Glueballs

At zero temperature and quark chemical potential the simplest effective Lagrangian describing a relevant part of the nonperturbative physics of the Yang-Mills (YM) theory is the glueball Lagrangian whose potential is [1-4] ... 

The spectrum in the 2SC state is made of 5 massive Gluons with a mass of the order of the gap, 3 massless Gluons confined (at zero temperature) into light glueballs and gapless up and down quarks in the direction (say) 3 of color. 

The SUC(2) gauge symmetry does not break spontaneously and confines. Calling H a mass dimension four composite field describing the scalar glueball we can construct the following Lagrangian [44] ... 

According to the present normalization of the glueball field A4 is v A4 with A the intrinsic scale of SUC(2) after the coordinates have been appropriately rescaled [46, 44] to eliminate the v dependence from the action. 

Using this Lagrangian one can estimate the SUC(2) glueball melting temperature to be [47] ... 

The term quarkonium is used to denote any qq bound state system in analogy to positronium in the e+e system. But it is only for heavy quarks that a non-relativistic approach can be justified. In this chapter we deal with the charmonium and bottomonium states whose data was analysed in Chapter 11. We also briefly consider glueballs. There exist several good reviews on the subject (Berkelman, 1986 Kwong et al., 1987 Lichtenberg, 1987 Schindler, 1986). 

Note that radiative J/ decays may be an ideal laboratory for glueball searches. This point will be briefly discussed in Section 12.4. 

We shall return to this point later (Section 12.5.1) but it is worth pointing out here the particular importance of Fig. 12.9(d). Should a resonance peak be observed in the energy distribution of the inclusive photon or in the mass of the hadronic final state, this would be an unequivocal signal for a glueball, i.e. for a flavourless bound state made of two gluons. 

Predictions for glueball masses have been made in all approaches lattice calculations, QCD sum rules, bag models, effective Lagrangians and potential models. There is an extensive literature on the subject see Kopke and Wermes (1989). 

Theoretical predictions for the masses of those glueballs, which have been most intensively searched for, are shown in Fig. 12.10. 

One can make a naive estimate of the production rate for the various species of particles, mesons (M), hybrids (H) and glueballs (Q) by simply counting powers of em and strong coupling constants (Chanowitz, 1987). 

As already mentioned, radiative J/ decay is the type of reaction where evidence for glueballs might be particularly clean. The 7 energy spectrum in... 

As can be seen, not all the resonances for which there is evidence are glueball candidates. But some are, noticeably the most famous glueball candidates, the pseudo-scalar t(1440), now renamed 7(1440) by the Particle Data Group, with = 0+(0 ), and the tensor (1690), now... 

Such an enormous discrepancy between theory and experiment is disastrous but, interestingly, a nice escape route exists (Brodsky et al., 1987). The trouble may be a signal for the existence of a glueball state of mass Mg close to the J/ (FVeund and Nambu, 1975). Looked at this way it is the JQir width that is enhanced by the nearby resonance. The calculated ratio of branching firactions (12.6.4) should now be multiplied... 

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