EFFECT OF QCD IN INTERMEDIATE ENERGY HADRON-HADRON SCATTERING AND THE EXPERIMENTAL SIGNATURES

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HADRON-HADRON SCATTERING AND THE EXPERIMENTAL SIGNATURES

E. Lomon

To cite this version:

E. Lomon. EFFECT OF QCD IN INTERMEDIATE ENERGY HADRON-HADRON SCATTERING AND THE EXPERIMENTAL SIGNATURES. Journal de Physique Colloques, 1985, 46 (C2), pp.C2- 329-C2-338. �10.1051/jphyscol:1985239�. �jpa-00224553�

JOURNAL DE PHYSIQUE

Colloque C2, supplement au n°2, Tome 46, fevrier 1985 page C2-329

EFFECT OF QCD IN INTERMEDIATE ENERGY HADRON-HADRON SCATTERING AND THE EXPERIMENTAL SIGNATURES*

E.L. Lomon

Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A

Résumé - La méthode de la matrice R est utilisée pour la détermin- ation des caractéristiques des résonances dues à la QCD dans les réactions hadroniques.

Abstract - In two-hadron reactions the system couples at short range to the asymptotically free multi-quark (exotic) configurations.

Given a model of their QCD behavior the effect of these configur- ations on the two-hadron reactions can be determined using R-matrix theory. Resonances are predicted whose width, dominant reaction channels, and relative masses are determined by the asymptotically free characteristics of the QCD model. The absolute positions of the resonances are determined by the range of transition to confinement of the quarks, as well as by the asymptotically free properties.

For the nucleon-nucleon system the lowest energy resonances are predicted to be in the 3S . and 1S _ channels. At resonance the wave functions are dominated by the free quark component. Signatures of the quark dominance include the 70 MeV mass difference between the states, their 50 MeV width and their strong coupling to the AA channel. The MIT and CHP Bag models are inconsistent with the known phase shifts at T_<800 MeV. The Cloudy Bag model is consistent and predicts the resonances to have 2.7 GeV mass. Detailed calculations for this model indicate detectable variations of elastic spin

observables such as A and in two-pion production.

I - Introduction

The general properties of QCD, especially that of asymptotic freedom, indicate that hadron reactions at intermediate energies will contain structures with properties dominated by short range quark-gluon degrees of freedom. The range of such dominance, and therefore the energy of the states will depend sensitively on the nature of the transition to confinement. Thus the observation of these structures can be verified by properties derived from asymptotic freedom, Having been identified, they will provide critical information on higher order aspects of QCD including confinement properties, quark and gluon self energies and configuration mixing.

As these multi-quark gluon states make the transition from the short-range quark gluon phase at short distances to the hadronically clustered phase at large separation of the hadrons, they are sensi- tive to details of the confinement process. Up to now there is little information on this process either from experiment or from theoretical calculations. Experimental information from hadron

This work is supported in part through funds provided by the U.S. Department of Energy (DOE) under contract DE-AC02-76ER03069.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985239

r e a c t i o n s w i l l l e a d t o b e t t e r models o f QCD and may s u g g e s t c a l c u - l a t i o n a l methods t h a t l e a d t o new QCD p r e d i c t i o n s .

Whether s t a r t i n g from models o r fundamental t h e o r y , q u a n t i t a t i v e p r e d i c t i o n s a r e l i k e l y t o t a k e a d v a n t a g e of t h e d i v i s i o n of t h e p h y s i c a l b e h a v i o r i n t o two r e g i o n s - - t h e a s y m p t o t i c freedom o f q u a r k s and g l u o n s a t s h o r t r a n g e , and t h e confinement of t h e i r c o n s t i t u e n t s i n t o hadrons a t l o n g r a n g e ( i n t e r a c t i n g v i a hadron e x c h a n g e ) . T h i s i n v i t e s t h e u s e o f many-body t e c h n i q u e s , developed i n n u c l e a r p h y s i c s , which r e l a t e s i n g l e p a r t i c l e and c o l l e c t i v e c o o r d i n a t e s . G e n e r a t o r c o o r d i n a t e , c l u s t e r model o r r e s o n a t i n g g r o u p methods have been a p l i e d ' , a s w e l l a s p r o j e c t i o n o p e r a t o r 2 and R-matrix

methodsP- 7. We have pursued t h e R-matrix method6' ' which t a k e s f u l l advantage of t h e s p a t i a l s e p a r a t i o n of t h e two r e g i o n s and e n a b l e s t h e t e s t i n g o f d e t a i l e d a s p e c t s o f dynamical models.

I n t h e f o l l o w i n g we b r i e f l y r e v i e w t h e r e l e v a n t a s p e c t s o f t h e R-matrix method. Then we a p p l y t h e method t o t h e l o w e s t e n e r a y r e s o n a n c e s i n nucleon-nucleon s c a t t e r i n g . b7e p r e s e n t s e v e r a l r e s u l t s i n c l u d i n g some d e t a i l e d p r e d i c t i o n s f o r e l a s t i c and p r o d u c t i o n s p i n o b s e r v a b l e s a t a few GeV. F u r t h e r a p p l i c a t i o n s t o nucleon-nucleon and o t h e r hadron-hadron r e a c t i o n s a r e mentioned.

I1 - Review of R-matrix method

I n t h e i n t e r i o r r e g i o n ( F i g . 1) a complete set o f s t a t e s o f e n e r g i e s Wi i s determined by a homogenous boundary c o n d i t i o n , which f o r t h e f - m a t r i x v e r s i o n o f t h e method i s i

I

) ( r = X o ) = O

I q

%I**=

Hadron exchange potential

Ffg. 1

-

f o r q u a r k c o o r d i n a t e ra. The e x t e r i o r wave f u n c t i o n s a r e expanded i n t h e s e and by u s i n g G r e e n ' s Theorem and c o n t i n u i t y c o n d i t i o n s one o b t a i n s r0+iT ( r o ) = WIT(r0)

where r, i s t h e r e l a t i v e two-hadron c o o r d i n a t e and i s r e l a t e d t o R o by a v e r a g i n g o v e r t h e e x t r a d e g r e e s o f freedom. The f - m a t r i x i s

g i v e n by i

Pa B f a B ( r 0 , w ) = f 0 ( l o ) + ^C -

a B _i

W-W i w i t h

where t h e ei a r e f r a c t i o n a l p a r e n t a g e c o e f f i c i e n t s o f e x t e r n a l c h a n n e l s a @ i t h r e s p e c t t o t h e i n t e r i o r s t a t e s i.

I n t h e e x t e r i o r r e g i o n t h e h a d r o n i c c h a n n e l s a r e c o u p l e d by one- boson and two-pion exchange p o t e n t i a l s . These a r e c a l c u l a b l e from t h e o r y and known t o b e a c c u r a t e f o r r a n g e s g r e a t e r t h a n a b o u t 0.8 fm.

When t h e S-matrix i s known from e x p e r i m e n t t h e n t h e e x t e r i o r wave f u n c t i o n i s d e t e r m i n e d f o r r l r , and c o n s i s t e n c y w i t h t h e boundary c o n d i t i o n energy dependence, d e t e r m i n e d by t h e i n t e r i o r Wamiltonian, can be checked.

I n t h e i n t e r i o r r e g i o n e a c h model o f QCD d e t e r m i n e s t h e wi and P U n t i l now we have used bag models, b u t c o n s t i t u e n t q u a r k models ^i' c o u l d j u s t a s w e l l b e used. These models a l r e a d y have t h e i r p a r a - m e t e r s d e t e r m i n e d by a f i t t o t h e meson and baryon s p e c t r a . One c a n , i n p r i n c i p l e , f u r t h e r improve t h e method by u s i n g l a t t i c e QCD c a l c u l a t i o n s f o r which r, can be l a r g e r t h a n t h e r a n g e o f a s y m p t o t i c freedom. That would i n c r e a s e c o n f i d e n c e i n t h e a c c u r a c y o f t h e hadron exchange p o t e n t i a l s f o r r > r o .

The c o n s t a n t t e r m s o f t h e £ - m a t r i x , f 0 a r e n o t d e t e r m i n e d by t h e i n t e r i o r Hamiltonian and may b e adjus@d i n t r y i n g t o f i t t h e a v a i l - a b l e d a t a . The r, i s n o t f u l l y determined b u t i s c o n s t r a i n e d by t h e t h e o r y t o 0. 8 r e u c r o < r The r e a , c o r r e s p o n d i n g t o t h e e q u i l i b r i u m

e a -

r a d i u s o f t h e bag modei R ( o r t h e r a d i u s o f confinement p o t e n t i a l eu

dominance i n c o n s t i t u e n t q i a r k m o d e l s ) , i s a s t r i c t upper bound on t h e r e q u i r e m e n t o f a s y m p t o t i c freedom i n t h e i n t e r i o r . I n f a c t l a t t i c e QCD c a l c u l a t i o n s i n d i c a t e a f i n i t e t r a n s i t i o n r a n g e between asymp- t o t i c freedom and c o n f i n e m e n t 8 , , s o t h a t r, needs t o b e l e s s t h a n r

e u l p r o b a b l y by 1 0 % o r more. The lower bound o f 0.8 reu i s imposed by t h e r e q u i r e m e n t t h a t t h e QCD model f i t t o t h e meson and baryon spec- trum be meaningful. That f i t assumed a s y m p t o t i c freedom, and h a l f t h e volume c o n t r i b u t i n g t o t h e mass i s i n t h e r e g i o n R>0.8 R

eq' The R-matrix method t h e n e n a b l e s o n e t o p o s e t h e f o l l o w i n g q u e s t i o n s :

1) Can one s a t i s f y a l l t h e above c o n s t r a i n t s and t h e a v a i l a b l e hadron r e a c t i o n d a t a w i t h a g i v e n QCD model?

2 ) I f q u e s t i o n 1 i s answered p o s i t i v e l y , what phenomena a r e p r e d i c t e d a t h i g h e r e n e r g y and how d o e s one r e c o g n i z e t h e i r QCD o r i g i n ?

I n t h e f o l l o w i n g a p p l i c a t i o n t o t h e nucleon-nucleon i n t e r a c t i o n we s h a l l s e e t h a t q u e s t i o n 1 d o e s n o t always have a p o s i t i v e answer, t h u s r u l i n g o u t some QCD models which a r e s u c c e s s f u l i n t h e meson and baryon spectrum s e c t o r . For t h o s e t h a t a r e s u c c e s s f u l , i n e l a s t i c r e s o n a n c e s a r e p r e d i c t e d w i t h p r o p e r t i e s c h a r a c t e r i s t i c o f t h e i r QCD o r i g i n .

I11 - A p p l i c a t i o n t o t h e Nucleon-Nucleon Svstem

J a f f e and LOW^ f i r s t a p p l i e d t h e R-matrix method t o t h e QCD d e g r e e s o f freedom i n t h e approximation t h a t r o = r and t h a t t h e e x t e r n a l

eu

i n t e r a c t i o n v a n i s h e d . A s such it i s c a l l e d t h e P-matrix method.

They chose r a s t h e y r e g a r d e d t h e boundary a s a dynamical conse- eq

quence o f confinement. We view i t , a s a p p r o p r i a t e t o R-matrix t h e o r y , t o b e a m a t h e m a t i c a l boundary c o n s t r a i n e d by t h e adequacy o f t h e H a m i l t o n i a n s i n t h e two r e g i o n s . I t h a s no r e l e v a n t dynamical c h a r a c t e r i s t i c s , such a s t h i c k n e s s , s u r f a c e t e n s i o n , e t c . I n Ref. 3 t h e P-matrix method was a p p l i e d t o t h e meson-meson s e c t o r and i n Ref. 4 t o t h e meson-baryon s e c t o r . The lower energy s t a t e s of t h e q 2 q 2 and q 4 q c o n f i g u r a t i o n s were r e l a t e d t o meson-meson and meson- baryon phase s h i f t s , b o t h r e s o n a n t and n o n - r e s o n a n t . The P-matrix

poles (wave function zeros) at r agreed with the energies of multi- eu

quark states w within 100 MeV ani the residues Pi were 20-100%

i

larger than the theoretical value. In spite of these differences the regularity of the identification in all channels was impressive.

However when the P-matrix approximation is applied to the nucleon- nucleon system5 the data requires that Pibe a factor of five times the theoretical value, in addition to a mismatch of the wi and the P-matrix poles by about 100 MeV. This difficulty is amellorated by including an external potential-matrix (that couples the nucleon and isobar channels)' and especially by allowing r o < r (under the constraints described in Section 2). eq

Fig. 2 illustrates how the experimental and theoretical constraints are imposed on the boundary condition. The solid curves are the

energies of the lowest s, corresponding

3.4

-

3.2 -

3.0 -

-

0 2

.c 1 2.6 -

b '-2.4

-

2.2 -

2.0 -

1.8 ^{I I I I I I I}

'0.6 0.8 10 1.2 1.4 1.6 1.8

r,,,, (f m) 1.14 R ( f rn)

Fig. 2 - Bag state energies (- ) and experimental f-matrix pole energies (----I as a function of relative radius for the 'so and 3 ~ 1

NN channels.

to the S1 and 'so nucleon-nucleon states. They are shown for three different QCD models; (i) the MIT ~ a g " , (ii) the Cloudy Bag" and

(iii) the CHP Bag12. The dashed lines are the shortest range zeros of the wave functions determined by the external interaction and the known phase shifts for TL<l GeV. It can be seen that the latter intersect the former for the MIT Bag, and a short extrapolation of the latter intersect the former for the Cloudy Bag at ra0.9 r

es

:

satisfying our criteria. The CHP Bag curves intersect the experl- mental ones at the unstable ro>rea position, which would collapse into (unseen) states just above eiastic threshold. A crossing at a smaller radius would have to be at ro<0.8 r even if the dashed lines were extrapolated in a very non-lineaFq fashion.

The predicted resonances of the CHP Bag are inconsistent with data.

The MIT Bag is inconsistent with the enerqy dependence of the phase shifts at TT,5800 MeV because of the large value of r, necessitated by

-

the energy match. Such a large value requires that the phase shifts decrease too rapidly with energy. The only way to cancel that effect is to make p so large5 that the pol& of the f-matrix dominates the constant term over the low energy region. i

The Cloudy Bag model has a smaller r, and there is a choice of the f0 which fits the phase shift data. Then resonant structures are pre- dicted at w.=2.63 GeV in the 3~ - 3 ~state and at w.=2.70 GeV in the

1 1 1 1

'so state. The phase shifts for these structures have been shown in Ref. 6, and the 'so result is reproduced in Fig. 3. The change of 6 ('SO) and of r l ( 'so) over the 50 PleV width of the structure is sub- stantial and the effects in the 3~ - 3 ~ 1 state are larger. Because

1

of the low weight of these partial waves among the many partial waves at this energy, the effect on observables is small, but observable, as we shall see.

Fig. 3 - The (a) phase shift S and (b) elasticity rl for the NN('s~) channel coupled to the NA ('DO), AA('So) and NN* (1440) ('s ) channels

0 and to the [q( ' ~ 1 ) - 1 configuration of the Cloudy Bag model.

2

Before looking at the consequences of the Cloudy Bag model pre- diction in,more detail we remark that one can surmise that models that have both quark self-energy (such as the CHP) and gluon self-

e n e r g y c a v i t y t e r m s , o r o t h e r v a r i a t i o n s , may have r, s m a l l e r t h a n i n t h e Cloudy Bag model. However, a lower l i m i t on r, i s t h e c o n s t a n t f - m a t r i x ~eshbach- omo on'^ r a d i u s o f 0 . 7 4 fm; a s t h e Wigner c a u s a l i t y c o n d i t i o n a p p e a r s t o be v i o l a t e d f o r s m a l l e r v a l u e s . Examination o f F i g . 2 i n d i c a t e s t h a t t h e e n e r g i e s o f t h e f - m a t r i x p o l e s , and hence o f t h e s e f i r s t QCD dominated r e s o n a n c e s a r e l i k e l y t o b e bounded by 1 . 5 GeV < T <4.5 G e V .

L

I V - QCD S i q n i f i c a n c e o f t h e Resonances

The dominance o f t h e QCD d e g r e e s o f freedom i s measured by t h e c o n t r i b u t i o n t o t h e p r o b a b i l i t y o f t h e wave f u n c t i o n f o r r<r,.

The c o n t i n u i t y c o n d i t i o n s and G r e e n ' s Theorem e n a b l e o n e t o r e l a t e t h i s p r o b a b i l i t y t o t h e f - m a t r i x p o l e p r o p e r t i e s and t h e wave

f u n c t i o n a t r,. The r e s u l t s a r e ~ i v e n i n Ref. 6 , and F i g . 5 o f t h a t r e f e r e n c e shows t h a t t h e f r e e q u a r k c o n t e n t i s indeed dominant o v e r t h e r e s o n a n c e , and s u p p r e s s e d e l s e w h e r e f a r below t h e f r e e wave f u n c t i o n l e v e l .

I t f o l l o w s t h a t t h e r e s o n a n c e p r o p e r t i e s a r e a d i r e c t r e f l e c t i o n o f t h e f r e e quark d e g r e e s o f freedom. On t h e o t h e r hand, f o r t h e d e u t e r o n t h e f r e e q u a r k p r o b a b i l i t y i s o n l y 9 % . Thus d e u t e r o n p r o p e r t i e s a r e dominated by n u c l e o n i c , i s o b a r i c and mesonic d e g r e e s of freedom u n t i l momentum t r a n s f e r s a r e l a r g e enough t o emphasize t h e s h o r t r a n g e r e g i o n .

V - Nucleon-Nucleon S p i n E f f e c t s f o r T, < 1 . 5 G e V

For T c 1 . 5 GeV some s t r u c t u r e s have.shown up i n s p e c i f i c s p i n L

o b s e r v a b l e s l ' s u c h a s AaL b u t complete s e t s o f d a t a a t s e v e r a l e n e r g i e s have been r e q u i r e d t o d e t e r m i n e t h e p a r t i a l wave p o s i t i o n , w i d t h and i n e l a s t i c i t y . The s t r u c t u r e s i n d and T) a r e n o t v e r y r o - nounced b u t do show r e s o n a n t f e a t u r e s i n an Argand p l o t f o r t h e 'D2 and 3 ~ c h a n n e l s , and p e r h a p s a l s o t h e 3 3 ~c h a n n e l , a s d i s c u s s e d 0 a t t h i s c o n f e r e n c e .

F i g . 4 - Re@s and I m @ s f o r pp s c a t t e r i n g , determined by t h e ' ₀

p h a s e s o f F i g . 3 and t h e o t h e r p a r t i a l waves e x t r a p o l a t e d from t h e models o f Ref. 9.

These low e n e r g y T=l s t r u c t u r e s a r e w e l l e x p l a i n e d , even r e q u i r e d , by i s o b a r c h a n n e l c o u p l i n g s among t h e N N , N A , A A and NN* (1440) c h a n n e l s . I n t h e T=O c h a n n e l s t h e l o w e s t i n e l a s t i c t h r e s h o l d s a r e i n t h e A A and NN* c h a n n e l s . Allowing f o r t h e w i d t h s o f t h e A and N*

one can p r e d i c t t h a t t h r e s h o l d e f f e c t s b e g i n a t TLzl.O GeV, a s shown i n F i g . 6 o f Ref. 6. T h i s may be t h e t r u e n a t u r e o f t h e s o - c a l l e d

"Kamae r e s o n a n ~ e " ~ ~ f o r which o t h e r d a t a 1 6 i n d i c a t e s an e f f e c t o v e r a l a r g e energy r a n g e above t h r e s h o l d r a t h e r t h a n a narrow r e s o n a n t s t r u c t u r e .

V I - S i g n a t u r e s o f t h e F r e e Quark Dominance

Using o u r r e s u l t s i n t h e ' S c h a n n e l f o r t h e Cloudy Bag model ( F i g 3 ) and t h e o t h e r T = l p h a s e s e x e r a p o l a t e d from t h e c o u p l e d c h a n n e l model o f Ref. 9 a s f i t t e d t o t h e d a t a f o r TL2800 MeV w e can p r e d i c t t h e s c a t t e r i n g a m p l i t u d e s and o b s e r v a b l e s i n t h e v i c i n i t y o f t h e r e s 0 n a n c e s . A ~ shown i n F i g . 4 t h e ReOs i s i n s e n s i t i v e t o t h e

r e s o n a n c e . But t h e I m O s v a r i e s by more t h a n 1 0 % o v e r t h e r e s o n a n c e w i d t h a t s m a l l a n g l e s (<15O) and n e a r 90°.

- -

a r e o b s e r v a b l e . The e f f e c t i s more s p e c i f i c i n AT,-, a t o t h e r a n g l e s

l l

a s shown i n Fig. 5. Bumps o f AA =0.1 a p p e a r a t 51.5O and 64.8c0, and a s m a l l e r bump a t 21.2O. YY

..ad. 1.93 GoV

-

--

-0.4

O* 30q 60' 90'

0c.m.

F i g . 5 - The s p i n c o r r e l a t i o n o b s e r v a b l e A a s ( a ) a f u n c t i o n o f a n g l e f o r e n e r g i e s n e a r r e s o n a n c e and ( b ) YYa f u n c t i o n o f energy f o r s e v e r a l s e n s i t i v e a n g l e s . The model i s t h a t o f F i g . 4 .

These are observable variations over a convenient energy interval.

(The detailed shapes of the energy dependence are sensitive to the background phases, which are for now a model extrapolation from lower energy data.) We have not spotted any other observable as sensitive as Avv. In particular, Ax, shows little sensitivity. A

1 1 1

similar prediction of observables for the T=O case has yet to be made, but the larger variation of the resonance phases in the 3 ~ 1 -

state suggest that larger variations in observables will be D1indicated.

The most obvious characteristics obtained from elastic scattering are the 50 MeV width of the structures and the 70 MeV splitting between the 'so and 3 ~ st.ructures. 1 The former is model independent

-

because it derives from the small fractional parentage coefficients (<Nk=.11,<Ai=.09). The latter is model independent because it is due to 'the color-magnetic splitting, which is fixed by the N-A splitting for each model.

Because of the importance of measuring the isospin splitting and because of the expected large T=O effects, it is important to measure the np as well as the pp observables.

Because the open channels in the core are entirely in the 'so NN and A A channels (the other 80% of the core is composed of hidden color channels), and because p,rENN i EAA,there must be a strong variation of the A A production as one passes through the resonance. One has the S wave AA production amplitude

The result is sensitive to the constant background term fONN,AA.

If that quantity is small, AAA increases slowly with w. If it is large, there is a sharp dip at an energy just below wD due to inter- ference of the pole with the background. Fig. 6 illustrates the result for our Cloudy Bag model case. One notes that in this case the large, sharp dip in the two-pion production through the AA channel would be compensated by the growth in two-pion production through the NN* channel (the channels affect each other through their common coupling to the NN channel). However the two-pion charge distribution, angular correlations to the final nucleons and the spin correlations of those nucleons differ for the two channels.

Therefore measurements can isolate the A A production dip. The strong variation of A A production is characteristic of the NN, AA content of six quarks in the IS+ state. The particular type of variation depends on the QCD model through foNNIAA.

VII

-

Other low lying NN channels will have resonances split fro? the 'so

and 3 ~ 1by model insensitive color-magnetic effects. The S2(AA) configuration (connected to the 5 ~(NA) 2 and 1 ~ (NN) via long range 2 interactions) and the 7 ~ 3 ( A A ) configuration (connected to D3 (NN) )

are expected to be about 110 MeV above the 'so in mass. Their

TL (MeV)

F i g . 6 - Two-pion p r o d u c t i o n from t h e NN ( ' s o ) model d e s c r i b e d i n Fig. 3 , t h r o u g h t h e A A ( ' s o ) c h a n n e l (-) and t h e NN* ( ' s ) c h a n n e l

- -

w i d t h s a r e e x p e c t e d t o b e narrow b e c a u s e t h e y a r e a l s o 80% hidden c o l o r and have an a n g u l a r momentum b a r r i e r t o t h e NN c h a n n e l . When s t r a n g e q u a r k s a r e i n c l u d e d i n t h e 'SI _- q u a r k s t a t e s t h e n t h e N-A s p l i t t i n g d e t e r m i n e s t h e s t r a n g e quark2mass and t h e r e s u l t a n t r e s o n a n c e s p l i t t i n g . Because ',<re, t h e s e s t a t e s a r e e x p e c t e d t o be s e v e r a l hundred. MeV abovs t h e p r e d i c t i o n s o f t h e M I T Bag model. We t h e r e f o r e e x p e c t t h e H ( A A ) t o be i n t h e continuum. E x p l o r i n g t h e s e r e s o n a n c e s r e q u i r e s A , C and ^E beams.

O r b i t a l e x c i t a t i o n s o f t h e q u a r k s w i l l l e a d t o s t a t e s w i t h a b o u t 0.5 GeV more mass t h a n t h e lower o r b i t a l e x c i t a t i o n . Col$.ective e f f e c t s such a s l e a d t o deformed bags may d e c r e a s e t h i s s p l i t t i n g .

I n t h e meson-meson and meson-baryon s e c t o r s t h e c h o i c e o f r, s l i g h t l y s m a l l e r t h a n re_ can improve on t h e r e s u l t s o f Refs. 3 and 4 . I n

=Y

t h e n u c l e o n - a n t i n u c l e o n s e c t o r p a s s a g e t h r o u g h q2q' c o n f i g u r a t i o n s w i l l l e a d t o narrow r e s o n a n c e s b e c a u s e o f t h e a n n i h i l a t i o n and c r e a t i o n o f q u a r k p a i r s . A Brookhaven np a n n i h i l a t i o n experiment by Lowenstein e t a 1 h a s seen a narrow s t r u c t u r e ( < I 7 MeV) j u s t above e l a s t i c t h r e s h o l d , a t 11:1980 MeV.

I f g l u o n s a r e added t o t h e c o n f i g u r a t i o n s one may e x p e c t s t r u c t u r e s a t s t e p s o f 100-200 MeV f o r e a c h gluon.

V I I I - C o n c l u s i o n

A v e r y r i c h s p e c t r u m o f QCD r e s o n a n c e s i s e x p e c t e d i n hadron-hadron r e a c t i o n s . Each o n e t h a t i s i d e n t i f i e d can g i v e v e r y s i g n i f i c a n t i n f o r m a t i o n a b o u t QCD.

The R-matrix method i s q u a n t i t a t i v e and p r e d i c t i v e . I t r e l a t e s m u l t i - h a d r o n p r e d i c t i o n s t o s i n g l e hadron r e s u l t s v i a a QCD model.

The r e s u l t i n g s t r u c t u r e p r e d i c t i o n s f o r T >800 MeV a r e n o n - t r i v i a l L

and o b s e r v a b l e ( a t l e a s t i n a p h a s e s h i f t a n a l y s i s , b u t sometimes a s bumps i n a n o b s e r v a b l e ) .

Some o f t h e o b s e r v a t i o n a l r e s u l t s c a n b e u s e d t o i d e n t i f y t h e QCD n a t u r e o f t h e s t r u c t u r e ( l e v e l s p l i t t i n g s , w i d t h s and p r o d u c t i o n c h a n n e l s ) . O t h e r r e s u l t s , s u c h a s t h e a b s o l u t e e n e r g y of r e s o n a n c e s and d e t a i l s o f t h e i r s h a p e and p r o d u c t i o n c h a n n e l s , w i l l p u t restric- t i o n s on t h e p r o p e r t i e s o f QCD models.

The e x p e r i m e n t s t h a t can i d e n t i f y a n d a n a l y z e t h e s e s t r u c t u r e s need p o l a r i z e d p r o t o n , n e u t r o n and a n t i - n u c l e o n beams up t o 1 0 GeV and p i o n and kaon beams o f a few GeV. T h i s r e q u i r e s an a c c e l e r a t o r t h a t p r o d u c e s a n i n t e n s e p r i m a r y beam o f p o l a r i z e d p r o t o n s .

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