Superconvergent Dispersion Relations and Electromagnetic Mass Differences

Using dispersion relations and the convergence properties of $t$-channel isospin amplitudes, we show that (a) $\Delta I=2\mathrm{}$ electromagnetic mass difference should be correctly obtained by summing the self-energy contributions of a few low-lying states; (b) $\Delta I=1\mathrm{}$ mass differences cannot be obtained in this way, and a subtraction term is always necessary; (c) the subtraction term has the correct sign for explaining the proton-neutron mass difference.