• No results found

Search for C violation in the decay eta -> pi(0)e(+)e(-) with WASA-at-COSY

N/A
N/A
Protected

Academic year: 2021

Share "Search for C violation in the decay eta -> pi(0)e(+)e(-) with WASA-at-COSY"

Copied!
7
0
0

Loading.... (view fulltext now)

Full text

(1)

Contents lists available atScienceDirect

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.

(2)

sDepartmentofPhysics,IndianInstituteofTechnologyIndore,KhandwaRoad,Simrol,Indore453552,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,JLNMargJaipur302017,Rajasthan,India

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

zDepartmentofPhysics,IndianInstituteofTechnologyBombay,Powai,Mumbai400076,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

r

a

c

t

Articlehistory:

Received12February2018 Receivedinrevisedform3June2018 Accepted10July2018

Availableonline14July2018 Editor:V.Metag

We reportonthesearchfor theraredecay

η

π

0e+ewhichisofinteresttostudyC 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.Intotal3×107eventsofthereactionpd3He

η

havebeen

recorded atan excessenergy of Q =59.8 MeV. Based onthisdata set the C parityviolatingdecay

η

π

0

γ

π

0e+eviaasingle-photonintermediate statehasbeen searchedfor,resulting innew

upperlimits of

η

π

0e+e−/

η

π

+

π

π

0<3.28×10−5 and

η

π

0e+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+evia 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, mU and

U

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 massmU

0

=

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+etheVMDmodelisdominatedbythe

ρ

mesonwitha mass of

=

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+ewas 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-COSY facil-ityhavebeenanalyzedwhichalsoconstitutedthebasisforstudies ofother

η

mesondecaychannelsalreadypublishedinRef. [11].

2. Experiment

TheWASA-at-COSYexperimentwasaninternalexperiment op-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,whichwasusedforthereconstructionofthe pro-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 layersofthinandthickplasticscintillatorsenablingparticle iden-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

(3)

inaddition.Duetothetriggerrelyingoninformationfromthe for-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+ewas basedon a

com-monanalysischainfor

η

decaystudiesdescribedinRef. [11].

Preselection. Before the selection conditions for the decay

η

π

0e+ewere 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 offtheCOSYbeamaxisandbya recon-structedinvariant massbelow8 to15 MeV

/

c2,dependingonthe reconstructedradial vertexpositionandassuminga vertexatthe COSYbeampipe.Those pairsarerejected, aswell.Moredetailsof theseconditionswerepublishedinRef. [11].

Besidesthesegeneralpreselectionconditions,acutonthe sig-natureofthe decay

η

π

0e+ewas 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+eareexpectedto

bebelowthisvalue.

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

η

π

0e+e, 1

.

8

×

108 MonteCarlo 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+ewere

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 thesimulateddecayηπ0e+e.Black

lined:decayviaηπ0γconsideringVMD.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+eandthetransitionformfactorfortheoff-shell

con-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 moredetailed

cal-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,fortheanalysis pre-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+eis basedonMonteCarlo

simulations.It isnecessarytoknowthecontributionsofthe vari-ousreactionstothecollecteddataforanoptimalchoice.Therefore, the2008and2009datasetswerefittedseparatelyindistributions of selected quantities by template distributions ofthe aforemen-tionedMonteCarlosimulationstodeterminethe contributionsof the individual reactions to the data. Indetail, thesedistributions are:

the missingmassmX,corresponding totheinvariant massof theprotonbeamandthedeuterontargetremaining afterthe 3He fourmomentum hasbeensubtracted andpeaksatthe

η

massforthereactionpd

3He

η

,

(4)

the invariant mass meeγ γ of an electron–positron pair

can-didate andtwo photons, which peaksat the

η

mass forthe decay

η

π

0e+ewith

π

0

γ γ

,

the invariant mass mγ γ oftwo photons, which peaks atthe

π

0massforreactionswith

π

0 mesonsproduced,

theinvariantmassmeeofanelectron–positronpaircandidate,

thesmallestinvariantmassmeγ ofallfourpossible

combina-tionsofanelectronorpositroncandidateandaphotonand

the missing mass squaredm2Xee, 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+ein thecombined datasets after preselection, considering the prese-lectionefficiency forthe signal decay. A fitby Monte Carlo sim-ulationsincludingthesimulateddecay

η

π

0e+eisconsistent withzeroeventsfromthissignaldecaychannel.Therefore,the de-cay

η

π

0e+ewasexcludedfromthefit.Whilethedifferential

distribution forthe reaction pd

3He

η

iswell known [15], the differentialdistributionsareknownonlywithhighuncertaintiesor notatallfordirectmulti-pionproductions.Hence,the datawere dividedintotenbins inangularranges ofcos

ϑ

3cmsHe.

5 MonteCarlo

simulations were fittedto datain theeight angularbins ranging from

1 to0

.

6.Theangularrange0

.

6

<

cos

ϑ

3cmsHe

1 wasexcluded becauseofthelowerenergyresolutionoftheforwarddetectorfor theseforwardscattered3He nuclei.Moreover,therelativeamount ofbackgroundfromthedirectpionproductionislargerinthis an-gularrange,whereaslessthan3% ofallpd

3He

η

eventshavea cos

ϑ

3cmsHe

>

0

.

6.

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

η

decayswereconstrainedtothebranchingratios accord-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

<

cos

ϑ

3cmsHe

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-pion pro-ductionreactions.NotethatMCsimulationswitheventoverlapare requiredforaproperdescriptionoftheshouldersoftheinvariant massdistributions.A collectionofallfitsisavailableinRef. [9].

Selectionconditions. Theselectionconditionsforthesearchforthe decay

η

π

0e+ewerebasedonthefollowingquantities:

themissingmassmX,

theinvariantmassesmeeγ γ ,mγ γ andmee,

the

χ

2probabilityofakinematicfitwiththehypothesispd

3He

γ γ

e+eand

theenergylossESECdepofthechargedparticlesinthecentral de-tector scintillator electromagneticcalorimeter(SEC) andtheir momentum p todiscriminatee± and

π

± (particle identifica-tion,PID).

5

ϑ3cmsHe isthepolarscatteringangleofthe

3He nucleusrelativetothebeamaxis inthecenterofmasssystem.

Fig. 2. MissingmassmX=Pp+ Pd− P3Heafterpreselectionforadatasampleof the2008periodfittedbyMonteCarlosimulations.Onlythemostcommon contri-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 ofthe selec-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,scaledaccordingtothefit ex-plainedinthepreviousparagraph.Thegraphicalcutforthe parti-cleidentification(seeFig.6)waschosenbyoptimizingtheproduct of the number of selected e+e− pairs (Ne+e−) and the ratio of

Ne+e− to thenumber of chargedpion pairs (Nπ+π−). While this cutwaschosenbeforehand,asitisacommoncututilizedforPID independent fromthe analyzed reaction,the selection conditions

(5)

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.Thisalgorithmisbasedontherelativeamountof simu-latedsignal events SR

=

NcutS

/

N

pres

S remaining afterall cuts(NcutS ) compared to the numberafter preselection (NpresS ) and the rela-tive amount of all simulatedbackground events BR

=

NBcut

/

N

pres B remainingafterallcuts(NBcut)inrelationtothenumberafter pre-selection(NpresB ).Incaseofthebackgroundreactionsthe contribu-tionsasobtainedinthedatadescriptionwere usedtodownscale theMonteCarlosimulationsandtoextractthenumbers.

Thecutoptimizationalgorithmmaximizestheevaluation func-tion

G

=

SR

·

SR

BR

(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)andforthesimulationsscaledtodataaccordingtothefittodataafter pre-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+ewasdeterminedtobe

ε

virtual

S

=

0

.

02331

(

7

)

(7)

foradecayvia

η

π

0

γ

assumingVMD,whereastheassumption ofadecayaccordingtopurethree-particlephasespaceresultsin

ε

Sphase

=

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.Accordingtothedata de-scriptionbyMonteCarlosimulationsandconsideringtheefficiency correctionfactorsforthepreselectionof

ε

ηpres.π+ππ0

γ γ,2008

=

0

.

03587

(

26

)

(9)

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

ε

ηpres.π+ππ0

γ γ,2009

=

0

.

03305

(

18

)

(10)

forthedatasetcollectedin2009therewere

Nproduced

ηπ+ππ0

γ γ

= (

6

.

509

±

0

.

018

)

×

10

6 (11)

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

η

π

0e+e,alluncertainties haveto be con-sideredandincorporatedintothecalculations.

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

(6)

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

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

η

π

0e+eandan 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



Varvirtual

rel

=

0

.

059 (12)

for a decay via

η

π

0

γ

assuming VMD whereas for a decay

accordingtopurethree-particlephasespaceonefinds



Varphaserel

=

0

.

057

.

(13)

Inthefollowinganalysisthesquare rootofthevariancewas con-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.

Theuncertaintiesforthenumberofbackgroundevents remain-ing after all cuts can be separated into a statistical uncertainty duetothefinitenumberofMonteCarlosimulations and system-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 parametersforbothdatasetsoriginatedmainlyfromdifferent ex-perimentalsettings,whichaffected,e.g.,theeventoverlapdueto differentluminosities.Todetermine the overallsystematic uncer-taintyforthe numberofremainingbackgroundevents,the prob-abilitydensityfunctions(pdf)oftheindividualuncertainties were folded. The resulting pdf for the nuisance parameters

λ2008

and

λ2009

correspondstotheoverallrelativesystematicuncertaintyfor the2008and2009datasetsandwasincorporatedintotheupper limitcalculations.InFig.8thedistributionofthenuisance param-etersareillustratedforbothdatasets.

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

expectationsaccordingtosimulationswerecomparedtothe num-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.

Adetaileddescriptionoftheuncertaintyinvestigationsis avail-ableinRef. [9].

Upperlimit. Theupperlimitfortherelativebranchingratioofthe decay

η

π

0e+ewascalculatedwiththeformula:





η

π

0e+e







η

π

+

π

π

0

 <

NS,up

Nηproducedπ+ππ0

·

εS

(14)

withtheupperlimitNS,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

NS,up

=

4

.

97

(

CL

=

90%

).

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

η

π

0e+evia

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 space dis-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+evia

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+eissmallerthan 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 utilizingthe

(7)

pro-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+ecould possibly occur via a

hypo-theticalC violatingdarkbosonUwherethepertinentformfactor isevenfurthersuppressedby



2q2

/



q2

m2

U

+

imUU



compared to the single-photonmechanismwithout a U [24]. Investigations withregardtothisdecayprocessarecurrentlyongoingforthe pre-sentedpd

3He

η

datasetsandthepp

pp

η

datasetsrecorded withWASA-at-COSYprovidinganorderofmagnitudehigher statis-tics.

Acknowledgements

Thiswork was supported in partby the EU Integrated Infras-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,andthe Founda-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-COSYcollaboration mem-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.

Figure

Fig. 1. Invariant mass of e + e − pairs for the simulated decay η → π 0 e + e − . Black lined: decay via η → π 0 γ ∗ considering VMD
Fig. 2. Missing mass m X = P p + P d − P 3 He  after preselection for a data sample of the 2008 period fitted by Monte Carlo simulations
Fig. 6. Energy loss of charged particles in the SEC plotted against their momentum times charge for the preselected data sets of the 2008 and 2009 periods
Fig. 8. Nuisance parameters λ 2008 (red) and λ 2009 (blue) for the systematic uncer- uncer-tainty of the number of background events remaining after all cuts in the 2008 and 2009 data sets.

References

Related documents

The increasing availability of data and attention to services has increased the understanding of the contribution of services to innovation and productivity in

Generella styrmedel kan ha varit mindre verksamma än man har trott De generella styrmedlen, till skillnad från de specifika styrmedlen, har kommit att användas i större

Industrial Emissions Directive, supplemented by horizontal legislation (e.g., Framework Directives on Waste and Water, Emissions Trading System, etc) and guidance on operating

Detta stämmer med litteraturen där incitamenten för låg produktion och låga kostnader ofta anges som mycket starka (Barnum m.fl. 1995) Även om kostnaderna blir låga antas

The ambiguous space for recognition of doctoral supervision in the fine and performing arts Åsa Lindberg-Sand, Henrik Frisk &amp; Karin Johansson, Lund University.. In 2010, a

i Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai 200443, People ’s Republic of China.. j Also

I kapitel fyra ger vi en introduktion till Sandvik koncernen och den avdelning som vi valt att studera närmare, Sandvik Financial Services (SFS). Här presenteras

Francis (2004) påpekar att risken för juridiska repressalier kan påverka revisorn till att frångå sitt oberoende och därav välja att avstå från att utfärda en anmärkning om