THEORETICAL ASPECTS OF THE NUCLEON-NUCLEON WORKSHOP

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THEORETICAL ASPECTS OF THE NUCLEON-NUCLEON WORKSHOP

R. Silbar

To cite this version:

R. Silbar. THEORETICAL ASPECTS OF THE NUCLEON-NUCLEON WORKSHOP. Journal de Physique Colloques, 1985, 46 (C2), pp.C2-389-C2-397. �10.1051/jphyscol:1985244�. �jpa-00224558�

THEORETICAL ASPECTS OF THE NUCLEON-NUCLEON WORKSHOP

R.R. Silbar

Theoretical Division, Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545, U.S.A.

Résumé - Ce rapport est centré sur l'étude des voies inêlastiques dans la diffusion N-N entre 300 et 1500 MeV. Les sujets couverts comprennent la manifestation de la structure en quarks, les dibaryons, la dépendence en modèle des i n é l a s t i c i t é s N-N prédites. Nous présentons une comparaison en- tre les résultats donnés par les modèles conventionnels e t un ensemble de données expérimentales en rapide expansion. Nous concluons q u ' i l n'y a, à présent, aucune évidence nette de la présence de résonances dibaryoniques non conventionnelles dans le système N-N aux énergies intermédiaires. Nous présentons aussi quelques remarques concernant d'une part une contribution théorique à la diffusion élastique e t , d'autre part, des résultats expé- rimentaux nouveaux pour la photodësintégration du deuteron et d'échange de charge dans le système pion-nucléon.

Abstract - This report concentrates on the inelastic NN system from 300 to 1500 MeV.Topics covered include the visibility of quark signals, dibaryons, the model dependence of predicted NN i n e l a s t i c i t i e s , and a review of how well present conventional models compare with a rapidly expanding database.

The general conclusion is that there is so far no clear evidence in the NN system at intermediate energies for unconventional dibaryon resonances.

Shortremarks are also made concerning one theoretical contribution on elastic scattering and on new experimental results for deuteron photo- disintegration and pion-nucleon charge exchange.

I - INTRODUCTION

Catherine LeLuc has just told you about some of the matters discussed at the Work- shop on NN Scattering at Intermediate Energies held a week ago last Wednesday.

These included antiproton-nucleon reactions and the database for elastic scattering, comparing especially the less-well-known np situation with pp scattering. She also reviewed the experimental programs underway at various laboratories active in this energy range and then the status of e l a s t i c phase shift analyses.

My job today is to cover all the rest, which largely means the theoretical aspects of the Workshop. There was only one contribution on elastic NN scattering, and I discuss that f i r s t . I then will say a few words about two experimental subjects which were discussed, photo-disintegration of deuterons and pion-nucleon charge exchange. The bulk of my talk, however, addresses the inelastic region from 300 to 1500 MeV, where single-pion production is the dominant inelasticity. This is the region of the con- troversal (non-strange) dibaryon resonances. Besides discussing dibaryons, I will comment on model-dependence in theoretical predictions of inelasticities in high-L partial waves. That will be followed by reviewing present-day conventional models, comparing them with the rapidly expanding database in this energy region.

II - ELASTIC SCATTERING

Various ambiguities and peculiarities of elastic NN amplitudes were discussed by A. Gersten in-a very compact ten minute presentation. He f i r s t explained his "zero method" for generating distinct phase shift solutions (given a cutoff angular momen-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985244

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tum Lmax). This leads t o a s e t o f d i s c r e t e ambiguities, many o f which can be e l i m i - nated f o r reasons o f c o n t i n u i t y and uni t a r i t y . Given an incomplete s e t o f experiments, such as a , ANO, ^{ANN, D} N, and KNN, these ambiguities can nonetheless plague a phase s h i f t a n a l y s ~ s . !he met!od i s probably more u s e f u l , he suggests, f o r a n a l y s i s o f r e a c t i o n s l i k e pp i n t o two pseudoscalar mesons than f o r e l a s t i c NN s c a t t e r i n g . Gersten a l s o described h i s "no exchange model" f o r NN e l a s t i c s c a t t e r i n g . By t h i s he means a p i o n exchange model b u t w i t h o u t any pions being exchanged when t h e two nucle- ons are c l o s e r than, say, 1.1 fm i n c o n f i g u r a t i o n space. I n t h i s way, i t i s p o s s i b l e t o p r o v i d e a very good d e s c r i p t i o n o f the experimental double-heli c i t y - f l i p ampli t u - de Q2 = <++ITI--> f o r pp s c a t t e r i n g from 100 t o 500 MeV. The p r e d i c t i o n s o f t h i s mo- d e l are s i m i l a r t o , b u t a considerable improvement upon, t h e "poor m n ' s absorption model", i n which powers o f t i n numerators a r e simply s e t equal t o pf. This a l l very i n t e r e s t i n g but, as Gersten emphasized, i t leaves us w i t h the,mystery as t o why no o t h e r mesons seem t o be i n v o l v e d i n the dynamics o f t h e 02 amplitude.

I n t h e discussion period, M. Moravcsik reminded us o f h i s r e c e n t l y p u b l i s h e d work w i t h G. Goldstein i n which t h e r e s o l u t i o n o f d i s c r e t e a m b i g u i t i e s i s shown t o r e q u i r e measurements o f spins along t h r e e independent d i r e c t i o n s .

I 1 1 - SOME RECENT, RELATED EXPERIMENTS

Somewhat i s o l a t e d from o t h e r s u b j e c t s a t t h e workshop was t h e d i s c u s s i o n by W. Meyer o f p h o t o d i s i n t e g r a t i o n o f the deuteron a t i n t e r m e d i a t e energies. A new experiment, done a t Bonn, has measured t h i s process u s i n g a v e c t o r - p o l a r i z e d deuteron t a r g e t w i t h a bremsstrahlung beam a t 550+50 MeV. The asymmetry i n t h e pn f i n a l s t a t e was measured a t 13 angles over the whole CM angular range and shows a r i s e through zero t o p o s i t i v e values o f about +.3 a t t h e most backward angle. Meyer compared t h i s data w i t h t h r e e t h e o r e t i c a l curves : a c a l c u l a t i o n done a t Bonn based on a few leading conventional Feynman diagrams, another conventional c a l c u l a t i o n by a Tokyo group, and t h e same Tokyo c a l c u l a t i o n w i t h added dibaryon terms ( f i t t e d t o reproduce t h e o l d Kamae data on r e c o i l p r o t o n p o l a r i z a t i o n /I/, one o f the f i r s t experiments c l a i - med t o show dibaryon resonances). Meyer concluded, " A l l analyses f a i l , w i t h o r w i t h o u t dibaryons", a1 though t o my eye t h e Bonn curves d o e s n ' t do so badly. I n view of t h e skimpy nature o f t h e t h e o r e t i c a l models so f a r a p p l i e d t o t h i s process, however, i t i s probably dangerous t o draw any conclusions. T h e o r e t i c a l work i s needed here.

Another p h o t o d i s i n t e g r a t i o n experiment, i n v o l v i n g a p o l a r i z e d photon beam on an unpolarized d e u t e r i urn t a r g e t and measuring the p o l a r i z a t i o n o f t h e r e c o i 1 neutron ( !), was r e p o r t e d by a Yerevan group headed by G. Vartapetyan. T h i s experiment a t 300 t o 500 MeV, the f i r s t such double-spin measurement i n t h i s f i e l d , i s s t i l l i n a p r e l i m i n a r y stage o f a n a l y s i s . No attempt was made t o conpare wi t h model p r e d i c t i o n s , and, indeed, i t would be s u r p r i s i n g i f any such p r e d i c t i o n s have y e t been made.

There has been one new development i n aN physics, g e n e r a l l y a s l o w l y changing f i e l d a t i n t e r m e d i a t e e n e r g i e s . 6. Nefkins described new r e s u l t s o f a p charge exchange using a p o l a r i z e d t a r g e t . Four i n c i d e n t momenta were s t u d i e d : 300, 470, 586 and 625 MeV/c. The lower-momentum r e s u l t s f o r t h e p o l a r i z a t i o n asymmetry agree w e l l w i t h the Karlsruhe-Helsi n k i and CMU-LBL phase s h i f t a n a l y s i s p r e d i c t i o n s . The data a t h i g h e r momenta, however, disagree s t r o n g l y . Moreover, t h e t r i a n g l e i n e q u a l i t y f o r the p o l a r i z a t i o n ( i t a p p l i e s t o AN as well a s t o d i f f e r e n t i a l cross s e c t i o n s ) i s "on t h e edge" o f showing an i s o s p i n symmetry v i o l a t i o n f o r the h i g h e r energies. With these data, one has t o wonder (again) i f t h e r e may n o t be something funny about t h e Roper resonance i n t h e PllaN p a r t i a l wave.

I t u r n now t o t h e main c o n s i d e r a t i o n i n t h i s r e p o r t , nucleon-nucleon r e a c t i o n s above t h e i n e l a s t i c threshold. The basic q u e s t i o n t o be faced i s whether a conventional i e s c r i p t i o n s u f f i c e s t o describe the experimental s i t u a t i o n . Here, and below, a

conventional model " means one i n v o l v i n g nucleons and & l t a s i n t e r a c t i n g by poten- t i a l s o r by meson exchanges. An "unconventional model" r e f e r s t o one which necessa- r i l y i n v o l v e s quark degrees o f freedom, such as t h e c o l o r quantum number.

A. R i n a t r e p o r t e d on a c a l c u l a t i o n o f t h e pptd~+ r e a c t i o n i n which he i n c o r p o r a t e d quark e f f e c t s i n t h e ANTI vertex1 by means o f a cloudy c h i r a l bag model.The changes

i n going t o t h i s more complicated d e s c r i p t i o n a r e small, o f the o r d e r o f 10% o r less.

R i n a t f e e l s -- now -- t h a t t h e amount o f e f f o r t i n v o l v e d i n such c a l c u l a t i o n s a t medium energies i s h a r d l y worth i t . For t h e energy regime under discussion, he says, i t i s probably most e f f i c i e n t c o m p u t a t i o n a l l y t o use t h e " c o l l e c t i v e c o o r d i - nates" o f baryons and mesons.

I n d i s c u s s i o n afterwards, E. Lomon suggested one should n o t be so p e s s i m i s t i c . Perhaps we haven't seen quark degrees o f freedom y e t because t h e i r major e f f e c t s l i e a t center o f mass energies above 2.5 GeV, somewhat higher than have been inves- t i g a t e d up t o now. You w i l l hear more about t h i s from Lomon l a t e r t h i s morning.

Altogether, I must confess t h a t I am p r e t t y sympathetic t o R i n a t ' s p o i n t o f view on t h i s question. C e r t a i n l y , a t t h i s point,, t h e r e i s no c l e a r and d i s t i n c t i v e s i g n a l fcr quarks i n intermediate-energy NN physics. There a r e a few suggestive experimental data t h a t , i f they prove t o be c o r r e c t , may r e q u i r e e v e n t u a l l y a quark-based explana- t i o n . I w i l l mention a few o f these as we go along, b u t , so f a r , conventional phy- s i c s seems t o be adequate t o describe the physics i n t h i s energy region.

V- THE DIBARYON PROBLEM

The question o f whether t h e r e are dibaryon resonances i n NN s c a t t e r i n g a t medium energies i s now almost e i h t years o l d . It i s c l e a r t h a t something i n t e r e s t i n g i s

S

happening i n t h e and F3 p a r t i a l wave amplitudes, b u t whether t h e u n d e r l y i n g dynamics i s conventional o r n o t i s s t i l l v e r y c o n t r o v e r s i a l . Besides discussion of these two well-known cases, t h e r e were a few suggestions a t t h e Workshop of new possi b i 1 i t i e s f o r d i baryon resonances.

I t was s t r o n g l y emphasized by P. K r o l l t h a t , as f a r as t h e P a r t i c l e Data Group's c r i t e r i o n f o r a r sonancegis concerneci (approximate Breit-Wigner behavior i n an f

Argand p l o t ) , t h e D2 and F3 waves have " f o u r - s t a r resonances". The counter-clock- wise looping behavior as t h e energy increases i s c l e a r . I t i s a l s o v e r y c l e a r t h a t these p a r t i a l waves a r e v e r y i n e l a s t i c , w i t h most o f t h a t i n e l a s t i c i t y coming from s i n g l e - p i o n production, NN-~NNTI. What i s n o t c l e a r i s whether t h i s behavior i s due t o " t h e o r e t i c a l resonances", i.e., poles on the second ( o r h i g h e r ) sheet of t h e com- p l e x energy plane. The basic m o t i v a t i o n f o r r a i s i n g such a q u e s t i o n i s t h e impor- tance o f the NN-tNA thresholds i n these p a r t i a l waves. The c o u p l i n g t o t h e i n e l a s t i c NA channel provides an a t t r a c t i v e f o r c e which may o r may n o t g i v e ' r i s e t o a reso- nance pole. C e r t a i n l y , much o f t h e motion on the Argand p l o t can be a t t r i b u t e d sim- p l y t o t h e thresholds, which a n a l y t i c a l l y correspond t o c u t s r a t h e r than poles.

K r o l l p o i n t e d o u t t h a t the D resonance appears t o be n e a r l y " p u r e l y conventional", 1 a m a n i f e s t a t i o n o f t h i s all-Praser i n e l a s t i c coup1 i n g mechanism. The s i t u a t i o n f o r t h e 3 ~he f e e l s , may be more i n t e r e s t i n g , since present conventional models do n o t ~ , seem q u i t e a b l e t o reproduce a l l the f e a t u r e s o f t h e data. Perhaps t h i s t r i p l e t resonance i s "mixed", having both a conventional and an unconventions component.

K r o l l showed transparencies o f how t h e a d d i t i o n o f a dibaryon resonance term i n t h i s p a r t i a l wave made dramatic improvements i n h i s Deck model p r e d i c t i o n s of c e r t a i n observables, such as AaL(pp+NN7i).

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I t i s probably u s e f u l t o be cautious about these conclusions. F i r s t , conventional mo- dels, e s p e c i a l l y f o r NN-tNNr, a r e few and l i m i t e d i n t h e physics they i n c l u d e . Also, u n i t a r i t y i s probably e s s e n t i a l f o r understanding odd-tensor observables l i k e ANQ, the s c a t t e r i n g asymmetry w i t h r e s p e c t t o t h e beam. 1 w i 11 show a f i g u r e i 1 lu s t r a t i n g t h i s p o i n t l a t e r on. K r o l l and h i s colleagues p l a n t o apply t h e i r model t o p r e d i c t AN and o t h e r such q u a n t i t i e s . F i n a l l y , besides comparing w i t h a l l a v a i l a b l e NbNNr data, f u t u r e analyses should e v e n t u a l l y a l s o i n c l u d e i n f o r m a t i o n on t h e s t r o n g l y - coupled NN+NN, NN-vrd (and i t s i n v e r s e ) , and ad-vrd r e a c t i o n s .

A f i r s t step towards such a u n i f i e d a n a l y s i s has a l r e a d y been taken by an Osaka group, as r e p o r t e d by N. Hiroshige. They have extended the K-matrix approach t o i n - clude pp+pp,ppwd, and ad-md amplitudes as determined by r e c e n t phase s h i f t analy- ses f o r each o f t h e e react'ons separately. Indeed, they f i n d h i g h l y i n e l a s t i c reso-

4

nance poles i n t h e D and F p a r t i a l waves. A b i t o f c a u t i o n i s i n order here as w e l l . The Osakagroup {as n o t ? y e t ) i n c l u d e d any pp-NNn i n f o r m a t i o n i n t h e i r analy- s i s , and t h a t i s t h e m a j o r i n e l a s t i c i t y i n t h i s region. Moreover, one can sometimes be f o o l e d by t h e K-matrix approach. Some "experiments" have been done /2/ i n which t h e o r e t i c a l models a r e used t o generate "data", which i n t u r n areused f o r a K-matrix f i t . The r e s u l t i n g o u t p u t amplitudes do n o t alwavs resemble t h e i n o u t a m ~ l i t u d e s . Are there any h i n t s o f new dibaryons, i .e. resonances o t h e r than t h e I = 1 'D and 3 ~ 3 ? Several suggestionScam u p d u r i n g the workshop, although none o f t h e fol?owing needs t o be taken s e r i o u s l y y e t . F i r s t , t h e r e was n o t h i n g s a i d about I = 0 dibaryom.

I n f a c t , t h e data and t h e o r e t i c a l curves shown by Meyer f o r yd+pn can be taken as evidence t h a t the Kamae data should not be i n t e r p r e t e d i n terms o f a resonance.

Things were more e x c i t i n g i n I = 1. Lomon p o i n t e d out, on t h e basis o f a vague wiggle i n t h e Saclay-Geneve phase s h i f t a n a l y s i s , t h a t t h e r e might be something resonating i n t h e 3P0 amplitude near 575 MeV. I was v e r y s u r p r i s e d n o t t o hear a discussion, i n the Workshop, o f t h e t h r e e narrow bumps found by an O G y - S a c l a y group /3/ i n the r e a c t i o n 3He(p,d) X. As r e p o r t e d a t t h e PANIC, the i n v a r i a n t mass o f X peaks a t 2124, 2189 and 2243 MeV, w i t h widths o f t h e o r d e r o f 20 MeV. A. Masaike t o l d us about a KEK p o l a r i z e d - t a r g e t experiment on e l a s t i c r d s c a t t e r i n g a t 740 MeV, which shows no t r a c e o f a p r e v i o u s l y r e p o r t e d 1~~ resonance. And f i n a l l y , n o t a t t h e Workshop b u t yesterday, M. Locher t o l d us o f another narrow bump a t M = 2020 MeV i n the photoproducti on o f pions from deuterons.

V I - MODEL DEPENDENCE OF INELASTICITY PREDICTIONS

The s p i n dependence o f t o t a l i n e l a s t i c cross sections has r e c e n t l y become a v a i l a b l e f o r t h e f i r s t time, and i t i s t e l l i n g us a g r e a t deal about the dynamics o f t h e i n e l a s t i c i t y . F i g u r e 1 shows Aa (pp+NNr) , another v e r s i o n o f which appeared several times d u r i n g t h e Workshop (and t h e week s i n c e ) . The t h r e e conventional model calcu- t i o n s miss e n t i r e l y t h e shape and s i g n o f t h e experimental data (which comes from

Geneve and ANL). Since i t i s t h e t r i p l e t (spins p a r a l l e l ) cross s e c t i o n t h a t has t h e negative sign, t h e lesson t o be drawn from Fig.1 i s t h a t t h e r e i s t r i p l e t i n e l a s t i c i - t y m i s s i n g from conventional model d e s c r i p t i o n s

.

One way o f i n c l u d i n g more t r i p l e t i n e l a s t i c i t y , e x p l o i t e d by K r o l l and h i s c o l l e a - gues, i s t o add an e x p l i c i t 3 ~ 3 dibaryon resonance t o the model. This gives, a f t e r f i t t i n g a few parameters, the dashed curve shown i n t h e f i g u r e . The f i t t o the data i s much improved.

Even more r e c e n t l y we have begun t o see AaT(pp+NN.rr) data. R. Hess showed us Geneve data f o r t h i s q u a n t i t y up t o 580 MeV, and i t t u r n s o u t t o be p o s i t i v e . Conventional model p r e d i c t i o n s f o r ~0;"' a r e a l s o p o s i t i v e and r i s i n g i n t h i s energy region.

Moreover, K. Imai e a r l i e r t h i s y e a r a t a conference i n Japan showed h i s e x t r a c t e d values o f Aoinel a t h i g h e r energies and has claimed them t o be i n "reasonable agreement" w i l h t h e Kloet-Si 1 bar p r e d i c t i o n . Thus we can draw an i m p o r t a n t conclusion:

Fig.1

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i f &,inel i s bad (compared with experiment) and ~o:"~' i s good, then the t r i p l e t i n e l a s t i c i t y missing i n the models has L = J .

A t a f i n e r level than t o t a l i n e l a s t i c cross sections, one can study the i n e l a s t i c i t parameters nLSJ i n s p e c i f i c N N p a r t i a l waves. Kroll showed a p l o t of n ( 3 ~ ~ ) versus Tlab, comparing three conventional models, plus his Deck model w i t h the added diba- ryon, with the values extracted from e l a s t i c phase s h i f t analyses. In general, the conventional models a1 1 underpredict the amount of i n e l a s t i c i t y i n t h i s L=J t r i p l e t wave. (The model with the f i t t e d di baryon, of course , does r a t h e r we1 1 . ) This i s quite consistent with the conclusion drawn i n the l a s t paragraph.

I t i s not obvious, however, that adding i n a dibar on i s the only way to get the 3

additional i n e l a s t i c i t y here. F i r s t note t h a t the F j partial wave i s not a periphe- ral wave, since the N N s t a t e can couple t o an NA s t a t e i n a r e l a t i v e p-wave (with channel spin coupled t o S=2). However, almost a l l the conventional models t h a t have predicted '1313 are of the one-pion-exchange type (including others not shown by Kroll). I t might be t h a t short-range forces not so f a r i n the models (such as P-

exchange) are responsible f o r the missing i n e l a s t i c i t y here ; t h a t needs t o be i n - ves t i gated.

In regard to the model predictions of n ( 3 F3), i t i s also worth noting t h a t there are big differences between them. For example, a t 800 MeV the Deck model n i s 0.9, while Lomon's n i s 0.73. Since the i n e l a s t i c cross section i n a p a r t i a l wave goes l i k e 1

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In f a c t , however, even the peripheral p a r t i a l waves show a wide variation i n predic- ted i n e l a s t i c i t i e s . This point was not really discussed a t the Workshop. I know of i t

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from a r e c e n t p r e p r i n t by K l o e t and Tjon / 4 / . For example, t h e 3 ~ 4 p a r t i a l wave i n e - l a s t i c i t y a t 800 MeV a l s o v a r i 6 s between' models by a f a c t o r o f t h r e e o r more i n t h e cross s e c t i o n . K l o e t and Tjon a t t r i b u t e t h e d i f f e r e n c e s t o two sources : d i f f e r e n c e s i n t h e treatment o f A propagators, and whether t h e c u t o f f f u n c t i o n s i n t h e models are functions o f v a r i a b l e s a p p r o p r i a t e t o a two-body coupled-channel approach o r t o a three-body Faddeev type approach. I t i s n o t obvious how the l a t t e r ambiguity can, o r should, be resolved.

This model dependence o f the i n e l a s t i c i t y parameters i s unfortunate, s i n c e we there- fore cannot now use theory t o f i x t h e p e r i p h e r a l p a r t i a l wave n ' s , thereby reducing the number o f parameters t h a t must be f i t i n a phase s h i f t a n a l y s i s . The b e s t t h a t can be s a i d i s t h a t people doing phase s h i f t analyses ought t o try searching on t h e

0's w i t h i n an " e r r o r band" i n d i c a t e d by t h e various d i f f e r e n t model p r e d i c t i o n s . V I I - HOW GOOD ARE PRESENT DAY CONVENTIONAL MODELS ?

I now want t o discuss how we1 1 t o d a y ' s f i r s t - g e n e r a t i o n conventional models compare w i t h experiment. For the r e a c t i o n s n&md and p p w d I w i l l be b r i e f , since these

t o p i c s were very n i c e l y covered i n Locher's t a l k yesterday. On t h e o t h e r hand, t h e pptNNrr r e a c t i o n has n o t so f a r been very e x t e n s i v e l y reviewed i n t h i s s e r i e s o f Spin Physics conferences. The b a s i c q u e s t i o n t o bear i n mind throughout t h i s discus- s i o n i s , t o what e x t e n t do disgreements w i t h data need t o be m o d i f i e d by unconven- ti onal dynamics ?

Regarding the TZ0 controversy i n e l a s t i c pion-deuteron s c a t t e r i n g , t h e r e i s l i t t l e t o say t h e o r e t i c a l l y . I f the ETH data do t u r n o u t t o be c o r r e c t , however, then t h e i r narrow s t r u c t u r e s wi 11 almost c e r t a i n l y r e q u i r e an unconventional explanation. On the o t h e r hand, i f t h e ANL data are t h e c o r r e c t ones, then Tzo can probably be under- stood w i t h conventional models.

Note a1 1 problems i n pion-deuteron s c a t t e r i n g are discrepancies between experiments.

Although he was n o t a p a r t i c i p a n t a t t h e Workshop, several people r e f e r r e d t o calcu- l a t i o n s by H. Garci l a z o /5/, which compare w e l l w i t h t h e i tll and (ANL) T20 data.

Unpublished work by him also does a good j o b i n r e p r e s e n t i n g the cross s e c t i o n s and v e c t o r p o l a r i z a t i o n s f o r pion-deuteron breakup, rd+rNN. The problem, however, i s t h a t Garcilazo has no absorption channel ( i .e. , ~ d - t N M d ) i n h i s model. I s t h i s , as Locher says, "a g i a n t step backwards"? O r , are the usual treatments o f the Pll nN i n p u t amplitude, which tend t o i n v o l v e a b i g on-shell c a n c e l l a t i o n between a pole- term and a background c o n t r i b u t i o n , wrong i n some unknown way. d o n ' t know, b u t t h e l a t t e r sounds a t l e a s t p l a u s i b l e t o me.

For the ppvrrd r e a c t i o n p r e s e n t t h e o r i e s are overwhelmed by very precise and numerous data.Conventiona1 models o n l y p r e d i c t the trends o f observables l i k e AN^ c o r r e c t l y . The agreement between model and data, ~och-wed us, can be much improved i f one simply adds, i n an ad hoc manner, some (non-resonant) t r i p l e t s t r e n g t h , which i n - h i s examples was i n t h e w n d 3~~ p a r t i a l waves. Again, t h i s i s q u i t e c o n s i s t e n t w l t h the conclusions drawn AUL and AOT. As f a r as I know , t h e r e are no unconventional models proposed f o r t h i s r e a c t i o n ( o t h e r than R i n a t ' s cloudy bag essay), and t h a t i s probably because the data p r o v i d e no compel 1 i ng reason t o propose them.

For c a l c u l a t i o n s o f t h e r e a c t i o n where most o f the i n e l a s t i c i t y occurs, NbNNlr, t h e r e are o n l y two a c t i v e groups. The t h e o r e t i c a l basis f o r a l l models i n t h i s energy r e g i o n i s t h e i s o b a r model, proposed i n 1958 by Lindebaum and Sternheimer and by Mandelstam. Here t h e i n i t i a l NN s t a t e makes a t r a n s i t i o n t o a ( s p e c t a t o r ) nucleon and an i s o b a r , which then propagates some distance and then decays i n t o a nucleon and a p i o n . The most i m p o r t a n t i s o b a r i s the A(3,3), f o r which the propagator i s l i k e a B r e i t-Wigner resonance f a c t o r . The Wuppertal group, headed by K r o l l , uses a form of t h i s model c a l l e d a Deck model (or, a F e r r a r i - S e l l e r i model), i n which t h e i s o b a r p r o d u c t i o n amplitude i s given by s i n g l e - p i o n exchange and t h e nN i n p u t i n f o r m a t i o n i s taken from t h e Karlsruhe-Helsinki a n a l y s i s . Our group 151 solves coupled-channel three-body equations f o r t h a t p r o d u c t i o n amp1 i tude, thus m a i n t a i n i n g (two- and three-

as we have seen, can add i n e x p l i c i t d i baryon terms, which, though a non-uni t a r y pro- cedure, d o e s n ' t h u r t them s i n c e t h e i r model i s n ' t u n i t a r y t o s t a r t w i t h . We, on t h e o t h e r hand, cannot add such terms ( v e r y e a s i l y ) , and have n o t y e t done so.

A c t u a l l y , the u n i t a r y OPE model does q u i t e w e l l i n d e s c r i b i n g a l a r g e pptnpat data base. A " t y p i c a l " comparison w i t h t h e extensive 800 MeV Rice-Houston data /6/ f o r an e x c l u s i v e d i f f e r e n t i a l cross s e c t i o n and t h e corresponding asymmetry parameter, ANO, i s shown i n Fig.2. For t h i s forward-angle p r o t o n case, t h e p r e d i c t e d cross-section i s a b i t low, b u t a t l a r g e r p r o on angles i t i s high. This r e f l e c t s t h e overpredic-

f

t i o n , i n t h i s model, o f t h e NN( D ~ ) + N A ( ~ s ~ ) i n e l a s t i c i t y , which i n t u r n means a too i s o t r o p i c NA f i n a l s t a t e . The peak i n the cross s e c t i o n around o u t o i n g p r o t o n mo-

9

mentum o f 600 MeV/c i s due t o an NN f i n a l s t a t e i n t e r a c t i o n i n t h e So o r 3 ~ 1 states.

Our model does n o t c o n t a i n any such dynamics ( y e t ) , whence i t misses t h i s peak. The u n i t a r y p r e d i c t i o n f o r ANO, shown as a s o l i d curve, has the r i g h t shape b u t i s d i s - placed downwards from the data. The dashed curve on t h a t graph i s o u r Born approxi- mation c a l c u l a t i o n o f ANOy and the d i f f e r e n c e between the two curves i l l u s t r a t e s my e a r l i e r p o i n t about t h e importance o f u n i t a r i t y f o r understanding such observables.

For o t h e r p r o t o n - p i o n angle p a i r s , the agreement between model and d a t a i s sometimes b e t t e r and sometimes worse than shown.

Fig.2 - E x c l u s i v e d i f e r e n t i a l cross s e c t i o n and asymmetry f o r pp+np7it a t 800 MeV, Op = 1 4 O and 0, = 42" ( l a b ) .

This u n i t a r y model has a l s o been compared, w i t h about t h e same degree o f success, t o many o t h e r k i n d s o f data on s i n g l e - p i o n p r o d u c t i o n from 420 t o 800 MeV. These i n c l u d e s p i n - s p i n c o r r e l a t i o n s /7/, s p i n - t r a n s f e r c o e f f i c i e n t s /8/ and p o l a r i z a t i o n asymmetry i n ppyp.rrO /9/ and i n i n c l u s i v e pp-tpX / l o / .

So, what are t h e problems i n t h e NFkNNa reactions? I have a l r e a d y discussed Aa (ppNNa) and t e m i s s i n g L = J t r i p l e t i n e l a s t i c i t y . Probably c l o s e l y r e l a t e d t o

t h h i s t h e w r o n d l s i g n p r e d i c t i o n f o r ALL a t 800 MeV, mentioned by K r o l l . A perhaps e n t i r e l y d i f f e r e n t problem i s t h e s p i n - t r a n s f e r c o e f f i c i e n t measured f o r the i n c l u - s i v e $p+?i~ r e a c t i o n a t O 0 a t 800 MeV /11/. F i g u r e 3 shows t h e KLL c o e f f i c i e n t , com- p a r i n g w i t h o u r u n i t a r y model. Again, the shape and magnitude a r e completely wrong.

I n t h i s case i t i s n o t c l e a r a t a l l how more L = J t r i p l e t i n e l a s t i c i t y can improve

C2-396 JOURNAL DE PHYSIQUE

the s i t u a t i o n . Nor i s i t c l e a r whether the trouble comes from t h e lack of short-range forces i n the model.

Fig.3 - Spin t r a n s f e r c o e f f i c i e n t KLL f o r ppnX a t 800 MeV, On = 0'.

What needs t o be done t o improve today's NkNh models? F i r s t , other unified-model builders should t u r n t h e i r a t t e n t i o n t o the unbound three-body f i n a l s t a t e . Kroll and company and Dubach, Kloet and S i l b a r badly need some competition! I t i s very hard t o know what the model dependence of certain predictions i s i f there are only two modelst A second major improvement would be t o go beyond one-pion-exchange forces. To put shorter-range forces i n t o these models, one could use phenomenological potentials o r , perhaps more s a t i s f y i n g , the exchange of heavier mesons. The nucleon-nucleon final s t a t e interactions a r e , as we have seen, sometimes important, and these should a l s o be brought i n t o the models. As mentioned e a r l i e r , i t might eventually be necessary t o include e x p l i c i t dibaryon resonances i n the models, and one would hope t h a t t h i s can be done i n way t h a t does not v i t i a t e u n i t a r i t y .

In the f a r t h e r o f f f u t u r e , say, i n about f i v e years, we might expect t o see unified amplitude analyses of a1 1 the I = 1 data i n the single-pion-production region. This would t r e a t N k N N , N h i and N k N r data simultaneously, using theory t o constrain o r f i x the high-L p a r t i a l waves.

VIII - CONCLUSION

In general, theoretical models of the i n e l a s t i c N N region a r e doing as well as ( o r b e t t e r than) could have been expected. This has been no easy task i n view of the re- cent flood of new experimental r e s u l t s . I see three major problems t h a t t h e o r i s t s must now face : the model dependence of t h e peripheral p a r t i a l wave i n e l a s t i c i t i e s , the missing S = 1, L = J i n e l a s t i c i t y , and the KCL problem i n forward pp+nX. Apart from these problems, which probably are soluble I n the usual way", my basic conclu- sion as a spectator a t the NN Workshop i s t h a t there i s no c l e a r evidence today i n the NN system a t intermediate energies f o r unconventional dibaryon resonances.

In closing, I would l i k e to thank C. Lechanoine-LeLuc f o r doing e s s e n t i a l l y a l l of the organizational work f o r t h i s Workshop. J . Soffer and F. Lehar were very helpful with t h e arrangements, support, and good advice. And M . Moravcsi k as chairman did a good job of keeping the Workshop on track, i n s p i t e of a very crowded schedule.

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3. B . Tatischeff e t a l . , contribution t o PANIC, Heidelberg ( J u l y 1984).

4. W.M. Kloet and J.A. Tjon, p r e p r i n t LA-UR-84-2132 (July 1984)

5. W . M . Kloet and R . R . S i l b a r , Nucl . Phys. A281(1980) 281 ; J . Dubach e t a1

.

Phys. L e t t . B106(1981) 29 and J . Phys. GT(T982) 475.

6. A.D. H a n c o c k e t a l . , Phys. Rev. C 27(1983r 2742.

7. R . Shypit e t a1 ., Phys. Lett. E V 9 8 3 ) 314 ; T. S. Bhatia e t a1 .,

Phys. Rev. C 28(1983) 2071.

8. C. Hollas, prfiate communication.

9. G. Mutchler, private communication.

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11. G. Glass e t a l . , Phys. Lett. E m 8 3 ) 27.