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.