On the OZI rule for baryons

Volume 230, number 1,2

PHYSICS LETTERS B

26 October 1989

ON THE OZI RULE FOR BARYONS J K STORROW Department of TheoretwalPhystcs, Untversltyof Manchester, OxfordRoad, 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 OkuboZwelg-hzuka (OZI) rule does not apply to baryonlc verhces because baryons contain a slgmficant number of strange quarkantlquark pairs, and they claim some phenomologxcalsupport for this proposal In the hght of this, the excellentdata 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 significancequestionable We also re-examinethe 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 ] ( E G K ) that the O k u b o Z w e l g - h z u k a ( O Z I ) rule does not apply to baryons because they contain a signtficant n u m b e r of strange q u a r k - a n t l q u a r k (sg) pairs even at low Q2 This gives rise to additional connected quark dtagrams which evade the OZI rule Neither of the two pieces of evidence quoted are entirely u n a m b i g u o u s The first is the discrepancy between the experimental value a n d theoretical estimates of the ~ - N sigma term However, the theoretical value of 25 MeV [2 ] involves the applicatton of first order perturbation 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 m e a s u r e m e n t of deep inelastic polarlsed jap scattering [8] combined with measurements ofgA and the value of the SU (3) F / D ratio measured in hyperon [3 decays leads to the surprising and counter-intuitive result that the total spin carried by all quarks a n d antiquarks in the 124

proton is consistent with zero [9,10], and that the proton has a significant sg content The sg c o m p o n e n t makes a significant c o n t r i b u t i o n to the proton spin ( A s = - 0 24_+0 07 [9,10] ) which is cancelled by the c o n t r i b u t i o n of the u and d quarks This line of argument is not u n a m b i g u o u s either it is possible to avoid the conclusion of this sizeable sg content by having the gluons playing a larger role [ 11 ], by invoking 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 investigating in its own right The m a i n evidence quoted by E G K in favour of OZI violation is a comparison of the data on 0 a n d c0 production in laP and l~n annihilation [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~ ( 1 5 2 5 ) ) productaon compared with f (1 e 1"2(1270) ) production in I~P a n n i h i l a t i o n [ 16 ] The problem with interpreting such effects as due to as sg c o m p o n e n t 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

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many parhcle nature o f the final state ~t ~s not clear that any effect found can be ascribed speofically to a violatmn o f the O Z I rule at a MBB vertex F o r example, ~t has been recently suggested that exohc ( q q ~ ) mesons could be the source o f the discrepancy in the anmhdatxon reacUons [ 17 ] ( b ) The calculatmn o f the deviation from magic mixing depends on whether a hnear or quadratic mass formula ~s assumed a n d this is translated into an uncertainty o f a factor o f 5 in the predxcted 0 cross section [ 1 ] We propose that a much cleaner test o f O Z I vmlataon lies m the excellent d a t a that exist for backward meson p r o d u c t m n m the lntermedmte energy ( 3 - 6 G e V / c ) regmn, where ~t is clear that the underlying m e c h a m s m ts baryon exchange [18], and that the relevant vertices are MBB. it 1s a strmghtforward and uncontroverslal fact that there ~s very httle evidence for the backward production o f ~ and f' mesons by meson (n or K ) or p h o t o n beams o f f p r o t o n s Th~s is normally interpreted as evidence for the OZI rule and the data used to put b o u n d s on the devmtlons from magic mixing, as reviewed m ref. [ 18 ] In sectmn 2 we re-examine these d a t a m the hght o f the proposal o f E G K and find that there xs some shght ewdence for violation o f the O Z I 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 ffthere is a significant sg component o f the proton then one would expect exotic baryons (qqqqC1) such as K + p resonances to exist They clmm some evidence for the exchange o f such states in backward lbp--+K+K - at PL-----0 5 G e V / 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 l m m e d by E G K

26 October 1989

laboratory m o m e n t a pL>~ 3 G e V / c At such energms these backward reactmns are expected to be dominated by reggelsed baryon exchange, m particular 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 o f Nv and N 0 exchange [ 18 ], these trajectories being associated with the j e = 3 / 2 - state N ( 1520 ) and the J P = 5 / 2 - state N ( 1 6 7 5 ) respectwely, but we can safely neglect t h e m [ 18 ] We define the cross section ratios Rv(M~B) =

aB(Mp~BO) aB(Mp~Bco) '

and RT(M-,B) =

ira ( M p - ~ B f ' ) an ( M p - , B f ) '

where 0a refers to the cross section integrated over H

B

(a)

K÷

p

K-

K-

p

!z

K

K÷

p

p

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 (respectively) produced m the backward hemisphere, for

Fig 1 Baryon exchange diagrams for various backward reacUons (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 +

125

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the backward peak U n d e r the a s s u m p t i o n o f the N~ d o m m a n c e , Rv (RT) should be given by the ratio o f the square o f the 9Nlq (f' N/q ) and e0Niq (fNiq) coupling constants i e , Rv = g~NN 2 go~NN

and g2, NN R T -- g 2 y '

where we have extrapolated from the phystcal region for the backward process (u-~ 0) to the nucleon pole at u = m ~ This p r o c e d u r e IS known to give a reliable estimate o f the ratto o f c o u p h n g constants g ~ N and gZNN from the ratio o f the backward cross sections for K - p - ~ A n ° and n N - - , N n [ 18,19] even f f a p p l l e d at laboratory m o m e n t a as low as 4 G e V / c The best data are in the K - i n d u c e d reacnons, obtained in a large exposure o f the C E R N 2 m HBC to a 4 2 G e V / c K - beam, and m e a s u r e d by the Amsterd a m - C E R N - N 0 m e g e n - O x f o r d and C E R N - C o l l b g e de F r a n c e - M a d r i d - S t o c k h o l m Collaborations They obtain [20] Rv(K-~A)=(1 Rv(K-~Z

6_+0 5)% ,

°) = ( 4 _ + 2 ) % ,

and [21 ] Rv ( K - - ~ A ( 1 5 2 0 ) ) = (3_+2)% They also find a backward cross section o f 0 5 p.b for K-p~0Z°(1385) [21], c o m p a r a b l e to the 0 cross sections in the above reactions. Older data on K - reactions [22], and also d a t a on n and p h o t o n induced reactions, is in the form o f bounds, though not so stringent as to affect the n u m b e r s given above [ 18 ] So we see that there is some e w d e n c e for violations o f the O Z I rule at the 9Nlq vertex at a r o u n d the 2% level for cross sections F o r the 0 reactions, the departure from magic mixing calculated from the observed masses o f the vector nonet [23] would give a contribution to Rv o f less than 0 5% (0 1%) using values o f the mixing angle based on a q u a d r a t i c (linear) mass formula For backward f' production, there are only u p p e r b o u n d s available [20,24,25] The most useful ones are those p r o v i d e d by the 4 2 G e V / c K - b e a m bub126

26 O c t o b e r 1989

ble c h a m b e r m e n t i o n e d above [20,24 ] and yield RT(K- ~A) <2%, R T ( K - ~ Z °) < 5 % Here, the expected contribution to RT from the calculated deviation from magic mtxlng [23 ] are significantly larger than in the 0 case, a r o u n d 1 5% (2 5%) if a q u a d r a t i c (linear) mass formula is used So we see, c o m p a r i n g these numbers with the first o f the above bounds, that there is very httle scope for O Z I violation in the f' case The predictions o f EGK, based on their estimate o f the sg content o f the proton and meson d o m i n a n c e assumptions, are that g, NN = 0 , and gf'NN--o 1 0 + 0 05 g~N Since this leads to predictions o f R v = 0 and RT-- 1% It would a p p e a r difficult to reconcile with the data we have presented Their predictions for the MBB vertex are in fact difficult to interpret when one o f the particles is reggeIsed By considering the case o f the reggelsed meson, we can argue that the 0N/q and f ' N l q vertices should be equal from c o n s i d e r a n o n s o f the strong exchange degeneracy o f the 0 and f' trajectories in the reaction N N - ~ N N F o r the case o f a reggeised baryon, the case in which we are specifically interested, then their statement 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 f c o u p h n g s are unreliable in other cases They estimate for the A2 (1 e a2(1320) ) gaA2NN --~0 10-+0 05 g~N which would imply this value for the ratio o f backward A2 to f production Experimentally, we find

[20] ~ a ( K - p ~ A A °) = 0 5 0 + 0 15 ~rB( K - p - - , A f )

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for a b e a m energy o f 4.2 G e V / c and value o f 0.6 + 0 2 for the corresponding reacUons with E ° replacang A [20], although the Z ° reactaons could have a small a m o u n t o f A~ exchange So we see that it would be surprising af the m o d e l o f E G K for MBB couplings were true, even a p a r t from its fadure to account for the data on backward ~ and f' p r o d u c t m n

3. Z ' e x c h a n g e We now turn to another p~ece o f evadence quoted by E G K m favour o f a large sg content o f the proton, the backward ~ peak observed m p p - - , 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 e w d e n c e for such states has been a r o u n d for over 15 years and two recent partml wave analyses have claimed [ 7 ] a P L3resonance a r o u n d 1800 MeV However, the Particle Data G r o u p has not as yet accorded It officml resonance status, c m n g the general prejudice against baryons not m a d e of three quarks [23] W h a t e v e r the status o f 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 o f mass 1940 MeV, as concluded by the experlmentahsts [6 ] We must look at hagher energaes for better 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) ~ t b ( G e V / c ) -2 There as a more s~gmficant backward peak observed an the related line reversed reaction K - p ~ p K with d e / d u l ~ = o ~ (0 2 0 + 0 07) l a b ( G e V / c ) -2 at PL=5 G e V / c [29,30] The latter peak, whach certainly could be due to Z* exchange (fig l c ) , ~s two orders o f magmrude 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. 1d ) However, before such peaks can be unambiguously ascribed to Z* exchange, we must check the energy dependence o f the cross section. Theoretacally, f f t h e Z* has mass 1800-1900 MeV and spin 3 / 2 we expect ~ By backward we mean small momentum transfer between ahe 15andtheK + (fig lb)

26 October 1989

a o c s n wath n ~ - 5 ,

assuming the universal slope o f or' = 0 9 G e V -2 for the Z* trajectory. Experimentally we find n = - ( 9 . 8 + 0 3) for the backward K - p - , p K - d a t a 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 p h e n o m e n o n m a n y reactaons, corresponding to both exotic and non-exotic exchange, show very steep energy dependence at low energies [ 31 ], particularly below 2 G e V / c , a feature that is not understood theoretically. Usually, at hagher energies, a transltaon to the more m o d e r a t e energy dependence associated with the Regge region is found [ 31 ] F o r both backward K - p - , p K - and f ~ p ~ K + K the 5 G e V / c data give some hint o f thas transition [ 29 ], but unfortunately, the only data above 5 G e V / c that exast for these reactions are m the form o f upper b o u n d s [32 ], which are not stringent enough to gave a useful hmat A n o t h e r note o f cautaon needs to sounded before associating these peaks w~th Z* exchange peaks also exist corresponding to other types o f 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 p p - ~ p p at P L = 5 G e V / c [29] Thas must mean that other dynamical m e c h a m s m s are operating whach simulate exotic exchange, such as Regge-Regge cuts For the case we are considerrag, Z* exchange could be simulated by a K * - N ~ cut, which would gave energy d e p e n d e n c e corresponding to n ~ - 4 and would thus be very difficult to disentangle from Z* exchange

4. Discussion To s u m m a n s e the phenomenologlcal analysis o f section 2, we have found some evidence o f violation o f the OZI rule at the 2% level m cross section for backward ¢ productaon but none for f' p r o d u c t i o n O u r findings are not consistent w~th the pattern predacted by E G K and we have presented i n d e p e n d e n t arguments why it would be surpnsang ffthear predactaons were reahsed W i t h such a low level o f vaolatlon o f the O Z I rule ~t as worth asking whether there ~s anything specml about baryons, since c o m p a r a b l e vaolataons are seen for mesons F o r 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

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PHYSICS LETTERS B

M e V a n d F ( K I ~ ) = 6 3 v5o/~+6° M e V [ 3 4 ] T h e q u o t e d v a l u e [23 ] o f t h e nrt to KI~ b r a n c h i n g ratio, b a s e d o n a n 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 ] B e a r i n g in m i n d t h a t in th~s case t h e rtr~ d e c a y ~s enh a n c e d r e l a n v e to t h e KI~ d e c a y b y a p h a s e s p a c e fact o r o f 3 6, we see t h a t t h e O Z I v i o l a t i o n s a r e r o u g h l y c o m p a r a b l e to t h o s e we f o u n d f o r b a r y o n s By c o n trast, E G K a r g u e t h a t O Z I v~olatlons s h o u l d b e O (No) larger in t h e b a r y o n case b e c a u s e o f q u a r k loop effects As r e g a r d s Z* e x c h a n g e , t h e r e is c e r t a i n l y b e t t e r evidence than that quoted by EGK which could 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 , f o r o t h e r p o s s i b l e m e c h a m s m s to b e r u l e d o u t we n e e d b e t t e r d a t a o n energy dependence and a better theoretical unders t a n d i n g o f t h e 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 react i o n s [ 31 ] In s u m m a r y we c a n c o n c l u d e t h a t w h a t e v e r t h e t h e o r e t i c a l m e r i t s or o t h e r w i s e o f a l a r g e r sg c o m p o nent of the proton, the s~tuanon concerning any cons e q u e n t v i o l a t i o n s o f t h e O Z I rule for b a r y o n s is n o t as c l e a r c u t as s t a t e d b y E G K In p a r t x c u l a r , a n y VlOl a n o n s o f t h e rule are small, a r o u n d 2% in rates, a n d d o n o t follow t h e p a t t e r n p r e & c t e d b y E G K B e t t e r d a t a w o u l d o f c o u r s e help, b u t m all cases we a r e c o n s~derlng v e r y s m a l l cross s e c t i o n s a n d so t h e e x p e r i m e n t s are r a t h e r d i f f i c u 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 t e e p l y w~th energy, at least as fast as ~ s - 3

Acknowledgement I w o u l d h k e to t h a n k m y c o l l e a g u e s m t h e T h e o r y G r o u p at M a n c h e s t e r , p a r t i c u l a r l y S a n d y D o n n a c h ~ e , for h e l p f u 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 t h i s p a p e r

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