SPIN EFFECTS IN LARGE ANGLE TWO-BODY REACTIONS AT HIGH ENERGY

HAL Id: jpa-00224532

https://hal.archives-ouvertes.fr/jpa-00224532

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

SPIN EFFECTS IN LARGE ANGLE TWO-BODY REACTIONS AT HIGH ENERGY

G. Nardulli

To cite this version:

G. Nardulli. SPIN EFFECTS IN LARGE ANGLE TWO-BODY REACTIONS AT HIGH ENERGY.

Journal de Physique Colloques, 1985, 46 (C2), pp.C2-211-C2-215. �10.1051/jphyscol:1985221�. �jpa- 00224532�

SPIN EFFECTS IN LARGE ANGLE TWO-BODY REACTIONS AT HIGH ENERGY G. Nardulli

Centre de Physique Théorique, CNRS, 13288 Marseille, France and

Dipartimento di Fisica, Università di Bari, I.N.F.N., Sezione di Bari, Italy

Résumé - Les effets de spin dans les réactions à deux corps à grands angles et hautes énergies constituent un moyen de discernement entre les différents modèles décrivant les processus exclusifs à courtes distances ; les résultats du modèle des quarks massifs sont comparés aux données expérimentales, à la QCD perturbative et aux prédictions du modèle de diffusion par échange d'un quark.

Abstract - Spin tests in the large angle two-body reactions at high energies can be used as a tool to discriminate among different models of exclusive processes at short distances ; results from the Massive Quark Model are compared to experimental data and perturbative QCD and Quark Interchange Model predictions.

In this paper I shall discuss a few two-body reactions at high energy and large angle, i.e. large s,t. From the theoretical point of view, the reason to study such processes lies on the fact that in this region perturbative QCD is available and several predictions of the theory can be tested. It is fair to say that at the present experimental energies (typically |t| ;£ 10 GeV ) one may still expect non asymptotic contributions (c»m/Q) and care must be taken in comparing QCD predictions with the experimental data ; nonetheless some trend should be seen in the data if we are using the correct, and correctly understood, theory of strong interactions.

For all the reactions we are dealing with, perturbative QCD has a very clean predict- ion, namely the helicity conservation sum rule, which states that, in the asympto- tic limit

51 \

= II,, (1)

initial final

i.e. the sum of all the helicities X of initial hadrons must be equal to the sum of all the hadron helicities X „ , in the final state / l / . This result holds at all the orders of the perturbative expansion and stems from two features of the QCD description of exclusive processes :

i) the fundamental QCD interaction is of the type Yu, , thus conserving active quark helicities if m = 0.

q

ii) the sum of the interacting quarks'spin along the hadron momentum is equal to the hadron spin.

The helicity conservation rule (1) has far-reaching consequences in the following reactions :

B1B2 - * B 3 B4 ( 2 )

MB » M'B' (3) at large s,t. Before discussing them, however, I wish to summarize the general

assumptions of an alternative approach to large angle high energy two-body reactions, which is based on the Massive Quark Model (MQM) and its more refined version Quark Geometro-Dynamics (QCD) /2/. The analysis of this model and its predictions for processes (2) and (3) will provide a theoretical contrast to perturbative QCD from

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985221

C2-212 JOURNAL DE PHYSIQUE

which, hopefully, a b e t t e r understanding of t h e r o l e played by t h e s p i n a t s h o r t d i s t a n c e w i l l emerge.

The MQM i s a phenomenological approach t o t h e s h o r t d i s t a n c e i n t e r a c t i o n s which i s e q u i v a l e n t by a n a p p r o p r i a t e mathematical transformation, t o t h e Quark Parton Model (QPM), b u t i n c o r p o r a t e s quark confinement e x p l i c i t l y . As an example of t h i s approach one can consider 6 ( e f e - 3 hadrons). I n t h i s c a s e , a s i n another s i m i l a r approach, Q 2 d u a l i t y between f r e e quarks and bound s t a t e s /3/, one d e s c r i b e s t h e process of production of hadrons from a highly v i r t u a l photon a s a two-step process, where t h e photon produces a J = 1 vector meson resonance, of mass Mn and electromagnetic coupling f n , which then decays i n t o hadrons. I t i s well known /3/, /4/ t h a t such a d e s c r i p t i o n i s e q u i v a l e n t t o QPM, giving t h e same r e s u l t f o r t h e r a t i o R :

ete- ^{~ ~} R = 3

'5-

.

P+P- - - 0

.

sum r u l e s /s/. S i m i l a r l y one can consider t h e quark quark s c a t t e r i n g amplitude G which i s depicted i n Fig. 1. The MQM describes i t a s a sum over i n f i n i t e l y many reso- qq nances belonging t o two f a m i l i e s : pseudoscalar (with a coupling d< t o t h e quarks) and v e c t o r family (with both l o n g i t u d i n a l and t r a n s v e r s e couplings t o t h e q u a r k s ) .

1

(a) (bl

F i g . 1

-

As a consequence, t h i s model p r e d i c t s t h e p o s s i b i l i t y of h e l i c i t y f l i p s among a c t i v e quarks, i n c o n t r a s t t o QCD-inspired models where, a s we have a l r e a d y s t r e s s e d , h e l i - c i t y i s conserved i n t h e quark-quark s c a t t e r i n g . I t must be s a i d t h a t l a r g e angle two-body r e a c t i o n s supply a f i e l d of i n v e s t i g a t i o n s where t h e MQM o r

du dual it^

models s e n s i b l y d i f f e r from QPM and QCD ; t h i s i s a t variance with t h e c a l c u l a t i o n of Re+e- o r t h e Weinberg sum r u l e s where h e l i c i t y f l i p s cannot appear. As a f i n a l comment on t h i s approach, couplings and masses of t h e resonances appearing i n F i g . 1 can be c a l c u l a t e d i f one has a reasonable p o t e n t i a l among quarks j f o r confining p o t e n t i a l s , r e g u l a r a t t h e o r i g i n , one o b t a i n s t h a t asymptotically masses a r e a s follows :

M : ~

where k i s a c o s t a n t and n , k a r e t h e r a d i a l and o r b i t a l quantum numbers ; a s f o r t h e wavefunctions, they can be c a l c u l a t e d by t h e same r e l a t i v i s t i c wave equations t h a t g i v e meson and baryon masses.

Let us now consider p r e d i c t i o n s of t h e MQM f o r processes ( 2 ) and ( 3 ) and compare them t o some c a l c u l a t i o n s based on t h e Quark lnterchange Model ( Q l M ) which, although not a d i r e c t consequence of p e r t u r b a t i v e QCD, nonetheless s h a r e s some of i t s features ( t h i s i s not s u r p r i s i n g a s one can e a s i l y show t h a t Q I M i s t h e l i m i t of QCD when

N c ->a).

I s h a l l consider only two c a s e s / 6 / : pp

+

a s discussed a t l e n g t h i n /6/ j from t h i s a n a l y s i s a s e t of h e l i c i t y amplitudes can be calcul.ated /6/ and t h e following r e s u l t s a r e obtained :

i ) t h e d i f f e r e n t i a l c r o s s s e c t i o n i s given by

where mo N 1-2 GeV i s a parameter and F($. a c a l c u l a b l e f u n c t i o n j t h e energy depen- dence i n e q . ( 5 ) reproduces q u i t e well t h e a v a i l a b l e experimental d a t a /6/.

i i ) For pp 4 pp s c a t t e r i n g t h e asymmetry parameters ANN, ALL, ASS a t

TcM

a r e given by

A = + 0.97

NN A = -0.02

LC A SS = -0.01 ( 6 )

These r e s u 1 . t ~ should be compared with t h e Q l M asymptotic p r e d i c t i o n s a t

qM=

Notice t h a t t h e h e l i c i t y conservation r u l e ( 1 ) only g i v e s A - -A

.

A _NN = 0.59

*

iii) I n t h e case of pn+pn s c a t t e r i n g t h e MQM p r e d i c t i o n s f o r t h e asymmetry parame- t e r s a t 90° a r e a s follows :

A N N = + 0.93 ALL = + 0.02 ASS = f 0.02 ( 9 )

whereas Q I M p r e d i c t s a t 90° /8/ :

A N N = - 0 . 4 4 A L L = + 0 . 4 4 A S S = + 0 . 4 4 ( 1 0 )

I want t o s t r e s s t h a t predictions ( 9 ) and (10) a r e q u i t e d i f f e r e n t j i n p a r t i c u l a r t h e MQM value f o r t h e parameter A N N d i f f e r s a l s o i n s i g n from t h e value predicted by QIM : a measurement of t h i s q u a n t i t y would c l e a r l y d i s c r i m i n a t e between t h e two models. F i n a l l y t h e p r e d i c t i o n f o r t h e r a t i o r = d G ( ~ n + pn)/d6(pp cp pp)1900

r = 0.48 (MQM) r = 0.59 (QIM)

whereas a t P ⁴ 12 GeV one has / l o / LAB

r = 0.50

*

MB+ M'B

C2-214 JOURNAL DE PHYSIQUE

Let us f i r s t l y c o n s i d e r some p r e d i c t i o n s from t h e MQM approach /6/ t h e r e l e v a n t diagrams a r e depicted i n Fig. 3 ; t h e r e l a t i v e normalization between

4,

4

$ =Ita

t b

Fig. 3

-

k

Let us consider t h e following processes

Reactions i n Eq.(14) a r e a l l suppressed i n t h e MQM a t l a r g e s , t j MQM p r e d i c t i o n s f o r d6/dt of processes i n Eq.(15) a r e g e n e r a l l y a f a c t o r of 2-4 lower than f o r f f A p e l a s t i c s c a t t e r i n g j t h e A+ production process i n Eq.(16) depends s t r o n g l y on t h e value of t h e parameter j f o r pLAB = 12 GeV and $CM= 90° one o b t a i n s

d6/dt N cm2/~ev2.

The case of 9 - production i s p a r t i c u l a r l y i n t e r e s t i n g a s i t provides a f u r t h e r s p l i t between p e r t u r b a t i v e QCD and MQM p r e d i c t i o n s . I f one looks a t t h e angular d i s t r i b u t i o n of &e 'If- coming from t h e $-decay i n t h e resonance r e s t frame one has g e n e r a l l y ( 8 t h e polar angle and IQ t h e azimuthal a n g l e ) :

-

d Z * ~ c o s 2 $ +

5

d c o s % d p

-

- 2 s i n ~ $ s i n \ p

'5/6= ^d+/k

(19)

G10/6_

*

i . e . t h e a n g u l z d i s t r i b u t i o n i s dominantly of t h e type s i n 2 $ s i n 2 y

This r e s u l t i s i n q u a l i t a t i v e agreement with t h e d a t a presented by t h e Brookhaven- Massachusetts-Minnesota c o l l a b o r a t i o n a t t h i s Symposium. On t h e c o n t r a r y , a s a consequence of t h e h e l i c i t y conservation r u l e ( 1 ) one o b t a i n s t h a t d ⁼ 6-, which generates a completely d i f f e r e n t angular d i s t r i b u t i o n where a c o s q 'contribution i s expected. Let us f i n a l l y mention a f u r t h e r p r e d i c t i o n of t h e MQM a t $CM= 90° :

G. Bunce a t t h i s Symposium has presented t h e r e s u l t R M 1 with some uncertainty from t h e Backwund, which does n o t r u l e out t h e p r e d i c t i o n ( 2 1 ) .

I n conclusion s p i n t e s t s f o r two-body r e a c t i o n s a t high energy and l a r g e angle provide a s e n s i t i v e way t o d i s c r i m i n a t e among d i f f e r e n t models of exclusive proces- s e s i n t h e p e r t u r b a t i v e region j more experimental d a t a i n t h e f u t u r e w i l l give us, hopefully, a deeper understanding of t h e quark dynamics a t s h o r t d i s t a n c e s .

REFERENCES

1 . BRODSKY S.J. and LEPAGE G.P., Phys. Rev. D24 (19811, 2848.

2. For a review s e e G. PREPARATA, ~ r o c e e d i n g a 9 7 4 Erice Summer School,

Ed. A . Z i c h i c h i ( ~ c a d e m i c P r e s s , New York 1975), p. 54, and Proceedings 1978 E r i c e Summer School, Ed. A . Z i c h i c h i (Academic P r e s s , New York, 1979), p. 727.

3. BRAMON A., ETIM E., and GRECO M., Phys. L e t t . 41B (1972)) 609.

4. CEA P . , NARDULLI G . , and PREPARATA G., Z. phys.G ( 1982), 135.

5. CEA P., COLANGELO P., NARDULLI G., PAIANO G., and PREPARATA G., Phys. Lett.

1288 (19831, 225.

6. ~ U L L I G., PREPARATA G., and SOFFER J . , "Large Angle Two-Body Reactions a t High Energy", t o be published i n Nuovo Cimento A .

7 . CHIAPPETTA P. and SOFFER J., Phys. Rev. !@ (1983), 2162.

8. FARRAR G.R., GOTTLIEB S., SIVERS D., and THOMAS G.H., Phys. Rev. D20 (1979)) 202 3 BRODSKY S. J

.

9. CRABB D.G. e t a l . , Phys. Rev. L e t t . 41 (1978)) 1257.

10. STONE J.L. e t a l . , Phys. Rev. L e t t .

3