the sixphoton invariant mass: 400<M6γ <

700 MeV;

Fig. 1. Recoilmassagainstthee⁺e⁻pairforthedatasampleafterpreselectioncuts.

Thefirstpeakontheleftcorrespondstotheηmass.Thesecondpeakat∼^{590 MeV} isduetoKS→π⁺π⁻eventswithawrongmassassignment.

(3) a3

σ

cutontherecoilmassagainstthee⁺e⁻pair,M_ee(recoil), showninFig. 1:536.5<Mee(recoil)<554.5 MeV¹;

(4) acutontheinvariantmassandthedistancebetweenthetwo tracksextrapolatedtothebeampipeandatthedriftchamber wallsurfaces,torejectphotonconversion;

(5) a cut based on the time of flight (TOF) of the tracks to the calorimeter to reject events with charged pions in the final state.

Thesecutsare describedindetails inRef.[13],whichreportsthe resultsfor a search ofa light vector boson using the same data sample. The M_ee andcosψ^∗2 distributions, after the M_ee(recoil) cutandattheendoftheanalysischain,areshowninFig. 2,com- paredtoMCexpectations.Theresidualbackgroundcontamination isconcentratedathighmassesandisdominatedbyφ→^KSKL→

π

⁺

π

⁻3

π

⁰ eventswithanearly K_L decay.

The analysis efficiency for signal events as a function of the e⁺e⁻ invariantmassisshowninFig. 3for5 MeV massbins.Itis about10%atlowmassesandincreasesto∼35% at460 MeV,due tothelargeracceptanceforhighermomentumtracks.

At the end of the analysis chain, 30,577 events are selected, with∼3% backgroundcontamination.Afterbintobinbackground subtraction, 29,625±¹⁷⁸ φ→

η

e⁺e⁻,

η

→³

π

⁰, candidates are presentinthedataset.

Thebranching ratio hasbeencalculated usingbin-by-bin effi- ciencycorrection:

BR



φ → η

e⁺e⁻

=

iNi

/ 

i

σ

φ

×

L

×

BR

( η →

3

π

⁰

) .

(4) The luminosity measurement is obtained using very large angle Bhabhascattering events[14],giving an integratedluminosity of L= (¹.68±⁰.01)fb⁻¹. The effective φ production cross section takes into account the center of mass energy variations (at 1%

level)[15]:

σ

= (³³¹⁰±¹²⁰)nb.ThevalueoftheBR(

η

→³

π

⁰)= (32.57±⁰.23)% istakenfrom[16].Ourresultis:

BR



φ → η

e⁺e⁻

= (

1

.

075

±

0

.

007

±

0

.

038

) ×

10⁻⁴

,

(5) where the error includes the uncertainties on luminosity and φ production cross section. The systematic error has been evalu- ated moving by ±¹

σ

the analysis cuts on the recoil mass and

1 We observed a shift of about 2 MeV with respect to the η mass (∼547.85 MeV).Theshiftisduetothetreatmentoftheenergylossfortheelec- tronsinthetrackingreconstruction,thatassumestheenergylossforpions.

2 Thecosψ^∗ variableisdefinedastheanglebetweentheηandthee⁺ inthe e⁺e⁻restframe.

TOF, and by ±^{20% thoserelated to conversion cuts (Table 1). In} ordertoevaluate thesystematicduetothevariationoftheanal- ysisefficiencyforlow M_ee values,the BRhasbeenmeasured for Mee>100 MeV, wherethe efficiency has a smoother behaviour.

Thesesystematicsarenegligiblewithrespecttothenormalization error.

4. Measurementoftheelectromagnetictransitionformfactor

Thefitprocedure,basedontheMINUITpackage[17],isapplied totheM_ee distribution,afterabin-by-binbackgroundsubtraction.

Analysisefficiencyandsmearingeffectshavebeenfoldedintothe theoreticalfunction ofEq.(1),usingasfree parametersΛφη with anoverallnormalizationfactor.TheM_eedistributionisthenfitted, inthewholerange,usinga binwidthof5MeV,byminimizinga

χ

² function,definedas:

χ

²

= 

N

i=1

(

Nⁱ_DATA

−

^N_expectedⁱ

)

²

σ

_i²

^,

⁽⁶⁾

where NDATA is the number of event in the reconstructed i-th M_eebinafterbackgroundsubtractionandN_expectedistheexpected numberofeventsinthesamebin,evaluatedbyperformingacon- volutionofthe theoreticalfunction withreconstruction effectsas follows:

N_expectedⁱ

= 

N

j=1

f_theory

(

mj

) ·

^p



M_ee^j

,

Mⁱ_ee

· 

j

,

(7)

where f_theory(mj)istheintegratedVMDspectruminthe j-thbin, p(M_ee^j,Mⁱ_ee) is the probability for an eventgenerated with mass m_jtobereconstructedinthei-thbinand



j isthereconstruction efficiencyinthe j-thbin.Theprobability p(Mee^j,M_eeⁱ )isshownin Fig. 4.Smearingeffectsareoftheorderoffew%.Theresolutionon the Mee variablehasbeenevaluatedforeach massbinapplyinga GaussianfittotheM_ee(rec.)−^Mee(true)distribution.Itis∼^{2 MeV} forMee<350 MeV andthenimprovesto1 MeVforhighervalues.

As a result of the fit procedure, we determine a value of the formfactorslopeb_φη= (¹.28±⁰.10)GeV⁻²,with

χ

²/ndf=¹.15 and a

χ

² probability of about13%. In Fig. 5 (top) the fit result is shown and compared with data. Fit normalized residuals, de- fined as (Nⁱ_DATA−^Ni_expected)/

σ

i, are shown in Fig. 5 bottom left:

thedistributionoftheirvalueshasthecorrectGaussianbehaviour, centeredat0with

σ

=^{1 (Fig. 5bottomright).}

SystematicsfortheMee(recoil), TOFandphotonconversioncuts havebeenevaluatedasfortheBRmeasurementandsummarized inTable 2.Systematicsrelatedtothefitprocedurehavebeeneval- uatedastheRMSofthedeviationfromthecentralvalueobtained byvaryingthemassrangeusedforthefit.Thetotalsystematicer- ror isthequadratureofallcontributions. Theresultforthe slope ofthetransitionformfactoris:

bφη=

1.28±⁰.10⁺₋⁰₀^._.⁰⁹₀₈

GeV⁻²

.

(8)

5. TransitionformfactorasafunctionofMee

The modulussquaredof thetransitionformfactor, |^Fφη(q²)|^2, asafunction ofthee⁺e⁻ invariant mass,isobtainedby dividing binby binthe M_ee spectrum ofFig. 5(top)by theone ofrecon- structed signal events, generated with F_φ^MCη =^{1, after all analysis} cuts. MCsample isnormalizedinorderto reproducethenumber ofeventsinthefirstbinofdata.InTable 3,thevaluesof|^Fφη(q²)|² asafunctionofthedileptoninvariantmass,withthecorrespond- ingstatisticalerrorsarereported.

Fig. 2. Data-MCcomparisonforMee(left)andcosψ^∗(right)distributionsaftertheMee(recoil)cut(top)andattheendoftheanalysischain(bottom).Thesignalproduction correspondstoanintegratedluminosityonehundredtimeslargerthancollecteddata.

Fig. 3. Analysisefficiencyasafunctionofe⁺e⁻invariantmassfordifferentsteps oftheselectionprocedure.TheToFcutis∼100% efficientonsignalevents,sothat thesymbolscorrespondingtoconversionandToFcutsarealmostsuperimposed.

Table 1

Systematicson thebranching ratio.Relativevariation ofeach contributionwith respecttotheMee(recoil),TOF,photonconversion,eventclassificationcutsarere- ported.

CUT BR variation

Mee(recoil) ±1σ (−0.1/+0.6)%

TOF ±1σ (+0.01/−0.1)%

Photon conversion ±^20% (−⁰.1/+⁰.1)%

Event classification Mee>100 MeV −⁰.1%

Total (−⁰.2/+⁰.6)%

The|^Fφη(q²)|² distributionhasbeenfittedasafunctionofthe invariantmasswithtwofreeparameters,onecorrespondingtothe normalizationandtheother toΛφη , asshownin Fig. 6,together withthepredictionsformtheVMDandfromRef.[3].Fromthisfit, thevalueoftheslopeb_φη is:

Fig. 4. Smearingmatrix:reconstructedvsgeneratedMeevaluesforφ→ηe⁺e⁻MC events.

b_φη

= (

¹

.

25

±

⁰

.

10

)

GeV⁻²

,

(9) in agreement within the uncertainties with the value obtained fromthe fitto the invariantmass spectrum(Eq. (8)) andconsis- tentwiththereproducibilityofthemeasurement.

6. Conclusions

Analyzing the φ→

η

e⁺e⁻ decay channel, a precise measure- ments of both,the BR(φ→

η

e⁺e⁻), andthetransition formfac- tor slope bφη are obtained. We measured a value of BR(φ→

η

e⁺e⁻)= (¹.075±⁰.007±⁰.038)×^{10−4 andavalueoftheslope} ofb_φη= (¹.28±⁰.10⁺₋⁰₀^._.⁰⁹₀₈)GeV⁻².

TheBR(φ→

η

e⁺e⁻)isinagreementwithVMDpredictions[7]

and with the SND and CMD-2 results [5,6]. The transition form factor slope is in agreement with VMD predictions [7], with a precision that is a factor of five better than previous SND mea- surement.

Thetransitionformfactorhasbeenused[18]toderivetheup- perlimitfortheproductionofalightdarkbosonU inφ→

η

U→

η

e⁺e⁻ decay. Present measurement confirms the exclusion plot

Fig. 5. Top:fittothe Mee spectrumfortheDalitzdecaysφ→ηe⁺e⁻,withη→ π⁰π⁰π⁰,inlogarithmicscale.Bottomleft:normalizedfitresidualsvsMee.Bottom right:distributionofnormalizedvalueswithsuperimposedaGaussianfit.

Table 2

Systematicson bφη. Relative variation ofeach contributionwith respect to the Mee(recoil),TOF,photonconversion,fitmassrangecutsarereported.

CUT bφηvariation

Mee(recoil) ±1σ (+4.4/−3.0)%

TOF ±1σ (+3.2/−1.5)%

Photon conversion ±20% (−4.1/+1.9)%

Fit limits Meefit range ±³.8%

Total (+⁶.9/−⁶.5)%

Fig. 6. Fittothe|Fφη|²distributionasafunctionoftheinvariantmassoftheelec- tronpositronpair,withabinningof5 MeV.Thebluecurveisthefitresult,andin dashedbluethefunctionsobtainedforΛφη= Λφη±¹σarereported.VMDexpec- tationsaresuperimposedinpinkdashedlinewhilethecurveobtainedfromRef.[3]

isreportedinredemptydots.(Forinterpretationofthereferencestocolorinthis figurelegend,thereaderisreferredtothewebversionofthisarticle.)

Table 3

Transitionformfactor|Fφη|²oftheφ→ηe⁺e⁻decay.

Mee(MeV) |Fφη|² δ|Fφη|² Mee(MeV) |Fφη|² δ|Fφη|² Mee(MeV) |Fφη|² δ|Fφη|²

2.50 1.00 0.01 157.50 1.17 0.09 312.50 1.57 0.17

7.50 1.05 0.02 162.50 1.13 0.09 317.50 1.28 0.16

12.50 1.03 0.02 167.50 0.98 0.08 322.50 1.19 0.16

17.50 0.99 0.03 172.50 1.03 0.09 327.50 1.38 0.18

22.50 0.97 0.04 177.50 1.28 0.10 332.50 1.21 0.18

27.50 1.00 0.04 182.50 1.03 0.09 337.50 1.35 0.19

32.50 0.93 0.04 187.50 1.21 0.10 342.50 1.39 0.20

37.50 1.03 0.05 192.50 0.90 0.09 347.50 2.08 0.26

42.50 0.95 0.05 197.50 1.25 0.10 352.50 1.50 0.25

47.50 0.95 0.05 202.50 1.12 0.10 357.50 1.30 0.24

52.50 1.01 0.05 207.50 1.05 0.10 362.50 1.13 0.28

57.50 1.01 0.05 212.50 1.13 0.10 367.50 1.20 0.27

62.50 1.03 0.05 217.50 1.04 0.10 372.50 1.87 0.29

67.50 1.08 0.06 222.50 1.14 0.10 377.50 1.76 0.29

72.50 1.04 0.06 227.50 1.27 0.11 382.50 1.02 0.29

77.50 0.96 0.06 232.50 1.18 0.11 387.50 1.49 0.31

82.50 1.09 0.06 237.50 1.06 0.10 392.50 1.58 0.36

87.50 1.06 0.06 242.50 0.83 0.10 397.50 1.79 0.38

92.50 1.01 0.06 247.50 1.20 0.11 402.50 1.54 0.37

97.50 1.08 0.07 252.50 1.11 0.11 407.50 2.08 0.43

102.50 0.98 0.07 257.50 1.52 0.13 412.50 1.40 0.48

107.50 1.06 0.07 262.50 1.33 0.12 417.50 2.24 0.59

112.50 0.97 0.07 267.50 1.39 0.13 422.50 1.40 0.59

117.50 1.12 0.08 272.50 1.24 0.13 427.50 −⁰.14 1.36

122.50 1.05 0.08 277.50 1.32 0.13 432.50 0.28 3.02

127.50 0.96 0.07 282.50 1.39 0.14 437.50 5.36 3.59

132.50 1.09 0.08 287.50 1.18 0.13 442.50 2.75 3.68

137.50 1.06 0.08 292.50 1.20 0.13 447.50 6.97 4.10

142.50 1.08 0.08 297.50 1.27 0.14 452.50 1.44 3.79

147.50 1.06 0.08 302.50 1.22 0.14 457.50 3.43 4.91

152.50 1.11 0.09 307.50 1.30 0.15

obtainedby KLOEinthemassrange(5<MU<470)MeV, where bφη=^{1 GeV−2 wasassumed[13].}

Acknowledgements

We warmly thank our former KLOE colleagues for the ac- cess to the data collected during the KLOE data taking cam- paign. We thank the DAΦNE team for their efforts in main- taining low background running conditions and their collabo- ration during all data taking. We want to thank our techni- cal staff: G.F. Fortugno and F. Sborzacchi for their dedication in ensuring efficient operation of the KLOE computing facili- ties; M. Anelli for his continuous attention to the gas system and detector safety; A. Balla, M. Gatta, G. Corradi and G. Pa- palino for electronics maintenance; M. Santoni, G. Paoluzzi and R. Rosellini forgeneral detectorsupport; C. Piscitelli forhis help during major maintenance periods. This work was supported in part by the EU Integrated Infrastructure Initiative Hadron Physics Project under contract number RII3-CT-2004-506078; by the European Commission under the 7th Framework Programme through the ‘Research Infrastructures’ action of the ‘Capacities’

Programme, Call: FP7-INFRASTRUCTURES-2008-1, Grant Agree- ment No.227431; by the PolishNational ScienceCentre through

the Grant Nos. DEC-2011/03/N/ST2/02641, 2011/01/D/ST2/00748, 2011/03/N/ST2/02652, 2013/08/M/ST2/00323, and by the Foun- dation For Polish Science through the MPD programme and the projectHOMINGPLUSBIS/2011-4/3.

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