Measurement of the φ→π0e+e- transition form factor with the KLOE detector

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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

a_INFN_Sezione_di_Bari,_Bari,_Italy b_INFN_Sezione_di_Catania,_Catania,_Italy

c_Institute_of_Physics,_Jagiellonian_University,_Cracow,_Poland d_Laboratori_Nazionali_di_Frascati_dell’INFN,_Frascati,_Italy

e_Dipartimento_di_Fisica_e_Scienze_della_Terra_{dell’Università}_di_Messina,_Messina,_Italy

f_Dipartimento_di_Scienze_Chimiche,_Biologiche,_{Farmaceutiche}_ed_Ambientali_{dell’Università}_di_Messina,_Messina,_Italy g_INFN_Gruppo_collegato_di_Messina,_Messina,_Italy

h_Dipartimento_di_Fisica_{dell’Università}_della_Calabria,_Rende,_Italy i_INFN_Gruppo_collegato_di_Cosenza,_Rende,_Italy

j_Dipartimento_di_Scienze_di_Base_ed_Applicate_per_{l’Ingegneria}_{dell’Università}_{“Sapienza”,}_Roma,_Italy k_Dipartimento_di_Scienze_e_Tecnologie_applicate,_Università_“Guglielmo_Marconi”,_Roma,_Italy l_Novosibirsk_State_University,₆₃₀₀₉₀_Novosibirsk,_Russia

m_Dipartimento_di_Fisica_{dell’Università}_{“Sapienza”,}_Roma,_Italy n_INFN_Sezione_di_Roma,_Roma,_Italy

o_Dipartimento_di_Fisica_{dell’Università}_“Tor_Vergata”,_Roma,_Italy p_INFN_Sezione_di_Roma_Tor_Vergata,_Roma,_Italy

q_Dipartimento_di_Matematica_e_Fisica_{dell’Università}_“Roma_Tre”,_Roma,_Italy r_INFN_Sezione_di_Roma_Tre,_Roma,_Italy

s_ENEA_UTTMAT-IRR,_Casaccia_R.C.,_Roma,_Italy

t_Department_of_Physics_and_Astronomy,_Uppsala_University,_Uppsala,_Sweden u_National_Centre_for_Nuclear_Research,_Warsaw,_Poland

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received26January2016

Receivedinrevisedform6April2016 Accepted7April2016

Availableonline11April2016 Editor:M.Doser

A measurement of the vector to pseudoscalar conversion decay φ→

π

0_e+_e−_{with the KLOE experiment}

is presented. A sample of ∼9500 signal events was selected from a data set of 1.7 fb−1 _of_e+_e−

collisions at √s∼mφ collected at the DANE e+e− collider. These events were used to perform the ﬁrst measurement of the transition form factor |F_φπ0(q2)| and a new measurement of the branching

*

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

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Keywords: e+e−collisions Conversiondecay Transitionformfactor

ratio of the decay: BR(φ→

π

0_e+_e−₎_{= (}₁_.₃₅_±₀_.₀₅+0.05 −0.10)×10−

5_{. The result improves signiﬁcantly on} previous measurements and is in agreement with theoretical predictions.

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-momentum trans-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,suchasthe calcu-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

−_TFF_{Fω π}₀

₍

_q2

_).

_Over theyears, severaltheoretical modelshave beendeveloped to ex-plainthisdiscrepancy[4–7]. Inorderto check theconsistencyof themodels,a measurementofthe F_φ_π0

(

q2

)

TFF,whichhasnever

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

φ

→

π

0_e+_e−_process_is_a_very_good benchmarktoinvestigatetheobservedsteepriseinNA60dataat

q2 closetothe

ρ

resonancemass.

Atpresent, theexistingdata on

φ

→

π

0_e+_e− _come _from_SND

[8]and CMD-2[9] experiments which were able to extract only thevalueoftheBranchingRatio(BR).TheF_φ_π0

(

q2

)

TFFhence,was

nevermeasuredsofar.Itsmodulussquareentersinthecalculation ofthe

φ

→

π

0_e+_e−_{double-differential}_decay_width:

d2

_(φ

_→

_π

0_e+_e−

₎

dq2_{d cos}

_θ

∗

=

3 8

q2 q2

₊

_2m2 e

(

2

− β

2sin2

θ

∗

)

×

d

(φ

→

π

0e+e−

)

dq2 (1) with

β

=

1

−

4m2 e

/

q2

1/2 and

[10]

: d

(φ

→

π

0_e+_e−

₎

dq2

= (φ →

π

0

_γ

₎

α

3

π

β

|

F_φ_π0

(

q2

)

|

2 q2

1

+

2m 2 e q2

×

⎡

⎣

1

+

q 2 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

0_mesons,_{respectively.}

_θ

∗ _is_the_angle_between_the

φ

and the e+ direction in the e+e− rest frame. Its cosine is an invariantquantitywhichcanbewrittenas

[11]

:

cos

θ

∗

=

(

q 2

₊

_m2 φ

−

m2π

)

−

4 pφ

·

pe+

β

q2

₋

_m2 φ

−

m2π

2

−

4 m2 πm2φ

,

(3)

wherepφ isthe4-momentumof

φ

andpe+ ofthepositron.

Thankstothelargeamountofcollected

φ

decays(

∼

5.6

×

109_), theKLOEexperimenthasbeenablebothtoperformtheﬁrst mea-surement of the F_φ_π0

(

q2

)

TFF and to signiﬁcantly improve the

determinationofthebranchingratioof

φ

→

π

0_e+_e−_.

2. TheKLOEdetector

DANE, 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 largecylindricalDrift Cham-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.Thecalorimeter

[13]

,withareadout granu-larityof

∼

(4.4

×

4.4) cm2_,_for_a_total_of₂₄₄₀_cells_arranged_in_ﬁve 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

σE

/

E

=

5.7%/

√

E

(GeV)

and

σ

t

=

57 ps/

√

E

(GeV)

⊕

100 ps, re-spectively.Thetrigger

[14]

usesbothcalorimeterandchamber in-formation.Inthisanalysistheeventsareselectedbythe calorime-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 statistical uncer-tainty anda systematicerrorof

∼

30 keV,isroutinelyperformed onthebasisof200 nb−1 ofintegratedluminosity.Thesystematic errorisinfactontheabsolutemomentumscale,derivedfromthe analysisofthe

φ

lineshape

[15]

.Thecenter-of-massenergy distri-butionwidthisabout330 keVfromthecontributionsofi)DANE beam energy spread (0.06%) and ii) radiative corrections/effects. Collected data are processedby an eventclassiﬁcation algorithm

[16],whichstreams various categoriesofevents indifferent out-putﬁles.

3. Dataanalysis

The analysisofthe decay

φ

→

π

0_e+_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

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Fig. 1. Data-MCcomparisonafteralltheanalysiscutsfortheinvariant-massspectrumofe+e−(left)andofthetwophotons(right).Blackdotsaredata,solidredlineisthe sumofMChistogramcomponents:signal(cyan),φ→π0_γ _background_(orange)_and_radiative_Bhabha_scattering_(green)._(For_{interpretation}_of_the_references_to_color_in_this ﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

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

|

F_φ_π0

(

q2

)

|

2

=

1). The radiative emission from

theleptonsintheﬁnalstateofthechannelunderstudyisalso in-cludedin thesimulationby means ofthe

PHOTOS

MCgenerator

[17].Thesignal productioncorresponds toanintegrated luminos-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

_with_the

_π

0 Dalitzdecayto

γ

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

φ

meson decays, the non-resonant

e+e−

→

ωπ

0 _process _and_the

_π

0 _production _via

_{γ γ}

_interaction,

e+e−

→

π

0_e+_e−_,_were_also_simulated,_resulting_fully_negligible_at theendoftheanalysispath.

Asaﬁrststepoftheanalysis,eventsareselectedrequiringtwo opposite-chargetracksextrapolatedtoacylinderaroundthe inter-actionpoint(IP)withradius4cmand20 cmlongandtwoprompt photoncandidatesfromIP(i.e.withenergyclustersEclu

>

7 MeV not associatedto anytrack, inthe angularregion

|

cos

θ

γ

|

<

0.92

andin the time window

|

Tγ

−

Rγ

/

c

|

<

min

(3

σt

,

2ns)). In order toenhance thesignal-to-background ratio,furtherconstraintsare appliedonthispreselecteddatasample:

•

a cut on the energies of the ﬁnal state particles requiring:

(30

<

Ee±

<

460) MeV, Eγ

>

70 MeV,

(300

<

Eγ1

+

Eγ2

<

670)MeV and

(470

<

Ee+

+

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

<

minv

γ γ

<

190)MeV and

(80

<

memiss+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

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

θ

e+e− and

θ

γ γ oftracksandclustersallowtostrongly

sup-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_,_in_which_the_ﬁnal _state_leptons _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_eBP,DC+e− ) and the distance

(d_eBP,DC+e− ) 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_eBP+e−

<

10 MeV andd

BP

e+e−

<

2 cm,orm

DC

e+e−

<

80 MeV and

dDC

e+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 ttrk

=

Ltrk

/β

c,where Ltrk 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,turnsouttobecrucialforreducingthe contam-inationfromthedecay

φ

→

π

+

π

−

π

0 _to_a_negligible_level.

Afteralltheabovedescribedcutstheoveralleﬃciency,as esti-mated bytheMC, is15.4%.Theeﬃciencyis19.5%atlowere+e−

invariant masses, decreasing to afew percent atthe highest val-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 the re-gion

q2

_>

_{400 MeV the}

_φ

_→

_π

0

_γ

_background_is _negligible_and onlytheBhabhabackgroundispresent.Furthermore,asacheckof Eq.(3),in

Fig. 2

weshow thedistributionof

|

cos

θ

∗

|

ascompared totheMCprediction.

(4)

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 of increas-ingwidth(topreservethestatistics ofsignalcandidates). Ineach binof

q2_,_the _mmiss

e+e− distribution is ﬁt by a sumof two

Gaus-sianfunctions,parametrizingthesignal,andathird-order polyno-mial,parametrizingthebackground.Someexamples oftheﬁtsto them_emiss+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_φ_π0

(

q2

)

|

2

ThemodulussquareoftheTFF,

|

F_φ_π0

(

q2

)

|

2,isafactorinfront

oftheq2differentialcrosssection(seeEq.(2)),henceitcanbe ex-tracted fromdataby dividing themeasured e+e− invariant-mass spectrumbythespectrumofreconstructedMCsignalevents, gen-erated with a constant F_φ_π0

(

q2

),

after all the analysis cuts. The

resultis reportedin

Table 1

.The measured TFFis normalizedso that

|

F_φ_π0

(

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. mmiss

e+e− distributions(unitsMeV)forsome

q2_bins_showing_the_total_background_contribution_(red_curve)_evaluated_from_a_fit_to_the_data_(black_points),_with_fixed signalshape(bluecurve).Thedashedgreencurverepresentstheglobalfitofdata,includingthebackgroundfunctionandthesignalparametrization.

(5)

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 _from_the _original_one. _The _relative_deviations _of countscomingfromthedifferentcutsarethensummedbinbybin inquadraturetogetthetotalrelativeuncertainty.Whenavariable isselectedwithinawindow,itsedgesarealwaysmovedoppositely inordertomakethewindowwiderornarroweraccordingtothe resolution.Theresultingfractional uncertaintyisofafewpercent inmostofthebinsoflower

q2_,_increasing_up_to_20%_in_some_of thebinsof higher4-momentumtransfer.There isnoevidence of asingledominantcutwithrespecttotheothers;thecontribution ofthevariousanalysiscutsisdifferentforeachbinof

q2_.

Thesystematicerrorassociatedtotheﬁttingprocedureis eval-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 _contribution_is _then propagated to F_φ_π0

(

q2

)

through the numberofsignal candidates

ineachbin,whichenters inthecomputation.The contributionin eachbinof

q2_is_of_a_few_percent.

In

Fig. 4

,our resultson

|

F_φ_π0

(

q2

)

|

2 are compared withthree

different theoretical predictions. The best agreement is obtained withthe Unconstrained ResonantChiralTheory (UChT), with pa-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“

q2_UChT”_in

_{Table 1}

_)._As_shown_in

_{Table 1}

_, withthegivenbinwidths,thebincenterisagoodapproximation ofthe weighted

q2 _in_each _bin,_with_the _exception _of_the_very ﬁrstbin,wheretheme+e− functionissteeper.

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

F

(

q2

)

=

1

−

q2

_/

2

,

(4)

Table 2

PreviousdeterminationofBR(φ→π0_e+_e−₎_by_SND_[8]_and_CMD-2_[9]_._The_PDG averageis(1.12±0.28)×10−5[20].Thetheoreticalpredictionsarealsoreported. ForRef.[5]“once”(“twice”)referstothedispersiveanalysiswithone(two) sub-tractions.

BR(φ→π0_e+_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

(

q 2

₎

dq2

q2₌₀

=

−2

_.

By ﬁtting our data according to (4), we get b_φ_π0

= (

2.02

±

0.11)GeV−2, to be compared with the one-pole approximation expectation,b_φ_π0

=

M_φ−2,andthepredictionofthedispersive

anal-ysis,b_φ_π0

= (

2.52

· · ·

2.68)GeV−2,ofRef.[5].

3.2. MeasurementofBR(φ

→

π

0_e+_e−

₎

The branching ratio of the

φ

→

π

0_e+_e− _decay _was _obtained

fromthebackground-subtractede+e− massspectrumbyapplying aneﬃciencycorrectionevaluatedbinbybin:

BR

(φ

→

π

0e+e−

)

=

iNi/

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]istheintegrated lumi-nosity ofdata,andBR(

π

0

_→

_{γ γ}

₎

_the_branching _ratio_of

_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₎_and_is_equal_to:

BR

(φ

→

π

0e+e−

;

q2

_<

_{700 MeV}

₎

_{= (}

₁

_.

₁₉

_±

₀

_.

₀₅+0.05

−0.10

)

×

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+₋0.05_0.10

)

×

10−5

.

(7)

This result improves the previous measurements by SND and

CMD-2experimentsandisinagreementwiththetheoretical pre-dictionsshownin

Table 2

.

4. Conclusions

Analyzingtheconversiondecay

φ

→

π

0_e+_e−_,_we_measured_for

theﬁrsttimethemodulussquareofthe F_φ_π0 transitionform

(6)

theoreticalpredictionbasedontheUnconstrainedResonantChiral Theory(UChT),withparameters extractedfromaﬁt oftheNA60

data. From the same data set we obtained a value of BR(φ

→

π

0_e+_e−

_;

_q2

_<

₇₀₀_MeV)

_{= (}

_1.19

_±

_0.05+0.05

−0.10

)

×

10−5.An extrap-olationbasedonthetheoreticalmodelinagreementwiththedata has been used to extend the result to the full

q2 _range. _The value obtained is BR

(φ

→

π

0_e+_e−

₎

_{= (}

_1.35

_±

_0.05+0.05

−0.10

)

×

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 DANEteamfortheireffortsinmaintaininglow back-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 continuous at-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.Wearealsovery grate-fultoDr.S.Ivashynforprovidingustheformulaforcos

θ

∗ andfor the many enlightening discussions during all the phases of the analysis.Thisworkwas supportedinpartbytheEUIntegrated

In-frastructureInitiativeHadronPhysicsProjectundercontract num-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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