  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.

Nuclear Theory;High Energy Physics - Lattice;High Energy Physics - Phenomenology