Study of the quasi-free np→npπ+π- reaction with a deuterium beam at 1.25 GeV/nucleon

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Study

of

the

quasi-free

np

→

np

π

+

π

−

reaction

with

a

deuterium

beam

at

1.25

GeV/nucleon

G. Agakishiev

g

,

A. Balanda

c

,

D. Belver

q

,

A.V. Belyaev

g

,

A. Blanco

b

,

M. Böhmer

j

,

J.L. Boyard

o

,

P. Braun-Munzinger

d

,

3

,

P. Cabanelas

q

,

E. Castro

q

,

S. Chernenko

g

,

T. Christ

j

,

M. Destefanis

k

,

J. Díaz

r

,

F. Dohrmann

f

,

A. Dybczak

c

,

L. Fabbietti

i

,

O.V. Fateev

g

,

P. Finocchiaro

a

,

P. Fonte

b

,

2

_,

_{J. Friese}

j

_,

_{I. Fröhlich}

h

_,

_{T. Galatyuk}

e

,

3

_,

_{J.A. Garzón}

q

_,

R. Gernhäuser

j

,

A. Gil

r

,

C. Gilardi

k

,

K. Göbel

h

,

M. Golubeva

m

,

D. González-Díaz

d

,

F. Guber

m

,

M. Gumberidze

e

,

T. Hennino

o

,

R. Holzmann

d

,

A. Ierusalimov

g

,

I. Iori

l

,

5

,

A. Ivashkin

m

,

M. Jurkovic

j

,

B. Kämpfer

f

,

4

,

T. Karavicheva

m

,

D. Kirschner

k

,

I. Koenig

d

,

W. Koenig

d

,

B.W. Kolb

d

,

R. Kotte

f

,

F. Krizek

p

,

R. Krücken

j

,

W. Kühn

k

,

A. Kugler

p

,

A. Kurepin

m

,

A. Kurilkin

g

,

∗

,

P. Kurilkin

g

,

V. Ladygin

g

,

∗

,

S. Lang

d

,

J.S. Lange

k

,

K. Lapidus

i

,

T. Liu

o

,

L. Lopes

b

,

M. Lorenz

h

,

L. Maier

j

,

A. Mangiarotti

b

,

J. Markert

h

,

V. Metag

k

,

B. Michalska

c

,

J. Michel

h

,

E. Morinière

o

,

J. Mousa

n

,

C. Müntz

h

,

L. Naumann

f

,

J. Otwinowski

c

,

Y.C. Pachmayer

h

,

M. Palka

c

,

Y. Parpottas

n

,

6

,

V. Pechenov

d

,

O. Pechenova

h

,

J. Pietraszko

h

,

W. Przygoda

c

,

B. Ramstein

o

,

∗

,

A. Reshetin

m

,

A. Rustamov

h

,

A. Sadovsky

m

,

P. Salabura

c

,

A. Schmah

j

,

1

,

E. Schwab

d

,

Yu.G. Sobolev

p

,

S. Spataro

k

,

7

,

B. Spruck

k

,

H. Ströbele

h

,

J. Stroth

h

,

d

,

C. Sturm

d

,

A. Tarantola

h

,

K. Teilab

h

,

P. Tlusty

p

,

M. Traxler

d

,

R. Trebacz

c

,

H. Tsertos

n

,

V. Wagner

p

,

T. Vasiliev

g

,

M. Weber

j

,

M. Wisniowski

c

,

T. Wojcik

c

,

J. Wüstenfeld

f

,

S. Yurevich

d

,

Y. Zanevsky

g

,

P. Zhou

f

a_{IstitutoNazionalediFisicaNucleare,LaboratoriNazionalidelSud,95125Catania,Italy}

b_{LIP-LaboratóriodeInstrumentaçãoeFísicaExperimentaldePartículas,3004-516Coimbra,Portugal} c_{SmoluchowskiInstituteofPhysics,JagiellonianUniversityofCracow,30-059Kraków,Poland} d_{GSIHelmholtzzentrumfürSchwerionenforschungGmbH,64291Darmstadt,Germany} e_{TechnischeUniversitätDarmstadt,64289Darmstadt,Germany}

f_{InstitutfürStrahlenphysik,Helmholtz-ZentrumDresden-Rossendorf,01314Dresden,Germany} g_{JointInstituteofNuclearResearch,141980Dubna,Russia}

h_{InstitutfürKernphysik,Goethe-Universität,60438Frankfurt,Germany}

i_{ExcellenceCluster‘OriginandStructureoftheUniverse’,85748Garching,Germany} j_{PhysikDepartmentE12,TechnischeUniversitätMünchen,85748Garching,Germany} k_{II.PhysikalischesInstitut,JustusLiebigUniversitätGiessen,35392Giessen,Germany} l_{IstitutoNazionalediFisicaNucleare,SezionediMilano,20133Milano,Italy} m_{InstituteforNuclearResearch,RussianAcademyofScience,117312Moscow,Russia} n_{DepartmentofPhysics,UniversityofCyprus,1678Nicosia,Cyprus}

o_{InstitutdePhysiqueNucléaire(UMR8608),CNRS/IN2P3–UniversitéParisSud,F-91406OrsayCedex,France} p_{NuclearPhysicsInstitute,AcademyofSciencesofCzechRepublic,25068Rez,CzechRepublic}

q_{LabCAF.Dpto.FísicadePartículas,Univ.deSantiagodeCompostela,15706SantiagodeCompostela,Spain} r_{InstitutodeFísicaCorpuscular,UniversidaddeValencia-CSIC,46971Valencia,Spain}

*

Corresponding authors.

E-mailaddresses:akurilkin@jinr.ru(A. Kurilkin), vladygin@jinr.ru(V. Ladygin), ramstein@ipno.in2p3.fr(B. Ramstein). 1 _{Also at Lawrence Berkeley National Laboratory, Berkeley, USA.}

2 _{Also at ISEC Coimbra, Coimbra, Portugal.}

3 _{Also at ExtreMe Matter Institute EMMI, 64291 Darmstadt, Germany.} 4 _{Also at Technische Universität Dresden, 01062 Dresden, Germany.} 5 _{Also at Dipartimento di Fisica, Università di Milano, 20133 Milano, Italy.} 6 _{Also at Frederick University, 1036 Nicosia, Cyprus.}

7 _{Also at Dipartimento di Fisica Generale and INFN, Università di Torino, 10125 Torino, Italy.}

http://dx.doi.org/10.1016/j.physletb.2015.09.016

0370-2693/©2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3_.

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Articlehistory:

Received 13 March 2015

Received in revised form 4 September 2015 Accepted 7 September 2015

Available online 11 September 2015 Editor: D.F. Geesaman

Keywords:

Two-pion production

np collisions

Resonance excitations

Thetaggedquasi-freenp→np

π

+

π

−reactionhasbeenstudiedexperimentallywiththeHighAcceptance Di-Electron Spectrometer (HADES) at GSI at a deuteron incident beam energy of 1.25 GeV/nucleon (√s∼2.42 GeV/c for the quasi-free collision). For the first time, differential distributions of solid statisticsfor

π

+

π

− productioninnp collisionshavebeencollectedintheregioncorresponding tothe largetransversemomentaofthesecondaryparticles.Theinvariantmassandangulardistributionsforthe

np→np

π

+

π

−reactionarecomparedwithdifferentmodels.Thiscomparisonconfirmsthedominanceof thet-channelwithcontribution.ItalsovalidatesthechangespreviouslyintroducedintheValencia model to describetwo-pion productiondata inother isospinchannels, although somedeviations are observed,especiallyforthe

π

+

π

− invariantmassspectrum.Theextractedtotalcrosssectionisalsoin muchbetteragreementwiththismodel.Ournewmeasurementputsusefulconstraintsfortheexistence oftheconjectureddibaryonresonanceatmassM_∼2.38 GeV andwithwidth∼70 MeV.

©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

Thetwo-pionproductioninnucleon–nucleon(NN)collisionsis arichsourceofinformationaboutthebaryonexcitationspectrum andthebaryon–baryon interactions. In additionto the excitation ofaresonancedecayingintotwopions,whichcanalsobestudied inthe

π

N

→

π π

N [1]and

γ

N

→

π π

N [2]reactions,the simul-taneous excitation oftwo baryons can be investigated inthe NN

reactions.Bygivingaccessto singleanddoublebaryon excitation processes,whichbothplayan importantroleintheNN dynamics

inthefewGeVenergyrangeandcontributesignificantlytomeson anddileptonproduction,thetwo-pionproductionappearsasakey process towardsa better understanding ofhadronic processes.In comparisontotheone-piondecaymode,itpresentsadifferent se-lectivitywithrespect tothevarious resonances.In particular,the excitationofbaryonicresonancescoupledtothe

ρ

mesoncanbe studied with the two pions in the isospin 1 channel. This is of utmostinterestforabetterunderstandingofthedilepton produc-tioninnucleon–nucleonreactions,wherethesecouplingsmanifest clearly

[3–5]

,andalsoinnucleonmatterduetotheexpected mod-ificationsofthe

ρ

mesonspectral functions

[6]

.Finally,the com-parisonoftwo-pionproductionin pp andnp channelscouldshed some light on theorigin ofthe surprisinglylarge isospin depen-denceofthedileptonemissionobservedbytheHADESexperiment

[7].Inparticular,the

ρ

productionmechanismvia



final state interaction,whichdoesnot contributeinthe pp channel,was re-centlyproposed asan explanationforthedifferentdileptonyield measuredin pp and pn channels

[8]

.It isthereforeimportantto checkthedescriptionofthedouble



processinthetwo-pion pro-ductionchannels.

Additionally, following the intriguing results obtained by the WASA Collaboration in the double pionic fusion reactions, a

re-newed interest on the study of the two-pion production in NN

collisionswassparked,inordertocheckthepossiblecontribution ofadibaryonresonance

[9,10]

.

The answer to all these open questions requires systematic

two-pion production measurements both in proton–proton and

neutron–proton collisions. Concerning proton–proton collisions,

a significant amount of data has been accumulated for various

two-pion final channels in bubble chamber experiments [11–23]

forproton incident energies fromthe thresholdup to 2.85 GeV. Precisedifferentialcross-sectionshavealsobeenobtainedrecently

at CELSIUS and COSY up to 1.4 GeV [24–34], with an emphasis

onthe

π

0

_π

0 _{production.The databaseforthe pn reactionfrom}

thebubblechamberexperimentsisevenmorescarce

[14,18,19,21,

35].Veryrecently,however,precisemeasurementsoftotaland dif-ferentialcross sectionsforthenp

→

pp

π

−

π

0 _andnp

_→

_np

_π

0

_π

0

became available from WASA at COSY at neutron energies from

1.075 to 1.36 GeV [36,37].In the np

→

np

π

+

π

− channel,

differ-ential cross-sections are also known from Dubna measurements

[38,39], covering the beam incident energy range from 0.624 to 4.346 GeV.

Since the chiral perturbation theory calculationsfor two-pion production in NN collisions are available only near threshold

[40], several phenomenological models have been suggested for the analysis of the double pion production in NN collisions in the GeV energy range.The first theoretical developments related tothetwo-pionproductionwerebasedontheone-pionexchange (OPE) model [41]. The reggeized

π

exchange model (OPER) [42, 43], which uses the partial wave analysis results for

π

N

elas-ticscattering

[44]

,constitutesits mostrecentandmostelaborate modification.Lagrangianmodelswerealsointroduced.The Valen-ciamodelbyAlvarez-Rusoetal.

[45]

wasfirstdeveloped.Itaimed atadescriptionofNN collisionsatenergieslowerthan1.4 GeVand included N

(1440)

and

(1232)

excitations. TheCao et al.model

[46],developed afterthepublicationofnewdataatCOSYand CEL-SIUS, has a larger range of applicability due to the inclusion of resonances with mass up to 1.72 GeV. Both models qualitatively reproducetheveryfastincreaseofthecrosssectionabove thresh-oldinthedifferenttwo-pionproductionchannelsandpredict the dominance of two processes above 1 GeV: the excitation of the

N

(1440)

resonanceandsubsequentdecayinto



π

orN

σ

andthe double



excitation.

However, both models [45,46] have failed to reproduce the

π

0

_π

0 _{spectra for the pp}

_→

_pp

_π

0

_π

0 _{reaction at beam energies}

above 1.0 GeV [32,34], which motivated the development of the so-called “modified Valencia model” [32], providing a much im-proved description ofthesedata.This newmodel hasbeenused bytheWASACollaborationfortheinterpretationofthedouble pi-onic fusion reactions, after some additional changes to take into account the deuteronformation. However, the observedresonant behaviorofthecrosssectionofthepn

→

d

π

0

_π

0 _{[9,10],associated}

with a structure atlow

π

0

_π

0 _{invariant mass(the so-calledABC}

effect) couldnot be explainedbysuch an approachandwere in-terpreted asbeingdue toa dibaryon resonancein theI

=

0 NN

channel,withamassof2.37 GeV/c2 andawidthof70MeV.This hypothesis was further supported by the isospin decomposition of the pn

→

d

π π

reaction [47]. The latterprovided a consistent description ofboth I

=

0 andI

=

1channels by takinginto ac-count the resonant contribution in addition to the conventional t-channel processes described by the “modified Valencia model”. Even more recently, the pn

→

pp

π

0

_π

− _{[36] reaction was also}

consistently described with the same model.The accuracy of d∗

analysisbased onnewpolarizednp scattering



data. Inthis anal-ysis a resonance pole in the 3D3–3G3 coupled partial waves at

(2380

±

10–i40

±

5)MeV havebeendiscovered

[48,49]

.

Considering the impact that the discovery of a dibaryon res-onance could have, this systematicstudy must be pursued. It is indeedimportanttoprovide,possiblyinindependentexperiments, constraintsforallpossiblechannelsofthe pn reaction,wherethe resonanceisexpectedtocontribute,inparticular

π

+

π

−or

π

0

_π

0

productionwithanunbound pn pair, butalsofor pp channels in order to check unambiguously the consistent description of the conventionalprocesses.

The experimentswithHADES

[50]

are particularlywell suited toanswersucharequest,sinceboth pp and pn experimentswere studiedintherelevantenergyrange.ThegoodcapacitiesofHADES forhadronidentificationwerealreadyshowninthestudyof one-pion andone-eta (measuredby its three pion decay) production channels

[5,51]

ofthepp reactionatdifferentenergies.Beyondthe searchforthedibaryonresonance,thestudyofthetwo-pion pro-ductionprocess by the HADESCollaboration isalso motivatedby theconnectionwiththedileptonproduction,asmentionedabove. As a first step in thisprogram, we report hereon the analy-sis ofthe tagged quasi-free pn

→

pn

π

+

π

− reaction from

exper-iments using a deuteron beamof 1.25 GeV/nucleon and present

precisetotal anddifferential cross-sections.According toprevious estimates

[14,18,19,21]

,thischannelisdominatedbytheisospin-0 contributions,inwhichtheresonanceshouldreveal.Inthepresent analysis, theresultswere averagedover theavailable rangeofnp

center-of-mass energies. Our strategy consists in comparing the various differential spectra to three different models introduced above:theOPERmodel,themodifiedValenciaandtheCaomodel andcheck whethera description of the data ispossible without contribution fromthe dibaryon resonance. The sensitivity ofour data to the differentmechanisms (double

(1232),

N

(1440)

ex-citation, aswell ashigher lying resonances) can be studied. The totalcross-sectioncanbeusedforconsistencychecksofthe differ-entanalysis,incomparisontothealreadymeasuredpn

→

d

π

+

π

− cross-section,asdiscussedin

[52,53]

.

Ourpaperisorganizedasfollows:Theexperimentalprocedure isdescribedinSection 2.Thefeatures ofthemodelsusedforthe description of the data are introduced in Section 3. We present anddiscusstheexperimentalresultsandthecomparisonwiththe modelsinSection4anddrawconclusionsinSection5.

2. Experimentalprocedure

The experimental data have been obtainedusing HADES [50]

locatedattheGSIHelmholtzzentrumfürSchwerionenforschungin

Darmstadt, Germany. HADES is a modern multi-purpose detector

currentlyoperating in the region ofkinetic beamenergies of up to2 A GeVfornucleus–nucleuscollisions.Thedetaileddescription oftheset-upcanbefoundin

[50]

,herewebrieflysummarizethe mainfeaturesrelevantforthepresentanalysis.

HADESisdividedinto6identicalsectorsdefinedbythe super-conductingcoils producing the toroidal geometry magnetic field.

The spectrometer has 85% of azimuthal acceptance and covers

polar angles from 18◦ to 85◦ measured relatively the beam di-rection.Each sector ofthe spectrometer contains a Ring Imaging Cherenkovdetector(RICH)operatinginthemagneticfield-free re-gion, 4 planes of the Multi-wire Drift Chambers (MDC) located beforeandafterthemagneticfield region,two plasticscintillator wallsforthepolarangleslarger(TOF)andsmaller(TOFINO)than 45◦, respectively, and an electromagnetic cascade detector (Pre-Shower) behind TOFINO for particle identification. A two-stage trigger system is employed to select events within a predefined chargedparticlemultiplicity interval,aswell astheelectron

can-didates. The investigationof thequasi-free np reactions withthe deuteronbeamisperformedbyusingaForwardWall(FW) scintil-latorhodoscopebyregisteringthespectatorprotons.TheFWisan array whichconsistsofnearly300scintillatingcellseach2.54 cm

thick. During the dp experiment the FW was located 7 meters

downstream the target covering polar angles from 0.33◦ up to 7.17◦.AMonteCarlosimulationfordeuteron–protonbreakuphas shownthatapproximately90% ofall spectatorprotonsarewithin theFWacceptance

[7]

.

In the present experiment, the deuteron beam withintensity up to 107 _{particles/s and 1.25 GeV/u of kinetic energy was}

di-rectedonto a 5cmlong liquid–hydrogentarget of1% interaction probability. The analysis of the deuteron induced quasi-free np

reactions was based on the first-level triggered events, with the requiredchargedparticlemultiplicity ofatleastthreeinTOFand TOFINO andasignal intheFWhodoscope. Theinformationfrom

RICH, TOF/TOFINO and Pre-Shower detectors was used to select

anddiscriminatethehadronsagainsttheleptons.Themomentum reconstruction was carriedout by measuringthe deflectionangle of the particle trajectoriesderived fromthe four hit positions in theMDCplanes(twobeforeandtwoafterthemagneticfieldzone)

using the Runge–Kutta algorithm [50]. The achieved momentum

resolutionwas2–3%forprotonsandpionsdependingontheir mo-mentumandscatteringangle.

Quasi-free np interactionshavebeenselectedby thedetection oftheprotonspectatorswithscatteringangles

≤

2◦ andmomenta between1.7 GeV/c and2.3 GeV/c reconstructed fromthe time-of-flight measurementinFW.The latterwindowiscentered onhalf ofthebeammomentumandhasahalfwidthequalstothreetimes thewidthofthemomentumresolution.Thenp

→

np

π

+

π

− chan-nelselectionwasbasedonidentificationofthreedetectedhadrons whereoneofthemhasthenegativemomentumpolarity.The par-ticle identification was based on eventhypotheses whereany of the three selectedhadronshas beenused asthereference parti-cle. The referenceparticletime-of-flight was calculatedusing the reconstructed momentum andtrajectory length. The velocities of the other two particles were thendeduced, usingonly the time-of-flight difference with the reference particle. The applicability of this time-of-flight reconstruction algorithm was checked in a dedicatedexperimentwithalow beamintensitybymeansofthe START detectorasdiscussedin

[50]

.Thecorrelationsbetweenthe velocityandreconstructedmomentumforallthreeparticleswere takenintoconsiderationto rejectthewrong hypotheses.The

cor-relationbetweenthe energylossesin MDCsandmomentumwas

additionallyappliedforthefinal selectionoftheprotonsand

π

+. Finally, thetotal numberof selected eventscorresponding to the

np

→

np

π

+

π

− channelwas

∼

8

·

105.

The normalization of the experimental yield has been

per-formed using thesimultaneously measured quasi-elastic pp

scat-teringyield

[54]

.The selectionof pp elastic eventswas basedon relationsbetweenthepolarangles

θ

1 and

θ

2andazimuthalangles

φ

1 and

φ

2 ofbothprotonsduetothemomentumconservationin

elasticscattering:

|φ1

− φ2| =

180◦

,

(1) tan

θ

1

·

tan

θ

2

=

1

γ

2 CM

,

(2)

where

γ

CMistheLorentzfactorofthecenter-of-mass(CM)system. Theelasticeventswereapproximatelyselectedbyanellipticcutin the

|φ

1

− φ

2

|

vs.tan

θ

1

·

tan

θ

2)planewithsemiaxescorresponding

to 3

σ

cut foreach variable. The quasi-free pp elastic data mea-suredbyHADESintheangularrange46◦–134◦ intheCMsystem have beencorrectedfor theefficiencyandacceptance byusing a

Fig. 1. Squared

missing mass distributions of the

pπ+π− system for the np→ npπ+π−reaction at 1.25 GeV. The experimental data are shown by the solid sym-bols. The shaded area displays the phase-space distributions at 1.25 GeV, corrected for the energy dependence of total cross section taken from [20].

Pluto[55,56]simulation whichuses thedatafrom [54] asan in-putandtakesinto accounttheprotonmomentum distributionin thedeuteronandthe dependenceofthe crosssection on the pp

centerofmassenergydependenceofthecrosssection.The result-ing factortaken to normalizethe differential cross section has a precisionofabout4%at1.25 GeV.Thedetailsofthenormalization procedureat1.25 GeVarediscussedin

[57]

.

Thepurity ofthe np

→

np

π

+

π

− channel selection is demon-stratedbythesquaredmissingmassdistributionofp

π

+

π

−shown assolid circlesin Fig. 1,which peaksclose tothe neutronmass. Theshaded area displays the resultofa simulationof the quasi-free np

→

np

π

+

π

− reaction,where theneutron momentum dis-tribution in the deuteron is taken into account using the Paris potential [58] and the

π

+

π

− production in the n

+

p reaction

istreatedusing phase-distributions andconsidering a rise ofthe crosssectionwiththenp center-of-massenergyaccordingto

[20]

. The direct comparison of theoretical and efficiency corrected experimental distributionshas beenperformedinside the HADES acceptanceusingdedicatedfilters,aswillbeshowninthe follow-ing.Forthispurpose,theacceptancesandefficienciesfordifferent particles(i.e.pionsandprotons)wereseparatelytabulatedin ma-tricesasfunctionsofthemomentum,azimuthalandpolarangles. TheacceptancematricesdescribeonlytheHADESfiducialvolume andcanbeappliedasafiltertotheeventsgeneratedbythe mod-els.Thematrixcoefficientshavebeendeterminedbymeansoffull GEANTsimulations,withpionsandprotonsprocessedthroughthe detectorandreconstructed bytracking,particle identificationand selectionalgorithmswiththesamepackageasitwasdoneforreal events.Theacceptanceof HADESforthe np

→

np

π

+

π

− reaction isabout6% incomparisonwiththefullphase-space.Theresulting detectionand reconstruction efficiencyis typically about90% for protonsandpions.Theseefficiencieshaveaverysmoothbehavior asa functionofthedifferentobservablesshowninthefollowing. Therefore,weonlyconsideraglobalsystematicuncertaintywhich willaffectthenormalizationofourdata,butnottheshapeofthe spectra.Thiseffectispartiallytakeninto accountby the normal-izationtotheelasticdata,andweestimatetheresidualuncertainty to2%.

3. Modelfeatures

FortheinterpretationanddiscussionofourresultsinSection4

below,weusedthemodifiedValencia

[33]

,theCao

[46]

andOPER models

[43]

.The Caoand modified Valenciamodelsare effective lagrangianmodelstakingintoaccountdifferentresonantand non-resonant graphs. The original Valencia model [45] includes only

N

(1440)

and

(1232)

resonances while the Cao model

consid-ers all known baryonic resonances with mass up to 1.72 GeV,

neglecting the interferences between the different contributions, included in the Valencia model. The practical differences in our

energy range are lower contributions for both



and N

(1440)

by about 30% in the Valencia model, which are partially

com-pensated by constructive interferences. In comparison with the original Valenciamodel,four mainchanges havebeen applied in the “modified”Valenciamodel.First, theratio R

= (

N

(1440)

→



π

)/ (

N

(1440)

→

N

σ

)

ofthebranchingratiosoftheRoper res-onance towards2

π

N via



π

or N

σ

hasbeenreducedfrom4in theinitial modelto1.Theinitialvalue correspondedtoPDG

[59]

estimates prior to 2012, anda newvalue was deduced from an

analysisof the

π

0

_π

0 _{openingangle andinvariant mass}

distribu-tionsobtainedinthepp

→

pp

π

0

_π

0 _{reactionbelow900MeV}

_[30]

assumingthedominanceoftheRoperexcitation.Thisnewvalueis alsoin agreementwitha recentPartialWave Analysis

[60,61]

. In themeantime,thePDGlimitsfortheratiohavealsobeenchanged andarenow between1and3.Thischangeseems thereforefully consistent.TheCaomodelusesavalue2forthisratio,hence favor-ing N

(1440)

→ 

π

by afactor2withrespectto N

(1440)

→

N

σ

decay, while they have equal weights in the modified Valencia

model.

The second changeisa readjustmentof the N

(1440)

strength in the modified Valencia modelaccording to the isospin decom-position of the two-pionproduction channels inthe pp reaction

at differentenergies between0.775 GeV and 1.36 GeV [31].The maximumreductionisobtainedexactlyforourincidentenergyof 1.25 GeVandamountstoafactor2.ThisbringstheN

(1440)

con-tributiontobe muchsmallerthanthedouble



excitation inthe modified Valencia modelandmakes a significant difference with the Cao model, where the N

(1440)

contribution corresponds to about40%ofthetotalpn

→

pn

π

+

π

− crosssectionatanincident energyof1.25 GeV.

The third modification is driven by the shape of the

π

0

_π

0

invariant mass distributionmeasured in pp

→

pp

π

0

_π

0 _{at an}

in-cidentenergylargerthan1 GeV, wherethedouble



mechanism dominates [32]. It consists in a reduction by a factor 12, and a changeofthesignofthe

ρ

exchangecontributioninthe



excita-tionmechanism. Thelatterindeedinducedatwo-humpstructure inthe

π

0

_π

0_{invariantmassdistribution,whichwasnotseen,}

nei-therinthedata

[32]

norintheCaomodelwhichhasaverysmall

ρ

exchangecontribution.

The fourth modification consists in the introduction of the

(1600)

→ (

1232)

π

contribution toimprovethedescription of the pp

→

nn

π

+

π

+ reaction. In thischannel, the N∗ decay does notcontribute,andthecrosssectionislargerbymorethana fac-tor 2 than expected for the double

(1232)

contribution only. The WASA Collaboration explained this feature by a large con-tribution of

(1600)

excitation, with a destructive interference withthedouble

(1232)

contribution.Afterintroducingthisnew contribution, the pp

→

nn

π

+

π

+ cross section could be repro-duced and the description of the differential spectra, especially the

π

+

π

− opening angle and invariant mass distributions mea-suredforthischannel at1.1 GeV

[33]

,improvedsignificantly.The

(1600)

→ (

1232)

π

process wasimplementedinasimilarway as

(1232)

→ (

1232)

π

, which was already takeninto account inthe Valenciamodel.However, such a large contributionof the

(1600)

resonanceatsuchlow energies issurprising.IntheCao model,itistakenintoaccount,butstartstocontributesignificantly tothe pp

→

nn

π

+

π

+reactionforenergieslargerthan1.6 GeV.It hasto be notedthat,while theoriginal Valenciamodel underes-timatesthe pp

→

nn

π

+

π

+ crosssection bymorethanafactor2, theCaomodelprovides goodpredictionsforbothtotalcross sec-tionsanddifferentialspectra

[46]

.Thisisrelatedtothelarger dou-ble



contributioninthismodel.However,suchalargedouble



Table 1

Main contributions in the Cao [46], “modified Valencia” [32]and OPER [43]models for the np→npπ+π−for a neutron incident energy of 1.25 GeV.

Cao mod. Valencia OPER

(1232)(1232) 47.0% 60% 38.0%

N(1440)→ (1232)π 23.0% 2.1% 4.5%

N(1440)→Nσ 20.0% 8.2% 0.2% (1600)→ (1232)π 3.0% 21.0% 4.5%

contributionleads toasignificantoverestimate ofthe pp

→

pp

π

0

π

0_{crosssection.Inbothmodels,thenucleonpoletermsarefound}

tobeverysmall,althoughtheyhaveamuchlargerrelative contri-butioninthepp

→

nn

π

+

π

+thaninotherchannels.

Asmentionedintheintroduction,theOPERmodelisbasedon a Reggeized

π

-exchange model and uses on-shell amplitudes of theelastic

π

N scatteringandoftheinelastic

π

N

→

π π

N reaction,

with form factors and propagators taking into account the off-shellnessoftheexchanged pion.Theelasticamplitudesare taken froma Partial Wave Analysis andthe inelastic onesare deduced fromaparametrizationobtainedintheframeworkofthe General-izedIsobarModel

[38,62]

.Thismodelprovidedagooddescription of differential spectra measured at Dubna in the np

→

np

π

+

π

− reaction at5.2 GeV/c andin p p

¯

→ ¯

p p

π

+

π

− at7.23 GeV/c [38]. TheOne-BaryonExchange(OBE)diagramswereintroduced,as de-scribedin [38],to improvethedescription ofthe np

→

np

π

+

π

− spectra below 3 GeV/c. Such diagrams correspond in Lagrangian modelstothe“pre-emissioncontribution”.Veryrecently,the con-tributionoftheso-called “hanged” diagrams,duetothetwo-pion productionfromtheexchange pionline,was alsoconsidered. For this, amplitudes for

π π

scattering were used. This addition was showntoimprovethedescriptionofthe

π π

invariantmass spec-trainthelowmassregion

[43]

.Suchgraphsaretakenintoaccount intheValenciamodel,butareneglectedintheCaomodel.

Table 1

displays the main resonant contributions in the three models at anincidentneutronenergyof1.25 GeV,disregardingthe contribu-tion viainterference terms.This makes a bigdifference withthe

OPER model, where the OBE diagrams, where at least one pion

is not emitted by a resonance,amount to41% of the totalyield. Althoughthesenumbersdonottakeintoaccountinterference ef-fects,they alreadypointtomajordifferencesbetweenthemodels whichwillbeinvestigatedfurtherwhencomparingtoourdata.

Totakeintoaccountthemomentumdistributionoftheneutron inside the deuteron, the Paris [58] deuteron wave functions has beenusedforthephase-spacecalculation,theHulthen

[63]

wave

function for modified Valencia [33] and CD-Bonn [64] for OPER

[43] and Cao [46] models. No significant difference is expected fromthesedifferentinputs.Asmentionedintheprevioussection, eventshavebeengeneratedaccordingtodistributions fromthese modelsandfilteredbytheHADESacceptance.

4. Experimentalresultsandcomparisonwithmodels

We first concentrate on the comparison of the shapesof the theoretical and experimental distributions and will discuss the crosssections atthe endof thissection. The invariant mass and angulardistributions forthe np

→

np

π

+

π

− reaction at1.25 GeV measured insidethe HADES acceptanceandcorrected forthe re-construction efficiencyare presented by solid circles in Figs. 2–3 and 4–5 respectively. Only statistical errors are shown. As ex-plainedabove,theglobaluncertaintytakingintoaccountboth nor-malizationandefficiencycorrectionisoftheorderof5%,withno significantdependenceonthedifferentobservables.

Thepredictions fromthe modifiedValencia

[33]

,Cao

[46]

and OPERmodels

[43]

havebeennormalizedthereforetothetotal ex-perimental yield and are presented as long-dashed, dashed and

Fig. 2. Distributions

of the

π+π− (a), pπ−(b), pπ+ (c) and pπ+π− (d) invari-ant masses for the np→npπ+π− reaction at 1.25 GeV. The experimental data are shown by solid symbols. The theoretical predictions within HADES acceptance from OPER [43], Cao [46]and modified Valencia models [33]are given by the solid, dashed and long-dashed curves, respectively. The shaded areas show the phase-space distributions.

Fig. 3. Experimental

data (full dots) for

np→npπ+π− at 1.25 GeV are compared to the total yield (solid curves) for the OPER model [43](left column) and modified Valencia model [32,33](right column). In each case, the (long-dashed), N(1400) (long dash-dotted) and (1600)(short-dashed) contributions are shown. a) and b): π+π−invariant mass, c) and d): pπ+invariant mass, e) and f): pπ+π−invariant mass distributions.

solid lines, respectively, in Figs. 2 and 4. The hatched areas cor-respondtophase-spacedistributionsobtainedinthesameway.In addition,thedifferentcontributionsintheOPERandmodified Va-lenciamodelsareshownin

Figs. 3 and 5

incomparisontoselected experimentaldistributionsexhibitedin

Figs. 2 and 4

.

Fig. 4. Same

as

Fig. 2, but for angular distributions: a) – opening angle of π+π− in the np rest

frame, b) – polar angle of

pπ+π− in the np rest

frame, c) – polar

angle of pπ−in the np rest

frame, d) – polar angle of

pπ+in the np rest

frame,

e) – polar angle of π−in the pπ−Gottfried–Jackson frame, f) – polar angle of π+ in the pπ+Gottfried–Jackson frame.

Fig. 5. Same

as

Fig. 3for opening angle of π+π−in the np rest

frame (a) and b))

and polar angle of pπ+system in the np rest

frame (c) and d)).

4.1.Invariantmassdistributions

Theexperimental p

π

−, p

π

+ and p

π

+

π

− invariant mass dis-tributions(panels b),c) andd)in Fig. 2)are all shiftedtohigher massesin comparison withthe phase-space calculations. In par-ticular, the invariant mass distribution of the p

π

+ subsystem (panel c)in

Fig. 2

) showsapronounced resonantbehaviorwitha positionofthemaximumintheexperimentaldistributionroughly correspondingtothe



++mass.Thisdistributioniswelldescribed bythedifferentmodels anddeviatessignificantly fromthephase

spacedistribution.Sucha resonantbehaviorofthe p

π

+invariant mass distribution is expected for the double



excitation pro-cess, sincethe isospinfactorsfavor theexcitation ofthe



++



− contributionwithrespecttothe



+



0 byaweightof8/5.A reso-nanceinthep

π

+systemisalsoexpectedfortheN

(1440)

+decay into



++

π

−,butwitha “smearing” dueto theexcitation of the

N

(1440)

0 _{andsubsequentdecayinto}

_

−

_π

+ _{whichhasthe same}

probability.In addition,the dominance withrespect tothe other isospin channels is alsolower than in the caseof the double



excitation. The situationissimilar forthe

(1600)

case, withan evenlowerrelativeweightforthedecayinvolvingthe

(1232)

++ excitation.Thesestatementsareconfirmedby thebehaviorofthe

N

(1440)

and

(1600)

contributionswhicharedisplayedin

Fig. 3

d

below in the case of the modified Valencia model. The overall

contribution ofthe double



excitation islarger inthe modified Valenciamodel than inthe Cao model.This isprobably the rea-sonwhythelatterpresentsaslightlybroaderp

π

+invariantmass distribution. Surprisingly, the p

π

+ invariant mass of the double

(1232)

contributioninthe OPER modelisslightlybroaderthan in theValencia model,ascan be seen in Fig. 3c. Theglobal dis-tributionwhich isfurtherbroadenedby theOBEcontributions, is similar to the one in the Cao model with an additional shift to higherenergies(see

Fig. 2

b).

Thedeviationsfromphase-spacedistributions areless spectac-ularforthe p

π

−andp

π

+

π

− invariantmassdistributions(panels b)andd)in

Fig. 2

).Noclearresonancebehaviorisindeedexpected forthe p

π

− system, since the

(1232)

0 _{isdisfavored by isospin}

withrespect to



++ inall channels(double

,

N

→ (

1232)

π

, and the

(1600)

→ (

1232)

π

). This also holds for the p

π

+

π

− system, duetothestrongdouble



contribution.In addition,the

N

(1440)

0 excitation,whichisasprobableasthe N

(1440)

+,is fa-voredbyacceptance.Thiscanbecheckedin

Figs. 3c

and 3d,where the N

(1440)

contributions are indeedshifted tolow p

π

+

π

− in-variantmass.Forthe

(1600)

excitation,thepositivechargestate, decaying into p

π

+

π

−,is favoredby acceptance.This isprobably the reason why the p

π

+

π

− invariant mass distribution for this contributionisshiftedinthemodelstothehigh-masspartofthe availablephasespace. TheOPERandCaomodelsgivesimilar pre-dictionsforthe p

π

− andp

π

+

π

−observablesandachievea rea-sonabledescriptionofthe p

π

− butpredictatoonarrow p

π

+

π

− invariantmassdistribution.InthecaseoftheValenciamodel,both the p

π

− and p

π

+

π

− areoverestimatedonthehighenergyside. This points to a too large

(1600)

contribution, as will be dis-cussedbelowinsomedetails.

Thethreemodelspresentthelargestdeviationsforthe

π

+

π

− invariant mass distribution. The sensitivityof this distributionto thetwo-pionproductionmechanisminNN

→

NN

π π

reactionshas alreadybeendemonstratedinprevious work

[46,30,32,34]

.Infact, thepuzzlingenhancementobservedinthelow-energypartofthe invariant massspectraoftwo pionsproduced in pn or pd fusion

reaction(theso-calledABCeffect)wasalsoamanifestationofthis sensitivity and triggered the onset of double



excitation mod-els [65]. The OPER model is not too far fromthe data, but has a slightly tooflat shape, while the Cao and Valenciamodels fail strongly to describe the shape of this distribution. The double-humpstructure which can be seenin thepredictions of theCao modeliscompletelyabsent inourdata.Averysimilar trendwas alreadyobservedforthecomparisonoftheCaomodelpredictions tothespectrameasuredinthepp

→

pp

π

+

π

−andpp

→

pp

π

0

_π

0

reactions above 1.1 GeV [46]. Since this double-hump structure is dueto the N

(1440)

→ 

π

process, theseresults indicatethat thiscontribution istoo large inthe Cao model.The OPER model gives the best description of the low mass part of this distribu-tion, which seems to be mainly dueto the addition of the OBE and“hanged”diagrams.However,thedouble



contributionisalso

muchbroaderthaninthecaseofthemodifiedValenciamodel(see

Fig. 3aandb).InthemodifiedValenciamodel,theexcessinthe re-gionabove350MeV/c2 _{isduetoboththe}

_(1600)

_andtheRoper

contributionsandtheirinterferencewiththedouble

(1232)

con-tribution. In particular, the interference between the Roper and double

(1232)

contributionissmallinoverall,buthasa signifi-cantconstructiveeffectofthelevel of10–15%inthisregion. Our datawouldbe betterdescribed by achangeof signofthis inter-ferencetogetherwithareductionofthe

(1600)

contribution.

4.2. Angulardistributions

Fig. 4exhibitstheangulardistributionsforthenp

→

np

π

+

π

− reaction at 1.25 GeV. Panels a), b), c), d) and e), f) correspond to the distributions ofthe opening angle of

π

+

π

−, polarangles of p

π

−, p

π

+, p

π

+

π

−subsystems inthenp CM systemand po-laranglesof

π

− and

π

+ inthe p

π

− and p

π

+ Gottfried–Jackson frames,respectively.TheCMframewasdefinedassumingthe neu-tronatrestinthedeuteronandtheanglesintheGottfried–Jackson framearedefinedwithrespecttothebeamdirection.

Theexcessofthemeasuredyieldsatsmall

π

+

π

− opening an-gles(cos

δ

CM_π+_π−

∼

1) withrespect tothepredictionsofallmodels

observed in Fig. 4 reflects the enhancement atsmall

π

+

π

− in-variant mass which was observed in Fig. 2a. Both variables are indeed strongly correlated. The large asymmetry ofthe distribu-tionin thecaseofthe Caomodel anditssteep peakingforback toback

π

+

π

− emission(cos

δ

_πCM+_π−

= −

1)arerelatedtothe

high-massstructure in

Fig. 2

a,which,asalreadymentioned, isdueto the N

(1440)

→ (

1232)

π

decay.As explainedin

[30]

, thiseffect isproducedbythedoublep-wavedecaywhichgivesanamplitude witha cos2

_δ

CM

π+π− behavior. For the other models, the backward

peakingis consistent withthe data.It can be checked in

Fig. 5

a andbthatthedistributionsarerathersmoothforallcontributions.

In the case of the modified Valencia model, the roughly

sym-metricdistributionresultsfromtheopposite trendsofthedouble

(1232)

and

(1600)

whichhaveyieldsrespectivelyforwardand

backward peakedinthe HADES acceptance.Forthe OPER model,

the anisotropy is mainly due to the OBE terms, all other con-tributions being very flat. Since the N

(1440)

contribution inthe

OPER model is dominated by the



π

decay, we were expecting

a larger anisotropy, following the arguments given above. In the case of the modified Valencia model, the N

(1440)

→ (

1232)

π

decayissuppressedwithrespecttothe

σ

N decay(see

Table 1

).It isthereforenotsurprisingthatthe N

(1440)

contributiondoesnot present a strong anisotropy. The difference of the shapes of the cos

δ

_πCM+_π− distributionsobtainedforthedouble



contributionsin

themodifiedValenciaandOPERmodelsisconsistentwiththe al-readymentioneddifferentbehaviorofthe

π

+

π

−invariantmasses (Fig. 5aandb).

The

θ

CM_pπ+π−,

θ

pCMπ− and

θ

pCMπ+ angular distributions shown in

panels b) and c) and d) in Fig. 4, respectively, present a

signif-icant forward/backward asymmetry. This asymmetry reflects the

fact that protons are emitted preferentially backward in the CM, whichismainlyduetothestrong



++



−contribution.This pro-cessismorelikelyforsmallfour-momentumtransfersbetweenthe targetprotonandthe



++ andthebeamneutronandthe



− re-spectively, hencethe peakingof the protons atbackward angles. Such a strong asymmetry is not present for the other contribu-tions. However, theeffectis alsoenhanced by the acceptance,as demonstrated by the distribution of the pure phase space. Due to the lacking detection capabilities for laboratory polar angles lowerthan 18◦,thedetectionofthe protonisindeedmore likely atbackwardcenter-of-massangles. TheCao modelgivesthebest overalldescriptionofthethreedistributions.The modified Valen-cia model is also doing rather well, however forward/backward

asymmetry is smaller than in experimental data. A much worse

descriptionoftheslopesof

θ

_pCM_π+_π−,

θ

pCMπ− and

θ

CM

pπ+ isobtainedin

OPERmodel.Asshownin

Figs. 5c

and5d,thedouble



contribu-tionismuchmorestronglybackwardpeakedthaninthemodified

Valencia model. However, the OBE and “hanged” contributions,

which are not displayed in the picture, are also responsible for the too steep total angular distribution.One of the possible rea-sons ofsuch a deviationcan be theomission ofthe interference between the“hanged” andother diagrams[43].The striking dif-ference withthe double



contributionin themodified Valencia modelisprobablyduetothemuchlowercut-offparametersinthe vertexformfactorswhichinduceamuchsteeper four-momentum transfer dependence. Worth to note is the strong difference be-tweenthe

θ

_pCM_π+ and

θ

pCMπ− distributions,incontrastwiththephase

space distribution,which allows toappreciate thesmall effectof thedifferent

π

+and

π

−acceptances.Again,themodifiedValencia modelgivesthebestsimultaneousestimateofthesedistributions, which we take as a hint that this modelcorrectly describes the differentisospinconfigurationsofthetwo-pionproduction mech-anisms.Itcanalsobenotedthat,similarlytothe

π

+

π

− invariant mass distributions,the descriptionofthe

θ

_pCM_π+ distribution could

beimprovedbyareductionofthe

(1600)

contribution.The dis-tributionsofthepionangles

θ

_πpπ−−

(

GJ

)

and

θ

pπ

+

π+

(

GJ

)

areshownin

panelse)andf)in

Fig. 4

,respectively.Thequantity

θ

i j_j denotesthe

angle between the thee-momentum of particle j and the

direc-tionofthebeaminthecenter-of-massofparticles i and j,taken relatively to the direction of the beam particle in this reference frame.Thesedistributionsalsopresentstrikingdifferencesfor

π

+

and

π

−.Itcanbenotedthatthe

θ

_πpπ−−

(

GJ

)

distributionisverywell

reproduced, especiallybytheOPER andmodifiedValenciamodel, while noneof themodels predict the observedenhancement for backward

θ

_πpπ++

(

GJ

).

To summarizetheanalysisof thesedistributions,the Valencia modelprovidesamuchbetterdescriptionthantheCaomodel.Our analysis thereforevalidates thechanges introduced by theWASA Collaboration in the original Valencia model, except perhaps for the

(1600)

contribution,whichseemstobetoolarge.TheOPER model, whichis basedon a very differentapproach, givesalso a gooddescriptionofthedata.Inparticular,itfitsbetterthe

π

+

π

− invariant massesthanthemodified Valenciamodel.However, the predictionsareworsefortheCMangulardistributionsofthep

π

+,

p

π

−andp

π

+

π

−subsystems.

4.3. Absolutecrosssections

We come now to the discussions of the absolute yields. The measured differentialcrosssectionintegratedovertheHADES ac-ceptance is 34.9

±

1.5 μb. The model [46] and [43] predictions, respectively 72.4 and 86 μb are larger by a factor more than 2, while the modified Valencia model [33] is in better agreement, with a cross section of 26.4 μb, i.e., about 30% lower than the experimental value. Acceptance correctionswere calculated using

the modified Valencia model

[33]

andOPER model whichgive a

reasonable description of the differential distributions, as shown in

Figs. 2–5

.Inpractice,eightdifferentdifferentialspectra, corre-sponding to the distributions in _Mπ+_π−, Mpπ+, Mpπ−, Mpπ+π−,

cosCM

δ_π+π−, cos

CM

pπ+π−, cosθCMpπ+ and cosθpCMπ− (Figs. 2 and 4 a–d)

were correctedforacceptanceusingboth models.Thedifferences betweentheintegratedyieldsobtainedforthesedifferent distribu-tionswereusedtodeterminethesystematicerrors.Followingthis procedure,weobtainforthetotalcrosssection0.65

±

0.03 mb us-ing themodifiedValenciamodeland0.795

±

0.040 mb usingthe OPERmodel.Ourfinalestimate,takingintoaccountthesetwo

val-Fig. 6. HADESmeasurement for the quasi-free np→npπ+π− reaction using a deuterium beam at 1.25 GeV/nucleon (full dot) compared to world data shown by various symbols. The horizontal error bars indicate the spread of the neutron momentum in the different measurements. The full and short dash-dotted curves display respectively the “Bistricky parametrization” used for the OPER model [20] normalization and the predictions of the modified Valencia model [33]. The long dash-dotted curve is the estimate from [53]for the contribution of the dibaryon res-onance. The dashed curve is the sum of the modified Valencia model and dibaryon resonance contributions.

uesis

σ

=

0.722

±

0.108 mb. Thiscross section isaveraged over neutronenergiesaccessibleinthequasi-freenp

→

np

π

+

π

− reac-tionatadeuteronbeamenergyof1.25 GeV/nucleon.Accordingto thefitofthemissingmass(Fig. 1),takingintoaccounttheneutron energyandmomentum distribution in the deuteron,the average neutron energyfor this measurement is 1.273

±

0.063 GeV. Our datapointisshowntogetherwiththeworlddatain

Fig. 6

.In con-trast to previous plots which can be found in the literature, we takeintoaccountthespreadoftheneutronmomentuminthe dif-ferentmeasurements. The Cao model overestimatesour point by a factor2.4, witha prediction of1.730 mb,which confirms that this model does not reproduce satisfactorily the np

→

np

π

+

π

− reaction in ourenergy range. The OPER modeldoes not provide crosssections andwas normalizedto the “Bistricky parametriza-tion”

[20]

(shownasablackcurvein

Fig. 6

),whichresultedfrom asimpleinterpolationbetweenmeasurementsoverawideenergy rangeupto2.2 GeV.Thisparametrizationlargelyoverestimatesthe NIMRODmeasurement

[14]

,whichwasobtainedatanincident en-ergyhigherbyabout120MeVthanourexperiment.Ontheother hand,itprovided a good predictionforthe measurement atKEK

[21]whichwasobtainedinthemeantime.Thelatterisofspecial interestforthepresentstudy,sinceitwasobtainedforanincident energyonly70MeVlowerthanourexperiment.Ourextrapolated crosssectionisapproximatelyafactor2.6lowerthanthe“Bistricky parametrization”thathasavalueof1.88mbat1.25 GeV.This re-sultisincontradictionwithasmoothlyincreasingcrosssectionas afunction oftheincident energy.This,aswe willseeinthe fol-lowing,couldbeexpectedinthepresenceofaresonanceatlower energies.Ourmeasurementishoweverhardlycompatiblewiththe KEK data (

σ

=

1.25

±

0.05 mb at Tn

=

1.17 GeV). A decrease of afactor 2in such asmall energyrangeis indeeddifficult to ex-plain.Ontheotherhand,themodifiedValenciagivesaprediction of 590 μb, i.e. much closer to our value. This model also rea-sonably reproduces not only the differential distributions for the

np

→

np

π

+

π

− channel, asshownin thispaper, butalsothe to-talcross sectionsanddifferentialdistributions for pp

→

pp

π

0

_π

0 [32]and pp

→

nn

π

+

π

+ [33]channelsmeasuredby WASAbelow 1.4GeV. However, thismodeldoes notdescribe satisfactorily the generalexcitationfunctionofthenp

→

np

π

+

π

−reaction.The un-derestimationofthedataathigherenergies mightwellbe dueto

thelackofhigherlyingresonances,suchasN

(1520)

andN

(1535)

in the model.However, another explanation hasto be found for theunderestimationatlowerenergies.

Inthehypothesisofadibaryonresonancewithamassaround 2.38 GeV, as claimed by the WASA Collaboration, a structure is expected at a neutron energy around 1.13 GeV. Using the cross sections for pn

→

d

_→

_d

_π

+

_π

− _{extracted by the WASA}

Collab-oration, Albaladejo et al. [53] have estimated the resonant cross section forthenp

→

np

π

+

π

− channel, i.e., pn

→

d

→

pn

π

+

π

− (seedash-dottedcurvein

Fig. 6

).Theyconcludedonthedifficulty toreconciletheexistingdatawiththeresonancehypothesis,taking into account thelarge non-resonant contributionwhich has nec-essarilyto be added.However, thisconclusion is,to ouropinion, stronglybiasedbytheKEKpointwhichisalreadybeyondthe reso-nanceandfavorsalargenon-resonantcontribution.Inthisrespect, ourmeasurement,whichprovidesamuchsmallercontribution,is inbetter agreementwiththedibaryon resonancehypothesis.The expectedresonantcontributionatourenergyisabout0.2 mb,less than one third of our measured cross section, andis compatible witha non-resonant contribution ofthe order of0.5 mb as pre-dicted by the modified Valenciamodel. Accordingto this model, thenon-resonantcontributionatthepeakoftheresonanceisonly of theorder of0.2 mb. The existing cross section measurements inthisregionarethereforenotinconsistentwitharesonant cross-sectionofabout0.7 mb,asdeducedfromtheWASAresultinthe

pn

→

d

π

+

π

− channel. Toillustrate that, we show in

Fig. 6

the excitation function obtainedby addingthe dibaryon contribution from [53] to the modified Valenciamodel prediction. Except for the KEKpoint, theresultdescribeswithin 20% thecross sections obtained for incident energies between1 and 1.3 GeV, which is theenergyrangeofthe pp

→

pp

π

0

_π

0 _andpp

_→

_nn

_π

+

_π

+ _data

usedto adjustthemodified Valenciamodel.In particular,itis in perfectagreementwithourmeasurement.The poorerdescription outside this energy range could probably be reduced by further adjustmentsoftheValenciamodel.Noconclusioncanhoweverbe drawnfromthisverycrudecalculation,duetotheunknowneffect ofinterferencesbetweent-channelands-channelprocesses.In ad-dition,itwouldbenecessarytoincludethedecayoftheresonance intoapn pairwithotherquantumnumbersthanthedeuteron. Ac-cordingtotheanalysisin

[66]

,thiscontributionisestimatedtobe of the order of0.1 mb. The effect of the resonance contribution on the differential distributions andin particular to the p

π

+

π

− invariant mass is also an open question. This can only be made usingafullmodel,includinginaconsistentwaythet-channel pro-cesses,based onthe“modifiedValencia”modelandtheresonant

s-channel although a phenomenological approach was presented

fortheanalysisofnp

→

np

π

0

_π

0_in

_[37]

_. 4.4. Acceptancecorrecteddistributions

Inorder toallow foramoredirect comparisonofourdata to differential cross sections forquasi-free np

→

np

π

+

π

− [39] and

np

→

np

π

0

_π

0 _{[37] reactions measured in other experimentsand}

possibly facilitate the comparison to other potential models key distributions have been corrected for acceptance. The correction

has been done by using modified Valencia [33] and OPER [43]

models.

Fig. 7

presentstheextrapolateddistributionsof

π

+

π

−

in-variant mass andopening angle betweenpions in CM frame for

np

→

np

π

+

π

− reaction at 1.25 GeV. The errors on extrapolated datatake into accountthe differencebetweenacceptance correc-tioncoefficientsformodifiedValencia

[33]

andOPER

[43]

models. The predictions ofthe different models in4

π

are also displayed in

Fig. 7

usingthe samenormalization asforthe comparison in-side HADES acceptance(Figs. 2–5). The differentyields therefore illustratethedifferentacceptancecorrectionfactors.Thesame

fea-Fig. 7. The

acceptance corrected distributions of the

π+π−invariant mass (a) and opening angle of π+π−in the np rest

frame (b) for the

np→npπ+π− reaction at 1.25 GeV. The experimental data are shown by solid symbols. The theoretical predictions in 4π region from OPER [43], Cao [46]and modified Valencia models [33]are given by the solid, dashed and long-dashed curves, respectively. The shaded areas show the phase-space distributions.

tures as described in Section 4.1 and Section 4.2 forthe results insideacceptance canbe observed fortheresultsextrapolatedin 4

π

.IndeedtheOPER

[43]

andmodifiedValencia

[33]

modelsgive thebestoveralldescriptionoftheshapeofbothdistributions.The OPER

[43]

andinalesserextentthemodifiedValencia

[33]

models give also good results for the

π

+

π

− invariant mass and open-ing angledistributions measured in the np

→

np

π

+

π

− at1 and 1.5 GeV. The results obtainedat the three energies allow to fol-low the evolution ofthe mechanisms, characterized inparticular bytheimportantroleofnon-resonantcontributionsat1 GeVand the dominance of double Delta excitation at 1.5 GeV. As forthe

np

→

np

π

0

_π

0 _{reactionat1.13 GeV}

_[37]

_{,whereadominanceofthe} d

∗

contributionisobserved,theshapeofthe

π π

invariantmassis similartoourmeasurement,whichconfirmstheratherlow sensi-tivityofthisobservabletothes-channelresonantcontribution,as stressedbytheauthors.

5. Conclusion

Wehavepresentedananalysisofhigh-statisticsdifferential dis-tributions obtained in the np

→

np

π

+

π

− reaction, using a

deu-terium beam at 1.25 GeV/nucleon and the HADES experimental

set-up atGSI. Inthischannel, inaddition tot-channel processes, mainlyduetotheRoperanddouble

(1232)

excitations,the con-tributionofas-channelprocess,withanintermediatedibaryon,as observedin thereaction pn

→

d

π

+

π

− might bepresent. In this paper, we focused on the compatibilityof our data withmodels includingt-channelprocessesonly.Theexperimentaldistributions

have therefore been compared with the predictions of two

La-grangianmodels,theCaomodel

[46]

andthe“modifiedValencia” model

[33]

andof theOPER model

[43]

,based on one-pion and one-baryonexchanges.Thisanalysisdemonstrates thehigh sensi-tivityofthe differentialdistributions tothedifferentcomponents

of the two-pion production mechanism. The modified Valencia

modelgivesamuchbetterdescriptionoftheshapesofthe distri-butionsthantheCaomodel.Thisgoodresultsupportsthechanges introduced by the WASA Collaboration to describe the total and differentialcrosssectionsinpp

→

pp

π

0

_π

0 _andpp

_→

_nn

_π

+

_π

+ _in

thesameenergyrange,especiallythereductionoftheN

(1440)

→

(1232)

π

contribution. The double



contribution seems to be ratherwelldescribedby themodel,whichisimportantsincethis process is expected to contribute to dilepton production in the

pn reaction

[8]

.However,some discrepanciesareobserved inour channel,like amissingstrength atsmall

π

+

π

− invariant masses andforward

θ

_pCM_π+ angles inthemodel.Thesediscrepancies could

beprobablyreducedby furtheradjustingthe

(1600)

andRoper contributions.However, suchchanges shouldalsobe validatedby ananalysisoftwo-pionproductioninotherisospinchannels. The OPER model gives also rather good results, except for the

po-lar angleof the p

π

+ systemin the np rest frame, witha lower relative contribution of the double

(1232)

contribution, and a significantcontributionofone-baryonexchangegraphs.Both mod-elshavebeenusedtocalculateacceptancecorrections,andobtain an estimate of the total cross section of the np

→

np

π

+

π

− re-action at 1.25 GeV beamenergy. Thismeasurement is important due to the scarce existing measurement in the relevant energy range. Thefound rather low value ofthe cross section isnot in-consistentwitharesonantstructureatlowenergies,asexpectedin presenceofthedibaryonresonance,withmassM

∼

2.38 GeV and width



∼

70 MeV reported bytheWASACollaboration.However, ourmeasurementishardlycompatiblewiththemeasurement

per-formed atKEK at an incident neutron energylower by 70 MeV.

The modified Valenciamodel, whichhas been now validatedfor

different channels, underestimates the total cross section in our measurement byonly 30%.Undertheresonancepeak, the under-estimationofthedataismuchlargerandisalsocompatiblewith theresonanthypothesis.However,thepresentsituation,bothfrom experimental andtheoretical aspects,isnot clearenough todraw conclusionsontheexistenceofthedibaryonresonance.Onthe ex-perimentalside,usefulconstraintsinthepresentexperimentcould be obtainedfromthe extractionofcrosssectionatdifferent neu-tron energies, the on-going analysis of the pp

→

pp

π

+

π

− and

pn

→

d

π

+

π

− channelswith HADES will allow for specific tests ofthe modified Valenciamodelandthedibaryon resonance con-tribution,respectively.Theexperimentalsituationshouldtherefore further become clearerin a nearfuture. On the theory side, we would liketo callforthe development ofa full model,including in a consistent waythe t-channel processes, based on the mod-ified Valencia model and the s-channel processes including the

dibaryon with above quoted parameters, which could provide a

solid frameworkfortheinterpretationofthetwo-pionproduction data.

Acknowledgements

We acknowledge valuable discussions with Dr. T. Skorodko

and are particularly indebted to her and Dr. Xu Cao for the

provided calculations. The collaboration gratefully acknowledges

the support by BMBF grants 06TM970I, 06GI146I, 06FY9100I,

and 05P12CRGHE (Germany), by GSI (TM-FR1, GI/ME3, OF/STR),

by Helmholtz Alliance HA216/EMMI, by grants MSMT LC07050,

LA316andGAASCRIAA100480803(CzechRepublic),bygrantNCN

2013/10/M/ST2/00042 (Poland), by INFN (Italy), by CNRS/IN2P3

(France), by grants MCYT FPA2000-2041-C02-02 and XUGAPGID

T02PXIC20605PN(Spain),bygrantUCY-10.3.11.12(Cyprus),by IN-TASgrant03-51-3208andbyEUcontractRII3-CT-2004-506078.

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