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Volume 230, number 1,2 PHYSICS LETTERS B 26 October 1989

ON THE OZI RULE FOR BARYONS

J K STORROW

Department of Theoretwal Phystcs, Untverslty of Manchester, Oxford Road, Manchester, M13 9PL, UK

Received 28 June 1989, revised manuscript received 2 August 1989

Elhs, Gabathuler and Karhner [Phys Lett B 217 (1989) 173 ] have recently proposed on theoretical grounds that the Okubo- Zwelg-hzuka (OZI) rule does not apply to baryonlc verhces because baryons contain a slgmficant number of strange quark- antlquark pairs, and they claim some phenomologxcal support for this proposal In the hght of this, the excellent data on backward meson production ~s critically re-examined We find some ewdence for OZI-evadmg couphngs for the case of the 0, and put bounds on any OZI-vlolatmg couphngs of the f~ (1525) The violations found do not follow the pattern predicted by Elhs et al and are also so small as to make their significance questionable We also re-examine the data on the related question of Z* (exotic baryon) exchange

1. Introduction

It has been proposed on theoretical grounds by Ellis, Gabathuler and Karhner [ 1 ] (EGK) that the Okubo- Zwelg-hzuka (OZI) rule does not apply to baryons because they contain a signtficant number of strange quark-ant lquark (sg) pairs even at low Q2 This gives rise to addit ional connected quark dtagrams which evade the OZI rule

Neither of the two pieces of evidence quoted are entirely unambiguous The first is the discrepancy between the experimental value and theoretical estimates of the ~ -N sigma term However, the theoretical value of 25 MeV [2 ] involves the applicatton of first order perturbat ion theory to the mass sphttings of the octet baryons, an assumption questioned by Jaffe [ 3 ] on the basis of chiral bag model results [ 4 ] The latter arguments have been supported by two recent calculations [5,6] Also the "experimental" value of 55 MeV involves a long extrapolatton and has been questioned by some authors [ 5,7]

The other piece of evidence concerns the so-called "spin crisis" in the proton. The EMC measurement of deep inelastic polarlsed jap scattering [8] com- bined with measurements ofgA and the value of the SU (3) F / D ratio measured in hyperon [3 decays leads to the surprising and counter- intui t ive result that the total spin carried by all quarks and antiquarks in the

proton is consistent with zero [9,10], and that the proton has a significant sg content The sg component makes a significant contr ibut ion to the proton spin (As= - 0 24_+0 07 [9,10] ) which is cancelled by the contr ibut ion of the u and d quarks This line of ar-

gument is not unambiguous either it is possible to avoid the conclusion of this sizeable sg content by having the gluons playing a larger role [ 11 ], by in- voking higher twist effects [ 12 ], or, even in the naive quark model, by having some D state admixture m the proton [ 13 ]

Even with the above caveats the question of OZI violation at baryomc vertices is clearly worth inves- tigating in its own right The main evidence quoted by EGK in favour of OZI violation is a comparison of the data on 0 and c0 production in laP and l~n annihi lat ion [14] and pp [15] reactions in all cases, the O eo ratios are too high compared to expectations based on the deviations from magic mixing calculated from the masses of the vector meson nonet They also claim similar results for f' (1 e f~ (1525)) productaon compared with f (1 e 1"2(1270) ) production in I~P annihi la t ion [ 16 ] The problem with interpret- ing such effects as due to as sg component of the proton is that there are uncertainties m the theoretical estimates for the following reasons

(a) The underlying dynamical mechanisms of such reactions are not clearcut m particular, due to the

124 0370-2693/89/$ 03 50 © Elsevier Science Publishers B V (North-Holland Physics Publishing Division)


many parhcle nature of the final state ~t ~s not clear that any effect found can be ascribed speof ica l ly to a v iola tmn of the OZI rule at a MBB vertex For example, ~t has been recently suggested that exohc ( q q ~ ) mesons could be the source of the discrepancy in the anmhdatxon reacUons [ 17 ]

(b) The calculatmn of the devia t ion from magic mixing depends on whether a hnear or quadrat ic mass formula ~s assumed and this is t ranslated into an un- certainty of a factor of 5 in the predxcted 0 cross sec- t ion [ 1 ]

We propose that a much cleaner test of OZI vmla- taon lies m the excellent da ta that exist for backward meson p roduc tmn m the ln termedmte energy (3 -6 G e V / c ) regmn, where ~t is clear that the underlying mechamsm ts baryon exchange [18], and that the relevant vertices are MBB. it 1s a strmghtforward and uncontroverslal fact that there ~s very htt le evidence for the backward product ion of ~ and f' mesons by meson (n or K) or photon beams o f fp ro tons Th~s is normally interpreted as evidence for the OZI rule and the data used to put bounds on the devmtlons from magic mixing, as reviewed m ref. [ 18 ] In sectmn 2 we re-examine these da ta m the hght o f the proposal of E G K and find that there xs some shght ewdence for violat ion of the OZI rule, though ~t is not of the form suggested by them, and it xs also not clear how significant ~t is

E G K also point that f f there is a significant sg component of the proton then one would expect exotic baryons (qqqqC1) such as K + p resonances to exist They clmm some evidence for the exchange of such states in backward lbp--+K+K - at PL-----0 5 GeV/c . In section 3 we examine the evidence for this m the higher energy data for th~s reactmn and also In the related hne reversed reacUon, backward K - p--, p K - Again we find that the phenomenologxcal sxtuauon is not as clearcut as c lmmed by E G K

2. Backward ~ and f' production

We consxder the processes

M + p - , B + (V, T ) ,

where M is a meson, B a baryon, and V ( = 0 or co) and T ( = f' or f ) are vector and tensor mesons (re- spectively) produced m the backward hemisphere, for

labora tory momen ta pL>~ 3 G e V / c At such energms these backward reactmns are expected to be domi- nated by reggelsed baryon exchange, m par t icular by the N~ trajectory (fig l a ) , the Regge trajectory assocmted with the nucleon and ~ts recurrences, the N ( 1 6 8 0 ) with Je=5/2+ and the N ( 2 2 2 0 ) with Je=9/2 + There are perhaps also small admixtures of Nv and N 0 exchange [ 18 ], these trajectories being associated with the je= 3 / 2 - state N ( 1520 ) and the J P = 5 / 2 - state N ( 1 6 7 5 ) respectwely, but we can safely neglect them [ 18 ] We define the cross section ratios

a B ( M p ~ B O ) R v ( M ~ B ) =

aB(Mp~Bco) '

and

ira ( M p - ~ B f ' ) R T ( M - , B ) =

an ( M p - , B f ) '

where 0a refers to the cross section integrated over

(a)

H B

K ÷

p K-

K- p

!z K

K ÷ p

p K ÷

Fig 1 Baryon exchange diagrams for various backward reac- Uons (a) No exchange m backward M + p ~ B + (0, o, f' or f) (b) Z* exchange m backward ~p-~K+K - (c) Z* exchange m backward K-p---,pK- (d) A and Z exchange in backward

K+B--,pK +

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Volume 230, n u m b e r 1,2 PHYSICS LETTERS B 26 October 1989

the backward peak Unde r the assumpt ion o f the N~ dommance , Rv (RT) should be given by the rat io o f the square of the 9Nlq (f ' N/q ) and e0Niq ( fNiq) cou- pling constants i e ,

Rv = g~NN 2

go~NN

and

g2, NN R T -- g 2 y '

where we have extrapola ted from the phystcal region for the backward process (u-~ 0) to the nucleon pole at u = m ~ This procedure IS known to give a reliable es t imate o f the ratto o f c o u p h n g constants g ~ N and gZNN from the rat io of the backward cross sections for K - p - ~ A n ° and nN-- ,Nn [ 18,19] even f f app l l ed at labora tory momen ta as low as 4 G e V / c

The best data are in the K - induced reacnons, ob- ta ined in a large exposure of the CERN 2 m HBC to a 4 2 G e V / c K - beam, and measured by the Amster- d a m - C E R N - N 0 m e g e n - O x f o r d and CERN-Col lbge de F r a n c e - M a d r i d - S t o c k h o l m Col laborat ions They obtain [20]

R v ( K - ~ A ) = ( 1 6_+0 5)% ,

R v ( K - ~ Z °) = (4_+2)%,

and [21 ]

Rv ( K - - ~ A ( 1 5 2 0 ) ) = (3_+2)%

They also f ind a backward cross section o f 0 5 p.b for K - p ~ 0 Z ° ( 1 3 8 5 ) [21] , comparab le to the 0 cross sections in the above reactions. Older data on K - react ions [22] , and also da ta on n and photon induced reactions, is in the form of bounds, though not so stringent as to affect the numbers given above [ 18 ] So we see that there is some ewdence for violat ions of the OZI rule at the 9Nlq vertex at a round the 2% level for cross sections For the 0 reactions, the de- par ture from magic mixing calculated from the observed masses of the vector nonet [23] would give a contr ibut ion to Rv of less than 0 5% (0 1%) using values of the mixing angle based on a quadra t ic (l inear) mass formula

For backward f ' product ion, there are only upper bounds avai lable [20,24,25] The most useful ones are those provided by the 4 2 G e V / c K - beam bub-

ble chamber ment ioned above [20,24 ] and yield

R T ( K - ~ A ) < 2 % ,

R T ( K - ~ Z °) <5%

Here, the expected contr ibut ion to RT from the calculated devia t ion from magic mtxlng [23 ] are signif- icantly larger than in the 0 case, a round 1 5% (2 5%) if a quadra t ic ( l inear) mass formula is used So we see, compar ing these numbers with the first of the above bounds, that there is very httle scope for OZI violat ion in the f' case

The predic t ions of EGK, based on their es t imate of the sg content of the proton and meson dominance assumptions, are that

g, NN = 0 ,

and

gf 'NN--o 1 0 + 0 05 g~N

Since this leads to predic t ions o f R v = 0 and RT-- 1% It would appear difficult to reconcile with the data we have presented Their predic t ions for the MBB vertex are in fact difficult to interpret when one of the part icles is reggeIsed By considering the case of the reggelsed meson, we can argue that the 0N/q and f 'Nlq vertices should be equal from cons ideranons of the strong exchange degeneracy of the 0 and f ' t rajecto- ries in the react ion N N - ~ N N For the case o f a reggeised baryon, the case in which we are specifically interested, then their s ta tement that g , NN = 0 whereas g, NN* ¢ 0 iS difficult to apply to the 9NN~ vertex as N~ exchange involves the exchange o f not only the nucleon, but also o f all o f its recurrences. In fact, the vanishing ofg0NN IS, as we saw above, undesirable on phenomenologlcal grounds We find that their estimates o fcouphngs are unrel iable in other cases They est imate for the A2 (1 e a2(1320) )

gaA2NN --~0 10-+0 05 g~N

which would imply this value for the rat io o f backward A2 to f product ion Experimental ly, we find [20]

~ a ( K - p ~ A A °) = 0 5 0 + 0 15

~rB ( K - p - - , A f )

126


for a beam energy of 4.2 G e V / c and value of 0.6 + 0 2 for the corresponding reacUons with E ° replacang A [20] , al though the Z ° reactaons could have a small amount of A~ exchange So we see that it would be surprising af the model of E G K for MBB couplings were true, even apar t f rom its fadure to account for the data on backward ~ and f' p roduc tmn

3. Z ' e x c h a n g e

We now turn to another p~ece of evadence quoted by E G K m favour of a large sg content of the proton, the backward ~ peak observed m pp - - ,K+K - at PL--~0 5 G e V / c [26] They cite thas as evadence o f a direct p - - , K - couphng, forbidden in the naive quark model It ~s related by crossing to the exotic channel K + p ~ Z *, where Z* Ls an exotic S = 1 (qqqqdl) state Some ewdence for such states has been around for over 15 years and two recent partml wave analyses have cla imed [ 7 ] a P L3 resonance a round 1800 MeV However, the Particle Data Group has not as yet ac- corded It officml resonance status, cmng the general prejudice against baryons not made of three quarks [23] Whatever the status of Z* resonances, the observed peak at PL----- 0.5 G e V / c is at too low an energy to be assocmted wtth anything other than a darect channel meson resonance of mass 1940 MeV, as con- cluded by the exper lmentahs ts [6 ] We must look at hagher energaes for bet ter evidence for Z* exchange. m fact there is a backward peak observed m f~p--,K+K - at pL=5 G e V / c [28,29] wath d a / d u l , = o ~ - (0 0 4 2 + 0 030) ~ tb(GeV/c) -2 There as a more s~gmficant backward peak observed an the related line reversed reaction K - p ~ p K - with d e / du l~=o~ (0 2 0 + 0 07) l ab (GeV/c) -2 at PL=5 GeV/ c [29,30] The lat ter peak, whach certainly could be due to Z* exchange (fig l c ) , ~s two orders of magm- rude smaller than the corresponding peak (also at PL = 5 G e V / c ) m the reaction K + p ~ p K + [ 18,29,30 ], where hyperon exchange is allowed (fig. 1 d)

However, before such peaks can be unambiguously ascribed to Z* exchange, we must check the energy dependence of the cross section. Theoretacally, f f the Z* has mass 1800-1900 MeV and spin 3 /2 we expect

~ By backward we mean small momentum transfer between ahe 15andtheK + (fig lb)

aocs n wath n ~ - 5 , assuming the universal slope of or' = 0 9 GeV -2 for the Z* trajectory. Experimental ly we find n = - ( 9 . 8 + 0 3) for the backward K - p - , p K - da ta with pLy<3 G e V / c [29,30] and the backward 0 p - , K + K - data is consistent with this [ 28,29] Thas could be a low energy phenomenon many reactaons, corresponding to both exotic and non-exotic exchange, show very steep energy dependence at low energies [ 31 ], part icularly below 2 GeV/c , a feature that is not understood theoretically. Usually, at hagher energies, a transltaon to the more modera te energy dependence associated with the Regge region is found [ 31 ] For both backward K - p - , p K - and f ~ p ~ K + K - the 5 G e V / c data give some hint of thas t ransi t ion [ 29 ], but unfortunately, the only data above 5 G e V / c that exast for these reactions are m the form of upper bounds [32 ], which are not stringent enough to gave a useful hmat

Another note of cautaon needs to sounded before associating these peaks w~th Z* exchange peaks also exist corresponding to other types of exotic exchange, for example, exotac meson exchange in K - p - ~ n + E - at PL = 4 G e V / c [ 33 ] and dr-baryon exchange an backward pp-~pp at PL=5 G e V / c [29] Thas must mean that other dynamical mechamsms are operat ing whach simulate exotic exchange, such as Regge-Regge cuts For the case we are consider- rag, Z* exchange could be s imulated by a K*-N~ cut, which would gave energy dependence corresponding to n ~ - 4 and would thus be very difficult to disen- tangle from Z* exchange

4. Discussion

To summanse the phenomenologlcal analysis of section 2, we have found some evidence of violat ion of the OZI rule at the 2% level m cross section for backward ¢ productaon but none for f ' p roduct ion Our findings are not consistent w~th the pat tern pre- dacted by E G K and we have presented independent arguments why it would be surpnsang ffthear predac- taons were reahsed

With such a low level of vaolatlon of the OZI rule ~t as worth asking whether there ~s anything specml about baryons, since comparable vaolataons are seen for mesons For example, the quoted [23] values o f the nn and K K widths o f the f' are F ( n n ) = 1 4 +1-o5°

t27


M e V a n d F ( K I ~ ) = 6 3 v 5o/~+6° M e V [ 3 4 ] T h e q u o t e d

va lue [23 ] o f the nrt to KI~ b r a n c h i n g rat io , b a s e d on

an i n d e p e n d e n t e x p e r t m e n t , is (7 5 + 3 5 ) % [ 3 5 ]

Bea r ing in m i n d t h a t in th~s case the rtr~ decay ~s en-

h a n c e d r e l a n v e to t he KI~ decay by a p h a s e space fac-

t o r o f 3 6, we see t h a t the O Z I v i o l a t i o n s a re rough ly

c o m p a r a b l e to t hose we f o u n d for b a r y o n s By con -

trast , E G K argue t ha t O Z I v~olat lons s h o u l d be O (No)

larger in the b a r y o n case because o f q u a r k loop effects

As rega rds Z* exchange , t he re is c e r t a i n l y b e t t e r

e v i d e n c e t h a n t h a t q u o t e d by E G K w h i c h cou ld be

a s c r i b e d to Z* e x c h a n g e H o w e v e r , for o t h e r poss ib l e

m e c h a m s m s to be ru led ou t we n e e d b e t t e r d a t a o n

energy d e p e n d e n c e a n d a b e t t e r t h e o r e t i c a l u n d e r -

s t a n d i n g o f t he m e c h a n i s m s o f e x o n c e x c h a n g e reac-

t i ons [ 31 ]

In s u m m a r y we can c o n c l u d e t h a t w h a t e v e r the

t heo re t i c a l m e r i t s or o t h e r w i s e o f a la rger sg c o m p o -

n e n t o f the p r o t o n , t h e s~ tuanon c o n c e r n i n g a n y con-

s e q u e n t v i o l a t i o n s o f the O Z I ru le for b a r y o n s is no t

as c l ea rcu t as s t a t e d by E G K In par txcular , any VlO-

l a n o n s o f the ru le are smal l , a r o u n d 2% in ra tes , a n d

do no t fo l low the p a t t e r n p r e & c t e d by E G K B e t t e r

da t a w o u l d o f cou r se help , b u t m all cases we are con-

s~derlng ve ry smal l cross s ec t ions a n d so t he exper i -

m e n t s are r a t h e r d i f f icu l t T h e r e l e v a n t n u m b e r s are

m all cases a r o u n d 0 5 tab at PL = 4 G e V / c a n d f a l h n g

s teeply w~th energy, a t least as fas t as ~ s - 3

Acknowledgement

I w o u l d h k e to t h a n k m y co l leagues m the T h e o r y

G r o u p at M a n c h e s t e r , pa r t i cu la r ly S a n d y Donnach~e ,

for he lp fu l c o m m e n t s o n a d r a f t v e r s i o n o f th i s p a p e r

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