Physics Letters B 273 ( 1991 ) 301-305 North-Holland PHYSICS LETTERS B

A test of the OZI-rule in proton-antiproton annihilation

R. D e c k e r and D. Woi t sch i t zky Institut ff~r Theoretische Teilchenphysik, Universitiit Karlsruhe, Pfi 6980, W-7500 Karlsruhe 1, FRG

Received 17 August 1991; revised manuscript received 2 October 1991

We show that the comparison of some two-body decay channels in proton-antiproton annihilation yields a good test of the validity of the OZI-rule in baryons and the presence of strangeness in the proton.

According to the naive quark model [ 1 ] the proton wave function contains two u quarks and a d quark. The model provides a good explanation of the hadron structure at small momenta transfers. On the other hand deep inelastic scattering yields a different picture with more constituents, notably sea quarks and gluons as predicted by QCD [ 2 ].

However, several experimental findings refute this naive picture at large distances. The first indication came from the pion-nucleon ~ term. Indeed the a term as derived from r~-N data and its computat ion in the frame- work ofchiral symmetry and using the Gel l -Mann-Okubo-mass formula disagree [ 3 ] unless the proton contains some strangeness,

(P I~s lP ) = 0 . 1 0 . (1) ( p l O u + d d l p )

Of course the reader should be aware that the former prediction relies heavily on the application of first-order perturbation theory to the baryon mass splittings, an assumption which can be easily questioned.

Further hints for strangeness in the proton are obtained from elastic scattering of electrons [4,5 ] or neutrinos [6,7 ] off protons. In these experiments the vector and axial-vector currents are tested. For instance sizeable contributions o f strange quarks to the magnetic moment

/~s/~tu -~ ¼/td/#u -----0.08 (2)

and to the charge radius

2 2 I ~ 2 / ~ 2 rs /ru 20 .10 (3)

of the proton are derived within a vector-meson dominance model for the electromagnetic form factors [5 ]. The predictions of this model can be verified in elastic scattering of polarized electrons [ 8 ]. Finally a precise determination of the axial-vector matrix element A s Mp' ( = ( p I STu ~5 S I P ) ) from neutrino scattering is veiled by the anomaly problem and also by SU ( 3 ) f breaking effects (F and D coupling constants). However, the general conclusion is that Mp A'S is not vanishing [ 7 ]. The same result is obtained from the EMC measurement [ 9 ] which indicates a violation of the Ellis-Jaffe sum rule [ 10 ]. A simple explanation of this violation is the presence of strange quarks in the proton. Note, however, that other explanations of the EMC data exist: either the presence of a strong gluonic contribution [ 11 ] or some special effects of chiral symmetry [ 12 ].

The application of the OZI-rule [ 13 ] to baryons has been discussed in great detail in a recent paper [ 14 ] and the predictions of OZI-evading couplings have been catalogued, especially for pion-nucleon scattering, pp an- nihilation and pp scattering. Some critical comment on this approach can be found in ref. [ 15 ].

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From the experimental side recent publications [ 16] observe an enhancement of 0 production in plb annihi- lation as compared to naive expectations. These authors conclude on strong violation of the OZI.

In this paper we would like to clarify what is meant by a strong violation of the OZI-rule and what can be deduced for the presence of strangeness in the proton. We will concentrate on some educated two-body decay channels in lOp annihilation.

First of all, we would like to emphasize once more [ 17 ] that it is a delicate point to conclude from a measure- ment of 0 production in lop annihilation on the kind of OZI-violation. In order to make our point let us consider the four decays

a (pp~co~) , a(pp--+coq), a(ISp--,0rt) and a(1)p~0rl) . (4)

For the time being we assume the OZI-rule (or the so-called quark line diagram method) and we derive some simple results. The two-body decays can be described by annihilation diagrams alone or by an admixture of annihilation and rearrangement diagrams (fig. 1 ). On the quark level both models forbid several flavour combinations

A ((yp--*QsQu) =A (15p~QsQd) =A (pp~QsQs) = 0, (5)

where Qj =qiqi. Furthermore the annihilation model predicts A (pp~QdQa) =0. Finally one ends up by a linear combination

of amplitudes with the quark content QuQu, QdQd and QaQu. The decay into mesons is obtained by the projec- tion of the quark flavours on the corresponding meson states

A (lop--*MI M2) = ~ A(fap~QiQ2) x <QiIMI > × (Q2 [M2 > , (6)

where we have suppressed all Lorentz and Dirac indices. If the OZI-rule holds exactly, then eq. (5) implies that the 0-meson production is forbidden in lop annihila-

tion. On the other hand it is well known that the OZI-rule is even slightly violated in the vector-meson sector: the 0-c0 mixing is not ideal. Therefore some produced O mesons can be explained through their tiny Ou + dd content. However, because of the uncertainties in the mixing angle (quadratic and linear mass formulae give quite different results) a determination of OZI-violation beside the vector-meson mixing is extremely difficult. The situation is worse for decays involving only pseudoscalar particles since there the deviation from ideal mixing is huge and therefore we expect no sizeable changes if the OZI-rule is violated beside the mixing. This explains our choice of the decays in eq. (4).

Finally the computation of the decays in eq. (4) cannot be done without a detailed model. In fact the decay states Vx and Vq have different isospin so that we do not expect a cancellation of the dynamics in the ratio of the amplitudes. On the other hand the ratios R j - a(pp--,OMj)/a(lbpocoMj) are free of the dynamics but depend strongly on the vector-meson mixing angle. Neglecting phase space differences (rn,o # m,) we obtain

R i =tan20, (7)

where tan 0 ( = 0.03) is the deviation from ideal mixing of the 0-co-system. As stated previously the hardly known mixing angle in eq. (7) does not allow to establish firmly OZI-violation beside the vector-meson mixing. On the other hand if we consider the ratio of R~ and R, tan 0 is cancelled and assuming no further OZI-violation we predict

I I Fig. 1. Annihilation diagrams contributing to the pp-+MI +M2 decay amplitude.

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R J R , ~- 1. (8)

Any deviation from eq. (8) must be explained by some specific OZI-violation in the baryon system. We analyze these deviations with respect to the strangeness content in the proton wave function.

Assume that the proton wave function has some strangeness content.

~Up = a l uud> +flluud~s> + .... (9)

Then the diagrams of fig. 2 contribute also to the previously considered decays. Diagrams which are propor- tional to f12 (strangeness in the proton and the antiproton) are neglected. Note that because of the smallness of the vector-meson mixing angle the contributions of fig. 2 are negligible in the decay amplitudes with an to meson. The situation is different for those decays involving a ¢. Indeed the dominant amplitude (fig. 1 ) is suppressed by mixing and therefore the new amplitudes can compete.

Since our model is very crude (but quite general), we will not be able to derive the strangeness content [fl of eq. (9) ] of the proton explicitly. On the other hand we are able to derive the relative strength of the different matrix elements (which are products offl and annihilation amplitudes) and we will show that they have reason- able sizes.

Let us briefly present our model, the double annihilation model [ 18 ] which has to be slightly modified for the present purpose. The structure of the hamiltonian of the double-annihilation model is obtained from the anni- hilation of two pairs of quarks and antiquarks into gluons. Note that in the isospin limit the contribution of the three-gluon coupling can be neglected. Then the SU (6) wave functions are used in order to reduce the matrix elements of < p~ I SI MM' >. Our extension of this model consists of modifying the SU (6) wave function of the proton in such a way that an sg contribution can be added. Then the double-annihilation model [ 18 ] contains the diagrams of fig. 2. In this framework we obtain

R, tr(pp--,ton) ( 1-sinOa<2Q.+Qa,n> )2 = ~ ( 0 p - ~ t o ~ ) - M<pfalSIto~>va~-sinOa<2Qu+Qolq>-sinOb<Qsl~> XPh. sp.,

R , = a ( p p ~ r t ) ( M<pf~ISIQn>va,+cosOa<2Qu+QoIn> )2 a ( 0 p ~ T I ) = M<pfalSICprl>va,+cosOa<2Qu+QalTl>+cosOb<Qsltl> ×Ph. sp., (10)

with M a normalization factor ( M = < PlblSI tore > ~a~ ) the matrix element of the valence quarks alone, a and b are the contributions (normalized to M) of the diagrams, figs. 2a and 2b, respectively. For details see ref. [ 19 ]. Note that the ratio R, depends on the to-~ mixing angle and therefore the fit of a and b is 0 dependent. On the other hand since the sg content of the to meson and a and b are small, it appears that Ro, is almost independent on 0.

Since the cross sections of eq. (4) are not yet experimentally known we assume two large values for the ratio

R J R n = 0.010 + 0.005, R J R n = 8 + 2, ( 11 a,b)

and then we solve our system of unknown amplitudes assuming them to be real. The results are given in table 1.

S S S I

I

' 1 0 '1 (a) (b)

S

Fig. 2. Supplementary diagrams due to the presence of non-valence ~s quarks.

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Table l Using the input parameters ofeq. ( 11 ) we derive the relative strength of the amplitudes which occur if some strangeness is present in the proton.

R~/Rq a/M b/M

8 +2 --v.v.O/~"/ + 0.04__0.O8 0 . 5 5 -~- _--0"701.27

0.010+0.005_ --0.11 + -o.o1+°'°5 --0.14 + -o.o3+°'14

Table 2 Using SU(3 )f symmetry we extend our results to other decay channels. The experimental values have been derived from ref. [20] by adding the errors linearly.

a(qp°)/a(q'p ° ) tr(rlp°)/a0t°p ° ) a(W p°)/tr(Tt°p ° )

R,JRn=8 _+2 5.2_+ -Tt~ 0.13_+-8.82 n n.~+o.o, . -- . v . v z . _ _ 0.01

7.3 _ +2.7 . . . . . O.Ol 0.02 _+ -o.ol RJRn=O.OIO+.O.O05 -0.7 n la+O.OO +o.oo valence quarks only 2.7 0.10 0.04 experiment 0 -~-o.t52a + o.2o 0.09 _+ olo5° os

Here a few c o m m e n t s are in order. In the OZI - l imi t a n d neglect ing phase space correct ions we have shown that R~/Rn ~ I. This impl ies that the values in eq. ( 11 ) are order of m a g n i t u d e v io la t ions of the OZI-rule . Therefore del icate cancel la t ions have to occur an d we expect that the ampl i tudes a a n d b depend strongly on the rat io in eq. ( 11 ). F ina l ly using SU (3) v a n d our inpu ts in eq. ( 11 ) we predict the results in table 2 and compare t hem with the OZI- ru le predict ions . Since d iagram 2b does no t con t r ibu te in react ions like p p - ~ M p °, the results for bo th values of eq. ( 11 ) are near ly the same. Note, however, that s t rangeness in the p ro ton has a wel l -def ined s ignature in these ratios. The q ' pO channe l is decreased while the qpO channe l is increased. The predic ted b ranch- ing ratios are of course in agreement with the poor expe r imen t [20 ]. Note that the a n n i h i l a t i o n mode l yields reasonable fits o f the exper imenta l ly bet ter k n o w n decay channels [ 18,19 ].

Conclusions. We have analyzed several two-body decays of p r o t o n - a n t i p r o t o n ann ih i l a t ion . We have po in t ed out that ~ p roduc t ion is a sign of OZI -v io la t ion bu t that a d e t e r m i n a t i o n of OZI- ru le v io la t ion beside the vector- meson mass mix ing needs a more careful t rea tment . We have advoca ted to cons ider the rat io of R~ and R , as a sensi t ive parameter . I f the comple te OZI -v io l a t i on is due to m eson mass mix ing then this rat io is predic ted to be one ( m o d u l o phase space correc t ions) . A conf l ic t ing m e a s u r e m e n t has to be seen as an OZI -v io la t ion in the ba ryon ic sector and is a fur ther i nd i ca t ion of s t rangeness in the pro ton .

We thank Dr. Nowakowski for helpful c o m m e n t s and careful reading of the paper. This work has been sup- por ted in par t by the Landesgraduie r tenf6rderung .

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