Problem of Neutron-Proton Mass Difference

The problem of the $n-p$ mass difference is carefully analyzed in the framework of dispersion theory. The author has studied the models recently used to obtain interesting properties of the electroproduction structure functions, in order to calculate an important piece of the mass shift coming from the subtraction constant that enters into the dispersion relation for the spin-nonflip forward Compton amplitude of the nucleon. It was hoped that in some simple model one might enhance this piece in the right direction and thereby obtain at least the required sign reversal. It is shown that this is not so. Thus, unless the contributions of the higher resonance states (in addition to the nucleon pole) or those of the fixed poles to the Compton amplitude are important, the $n-p$ mass shift cannot be understood from the viewpoint of dispersion theory.