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7.1 VMD for near the resonance region

A general review on VMD and many of its results can be found in ref. [1]. Here, we simply concentrate on the main formulae for annihilations. In this case, the crucial point in the model is the assumption that the blob in Fig.(1), connecting the intermediate photon to the final hadronic state, reduces to a vector meson (or sum over vector mesons) propagator(s). More precisely, the diagram is assumed to contain a conversion vertex (with a coupling given by ), followed by the V-propagator and the final V-decay vertex into f (with a coupling constant). The cross-section turns out to be

with the sum extending over the relevant V-mesons, F(s) being the final phase space factor and

The values of the couplings can be extracted from data [11] through and are essentially compatible with the nonet symmetry and ideal mixing predictions . For the various final states f, one has in such a way that the -cross section factorizes into a V-production and V-decay factor. More explicitly, at a resonance peak, one has

The particularization of the above formulae to the pseudoscalar form factor case is extremely simple. For pions one has

where the VMD relation has been used. For kaons one similarly obtains

where the numerical coefficients follow from SU(3) Clebsch-Gordans and quark charges. These F.F. satisfy the simple VMD relation .

The above simple equations give a quite reasonable description of pseudoscalar pair production below , thus showing the adequacy of the naive VMD hypothesis. For a more accurate description further details and fine tuning of parameters is required. This proceeds in two main directions. One consists in extending the sum not only to the lowest-lying V-mesons but also to their high-mass recurrencies or radial excitations. Small improvements are then obtained along the lines of refs. [18] [4] and [14]. A second line of improvement consists in introducing SU(3)-breaking effects as described in detail in a next section [15]. The later are of interest in Daphne, where and mixings (or, equivalently, the precise quark content of the ) should be accurately measured.

The transition form factors are readily obtained in the VMD context. Now one has

leading to an economical and reasonable description of the data. Again, some improvements can be performed along the same lines as before. Details can be found in refs. [16] and [15] in these proceedings.



next up previous
Next: 7.2 Models for F.F. Up: 7 Models for form Previous: 7 Models for form



Carlos E.Piedrafita