The paper reviews the Cottingham formula, its renormalization issues, and two models for the required subtraction function to estimate the electromagnetic part of the proton-neutron mass splitting.
The Electromagnetic Self-Energy Contribution to M_p - M_n and the Isovector Nucleon Magnetic Polarizability
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abstract
We update the determination of the isovector nucleon electromagnetic self-energy, valid to leading order in QED. A technical oversight in the literature concerning the elastic contribution to Cottingham's formula is corrected and modern knowledge of the structure functions is used to precisely determine the inelastic contribution. We find \delta M_{p-n}^\gamma = 1.30(03)(47) MeV. The largest uncertainty arises from a subtraction term required in the dispersive analysis, which can be related to the isovector magnetic polarizability. With plausible model assumptions, we can combine our calculation with additional input from lattice QCD to constrain this polarizability as: \beta_{p-n} = -0.87(85) x 10^{-4} fm^3.
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On the Cottingham formula and the electromagnetic contribution to the proton-neutron mass splitting
The paper reviews the Cottingham formula, its renormalization issues, and two models for the required subtraction function to estimate the electromagnetic part of the proton-neutron mass splitting.