## Dissertations, Theses, and Masters Projects

1994

Dissertation

#### Degree Name

Doctor of Philosophy (Ph.D.)

Physics

Franz L Gross

#### Abstract

Pion nucleon scattering is described by a manifestly covariant wave equation in which the pion is restricted to its mass-shell. The kernel of the equation includes nucleon (N), Roper (N*), delta ({dollar}\Delta{dollar}) and {dollar}D\sb{lcub}13{rcub}{dollar} poles, with their corresponding crossed pole terms approximated by contact interactions, and contact {dollar}\sigma{dollar}- and {dollar}\rho{dollar}-like exchange terms. The {dollar}\pi NN{dollar} vertex is treated as a mixture of {dollar}\gamma\sp5{dollar} and {dollar}\gamma\sp\mu\gamma\sp5{dollar} coupling, with a mixing parameter {dollar}\lambda{dollar} chosen so that the dressed nucleon pole will be unshifted by the interaction. Chiral symmetry is maintained at threshold. The resonance contributions are fully unitarized by the equation, with their widths determined by the dynamics included in the model. The {dollar}\Delta{dollar} and {dollar}D\sb{lcub}13{rcub}{dollar} are treated as a pure spin 3/2 particles, with no spin 1/2 amplitude in the S-channel. Pion photoproduction is also described by a manifestly covariant wave equation, which includes a treatment of the final state {dollar}\pi N{dollar} interactions consistent with the covariant, unitary, resonance model of {dollar}\pi N{dollar} scattering. The model is exactly gauge invariant to all orders in the strong coupling, g and satisfies the Low Energy Theorem. Unitarity is maintained up to first order in the charge e (Watson theorem). The complete development of the model which gives a good fit to all the data up to 770 MeV photon energy lab, is presented.

#### DOI

https://dx.doi.org/doi:10.21220/s2-jszh-8v58