Deep sub-threshold $\phi$ production in Au+Au collisions

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Physics Letters B

www.elsevier.com/locate/physletb

Deep sub-threshold φ production in Au + ^{Au collisions}

HADES Collaboration

J. Adamczewski-Musch

^d

, O. Arnold

^j,i

, C. Behnke

^h

, A. Belounnas

^o

, 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,7

, L. Chlad

^p

, 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

^q

, R. Gernhäuser

^j

, M. Golubeva

^l

, R. Greifenhagen

^f,3

, F. Guber

^l

,

M. Gumberidze

^e,2

, S. Harabasz

^e,c

, T. Heinz

^d

, T. Hennino

^o

, S. Hlavac

^a

, C. Höhne

^k

, R. Holzmann

^d

, A. Ierusalimov

^g

, A. Ivashkin

^l

, B. Kämpfer

^f,3

, 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

, W. Kühn

^k

, A. Kugler

^p

, T. Kunz

^j

, A. Kurepin

^l

, A. Kurilkin

^g

, P. Kurilkin

^g

, V. Ladygin

^g

, R. Lalik

^j,i

, 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,4

, C. Müntz

^h

, R. Münzer

^j,i

, L. Naumann

^f

, K.N. Nowakowski

^c

, M. Palka

^c

, Y. Parpottas

^n,5

, V. Pechenov

^d

, O. Pechenova

^h

, O. Petukhov

^l,4

, J. Pietraszko

^d

,

W. Przygoda

^c

, S. Ramos

^b

, B. Ramstein

^o

, A. Reshetin

^l

, P. Rodriguez-Ramos

^p

, P. Rosier

^o

, A. Rost

^e

, A. Sadovsky

^l

, P. Salabura

^c

, T. Scheib

^h

, H. Schuldes

^h

, E. Schwab

^d

, F. Scozzi

^e,o

, F. Seck

^e

, P. Sellheim

^h

, J. Siebenson

^j

, L. Silva

^b

, Yu.G. Sobolev

^p

, S. Spataro

⁶

, H. Ströbele

^h

, J. Stroth

^d,h

, P. Strzempek

^c

, C. Sturm

^d

, O. Svoboda

^p

, M. Szala

^h

, P. Tlusty

^p

, M. Traxler

^d

, H. Tsertos

ⁿ

, E. Usenko

^l

, V. Wagner

^p

, C. Wendisch

^d

, M.G. Wiebusch

^h

, J. Wirth

^j,i

, Y. Zanevsky

^g,7

, 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 nDepartmentofPhysics,UniversityofCyprus,1678Nicosia,Cyprus

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

qLabCAF.F.Física,Univ.deSantiagodeCompostela,15706SantiagodeCompostela,Spain

E-mailaddress:hades-info@gsi.de(R. Holzmann).

1 AlsoatISECCoimbra,Coimbra,Portugal.

2 AlsoatExtreMeMatterInstituteEMMI,64291 Darmstadt,Germany.

3 AlsoatTechnischeUniversitätDresden,01062 Dresden,Germany.

4 AlsoatMoscowEngineeringPhysicsInstitute(StateUniversity),115409 Moscow,Russia.

5 AlsoatFrederickUniversity,1036 Nicosia,Cyprus.

6 AlsoatDipartimentodiFisicaandINFN,UniversitàdiTorino,10125 Torino,Italy.

7 Deceased.

https://doi.org/10.1016/j.physletb.2018.01.048

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

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

Articlehistory:

Received15January2018 Accepted16January2018 Availableonline3February2018 Editor:D.F.Geesaman

We presentdata onchargedkaons(K^±)and φmesonsinAu(1.23A GeV)+^Aucollisions.It isthefirst simultaneousmeasurementofK⁻andφmesonsincentralheavy-ioncollisionsbelowakineticbeamen- ergyof10A GeV.Theφ/K⁻multiplicityratioisfoundtobesurprisinglyhighwithavalueof0.52±⁰.16 andshowsnodependenceonthecentralityofthecollision.Consequently,thedifferentslopesoftheK⁺ and K⁻ transverse-massspectracanbeexplainedsolelybyfeed-down,whichsubstantiallysoftensthe spectraofK⁻mesons.Hence,incontrasttothecommonlyadaptedargumentationinliterature,thedif- ferentslopesdonotnecessarilyimplydivergingfreeze-outtemperaturesofK⁺and K⁻ mesonscaused bydifferentcouplingstobaryons.

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

Until now, hadron properties and interactions at high baryon densities – as reached in relativistic heavy-ion collisions (HICs) –cannot be addresseddirectly by ab-initio QCD calculationsand thus have to be modeled using effective Lagrangians. Both the equation of state andthe kinetic description of the HIC dynam- ics provide severe challenges with far reaching implications for astrophysicalobjects,e.g.forneutronstarstructureandmergerdy- namics[1–4].

Strangeness-carryingexcitations–withafocusonkaonsinthe energyregimebelow10A GeV–areconsideredsuitableprobesof thepropertiesof compressednuclearmatter andtherelatedcol- lision dynamics [5]. In strong interaction processes one observes strangenessproductionassimultaneousappearanceofass pair,¯ ei- therasastrangenessneutralboundstateliketheφmesonorwith subsequentredistributiontobaryonsandmesons(associated pro- duction).ArgumentsbasedontheOZIruledisfavortheproduction ofthebound φ=^s¯s state[6,7]. Keyquantitiesof strangemesons aredeterminedbytheirspectralfunctionrelatedtotheirso-called nuclear potentials. Various approaches [8–13] predict a net at- tractive K⁻-nucleon (N)potential. However, dueto the presence of baryon resonances [14,15], the resulting K⁻ spectral function mayhavean intricateshape and, dueto thelackof ab-initioap- proaches,itneedstobe controlledbyexperimentaldata.Thefirst high-quality data on sub-threshold K⁻ production in HICs have become available in the late 1990s [16–19].The data revealed a similarriseofK⁺and K⁻yieldswithincreasingcentralityofthe collision, and systematically softer K⁻ spectra compared to the ones of the K⁺. Comparisons between data and transport mod- els suggestedthat the K⁻ decouples from the systemlater than the K⁺ due to the large cross section of strangeness exchange reactions, e.g.

π

→N K⁻, which were predicted in[20] asthe dominantsourceforsub-threshold K⁻production.Thiswastaken asanexplanationforboth,thesofterspectraoftheK⁻(duetothe laterfreeze-out)aswellasthesimilardependenceonthesystem size(couplingof K⁻yieldtotheoneoftheK⁺ viathehyperons) [21]. Alater freeze-out ofthe K⁻ compared to the K⁺ hasthus becomeaparadigmofsub-thresholdstrangenessproduction.

Attempting to extract the K⁻-N potential from experiment, mostcomparisonsbetweenK⁻dataandtransportmodelsfavorin fact an attractive potential. However, quantitative statements are difficult, e.g. due to differences between the various models [5, 22–24]w.r.t.theextractedobservabledistributions.

Theφ mesonsasapossiblesourceof K⁻ mesonsatSISener- giesisdiscussedforthefirsttime in[25,26].Recentdatainlight collision systems reveal, indeed, that a sizable fraction of about 20%oftheobserved K⁻ yieldresultsfromφdecays[27–31].The observed differencein theslopes ofthe K⁺ and K⁻ spectracan be explained by taking the K⁻ contribution from φ decays into accountinlightcollisionsystems,asthoseK⁻haveasubstantially

softerspectrum[32],asconfirmedin[29–31].Severalexplanations for the large φ/K⁻ ratio in light systems have been proposed, based on both macroscopic [33,34] and microscopic models [35, 36] butwithouttheemergence ofa commonpicture,andthere- lationtoheavysystemsremainedvagueuntilnow.

In this letter, we present data on charged kaons (K^±) and φ mesonsinAu+^{Aucollisionsatakineticbeamenergyof1.23A GeV.}

It is the only simultaneous measurement of K⁻ and φ in cen- tralheavy-ioncollisionsbelowakineticbeamenergyof10A GeV.

Mesons with strange quark content are produced deeply below their corresponding free nucleon-nucleonthresholds witha clear hierarchy inenergydeficitsof−150 MeV(K⁺), −450 MeV(K⁻) and−^{490 MeV(}φ).Hence, thefireball producedinAu+^Aucolli- sions at1.23AGeVistheidealenvironmenttostudysub-threshold strangenessproduction.

TheHigh-Acceptance Di-ElectronSpectrometer(HADES) [37]is acharged-particledetectorlocatedattheGSIHelmholtzCenterfor Heavy IonResearch inDarmstadt,Germany. It comprises a6-coil toroidal magnetcentered around thebeamaxis andsixidentical detection sectionslocated between the coils covering almost the full azimuthal angle. Low-mass Mini-Drift Chambers (MDCs) are the main tracking detectors,while a scintillator hodoscope (TOF) and a Resistive Plate Chamber (RPC) are used for time-of-flight measurements incombination with a diamond start detectorlo- catedinfrontofa15-foldsegmentedtarget.Themultiplicitytrig- ger is based on the hit multiplicity in the TOF covering a polar anglerangebetween45^◦and85^◦.

In total 2.1×^{109 Au}+^{Au events have been collected corre-} spondingto the40% mostcentral eventsestimatedbyelaborated studies using a Glauber model [38]. Charged particle trajecto- ries werereconstructedusingtheMDCinformation.Theresulting tracks weresubjectto severalselectionsbased onquality param- eters delivered by a Runge–Kutta track fittingalgorithm. Particle identificationisbased onthemeasurements oftime-of-flightand track length. Additional separation power forkaons isgained by the energy-loss information from MDC and TOF detectors. K⁺ mesons are identified in the center-of-mass rapidity interval of

ycm= −⁰.65· · ·+⁰.25 inseveraltransversemass(mt= p_t²+^m2₀⁾ binsof25 MeV/c² width.Theunderlyingbackgroundisestimated inaniterativefittingprocedure.Thefitparametersareobservedto showlittleincreasewithincreasingmomentum,exhibitingquanti- tativeagreementwiththeMonte-Carlosimulation.Thisprocedure allowstoobtainthestatisticalerrorofthesignalandtotake into account thequalityofthebackgrounddescription ofthefitfunc- tion. Additional variations of the number of parameters, the fit and theintegration ranges turned out to be well covered by the error given by the fit. An example of a K⁺ signal and the cor- responding background is displayed in the upper inset of Fig. 1 fortheregioncoveringmid-rapidityandreducedtransversemass

Fig. 1. Left:Acceptance and efficiencycorrectedtransverse-mass spectraaround mid-rapidity.Thenumberofcountsperevent,pertransversemassandperrapid- ityregion,dividedbym²_t togetherwithafittothedatapointsaccordingtoEq.(1) forthe 0–40%mostcentraleventsisdisplayed.Upper right: K⁺ signaland the correspondingbackgroundfitfortheregioncoveringmid-rapidityandmt−m0be- tween25and50 MeV/c².TheredcurvecorrespondstotheGaussianpartandthe blueonetothepolynomialpartofthecombinedfunctionusedforsignalextrac- tion.Middleright:Sameasupperonebutfor K⁻ andmt−^m0 between50and 75 MeV/c².Lowerright:K⁺K⁻invariantmassdistributionforthemid-rapidityre- gionandmt−m0between0and100 MeV/c²aftersubtractionofthebackground.

(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisre- ferredtothewebversionofthisarticle.)

mt−^m0 between25 and50 MeV/c². K⁻ are identified similarly as K⁺ but in a range of ycm= −⁰.7 to +⁰.1. An example of a K⁻ signal includingthebackgroundfitisdisplayedinthemiddle insetof Fig. 1 forthe region covering mid-rapidity andmt−^m0 between50and75 MeV/c².φmesonsareidentifiedviatheir de- caysintochargedkaons.Thisanalysisisdone inarapidity region rangingfrom ycm= −⁰.5 to+⁰.1.The combinatorialbackground is described with the mixed-event technique. For systematic er- ror evaluationonthe count rate, thenormalizationregion ofthe mixed-event and the integration range are varied. The error of theextractedcountrateisthendefinedinthesamewayasdone for K^±.AnexampleofaφsignalintheK⁺K⁻invariantmassaf- tersubtractionofthe backgroundisdisplayed onthelower inset ofFig. 1forthemid-rapidity regionandmt−^m0 between0 and 100 MeV/c².

Therawcountratesare correctedineachphasespacecell for acceptanceandefficiencybasedonMonte-CarloandGeant 3sim- ulations,subjecttothesame reconstructionandanalysissteps as theexperimentaldata.Theaverageefficiencyandacceptancecor- respond to ≈ ^{0.2 for kaons and about 0.04 for} φ mesons, for detailssee[39].Asinputforthesimulation,thermallydistributed K⁺,φ(T=^{100 MeV)andK− (T}=^{80 MeV)wereembeddedinto} Au+^{AucollisioneventsgeneratedwiththetransportcodeUrQMD} [40]serving asbackground.Thesystematicbiasanduncertainties ofthecorrectionarecheckedbasedonthemoreabundantproton andpiontracksaswellasonthedifferencebetweenthedifferent sectorsofHADESandare eithercorrected ortakenassystematic error.Thetotalsystematicuncertaintyonthechargedkaonyields

Fig. 2. Upperleft:RapiditydistributionsofK⁻ andφandtheGaussianfunctions (dashedcurves)usedforextrapolationinycm.Pointsreflectedatmid-rapidityare displayedas opensymbols.Upperright:Extractedinverseslope parametersob- tainedfromthe Boltzmannfitstothe mt spectra.Thedistributionsareadapted usingTB=cosh^{Te f f}(y_cm),displayedasdashedcurve.Bothfiguresshowresultsforthe 0–40%mostcentralevents.Incaseofthe K⁻,alsotheyieldsandthe extracted inverseslopes ofthe two-componentmodelaredisplayed: direct thermal(blue dotted),feed-downfromφdecays(reddashed),sumofboth(greensolid).Lower panel:K⁻transverse-massspectraaroundmid-rapiditycomparedtothedifferent cocktailcontributionsinthesamecolorcode.(Forinterpretationofthereferences tocolorinthisfigure,thereaderisreferredtothewebversionofthisarticle.)

within theacceptancecorresponds to 4%. Theacceptance andef- ficiency corrected transverse mass spectra of K^± and φ for the mid-rapidity bin are presented in Fig. 1 in terms of counts per event,pertransversemassandperunitinrapidity,dividedbym_t². This representation ischosen to ease acomparison withthermal distributionsaccordingto

1 m_t²

d²N

dmtdycm

=

^C

(

ycm

)

exp



− (

mt

−

^m0

)

TB

(

ycm

)



,

(1)

whereC(y_cm)isarapiditydependentnormalization,andtheslope parameter TB depends on the rapidity too. Using Eq. (1) for an extrapolationin mt−^m0 andintegratingthe datapoints, the ra- piditydensitydistributionsforthedifferentparticlesareobtained, seeFig. 2.Theuncertaintyoftheextrapolationisestimatedto1.5%

fromthedifferencebetweentheextrapolationbasedonEq.(1)and aSiemens–Rasmussenmodelfunctionincludingaradialexpansion velocityasparameterfixedby usingthekinematicdistributionof theprotonsinthesamecollisionsystem[39].Addingupthediffer- enterrorsquadratically,wefindan overallsystematicuncertainty ontheyieldwithinthecoveredrapidityrangeof≈^5%forcharged kaons andof≈^{10% forthe K± and}φ mesons. Multiplicitiesare obtained integratingover ycm and using a Gaussian for extrapo- lationtofull phasespace. Theuncertaintyofthisextrapolationis estimatedbasedontherelativedifferenceofextrapolatedyieldob- tainedfortheGaussandthescaleddistributionfromUrQMD.The obtainedtotalmultiplicitiesarelistedinTable 1.The rapiditydis- tributions andthe Gauss functions used for the extrapolation in

Table 1

MultiplicitiesandeffectiveinverseslopesTe f fatmid-rapidityaswellasmultiplicity ratiosforgivencentralityclasses.Thefirstgivenerrorcorrespondstothestatistical, thesecondtothesystematicerrorwithintherapidityrangecoveredbyHADESand thelastonetotheextrapolationuncertaintytofullphasespace.Ifthesecondor thirderroris notgiven,itisfoundtobewellbelowthestatisticalerrorandis henceneglected.Theerroronthemultiplicityratioscorrespondstothequadratic sumofthesingleerrorsources.

K⁺ Yield [10⁻²/evt] Te f f [MeV]

0–40% 3.01±^0.03±^0.15±^{0.30 104}±¹±¹

0–10% 5.98±^0.11±^0.30±^{0.60 110}±¹±¹

10–20% 3.39±^0.05±^0.17±^{0.34 103}±¹±¹

20–30% 1.88±0.02±0.09±0.19 97±1±1

30–40% 1.20±0.02±0.06±0.12 91±1±1

K⁻ Yield [10⁻⁴/evt] Te f f [MeV]

0–40% 1.94±^0.09±^0.10±^{0.10 84}±⁶

0–20% 3.36±^0.31±^0.17±^{0.17 84}±⁷

20–40% 1.28±^0.11±^0.06±^{0.06 69}±⁷

φ Yield [10⁻⁴/evt] Te f f [MeV]

0–40% 0.99±0.24±0.10±0.05 108±7

0–20% 1.55±0.28±0.15±0.11 99±8

20–40% 0.53±^0.08±^0.05±^{0.04 91}±⁷

K⁻/K⁺×¹⁰³ φ/K⁻

0–40% 6.45±^{0.9 0.52}±^0.16

0–20% 7.17±^{1.1 0.46}±^0.12

20–40% 8.31±1.3 0.44±0.10

y_cm aredisplayedontheupperleftpanel ofFig. 2for K⁻ andφ. Theerrorbarsdisplaythestatisticalerror,whilethesystematicer- ror isindicated by boxes.The extractedinverseslope parameters obtainedfromtheBoltzmannfitsto them_t spectraare displayed ontheupperrightpanel ofFig. 2.Thedependenceisfittedusing

T_B= _cosh^{Te f f}_(ycm) ^{in orderto obtain theeffective inverseslope T}e f f.

While T_{e f f} is extracted to (104±¹stat±¹sys) MeV for K⁺ and to (108±⁷stat) MeV for φ mesons, the obtained value for K⁻ of(84±⁶stat) MeVis significantlylower.This isinlinewiththe previously obtainedsystematics[19].The systematicerroronthe inverse slope of the K⁺ is obtained by comparison of the spec- traextractedinthedifferentsectorsseparately.Incaseofthe K⁻ andφ,asimilarcheckgivesvariationswellbelowthestatisticaler- rorsandhenceareneglected.Inaddition,theanalysisprocedureis repeatedinfourandtwocentralityclassesforthe K⁺ andK⁻,φ, respectively,whichcorrespondto10% (20%)stepsincentrality.The resultsare summarized inTable 1. For T_{e f f} of K⁻,we take into account the larger extrapolation inmt−^m0,due to the reduced statistics,byanadditionalsystematicerror.

Thehierarchyinenergydeficitsisreflectedintheyieldsofthe threemesons: K⁺ mesons arefound to betwo orders ofmagni- tudemoreabundantlyproducedthanthedeepsub-thresholdpro- ducedK⁻ andφmesons.Duetothesimilarriseofchargedkaon yieldswithincreasingcentrality,onecandirectlycomparetheex- tractedratioK⁻/K⁺= (⁶.45±⁰.77)×^{10−3 tovaluesobtainedby} theKaoScollaboration athigherbeamenergiesandvariouscolli- sionsystems[19,28]withoutcorrectingforthedifferentcentrality selections. Theratio showsalinear increase with√

sN N, andour datapoint isconsistent withthe extrapolationfromhigherener- giesusing a linear regression [28]. The yield andslope of the φ mesonhaveneverbeforebeenmeasuredincentralheavy-ioncol- lisions below a kinetic beam energy of 10A GeV. The excitation function ofthe φ/K⁻ ratio isdepicted inFig. 3 asa function of

√sN N,including datafromhigherenergies [41,42].Assumingthe validityofthepreviousparadigmofsub-thresholdstrangenesspro- duction presented in the introduction, one expects the φ/K⁻ to

Fig. 3. Multiplicityratioφ/K⁻ asfunctionof√

sN Nforcentralheavy-ioncollisions [41,42];theHADESdataisdepictedasfilledsymbol.

decrease withdecreasing energy, as it becomes increasingly un- likely to accumulate enough energy for φ production, while K⁻ can still be produced via strangeness exchange reactions, which should have sufficient time to occur in large systems. However, while the ratio is constant ≈ ^{0.15 for} √

s_{N N}≥^{4 GeV, our data} indicate astrongincreasetowards lowenergies:Wefinda φ/K⁻ ratioof0.52±⁰.16.

Thisrisesquestionsonthewidespreadassumptionofasmallφ productioncrosssection[7]duetotheOZIruleandshowsthatin- deedcorrelatedkaonproductionviaφ mesonsisasizablesource of K⁻ ((26±⁸)% of all K⁻ mesons) in large collision systems atlow energies. Hence,thefeed-down fromφ mesondecayscan notbeneglected inthe K⁻ channel.Toinvestigatethefeed-down effect we built a simple K⁻ cocktail using the event generator Pluto [43]. We generate two static thermal sources, one for di- rect K⁻andoneforφmesonswithtemperaturesofT=^{104 MeV} andT=^{108 MeV,}respectively,accordingtothemeasuredinverse slopesof K⁺andφ.Duetothehierarchyinproductionyieldsthe feed-downonthe K⁺ spectraisnegligible.Incaseofthe K⁻,we scale thetwo contributions accordingto themeasured φ/K⁻ ra- tio.Thedifferentcocktailcontributionstothe K⁻transverse-mass spectra around mid-rapidity are displayed in the lower panel of Fig. 2: direct thermal(blue), resulting from φ decays (red), sum of both (green). It turns out that the K⁻ resulting from φ de- cays have amuch softerspectrum andhencesubstantially “cool”

the finally observed spectrum. The sum of both contributions is then fitted using Eq. (1) (black) in a similar mt−^m0 range be- tween 0 and 200 MeV/c² as used for experimental data (green triangles), both displayed in Fig. 2. The rapidity dependences of theextractedinverseslopesfordifferentK⁻sourcesaredisplayed on the right panel inFig. 2 with the same colorcode as above.

Theinverseslopeof(84±^{5)MeVagreeswiththe}measurementof (84±⁶)MeV.Theerrorisobtainedbyvariationoftheφ/K⁻ratio within the given errors. The error on the inverse slope parame- teroftheexperimentalspectrum ispropagatedby makinguseof the covariancematrix when determiningthe yields andhence is notvariedexplicitly.Wefindtheshapeoftherapiditydistribution tobereproducedaswell,displayed togetherwiththe K⁻dataon the left panel of Fig. 2, where a comparison of the data to the fullcocktail(greencurve),thedirect(bluecurve)andcontribution from φ decays (red curve) is shown. The different slopes of the K⁺ and K⁻ transverse-mass spectra can be explained solely by feed-down,whichsubstantiallysoftens thespectraof K⁻ mesons anddohencenot implydifferentfreeze-outtemperaturesofboth mesonsresultingfromtheirunequalcouplingstobaryons.

The general understanding of sub-threshold strangeness pro- ductionisfurtherchallengedbytheinvestigationofthecentrality dependenceoftheφ/K⁻ andK⁻/K⁺ ratios.Withintheprevious paradigm, one also expects the relative yields to show different scalings withthe system size as the K⁻ yield is coupled to the one of K⁺ via strangenessexchangereactions, while nosuch re- actions arepresentincaseoftheφmeson(notethattheaverage amount of produced strange quark pairs is at theorder of 10⁻²

perevent).Hence,asignificantlyhigheramountofenergymustbe accumulatedbeforeφ meson productioncan occurandtherefore astronger scalingwithincreasing centralityis expected, thanfor thechargedkaons.However, both theφ/K⁻ andthe K⁻/K⁺ ra- tiosextracted within the two centralityclasses donot show any increasetowardscentralevents,seeTable 1.Thisimpliesthat en- ergyismuchmoreeasilyredistributedinthecreatedfireballthan previously assumed, suggesting a universal scaling of produced strangenesswithincreasingsystemsize.

Several ongoing calculations promise to improve our under- standingofsub-thresholdstrangenessproductionandwillbecon- fronted with the data for more quantitative comparisons in the future: An improved version of the transport code UrQMD [36]

candescribe the observed φ/K⁻ forenergies at low energies by increasingthe φ-Ncouplingvia higherbaryon resonances,which decaytofinalstatesincludingaφmesonandactasenergyreser- voir at the same time. As such decay branches are not directly observed,their branching ratios are tuned to matchdataon ele- mentaryφproductioncrosssections[44].Insupportofthis,recent datafromelementarycollisions [45] andinvestigations aboutthe φ meson self-energy in nuclear matter [46] show stronger φ-N couplings than expected by the OZI rule. Also statistical models canreproducetherise oftheφ/K⁻ ratiowhenincludingtheso- calledstrangenesscorrelationradius Rc,whichgovernsthecanon- icalsuppression.Astheφ mesonhasnonet-strangeness,itisnot affected by strangeness conservationin the reduced volume and thereforenotsuppressed,whiletheK⁻mesonis.Thisresultsinan increaseoftheφ/K⁻ ratiowithdecreasing √

sN N,wherethesize of R_c determines the strength of the decrease. Also, the similar dependenceof chargedkaon andφ production withthe central- ityofthecollision isnaturally reproducedasthetotalamountof producedstrangenessincreaseswithdecreasingimpactparameter ofthecollision, prior toits redistribution tothe differenthadron species at freeze-out [47]. In summary, we have presented first combineddata on chargedkaons (K^±) andφ mesons in Au+^Au collisions at √

s_{N N}=².4 GeV. The φ/K⁻ ratio showsa increase withdecreasing center-of-massenergy √

sN N and is found to be 0.52±⁰.16 inourexperiment.Hence,withafraction(26±⁸)% of K⁻ mesons resulting fromφ mesondecays, thelatter one turns out to be a sizable source of antikaon production. The different slopesofthetransverseK⁺andK⁻spectracanbefullyexplained by feed-down.The φ/K⁻ ratio is constant as a function of cen- trality,suggestingauniversalscalingofproducedstrangenesswith increasing system size. Both observations have not been taken properlyintoaccountbyphenomenologicalmodelsinthepastand thusfurtherdevelopmentsareneededtoarriveatfirmconclusions onthe K⁻-Npotential, whichisan importantingredient, e.g. for thedescriptionofastrophysicalobjects,asmentionedintheintro- duction.Conclusionsbasedonthat potential mustbetestedwith regard to their consistency with our findings. An improved un- derstanding ofstrangeness dynamics in HICs is also a necessary prerequisiteforsharpeningthesciencecaseofexperimentsatthe upcominglarge scale facilitiesas FAIR,NICA,J-PARC andthe low energyrunsofRHIC.

Acknowledgements

The HADES collaboration gratefully acknowledges the support by the grants SIP JUC Cracow (Poland), 2013/10/M/ST2/00042;

TU Darmstadt (Germany), VH-NG-823; GU Frankfurt (Germany), BMBF:05P15RFFCA,HIC forFAIR, ExtreMe Matter Institute EMMI;

TUMünchen,Garching(Germany),MLLMünchen,DFGEClust 153, DFG FAB898/2-1, BmBF 05P15WOFCA; JLU Giessen (Germany), BMBF:05P12RGGHM; IPN, IN2P3/CNRS (France); NPI CAS Rez (CzechRepublic),GACR13-06759S,MSMTLM2015049.

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