Electromagnetic Contribution to the Proton-Neutron Mass Splitting

Abstract

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 $\delta M_{p-n}^{\gamma }=1.04\pm 0.11\mathrm{MeV}$, which represents a significant improvement in precision.

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