Calculation of the Proton-Neutron Mass Difference byS-Matrix Methods

Abstract

The proton-neutron mass difference is calculated using $S$-matrix methods developed in the previous paper. 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 electromagnetic 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.