https://doi.org/10.1140/epja/i2014-14130-x
Regular Article - Theoretical Physics
On kinematical constraints in the hadrogenesis conjecture for the baryon resonance spectrum
GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planck Str. 1, 64291, Darmstadt, Germany
* e-mail: y.heo@gsi.de
Received:
7
May
2014
Revised:
18
July
2014
Accepted:
21
July
2014
Published online:
22
August
2014
We consider the reaction dynamics of bosons with negative parity and spin 0 or 1 and fermions with positive parity and spin 
or 
. 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.
© SIF, Springer-Verlag Berlin Heidelberg, 2014
