Table Of Content

EPJ manus ript No. (will be inserted by the editor) pp Single-Pion Produ tion in Collisions at 0.95 GeV/ (II) 8 6 2 6 6 6 5,2 9 S.AbdEl-Sa6mad ,R.Bilge6r ,K.-Th.B3rinkmann ,H7.Clement ,M.D2ietri h ,E.D3,o1roshkevi h4,S.Dshemu h4adse , 0 K. Ehrha3rdt , A. Erhardt4, W. Eyri h2 , A. Filip2pi , H. Freie2sleben , M.4Frits h 6, R. Geyer , A.2Gillitzer , 7 0 J. Hau(cid:27)e , D4. Hesselbart6h , R. Jaeke5l , B. Jakob ,4L. Kars h , K.5Kilian , J. K4ress , E. Kuhlm4ann , S. Mar el2lo,3, 2 S. Marwinski , R. Meier2, K. Möller , H3.P. Mors h , L3. Naumann2, J. Ritman 3, E. Roderburg6, P. S hönme3ier , n M. S hulte-6Wissermann1, W. S hr3oeder , F. S6tainzing , G.Y. Sun ,9J. Wä hter , G.J. Wagner , M. Wagner , a U. Weidli h , A. Wilms , S. Wirth , G. Zhang , and P. Zupranski J 1 2 Ruhr-UniversitätBo hum, Germany 5 3 Te hnis heUniversität Dresden, Germany 1 4 Friedri h-Alexander-UniversitätErlangen-Nürnberg, Germany ] 5 Fors hungszentrumJüli h, Germany x 6 Fors hungszentrumRossendorf, Germany e 7 Physikalis hes Institut derUniversität Tübingen, Tübingen,Germany l- 8 Universityof Torino and INFN,Sezione di Torino, Italy c 9 Atomi Energy AuthorityNRCCairo, Egypt u Soltan Institute for Nu lear Studies, Warsaw, Poland n (COSY-TOF Collaboration) [ 2 January 15, 2009 v pp→dπ+ pp→npπ+ pp→ppπ0 9 Abstra t. Thesingle-pionprodu tionrea tions , and weremeasuredata 8 Tp ≈ beammomentumof0.95GeV/ ( 400 MeV)usingtheshortversionoftheCOSY-TOFspe trometer. 1 The entral alorimeter provided parti le identi(cid:28) ation, energy determination and neutron dete tion in 1 addition to time-of-(cid:29)ight and angle measurements from other dete tor parts. Thus all pion produ tion . 7 hannelswenrepπre+ ordedwith1-4over onstraints.Themainemphasisisputonthepresentationanddis us- 0 sion of the hannel, sin e the results on the other hannels have already been published previously. 8 Theptpoπt0al and di(cid:27)erential ross se tinopnπs+obtained are ompared to theoreti ∆al al ulations. In ontrast to 0 : the hannelwe observe in the (3 cos 2hΘan+ne1l)a strong in(cid:29)uen eofthe ex itation. Inp∆arti ular the v pion angular distribution exhibits a dπ+ dependen e, typi al for a pure s- hannel ex itation Xi andide1nDti2 aplntothatobservedinthe hannel.Sin ethelatter isupnndπe+rstoodbyas- hannelresonan e in the partial wave, we dis uss ananalogous s enario for the hannel. r a PACS. 13.75.Cs (cid:21) 14.20.Gk (cid:21) 14.20.Pt (cid:21) 25.10.+s (cid:21) 25.40.Ep ∆ 1 Introdu tion ate the presen e ofsigni(cid:28) ant produ tionin a relative p-wavealready lose to threshold. pp→pnπ+ Single-pion produ tion in the ollision between two nu- In this workwepresentourresultsforthe leons is thought to be the simplest inelasti pro ess be- hannel at th∆e same in ident energy. We will show that tween two baryons, nevertheless its understanding is still here, where produ tion in relative s-wave is allowed, far from being satisfa tory - both from the theoreti al indeed this produ tion pro ess is overwhelmingly domi- and the experimental point of view. In a re ent publi- nant and hara terizes the di(cid:27)erential observables in this ation [1℄ (cid:21) in the following denoted by (I) (cid:21) we have hannel. presentepdpt→hepp(cid:28)πrs0t kinemati ally omplete measurement The rea tion of interest here has been investigated in for the hanneTl a=t a beam momentum o∆f 0.95 thenear-thresholdregionalreadypreviouslybyaseriesof p GeV/ ( orrespondingto 397MeV).Although pro- measurementsatJINR[2℄,KEK[3,4℄,TRIUMF[5℄,CEL- du tion in a relative s-wave is prohibited in this rea tion SIUS [6℄ and notably at IUCF [7,8,9,10℄, sin e there ex- hannel, wehaveseen that the angular distributions indi- perimentshavebeen arriedoutbothwithpolarizedbeam a andtarget.Inthesemeasurementsvery losetothresThold p present address: Peking University it was already noted [7℄ that at beam energies of = Corresponden e to: H. Clement 320 MeV, i.e. only 20 MeV above threshold, an onset of ∆ email: lementpit.physik.uni-tuebingen.de the ex itation is seen in the pion angular distribution. pp 2 S. AbdEl-Samadet al.: Single-Pion Produ tion in Collisions at 0.95 GeV/ (II) p ∆ N dete tor system onsists of the so- alled Quirl, a 3-layer π q s intillator system 1081 mm downstream of the target (cid:21) p and in its peripheral part of the so- alled Ring, also a 3- N layers intillatorsystembuiltin adesignanalogoustothe Quirl,however,withinnerandouterradiiof560and1540 N mm, respe tively. Finally behind the Quirl a alorimeter p ∆ π was installed for identi(cid:28) ation of harged parti les and of neutrons as well as for measuring the energy of harged p parti les. The alorimeter onsists of 84 hexagon-shaped N s intillatorblo ksoflength450mm,whi hsu(cid:30) estostop deuterons, protons and pions of energies up to 400, 300 and 160 MeV, respe tively. The energy alibration of the Fig. 1. Graphs used for the theoreti al al ulations. Top: t- alorimeter was performed by dete ting osmi muons. hannelapproa h(PWIA,dire tpartonly),bottom:s- hannel approa h. 2.2 Parti le identi(cid:28) ation and event re onstru tion The latter hanges from isotropi at energies below 300 IntheexperimentthetriggerrequiredtwohitsintheQuirl MeV to anisotropi at 320 MeV suggesting there a 30 - % ∆ and/or Ring asso iated with two hits in the start dete - 40 ontribution of the ex itation. In the TRIUMF tor. Tra ks of harged parti les are re onstru ted from measurements,whi hwereperformedat beam energiesof Tp straight-line (cid:28)ts to the hit dete tor elements. They are = 420 and 500 MeV, it was noti ed thpapt→at tdhπe+se en- a epted as good tra ks, if they originate in the target perpgi→esptnhπe+pion angular distributions of and and have a hit in ea h dete tor element the tra k passes rea tions are not only very similar, but also th◦rough.In this waythe angularresolutionisbetter than very losetotheangulardistributionexpe tedfromapure ∆ 1 both in azimuthal and in polar angles. If there is an ex itation. In te1rDm2s opfppartial waves this means a pre- isolated hit in the alorimeter with no asso iated hits in dominan e of the partial wave at these energies the pre eding dete tor elements, then this hit quali(cid:28)es as as is in fa t thepopu→t omdπe+of the SAID [11℄ partial wave aneutron andidate(further riteriawill bedis ussed be- analysis for the rea tion. Hen e after presen- low). In this ase the angular resolution of the neutron tation and dis ussion of our data we will onfront them tra k is g◦iven by the size of the hit alorimeter blo k, i.e. withtheoreti alt- hannel al ulations(Fig.1,top)aswell by 7 - 8 . By onstru tion of the alorimeter a parti le as with s- hannel al ulation1sD(2Fig. 1, bottom). The lat- will hit one or more alorimeter blo ks. The number of ter a ount for the striking partial wave dominan e blo ks hit by a parti ular parti le is given by the tra k andassumeforsimpli itythatallotherpartialwavesgive re onstru tion. The total energy deposited by this parti- negligible ontributions.Inboth asesanex itationofthe ∆ le in the alorimeter is then just the ( alibrated) sum of resonan e is assumed. energiesdepositedinallblo ksbelongingtotheparti ular tra k. In order to have maximum angular overage by the 2 Experiment dete torelements andtominimizethefra tionof harged pions de aying in (cid:29)ight before rea hing the stop dete - 2.1 Dete tor setup tors,theshortversionoftheTOFspe tromete◦r≤waΘsluasbed≤. In◦this way a total polar angle overage of 3 Sin e the experimental setup has been dis ussed in detail 49 was◦a ≤hieΘvleadb w≤ith◦the entral alorimeter overingthe alreadyin(I),wegivehereonlyashorta ount.Themea- region 3 28 . For fast parti les the energy res- surementshavebeen arriedoutattheJüli hCoolerSyn- olution of the alorimeter amounting to 4% is superior to hrotronCOSYusingthetime-of-(cid:29)ightspe trometerTOF that from time-of-(cid:29)ight measurements due to the short atoneofitsexternalbeamlines.Attheentran eofthede- path length. However, the time-of-(cid:29)ight resolution is still ∆E te torsystemthebeam- ollimatedtoadiametersmaller mu hbetterthanthe resolutionoftheQuirlelements. 2 ∆E than 2 mm - hits the LH target, whi h has a length of Hen e, for parti le identi(cid:28) ation, instead of plotting µm E cal 4 mm, a diameter of 6 mm and 0.9 thi k hostaphan versus , the un orre ted parti le en∆eErgy∼d(ezp/oβs)i2ted in foils as entran e and exit windows. At a distan e of 22 the alorimeter,wezu=tili1ze the rela1t/ioβn2 E with cal mm downstream of the target the two layers of the start theparti le harge andplot versus ,where β = v/c dete tor (ea h onsisting of 1 mm thi k s intillators ut the parti le velo ity is derived from the time-of- into 12 wedge-shaped se tors) were pla ed followed by a (cid:29)ight measurement. two-plane (cid:28)ber hodos ope (96 x 96 (cid:28)bers, 2 mm thi k Byidentifyingandre onstrduπ +tinngptπh+etwo phpaπrg0edtra ks ea h ) at a distan e of 165 mm from target. Whereas the of an event the exit hannels , and an be startdete tormainlysuppliesthestarttimesignalsforthe separated. Kinemati ally th≈e9m◦aximum possible la≈bo3r2a◦- time-of-(cid:29)ight (TOF) measurements, the (cid:28)ber hodos ope tory (lab) polar angles are for deuterons and primarily provides a good angular resolution for the de- forprotons(andneutrons).Hen e86%oftheangular ov- te ted parti le tra ks. In its entral part the TOF-stop erage for protons and neutrons from single pion produ - pp S. AbdEl-Samadet al.: Single-Pion Produ tion in Collisions at 0.95 GeV/ (II) 3 tion arewithin the angulara eptan eofthe alorimeter. For harged pions the angular overage has been mu h ] b lower withΘthlaibs s=etup,◦sin e kinemati ally they an ex- µ tend up to 180 . Hen e within the angularπ +over- [π 20 age of≈Qui%rl and Ring the angular a eptan e for has φp been 40 only. Nevertheless most of the phase spa e ∆ d part ne essary for a full overage of the physi s in sin- / 15 glepionprodu tionhasbeen overed(seebelow)bythese σ d measurements due to the ir umstan e that the enter- of-mass ( ◦m) angular distributions have to be symmetri 10 about 90 be ause of identi al ollision partners in the in ident hannel. 5 npπ+ 2.3 Sele tion of the hannel 0 0 50 100 150 npπ+ ∆φ The hannel is sele ted by identifying proton and pπ pioninthe alorimeteroronlytheprotoninthe alorimeter, when the se ond harged tra k is in the Ring. In ad- pπ MM pπ dition, the missi/ncg2 ≤ mMaMss ≤ has to m/ce2et the on- pπ dition 900 MeV dπ+980 MeV . Also to ∆φ suppress ba kground from the hannel - in parti u- Fig. 2. Distribution of the pplapn→aritpynπa+ngle de(cid:28)ned in the enter-of-masssystemforthe rea tion.Dataofthis lar when the deuteron brpeπa+ksup and appearsasa proton work are shown by full ir les and phase spa e by the shaded in the alorimeter - the tra k is required to be non- ∆Φ area. Solid and dashed lines denote s- hannel and t- hannel oplanar.Tothisendwedeterminethevariable ,whi h al ulations, respe tively, as dis ussed in the text. For ease is de(cid:28)ned as the proje tion of the opening angle between twotra ksontothep∆laΦne≤no1r8m0◦altothebeamve tor.That oexfp eormimpeanritsaolntotthael arol suslastei otniosnh.aTvheeb eoennstnroarinmtal∆izΦed<to16th0◦e waywehavealways . Thpeπa+ ordinghistogram fortheeliminationofeventsstemmingfromdeuteronbreakup is displayed in Fig.2. We see that events stemmin◦g 180 is indi atedbytheverti al dash-dottedline. fromdeuteronbreakupgiverisetoalargepeaknear . In order to get rid◦ of these events we introdu e the on- ∆Φ < 160 straint∆Φ<170◦ . From Fig. 2 we see that in prini ple over onstraintsforthis hannel.Correspondingkinemati a ut would already be su(cid:30) ient to eliminate (cid:28)ts were applied. this ba kground.However, in order to bepopn→thedπsa+fe side Theluminosityoftheexperimentwasdeterminedfrom pp and to have no per eptible tails from the rea - the analysisof elasti s attering, see (I). All data have tion in the (cid:28)nal data sample, we used the more rigorous been e(cid:30) ien y orre ted by MC simulations of the de- onstraint. From Fig. 2 we see that this onstraint does te tor setup by using the CERN GEANT3 [12℄ dete tor 1 not ut away signi(cid:28) ant pie es of physi s information . simulation pa kage, whi h a ounts both for ele tromag- Any extrapolation into the ut region, be it by model or neti and hadroni intera tions of the eje tiles with the by phase spa e, will introdu e un ertainties on the level dete tor materials. of less than two per ent. Aside from this physi s ba kground due to deuteron breakup we do not (cid:28)nd any sizable ba kground in the 2.4 Un ertainties (cid:28)nal data sample, as has been he ked by ontrol measurements, where the target ell was empty. Furtheron,theneutron4-momentumisre onstru ted The (cid:28)nal data sample ontains about 80000 good events, fromthe 4-momentaofprotonandpionandit is he ked, i.e.thestatisti alerrorsareontheper entlevelandhen e Θ Φ whether a alorimeter blo k in the orresponding ( , ) of minor importan e in omparisonwith systemati alun- regionre ordedahitwithoutanyadditionalentriesre orded ertainties.Onesour eofsystemati errorsarebeamalign- in the pre eding dete tor elements of the Quirl. If these ment and quality. The requirement that the beam has to onditionsaremet,aneutrontra kisassumed. Thatway pass a 2 mm ollimator without signi(cid:28) ant halo assures Θ Φ nand naredeterminedbythelo ationofthis alorime- good alignment and quality of the beam. The alignment ter blo k. By this method we obtain a neutron dete tion is also veri(cid:28)ed by the fa t that the angular distributions % e(cid:30) ien y of 36 . Thus having only the neutron energy intheover◦all enter-of-masssystemhavetobesymmetri undetermined experimentallyweend upwith3kinemati about 90 , see next se tion. In addition polarized beam measurementswith the identi al dete torsetup usedhere 1 we note that the data sample with the ut ∆Φ < 170◦ also give no hint for noti eable misalignments [13℄. leads to results, whi h are pra ti ally indistinguishable from A mu h more severe sour e for systemati un ertain- those shown here ties on erns the a eptan e and e(cid:30) ien y orre tions of pp 4 S. AbdEl-Samadet al.: Single-Pion Produ tion in Collisions at 0.95 GeV/ (II) lptahlreetredaanmtgaoe.mAoefsnttdhuiesm ruersaas netgdioean,bohofovwienettvheerere,dstne.toeTt htthoisrem ooevmaenrpssl,etttheheaa tnogtmhue-- 2)]MeV/c 30 µΩb/sr] [ 60 a2 = 0.96(2) ua n mepeatasunr eed oarnrgeu tlaiornrehgaisontso. rFerloymontheextDraapliotzlatpiloontss idnitso- µb/( [Mpn20 σ /dd 40 a’2 = 0.79(2) d played in Fig. 4 we see that (cid:21) a ording to all we know σ / 10 20 d fromthisrea tion(cid:21)theseunmeasuredregionsaretheones with the lowest ross se tion. Hen e systemati errors in- 0 1880 1900 1920 0-1 -0.5 0 0.5 1 trodu edbytheseextrapolationsoughttobeofminorim- Mpn [MeV/c2] cosθCπM portan e.Toquantifythisstatementwe omparethedata resultingfrom orre tionswithMCsimulations,whi hare based either on pure phapspe→span peπo+r alternatively on a Fig. 3. Di(cid:27)erMential ross se tions in dependen e on thΘeCinM- model des ription of the rea tion. A model, variant mass pn (left) and the pion s atterpinpg→anpgnleπ+π whi h is trimmed to des ribe all essential features of the (right) in the enter-of-mass system for the re- data,is the appropriatetoolfora reliable a eptan eand a tion. The full ir les show our data properly orre ted by e(cid:30) ien y orre tionbyaMCsimulation,whi hpassesthe a self- onsistent MC simulation, i.e. using a rea tion model, eje tiles from the rea tion of interest through the virtual whi h is in agreement with the (cid:28)nal data. The open ir les dete tor. It has the potential of providing a self onsistent derive from MC simulations using just pure phase spa e. The pro edureforthese orre tions.Contraryto this the pure phasespa edistributionsforthedi(cid:27)erentialspe traareshown phase spa e des ription of the rea tion is (cid:21) as we easily by the shaded area. Solid and dashed lines in the right (cid:28)ag2ure anseefromtheexperimentalresultsdisplayedinFigs.2- show Legendre (cid:28)ts to the (cid:28)lled and open ir les yielding = 6 (cid:21)inadequate though onvenient.It may serve,however, 0.96(2) and =0.79(2), respe tively. as a very onservative estimate of the systemati un ertainties due to the a eptan e and e(cid:30) ien y orre tions. As epxnamplesMwepndisplay in Fig. 3 our data for the invari- in (Ip).pI→t isdrπo+ughly a fa tor of two smaller than that for ant mass and forthσe(ΘpiCoMna)ngular distribution in the pp → pp πh0annel and (cid:28)ve times larger than that π the enter-of-mass system evaluated (properly) for the hannel, see Table 1 in (I). For the by use of a model, whi h (cid:28)ts the (cid:28)nal data (solid ir les), omparison with data at neighbouring energies [14,3,5,8℄ andalternativelybyuseofpurephasespa e(open ir les), see dis ussion in the next se tion. respe tively. The use of the latter for the extrapolation Di(cid:27)erentialdistributionsareshowninFigs.3-6.Sin e into unmeasuredregionsbringsthe data,of ourse,some- a 3-body system in the (cid:28)nal state has (cid:28)ve independent what loser to the phase spa e predi tions. However, de- variables, we hoose to present the three invariant mass M M M spite the fa t that phase spa e and model predi tions are spe tra pn, pπ+ and nπ+ as well as the proton and vastly di(cid:27)erent, the e(cid:27)e t of the inadequate phase spa e pion angular distributions in the overall enter-of-mass orre tion on the data is still very moderate. A realisti system ( ms). Be ause of th0e◦l<imiΘtecdma≤ e9p0t◦an e for pi- upperlimitforsystemati un ertaintiesduetoa eptan e ons only the angular range π is overed◦. and e(cid:30) ien y orre tion will be mu h smaller than the However, as pointed out above, due to the required 90 di(cid:27)eren es between open and solid ir les in Fig. 3. As a symmetry of the angular distributions the full informa- realisti estimate for this kind of systemati un ertainties tion is ontained in the data. we on lude that they are within the size of the symbols, ppπ0 whi h are used in Figs. 2 - 6 for displaying our experi- Ipnnπ o+ntrast to the hannel the Dalitz plots for the hannelarefarfrom being (cid:29)at(cid:21)seeFig.4.This mental results. We note that the use of either t- hannel is also borne out in the proje tions, the invariant mass or s- hannel al ulations in the MC simulations does not Mpπ+ Mnπ+ spe tra and (see Fig. 5, top), whi h peak at lead to any noti eable di(cid:27)eren es in the a eptan e and the highest kinemati ally available masses. In ontrast to e(cid:30) ien y orre ted data. Mpn these the spe trum (Fig. 5, bottom) peaks at the lowest masses. Note that the high-mass enhan ement is M M pπ+ nπ+ similarin both and spe tra. Thisisin agree- 3 Results ment with the trend observed in bubble hamber data at T p = 432 MeV [4℄. Duetotheidentityofthe ollisionpartnersintheentran e hannel the angular distributions in the over◦all enter-of- Whereas the proton angular distribution is lose to masssystemhavetobesymmetri about90 ,i.e.thefull (cid:29)at, the pion angular distribut(i3ocnosis2Θstcrmon+g1ly) anisotropi . information about t0h◦e≤reaΘ ctmion≤ 9h0a◦nnels is ontained al- Itis(cid:28)ttedverywellbyapure π+ distribution readyintheinterval .Deviationsfromthis (solid line in Fig.3, right). symmetryinthedataindi atesystemati un ertaintiesin Our results are in good agreement with the results the measurements. Hen e we plot - where appropriate - from PROMICE/WASA [6℄T, w≈hi harethe only other un- p the full angular range, in order to show the absen e of polarizeddataavailableat 400MeV.Note,however, major systemati errors in our measurement. pp → thatthosemeasurementswere arriedoutinaverylimited pnπT+he total rossTse= ti4o0n0Mofe0V.47(2) mb for the phase spa e region only. E.gc.o,s(tΘhecmp)io≥n angular distribu- rea tion at p has already been given tion was only measured for π+ 0.79. pp S. AbdEl-Samadet al.: Single-Pion Produ tion in Collisions at 0.95 GeV/ (II) 5 M2pπ vs M2pn M2pπ vs M2nπ 18000 sr] sr] 16000 10000 b/ b/ 42]/cGeV1.25 111024000000000 42]/cGeV1.25 68000000 µΩσ [ /dd 4600 a2 = 0.20(2) µΩσ [ /dd 4600 a2 = 0.96(2) 2 [Mπ+p1.2 68000000 2 [Mπ+p1.2 4000 20 20 4000 2000 2000 1.15 1.15 3.5 3.55 3.6 3.65 3.7 0 1.15 1.2 1.25 0 0-1 -0.5 0 0.5 1 0-1 -0.5 0 0.5 1 Mp2n [GeV2/c4] Mn2π+ [GeV2/c4] cosθCpM cosθCπM M2pπ vs M2pn M2pπ vs M2nπ 4500 2500 4000 Fig.6.Angulardistributionsofprotpopns→(lepfnt)πa+ndpions(right) 422]/c [GeVMπ+p1.12.52 12233505050000000000 422]/c [GeVMπ+p1.12.52 112050000000 siopnufhltatthhsseei[s6s ℄pewbnaoyt reekorb-paoyerfn-etmh seaihrso sshlwesasnyds(ebtrdeeymnaforufreolmalr.a tSilhrioz eleliedds,taonWdσAtdoStaAsoh/fePtrdheRailsO intwMieoosInrCdk.e)EDnaaornttedae- 1000 500 s- hannelandt- hannel al ulations,respe tively,asdis ussed 500 1.15 1.15 in thetext.For ease of omparison the al ulations have been 3.5 3.55 3.6 3.65 3.7 0 1.15 1.2 1.25 0 normalized to the experimental total ross se tion. Given are Mp2n [GeV2/c4] Mn2π+ [GeV2/c4] alsotheLegendre oe(cid:30) ientsa2 fromaLegendre(cid:28)ta ording to eq. 2 in (I) tgether with statisti al errors. M2 Fig.4. Dalitzplotsfortheinvariantmass ombinations pπ+ versus Mp2n (left) and Mp2π+ versus Mn2π+ (right) as obtained 2)]c 4 2)]c 4 pp→pnπ+ V/ V/ forthe rea tion:dataareshownontopandtheMC Me 3 Me 3 s- hannel al ulation (see text) at the bottom. Note that the b/( b/( µ µ plots for the data are e(cid:30) ien y but not a eptan e orre ted. [Mpp 2 M [π0p 2 Tohrenetrinsyadreevdiuateiotnostfhreomext hluedeelldipbtie a mir- huomleferreegnio ne.attheupper σ /dd 1 σ /dd 1 0 1880 1900 1920 0 1080 1100 1120 2)]c 2)]c Mpp [MeV/c2] Mpπ0 [MeV/c2] V/ V/ Me 20 Me 20 b/( b/( µ µ [dMπ+p10 dM [π+n10 mFiags.se7s.MDpip(cid:27)e(rleefntt)iaalnd rMosspπs0e (triiognhst)infordetpheenpdpe→n eppoπn0inrevaa rtiaionnt σ /d σ /d (from (I)). Phase spa e is shown by the shaded area. For the explanationof the urves see (I). 0 1080 1100 1120 0 1080 1100 1120 Mpπ+ [MeV/c2] Mnπ+ [MeV/c2] 4 Dis ussion of Results 2)]c 30 ppπ0 eV/ 4.1 Comparison with the hannel M µb/( 20 pnπ+ ppπ0 [Mpn For the omparison of and hannels we show σ /d 10 on e more resultspipnπ0Figs. 7 and 8, whi h we obtained d previously for the hannel, see (I). pnπ+ 0 1880 1900 1920 ppπT0he proton angular distributions both in and M [MeV/c2] hannelsare losetoisotropi (seeFigs.6and8,left). pn Theyneverthelessshowatenden y ofopposite urvature, whi h just may be some re(cid:29)e tion of the very di(cid:27)erent pion angular distributions in both hannels. At these low mFiags.se5s.MDpi(cid:27)ne,rMenptπia+l arnodssMsen πt+ionfsorinthdeeppepnd→enp enπo+n irnevaa rtiiaonnt. energies the pion angular distributions aredes ribed on- Dataofthisworkareshownbyfull ir les andphasespa e by venσie(nΘtlπcym0b)y∼th1e+Lae2ge∗n(d3rceosa2nθsπcam0tz−1)/2, the shaded area. Solid and dashed lines denote s- hannel and a2 where the parameter is (cid:28)tted to the data. This t- hannel al ulations, respe tively, as dis ussed in the text. For ease of omparison the al ulations have been normalized papnπsa0tz has also been used in (I) for the analysis of the to theexperimental total ross se tion. a 2hannel(cid:21)seeeq. 2in (I). Other notationsrelatedto our parameter are as follows: in the notation of Ref. a2 =A2/A0 [5℄, Table III wehave , in the notationof Ref. pp 6 S. AbdEl-Samadet al.: Single-Pion Produ tion in Collisions at 0.95 GeV/ (II) cosθ cosθ sr] sr] hannel,wedonot(cid:28)ndsu habehaviorhere.Thepionan- b/ a2 = -0.14(2) b/ a2 = -0.12(1) gular distributions stay essentially the same for di(cid:27)erent µΩ [ 10 µΩ [ 10 q-regions. This again is in support of a single dominant d d σ / σ / me hanism pro eeding via a single partial wave. d d 5 5 Whereas we (cid:28)nd good agreement in the anisotropy of the pion angular distribution with the ones measured at T p TRIUMF at = 420 and 500 MeV [5℄, we fa e a pro- 0-1 -0.5 0 0.5 1 0-1 -0.5 0 0.5 1 founddis repan ywithIUCFresults[10℄.Therekinemat- cosθCpM cosθCπM i ally omplete measurements with both polarized beam T p and target are presented for = 325, 350, 375 and 400 MeVtogetherwithLegendrepolynomial(cid:28)ts,whi hrepro- Fig.8.Angulardistributionsofprotopnps→(lepftp)πa0ndpions(right) du e the measured angular distributions of the polariza- inthe enter-of-masssystemforthe rea tion (from tion observables. In Table II of Ref. [10℄ the oe(cid:30) ients (I)). The solid urves representLegendre (cid:28)ts, see (I). resulting from these (cid:28)ts are listed. This list also ontains b00 = a2/2 the anisotropy parameterσ(ΘCM) for the unpolarized π a2 =B/A di(cid:27)erential ross se tion . Sin e that paper on- [8℄,TableVwehave a2 =2∗ba0n0dinthean0o0t=ati1onofRef. entrates on the polaσr(izΘaCtiMon)observables, it does not di- [10℄, Table II we have (sin e pthpπer0e). usstheunpolarized π datain anydepta+il.nItisjust For the pion angular distribution in aseao2f we noted that these have been dedu ed from oin i- (cid:28)nd a slightly on ave shape (Fig. 8, right; = -0.12), den es. As a result of their Legendreanalysisthey obtain pwnhπe+reas we get a strongly ao2nvex shape in ase of the a2=0.39(9)forTp=400MeV,avalue,whi hislessthan hannel (Fig. 6, right; p=pπ+00.96(2)). half of our value. The di(cid:27)eren e amounts to six standard A striking ∆di(cid:27)eren e to the pn πh+annel is the dom- deviations.Wefa ehereperhapsasimilarproblemasdis- ipnpaπn0 e of the∆ ex itation in the hannel. In the ussed in (I) for thppe s→itupaptπio0n of the experimental data hannel produ tionin a s-waverelativeto the a - with the rea tion at the same beam energy T p ompanying nu leon is prohibited by quantum numbers. of = 400 MeV. There also a large dis repan y exists ∆ a2 However,asdemonstratedin(I),the produ tioninrela- between the asymmetry parameter found in the IUCF tivep-waveisallowedandindeed ontributessigni(cid:28) antly analysisand the one we found at COSY-TOF. Our result to this hannel alread∆y lose to threshold. pnπ+ has meanwhile been on(cid:28)rmed by CELSIUS/WASA data The signature of produ tion in the hannel [15℄. In both these worksit has been shownthat previous is seen in all di(cid:27)erential observables shown in Figs. 3 - 6. results (cid:21) like the one obtained at PROMICE/WASA [16℄ M pn The Mspe trum (Fig. 5, botptpoπm0) is markedlydi(cid:27)erent (cid:21)su(cid:27)eredfrominsu(cid:30) ientphasespa e overage ombined pp from the spe trum in the hannel (Fig. 7, left). withinappropriateextrapolationsintotheunmeasuredre- pn Though the (cid:28)nal state intera tion (FSI) is somewhat gions. pp larger than the FSI, it annot a ount for the huge Wenotethefollowingsurprisingtrendintheresultsof di(cid:27)eren e between both spe tra at low masses. It rather a2 M theIUCFanalyses on erningthe parameter.Inagree- pπ+ is a re(cid:29)e tion from the omplementaryspe tra and M mentwithpreviousIUCFworkvery losetothreshold[8℄, nπ+, whi h peak just at the highest available masses a2 M where a strong in rease in the value with energy is ob- (sFpeig .tr5u,mtopob)sienr voendtirnastthetoptphπe0m hoarnenpehla(sFei-gs.p7a, erilgihket).Tphπe0 sMerevVe,dre(asp2e= ti0v,el0y.)1,2aavnadlu0e.3o1f aat2T=p 0=.3249(74), 2a9t9Tpan=d 332159 high-m∆ass enhan ement in turn is most likely asso iated MeV is reported in Ref. [10℄, Table II. Th∆is in rease just with ex itation. re(cid:29)ep pts→thenpinπ +reasing importan e of the T ex itation in p the rea tion. However, above = 325 MeV a2 Ref. [10℄(see again Table II) (cid:28)nds that the parameter 4.2 Pion angular distribution nolongerin reases,butrathersaturatesatavalueof0.39. ∆ This implies that the ontribution also suddenly satu- pnπ+ T ∆ The most s(t3rickoins2gΘfecmat+ur1e)in our data at p = 400 rates despite the fa t the pole is still far from being MeVisthe π+ dependen eofthepionangular rea hed at these energies. Also the Jüli h model al ula- distribution. It is exa tly this dependen e, whi h is seen tions[17℄, whi hareusedin Ref.[10℄ for omparisonwith πN ∆ in s attering in pthpe→drπe+sonan e region and whi h is thepolarizat∆iondatapredi t astronglyin reasingimpor- alsoobservedinthe rea tionoveralargerange tan e ofthe ex itation at these beam energies(cid:21)asalso of in ident energies. We note that also the pion angular expe ted intuitively. T p distributions at = 420 anpdp5→00pMnπe+V, dedu ed from InRef.[10℄thedis repan yTbetweentheir400MeVre- p in lusivemeasurementsofthe rea tioninRef. sult and the TRIUMF data at = 420 MeV [5℄ was not [5℄ are basi ally in a ord with this dependen e. dis ussed. The TRIUMF measurements were performed We also noptepπi0n passing, that in ontrast to the sit- asasingle-armexperimentwithamagneti spe trometer, uation in the hannel, where we observe a strong whi h measures a 3-body rea tion only in lusively. Su h dependen e of the pion angular distribution on the rel- measurements are known to be very reliable for the de- ative momentum q between the two nu leons in the exit termination of single-parti le angular distributions, sin e pp S. AbdEl-Samadet al.: Single-Pion Produ tion in Collisions at 0.95 GeV/ (II) 7 ht2 exa tlythesamedete torisusedfortheparti ledete tion at all angles minimizing thus the problem of a eptan e ] and e(cid:30) ien y orre tions. b a2 m Tosummarizethedis ussionabout wefa easevere s+t [ Tpdpips →=repn4a0pn0π +MybeVetwfoerenbotthheItUheCpFpa→ndpCpOπ0SYre-aT OtiFonreasnudltsthaet σ tot 10 t pnπ+ rea tion.However,thereisgoodagreementof ourresultforthe(cid:28)rstrea tionwiththe orrespondingone s from CELSIUS/WASA and for the se ond rea tion with the one obtained at TRIUMF. We (cid:28)nally note that the 1 a2 un ertainty of quoted in Fig.6 onlyin ludes the statisti al un ertainties of the data. If we in lude an estimate dπ+ onsystemati un ertainties(asdis ussedaboveinthese - tio∆na22.4≈), we end up with an estimated total un ertainty 10-1 s of 0.08. dπ+ Tphneπ +losesimilarityintheangulardistributionsof and hannels is in agreement with the predi tions of Fäldt and Wilkin [18℄, a ording to whi h the meson 10-20 0.2 0.4 0.6 0.8 1 1.2 1.4 angular distributions oin ide losely in bound state and T [GeV] breakup( 3hcaonsn2eΘlscmne+ar1t)hreshold. pp→dπ+ p The π+ 1D2dependen e in the rpep- a tion is due to the partial wave in the in ident hannel ombinedwiththe onstraintofap-wavepionrel- ative to the deuteron in the exit hannel. As kn1oDw2nPfrom Fig. 9p.pE→nedrgπy+dependen eoftpopta→l pronsπs+se tionsfortherea - phaseshiftanalysesofthpispr→ea dtπio+n[11,19℄this par- tions (squares) and ( ir les). The (cid:28)lled tialwavedominaTtes≈the rea tionbasi allyfrom symbolsdenoteresultsofthiswork,opensymbolsarefrom[14, p threshold up to 900 MeV. It is responsible for the 3,8℄. Dash-ddπo+tted anpdnπd+ashed lines represent s- hannel al u- resonan e-like energy dependen e of the total ross se - lationsfor and hannels,respe tively,normalizedto T tion and performs a perfe t looping in the Argand dia- pthneπ+data at p = 400 MeV. The t- hannel al ulation for the gram[11℄. Thus this partialwavepossesIs(eJsPa)ll=fea1t(u2r+e)sto hTann≥elisgivenbythedottedlineandnormalizedtothe p qualify for apsp- hannel resonan edwπi+th in dataat 1GeV,whereitisknowntoprovideareasonable thein identN∆ hannel,the (cid:28)nal hannel and thein- des ription.Thesolid urvedepnpot→edpbnyπs++tisthein oherent termediate hannel (cid:21) see also d1iDs 2uPssion in Ref. [27℄. sumof both pro esses for the hannel. Fromppt→hedtoπt+al ross se tion of the partial wave in the rea tion [11℄ we see that the resonan e en- N∆ ergy is some 60 MeV below the≈nominal threshold, 4.4 Comparison to t- and s- hannel al ulations whereas the resonan e width of 110 MeV orresponds ∆ Finallywe onfrontthedatawithsimpletheoreti al al u- to that of the resonan e. T p lations a ording to the graphsdepi ted in Fig. 1. In this Theexper(i3mceonst2aΘlocmbs+erv1a)tionthatupto =500MeV essentiaplply→a pnπ+ π+ dependen e is observed also wexipther imomenptleaxlp aapl eurlaittiiosnnso,twohui rhaaimretboe yoomndpatrheeosu orpdeatoaf in the 1D2P rea tion points to the predominan e this work.We rather wantto use these al ulations in or- of the partial wave in this rea tion, too, as was derextra tthemainphysi smessageresidinginthedata. already noted in Ref. [5℄. From this also follows that the ∆ pn Sin ewehaveseeninthedis ussionabovethat ex i- likesyqsutaenmtuamt tshtaestee eIn(JerPg)ie=s i0s(p1r+e)f.erably in the deuteron- t1aDt2ionandde ayisthedominantrea tionme hanismand is by far the dominant partial wave at least in the T p energy region = 400 - 500 MeV, we expli itly negle t any non-resonant terms in the rea tion pro ess. 4.3 Total ross se tion We start with a (properly antisymmetrized) t- hannel approa h in (cid:28)rst-order impulse approximation, whi h is pTphe→endeπr+gy deppepnd→enn peπo+f the total ross se tions for the known to provide reasTona≥ble results for the angular dis- p ppa→ndpnπ+ hanTnelsisdisplayedin Fig.9. tributions at energies 1 GeV [20,21,22,23,24℄. For p Forthe hannelat =400MeVthereareno our energy we show su h a t- hannel al ulation by the experimental data to ompare with. However, our result dashed lines in Figs. 2, 3, 5 and 6. We see that the pion (cid:28)ts well to the trend given by the experimental results angular distribution is not reprodu ed orre tly. The rea- ∆ [14,3,5,8℄ at neighbouring energies.In orderto dis uss in sonforthisfailureissimple.Sin einthisapproa hthe is the next se tion the energy dependen e in som1De2broader ex itedbypionex hangebetweenthetwo ollidingnu l∆e- ontext with regard to the dominan e of the partial ons,thereferen eaxisforthepionde ayoftheex ited wave,weplotinFig.9theenergyrangefromthresholdup resonan e is the momentum transfer q and not the beam T ∆ p to = 1.5 GeV, i.e. overthe full region of ex itation. axis. Note that the latter, however, is the referen e axis pp 8 S. AbdEl-Samadet al.: Single-Pion Produ tion in Collisions at 0.95 GeV/ (II) ht2 gooda ount of the di(cid:27)erential distributions both for the ] invariant masses and for the parti le emission anIg(leJsP. )= b m 1(2+M)ass(2.07GeV) andwidth(160MeV) ofthe resonan einthiss- hannelansatzhavebeen hosen σ [tot 10 pnπ1D+2 SP40 dttoioomrneiponrfaontdh uee ,pei.peth.→uepedntπoe+rTgprye≈da e7tpi0eo0nndMienenV teh.eTofhretahgteiwotnaoytoafwlte hrseoims1sDusl2teaP -- 1D SP07 2 neouslyget a good des ription fpopr→thepennπe+rgy dependen e s Tofpt≈hetotal rossse tionforthe rea tionupto 1 600 MeV. If ombined with the amplitude of the t- hannelapproa hweevenobtainareasonabledes ription of the total ross se tions up to the GeV region (Fig. 9). dπ+ 10-1 1D SP93 al Fuilnaatilolynswfoer tohmep1aDr2epinartFiaigl.w1a0veoiunrtshiemnppleπ+s- hhaanNnnnNeell 2 s to the results opfpS→AIdDπ+[11℄ partial wave analyses of s at1teDri2ngand rea tion. The imaginary part of the partialwave,whi h is obtained from the analysis NN 10-20 0.2 0.4 0.6 0.8 1 1.2 1.4 of elasti σisn ealt(t1eDri2n)g, gives r1isDe2to the total inelasti ross se tion for the partial wave, whi h T [GeV] p in turn is given by the sum of the pion-pprpod→u ptpioπn0 ross se tionsi1nDt2his partialwave.Sin e in the rea - tion the partial wave is highly suppressed due to the ∆ suppression of the ex itation, we have in good approx- Fig. 10. Energy dependen e of total rosspspe →tiondsπa+s al u- imaσtipopn→npπ+(1D2)≈σinel(1D2)−σpp→dπ+(1D2) lated with opupr→s- phnanπn+el approa h for the (dash- The thus derived results are shown in Fig. 10 for the dotted)and (dashed ureve)rea tions,normalized NN T tothedatapointsfromthisexperimentat p=400MeV((cid:28)lled SAIDsolutionsSP07andSP40from s atteringa1nDal2- squareand ir le,respe tively;seealsoFig.9).For omparison yses together withdtπh+e SAID solution SP93 for the tluhteiosnhsonrSptPπd0+a7sha-nddotStPed40a,nrdesdpoet tteivdelliyn,efsorgitvheet1hDe2SApaIrDtia[1l1w℄asvoe- apnasratitazlwovaevrepirnedtih ets the 1hDan2npela.rWt oefsetehethpapto→urdsπ- +ha nronsesl inthe hannel(seetext),w1hDe2reas thesolid urveshdoπw+s se tion at higher energies as expe ted, sin e we have as- the SAID solution SP93 for the partial wave in the sumedfornspiπm+pli itythatonlythispartialwave ontributes. hannel. For the hannel the SP07 solution underpredi ts the ross se tion in the near-threshold region strongly, Twhe≤reas the SP40 solution, whi h is made for the region p 400MeV,providesaproperenergydependen e,how- for angles in the enter-of-mass frame. Sin e the momen- ever, is in the absolute s ale substantially above the data tum transfer varies in dependen e of the nu leon s atter- and the s- hannel al ulation in this energy region. At ing angles, whi h are integrated over(i3nctohse2Θpiqon+an1g)ular distribution, the al ulated intrinsi π+ de- higher energies up to 800 MeV our al ulation is essen- penden einthet- hannelapproa happearstobesmeared tially between both solu1tDio2ns. This omparison with the SAID solutions for the partial wave shows that our out in the ms pion angular distribution. simple model des ription is not in severe ontradi tion to In order to establish the beam dire tion as the appro- the SAID results, where the large spread between both NN priate referen e axis for the pion angular distribution in solutionspointstostillsubstantialambiguitiesinthe the al ulation one either has to reiterate the pion ex- partial wave analyses on erning the imaginary parts of hanges and sum them up to in(cid:28)nity or simply make a partial waves. s- hannel ansatz. The l1aDtt2er is easily made by a Breit- Wigner ansatz for the resonan e (Fig. 1, bottom), N∆ whi hdisso iatesintoa systemin relatives-wavefol- ∆ lowed by(t3hceods2eΘ acymo+f1t)he resonan e. This grants the 5 Summary observed π+ dependen eforthepionsaswell pp → pnπ+ asthedespirped→shdaπp+eoftheinvariantmassspe tra.Tosim- We have pTres≈ented measurements of the re- p ulatethe rea tionwithinthisansatzweimpose a tion at 400 MeV. In this energy region they are theHulthen wavefun tion as onditionforthepFpe→rmpinmπo+- the (cid:28)rst ex lusive ones of solid statisti s to over most mentumbetweenprotonandneutron.Forthe of the rea tion phase spa e. The di(cid:27)erential distributions rea tion we impose a FSI intera tion of Migdal-Watson are hara terized by the overwhelming dominan e of the pn ∆ type [25,26℄ on the system. These al ulations (Tnor- ex itation.Thepionppan→gudlaπr+distribution oin ideswith p malized to our results for the total ross se tions at = that observed in the 1D h2aPnnel, whi h in turn is 400MeV) areshownby the Dalitzplotsin Fig.4,bottom dominated by the resonating partiaplnwπa+ve. From and by the solid lines in Figs. 2,3, 5 and 6. They give a this oin iden e we on lude that also the hannel pp S. AbdEl-Samadet al.: Single-Pion Produ tion in Collisions at 0.95 GeV/ (II) 9 isdominatedbythesames- hannelresonan einthenear- thresholdregion.The orrelationbetweenboundstateand breakup hannelsisina ordan ewiththe predi tionsby Fäldt and Wilkin [18℄. This work has been supported by BMBF, DFG (Europ. Gra- duiertenkolleg683)andCOSY-FFE.Wea knowledgevaluable dis ussions with R. A. Arndt, L. Alvarez-Ruso, D. Bugg, C. Hanhart,M.Kaskulov,V.Kukulin,E.Oset,I.Strakovsky,W. Weise and C. Wilkin. Referen es 1. S. AbdEl-Samadet al., Eur. Phys.J. A30, 443 (2006) 2. B.Neganov,O.Sav henko,Sov.Phys.JETP5,1033(1957) 3. F. Shimizuet al., Nu l. Phys.A386, 571 (1982) 4. F. Shimizuet al., Nu l. Phys.A389, 445 (1982) 5. R. G. Pleydonet al., Phys.Rev. C59, 3208 (1999) 6. A. Bets h et al., Phys. Lett. B446, 179 (1999) 7. W. W. Daehni ket al., Phys. Rev. Lett. 74, 2913 (1995) 8. J. G. Hardie et al., Phys.Rev. C56, 20 (1997) 9. R. 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