Sub-threshold production of $K_{s}^{0}$ mesons and $\Lambda$ hyperons in Au+Au collisions at $\sqrt{^{s}NN}=2,4 $ GeV

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Physics Letters B

www.elsevier.com/locate/physletb

Sub-threshold production of K ⁰ _s mesons and  hyperons in Au + ^Au collisions at √

s _NN = ² . 4 GeV

HADES Collaboration

J. Adamczewski-Musch

^d

, O. Arnold

^j,i

, C. Behnke

^h

, A. Belounnas

^p

, A. Belyaev

^g

, J.C. Berger-Chen

^j,i

, J. Biernat

^c

, A. Blanco

^b

, C. Blume

^h

, M. Böhmer

^j

, P. Bordalo

^b

,

S. Chernenko

^g,4

, L. Chlad

^q

, C. Deveaux

^k

, J. Dreyer

^f

, A. Dybczak

^c

, E. Epple

^j,i

, L. Fabbietti

^j,i

, O. Fateev

^g

, P. Filip

^a

, P. Fonte

^b,1

, C. Franco

^b

, J. Friese

^j

, I. Fröhlich

^h

, T. Galatyuk

^e,d

,

J.A. Garzón

^r

, R. Gernhäuser

^j

, M. Golubeva

^l

, R. Greifenhagen

^f,2

, F. Guber

^l

,

M. Gumberidze

^d,e

, S. Harabasz

^e,c

, T. Heinz

^d

, T. Hennino

^p

, S. Hlavac

^a

, C. Höhne

^k,d

, R. Holzmann

^d

, A. Ierusalimov

^g

, A. Ivashkin

^l

, B. Kämpfer

^f,2

, T. Karavicheva

^l

, B. Kardan

^h

, I. Koenig

^d

, W. Koenig

^d

, B.W. Kolb

^d

, G. Korcyl

^c

, G. Kornakov

^e

, R. Kotte

^f

, A. Kugler

^q

, T. Kunz

^j

, A. Kurepin

^l

, A. Kurilkin

^g

, P. Kurilkin

^g

, V. Ladygin

^g

, R. Lalik

^c

, K. Lapidus

^j,i

, A. Lebedev

^m

, L. Lopes

^b

, M. Lorenz

^h

, T. Mahmoud

^k

, L. Maier

^j

, A. Mangiarotti

^b

,

J. Markert

^d

, S. Maurus

^j

, V. Metag

^k

, J. Michel

^h

, D.M. Mihaylov

^j,i

, S. Morozov

^l,n

, C. Müntz

^h

, R. Münzer

^j,i

, L. Naumann

^f

, K. Nowakowski

^c

, M. Palka

^c

, Y. Parpottas

^o,3

, V. Pechenov

^d

, O. Pechenova

^d

, O. Petukhov

^l

, J. Pietraszko

^d

, W. Przygoda

^c

, S. Ramos

^b

, B. Ramstein

^p

, A. Reshetin

^l

, P. Rodriguez-Ramos

^q

, P. Rosier

^p

, A. Rost

^e

, A. Sadovsky

^l

, P. Salabura

^c

, T. Scheib

^h

, H. Schuldes

^h

, E. Schwab

^d

, F. Scozzi

^e,p

, F. Seck

^e

, P. Sellheim

^h

,

I. Selyuzhenkov

^d,n

, J. Siebenson

^j

, L. Silva

^b

, Yu.G. Sobolev

^q

, S. Spataro

^s

, S. Spies

^h

, H. Ströbele

^h

, J. Stroth

^h,d

, P. Strzempek

^c

, C. Sturm

^d

, O. Svoboda

^q

, M. Szala

^h

, P. Tlusty

^q

, M. Traxler

^d

, H. Tsertos

^o

, E. Usenko

^l

, V. Wagner

^q

, C. Wendisch

^d

, M.G. Wiebusch

^h

, J. Wirth

^j,i

, Y. Zanevsky

^g,4

, P. Zumbruch

^d

aInstituteofPhysics,SlovakAcademyofSciences,84228Bratislava,Slovakia

bLIP-LaboratóriodeInstrumentaçãoeFísicaExperimentaldePartículas,3004-516Coimbra,Portugal cSmoluchowskiInstituteofPhysics,JagiellonianUniversityofCracow,30-059Kraków,Poland dGSIHelmholtzzentrumfürSchwerionenforschungGmbH,64291Darmstadt,Germany eTechnischeUniversitätDarmstadt,64289Darmstadt,Germany

fInstitutfürStrahlenphysik,Helmholtz-ZentrumDresden-Rossendorf,01314Dresden,Germany gJointInstituteofNuclearResearch,141980Dubna,Russia

hInstitutfürKernphysik,Goethe-Universität,60438Frankfurt,Germany iExcellenceCluster‘OriginandStructureoftheUniverse’,85748Garching,Germany jPhysikDepartmentE62,TechnischeUniversitätMünchen,85748Garching,Germany kII.PhysikalischesInstitut,JustusLiebigUniversitätGiessen,35392Giessen,Germany lInstituteforNuclearResearch,RussianAcademyofScience,117312Moscow,Russia mInstituteofTheoreticalandExperimentalPhysics,117218Moscow,Russia

nNationalResearchNuclearUniversityMEPhI(MoscowEngineeringPhysicsInstitute),115409Moscow,Russia oDepartmentofPhysics,UniversityofCyprus,1678Nicosia,Cyprus

pInstitutdePhysiqueNucléaire,CNRS-IN2P3,Univ.Paris-Sud,UniversitéParis-Saclay,F-91406OrsayCedex,France qNuclearPhysicsInstitute,TheCzechAcademyofSciences,25068Rez,CzechRepublic

rLabCAF.F.Física,Univ.deSantiagodeCompostela,15706SantiagodeCompostela,Spain sDipartimentodiFisicaandINFN,UniversitàdiTorino,10125Torino,Italy

Y. Leifels

GSIHelmholtzzentrumfürSchwerionenforschungGmbH,64291Darmstadt,Germany

https://doi.org/10.1016/j.physletb.2019.03.065

0370-2693/©^{2019TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

Relativisticheavy-ioncollisions(HICs)provideauniqueoppor- tunity tostudymatter at2–3timesnuclear groundstate density (similar asexpected forneutron star mergers [1,2]) in the labo- ratory.Inparticular, kaonsand hyperonsare promisingprobes withrelevance forvariousastrophysicalprocesses[3–8].However, HICs are highly dynamical processes and therefore it is difficult to directly address fundamental aspects. Numerous works inves- tigated kaon production in HICs in the few-GeV energy regime in the past.Comparisons ofexperimental data (spectra andflow anisotropies)[9–13] totransport modelcalculationsseemto con- firm arepulsive K-Npotential [14–21],whichhas beenpredicted by various effective approaches. Furthermore,constraints for the equation-of-state(EOS)ofnuclearmatterhavebeendeducedfrom kaonproduction,undertheassumptionofenergyaccumulationin sequentialnucleon-nucleoncollisions,e.g.NN→ ^N[22–24].

DataonproductionfromHICsatlow energiesarescarce.At SIS18energies(1–2AGeV)onlydatafromsmallcollisionsystems are available [25,26].While the -nucleonpotential is knownto beattractiveatgroundstatedensitiesfromhypernucleiformation [27],itsdensitydependencethereforestillremainsvague[28].

Inthispaper,we reportthe firstobservationofK⁰_s andhy- peronsemittedfromcentralAu+^{Aucollisionsat}√

sNN=².4 GeV.

Both kaons and  hyperons are produced about 150 MeV be- low their free NN-threshold and hence are sensitive to the en- ergy dissipation in the collision system. We compare the scaling ofthe multiplicitiesasfunction ofthe centralityofthe collisions tothepreviouslypublished dataonchargedkaonsandφmesons [29] andthespectraandrapiditydistributionstopredictionsfrom threestate-of-the-artmicroscopictransportmodels(UrQMD,HSD, IQMD) [30–32].Based onthiswe discussthe validityof thepre- viouslydrawnconclusionsabouttheK-Npotentialandtheenergy dissipationduringthecollisioninlightofthenewdata.

The data have been collected with HADES, located at the GSI Helmholtz Center forHeavy Ion Researchin Darmstadt, Ger- many.HADES is acharged-particle detector consistingofa 6-coil toroidal magnet centered around the beam axis and six identi- cal detectionsections located betweenthe coils covering almost the full azimuthal angle. Each sector is equipped with a Ring- ImagingCherenkov(RICH)detectorfollowed byMini-Drift Cham- bers(MDCs),twoinfrontofandtwobehindthemagneticfield,as wellasascintillator hodoscope(TOF)andaResistivePlateCham- ber(RPC).Attheendofthesystemaforwardhodoscopeusedfor event plane determination is located. The RICH detector is used mainlyforelectron/positronidentification,theMDCsarethemain tracking detectors, while the TOF and RPC are used fortime-of- flightmeasurementsincombinationwithadiamondstart-detector

E-mailaddress:hades-info@gsi.de(J. Stroth).

1 AlsoatCoimbraPolytechnic–ISEC,Coimbra,Portugal.

2 AlsoatTechnischeUniversitätDresden,01062 Dresden,Germany.

3 AlsoatFrederickUniversity,1036 Nicosia,Cyprus.

4 Deceased.

located in front of the 15-fold segmented target. The trigger is based on the hit multiplicity in the TOF covering a polar angle rangebetween45^◦ and85^◦. AdetaileddescriptionoftheHADES detectorisgivenin[33].

Intotal,2.2×^{109 Au}+^{Aueventsareusedinthepresentanal-} ysis corresponding to the 40% most central events.The latter is estimated based on comparison of the event-by-event hit multi- plicityintheTOFandRPCdetectorscomparedtoaGlaubermodel, fordetailssee[34].

K⁰_s mesons are identified via their decayto

π

⁺+

π

⁻ (BR = 69.2%, c

τ

₌2.68 cm).  hyperons are identified through their decay to p+

π

⁻ (BR =⁶³.9%, c

τ

₌7.89 cm). Note that the re- constructedyieldcontainsalsoacontributionfromthe(slightly heavier)⁰ baryondecayingelectromagneticallyexclusivelyintoa

anda photon.Thisdecayprocesscannot bedetectedwiththe presentexperimental setup; hence, the yieldhasto be under- stood asthat of + ^{0 throughout the paper. Pion and proton} candidates used for the invariant mass analysisare identified by thecurvatureoftheir trackinthemagneticfield,averyloosecut on the reconstructed particle mass,and a careful track selection based on several quality parameters delivered by a Runge-Kutta tracking algorithm. The following conditions on the decaytopol- ogy of both hadrons are required to suppress the combinatorial backgroundofuncorrelatedpairs:(1)Aminimaldistancebetween theprimaryeventvertexandthedecayvertex,(2)aminimaldis- tance ofclosest approach(DCA) betweenthe proton,respectively thepiontrack,andtheprimaryvertex,(3)amaximalvalueonthe DCAbetweenthetwodecaytracksofonemotherparticleandon theDCAofthereconstructedmotherparticletrajectorytothepri- maryvertex,aswellasaminimumopeningangle[36].

The remaining background is subtracted using a mixed-event technique where onlytracks fromeventswithin the samemulti- plicity class and fromthe same target stripeare combined [36].

Examples of the invariant mass distributions used for signal ex- tractions are displayed in Fig. 1.The signal counts are extracted by fittinga Gaussian and integratingthe data in a ±²

σ

-region around thenominalmass,whilethe normalizationregion forthe mixed-eventbackgroundisplacedbetweenfour-five

σ

outsidethe signalregion.Typicalsignal-to-backgroundratiosareabout1–9for K⁰_s andabout0.5–5 for.Intotal,about190000 K⁰_s mesonsand about290000hyperonsarereconstructed.

K⁰_s yieldsaredeterminedin15rapiditybins,coveringthecen- ter of mass rapidity y_cm= ^y−⁰.74 between −^{0.65 and} +^0.85 in steps of 0.1 units in rapidity, and up to 19 transverse mass (mt=

p²_t +^m20)binsinstepsof40MeV/c².hyperonsareiden- tified in12 rapidity bins,ranging from y_cm= −⁰.65 to+^0.55in steps of 0.1units in rapidity,andup to 16 transverse mass bins instepsof50MeV/c².Therawsignalyieldsarecorrectedineach phase space cell foracceptanceand efficiencyusing Monte-Carlo simulations basedon Geantanda detaileddescriptionofthede- tector response, exposed to exactly the same reconstruction and analysis steps asthe experimental data.As input forthe simula-

Fig. 1. ExamplesofK⁰s (left)and(right)signalsfor0–40%mostcentralevents, overmixed-eventbackgroundforthebin−0.05<ycm<0.05 andreducedtrans- versemassesbetween80–120MeV/c²and100–150MeV/c²,respectively.

Fig. 2. Reducedtransversemass(mt−m0)spectraofK⁰_s(left)and(right)forthe 0-40%mostcentral events.Forabetterrepresentation,the spectraarescaledby consecutivefactorsof10foreachrapiditybinasindicatedinthelegendandonly statisticalerrorsareplotted.ThedottedcurvesarefitswithEq. (1) tothedata.

tion,thermaldistributionsofK⁰_s andhyperonswithaninverse slopeof90MeVwere embeddedintotheexperimental data.The combinedcorrectionfactorsfortheefficiencyandacceptancecor- respond to about 50 for K⁰_s and about 100 for  hyperons at mid-rapidity, including the branching ratio to the

π

⁺₊

π

⁻ and

π

⁻+^{p final state,} respectively [35,36]. In order to suppressthe largercombinatorialbackgroundinthep+

π

⁻sample,morestrin- gentcutsonthedecaytopologywereapplied thanincaseofthe

π

⁺

π

⁻sample,resultinginthelowerdetectionefficienciesforthe

comparedtotheK⁰_s.

Theacceptanceandefficiencycorrecteddistributionsofreduced transversemassspectraforsubsequentslicesofrapidityforK⁰_s and

hyperons are presented in Fig. 2. Displayed is the number of countsperevent,pertransversemassandperunitinrapidity,di- videdby m²_t. Thisrepresentation ischosen to ease a comparison withsingle slope Boltzmann fits to the resultingdistribution ac- cordingto

1 m²_t

d²N

dmtdycm

=

^C

(

ycm

)

exp



− (

m_t

−

^m0

)

c² TB

(

ycm

)



,

(1)

whichdescribethespectrasatisfactorily.Therapiditydistributions, shownin Fig.3 are obtained by integratingthe dataas function ofthetransversemomentum p_t andusingBoltzmannfitfunctions forextrapolationsinthenotcovered pt regions.Thesystematicer- rorsoftheyieldsineachrapidity binareduetothevariationsof topologycuts, the normalizationregionof themixed-event back-

Fig. 3. RapiditydistributionofK_s⁰(left)and(right).Theclosedsymbolsdepictthe measureddatapoints,whereastheopensymbolsshowthedatapointsreflected aroundthecenter-of-massrapidityycm=0.Theerrorbarsdisplaythestatistical errorswhilethesystematicuncertaintiesareindicatedbytheopenboxes.Forthe extrapolationtounmeasuredrapidityvaluesaGaussian functionisused(dotted curve).

ground and by the comparison of the spectra measured in the forwardandbackwardhemisphere.Thedecaylengthdistributions of the two hadrons are determined to ensure the quality of the correctionprocedure.Weobservelifetimesinagreementwiththe PDGvalues,i.e.K⁰_s:

τ

exp=⁸⁷.1±¹.1 ps,

τ

P D G=⁸⁹.6±¹.6 ps;:

τ

exp=²⁵⁵±^{7 ps,}

τ

P D G=²⁶³±^{2 ps[37].}

Multiplicitiesare obtainedbyintegratingtherapidity distribu- tionandusingaGaussianfitforextrapolationtofullphasespace, see dottedcurve in Fig. 3. The statisticalerroris takenfrom the fit directly.The systematicuncertaintyof theextrapolation ises- timatedbasedonvariationwithinthesystematicerrorsandusing inaddition tothe Gaussian fittherapidity distributions obtained fromthethreedifferenttransportmodelsforextrapolation,asde- scribedbelow.

Weobtainatotalmultiplicityof(1.56±⁰.03stat+0.12

−0.12sys)×¹⁰⁻² K⁰_s and(4.72±⁰.06_stat⁺₋⁰₀^._.²¹_75sys)×¹⁰⁻².

The extracted inverse slope parameters obtained from the Boltzmannfitstothemtspectraforeachrapidityintervalarefitted usingtheansatz T_B=_cosh^{Te f f}_(ycm) ^{inordertoobtaintheeffectivein-} verseslopeT_{e f f}.Astheinverseslopecontainsacontributionfrom the velocity ofthe radial expansion ofthe fireball,whichis pro- portionalto theparticle mass,one expectsa largerinverseslope for the  hyperons. We find T_{e f f} =⁹³±¹±^{4 MeV for the K0}s and T_{e f f} =⁹⁸±¹±^{4 for the}  hyperons,suggesting no strong differencebetweenradialflowoftheK⁰_s andhyperons.

Inaddition,theanalysisprocedureisrepeatedinthesameway forfour centrality classes.These classescorrespond to 10% steps incentrality,which canbetranslatedintothe averagenumberof participants^Apart^{[34].TheresultsaresummarizedinTable1.}

A comparisonto theworld data is presentedin Fig.4, where the mid-rapidity yields for central Au+^{Au (Pb}+^{Pb) collisions as} function of√

sNN aredisplayed. Whileonly experimentaldataon K⁰_s productionexistsforcentralHICsatenergies√

s_NN>17.2 GeV [38–41],thehyperonwasstudiedmoreextensively[40,42–48].

Its yield rises almost exponentially with energy up to √ sNN≈ 5 GeVandthenlevelsoff.

As both the K⁰_s and  are produced below their free NN- threshold,therequiredenergymustbesuppliedfromthecollision system. Hence, one expects their yields to rise as a function of thegeometricaloverlapofthenuclei, whichisanapproximateof thenumberofnucleonstakingpartinthecollision.Toinvestigate this,weanalysethemultiplicitiespermeannumberofparticipants Mult/^Apart^{asafunctionof}^Apart^{,asshowninFig.5andinclude} also themultiplicities of chargedkaons andφ mesonsmeasured in the same collision system[29]. If final state interactions play a minor role, the strength of this rise characterizes the amount

−0.06

 0–40% 4.72±0.06⁺₋⁰₀^._.²¹₇₅ 98±1±5

0–10% 8.22±0.11⁺₋⁰₀^._.⁵⁵₉₂ 106±1±2 10–20% 4.90±^0.09+₋⁰0^..²¹70 97±¹±² 20–30% 3.17±0.08⁺₋⁰₀^._.¹⁴₃₆ 90±1±3 30–40% 1.92±0.08⁺₋⁰₀^._.⁰⁹₂₈ 84±1±4

Fig. 4. Compilationofmid-rapidityyieldsforcentralAu+^Au(Pb+^{Pb)collisionsasa} functionof√

sNNofK⁰_s (red)and(blue)from[38–48].Ourresultsareshownby thetwoleftmostbullets.

Fig. 5. MultiplicitiespermeannumberofparticipantsMult/Apartasafunctionof

Apart.AllhadronyieldsarefittedsimultaneouslywithafunctionoftheformMult

∝ Apart^αwiththeresult:α=1.45±0.06.

of surplusenergy provided by the system, over the contribution fromfirstchance NNcollisions.Ifone assumesthatenergyaccu- mulates insequential nucleon-nucleoncollisions (asdiscussed in theintroduction)incombinationwiththesteepenergyexcitation function for strange hadron production, one expects to observe significantlydifferentslopes,duetotheclearhierarchyinthepro- duction thresholds,≈ −^{150 MeV forK+,K0,} (NN→^NK) and

≈ −^{450 MeV,} ≈ −^{490 MeV forthe K− (NN}→^{NNK+K−) andthe} φmeson(NN→^NNφ).However,theglobalfitofthefunctionMult

Fig. 6. MultiplicitiespermeannumberofparticipantsMult/^Apart^{,asafunctionof}

^Apart^forK0s(left)and(right)comparedtovarioustransportmodelcalculations (seelegends).

Table 2

ValuesoftheparameterαextractedforK⁰_sand dataandvariousmodels,asdisplayedinFig.6.

α data (K^+,−,0,,φ) 1.45±^0.06

UrQMD (K⁰_s,) 1.69±^0.04 HSD no pot. (K⁰_s,) 1.35±^0.02 IQMD no pot. (K⁰s,) 1.51±0.03 HSD pot. (K⁰s,) 1.30±0.02 IQMD pot. (K⁰_s,) 1.42±0.03

∝ ^Apart^{α toall thehadron yields returnsa} satisfactoryvalue of

χ

²/NDF=0.59,with

α

=¹.45±⁰.06.⁵

This points to a more involved picture than assumed in the past, asthetotal amountofproduced strangenessincreaseswith thenumberofparticipantsandmightbeonlyredistributed(statis- tically)tothefinal hadronspeciesatfreeze-out[49].Thisimplies that thecreatedsystemismoreinterrelatedthanexpectedinthe past.

In the following,we will comparethe K⁰_s and datato pre- dictionsfromthreestate-of-the-arthadronictransportmodels,the Isospin QuantumMolecularDynamicsmodel(IQMDv.c8)[31],the HadronStringDynamics(HSDv.711n)model[30] andtheUltrarel- ativistic QuantumMolecular Dynamics model(UrQMDv 3.4)[32].

It has been shown that none of the standard code versions can reproduce the observed φ/K⁻ multiplicity ratio measured in the sameexperiment[50].⁶

All three are semi-classical models simulating a HIC on an event-by-event basis. While UrQMD produces particles via inter- mediate resonanceexcitations, inHSDandIQMD alsodirectpro- ductionviatwo-to-threeparticleprocessesisincludedhoweverin IQMD only (1232) resonances are implemented. In contrast to IQMDandHSD,neithermean-fieldN-NpotentialsnorexplicitK-N potentialsareincludedinthepresentedversion ofUrQMD. IQMD is, due to missinghigh-energy processes, not applicable at ener- giesbeyond2 A GeV,butitisverywelltestedintheSIS18energy regime. HSDallowsinaddition,thepropagationofoff-shellparti- cles,however,thisismorerelevantforantikaonproduction.

WetrytoextractparticlespecificpropertiesofK⁰_s mesonsand

hyperonsliketheK-Nand-Npotential,whichaffectboththeir productionandpropagationinthemedium.

We startwiththecomparisonofcentrality dependenceofthe integrated yield, see Fig. 6 and Table 2. We find that HSD and IQMDwithoutan implementationoftheK-Npotential,aswellas

5 WhileincaseoftheK⁻thesimilarscalingwasexplainedbyacouplingtothe K^+,0yieldviastrangenessexchangereactions,e.g.π⁰+ →K⁻+p [12],nosuch processispossibleincaseoftheφmeson.

6 TheUrQMDversionpredictingthemeasuredφ/K⁻[29] ratioaftertuningthe cross-sectionstomatchdatafromp+pcollisionsisnotpubliclyavailableyet[50].

Fig. 7. ComparisonoftheshapeoftherapiditydistributionofK⁰s(left)and(right) tovarioustransportmodelversions.Themodelcurvesarenormalizedtotheinte- gralofthedata,seetextfordetails.Dataaresymmetrizedaroundmid-rapidity.

UrQMD, overpredict the yields by a large factor. Also the model curvesdifferamongeachotherbyuptoafactor2.5,whichpoints totheuseofdifferentparametrizations forelementary crosssec- tions.

InHSDandIQMD,arepulsive K-Npotentialof40MeV atnu- cleargroundstate density

ρ

0 isincluded,whichincreaseslinearly withdensity.Ifturnedon,theK⁰_s curvescomemuchclosertothe dataandalsothe

α

parameteris reduced. TheIQMD predictions arebyfartheclosesttothedatawithadeviationoftheyieldsof theorderof10%⁷ andanagreementwithinerrorsoftheextracted valuesof

α

.Thereductionoftheyieldand

α

valuescanbeunder- stoodqualitativelybyaneffectiveshiftintheproductionthreshold of kaons. As the effect of the density dependence is more pro- nouncedforcentral events,also therise with^Apart^{is reduced.}

Dueto the associated productionof kaons and hyperons,also theyieldsareaffectedbytheinclusionofaK-Npotential.Note thattheemployedversionofUrQMDdoesnot includeanypoten- tial,whilebothversionsofHSDandIQMDassumethestrengthof the-Nmeanfieldtobe2/3oftheN-Nmeanfield,motivatedby theadditivequarkmodel[14].

Next, we compare the shape of the rapidity distributions for 0–10%mostcentralevents.Forthis,wehavesymmetrizedthedis- tributions with respect to mid-rapidity. In order to compare the shapes, the model curves are normalized to the area of the ex- perimentalones, seeFig.7.Thewidthoftherapiditydistribution isparticularlysensitivetothestoppingofbaryonsinthecollision zone.Repulsive potentialsinfluence theshape ofthe distribution further by pushing the particles away from the bulk of matter atmid-rapidity. Indeed,we findthat the inclusion of apotential improvesthe descriptionsignificantly. Incontrast tothe previous observable,alsotheUrQMDcalculation givesafairdescriptionof theshape, without anypotential. Incase ofthe ,the inclusion ofthe K-N potential does not affect the shape and we find that UrQMDdescribesthedatabest.

Finally,westudythetransversemomentumdistributionatmid- rapidity for the most central eventclass, see Fig. 8. Besides the

7 Note,thatpreliminarydataonyieldsofchargedpionsshowadeviationatthe orderof20%todataoftheFOPIexperiment,whicharewelldescribedbyIQMD [51].Dueto π induced strangenessproduction channels, this differenceis also transportedtotheK⁰_sandyields.

Fig. 8. Comparisonoftheshapeofthept-spectrafor±^{0.15rapidityunitsaround} mid-rapidityofK⁰_s (left)and (right) tovarioustransportmodelversions.The modelcurvesarenormalizedtotheintegralofthedata.

Table 3

Summaryofthecomparisonofdatatomicroscopictransportmodelsbasedonthe χ²normalizedtothenumberofdatapoints.

Model KN potential K⁰_s  α

pt y Mult pt y Mult

UrQMD no 105 4.1 1619 2.3 3.6 3020 16

HSD yes 7.0 2.7 670 39 6.3 626 6.3

IQMD yes 6.0 2.0 99 38 12 214 0.3

production mechanism [52] and the radial expansion velocity of thesystem,thelowtransversemomentumpartisparticularlysen- sitivetotheK/-Npotentials[10].⁸

Onceagain, inordertocomparetheshapes, themodelcurves arenormalizedtotheareaoftheexperimentalones.Clearly,forK⁰_s the data favourmodels which includepotentials. However, again UrQMDwithoutanypotentialshowsacompletelydifferentbehav- ior comparedtothetwo othercalculationswithoutthepotential, undershootingthelow pt partofthespectrum.Hence,production via intermediate resonances seems to(over-) mimic theeffect of thepotential.

In addition, similar as in case of the rapidity distribution, UrQMDoffersthebestdescriptionofthept spectra.

In total, we find that none of the model predictions can de- scribethe yield,the^Apart ^{scalingandtheshape oftherapidity} andpt spectraofK⁰_s andsimultaneously,seealsothe

χ

² values normalizedtothenumberofdatapointslisted inTable3forthe investigated observables.Furthermore, we observe that effects of arepulsive K-Npotential canbe tosome extendcompensatedby production via intermediate resonances. Hence, any further con- clusionsareweakenedbytheambiguitiesofdifferentmicroscopic effects and the incomplete description of the presented observ- ables within all investigated models. Therefore, it is premature to drawconclusions on thestrength ofthe potentialsbased only thepresentedobservables, anditisnecessarytocompareandde- scribeasmany (related) observablesaspossiblewithin the same model.Toenableacomprehensiveadjustmentofmodelsandnew approacheswhichareunderdevelopment[53–56] toourdata,dif- ferential transverse massversus rapidity yields are shownin the Appendixandafurtheranalysisondirectedflowofhadrons,which isknowntobe stronglyinfluencedby mean-fieldpotentials,isin preparation.

8 Notethatthisdependsontheformoftheimplementedpotentialandhence doesnotholdtrueforallmodels,seee.g.[11].

lationinsequentialnucleon-nucleoncollisionsshouldthereforebe revisited.

Our comparison of the yields, the universal scaling and the shapesof rapidity and pt spectra to three microscopic transport models doesnot yet lead toa consistent picture. Includinga re- pulsiveKNpotentialtheIQMDpredictionsarebyfarclosesttothe data,witharemainingdeviationoftheyieldsoftheorderof10%

andan agreementwithin errorsoftheextractedvaluesof

α

.The shapeofthekaonrapiditydistributioniswelldescribedifarepul- siveK-NpotentialisincludedinHSDandinparticularinIQMD.On theotherhand,UrQMDreproducestherapiditydistributionwith- out such a potential,probably becauseofthe particleproduction through intermediate resonances, but fails to reproduce the ob- served scalingof theyields with centrality.Yet, theshape ofthe

rapidity distributionsandthe p_t spectraare bestdescribed by UrQMD. Due to the observed ambiguities andthe imperfect de- scription of the presented observables, it is premature to adjust the strength ofthe potential basedon the presented observable.

Furthermodelrefinements anddata-to-modelcomparisonsbased onadditionalobservablese.g.directedflowofstrangehadronsare necessarybeforefirmconstraintscanbededuced.

Acknowledgements

The HADES collaboration thanks J. Aichelin, M. Bleicher, E.

Bratkovskaya,C.HartnackandJ.Steinheimerforelucidatingdiscus- sions.Wegratefullyacknowledgesupportbythefollowinggrants:

LIP Coimbra, PTDC/FIS/113339/2009; SIP JUC Cracow, Cracow (Poland) National Science Center, 2016/23/P/ST2/040 POLONEZ, 2017/25/N/ST2/00580,2017/26/M/ST2/00600;TUDarmstadt,Darm- stadt (Germany) and J. W. Goethe-University, Frankfurt (Ger- many), ExtreMe Matter Institute EMMI at GSI Darmstadt; TU München, Garching (Germany), MLL München, DFG EClust 153, GSITMLRG1316F,BmBF05P15WOFCA,SFB1258,DFGFAB898/2-2;

NRNU MEPhI Moscow, Moscow (Russia), in framework of Rus- sian Academic Excellence Project 02.a03.21.0005, Ministry of Sci- enceandEducationoftheRussianFederation3.3380.2017/4.6;JLU Giessen,Giessen(Germany),BMBF:05P12RGGHM;IPNOrsay,Orsay Cedex (France), CNRS/IN2P3; NPI CAS, Rez, Rez (Czech Repub- lic),MSMTLM2015049,OPVVVCZ.02.1.01/0.0/0.0/16013/0001677, LTT17003.

Appendix

Theobservablesshownin thetext arebasedon thedatapre- sentedinFigs.9and10.Thedataareorganizedinbinsofmt−^m0 vs. ycm forfourcentralityclasses.Thedetailsofthecentralityse- lectionaredescribedin[34].

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