S-Matrix Methods for Electromagnetic Corrections to Strong Interactions with an Application to the Proton-Neutron Mass Difference

Citation

Dashen, Roger Frederick (1964) S-Matrix Methods for Electromagnetic Corrections to Strong Interactions with an Application to the Proton-Neutron Mass Difference. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/18GW-XP34. https://resolver.caltech.edu/CaltechETD:etd-10032002-102733

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The first half of this thesis is devoted to the derivation of an S-matrix method for calculating the effect of small perturbations on a partial wave amplitude, and, in particular, on the positions and residues of bound states. The method is applicable to both non-relativistic and relativistic problems. It has, as a particular virtue, rapid convergence of the dispersion integrals. Electromagnetic corrections to strong interactions will be an important application and modifications useful for handling the infrared divergence that occurs in this case are described in detail. The second half of this work is a detailed, quantitative application to the neutron-proton mass difference. Neutrons and protons are treated as bound state poles in the [pi]-N scattering amplitude and the mass difference is obtained by finding the electromagnetic corrections to their binding energies. The results are in good agreement with experiment. No cutoffs or other purely theoretical parameters are involved. All the long range corrections to the [pi]-N interaction are investigated. Photon exchange turns out to be the most important. Form factors appear as short range modifications of the photon exchange force. The results of the calculation are not sensitive to the detailed behavior of the form factors at large momentum transfer.

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