On kinematical constraints in the hadrogenesis conjecture for the baryon resonance spectrum
arXiv:1405.1597 · doi:10.1140/epja/i2014-14130-x
Abstract
We consider the reaction dynamics of bosons with negative parity and spin or 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.
arXiv comment18 pages
References in corpus (34)
- Modern Theory of Nuclear Forces
- The Two-Nucleon Potential from Chiral Lagrangians
- Relativistic chiral SU(3) symmetry, large N_c sum rules and meson-baryon scattering
- Chiral Dynamics and the Nucleon Resonance
- On meson resonances and chiral symmetry
- Quark mass dependence of s-wave baryon resonances
- Bethe-Salpeter Approach for Unitarized Chiral Perturbation Theory
- On baryon resonances and chiral symmetry
- The (1535) and (1650) Resonances in Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory
- Chiral dynamics of the S11(1535) and S11(1650) resonances revisited
- Radiative and isospin-violating decays of Ds mesons in the hadrogenesis conjecture
- Charmed and strange baryon resonances with heavy-quark spin symmetry
- Photon- and pion-nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian
- Self consistent propagation of hyperons and antikaons in nuclear matter based on relativistic chiral SU(3) dynamics
- Baryon resonances from chiral coupled-channel dynamics
- On the radiative decays of light vector and axial-vector mesons
- Effective chiral theory of nucleon-nucleon scattering
- Baryon self energies in the chiral loop expansion
- Dynamical light vector mesons in low-energy scattering of Goldstone bosons
- Electromagnetic transitions in an effective chiral Lagrangian with the eta-prime and light vector mesons
- Antikaons and hyperons in nuclear matter with saturation
- Compton scattering from chiral dynamics with unitarity and causality
- Covariant meson-baryon scattering with chiral and large N_c constraints
- Two-nucleon scattering: merging chiral effective field theory with dispersion relations
- On causality, unitarity and perturbative expansions
- Photon-fusion reactions from the chiral Lagrangian with dynamical light vector mesons
- Large-N_c operator analysis of 2-body meson-baryon counterterms in the chiral Lagrangian
- On kinematical constraints in boson-boson systems
- Covariant and self consistent vertex corrections for pions and isobars in nuclear matter
- Combined large-N_c and heavy-quark operator analysis for the chiral Lagrangian with charmed baryons
- On kinematical constraints in fermion-antifermion systems
- Combined large- and heavy-quark operator analysis of 2-body meson-baryon counterterms in the chiral Lagrangian with charmed mesons
- Chiral symmetry, strangeness and resonances
- Quark-mass dependence of baryon resonances