Charge symmetry breaking in $dd\rightarrow ^{4}He\pi ^{0}$ with WASA-at-COSY

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Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Charge symmetry breaking in dd → ⁴ ^He π ⁰ with WASA-at-COSY

WASA-at-COSY Collaboration

P. Adlarson

^a^,¹

, W. Augustyniak

^b

, W. Bardan

^c

, M. Bashkanov

^d^,^e

, F.S. Bergmann

^f

, M. Berłowski

^g

, H. Bhatt

^h

, A. Bondar

ⁱ^,^j

, M. Büscher

^k^,^l^,²^,³

, H. Calén

^a

, I. Ciepał

^c

, H. Clement

^d^,^e

, D. Coderre

^k^,^l^,^m^,⁴

, E. Czerwi ´nski

^c

, K. Demmich

^f

, E. Doroshkevich

^d^,^e

, R. Engels

^k^,^l

, A. Erven

ⁿ^,^l

, W. Erven

ⁿ^,^l

, W. Eyrich

^o

, P. Fedorets

^k^,^l^,^p

, K. Föhl

^q

, K. Fransson

^a

, F. Goldenbaum

^k^,^l

, P. Goslawski

^f

, A. Goswami

^k^,^l^,^r

, K. Grigoryev

^k^,^l^,^s^,⁵

, C.-O. Gullström

^a

, C. Hanhart

^k^,^l^,^t

, F. Hauenstein

^o

, L. Heijkenskjöld

^a

, V. Hejny

^k^,^l^,^∗

, B. Höistad

^a

, N. Hüsken

^f

, L. Jarczyk

^c

, T. Johansson

^a

, B. Kamys

^c

, G. Kemmerling

ⁿ^,^l

, F.A. Khan

^k^,^l

, A. Khoukaz

^f

,

D.A. Kirillov

^u

, S. Kistryn

^c

, H. Kleines

ⁿ^,^l

, B. Kłos

^v

, W. Krzemie ´n

^c

, P. Kulessa

^w

, A. Kup´s ´c

^a^,^g

, A. Kuzmin

ⁱ^,^j

, K. Lalwani

^h^,⁶

, D. Lersch

^k^,^l

, B. Lorentz

^k^,^l

, A. Magiera

^c

, R. Maier

^k^,^l

,

P. Marciniewski

^a

, B. Maria ´nski

^b

, M. Mikirtychiants

^k^,^l^,^m^,^s

, H.-P. Morsch

^b

, P. Moskal

^c

, H. Ohm

^k^,^l

, I. Ozerianska

^c

, E. Perez del Rio

^d^,^e

, N.M. Piskunov

^u

, P. Podkopał

^c

,

D. Prasuhn

^k^,^l

, A. Pricking

^d^,^e

, D. Pszczel

^a^,^g

, K. Pysz

^w

, A. Pyszniak

^a^,^c

, C.F. Redmer

^a^,¹

, J. Ritman

^k^,^l^,^m

, A. Roy

^r

, Z. Rudy

^c

, S. Sawant

^k^,^l^,^h

, S. Schadmand

^k^,^l

, T. Sefzick

^k^,^l

, V. Serdyuk

^k^,^l^,^x

, B. Shwartz

ⁱ^,^j

, R. Siudak

^w

, T. Skorodko

^d^,^e

, M. Skurzok

^c

, J. Smyrski

^c

, V. Sopov

^p

, R. Stassen

^k^,^l

, J. Stepaniak

^g

, E. Stephan

^v

, G. Sterzenbach

^k^,^l

, H. Stockhorst

^k^,^l

, H. Ströher

^k^,^l

, A. Szczurek

^w

, A. Täschner

^f

, A. Trzci ´nski

^b

, R. Varma

^h

, M. Wolke

^a

,

A. Wro ´nska

^c

, P. Wüstner

ⁿ^,^l

, P. Wurm

^k^,^l

, A. Yamamoto

^y

, L. Yurev

^x^,⁷

, J. Zabierowski

^z

, M.J. Zieli ´nski

^c

, A. Zink

^o

, J. Złoma ´nczuk

^a

, P. ˙Zupra ´nski

^b

, M. ˙Zurek

^k^,^l

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

cInstituteofPhysics,JagiellonianUniversity,ul.Reymonta4,30-059Kraków,Poland

dPhysikalischesInstitut,Eberhard-Karls-UniversitätTübingen,AufderMorgenstelle14,72076Tübingen,Germany

eKeplerCenterforAstroandParticlePhysics,EberhardKarlsUniversityTübingen,AufderMorgenstelle14,72076Tübingen,Germany fInstitutfürKernphysik,WestfälischeWilhelms-UniversitätMünster,Wilhelm-Klemm-Str.9,48149Münster,Germany

gHighEnergyPhysicsDepartment,NationalCentreforNuclearResearch,ul.Hoza69,00-681,Warsaw,Poland hDepartmentofPhysics,IndianInstituteofTechnologyBombay,Powai,Mumbai,400076,Maharashtra,India iBudkerInstituteofNuclearPhysicsofSBRAS,11akademikaLavrentievaprospect,Novosibirsk,630090,Russia jNovosibirskStateUniversity,2PirogovaSt.,Novosibirsk,630090,Russia

kInstitutfürKernphysik,ForschungszentrumJülich,52425Jülich,Germany lJülichCenterforHadronPhysics,ForschungszentrumJülich,52425Jülich,Germany

mInstitutfürExperimentalphysikI,Ruhr-UniversitätBochum,Universitätsstr.150,44780Bochum,Germany nZentralinstitutfürEngineering,ElektronikundAnalytik,ForschungszentrumJülich,52425Jülich,Germany

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

pInstituteforTheoreticalandExperimentalPhysics,StateScientiﬁcCenteroftheRussianFederation,BolshayaCheremushkinskaya25,117218Moscow,Russia

*

Correspondingauthorat:InstitutfürKernphysik,ForschungszentrumJülich,52425Jülich,Germany.

E-mailaddress:v.hejny@fz-juelich.de(V. Hejny).

1 Presentaddress:InstitutfürKernphysik,JohannesGutenberg-UniversitätMainz,Johann-Joachim-BecherWeg45,55128Mainz,Germany.

2 Presentaddress:PeterGrünbergInstitut,PGI-6ElektronischeEigenschaften,ForschungszentrumJülich,52425Jülich,Germany.

3 Presentaddress:InstitutfürLaser- undPlasmaphysik,Heinrich-HeineUniversitätDüsseldorf,Universitätsstr.1,40225Düsseldorf,Germany.

4 Presentaddress:AlbertEinsteinCenterforFundamentalPhysics,UniversitätBern,Sidlerstrasse5,3012Bern,Switzerland.

5 Presentaddress:III.PhysikalischesInstitutB,Physikzentrum,RWTHAachen,52056Aachen,Germany.

6 Presentaddress:DepartmentofPhysicsandAstrophysics,UniversityofDelhi,Delhi,110007,India.

7 Presentaddress:DepartmentofPhysicsandAstronomy,UniversityofSheffield,HounsfieldRoad,Sheffield,S37RH,UnitedKingdom.

http://dx.doi.org/10.1016/j.physletb.2014.10.029

0370-2693/©²⁰¹⁴^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/3.0/).Fundedby SCOAP³.

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qII.PhysikalischesInstitut,Justus-Liebig-UniversitätGießen,Heinrich-Buff-Ring16,35392Giessen,Germany rDepartmentofPhysics,IndianInstituteofTechnologyIndore,KhandwaRoad,Indore,452017,MadhyaPradesh,India sHighEnergyPhysicsDivision,PetersburgNuclearPhysicsInstitute,OrlovaRosha2,Gatchina,Leningraddistrict188300,Russia tInstituteforAdvancedSimulation,ForschungszentrumJülich,52425Jülich,Germany

uVekslerandBaldinLaboratoryofHighEnergy Physics,JointInstituteforNuclearPhysics,Joliot-Curie6,141980Dubna,Moscowregion,Russia vAugustChełkowskiInstituteofPhysics,UniversityofSilesia,Uniwersytecka4,40-007,Katowice,Poland

wTheHenrykNiewodnicza´nskiInstituteofNuclearPhysics,PolishAcademyofSciences,152RadzikowskiegoSt,31-342Kraków,Poland xDzhelepovLaboratoryofNuclearProblems,JointInstituteforNuclearPhysics,Joliot-Curie6,141980Dubna,Moscowregion,Russia yHighEnergyAcceleratorResearchOrganization KEK,Tsukuba,Ibaraki305-0801,Japan

zDepartmentofCosmicRayPhysics,NationalCentreforNuclearResearch,ul.Uniwersytecka5,90-950Łód´z,Poland

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

Articlehistory:

Received10July2014

Receivedinrevisedform10September 2014

Accepted10October2014 Availableonline16October2014 Editor:V.Metag

Keywords:

Chargesymmetrybreaking Deuteron–deuteroninteractions Pionproduction

Chargesymmetrybreaking(CSB)observablesareasuitableexperimentaltooltoexamineeffectsinduced byquarkmassesonthenuclearlevel.PrevioushighprecisiondatafromTRIUMFandIUCFarecurrently usedtodevelopaconsistentdescriptionofCSBwithintheframeworkofchiralperturbationtheory.In thiswork the experimentalstudies onthe reactiondd→⁴^Heπ⁰have been extendedtowards higher excessenergiesinordertoprovideinformation onthecontributionof p-waves inthefinalstate. For this,anexclusivemeasurementhasbeencarriedoutatabeammomentumofpd=¹.2 GeV/c usingthe WASA-at-COSYfacility.Thetotalcrosssectionamountstoσtot= (¹¹⁸±¹⁸^stat±¹³^sys±⁸êxt)pb andfirst dataonthedifferentialcrosssectionareconsistentwiths-wavepionproduction.

©²⁰¹⁴^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (http://creativecommons.org/licenses/by/3.0/).FundedbySCOAP³.

1. Introduction

Within the Standard Model there are two sources of isospin violation,⁸ namely the electro-magnetic interaction and the dif- ferences in the masses ofthe lightest quarks [1,2]. Especiallyin situationswhereoneisabletodisentanglethesetwosources,the observation of isospin violation in hadronic reactions is a direct windowtoquarkmassratios[2–4].

The effectiveﬁeld theory forthe Standard Model in the MeV rangeischiralperturbationtheory(ChPT).Itmapsallsymmetries ofthe Standard Model onto hadronic operators — their strength thenneedstobeﬁxedeitherfromexperimentorfromlatticeQCD calculations. At leading order the only parameters are the pion massandthepiondecayconstantwhicharethebasisforaseries offamouslow energytheoremsinhadron–hadron scattering(see, forexample,Ref. [5]). Althoughat subleadingorders thenumber ofaprioriunknownparametersincreases,thetheorystillprovides non-trivial links between different operators. A very interesting exampleisthecloselinkbetweenthequarkmassinducedproton–

neutronmassdifference,M^qmpn,and, atleading order,isospinvi- olating

π

N scattering,theWeinbergterm.Ingeneral,itisdiﬃcult togetaccesstoquark masseffectsinlow energyhadronphysics:

byfar the largestisospin violating effectisthe pionmass differ- ence,whichalsodrivesthespectacularenergydependenceofthe

π

⁰-photoproduction amplitude near threshold (see Ref. [6] and the references therein). Thus, it is important to use observables wherethepion massdifference doesnot contribute. Anexample is chargesymmetry breaking(CSB)observables—charge symmetry isan isospin rotationby 180degrees that exchangesup and downquarks—asthepionmasstermis invariantunderthisro- tation.Forthiscase, theimpactofsoftphotonshasbeenstudied systematically[7–11]andcanbecontrolled.Alreadyin1977Wein- bergpredictedahugeeffect(upto30%differenceinthescattering lengthsfor p

π

⁰ andn

π

⁰)of CSBin

π

⁰N scattering [1](seealso Ref.[12] fortherecentextraction ofthesequantitiesfrompionic atomsdata).

8 Ignoringtinyeffectsinducedbytheelectro-weaksector.

While the

π

⁰p scattering length might be measurable in po- larized neutralpion photoproductionvery near threshold[13], it isnotpossible tomeasurethen

π

⁰ channel. Asan alternativeac- cessto CSBpion–nucleonscatteringitwas suggestedinRef. [14]

to use N N induced pion production instead. There have been two successful measurements of corresponding CSB observables, namely a measurement of Af b(pn→^d

π

⁰) [15] — the forward–

backwardasymmetryinpn→^d

π

⁰—and ofthetotalcrosssection ofdd→⁴^He

π

⁰ closetothereactionthreshold[16].

TheﬁrstexperimentwasanalyzedusingChPTinRef.[17](see also Ref. [18]), where it was demonstrated that A_{f b}(pn→^d

π

⁰) isdirectly proportionalto M^qmpn,while theeffectof

π

₋

η

mix- ing, previously believedto completelydominate thisCSBobserv- able [19], was shownto be subleading.The value for M^qm_pn ex- tractedturned outtobe consistentwithother,directcalculations of thispart based on dispersiveanalyses [2,20,21] andfromlat- tice.SeeRef.[22]forthelatestreview.Inordertocross-check the systematicsandtoeventually reduce theuncertainties, additional experimentalinformationneedstobeanalyzed.

The ﬁrst theoretical results for dd→⁴^He

π

⁰ are presented in [23,24]. The studies show that the relative importance of the various charge symmetry breaking mechanisms is very different compared to pn→^d

π

⁰. Forexample, softphoton exchange may signiﬁcantlyenhancethecrosssectionsfordd→⁴^He

π

⁰[25].Fur- thermore, a signiﬁcant sensitivity of the results to the nuclear potential model was reported in Ref. [26], which calledfor a si- multaneous analysis of CSB in the N N scattering length and in dd→⁴^He

π

⁰[26].Thus,aspartofaconsistentinvestigationofCSB inthetwonucleonsector,pn→^d

π

⁰anddd→⁴^He

π

⁰shouldhelp tofurtherconstraintherelevantCSBmechanisms.

Themainchallengeinthecalculationofdd→⁴^He

π

⁰ istoget theoreticalcontrolovertheinitialstateinteractions:highaccuracy wave functions are needed fordd→^{4N in} ^low ^partial ^waves ^at relativelyhighenergies.Oneprerequisitetocontrolthisistheear- lier WASA-at-COSY measurement ofdd→³^Hen

π

⁰ [27], which is allowed by charge symmetry and partially shares the same ini- tial state as dd→⁴^He

π

⁰. In addition, higher partial waves are predicted to be very sensitive to the CSB N N→^N transition potential that is diﬃcult to access in other reactions. In leading order in chiral perturbation theory this potential is known.

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Fig. 1. Cumulativeprobabilitydistributionsfrom thekinematicﬁtusedforevent selectionplottedasprobabilityfor the⁴He hypothesisversus theprobabilityfor the 3He hypothesis.Left:distributionforMonte-Carlosimulatedsignaleventsfordd→⁴^Heπ⁰,middle:distributionforMonte-Carlosimulatedeventsfordd→³^Henπ⁰,right:

distributionfordataandtheappliedprobabilitycut.

Thus, a measurement of, for example, p-waves provides an additional, non-trivial test of our current understanding of isospin violation in hadronic systems. Future theoretical CSB studies for dd→⁴^He

π

⁰ can be based on recent developments in effective ﬁeld theoriesforfew-nucleon systems[28] aswell asforthere- actionN N→^{N N}

π

[29–31],thus promisingamodel-independent analysisofthedata.

Whiletheprevious measurementsofdd→⁴^He

π

⁰ closeto reaction threshold were limited to the total cross section [16], in ordertoextractconstraintsonhigherpartialwavesanynewmea- surementathigherexcess energiesinadditionhastoprovide in- formation on the differential cross section. Forthis, an exclusive measurementdetecting the⁴He ejectile aswellasthetwo decay photonsofthe

π

⁰ hasbeen carriedout utilizingthe samesetup usedfordd→³^Hen

π

⁰ [27].Thelatterreactionwas alsousedfor normalization.

2. Experiment

The experiment was carried out at the Institute for Nuclear Physics of the Forschungszentrum Jülich in Germany using the CoolerSynchrotron COSY[32] together withthe WASA detection system [33]. For the measurement of dd→⁴^He

π

⁰ at an excess energy of Q ≈^{60 MeV a} ^deuteron ^beam ^with ^a ^momentum ^of 1.2 GeV/c wasscatteredonfrozendeuteriumpellets providedby an internal pellet target. The ⁴He ejectile and the two photons from the

π

⁰ decay were detected by the Forward Detector and theCentralDetectoroftheWASAfacility,respectively.Theexperi- mentalsetupandtriggerconditionswerethesameasdescribedin Ref.[27].

3. Dataanalysis

The basic analysis leading to eventsamples with one helium andtwophotonsinﬁnalstatefollowsthestrategyusedfordd→

3Hen

π

⁰ outlinedinRef.[27].Comparedtothisreaction,however, the charge symmetry breaking reactiondd→⁴^He

π

⁰ has a more thanfourordersofmagnitudesmallercrosssection.Theonlyother channelwith⁴He andtwophotonsinﬁnalstateisthedoublera- diativecapturereactiondd→⁴^He

γ γ

.The crosssectionsforboth reactionsarenotlargeenough toprovideavisualsignaturefor⁴He in thepreviously used E–E plots from the ForwardDetector.

Thus, all ³He and ⁴He candidatestogether withthe two photons havebeen testedagainst the hypotheses dd→⁴^He

γ γ

(“⁴He hypothesis”) anddd→³^Hen

γ γ

(“³He hypothesis”) by means of a kinematicﬁt.Besidestheoverallenergyandmomentumconserva- tion noother constraintshave beenincluded. Especially, thereis no constraintonthe invariant mass ofthe two photonsin order

Fig. 2. Missingmassplotforthereactiondd→⁴^{He X .}^The^differentcontributions ﬁttedtothespectrumaredoubleradiativecapturedd→⁴^Heγ γ (greendashed), thereactiondd→³^Henπ⁰ (bluedotted,added)andthesumofallcontributions includingthesignal(redsolid).

to leavea decisivemissing-mass plotandnot tointroducea fake 4He

π

⁰ signal.

Forﬁnaleventclassiﬁcationthecumulativeprobabilities P(

χ

², n.d.f.) for the two hypotheses have been plotted as probability for the ⁴He hypothesis versus the probability for the ³He hypothesis (see Fig. 1). The data (right plot) have been compared to Monte-Carlo generated samples of dd→⁴^He

π

⁰ events (left plot) and dd→³^Hen

π

⁰ events (middle plot). Events originating fromdd→⁴^He

π

⁰populatethelowprobabilityregionforthe³He hypothesis andform a uniformdistribution forthe ⁴He hypothesis. As there is no pion constraint in the ﬁt, events from the double radiative capture reaction show the same signature. For dd→³^Hen

π

⁰ thesituationisopposite.Theindicatedcutisbased ontheMonte-Carlosimulations,buthasbeenoptimizedbymaxi- mizingthestatisticalsigniﬁcanceofthe

π

⁰ signalinﬁnalmissing mass plot.In addition,ithasbeen checkedthatthe resultissta- blewithinthestatisticalerrorsagainstvariationsoftheprobability cut. For the simulations the standard Geant3 [34] based WASA Monte-Carlopackagehasbeenused,whichincludesthefulldetec- torsetupandwhichhasalreadybeenbenchmarkedagainstawide rangeofreactionsfromtheWASA-at-COSYphysicsprogram.After thisanalysisstepthecontributionfrommisidentiﬁed³He wasre- ducedbyaboutfourordersofmagnitude.

In a next step, the resulting four momenta based on the ﬁt hypothesis dd→⁴^He

γ γ

havebeenusedto calculatethemissing massm_X indd→⁴^{He X as}^a^function^of^the center-of-massscat- teringangleθ^∗ ofthe particle X .Fig. 2showsapeakatthepion

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Fig. 3. Missingmassplotsforthefourdifferentangularbins(scatteringangleofthepioninthec.m.system).Thecolorcodefortheindividualcontributionsisthesameas inFig. 2.

massontopofabroadbackground.Inordertoextractthe num- berofsignal eventsthebackgroundinthepeak regionhasto be described andsubtracted. Instead ofa (rather arbitrary) ﬁtusing a polynomial, the shape of signal and background has been re- producedusinga composition ofphysics reactions withadouble chargednucleus and two photons in the ﬁnal state. Any further sources ofbackground— physics aswell asinstrumental —have alreadybeeneliminatedbytheanalysisstepsdescribedinRef.[27]

and the subsequent kinematic ﬁt. The signal has then been ex- tractedbyﬁttingalinearcombinationofthecorrespondingMonte- Carlogeneratedhigh-statisticstemplatedistributionsforthethree reactions

•^dd→⁴^He

γ γ

(double radiative capture) using 3-body phase space(greendashed),plus

•^dd→³^Hen

π

⁰ using the model described in Ref. [27] (blue dotted)forwhichthe³He isfalselyidentiﬁedas⁴He,plus

•^dd→⁴^He

π

⁰ using2-bodyphase space(i.e. plains-wave, red solid).

PleasenotethatinFig. 2aswell asinFig. 3thecumulated distri- butionsare shown,e.g. thered solid curverepresentsthe sumof allcontributions.

For the differential cross section the data have been divided into four angular bins within the detector acceptance (−⁰.85≤ cosθ^∗≤⁰.75).Independentﬁtsofthedifferentcontributionslisted

above have been performed for each bin to address possible anisotropies. In the course of theﬁt two systematic effects have beenobserved,whicharediscussedinthefollowing.

First, the background originating from misidentiﬁed ³He is slightlyshiftedcompared totheMonte-Carlo simulations.Theef- fectisangulardependentandislargestatforwardangles.Possible reasons are a mismatch in the actual beam momentum, a different amountof insensitive material inMonte-Carlo simulations compared totherealexperiment orsystematicdifferencesin the simulateddetectorresponsefor³He and⁴He —thelimitedstatis- ticsdidnot allowfora detailedstudyoftheoriginofthat effect.

Thebackgroundstemmingfromdd→³^Hen

π

⁰issensitivetothese effectsastheenergylossesfroma(true)³He ejectileareusedfor energyreconstruction of a (falselyidentiﬁed)⁴He.The mismatch canbe compensatedby introducinganangulardependentscaling factoronthemissingmassaxisforthe³Hen

π

⁰background,which hasbeenincluded intheﬁtasadditionalfree parameter.Forthe angularbinsfrombackwardtoforwardthesefactorsare1.0,0.99, 0.97 and0.94,respectively.Astheresultingﬁtsdescribetheshape ofthedataespeciallyintheregionofthepionpeak,noadditional systematicerrorhasbeenassignedtothiseffect.

The second systematiceffect concerns a mismatchinthe low mass rangem≤⁰.11 GeV/c² in the mostbackward angular bin.

According to the ﬁt only events fromthe reaction dd→⁴^He

γ γ

contribute in thismass region. The model used forthis channel was3-bodyphasespace,whichwasnotexpectedtoprovideaper- fect description. However, with the dominatingbackground from

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dd→³^Hen

π

⁰ in a wide mass range,it is currently not possible todisentangle thetwocontributions preciselyenoughinorderto verifyany moreadvanced theoretical model —this issuewill be addressedinafollow-upexperiment,seebelow.Consequently,the final fit excludes the corresponding missing mass range (consis- tentlyinall angularbins).Basedon thedifferencetothefit with the low mass region included a corresponding systematic uncer- taintyforthiseffecthasbeenassignedintheresult.

Fig. 3shows the fittedmissing massspectra for the different binsincosθ^∗ together withthefitresult. Thechosenansatz pro- videsagood overalldescriptionofthe fulldataset.Any testsfor furthersystematiceffects(accordingtothedefinitioninRef.[35]), forexample concerningrateeffects andselection cutsin theba- sicanalysis(seeRef.[27]),didnotrevealanyadditionalsystematic uncertainties.

4. Results

For the acceptance correction an isotropic angular distribu- tion has been assumed. For absolute normalization the reaction dd→³^Hen

π

⁰ hasbeenused. Theresultingdifferential crosssec- tionsextractedfromFig. 3are

d

σ

d

Ω

−

⁰

.

85

≤

^cos

θ

^∗

≤ −

⁰

.

45

= (

¹⁷

.

1

±

³

.

8

±

⁴

.

0_ﬁt

)

pb

/

sr

,

(1) d

σ

d

Ω

−

⁰

.

45

≤

^cos

θ

^∗

≤ −

⁰

.

05

= (

⁶

.

6

±

²

.

4

)

pb

/

sr

,

(2) d

σ

d

Ω

−

⁰

.

05

≤

^cos

θ

^∗

≤

⁰

.

35

= (

⁵

.

5

±

²

.

2

)

pb

/

sr

,

and (3) d

σ

d

Ω

0

.

35

≤

cos

θ

^∗

≤

0

.

75

= (

8

.

4

±

2

.

8

)

pb

/

sr

.

(4)

Ingeneral,onlystatisticalerrorsaregiven, exceptfortheﬁrstbin wheretheuncertaintycausedby thesystematiceffectinthelow massregion hasbeenincluded.Asystematicerrorof 10% forlu- minositydetermination and7% for the normalizationto external dataiscommontoall numbers.Integratingtheindividualresults, the (partial) total cross section within the detector acceptance amounts to

σ

_tot^acc

= (

⁹⁴

±

¹⁴stat

±

¹⁰sys

±

⁶ext

)

pb (5) withthesystematicerror originatingfromluminosity determina- tionandtheuncertaintyfromthedifferentﬁtmethods.Theexter- nalnormalizationerrorhasbeenpropagated fromtheluminosity determination for dd→³^Hen

π

⁰ (see Ref. [27]). Extrapolation to thefull phasespacebyassuminganisotropicdistributionyields

σ

tot

= (

¹¹⁸

±

¹⁸stat

±

¹³sys

±

⁸ext

)

pb

.

(6) This result can be compared with the values measured close to thresholdbydividingoutphasespace(seeFig. 4).Aconstantvalue couldbeinterpretedasadominatings-wave,butonehastokeep inmindthat theenergydependenceoftheformationofa⁴He in the4N ﬁnalstatemighthavesomeinﬂuencehere,too.

Fig. 5showsthedifferentialcrosssection.Duetotheidentical particlesintheinitialstate,oddandevenpartialwavesdonotin- terfereandthe angulardistribution issymmetric withrespectto cosθ^∗=^0. ^As ^the ^p-wave ^ands–d interference terms contribute to the quadraticterm andthe p-wave also addsto the constant term, the differentpartial wavescannot be directly disentangled.

However,a ﬁtincludingtheLegendrepolynomials P0(cosθ^∗)and P2(cosθ^∗) — although not excluding — doesnot show any evi- denceforcontributionsofhigherpartialwaves:

Fig. 4. Energydependenceofthereactionamplitudesquared|A|².Intheabsenceof initialandﬁnalstateinteractions aconstantamplitudewouldindicatethatonly s-waveis contributing.Theredfullcirclecorrespondstothetotalcross section giveninthetext.(Forinterpretationofthereferencestocolorinthisﬁgureleg- end,thereaderisreferredtothewebversionofthisarticle.)

Fig. 5. Differentialcrosssection.Theerrorsbarsshowthestatisticaluncertainties.In thefirstbintheadditionalsystematicuncertaintyfromthefithasbeenadded(see text).Thebluedashedlinerepresentsthetotalcrosssectiongiveninthetextas- suminganisotropicdistribution,thesolidredcurveshowsthefitwiththeLegendre polynomialsP0andP2.

d

σ

d

Ω = (

⁹

.

8

±

²

.

6

)

pb

/

sr

·

^P0

cos

θ

^∗

+ (

9

.

5

±

7

.

4

)

pb

/

sr

·

P2

cos

θ

^∗

.

(7)

Here, the twocoeﬃcients are stronglycorrelated withthecorre- lationparameter0.85,i.e. thereadershould notinterpretthetwo contributionsasindependentresults.

Based on theﬁtresults aﬁrst estimate ofthe totalcross sec- tionofdd→⁴^He

γ γ

hasbeenextractedassumingahomogeneous 3-bodyphasespace.Itamountsto

σ

tot

= (

⁰

.

92

±

⁰

.

07stat

±

⁰

.

10sys

±

⁰

.

07norm

)

nb

.

(8) Itshouldbenotedthatthisresultdependsontheunderlyingmod- els forthereactionsdd→³^Hen

π

⁰ anddd→⁴^He

γ γ

.Thismodel dependenceisnotincludedinthegivensystematicerror.

5. Summaryandconclusions

In this letter results were presented for a measurement of the chargesymmetry breakingreactiondd→⁴^He

π

⁰ atan excess

(6)

energy of60 MeV. The energy dependence ofthe square of the productionamplitude mightindicate the on-set ofhigher partial wavesorsome unusualenergydependenceof thes-wave amplitude — given the current statistical error, no conclusion on the strength of the higher partial waves is possible from the differ- entialcrosssection.

However, since within chiral perturbation theory the leading andnext-to-leading p-wave contribution does not introduce any newfreeparameter(it isexpectedtobedominatedbytheDelta- isobar),thedataonthestrengthofhigherpartialwavespresented in this work will still provide a non-trivial constraint for future theoreticalanalyses.

The results presented hereare based on a two-week run using the standard WASA-at-COSY setup. Based on the experiences gainedduringthisexperimentanother8weekmeasurementwith amodiﬁeddetectorsetupoptimizedforatime-of-ﬂightmeasure- mentoftheforward goingejectiles hasbeenperformedrecently.

In total, an increase of statistics by nearly a factor of 10 and signiﬁcantlyreducedsystematicuncertainties canbe expected. In particular,the experimenthas beendesigned toprovide a better discriminationofbackgroundeventsfromdd→³^Hen

π

⁰.

Acknowledgements

Wewouldliketothankthetechnicalandadministrativestaffat theForschungszentrumJülich,especiallyattheCOolerSYnchrotron COSYandattheparticipatinginstitutes. Thisworkhasbeensup- portedin partby the German Federal Ministryof Education and Research(BMBF), the PolishMinistry ofScience andHigher Edu- cation(grantNos. NN202078135 andNN202285938),thePol- ishNational ScienceCenter (grant No.2011/01/B/ST2/00431), the Foundation For Polish Science (MPD), Forschungszentrum Jülich (COSY-FFE) and the European Union Seventh Framework Pro- gramme(FP7/2007–2013)undergrantagreementNo.283286.

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Charge symmetry breaking in $dd\rightarrow ^{4}He\pi ^{0}$ with WASA-at-COSY

Physics Letters B

Charge symmetry breaking in dd → 4 He π 0 with WASA-at-COSY

WASA-at-COSY Collaboration

P. Adlarson

, W. Augustyniak

, W. Bardan

, M. Bashkanov

, F.S. Bergmann

, M. Berłowski

, H. Bhatt

, A. Bondar

, M. Büscher

, H. Calén

, I. Ciepał

, H. Clement

, D. Coderre

, E. Czerwi ´nski

, K. Demmich

, E. Doroshkevich

, R. Engels

, A. Erven

, W. Erven

, W. Eyrich

, P. Fedorets

, K. Föhl

, K. Fransson

, F. Goldenbaum

, P. Goslawski

, A. Goswami

, K. Grigoryev

, C.-O. Gullström

, C. Hanhart

, F. Hauenstein

, L. Heijkenskjöld

, V. Hejny

, B. Höistad

, N. Hüsken

, L. Jarczyk

, T. Johansson

, B. Kamys

, G. Kemmerling

, F.A. Khan

, A. Khoukaz

,

D.A. Kirillov

, S. Kistryn

, H. Kleines

, B. Kłos

, W. Krzemie ´n

, P. Kulessa

, A. Kup´s ´c

, A. Kuzmin

, K. Lalwani

, D. Lersch

, B. Lorentz

, A. Magiera

, R. Maier

,

P. Marciniewski

, B. Maria ´nski

, M. Mikirtychiants

, H.-P. Morsch

, P. Moskal

, H. Ohm

, I. Ozerianska

, E. Perez del Rio

, N.M. Piskunov

, P. Podkopał

,

D. Prasuhn

, A. Pricking

, D. Pszczel

, K. Pysz

, A. Pyszniak

, C.F. Redmer

, J. Ritman

, A. Roy

, Z. Rudy

, S. Sawant

Charge symmetry breaking in dd → ⁴ ^He π ⁰ with WASA-at-COSY