Search for an isospin I=3 dibaryon

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Physics

Letters

B

www.elsevier.com/locate/physletb

Search

for

an

isospin

I

=

3 dibaryon

The

WASA-at-COSY

Collaboration

P. Adlarson

a,1

,

W. Augustyniak

b

,

W. Bardan

c

,

M. Bashkanov

d,

∗

,

F.S. Bergmann

e

,

M. Berłowski

f

,

H. Bhatt

g

,

A. Bondar

h,i

,

M. Büscher

l,2,3

,

H. Calén

a

,

I. Ciepał

c

,

H. Clement

j,k

,

E. Czerwi ´nski

c

,

K. Demmich

e

,

R. Engels

l

,

A. Erven

m

,

W. Erven

m

,

W. Eyrich

n

,

P. Fedorets

l,o

,

K. Föhl

p

,

K. Fransson

a

,

F. Goldenbaum

l

,

A. Goswami

l,q

,

K. Grigoryev

l,r,4

,

C.-O. Gullström

a

,

L. Heijkenskjöld

a

,

V. Hejny

l,1

,

N. Hüsken

e

,

L. Jarczyk

c

,

T. Johansson

a

,

B. Kamys

c

,

G. Kemmerling

m,5

,

F.A. Khan

l

,

G. Khatri

c

,

A. Khoukaz

e

,

O. Khreptak

c

,

D.A. Kirillov

s

,

S. Kistryn

c

,

H. Kleines

m,5

,

B. Kłos

t

,

W. Krzemie ´n

c

,

P. Kulessa

u

,

A. Kup´s ´c

a,f

,

A. Kuzmin

h,i

,

K. Lalwani

v

,

D. Lersch

l

,

B. Lorentz

l

,

A. Magiera

c

,

R. Maier

l,w,x

,

P. Marciniewski

a

,

B. Maria ´nski

b

,

H.-P. Morsch

b

,

P. Moskal

c

,

H. Ohm

l

,

E. Perez del Rio

j,k,6

,

N.M. Piskunov

s

,

D. Prasuhn

l

,

D. Pszczel

a,f

,

K. Pysz

u

,

A. Pyszniak

a,c

,

J. Ritman

l,w,x,y

,

A. Roy

q

,

Z. Rudy

c

,

O. Rundel

c

,

S. Sawant

g,l

,

S. Schadmand

l

,

I. Schätti-Ozerianska

c

,

T. Sefzick

l

,

V. Serdyuk

l

,

B. Shwartz

h,i

,

K. Sitterberg

e

,

T. Skorodko

j,k,z

,

M. Skurzok

c

,

J. Smyrski

c

,

V. Sopov

o

,

R. Stassen

l

,

J. Stepaniak

f

,

E. Stephan

t

,

G. Sterzenbach

l

,

H. Stockhorst

l

,

H. Ströher

l,w,x

,

A. Szczurek

u

,

A. Trzci ´nski

b

,

R. Varma

g

,

M. Wolke

a

,

A. Wro ´nska

c

,

P. Wüstner

m

,

A. Yamamoto

aa

,

J. Zabierowski

ab

,

M.J. Zieli ´nski

c

,

A. Zink

n

,

J. Złoma ´nczuk

a

,

P. ˙Zupra ´nski

b

,

M. ˙Zurek

l a_{Division of Nuclear Physics, Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden} b_{Department of Nuclear Physics, National Centre for Nuclear Research, ul. Hoza 69, 00-681, Warsaw, Poland}

c_{Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland}

d_{School of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom} e_{Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany}

f_{High Energy Physics Department, National Centre for Nuclear Research, ul. Hoza 69, 00-681, Warsaw, Poland} g_{Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Maharashtra, India} h_{Budker Institute of Nuclear Physics of SB RAS, 11 akademika Lavrentieva prospect, Novosibirsk, 630090, Russia} i_{Novosibirsk State University, 2 Pirogova Str., Novosibirsk, 630090, Russia}

j_{Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany}

k_{Kepler Center for Astro and Particle Physics, Eberhard Karls University Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany} l_{Institut für Kernphysik, Forschungszentrum Jülich, 52425 Jülich, Germany}

m_{Zentralinstitut für Engineering, Elektronik und Analytik, Forschungszentrum Jülich, 52425 Jülich, Germany}

n_{Physikalisches Institut, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erwin-Rommel-Str. 1, 91058 Erlangen, Germany}

o_{Institute for Theoretical and Experimental Physics, State Scientific Center of the Russian Federation, Bolshaya Cheremushkinskaya 25, 117218 Moscow, Russia} p_{II. Physikalisches Institut, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany}

q_{Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Indore 452017, Madhya Pradesh, India} r_{High Energy Physics Division, Petersburg Nuclear Physics Institute, Orlova Rosha 2, Gatchina, Leningrad district 188300, Russia}

s_{Veksler and Baldin Laboratory of High Energiy Physics, Joint Institute for Nuclear Physics, Joliot-Curie 6, 141980 Dubna, Moscow region, Russia} t_{August Chełkowski Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007, Katowice, Poland}

u_{The Henryk Niewodnicza´nski Institute of Nuclear Physics, Polish Academy of Sciences, 152 Radzikowskiego St, 31-342 Kraków, Poland}

*

Correspondingauthor.

E-mail address:mikhail.bashkanov@ed.ac.uk(M. Bashkanov).

1 _{Presentaddress:InstitutfürKernphysik,JohannesGutenberg-UniversitätMainz,Johann-Joachim-BecherWeg 45,55128Mainz,Germany.} 2 _{Presentaddress:PeterGrünbergInstitut,PGI-6ElektronischeEigenschaften,ForschungszentrumJülich,52425Jülich,Germany.}

3 _{Presentaddress:InstitutfürLaser- undPlasmaphysik,Heinrich-HeineUniversitätDüsseldorf,Universitätsstr. 1,40225Düsseldorf,Germany.} 4 _{Presentaddress:III. PhysikalischesInstitut B,Physikzentrum,RWTHAachen,52056Aachen,Germany.}

5 _{Presentaddress:JülichCentreforNeutronScienceJCNS,ForschungszentrumJülich,52425Jülich,Germany.} 6 _{Presentaddress:INFN,LaboratoriNazionalidiFrascati,ViaE. Fermi,40,00044Frascati(Roma),Italy.}

http://dx.doi.org/10.1016/j.physletb.2016.09.051

0370-2693/©2016TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Accepted26September2016 Availableonline5October2016 Editor:V.Metag

Keywords: Dibaryons Four-pionproduction

N N-decoupledstateindataonthepp→pp

π

+

π

+

π

−

π

−reaction.Sincenoclear-cutevidencehasbeen found, wegive upper limits for the productioncross sectionof sucharesonance in the massrange 2280–2500MeV.

©2016TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Recently, exclusive and kinematically complete measurements ofthe reactions pn

→

d

π

0

_π

0 _{and pn}

_→

_d

_π

+

_π

− _revealeda nar-rowresonance-likestructure in thetotal cross section [1–3] ata

massm

≈

2380 MeV with a width of



≈

70 MeV and quantum

numbersI

(

JP

)

=

0

(

3+

)

.Additionalevidenceforithadbeentraced subsequentlyinthetwo-pionproductionreactions pn

→

pp

π

0

_π

− [4], pn

→

pn

π

0

_π

0 _{[5]and pn}

_→

_pn

_π

+

_π

− _{[6–8]. Finally,} analyz-ing power measurements ofnp elastic scatteringestablished this structuretorepresentatrues-channelresonance,whichproduces apoleinthe3_D

3 partialwave –denotedsincethen byd∗

(

2380

)

[9–12].

Such a dibaryon resonance, which asymptotically resembles a deeplybound



system, waspredictedfirst–andastonishingly precise asit turns out now –by Dyson and Xuong [13] in 1964 basedon SU

(

6

)

symmetrybreaking.Later-on,Goldmanetal.

[14]

called this state the “inevitable dibaryon” pointing out that due toitsparticularquantumnumbersanditsassociatedspecial sym-metries,such a state mustbe predictedin anytheoreticalmodel basedonconfinement andone-gluon exchange. Indeed,thereare now quite a number of QCD-based model calculations available, whichfindd∗

(

2380

)

ataboutthecorrectmass

[15–22]

.Also, rel-ativisticFaddeev-type calculationsbased on hadronicinteractions find this state at the observed mass [23,24]. The observed rela-tively narrow widthof about70 MeV is obviously moredifficult tounderstandtheoretically.Untilrecently,GalandGarcilazocame closestwithabout100MeV

[24]

.Dongetal.

[18]

succeededin re-producingtheexperimentalwidthby accountingforhiddencolor effects–ashadbeenspeculatedalreadyinRef.[25].

Part of the theoretical calculations, which successfully obtain the d∗

(

2380

)

state, predicts also a dibaryon state with mirrored quantumnumbers I

(

JP

₎

₌

₃

₍

₀+

₎

_{ata similar mass}

_{[13,15,16,24]}

_.

Intendency,thisstate, whichisexpectedto beagaina



con-figurationasymptotically,appearstobesomewhatlessboundthan

d∗

(

2380

)

,butstillbelowthe



thresholdof2m.Thepredicted

widthvariesfromabout90MeV

[24]

toabout180MeV

[15]

.Only thecalculationoftheNijmegengroup

[22]

predictsthisstatetobe farabovethe



threshold.

2. Experiment

Inordertoinvestigatethisissueexperimentally,wefollowthe suggestionofDyson andXuong (whocalledthestate inquestion

the D30,wherethefirstindexdenotestheisospinandthesecond

one the spin) and consider the four-pion production in proton-protoncollisions,inparticularthe pp

→

pp

π

+

π

+

π

−

π

−reaction. Becauseofitsisospin I

=

3 suchastateisisospin-decoupledfrom the nucleon–nucleon(N N) system. Therefore,inorder tobe able toreachsucha stateby N N collisions,itsproductioninthe colli-sionprocessneedstobeassociatedbythegenerationofparticles, which takeaway two unitsofisospin.Thisappearsto be accom-plished mosteasily by the productionoftwo extra pions.So the processweaimatreadsaspp

→

D30

π

−

π

−

→ 

++



++

π

−

π

−

→

pp

π

+

π

+

π

−

π

−.Due to I

=

3 the



++



++ configuration is the mostpreferred



combination,whereD30decaysinto–seenext

section.

The measurementsofthisreactionhavebeencarriedoutwith theWASAdetectorincludingahydrogenpellettarget

[26,27]

atthe cooler synchrotronCOSY (ForschungszentrumJülich) usingproton beams with energies of Tp

=

2

.

063 and 2.541 GeV. These

cor-respond to center-of-mass energies of

√

s

=

2

.

72 and 2.88 GeV, respectively.ThelatterdenotesthehighestenergyusedwithWASA atCOSY.

Thetriggerwassettotwo(andmore)chargedhitsbothinthe forwardandinthecentraldetector.Sincethemaingoalsofthese runs,whichcomprise3weeksofbeam-time,wasnotthefour-pion production,but

ω

and

η

 production,alsoa missingmasstrigger was activeduringthemeasurementsat2.541GeV.Itrequiredthe deposited energyofeach ofthe two protonsdetected in the for-warddetectortobelargerthan150MeV–acondition,whichdid notaffectthefour-pionproductionevents.

The four-momenta ofthe two emitted protons were detected

in the Forward Detector, whereas the four-momenta of the four chargedpionswererecordedintheCentralDetector,wherea

mag-netic field allowed for charge identification and momentum

de-termination. That way, the reaction was measured kinematically complete withfouroverconstraints,which allowed a correspond-ingkinematicfitoftheevents.Finally,atotalof136(1017)events atTp

=

2

.

063 (2.541)GeVpassedthe

χ

2criterionofthekinematic

fit, whichisa cut ofthe probabilityfunction at10%. Despitethe kinematicfitcondition,MonteCarlo(MC)simulationssuggestthat thefinalsampleatTp

=

2

.

063 GeV iscontaminatedwithabout50

eventsoriginatingfromthree-pionproduction,wherethephotons from

π

0_{decayhaveundergoneconversionorDalitzdecay.The}

dis-tributionofthoseeventsisnotnoticeablydifferentfromtheother events.The acceptanceofthe WASAdetectorfor pp

π

+

π

+

π

−

π

−

Fig. 1. (Coloronline.) Measured spectrumofthe pp →ppπ+π0_π− _{reaction at} Tp=2.063 (top)and2.541GeV(bottom).Thefilledcirclesrepresentthedatafrom

thiswork.Dottedanddashedlinesgivethefittedηandωcontributions,whereas theshadedareainthetoppanelshowsthepurephase-spacedistribution.The dash-dottedlineinthebottompanelisapolynomialfitofdirectthree-pionproduction. Thesolidlineisthesumofη,ωanddirectthree-pionproduction.

withan uncertaintyof less than 1%. The detection efficiencyfor

pp

π

+

π

+

π

−

π

−eventshasbeen0.1%atTp

=

2

.

063 GeV and0.5%

atTp

=

2

.

541 GeV,alsoevaluated viacomprehensive MC

simula-tionsofthedetectorperformance.

Theabsolutenormalizationofthefour-pionproductiondatahas

been done via the simultaneous measurement of the three-pion

production(

π

+

π

−

π

0 _with

_π

0 _{decayintotwophotons)including}

η

and

ω

productioninthischannel.Thespectraofthethree-pion invariantmass _Mπ+_π0_π− at Tp

=

2

.

063 GeV and Tp

=

2

.

541 GeV

are shown in Fig. 1. Since the cross section for three-pion pro-ductionistwoorders ofmagnitudelarger thanthat forfour-pion production, it was sufficient to use only a small sample of the availablethree-pionproductiondataforthisprocedure.

AtTp

=

2

.

063 GeV,thedataforthethree-pionproduction

(in-cluding

η

and

ω

production)havebeennormalizedtothevalueof 220μbobtainedinRefs.[28,29]forthisreactionatTp

=

2 GeV.As

aresult,thefittedcontributionsfrom

η

and

ω

production(dotted and dashed lines in Fig. 1) correspond to production cross sec-tionsof111

±

20 μb and5

.

6

±

1

.

0 μb,respectively.Thefirstvalue agreesreasonablywellwiththevalueof142

±

22 μb obtainedat

Tp

=

2

.

2 GeV bytheHADES Collaboration

[30]

.The second value

isingoodagreementwiththevalueof5.7μbobtainedinRef.[31]. AtTp

=

2

.

541 GeV,where

ω

productionprovidesalreadya

sub-stantialcontributiontothree-pionproduction,thedatahavebeen normalizedtothisprocessusingforthe

ω

productioncrosssection thevalue35μbinterpolatedfromthevaluesgiveninRefs.[32,33]. As a result of this normalization procedure, we obtain total four-pioncrosssectionsof0

.

7

±

0

.

3 and5

.

2

±

1

.

0 μb atTp

=

2

.

063

and2.541 GeV, respectively, which are two orders ofmagnitude smallerthanthethree-pionproductioncrosssectionsatthese en-ergies.

Thequoteduncertaintiesoriginatepredominantlyfrom system-aticuncertaintiesinthedeterminationofbackgroundbeneaththe

Fig. 2. (Coloronline.)Energydependenceofthetotalcrosssectionforthe

pp

→ ppπ+π+π−π−reaction.Thefilledcirclesarefromthis work,theopensymbols from Refs.[34–38].Thedrawn linegivesthe energydependence ofpure phase spacenormalizedtothedatapointat

T

p=2.541 GeV.

η

and

ω

peaks,thedeterminationoftheWASAacceptanceand ef-ficiencyandtheextrapolationofcrosssectionstofullphasespace, whichhasbeendonebyMCsimulationsassumingphase-spaceor modeldistributions–seenextsection.

Due to the small statistics for the four-pion production reac-tion, all systematical effects hadto be evaluated by Monte Carlo simulations only. However, some of thesesystematic effects,like influenceofmissing-masstriggercouldbecross-checkedwiththe

pp

→

pp

π

+

π

0

_π

− _{reaction due to much higher statistics, same} multiplicity(

π

0 _{decaysintotwophotons,hencetherearealsosix}

particles detected in the final state)and verysimilar kinematics. Thereforesystematical errorsrelatedtotriggering,errors parame-terization, kinematicalfitting, etc. were evaluated basedon large samplesofthree-pion productiondata.

Thewidthsofabout30MeVforthe

η

and

ω

linesinthe three-pionspectrumgive ameasure ofthe massresolutionachievedin thisdataanalysis.

3. Resultsanddiscussion

Theenergydependenceofthetotalcrosssectionforthe pp

→

pp

π

+

π

+

π

−

π

− reaction isdisplayed in

Fig. 2

,whereour results arecomparedto earlierpublished data

[34–38]

obtainedahigher energies.Thesolidlinerepresentstheenergydependenceofpure phasespace. It accountsatleastqualitativelyforthetrend ofthe data.

Havingmeasured thefour-pionproductionkinematically com-plete,weareabletoconstructallkindsofdifferentialdistributions. Of relevance in the search for the I

=

3 dibaryon D30 are the

spectra of the pp

π π

-invariant masses Mppπ+π+, Mppπ−π− and Mppπ+π−.Forthelatterthestatisticsquadruplesdueto

combina-torics.Thesespectraaredisplayedin

Fig. 3

forbothincident ener-gies. TheyareshownwithinWASAacceptance,i.e. notacceptance corrected,inordertoavoidanymodeldependenceintroducedby thecorrespondingcorrectionprocedure.

Thespectrain

Fig. 3

showverysmoothmassdistributionsand donotexhibit anyunusualstructures.However, theydeviate sys-tematically from pure six-body phase-space distributions, which

are shown (again within WASA acceptance) by the shaded

his-togramsin

Fig. 3

.Thisisnot surprising,since alreadysingle- and two-pionproductionsareknowntobedominatedbybaryon exci-tationsstartingrightfromthreshold

[39–45]

.

The lowest-lying baryon resonance,which decaysby emission of two pions, is the Roper resonance N∗

(

1440

)

with its

two-pion decay routes N∗

→

N

σ

→

N

π π

and N∗

→ 

π

→

N

π π

.

It is known to dominate the two-pion production for energies

ex-Fig. 3. (Coloronline.) DistributionsofinvariantmassesMppπ+π+ (top),

M

ppπ+π−

(middle)and Mppπ−π− (bottom)for √s=2.72 GeV (left)and 2.88 GeV(right) withinWASAacceptance.Soliddotsdenotethedatafromthiswork,theshaded histogramsrepresentphase-spacedistributions, whereasthecalculated

t-channel

N∗(1440)N∗(1440)distributionisshownbythesolidlines.Thedottedcurvesshow theeffectofan

I

=3 resonancewithmass

m

=2380 MeV andwidth=70 MeV scaledarbitrarilyinheighttoa5%contributionofthetotalcrosssection.

changestartstodominateatenergiesabove1 GeV.Sincethelatter configuration can produce only two pions in its decay, the only resonance process eligible for four-pion production is the dou-ble N∗

(

1440

)

excitation, i.e. the N∗

(

1440

)

N∗

(

1440

)

excitation by

t-channel meson exchange betweenthe colliding incident nucle-ons. Also, the nominal mass of 2mN∗(1440) for this configuration

fitsverywelltothecenter-of-massenergiesofthemeasurements discussedhere.Amodelcalculationbasedonanextendedversion ofthe modified Valenciamodel

[44,42]

reproduces themeasured totalcrosssectionswithin30%.

Thesolidlinesin

Fig. 3

show acalculationofthe N∗

(

1440

)

N∗

(

1440

)

processadjustedinheighttothedata.Forthelowerenergy,

√

s

=

2

.

72 GeV,thiscalculationgives alreadyapractically perfect descriptionofallthreeinvariant-massspectrawithinuncertainties. Forthehigherenergythisdescriptionisnotquiteasgood,since it misses strength at low pp

π

+

π

+ and high pp

π

−

π

− invariant masses.Thesituationcouldpossiblybeimproved,ifwewouldfita contributionfromthenexthigher-lying N∗ excitation(providinga

N∗

(

1520

)

N∗

(

1440

)

configurationintheintermediatestate)tothe data. But we refrain here from a fine tuning of the background descriptionduetothemuchincreasedcomplexityofthe theoret-ical description, which necessarily introduces new uncertainties. We justnote that the behavior of the shapesgiven by the solid

Fig. 4. (Coloronline.)DistributionofMC-simulatedeventsplottedintheplaneof Mppπ−π− versus

M

ppπ+π+ foran

I

=3 resonancewithmass

m

=2380 MeV and width=70 MeV.Thetoppanelexhibitsthesituationat√s=2.72 GeV,the bot-tompanelthatat√s=2.88 GeV.

lines ischaracteristicforadominanceofthe



++



++ excitation insofarastheMppπ+π+ spectrumisnarrowerthanthepure

phase-spacespectrum andpeakingaround 2m,whereas the Mppπ−π−

spectrumexhibitingdominantlythereflectionofthe



++



++ ex-citationpeaksatsubstantiallowermass.

Next,we investigate, how an I

=

3 resonance would showup inthesespectra.Fromisospincouplingarguments,wededucethe relative crosssections,withwhichsuch aresonanceshouldshow upinthevariousinvariant-massspectra,namely:

σ

ppπ+π+

:

σ

ppπ+π−

:

σ

ppπ−π−

=

1

:

2 225

:

1

225

.

(1)

I.e., such a resonancecontributespractically only to the spec-trumwiththehighestcharge inadirectway.However, sincethe three invariant-mass spectra are interrelated, reflections of such a resonance also appear in the Mppπ+π− and Mppπ−π− spectra – as illustrated in Fig. 4, where MC generated events are plot-tedintheplane Mppπ−π− versus Mppπ+π+.Itdisplaystheresults

of a simulation of an I

=

3 resonance with m

=

2380 MeV and



=

70 MeV.The simulated resonance is shownin Fig. 3 by the dashed curves scaled in height corresponding to a 5% contribu-tion of the resonance to the total cross section. Whereas in the

Mppπ+π− spectrumthereflectioncausesabroadphase-spacelike continuum, itproducesapeak-likestructure inthe Mppπ−π−

dis-tribution,thoughsomewhat broaderthantheoriginalpeakinthe

Mppπ+π+ spectrum and located in the complementary region of

thekinematicalmassrange.

Knowing now the kinematic behavior of such an I

=

3

reso-nance, we further inspect the data shown in Fig. 3. We observe no obvious narrow structures, which fulfill the kinematical con-ditions for apossible I

=

3 resonance. However, we immediately also notice that a contribution of a dibaryon resonance as

illus-Fig. 5. (Coloronline.)Upperlimits(C.L.95%)inpercentageofthetotalcrosssection fromthesearchforan I=3 resonancestructureconductedontheinvariantmass spectraofFig. 3at√s=2.72 GeV (top)and2.88GeV(bottom)assumingthe con-ventionalprocessestobehavelikethe

N

∗(1440)N∗(1440)distributions.Thesolid, dottedanddashedlinesrefertoafitsearchwithalinewidthof=50,100and 150MeV,respectively.

trated by the dashed lines in Fig. 3 wouldcertainly give an im-proveddescription ofthe data.Thoughthisis certainly a model-dependent statement, it demonstrates the difficulty of excluding a dibaryon resonance contribution of smaller than 5% of the to-talcrosssection –inparticular fordibaryon massessmallerthan 2380 MeV.

Inanidealcasethepeak tobesearched forisexpectedto sit upon a flat orsmoothly rising orfalling background witha cur-vature, which is small compared to the peak width. This is far frombeingthecasehere. Ontheoreticalgrounds wecan not ex-pectthe dibaryon resonanceto havea width muchsmaller than

50 MeV, more likely is a width in the region of 100 MeV or

even above, if this resonance happens to be close to the



threshold. The background due to conventional processes is not flat or smoothly rising/falling in the range of interest as we see from the distributions displayed in Fig. 3. Moreover shape and strength ofthe background can not be calculated sufficiently re-liable within contemporary theoretical approaches. Though the width of these distributions is still broader than the dibaryon signal we look for, it is not broader by an order of magnitude.

We are not aware of any model-independent peak search

anal-ysis for such a case. Hence we will proceed by assuming two

scenarios,wherethebackgroundisaccountedforeitherbyphase space-likeprocesses(meaningprocesses,whichgiveidentical con-tributions in all MN Nπ π spectra, e.g. chiral terms, various

con-tactterms,etc.)orbythe N∗

(

1440

)

N∗

(

1440

)

processdisplayedin

Fig. 3.The N∗

(

1440

)

N∗

(

1440

)

scenario representsa theoretically-motivatedbackgrounddescription,though possibly oversimplified asdiscussedabove.

Asusualinsuchpeaksearches,weassume interferencestobe smallandaddtheresonancetermincoherentlytothebackground term.Undertheseassumptionsthe shapesofbothresonanceand

Fig. 6. (Color online.) Difference spectraas defined inthe text in dependence of Mppπ π. The dashed curve represents the simulation ofan I=3 resonance

with mass

m

=2380 MeV andwidth=70 MeV, the solidlinethe

t-channel

N∗(1440)N∗(1440) excitation. The left panel exhibits the situation at √s=

2.72 GeV,therightpanelthatat√s=2.88 GeV.

backgroundcanbeconsideredtobeknown(alsowithinWASA ac-ceptance). Then for givenmass andwidth ofthe resonanceonly the relativecontributions ofresonance andbackgroundenter the simultaneous fit of all three invariant mass spectra. The upper limits(95%C.L.)resultingfromthesesingle-parameterfitsare dis-played in Fig. 5 in dependence of a hypothetical dibaryon mass

Mdibar yon for assumed resonancewidths of 50 MeV (solid lines),

100MeV(dotted)and150MeV(dashed).

In order to investigatethe case, where the backgroundis as-sumedtobedistributedphase-spacelike,weconsiderthe follow-ingdifference spectraconstructedoutofthethreeinvariant-mass spectra:

σpp

π+π+

−

σ

ppπ−π−,

σpp

π+π+

−

σ

ppπ+π− and

σpp

π−π−

−

σ

ppπ+π−, since they have the advantage that there the contri-butions fromphase-space likedistributions cancel.Note that any possible contaminations from misreconstructed background, like three-pion production with subsequent

π

0 _{Dalitz decay, cancels}

outinthedifferencespectraaswell.

Inthesedifferencespectra,whichareplottedin

Fig. 6

forboth beam energies, double baryon excitations due to t-channel me-son exchange produce an antisymmetric pattern (see solid lines in

Fig. 6

),whereas an I

=

3 resonanceinthe pp

π

+

π

+ subsystem shouldshowupingeneralbyanasymmetricpatternformedbyits directpeakanditsreflection–asindicatedbythedashed curves in

Fig. 6

.

Fig. 7. (Coloronline.)Upperlimits(C.L.95%)inpercentageofthetotalcrosssection fromthesearchforan I=3 resonancestructureconductedonthedifference spec-tradefinedineqs.(2)–(4)at√s=2.72 GeV (top)and2.88GeV(bottom).Thesolid, dottedanddashedlinesrefertoafitsearchwithapeakwidthof=50,100and 150MeV,respectively.

Since we know the expected signature of such a resonance

inthe difference spectra,we can perform againsingle-parameter peakfindingfitssimultaneouslytoall threedifferencespectraper beam energyand thus obtain upperlimits for such a resonance independenceofits massandwidth.The resultsforthe95%C.L. upperlimitsofthispeakfindingsearcharedisplayedin

Fig. 7

.

Bothin

Fig. 5

andin

Fig. 7

the95%C.L.upperlimitsareplotted inpercentageofthetotalcrosssection.Theextrapolationofour re-sultsobtainedwithin theWASAacceptancetototalcrosssections introducessystematicuncertainties,asdiscussedinthe experimen-talsection.Theyamountto40%forthelower energyand20%for thehigherenergy.

Forboth scenarios – N∗

(

1440

)

N∗

(

1440

)

and phase-spacelike background – we obtain qualitatively similar results. Due to the muchsuperior statisticsatthehigherenergy,the resultingupper limits are much more stringent there. As expected, the data are most sensitive to the signature of a narrow resonance. Also, for largedibaryonmassestheupperlimitsareingeneralsubstantially lower than for smallmasses. The largest upper limit happensin the N∗

(

1440

)

N∗

(

1440

)

background scenario fora dibaryon mass

of about 2380 MeV and a width of 100 MeV, where the upper

limitreaches40%ofthetotalcrosssection.

Comparedto the formation cross section of1.7 mb found for

d∗

(

2380

)

[46], theupper limitsfound herefor theproduction of an I

=

3 dibaryonresonancearesmallerbythreetofourordersof magnitude.

Moreinformative should bethe comparisonto

formation/pro-duction of a



system by conventional t-channel meson

ex-change. In two-pion production (isoscalar part) the peak cross section for d∗

(

2380

)

formation is roughly one order of magni-tude largerthan the one fortheconventional



process [2]at the d∗

(

2380

)

peak energy. If we assume that the four-pion

pro-duction at the beam energies considered here is dominated by

tained at the higher incident energy are in general significantly smaller – with the exception of the case Mdibar yon

≈

2380 MeV

and



=

100 MeV forthe N∗

(

1440

)

N∗

(

1440

)

scenario,wherethe upper limit is of the same order as the conventional



++



++

production. The results for the higher incident energy appear to be quite significant. If the interaction between the two



++

particles produced side-by-side in the decay ofthe intermediate

N∗

(

1440

)

N∗

(

1440

)

systemwouldbeattractive,thenthe probabil-itytoforma dibaryonshouldbe substantiallylarger thanforthe conventionalprocess–asitisobviouslythecaseford∗

(

2380

)

for-mation in the presence of an isoscalar



+



0 system. However, our results suggest that the probability for dibaryon formation in the presence of a



++



++ system in the intermediate state is smaller (with the possible exception of the above mentioned case). This is in support of the findings of Ref. [14], which pre-dicted an attractive interaction between the



pair in case of

d∗

(

2380

)

,butrepulsionincaseofD30andhencenodibaryon

for-mation.

4. Summaryandconclusions

We havesearchedforan I

=

3 dibaryon resonance,whichhas

been predictedby Dyson andXuong as well asby various

QCD-based andhadronic modelcalculations todecay into the N N

π π

system. The mass range of our search covers the region from

2.2–2.5 GeV, i.e. from near-to two-pionthreshold tothe nominal



thresholdof2mandabove.Toourknowledgethishasbeen

thefirstsuchsearch–withtheexceptionofsome earlierattempt byuseofproton–nucleuscollisions

[49]

.

We have found no apparent indication for such a resonance

in our data.The deduced upper crosssection limitsforthe pro-duction of such a resonance are three to four orders of magni-tude smaller than the formation cross section of 1.7 mb found ford∗

(

2380

)

.Theyalsoareuptoone orderofmagnitudesmaller thanthecrosssectionforconventional



++



++productioninthe

pp

→

pp

π

+

π

+

π

−

π

− reaction – again in sharp contrast to the corresponding situationfor d∗

(

2380

)

formation, wherethis is an orderofmagnitudelargerthaninconventional



formation.

An improved, reliable background descriptionby conventional

t-channelmesonexchangeprocesseswouldcertainlyhavethe po-tentialtolowertheseupperlimitsconsiderably.

With only upper limits at present we, of course, cannot ex-cludetheexistenceofsucharesonance.However,ifexistent,either theproductionprocessofthe I

=

3 resonanceassociatedwiththe emissionoftwopionshasanunusuallysmallcrosssectionorsuch aresonancehasamassabovetheenergyregioninvestigatedhere –aspredicted,e.g. inRef.[22].However,insuchacase,whenthe resonance lies significantly above the



threshold,its width is expectedto bevery broadduetoits fall-partdecayandhenceit will be very hard to distinguish such a resonance from conven-tionalprocesses.

Acknowledgements

Weacknowledgevaluable discussionswithSt. Brodsky,A.Gal, I.Strakovsky,F.Wang,C.WilkinandZ.Zhangonthisissue.Weare indebted to Luis Alvarez-Ruso for using his code. This work has beensupportedbyDFG(CL214/3-1),STFC(ST/L00478X/1)andby thePolishNationalScienceCenter throughgrantsNos.DEC-2013/ 11/N/ST2/04152and2011/03/B/ST2/01847.

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