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 ${\ensuremath{\beta}}_{p\text{\ensuremath{-}}n}=(\ensuremath{-}1.12\ifmmode\pm\else\textpm\fi{}0.40)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{3}$, which is in agreement with the empirical result, albeit with a somewhat smaller error. As a result, we find $\ensuremath{\delta}{M}_{p\text{\ensuremath{-}}n}^{\ensuremath{\gamma}}=1.04\ifmmode\pm\else\textpm\fi{}0.11\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, which represents a significant improvement in precision.