Measurement of the $\phi \rightarrow \pi^{0}e^{+}e^{-}$ transition form factor with the KLOE detector

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Measurement of the φ → π ⁰ e ⁺ e ⁻ transition form factor with the KLOE detector

KLOE-2 Collaboration

A. Anastasi

^e

^,

^d

, D. Babusci

^d

^,

^∗

, G. Bencivenni

^d

, M. Berlowski

^u

, C. Bloise

^d

, F. Bossi

^d

,

P. Branchini

^r

, A. Budano

^q

^,

^r

, L. Caldeira Balkeståhl

^t

, B. Cao

^t

, F. Ceradini

^q

^,

^r

, P. Ciambrone

^d

, F. Curciarello

^e

^,

^b

^,

^l

, E. Czerwi ´nski

^c

, G. D’Agostini

^m

^,

ⁿ

, E. Danè

^d

, V. De Leo

^r

, E. De Lucia

^d

, A. De Santis

^d

, P. De Simone

^d

, A. Di Cicco

^q

^,

^r

, A. Di Domenico

^m

^,

ⁿ

, R. Di Salvo

^p

,

D. Domenici

^d

, A. D’Uffizi

^d

, A. Fantini

^o

^,

^p

, G. Felici

^d

, S. Fiore

^s

^,

ⁿ

, A. Gajos

^c

, P. Gauzzi

^m

^,

ⁿ

, G. Giardina

^e

^,

^b

, S. Giovannella

^d

, E. Graziani

^r

, F. Happacher

^d

, L. Heijkenskjöld

^t

,

W. Ikegami Andersson

^t

, T. Johansson

^t

, D. Kami ´nska

^c

, W. Krzemien

^u

, A. Kupsc

^t

, S. Loffredo

^q

^,

^r

, G. Mandaglio

^f

^,

^g

, M. Martini

^d

^,

^k

, M. Mascolo

^d

^,

^∗

, R. Messi

^o

^,

^p

, S. Miscetti

^d

, G. Morello

^d

, D. Moricciani

^p

, P. Moskal

^c

, M. Papenbrock

^t

, A. Passeri

^r

, V. Patera

^j

^,

ⁿ

, E. Perez del Rio

^d

, A. Ranieri

^a

, P. Salabura

^c

, P. Santangelo

^d

, I. Sarra

^d

, M. Schioppa

^h

^,

ⁱ

, M. Silarski

^d

, F. Sirghi

^d

, L. Tortora

^r

, G. Venanzoni

^d

, W. Wi´slicki

^u

, M. Wolke

^t

aINFNSezionediBari,Bari,Italy bINFNSezionediCatania,Catania,Italy

cInstituteofPhysics,JagiellonianUniversity,Cracow,Poland dLaboratoriNazionalidiFrascatidell’INFN,Frascati,Italy

eDipartimentodiFisicaeScienzedellaTerradell’UniversitàdiMessina,Messina,Italy

fDipartimentodiScienzeChimiche,Biologiche,FarmaceuticheedAmbientalidell’UniversitàdiMessina,Messina,Italy gINFNGruppocollegatodiMessina,Messina,Italy

hDipartimentodiFisicadell’UniversitàdellaCalabria,Rende,Italy iINFNGruppocollegatodiCosenza,Rende,Italy

jDipartimentodiScienzediBaseedApplicateperl’Ingegneriadell’Università“Sapienza”,Roma,Italy kDipartimentodiScienzeeTecnologieapplicate,Università“GuglielmoMarconi”,Roma,Italy lNovosibirskStateUniversity,630090Novosibirsk,Russia

mDipartimentodiFisicadell’Università“Sapienza”,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

tDepartmentofPhysicsandAstronomy,UppsalaUniversity,Uppsala,Sweden uNationalCentreforNuclearResearch,Warsaw,Poland

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

Articlehistory:

Received26January2016

Receivedinrevisedform6April2016 Accepted7April2016

Availableonline11April2016 Editor:M.Doser

Ameasurementofthevectortopseudoscalarconversiondecayφ→

π

⁰e⁺e⁻withtheKLOEexperiment is presented. A sample of ∼9500 signal events was selectedfrom a data set of 1.7 fb⁻¹ of e⁺e⁻ collisions at√

s∼^mφ collectedatthe DANEe⁺e⁻ collider. Theseevents wereusedto performthe first measurement ofthe transition formfactor|^Fφπ⁰(q²)| ^{anda new}measurement of thebranching

*

Correspondingauthors.

E-mailaddresses:danilo.babusci@lnf.infn.it(D. Babusci),mascolo.matteo@gmail.com(M. Mascolo).

http://dx.doi.org/10.1016/j.physletb.2016.04.015

0370-2693/©^{2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

Keywords:

e⁺e⁻collisions Conversiondecay Transitionformfactor

ratioofthedecay:BR(φ→

π

⁰e⁺e⁻)= (¹.35±⁰.05⁺₋⁰₀^._.⁰⁵₁₀)×^{10−5.Theresultimproves}significantlyon previousmeasurementsandisinagreementwiththeoreticalpredictions.

©^{2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The conversion decays of a light vector resonance (V) into a pseudoscalarmeson (P) anda lepton pair, V →^P

γ

^∗→^P



⁺



⁻, represent a stringent test for theoretical models of the nature of mesons. In these processes, the squared dilepton invariant mass,m²_,correspondstothevirtual photon4-momentumtrans- fer squared, q². The q² distribution depends on the underlying electromagneticdynamicalstructureofthetransitionV→^P

γ

^∗.

Thedescription ofthe couplingofthe mesonsto virtual pho- tons is typically parametrized by the so-called Transition Form Factor(TFF), FV P

(

q²

)

.TFFs arefundamental quantities playingan importantroleinmanyfieldsofparticlephysics,suchasthecalcu- lationofthehadronicLight-by-Lightcontributionto theStandard Modelpredictionofthemuonanomalousmagneticmoment[1].

Recently, the increasing interest in conversion decays was mostly drivenby the discrepancybetweentheexperimental data from NA60 [2] and Lepton G [3], and the Vector Meson Domi- nance(VMD)predictionforthe

ω

→

π

⁰

μ

⁺

μ

⁻TFFFω π⁰

(

q²

)

.Over theyears, severaltheoretical modelshave beendeveloped toex- plainthisdiscrepancy[4–7]. Inorderto check theconsistencyof themodels,a measurementofthe F_φπ⁰

(

q²

)

TFF,whichhasnever been measured so far, was strongly recommended. In particular, becauseofitskinematics,the

φ

→

π

⁰e⁺e⁻processisaverygood benchmarktoinvestigatetheobservedsteepriseinNA60dataat q² closetothe

ρ

resonancemass.

Atpresent, theexistingdata on

φ

→

π

⁰e⁺e⁻ come fromSND [8]and CMD-2[9] experiments which were able to extract only thevalueoftheBranchingRatio(BR).TheF_φπ⁰

(

q²

)

TFFhence,was nevermeasuredsofar.Itsmodulussquareentersinthecalculation ofthe

φ

→

π

⁰e⁺e⁻double-differentialdecaywidth:

d²

(φ → π

⁰e⁺e⁻

)

dq²d cos

θ

^∗

=

³

8



q²

q²

+

^2m2e



(

2

− β

^2sin2

θ

^∗

)

×

^d

(φ → π

⁰e⁺e⁻

)

dq² (1)

with

β

=

1−^4m2e

/

q²1/2

and[10]:

d

(φ → π

⁰e⁺e⁻

)

dq²

= (φ → π

⁰

γ ) α

3

π ^β

|

F_φπ0

(

q²

)|

² q²



1

+

^2m2e

q²



×

⎡

⎣



1

+

^q2 m²_φ

−

m²_π

2

−

^4m

2 φq²

(

m²_φ

−

m²_π

)

²

⎤

⎦

3/2

,

(2)

whereme isthemassoftheelectron,andmφ,mπ arethemasses ofthe

φ

and

π

⁰mesons,respectively.

θ

^∗ istheanglebetweenthe

φ

and the e⁺ direction in the e⁺e⁻ rest frame. Its cosine is an invariantquantitywhichcanbewrittenas[11]:

cos

θ

^∗

= (

q²

+

^m2_φ

−

^m2_π

) −

^{4 p}φ

·

^pe⁺

β 

q²

−

^m2_φ

−

^m2_π



2

−

^{4 m2}_π^m2_φ

,

(3)

wherep_φ isthe4-momentumof

φ

andp_e+ ofthepositron.

Thankstothelargeamountofcollected

φ

decays(∼⁵

.

6×^109), theKLOEexperimenthasbeenablebothtoperformthefirstmea- surement of the F_φπ⁰

(

q²

)

TFF and to significantly improve the determinationofthebranchingratioof

φ

→

π

⁰e⁺e⁻.

2. TheKLOEdetector

DA



NE, the Frascati

φ

-factory,is an e⁺e⁻ colliderrunning at a center-of-mass energy of ∼^{1020 MeV. Positron and electron} beams collide at an angle of

π

-25 mrad, producing

φ

mesons nearlyatrest.

TheKLOE apparatusconsistsofa largecylindricalDriftCham- ber (DC) surrounded by a lead-scintillating fiber electromagnetic calorimeterbothinsertedinside asuperconductingcoil, providing a 0.52 Taxial field. The beampipe attheinteraction region isa sphere with 10 cm radius, made of a 0.5 mm thick Beryllium–

Aluminum alloy. The drift chamber [12], 4 m in diameter and 3.3 mlong,has12,582all-stereotungsten sensewiresand37,746 aluminum field wires, with a shell made of carbon fiber-epoxy compositewithaninternalwallof∼^{1 mmthickness.Thegasused} is a 90% helium,10% isobutane mixture. The momentum resolu- tionis

σ (

p_⊥

)/

p_⊥≈⁰

.

4%.Verticesarereconstructedwithaspatial resolutionof∼^{3 mm.The}calorimeter[13],withareadoutgranu- larityof∼^(4.4×^{4.4) cm2,foratotalof2440cellsarrangedinfive} layers,covers98% ofthesolid angle.Eachcellisreadout atboth endsbyphotomultipliers,bothinamplitudeandtime.Theenergy depositsare obtainedfromthesignal amplitude whilethearrival timesandtheparticlepositionsareobtainedfromthetimeofthe signals collected at the two ends. Cells close in time and space aregroupedintoenergyclusters. Energyandtime resolutionsare

σ

E

/

E=⁵

.

7%

/

√

E

(

GeV

)

and

σ

t=^{57 ps}

/

√

E

(

GeV

)

⊕^{100 ps, re-} spectively.Thetrigger[14] usesbothcalorimeterandchamberin- formation.Inthisanalysistheeventsareselectedbythecalorime- tertrigger,requiringtwoenergydepositswithE

>

50 MeV forthe barrelandE

>

150 MeV fortheendcaps.

Large angle Bhabha scattering events are used to obtain lu- minosity,center-of-massenergyandcrossingangleof thebeams.

Aprecision measurement of√

s,withnegligible statisticaluncer- tainty anda systematicerrorof∼^{30 keV,isroutinelyperformed} onthebasisof200 nb⁻¹ ofintegratedluminosity.Thesystematic errorisinfactontheabsolutemomentumscale,derivedfromthe analysisofthe

φ

lineshape[15].Thecenter-of-massenergydistri- butionwidthisabout330 keVfromthecontributionsofi)DA



NE beam energy spread (0.06%) and ii) radiative corrections/effects.

Collected data are processedby an eventclassification algorithm [16],whichstreams various categoriesofevents indifferentout- putfiles.

3. Dataanalysis

The analysisofthe decay

φ

→

π

⁰e⁺e⁻ (

π

⁰→

γ γ

),has been performedonadatasampleof1.69 fb⁻¹ fromthe2004/2005data takingcampaign.

The simulationofboth signal andbackgroundeventsis based on the KLOE Monte Carlo (MC), GEANFI [16], that includes ra- diative contributions to the process under study and takes into account variations of beam energy, crossing angle and machine backgroundconditions ona run-by-runbasis. The MC simulation

Fig. 1. Data-MCcomparisonafteralltheanalysiscutsfortheinvariant-massspectrumofe⁺e⁻(left)andofthetwophotons(right).Blackdotsaredata,solidredlineisthe sumofMChistogramcomponents:signal(cyan),φ→π⁰γ background(orange)andradiativeBhabhascattering(green).(Forinterpretationofthereferencestocolorinthis figurelegend,thereaderisreferredtothewebversionofthisarticle.)

ofthesignal hasbeenproduced accordingtoEq.(1),assuming a point-like TFF (i.e. |^Fφπ⁰

(

q²

)

|²=^{1). The radiative emission from} theleptonsinthefinalstateofthechannelunderstudyisalsoin- cludedin thesimulationby means ofthePHOTOS MCgenerator [17].Thesignal productioncorresponds toanintegratedluminos- ity 1000 times larger than for the collected data. The dominant contributions to background events originate fromdouble radia- tiveBhabhascattering(e⁺e⁻→^e+e−

γ γ

)andfromthe

φ

→

π

⁰

γ

decay,wherethe

γ

convertstoae⁺e⁻pairintheinteractionwith thebeampipeordriftchamberwalls.(The

φ

→

π

⁰

γ

withthe

π

⁰

Dalitzdecayto

γ

e⁺e⁻alsocontributestothebackgroundbutitis almostcompletelysuppressedbytheanalysiscuts.) Allotherback- ground events, i.e. the other

φ

meson decays, the non-resonant e⁺e⁻→

ωπ

⁰ process andthe

π

⁰ production via

γ γ

interaction, e⁺e⁻→

π

⁰e⁺e⁻,werealsosimulated,resultingfullynegligibleat theendoftheanalysispath.

Asafirststepoftheanalysis,eventsareselectedrequiringtwo opposite-chargetracksextrapolatedtoacylinderaroundtheinter- actionpoint(IP)withradius4cmand20 cmlongandtwoprompt photoncandidatesfromIP(i.e.withenergyclustersE_clu

>

7 MeV not associatedto anytrack, inthe angularregion |^cos

θ

_γ|

<

0

.

92 andin the time window |Tγ−Rγ

/

c|

<

min

(

3

σ

t

,

2ns

)

). In order toenhance thesignal-to-background ratio,furtherconstraintsare appliedonthispreselecteddatasample:

• ^{a cut on the energies of the final state particles requiring:}

(

30

<

E_e±

<

460

)

MeV, Eγ

>

70 MeV,

(

300

<

_Eγ1 +Eγ2

<

670

)

MeV and

(

470

<

E_e++^Ee⁻

<

750

)

MeV;

• ^{angular cuts: 45◦}

< θ

_e±

, θ

_γ

<

135^◦,

θ

_e+e⁻

<

145^◦ and 27^◦

<

θ

γ γ

<

57^◦;

• ^{two cuts on the invariant mass of the two photons and on} the recoil mass against e⁺e⁻ to select events with a

π

⁰ in thefinalstate,i.e.

(

90

<

mγ γ^inv

<

190

)

MeV and

(

80

<

m_e^miss_+e−

<

180

)

MeV;

• ^{acutontheinvariantmassandthedistancebetweenthetwo} trackscalculated atthe surfacesofthe beampipe (BP)or of theDCwallsurfaces;

• ^{a cut based on the time of flight (ToF) of the tracks to the} calorimeter.

All the cuts have been optimized in order to maximize the available rangeof the e⁺e⁻ invariant mass spectrum fortheTFF extraction.The constraints on angularand energyvariables have beenobtained looking atthe differencesbetween thesignal and

Bhabhareconstructedangularandenergydistributionsoffinallep- tons and photons. The cuts on the energies and on the opening angles

θ

e⁺e⁻ and

θ

γ γ oftracksandclustersallowtostronglysup- press the dominant background (S/B∼⁵×^{10−4) from the QED} process e⁺e⁻→^e+e−

γ γ

. The

θ

_e+e⁻ ≤^145◦ requirement is also very effectiveinrejecting oftheirreducible backgroundfromthe

γ γ

processe⁺e⁻→^e+e−

π

⁰,inwhichthefinal stateleptons are emitted in the forward direction(i.e. atsmall polar angles with respect to the beam line) forthis kind ofevents. The

φ

→

π

⁰

γ

contamination, withthe

γ

converting on the BP or DCwalls, is suppressed by tracing back the tracks of the e⁺

/

e⁻ candidates, by reconstructing the invariant mass (m_e^BP_+e^,DC₋ ) and the distance (d_e^BP_+e^,DC₋ ) of the track pair both at the BP and DC wall surfaces.

Both variables are expected to be small for photon conversion events,so that thisbackgroundis suppressedby rejecting events with:m_e^BP_+e−

<

10 MeV andd_e^BP_+e−

<

2 cm,orm_e^DC_+e−

<

80 MeV and d_e^DC_+e−

<

3 cm. Thecut on the time offlight tothe calorimeteris usedtoremoveresidualbackgroundeventswithmuonsorcharged pions in the final state. When an energy cluster is associated to a track, the ToF to the calorimeter is evaluated using both the calorimeter timing (tclu) and the time along the tracktrajectory, namely t_trk=^Ltrk

/β

c,where L_trk is the length ofthe trackpath.

The difference



t=^ttrk−^tclu is then evaluated in the electron hypothesis; all events with



t

<

0

.

8 ns are retained for further analysis. Thisalgorithm, together withthe cut ontheenergies of thefinalparticles,turnsouttobecrucialforreducingthecontam- inationfromthedecay

φ

→

π

⁺

π

⁻

π

⁰ toanegligiblelevel.

Afteralltheabovedescribedcutstheoverallefficiency,asesti- mated bytheMC, is15.4%.Theefficiencyis19.5%atlowere⁺e⁻ invariant masses, decreasing to afew percent atthe highestval- uesofmomentumtransfer. Forthisreasontheanalysisislimited up to 

q²=^{700 MeV. At the end of the analysis chain, 14670} events areselected, witharesidual backgroundcontamination of

∼^{35%,equallydividedbetweentheBhabhaand}

φ

→

π

⁰

γ

compo- nent,correspondingtoabout9500signalevents.

The agreement betweendata andMonte Carlosimulation, af- ter all selection cuts, is shown in Fig. 1 for the 

q² and mγ γ distributions. Asshownintheleft panelofthisFigure,in there- gion 

q²

>

400 MeV the

φ

→

π

⁰

γ

backgroundis negligibleand onlytheBhabhabackgroundispresent.Furthermore,asacheckof Eq.(3),inFig. 2weshow thedistributionof|^cos

θ

^∗|^ascompared totheMCprediction.

Fig. 2. Data-MCcomparisonafteralltheanalysiscutsfor|cosθ^∗|.Codeofsymbols andcolorsasinFig. 1.(Forinterpretationofthereferencestocolorinthisfigure legend,thereaderisreferredtothewebversionofthisarticle.)

In order to subtract the residual background from data, the e⁺e⁻ invariant-massspectrum isdivided into15bins ofincreas- ingwidth(topreservethestatistics ofsignalcandidates). Ineach binof 

q²,the m_e^miss_+e− distribution is fit by a sumof two Gaus- sianfunctions,parametrizingthesignal,andathird-orderpolyno- mial,parametrizingthebackground.Someexamples ofthefitsto them_e^miss_+e− distributions are shownin Fig. 3. Apartfrom a global normalization,theparameters oftheGaussian functionsare fixed by a fit of the MC signal distribution. The background contribu- tionisevaluatedbinbybin,withoutanyassumptionorconstraint for the polynomial parameters. Once the residual background is parametrized,itisbinbybinsubtractedfromdata.

Table 1

KLOEmeasurementofthetransitionformfactor|^Fφπ⁰(q²)|^ofthe φ→π⁰e⁺e⁻ decay.

Bin # 

q²-range (MeV)

Bincenter (MeV)

q²(UChT) (MeV)

|^Fφπ⁰(q²)|²

1 2me÷^{30 15}.5 9.0 1.00±^0.11

2 30÷^{60 45 43}.3 1.18±^0.22

3 60÷90 75 74.0 0.93±0.21

4 90÷120 105 104.2 1.09±0.19

5 120÷150 135 134.4 1.19±0.23

6 150÷^{190 170 169}.0 1.42±^0.33

7 190÷^{230 210 209}.1 1.46±^0.47

8 230÷^{270 250 249}.1 1.22±^0.58

9 270÷^{310 290 288}.8 2.30±^0.53

10 310÷350 330 327.5 2.17±0.65

11 350÷400 375 380.0 3.01±1.34

12 400÷450 425 426.6 3.14±1.71

13 450÷^{500 475 476}.1 6.07±^2.05

14 500÷^{550 525 526}.0 8.49±^4.27

15 550÷^{700 625 632}.9 17.4±^10.3

3.1. Measurementof|F_φπ⁰

(

q²

)|

²

ThemodulussquareoftheTFF,|^Fφπ⁰

(

q²

)|

^{2,isafactorinfront} oftheq²differentialcrosssection(seeEq.(2)),henceitcanbeex- tracted fromdataby dividing themeasured e⁺e⁻ invariant-mass spectrumbythespectrumofreconstructedMCsignalevents,gen- erated with a constant F_φπ⁰

(

q²

)

, after all the analysis cuts. The resultis reportedinTable 1.The measured TFFis normalizedso that |^Fφπ⁰

(

q²

)

|²=^{1 inthefirst bin.The errors includeboth the} statisticalandthesystematicuncertainty.

Thesystematicuncertaintyconsistsoftwomajorcontributions:

the first due to the experimental resolution of the variables to whichtheanalysiscutsare applied,andthe secondassociatedto thebackgroundfittingprocedure.

Fig. 3. m^miss_e+e− distributions(unitsMeV)forsome

q²binsshowingthetotalbackgroundcontribution(redcurve)evaluatedfromafittothedata(blackpoints),withfixed signalshape(bluecurve).Thedashedgreencurverepresentstheglobalfitofdata,includingthebackgroundfunctionandthesignalparametrization.

Fig. 4. Comparisonbetweenthemeasurementof|^Fφπ⁰(q²)|^{2(blackpoints)andthe} theoreticalpredictionsforthisquantitybasedon:thedispersiveanalysisofRef.[5]

(orangeandcyanbands)andRef.[7](bluedashedline),thechiraltheoryapproach ofRef.[6](greenband),andtheone-poleVMDmodel(solidredline)(seeEqs. (49) and(50)ofRef.[7]).(Forinterpretationofthereferences tocolorinthis figure legend,thereaderisreferredtothewebversionofthisarticle.)

Thesystematicuncertaintyduetotheanalysiscutsisevaluated moving by±¹

σ

allthevariables onwhicha selectionisapplied.

Cutsaremovedonceatatime,loggingthedeviationofcountsin each binof

q² fromthe originalone. The relativedeviations of countscomingfromthedifferentcutsarethensummedbinbybin inquadraturetogetthetotalrelativeuncertainty.Whenavariable isselectedwithinawindow,itsedgesarealwaysmovedoppositely inordertomakethewindowwiderornarroweraccordingtothe resolution.Theresultingfractional uncertaintyisofafewpercent inmostofthebinsoflower

q²,increasingupto20%insomeof thebinsof higher4-momentumtransfer.There isnoevidence of asingledominantcutwithrespecttotheothers;thecontribution ofthevariousanalysiscutsisdifferentforeachbinof

q². Thesystematicerrorassociatedtothefittingprocedureiseval- uated computing the deviation of the yield of the background function,withrespecttothenominalone,wheneach ofthefour parametersismovedby±¹

σ

whilefixingtheotheronesaccording tothecorrelationmatrix.Thefourcontributionsthusobtainedare summed in quadrature to get the total uncertainty on the back- groundyield in each bin of 

q². This error contributionis then propagated to F_φπ⁰

(

q²

)

through the numberofsignal candidates ineachbin,whichenters inthecomputation.The contributionin eachbinof

q²isofafewpercent.

InFig. 4,our resultson |^Fφπ⁰

(

q²

)

|^{2 are compared withthree} different theoretical predictions. The best agreement is obtained withthe Unconstrained ResonantChiralTheory (UChT), withpa- rametersextractedfromafitoftheNA60 data[6].We notethat, asa consequence of the steepness and nonlinearityof the e⁺e⁻ invariant-mass spectrum, theTFF measured in a 

q² bin cannot be associated to the corresponding bin center. For this reason, each experimental pointof Fig. 4 isassociated witha 

q² value weighted according to the theoretical shape predicted by UChT (seecolumnlabeled“

q²UChT”inTable 1).AsshowninTable 1, withthegivenbinwidths,thebincenterisagoodapproximation ofthe weighted 

q² ineach bin,withthe exception ofthevery firstbin,wherethem_e+e⁻ functionissteeper.

The transitionformfactors areoften representedby a simple, VMD-inspired,one-poleparametrization:

F

(

q²

) =

¹

1

−

^q2

/

²

,

(4)

Table 2

PreviousdeterminationofBR(φ→π⁰e⁺e⁻)bySND[8]andCMD-2[9].ThePDG averageis(1.12±0.28)×10⁻⁵[20].Thetheoreticalpredictionsarealsoreported.

ForRef.[5]“once”(“twice”)referstothedispersiveanalysiswithone(two)sub- tractions.

BR(φ→π⁰e⁺e⁻)×10⁵

Experiment SND 1.01±0.28±0.29

CMD-2 1.22±0.34±0.21

Theory Schneider et al.[5](“once”) (1.39 . . . 1.51) Schneider et al.[5](“twice”) (1.40 . . . 1.53)

Danilkin et al.[7] 1.45

fromwhichtheformfactorslopeparameterisobtained:

b

=

^dF

(

q²

)

dq²

 

q²=⁰

= 

⁻²

.

By fitting our data according to (4), we get b_φπ⁰ = (²

.

02± 0

.

11

)

GeV⁻², to be compared with the one-pole approximation expectation,b_φπ⁰=^M−φ²,andthepredictionofthedispersiveanal- ysis,b_φπ⁰= (²

.

52· · ·²

.

68

)

GeV⁻²,ofRef.[5].

3.2. MeasurementofBR

(φ

→

π

⁰e⁺e⁻

)

The branching ratio of the

φ

→

π

⁰e⁺e⁻ decay was obtained fromthebackground-subtractede⁺e⁻ massspectrumbyapplying anefficiencycorrectionevaluatedbinbybin:

BR

(φ → π

⁰e⁺e⁻

) =



iN_i

/ 

i

σ

φ

× L

int

×

^BR

( π

⁰

→ γ γ ) ,

(5) where

σ

φ istheeffective

φ

productioncross-section,

σ

φ= (³³¹⁰± 120

)

nb[18],

L

int= (¹

.

69±⁰

.

01

)

fb⁻¹[19]istheintegratedlumi- nosity ofdata,andBR

( π

⁰→

γ γ )

thebranching ratioof

π

⁰ into twophotons[20].Niisthenumberofsignalcandidatesintheith binof

q² and



i isthecorrespondingselectionefficiency,evalu- atedasthenumberofMCsignaleventsintheithbinafterallthe analysis steps, divided by the numberof the corresponding gen- erated events. The result covers the range 

q²

<

700 MeV (the upperedgeofthehigherbinof

q²)andisequalto:

BR

(φ → π

⁰e⁺e⁻

; 

q²

<

700 MeV

) = (

¹

.

19

±

⁰

.

05⁺₋⁰₀^._.⁰⁵₁₀

) ×

¹⁰⁻⁵

.

(6) Here,thefirsterrorresultsfromthecombinationofthestatistical one (2.2%infraction) withtheabove quoted uncertaintieson

σ

φ and

L

int.The secondisa systematiconeduetotheanalysiscuts andbackgroundsubtraction(see sec. 3.1). The erroron



i dueto theparametrizationoftheTFFintheMCisnegligible.

The result can be extended to the full 

q² range evaluating the fraction ofthe integral in thee⁺e⁻ invariant-mass spectrum which isnot covered bythe analysis. Theextrapolation hasbeen computedaccordingtothetheoreticalmodelthatbestfitsthedata [6].Theestimateofthetotalbranchingratiois:

BR

(φ → π

⁰e⁺e⁻

) = (

1

.

35

±

0

.

05⁺₋⁰₀^._.⁰⁵₁₀

) ×

10⁻⁵

.

(7) This result improves the previous measurements by SND and CMD-2experimentsandisinagreementwiththetheoreticalpre- dictionsshowninTable 2.

4. Conclusions

Analyzingtheconversiondecay

φ

→

π

⁰e⁺e⁻,wemeasuredfor thefirsttimethemodulussquareofthe F_φπ⁰ transitionformfac- tor for

q² below700 MeV.The dataare inagreementwiththe

theoreticalpredictionbasedontheUnconstrainedResonantChiral Theory(UChT),withparameters extractedfromafit oftheNA60 data. From the same data set we obtained a value of BR

(φ

→

π

⁰e⁺e⁻;

q²

<

700MeV

)

= (1

.

19±0

.

05⁺₋⁰₀^._.⁰⁵₁₀

)

×10⁻⁵.Anextrap- olationbasedonthetheoreticalmodelinagreementwiththedata has been used to extend the result to the full 

q² range. The value obtained is BR

(φ

→

π

⁰e⁺e⁻

)

= (¹

.

35±⁰

.

05⁺₋⁰₀^._.⁰⁵₁₀

)

×^10−5, thatimprovessignificantlytheresultsobtainedbySNDandCMD-2 experiments,andisinagreementwiththeoreticalpredictions.

Acknowledgements

We warmly thank our former KLOE colleagues forthe access tothe data collected during the KLOE datataking campaign. We thankthe DA



NEteamfortheireffortsinmaintaininglowback- groundrunning conditionsandtheir collaboration during alldata taking. We want to thank our technical staff: G.F. Fortugno and F. Sborzacchi for their dedication in ensuring efficient operation oftheKLOE computingfacilities;M. Anelliforhis continuousat- tentionto thegas systemanddetectorsafety;A. Balla, M. Gatta, G. Corradi and G. Papalino forelectronics maintenance; M. San- toni, G. Paoluzzi and R. Rosellini for general detector support;

C. Piscitelli for his help during major maintenance periods. We thankProf.B.KubisandDr.I.Danilkinforthedetailedresultofthe calculationofRefs.[5]and[7],respectively.Wearealsoverygrate- fultoDr.S.Ivashynforprovidingustheformulaforcos

θ

^∗ andfor the many enlightening discussions during all the phases of the analysis.Thisworkwas supportedinpartbytheEUIntegratedIn-

frastructureInitiativeHadronPhysicsProjectundercontractnum- berRII3-CT-2004-506078;bytheEuropeanCommissionunderthe 7thFramework Programme through the‘Research Infrastructures’

actionofthe‘Capacities’Programme,Call:FP7-INFRASTRUCTURES- 2008-1, Grant Agreement No. 227431; by the Polish National Science Centre through the Grants Nos. 2011/03/N/ST2/02652, 2013/08/M/ST2/00323,2013/11/B/ST2/04245,2014/14/E/ST2/00262, 2014/12/S/ST2/00459.

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