Investigations in hadron physics: bound state models for fermions; radiative corrections to pion--pion scattering

Trajectories of fermion Regge poles are calculated in a model in which a spin 1/2 particle is bound to a spin 0 core. The Bethe-Salpeter equation in the ladder approximation provides a relativistic description of the model in which a fundamental interaction is unitarized. Results are obtained numerically from a coveriant separable approximation to the kernel of the partial-wave integral equation. Two kinds of interactions are considered: the single particle exchange kernel and an exponentially damped kernel. In both interactions the leading trajectory with parity (-1)/sup j/-1/2 is much like the boson trajectory generated by similar interactions. The opposite trajectory satisfies the constraints of MacDowell symmetry, yet is totally distinct for s>0. With the exponential kernel the model produces a trajectory which above the elastic threshold has a small negative Imα and an increasing Reα. Such a trajectory produces poles on the physical sheet of the energy plane. Arguments are presented which suggest that an analogous effect might be observed in unitarized dual models.A chiral SU(s)xSU(2) Lagrangian is used to describe low-energy π-π scattering. Radiative corrections are calculated by modifying in a gauge invariant way the strong interaction Lagrangian in the presence of the electromagnetic field. Corrections to the cross section are calculated to 0(α). The results are expanded in powers of the center-of-mass momentum to obtain a direct channel threshold expansion. All the ultraviolet divergences cancel and the results are independent of cut-off parameters. The infrared divergences cancel term by term in the low-momentum expansion. Corrections to the Weinberg scattering lengths of the order of 3% are defined by removal of the Coulomb pole terms. The field theoretic calculation is compared with a potential theory approach. It is argued that both methods produce the same dominant terms in the expansion of the radiative corrections