On the n-p Mass Difference in QCD

Abstract

With the advent of unified gauge theories, quantum chromodynamics, dynamical symmetry breaking and the like, the old and, as yet, unsolved problem of the n-p mass difference has been cast in a new light. Traditional attempts to explain the infamous sign reversal have invariably been based upon the assumption that the mass splitting was electromagnetic in origin.1 However, all attempts along these lines agree with naive Coulomb energy considerations and, therefore, fail. Nowadays one has an equally important origin of isospin symmetry breaking, namely, the quark masses themselves.2 Thus, the problem of the n-p mass difference becomes intimately related to the problem of quark mass splitting and these presumably arise from the dynamical breaking of an assumed unified symmetry. From this point of view, the smallness of isospin splitting appears accidental, being merely a reflection of the smallness of the current quark masses relative to more typical hadronic mass scales. This view leads to a remarkable conclusion, namely, that the formidable macroscopic consequences of the neutron being heavier than the proton have their origins at energies relevant to the breaking of a grand unified group. Regardless of the role played by the masses themselves, the conventional electromagnetic contribution has to be reckoned with; indeed, all quark mass splittings have two such contributions, namely those from dynamical symmetry breaking and those from gauge boson radiative corrections.