Strong-Isospin Breaking in the Neutron-Proton Mass Difference

We determine the strong-isospin violating component of the neutron-proton mass difference from fully-dynamical lattice QCD and partially-quenched QCD calculations of the nucleon mass, constrained by partially-quenched chiral perturbation theory at one-loop level. The lattice calculations were performed with domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at a lattice spacing of b ∼ 0.125 fm, lattice spatial size of L ∼ 2.5 fm and pion masses ranging from mπ ∼ 290 MeV to ∼ 350 MeV. At the physical value of the pion mass, we predict Mn−Mp|(d−u) = 2.26±0.57±0.42±0.10 MeV where the first error is statistical, the second error is due to the uncertainty in the ratio of light-quark masses, η = mu/md , determined by MILC [1], and the third error is an estimate of the systematic due to chiral extrapolation.