The Bethe Salpeter equation provides the most widely used technique to extract bound states and resonances in a relativistic quantum field theory. Nevertheless a thorough discussion of how to identify its solutions with physical states is still missing. The occurrence of complex eigenvalues of the homogeneous Bethe Salpeter equation complicates this issue further. Using a perturbative expansion in the mass difference of the constituents we demonstrate for scalar fields bound by a scalar exchange that the underlying mechanism which results in complex eigenvalues is the crossing of a normal (or abnormal) with an abnormal state. Based on an investigation of the renormalization of one-particle properties we argue that these crossings happen beyond the applicability region of the ladder Bethe Salpeter equation. The implications for a fermion antifermion bound state in QED are discussed, and a consistent interpretation of the bound state spectrum of QED is proposed. Academic Press

We introduce diquarks as separable correlations in the two-quark Green's function to facilitate the description of baryons as relativistic three-quark bound states. These states then emerge as solutions of Bethe-Salpeter equations for quarks and diquarks that interact via quark exchange. When solving these equations we consider various dressing functions for the free quark and diquark propagators that prohibit the existence of corresponding asymptotic states and thus effectively parameterize confinement. We study the implications of qualitatively different dressing functions on the model predictions for the masses of the octet baryons as well as the electromagnetic and strong form factors of the nucleon. For different dressing functions we in particular compare the predictions for kaon photoproduction, γp → KΛ, and associated strangeness production, pp → pKΛ, with experimental data. This leads to conclusions on the permissibility of different dressing functions.

Abstract. We treat baryons as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. This description results as an approximation to the relativistic Faddeev equation for three quarks which yields an effective Bethe-Salpeter equation. Octet and decuplet masses and fully fourdimensional wave functions have been computed for two cases: assuming an essentially pointlike diquark on the one hand, and a diquark with internal structure on the other hand. Whereas the differences in the mass spectrum are fairly small, the nucleon electromagnetic form factors are greatly improved assuming a diquark with structure. First calculations to the pion-nucleon form factor also suggest improvements. I MOTIVATIONTwo approaches to the rich structure of strong interaction phenomena have been the topic of this workshop. The first one, effective theories like Chiral Perturbation Theory, resorts to including only physical fields with a suitable expansion parameter. The second approach, the building of effective models, often tries to interpolate between QCD and observable degrees of freedom by taking loans from the latter in terms of the assumed relevant degrees of freedom, such as (constituent) quarks. Different types of these models describe various aspects of baryon physics. Among them are nonrelativistic quark models, various sorts of bag models and approaches describing baryons by means of collective variables like topological or non-topological solitons [1]. Most of these models are designed to work in the low-energy region and generally do not match the calculations within perturbative QCD. Considering the great experimental progress in the medium energy range

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We treat baryons as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. We obtain fully four-dimensional wave functions for both octet and decuplet baryons as solutions of the corresponding BetheSalpeter equation. Applications currently under investigation are: electromagnetic and strong form factors and strangeness production processes. MotivationDifferent types of hadronic models describe various aspects of baryon physics. Among them are nonrelativistic quark models, various sorts of bag models and approaches describing baryons by means of collective variables like topological or non-topological solitons [1]. Most of these models are designed to work in the low energy region and generally do not match the calculations within perturbative QCD. Considering the great experimental progress in the medium energy range [2], there is a high demand for models describing baryon physics in this region that connects the low and high energy regimes. To make progress in this direction we investigate a covariant formulation of a diquark-quark-model of baryons.Our motivation to choose such an approach is fed from two sources. On the one hand, when starting with the fully relativistic Faddeev equation for bound states of three quarks, diquarks appear as effective degrees of freedom. These diquarks stand for correlated quark-quark pairs inside baryons. Thus they should not be confused with the notion of diquark condensates in the context of colour superconductivity. On the other hand, diquarks as constituents of baryons are naturally obtained when one starts with an NJLtype of model of colour octet flavour singlet quark currents [3]. Although in the limit N c → ∞ baryons emerge as solitons of meson fields [4], it can be shown for the case of three colours that both effects, binding through quark exchange in the diquark-quark picture and through mesonic effects, contribute equally [5]. * Supported by the BMBF (06-TU-888) and by the DFG (We 1254/4-1). Talk given by R. Alkofer at PANIC 99.