L~TT:ER~E AL NUOVO CIMENTO VOL. 33, S . 13 27 M a t z o 1982

1- Glueball and OZI-Violating Couplings.

S, M~NA~I

Department , of Phys ics , Osaka City Univers i ty - S u m i y o s h i - k u , Osaka 558, J a p a n

( r i cevu to il 13 Genna io 1982)

Since t h e (KK~) p e a k a t 1.44 GeV (1) was o b s e r v e d in J / ~ - ~ v X , v a r i o u s a p p r o a c h e s to g luon -g luon i n t e r a c t i o n s h a v e b e e n m a d e b y m a n y a u t h o r s (~). B u t we t h i n k i t is n e c e s s a r y to s t u d y n o t on ly t h e g lueba l l s w i t h even C, b u t also t h o s e w i t h o d d C. P re - v ious ly we h a v e i n v e s t i g a t e d t h e h a d r o n i c J / ~ p r o d u c t i o n (8) due to t h e o r d i n a r y q u a r k - a n t i q u a r k fus ion v i a 0 Z I - v i o l a t i n g coupl ings (4) for w h i c h t h r ee -g luon e x c h a n g e is re- spons ib le . I f t h e 1- g lueba l l ex is ts , howeve r , i t also p l ays an i m p o r t a n t ro le in t h e r eac t ion .

T h e p u r p o s e of t h i s p a p e r is to sugges t a poss ib le v e c t o r d o m i n a n c e m o d e l for t h e i n t e r a c t i o n s b e t w e e n t h e 1- g lueba l l a n d t h e v e c t o r q~(QQ) s t a t e a n d to p o i n t o u t a pos- s i b i l i t y t h a t a p a r t f r o m t h e J / ~ p r o d u c t i o n a s soc ia t ed w i t h t h e p h o t o n , t h e h a d r o n i c p r o d u c t i o n of J/d/ p roceeds m a i n l y v i a 1- g lueba l l r a t h e r t h a n t h e p rocess of th ree - g luon exchange , t h a t is t h e m a i n r e a c t i o n m e c h a n i s m is s im i l a r to t h a t of t h e J / ~ p r o d u c t i o n v i a a p h o t o n in e+e - coll isions.

F i r s t we d iscuss t h e fo l lowing p r o b l e m : Is i t t h e g luon or t h e 1 - g l u e b a l l in QCD t h a t p l ays t h e role t h e p h o t o n p l ays in Q E D ? As is seen f r o m t h e r e a c t i o n m e c h a n i s m for e+e--~ ---> ~t+~-(~+T-), t he l ep tons be long ing to d i f fe ren t g e n e r a t i o n can be p r o d u c e d t h r o u g h a p h o t o n in t h e i n t e r m e d i a t e s ta te . Since t h e p h o t o n can couple w i t h q u a r k s as wel l as lep- tons , t h e r e a re also t h e o t h e r processes , for example , A) t h e ~ - a n d ~+ in t h e a b o v e reac- t i o n are r ep l aced b y Q a n d Q, respec t ive ly , or B) t h e e-(e+) a n d ~t-(~+) a re r ep l aced b y q (~) a n d Q (~) , respec t ive ly . I f Q a n d ~ in t h e A) process a re in a b o u n d s t a t e such as t h e J /~ , th i s m e a n s t h e J / q / p r o d u c t i o n in e+e - col l is ions wh ich is d e s c r i b e d b y t h e vec- t o r d o m i n a n c e m o d e l (see fig. l a ) ) a n d t h e V in t h e i n t e r m e d i a t e s t a t e is of course t h e mass ive p h o t o n .

(1) D. L. SaHAttRE: in Proceedings ~] the Sixth International Con]erence on Meson Spectroscopy, May1980, SLAC-PUB-2519 (1980). (~) ]~. ISHIK~.WA: Phys. Rev. Lett., 46, 978 (1981); Phys. Left. B, 101, 344 (1981); M. C~ANOWI~Z: Phys. Rev. L~tt., 46, 981 (1981); T. BARNES: Z. Phys. C, 10, 275 (1981); C. E. CARLSON, J. J. COYNE, P. M. FISHBA~E, F. GROSS and S. MESHKOV: Phys. Lett. B, 98, llO (1981); H. J. LIPKIN: Phys. Left. B, 106, 114 (1981); T. F. ~VALSH: CERN Report, TH. 3027-CERN (1981); F. E. CLOSE: preprint RL-81-066 (1981); S. MINAMI: preprint OCU-79, OCU-80 and OCU-81 (1981); S. IwAo: preprint HPICt~-093 (1981). (3) S. MINAMI and R. NAKASHI~A: Left. Nuovo Cimento, 31, 305 (1981); and Pros. Theor. Phys., in press. (') S. OKUBO: Phys. Left., 5, 165 (1963); G. ZWEI•: CERN Report TH. 412 (1964); I. IIZUKA: Pros. Theor. Phys. Suppl., 37 and 38, 21 (1966).

421

4 2 2 s . MI~AlVlI

- - " ~ - - - , s l y J~

a) b)

Fig. 1. - Process of J/'~ p r o d u c t i o n v i a a p h o t o n (a 1- g luebal l ) in c+e- (q~) collisions.

I t seems tha t in QCD, the gluon has been regarded as the part icle corresponding to the~ photon in QED. However, i t should be nof, ed tha t i) the Y in the process B) can be replaced not only by a gluon, but also by a 1- glueball and ii) the bound Q~ states such as the J /~ cannot be produced through a gluon, but through a vector g luebal l in q~ col- lisions (see fig. lb)) because gluon and glueball are the part icles with and without colour~ respectively.

Thus we can say what follows: If the 1- glueball exists, i) i t is the vector glueball ra ther than the gluon in QCD tha t p lays the role of photon in QED and ii) a possible vector dominance model can be proposed with respect to the interactions between 1- glueball and vector q~(Q~) states. Such a vector dominance model suggests a new reaction mechanism for the hadronic production or decay of the J/d/ (in general vector mesons. in the ~ Q system).

Taking the new reaction mechanism into consideration, in th is paper we wish to re-examine the description of hadronie J /~ production. Although it is said tha t at h igh energies, the reaction proceeds mainly via t h e / ' - w a v e in termedia te s tates and about 5 0 ~ of the ~'s are produced together with a photon, i t is of course impor tan t to examine the process of ord inary quark-ant iquark fusion via the OZI-violating couplings, where. the cross-section for the subprocess q~ --~ J /~ is re la ted to the width I'(J/d/--~ q~).

CAP, LSO~ and SUAYA (5) have es t imated from the simplest connected Born d iagram the rat io of q~ producing J [~ via the in termedia te state compared to q~ producing J/d/ d i rec t ly and have given a very small value of T(J /d / -~ q~) such as

(1) F(J/d/--~ q~) _~ 1 keV.

On the other hand, we have also es t imated the width from other phenomenologica~ viewpoints (z) and have obtained

(2) /~(Jld/--~ q~) _ 11 keY.

This value is considerably larger than tha t given in eq. (1). In order to examine the difference between them, we pay at tent ion to the reac t ion

mechanisms for the subproeess q~ ~ J/d/. When a c~ pa i r is created by the p roces , qq --~ 3g --~ e~ shown in fig. 2a) i t may be supposed tha t the probabi l i ty of finding the bound e~ states is considerably smaller than tha t of finding the unbound e~ states. re levant to production of charmed mesons. Probably this is one of the reasons why the value of /~(J/d/--~ q~) is p re t ty small.

Owing to the new vector dominance model suggested in this paper, however, we have another react ion mechanism

(~) C. E. CARLSOI~ a nd R. SUAYA: Phys. Rev. D, 18, 760 (1978).

1- GLU]BBALL AND 0ZI-VIOLATING COUPLINGS 4 2 ~

q:_ c a)

P

�9 "';":':-'vr Y / / / / / A ~ h c z o L r o n s ~ e + "$ hac~rons - - - - -~/JJJJJJ/JJfJ~~

o) c)

Fig. 2. - a) Reaction mechanism for creation of a c~ pair in p~ collisions, b) reaction mechanism for the J]r production via a 1- glueball in pp collisions and c) process of J]r production in e+e - colli- sions.

for t h e h a d r o n i c p r o d u c t i o n of J / ~ w h i c h is s imi l a r to t h a t for t h e J / ~ p r o d u c t i o n in e+e - col l is ions (see fig. 2b) a n d c)), w h e r e G i n d i c a t e s t h e 1- g luebal l . T h e n , eq. (2) s h o u l d b e i n t e r p r e t e d as

(2') / ' (J/~b -+ 3g --)- q~) + / ' ( J /{ , --+ G -+ q~) ,-~ 11 k e V .

A n d i t is n e c e s s a r y to c o m p a r e t h e c ross -sec t ions for J / ~ p r o d u c t i o n v i a 1- g lueba l l w i t h t h o s e due to t h e t h r e e - g l u o n e x c h a n g e process .

To t h i s pu rpose , le t us cons ide r t h e v e c t o r d o m i n a n c e m o d e l for g lueba l l t o g e t h e r w i t h t h a t for p h o t o n a n d e x a m i n e t h e r a t i o of F ( J / ~ --~ G --~ qq) to F ( J / ~ - ~ 3g -+ qq) . As is wel l known , t h e yVQ coupl ing in t h e v e c t o r d o m i n a n c e m o d e l i s exp re s sed in t h e f o r m

(3) H = ]vv V~A~ ,

a n d t h e R o y e n - W e i s s k o p f f o r m u l a (6)

(4) /~(VQ --~ e+e-) = 16ua 2

, l~(O)iSe~ ~r6 v

can be d e r i v e d f rom t h e mode l , w h e n t h e coup l ing c o n s t a n t is g i v e n b y

(5) & ~ = 2eQ~(O)m~ ~ ,

w h e r e VQ is t h e lowest v e c t o r m e s o n in t h e QQ sys tem, m v is t h e mass of t h e VQ, 9(0) is t h e v a l u e of t h e wave f u n c t i o n a t t h e o r ig in for t h e VQ, a n d eQ is t h e q u a r k charge .

(,) I~. VAN ROYEN and V. F. WEISBKOPF: NU0~)0 Cim'ento, 50, 617 (1967).

424 s. MINAMI

AS a 1- glueball-VQ in terac t ion , we can consider

(6) H = lvar~G~

w i t h the coupl ing cons tant g iven by

(7) ]vG----- ]~(O)mv',

where n is a pa rame te r . I n a p rev ious pape r (7) we h a v e shown the fol lowing results . W h e n n is equal to t as in t h e case of /wr (see eq. (5)), good fits to the d a t a for decays of the J / ~ and T can he ob ta ined and

(8) P ( J / ~ --~ G --~ hadrons)/F(J/d~ --~ 3g --~ hadrons) _~ 8 /5 .

Needless to say, t he 1- g luebal l can decay into three gluons, and P(VQ--~ 3g(G) --~hadrons) consis ts of P(VQ --~ 3g(G) --~ qq) and F(VQ-~ 3 g jets). F o r t he J/~/, however , t he ra t io o f F ( J / ~ - ~ 3g jets) to F ( J / ~ - - ~ h a d r o n s ) is p r e t t y small . T h e n we assume t h a t

(9) T ( J / 4 --~ G --~ q-q)/F(J/~/--~ 3g --~ q~) --~

,-~ F ( J / ~ -+ G --~ h a d r o n s ) / F ( J / ~ --* 3g -* hadrons) .

F r o m eqs. (2r), (8) and (9) i t fol lows tha t

(10) /~ ( J /g / -* G --~ qq) ~-- 7 k e V , and f ( J / ~ --~ 3g --~ qq) _~ 4 k e V .

On the basis of these resul ts we wish to po in t out t h a t as a reac t ion mechan i sm %hrough which ~'s are p roduced direct ly , the process v i a t he 1- gluebal l m a y be more i m p o r t a n t t h a n the three-g luon exchange process. Moreover , i t can be said t h a t in the hadron ic T produc t ion , th is t endency would be more remarkable , t h a t is t h e contr ibu- t ions f rom the fo rmer process become much la rger t h a n those f rom the l a t t e r process, since

F ( T --~ G --~ hadrons) >> F ( ~ -~ 3g --~ hadrons) for n ~

as was shown in ref. (~).

(7) S. MI~AMI: Prog. Theor. Phys, 65, 771 (1981).