Strong-isospin violation in the neutron–proton mass difference from fully-dynamical lattice QCD and PQQCD

Abstract

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 m π ∼ 290 MeV to ∼ 350 MeV . At the physical value of the pion mass, we predict M n − M p | 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 = m u / m d , determined by MILC [C. Aubin, et al., MILC Collaboration, Phys. Rev. D 70 (2004) 114501, hep-lat/0407028], and the third error is an estimate of the systematic due to chiral extrapolation.