Abstract
A procedure has been suggested for computing $\ensuremath{\Delta}I=1$ electromagnetic mass differences by using a finite-energy sum rule to compute the subtraction function in the dispersion relation for the amplitude ${t}_{1}({q}^{2},\ensuremath{\nu})$ which appears in the Cottingham formula; Regge residues appearing in the subtraction function are found from a superconvergence relation. The present work considers the effect of the inclusion of asymptotic nonleading power behavior on the results of this procedure; we find a surprising sensitivity. In particular, we show that in evaluating the superconvergence relation, the hypothesis of ${A}_{2}$ dominance of high-energy virtual Compton scattering from $K$ mesons is only tenable for an extremely narrow range of the ratio of the longitudinal to transverse total virtual Compton cross sections. (This range does not include zero.) We also discuss the effects of O(4) symmetry, comment on the more complicated nucleon mass-difference problem, and apply the Cottingham formula to nuclear mass differences.
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