IL NUOVO CIMENT0 VOL. 65A, N. 2 21 Settembre 1981

The OZI Rule and Glueballs.

S . J . LI~DE~]3AXY~Cf

Brookhaven National Laboratory (*) - Upton, 2V. jr. City College (**) - _/Yew York, N. Jr.

(ricevuto il 5 Giugno 1981)

Summary. - - The 0ZI rule works rather well but is peculiar in that an OZI-forbidden process can proceed via two successive 0ZI-allowed processes. This implies circumventing the 0ZI-forbidden diagram and also implies violation of crossing symmetry and unitarity. These pecu- liarities of the 0ZI rule are attributed to the facts of life of color con- finement. The patent failure of the OZI rule in ~-p--~$on is demonstrated in detail. I t is pointed out that, within the context of QCD, a logical explanation for this failure is the intervention of glueballs (multigluon resonances). A discussion of how to make and recognize glueballs and their importance to QCD is included.

1 . - I n t r o d u c t i o n .

The OZI rule (1), which is also referred to as the quark line rule (2), has

been of considerable value in nnders tanding certain aspects of particle phe-

nomena. I n particular, the sizable suppression of ~ decay into particles con-

ta ining no strange quarks, the even larger suppression of ~ product ion in

(*) This research was supported by the U.S. Department of Energy under Contract No. DE-AC02-76CH00016. (**) Research supported by the National Science Foundation. (1) S. OKUBO: Phys. Lett., 5, 165 (1963); G. Zw~IG: CERN Report Th 401 a114 412 (1964); J. IIZUBA: Prog. Theor. Phys. Suppl., 37-38, 21 (1966); J. hzuBA, K. OKUDA and O. Sm~o: Prog. Theor. Phys., 35, 1061 (1966). (2) S. OKU•O: A Survey o] the Quark Zine Rule (U.R. 641, Department of Physics and Astronomy, University of Rochester, N.Y., 1977).

222

THE OZI RULE AND GLUEBALLS 223

~ - p -+ qn, the suppression of J /~ decay into part icles containing no charmed quarks and the suppression of T decay into part icles containing no b o t t o m quarks follow this rule (3).

As poin ted out by the author , the OZI rule is not topological ly self-con- sistent and, in fact , two addi t ional rules had to be pos tu la ted to obta in in ternal

consis tency (4). However , the end result was t h a t the OZI rule or rules violated crossing

s y m m e t r y and uni ta r i ty . Fu r the rmore , an analysis of a BNL/CCNY collab-

orat ion exper imen t (5,6) which studied (23GeV/c) ~ : - p - > q q n was clearly

shown (7) to imply evidence for the in te rvent ion of gluebM1 resonances in the

react ion. The ma jo r purposes of th is pape r will be

1) to examine the OZI rule in the context of QCD,

2) to possibly explain its peculiar behavior (i.e. apparen t violations of crossing s y m m e t r y and nni tar i ty) as resul t ing f rom color confinement ,

3) to point out t h a t the mos t logical explana t ion for the failure of the

OZI rule in ~ - p -~ ~qn is the in te rven t ion of gluebM1 resonances and, in fact ,

point out t h a t tl~e qq sys tem in the 7:-]? -+ ~ n exper iment (5,6) is an excellent

place to search for g luebMls - - the effects of which m a y a l ready have been seen.

2. - The O Z I rule .

The OZI rule was originMly applied to part icle decays and product ion involving the singlets of ideally mixed S U3 nonets. I n these cases the singlet was an Mmost pure s~ pair . The q-meson of the 1 - - uonet was the first example .

Le t ns consider the Zweig approach for the quark line diagrams. We see t h a t

(3) a) T. APFLEQUIST, K. KANE and M. BARNETT: Annu. Rev. Nucl. Sci., 28, 387 (1978); b) W. MARCIANO and H. ])AGELS: Phys. Rep., 36, 137 (1978); c) I. J. MUZlN1CtI and F. E. PAIGE: Phys. Bey. D, 21, 1151 (1980). (4) S. J. LII~DENBAUM: Quark line diagrams, rules and some recent data, BNL 50812 (December 1977). (5) A. ETKIN, I~. J. FOLEY, J. H. GOLDMAN, W. A. LOVE, T. W. MORRIS, S. 0ZAKI, ]~. D. PLATNER, A. C. SAULYS, C. D. WHEELER, ]~. H. WILLEN, S. J. L1NDENBAUM, M. A. KRAMER and U. MALLIK: Phys. Bey. Lett., 40, 422 (1978). (6) A. ]~TKIN, I~. J. FOLEY, J. H. GOLDMAN, W. A. LOVE, T. W. MORRIS, S. 0ZAKI, ~E. D. PLATNER, A. C. SAULYS, C. D. WHEELER, E. H. WILLEN, S. J. L1NDENBAUM, M. A. KRAMER and U. MALLIK: Phys. Rev. Lett., 41, 784 (1978). (7) S. J. LINDENBAUM: ttadronic physics o] q~ light quark mesons, quark molecules and glueballs, lecture presented in X V I I I Course: The High Energy Limit, July 31- August 11, 1980, The International School o] Subnuclear Physics, Erice (London, 1981); also BNL 28498 (October 1980).

224 s . J . LINDENBAU~

r 7:+~o~- can be d r a w n as a g r a p h con ta in ing on ly connec ted q u a r k lines

(fig. l a ) ) which is considered an OZI-a l lowed process, whereas for ? - > ~:+::o~-

t h e q u a r k l ines are d is jo in ted (fig. lb)) , g iv ing us t h e so-called ha i rp in dia-

g r a m which is considered an O Z L f o r b i d d e n process (at least to a subs tan t i a l

suppress iou factor) . F igu re lc) shows the ? decay to K + K - which is an OZI-

a l lowed process.

o{ u

lu

U

U

cL } n o

I a U

.

5

~{ ' I S

U

I ~ }~~ ~cL - }~-

U

o)

Fig. 1. - a) r an OZI-al lowed process; eess; e) ? - ~ K + K -, an OZI-al lowed process.

S

}K- )S I .i{ u

S

c)

b) ?_)..~+=o=- an OZI-forbidden pro-

U

s ~ }e +

a)

S U

( }u ; j _ _ d . I �9 - _ ,. } ~ +

S U

b)

Fig. 2. - a) r an OZI-forbidden process; b) ?--~K-K+-+v:-O + via a two-step process, each of which is 0ZI allowed. ?-~K-K+--*=+=~ - (not shown) is also a two-step process, each step of which is OZI allowed.

T H E OZI RULE AND GLUEBALLS 2 2 5

l~igure 2a) shows t ha t ~ --> ~-p+ is an OZI-forbidden process. However , if we consider ~0 -~ K - K + --> ~:-p+, we have fig. 2b), which is a two-step process each of which appears to be OZI allowed and is topologically equivalent to the OZI-forbidden diagram (fig. 2a)).

Thus, in order to obtain the suppression of this process which would negate the OZI rule, the au thor postulated (4) QLR 1~o. 2, namely tha t quark lines which s ta r t in the initial s tate can only be joined together or annihi late in the initial s tate before t hey in teract with quark lines in the final state. Otherwise, one could always tu rn a disjointed diagram of the hairpin type into a topologically equivalent connected diagram.

Of course, the price of prevent ing these two-step processes is t h a t we violate crossing symmet ry and uni tar i ty . The fact t h a t the OZI rule works in spite of these ugly features and exhibits a suppression to over ~ 100 for hairpin diagrams has been considered a mystery . Later in the paper, when I consider the OZI rule in the context of QCD, I will show th a t the requirements of color confinement can probably explain this situation.

3. - QCD and OZI.

The OZI rule has found a na tura l explanat ion in the context of QCD (s). The connected diagrams for OZI-allowed processes allow a series of one -ghon exchanges wi thout violat ing color confinement; on the other hand, the disjoint

cL

1"[--{ l~ U S ~s }cp

U

I " I U n eL

a)

_ { . �9 d. / K -

U ~..

{ " 1 p ~ u ~ u n

~cL >cL ~)

Fig. 3. - a) =-p-+~n, an 0ZI-forbidden process; b) ~-p--~K+K-n-~on via a two- step process, each step of which is 0ZI allowed.

226 s . J . LINDENBAUM

or hairpin diagram requires 3-gluon exchange since the ~ is a vector (2-gluon exchange would be permissible if the ~ were a scalar).

Therefore, the OZI suppression is a t t r ibutable to the factor g6 involved in going f rom quarks to quarks via 3-gluon exchange.

We have, however, a l ready seen tha t two OZI-allowed processes can be used to el iminate the OZI-forbidden diagram and this has been shown (4.7) to be a quite general phenomenon occurring in product ion as well as decay.

For example, the typica l OZI suppression factor ~ 100 has been found (2) in the react ion ~:-p-+ ~0n, which is shown in fig. 3a).

However , this react ion can occur via a two-step process (4,7), each step of which is allowed, as shown in fig. 3b), ~-p -+ K + K - n -+ q0n.

I would like to point out t ha t what is unique here is t ha t by the two steps we have conver ted a process which requires 3-gluon exchange into one which can go by a series of single-gluon exchanges (7). This evident ly is not allowed and thus the crossing symmet ry and uni ta r i ty arguments made without taking into account this QCD fact of life are probably only applicable when one does not change the nature of a gluon exchange. I view this as an added require- men t due to color confinement.

I pointed out (a,7) tha t , if in fig. 2b) and 3b) one pulled the par t o f t h e quark

line diagram containing the ~o far enough to the left, one would again obtain the disjointed diagrams of fig. 2a) and 3a). In part icular , you cannot use a final- s ta te in teract ion as a second step or you defeat the OZI rule.

A th i rd quark line rule (7,8) is t ha t you m ay have to pay a pena l ty factor when you create a new type of quark pair (such as, for example, a ss pair) which did not exist in your initial state. In this paper we will be pr imari ly concerned wi th comparing processes in which no new types of quarks are in t roduced and thus this rule will not be relevant .

4. - The failure of the OZI rule i n (23 GeV/c) ~ - p - > ~ n .

The quark line diagrams relevant to the B ~ L / C C N Y experiments are shown in fig. 4. Inc ident ~ - mesons of 22.6 GeV/c in terac ted with protons to produce

the reactions

a) 7:-p --> K+K-K+K-n~

b) 7:-p --> ~0K+K-n,

e) ~-p -+ ~ n .

(8) H. J. LIPI(I~: Phys. Lett. B, 60, 371 (1976).

T H E OZI R U L E A N D CrLUEBALLS ~ 2 7

Figures 4a) and b) are rearrangement diagrams that are expected to have the a l lowed order of cross-section. An explicit check of the assumpt ion that rearrangement diagrams have the OZI-al lowed order of cross-section is obtained by comparing = - p - ~ K+K-~7: -p corresponding to a planar diagram from a C E R N exper iment at comparable energies wi th the B N L ~ - p - > K + K - ~ n which corresponds to a rearrangement diagram. The cross-sections obta ined for the two react ions are a ~ 0.4 ~b and a N 0.3 ~b, respectively, which shows there is no essential difference in cross-section (~,7).

r ( -

u u

�9 ~ K- ~ ~ . s~ K+

~'cl.. uA K -

s~ K+

u

1,, u cL

n a )

n -

p -

U �9

U

b)

~b

cp

K +

d

ql u

>U �9

~Ct

Fig. 4. - a) =-p-~ K+K-K+K-n,

cL > U �9 rl

~'ct

c)

b) rc-p--~ 0K+K-n,

A scatter plot of the mass of one K + K - pair chosen in a random w a y on the x-axis vs. the mass of the second K + K - pair p lot ted on the y-axis is shown in fig. 5. Thus each event is p lot ted twice. An e n h a n c e m e n t over background is seen in each of the t w o ~ mass bands. An enormous e n h a n c e m e n t over back- ground is seen where the two ~ mass bands cross. This region (i.e. the ~9 region)

2 2 8 S . J . L I N D E N B A U M

appears as a very densely populated area which is amost black. When correc- tions for resolution and double counting are made, the peak intensity in the ~ region is approximately 1500 times the adjoining background level. This clearly implies that the OZI suppression is ~pparently not working, since, if the OZI suppression were perfect, there would be no ~ events at all and thus no enhacement in the ~ region.

1.49

I

- I "

1.39

1.29 �9 : . "L . " . ' �9 . " �9 "

: : : �9 : :i : �9 . . . . . . . . . . . . . : . . . . .

. �9 . . .

. . . : . 1.19 -

i . �9 . . - . . . . . . . .

. . . . . : . . . . : � 9 : ' : . . , . " . . . . . . . '

- ,:~:.:. - . . . . : ' , , , � 9 . ' : . , :...,: - . " : . - : : . �9 . - , " . . . - . .

} . . ' - . . . " : � 9 ' . - . . : . . . .

�9 i " / . : . ' . . ' " . '" : ' : . . . . : . 1.0!

:'." " .'~: . �9 .: . : �9 . .. ". �9 . . , " . . . . . . �9 .

: ~ . . . . - . �9 . . , . . ~ ; . �9 . �9 . ".

. . . . . . . . . . . . . . . . . . . . . . �9 .

. . . , .

. . . . . �9 . . �9 �9 . . . " . �9 - .

�9 . - . �9 . . . �9 . " : " . . - . .

�9 . . . . . .

�9 . . .

�9 . - . �9

�9 ' . . : . , . ' . ' : ' . " . i ~ . ~ . . . . ' ~ . �9 " . , .

�9 . . . . . , . . . : . , - , . . .

.. : . , " . . . . . , .

:" . . . . . . , . , . . . , . . - . . . . : ) - �9 . �9 . �9 �9 .

, . . . - . . . . : , . . ~ . . . . . . ' . . �9 . . . " �9 . �9 . " . . . ..

. : . . . . . . " . ." . . . : : . . . �9 . . . - ~ .

�9 : . , . ' / ' . " - . : : . . ":: . , . '" . : . . ' : ! : :~."..: '::,:';'.','.:~" : ..."..

�9 �9 " " �9 �9 �9 �9 " - " I

1.09 1.19 1.29 1:39 1.4.9 N ( K + K - ) I

0.99

Fig. 5. - Scatter plot of K+K - effective mass for effective masses ((K+K-)I and (K+K-)=) less than 1.49 GeV/e ~. Two randomly chosen mass combinations are plotted for each event. Clear bands of $(1019) are seen with an enormous enhancement where they

overlap (i.e. ~ ) .

To see more quant i ta t ive ly w h a t is happening , we plot in fig. 6 the m a s s

spec trum of K + K - pairs f rom the react ion 7~-p --> K + K - K + K - n . l~our K + K -

combinat ions are p lo t ted for each event . In addit ion, the shaded curve is t h e

mass spectrum of l ike-sign K pairs, which can be used as an indicat ion of the ex tra background due to mul t ip le combinat ions . A v e r y clear ~ s ignal is ob-

ta ined corresponding to a peak- to -background ratio of about 4:1 . W e then

THE 0Zl R U L E AND GLUEBALLS 229

120

8O

>

~40

i I

1.0 1.1 1.2 P/(K + K-)(GeV/c 2)

Fig. 6. - The effective-mass spectrum of K+K - pairs after removing $$ events for =--p-+ K+K-K+K-n. The shaded histogram is the sum of like-sign K pairs and is an indication of background due to multiple combinations.

80

6O

:E

2O

0.99 t.09 1.19 M(K+ K-)(GoV/J)

Fig. 7. - The effective mass of each K+K - pair for which the other pair was in the $ mass band in the reaction =-p--~K+K-K+K-n.

230 S . J . LINDENBAUI~

correct b y a fac tor of two to allow for mul t ip le combinat ions, which gives 8:1. We then correct for our mass resolution~ which is abou t three t imes the ? mass

width , thus the t rue ? peak- to -background rat io is ~-- 25. Hence we see a large enhancemen t factor ~ 25 a t the ? mass.

Reac t ion c) corresponds to fig. 4c) and is an OZLforb idden reaction. To

s tudy react ion c), we select events wi th a K + K - pair in the ? mass band and

p lo t the effective mass of the other K + K - pair , and obta in the mass spec t rum

shown in fig. 7 which exhibi ts a huge ? signal corresponding to react ion c). The peak- to -background rat io is abou t 20 : 1. When corrected for the resolution,

the t rue peak- to -background ra t io is about 60:1. I f the OZI suppression were

100 %, no ? signal would be seen in fig. 4c). We, therefore, have the unusual s i tua t ion t h a t the forbidden react ion c) produces a higher ? enhancemen t over K + K - background t h a n the allowed react ion b), a l though equal enhancements

cannot be ruled out because of the possible con tamina t ion of the da ta wi th ~p pairs and the errors in corrections for combinat ional problems.

F igure 8 shows the mass spectra f o r the effective masses ( ?K+K -) and ? ?

:for o u r publ ished spec t rum (~) of ~ 100 ? ? events. The ? K + K - mass spec t rum

60O

4O0

o 200 6

I

20c

2.0 3.0

~)

i I 4.0

M (4 K )(GeV/c 2)

I 5 . 0

Fig. 8. - a) Effective-mass spectrum (corrected for acceptance) of the 0K+K - system where the K+K - does not lie in the ? band; ~:-p--~?K+K-n. b) ?? effective-mass spectrum (corrected for acceptance); ~-p-~??n.

THE 0ZI RULE AND GLUEBALLS 231

shows a broad distribution which occupies most of the available phase space,

while the T9 mass spectrum has a low effective mass peak and is restricted

to relatively low energies. Thus the 99 spectrum has a distinctly different

character t h a n the ~K+K -. Furthermore~ there is some indication tha t there

m a y possibly be some structure in the neighborhood of 2.4 GeV. I f we integrate

the two spectra, we get a ratio of reaction b) to reaction c) of less t han five,

which is a typical value for resonance-to-background ratios in allowed reac- t ions (*).

Hence we have clear evidence tha t there is no OZI suppression (perhaps

even an enhancement) in our K+K - effective-mass studies and we find even

in comparing to ta l cross-sections we are consistent with normal resonance

behavior for the second K+K - pair (after the first has made a 9) with no evidence

for OZI suppression for creation of a second ~. Therefore, we conclude tha t

OZI suppression is absent in these processes.

I shall now proceed to t reat the observations from the point of view of the

isobar model (9) which we proposed over 2 decades ago. The isobar model

never heard of OZI suppression and ignores it. We will shortly find quan-

t i ta t ive agreement of the present observations with these isobar model cal-

culations. The agreement will depend on final-state K+K - resonant inter-

actions built into the isobar model t reatment . I showed earlier in this paper

tha t such final-state interactions completely defeat the OZI rule and thus we

will show tha t the OZI rule is inoperative in these reactions.

Let us now calculate the enhancement factor expected from the point of

view of the isobar model where the 9 isobar formation probabil i ty is related

to the K+K - resonant scattering to form a % We consider the 9 as a L ~ 1,

I ---- 0 resonance of the K+K - scattering which decays back into K+K - with a branching ratio of 0.47 and into K~ ~ with a BR of 0.35. Off resonance we

assume the K+K - scattering cross-section is estimable by using the addi-

t ive quark model (AQM) to determine a(K+K -) ~ ~ a ( K J ~ ) ~ 8 mb (non-

resonance). The max im um cross-section for K+K - scattering at the resonance can then be est imated to be

a(K+K - -+ K+K -) ~ 12~ 2 X �89

t T----0

Inelas t ic i ty factor • effective BR ~ 200 mb.

(*) For example, C. BALTAY, C. V. COVTIS and M. KALELKAR: Phys. Rev. Lett., 40, 87 (1978), find that ~ production accounts for about 5% of the ~+~-~o spectrum in the reaction T:-p-+A++7:+7:-uo at 15 GeV/c. Resonance production is typically one tenth of a reaction. (9) S, J. LINDE~BAUM and R. M. STER~REIMER: Phys. Rev., 105, 1874 (1957); 106, 1107 (1957); 109, 1723 (1958); 123, 333 (1961).

2 3 2 s . J . LINDENBAUM

E s t i m a t e d enhancemen t fac tor a t the p e a k - ~

200 m b (peak resonant cross-section) 25 . 8 m b (nonresonant cross-section)

Thus we predic t an enhancemen t fac tor over background ~ 25 for the 9 peak

over background. This is indeed what we find for the first ~0.

Fo r the second % employing the isobar model, we would expect the same

enhancemen t fac tor and, as s ta ted, observe ~ 60. This t r e a t m e n t f rom the

isobar model viewpoint has no OZI suppression in it and thus the fac t t h a t

the enhancemen t found for the second ~ peak is if any th ing greater t h a n the first, bu t a t least comparab le and thus in general agreement with the isobar

model shows clearly t h a t the OZI suppression is effectively absent .

5 . - G l u e b a l l s a n d f a i l u r e o f O Z I .

My explana t ion for this comple te fai lure of the OZI suppression in ~ - p - >

--> T~n is the following. I n an OZI-forbidden react ion the in te rmedia te s ta te which connects the

two disconnected par t s of the d iagram is a collection of gluons. I f a var iable

15

10 -.....

: l o -G-

0 2.o

llnn 2.4

M(r (p)(GeV/c 2) 2.8 3.2

Fig. 9. - Observed ~ mass spectrum for the final sample ~170 r events. This spectrum is uncorrected for acceptance. ~-p--~@n, 22.6 GeV/c.

T H ~ OZI R U L E AND G L U E B A L L S 233

mass of this in termediate s tate is allowed by the reaction (as in ??) and some par t of the mass region covers existing glueball resonances, the resonances m a y lead to effectively strong coupling and the OZI rule m ay be defeated. In essence we would be looking at a diagram in which exchange of glueballs would occur. This is obviously a ve ry good way to look for glueballs and the complete failure of the OZI rule and the different shape of the ~07 and ? K + K - effective-mass spectra indicate tha t we may well have seen t h em in this reaction.

Figure 9 shows the observed ? ? spectrmn with the addit ional (unpublished) events we have obtained by fur ther analysis. Approximate ly 170 ? ? events are p lo t ted in 20 N[eV mass bins which is ~ our full-width ha l f -maximum resolution. This spect rum m a y well contain glueballs. Although there is some indication (not statist ically significant) of possible s tructure, it is clear we need much more statistics to form a conclusion.

The BNL/CCNY collaboration is prepar ing for a new exper iment with the B NL MPS I I , where drif t chambers replace the present spark chambers. We should obtain 20 t imes more statistics and thus gather ~ (3.000--4.000)~o? events in 7:-p -~ ~o?n. We believe this nmnber will allow significant observation of possible s t ructure in the spectrum and also an effective part ial-wave analysis. Therefore, we hope to be able to demonst ra te the existence of glueballs.

6. - H o w necessary are gluebal ls for QCD.

QCD is a non-Abelian gauge theory which has the following novel charac- teristics.

I) The gauge bosons which are an octet of colored vector massless gluons self-interact.

I I ) Asymptot ic freedom.

Gluon-gluon and mult igluon interactions occur with the same coupling constant as the quark-gluon interact ion and these interact ions become stronger as the energy decreases (and weaker as the energy increases).

Characteristics I) and I I ) follow from the nature of the non-Abelian gauge theory and do not occur in an Abelian gauge theory such as QED.

I I I ) In addition, QCD has a th i rd characteristic, namely color con- finement.

When considering the propert ies of gluon-gluon interactions, which be- come stronger as the energy becomes lower, and the characterist ic of con- finement, I believe one would almost inescapably be led to expect to find multi- gluon gluebM1 resonances at low energies. I n a str ict sense, there is no gauge- invar iant separation into 2g, 3g, etc. due to the self-couplings of gluons. Any numbers of gluons can couple together and t ransform into a different number.

234 s . z . LIND~NBAUM

However , a gauge- invar iant description is possible (~o). ~ever theless , the

classification b y n u m b e r of glnons is physical ly appeal ing and m a y well be meaningfu l if we judge by the success of quark model classifications. I t should

be noted t h a t simple confinement a rguments , the bag model, the quark po- t en t i a l model and lat t ice calculat ions all predic t glueball resonances (l~a3).

Therefore, if glneball resonances are NOt found, it wonld be difficnlt not

to conclude QCD is in trouble. On the other hand, the discovery of real glueballs

would be a great t r i u m p h for QCD.

7. - H o w would y o u recognize a g luebal l ?

Gluebal l s ta tes are color singlets wi th I - - - -0 , B--~ 0 (u, d, s, c, b--~ 0), d ~ can be ei ther nonexot ic or exotic. Manifes t ly exotic jpo combinat ions

occur na tu ra l ly in 2g and 3g combinat ions in cont ras t to the quark ease in which, for example , to ob ta in an exotic jPc one mns t go f rom a qq (2-quark

s ta te) to a qqqq (four-quark state). Thus, if the JPe is not exotic, t hey could appear as addi t ional singlets

resembl ing the I ~ 0 singlet of a S U3 nonet. These states could mix with

ord inary qcl mesons. One would expect the full width /~ to be reduced compared to the typ ica l

hadronic width by ~ %/OZI suppression factor for vector gluons, since you go f rom q q to glue only once. The OZI suppression factor was de te rmined for vec tor part icles which require a three-gluon in te rmedia te state. 1f one had a scalar glueball , only two gluons would be involved in the in te rmedia te state, therefore one would expect t h a t the typ ica l hadronic width would be rednced

b y ~ ~ / O Z I suppression factor. Tak ing the OZI suppression fac tor of ~ 100 and a typ ica l hadronic width

200 MeV, a ba l lpa rk figure for the expected glueball widths would be F

( 3 0 ~ 10)MeV. CA_~LSON et al. (~3) use pe r tu rba t ion theory calculations to conclude thn t

(lo) j . D. BJORKEN: SLAC-PUB-2366 (August 1979); SLAC Summer Institute on Particle Physics (1979). (11) a) H. FRITZSCH and P. MINKOWSKI: 2YUOVO Cimento A, 30, 393 (1975); b) R. L. JAFFE and K. JOHNSON: Phys. Lett. B, 60, 201 (1976); c) J. KOGUT, D. K. SINCLAIR and L. SUSSKIND: 2r Phys. B, 114, 199 (1970); d) D. ROBSON: Nucl. Phys. B, 130, 328 (1977). (1~) j . DONOGHUE: Proceedings o/ the VI International Con/erence on Experimental Meson Spectroscopy, Brookhaven National Laboratory, April 25-26, 1980 (to be published in Al l ) Con/erence Proceedings, Subseries on Particles and Fields). (13) a) J. COYNE, P. FISHBAN~ and S. MESHKOV: Phys. Left. B, 91, 259 (1980); b) C. E. CARLSON, J. J. COYNE, P. M. FISnBANE, F. GROSS and S. M~SHKOV: pre- print (1980).

THE OZI RULE AND GLUEBALLS 2 ~ 5

J = 0 and J----1 or 2g glueballs are as narrow as a few MeV or less and the ex- otics have f ' ~ 1 MeV. The use of pe r tu rba t ion theory in decays of resonant

s ta tes m a y not be accurate. They have not considered 3g glueballs and the 2g ~_ 3g t ransformat ions .

Table I (based on the da ta of COY~E et al. (,3)) shows jpc values th rough spins of 3 which are allowed (5/) and forbidden ( X ) for qq (quark model states) 2g glue-

balls and 3g glucballs. Arrows on the side of the table indicate exotic states. I f the arrow is solid, the j v c is exotic in the quark model , bu t allowed only for

3g glueballs which allow all jPc combinat ions. I f there is a do t ted arrow under the solid arrow, the s ta te is allowed for 2g as well as 3g glueballs. One should,

of course, bear in mind t h a t qq, 2g and 3g s tates of the same j p c all mix to a cer ta in extent , bu t one can expect , based on quark model classification success

and general considerations, t ha t to a reasonable ex ten t these classifications m a y hold.

Thus the discovery of a boson s ta te wi th I = 0 and the other quan tum numbers corresponding to a glneball wi th a re la t ively nar row width would m a k e it an excellent candidate for a glueball. I f it should tu rn out to have an exotic jpc, the a rgumen t would be even more compelling.

TABLE I. -- List o/ states (jPv) /or quark model and glueballs. %/ ( x ) indicates allowed (disallowed). 2g (3g) correspond to glueball states formed by 2 (3) gluons. Solid arrow (-+) indicates quark model exotics in 3g states. Dashed arrow (->) indicatcs exotics in 2g states.

State qq 2g 3g

o++ %/ %/

"--> 3~0+ - X X %/

o-+ V %/ %/

--> 3gO-- X X %/

1 ++ %/ %/ %/

1+- %/ X %/

--~a'l-+ X %/ %/

1 - - V x V

2++ V V V

'-->" 8~2+- X X

2-+ V V V

2-- V x V

3++ V V V

3+- %/ x

~ ~ x V V

3-- V X %/

236 s . J . LIND:ENBAUM~

8. - H o w w o u l d you expect to m a k e a gluebal l preferential ly ?

8"1. J/~b radiative decay. - One suggested way (1~,13) is in invest igat ing ra- diat ive J/~b decay (14). Pe r tu rba t ion theory t r ea tments indicate t h a t the im- por t an t diagram is tha t shown in fig. 10. One would expect to find evidence for the glueball by plot t ing d N / d E as a funct ion of y-ray energy, as shown in fig. 10. The rat ionale for fig. 10 allowing enhanced product ion of glueballs is t ha t the 7 can have a variable energy, so tha t the effective mass of the two gluons could sweep over a range of masses and thus, if there is a gg resonance corresponding to a glueball, one would favor forming it.

C

r 1 oooooooooooooooo~ l.,..,.+ ....... +

E~

Fig. 10. - The dominant diagram in radiative J/~ decay, and on the r.h.s, of it a plot of d]g/dE vs. E v.

The plot of d N / d E vs. E~ {fig. 10) might show a s t ructure corresponding

to glueballs. In regard to the radiat ive decay of the J/~, it has been considered (1~-1~)

t h a t the E observed in J/~b -+ v+E(1420) may be a glueball. There is con- siderable uncer ta in ty and lack of convincing evidence about this par t icular in terpre ta t ion for this low-statistics experiment . Therefore, we will not discuss it in this paper, bu t refer the reader to ref. (1++-1,).

8"2. The OZI-]orbidden 7:-p--> ~ n . - Another way suggested by the au thor (*) some t ime ago is shown by the diagram in fig. 11.

The GoT system forms a hairpin diagram disjoint f rom the rest of the quark

line diagram, thus it is OZI suppressed. I n the context of QCD it proceeds via exchange of 2 gluons, if V~0 is a scalar system, or 3 gluons, if ~0~ is a vector system. The key point is to have a mult igluon intermediate s ta te of variable

mass so that , if glueball resonances exist, they can be produced enhanced rel- at ive to o ther states. This exper iment was performed some t ime ago by the BNL/CCSTY collaboration (5,6). I t was shown tha t the OZI rule was pa ten t ly violated (~.6) and, in fact, there was no evidence for OZI suppression. My ex- p lanat ion for this is the in tervent ion of glueball resonances. In case of a res-

(14) D. L. SCI~AI~RE: Proceedings o] the VI International Con]erence on Experimental Meson Spectroscopy, Brookhaven National Laboratory, April 25-26, 1980 (to be published in A I P Conference Proceedings, S~ebseries on Particles and .Fields). (*) Reference (7) and various prior conferences.

THE OZI RULE AND GLUXBAL.LS 2 3 7

onance, the coupling can become effectively s t rong and what we would be looking

a t is a d iagram in which a glueball is exchanged. This could defeat the OZI

rule and thus we m a y well have seen the in tervent ion of glueball resonances

s

d

P ~ c t cL _ _ n

c t c t _ _ J

Fig. 11. - =-p-~ ~?n, an OZI-forbidden diagram in which the multigluon intermediate state (which leads to ~ production) can have ~ variable mass.

in this interact ion. I believe the mos t logical explanat ion (~5) in the context of

QCD for the absence of OZI suppression in ~ - p -> ? ? n is the in tervent ion of glueball exchange and tha t this process is t ak ing place. Therefore, this is p robab ly an excellent channel in which to find gluebMls.

9 . - C o n c l u s i o n s .

1) The OZI rule works, bu t it has a pecul iar i ty whereby two OZI-al lowed processes can ~void an OZI-forbidden process and thus c i rcumvent the OZI rule. This violates crossing s y m m e t r y and un i ta r i ty and necessitates an ad hoc el iminat ion of these a l te rna te possibil i ty (the au thor ' s Q L R No. 2) (~).

I n this pape r the au thor a t t r ibu tes this pecul iar i ty to the fac t of life of color confinement and points out t h a t using the two steps of OZI-al lowed proc- esses allows one to t r ans form a two-gluon or more-gluon exchange process

into one which can go by a series of one-gluon exchanges. Thus it is concluded tha t the crossing s y m m e t r y and un i ta r i ty a rguments made wi thout t ak ing into

account this QCD fact of life are p robab ly only applicable when one does not

change the na tu re of ~ gluon exchange. I view this as an added requi rement due to color confinement.

2) The mos t logical explanat ion in the context of QCD for the failure

of the OZI rule in s - p -~ ? ? n is the in tervent ion of glueball resonances. The

? ? sys tem in this exper iment is thus an excellent place to search for glueballs.

(15) S. J. LINDENBAUM : QCD , OZI and evidence ]or glueballs, in X V I Recontre de Moriond, Elementary Particle Physics Meetings, Les Arcs, Savoie, France, March 15-27, 1981 (to be published in the proceedings, 1981).

16 - I I N u o v o Clmen~o A .

238 S . J . LINDENBAU'M

A p p r o x i m a t e l y 170 , ~ - p - + ~ n even t s have been observed. A p l a n n e d

second e x p e r i m e n t wi th ~ 20 t imes more d a t a is expec ted to al low de te r ln ina -

t ions of J" . C is k n o w n to be -f- for ~r a n d I is k n o w n to be zero. Thus all

t he q u a n t u m n u m b e r s m a y be d e t e r m i n e d a n d th i s allows a n excel lent pos-

s ib i l i ty for expl ic i t d iscovery of g luebal ls , especial ly if j e c is exotic.

�9 R I A S S U N T O (*)

La regola di OZI funziona abbastanza bene ma la sun peculiarith eonsiste nel fatto che un processo proibito secondo OZI pub avvenire mediante due processi successivi per- messi secondo OZI. Questo implica l 'aggiramento del diagramma proibito secondo OZI ed anehe la violazione delia simmetria inerociata e dell 'unitarieth. Quests peeuliarith della regola di OZI si attribuiscono ai fatt i della vi ta del confinamento di colore. Si di- mostra in dettaglio l 'evidente insueeesso della reg(fla di OZI nella reazione =-p ~ ~ n . Si sottolinea ehe, nell 'ambito della QCD, una spiegazione logica di questo insuecesso

l ' intervento della sfere di gluoni (risonanze a molti gluoni). Segue una diseussione su eorae fare a rieonoscere le sfere di gluoni e sulla h)ro importanza per la QCD.

(*) 7',raduzione a cura della Redazio~e.

l-IpaBKao O Z I u K.aeenb~e mapm.

Pe3mMe (*). - - YIpaBnnO OZI pa6oTaeT ~OCTaTOqHO xopoIIIO, HO cneuHdpHKa 3aKnloqaeTcs B TOM, qTO IIpOI.[ecc, 3arlpetReaHbi~ HpaHBYIOM O ZI , Mo~KeT npoHcxo~HTb qepe3 ~na nocJIe~OBaTeJ~bHbIX pa3pemeHHblX npaBnnOM 0 g I npotlecca. 9TO O~CTORTeJ1bCTBO yKa- 3binaeT nyTb o6xo~a ~HaFpaMM, 3alpeIIIeHHbIX npaBaaOM 0ZI , a TaK~e r[o]ipa3yMeBaeT HapymeHHe CHMMeTpHH H yHHTapHOCTH. ~TH xapaKTeph~ble OCO~eHHOCTH npaBHna 0Z[ Iipm'mCbXBatOTCa qbaKTy << ~BeTHOrO >> y~ep~aHHa. I'[o~po6Ho aHanH3HpyeTca aBHa~l HecOC- TO~ITeYlbHOCTb npam4na OgI e upottecce 7~-p ~ q~n. OTMeqaeTc~I, HTO B KOHTeKCTe KBaH- TOBO~ XpOMO~HHaMaKH ~iorHqecKoe o6~acaeaHe 3TO~ ~ecoeroaTeabaOCTa cBa3ano r yqacT~eM xaeeBbiX mapos (~ym, THrayoHmax pe3oHarlcoB). 06cya<aaeTca Bonpoc H~eH- THdpal~atlHH KneeBbIX tHapoB H Ba~HOCTb HX BKYIIOtleHHff B KBaHTOByIO XpOMO~HHaMHKy.

(*) Hepeaec)eno pec)amlue(t.