A MECHANISM for GLUEBALL PRODUCTION Ccnposed of Quark-Aituijark
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IC/84/112 Internal Report (Limited Distribution) 1. INTRODUCTION: Quantum Chromodynamics (QCD) is now accepted as the theory of strong , Iriternational Atocaic Energy Agency •••••• • - l)-2).- • ] and interactions. Since gluohs also carry colour, existence o:f glueballs . : United Nations Educational Scientific and Cultural Organization as a colour singlet multigluon resonant state was predicted within QCD -SljfTERNATIONAL CENTRE FOR THEORETICAL PHYSICS framework. Since gluons do not possess charge or flavour quantum numbers, any ccrrpcsite states of glucns must be neutral, flavourless and of baryon nuitjer zero, ttowever, a neutral, flavourless state can in general be either a glueball or an ordinary or exotic meson A MECHANISM FOR GLUEBALL PRODUCTION ccnposed of quark-aitUijark. This gives rise to the problem of finding some way of distinguishing neutral flavourless mesons made of quark-antiquark pairs *• C.P. Singh from glueballs. As the field of glueballs is maturing fast, the experimental International Centre for Theoretical Physics, Trieste, Italy. search for such states has proven to be a difficult one. So far we do not and have any easy test for experimentally establishing the existence of a S.N.. Ram gluonium or glueball state. In the past, a number of guiding principles Department of Physics, Banaras Hindu University, Varanasi 221005, India. have been put forward to test experimentally the production of a gluonium e.g. the width of the gluoniura state should be of the order qf geometric »ean of OZI rule allowed and OZI rule suppressed decay widths; quarkonia ABSTRACT states should decay into gluonium states and finally a gluonium should have A production mechanism is suggested to test the production of a flavour independent couplings to its decay channels. However, these criteria glueball resonance in the process TT p—» 0^h. • Our results 4) have been debated quite recently and it was shown that gluonia can have indicate that g resonance in this process corresponds to a quarkonium typical hadronic widths ( ** 100 HeV). It was also pointed out that the (ss) state. mixing with quarkonia states with similar quantum numbers would influence the decay channel of agluonium resonance. At present there are several experimental candidates for glueballs, but no conclusive evidence for them exists. Recently Etkin et al. have studied an OZI-rule forbidden reaction TT~ p—• <p<$ n and observed the MIRAMARE - TRIESTE enhancement around 2.20 GeV in the mass plot. They have shown that their August 1984 results can be explained well in terms of three tensor resonances g (2120), g'{2220) and g"(236O) which they claim as possible candidates for glueballs. The main reason for considering these states as glueballs is that although they are produced in reactions which are doubly forbidden by * To be submitted for publication Zweig's rule, their cross-sections are substantial and comparable to those •• Permanent Address: Department of Physics, Banaras Hindu University, for Zweig allowed reactions. This interpretation for the identification of Varanasi 221005, India. a glueball has sparked controversies in the literature . In view of - 2 - such a confusing situation, it looks worthwhile to outline a dynamical through at least two-gluon exchanges. Moreover, TIT—> gg apralitude in mechanism for the production of gm resonances in "T"? interaction and Fig. l(b) for the gluonium production can be approximated by a resonance T which couples to both channels. Thus after combining these two effects, we which may servo as a necessary criterion for the experimental search of a 2 glueball statf. find that g coupling would be suppressed by a larger factor g<yi * TT TT The ha-J:onie production of g.luebaJ.1 resonances has been recently 4 11)-14) than ck (;£> 1/10O) if g is a quarkonium resonance. Considering the discussed by many people. However, almost all these mechanisms S 6) T experimental nature of peripheral production and neglecting the spin suggested Tor the central production of glueballs in pp or pp complications, we can parametrize the "TT-Regge exchange amplitude for the collisions are based on the consideration of gluon fusion diagrams. peripheral production of g resonance as The theoretical results indicate that the ulueball production in pp -*• ex is copious and the cross-section is comparable to any other hadronic reaction crt>Ss-se.?tion ("several, mb). However, these mechanisms hardly distinguish between a glueball resonance and a quarkonium state. The A IT ») - purpose of this paper is to suggest a peripheral production mechanism which can distinguish between gluonium and quarkonium production and thus to (2) lay down the criterion for the experimental search of a glueball state. 14 5 s 1 = where i^-p*^ ' ' 0 ° ^' § +1, and Regge trajectory ^(t) = 0.72 ( t - n^j. ). We finally get 2. METHOD OF CALCULATION (3) The production mechanism is clearly shown in quark line diagrams of 1 -2.8 nsK' Figs. 1. We suggest that the difference between a quarkonium and a gluonium where K is the squared cm. momentum of initial pion and s, t are the production lies at the vertex g TT IT as shown in Fig. l(a) and l(b), T usual Mandelstam variables. The decay width of a tensor meson is related respectively. We consider that the decay g —» A <& in the process: to the coupling constant as follows: 71 7T (1) is unimportant for our phenomenological scheme, since if g is a where we have also considered a phase space factor of - for identical quarkonium (ss) state, g—* <f> <y> decay does not involve hairpin diagram particles and a factor of 3 for summation over three states. Here p is and therefore, it should not be suppressed. On the other hand, if g is the momentum of pion in the rest frame of g . a gluonium state with very large width, Ig —* rf><i can be of the order of hadronic decay width ( /"* 50 MeV). However, the difference between a quarkonium and a gluonium state becomes prominent for the g —• Ti~TT decay. 3. RESULT AND DISCUSSION In case g is an ss quarkonium state, it couples to TT TT states Result of our calculation is shown in Fig.2. We have taken in our — 3 — to be alculation the value or ' ST T i-e.fthe minimum value for behaviour of a gluonium which is considered/its main feature. Moreover, a 17),IB) any hadronic width. The cross-section 0" (n~*p —» <p <J> 0 } is more complete analysis including three body mixing was performed in experimentally reported as 20 nanobarns which is far below our values for the case of another glueball candidate © (1640)—^"TTTT decay and it g production. However, if we take a suppression factor larger than 1/100 does not seem to be consistent with experiment. into our calculation, the numerical results would become compatible with the In a future publication we plan to calculate the consequences of our experimental value. Thus according to our scheme, e corresponds to a model to test the suppression of production cross-sections of all OZI-rule 19) quarkonium (ss) resonance. The failure to observe this resonance in J/y violating processes which require two-step unitary diagrams to explain decays supports our prediction. their dynamical origin. In our calculation, we have considered g t TTTT We have shown in Fig.2, the differential cross-section from Eq.(3) as a dynamical vertex as shown in Fig. l(b) for quarkonium production. In when the partial width I g _^—. = 1 MeV. Thus we believe that if g is our scheme, the threshold enhancement of the production cross section for a gluonium, its decay/into TT Tr cannot be less than 1 MeV because of its OZI-rule violating processes is related to the increase in the strong flavour symmetrical decays. Therefore, in our opinion the graph in Fig.2 interaction coupling 0^ . As the energy for TT~~p interaction increases. shows the lower limit on the cross-section for gluonium resonance production. the energy of the resonance increases and the value of decreases. Since quarkonium production i.s suppressed, it can be safely considered that Apart from the usual Regge energy dependence, the variation of the coupling the quarkonium production will lie far below the curve shown in Fig.2. 2 g TrTr ^n our sc'r!eme w<>uld also contribute to the energy dependence Thus our scheme clearly lays down a limit for a gluonium production in TT~p of the OZI-rule violating processes. This can be considered as an added production and makes a distinction between a quarkonium and a gluonium feature of our model. production. It Bhould be mentioned here that the validity of our phenomenological scheme rests on the Hegge parametrization of the high energy TT p—• g_n ACKNOWLEDGMENTS scattering amplitude and also on the consideration . that there is no One of the authors (C.P.S.) is-grateful to Professor Abdus Salam, the mixing present in the quarkoniuia and gluonium states around the energy International Atomic Energy Agency and UNESCO for hospitality at the region7"2.2 GeV. It has been shown by Caruso et al. that a similar International Centre for Theoretical Physics, Trieste. Regge parametrization gives good qualitative account of the total invariant mass distribution of <p <i in the process "n"""f>—» <j> ^ n . However, we emphasize here the quantitative aspect of the prediction which would change their interpretation of the resonance as a gluebs.ll. The problem would certainly' be complicated if a has both giuonic as well as quark-anti- 16) quark components in its wave function . In that case we do not find any way to distinguish, between quarkonium and gluoniutn states. Moreover, by adjusting the mixing angle one can suppress any hadronic decay mode such as g —» TTTf so that our quantitative results are reproduced.