DOI 10.1140/epja/i2002-10298-x Eur. Phys. J. A 18, 189–192 (2003) T HE EUROPEAN P HYSICAL JOURNAL A The spectrum and strong decays of baryons in a relativistic quark model B. Metsch a , U. L¨oring, D. Merten, and H. Petry Helmholtz-Institut f¨ ur Strahlen- und Kernphysik, Universit¨at Bonn, Nußallee 14-16, D-53115 Bonn, Germany Received: 30 September 2002 / Published online: 22 October 2003 – c  Societ` a Italiana di Fisica / Springer-Verlag 2003 Abstract. On the basis of the three-particle Bethe-Salpeter equation we formulated a relativistic quark model for baryons. With free constituent-quark propagators and instantaneous interaction kernels a good description of the overall baryonic mass spectrum up to the highest spin states is obtained. Preliminary results on strong two-body decays of baryon resonances are discussed. PACS. 11.10.St Bound and unstable states; Bethe-Salpeter equations – 12.39.Ki Relativistic quark model – 12.40.Yx Hadron mass models and calculations – 13.30.Eg Hadronic decays 1 Introduction The baryonic resonance spectrum exhibits some striking features: Linear Regge trajectories, which hint at a linear confinement potential; moderately large hyperfine split- tings (e.g. the N -Δ splitting) hinting at a strong spin- spin interaction; parity doublets, such as e.g. N * 5 2 + (1680)- N * 5 2 - (1675), which all are a challenge to explain theoreti- cally. The most successful approaches to account for these have been constituent-quark models (in non-relativistic or “relativized” versions), see e.g. the excellent review by Capstick and Roberts [1] and references therein, which use one-gluon exchange or Goldstone-boson exchange as quark interaction in addition to a linear confinement po- tential. Although the results from such calculations are in general satisfactory, they do not reproduce the details of the N Regge trajectory nor explain the parity doublets found. Moreover, the role of the spin-orbit parts of the residual interactions remains obscure. On top of this, the conventional constituent-quark models have no real field- theoretical basis and lack relativistic covariance. As an extension of an earlier relativistic quark model descrip- tion of mesons [2], we therefore developed a relativistic quark model for baryons on the basis of the three-particle Bethe-Salpeter equation. 2 A relativistic quark model The details of our approach are extensively described in [3]; here we shall merely quote the basic assump- tions and features. Starting point is the Bethe-Salpeter a e-mail: metsch@itkp.uni-bonn.de equation for bound states of three fermions, which is a homogeneous integral equation involving full quark propagators and irreducible interaction kernels in terms of the 8 relative momentum variables of the quarks. In order to solve this equation we made the following assumptions, which were inspired by the non-relativistic constituent- quark model being quite successful in describing the baryon spectrum. It is assumed that the self-energy in the quark propagators can be suitably approximated by introducing an effective, constituent-quark mass in the free Feynman propagator. Furthermore, we assume that interaction kernels do not depend on the relative energy variables of the quarks in the rest frame of the baryon. Although this also implies a technical simplification (Salpeter equation), the main reason is that we want to implement confinement by an instantaneous linearly rising three-body potential. These assumptions, after introducing an effective instantaneous kernel that approx- imates retardation effects in two-body interactions, allow for a formulation of the resulting Salpeter equation as an eigenvalue equation. The latter is solved by expanding the amplitudes in a suitable large, but finite, basis. Confinement is implemented by a string-like three- body potential, which rises linearly with inter-quark dis- tances and comprises a spin structure chosen such that spin-orbit splittings are suppressed, see [4] for details. In order to account for the hyperfine structure we adopted an effective two-body interaction based on instanton ef- fects, which has the decisive property to solve the U A (1)- problem in the pseudoscalar meson spectrum [2]. For two quarks it is a short-range two-body interaction acting on quark pairs with vanishing spin that are antisymmetric in flavour. Consequently, this force does not act on the flavour symmetric Δ-resonances. The Regge trajectory in