First observation and study of the K± → π±π0e+e− decay

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

First

observation

and

study

of

the

K

±

→

π

±

π

0

e

+

e

−

decay

The

NA48/2

Collaboration

J.R. Batley,

G. Kalmus,

C. Lazzeroni

1

,

2

,

D.J. Munday

1

,

M.W. Slater

1

,

S.A. Wotton

1 CavendishLaboratory,UniversityofCambridge,Cambridge,CB30HE,UK3

R. Arcidiacono

4

,

G. Bocquet,

N. Cabibbo

†

,

A. Ceccucci,

D. Cundy

5

,

V. Falaleev

6

,

M. Fidecaro,

L. Gatignon,

A. Gonidec,

W. Kubischta,

A. Maier,

A. Norton

7

,

M. Patel

8

,

A. Peters

CERN,CH-1211Genève23,Switzerland

S. Balev

†

,

P.L. Frabetti,

E. Gersabeck

9

,

E. Goudzovski

1

,

2

,

10

,

P. Hristov

11

,

V. Kekelidze,

V. Kozhuharov

12

,

13

,

L. Litov

12

,

D. Madigozhin,

M. Misheva

∗

,

14

,

N. Molokanova,

I. Polenkevich,

Yu. Potrebenikov,

S. Stoynev

15

,

A. Zinchenko

†

JointInstituteforNuclearResearch,141980Dubna(MO),Russia

E. Monnier

16

,

E. Swallow

†

,

R. Winston

17 TheEnricoFermiInstitute,TheUniversityofChicago,Chicago,IL60126,USA

P. Rubin

18

,

A. Walker

DepartmentofPhysicsandAstronomy,UniversityofEdinburgh,Edinburgh,EH93JZ,UK

P. Dalpiaz,

C. Damiani,

M. Fiorini,

M. Martini,

F. Petrucci,

M. Savrié,

M. Scarpa,

H. Wahl

DipartimentodiFisicaeScienzedellaTerradell’UniversitàeSezionedell’INFNdiFerrara,I-44122Ferrara,Italy

W. Baldini,

A. Cotta Ramusino,

A. Gianoli

Sezionedell’INFNdiFerrara,I-44122Ferrara,Italy

M. Calvetti,

E. Celeghini,

E. Iacopini,

M. Lenti,

G. Ruggiero

19 DipartimentodiFisicadell’UniversitàeSezionedell’INFNdiFirenze,I-50125SestoFiorentino,Italy

A. Bizzeti

20

,

M. Veltri

21

Sezionedell’INFNdiFirenze,I-50019SestoFiorentino,Italy

M. Behler,

K. Eppard,

M. Hita-Hochgesand,

K. Kleinknecht,

P. Marouelli,

L. Masetti,

U. Moosbrugger,

C. Morales Morales,

B. Renk,

M. Wache,

R. Wanke,

A. Winhart

1 InstitutfürPhysik,UniversitätMainz,D-55099Mainz,Germany22

https://doi.org/10.1016/j.physletb.2018.11.046

0370-2693/©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

D. Coward

23

,

A. Dabrowski

11

,

T. Fonseca Martin,

M. Shieh,

M. Szleper

24

,

M. Velasco,

M.D. Wood

23

DepartmentofPhysicsandAstronomy,NorthwesternUniversity,Evanston,IL60208,USA

G. Anzivino,

E. Imbergamo,

A. Nappi

†

,

M. Piccini,

M. Raggi

25

,

M. Valdata-Nappi

DipartimentodiFisicadell’UniversitàeSezionedell’INFNdiPerugia,I-06100Perugia,Italy

P. Cenci,

M. Pepe,

M.C. Petrucci

Sezionedell’INFNdiPerugia,I-06100Perugia,Italy

F. Costantini,

N. Doble,

L. Fiorini

26

,

S. Giudici,

G. Pierazzini

†

,

M. Sozzi,

S. Venditti

DipartimentodiFisicadell’UniversitàeSezionedell’INFNdiPisa,I-56100Pisa,Italy

G. Collazuol

27

,

L. DiLella

28

,

G. Lamanna

28

,

I. Mannelli,

A. Michetti

ScuolaNormaleSuperioreeSezionedell’INFNdiPisa,I-56100Pisa,Italy

C. Cerri,

R. Fantechi

Sezionedell’INFNdiPisa,I-56100Pisa,Italy

B. Bloch-Devaux

∗

,

29

,

C. Cheshkov

30

,

J.B. Chèze,

M. De Beer,

J. Derré,

G. Marel,

E. Mazzucato,

B. Peyaud,

B. Vallage

DSM/IRFU–CEASaclay,F-91191Gif-sur-Yvette,France

M. Holder,

M. Ziolkowski

FachbereichPhysik,UniversitätSiegen,D-57068Siegen,Germany31

S. Bifani

1

,

M. Clemencic

11

,

S. Goy Lopez

32 DipartimentodiFisicadell’UniversitàeSezionedell’INFNdiTorino,I-10125Torino,Italy

C. Biino,

N. Cartiglia,

F. Marchetto

Sezionedell’INFNdiTorino,I-10125Torino,Italy

H. Dibon,

M. Jeitler,

M. Markytan,

I. Mikulec,

G. Neuhofer,

L. Widhalm

† ÖsterreichischeAkademiederWissenschaften,InstitutfürHochenergiephysik,A-10560Wien,Austria33

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received11September2018

Receivedinrevisedform23November2018 Accepted26November2018

Availableonline29November2018 Editor:W.-D.Schlatter

TheNA48/2 experimentatCERN reportsthefirstobservationofthe K±→

π

±

π

0_e+_e− _decayfroman

exposureof1.7×1011chargedkaondecaysrecordedin2003–2004.Asampleof4919candidateswith 4.9%background contamination allowsthe determination ofthe branchingratioin thefull kinematic region,B R(K±_→

π

±

π

0_e+_e−_{)= (4.24±0.14)×10}−6_{.Thestudyofthekinematicspaceshowsevidence}

forastructuredependentcontributioninagreementwithpredictionsbasedonchiralperturbationtheory. SeveralP- andCP-violatingasymmetriesarealsoevaluated.

©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

*

Correspondingauthors.

E-mailaddresses:milena.misheva@cern.ch(M. Misheva),brigitte.bloch-devaux@cern.ch(B. Bloch-Devaux). † _Deceased.

1 _{Nowat:SchoolofPhysicsandAstronomy,UniversityofBirmingham,Birmingham,B152TT,UK.} 2 _{SupportedbyaRoyalSocietyUniversityResearchFellowship(UF100308,UF0758946).} 3 _{FundedbytheUKParticlePhysicsandAstronomyResearchCouncil,grantPPA/G/O/1999/00559.} 4 _{Nowat:UniversitàdegliStudidelPiemonteOrientaleeSezionedell’INFNdiTorino,I-10125Torino,Italy.} 5 _{Nowat:IstitutodiCosmogeofisicadelCNRdiTorino,I-10133Torino,Italy.}

1. Introductionandtheoreticalframework

Kaondecayshaveplayedamajorroleinestablishingthequark mixingflavourstructureoftheStandardModel[1].Radiativekaon decaysareofparticularinterest intestingmodelsdescribing low-energyquantumchromodynamics(QCD)suchasthechiral pertur-bationtheory (ChPT),an effectivefield theoryvalidbelowascale

O

(1GeV).

The radiative decay K±

→

π

±

π

0_e+_e−_{, never observedso far,}

proceeds through virtual photon exchange followed by internal conversion into an electron-positron pair, i.e. K±

→

π

±

π

0

_γ

∗

_→

π

±

π

0_e+_e−_{. The virtual}

_γ

∗ _{can be produced by two different}

mechanisms: Inner Bremsstrahlung (IB)where the

γ

∗ isemitted byoneofthechargedmesonsintheinitial orfinal state,and Di-rectEmission(DE)wherethe

γ

∗isradiatedoffattheweakvertex. Consequently, the differential decayrate consistsof three terms: the dominant long-distance IB contribution, the DE component (electricEandmagnetic Mparts), andtheir interference.The in-terferencetermINTincludesthedifferentcontributions,IB-E,IB-M andE-M.TheIB-MandE-MtermsareP-violatingandcancelupon angularintegrationinthetotalrate.

There are few theoretical publications related to the K±

→

π

±

π

0_e+_e−_{mode[2–4] andnoexperimentalobservation.The}

au-thorsof[3] predicted,onthebasisoftheNA48/2measurementof

6 _{Nowat:JointInstituteforNuclearResearch,141980Dubna(MO),Russia.} 7 _{Nowat:DipartimentodiFisicaeScienzedellaTerradell’UniversitàeSezione} dell’INFNdiFerrara,I-44122Ferrara,Italy.

8 _{Nowat:DepartmentofPhysics,ImperialCollege,London,SW72BW,UK.} 9 _{Nowat:SchoolofPhysicsandAstronomy,TheUniversityofManchester,} Manch-ester,M139PL,UK.

10 _{SupportedbyERCStartingGrant336581.} 11 _{Nowat:CERN,CH-1211Genève23,Switzerland.}

12 _{Nowat:FacultyofPhysics,UniversityofSofia“St.Kl.Ohridski”,BG-1164Sofia,} Bulgaria,fundedbytheBulgarianNationalScienceFundundercontractDID02-22.

13 _{Alsoat:LaboratoriNazionalidiFrascati,I-00044Frascati,Italy.}

14 _{Nowat:InstituteofNuclearResearchandNuclearEnergyofBulgarianAcademy} ofScience(INRNE-BAS),BG-1784Sofia,Bulgaria.

15 _{Nowat:FermiNationalAcceleratorLaboratory,Batavia,IL60510,USA.} 16 _{Nowat:CentredePhysiquedesParticulesdeMarseille,IN2P3-CNRS,Université} delaMéditerranée,F-13288Marseille,France.

17 _{Nowat:SchoolofNaturalSciences,UniversityofCalifornia,Merced,CA95343,} USA.

18 _{Nowat:SchoolofPhysics,AstronomyandComputationalSciences,George} Ma-sonUniversity,Fairfax,VA22030,USA.

19 _{Nowat:PhysicsDepartment,UniversityofLancaster,Lancaster,LA14YW,UK.} 20 _{AlsoatDipartimentodiScienzeFisiche,InformaticheeMatematiche,Università} diModenaeReggioEmilia,I-41125Modena,Italy.

21 _{AlsoatIstitutodiFisica,UniversitàdiUrbino,I-61029Urbino,Italy.}

22 _{FundedbytheGermanFederalMinisterforEducationandresearchunder} con-tract05HK1UM1/1.

23 _{Nowat:SLAC,StanfordUniversity,MenloPark,CA94025,USA.} 24 _{Nowat:NationalCenterforNuclearResearch,P-05-400´Swierk,Poland.} 25 _{Nowat:UniversitàdiRoma“LaSapienza”,I-00185Roma,Italy.}

26 _{Nowat:InstitutodeFísicaCorpuscularIFIC,UniversitatdeValència,E-46071} València,Spain.

27 _{Nowat:DipartimentodiFisicadell’UniversitàeSezionedell’INFNdiPadova,} I-35131Padova,Italy.

28 _{Now at: Dipartimento di Fisica dell’Università e Sezione dell’INFN di Pisa,} I-56100Pisa,Italy.

29 _{Nowat:DipartimentodiFisicadell’UniversitàdiTorino,I-10125Torino,Italy.} 30 _{Nowat:InstitutdePhysiqueNucléairedeLyon,IN2P3-CNRS,UniversitéLyonI,} F-69622Villeurbanne,France.

31 _{Fundedbythe GermanFederalMinisterforResearchandTechnology(BMBF)} undercontract056SI74.

32 _{Nowat:CentrodeInvestigacionesEnergeticasMedioambientalesyTecnologicas,} E-28040Madrid,Spain.

33 _{FundedbytheAustrianMinistryforTrafficandResearchunderthecontractGZ} 616.360/2-IVGZ616.363/2-VIII,andbytheFondsfürWissenschaftundForschung FWFNr. P08929-PHY.

themagneticandelectrictermsinvolvedintheK±

→

π

±

π

0

_γ

de-cay [5],thebranchingratiosofIB,DE andINTcomponentsofthe

K±

→

π

±

π

0_e+_e− _{decay andposted recently a revised work [6]}

where the interference term is re-evaluated using more realistic inputsbasedonadditionalexperimentalresultsandfewer theoret-icalassumptions.

It is worth writing explicitly the various contributions to the squaredamplitudeofthedecay[3]:



spins

|

M

|

2

=

2e 2 q4

⎡

⎣



3 i=1

|

Fi

|

2Tii

+

2Re 3



i<j

(

F_i∗Fj

)

Ti j

⎤

⎦ ,

(1)

where FiarecomplexformfactorsandTi j arekinematic

expres-sions(asdefinedin[3])whichdependonthefour-momentaofthe

e+e− systemandthe chargedandneutralpionsinthe kaonrest frame.Forconvenience,onealsowrites:

F1

=

F1I B

+

F1D E

,

F2

=

F2I B

+

F2D E

,

F3

=

F3D E

.

(2)

The form factors F₁I B

,

F₂I B include a strongphase

δ

₀2 correspond-ing to the S-waveand isospin 2 state of the dipion system. The complex formfactors F₁D E

,

F₂D E correspond totheelectricpartof DE and make use of the ChPT counterterms N_E(0,1,2) while FD E 3

corresponds to the magnetic part of DE and makes use of the counterterm N(_M0).Theseformfactorscarry astrongphase

δ

1₁ cor-respondingtotheP-waveandisospin1stateofthedipionsystem. Numericalvaluesofthecountertermswereestimated[6] using experimental measurements offormfactors intherelatedmodes

K±

→

π

±

γ

∗,KS

→

π

0

γ

∗andK±

→

π

±

π

0

γ

.

2. Kaonbeamlineanddetector

The NA48/2 experiment atthe CERN SPS was specifically

de-signed for charge asymmetry measurements in the K±

→

3

π

decaymodes[7].Largesamplesofchargedkaondecayswere col-lected during the2003–2004 data takingperiod.The experiment beamline wasdesignedto deliversimultaneous narrow momen-tumband K+and K−beamsoriginatingfromprimary 400GeV/c protonsextractedfromtheCERNSPSandimpingingonaberyllium target. Secondary unseparated hadron beams with central

mo-menta of60 GeV/c anda momentumbandof

±

3.8%(rms) were

selected andbroughttoa commonbeamaxisby two systemsof dipole magnetswithzerototaldeflection(called“achromats”), fo-cusingquadrupoles,muonssweepersandcollimators.Thefraction of beamkaons decayingin the114 mlong cylindricalevacuated tankwas22%.

The momenta of chargeddecayproducts were measured in a magnetic spectrometer, housed in a tank filled with helium at nearly atmosphericpressure. The spectrometer was composed of pairs of drift chambers (DCH) on each side of a dipole magnet providing a momentum kick



p

=

120 MeV/c to charged parti-cles in the horizontalplane. The momentum resolution achieved was

σ

p

/

p

= (

1

.

02

⊕

0

.

044

·

p

)

%(p inGeV/c).

A hodoscope(HOD)consistingoftwo planesofplastic scintil-lators,eachsegmentedinto64strip-shapedcounters,followedthe spectrometer andprovided timemeasurements forcharged parti-cles with a resolution of150 ps. Grouping the counters of each plane ineight subsets, the HOD surface was logically subdivided into16exclusiveregionsproducingfastsignalsusedtotriggerthe detectorreadoutonchargedtracktopologies.

Further downstream was a liquid krypton electromagnetic

calorimeter (LKr), an almost homogeneous ionization chamber with an active volume of 7 m3_{, segmented transversally into}

13248 projective 2

×

2 cm2 cells with no longitudinal segmenta-tion. The energies ofphotons andelectrons were measured with

resolutions

σ

E

/

E

= (

3

.

2

/

√

E

⊕

9

.

0

/

E

⊕

0

.

42

)

%.Thetransverse posi-tionsofisolatedshowersweremeasuredwithaspatialresolution

σ

x

=

σ

y

= (

0

.

42

/

√

E

⊕

0

.

06

)

cm, andtheshower time resolution was2.5ns

/

√

E (E inGeV).Aniron/scintillatorhadronic calorime-terandmuondetectorswere locatedfurtherdownstream.Neither ofthemwasusedinthepresentanalysis.

A dedicated two-level trigger was used to collect K± decays into three charged tracks with high efficiency: at the first level (L1),eventscontaining chargedtracks were selectedby requiring spaceandtime coincidencesofsignalsinthetwo HODplanesin atleasttwoofthe 16exclusiveregions;atthe secondlevel (L2), afarmofasynchronousmicroprocessorsperformedafasttrack re-constructionandranavertexfindingalgorithm.

Moredetails about thebeam lineand triggerimplementation canbefound in[7].Adetaileddescriptionofthedetectorcan be foundin[8].

3. Dataanalysis 3.1.Measurementmethod

The K±

→

π

±

π

0_e+_e− _{decay rateis measured relative to the}

normalizationdecay K±

→

π

±

π

0 _{collectedconcurrently withthe}

same trigger logic. This method does not rely on an absolute kaonfluxmeasurement.Inthesignalsample, the

π

0 _{isidentified}

throughthe

π

0

_→

_{γ γ}

_mode

₍

_π

0

γ γ

)

.Inthenormalizationsample,

the

π

0 _{is identifiedthroughthe}

_π

0

D

→

e+e−

γ

Dalitz mode

(

π

D0

)

.

Theratioofpartialrates(andbranchingratios)isobtainedas:

B R

(

K±

→

π

±

π

0e+e−

)/

B R

(

K±

→

π

±

π

0

)

=

Ns

−

Nbs Nn

−

Nbn

·

An

×

ε

n As

×

ε

s

·

(

π

_D0

)

(

π

0 γ γ

)

,

(3)

whereNs

,

Nn arethenumbersofsignalandnormalization

candi-dates;Nbs

,

Nbnarethenumbersofbackgroundeventsinthesignal

andnormalizationsamples; Asand

ε

saretheacceptanceandthe

triggerefficiencyforthesignalsample;Anand

ε

narethoseforthe

normalizationsample.

The branching ratio of the normalization mode is B R

(

K±

→

π

±

π

0

₎

_{= (}

₂₀

_.

₆₇

_±

₀

_.

₀₈

₎

_{% and the ratio of}

_π

0 _{partial rates is}

(

π

0

D

)/(

π

γ γ0

)

= (

1

.

188

±

0

.

035

)

% [9]. Acceptances are obtained

from a detailed Monte Carlo (MC) simulation based on GEANT3 [10].The simulationincludesfull detectorgeometryandmaterial description,straymagneticfields,DCHlocalinefficienciesand mis-alignment,LKrlocalinefficiencies,accuratesimulationofthekaon beamlineandvariations oftheabovethroughoutthedata-taking period.

EfficienciesoftheL1andL2triggersaremeasuredfrom down-scaledcontrolsamples,recordedconcurrentlywiththethree-track trigger. The control trigger condition for the L1 efficiency mea-surementrequires atleast one coincidence of signalsin the two planesoftheHOD.ThecontroltriggersamplefortheL2efficiency measurementconsistsofL1triggersrecordedregardlessoftheL2 decision.Thetriggerdecisionisalsoavailableinthesimulationfor comparison.

3.2.Eventreconstructionandselection

ThestandardNA48/2softwarehasbeenusedincludingcharged track,LKrenergyclusterandthree-trackdecayvertex reconstruc-tion [7]. Fully reconstructed K±

→

π

±

π

+

π

− decays have been usedto monitorthe DCHalignment, the spectrometer field inte-gralandthe mean beampositionat each DCHplane throughout thedatataking.

Signal and normalization candidates are reconstructed from threetracks: twosame-sign tracksandone opposite-chargetrack forming a commonvertex inthe fiducial decayvolume, the ver-tex charge being thereforeqvtx

= ±

1. The vertextime is defined

as the average of the three HOD signal times associated to the tracks. The tracks are required to be in time within 5 ns of the vertextime.Theirimpactpointsarerequiredtobewithinthe ge-ometricalacceptanceofthedriftchambers.Inparticular,thetrack distancetothemonitoredbeampositioninDCH1planeisrequired tobelargerthan12cm.Thetrackmomentaarerequiredtobein therange(2–60)GeV

/

c andtrack-to-trackdistancesatDCH1tobe largerthan2 cmtosuppressphotonconversionstoe+e− pairsin theupstreammaterial.

Configurationswherethethreeconsideredtracks,extrapolated totheHODfrontface,havetheirimpactpointsinasingle trigger region are rejected to avoidL1 inefficiencies of purely geometri-cal origin.Becauseofthedifferentkinematics,thisaffects2.3%of thesignalsampleandhasanegligibleeffectonthenormalization sample.

All vertices considered for further analysisare required to be reconstructedina98mlongfiducialvolume,starting 2m down-streamofthelastcollimatorexit,andwithin3 cmfromthebeam axis.

Photonclustersmatchingthevertextimewithin5 nsare con-sideredasphotoncandidatesiftheirenergyisintherange(3–60) GeV, their position is within the LKrgeometrical acceptanceand their distancetothenearestLKrinactivecell islargerthan2cm. Photon four-momenta are reconstructed assuming they originate fromthethree-trackvertex.Photontrajectoriesarerequiredto in-terceptthe DCH1plane ata radialposition largerthan 11cm to avoidpossibleinteractionswiththeDCHflangeresultingina de-gradedenergymeasurement.

Signal and normalization modes differ in their final state by one photon, whilesatisfyingsimilar kinematicconstraints onthe reconstructed

π

0 _{and kaon masses, although with different}

res-olutions because of different numbers of participating particles.

The mass resolutions (Gaussian rms) obtained from the data

agreewiththose fromsimulationandare foundto be

σ

m

(

π

_D0

)



1

.

7 MeV

/

c2

,

σ

m

(

π

±

π

D0

)



4

.

2 MeV

/

c2and

σ

m

(

π

γ γ0

)



2

.

7 MeV

/

c2,

σ

m

(

π

±

π

γ γ ee0

)



6

.

1 MeV

/

c2 for the normalization and signal

modes,respectively.

Very loose requirements are applied to the reconstructed masses, required to be within 15 MeV

/

c2 _{(45 MeV}

_/

_c2_{) from the}

nominal

π

0 _(K±_{) mass[9], respectively, ensuring a minimal}

de-pendence of the selection on momentum or energy calibration effects,aswellasonanyresolutionmismatchesbetweendataand simulation.Acommonconstraint,takingintoaccount the correla-tionbetweenthereconstructed_mπ0 andmK massesanddefined

as

|

m_π0

−

0

.

42

·

mK

+

72

.

3

| <

6

(

all masses in MeV

/

c2

),

(4)

contains more than 99% of the normalization events and about 96.5%ofthesignalevents.

In both modes, the single track with its charge opposite to

qvtxisconsideredtobeanelectron(positron).Theremaininge

/

π

ambiguity forthetwo same-sign tracks isthen solved by testing the two mass hypothesesagainst the full selection. When a par-ticular mass assignment is considered, an extra requirement on thedistanceofanyphoton cluster tothetrackimpactatthe LKr frontface isappliedtoguaranteephoton showerisolation, avoid-ing potential overlap with other showers: the distance between the photon position andthe electron and positron trackimpacts isrequiredtobelargerthan10cmandthedistancebetweenthe photonpositionandthepiontrackimpacttobelargerthan20cm.

ThisrequirementisenforcedonlyfortrackimpactswithintheLKr geometricalacceptance.

Noupperlimitonthenumberoftracksandclustersisset,all three-trackverticesbeingconsideredandcombinedwithany pho-tonclusterunderthetwopossiblee

/

π

masshypothesesuntilone combinationsatisfieseitherofthefollowingselections (normaliza-tionor signal)below, theeventbeingrejectedotherwise. Ifboth mass combinations are accepted, the one with the tighter con-straintofEq. (4) iskept.

Normalizationselection The

π

0

D candidateisreconstructed froma

pairofelectronandpositrontracksandaphotonoriginatingfrom the three-track vertex. The kaoncandidate is reconstructed from the

π

±

π

0

D system.

Theconsistencyofthefinal statewithakaondecayalongthe beamaxisischeckedfurtherby consideringtheenergy-weighted coordinates ofthe centreof gravity (COG)ofthe particles atthe LKrfront planecomputedfromthephotonpositionandthetrack extrapolations obtained from track parameters measured before the magnet (undeviated trajectories). The radial distance of the COGtothenominalbeampositionisrequiredtobesmallerthan 2 cm.Thepionmomentumisrequiredtobelargerthan10 GeV

/

c

and the total momentum of the system to be in the beam

mo-mentum range (54–66) GeV

/

c. The e+e− massis required to be larger than 10 MeV

/

c2 _{to ensure good agreement between data}

andsimulation.Asampleof16316690candidatessatisfiesthe nor-malizationselectioncriteria.

Signalselection The

π

0

γ γ candidateisreconstructedfromtwo

pho-tonsoriginatingfromthethree-trackvertex.Thekaoncandidateis reconstructedfromthe

π

±

π

0_e+_e− _{system. The twophoton}

clus-tersarerequiredto beseparatedby morethan10 cm attheLKr front plane to avoid shower overlap. The event COG coordinates arethenobtainedincludingthetwophotonsandthethreecharged tracks,andsubjectedtothesamerequirementasabove.Thetotal momentumofthesystemisrequiredtobe inthebeam momen-tumrange(54–66) GeV

/

c.Thee+e− massisrequiredtobelarger than3 MeV

/

c2.

Twomainsourcesofbackgroundcontribute tothesignal final state: K±

→

π

±

π

0

γ γ

π

D0 (K3πD)where oneof thephotonsislost

(ormergedwithanotherparticle),andK±

→

π

±

π

0

D

(

γ

)

(K2πDγ ),

wheretheradiative photonandthe Dalitzdecayphoton mimica

π

0

_→

_{γ γ}

_{decay. Suppression of the K}

3πD background eventsis

achieved by requiring the squaredmass of the

π

+

π

0 _systemto

be greaterthan 0.12

(

GeV

/

c2

₎

2_{,exploitingthe largerphase space}

availableinthesignalmode.Thiscutalonerejects94%oftheK3πD

simulated eventsand

∼

1% ofthe IB signal. To reject the K2πDγ

background,each ofthetwo possiblemassesmeeγ isrequiredto

bemore than7 MeV

/

c2 _{away fromthe nominal}

_π

0 _mass

(corre-spondingto about4

σ

ofthe massresolution). Asample of 4919 candidatessatisfiesthesignalselectioncriteria.

3.3. Backgroundevaluation

The background processes contributing to the normalization mode (K2πD) are semi-leptonic decays followed by a Dalitz

de-cay ofthe

π

0_{: K}±

_→

_μ

±

_νπ

0

D (Kμ3D) and K±

→

e±

νπ

0 D (Ke3D),

collectivelydenoted Kl3D,wherethe

π

D0 decayiscorrectly

recon-structedbutthelepton(

μ

±

,

e±)iserroneouslyattributedthe

π

+ mass.Theacceptances ofsuchprocesses inthenormalization se-lectionare

O

(10−4_{)andobtainedfromlargesimulatedsamples.}

Foreachbackgroundprocess,thenumberofeventsNbn is

esti-matedrelativetothenumberofobservedeventsinthe normaliza-tionmodeNn usingtheacceptancesinthenormalizationselection

andtheworldaveragebranchingratios[9]:

Kl3D

:

Nbn

/

Nn

= (

AKl3D

/

An

)

·

B R

(

Kl3D

)/

B R

(

K2πD

)

(5)

wherethetriggerefficienciescanceltofirstorderduetothe simi-lartopologies.

The number of backgroundevents in the signal selection Nbs

isestimatedrelativetothenumberofobservedeventsinthe nor-malization selection Nn and is obtained as in Eq. (5), using the

acceptancesinthesignalselection,both

O

(10−6):

K3πD

:

Nbs

/

Nn

=

2

× (

AK3πD

/

An

)

·

B R

(

K3πD

)

×

B R

(

π

0

→

γ γ

)/

B R

(

K2πD

),

(6)

K2πDγ

:

Nbs

/

Nn

=

AK2πDγ

/

An

.

(7)

Note the factor of two in Eq. (6) due to the two

π

0 _{mesons in}

the K3πD mode.Anorderofmagnitudesmallercontributionfrom Ke3D isalsoconsidered.Inall contributionsbothbackgroundand

normalizationbranchingratiosincludethe

π

0_{Dalitzdecaypartial}

ratewhosevalueanduncertaintycancelintheestimation.

4. Branchingratiomeasurement

Candidatesandbackground Samplesof16

.

3

×

106_K

2πD candidates

and 4919 signal candidates have been selected froma subset of a 1

.

7

×

1011kaondecayexposurein2003–2004. Thebackground estimatesfromsimulationamount to(10437

±

119) Kμ3D events

and(6851

±

106) Ke3D events inthe normalizationmode,

corre-sponding to a total relative backgroundcontribution of 0.11%. In the signal mode, they amount to (132

±

8) events from K3πD,

(102

±

19) events from K2πDγ and (7

±

3) from Ke3D, adding

up to arelative backgroundcontribution of(4.9

±

0.4)%.The re-constructed

γ

e+e−

(

γ γ

)

and

π

±

π

0

D (

π

±

π

0e+e−) mass

distribu-tionsaredisplayed inFig.1(Fig.2) fortheselectednormalization (signal)candidates.Backgroundandnormalization(signal) simula-tions, scaled tothenumber ofobservedcandidates,show a good agreementwiththedatadistributions.

Acceptances Because the selection acceptance is not uniform acrossthephasespace,itsoverallvaluedependsonthedynamics oftheconsideredprocess.TheacceptanceAn (3.981%)iscomputed

using the simulation of K±

→

π

±

π

0 _{accordingto [11] followed}

by

π

0

D decayaccordingtothemostrecent“Prague”radiativedecay

calculation[12].

TheMCsamplesforthedifferentK±

→

π

±

π

0_e+_e−_signal

con-tributionsIB,DEandINThavebeengeneratedseparatelyaccording to the theoretical description givenin [3,6]: the DE contribution consistsmainlyofthemagneticMterm,withtheEtermexpected to befifteentimeslower; theINT termincludes onlytheelectric interferenceIB-E,astheotherinterferencetermsIB-MandE-Mdo notcontributetothetotalrateinthelimitoffullangular integra-tion(Section1).Particularcarehasbeentakeninthegenerationof theIB-Etermwhichcontributesconstructivelyordestructively to thedifferentialratedependingonthekinematicspaceregion con-sidered. Thispropertyis illustratedinFig.3-left. Radiativeeffects areimplementedusingthe

PHOTOS

package[13].

Global acceptances are obtained for each of the three main componentsofthesignalprocess:IB

(

0

.

645

±

0

.

001

)

%,M

(

1

.

723

±

0

.

003

)

% and IB-E

(

0

.

288

±

0

.

001

)

%. The signal acceptance As is

then obtained from a weighted average of the single-component acceptances,usingasweights,w,theirrelativecontributionstothe totalratewithrespecttoIBcomputedin[3,6]:

As

=

AIB

+

AM

·

wM

+

AIB-E

·

wIB-E

1

+

wM

+

wIB-E

Fig. 1. Normalizationcandidates.Left:reconstructedγe+e−mass.Right:reconstructedπ±π0

D mass.Fulldotscorrespondtodatacandidates;stackedhistogramsare,from

bottomtotop,theexpectedKμ3D(green)andKe3D(blue)backgroundsmultipliedbyafactorof50tobevisible.Thenormalizationsimulation(red)includesradiativeeffects

inbothkaonandπ0

Ddecaysthatreproducetheasymmetrictailsofbothdistributions.

Fig. 2. Signalcandidates.Left:reconstructedγ γmass.Right:reconstructedπ±π0_e+_e−_{mass.Fulldotscorrespondtodatacandidates;stackedhistogramsare,frombottom}

totop,theexpectedK3πD(green),K2πDγ (lightblue)andKe3D (darkblue)backgroundsandIBsignal(red)estimatedfromsimulation.Allquotederrorsarestatistical.

where wM and wIB-E are equalto 1/71and

−

1

/

253 respectively.

Theresulting signal acceptanceisobtainedas As

=

0

.

9900 AIB

+

0

.

0139 AM

−

0

.

0039 AIB-E

= (

0

.

662

±

0

.

001

)

%.

Both normalization and signal acceptances are obtained with respecttothefullmee kinematicrange.

Triggerefficiencies Trigger efficiencies are measured from control data samples for the normalization mode (L1:

(

99

.

75

±

0

.

01

)

%, L2:

(

97

.

66

±

0

.

04

)

%)andcross-checkedagainst thesimulated es-timations (L1:

(

99

.

767

±

0

.

003

)

%, L2:

(

98

.

495

±

0

.

006

)

%) which providealso an accurate description oftheir time variations due tolocalandtemporary inefficienciesoftheHODorDCHs.Dueto thelow statistics ofthe signal candidate sample, it is not possi-bletoobtain thetriggerefficiencies fromthedownscaled control samples. Trigger efficiencies for the signal candidates are there-foreestimatedfromthesimulatedsamples(L1:

(

99

.

729

±

0

.

009

)

%, L2:

(

98

.

604

±

0

.

021

)

%)andnot affectedbyotherwiselarge

statis-tical uncertainties. The full trigger efficiency in each selection is obtainedastheproductofL1andL2efficienciesthatarebasedon differentdetectorsandthereforeuncorrelated.

Systematicuncertainties Thestatisticaluncertaintiesonacceptance andtriggerefficiencyvaluesare accountedaspartofthe system-aticuncertainties.

Thecontrolofthegeometricalacceptancesisevaluatedby con-sideringthreeexclusiveregionsofthedecaylongitudinalposition (showninFig.3-right)withdifferentacceptancesandbackground conditionsforbothsignal andnormalizationchannels. The differ-ence betweenthe statisticalcombination ofthe three B R values

andtheglobalvalueisquotedassystematicuncertainty.

Thecontroloftheacceptancedependencewithtimeandkaon charge is quantified by considering four exclusive B R

quot-Fig. 3. AcceptancesoftheIB,MandIB-Ecomponentsprojectedalongthemee andthelongitudinal vertexposition Zvertex variables(the Z axisoriginislocated18m

downstreamofthelastcollimatorexit).FortheIB-Ecomponent,theacceptanceisformallyplottedwithanegative(positive)valuewhentheinterferenceisdestructive (constructive).Thearrowscorrespondtothethreeexclusiveregionsconsidered.

ingassystematicuncertaintythedifferencebetweenthestatistical combinationofthefourB R valuesandtheglobalvalue.

An evaluation of the background control level is obtained by tightening the constraintof Eq. (4) to reduce the background to signalcontributionfrom4.9%to3%whiledecreasingthesignal ac-ceptancebyarelativefractionof8%.Thequoteduncertaintycovers alsotheeffectoftheresidualdisagreementbetweendataand sim-ulatedreconstructedmasses.

Trigger efficiencies obtained from simulation are used in the

B R calculation.The difference betweenthe measured and simu-latedefficienciesofthenormalizationcandidatesisconsidered as asystematicuncertainty.

Themodeldependenceofthesignalacceptanceisinvestigated by varying in turn each input (N(_M0)

,

N(_E0,1,2)) within its theoreti-caluncertaintyestimate.Theresultingvariationsinacceptanceare addedinquadraturetoobtaintheoverall contributionto system-atics.

Accordingtotheauthorsofthe

PHOTOS

package[14],the un-certainty on the photon emission implementation cannot exceed 10%ofthefulleffect(here4

.

9

×

10−2relativeinthesignalmode), which is quoted as systematic uncertainty. In the normalization mode,intheabsenceofanyprescriptionfromtheauthorsofthe “Prague”

π

0

D decayimplementation,10%ofthe0

.

53

×

10−2relative

difference between the

PHOTOS

and“Prague” K2πD acceptances

is conservativelyassigned asa systematicuncertainty andadded quadratically to the signal

PHOTOS

uncertainty. The agreement betweendata andsimulationcan be judgedfrom themee

distri-butionsofFig.4.

Externalerrorsstemfromrelative errorson B R(K±

→

π

±

π

0₎

andon

(

π

0

D

)

/

(

π

γ γ0

)

.

Table1summarizestheconsideredsourcesofuncertainty.

Result Thefinalresultisobtainedas:

B R

(

K±

→

π

±

π

0e+e−

)

= (

4

.

237

±

0

.

063stat

±

0

.

033syst

±

0

.

126ext

)

×

10−6

,

(9)

wherethestatisticalerrorisdominatedbythesignalstatistics,the systematicerrorbytheradiative effectsandtheexternalerrorby the

π

0

D branchingratiouncertainty.

This value can be compared to the predictions from [3,6]:

B R

(

K±

→

π

±

π

0_e+_e−

₎

₌

₄

_.

₁₈₃

_×

₁₀−6 _{for IB only, B R}

₍

_K±

_→

Table 1

Statistical, systematic and external uncertainties to the K±→

π±π0_e+_e− _{branchingratiomeasurement.The uncertainties}

re-latedtothemodeldependenceandtoradiativeeffectscanalso beconsideredasexternalerrorsasbeingunrelatedtoourdata.

Source δB R/B R×102 Ns 1.426 Nbs 0.416 Nn 0.025 Nbn negl. Total statistical 1.486 As(MC statistics) 0.171 An(MC statistics) 0.051 ε(L1s×L2s) (MC statistics) 0.023 ε(L1n×L2n) (MC statistics) 0.007

Acceptance geometry control 0.083 Acceptance time variation control 0.064 Background control 0.280 Trigger efficiency (systematics) 0.400

Model dependence 0.285 Radiative effects 0.490 Total systematic 0.777 B R(K2π) 0.387 (π0 D)/(πγ γ0 ) 2.946 Total external 2.971

π

±

π

0_e+_e−

₎

₌

₄

_.

₂₂₉

_×

₁₀−6 _{whenincludingallDEandINTterms.}

Theobtainedvalueiscompatiblewithbothpredictionswithinthe experimental errors.However itshouldbenotedthat noneofthe abovepredictionsincludesanyradiativeorisospinbreakingeffects.

5. Kinematicspacestudy

The current data statistics does not allow a precise enough measurementtoquantifythecontributionoftheDEmagneticterm Mtothetotaldecayrate(expectedtobeabout1%).However,the authorsof[3,6] havepointedoutthatthecontributionsofIB, mag-neticM,andinterferenceIB-Etermshavedifferentdistributionsin the Dalitz plot (T∗_{π ,}E_{γ )}∗ for different ranges ofq2 values, where T∗_{π ,} E∗_{γ and} q2 are the charged pion kinetic energy and the vir-tual photon energy in the kaon rest frame, and the e+e− mass squared, respectively. The differences remain relevant even after the analysis selection acceptanceis applied. A method based on

Fig. 4. Reconstructede+e− massdistributionfor thenormalization(left)andsignal(right)candidateswith thelowercutsof10and3 MeV/c2_{,respectively.Simulated} backgroundandnormalization(signal)contributionsarealsodisplayed.

the population of 3d-boxes in the kinematic space (q2_{, T}∗

π , E∗γ )

isusedtodeterminetherelativefractionofeachcomponentthat wouldadd upto reproducethedatasample population.Thedata 3d-spaceis first split into N1 slices along q2, then each slice is splitintoN2slicesalong T∗_{π and}thenintoN3E∗_{γ slices,} all with equalpopulations.TheresultisagridofN1

×

N2

×

N3exclusive 3d-boxesofvariablesizebutidenticalpopulation.Thebackground contributionsandthevarioussimulatedsignalcomponentsare dis-tributedaccordingto thedata griddefinition,each resulting ina setof3d-boxes ofunequal population. Toaccount forthe poten-tially different sizes of the simulation samples, scale factors

ρ

M

and

ρ

IB-EaredefinedastheratiosoftheIBtotheMandIBtothe

IB-Esimulatedsamplesizes.

To obtain the fractions (M)/IB and (IB-E)/IB reproducing the data,a

χ

2_{estimatorisminimized:}

χ

2

₌

N1×

_

N2×N3 i=1

(

Ni

−

Mi

)

2

/(δ

N2i

+ δ

M2i

),

(10)

where Ni

(δ

Ni

)

is the data population (error)and Mi

(δ

Mi

)

the

expectedpopulation(error)inboxi.Thedenominatorofeachterm isdominatedbythenumberofdataevents

δ

N2

i

=

Ni,thesamein

eachbox.Theexpectednumberofeventsinboxi iscomputedas:

Mi

=

N

× (

NiIB

+

a

·

NMi

+

b

·

NIB-Ei

)

+

N Bkg

i

,

(11)

whereN is aglobalscalefactortoguaranteethat thesumofthe simulated events andbackground contributions is normalized to thetotalnumberofdatacandidates.Attheendofthe minimiza-tion,theobtainedvaluesofa andb canberelatedtotherelative contributions(M)/IBand(IB-E)/IBby:

(

M)/IB

= (

a

± δ

a

)/

ρ

M

,

(IB-E)/IB

= (

b

± δ

b

)/

ρ

IB-E

.

(12)

Themethodhasnosizeabledependenceontheprecisegrid struc-tureaslong asthe granularityensures sensitivity to the popula-tionvariation within theresolution(at least3q2 _slicesand5or

6 slices along the two other variables) and large enough statis-tics per box to consider Gaussian errors. The grid configuration 3

×

5

×

6 has been employed and the resultsare obtainedwith a

χ

2 _{probability of 19% for a value of 98.2/87 degrees of}

free-dom anda correlation C

(

a

,

b

)

=

0

.

06.The obtainedvalue (M)/IB =0

.

0114

±

0

.

0043stat isconsistent withthe predictedvalue from

[3], 1

/

71

=

0

.

0141

±

0

.

0014ext, obtained using the experimental

measurementof N(_M0).The (IB-E)/IBvalue of

−

0

.

0014

±

0

.

0036stat

shows that there is no sensitivity to this contribution within the current data statistics and agrees with the value from [6],

−

1

/

253

= −

0

.

0039

±

0

.

0028ext, obtained using experimental

in-putstoN(_E0,1,2)values.Theexternalerrorsonthepredictedvalues stemfromtheuncertaintiesofthemeasurementsusedasinputin theevaluations.

6. Asymmetryinvestigations

Electroweak (or beyond Standard Model) phases change sign underchargeconjugationwhenswitchingfrom K+ to K−,unlike the strongphase

δ

= δ

2₀

− δ

1₁ that governsthe final state interac-tionofthepionsystem.Thesephasescanbeinvestigatedthrough asymmetriesbetweenK+andK−partialrates.

ThesimplestCP-violatingasymmetry isthecharge asymmetry betweenK+andK−partialratesintegratedoverthewholephase space:

AC P

=

(

K+

→

π

+

π

0_e+_e−

₎

_{− (}

_K−

_→

_π

−

_π

0_e+_e−

₎

(

K+

→

π

+

π

0_e+_e−

₎

_{+ (}

_K−

_→

_π

−

_π

0_e+_e−

₎

.

(13)

Thevalueof AC P canberelatedtotheinterferenceIB-Etermand

isproportionaltosin

δ

sin



E,where



E isapossibleCP-violating

phaseappearingintheformfactorsF₁D E,F₂D Einaddition (subtrac-tion)tothestrongphase

δ

1₁(Section1).Theasymmetryisobtained from the statistically independent measurements of K+ and K−

branching ratios,that takeinto accountthepossible biases intro-ducedbythedetectoracceptances.Thevalues

B R

(

K+

)

= (

4

.

151

±

0

.

078stat

)

×

10−6

,

B R

(

K−

)

= (

4

.

394

±

0

.

108stat

)

×

10−6 (14)

leadto AC P

= −

0

.

0284

±

0

.

0155,wheretheerrorisstatisticalonly,

asthesystematicandexternalerrorscancelintheratio.Thisvalue isconsistentwithzeroandistranslatedtoasingle-sidedlimit:

Other asymmetries are defined in [3] using the so-called Cabibbo-Maksymowicz[15] variables34 to describe the kinematic spaceofthe decayandselecting particularintegration regions of the

φ

angularvariable:

Aφ_{C P}∗

=

2π



0 d



(K+−K−) d

φ

d

φ

∗ 2π



0 d



(K++K−) d

φ

d

φ

,

where 2π



0 d

φ

∗

≡

⎡

⎢

⎣

π/2



0

−

π



π/2

+

3

_

π/2 π

−

2π



3π/2

⎤

⎥

⎦

d

φ,

(16) A_{C P}˜φ

=

2π



0 d



(K+−K−) d

φ

d

˜φ

2π



0 d



(K++K−) d

φ

d

φ

,

where 2π



0 d

˜φ ≡

⎡

⎢

⎣

π/2



0

+

π



π/2

−

3

_

π/2 π

−

2π



3π/2

⎤

⎥

⎦

d

φ.

(17)

These asymmetriescan be obtainedby combiningthe branching ratios measured in various parts of the

φ

variable space. Defin-ing sectors of the

φ

space between 0 and 2

π

as



1

(

0

,

π

/

2

)

,



2

(

π

/

2

,

π

)

,



3

(

π

,

3

π

/

2

)

and



4

(

3

π

/

2

,

2

π

)

, and combin-ing them as statistically independent sector sums (



13

= 

1

+



3

,



24

= 

2

+ 

4)and(



12

= 

1

+ 

2

,



34

= 

3

+ 

4)one canobtaintheaboveasymmetries.

The

φ

∗ integralhastheinteresting propertyofsubtractingthe contribution of sector sum



24 from the contribution of sector sum



13. The interference termIB-M (Section 1) equally popu-lates sectors



1 and



3 when positive anddepopulates sectors



2 and



4 when negative. The Aφ_{C P}∗ asymmetry is then related tothe interferenceIB-Mtermandisproportional tocos

δ

sin



M,

where



M isapossibleCP-violatingphaseappearing intheform

factor F₃D E (Section1). The interference IB-M termhas not been generatedinthesimulationasitisnotexpectedtocontribute sig-nificantlytothe totalrate. Howeverithasbeen checkedthatthe wholerangeof the

φ

variableisalways considered inthe accep-tancecalculation,apart fortheregionq2

<

3 (MeV/c2

)

2 excluded fromthesignalselection. TheCPasymmetries definedinEq. (16,

17)aremeasured,althoughtoalimitedprecisiongiventhecurrent datastatistics,as:

Aφ_{C P}∗

=

0

.

0119

±

0

.

0150stat and A_{C P}˜φ

=

0

.

0058

±

0

.

0150stat

.

(18)

Allasymmetriesareconsistentwithzero,single-sidedupperlimits canbesetas

|

Aφ_{C P}∗

| <

3

.

11

×

10−2

,

|

A_{C P}˜φ

| <

2

.

50

×

10−2at 90% CL

.

(19)

34 _{For K}± _{decays,the variables arethe squaredinvariant dipion and dilepton}

masses,theangleoftheπ±(e±)inthedipion(dilepton)restframewithrespect totheflightdirectionofthedipion(dilepton)inthe K± restframe,theangleφ betweenthedipionanddileptonplanesinthekaonrestframe.

Following another prescriptionof [3], a long-distance P-violating

asymmetrydefinedas A(_PL)

=

2π



0 d



d

φ

d

φ

∗ 2π



0 d



d

φ

d

φ

=

(

13

)

− (

24

)



(20)

can be obtainedfrom the asymmetry between sector sums



13 and



24 when considering K+ or K− alone, and combined if found consistent. The A(_PL) asymmetry isproportional to N(_M0) [3] andsin

δ

.Aprecise A(_PL) measurementwouldallowacheckofthe signofN(_M0)andameasurementofsin

δ

.

Ourdataleadto A(_PL)

(

K+

)

=

0

.

0059

±

0

.

0180stat andA(PL)

(

K−

)

=

−

0

.

0166

±

0

.

0237stat, both consistent with zero. The combined

valueis A(_PL)

(

K±

)

= −

0

.

0023

±

0

.

0144stat.Theerrorsarestatistical

only as both systematic and external uncertainties cancel in the ratios.Thisvaluecanbetranslatedintoasingle-sidedupperlimit:

|

A(_PL)

| <

2

.

07

×

10−2at 90% CL

.

(21) 7. Resultsandconclusion

The data sample recorded by the NA48/2 experiment in

2003–2004 has been analyzed, searching for the unobserved

K±

→

π

±

π

0_e+_e− _{decaymode inan exposureof1}

_.

₇

_×

₁₀11_kaon

decays.Asample of4919decaycandidateswith4.9%background has been identified, resulting in the first observation of this de-cay mode.The branchingratiohasbeenmeasured relativeto the

K±

→

π

±

π

0 _{modefollowed byaDalitz decay}

_π

0

D

→

e+e−

γ

and

found to be

(

4

.

237

±

0

.

063stat

±

0

.

033syst

±

0

.

126ext

)

×

10−6, in

agreementwithpredictionsfromChPT.

Despitethelimitedstatisticsavailable,astudyofthekinematic spaceofthedecayhasbeenperformedtoextract informationon thefractionofmagnetic(M)andinterference(IB-E) contributions with respect to inner bremsstrahlung (IB). The relative contribu-tion,(M)/IB

= (

1

.

14

±

0

.

43stat

)

×

10−2,isfoundconsistentwiththe

theoreticalexpectationof

(

1

.

41

±

0

.

14ext

)

×

10−2.TherelativeIB-E

contribution,(IB-E)/IB

= (−

0

.

14

±

0

.

36stat

)

×

10−2,isalsoin

agree-ment with the prediction of

(

−

0

.

39

±

0

.

28ext

)

×

10−2 but with

limited significancedue to the lackof data statistics inthe high

mee region.

Several CP-violating asymmetries and a long-distance P-vio-latingasymmetryhavebeenevaluatedandfoundtobe consistent with zero, leading to upper limits

|

AC P

|

<

4

.

8

×

10−2

,

|

Aφ

∗ C P

|

<

3

.

1

×

10−2

_,

_|

_A˜φ C P

|

<

2

.

5

×

10−2

,

|

A (L) P

|

<

2

.

1

×

10−2at90%CL.

If larger data statistics becomes available (for example at the NA62 experiment),more detailed studies of the kinematic space willallowforanimprovedevaluationoftheDEtermcontribution. A studyofthe P-violatingasymmetrycould bring informationon the signofthe DE magnetictermand onthe strongphase

δ

in-volvedinthefinalstateinteractionofthetwopions.

Acknowledgements

WegratefullyacknowledgetheCERNSPSacceleratorandbeam linestafffortheexcellent performanceofthebeamandthe tech-nical staff of the participating institutes for their efforts in the maintenance andoperation of the detector, anddata processing. We thank M. Koval for making the “Prague” radiative

π

0 _Dalitz

decay code available in the NA48/2 simulation software. Discus-sions with G. D’Ambrosio and O. Catà were most stimulating in clarifyingtheimpactofinterferencetermsonourmeasurement.

References

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