$K^{-}$ absorption on two nucleons and $ppK^{-}$ bound state search in the $\Sigma^{0}p$ final state

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Physics Letters B

www.elsevier.com/locate/physletb

K ⁻ absorption on two nucleons and ppK ⁻ bound state search in the ⁰ p ﬁnal state

O. Vázquez Doce

^a^,^b^,^∗

, L. Fabbietti

^a^,^b

, M. Cargnelli

^c

, C. Curceanu

^d

, J. Marton

^c

, K. Piscicchia

^d^,^e

, A. Scordo

^d

, D. Sirghi

^d

, I. Tucakovic

^d

, S. Wycech

^f

, J. Zmeskal

^c

, A. Anastasi

^d^,^g

, F. Curciarello

^g^,^h^,ⁱ

, E. Czerwinski

^j

, W. Krzemien

^f

, G. Mandaglio

^g^,^k

, M. Martini

^d^,^l

, P. Moskal

^j

, V. Patera

^m^,ⁿ

, E. Pérez del Rio

^d

, M. Silarski

^d

aExcellenceCluster‘OriginandStructureoftheUniverse’,85748Garching,Germany bPhysikDepartmentE12,TechnischeUniversitätMünchen,85748Garching,Germany cStefan-Meyer-InstitutfürSubatomarePhysik,1090Wien,Austria

dINFN,LaboratoriNazionalidiFrascati,00044Frascati,Italy eMuseoStoricodellaFisicaeCentroStudieRicercheEnricoFermi,Italy fNationalCentreforNuclearResearch,00681Warsaw,Poland gDipartimentoM.I.F.T.dell’UniversitàdiMessina,98166Messina,Italy hNovosibirskStateUniversity,630090Novosibirsk,Russia

iINFNSezioneCatania,95129Catania,Italy

jInstituteofPhysics,JagiellonianUniversity,30-059Cracow,Poland kINFNGruppocollegatodiMessina,98166Messina,Italy

lDipartimentodiScienzeeTecnologieapplicate,Università‘GuglielmoMarconi’,00193Roma,Italy mDipartimentodiScienzediBaseeApplicateperl’Ingegneria,Università‘Sapienza’,00161Roma,Italy nINFNSezionediRoma,00185Roma,Italy

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

Articlehistory:

Received17November2015 Receivedinrevisedform21April2016 Accepted1May2016

Availableonline4May2016 Editor:V.Metag

We reportthe measurementofK⁻ absorption processesinthe ⁰p finalstateandthe firstexclusive measurementofthe twonucleonabsorption (2NA)withthe KLOEdetector.The 2NAprocesswithout furtherinteractionsisfoundtobe9%ofthesumofallothercontributingprocesses,includingabsorption onthreeandmorenucleonsor2NAfollowedbyfinalstateinteractionswiththeresidualnucleons.We alsodetermine thepossible contributionofthe ppK⁻boundstate tothe⁰p finalstate. Theyieldof ppK⁻/K⁻_stopisfoundtobe(0.044±⁰.009stat⁺₋⁰₀^._.⁰⁰⁴₀₀₅syst)·¹⁰⁻²^butîtsstatisticalsignificancebasedonan F-testisonly1σ.

©²⁰¹⁶^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

ThestudyoftheK-nucleus¯ interactionatlowenergiesisofin- terest not only for quantifying the meson–baryon potential with strangecontent [1],butalsobecauseofitsimpact onmodelsde- scribing the structure of neutron stars (NS) [2]. The K-nucleus¯ potentialisattractive,astheorypredicts[3]andkaonicatomscon- ﬁrm[4],andthisfactleadstotheformulationofhypothesesabout antikaon condensates inside the dense interior of neutron stars.

Althoughrecently measured heavy NS [5]constrain the equation of state of the latter as being rather stiff andhence degrees of

*

Correspondingauthor.

E-mailaddress:oton.vazquez.doce@cern.ch(O. Vázquez Doce).

freedomotherthanneutronsaredisfavouredandtheoreticalcalcu- lations aboutnuclear systemswithhighmultiplicity ofantikaons present upper limitsthat disfavour the appearance ofa conden- sate[6],experimentalstudiesoftheantikaonbehaviourinnuclear matter are needed. The studyof antikaons production in heavy- ion reactions at moderate energies (EKIN≈^GeV), ^with ^maximal reachedbaryondensitiesof

ρ

≈ (^3–4)·

ρ

0(with

ρ

0beingthenor- mal nuclear matter density) was carried out to ﬁnd evidence of a strong attractivepotential betweenantikaons within densenu- clear matter [7].However, the statistics collected so far [8]does not allow forany conclusive statement about the role played by kaonswithindensenuclearmatter.Inthiscontextitiscrucialthat thetheoreticalmodelsusedtointerpretthedataproperlyinclude both the ratherlarge cross-sectionsfor antikaon absorption pro- cessesonnucleonsandthepresenceofthe(1405)resonance[1].

http://dx.doi.org/10.1016/j.physletb.2016.05.001

0370-2693/©²⁰¹⁶^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

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Indeed,anantikaon producedwithin nuclearmatter canundergo absorption upon one or more nucleons andthe measurement of suchprocessesisnotyetexhaustive,evenatnormalnucleardensi- ties[9,10].Absorptionprocessesalsoplayanimportantroleinthe understandingofkaonicatoms,whereasubstantialmulti-nucleon componentis put forward by some theoretical models [11]. The

(1405) link to the antikaon–nucleon interaction resides in the factthattheorydescribesthisresonanceasgenerateddynamically fromthecouplingoftheK–N¯ andthe–

π

channels[12].Hence the(1405)canbeseen,atleastpartially,asaK–N¯ boundstate.

Despiteofseveralexperimentalmeasurements [13],not eventhe vacuumpropertiesofthe(1405) areyetpinneddownprecisely andthose canalso be modiﬁed at ﬁnitebaryonic densities,with majorimplicationsfortheK dynamics¯ inthemedium.

Following the line of thought employed to interpret the

(1405), one or more nucleons could be kept together by the strongattractive interactionbetweenantikaonsandnucleons,and then so-calledkaonic bound states asppK⁻ or ppnK⁻ might be formed. The observation of such states and the measurement of their binding energies and widths would provide a quantitative measurementoftheK-nucleon¯ interactioninvacuum,providingan importantreferencefortheinvestigationofthein-mediumproper- tiesofK.¯ Forthedi-baryonickaonicboundstateppK⁻,theoretical predictions deliver a wide range of binding energies andwidths [14]andexperimentalresultsarecontradictory[15].Forthesearch ofsuchstatesinK⁻-absorptionexperiments,thecompetingmulti- nucleonicabsorptionplaysafundamentalrole.

Thiswork focuseson the analysis ofthe ⁰p finalstate produced in absorption processes of K⁻ on two or more nucleons and the search for a signature of the pp K⁻→ ⁰+^{p kaonic} bound state. The chosen ⁰p final state is free from the am- biguities present in the analysis of the p state considered in previous works[10]. Moreover, thisstudyrepresentsthe first at- temptofcombiningaquantitativeunderstandingoftheabsorption processesandcontributingbackgroundsourceswiththetestofdif- ferenthypothesesfortheppK⁻boundstateproperties.

2. ⁰p selectionandinterpretation

Theanalyseddatacorrespondsto atotalintegratedluminosity of1.74 fb⁻¹ collected in2004–2005 withtheKLOE detector[16]

locatedattheDANEe⁺e⁻collider[17].There,φmesonsarepro- ducednearlyatrest,providinganalmostmonochromaticsourceof K⁻withamomentumof∼^{127 MeV}/c.

The data here presented was taken by the KLOE Collabora- tion and provided to the authors for an independent analysis.

TheKLOE detector consistsofa large acceptance cylindricaldrift chamber (DC) of 3 m length and2 m radius surrounded by an electromagneticcalorimeter (EMC) inside an axial magnetic ﬁeld of 0.52 T. The DC provides a spatial resolution of 150 μm and 2 mmintheradialandlongitudinalcoordinates,respectively,anda transversemomentumresolutionof

σ

pT/p_T∼⁰.4% forlargeangle tracks.The EMCiscomposedofbarrelandend-capmodulescov- ering98%of thesolid anglewithenergy andtimeresolutions of

σ

E/E=⁵.7%/√

E(GeV)and

σ

t=^{54 ps}/√

E(GeV),respectively.The DCentrancewalliscomposed of750 μmcarbonfibrewithinner andouter layersof aluminiumof100 μm thickness. Thenumber ofstoppedK⁻ in thiswall iscalculatedby combiningthe experimental K⁺ tagging efficiency, the luminosity information and a Monte Carlo simulation to determine the rate of K⁻ stopped in the DCwall. The decay nearly at restof the φ meson allows to tag K⁻ events by the identification of a K⁺ track in the oppo- sitehemisphereoftheDC.Theextractedtotalnumberofstopped K⁻ isequalto(3.25±⁰.06)·¹⁰⁸^.^This^valueîsûsed^to^normalise themeasured yieldsofthedifferentabsorptionprocesses.Bothin

Fig. 1. (Colour online.)γinvariantmassdistribution.Theblacksymbolsrepresent theexperimentaldata,theblueandtheredhistogramsarethecontributionfrom themachinebackgroundandeventsthatcontainaπ⁰p intheﬁnalstate,respectively.Thegrayhistogramshowsthesimulated⁰ signalandthegreenonethe overallﬁttothedata(seetextfordetails).

ﬂightandatrestK⁻absorptionscanoccurandaweightof50%is assignedtoeachprocessforthenormalisation.

Thestarting pointfortheselection ofK⁻ absorptionprocesses leading to ⁰p final state isthe identification of a (1116) hy- peron through its decay into protons and negative pions (BR = 63.8%). Proton and pion track candidates are selected via dE/dx measurement in the DC. For each proton and pion candidate a minimum tracklength of atleast 30 and50 cm is required,respectively. The track length must also be larger than 50% ofthe expected length value calculated by extrapolating the measured momentum at the DC entrance. Additionally, proton candidates musthaveamomentumhigherthan170 MeV/c.Theseselections aimto improvethepurityofthe particleidentification, minimise the pion contamination in the proton sample and minimise the contributionfromlowmomentumtracksthatareemittedparallel totheDCwiresandreachtheEMCbarrel.ThereconstructedM_pπ⁻ invariant mass showsa meanvalue of 1115.753±⁰.002 MeV/c² forthemass,witharesolutionof

σ

=⁰.5 MeV/c²,well inagree- mentwiththePDGvalue[18].Thecandidatesareselectedusing thefollowingcut:1112<M_pπ⁻<1118 MeV/c².

Acommonvertexbetweenthecandidateandan additional protontrackis thensearched for.The obtainedresolutiononthe radialcoordinate(

ρ

p)forthep vertexis12 mm,andthistopo- logicalvariableisusedtoselecttheK⁻absorptionprocessesinside theDCwall.Thecontaminationofeventsofabsorptionsinthegas volume oftheDCis below 1%. Thep invariantmass resolution isevaluatedwithaphasespaceMonteCarlosimulationwherethe protonandmomentaarevaried from100 to700 MeV/candis foundtobeequalto1.1 MeV/c².Thecontaminationtotheproton sample forthe p ﬁnal state duetoheavierparticles (deuterons or tritons)is estimatedto be lessthan 2% by MC simulations of absorptioneventswithd andt ﬁnalstate.

The ⁰ candidates are identiﬁed through their decay into

γ

pairs. Afterthe reconstruction of a p pair, the photon se- lectioniscarriedoutviaitsidentiﬁcationintheEMC.Photoncan- didatesare selected byapplying acut on thedifference between the EMC time measurement and the expected time of arrival of thephotonwithin−¹.2< t<1.8 ns.Theresulting

γ

invariant massdistributionisshowninFig. 1,wherethe⁰ signalisvisible aboveabackgrounddistribution.

The following kinematic distributions are considered simulta- neouslyinaglobalﬁttoextract thecontributionsofthedifferent absorptionprocesses:the⁰p invariantmass,therelativeangleof the⁰ andprotoninthelaboratorysystemcos(θ0p),the⁰and theprotonmomenta.Theprocessesthataretakenintoaccountin theﬁtoftheexperimentaldataare:

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1. K⁻A→ ⁰^-(

π

)pspec(A), 2. K⁻pp→ ⁰^{-p (2NA),} 3. K⁻ppn→ ⁰-p-n (3NA), 4. K⁻ppnn→ ⁰-p-n-n (4NA).

This list includes the K⁻ absorption on two nucleons with and without ﬁnal state interaction for the ⁰p state and processes involvingmorethan two nucleonsin theinitial state.These con- tributionsare eitherextractedfromexperimentaldatasamplesor modelled via simulations and digitised. Nevertheless, the back- groundcontributions mustbe determinedandsubtracted priorto theglobalﬁt.

Twokindsofbackgroundcontribute totheanalysed ⁰p ﬁnal state:themachine backgroundandthe eventswith

π

⁰p inthe ﬁnal state. Both are quantiﬁed using experimental data.The machine background originates from spurious hitsin the EMC that enter the photon time coincidence window. It is emulated by a sidebandanalysis, selectingeventswithEMChitsoutsidetheco- incidence window (−⁴< t<−^{2 ns and} ³< t<8.2 ns). The

π

⁰p backgroundoriginateseitherfromasinglenucleonabsorp- tion followed by the creation of a

π

⁰ or a ⁰

π

⁰ pair. In the ﬁrst casealsoa rescatteringof the /

π

⁰ withone orseveral of the spectator nucleons could occur while in second case the ⁰ hypeonundergoesaninternalconversionprocessonaresidualnu- cleon(N→ ^N)^leading^to^a

π

⁰p ﬁnalstate.Eventswithtwo photon candidates within the selected time window andwith a

γ γ

invariant mass around the

π

⁰ nominalmass (3

σ

of the ex- perimentalresolution of 17 MeV/c²) are selected to emulatethe

π

⁰p background.Both experimental samples are used together witha simulationof the ⁰ signal to ﬁt the-photon invariant massdistributioninordertoextractthemachineand

π

⁰p back- groundcontributions. Events originatingfrom the ⁰

π

⁰ production aftera single nucleon absorption followedby the emission of a proton via the ﬁnal state interaction of the ⁰ or

π

⁰ con- tributeto the low energy part ofour spectra witha contamination of 3±^2%. ^Full ^scale simulations of the ⁰ reconstruction in the

γ

channel lead to a mass mean value and

σ

of 1189 and14.5 MeV/c²,respectively. Themean value isslightlyshifted withrespectto the⁰ nominalmassreportedin[18] becauseof thesmallbiasintroducedbythereconstruction.Thissimulationis usedtoﬁtthe⁰signalonthe

γ

distributionshowninFig. 1.

Fig. 1 showsthe results of the ﬁt to the

γ

invariant mass, with the background and signal components. The black symbols refer to the experimental data, the blue histogram to the ﬁt- ted machine background, the red histogram to the

π

⁰p background, the gray one to the simulated ⁰ signal and the green histogram to the sum of all ﬁt contributions. The errors shown forthebackgrounddistributionsrepresentthestatisticalerrorsof the ﬁt. To enhance the purity of the experimental data for the following analysissteps, a cut onthe

γ

invariant massaround thenominal⁰ mass isapplied.Theapplied cut,1150<Mγ<

1235 MeV/c²,corresponds to 3

σ

ofthe experimental resolution, andis veriﬁed with MC simulation. The contribution ofthe machine and

π

⁰p backgrounds within the selected

γ

invariant massis(14.6±⁰.8)% and(26.1±².7)%,respectively.Themachine backgroundis directlysubtracted from theexperimental data for each kinematic distributions used forthe globalﬁt. The ﬁt error is added to the statistical errors of the experimental data after the backgroundsubtraction. The

π

⁰p backgroundis considered intheglobalﬁtusingtheobtainedyieldasastartingvalue.

3. Determinationoftheabsorptionprocesses

The cocktail of processes considered for the global ﬁt is ob- tainedasfollows.Process 1corresponds tothe uncorrelatedpro-

ductionofaprotonfromthefragmentationoftheresidualnucleus together witha ⁰ productionfromtheK⁻absorption.Thiscon- tributionisobtainedfromexperimentaldatacontaining–triton–

proton,–deuteron–protonor–proton–proton intheﬁnalstate toemulatethecasewheretheselectedprotonisbarelycorrelated withthe.

Forthesimulationoftheabsorptionprocesses2–4a¹²Ctarget is considered. The Fermi momentum of the interacting nucleons insidethe¹²C,theinitialmomentumoftheabsorbedK⁻andthe mass difference betweenthe initial and residual nucleiare used in the calculation of the eventkinematic. The Fermi momentum distribution of the nucleons in ²⁷Al target is only 9% higher in comparisonwith¹²C.Themassdifferenceoftheinitialandresid- ualnucleivariesonlyby0.3%whenconsidering²⁷Alincomparison with¹²Candthisvalue islower thantheexperimentalresolution of the ⁰p invariant mass. For all the considered reactions, the emitted nucleons are required to have a total momentum above the¹²CFermimomentumtobeabletoleavethenucleus.

Forthe 2NA (process2),two casesare studied.One including theﬁnal state interaction(2NA-FSI)ofthe⁰ orprotonwiththe residualnucleus, andthesecondassuming noFSIatall(2NA-QF).

In the caseof the FSI-free productionof the ⁰p pair, only the fragmentationoftheresidualnucleusisconsidered.Thefollowing cases for the fragmentation for the spectator nucleus have been consideredinthesimulations:K⁻+¹²^C→ ⁰^p(¹⁰Be,⁴He+⁴^He+ 2n,⁴He+^2p+⁴ⁿ,4p+⁶ⁿ).Therelativeamplitudes ofthesecon- tributionsareleftfreeintheglobalﬁtandtheyareclearlyvisible inthe⁰p invariantmassdistributionasalowmasstail.Allother kinematic variablesstay unaffectedby the fragmentationprocess.

TheFSIforthe⁰ andpisimplementedbyallowingtheoutgoing protonor⁰ toscatterelasticallywiththeresidualnucleons.The nucleon momentum is sampled accordingto the Fermi distribution andthescatteringprobability isassumedto beequalto50%

for both thecases ofone andtwo collisions. The modiﬁed kinematic variables of the ⁰ or proton are then considered in the simulatedeventsusedintheglobalﬁt.Amoresophisticatedprop- agationofthehitprobabilitywasinvestigated[19],buttheresults shownomajordifferencesintheresultingkinematicdistributions.

This motivates the simplification. Reactions resulting into a ⁰n final state followed by a rescattering np→^{np have} âlsoînvesti- gated. Theyresultin thesamekinematicdistributions mentioned abovemodulusthesmalln-pmassdifference.

Theprocesses1–4togetherwiththe

π

⁰p backgroundsample are usedforthe globalﬁt.Thestarting value forthe

π

⁰p yield is extractedfromtheﬁtto the

γ

invariant massbutthiscom- ponent is free to varywithin 2

σ

in theglobal fit.Panels (a)–(d) inFig. 2showtheexperimentaldistributionsforthe⁰p invariant mass, the cos(θ0p), and the ⁰ andproton momenta, together with the fit results.The blackpoints representthe experimental data after the subtraction of the machine background with the systematicerrors shownby boxes. The grayfilledhistogram rep- resents the

π

⁰p background. The cyan distributions show the sum of the 4NA simulation together with the uncorrelated pro- ductionofthe⁰p finalstate.Thebluedistributionrepresentsthe 3NAandthemagentahistogramthe2NA-FSI.Thereddistribution showsthe2NA-QF.Thegraylineistheresultingtotalfit.Foreach fitted distribution the light errorband corresponds to the statis- ticalerrorresultingfromthefit,whilethedarkerband visualises thesymmetrised systematicerror.

The systematicerrorsforthe experimental andsimulateddis- tributions are obtainedby varying the minimum momentum required for the proton track selection, the time window for the selectionofsignalandmachinebackground,theyieldsofthema- chine backgrounddistributionsandtheselection ofthe⁰ mass.

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Fig. 2. (Colour online.)Experimentaldistributionsofthe⁰p invariantmass,cos(θ⁰p),⁰momentumandprotonmomentumtogetherwiththeresultsoftheglobalﬁt.

Theexperimentaldataafterthesubtractionofthemachinebackgroundareshownbytheblackcircles,thesystematicerrorsarerepresentedbytheboxesandthecoloured histogramscorrespondtotheﬁttedsignaldistributionswherethelight-colouredbandsshowtheﬁterrorsandthedarkerbandsrepresentthesymmetrisedsystematicerrors.

Thegraylineshows thetotalﬁtdistributions(seetextfordetails).

The obtainedresolution for the

γ

invariant mass and⁰ mo- mentumisequalto3.5 MeV/c² and6 MeV/c,respectively.

Theminimummomentumfortheprotontracksisvariedwithin 10 MeV/c of the central value of 170 MeV/c. Variations of 15%

aretestedforthetimewindowsusedtoselectthemachineback- ground,the photon signaland

π

⁰ background selectionindepen- dently.Asforthemachinebackgroundsubtraction, thesystematic erroris evaluated by repeating theﬁt allowing variations within 1

σ

of theinitial ⁰ mass ﬁt parameters. Forwhat concerns the simulateddistributions,thesystematicerrorsarealsoevaluatedfor theminimummomentumofthenucleonsrequiredtoexitthenu- cleus in the absorption simulation and the probability of having morethanonecollisionwhensimulatingtheFSIwiththeresidual nucleusfollowinga2NAprocess.

The minimum momentum for the nucleons is sampled according to the Fermi momentum distribution between 170 and 220 MeV/c.The systematicerroris evaluated by varyingthe two boundariesby15%inbothdirections.Forthesystematicvariation ofthe probabilityofhavingone ortwo collisionsfortheFSIpro- cesstwocases,40/60%and60/40%,areevaluatedrespectively.

The final fit results deliver the contribution of the different channelsto the analysed ⁰p final state. The best fit delivers a

χ

²/ndf of 0.85. The emission rates extracted from the fit are normalised to the total number of stopped antikaons, as sum- marisedinTable 1.Thefitresultslead tothefirst measurements of the genuine 2NA-QF for the final state ⁰p in reactions of stoppedK⁻ontargetsof¹²C and²⁷Al.Thiscontributionisfound tobeonly9% ofthetotal absorptioncross-sectionincluding2NA, 3NA and4NA processeswith alsothe contribution ofthe uncorrelated background leading to a ⁰p final state taken into ac- count.

Table 1

Productionprobabilityofthe ⁰p ﬁnalstatefordifferentintermediateprocesses normalisedtothenumberofstoppedK⁻intheDCwall.Thestatisticalandsystem- aticerrorsareshownaswell.“Tot2NA”standsforthesumofthe2NA-QFandthe 2NA-FSIprocesses.“Tot3body”standsforthesumof2NA-FSIand3NAprocesses.

yield/K⁻_stop·¹⁰⁻² σstat·¹⁰⁻² σsyst·¹⁰⁻²

2NA-QF 0.127 ±0.019 ⁺₋⁰₀^._.⁰⁰⁴₀₀₈

2NA-FSI 0.272 ±0.028 ⁺₋⁰₀^._.⁰²²₀₂₃

Tot 2NA 0.399 ±⁰.033 ⁺₋⁰₀^._.⁰²³₀₃₂

3NA 0.274 ±⁰.069 ⁺₋⁰₀^._.⁰⁴⁴₀₂₁

Tot 3 body 0.546 ±⁰.074 ⁺₋⁰₀^._.⁰⁴⁸₀₃₃ 4NA+^bkg. ^0.773 ±⁰.053 ⁺₋⁰₀^._.⁰²⁵₀₇₆

Similar measurements have been carried out and reported in [9,20].In[9]stoppedK⁻ina⁴Hetargethavebeenconsideredand theintegratedcontributiontothefinal state⁰() withnopion emission was extracted and found to be equal to 0.117±⁰.024 perstoppedK⁻.Thislargenumberisduetothecontamination in the sample and to the fact that absorptions on p-n pairs are included.Thedatain[20] show themeasurementofthe⁻p final state from a ¹³C target. There, a yield of 0.46±⁰.09(stat)± 0.02(syst)·¹⁰⁻²^per^stopped^K⁻îsattributed totheK⁻absorption onap-npair.

Even if the employed simulation model is rather simpliﬁed, the treatment of 2NA-QF is satisfactory forour purpose and the signature of thiscomponent well distinguishable from the other contributions,especiallyinthe⁰p invariantmassdistribution.On theother hand,acleardisentanglementof the3NAprocess from the2NAfollowedbyFSIisdiﬃcult,duetotheoverlapoftherel- evant kinematic variables over a wide rangeof the phase space.

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Fig. 3. (Colour online.)⁰p invariantmassandprotonmomentumdistributionstogetherwiththeresultsoftheglobalﬁtincludingtheppK⁻.Thedifferentcontributionsare labeledasinFig. 2andthegreenhistogramsrepresenttheppK⁻signal.

Two tests were performed that demonstrate that both physical processes should be included in the ﬁt. First, if the 3NA contri- butionisswitchedoffa variationofthereduced

χ

² of0.19from 0.85(the best ﬁt) to 1.05 is observed. Such effect is mainly due to the fact that the ⁰ andthe proton momentum distributions arenolongerwelldescribed.Theotherkinematicdistributionsare lesssensitivetothiscontribution.Inparticular,the

χ

² calculated fortheﬁtresultoftheprotonmomentumdistributiononlyisde- terioratedby 47%when excludingthe 3NAcontributionfromthe ﬁt.Asasecond limitingcasethe2NA+ ^FSIcontributionwasdis- carded,leadingtoareduced

χ

² of1.18.Inthiscasethecos(θ0p) and⁰p invariantmassdistributionsarenotproperlyreproduced.

The uncorrelatedemission ofthe ⁰p isalso notdistinguish- ablefromthe4NAprocessandhencethesetwocontributionsare addedup.

4. SearchfortheppK⁻boundstatesignal

The last step of the analysis consists in the search of the ppK⁻ bound state produced in K⁻ interactions with nuclear tar- gets,decaying intoa ⁰p pair.The ppK⁻ are simulatedsimilarly to the2NA-QF process butsamplingthe massof the ppK⁻ state withaBreit–Wignerdistribution,ratherthantheFermimomenta of the two nucleons in the initial state. The event kinematic is implemented by imposing the momentum conservation of the ppK⁻-residualnucleussystem.Differentvaluesforthebindingen- ergyandwidth varyingwithin 15–75 MeV/c² and30–70 MeV/c² insteps of15and20 MeV/c², respectively,are tested. Thisrange is selected according to theoretical predictions [14] and taking intoaccounttheexperimentalresolution.Theglobalﬁtisrepeated addingtheppK⁻statetotheprocesses1–4.Thebestﬁt(

χ

²/ndf= 0.807) isobtainedforappK⁻candidatewithabindingenergyof 45 MeV/c² anda width of30 MeV/c²,respectively. Fig. 3 shows theresults ofthebest ﬁtforthe ⁰p invariantmass andproton momentumdistributionswheretheppK⁻boundstatecontribution isshownin green.The resultingyield normalisedto the number ofstoppedK⁻isppK⁻/K⁻_stop= (⁰.044±⁰.009stat⁺₋⁰₀^._.⁰⁰⁴₀₀₅syst)·¹⁰⁻²^. Fig. 4showstheyieldresultsfromthetwobestﬁtsofthebound statewitha widthof30 MeV/c² andabinding energyof45and 60 MeV/c², respectively, with statisticalerrors calculated by MI- NOSat1

σ

(black line),2

σ

(blue boxes)and3

σ

(redboxes). The inclusionof theppK⁻ boundstate to theglobalﬁtintroduces an additional parameter andthis improves the ﬁt quality. Consider- ing also that the improvement of the

χ

² is only marginal, an F-Testiscarriedouttocomparethetwomodels:withandwithout ppK⁻ bound state. This test consists in evaluating the statistical signiﬁcance ofthe model withthe ppK⁻,accounting forthe ad-

Fig. 4. (Colour online.)ppK⁻yieldnormalisedtothenumberofstoppedK⁻forthe twobestﬁtscorrespondingtobindingenergiesof45and60 MeV/c²andwidthof 30 MeV/c²fortheppK⁻ boundstate.Theerrorsareonlystatisticalcalculatedby MINOSat1(blackline),2(blueboxes)and3(redboxes)σ.

Fig. 5. (Colour online.)p-ValueresultingfromtheF-testthatcomparesthetwoﬁt- tinghypotheses.Horizontallinesshowingupto3σaredrawn.

ditionalﬁtparameter, by comparingtheresiduals andnumberof degreesoffreedom oftwomodels.Theresulting F valuereadsas follows:

F

= (

S S E₁

−

^{S S E}2

)/(

ndf₁

−

^ndf2

)

S S E₂

/

ndf₂ (1)

withS S E beingthequadraticsumoftheresidualsbinperbinand ndf thenumberofdegreesoffreedom ofeachmodel.Theglobal p-value associatedto theobtained F valueandfromthenumber of parameters ineach model is shownin Fig. 5 for bound state simulationswithawidthof30,50and70 MeV/c²asafunctionof thebindingenergy.Onecanseethateventhebestﬁtcorresponds toap-valueequalto0.25 andhencetoasigniﬁcanceof1

σ

.

Thisimpliesthatalthoughtheﬁtfavoursthepresenceofanad- ditionalcomponentthatcanbeparametrisedwithaBreit–Wigner

(6)

distributionwithacertain massandwidth, its signiﬁcanceisnot suﬃcienttoclaimtheobservationoftheboundstate.Thepresent datalacks ofsensitivityforinvestigatingtheexistenceofabound statewithalargerbindingenergyand/orwidththanthoseconsid- eredinthedescribedanalysis.

5. Summary

WehavepresentedtheanalysisoftheK⁻absorptionprocesses leadingtothe⁰p finalstatemeasuredwiththeKLOEdetector.It isshownthat thefullkinematics ofthisfinal state canberecon- structed anda globalfitof thekinematic variablesallows to pin down quantitatively the different contributingprocesses. A cocktail of processes including simulations of the K⁻ absorption on twoormorenucleonswithorwithoutfinalstateinteractionsand backgroundprocessesestimatedwithexperimentaldataisusedfor theglobalfit.The absorptionontwonucleons withoutfinalstate interaction (2NA-QF) is isolated and the yield normalised to the number of absorbed K⁻ is presented in this work for the first time. It is shown that it is difficult to distinguish between the case where K⁻ are absorbed on three nucleons (3NA) or when thetwo-nucleonabsorptionisfollowedbyafinalstateinteraction (2NA-FSI).Forthispurposethedatashouldbefurtherinterpreted withthehelpoftheoreticalcalculations.The2NA-QFyieldisfound tobeabout20%ofthesumofthe3NA and2NA-FSIprocesses.If oneconsidersthe ratioofthe2NA-QFtoall othersimulatedpro- cessesavalueofabout9%isobtained.Hence,weconcludethatthe contributionofthe2NA-QFprocessesforK⁻momentalowerthan 120 MeV/cismuchsmallerincomparisonwithotherprocesses.

Asecondﬁtoftheexperimentaldataincludingthecontribution ofa ppK⁻ bound state decayinginto a ⁰p ﬁnal state iscarried out. A systematic scan of possible binding energies and widths varying within 15–75 MeV/c² and30–70 MeV/c²,respectively, is performedandthebestvalue ofthetotalreduced

χ

² isachieved forthehypothesisofappK⁻withabindingenergyof45 MeV/c² andawidthof30 MeV/c².ThecorrespondingppK⁻yieldextracted fromthefitisppK⁻/K⁻_stop= (⁰.044±⁰.009stat⁺₋⁰₀^._.⁰⁰⁴₀₀₅syst)·¹⁰⁻²^.Ân F-test is conducted to compare the simulation models withand withouttheppK⁻ signalandtoextractthesignificanceofthere- sult. A significance of only 1

σ

is obtained for the ppK⁻ yield result.Thisshowsthatalthoughthemeasuredspectraarecompat- iblewiththehypothesisofacontributionofthechannel pp K⁻→

⁰+^p,^thesigniﬁcanceoftheresultisnotsuﬃcienttoclaimthe observationofthisstate.

Acknowledgements

Weacknowledge theKLOECollaboration fortheir supportand forhavingprovidedusthedataandthetoolstoperformtheanal- ysis presentedinthispaper.

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