Total and differential cross sections of $\eta$-production in proton-deuteron fusion for excess energies between $Q_{\eta} = 13$ MeV and $Q_{\eta} = 81$ MeV

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Physics Letters B

www.elsevier.com/locate/physletb

Total and differential cross sections of η -production in

proton–deuteron fusion for excess energies between Q _η = ^{13 MeV and} Q _η = ^{81 MeV}

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

, C. Wilkin

^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,UnitedKingdom eInstitutfürKernphysik,WestfälischeWilhelms-UniversitätMünster,Wilhelm-Klemm-Str.9,48149Münster,Germany

fHighEnergyPhysicsDepartment,NationalCentreforNuclearResearch,ul.Hoza69,00-681,Warsaw,Poland gBudkerInstituteofNuclearPhysicsofSBRAS,11akademikaLavrentievaprospect,Novosibirsk,630090,Russia hNovosibirskStateUniversity,2PirogovaStr.,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

qInstituteforTheoreticalandExperimentalPhysicsnamedafterA.I.AlikhanovofNationalResearchCentre“KurchatovInstitute”,25Bolshaya Cheremushkinskaya,Moscow,117218,Russia

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

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

*

Correspondingauthor.

E-mailaddress:n_hues02@uni-muenster.de(N. Hüsken).

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.2018.05.036

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

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

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

wDepartmentofPhysics,MalaviyaNationalInstituteofTechnologyJaipur,JLNMargJaipur302017,Rajasthan,India

xJARA-FAME,JülichAachenResearchAlliance,ForschungszentrumJülich,52425JülichandRWTHAachen,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 adPhysicsandAstronomyDepartment,UCL,GowerStreet,LondonWC1E6BT,UnitedKingdom

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

Articlehistory:

Received20January2018

Receivedinrevisedform23April2018 Accepted13May2018

Availableonline18May2018 Editor: V.Metag

Keywords:

Mesonproduction Proton–deuteroninteractions ηmeson

Newdataonbothtotalanddifferentialcrosssectionsoftheproductionofηmesonsinproton–deuteron fusionto³Heηintheexcessenergyregion13.6 MeV≤^Qη≤⁸⁰.9 MeV arepresented.Thesedatahave been obtainedwith the WASA-at-COSYdetectorsetup located atthe ForschungszentrumJülich, using aprotonbeamat15 differentbeammomentabetweenpp=¹.60 GeV/c andpp=¹.74 GeV/c.While significantstructureofthetotalcrosssectionisobservedintheenergyregion20 MeV^Qη^{60 MeV,} apreviouslyreportedsharpvariationaround Qη≈50 MeV cannotbeconfirmed.Angulardistributions show thetypicalforward-peakingthatwasnotedearlier.Forthefirsttime,it ispossibletostudythe developmentoftheseangulardistributionswithrisingexcessenergyoverawideinterval.

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

1. Introduction

The production of

η

mesons off nuclei has been a topic of active research overat leasttwo decades.Inspired by the attrac- tive interaction between

η

mesons and nuclei, first studied by Bhalerao, Haiderand Liu[1,2], extensiveexperimental effort was putinto the studyof near-thresholdproduction of

η

mesons off various nuclei. Although the original work suggested studies on heavier nuclei, already the

η

production off light nucleisuch as thedeuteron[3–6],³He or⁴He [7,8] revealedsignsofastrongfi- nalstate interaction.Thereaction pd→^3He

η

isone ofthemost discussed dueto its markedly enhanced cross section very close to the production threshold,a feature that can also be found in photoproduction of

η

mesons off ³He [9,10]. In proton–deuteron fusion,it was observed that theproduction crosssection

σ

rises fromzeroatthresholdtoaround400 nb within lessthan 1 MeV ofexcessenergy[11–14].Thiscuriousbehaviouroftheproduction crosssectionhasfirstbeendiscussedinthecontextofastrongfi- nalstateinteraction andthepresenceofapossible(quasi-)bound

η

³He stateclosetothethresholdin[15],whichwaslaterfollowed upon,e.g.,in[16,17].However,whiletheproductioncrosssection ofthereaction pd→^3He

η

hasbeenstudiedingreatdetail close tothreshold,athigher excessenergies theavailable databasebe- comessparse.MeasurementsbytheCELSIUS/WASA[18], COSY-11 [19] andANKE[20] groupsseemtosuggestacrosssectionplateau awayfromthreshold,whereasameasurementbytheGEMcollab- oration [21] yielded a larger cross section, albeit with a sizable uncertainty.

A sharp variation of the total cross section between Q η= 48.8 MeV and Q η=⁵⁹.8 MeV has recently been reported [22].

In order to investigate further the existence and cause of this cross section variation, a new measurement was performed at 15differentbeammomenta between pp=¹.60 GeV/c and pp= 1.74 GeV/c,usingtheexperimentalapparatusWASAattheCOoler SYnchrotronCOSY.Apartfromdeterminingthetotal crosssection of theproton–deuteron fusion to the ³He

η

final state, thefocus ofthe new measurement is onthe precise determination of dif- ferential cross sectionsand the studyof their development with

rising excessenergy. Such acomparisonbetweendifferential dis- tributions atdifferentexcessenergies hasthus farbeenhindered by large systematic differences between the individual measure- ments performed in the various experiments mentioned above.

For this reason, a consistent measurement over a wide range of higher excessenergies ina single experimentallows forthe first timeanin-depthstudyofthedependenceofthedifferentialcross section on the excess energy. High quality data are of great im- portancein ordertofacilitatetheoretical workon theproduction mechanismof

η

mesonsinproton–deuteronfusion,ashasrecently beenclaimedin[23].Uptonow,nomodelexiststhatmanagesto correctly reproduce thetotal anddifferential cross sectionsaway from the production threshold. While the two-step model, first studied by [24] in a classical framework and by [25] quantum- mechanically, hassome success indescribing near-thresholddata (see, e.g., [23,25]),at larger excess energies themodel no longer describestheavailabledata[26,27].

In [28], it was claimed that the GEM data can be adequately describedbyaresonancemodel,inwhich

η

mesonsareproduced fromthedecayofa N^∗ resonance.Suchamodelis,however,un- likely to have a large contribution closeto threshold due to the large momentumtransfernecessarytocompensateforthe

η

me- son mass. It remains to be seen ifthe production mechanismof thereaction pd→^3He

η

changeswithenergyand,ifso,why.Itis for thesereasonsthat in [23] newdata atlarger excess energies wereassessedtobeofhighpriority.

2. Experiment

The measurement was performed using the WASA detector setup(whichisdescribedindetailin[29])atthestorageringCOSY oftheForschungszentrumJülich.Utilizingtheso-calledsupercycle mode of thestorage ring,the momenta ofthe beamprotons are changedateachinjectionofanewprotonbunch.Eightbeamset- tings canbe storedatonceandthemeasurement wascomposed oftwosuchsupercycles(SC),eachcontainingtheeightbeammo- menta(flat-tops) indicatedinTable1.Intotal,datawere takenat 15 differentbeammomentabetween p_p=¹.60 GeV/c and p_p=

Table 1

Nominalbeammomentappforeachsupercycleandflat-topinGeV/c.

FT0 FT1 FT2 FT3 FT4 FT5 FT6 FT7

SC0 1.60 1.62 1.64 1.66 1.68 1.70 1.72 1.74 SC1 1.61 1.63 1.65 1.67 1.69 1.70 1.71 1.73

SC2 1.70

Fig. 1. Distributionofpolarangleθ3HeversuskineticenergyT3Heof³He candidates stoppedinthefirstlayeroftheWASAForwardRangeHodoscopefromthemea- surementat pp=1.70 GeV/c.Thegreylineshowsthekinematicalexpectationfor thereactionpd→³Heηatpp=1.70 GeV/c,whereasthecolourofthehistograms reflectsthenumberofreconstructed³He nuclei.(Forinterpretationofthecolours inthefigure(s),thereaderisreferredtothewebversionofthisarticle.)

1.74 GeV/c withamomentumspreadofaroundp/p=^10−3[30]

andastepsizeof10 MeV/c.Themeasurementatamomentumof pp=¹.70 GeV/c wasrepeatedinbothsupercyclesandinan ad- ditionalsingle-energy measurement for systematicchecks. Inside theWASACentralDetectorthebeamprotonsaresteeredtocollide withadeuterium pellet target.Due to thefixed-targetgeometry, heavy ejectiles like ³He are produced nearthe forward direction andsubsequentlystoppedinsidetheWASAForwardDetector.Here, usinga proportionalchamberandvariouslayersofplasticscintil- lator,boththeproductionangles θ and

ϕ

,andtheenergydeposit offorward-going particles are reconstructed. Doubly-charged He- liumionscanbeefficientlyseparatedfromprotons,deuteronsand chargedpionsbytheirenergydeposit.Fromthedepositedenergy, thekinetic energyof³He nucleiisalsoevaluated,thus,incombi- nationwiththedeterminedscatteringangles,fullyreconstructing theirfour-momenta.

3. Dataanalysis

Foratwo-particlefinalstatesuchas³He

η

,thepolarangleθ³_He andthe kinetic energy T3He of the Helium nuclei are kinemati- cally correlated. Using this relation, the precise measurement of thepolarangleθ3He(θ3He≈⁰.2^◦)canbeexploitedtogiveavery accuratecalibration ofthereconstructed energy.Acomparisonof thetwo-dimensionaldistributionofθ3Heversus T3He betweenthe kinematicalexpectationforthesignalreactionpd→^3He

η

andthe dataobtainedatpp=¹.70 GeV/c canbefoundinFig.1.

Thereactionofinterestisidentifiedfromthespectraofthefi- nal state momentum of ³He nuclei in the centre-of-mass frame p^∗_3Heinamissing-massanalysis.Thus,noassumptiononthe

η

de- cayis made. Dividing thecosine ofthe centre-of-mass scattering anglecosθ_{η into}^∗ 100equallysizedbins,thefinalstatemomentum spectra are fitted by a background function, excluding the peak region.Here,thebackgroundisasumofMonteCarlo(MC)simu- lationsoftwo- andthree-pionproductionaswellasathirdorder polynomial, accounting both for other possible background reac-

Fig. 2. Exampleofabackgroundfittothefinalstatemomentumspectrumof³He nucleifor0.50≤cosθ_η^∗<0.52 at pp=1.70 GeV/c.Blacktriangleswithblacker- rorbarsrepresentmeasureddata,the bluedashedlinerepresentstheestimated background,greydownwardtriangleswithgreyerrorbarsshowthesamedata,sub- tractedbythebackgroundexpectation.Thebackgroundsubtractedsignalisfittedby adouble-Gaussian(greensolidline),whoseindividualcontributionsaredisplayed bydashedgreenlines.TheredhistogramshowsaMCsimulationofthesignalre- actionpd→³Heη.

tions anddeviationsfromsimplephasespacedistributions inthe caseofthethree-pionproduction.Thesimulationoftwo-pionpro- ductionwasperformedusingamodelincorporatingtheABCeffect and t-channeldouble-(1232) excitation, developed for[31]. An exampleofsuchafitcanbefoundinFig.2.

Inordertodeterminethesignal yieldinagivenbinincosθ_{η ,}^∗ the background subtracted data are summed over the interval p^∗η−³

σ

≤^p∗3He≤^p∗_η+³

σ

,where p^∗η and

σ

arethepositionand widthofthe signalpeak determined froma fitofan appropriate peakfunction tothebackgroundsubtracted data.Formostvalues ofcosθ_{η a}^∗ simpleGaussian ischosen.However, closetothemax- imumscatteringanglethebreak-upof ³He nucleiinthedetector leadstoasymmetricpeaks(seeFig.2)thatarefittedbyadouble- Gaussian.Inthesecases,peakpositionandwidthofthedominant signalcontributionareused.

Beforephysicallymeaningfulangulardistributionsareobtained, the signal yield needs to be corrected for the product of detec- toracceptanceandreconstructionefficiency,whichcanbederived fromMCsimulations.Incontrasttoearlierwork[22],anextension to theGEANT3 softwarepackage [32] providedby theauthors of [18] was used to simulatenuclear break-up of ³He nucleiin the scintillatormaterial.Inaddition,thepossibilitythattheinteraction occurson the evaporated target gasrather than thepellet target wasaccountedfor.

Simulations of the signal reaction pd→^3He

η

were first per- formedwithcosθ_{η equally}^∗ distributedoverall valuesfrom−^{1 to} +^{1.From thissetof}simulations,theproductofacceptancetimes reconstructionefficiencywascalculatedastheratioofthenumber ofeventsreconstructed ina binofcosθ_{η divided}^∗ by thenumber ofeventsthatweregeneratedinthatbin.However,onlyifthede- tectorresolutionwereperfectwouldthisratiodirectlycorrespond to the sought-after product of acceptanceand reconstruction ef- ficiency. Otherwise,the finite detectorresolution,in combination withasignal thatexhibitsa strongangulardependence,causesa binmigration effectin theopposite directionto theslope ofthe angulardistribution.Inaddition,thenuclearbreak-upintroducesa tendencyto reconstructthe ³He nuclei atslightlysmallerkinetic energies.Toaccountfortheseeffects,theacceptancecorrectionis doneinaniterativemanner.Forthis,theangulardistributionsob- servedindata,aftercorrectingfortheacceptancederivedfromthe

Fig. 3. Angulardistributionofthereactionpd→^3Heηat pp=¹.70 GeV/c.Black trianglesrepresentdata andthe bluelineapolynomialfitofthe typegivenin Eq. (1).Theshadedhistogramdisplaysthecorrespondingproductofacceptanceand reconstructionefficiencyineachbinincosθ_η^∗,withthescalebeingdisplayedonthe righthandaxis.Onlystatisticaluncertaintiesareshown.

MCsampleequallydistributedincosθ_{η ,}^∗ arefittedbyathirdorder polynomial

f

(

cos

θ

_η^∗

) =

^N0



1

+ α

cos

θ

_η^∗

+ β

^cos2

θ

_η^∗

+ γ

cos³

θ

_η^∗



.

(1)

These polynomials are subsequently used to generate a new set ofMC simulations withwhichtheproduct ofacceptanceandre- constructionefficiencycanagainbedetermined.Thisprocedureis repeateduntilconvergenceofallangulardistributions isreached.

Theangulardistribution,alongwiththeproductofacceptanceand reconstructionefficiencyofthesumofthethreemeasurementsat pp=¹.70 GeV/c,isdisplayedinFig.3.

4. Normalization

For the measurement presented here, the normalization was carriedoutintwo stages.Theluminosity ofthesumofthethree measurements at p_p =¹.70 GeV/c ( Q η =⁶¹.7 MeV) is deter- mined by comparing the integral over the fit to the ³He

η

an- gular distribution displayed in Fig. 3 and the value of the total cross section

σ

= (³⁸⁸.1±⁷.2stat.) nb (with an additional 15%

normalization uncertainty), measured by the ANKE collaboration at Q η=60 MeV [20]. The measurements at the 14 remaining beam momenta are then normalized relative to the luminosity derived for pp=¹.70 GeV/c using proton–deuteron elastic scat- tering.Withinexperimental uncertainties, datainourenergyand momentum-transferrange[33–37] suggestthatthe pd elasticdif- ferentialcrosssectiond

σ

/dt islargelyindependentoftheincident protonmomentum pp.Inaddition,asoneoftheobjectivesofthis new measurement is to examine the cross section variation ob- servedin[22],itisdesirabletouseanormalizationmethodthatis differentfromthesinglepionproductionpd→^3He

π

⁰usedthere.

Elastic pd scatteringcanbeidentifiedbydemandingcoincident chargedparticles inthe forward andcentral detector andstudy- ing their angles. Since the forward-going protons are minimum ionizing,a measurementoftheir energydepositdoesnot helpto determine their kinetic energy. A loose cut was first set on the azimuthal angles of the two tracks, 120^◦<|

ϕ

FD−

ϕ

CD|<240^◦, before comparing the polarangles of the two tracks.For a two- particlefinal state,the polarangles of both particlesare directly related and this connection is evident in Fig. 4a for data corre- sponding to quasi-free pd→^ppnspec and pd→^{pd. In the case} ofproton–deuteronelasticscattering,themomentum transfert is

Fig. 4. a) Pairsofpolaranglesofcoincidentallymeasuredchargedparticlesinthe forwardandcentraldetectors,comparedtothekinematicalexpectationsforquasi- elastic pd→ppnspecscattering(blackdottedline)and pd→pd elasticscattering (greyline). b) Projectionontotheminimumdistance d ofagivenpairofpolar anglestothekinematicrelationfor pd elasticscattering,fittedbyafourthorder polynomial(blueline). c) Distributionofpd elasticscatteringeventsasafunction ofthemomentumtransfert,fittedbyascaledfittotheliteraturedata.Thehis- togramrepresentstheproductofacceptanceandreconstructionefficiency.

calculatedfromtheprotonpolarangle.Inaddition,theminimum distanced tothekinematicexpectationfor pd elasticscatteringis calculatedforeachpairofmeasuredpolaranglesθFD andθCD.As seen fromFig.4b,thedistanced exhibitsa narrowpeak closeto d=^{0 formomentumtransfersintheregion0}.140(GeV/c)²≤ |^t|≤ 0.215(GeV/c)²ontopofastrongbackgroundcontributiondueto quasi-elasticproton–protonscattering.

After excluding the signal region, the background in d is fit- ted by a fourthorder polynomial and, after subtracting this, the acceptance-correctedeventyieldforproton–deuteronelasticscat- tering is determined asa function of |^t|^{for each beam momen-}

Fig. 5. Totalcrosssectionofthereactionpd→³Heη.Cyanstarsarefrom[11],blueboxesfrom[12],greyopentrianglesfrom[21],orangeopendiamondsfrom[18],dark purplefilledcirclesfrom[13],lightpurpleupwardfilledtrianglesfrom[19],blackdownwardfilledtrianglesfrom[14,20],andgreenopencirclesfrom[22].Fortheredfilled diamondsfromthepresentwork,theerrorbarsindicatethestatisticalpoint-to-pointuncertainty,redboxesindicatethestatisticalchain-to-pointuncertaintyrelativetothe fixedcrosssectionatQη=⁶¹.7 MeV andgreyboxesindicatethesystematicuncertainty.Inaddition,anormalizationuncertaintyof16.3% istobeunderstood.Similarly,the normalizationuncertaintiesoftheearlierdataarealsonotdisplayed.

Table 2

Totalcrosssectionofthereactionpd→^3Heη,includingstatistical point-to-pointuncertaintiesσstat^{P 2P},theuncertaintyofthewhole datasetrelativetothefixedpointat Qη=⁶¹.7 MeVσstat^{C 2P},and thesystematicuncertaintiesσ_sys^±.Thebehaviourofthesystem- aticuncertaintychangesdirectionatQη=61.7 MeV,asindicated bythesign.Inaddition,thereisanoverallnormalizationuncer- taintyof16.3%.

Qη in MeV

σ in nb

σ_stat^{P 2P} in nb

σ_stat^{C 2P} in nb

σ_sys⁻ in nb

σ_sys⁺ in nb

13.6(8) 300.3 6.5 3.4 −14.9 12.5

18.4(8) 292.2 5.8 3.3 −¹¹.8 11.0

23.2(8) 292.8 5.8 3.3 −¹⁰.3 9.8

28.0(8) 312.9 6.0 3.5 −⁸.1 9.3

32.9(8) 352.6 7.0 4.0 −⁷.3 8.9

37.7(8) 374.7 7.3 4.2 −4.3 8.0

42.5(8) 394.0 8.0 4.4 −3.7 6.7

47.3(8) 399.8 7.6 4.5 −2.8 5.1

52.1(8) 408.0 8.1 4.6 −².1 3.5

56.9(8) 392.7 7.2 4.4 −⁰.1 1.7

61.7(8) 388.1

66.5(8) 403.3 7.8 4.5 2.6 −¹.8

71.3(8) 412.0 8.4 4.6 2.8 −3.6

76.1(8) 402.5 7.7 4.5 3.3 −5.4

80.9(8) 408.7 7.9 4.6 2.3 −7.4

tum (see Fig. 4c). The combined database[33–37] can be fitted byd

σ

/dt=^exp(12.45−²⁷.24|^t|+²⁶.31|^t|²),wheret ismeasured in (GeV/c)² [38], and thisis scaled to the observed distribution dN/dt to determine the luminosity. There is good evidence that the pd elasticcrosssection d

σ

/dt islargelyindependentofbeam momentuminourkinematicregion[39].Inthiscasetherelative luminosityattwodifferentmomentaisdirectlygivenbytheratio ofthetwoscalingfactors.

5. Results

Our total cross sections at all 15 excess energies are given in Table 2 and displayed in Fig. 5, where they are compared to the data available in the literature. Since the cross section at Q η=⁶¹.7 MeV isfixedtotheANKEvalue[20],thestatisticalun- certainty ofour measurement atthat Q η must be considered as acollective uncertainty 

σ

_stat^{C 2P} ofour whole dataset.In the su- percyclemode, relative systematic effects,due to changes to the

experimental orenvironmentalconditions,can generallyberuled out.Acarefulstudyofthethreemeasurementsatp_p=¹.70 GeV/c shows no systematic changes between the data-taking periods.

Systematic effects due to inefficiencies are also largely canceled out in the relative normalization. Uncertainty relatedto the ³He break-upwasestimatedtobearound5% [18] butthisismuchre- ducedwhenusingarelativenormalization.

Two main sources ofsystematic uncertainty remain. The dis- tribution and density of evaporated target gas in the scattering chamber is not known to high precision. As a shift of the ver- tex along the beamaxis leads to a loss of information forlarge polarangles,variation ofdensityanddistribution inMonteCarlo simulationshasimplicationsonthegeometricalacceptance.These arelargerathigherQ η whenthemaximum³He productionangle is greater. Secondly, the assumption that the pd elastic scatter- ing cross section d

σ

/dt is constant as a function of the beam momentum, which is consistent with the precision of the avail- able data, has been tested in model calculations [40,41]. These suggest that the integrated cross section over 0.140 (GeV/c)²≤

|^t|≤⁰.215(GeV/c)² changes slightlybutlinearlywithbeammo- mentum. Relative to the value at p_p=¹.70 GeV/c, this would change the luminosity by ≈^{4% at p}p=¹.60 GeV/c and −^{2% at} pp=¹.74 GeV/c. Both these systematic uncertainties are asym- metric and Gaussian error propagation leads to the values of



σ

_sys⁻ and 

σ

_sys⁺ given in Table 2. Here, the sign in 

σ

_sys^± in- dicates the sign of the systematic uncertainty at the smallest energy. Due to the relative normalization, the systematic uncer- taintychangessignwhencrossingthereferencemomentum pp= 1.70 GeV/c.

Inaddition,theoverallnormalizationfactorfromthecompari- son ofthe Q η=⁶¹.7 MeV datawiththetotal crosssectionpub- lishedin[20] comeswithan uncertaintyof16.3%.Ofthis,15% is associatedwiththeliteraturecrosssectionandanadditional6.3%

uncertaintywas found whendifferentsubparts ofthedifferential crosssectionwereusedfornormalizationinsteadofthetotalcross section.These 16.3% are,however,irrelevantwhen discussingthe energydependenceofthetotalcrosssection.

From Fig. 5, it is apparent that the abrupt change in the to- tal cross section between 40 and 50 MeV, that was previously reported in[22], isnot confirmedby the present analysis. How- ever, by repeating the normalization procedure used in [22] on

Fig. 6. Differentialcrosssectionsofthereactionpd→³Heηat15excessenergies betweenQη=13.6 MeV andQη=80.9 MeV.Theblacklinerepresentsafitofa thirdorderpolynomialasgiveninEq. (1).Whereverpossible,earlierdataareshown forcomparison,usingthesamecolourcodeasinFig.5.Datafrom[21] areomitted duetotheirlargeuncertainties.

thepresentdata,itcouldbeshownthattheanomalousbehaviour wasduetoanincorrectassumptionregardingthedifferentialcross section for single pion production rather than an error in the measurementitself [42].Inreality thebackward crosssection for pd→^3He

π

⁰ hasaminimumintheenergyregionofinterestand thevariationwithenergyisverystrong [43].

Intheexcess energyinterval 20 MeVQ η^{60 MeV, the in-} creaseandsubsequentleveling offofthetotal crosssection, that was observedin[18,20], isalsoseen inthepresentwork. Itcan, however,bestudiedinalotmoredetailthanwaspreviouslypos- sible.

Thedifferential crosssectionsderived inthepresentworkare displayed inFig.6.Generally,the distributionsatall energies ex- hibittheforward-peakingthatwasobservedinotherexperiments, thoughthemaximaaretypically atcosθ≈⁰.7 ratherthan inthe forwarddirection. Dueto the largeamount ofdatagathered,the angular distributions as well as their energy dependence can be studied in unprecedented detail. At all energies, the differential cross sections can be well described by the third order polyno- mial of Eq. (1) and the valuesof thefit parameters are given in Tables 3–5. Theerror barsshownthere were discussedearlierin thissection.

The asymmetry parameter

α

isof special importance,as it is oftenused to study the interferencebetween s- and p-waves in thenear-thresholddata(see,e.g.,[14,16]),whichmightreflectthe influence of

η

-mesic states below threshold. In Fig. 7, the val-

Table 3

Valuesofthefit parameterN0ofEq. (1) atall15excess energies.

Qη in MeV

N0 in nb/sr

N0,stat in nb/sr

N⁻_0,sys in nb/sr

N₀⁺_,sys in nb/sr

13.6(8) 26.81 0.46 0.84 0.20

18.4(8) 26.22 0.40 0.54 0.15

23.2(8) 25.96 0.40 0.30 0.15

28.0(8) 27.72 0.44 0.17 0.10

32.9(8) 31.68 0.58 0.17 0.17

37.7(8) 33.78 0.64 0.21 0.51

42.5(8) 35.77 0.74 0.14 0.62

47.3(8) 36.29 0.71 0.14 0.72

52.1(8) 36.72 0.77 0.14 0.67

56.9(8) 35.49 0.67 0.14 0.84

61.7(8) 34.71 0.63 0.12 0.75

66.5(8) 35.68 0.72 0.13 0.96

71.3(8) 36.02 0.78 0.12 0.94

76.1(8) 35.03 0.70 0.13 0.97

80.9(8) 35.29 0.72 0.18 0.83

Table 4

ValuesofthefitparameterαofEq. (1) atall15ex- cessenergies.

Qηin MeV

α αstat αsys⁻ αsys⁺

13.6(8) 0.517 0.017 0.012 0.015 18.4(8) 0.619 0.014 0.009 0.018 23.2(8) 0.736 0.015 0.009 0.022 28.0(8) 0.804 0.014 0.011 0.023 32.9(8) 0.894 0.014 0.008 0.026 37.7(8) 0.948 0.013 0.010 0.023 42.5(8) 1.025 0.014 0.008 0.022 47.3(8) 1.054 0.013 0.008 0.026 52.1(8) 1.101 0.013 0.009 0.027 56.9(8) 1.118 0.013 0.007 0.022 61.7(8) 1.183 0.008 0.009 0.023 66.5(8) 1.253 0.014 0.009 0.022 71.3(8) 1.257 0.014 0.008 0.017 76.1(8) 1.285 0.014 0.008 0.020 80.9(8) 1.306 0.015 0.008 0.017

Table 5

Valuesofthefitparametersβandγofthefunction givenEq. (1) atall15excessenergies.Systematicun- certaintiesomittedherecanbefoundin[42].

Qηin MeV

β βstat γ γstat

13.6(8) −0.326 0.016 −0.098 0.041 18.4(8) −0.339 0.012 −0.180 0.028 23.2(8) −⁰.307 0.012 −⁰.213 0.030 28.0(8) −⁰.305 0.012 −⁰.255 0.028 32.9(8) −⁰.343 0.011 −⁰.296 0.027 37.7(8) −⁰.352 0.011 −⁰.356 0.026 42.5(8) −0.371 0.011 −0.463 0.026 47.3(8) −0.370 0.010 −0.438 0.024 52.1(8) −0.347 0.011 −0.480 0.025 56.9(8) −⁰.358 0.010 −⁰.511 0.024 61.7(8) −⁰.331 0.010 −⁰.560 0.016 66.5(8) −⁰.302 0.011 −⁰.652 0.026 71.3(8) −⁰.269 0.012 −⁰.599 0.027 76.1(8) −0.257 0.012 −0.624 0.029 80.9(8) −0.235 0.013 −0.605 0.031

ues at the three lowest energies of the present work are com- pared to published asymmetry parameters [14,20,13]. The agree- mentwiththehighervaluesfromCOSY-11 [13] mightbeslightly preferred comparedto the ANKEresults [14]. TheANKE value at Q η=¹⁹.5 MeV isinstrongconflicttothefindingsreportedhere, but, asalready argued in [20], the inclusion of this point into a