The European Physical Journal A

, 50:130

On kinematical constraints in the hadrogenesis conjecture for the baryon resonance spectrum

Authors

    • GSI Helmholtzzentrum für Schwerionenforschung GmbH
  • Matthias F. M. Lutz
    • GSI Helmholtzzentrum für Schwerionenforschung GmbH
Regular Article - Theoretical Physics

DOI: 10.1140/epja/i2014-14130-x

Cite this article as:
Heo, Y. & Lutz, M.F.M. Eur. Phys. J. A (2014) 50: 130. doi:10.1140/epja/i2014-14130-x

Abstract

We consider the reaction dynamics of bosons with negative parity and spin 0 or 1 and fermions with positive parity and spin \(\tfrac{1} {2}\) or \(\tfrac{3} {2}\). Such systems are of central importance for the computation of the baryon resonance spectrum in the hadrogenesis conjecture. Based on a chiral Lagrangian the coupled-channel partial-wave scattering amplitudes have to be computed. We study the generic properties of such amplitudes. A decomposition of the various scattering amplitudes into suitable sets of invariant functions expected to satisfy Mandelstam’s dispersion-integral representation is presented. Sets are identified that are free from kinematical constraints and that can be computed efficiently in terms of a novel projection algebra. From such a representation one can deduce the analytic structure of the partial-wave amplitudes. The helicity and the conventional angular-momentum partial-wave amplitudes are kinematically constrained at the Kibble conditions. Therefore an application of a dispersion-integral representation is prohibitively cumbersome. We derive covariant partial-wave amplitudes that are free from kinematical constraints at the Kibble conditions. They correspond to specific polynomials in the 4-momenta and Dirac matrices that solve the various Bethe-Salpeter equations in the presence of short-range interactions analytically.

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2014