Superconvergent Dispersion Relations and Electromagnetic Mass Differences

Abstract

Using dispersion relations and the convergence properties of $t$-channel isospin amplitudes, we show that (a) $\ensuremath{\Delta}I=2$ electromagnetic mass difference should be correctly obtained by summing the self-energy contributions of a few low-lying states; (b) $\ensuremath{\Delta}I=1$ 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.