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We update the determination of the isovector nucleon electromagneticself-energy, valid to leading order in QED. A technical oversight in theliterature concerning the elastic contribution to Cottingham's formula iscorrected and modern knowledge of the structure functions is used to preciselydetermine the inelastic contribution. We find \delta M_{p-n}^\gamma =1.30(03)(47) MeV. The largest uncertainty arises from a subtraction termrequired in the dispersive analysis, which can be related to the isovectormagnetic polarizability. With plausible model assumptions, we can combine ourcalculation with additional input from lattice QCD to constrain thispolarizability as: \beta_{p-n} = -0.87(85) x 10^{-4} fm^3.

The Electromagnetic Self-Energy Contribution to M_p - M_n and the Isovector Nucleon Magnetic Polarizability