Measurement of the $np\rightarrow np\pi^{0} \pi ^{0}$ reaction in search for the recently observed $d^{\ast}$ (2380) resonance

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Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Measurement of the np → ^np π ⁰ π ⁰ reaction in search for the recently observed d ^∗ ( 2380 ) resonance

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

, 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

, 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^,^y

, 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

, G.J. Wagner

^d

, M. Wolke

^a

, A. Wro ´nska

^c

, P. Wüstner

ⁿ^,^l

,

P. Wurm

^k^,^l

, A. Yamamoto

^z

, J. Zabierowski

^aa

, 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.Hoza 69,00-681,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,2PirogovaStr.,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

*

Correspondingauthor.

E-mailaddress:heinz.clement@uni-tuebingen.de(H. Clement).

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

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

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

4 Presentaddress:AlbertEinsteinCenterforFundamentalPhysics,UniversitätBern,Sidlerstrasse 5,3012Bern,Switzerland.

5 Presentaddress:III. PhysikalischesInstitut B,Physikzentrum,RWTHAachen,52056Aachen,Germany.

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

http://dx.doi.org/10.1016/j.physletb.2015.02.067

0370-2693/©²⁰¹⁵^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

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Articlehistory:

Received9September2014

Receivedinrevisedform29January2015 Accepted27February2015

Availableonline3March2015 Editor: V.Metag

Keywords:

Two-pionproduction

ABCeffectandresonancestructure Dibaryonresonance

Exclusivemeasurementsofthequasi-freenp→^npπ⁰π⁰reactionhavebeenperformedbymeansofdp collisionsatTd=².27 GeV usingtheWASAdetectorsetupatCOSY.Totalanddifferentialcrosssections have been obtained covering the energy region √

s= (².35–2.46) GeV, which includes the regionof the ABC effectand itsassociated d^∗(2380)resonance. Addingthe d^∗ resonance amplitudetothat for theconventionalprocessesleadstoareasonabledescriptionofthedata.Theobservedresonanceeffect inthetotalcrosssectionisinagreementwiththepredictionsofFäldtand Wilkinas wellwiththose of Albadajedo and Oset.The ABC effect, i.e. the low-massenhancement in the π⁰π⁰-invariant mass spectrum, isfoundto beverymodest–ifpresentatall,whichmightposeaproblemtosomeofits interpretations.

©²⁰¹⁵^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Recentdata onthe basicdouble-pionicfusion reactions pn→ d

π

⁰

π

⁰ and pn→^d

π

⁺

π

⁻demonstratethattheso-calledABCef- fectistightlycorrelatedwithanarrowresonancestructureinthe totalcrosssectionofthesereactions[1–3].TheABCeffectdenoting ahugelow-massenhancementinthe

π π

invariantmassspectrum is observed to occur, if the initial nucleons or light nuclei fuse toa bound final nuclearsystemand iftheproduced pionpairis isoscalar.TheeffecthasbeennamedaftertheinitialsofAbashian, BoothandCrowe,who firstobserveditinthe inclusivemeasure- mentofthepd→³HeX reactionmorethanfiftyyearsago[4].

TheresonancestructurewithI(J^P)=⁰(3⁺)[1]observedinthe pn→^d

π π

totalcrosssectionat√

s≈².38 GeV issituatedabout 80MeV below√

s=^2m, thepeak position ofthe conventional t-channel process, which is also observed in this reaction.

The resonance structure has a width of only 70 MeV, which is about three times narrower than the conventional process. Nev- ertheless, from the Dalitz plotof the pn→^d

π

⁰

π

⁰ reaction it is concludedthat thisresonance decaysviatheintermediate ⁺⁰ system(atleastpredominantly) intoits ﬁnal d

π

⁰

π

⁰ state.Inthe pn→^pp

π

⁰

π

⁻ reaction the resonance has been sensed, too [5], though in this case, there is no ABC effect associated with the resonance. In consequence it has no longer be called ABC resonance, butd^∗ – adopting the notation of thepredicted so-called

“inevitabledibaryon”[6]withidenticalquantumnumbers.

Bysubsequentquasifreepolarizednp scatteringmeasurements, it has been demonstrated that there is a resonance pole in the coupled³D3–³G3partialwavescorrespondingtothed^∗ resonance structureinmass,widthandquantumnumbers[7,8]–supporting thusitss-channelcharacter.

Ifthescenarioofas-channelresonanceinthenp systemiscor- rect, then also thenp→^np

π

⁰

π

⁰ reaction should be affected by thisresonance, since thischannel may proceed via the samein- termediate⁰⁺systemasthenp→^d

π

⁰

π

⁰ andpn→^pp

π

⁰

π

⁻

reactions do.From a simple isospinpoint ofview we expectthe resonance effect in the np

π

⁰

π

⁰ system to be identical in size to that in the d

π

⁰

π

⁰ system. From more reﬁned estimates in

Refs. [9,10],whichaccountalsofordifferencesinphasespace, we expect the resonance effect in the np

π

⁰

π

⁰ channel to be about 85% ofthat inthed

π

⁰

π

⁰ system. Sincethepeakresonancecross section inthelatteris270 μb[3]sittinguponbackgrounddueto conventionalt-channelRoperandexcitations,weestimatethe peak resonance contribution in thenp

π

⁰

π

⁰ systemto be in the orderof200 μb.

2. Experiment

Since there exist no data at all for the np→^np

π

⁰

π

⁰ channel, we have investigated this reaction experimentally with the WASA detector at COSY (FZ Jülich) by using a deuteron beam with an energy of Td=².27 GeV impinging on a hydrogen pel- let target [11,12]. By exploiting the quasi-free scattering process dp→^np

π

⁰

π

⁰₊pspectator, we coverthe full energy range of the conjectured resonance. In addition, the quasi-free process in in- verse kinematics gives usthe opportunity to detect alsothe fast spectatorprotonintheforwarddetectorofWASA.

The hardware triggerutilizedin thisanalysisrequiredatleast two chargedhits inthe forward detector aswell as two neutral hitsinthecentraldetector.

The quasi-free reactiondp→^np

π

⁰

π

⁰+^pspectator hasbeense- lectedintheoﬄineanalysisbyrequiringtwoprotontracksinthe forwarddetectoraswellasfourphotonhitsinthecentraldetec- tor, which can be traced back to the decay of two

π

⁰ particles.

Thatway,thenon-measuredneutronfour-momentumcouldbere- constructed by a kinematicﬁt withthreeover-constraints, which derive fromthe conditions forenergy andmomentum conserva- tion andthe

π

⁰ mass. The achievedresolution in √

s was about 20MeV.

Forthe reconstructionofthe two

π

⁰ particles out ofthefour

γ

quanta,allcombinationshavebeenconsideredandtheoptimal combination has been chosen, where both of the reconstructed

γ γ

-invariant masses Mγ γ are closest to the nominal

π

⁰ mass.

For all selected events this leads to a narrow peak in the two- dimensional plotof Mγ γ versus Mγ γ ,see,e.g. Fig. 2 inRef.[13]

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Fig. 1. Plotofthe energylossElayer 4ofparticlesinlayer4ofthesegmented RangeHodoscope versus thatin layer 5(Elayer 5).The bands ofstopped and punch-throughprotonsanddeuteronsareindicated.

andFig. 3inRef.[14].Withthisprocedurethecombinatorialback- groundisverysmall,intheorderofafewpercent.

ThechargedparticlesregisteredinthesegmentedForwardDe- tector of WASAare identiﬁed by useof the E−^{E energy} ^loss method.Forits applicationin thedata analysis, all combinations ofsignalsstemmingfromtheﬁvelayersoftheForwardRangeHo- doscope are used. As an example, Fig. 1 shows the plot of the energy loss in layer 4 versus that in layer 5. As can be seen, deuteronsandprotonscanbewellseparatedingeneral.

Adiﬃcultyemerges fromdeuterons,which originatefromthe np→^d

π

⁰

π

⁰ reactionandwhichpartlyalsobreakupwhilepass- ing the detector. Since in the energyloss plots used for particle identiﬁcationprotonanddeuteronbandsdohavesome smallbut ﬁniteoverlaps,deuteronscannot beseparatedcompletelyfromnp pairsstemmingfromthenp→^np

π

⁰

π

⁰ reaction.Tosuppresssuch misidentiﬁed eventswe requirethe angle betweenemitted neu- tronandprotontobelargerthanﬁvedegreesandalsotheirener- giestobeintheexpectedrange.Nevertheless,aMonteCarlo(MC) simulationof thenp→^d

π

⁰

π

⁰ reaction,which is known experi- mentallyand alsocan be modeled very well [1], showsthat we havetoexpect stillacontamination ofabout5% inthespectraof

Fig. 2. Eﬃciencycorrecteddistribution ofthe spectatorproton momentain the dp→npπ⁰π⁰+pspectatorreactionwithintheWASAacceptance,whichallowsthe detectionofthespectatorprotononlyforlabangleslargerthanthreedegrees.In addition,theconstraintforthesuppressionofbreakupeventshasbeenapplied(see text).Dataaregivenbysolid circles.Thehatchedhistogram (visibleatthe bot- tomoftheﬁgure)givestheestimatedsystematicuncertaintyduetotheincomplete coverageofthesolidangle.Thesolidlineshowstheexpecteddistributionforthe quasifreeprocessbasedontheCDBonnpotential[15]deuteronwavefunction.For comparison,thedashedlinegivesthepurephase-spacedistributionasexpectedfor acoherentreactionprocess.

thenp→^np

π

⁰

π

⁰ reaction.InFigs. 2–7theobservablesareshown with the MC-generated contamination events alreadysubtracted.

Inthe pn invariant-massspectrum Mpn,wherethecontamination showsupmostpronounced, thisconcerns onlytheﬁrst twobins (Fig. 7).

In Fig. 2, the measured eﬃciency and acceptance corrected spectatormomentum distributionisshownin comparisonwitha MC simulationof thequasifree dp→^np

π

⁰

π

⁰₊pspectator process.

Duetothebeam-pipe,ejectilescanonlybedetectedintheWASA forwarddetectorforlabangleslargerthanthreedegrees.Thegood agreementbetweendataandsimulationprovides conﬁdencethat the dataindeedreﬂect aquasifree process. Systematicuncertain-

Fig. 3. (Coloronline.) Totalcrosssectionsforthereactionspp→ppπ⁰π⁰(left)andnp→npπ⁰π⁰(right).Theresultsofthisworkareshownbythefullcirclesintheright ﬁgure.Statisticalandsystematicuncertainties(Table 1)aresmallerthanthesymbolsize.Theuncertaintyintheabsolutenormalizationintheorderof20%isnotshown.

PreviousWASAresultsontheppπ⁰π⁰channelareshownbyfullcircles[18]andfullsquare[14],respectively,intheleftﬁgure,previousbubble-chambermeasurements fromKEK[16]byopencircles.ThemodiﬁedValenciamodelcalculationisshownbythesolidlines.Thedash-dottedcurveshowstheresult,ifthes-channeld^∗resonance amplitudeisadded.Thed^∗contributionitselfisgivenbythedottedcurve.

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Fig. 4. (Coloronline.) Distributionsofthec.m.angles^cp^.^m^. (top)and ^c_π^.^m0^. (bottom)forthepn→^npπ⁰π⁰reactionatTn=¹.135 GeV.Sincethedataareshown withoutseparationinto√

s bins,theycorrespondtotheaverageovertheenergyre- gioncoveredbythequasifreecollisionprocess,whichis2.35 GeV<√

s<2.41 GeV (1.07 GeV<Tn<1.23 GeV).Filledcirclesrepresenttheexperimentalresultsofthis work.Thehatchedhistogramsgiveestimatedsystematicuncertaintiesduetothe incompletecoverageofthesolidangle.Theshadedareasdenotephase-space distributions.ThesolidlinesarecalculationswiththemodiﬁedValenciamodel.The dashed(dash-dotted)linesshowstheresult,ifthed^∗ resonanceamplitudewith (without)inclusionofthevertexfunction[1]isadded.Notethatinthebot- tompaneldashedanddash-dottedcurvesliepracticallyontopofeachother.All calculationsarenormalizedinareatothedata.

ties dueto eﬃciency andacceptance corrections are very small.

Theyareshownashatchedhistogram,barelyvisibleatthebottom lineofFig. 2.Theconstraintforthesuppressionofbreakupevents (see above) causes the maximumaccepted spectator momentum to be < 0.14GeV/cfulﬁlling the spectator momentum condition used in previous works [1,3,7]. This implies an energy range of 2.35GeV≤√

s≤^2.41^GeV^being^covered^due^to^the^Fermi^motion ofthenucleonsinthedeuteron.Thisenergyrangecorrespondsto incidentlabenergiesof1.07GeV<T_n<1.23GeV.

Intotalasampleofabout24 000goodeventshasbeenselected.

The requirement that the two protons have to be in the angular rangecovered by the forward detectorand that the gammas resulting from

π

⁰ decay have to be in the angular rangeof the central detector reducesthe overall acceptanceto about 7%. The total reconstruction efficiency including all cuts and kinematical fittinghasbeenabout 1%.Efficiencyandacceptancecorrectionsof thedatahavebeenperformedbyMCsimulationsofreactionpro- cessanddetectorsetup.FortheMCsimulationsmodeldescriptions havebeenused,whichwillbediscussedinthenextchapter.Since WASAdoesnot coverthefull reactionphase space,albeit alarge

Fig. 5. (Coloronline.) SameasFig. 4butforthedistributionsoftheinvariantmasses Mpπ⁰(top)andMnπ⁰ (bottom).

fraction of it, the corrections are not fully model independent.

The hatched grey histogramsin Figs. 2,4–7 give an estimate for systematic uncertainties due to theuse of differentmodels with andwithoutd^∗ resonancehypothesisfortheeﬃciencycorrection.

Comparedtotheuncertaintiesinthesecorrections,systematicer- rors associated withmodeling the reconstruction of particles are negligible.

The absolute normalization of the data has been performed by the simultaneous measurement of the quasi-free single pion production process dp→^pp

π

⁰+ⁿspectator and its comparison to previous bubble-chamberresultsforthe pp→^pp

π

⁰ reaction[16, 17].Thatway,theuncertaintyintheabsolutenormalizationofour dataisessentiallythatoftheprevious pp→pp

π

⁰ data,i.e. inthe orderof 20%.

3. Resultsanddiscussion

Inordertodeterminetheenergydependenceofthetotalcross sectionwe havedividedourdatasampleinto10MeVbinsin√

s.

Theresultingtotalcrosssectionstogetherwiththeirstatisticaland systematicuncertaintiesarelistedinTable 1.

Fig. 3exhibitstheenergydependenceofthetotalcrosssection forthenp→^np

π

⁰

π

⁰reaction(right)incomparisontothatofthe pp→^pp

π

⁰

π

⁰ reaction (left). The previous WASAresults [18,14]

and theones ofthis work aregiven by the full circles.They are compared to previous bubble-chamber measurements from KEK (opencircles)[16]incaseofthe pp

π

⁰

π

⁰ channel.

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Fig. 6. (Coloronline.) SameasFig. 4butforthedistributionsoftheinvariantmasses Mnπ⁰π⁰(top)andMpnπ⁰(bottom).

Incaseof thenp

π

⁰

π

⁰ channel, there existno dedicateddata fromprevious investigations. However, thereare some connected datafromthePINOTexperimentatSaclay,wheretheinclusivere- actions pp→

γ γ

X and pd→

γ γ

X were measured at Tp=¹.3 and1.5 GeV[19].Byexcludingthetwo-photoninvariantmassre- gions correspondingto single

π

⁰ or

η

production,the remaining two-photon events populating the combinatorial background are likelytooriginatefrom

π

⁰

π

⁰ production.Byusingthisfeature,a measureoftheratioofthecrosssectionspn→^pn

π

⁰

π

⁰+^d

π

⁰

π

⁰

to pp→^pp

π

⁰

π

⁰ has beenobtained. This leads to a crude estimate for the pn→^pn

π

⁰

π

⁰ cross section to be larger than the pp→^pp

π

⁰

π

⁰ crosssectionbyroughlyafactoroftwo–inquali- tativesupportofourresultsfromtheexclusivemeasurements[20].

InFig. 3,wecomparethedatatotheoreticalcalculationsinthe framework of the Valencia model [21], which incorporates both non-resonantandresonantt-channel processesfortwo-pionproduction in N N collisions. The t-channel resonance processes of interest hereconcern ﬁrst of all the excitation of the Roper resonance and its subsequent decay either directly into the N

π π

systemorviathe

π

systemaswellastheexcitationanddecayof the system. Deviatingfromthe originalValenciacalculations [21],thepresentcalculationshavebeentuned todescribequanti- tativelytheisovectortwo-pionproductionreactions pp→^{N N}

π π

[18],inparticularthepp

π

⁰

π

⁰[22]andnn

π

⁺

π

⁺[23]channelsby thefollowingmodiﬁcations:

•relativistic corrections for the propagator as given by Ref.[24],

Fig. 7. (Coloronline.) ThesameasFig. 4,butforthedistributionoftheinvariant massesM_π0π⁰(top)andMpn(middle).ThebottompanelshowstherawMpnspec- trumwithouteﬃciencyandacceptancecorrections.

• ^strongly ^reduced

ρ

-exchange contribution in the t-channel

process–inagreementwithcalculationsfromRef.[25],

• ^reduction ^of ^the ^N^∗→

π

amplitude by a factorof two in agreementwiththeanalysisofphoton- andpion-inducedpion productiononthenucleon[26]andinagreementwith pp→ pp

π

⁰

π

⁰andpp→^pp

π

⁺

π

⁻measurementsclosetothreshold [27–30] aswellasreadjustment ofthetotalRoper excitation according to the results of the isospin decomposition of the pp→^{N N}

π π

crosssections[18],

• înclusionôf^the^t-channel êxcitationôf^the(1600)P₃₃ resonance.

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The lattermodiﬁcation was necessary,in orderto account for theunexpectedlylargepp→ⁿⁿ

π

⁺

π

⁺crosssection[23].Thepre- dictive power of these modiﬁcations has been demonstrated by its successful applications to the recent pp→^pp

π

⁰

π

⁰ data at Tp=¹.4 GeV[14]andtothe pn→^pp

π

⁰

π

⁻reaction[5].

Finalstateinteraction(FSI)intheemittedN N systemhasbeen taken into account in the Migdal and Watson [31,32] factorized form.

The N N FSI is by far strongest in the isovector ¹S0 pn state andlessstrongin¹S0 pp and ³S1 pn statesasapparentfromthe scatteringlengthsin thesesystems.At energies above 1GeVthe t-channel process isthe dominatingone.Isospin decomposi- tionofitscontributiontothetotalnp→^np

π

⁰

π

⁰crosssection[33, 34,18]showsthatinthisprocess the¹S0 ﬁnal stateis muchless populatedthantheisoscalar³S1 state.Thesituationissomewhat differentinthenear-thresholdregion, wheretheRoperexcitation processdominates.Inthisprocess,equalamountsof pn pairsare emittedin¹S0and³S1 states.

SincethemodiﬁedValenciacalculationshavebeentunedtothe pp→^pp

π

⁰

π

⁰ reaction,itisnosurprisethatitstotalcrosssection is fairly well described – see left panel in Fig. 3.For the closely relatednp→^np

π

⁰

π

⁰ reaction, thecalculations predict a similar energydependence,butanabsolutecrosssection,whichislarger byroughlya factoroftwo–whereasthedataarelargerbymore thananorderofmagnitude–seeFig. 3,rightpanel.

As an independent check of these calculations we may per- formanisospindecompositionofcrosssectionsusingtheformulas giveninRefs. [33,34] andthe matrixelements deducedfromthe analysisofthe pp inducedtwo-pionproduction[18].Asan result ofsuchan exercisewegetagreementwiththemodiﬁed Valencia calculationwithinroughly 30%.

AsweseefromFig. 3,theexperimentalcrosssectionsobtained inthisworkforthenp→^np

π

⁰

π

⁰reactionarethreetofourtimes largerthanpredicted. Thisfailurepoints toanimportantreaction component not included in the t-channel treatment of two-pion production.Itisintriguingthat wedeal herewiththeenergyre- gionwherethe d^∗ resonancehasbeenobserved bothinnp scattering[7]andin theisoscalarpartofthedouble-pionicfusionto deuterium[1,3].Alsoithasbeenshownthatthedescriptionofthe pn→^pp

π

⁰

π

⁻ cross section improves greatly in this energyre- gion,ifthisresonanceisincluded[5].Henceweaddalsoherethe amplitudeofthisresonancetotheconventionalamplitude.Accord- ingtothepredictionsofFäldtandWilkin[9]aswellasAlbaladejo andOset[10],its contributionattheresonancemaximumshould beabout200 μb(dottedcurveinFig. 3)asdiscussedintheintro- duction.It isamazing,how well theresultingcurve (dash-dotted lineinFig. 3) describesthedata.Ofcourse,itisapitythatthere arenodataoutsidetheenergyregioncoveredbyourdata.Inpar- ticular at energies below 1 GeV and above 1.3 GeV, i.e. outside theresonanceregion,suchdatawouldbeveryhelpfultoexamine

entialobservables.Wechoosetoshowinthispaperthedifferential distributions forthe invariant masses Mπ⁰π⁰, Mpn, M_pπ⁰, M_nπ⁰, M_nπ⁰π⁰ andM_ppπ⁰ aswellasthedifferentialdistributionsforthe center-of-mass (cm) angles for protons and pions, namely ^c_p^.^m^. and^c^.^m^.

π⁰ .ThesedistributionsareshowninFigs. 4–7.

All measured differential distributions are markedly different in shape from pure phase-space distributions (shaded areas in Figs. 3–6), but close to the predictions both with (dashed and dash-dottedlines)andwithout(solidlines)inclusionofthed^∗ resonance.

Thepionangulardistribution(Fig. 4)behavesasexpectedfrom the p-wavedecayoftheresonance.Andalsotheprotonangu- lardistributionissimilarlycurved.Botht-channelmesonexchange andthe J^P=³⁺requirementford^∗ formationpredictcomparable shapesinagreementwiththedata.

TheinvariantmassspectraforM_pπ⁰,M_nπ⁰,M_nπ⁰π⁰ andM_pnπ⁰ (Figs. 5–6)arecharacterizedby and Ndynamicsastheynat- urally appearin the deexcitationprocess of an intermediate

system created either by d^∗ decay or via t-channel meson exchange.

The Mpn and Mπ⁰π⁰ spectra (Fig. 7) need a more thor- ough discussion. The data of the Mπ⁰π⁰ spectrum appear to be quite well described by the calculations, which hardly devi- ate from each other. At small invariant masses though, in the range 0.3–0.4 GeV/c², there is an indication of a small surplus of strength. Taken the uncertainties inherent in the data and in thetheoretical description,thesedeviationsappearnottobepar- ticularlysigniﬁcant.Therefore,ifthisconstitutesasignoftheABC effect, then it is obviously very small in this reaction. Note that contrarytothesituationinthe pn→^pp

π

⁰

π

⁻reaction,wherethe pion pair hasto be in relative p-waveand hencethe ABC-effect isabsent,thepionpairhereispreferentiallyinrelatives-waveal- lowingthus,inprinciple,theoccurrenceoftheABCeffect.Hence, the ﬁnding that there is no or nearly no ABC effect comes as a surpriseatleastforsomeofitsinterpretations–see,e.g. Ref.[35].

This ﬁndingis ofno surprise, ifthe ABC effectis described by a formfactor atthe vertexofthed^∗ decay[1].However, thena problem ariseswiththe description ofthe Mpn spectrum,as we discussinthefollowing.

The Mpn spectrum peaks sharply at its low-mass threshold, whichischaracteristicforastrongnp FSIasdiscussedabove.This low-mass peakingiswellaccountedforby themodiﬁed Valencia calculations(solidlinesinFigs. 4–7).Inclusionofthed^∗resonance as outlined in Ref. [1] (dashed lines) exaggerates the low-mass peakingdeterioratingthus theagreementwiththedata.The rea- son for this behavior is the formfactor at the decay vertex ofd^∗ introduced inRef. [1]forthedescription ofthe ABCeffect, i.e. thelow-massenhancementinthe M₍π π)⁰ spectraobservedin double-pionic fusion reactions. However, as already pointed out in Ref. [5], this formfactor acts only on the Mπ⁰π⁰ and Mπ⁺π⁻ spectra, ifthenucleon pairis boundin a ﬁnal nuclearsystem. If this is not the case, then the formfactor acts predominantly on

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theinvariant-massspectrumofthenucleonpair.Thisisillustrated bycomparisonofthecalculationsincludingd^∗ with(dashed) and without (dash-dotted)this formfactor. As we see,the formfactor hardly changes the Mπ⁰π⁰ distribution, but shuﬄes substantial strengthinthe M_pn spectrumto lowmasses–thusovershooting theobservedlow-massenhancement.

Unfortunately, also the model-dependence of the acceptance and efficiency corrections is largest near the low-mass threshold hampering thus a definite statement about a failure of the formfactoransatz. In ordertocircumvent thismodeldependence somewhat, we plotthe data inFig. 7, bottom, beforeacceptance andefficiencycorrections. The calculationsshown are nowgiven withintheacceptanceoftheWASAdetector.We seethat,firstof all, the corrections do not change the shape of the distribution profoundly,andsecondthatthecalculationswithformfactorover- shootthelow-masspeakinsimilarmannerasbefore,whereasthe calculationswithoutthisformfactoragreeagainwellwiththedata.

This overshooting indicates that the formfactor introduced in Ref.[1]onpurelyphenomenologicalgroundsforthedescriptionof theABC effect is possibly atvariance withthe data forisoscalar two-pionproductioninnon-fusionchannels.Hencealternativeso- lutionsfor thisphenomenon may haveto be looked for,such as d-wave contributionsintheintermediate systemand/or ﬁnal nucleon-pair[36,37].

Another alternative involving d-waves has been proposed recently by Platonova and Kukulin [35]. In their ansatz they as- sumethe d^∗ resonance not only to decayinto the d

π

⁰

π

⁰ chan- nelvia theroute d^∗→ ⁺⁰→^d

π

⁰

π

⁰,⁷ butalso via the route d^∗→^d

σ

_→d

π

⁰

π

⁰.Since

σ

is aspin zeroobject,ithasto bein relatived-waveto thedeuteroninthisdecayprocess,inorderto satisfythe resonancecondition of J^P = ³⁺^.^Inconsequencethe availablemomentum inthisdecayprocess isconcentrated inthe relativemotionbetweend and

σ

leavingthus onlysmallrelative momentabetweenthetwo emergingpions.Therefore the Mπ⁰π⁰ distributionisexpectedtobepeakedatlowmasses–i.e.,thelow- massenhancement(ABCeffect) inthismodelismadebythed

σ

decaybranch(intheamountofabout5%)andnotbyaformfactor asintroduced in Ref. [1]. The enhancement in thismodel is fur- therincreasedbyaninterferenceofthed

σ

decayamplitude with thedecayamplitude viathe⁺⁰ system. Itappearsstraightfor- ward to extend this ansatz also to reaction channels, where the np system is unbound. However, since we hardly observe a low- massenhancement(ABCeffect)intheMπ⁰π⁰ spectrum,muchless d^∗→^d

σ

contribution is needed here than in the pn→^d

π

⁰

π

⁰

reaction – which possibly poses a consistency problem for this ansatz[35].

Another point of concern with this ansatz is that mass and widthof the sigmameson havebeen ﬁtted to the pn→^d

π

⁰

π

⁰

data in Ref. [35] withthe resultthat mσ ≈300 MeV and σ ≈ 100 MeV. Both values are much smaller than the generally accepted values for the sigma meson [38], which are mσ = (400–550)MeV and σ= (^400–700)MeV.InRef.[35]ithasbeen arguedthat thesedeviations couldbe a signofchiral restoration inthehadronic/nuclearenvironment–inparticularwithinthesix- quark bag. However, anyevidence forthishypothesis fromother experiments is lacking so far. Whether the enhanced ABC effect observedinthedouble-pionic fusionto⁴He [39] isinsupportof suchanargumentationisanopenquestion.

7 Actuallytheyconsider thedecayd^∗→^D⁺⁺12π⁰→^dπ⁰π⁰ with D⁺⁺₁₂ beinga I(J^P)=1(2⁺)stateneartheNthreshold,butsincethepionemittedinthed^∗ decayisinrelativep-wavetoD12,thisrouteispracticallyindistinguishablefroma d^∗→ ⁺⁰decayatthegivenkinematicconditions.

4. Conclusions

The np→^np

π

⁰

π

⁰ reaction, for which no dedicated previous data exist, has been investigated by exclusive and kinematically complete measurements.Theyhavebeen carriedout inquasifree kinematics with a deuteron beamimpinging on a hydrogen pel- let target. Utilizing the nucleons’ Fermi motion in the deuteron projectile an energy region of 2.35 GeV<√

s<2.41 GeV could be covered corresponding to an incident lab energy range of 1.07–1.23 GeV.Thisenergyregioncoverstheregionofthed^∗resonance. Thedataareinagreement witha resonancecontribution ofabout200 μb,aspredictedbyFäldtandWilkin[9]aswellasby AlbaladejoandOset[10].Thed^∗ contributionisbyfarlargerthan that fromconventional processes. Calculations based on conventionalt-channelmesonexchangeunderpredictthedatabyfactors three to fourand inaddition are at variance withthe measured energydependenceofthetotalcrosssection.Thoughthosecalcu- lations havebeen tuned to two-pionproduction channels, where d^∗ doesnot contribute,they still mayhavesome inherent model dependence.But,evenifweassumetheassociateduncertaintyto beaslargeas 50%,westillarriveatanuncertaintyofonly15%for therequiredd^∗contribution,i.e. 200±^{30 μb.}

In general, the differential data are reasonably well described bycalculations,whichincludeboththed^∗ resonanceandthecon- ventionalt-channelprocesses.

Thedatadonot exhibitanysigniﬁcantlow-massenhancement (ABCeffect)inthe

π

⁰

π

⁰-invariantmassdistribution.Thoughthis is not in disagreement with the phenomenological ansatz of a formfactor at the d^∗→ ^decay ^vertex ^introduced ⁱⁿ ^Ref. ^[1], the worseningof thedescription ofthe Mpn spectrumby use of thisformfactor calls possibly foran improved explanation ofthe ABCeffectinconnectionwiththed^∗ resonance.

After having found evidences for the d^∗ resonance in the d

π

⁰

π

⁰, d

π

⁺

π

⁻ and pp

π

⁰

π

⁻ channels, the channel investigated here has been one of the two remaining two-pion production channels, wherethe predicted contributions of the d^∗ resonance hadnotyetbeencheckedexperimentally.Aswehaveshownnow, the datafor thenp

π

⁰

π

⁰ channel are consistent withthe d^∗ hy- pothesis andprovide an experimentally determined branching of about 12% for the d^∗ decay into thischannel. A preliminary list ofdecay branchesis giveninRef. [40],an update of whichis in preparation.

Sinced^∗ hasbeenobservedmeanwhilealsointheelasticchan- nelbypolarizednp scattering, theonlyremainingunexploredde- caychannelisnp

π

⁺

π

⁻.Thischannelhasbeenmeasuredrecently at HADES and preliminary results have been presented already at conferences [41–43]. It will be highly interesting, not only to obtain total cross sections for this channel, but also differential distributions. Of particular interest will be the Mpn and Mπ⁺π⁻ distributionsasdiscussedinthiswork.

Acknowledgements

We acknowledgevaluable discussions withV.Kukulin,E.Oset and C. Wilkin on this issue. We are particularly indebted to L. Alvarez-Ruso for using his code. This work has been sup- portedbyForschungszentrumJülich(COSY-FFE),DFG(CL214/3-1), the Foundation For Polish Science through the MPD programme and by the Polish National Science Centre through the Grants Nos. 2011/01/B/ST2/00431and2013/11/N/ST2/04152.

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Measurement of the $np\rightarrow np\pi^{0} \pi ^{0}$ reaction in search for the recently observed $d^{\ast}$ (2380) resonance

Physics Letters B

Measurement of the np → np π 0 π 0 reaction in search for the recently observed d ∗ ( 2380 ) resonance

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

, 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

, J. Ritman

, A. Roy

, Z. Rudy

, S. Sawant

, S. Schadmand

, T. Sefzick

, V. Serdyuk

, B. Shwartz

Measurement of the np → ^np π ⁰ π ⁰ reaction in search for the recently observed d ^∗ ( 2380 ) resonance