We study the coupled scalar-gauge soliton of FOX Theory as a model of the nucleon. The coupled system consists of the FOX scalar field φ(r) and an SU(2) gauge field K(r), subject to two classes of boundary conditions at the stasis sphere r*: Neumann (K′(r*) = 0, proton) and Dirichlet (K(r*) = 1, neutron). Three principal results are established: (i) the BPS incompatibility theorem; (ii) the BVP numerical solution yielding K*₂ = −1.7007, r* = 0.885 fm; (iii) the mass splitting ΔE = 1.015 MeV at 78.5% of the experimental neutron-proton mass difference, without free parameter. Part of the FOX Theory series (Branches A–D).
Adrien le Hardÿ de Beaulieu (Tue,) studied this question.