Electromagnetic Contribution to the Proton-Neutron Mass Splitting

We study the electromagnetic contribution to the proton-neutron mass splitting by combining lattice simulations and the modified Cottingham sum rule of Walker-Loud, Carlson and Miller. This analysis yields an estimate of the isovector nucleon magnetic polarizability as a function of pion mass. The physical value, obtained by chiral extrapolation to the physical pion mass, is $\beta_{p-n}=(-1.12 \pm 0.40)\times 10^{-4}\ \mathrm{fm}^3$, which is in agreement with the empirical result, albeit with a somewhat smaller error. As a result, we find $\delta M^{\gamma}_{p-n}=1.04 \pm 0.11\ \mathrm{MeV}$, which represents a significant improvement in precision.