A Classic Thesis Style - Johannes Gutenberg-Universität Mainz

1.4 theoretical models 11
For those processes in which the quark masses can be neglected and
the external momenta are small, the effective field theory constructed
with a Lagrangian consistent with the (approximate) chiral symmetry
of QCD, called Chiral perturbation theory (ChPT), provides a valid
computational scheme [12]. Chiral lagrangians result very successful
for pion electroproduction but due the relatively large strange quark
mass serious difficulties appear in the calculation of processes involving
kaons. ChPT kaon production calculations have been performed
only up to 100 MeV over threshold. The results are encouraging as
the comparison with the existing data is reasonably good but still
insufficient for a theoretical description of Kaos measurements where
energies over threshold of 150 MeV have been used [13].
A successful description of photoproduction has been obtained with
hadronic field theories. This approach is based on effective degrees
of freedom, mesons and baryons treated as a single entities, characterized
by properties such as mass, charge, spin, form factors, and
coupling constants (e.g. [14, 15, 16]). As we have seen, electroproduction
processes can be formally reduced to the binary process of
photoproduction by a virtual photon.
The different s, t and u diagrams for the lowest-order p(γ ∗ ; K)Y
amplitude can be classified in non-resonant and resonant types, and
are shown in Figs. 3 and 4 respectively. The names of the different
channels correspond to the relevant Mandelstam variable describing
the momentum exchanged in a particular diagram. Only hyperon
resonances can be exchanged in the u-channel due to the conservation
of strangeness. Finite decay widths are taken into account by
modifying the propagator denominators in the s channel with the
substitution: s − m 2 R → s − m2 R + imrΓR where mR is the mass of the
interchanged particle in the diagram and ΓR its width. Also visible in
Fig. 4 is a high precision measurement by the CLAS collaboration for
the total photoproduction cross-section as a function of the CM energy.
A clear resonance structure sitting on a continuous background near
threshold can be observed. This general structure is nicely explained
by the isobaric model as only the propagators in the s-channel terms
involving an excited state can reach their poles. The t- and u-channel
diagrams and the ground state nucleon s-channel term can not reach
their poles because of energy-momentum conservation and can be
seen as background contributions.
There is some ambiguity with respect to the structure of the KYN
vertex in the sense that pseudo-scalar or pseudo-vector coupling for
the interaction Lagrangians are possible. This issue has been studied
by several authors but neither of the two possibilities has yet been
confirmed as correct [17].
This approximation, where unitarity is lost, gives rise to the so called
isobaric models (originally introduced by [18]). Coupled-channels (or
rescattering) effects can be analyzed in the more general framework