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

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