Search for C violation in the decay $\eta \rightarrow \pi ^{0}e^{+}e^{-}$ with WASA-at-COSY

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Physics Letters B

www.elsevier.com/locate/physletb

Search for C violation in the decay η _→ π ⁰ e ⁺ e ⁻ with WASA-at-COSY

The WASA-at-COSY Collaboration

P. Adlarson

^a

, W. Augustyniak

^b

, W. Bardan

^c

, M. Bashkanov

^d

, F.S. Bergmann

^e,∗

, M. Berłowski

^f

, A. Bondar

^g,h

, M. Büscher

^i,j

, H. Calén

^a

, I. Ciepał

^k

, H. Clement

^l,m

,

E. Czerwi ´nski

^c

, K. Demmich

^e

, R. Engels

ⁿ

, A. Erven

^o

, W. Erven

^o

, W. Eyrich

^p

, P. Fedorets

^n,q

, K. Föhl

^r

, K. Fransson

^a

, F. Goldenbaum

ⁿ

, A. Goswami

^n,s

, K. Grigoryev

^n,t

, C.-O. Gullström

^a

, L. Heijkenskjöld

^a,1

, V. Hejny

ⁿ

, N. Hüsken

^e

, L. Jarczyk

^c

, T. Johansson

^a

, B. Kamys

^c

,

G. Kemmerling

^o,2

, G. Khatri

^c,3

, A. Khoukaz

^e

, A. Khreptak

^c

, D.A. Kirillov

^u

, S. Kistryn

^c

, H. Kleines

^o,2

, B. Kłos

^v

, W. Krzemie ´n

^f

, P. Kulessa

^k

, A. Kup´s ´c

^a,f

, A. Kuzmin

^g,h

, K. Lalwani

^w

, D. Lersch

ⁿ

, B. Lorentz

ⁿ

, A. Magiera

^c

, R. Maier

^n,x

, P. Marciniewski

^a

, B. Maria ´nski

^b

,

H.-P. Morsch

^b

, P. Moskal

^c

, H. Ohm

ⁿ

, W. Parol

^k

, E. Perez del Rio

^l,m,4

, N.M. Piskunov

^u

, D. Prasuhn

ⁿ

, D. Pszczel

^a,f

, K. Pysz

^k

, A. Pyszniak

^a,c

, J. Ritman

^n,x,y

, A. Roy

^s

, Z. Rudy

^c

, O. Rundel

^c

, S. Sawant

^z

, S. Schadmand

ⁿ

, I. Schätti-Ozerianska

^c

, T. Sefzick

ⁿ

, V. Serdyuk

ⁿ

, B. Shwartz

^g,h

, K. Sitterberg

^e

, T. Skorodko

^l,m,aa

, M. Skurzok

^c

, J. Smyrski

^c

, V. Sopov

^q

, R. Stassen

ⁿ

, J. Stepaniak

^f

, E. Stephan

^v

, G. Sterzenbach

ⁿ

, H. Stockhorst

ⁿ

, H. Ströher

^n,x

, A. Szczurek

^k

, A. Trzci ´nski

^b

, M. Wolke

^a

, A. Wro ´nska

^c

, P. Wüstner

^o

, A. Yamamoto

^ab

, J. Zabierowski

^ac

, M.J. Zieli ´nski

^c

, J. Złoma ´nczuk

^a

, P. ˙Zupra ´nski

^b

, M. ˙Zurek

ⁿ

and

A. Wirzba

^n,ad

aDivisionofNuclearPhysics,DepartmentofPhysicsandAstronomy,UppsalaUniversity,Box516,75120Uppsala,Sweden bDepartmentofNuclearPhysics,NationalCentreforNuclearResearch,ul.Hoza69,00-681,Warsaw,Poland

cInstituteofPhysics,JagiellonianUniversity,Prof. StanisławaŁojasiewicza11,30-348Kraków,Poland

dSchoolofPhysicsandAstronomy,UniversityofEdinburgh,JamesClerkMaxwellBuilding,PeterGuthrieTaitRoad,EdinburghEH93FD, United Kingdom of Great Britain andNorthernIreland

eInstitutfürKernphysik,WestfälischeWilhelms-UniversitätMünster,Wilhelm-Klemm-Str.9,48149Münster,Germany fHighEnergyPhysicsDepartment,NationalCentreforNuclearResearch,ul.Hoza69,00-681,Warsaw,Poland gBudkerInstituteofNuclearPhysicsofSBRAS,11Akademika Lavrentievaprospect,Novosibirsk,630090,Russia hNovosibirskStateUniversity,2 PirogovaStr.,Novosibirsk,630090,Russia

iPeterGrünbergInstitut,PGI-6ElektronischeEigenschaften,ForschungszentrumJülich,52425Jülich,Germany

jInstitutfürLaser- undPlasmaphysik,Heinrich-HeineUniversitätDüsseldorf,Universitätsstr.1,40225Düsseldorf,Germany kTheHenrykNiewodnicza´nskiInstituteofNuclearPhysics,PolishAcademyofSciences,Radzikowskiego152,31-342Kraków,Poland lPhysikalischesInstitut,Eberhard-Karls-UniversitätTübingen,AufderMorgenstelle14,72076Tübingen,Germany

mKeplerCenterfürAstro- undTeilchenphysik,PhysikalischesInstitutderUniversitätTübingen,AufderMorgenstelle14,72076Tübingen,Germany nInstitutfürKernphysik,ForschungszentrumJülich,52425Jülich,Germany

oZentralinstitutfürEngineering,ElektronikundAnalytik,ForschungszentrumJülich,52425Jülich,Germany

pPhysikalischesInstitut,Friedrich-Alexander-UniversitätErlangen-Nürnberg,Erwin-Rommel-Str.1,91058Erlangen,Germany

qInstituteforTheoreticalandExperimentalPhysicsnamedbyA.I.AlikhanovofNationalResearchCentre“KurchatovInstitute”,25BolshayaCheremushkinskaya, Moscow,117218,Russia

rII.PhysikalischesInstitut,Justus-Liebig-UniversitätGießen,Heinrich-Buff-Ring16,35392Giessen,Germany

*

Correspondingauthor.

E-mailaddress:florianbergmann@uni-muenster.de(F.S. Bergmann).

1 Presentaddress:InstitutfürKernphysik,JohannesGutenberg-UniversitätMainz,Johann-Joachim-BecherWeg 45,55128Mainz,Germany.

2 Presentaddress:JülichCentreforNeutronScienceJCNS,ForschungszentrumJülich,52425Jülich,Germany.

3 Presentaddress:DepartmentofPhysics,HarvardUniversity,17 OxfordSt.,Cambridge,MA 02138,USA.

4 Presentaddress:INFN,LaboratoriNazionalidiFrascati,ViaE. Fermi,40,00044Frascati,Roma,Italy.

https://doi.org/10.1016/j.physletb.2018.07.017

0370-2693/©^{2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

sDepartmentofPhysics,IndianInstituteofTechnologyIndore,KhandwaRoad,Simrol,Indore–453552,MadhyaPradesh,India

tHighEnergyPhysicsDivision,PetersburgNuclearPhysicsInstitutenamedbyB.P.KonstantinovofNationalResearchCentre“KurchatovInstitute”, 1 mkr. Orlova roshcha,LeningradskayaOblast,Gatchina,188300,Russia

uVekslerandBaldinLaboratoryofHighEnergy Physics,JointInstituteforNuclearPhysics,6Joliot-Curie,Dubna,141980,Russia vAugustChełkowskiInstituteofPhysics,UniversityofSilesia,Uniwersytecka4,40-007,Katowice,Poland

wDepartmentofPhysics,MalaviyaNationalInstituteofTechnologyJaipur,JLNMargJaipur–302017,Rajasthan,India

xJARA–FAME,JülichAachenResearchAlliance,ForschungszentrumJülich,52425Jülich,andRWTHAachen,52056Aachen,Germany yInstitutfürExperimentalphysikI,Ruhr-UniversitätBochum,Universitätsstr.150,44780Bochum,Germany

zDepartmentofPhysics,IndianInstituteofTechnologyBombay,Powai,Mumbai–400076,Maharashtra,India aaDepartmentofPhysics,TomskStateUniversity,36LeninaAvenue,Tomsk,634050,Russia

abHighEnergyAcceleratorResearchOrganisationKEK,Tsukuba,Ibaraki305-0801,Japan acAstrophysicsDivision,NationalCentreforNuclearResearch,Box447,90-950Łód´z,Poland

adInstituteforAdvancedSimulationandJülichCenterforHadronPhysics,ForschungszentrumJülich,52425,Germany

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

Articlehistory:

Received12February2018 Receivedinrevisedform3June2018 Accepted10July2018

Availableonline14July2018 Editor:V.Metag

We reportonthesearchfor theraredecayη→π⁰e⁺e⁻ whichisofinteresttostudyC violation in the electromagneticinteractionwhichwould indicatecontributions fromphysicsbeyondthe Standard Model, since the allowed decay viaa two-photon intermediate stateis strongly suppressed. The ex- perimenthasbeenperformedusingtheWASA-at-COSYinstallation,locatedattheCOSYacceleratorof theForschungszentrum Jülich,Germany.Intotal3×^{107eventsofthereactionpd}→^3Heηhavebeen recorded atan excessenergy of Q =⁵⁹.8 MeV. Based onthisdata set the C parityviolatingdecay

η→π⁰γ^∗→π⁰e⁺e⁻ viaasingle-photonintermediate statehasbeen searchedfor,resulting innew upperlimits of

η_→π⁰e⁺e⁻ /

η_→π⁺π⁻π^0<3.28×^{10−5 and}

η_→π⁰e⁺e⁻

/(η_→all) <

7.5×^10−6(CL=^90%),respectively.

©^{2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

According to the standard model, strong and electromagnetic interactions have to conserve C parity. This concept particularly restrictsthe decay modes of mesons and, as an instance,highly suppresses

η

_→

π

⁰e⁺e⁻. However, corresponding measurements ofthe relative branching ratio date back to the seventies of the last century and their sensitivity is limited to many orders of magnitudes above the standard model predictions. The process

η

_→

π

⁰e⁺e⁻ via thesingle-photonintermediatestate

η

_→

π

⁰

γ

^∗

would violate C parityconservation whereas a two-photon pro- cessasaphysicalbackgroundhasanexpectedbranchingrationot largerthan10⁻⁸accordingtotheoreticalcalculations[1–3].

A modern model for this process includes the coupling of a hypothetical massive dark U boson [4–6] to the virtual pho- ton where the corresponding interaction strength scales with

∼



²q²/

q²−^m2_U+^imUU

 rather than with ∼^q2/(q²+ⁱ

ε

)∼¹ asincaseof aphoton propagator.Here, q² denotes the momen- tumtransfer square of the photon, m_U andU are the U boson massandtotalwidth,respectively,and



isthecouplingconstant of the

γ

–U interaction. A searchfor a resonance peak structure resulting from the considered

η

decay is limited to a U boson massm_U≤mη−mπ⁰=^{413 MeV}/c². However, in thisletter re- sults based on a vector meson dominance model (VMD) for a decayvia a virtual photon will be presented. In case of the de- cay

η

_→

π

⁰

γ

^∗_→

π

⁰e⁺e⁻ theVMDmodelisdominatedbythe

ρ

mesonwitha mass ofmρ=⁷⁷⁵.26(25) MeV/c² [7]. Further de- tailsabouttheusedVMDmodelaregiveninRefs. [8,9].

Apparently, the

η

meson is well suited for the study of rare processesandthesearch forC , P and C P breakingdecays,since itisnotonlya C and P eigenstate ofstrongandelectromagnetic interactionbutallstrongandelectromagneticdecaysofthe

η

me- sonareeithersuppressedorforbiddentofirstorder.Nevertheless, thepresentexperimentalupperlimitforthebranchingratioofthe decay

η

→

π

⁰e⁺e⁻ was obtainedin 1975 withan optical spark

chamber experimentandamounts onlyto 4.5×^{10−5 (CL}=^90%) [10]. To determine a more stringent upper limit for the decay channel

η

→

π

⁰e⁺e⁻,datacollectedwiththeWASA-at-COSYfacil- ityhavebeenanalyzedwhichalsoconstitutedthebasisforstudies ofother

η

mesondecaychannelsalreadypublishedinRef. [11].

2. Experiment

TheWASA-at-COSYexperimentwasaninternalexperimentop- erated at the accelerator COSY of the Forschungszentrum Jülich, Germanyfrom2006to2014[12].Forthemeasurementsdiscussed here, a protonbeamwas acceleratedtoakinetic beamenergyof Tp=^{1 GeV andcollided withdeuterium pellets provided by the} internalpellettarget.The

η

mesonswereproducedinthereaction pd→^3He

η

.

The WASAdetectorsetup is divided intotwo main parts.The centraldetector,whichwasusedforthereconstructionofthepro- ducedmesonsandtheirdecayparticles,consistsofadriftchamber ina solenoidfield surroundedby an electromagneticcalorimeter.

This setup provided an energy resolution of 3% for charged and 8% for neutral particles as well as a geometrical acceptance of 96%.The forwarddetectorused forthemeasurement ofthe four- momenta of the forward scattered ³He nuclei comprised several layersofthinandthickplasticscintillatorsenablingparticleiden- tification and energy reconstruction with a 3% accuracy as well asaproportionalchambergivingpreciseangularinformationwith 0.2% accuracy.A moredetailed descriptionof the WASA-at-COSY experimentalsetupcanbefoundinRefs. [11–13].

The dataforthestudies presentedherewere obtainedintwo measurementperiods,oneoffourweeksin2008andoneofeight weeks in2009. A large energyloss in subsequent scintillator el- ements ofthe forward detector was required to trigger the data acquisition. Since the ³He nucleus stemming from the reaction pd→^3He

η

isstoppedinthefirstlayeroftheWASAforwardrange hodoscope,a vetoonthesignalsfromthesecond layerwas used

inaddition.Duetothetriggerrelyingoninformationfromthefor- warddetectoronly,theutilizedtriggerwasunbiasedwithrespect to a decay mode of the

η

meson. In total about3×^{107 events} containing an

η

meson were recordedwith 1×^{107 events orig-} inatingfrom the2008 periodand 2×^{107 events fromthe 2009} period[11].

3. Dataanalysis

The analysisofthe decay

η

_→

π

⁰e⁺e⁻ was basedon a com- monanalysischainfor

η

decaystudiesdescribedinRef. [11].

Preselection. Before the selection conditions for the decay

η

→

π

⁰e⁺e⁻ were determined, the data collected in 2008 and 2009 were preselected with conditions common to all recorded reac- tions.Forinstance,conditionsontime correlationswere used,re- quiringchargedandneutralparticlestobedetectedwithinatime window ofless than 40 ns and15 ns, respectively,compared to the ³He nucleus measured in theforward detector. Furthermore, hitsthatwere wronglyidentifiedasadditionalparticles(so-called split-offs) are rejected. Electron–positron pairs fromphoton con- versionattheCOSYbeampipecanbeidentifiedbyareconstructed vertexmorethan28 mm offtheCOSYbeamaxisandbyarecon- structedinvariant massbelow8 to15 MeV/c²,dependingonthe reconstructedradial vertexpositionandassuminga vertexatthe COSYbeampipe.Those pairsarerejected, aswell.Moredetailsof theseconditionswerepublishedinRef. [11].

Besidesthesegeneralpreselectionconditions,acutonthesig- natureofthe decay

η

→

π

⁰e⁺e⁻ was appliedrequesting atleast onepositivelyandone negativelychargedparticledetected inthe centraldetector,aswellasatleasttwoneutralparticlesoriginating fromthe

π

⁰mesondecay

π

⁰→

γ γ

.Thelastconditionappliedfor data preselection requires the maximumconsidered momenta of thechargeddecayparticlestobebelowp=^{250 MeV}/c,sincethe momentaoftheleptonsofthedecay

η

→

π

⁰e⁺e⁻areexpectedto bebelowthisvalue.

MonteCarlosimulations. In orderto determine optimalselection conditions for the search for the decay channel

η

→

π

⁰e⁺e⁻, 1.8×^{108 Monte}Carlo events ofall non-signal

η

decaysobserved yetwerecreatedwithrespecttotheir relativebranchingratio[7], as well astwo million events for the signal decay. These simu- lations were generated with the pluto++ software package [14]

consideringtheangulardistributionof pd→^3He

η

at T_p=^{1 GeV} according to Ref. [15]. Forthe various

η

decay channels physics models asincludedin pluto++ wereused. Thereader isreferred toRef. [11] forfurtherdetails.

In addition to the simulations of

η

decays, about 4.3×¹⁰⁹ events for the direct pion production were created, with most events for the production reactions pd→^3He

π

⁰

π

⁰ and pd→

3He

π

⁺

π

⁻,asthesecontribute mostto the non-

η

background at thegivenkineticbeamenergy.Forthesetwo-pionproductionsthe ABCeffectwasincorporatedintothesimulationsaccordingtothe modeldiscussedinRef. [16].

The simulations for the signal decay

η

→

π

⁰e⁺e⁻ were gen- erated with two different model assumptions. The first one is a decay according to pure three-particle phase space. The second is basedon the VMDmodel forthe intermediate virtual photon.

The directdecay

η

→

π

⁰

γ

to an on-shell photonviolatesboth C parityandangularmomentum conservationplus globalgauge in- variance.The violationofthe angularmomentum originatesfrom the general rule that a radiative 0→0 transition via the emis- sionorabsorptionofarealphotonisstrictlyforbidden,ascanbe readinmoredetailinRef. [17].Theglobalgaugeinvarianceisthe reasonthat thedivergence ofthe electromagnetic

ηπ

⁰ transition

Fig. 1. Invariantmassofe⁺e⁻ pairsfor thesimulateddecayη→π⁰e⁺e⁻.Black lined:decayviaη→π⁰γ^∗consideringVMD.Shadowedinorange:decayaccording tothree-particlephasespace.(Forinterpretationofthecolorsinthefigure(s),the readerisreferredtothewebversionofthisarticle.)

currenthasto vanish.Thisin turnimpliesthat theon-shelllimit ofthe

ηπ

⁰ couplingtoa photonhasto vanishaswell,since the onlytermthat isnotdirectlyproportional toq² corresponds toa longitudinallypolarizedphoton,whichthereforecannotcontribute toan on-shell-photonamplitude,seee.g. [18] formoredetails.In summary,thereisno

η

→

π

⁰

γ

on-shellcontributionforthedecay

η

_→

π

⁰e⁺e⁻andthetransitionformfactorfortheoff-shellcon- tribution vanishes at zero virtuality, such that the single-photon pole iscompletely removed [19–21]. InFig. 1the invariant mass of the e⁺e⁻ pair produced in the decay is plotted according to three-particlephasespace(shadowedinorange)andthedecayvia

η

_→

π

⁰

γ

^∗ accordingtothediscussedmodel.A moredetailedcal- culationofthemodelcanbefoundinRef. [9].

To simulate the WASA detector responses, the WASA Monte Carlopackage wmc wasused,whichisbasedon geant3[22].The settingsforthespatial,timingandenergyresolutionin wmc were settoagreewiththeresolutionobservedindata.

DuetothehighluminositiesoftheWASA-at-COSYexperiment, it is possible that detector responses from one event can over- lapwithanotherevent. InRef. [11] theeventselection wasdone without takingthis effect into account. Any remaining effect on therelativebranchingratiosreportedwascheckedbystudyingthe luminositydependenceoftheresult.However,fortheanalysispre- sentedinthispapereventoverlapcouldnotbeignored,becauseit influences alldifferential distributionswhich wereusedforevent selection andcut optimization. Therefore, the effect was consid- eredinthesimulationsandtheamountofeventoverlapwasleft asafreeparameterforthefitofthesimulationstodata(seenext paragraph).

All Monte Carlosimulations were preselected withconditions identicaltothosefordatapreselection.

Datadescription. The choice of the selection conditionswith re- gard to thedecaychannel

η

→

π

⁰e⁺e⁻ is basedonMonteCarlo simulations.It isnecessarytoknowthecontributionsofthevari- ousreactionstothecollecteddataforanoptimalchoice.Therefore, the2008and2009datasetswerefittedseparatelyindistributions of selected quantities by template distributions ofthe aforemen- tionedMonteCarlosimulationstodeterminethe contributionsof the individual reactions to the data. Indetail, thesedistributions are:

•^{the missingmassm}X,corresponding totheinvariant massof theprotonbeamandthedeuterontargetremaining afterthe 3He fourmomentum hasbeensubtracted andpeaksatthe

η

massforthereactionpd→^3He

η

,

•^{the invariant mass m}eeγ γ of an electron–positron pair can- didate andtwo photons, which peaksat the

η

mass forthe decay

η

→

π

⁰e⁺e⁻with

π

⁰→

γ γ

,

•^{the invariant mass} mγ γ oftwo photons, which peaks atthe

π

⁰massforreactionswith

π

⁰ mesonsproduced,

•^{theinvariantmassm}eeofanelectron–positronpaircandidate,

•^{thesmallestinvariantmassm}eγ ofallfourpossiblecombina- tionsofanelectronorpositroncandidateandaphotonand

•^{the missing mass squaredm2}_Xee^{, whichis the invariant mass} squaredoftheprotonbeamandthedeuterontargetremaining afterthe ³He fourmomentumandtheelectron–positronpair candidatemomentum havebeensubtractedandpeaksatthe

π

⁰masssquaredforthereactionofinterest.

Undertheassumption ofa branchingratioofthedecaybelow thecurrent upper limit of 4.5×^{10−5 (CL}=^{90%) [10], there are} less than 150 events expected from the decay

η

→

π

⁰e⁺e⁻ in thecombined datasets after preselection, considering theprese- lectionefficiency forthe signal decay. A fitby Monte Carlosim- ulationsincludingthesimulateddecay

η

→

π

⁰e⁺e⁻ isconsistent withzeroeventsfromthissignaldecaychannel.Therefore,thede- cay

η

→

π

⁰e⁺e⁻ wasexcludedfromthefit.Whilethedifferential distribution forthe reaction pd→^3He

η

iswell known [15], the differentialdistributionsareknownonlywithhighuncertaintiesor notatallfordirectmulti-pionproductions.Hence,the datawere dividedintotenbins inangularranges ofcosϑ₃^cms_He.⁵ MonteCarlo simulations were fittedto datain theeight angularbins ranging from−^{1 to0}.6.Theangularrange0.6<cosϑ3^cmsHe≤^{1 wasexcluded} becauseofthelowerenergyresolutionoftheforwarddetectorfor theseforwardscattered³He nuclei.Moreover,therelativeamount ofbackgroundfromthedirectpionproductionislargerinthisan- gularrange,whereaslessthan3% ofallpd→^3He

η

eventshavea cosϑ3^cmsHe>0.6.

The fit of the Monte Carlo simulations to the data was per- formed simultaneously for all angular ranges and distributions withidenticalscalingparametersforthesimulationsforalldistri- butionswithin one angularrange.Furthermore,theratiosforthe various

η

decayswereconstrainedtothebranchingratiosaccord- ing to Ref. [7] withinthe givenuncertainties. These were set to beidenticalforall angularranges. Similarly,theamountofevent overlapwasincludedasoneglobalfitparameter.InFig. 2,Fig.3, Fig.4 andFig. 5 the resultingMonte Carlofits to the 2008data are plotted for mX, meeγ γ , mγ γ and mee for the angular range 0.2<cosϑ3^cmsHe≤⁰.4.According to thisfit mostevents remaining afterpreselection originate fromthe

η

decay

η

→

π

⁺

π

⁻

π

⁰,the directpd→^3He

π

⁺

π

⁻

π

⁰ productionandthedirecttwo-pionpro- ductionreactions.NotethatMCsimulationswitheventoverlapare requiredforaproperdescriptionoftheshouldersoftheinvariant massdistributions.A collectionofallfitsisavailableinRef. [9].

Selectionconditions. Theselectionconditionsforthesearchforthe decay

η

→

π

⁰e⁺e⁻ werebasedonthefollowingquantities:

•themissingmassmX,

•^{theinvariantmassesm}eeγ γ ,mγ γ andmee,

•^the

χ

²probabilityofakinematicfitwiththehypothesispd→

3He

γ γ

e⁺e⁻and

•^{theenergylossESEC}_dep^{ofthechargedparticlesinthecentralde-} tector scintillator electromagneticcalorimeter(SEC) andtheir momentum p todiscriminatee^± and

π

^± (particle identifica- tion,PID).

5 ϑ3^cmsHe isthepolarscatteringangleofthe³He nucleusrelativetothebeamaxis inthecenterofmasssystem.

Fig. 2. MissingmassmX=Pp+ Pd− P³Heafterpreselectionforadatasampleof the2008periodfittedbyMonteCarlosimulations.Onlythemostcommoncontri- butionsofthevariousreactionstothefitareplottedseparately.

Fig. 3. Invariantmassofe⁺e⁻γ γafterpreselectionforadatasampleofthe2008 periodfittedbyMonteCarlosimulations.ForthelegendseeFig.2.

Fig. 4. Invariantmassofγ γafterpreselectionforadatasampleofthe2008period fittedbyMonteCarlosimulations.ForthelegendseeFig.2.

Since only very few events were expected to remain in the analysisafterthe eventselection,an optimalchoice oftheselec- tionconditionsisimportantforthebestpossibleresult.Thechoice of the cut conditions was performed with 40% of the generated MonteCarlosimulations,whereastheremainingMonteCarlodata sample was used later forthe selection efficiency determination.

Note that therelative amounts ofthe differentreaction channels arethesameforbothMCsamples,scaledaccordingtothefitex- plainedinthepreviousparagraph.Thegraphicalcutfortheparti- cleidentification(seeFig.6)waschosenbyoptimizingtheproduct of the number of selected e⁺e⁻ pairs (N_e+e⁻) and the ratio of N_e+e⁻ to thenumber of chargedpion pairs (Nπ⁺π⁻). While this cutwaschosenbeforehand,asitisacommoncututilizedforPID independent fromthe analyzed reaction,the selection conditions

Fig. 5. Invariant massofe⁺e⁻ afterpreselectionforadata sampleofthe 2008 periodfittedbyMonteCarlosimulations.ForthelegendseeFig.2.

Fig. 6. EnergylossofchargedparticlesintheSECplottedagainsttheirmomentum timeschargeforthepreselecteddatasetsofthe2008and2009periods.A graphical cutaroundtheelectronandpositronbandisindicatedbyblacklines.

fortheother five quantitieswere determined by an optimization algorithm.Thisalgorithmisbasedontherelativeamountofsimu- latedsignal events SR=^NcutS /N^pres_S remaining afterall cuts(N^cut_S ) compared to the numberafter preselection (N^pres_S ) and the rela- tive amount of all simulatedbackground events B_R=^N_B^cut/N^pres_B remainingafterallcuts(N_B^cut)inrelationtothenumberafterpre- selection(N^pres_B ).Incaseofthebackgroundreactionsthecontribu- tionsasobtainedinthedatadescriptionwere usedtodownscale theMonteCarlosimulationsandtoextractthenumbers.

Thecutoptimizationalgorithmmaximizestheevaluationfunc- tion

G

=

^SR

·

^SR

B_R (1)

by varyingthe selectionconditions forallchosen quantities. This wayanoptimalsignaltobackgroundratioisachievedwhileatthe sametime an optimalnumberofremaining signal eventscan be obtained.

With the aid of the cut optimization algorithm the following selectionconditionsweredetermined:

0

.

5414 GeV

/

c²

≤

^mX

≤

⁰

.

5561 GeV

/

c²

,

(2) 0

.

507 GeV

/

c²

≤

^meeγ γ

≤

⁰

.

646 GeV

/

c²

,

(3) 0

.

0923 GeV

/

c²

≤

^mγ γ

≤

⁰

.

1574 GeV

/

c²

,

(4) mee

≥

⁰

.

096 GeV

/

c²and (5)

χ

²prob.

≥

⁰

.

05

.

(6)

Fig. 7. Invariantmassofe⁺e⁻γ γ afterallcutsforthe2008and2009datasets (black)andforthesimulationsscaledtodataaccordingtothefittodataafterpre- selection(red).Thebluedashedlinesindicatethechosenselectionconditions.

4. Results

Afterapplyingtheselectionconditionstothedata,threeevents were left, whereastwo eventswereexpectedto remainfromthe direct two-pion production pd→^3He

π

⁰

π

⁰ according to Monte Carlo simulations. All other background reaction channels were foundtogivenosizeablecontributionafterapplyingthecuts.The invariant mass, meeγ γ , for these events are plotted in Fig. 7 to- gether withsimulateddata.Note thatthe generatedMonteCarlo events were scaled accordingto thefit to dataafterpreselection andthatthesumofallMonteCarloeventsremainingafterallcuts isequaltotwoevents.

The overall reconstruction efficiencyforthe signal decay

η

→

π

⁰e⁺e⁻wasdeterminedtobe

ε

_S^virtual

₌

0

.

02331

(

7

)

(7)

foradecayvia

η

→

π

⁰

γ

^∗assumingVMD,whereastheassumption ofadecayaccordingtopurethree-particlephasespaceresultsin

ε

_S^phase

=

⁰

.

01844

(

7

).

(8)

Thegivenuncertaintiesarepurelystatisticalones.

In order to calculate the upper limit for the branching ratio

(

η

_→

π

⁰e⁺e⁻)/(

η

_→all), the decay channel

η

→

π

⁺

π

⁻

π

⁰

with

π

⁰_→

γ γ

was utilized for normalization. This is a reason- able choice as thisdecay channel hasthe same signature as the signal decay and, thus, possible systematic effects introduced by differencesofthesignature areavoided.Accordingtothedatade- scriptionbyMonteCarlosimulationsandconsideringtheefficiency correctionfactorsforthepreselectionof

ε

_η^pres._{→π+π−π}0

γ γ,2008

=

⁰

.

03587

(

26

)

(9) determined by Monte Carlo studies for the data set collected in 2008and

ε

_η^pres._{→π+π−π}0

γ γ,2009

=

⁰

.

03305

(

18

)

(10) forthedatasetcollectedin2009therewere

N^produced

η→π⁺π⁻πγ γ⁰

= (

⁶

.

509

±

⁰

.

018

) ×

^{106 (11)}

events in data.In order to determine a final upperlimit for the branching ratioof

η

→

π

⁰e⁺e⁻,alluncertainties haveto becon- sideredandincorporatedintothecalculations.

Systematics. The systematic and statistical uncertainties, which need to be considered for theupper limit determination, can be

Fig. 8. Nuisanceparametersλ2008(red)andλ2009(blue)forthesystematicuncer- taintyofthenumberofbackgroundeventsremainingafterallcutsinthe2008and 2009datasets.

separated into uncertainties by multiplicative effects and uncer- taintiesby offseteffects.Theformerincludeanuncertaintyofthe reconstructionefficiencyofthedecay

η

→

π

⁰e⁺e⁻ andan uncer- tainty in the number of

η

→

π

⁺

π

^−

π

⁰_→

γ γ

^ events in data.

The latter ones are uncertainties of the number of background eventsremainingafterallcuts.

Todetermine the systematicuncertainty forthe signal recon- struction efficiency, the resolution settings for the Monte Carlo simulationswerevariedwithin theuncertaintiesoftheindividual detectorresolutionsobservedindata.Theextractedsquarerootof therelativevarianceofthereconstructionefficiencywas foundto be



Var^virtual_rel

=

⁰

.

059 (12)

for a decay via

η

→

π

⁰

γ

^∗ assuming VMD whereas for a decay accordingtopurethree-particlephasespaceonefinds



Var^phase_rel

=

⁰

.

057

.

(13)

Inthefollowinganalysisthesquare rootofthevariancewascon- sideredasthesystematicuncertainty.

The uncertainty for the efficiency corrected number of

η

→

π

⁺

π

^−

π

⁰→

γ γ

^ events in data was obtained by a compari- son to the efficiency corrected number determined utilizingless strictpreselection conditions,namelynocutstorejectconversion or split-off events, no cut on the momentum of charged decay particles andless strict cuts on the particles’ energies. Hereby a systematicuncertaintyof2.3% wasdetermined.

Theuncertaintiesforthenumberofbackgroundeventsremain- ing after all cuts can be separated into a statistical uncertainty duetothefinitenumberofMonteCarlosimulations andsystem- aticuncertainties introduced by uncertainties of thefit ofMonte Carlosimulationsto data.Thelatteraredominatedby differences betweenthe Monte Carlo fit parameters forthe 2008 and 2009 data sets, leading to asymmetric uncertainties. Such different fit parametersforbothdatasetsoriginatedmainlyfromdifferentex- perimentalsettings,whichaffected,e.g.,theeventoverlapdueto differentluminosities.Todetermine the overallsystematicuncer- taintyforthe numberofremainingbackgroundevents,the prob- abilitydensityfunctions(pdf)oftheindividualuncertainties were folded. The resulting pdf for the nuisance parameters λ2008 and λ2009correspondstotheoverallrelativesystematicuncertaintyfor the2008and2009datasetsandwasincorporatedintotheupper limitcalculations.InFig.8thedistributionofthenuisanceparam- etersareillustratedforbothdatasets.

Inorder to investigate further possible systematiceffects, the selection conditions used for the analysis were varied and the

expectationsaccordingtosimulationswerecomparedtothenum- ber ofevents seen indata.Since the expectednumberof events agreed with the number of events seen in data within the sta- tistical uncertainties, no additional systematic effect needs to be considered.

Adetaileddescriptionoftheuncertaintyinvestigationsisavail- ableinRef. [9].

Upperlimit. Theupperlimitfortherelativebranchingratioofthe decay

η

→

π

⁰e⁺e⁻wascalculatedwiththeformula:

 

η → π

⁰e⁺e⁻



 

η _→ π

⁺

π

⁻

π

⁰

^{ <}

N_S,up N_η^produced_{→π+π−π0}

· ε

S

(14)

withtheupperlimitN_S,up forthenumberofsignalevents,which depends on the number of observed events and the number of expectedbackgroundevents.ForthecalculationofNS,upaBayesian approachwaschosenasgiveninRef. [23] withaflatpriorpdfand incorporating the determined uncertainties and the pdfs for the nuisanceparameters,resultingin

N_S,up

=

⁴

.

97

(

CL

=

^90%

).

(15) As a result the relative branching ratio of the decay

η

→

π

⁰e⁺e⁻ via

η

→

π

⁰

γ

^∗ andassumingVMDwasfoundtobe

 

η → π

⁰e⁺e⁻



virtual

 

η → π

⁺

π

⁻

π

⁰

^{ <}

³

^.

²⁸

^×

¹⁰

−⁵

(

CL

=

^90%

)

(16)

whereas theassumptionofapure three-particlephase spacedis- tributionoftheejectilesresultsin

 

η → π

⁰e⁺e⁻



phase

 

η → π

⁺

π

⁻

π

⁰

^{ <}

⁴

^.

¹⁴

^×

¹⁰

−⁵

(

CL

=

^90%

).

(17)

Considering the branching ratio of the decay

η

→

π

⁺

π

⁻

π

⁰ of



η

→

π

⁺

π

⁻

π

^0/(

η

→^all)=⁰.2292(28) [7], the new upper limit forthe branching ratio ofthe decay

η

→

π

⁰e⁺e⁻ via

η

→

π

⁰

γ

^∗ resultsin

 

η _→ π

⁰e⁺e⁻



virtual

 ( η →

^all

) <

7

.

5

×

¹⁰⁻⁶

(

CL

=

^90%

).

(18) For comparison the assumption of a pure three-particle phase spacedistributionoftheejectileswouldleadto

 

η → π

⁰e⁺e⁻



phase

 ( η _→

all

) <

9

.

5

×

¹⁰⁻⁶

(

CL

=

^90%

).

(19) These values are smaller than the previous upper limit of 4.5×^10−5(CL=^{90%)[10] byafactorofsixandfive,}respectively.

5. Summary

We have presented new studies with the WASA-at-COSY ex- periment onthe C parityviolating

η

mesondecay

η

→

π

⁰e⁺e⁻. The obtained upper limit for the branching ratio of the decay

η

_→

π

⁰e⁺e⁻ issmallerthan thepreviously available upperlimit bya factoroffiveto six[10]. Theresultsoftheanalysisare con- sistent withno events seen in data, andthus give no hinton a C violation in anelectromagnetic process.Similarly, no processes fromphysics beyond theStandard Model are requiredto explain theresults.

In order to further decrease this value and to continue the search fora C parityviolationinan electromagneticprocess,ad- ditionaldatawerecollectedwithWASA-at-COSY utilizingthepro-

ductionreactionpp→^pp

η

.Overthreeperiodsin2008,2010and 2012 in total about 5×^{108 such events were recorded and are} currentlybeinganalyzedwithregardtothedecay

η

_→

π

⁰e⁺e⁻.

Besides a decay via one virtual photon according to a VMD model,the decay

η

→

π

⁰e⁺e⁻ could possibly occur via a hypo- theticalC violatingdarkbosonUwherethepertinentformfactor isevenfurthersuppressedby



²q²/

q²−^m2_U+^imUU

compared to the single-photonmechanismwithout a U [24]. Investigations withregardtothisdecayprocessarecurrentlyongoingforthepre- sentedpd→^3He

η

datasetsandthepp→^pp

η

datasetsrecorded withWASA-at-COSYprovidinganorderofmagnitudehigherstatis- tics.

Acknowledgements

Thiswork was supported in partby the EU IntegratedInfras- tructure Initiative HadronPhysics Project under contract number RII3-CT-2004-506078;bytheEuropeanCommissionunderthe7th Framework Programme through the Research Infrastructures ac- tion of the Capacities Programme, Call: FP7-INFRASTRUCTURES- 2008-1,GrantAgreementN. 227431;bythePolishNationalScience Centrethrough thegrants 2016/23/B/ST2/00784,andtheFounda- tionforPolishScience(MPD),co-financedbytheEuropeanUnion within the European Regional Development Fund. We gratefully acknowledgethe supportgivenby the SwedishResearchCouncil, the Knut and Alice Wallenberg Foundation, and the Forschungs- zentrum Jülich FFE Funding Program. This work is based on the PhDthesisofFlorianSebastianBergmann.

FinallywethankallformerWASA-at-COSYcollaborationmem- bersfortheircontributiontothesuccessofthemeasurements,as wellasthecrewoftheCOSY acceleratorfortheir supportduring bothmeasurementperiods.

References

[1] T.P.Cheng,Phys.Rev.162(1967)1734–1738,https://doi.org/10.1103/PhysRev.

162.1734.

[2] J.Smith,Phys.Rev.166(1968)1629–1632,https://doi.org/10.1103/PhysRev.166. 1629.

[3] J.N.Ng,D.J.Peters,Phys.Rev.D47(1993)4939–4948,https://doi.org/10.1103/ PhysRevD.47.4939.

[4] P. Fayet, Phys. Lett. B 95 (1980) 285–289, https://doi.org/10.1016/0370- 2693(80)90488-8.

[5] M.I.Dobroliubov,A.Y.Ignatiev,Phys.Lett.B206(1988)346–348,https://doi. org/10.1016/0370-2693(88)91519-5.

[6]L.B.Okun’,Sov.Phys.JETP56(1982)502–505.

[7] C.Patrignani, etal.,Chin.Phys.C40(2016)100001,https://doi.org/10.1088/ 1674-1137/40/10/100001.

[8]T.Petri,Master’sthesis,RheinischeFriedrich-Wilhelms-UniversitätBonn,Ger- many,2010,arXiv:1010.2378.

[9]F.S.Bergmann,Ph.D.thesis,WestfälischeWilhelms-UniversitätMünster,Ger- many,2017.

[10] M.R.Jane,etal.,Phys.Lett.B59(1975)99–102,https://doi.org/10.1016/0370- 2693(75)90167-7.

[11] P. Adlarson, et al., Phys. Rev. C94 (2016) 065206, https://doi.org/10.1103/ PhysRevC.94.065206.

[12]B. Hoistad, J. Ritman, et al., WASA-at-COSY Collaboration, arXiv:nucl-ex/ 0411038,2004.

[13] C.Bargholtz,etal.,Nucl.Instrum.MethodsA594(2008)339–350,https://doi. org/10.1016/j.nima.2008.06.011.

[14]I.Fröhlich,etal.,PoSACAT2007(2007)076,arXiv:0708.2382.

[15] P.Adlarson,etal.,Eur.Phys.J.A50(2014)100,https://doi.org/10.1140/epja/ i2014-14100-4.

[16] P. Adlarson, et al., Phys. Rev.C 91 (2015) 015201, https://doi.org/10.1103/ PhysRevC.91.015201.

[17]J.J.Sakurai,InvariancePrinciplesandElementaryParticles,PrincetonUniversity Press,Princeton,NewJersey,1964.

[18] E. Leader,E.Predazzi, J. Phys.G 40(2013) 075001,https://doi.org/10.1088/ 0954-3899/40/7/075001.

[19] J.Bernstein,G.Feinberg,T.D.Lee,Phys.Rev.139(1965)B1650–B1659,https://

doi.org/10.1103/PhysRev.139.B1650.

[20] B. Barrett, et al.,Phys. Rev.141(1966) 1342–1349,https://doi.org/10.1103/ PhysRev.141.1342.

[21] M.J.Bazin,etal.,Phys.Rev.Lett.20(1968)895–898,https://doi.org/10.1103/ PhysRevLett.20.895.

[22] R.Brun,et al.,CERNReportNo.W5013,1994,URLhttp://cds.cern.ch/record/ 1082634.

[23] Y.Zhu,Nucl.Instrum.MethodsA578(2007)322–328,https://doi.org/10.1016/ j.nima.2007.05.116.

[24] A.Kup´s ´c,A.Wirzba,J.Phys.Conf.Ser.335(2011)012017,https://doi.org/10. 1088/1742-6596/335/1/012017.