Mass Splittings and Ghost Tadpoles

The neutron-proton mass difference is expressed, on the assumption that it is purely electromagnetic in origin, in terms of partial-wave amplitudes for the process $N\overline{N}\to \gamma \gamma$ at zero total energy, and also in terms of the single $n=0\mathrm{}$, $M=0\mathrm{}$ $O\left(4\right)\mathrm{}$ amplitude for the same process. This representation allows quite directly a qualitative understanding of the sign of the $n-p$ mass difference, and also allows, with more drastic assumptions, an approximate numerical evaluation of the mass difference based on experimentally determined parameters from the $A_2$ Regge trajectory. This numerical estimate is in reasonable agreement with experiment. The approach is easily generalized to other electromagnetic mass differences, and is shown to yield the tadpole model.