The strong interactions of fundamental particles have been successfully described by Quantum ChromoDynamics (QCD). It is a non-Abelian gauge theory, based on the SU(3) gauge group. QCD involves the gauge fields and the fields of spin 1/2 particles as gluons and quarks, respectively. Quarks are fermions in the fundamental representation of the color SU(3) gauge group. Gluons are boson fields in the adjoint (octet) representation. Moreover, quarks carry flavour degrees of freedom which are independent of the color. A distinguished feature of QCD is asymptotic freedom. Politzer, Gross and Wilczek, and 't Hooft discovered the property of asymptotic freedom in non-Abelian gauge field theories. It allows QCD to be treated perturbatively at high energies. On the other hand, the strong interaction becomes nonperturbative at low energies, because the coupling constant of QCD increases rapidly in that regime. This problem can be overcome in the framework of effective field theories.
A remarkably successful effective Lagrangian approach to low-energy QCD is that of Chiral Perturbation Theory (χPT). The effective degrees of freedom of χPT are hadrons rather than quarks and gluons. χPT has been applicable in the flavour SU(2) sector of low-energy QCD. This effective field theory is based on the simple observation that QCD is chirally symmetric in the limit where the up and down current quark masses vanish. This implies that the handedness of quarks is a conserved property in that limit. However, the QCD vacuum is spontaneously broken. Since the pion masses (~140 MeV) are much smaller than the nucleon masses (~939 MeV), the pions can be identified to be the Goldstone bosons of the spontaneously broken chiral symmetry. The SU(2) χPT relies on the principles of quantum field theory and on the symmetries of QCD. A generalization of the chiral SU(2) scheme to the SU(3) flavour group which includes the strangeness sector is mathematically straightforward and has been done. Though the mass of the strange quark is much larger than the up and down quark masses, it is still small on the typical chiral scale of 1 GeV. The required approximate Goldstone boson octet is readily found with the pions, the kaons, and the eta-meson. But the domain of validity of χPT is restricted to a small neighbourhood of threshold energies. A generalization to higher energies is desired.
We study the on-shell scattering processes for two-body systems involving bosons with negative parity and spin 0 or 1 and fermions with positive parity and spin 1/2 or 3/2. A problem may be caused from the fact that helicity partial-wave scattering amplitudes are kinematically constrained. We solve such a problem by derivation of suitable transformations which eliminate all kinematical constraints. Resulting amplitudes are useful for partial-wave analysis and construction of effective field theories based on unitarity and micro causality. The procedure requires a parameterization of scattering amplitudes in terms of invariant functions free of kinematical singularities. We develop a novel algebra, so that it leads to the efficient computation of such functions by virtue of computer algebra codes.
We examine the hadrogenesis conjecture. It gives a systematic framework that various resonances can be conjectured to be a result of coupled-channel dynamics. It relies on a selection of a few fundamental hadronic degrees of freedom. The selection is guided by properties of QCD in the large-Nc limit. Starting with the relativistic chiral SU(3) Lagrangian, coupled-channel interactions are analytically extrapolated to higher energies by means of unitarity and micro causality. Our calculation contains not only the parameter-free term, i.e. the Weinberg-Tomozawa interaction, but also the s-, t-, and u-channel exchanges. At present, we restrict ourselves to a fermion with a spin-one-half in the calculation. We argue that further computation involving a spin-three-half fermion is required, because it is part of the baryon ground state multiplet which arises in the large-Nc limit of QCD
