Charge symmetry breaking in dd -> He-4 pi(0) with WASA-at-COSY

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

a_{DivisionofNuclearPhysics,DepartmentofPhysicsandAstronomy,UppsalaUniversity,Box516,75120Uppsala,Sweden} b_{DepartmentofNuclearPhysics,NationalCentreforNuclearResearch,ul.Hoza69,00-681,Warsaw,Poland}

c_{InstituteofPhysics,JagiellonianUniversity,ul.Reymonta4,30-059Kraków,Poland}

d_{PhysikalischesInstitut,Eberhard-Karls-UniversitätTübingen,AufderMorgenstelle14,72076Tübingen,Germany}

e_{KeplerCenterforAstroandParticlePhysics,EberhardKarlsUniversityTübingen,AufderMorgenstelle14,72076Tübingen,Germany} f_{InstitutfürKernphysik,WestfälischeWilhelms-UniversitätMünster,Wilhelm-Klemm-Str.9,48149Münster,Germany}

g_{HighEnergyPhysicsDepartment,NationalCentreforNuclearResearch,ul.Hoza69,00-681,Warsaw,Poland} h_{DepartmentofPhysics,IndianInstituteofTechnologyBombay,Powai,Mumbai,400076,Maharashtra,India} i_{BudkerInstituteofNuclearPhysicsofSBRAS,11akademikaLavrentievaprospect,Novosibirsk,630090,Russia} j_{NovosibirskStateUniversity,2PirogovaSt.,Novosibirsk,630090,Russia}

k_{InstitutfürKernphysik,ForschungszentrumJülich,52425Jülich,Germany} l_{JülichCenterforHadronPhysics,ForschungszentrumJülich,52425Jülich,Germany}

m_{InstitutfürExperimentalphysikI,Ruhr-UniversitätBochum,Universitätsstr.150,44780Bochum,Germany} n_{ZentralinstitutfürEngineering,ElektronikundAnalytik,ForschungszentrumJülich,52425Jülich,Germany}

o_{PhysikalischesInstitut,Friedrich-Alexander-UniversitätErlangen–Nürnberg,Erwin-Rommel-Str.1,91058Erlangen,Germany}

p_{InstituteforTheoreticalandExperimentalPhysics,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/©2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/3.0/).Fundedby SCOAP3_.

q_{II.PhysikalischesInstitut,Justus-Liebig-UniversitätGießen,Heinrich-Buff-Ring16,35392Giessen,Germany} r_{DepartmentofPhysics,IndianInstituteofTechnologyIndore,KhandwaRoad,Indore,452017,MadhyaPradesh,India} s_{HighEnergyPhysicsDivision,PetersburgNuclearPhysicsInstitute,OrlovaRosha2,Gatchina,Leningraddistrict188300,Russia} t_{InstituteforAdvancedSimulation,ForschungszentrumJülich,52425Jülich,Germany}

u_{VekslerandBaldinLaboratoryofHighEnergy Physics,JointInstituteforNuclearPhysics,Joliot-Curie6,141980Dubna,Moscowregion,Russia} v_{AugustChełkowskiInstituteofPhysics,UniversityofSilesia,Uniwersytecka4,40-007,Katowice,Poland}

w_{TheHenrykNiewodnicza´nskiInstituteofNuclearPhysics,PolishAcademyofSciences,152RadzikowskiegoSt,31-342Kraków,Poland} x_{DzhelepovLaboratoryofNuclearProblems,JointInstituteforNuclearPhysics,Joliot-Curie6,141980Dubna,Moscowregion,Russia} y_{HighEnergyAcceleratorResearchOrganization KEK,Tsukuba,Ibaraki305-0801,Japan}

z_{DepartmentofCosmicRayPhysics,NationalCentreforNuclearResearch,ul.Uniwersytecka5,90-950Łód´z,Poland}

a

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t

i

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l

e

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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→4He

π

0_{have been extendedtowards higher}

excessenergiesinordertoprovideinformation onthecontributionof p-waves inthefinalstate. For this,anexclusivemeasurementhasbeencarriedoutatabeammomentumofpd=1.2 GeV/c usingthe

WASA-at-COSYfacility.Thetotalcrosssectionamountsto

σ

tot= (118±18stat±13sys±8ext)pb andfirst

dataonthedifferentialcrosssectionareconsistentwiths-wavepionproduction.

©2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (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,



Mqmpn,and, atleading order,isospin vi-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 symme-try isan isospin rotationby 180degrees that exchangesup and downquarks—asthepionmasstermis invariantunderthis ro-tation.Forthiscase, theimpactofsoftphotonshasbeenstudied systematically[7–11]andcanbecontrolled.Alreadyin1977 Wein-bergpredictedahugeeffect(upto30%differenceinthescattering lengthsfor p

π

0 _andn

_π

0_{)of CSBin}

_π

0_{N scattering [1](seealso}

Ref.[12] fortherecentextraction ofthesequantitiesfrompionic atomsdata).

8 _{Ignoringtinyeffectsinducedbytheelectro-weaksector.}

While the

π

0_{p scattering length might be measurable in}

po-larized neutralpion photoproductionvery near threshold[13], it isnotpossible tomeasurethen

π

0 _{channel. Asan alternative}

ac-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

→

4He

π

0 _{closetothereactionthreshold[16].}

ThefirstexperimentwasanalyzedusingChPTinRef.[17](see also Ref. [18]), where it was demonstrated that Af b

(

pn

→

d

π

0

)

isdirectly proportionalto



Mqmpn,while theeffectof

π

−

η

mix-ing, previously believedto completelydominate thisCSB observ-able [19], was shownto be subleading.The value for



Mqmpn ex-tractedturned outtobe consistentwithother,directcalculations of thispart based on dispersiveanalyses [2,20,21] andfrom lat-tice.SeeRef.[22]forthelatestreview.Inordertocross-check the systematicsandtoeventually reduce theuncertainties, additional experimentalinformationneedstobeanalyzed.

The first theoretical results for dd

→

4He

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

→

4He

π

0_{[26].Thus,aspartofaconsistentinvestigationofCSB}

inthetwonucleonsector,pn

→

d

π

0_anddd

_→

4_He

_π

0_shouldhelp

tofurtherconstraintherelevantCSBmechanisms.

Themainchallengeinthecalculationofdd

→

4He

π

0 _istoget

theoreticalcontrolovertheinitialstateinteractions:highaccuracy wave functions are needed fordd

→

4N in low partial waves at relativelyhighenergies.Oneprerequisitetocontrolthisisthe ear-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 lead-ing order in chiral perturbation theory this potential is known.

Fig. 1. Cumulativeprobabilitydistributionsfrom thekinematicfitusedforevent selectionplottedasprobabilityfor the4_{He hypothesisversus theprobabilityfor the} 3_{He hypothesis.Left:distributionforMonte-Carlosimulatedsignaleventsfordd→}4_Heπ0_{,middle:distributionforMonte-Carlosimulatedeventsfordd→}3_Henπ0_,right:

distributionfordataandtheappliedprobabilitycut.

Thus, a measurement of, for example, p-waves provides an ad-ditional, non-trivial test of our current understanding of isospin violation in hadronic systems. Future theoretical CSB studies for

dd

→

4He

π

0 _{can be based on recent developments in effective}

field theoriesforfew-nucleon systems[28] aswell asforthe re-actionN N

→

N N

π

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

Whiletheprevious measurementsofdd

→

4_He

_π

0 _closeto

re-action threshold were limited to the total cross section [16], in ordertoextractconstraintsonhigherpartialwavesanynew mea-surementathigherexcess energiesinadditionhastoprovide in-formation on the differential cross section. Forthis, an exclusive measurementdetecting the4_{He ejectile aswellasthetwo decay}

photonsofthe

π

0 _{hasbeen carriedout utilizingthe samesetup}

usedfordd

→

3Hen

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.The experi-mentalsetupandtriggerconditionswerethesameasdescribedin Ref.[27].

3. Dataanalysis

The basic analysis leading to eventsamples with one helium andtwophotonsinfinalstatefollowsthestrategyusedfordd

→

3_Hen

_π

0 _{outlinedinRef.[27].Comparedtothisreaction,however,}

the charge symmetry breaking reactiondd

→

4_He

_π

0 _{has a more}

thanfourordersofmagnitudesmallercrosssection.Theonlyother channelwith4He andtwophotonsinfinalstateisthedouble ra-diativecapturereactiondd

→

4He

γ γ

.The crosssectionsforboth reactionsarenotlargeenough toprovideavisualsignaturefor4He in thepreviously used



E–



E plots from the ForwardDetector. Thus, all 3_{He and} 4_{He candidatestogether withthe two photons}

havebeen testedagainst the hypotheses dd

→

4_He

_{γ γ}

_(“4_He

hy-pothesis”) anddd

→

3Hen

γ γ

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

Fig. 2. Missingmassplotforthereactiondd→4_{He X .Thedifferentcontributions}

fittedtothespectrumaredoubleradiativecapturedd→4_{Heγ γ (greendashed),}

thereactiondd→3_Henπ0 _{(bluedotted,added)andthesumofallcontributions}

includingthesignal(redsolid).

to leavea decisivemissing-mass plotandnot tointroducea fake

4_He

_π

0 _signal.

Forfinaleventclassificationthecumulativeprobabilities P

(χ

2

_,

n

.

d

.

f

.)

for the two hypotheses have been plotted as probability for the 4_{He hypothesis versus the probability for the} 3_He

hy-pothesis (see Fig. 1). The data (right plot) have been compared to Monte-Carlo generated samples of dd

→

4He

π

0 _{events (left}

plot) and dd

→

3Hen

π

0 _{events (middle plot). Events originating}

fromdd

→

4He

π

0_{populatethelowprobabilityregionforthe}3_He

hypothesis andform a uniformdistribution forthe 4He hypoth-esis. 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,buthasbeenoptimizedby maxi-mizingthestatisticalsignificanceofthe

π

0 _{signalinfinalmissing}

mass plot.In addition,ithasbeen checkedthatthe resultis sta-blewithinthestatisticalerrorsagainstvariationsoftheprobability cut. For the simulations the standard Geant3 [34] based WASA Monte-Carlopackagehasbeenused,whichincludesthefull detec-torsetupandwhichhasalreadybeenbenchmarkedagainstawide rangeofreactionsfromtheWASA-at-COSYphysicsprogram.After thisanalysisstepthecontributionfrommisidentified3He was re-ducedbyaboutfourordersofmagnitude.

In a next step, the resulting four momenta based on the fit hypothesis dd

→

4He

γ γ

havebeenusedto calculatethemissing massmX indd

→

4He X asafunctionofthe center-of-mass scat-teringangle

θ

∗ ofthe particle X .

Fig. 2

showsapeakatthepion

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-tractedbyfittingalinearcombinationofthecorresponding Monte-Carlogeneratedhigh-statisticstemplatedistributionsforthethree reactions

•

dd

→

4_He

_{γ γ}

_{(double radiative capture) using 3-body phase}

space(greendashed),plus

•

dd

→

3Hen

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).

Pleasenotethatin

Fig. 2

aswell asin

Fig. 3

thecumulated 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

≤

cos

θ

∗

≤

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.The ef-fectisangulardependentandislargestatforwardangles.Possible

reasons are a mismatch in the actual beam momentum, a

dif-ferent amountof insensitive material inMonte-Carlo simulations compared totherealexperiment orsystematicdifferencesin the simulateddetectorresponsefor3He and4He —thelimited statis-ticsdidnot allowfora detailedstudyoftheoriginofthat effect. Thebackgroundstemmingfromdd

→

3_Hen

_π

0_{issensitivetothese}

effectsastheenergylossesfroma(true)3He ejectileareusedfor energyreconstruction of a (falselyidentified)4_{He.The mismatch}

canbe compensatedby introducinganangulardependentscaling factoronthemissingmassaxisforthe3_Hen

_π

0_{background,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

→

4He

γ γ

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

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 binsincos

θ

∗ together withthefitresult. Thechosenansatz pro-videsagood overalldescriptionofthe fulldataset.Any testsfor furthersystematiceffects(accordingtothedefinitioninRef.[35]), forexample concerningrateeffects andselection cutsin the ba-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 cross}

sec-tionsextractedfrom

Fig. 3

are

d

σ

d

Ω



−

0

.

85

≤

cos

θ

∗

≤ −

0

.

45



= (

17

.

1

±

3

.

8

±

4

.

0fit

)

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% for lu-minositydetermination and7% for the normalizationto external dataiscommontoall numbers.Integratingtheindividualresults, the (partial) total cross section within the detector acceptance amounts to

σ

_totacc

= (

94

±

14stat

±

10sys

±

6ext

)

pb (5)

withthesystematicerror originatingfromluminosity determina-tionandtheuncertaintyfromthedifferentfitmethods.The exter-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(see

Fig. 4

).Aconstantvalue couldbeinterpretedasadominatings-wave,butonehastokeep inmindthat theenergydependenceoftheformationofa4_{He in}

the4N finalstatemighthavesomeinfluencehere,too.

Fig. 5showsthedifferentialcrosssection.Duetotheidentical particlesintheinitialstate,oddandevenpartialwavesdonot in-terfereandthe angulardistribution issymmetric withrespectto cos

θ

∗

=

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

(

cos

θ

∗

)

and P2

(

cos

θ

∗

)

— although not excluding — doesnot show any

evi-denceforcontributionsofhigherpartialwaves:

Fig. 4. Energydependenceofthereactionamplitudesquared|A|2_{.Intheabsenceof}

initialandfinalstateinteractions aconstantamplitudewouldindicatethatonly s-waveis contributing.Theredfullcirclecorrespondstothetotalcross section giveninthetext.(Forinterpretationofthereferencestocolorinthisfigure leg-end,thereaderisreferredtothewebversionofthisarticle.)

Fig. 5. Differentialcrosssection.Theerrorsbarsshowthestatisticaluncertainties.In thefirstbintheadditionalsystematicuncertaintyfromthefithasbeenadded(see text).Thebluedashedlinerepresentsthetotalcrosssectiongiveninthetext as-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 withthe corre-lationparameter0.85,i.e. thereadershould notinterpretthetwo contributionsasindependentresults.

Based on thefitresults afirst estimate ofthe totalcross sec-tionofdd

→

4He

γ γ

hasbeenextractedassumingahomogeneous 3-bodyphasespace.Itamountsto

σ

tot

= (

0

.

92

±

0

.

07stat

±

0

.

10sys

±

0

.

07norm

)

nb

.

(8)

Itshouldbenotedthatthisresultdependsontheunderlying mod-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}

energy of60 MeV. The energy dependence ofthe square of the productionamplitude mightindicate the on-set ofhigher partial wavesorsome unusualenergydependenceof thes-wave ampli-tude — 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 isexpectedtobedominatedbythe Delta-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 us-ing the standard WASA-at-COSY setup. Based on the experiences gainedduringthisexperimentanother8weekmeasurementwith amodifieddetectorsetupoptimizedforatime-of-flight measure-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. Thisworkhasbeen sup-portedin partby the German Federal Ministryof Education and Research(BMBF), the PolishMinistry ofScience andHigher Edu-cation(grantNos. NN202078135 andNN202285938),the Pol-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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