Volume 68B, number 2 PHYSICS LETTERS 23 May 1911

THE SUPPRESSION OF tiDjj PRODUCTION AND ITS IMPLICATIONS FOR THE OZI RULE

M. TEPER Laboratoire de Physique Thiorique et Particules Elkmentaires, BLtiment 21 I, Universitk de Paris&d, 91405 Orsay, France’

Received 7 March 1977

The observed suppression of associated charm production is shown to be explained naturally within the framework of asymptotic freedom; implications for the OZI rule are discussed.

One of the surprising experimental results on ha- dronic $ pr,oduction has been the non-observation of associated charmed meson (D) production [ 11. Exper- iments (at s - 500 to 600 GeV2) find [2, 31 .

“p~p+Dc+..- 2 o(10-2),

pp’ $ + . . . (1)

using reasonable estimates of semileptonic branching ratios for the D. Theoretical predictions on the other hand have favoured a ratio for (1) that is much greater than unity (at s x 600 GeV2). This is true of Drell-Yan

models involving quark interactions (charmed [4] or

not). More significantly perhaps this is also true of

standard multiperipheral calculations [5] : a descrip-

tion in terms of hadrons is surely correct, being com- plementary to the correct microscopic Drell-Yan de- scription. In fig. 1 we display the results of a numeri-

cal multiperipheral calculation [5] which of course incorporate correct kinematics and Imin effects.

The band is the prediction for $DD production;

the width of the band is a measure of the expected theoretical error. Broken W(4) couplings were used in the calculation: these couplings (following the usual pattern of SU(3) coupling breaking) give a good value for $ photoproduction [6]. Pure SU(4) couplings would lower the band by a factor of ten, but are not acceptable in view of the correspondingly small pre- dicted J/ photoproduction cross-section (however, the following arguments are not at all affected by this). The lower line is an estimate of non-associated $ pro-

1 Laboratoire associd au Centre National de la Recherche Scientifique.

duction: since the $ width is about low4 of usual widths and since the mass of a pi5 pair (typically a AA, say - excpet at lows -with some relative kinetic energy) is close to the $ mass, we have made the esti- mate by simply plotting 10e4 X (np). The data shown does indeed demonstrate that this is a reasonable esti- mate. The problem resides of course in (1): a discrep- ancy of several orders of magnitude between theory

Fig. 1. Multiperipheral predictions for hadronic $ production: associated (band) and an estimate of non-associated produc- tion (line). The data points are from the compilation in ref. [l].

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Volume 68B, number 2 PHYSICS LETTERS 23 May 1977

and experiment. It is not conceivable that this is due to the unusual kinematics: the multiperipheral model describes reasonably well pj$ production at energies, s’, such that mpp/(fi- 2mp) is comparable to

mQD~/(&-2mp) with s a 600GeVZ. We can only conclude that the transition of ordinary hadrons to

$DD, which involves only a connected planar quark

diagram, and should thus not be suppressed by usual OZI criteria [7] does in fact suffer a drastic and mys- terious suppression.

One might accordingly suspect - since $DD is very much like two DD pairs - that we shall have another, although less dramatic, experimental surprise with the hadronic production of charmed particles. There is al- ready some indication for this: an emulsion experi- ment [8] finds that oDjj ~1.5ybats=600GeV2

provided that the D lifetime lies between lo-l2 and

lo-l4 s. In contrast, the multiperipheral prediction gives a value about an order of magnitude higher than may be estimated below. Consider fig. 2 for the pro- duction of heavy pairs A, A. The number of pairs equals approximately the number of links. Applying this to DD and pp pairs we have

Using o&, x 8 mb, as required to obtain a reasonable

J/ photoproduction cross-section [6], we find oDc e 10 pub. A better calculation [5] obtains a slightly

larger answer. There seems to be an order of magni- tude discrepancy developing between theory and experiment (the Drell-Yan calculation in ref. [4] also gives about 10pb).

To understand what is happening we must go to a more dynamical level than is possible through macro- scopic multiperipheral considerations. In the usual field theory of strong interactions [9] one calculates

P

I A A t

A

P Fig. 2. Multiperipheral amplitude for producing a heavy pair of particles A and A.

184

P

Fig. 3. Amplitude for producing J/ in a pp collision, assuming it goes by the inverse of $ decay (and assuming an asymptoti- cally free theory). g denotes a gluon and c the charmed quark.

$ decay using lowest order perturbation theory, since the running coupling (appropriate to calculating the

photon self-energy with external legs scaled to q2 = rng = hqi) is small, os (m$) X l/4. One may imagine

the inverse of this process as being responsible for

J/ production, see fig. 3. The coupling of the gluons to the incident hadron

system is not made specific since the perturbation theory arguments do not permit being so explicit. Such a scheme has been used [lo] with the assump tion that the gluons come from the gluon component of the parton sea, and predicts oDIj x !j - 2 mb at s = 600 GeV2 which is consistent with the experimental results mentioned earlier. To calculate $DD produc- tion within such a scheme, we first observe that the formation diagram is as in fig. 4a. However, to go any

further would seem to involve many assumptions. We. find it more convenient and model independent to return, at this point, to our macroscopic multiperiph- era1 description. Before doing so, however, we require one more observation. The production of $DD in fig. 4a is almost identical (from the point of view of

the field theory) to the production of $J, via a loop

p P

_ ”

P P

(0) (b)

Fig. 4. (a) Hadronic production of $DD from the field theory viewpoint. (b) Fig. 4(a) redrawn to look like $$ production.

Volume 68B, number 2 PHYSICS LETTERS 23 May 1977

as in fig. 4b (note that the production of two separate

$‘s is much smaller since it involves extra gluons and wavefunction factors). The difference is that J/DD arises when one of the legs of the loop is excited and dissociated into a DE pair. This kinematical difference will not be important if we are only interested in an

approximate estimate, especially since the kinematics

limits the relative subenergies of the $, D and D. Thus, the lesson of our microscopic excursion is

that $Do production is indeed suppressed, and that an estimate of its cross-section may be obtained by calculating instead the production of a $ loop. This can be readily done in the multiperipheral model, in an essentially model independent way. Turn back to

fig. 2 and let A now be $ and p respectively. Then

If we are interested in s = 600 GeV2, then the cross-

sections are to be evaluated at energies of -35 GeV2, and there we know from experiment [6] that roughly

%P-+LLX - 10e2 mb. So

a pp-+$DfiX ~ aPP-QILX

(5 PP-*tiX Opp+ X

z (+$ j, aPP x4x 10-3’1 ) Olcl

where we have inserted an error of +l in the exponent to cater both to the errors mentioned above which would tend to increase our result, and off-shell effects which would tend to decrease our result (for example [6] continuing the J/ legs in uQp to zero mass gives a

factor of about l/4). We now have a result entirely consistent with experiment.

This calculation highlights the difference between the S-matrix and field theoretic interpretations of the OZI rule. The production of $DD involves only con-

netted planar diagrams and is thus not suppressed from the S-matrix point of view. The field theory, on the other hand, does not care about the topological structure of quark diagrams, but only about whether heavy quark loops are being created, and so, predicts

a dramatic suppression of $DD. Experiment appears to be unequivocal in its support of the latter viewpoint

in this instance. We may conclude, then, that for charm the OZI rules are primarily effected through the field theoretic mechanism. One could obviously speculate about strange quarks but the theoretical extension is not well enough justified to motivate us to do so here.

We thank Tran Thanh Van for discussions, and the CNRS for financial support.

References

[l] For reviews see: D. Hitlin, lectures at the 1976 SLAC Summer School, SLAC publications; K.C. Stanfield, rapporteur’s talk at Meeting of Division of particle and fields, October 6, 1976; Purdue preprint COO-1428-439 (Dec. 1976).

[2] M. Binkley et al., Phys. Rev. Lett. 37 (1976) 578. [3] K.J. Anderson et al., submitted to XVIII Conf. on High

energy physics, Tbilisi, USSR (1976). [4] D. Sivers, Nucl. Phys. B106 (1976) 95. [5] G. Aubrecht, J.W. Dash, M.S.K. Razmi and M. Teper,

Phys. Rev. D14 (1976) 2304. [6] M. Teper, J.W. Dash and M.S.K. Razmi, Phys. Lett. B57

(1975) 51; G. Aubrecht, J.W. Dash, M.S.K. Razmi and M. Teper, (Oregon Preprint), Phys. Rev. D, to be published.

[7] For a recent review see: H.J. Lipkin, Proc. XI Rencontre de Moriond, 1976. Vol. I, p. 327.

[8] G. Coremans-Bertrand et al., Phys. Lett. 65B (1976) 480.

[9] T. Appelquist and H.D. Politzer, Phys. Rev. Lett. 34 (1975) 43.

[lo] M.B. Einhorn and S.D. Ellis, Phys. Rev. D12 (1975) 2007.

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