“K−pp”, a K-meson nuclear bound state, observed in 3He(K−, Λ p)n reactions

Citation for this paper:

Ajimura, S., Asano, H., Beer, G., Berucci, C., Bhang, H., Bhang, H. & Zmeskal, J.

(2018). “K

−

_{pp”, a K-meson nuclear bound state, observed in}

3

_He(K

−

_{, Λ p)n}

reactions. Physics Letters B, (789), 620-625.

https://doi.org/10.1016/j.physletb.2018.12.058

UVicSPACE: Research & Learning Repository

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Faculty of Science

Faculty Publications

_____________________________________________________________

“K

−

_{pp”, a K-meson nuclear bound state, observed in}

3

_He(K

−

_{, Λ p)n reactions}

J-PARC E15 collaboration, S. Ajimura, H. Asano, G. Beer, C. Berucci, H. Bhang, M.

Bragadireanu, P. Buehler, L. Busso, M. Cargnelli, S. Choi, C. Curceanu, S. Enomoto,

H. Fujioka, Y. Fujiwara, T. Fukuda, C. Guaraldo, T. Hashimoto, R.S. Hayano, T.

Hiraiwa, M. Iio, M. Iliescu, K. Inoue, Y. Ishiguro, T. Ishikawa, S. Ishimoto, K.

Itahashi, M. Iwasaki, K. Kanno, K. Kato, Y. Kato, S. Kawasaki, P. Kienle, H. Kou, Y.

Ma, J. Marton, Y. Matsuda, Y. Mizoi, O. Morra, T. Nagae, H. Noumi, H. Ohnishi, S.

Okada, H. Outa, K. Piscicchia, Y. Sada, A. Sakaguchi, F. Sakuma, M. Sato, A.

Scordo, M. Sekimoto, H. Shi, K. Shirotori, D. Sirghi, F. Sirghi, K. Suzuki, S. Suzuki,

T. Suzuki, K. Tanida, H. Tatsuno, M. Tokuda, D. Tomono, A. Toyoda, K. Tsukada, O.

Vazquez Doce, E. Widmann, T. Yamaga, T. Yamazaki, Q. Zhang, J. Zmeskal

February 2019

© 2018 Published by Elsevier B.V. This is an open access article under the CC BY

license (

http://creativecommons.org/licenses/by/4.0/

)

This article was originally published at:

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

“K

−

pp”,

a

K -meson

nuclear

bound

state,

observed

in

3

He

(

K

−

,



p

)

n

reactions

J-PARC

E15

collaboration,

S. Ajimura

a

,

H. Asano

b

,

G. Beer

c

,

C. Berucci

d

,

H. Bhang

e

,

M. Bragadireanu

f

,

P. Buehler

d

,

L. Busso

g

,

h

,

M. Cargnelli

d

,

S. Choi

e

,

C. Curceanu

i

,

S. Enomoto

j

,

H. Fujioka

k

,

Y. Fujiwara

l

,

T. Fukuda

m

,

C. Guaraldo

i

,

T. Hashimoto

n

,

R.S. Hayano

l

,

T. Hiraiwa

a

,

M. Iio

j

,

M. Iliescu

i

,

K. Inoue

a

,

Y. Ishiguro

o

,

T. Ishikawa

l

,

S. Ishimoto

j

,

K. Itahashi

b

,

M. Iwasaki

b

,

k

,

∗

,

K. Kanno

l

,

K. Kato

o

,

Y. Kato

b

,

S. Kawasaki

a

,

P. Kienle

p

,

1

,

H. Kou

k

,

Y. Ma

b

,

J. Marton

d

,

Y. Matsuda

l

,

Y. Mizoi

m

,

O. Morra

g

,

T. Nagae

o

,

H. Noumi

a

,

H. Ohnishi

q

,

b

,

S. Okada

b

,

H. Outa

b

,

K. Piscicchia

i

,

Y. Sada

a

,

A. Sakaguchi

a

,

F. Sakuma

b

,

∗

,

M. Sato

j

,

A. Scordo

i

,

M. Sekimoto

j

,

H. Shi

i

,

K. Shirotori

a

,

D. Sirghi

i

,

f

,

F. Sirghi

i

,

f

,

K. Suzuki

d

,

S. Suzuki

j

,

T. Suzuki

l

,

K. Tanida

n

,

H. Tatsuno

r

,

M. Tokuda

k

,

D. Tomono

a

,

A. Toyoda

j

,

K. Tsukada

q

,

O. Vazquez Doce

i

,

p

,

E. Widmann

d

,

T. Yamaga

b

,

a

,

∗

,

T. Yamazaki

l

,

b

,

Q. Zhang

b

,

J. Zmeskal

d

a_{OsakaUniversity,Osaka,567-0047,Japan} b_{RIKEN,Wako,351-0198,Japan}

c_{UniversityofVictoria,VictoriaBCV8W3P6,Canada}

d_{Stefan-Meyer-InstitutfürsubatomarePhysik,A-1090Vienna,Austria} e_{SeoulNationalUniversity,Seoul,151-742,SouthKorea}

f_{NationalInstituteofPhysicsandNuclearEngineering–IFINHH,Bucharest,Magurele,Romania} g_{INFNSezionediTorino,10125Torino,Italy}

h_{Universita’diTorino,Torino,Italy}

i_{LaboratoriNazionalidiFrascatidell’INFN,I-00044Frascati,Italy}

j_{HighEnergyAcceleratorResearchOrganization(KEK),Tsukuba,305-0801,Japan} k_{TokyoInstituteofTechnology,Tokyo,152-8551,Japan}

l_{TheUniversityofTokyo,Tokyo,113-0033,Japan}

m_{OsakaElectro-CommunicationUniversity,Osaka,572-8530,Japan} n_{JapanAtomicEnergyAgency,Ibaraki319-1195,Japan}

o_{KyotoUniversity,Kyoto,606-8502,Japan}

p_{TechnischeUniversitätMünchen,D-85748,Garching,Germany} q_{TohokuUniversity,Sendai,982-0826,Japan}

r_{LundUniversity,Lund,22100,Sweden}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received9August2018

Receivedinrevisedform25October2018 Accepted4December2018

Availableonline2January2019 Editor:V.Metag

Keywords:

Kaon Strangeness

Mesonicnuclearboundstate

Weobservedadistinctpeakinthep invariantmassspectrumof3_He(K−_{,p)n,wellbelowmK+2mp,} i.e.,themassthresholdoftheK−tobeboundtotwoprotons.Byselectingarelativelylarge momentum-transfer region q=350∼650 MeV/c, one can kinematically separate the peak from the quasi-free process,K N→K N followedbythenon-resonantabsorptionbythetwospectator-nucleonsK N N→ N. We foundthat thesimplestfitto theobserved peakgives usaBreit–Wignerpole positionat BKpp=

47±3(stat.)₋+₆3(sys.)MeVhavingawidthKpp=115±7(stat.)₋+2010(sys.)MeV,andtheS-waveGaussian reactionform-factorparameter QKpp=381±14(stat.)₋+570 (sys.)MeV/c,as anewform ofthenuclear boundsystemwithstrangeness–“K−pp”.

©2018PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

*

Correspondingauthorsat:RIKEN,Wako,351-0198,Japan.

E-mailaddresses:masa@riken.jp(M. Iwasaki),

sakuma@ribf.riken.jp

(F. Sakuma),

takumi.yamaga@riken.jp

(T. Yamaga).

1 _Deceased.

https://doi.org/10.1016/j.physletb.2018.12.058

1. Introduction

Sincethepredictionofthe

π

-mesonbyYukawa[1], the long-standingquestionhasbeenwhetheramesonicnuclearboundstate exists, i.e., whethera meson forms aquantumstate at an eigen-energyEM belowtheintrinsicmassm withoutpromptlyvanishing

innuclearmedia.Ifit exists,itmeansthat ameson(qq) formsa quantumstatewithin thenuclearmedium constitutedofbaryons (qqq).Therearemanyimportantsubjectstostudy,e.g.,howhadron massesaregeneratedfrom

∼

masslessparticles[quarks(mq

∼

few

MeV/c2)andgluons(mg

=

0)];howthepropertiesofthesemesons

changeinthe nuclearmedium;how hadronsare confinedinthe nuclearmedia;andtheequation-of-stateinnuclear(orstar) mat-ter. Therefore, many mesons have been examined over the past century,to seewhetheramesonicnuclearbound stateexists be-lowthemassthresholdwithabindingenergy BM

≡

m

−

EM,but

therehasbeennoclearevidencefortheirexistence.

The

π

N S-wave interaction is repulsive, so there is no nu-clearbound state much deeper than the atomicstates[2]. What aboutthe second-lightestmeson with an s-quark, the kaon? Af-terthe longstanding “kaonichydrogenpuzzle” wasresolved [3–5], thestrongK N attractiveinteractionwasestablishedintheisospin

I

=

0 channel. This leads us naturally to the ansatz that the

(

1405

)

couldbea K−p nuclearboundstate,ratherthana three-quark



-baryonic-stateasitisnamed,i.e.,thenameimpliesthatit isafirstexcited stateofthe



baryon whoseexcitation iscaused bytheconstituent-quarkinternal-motion.ArecentlatticeQCD cal-culationalsosupportsthe K−p picture[6].Akaishi–Yamazaki pre-dictedtheexistence ofkaonic nuclearboundstatesassuming the

(

1405

)

bea K−p boundstate[7].Thesimplestpredictedkaonic nuclearsystem, K N N symbolicallydenotedas“K−pp”,hascharge

+

1, I

=

1₂ and JP

=

0−, with a binding energy BKpp

=

48 MeV

(measuredfrom M

(

K pp

)

≡

mK

+

2mp

≈

2370 MeV/c2) anda

par-tialmesonicdecaywidth



πY N

=

61 MeV[8].

Triggered by this prediction, many studies were undertaken. Theoretically, the existence of the kaonic bound states is well supported, butthe resultsare widely scattered: binding energies (BKpp

≈

10

∼

100 MeV)andpartialmesonicdecaywidths(



πY N

≈

40

∼

100 MeV), e.g., [9–12], while the total decay width



K pp

(includingnon-mesonic decaychannels) hasyet tobe calculated. Experimentally,there havebeenmanysearchesfor“K−pp”, with reportsofpossiblecandidates[13–15] aswellascontradictory re-sults[16,17],leavingthematterbothcontroversialandunsettled.

2. J-PARCE15experiment

We have conducted an experimental search for the “K−pp”

by bombarding a 3He target witha 1 GeV/c K− beamto knock out a nucleon with the kaon, and directly introduce a recoiled virtual-K -meson into the residual nucleus. At this momentum (

√

s

∼

1

.

8 GeVfor K N),thesingle-nucleonelastic-reaction K N

→

K N has a very large cross-section, helped by the presence of

Y∗-resonances(mY∗

∼

1

.

8 GeV/c2)[18].Ontheotherhand,dueto

theshrinkageof thede Broglie wave-lengthofthe projectile, di-rectmulti-nucleonabsorption(multi-NA),whichproducesasevere backgroundinan at-rest-kaon-absorption experimenttosearch for “K−pp”[17,19],willberelativelysuppressed.

Themomentumofthevirtual ‘K ’isgivenasq_K

=

qK n

≡ |

qK n

|

(i.e. the momentum difference of an incident kaon and the for-wardneutronqK n

≡

pLab_K−.

−

pnLab.),wherethesuperscriptrepresents

thatit isinthelaboratory-frame,andthe singlequotation marks representthat it is within the strong interaction range in a nu-cleus.When the‘K ’ is backscattered, theq_K can be assmall as

∼

200MeV/c (theminimumq amongthesearchexperiments per-formed). With this condition, a successive reaction between the

virtual‘K ’andtwo‘spectatornucleons’at-restinthelaboratory-frame

canbe efficientlyrealized.Thisway,a“K−pp” canbe formed al-mostat-rest in thelaboratory-frame, whichmakes the formation probabilitylarge.Inthisreactionchannel,onecanreducethe pos-siblecombinationsof“K−pp”decayparticles,becausethes-quark

isconserved inthestronginteraction andthusa hadronwithan

s-quark should exist in its decay. Thus, one can efficiently con-duct invariant mass spectroscopy (decay channel) by having the detector surrounding the target, and missing mass spectroscopy (formation channel) usinga forward neutroncounter (NC)anda spectrometertosimultaneouslydetectaforwardgoingneutron(or proton) coming from K N

→

K N reaction. We designed our ap-paratus toachieve a mass resolutionof

σ

M

∼

10 MeV/c2 both in

missingandininvariantmass[20].

Thefirst-stageexperiment,J-PARCE151st,exhibitedahugepeak aboveM

(

K pp

)

byobservingtheneutroninNC(

θ

NC

∼

1

/

20)[21].

This spectral peak has a very large cross-section of



6 mb/sr in the semi-inclusive quasi-elastic K N

→

K N channel at

θ

n

=

0.

Thus, we confirmed that the forward nucleon knockout reaction,

K N

→

K N, isthe dominant process at pK

=

1 GeV/c.It also

re-vealed that there was a large event-excess extending from the quasi-elasticK bumptothelowermassregion.Thetailreachedto

∼

100MeV below M

(

K pp

)

(

∼

1mb/sr). However, nosignificant structurewas observedinthistailatanylocation,where“K−pp”

candidateswerereported[13–15].

On the contrary, we found a kinematical anomaly: a peak-like structure was observed in the



p invariant mass (IMp

≡

M

,

hereafter)spectrum ofthenon-mesonic



pn finalstate below theM

(

K pp

)

massthresholdatlowqp

(

=

qK n

≡

q

,

hereafter

)

[22].

This is the simplest final state, which consists of the minimum numberof lowest massbaryons withoutmeson emission, sothe possibleinterpretations arelimited. Themostpromising interpre-tationis:the“K−pp”isformedbyknockingoutaneutron,decays to



p, and thus a corresponding peak is seen in the M

spec-trum.

Tosignificantlyimprovethestatisticsofthe



pn finalstate per-mittingustoexaminethisinterpretation,wesetahigherpriority onaccumulatingeventshavingthreechargedparticlehitsaround the target withoutrequiringforwardneutrondetection. To identify the



pn finalstate,weobservedthembythe pp

π

−-events with-out requesting an NC hit, andwe conductedthe kinematical re-fit of p

π

−p (

+

nmissing) to the



pn finalstate using energy– momentum conservation atthe analysis stage to prevent biasing thedata.Wesucceededinaccumulating30timesasmuchdataon

p

π

−p eventscomparedtoE151st.

The formation channel, K−

+

3 _He

_→

_“K−_pp”

₊

_{n, can be} uniquely definedby the following two parameters;the



p-inva-riant mass M and the momentum transfer q. The event dis-tributions over M and q are given in Fig. 1. As shown in the figure, a strong event-concentration observed previously [22] is confirmed near the mass threshold M

(

K pp

)

at the lower-q side

(

Mc2

_,

_qc

₎

_{∼ (}

₂

_.

₃₇

_,

₀

_.

₂₅

₎

_GeV.

To our surprise, however, the structure near M

(

K pp

)

cannot be represented as a single Breit–Wigner (B.W.) function, as was naïvelyassumedinthepreviouspaper[22].Instead,itismore nat-uraltointerpret thisstructureasconsistingofat-leasttwo inter-nal substructuresoriginatingfromdifferentreaction mechanisms. However, the primary reaction K−N

→

‘K ’n (n forward) would be the same, because both substructures are close to

(

M

,

q

)

≈

(

mK

+

2mp

,

lower limit

)

.

The2Dplot(Fig.1a)showsthattheeventdistributionpatterns change at M

(

K pp

)

. The yield of a region-of-interest just below

M

(

K pp

)

is reduced as a function of q, but extends to q

∼

650 MeV/c.ThedistributioncentroidofM doesnotdependonq within

interpre-Fig. 1. a)2DeventdistributionplotontheM (=IMp)andthemomentumtransferq (qp)forthepn finalstate.TheMF(q)giveninEq. (2),themassthresholdM(K pp),

andthekinematicalboundaryforpn finalstate,areplottedinthefigure.Thelowerq boundarycorrespondstoθn=0 (forwardn),andtheupperboundarycorrespondsto

θn=π(backwardn).ThehistogramsofprojectionontotheM axisb),andontoq axisc)arealsogiventogetherwiththedecompositionsofthefitresult.

tation. On the other hand, the distribution centroid of M above M

(

K pp

)

dependsonq,andtheyieldvanishesrapidlyasafunction ofq.ThecentroidshiftstotheheavierM sideforthelargerq, sug-gestingitsnon-resonantfeature,i.e. thepropagator’skineticenergy isconvertedtotherelativekineticenergybetween



andp,near thelowerq boundary.Thus,themostnaturalinterpretationwould benon-resonantabsorptionofquasi-free‘K ’bythe‘N N’spectator (QF_KA)duetothefinalstate interaction(FSI).Thisprocesscanbe understoodasapart ofthequasi-free K reaction,in whichmost

K sescape from the nucleus, aswe published in [21]. Note that thereisanotherchangeineventdistributions atM

(

K pp

)

,i.e.,the eventdensityislowclosetothe

θ

n

=

0 linebelowM

(

K pp

)

,while

itishighabove M

(

K pp

)

(thispointwillbeseparatelydiscussedin thelastsection).

Thisspectralsubstructureisinrelativelygoodagreementwith that of Sekihara–Oset–Ramos’s spectroscopic function [23] to ac-count fortheobserved structure in[22]. Actually,their spectrum has two structures, namely A) a “K−pp” pole below the mass threshold M

(

K pp

)

(meson bound state), and B) a QF_KA process above the M

(

K pp

)

. Thus, the interpretation of the internal sub-structuresnearM

(

K pp

)

isconsistentwiththeirtheoreticalpicture.

3. Fittingprocedure

We first describe what we can expect if point-like reactions happenbetweenan incoming K− and3_{He,whichgoesto a}

_

_pn finalstate.Theeventsmustdistributesimplyaccordingtothe



pn

Lorentz-invariantphase space

ρ

3

(

M

,

q

)

,as shownin Fig. 2a. We fullysimulatedtheseeventsbasedonourexperimental setupand analyzed the simulated events by the common analyzer applied to the experimental data. The result is shown in Fig. 2b, which is simply

E(

M

,

q

)

×

ρ

3

(

M

,

q

)

, where

E(

M

,

q

)

is the experimen-tal efficiency. One can evaluate

E(

M

,

q

)

by dividing Fig. 2b by Fig.2a bin-by-bin,which isgiveninFig. 2c.Asshownin Fig.2c, we havesufficient andsmooth experimental efficiencyat the re-gion of interest, M

≈

M

(

K pp

)

at lower q, based on the careful designoftheexperimentalsetup.Ontheotherhand,theefficiency

is rather low at the dark blue region and even less toward the kinematicalboundary,asshowninFig.2c.Ifwe simplyapplythe acceptance correction, thestatistical errors ofthose bins become hugeandveryasymmetric.Thisfactmakestheacceptance correc-tion oftheentire

(

M

,

q

)

regionunrealistic.Therefore,we applied areverseprocedure,i.e.,wepreparedsmoothfunctions f_{j}

(

M

,

q

)

(toaccountforthe j-th physicalprocess)andmultipliedthatwith

E(

M

,

q

)

×

ρ

3

(

M

,

q

)

(

=

Fig. 2b) bin-by-bin. In this manner, one canreliably estimatehowthephysicsprocessshould beobserved in ourexperimental setup,andthispermitted usto calculatethe mean-event-numberexpectedineach2Dbin.Thethreeintroduced modelfunctions(atthebestfitparameterset)areshowninFig.3. A veryimportant andstriking structureexists below M

(

K pp

)

, whichcouldbeassignedasthe“K−pp”signal.Tomakethefitting function as simple as possible, let us examine the event distri-bution by usingthe same function aswas applied in [22], i.e., a product ofB.W.depending onlyon M, andan S-wave harmonic-oscillatorform-factordependingonlyonq as:

f_{Kpp}

=

CKpp





Kpp

/

2



2



M

−

MKpp



2

+





Kpp

/

2



2 exp



−



q QKpp



2



,

(1)

where MKpp and



Kpp are the B.W. poleposition and thewidth,

QKpp is the reaction form-factor parameter, and CKpp is the

nor-malizationconstant,asshowninFig.3a.

Amodel-functionoftheQF_KAchannel, f_{Q F_KA}

(

M

,

q

)

,is

intro-duced asfollows.As described, we assume that a ‘K ’propagates between the two successive reactions. It consists of 1) K−N

→

‘K ’N and2)non-resonant‘K ’

+

‘N N’

→ 

+

p intheFSI.Whenthe ‘K ’propagatesatmomentumq asanon-shellparticleinthe spec-tator’srestframe(

≡

laboratory-frame),thentheresultinginvariant massM (

≡

I Mp

(

‘K

+

N N’

)

)canbegivenas:

MF

(

q

)

=



4m2_N

+

m2_K

+

4mN

Fig. 2. Simulatedspectraofa)Lorentz-invariantpn phasespaceρ3(M,q)bytakingintoaccountthekaonbeammomentumbite,b)E(M,q)×ρ3(M,q),andc)experimental

efficiency,E(M,q),evaluatedbythebin-by-binratiobetweena)andb).Theunitofz-axis(colorcode)isperonegeneratedeventsbothfora)andb).Forc),theratiois given.

Fig. 3. Individual2Dfitfunctionsofthethreephysicalprocesses,a)“K pp”,b)QFKAandc)B G intheformofE(M,q)ρ3(M,q)fj(M,q)atthebestfitparameterset.The z-axis(colorcode)istheexpected-meaneventnumbertobeobserved.Thepale-blueisfortheregionwheretheexpectednumberisbelowone.Thez-axis’colorcodeofc) ischangedtoshowits(M,q)-dependenceclearly.

where mN and mK are the intrinsic mass of the nucleon and

the kaon, respectively. The curve originating at M

=

M

(

K pp

)

in Fig.1a is the MF

(

q

)

, which isconsistent with the q-dependence

of QF_KA as shown in the figure. Along the line, there are two strongevent-concentrationsobservedat

θ

n

=

0 (backward‘K ’)and

θ

n

=

π

(forward ‘K ’). To account for the distribution, we

de-fined f_{Q F_KA}

(

M

,

q

)

asfollows.Fortheq-direction,weintroduced Gaussian and exponential distributions at around the minimum andmaximum,respectively, with a constant inbetween. Forthe

M-direction, a Gaussian around MF

(

q

)

is applied to account for

thespectator’sFermi-motion.

Thereisanothercomponent,widelydistributingoverthe kine-matically allowed region of M and q, which was previously ob-served[22].Inreference[22],wesimplyassumedthattheyieldof thiscomponentwasproportional to

ρ

3

(

M

,

q

)

. However,withthe presentmuchimprovedstatistics,wefoundthatwecannotfitthis componentwith

ρ

3

(

M

,

q

)

.Comparedto

ρ

3

(

M

,

q

)

,theyieldsinthe heavierM regionandlowerq regionaremuchweaker, asshown inthefitcurvegiveninFig.1bandc.Thus,wephenomenologically

introduceda distributionfunction, f_{BG}

(

M

,

q

)

, similarto Eq. (1), butweexpandedtheq-dependentharmonicoscillatortermto al-lowangularmomentumupto P -wave,asshowninFig.3c.

Thedata D

(

M

,

q

)

can be fittedby usingthe maximum likeli-hoodmethod,whoselikelihoodlnL_{fit}isgivenbyaPoisson

distri-bution P

(

X

=

D

(

M

,

q

)

;

λ

D

(

M

,

q

))

havingmeanvalue

λ

D

(

M

,

q

)

at

each

(

M

,

q

)

-binas: lnL_{fit}

= −

M

q ln P

(

X

=

D

(

M

,

q

)

; λ

D

(

M

,

q

)).

(3)

Thefittingfunction

λ

D

(

M

,

q

)

isdefinedas:

λ

D

(

M

,

q

)

=

E

(

M

,

q

)

ρ

3

(

M

,

q

)

⎛

⎝

j yjfj

(

M

,

q

)

⎞

⎠ ,

(4)

where yj is the yield of the j-th physical process, and the first

term

E(

M

,

q

)

ρ

3

(

M

,

q

)

issimplyFig.2b.

To examine whether we should introduce more sophisticated model functions, we also studied the following distributions. In the3He

(

K−

,



p

)

n reactionfollowedby



→

p

π

−decay,thereare five kinematically independent observables in total. The remain-ingthreekinematicalparameters,independentofM andq,define the decay kinematics of “K−pp”

→ 

p and the



→

p

π

− de-cayasymmetry.Thus, theseparameters aresensitiveto JP ofthe reaction channels. For the “K−pp” signal, we analyzed events in thewindow M

=

2

.

28

∼

2

.

38 GeV/c2 wherethemajorpartofthe componentislocated,andq

=

350

∼

650 MeV/c wherenosevere interferenceisexpectedwith f_{Q F_KA}.Theangulardistributionsare fairly flat forany ofthe three kinematicalparameters. Therefore, the angulardistributionis consistent with S-wave.Thus, there is

Fig. 4.p invariantmassspectrumforpn finalstateproducedinthemomentum transferwindowof350<q<650 MeV/c.The efficiencyE(M,q)wascorrected basedonthesimulationbeforetheq integrationofthedata.Eachfittedphysical process,whichisefficiencycorrectedandintegratedovertheq-windowafterthe fit,isalsogiven.

nospecificreasontointroduceanysophisticatedtermsinaddition to Eq. (1). In fact, a flat distribution is naturally expected ifthe pole’squantum-numberis JP

=

0−.Wealsoanalyzedtheangular distributions for f_{Q F_KA} and f{BG}. However, againwe found no

specificreasontointroducefurtherterms.

We haven’t considered the interference terms between the three physical processes as given in Eq. (4), to avoid over fit-ting of our statistically limited data. Instead, we applied a peak fitting window to reduce the interference effect on our fit re-sult by the following procedures. We conducted i) thepeak fit,

where f_{Q F_KA}

(

M

,

q

)

is fitted by fixing all the parameters of

f_{Q F_KA}

(

M

,

q

)

and f_{BG}

(

M

,

q

)

within the q-window where no severe interference with QF_KA is expected. We then iterated this procedure together with procedure ii) aglobalfittoevaluate f_{Q F_KA}

(

M

,

q

)

and f_{BG}

(

M

,

q

)

(byfixing parameters in f_{Kpp} ex-ceptforthepeakyieldCKpp),untilproceduresi)andii)converged.

Toexhibit this “K−pp” candidateand topresentthe M

spec-trumfreefromexperimentalacceptance,weplottedthespectrum by correcting our detector efficiency for the events in the mo-mentum transfer windowof 350

<

q

<

650 MeV/c where mostly

E(

M

,

q

)



0,asshowninFig.4.Tomake fitvaluesinsensitiveto theacceptancecorrectionprocedure,we correctedtheacceptance asfollows.The data D

(

M

,

q

)

was divided by

E(

M

,

q

)

bin-by-bin andintegratedoverq atgivenM.Weappliedthesameprocedure forthedataerrortakingerror-propagationintoaccount.Foreach projectedphysicsprocess

ρ

3fj (plottedasthecurvedlinesinthe

figure), we integrated over q, by replacing the

E(

M

,

q

)

ρ

3

(

M

,

q

)

function(giveninFig.2b)with

ρ

3

(

M

,

q

)

(Fig.2a)tobemultiplied by fj

(

M

,

q

)

,cf.,Eq. (4).

In this window, the yield of other processes is largely sup-pressedincontrastto“K−pp”.TheQF_KAdistributionisalsoclearly separatedfromthe“K−pp”peakregion,becausetheQF_KAcentroid iskinematicallyshiftedtotheheavierside,accordingtoEq. (2),cf.,

acomparisonofthespectraldifferenceoftheQF_KA component in-settedin bluecurvesin Fig.1b andFig.4. As aresult, a distinct peakisobservedbelowM

(

K pp

)

.

4. Fitresult

The S-wave parameters obtained were; the mass eigenvalue

MKpp

=

2324

±

3

(

stat

.)

+₋6₃

(

sys

.)

MeV/c2 (i.e. BKpp

≡

M

(

K pp

)

−

MKpp

=

47

±

3

(

stat

.)

₋+63

(

sys

.)

MeV), the width



Kpp

=

115

±

7

(

stat

.)

+₋10₂₀

(

sys

.)

MeV, and the reaction form-factor parameter

QKpp

=

381

±

14

(

stat

.)

₋+570

(

sys

.)

MeV/c.The q-integrated“K−pp” formationyieldbelowthethresholdgoingtothe



p decay chan-nel is evaluated to be

σ

Kpp

·

Brp

=

7

.

2

±

0

.

3

(

stat

.)

+₋0₁._.6₀

(

sys

.)

μb (for M

<

M

(

K pp

)

). For the complete integration over all

q and M, the cross-section becomes

σ

tot

Kpp

·

Brp

=

11

.

8

±

0

.

4

(

stat

.)

+₋0_1..2₇

(

sys

.)

μb.

Weevaluatedthesystematicerrorscausedbythespectrometer magnetic field strength calibrated by invariant masses of



and

K0 _{decay, binningeffect ofthe spectrum, andthecontamination} effectsoftheotherfinalstates(

0pn and

−pp)tothe



pn event

selection.Tobeconservative,theeffectstothefitvaluesareadded linearly.Moredetailedanalysiswillbegiveninaforthcomingfull paper.

The BKpp

∼

50 MeVismuchdeeperthan reportedinourfirst

publication since the assumption of a single pole structure was invalid. It isalso muchdeeper than chiral-symmetry-based theo-retical predictions. The



Kpp

∼

110 MeV is rather wide, meaning

veryabsorptive.Ontheotherhand,itshouldbesimilartothatof

(

1405

)

→

π

, if“K−pp” decays like‘

(

1405

)

’

+

‘p’

→

π

p.

Thus,theobservedlargewidthindicatesthatthenon-mesonicY N

channelswouldbethemajordecaymodeofthe“K−pp”. Interest-ingly,theobservedQKpp

∼

400MeV/c isverylarge.Thelarge QKpp

value impliestheformationofavery compact(

∼

0

.

5 fm)system referring to

¯

h

∼

200 MeV/c fm.The compactnessofthe systemis also supportedby thelarge BKpp. However,the present QKpp can

bestronglyaffectedbytheprimary K N

→

K N reactioninthe for-mation process, so one needs more study to evaluate the static form-factor parameter of “K−pp” to deduce its size (or nuclear density)morequantitatively.

5. Discussionandconclusion

We have demonstrated the existence of a peak structure in

IMp below M

(

K pp

)

,which can be kinematically separated very

clearly from QF_KA by selecting the momentum transfer window of 350

<

q

<

650 MeV/c. As shown in Fig. 1a, the “K−pp” dis-tribution yield reduces near

θ

n

=

0 as a function of q, and it is

∼

proportionaltothephasespacevolumedefinedbyJacobian(cf., Fig.2a(or b)).Thisisnaturally expectedifthe S-wave harmonic-oscillatorform-factor giveninEq. (1) isvalid.Onthe otherhand, the QF_KA distributionishighly concentrated at

θ

n

=

0,wherethe

phasespace

ρ

3

(

M

,

q

)

isvanishing.Thisisconsistentwithour pre-vious result[21],inwhichnostructurewas foundbelowM

(

K pp

)

at

θ

n

=

0,i.e.,theleaking-tailofQFKAintotheboundregionhides thestructurebelowM

(

K pp

)

at

θ

n

=

0.

Thepresent



pn finalstate isthesimplestchannelforK− in-teracting with 3_{He. In this final state, the “kinematicalanomaly”} is only seen in IMp having an angular distribution consistent

withS-wave.Thus,thereisnoreasonableexplanationastowhya peakstructurecouldbeformedbelowM

(

K pp

)

otherthan“K−pp”.

However,onemaywonderwhetheraspuriousbumpnearM

(

K pp

)

mightbeformedfromsomeintermediatestateconverging(or con-verting)toa



pn finalstateintheFSI.

Here we discuss possible candidates for such an intermedi-ate state. Energetically, the possible intermediate states could be ‘



+

p’, ‘

+

N’ and ‘

(

1405

)

+

N’ below ‘K−

+

p

+

p’, which has an s-quark andtwo baryons (‘

(

1385

)

+

N’ is excluded be-cause it requires P -wave). In other words, a Y(∗) _{(baryon with} an s-quark)could begeneratedbythe primary2NAreaction,and theY(∗)_{couldmakeasuccessiveconversionreactionwithanother} spectatornucleon,toforma



pn finalstateduetotheFSI.Similar toEq. (2),theIMp ofthesechannelscanbegivenas:

IMp



‘Y(∗)

+

N’



≈



m2_N

+

m2_Y(∗)

+

2mN

m2_Y(∗)

+

q2

.

(5) First of all, observed “K−pp” event concentration does not have the q-dependence required by Eq. (5). Moreover, the IMp of

‘



+

p’ (

∼

2100), ‘

+

N’ (

∼

2175 MeV/c2) channels are much too small at the kinematical boundary of q

∼

500 MeV/c. The

IMp of ‘

(

1405

)

+

N’ is

∼

2371 MeV/c2 at the observed

aver-ageq distributionof q

∼

450 MeV/c (assuming

(

1405

)

mass

=

1405.1 MeV/c2 _{(PDG [24])).Thus theerror inthedifference from}

MKpp(

∼

2324 MeV/c2)isaslargeasfivestandarddeviations.A

di-rect



p formationdueto2NA(K−

+

‘pp’

→ 

+

p)couldbe possi-ble.Inthisreaction,kaonmomentumis1GeV/c andtheresulting



p invariantmassM calculatedfromEq. (2) is2.8GeV/c2.Infact, an eventconcentration isobserved at

(

Mc2

_,

_qc

₎

_{∼ (}

₂

_.

₈

_,

₁

_.

₀

₎

_GeV as shown in Fig. 1, but it is well separated from the region of interest. Therefore, none of these can be valid candidates. More complicated channels are even less likely to form a kinematical anomalyatthespecificenergynearM

(

K pp

)

.

The “K−pp” signal is significantly above the M

(

p

)

thresh-old, so it is unreasonable to explain it as a



-hypernucleus. One maystill wonder if the “K−pp” signal could be due to the

(

1405

)

–protonhypernucleus (_(14052₎H),sothat themeson(or constituent anti-quark) degree-of-freedom is already quenched in thesystem. However, this isnot consistent withpresent data.In theq distribution,the“K−pp”signallocatedatlowerq extendsup

∼

650 MeV/c. Thusa tightlybound“K−pp”ismorenaturalthan alessbound 2

(1405)H measuredfrom M

((

1405

)

p

)

. It wouldbe evenlessboundifthepolepositionof

(

1405

)

is

∼

1425rather than 1405 MeV/c2 _{as the chiral-unitary model suggests [24]. In} theM distribution,thesignalismuchwiderthanthatof

(

1405

)

, so the major decay channel should be Y N rather than

π

N, in contrastto

(

1405

)

→

π

(100%).Thisdrasticchangeofthe de-cay property is also not consistent with 2

(1405)H interpretation. Moreover, if

(

1405

)

is a “K−p” bound system, as recently ac-ceptedratherwidely,thediscriminationofthetwointerpretations ismeaninglessfromthebeginning.

It ismore naturalto interpret that the K in “K−pp” is ener-getically stabilized(BKpp

∼

50 MeV) compared to that in “K−p”

(

≡ (

1405

)

: BKp

≈

5

∼

25 MeV), becauseofthe presence oftwo

protons (nucleons) nearby. At the same time, the decay width becomes large (



Kpp

∼

110 MeV in respect to



Kp

∼

50 MeV),

forthe samereason. The existence ofthe QF_KA channel adjacent to “K−pp” also supports this interpretation, because if the sub-thresholdvirtual ‘K ’canformanuclearboundstate bycapturing spectatornucleons,then itisnaturaltoexpect higher-energy vir-tual ‘K ’production in‘vacuum’ (above M

(

K pp

)

), which could be followedby‘K−’

+

pp

→ 

p inFSI.Thus,thesimplestandnatural

interpretation is a kaonic nuclear bound state “K−pp”;a system composed of a K−-meson and two protons with JP

=

0−, i.e. a

highly excited novel form of nucleus with a kaon, in which the mesonicdegree-of-freedom stillholds.

Insummary,thequasi-freevirtual‘K ’productionK−‘N’

→

‘K ’N is the key reaction in the formation reaction, and M

(

K pp

)

is a doorway below which the “K−pp” is formed. Naïvely speak-ing, iftheenergy ofthe ‘K ’produced isbelow itsintrinsic mass (EK

<

mK), then the“K−pp” willbe formed.On theother hand,

ifitisabovetheintrinsicmass(EK

>

mK),thentheQFKA reaction happens(orthekaonescapesfromnuclei).

Acknowledgements

The authors are grateful to the staff members of J-PARC/KEK fortheirextensiveeffortsespeciallyonthestableoperationofthe facility. Weare also grateful tothe fruitful discussions with Pro-fessors Akinobu Dote, Toru Harada, Takayasu Sekihara, Khin Swe Myint and Yoshinori Akaishi. This work is partly supported by MEXT Grants-in-Aid 26800158, 17K05481, 26287057, 24105003, 14102005,17070007and18H05402.Partofthisworkissupported by the Ministero degli Affari Esteri e della Cooperazione Inter-nazionale,DirezioneGeneraleperlaPromozionedelSistemaPaese (MAECI),StrangeMatterproject.

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