The Alexander-Zweig (OZI) in multiparticle production. Are there strange quarks in nucleons and pions?

Volume 225, number 3 PHYSICS LETTERS B 20 July 1989

T H E A L E X A N D E R - Z W E I G (OZI) I N M U L T I P A R T I C L E P R O D U C T I O N . ARE T H E R E S T R A N G E QUARKS IN N U C L E O N S A N D P I O N S ?

Harry J. L I P K I N Department of Nuclear Physics, Weizmann Institute of Science, 76100, Rehovot, Israel and School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69 978 Tel Aviv, Israel

Received 1 April 1989; revised manuscript received 10 May 1989

Predictions, theoretical basis, experimental tests and violations of various versions of the A-Z (OZI) rule are examined. For- bidden production processes for ~ and f' mesons are shown on general grounds to be less suppressed than forbidden decays, without assuming the presence of strange quarks in baryons. Dynamical mechanisms responsible for violations include allowed two-step transitions via intermediate states containing ordinary hadrons, gluons, flavor-mixed hadrons like q, "q' or fo(S* ), and exotic hadrons like glueballs, multiquark states and hybrids. Each case is described by a different mechanism with a different suppression factor.

Recent suggestions that apparen t violat ions [ 1 ] of the OZI rule [2,3 ] might p rovide evidence for a con- siderable strange quark content in the pro ton are crit- ically examined and found to be unreliable. The Alexander -Zweig rule [ 3-5 ] (usually referred to as OZI; [2,3] we denote it by " A - Z " as in ref. [5] , so that the reader can fill in the names o f his favori te contr ibutors in a lphabet ical o rder ) has several different formulat ions and different cri teria for validity. No theoret ical prescr ipt ion nor unambiguous experimental test exists for the quant i ta t ive degree of suppression of forb idden processes nor for its varia- t ion from one react ion to another .

An early phenomenologica l "universa l mixing mode l" gave the predic t ions [ 6 ]

a (nN- - ,0X ) a ( N N ~ 0 X ) a ( l q N - , 9X ) a (nN- ,o~X) - a(NN--*coX) - a(lq-N--,toX)

= tan20v,

a ( n N - , f ' X ) a ( N N - , f ' X ) a ( N N - , f ' X )

( l a )

o ( n N - , f X ) - a ( N N - , f X ) - a ( lqN- - , fX)

= tan20T, ( l b )

where X denotes any single or mult ipart icle final state containing no strange part icles and the parameters 0v

and OT are the devia t ions from the ideal mixing an- gles which define the nonstrange admixtures in the and f' wave functions assumed to be responsible for their couplings to nonstrange hadrons and the violating ~ p n and f ' - onn decays.

Serious disagreements with the relat ions ( 1 ) in re- suits o f exper iments involving baryons like

Op- , f ' + n n , (2a)

p p - , p p 0 + n n , (2b )

have been used to support the suggestion that the OZI rule does not hold for baryons and as evidence for the existence o f strange quark pairs in protons which can be " l ibe ra ted" as ~ or f ' mesons [ 1 ]. However, other predic t ions ( 1 ) disagree with exper iment almost in all cases, including meson react ions [ 7 -10 ] ; e.g.

n - n+ ~¢~¢~ , (3a)

n - n + - - , O n ° , (3b)

7 ~ O n + n - . (3c)

These are not in terpreted as indicat ing that there are strange quarks in the pion, but rather as indicat ions for exotic or mixed-f lavor resonances which can couple to both strange and nonstrange qft pairs

0370-2693 /89 /$ 03.50 © Elsevier Science Publishers B.V. ( Nor th -Hol land Physics Publishing Divis ion )

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[ 7,8,10,11 ] or for a topological hierarchy involving semi-forbidden and doubly-forbidden transitions [9,10,12 ]. These interpretations can also apply to the baryon cases (2).

A full description of the selection rule and the suppression factors is expected but not yet obtained from QCD. The one successful QCD calculation, the hadronic J/~g decay, assumes without complete jus- tification the dominance of a three-gluon annihilation diagram [ 13 ]. Other gluonic contributions have been needed to describe higher heavy quarkonium decays; e.g.

~g '~GGJ/~g~nnJ /~g , (4)

where GG denotes two gluons, but so far without complete success. Similar diagrams with glueballs and exotics for the reactions (2) can also lead to violations of the relations ( 1 ) in the reactions (2) without requiring strange quarks in the proton; e.g.

~p ~ G G n n ~ f' nn , (5a)

(~p~ ( 4q)n--,f ' nn , (5b)

where 4q denotes a four-quark exotic state. A simple explanation can be given for the violation

of the predictions (1) in the reactions (2) without requiring strange quarks in the proton. The A-Z violating f' ~ n n decay has been successfully described [ 14-16 ] by phenomenological calculations of the cascade of allowed transitions

f' ~ K I ( ~ f - ~ n n , (6a)

using experimentally observed couplings and assuming that the K K ~ n n transition is dominated by the f pole in the s-channel [ 14,16 ]. The transition matrix element is obtained by a simple perturbation treatment using the Fermi golden rule,

( n n [ M [ f ) x" ( f [ M ] i ) ( i [ M [ f ' ) < n n l M I f ' ) - Mf,--Mf Z~i Mf,-Ei

(6b)

where i denotes all intermediate states which couple to both the f and f '. The sum in (6b) has a pole for the intermediate KI( state at the mass of the f'. Eval- uating this pole contribution has given a result in agreement with experiment.

The naive mixing result ( lb ) for the reactions (2a)

is obtained from an analogous treatment assuming dominance of the transition

p p ~ f + nn-- ,KK + n n ~ f ' + nn , ( 7a)

with spectator pions for the last two transitions,

<f' + n n l M l p p )

( f + n n [ M [ p p ) y, ( f ' [ M [ i ) ( i [ M [ f ) , (7b) M r , - M f "T' M r . - E l

( f ' + n n [ M [ p p ) _ ( u n [ M [ f ' ) (8) ( f + n n [ M [ p p ) ( n n [ M [ f ) "

However, this result (8) will be violated by other neglected contributions which have no analog in the f ' ~ x n decay and can be appreciable; e.g.

~ p ~ f ' K I ( + ( n - 2)n--,f' + n n . (9)

This simple perturbation treatment can be generalized and made more rigorous by writing the unitarity relation for the general forbidden transition

A + B ~ S + C , (10)

where A, B and C are any hadron states containing no strange quarks and S denotes any meson com- posed of a strange quark-antiquark pair like the ~ or f'. Assuming the unitarity sum to be dominated by two-step transitions which are both allowed gives

Im(SC[ TIAB)

=tc(SC[ T*[ (KI()SC) ( (KI()SC [ T[AB)

+K(SC[ T* [ S (KI() c ) (S (KI()C [ T[AB) + .... (11)

where tc is the usual kinematic factor and (KI() s and (KI() c denote kaon pair states with the quantum numbers including momentum and mass of the S and C, respectively. The naive mixing result analogous to (8) is obtained by considering only the first term on the right hand side ofeq. ( 11 ) and assuming that the transition matrix element ( (KI ( )SCIT[AB) is dominated by a nonstrange pole analogous to the f in eq. (7b) and that the multihadron state C is a spectator. However, there is no obvious reason for ne- glecting more complicated transitions and in partic- ular the second term, a generalization of (9) whose strength can depend upon the state C and be different from states C containing the same hadrons in different partial waves.

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The ~--,pn decay has also been treated by the method ofeqs. ( 6 ) - ( 11 ). The contribution of the on- shell KI( intermediate state is too small and much smaller than for f ' --,Ttn because of the difference in the available phase space for the on-shell intermediate state [ 16 ]. Additional contributions seem to be needed and the problem is still open. The hadronic J / ~ decay successfully described by a three-gluon QCD annihilation diagram [13 ] has no analogous contribution as it has no allowed on-shell intermediate state and no unitarity relation analogous to ( 11 ). The off-shell contributions have been neglected in all these decays, with arguments for their neglect based on cancellations between contributions of different intermediate states [ 17,18 ]. However, on-shell contributions cannot be cancelled by off-shell contributions, and can be used via unitarity to obtain model- independent constraints on suppression factors.

There are many examples of A-Z violation via flavor-mixed intermediate states produced via one flavor component and decaying via another [ 19 ], with no degenerate partners available to produce cancellations [17,18]; e.g. n °, n, 1]' and fo(975) (formerly S*). The J / ~ n + n - decay, for example, is dominated by the ~fo configuration [20]. Pion pairs produced in A-Z violating reactions like ( 2 b ) - (2d) should be checked for fo decays.

Further experimental investigations of forbidden processes can lead to a better understanding of the underlying QCD dynamics. Different A-Z violating transitions proceed via different mechanisms, with no simple relation between forbiddenness factors. Mul- tiparticle processes like (2) have additional violating diagrams absent in three-point functions. Data from experiments leading to multiparticle final states can be useful if invariant mass spectra of various com- ponents of the final state are available together with detailed partial wave analyses to determine spins and parities. Detailed analyses also including data for the allowed transitions related to the forbidden transition by unitarity can check the importance of two- step transitions like (9). But cookbook A-Z recipes cannot provide convincing evidence for the presence of strange quarks in nucleons and pions.

Further insight is obtained into different aspects of A-Z phenomenology by examining the following set of typical forbidden processes which can go via two steps in which each is allowed:

n -p~K°A-- ,On ,

7t-p--,n°n--,Tt+A - ,

K+A- ~K*+9°A- ~K*+ A- ,

K+A - ~ K * + o A - ~ K * + A - ,

K+A--oK*+~°A--- ,K*+A - .

(12a)

(12b)

(13a)

(13b)

(13c)

Three qualitatively different formulations of the A- Z rule which all forbid the ¢--,pn and f '--,nn decays have different implications elsewhere. The original "Okubo ansatz" [2 ] is defined for three-point nonet couplings and can be generalized to include charm. It applies to four-point functions only in models which factorize the amplitude into two three-point nonet couplings and thus forbids the reactions (12) and (13) only in a peripheral meson-exchange model with nonet symmetry at the quark level for the exchanged mesons. The topological formulation [3 ] forbids all "disconnected diagrams". This includes the four- point functions (12a) and ( 13 ) but not the four-point function (12b). The additive-quark-model (AQM) [21 ] formulation applied to neutral meson mixing by Alexander et al. [4 ] requires all reactions and couplings to currents to involve only one "active" quark in each hadron, with the remaining quarks being spectators. AQM forbids the four-point functions (12) but allows the four-point functions (13). There are no quantitative predictions for the suppression factors of forbidden processes which can occur as two-step processes (12), (13) where both steps are allowed [ 5,10,14 ].

The rho and omega exchanges (13a) and (13b) are both allowed but exactly cancel in the nonet symmetry limit to preserve the A- Z rule. The pion exchange (13c) cannot be cancelled by other exchanges like q and q ' because of large mass differences and should occur with the same strength as any other allowed pion exchange reaction. Thus A-Z violations occur when two-step processes arise without higher symmetries and degeneracies needed to cancel forbidden amplitudes as in (13a), (13b).

The reaction (12b) of double-charge exchange is forbidden by AQM but described by a connected diagram and not topologically forbidden. Theoretical arguments relate this type of "exotic exchange" reaction and reactions of the type (12a) which are described by a disconnected diagram [ 18 ]. The two-step

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ampl i t udes (12a ) and (12b ) are cance led by o the r

ampl i tudes unde r cer ta in s y m m e t r y assumpt ions , in

the same way that none t s y m m e t r y p roduces the can-

cel la t ions be tween (13a ) and (13b ) . But the same

symmet ry a rguments apply to bo th (12a ) and (12b) ,

which p roduce A - Z v io la t ing and exot ic exchange

t rans i t ions respect ively. Th is suggests that the two re-

ac t ions mus t be fo rb idden on s imi la r g rounds and

impl ies an incons i s tency or i ncomple t enes s in the

topologica l rule which forbids one reac t ion and not

the other. The A Q M f o r m u l a t i o n t reats the two on

the same foot ing.

References

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[ 20 ] G.J. Feldman, in: Experimental meson spectroscopy 1977, Proc. Fifth Intern. Conf. (Northeastern University, Boston, 1977), eds. E. von Goeler and R. Weinstein (Northeastern University Press, Boston, 1977) p. I.

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The Alexander-Zweig (OZI) in multiparticle production. Are there strange quarks in nucleons and pions?