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The Cottingham formula expresses the leading contribution of theelectromagnetic interaction to the proton-neutron mass difference as anintegral over the forward Compton amplitude. Since quarks and gluons reggeize,the dispersive representation of this amplitude requires a subtraction. Weassume that the asymptotic behaviour is dominated by Reggeon exchange. Thisleads to a sum rule that expresses the subtraction function in terms ofmeasurable quantities. The evaluation of this sum rule leads to$m_{QED}^{p-n}=0.58\pm 0.16\,\mbox{MeV}$.

Sum rule for the Compton amplitude and implications for the proton-neutron mass difference