Resonances and decay widths within a relativistic coupled channel approach
We present a microscopic model for hadron resonances which contains, in addition to constituent (anti)quarks, mesonic degrees of freedom. It is assumed that the (anti)quarks are confined by an instantaneous potential and that the mesons can couple directly to the (anti)quarks. This system is treated within a relativistic coupled-channel formalism in order to take the dynamics of the mesonic degrees of freedom fully into account. It is demonstrated that the mass eigenvalue problem for such a system can be reformulated as a purely hadronic eigenvalue problem in which bare hadrons, i.e. eigenstates of the pure confinement problem, are coupled via meson loops. The substructure of the bare hadrons is then hidden in (bare) hadron-meson vertex form factors. It is shown for a simple toy model that such a kind of approach may lead to reasonable (non-perturbative) decay widths for hadron resonances.