K- absorption on two nucleons and ppK- bound state search in the σ0p final state

(1)

Contents lists available atScienceDirect

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

a_Excellence_Cluster_‘Origin_and_Structure_of_the_Universe’,₈₅₇₄₈_Garching,_Germany b_Physik_Department_E12,_Technische_Universität_München,₈₅₇₄₈_Garching,_Germany c_{Stefan-Meyer-Institut}_für_Subatomare_Physik,₁₀₉₀_Wien,_Austria

d_INFN,_Laboratori_Nazionali_di_Frascati,₀₀₀₄₄_Frascati,_Italy e_Museo_Storico_della_Fisica_e_Centro_Studi_e_Ricerche_Enrico_Fermi,_Italy f_National_Centre_for_Nuclear_Research,₀₀₆₈₁_Warsaw,_Poland g_Dipartimento_M.I.F.T._{dell’Università}_di_Messina,₉₈₁₆₆_Messina,_Italy h_Novosibirsk_State_University,₆₃₀₀₉₀_Novosibirsk,_Russia

i_INFN_Sezione_Catania,₉₅₁₂₉_Catania,_Italy

j_Institute_of_Physics,_Jagiellonian_University,_30-059_Cracow,_Poland k_INFN_Gruppo_collegato_di_Messina,₉₈₁₆₆_Messina,_Italy

l_Dipartimento_di_Scienze_e_Tecnologie_applicate,_Università_‘Guglielmo_Marconi’,₀₀₁₉₃_Roma,_Italy m_Dipartimento_di_Scienze_di_Base_e_Applicate_per_{l’Ingegneria,}_Università_{‘Sapienza’,}₀₀₁₆₁_Roma,_Italy n_INFN_Sezione_di_Roma,₀₀₁₈₅_Roma,_Italy

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received17November2015 Receivedinrevisedform21April2016 Accepted1May2016

Availableonline4May2016 Editor:V.Metag

We reportthe measurementofK− absorption processesinthe 0_{p ﬁnal}_state_and_the _ﬁrst_exclusive

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+0.004

−0.005syst)·10−2butitsstatisticalsigniﬁcancebasedonan

F-testisonly1

σ

.

1. Introduction

ThestudyoftheK-nucleus

¯

interactionatlowenergiesisof in-terest not only for quantifying the meson–baryon potential with strangecontent [1],butalsobecauseofitsimpact onmodels de-scribing the structure of neutron stars (NS) [2]. The K-nucleus

¯

potentialisattractive,astheorypredicts

[3]

andkaonicatoms con-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).

freedomotherthanneutronsaredisfavouredandtheoretical calcu-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

0beingthe

nor-mal nuclear matter density) was carried out to ﬁnd evidence of a strong attractivepotential betweenantikaons within dense nu-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

(2)

Indeed,anantikaon producedwithin nuclearmatter canundergo

absorption upon one or more nucleons andthe measurement of

suchprocessesisnotyetexhaustive,evenatnormalnuclear densi-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-medium proper-tiesofK.

¯

Forthedi-baryonickaonicboundstateppK−,theoretical predictions deliver a wide range of binding energies andwidths

[14]andexperimentalresultsarecontradictory

[15]

.Forthesearch ofsuchstatesinK−-absorptionexperiments,thecompeting multi-nucleonicabsorptionplaysafundamentalrole.

Thiswork focuseson the analysis ofthe

0p ﬁnalstate

pro-duced 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 processesandcontributingbackgroundsourceswiththetestof dif-ferenthypothesesfortheppK−boundstateproperties.

2.

0p selectionandinterpretation

Theanalyseddatacorrespondsto atotalintegratedluminosity of1

.

74 fb−1 collected in2004–2005 withtheKLOE detector[16]

locatedattheDA

NEe+e−collider

[17]

.There,

φ

mesonsare pro-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

/

pT

∼

0

.

4% forlargeangle tracks.The EMCiscomposedofbarrelandend-capmodules cov-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 exper-imental 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.Thisvalueisusedtonormalise themeasured yieldsofthedifferentabsorptionprocesses.Bothin

Fig. 1. (Colour online.)γinvariantmassdistribution.Theblacksymbolsrepresent

theexperimentaldata,theblueandtheredhistogramsarethecontributionfrom themachinebackgroundandeventsthatcontainaπ0_{p in}_the_ﬁnal_state, respec-tively.Thegrayhistogramshowsthesimulated0 _signal_and_the_green_one_the 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, re-spectively. 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.ThereconstructedMpπ−

invariant mass showsa meanvalue of 1115

.

753

±

0

.

002 MeV

/

c2 forthemass,witharesolutionof

σ

=

0

.

5 MeV

/

c2,well in agree-mentwiththePDGvalue

[18]

.The

candidatesareselectedusing thefollowingcut:1112

<

Mpπ−

<

1118 MeV

/

c2.

Acommonvertexbetweenthe

candidateandan additional

protontrackis thensearched for.The obtainedresolutiononthe radialcoordinate(

ρ

p)forthe

p vertexis12 mm,andthis

topo-logicalvariableisusedtoselecttheK−absorptionprocessesinside theDCwall.Thecontaminationofeventsofabsorptionsinthegas volume oftheDCis below 1%. The

p invariantmass resolution isevaluatedwithaphasespaceMonteCarlosimulationwherethe

protonand

momentaarevaried 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 absorptioneventswith

d and

t ﬁnalstate.

The

0 candidates are identiﬁed through their decay into

γ

pairs. Afterthe reconstruction of a

p pair, the photon se-lectioniscarriedoutviaitsidentiﬁcationintheEMC.Photon can-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 massdistributionisshownin

Fig. 1

,wherethe

0 signalisvisible aboveabackgrounddistribution.

The following kinematic distributions are considered simulta-neouslyinaglobalﬁttoextract thecontributionsofthedifferent absorptionprocesses:the

0p invariantmass,therelativeangleof the

0 _and_proton_in_the_laboratory_system_cos

_(θ

0_p

)

,the

0and

theprotonmomenta.Theprocessesthataretakenintoaccountin theﬁtoftheexperimentaldataare:

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1. K−A

→

0_-

₍

_π

₎

_p spec(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

0_{p in}_the

ﬁnal state. Both are quantiﬁed using experimental data.The ma-chine background originates from spurious hitsin the EMC that enter the photon time coincidence window. It is emulated by a sidebandanalysis, selectingeventswithEMChitsoutsidethe co-incidence window (

−

4

<

t

<

−

2 ns and 3

<

t

<

8

.

2 ns). The

π

0_{p background}_originates_either_from_a_single_nucleon

absorp-tion followed by the creation of a

π

0 _or _a

0

_π

0 _pair. _In _the

ﬁrst casealsoa rescatteringof the

/

π

0 _with_one _or_several _of

the spectator nucleons could occur while in second case the

0

hypeonundergoesaninternalconversionprocessonaresidual nu-cleon(

N

→

N)leadingtoa

π

0_{p ﬁnal}_state._Events_with_two

photon candidates within the selected time window andwith a

γ γ

invariant mass around the

π

0 _nominal_mass ₍₃

_σ

_of _the

ex-perimentalresolution of 17 MeV

/

c2₎ _are _selected _to _emulate_the

π

0_{p background.}_Both _experimental _samples _are _used _together

witha simulationof the

0 signal to ﬁt the

-photon invariant massdistributioninordertoextractthemachineand

π

0_p

back-groundcontributions. Events originatingfrom the

0

π

0

produc-tion 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 contamina-tion 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 the

0 nominalmassreportedin

[18]

becauseof thesmallbiasintroducedbythereconstruction.Thissimulationis usedtoﬁtthe

0signalonthe

γ

distributionshownin

Fig. 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

0_p

back-ground, 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 thenominal

0 mass isapplied.Theapplied cut,1150

<

Mγ

<

1235 MeV

/

c2_,_corresponds _to ₃

_σ

_of_the _experimental _resolution,

andis veriﬁed with MC simulation. The contribution ofthe ma-chine and

π

0_{p 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

0_{p background}_is _considered

intheglobalﬁtusingtheobtainedyieldasastartingvalue. 3. Determinationoftheabsorptionprocesses

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

pro-ductionofaprotonfromthefragmentationoftheresidualnucleus together witha

0 _production_from_the_K−_absorption._This

con-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 27_Al _target _is _only _9% _higher _in

comparisonwith12_C._The_mass_difference_of_the_initial_and

resid-ualnucleivariesonlyby0.3%whenconsidering27_Al_in_comparison

with12_C_and_this_value _is_lower _than_the_experimental_resolution

of the

0p invariant mass. For all the considered reactions, the

emitted nucleons are required to have a total momentum above

the12_C_Fermi_momentum_to_be_able_to_leave_the_nucleus.

Forthe 2NA (process2),two casesare studied.One including theﬁnal state interaction(2NA-FSI)ofthe

0 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−

+

12C

→

0p

(

10Be

,

4He

+

4He

+

2n

,

4He

+

2p

+

4n

,

4p

+

6n

)

.Therelativeamplitudes ofthese con-tributionsareleftfreeintheglobalﬁtandtheyareclearlyvisible inthe

0p invariantmassdistributionasalowmasstail.Allother kinematic variablesstay unaffectedby the fragmentationprocess. TheFSIforthe

0 andpisimplementedbyallowingtheoutgoing protonor

0 toscatterelasticallywiththeresidualnucleons.The

nucleon momentum is sampled accordingto the Fermi

distribu-tion andthescatteringprobability isassumedto beequalto50% for both thecases ofone andtwo collisions. The modiﬁed kine-matic variables of the

0 _or _proton _are _then _considered _in _the

simulatedeventsusedintheglobalﬁt.Amoresophisticated prop-agationofthehitprobabilitywasinvestigated

[19]

,buttheresults shownomajordifferencesintheresultingkinematicdistributions. This motivates the simpliﬁcation. Reactions resulting into a

0n ﬁnal state followed by a rescattering np

→

np have also investi-gated. Theyresultin thesamekinematicdistributions mentioned abovemodulusthesmalln-pmassdifference.

Theprocesses1–4togetherwiththe

π

0_{p background}_sample

are usedforthe globalﬁt.Thestarting value forthe

π

0_{p yield}

is extractedfromtheﬁtto the

γ

invariant massbutthis com-ponent is free to varywithin 2

σ

in theglobal ﬁt.Panels (a)–(d) in

Fig. 2

showtheexperimentaldistributionsforthe

0p invariant mass, the cos

(θ

0_p

)

, 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

0_{p background.} _The _cyan _{distributions} _show _the

sum of the 4NA simulation together with the uncorrelated pro-ductionofthe

0p 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 andsimulated

dis-tributions are obtainedby varying the minimum momentum

re-quired for the proton track selection, the time window for the selectionofsignalandmachinebackground,theyieldsofthe ma-chine backgrounddistributionsandtheselection ofthe

0 mass.

(4)

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

Theexperimentaldataafterthesubtractionofthemachinebackgroundareshownbytheblackcircles,thesystematicerrorsarerepresentedbytheboxesandthecoloured histogramscorrespondtothefittedsignaldistributionswherethelight-colouredbandsshowthefiterrorsandthedarkerbandsrepresentthesymmetrisedsystematicerrors. Thegraylineshows thetotalfitdistributions(seetextfordetails).

The obtainedresolution for the

γ

invariant mass and

0 mo-mentumisequalto3.5 MeV/c2 _and_{6 MeV/c,}_{respectively.}

Theminimummomentumfortheprotontracksisvariedwithin 10 MeV/c of the central value of 170 MeV/c. Variations of 15% aretestedforthetimewindowsusedtoselectthemachine back-ground,the photon signaland

π

0 _background _selection

indepen-dently.Asforthemachinebackgroundsubtraction, thesystematic erroris evaluated by repeating theﬁt allowing variations within 1

σ

of theinitial

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

The minimum momentum for the nucleons is sampled

ac-cording to the Fermi momentum distribution between 170 and

220 MeV/c.The systematicerroris evaluated by varyingthe two boundariesby15%inbothdirections.Forthesystematicvariation ofthe probabilityofhavingone ortwo collisionsfortheFSI pro-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-marisedin

Table 1

.Thefitresultslead tothefirst measurements of the genuine 2NA-QF for the final state

0_{p in} _reactions _of

stoppedK−ontargetsof12C and27Al.Thiscontributionisfound tobeonly9% ofthetotal absorptioncross-sectionincluding2NA, 3NA and4NA processeswith alsothe contribution ofthe uncor-related background leading to a

0p ﬁnal state taken into ac-count.

Table 1

Productionprobabilityofthe 0p ﬁnalstatefordifferentintermediateprocesses normalisedtothenumberofstoppedK−intheDCwall.Thestatisticaland system-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 +0.023 −0.032 3NA 0.274 ±0.069 +0.044 −0.021 Tot 3 body 0.546 ±0.074 +0.048 −0.033 4NA+bkg. 0.773 ±0.053 +₋00..025076

Similar measurements have been carried out and reported in

[9,20].In

[9]

stoppedK−ina4_He_target_have_been_considered_and

theintegratedcontributiontotheﬁnal state

0

₍₎

_with_no_pion

emission was extracted and found to be equal to 0

.

117

±

0

.

024 perstoppedK−.Thislargenumberisduetothe

contamination in the sample and to the fact that absorptions on p-n pairs are included.Thedatain

[20]

show themeasurementofthe

−p ﬁ-nal state from a 13C target. There, a yield of 0

.

46

±

0

.

09

(

stat

)

±

0

.

02

(

syst

)

·

10−2perstoppedK−isattributed 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,especiallyinthe

0p invariantmassdistribution.On theother hand,acleardisentanglementof the3NAprocess from the2NAfollowedbyFSIisdiﬃcult,duetotheoverlapofthe rel-evant kinematic variables over a wide rangeof the phase space.

(5)

Fig. 3. (Colour online.)0_{p invariant}_mass_and_proton_momentum_{distributions}_together_with_the_results_of_the_global_ﬁt_including_the_ppK−_._The_different_{contributions}_are

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 _of_0.19_from

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

fortheﬁtresultoftheprotonmomentumdistributiononlyis de-terioratedby 47%when excludingthe 3NAcontributionfromthe ﬁt.Asasecond limitingcasethe2NA

+

FSIcontributionwas dis-carded,leadingtoareduced

χ

2 _of_1.18._In_this_case_the_cos

_(θ

0_p

)

and

0_{p invariant}_mass_{distributions}_are_not_properly_reproduced.

The uncorrelatedemission ofthe

0p isalso not distinguish-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.Differentvaluesforthebinding en-ergyandwidth varyingwithin 15–75 MeV/c2 and30–70 MeV/c2 insteps of15and20 MeV/c2_, _{respectively,}_are _tested. _This_range

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 _and_a _width _of_{30 MeV/c}2_,_{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 _and_a_binding _energy_of₄₅_and

60 MeV/c2_, _{respectively,} _with _statistical_errors _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/c2_and_width_of 30 MeV/c2_for_the_ppK− _bound_state._The_errors_are_only_statistical_calculated_by

MINOSat1(blackline),2(blueboxes)and3(redboxes)σ.

Fig. 5. (Colour online.)p-ValueresultingfromtheF-testthatcomparesthetwo

ﬁt-tinghypotheses.Horizontallinesshowingupto3σaredrawn.

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

F

=

(

S S E1

−

S S E2

)/(

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/c2_as_a_function_of

thebindingenergy.Onecanseethateventhebestﬁtcorresponds toap-valueequalto0

.

25 andhencetoasigniﬁcanceof1

σ

.

Thisimpliesthatalthoughtheﬁtfavoursthepresenceofan ad-ditionalcomponentthatcanbeparametrisedwithaBreit–Wigner

(6)

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

5. Summary

WehavepresentedtheanalysisoftheK−absorptionprocesses leadingtothe

0_{p ﬁnal}_state_measured_with_the_KLOE_detector._It

isshownthat thefullkinematics ofthisfinal state canbe recon-structed anda globalfitof thekinematic variablesallows to pin down quantitatively the different contributingprocesses. A cock-tail 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 othersimulated pro-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 _is_achieved

forthehypothesisofappK−withabindingenergyof45 MeV/c2

andawidthof30 MeV/c2.ThecorrespondingppK−yieldextracted fromtheﬁtisppK−

/

K−_stop

= (

0

.

044

±

0

.

009stat+₋0₀._.004₀₀₅syst

)

·

10−2.An F-test is conducted to compare the simulation models withand withouttheppK− signalandtoextractthesigniﬁcanceofthe re-sult. A signiﬁcance of only 1

σ

is obtained for the ppK− yield result.Thisshowsthatalthoughthemeasuredspectraare compat-iblewiththehypothesisofacontributionofthechannel pp K−

→

0

+

p,thesigniﬁcanceoftheresultisnotsuﬃcienttoclaimthe observationofthisstate.

Acknowledgements

Weacknowledge theKLOECollaboration fortheir supportand forhavingprovidedusthedataandthetoolstoperformthe anal-ysis presentedinthispaper.

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